Page 1
Page 2
Page 3
The Project Gutenberg eBook of Physics
This eBook is for the use of anyone anywhere in the United States and most
other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms of
the Project Gutenberg License included with this eBook or online at
www.gutenberg.org. If you are not located in the United States, you will
have to check the laws of the country where you are located before using
this eBook.
Title: Physics
Author: Willis E. Tower
Thomas D. Cope
Charles H. Smith
Charles M. Turton
Release date: July 9, 2012 [eBook #40175]
Most recently updated: October 23, 2024
Language: English
Other information and formats: www.gutenberg.org/ebooks/40175
Credits: Produced by Anna Hall, Albert László and the Online
Distributed Proofreading Team at http://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)
*** START OF THE PROJECT GUTENBERG EBOOK PHYSICS ***
PHYSICS
This eBook is for the use of anyone anywhere in the United States and most
other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms of
the Project Gutenberg License included with this eBook or online at
www.gutenberg.org. If you are not located in the United States, you will
have to check the laws of the country where you are located before using
this eBook.
Title: Physics
Author: Willis E. Tower
Thomas D. Cope
Charles H. Smith
Charles M. Turton
Release date: July 9, 2012 [eBook #40175]
Most recently updated: October 23, 2024
Language: English
Other information and formats: www.gutenberg.org/ebooks/40175
Credits: Produced by Anna Hall, Albert László and the Online
Distributed Proofreading Team at http://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)
*** START OF THE PROJECT GUTENBERG EBOOK PHYSICS ***
PHYSICS
Page 4
TOWER, SMITH, TURTON,
AND
COPE
(See p.441)
Three-color Printing
Y. Yellow impression; negative made through a
blue-violet filter. R. Crimson impression;
negative made through a green filter. RY.
Crimson on yellow. B. Blue impression;
negative made through a red filter. YRB.
Yellow, crimson, and blue combined; the final
product. (Courtesy of Phototype Engraving
Co., Philadelphia.)
PHYSICS
BY
AND
COPE
(See p.441)
Three-color Printing
Y. Yellow impression; negative made through a
blue-violet filter. R. Crimson impression;
negative made through a green filter. RY.
Crimson on yellow. B. Blue impression;
negative made through a red filter. YRB.
Yellow, crimson, and blue combined; the final
product. (Courtesy of Phototype Engraving
Co., Philadelphia.)
PHYSICS
BY
Page 5
WILLIS E. TOWER, M. SCI. (Univ. of Illinois)
HEAD OF THE DEPARTMENT OF PHYSICS, ENGLEWOOD
HIGH SCHOOL, CHICAGO
CHARLES H. SMITH, M. E. (Cornell)
HEAD OF THE DEPARTMENT OF PHYSICS AND ASSISTANT
PRINCIPAL, HYDE PARK SCHOOL, CHICAGO
CHARLES M. TURTON, A. M. (Syracuse)
HEAD OF THE DEPARTMENT OF PHYSICS, BOWEN
HIGH SCHOOL, CHICAGO
IN COLLABORATION WITH
THOMAS D. COPE, Ph.D. (Pennsylvania)
ASSISTANT PROFESSOR OF PHYSICS, UNIVERSITY
OF PENNSYLVANIA
BASED UPON
PRINCIPLES OF PHYSICS
BY
TOWER, SMITH and TURTON
WITH 7 PLATES AND 448 OTHER ILLUSTRATIONS
PHILADELPHIA
P. BLAKISTON'S SON & CO.
1012 WALNUT STREET
Copyright, 1920, by P. Blakiston's Son & Co.
HEAD OF THE DEPARTMENT OF PHYSICS, ENGLEWOOD
HIGH SCHOOL, CHICAGO
CHARLES H. SMITH, M. E. (Cornell)
HEAD OF THE DEPARTMENT OF PHYSICS AND ASSISTANT
PRINCIPAL, HYDE PARK SCHOOL, CHICAGO
CHARLES M. TURTON, A. M. (Syracuse)
HEAD OF THE DEPARTMENT OF PHYSICS, BOWEN
HIGH SCHOOL, CHICAGO
IN COLLABORATION WITH
THOMAS D. COPE, Ph.D. (Pennsylvania)
ASSISTANT PROFESSOR OF PHYSICS, UNIVERSITY
OF PENNSYLVANIA
BASED UPON
PRINCIPLES OF PHYSICS
BY
TOWER, SMITH and TURTON
WITH 7 PLATES AND 448 OTHER ILLUSTRATIONS
PHILADELPHIA
P. BLAKISTON'S SON & CO.
1012 WALNUT STREET
Copyright, 1920, by P. Blakiston's Son & Co.
Page 6
PREFACE
In the preparation of this text, the pupil, his experience, needs, and interests
have been constantly kept in mind. The order of topics, illustrations, and
problems have been selected with the purpose of leading the pupil into a
clear understanding of the physical phenomena continually taking place
about him.
The recommendations and conclusions reached by the "New Movement in
the Teaching of Physics" have been incorporated into the book as a whole.
These conclusions indicate that the most efficient teaching in physics
involves a departure from the quantitative, mathematical methods of
presentation that were in general use a dozen or more years ago, toward a
method better adapted to the capabilities, interests, and requirements of the
young people in our physics classes.
The older methods are effective with a portion of the student body which
has the greater mathematical ability and training, but they discourage a
large majority of the pupils who are not gifted or prepared for severe
mathematical analysis. For this reason, many of the more difficult
mathematical demonstrations often given in physics texts are omitted. Most
of the problems involve only the units employed in practical every-day
measurements.
The portions of Mechanics that are ordinarily so difficult for the average
pupil are not taken up until he has covered considerable ground with which
he is more or less familiar and not until he has become somewhat
accustomed to the methods of study and the technical terms of the subject.
The pupil comes to the study of physics with a great number of experiences
and impressions of physical phenomena continually occurring about him. In
recognition of this fact, it has been thought best to consider first the
explanation of common things well known to all pupils, such as the
diffusion of gases, evaporation of liquids, expansion of bodies when heated,
and capillary action. Since the molecular theory of matter is now supported
by so many conclusive evidences, we have not hesitated to make free use of
it in the early chapters. The applications of this theory are extremely helpful
In the preparation of this text, the pupil, his experience, needs, and interests
have been constantly kept in mind. The order of topics, illustrations, and
problems have been selected with the purpose of leading the pupil into a
clear understanding of the physical phenomena continually taking place
about him.
The recommendations and conclusions reached by the "New Movement in
the Teaching of Physics" have been incorporated into the book as a whole.
These conclusions indicate that the most efficient teaching in physics
involves a departure from the quantitative, mathematical methods of
presentation that were in general use a dozen or more years ago, toward a
method better adapted to the capabilities, interests, and requirements of the
young people in our physics classes.
The older methods are effective with a portion of the student body which
has the greater mathematical ability and training, but they discourage a
large majority of the pupils who are not gifted or prepared for severe
mathematical analysis. For this reason, many of the more difficult
mathematical demonstrations often given in physics texts are omitted. Most
of the problems involve only the units employed in practical every-day
measurements.
The portions of Mechanics that are ordinarily so difficult for the average
pupil are not taken up until he has covered considerable ground with which
he is more or less familiar and not until he has become somewhat
accustomed to the methods of study and the technical terms of the subject.
The pupil comes to the study of physics with a great number of experiences
and impressions of physical phenomena continually occurring about him. In
recognition of this fact, it has been thought best to consider first the
explanation of common things well known to all pupils, such as the
diffusion of gases, evaporation of liquids, expansion of bodies when heated,
and capillary action. Since the molecular theory of matter is now supported
by so many conclusive evidences, we have not hesitated to make free use of
it in the early chapters. The applications of this theory are extremely helpful
Page 7
in explaining every-day phenomena. Our experience shows that beginners
in physics understand and apply this theory without difficulty.
The illustrations and drawings have been selected from a pedagogical rather
than a spectacular point of view. Practically all of them are new. The
problems and exercises have been selected for the distinct purpose of
illustrating the principles taught in the text and for their practical
applications.
Many direct applications to common every-day experiences are given in
order to connect the subject matter with the home environment and daily
observation of physical phenomena. Some phenomena are mentioned
without detailed explanation as it is felt that the presentation of these
subjects in this manner is better for this grade of student than a complete
analysis.
Some of the special features of the text may be briefly summarized as
follows:
(A) Simplicity of presentation is emphasized. The methods of attack, the
illustrations and examples employed in developing the subjects are
particularly adapted to beginners in physics.
(B) The text is divided into some seventy-seven sections, each containing
material enough for one recitation.
(C) Each of these sections is summarized by a list of important topics which
point out to the pupil the principles and subject matter requiring most
careful attention. The lists of important topics are also of assistance to the
teacher in assigning recitations.
(D) The problems and practical exercises emphasize physical principles as
distinguished from mathematical training. A list of exercises is placed at the
end of the several sections. They are in sufficient number to permit testing
at many points and of a choice of problems by teachers.
The authors wish to express their appreciation for suggestions and helpful
criticisms to many who have read the text in manuscript or proof.
Especially to Professor A. P. Carman of the University of Illinois and his
associate, Professor F. R. Watson, who have gone carefully over the whole
text; and to Mr. Chas. M. Brunson, Scott High School, Toledo, Ohio, Mr.
Frank E. Goodell, North High School, Des Moines, Iowa, and to Mr. Walter
in physics understand and apply this theory without difficulty.
The illustrations and drawings have been selected from a pedagogical rather
than a spectacular point of view. Practically all of them are new. The
problems and exercises have been selected for the distinct purpose of
illustrating the principles taught in the text and for their practical
applications.
Many direct applications to common every-day experiences are given in
order to connect the subject matter with the home environment and daily
observation of physical phenomena. Some phenomena are mentioned
without detailed explanation as it is felt that the presentation of these
subjects in this manner is better for this grade of student than a complete
analysis.
Some of the special features of the text may be briefly summarized as
follows:
(A) Simplicity of presentation is emphasized. The methods of attack, the
illustrations and examples employed in developing the subjects are
particularly adapted to beginners in physics.
(B) The text is divided into some seventy-seven sections, each containing
material enough for one recitation.
(C) Each of these sections is summarized by a list of important topics which
point out to the pupil the principles and subject matter requiring most
careful attention. The lists of important topics are also of assistance to the
teacher in assigning recitations.
(D) The problems and practical exercises emphasize physical principles as
distinguished from mathematical training. A list of exercises is placed at the
end of the several sections. They are in sufficient number to permit testing
at many points and of a choice of problems by teachers.
The authors wish to express their appreciation for suggestions and helpful
criticisms to many who have read the text in manuscript or proof.
Especially to Professor A. P. Carman of the University of Illinois and his
associate, Professor F. R. Watson, who have gone carefully over the whole
text; and to Mr. Chas. M. Brunson, Scott High School, Toledo, Ohio, Mr.
Frank E. Goodell, North High School, Des Moines, Iowa, and to Mr. Walter
Page 8
R. Ahrens, Englewood High School, Chicago, for assistance in reading the
proofs. Also to Mr. W. H. Collins, Jr., Bowen High School, Chicago, who
supervised the preparation of drawings for the diagrams and figures; and to
many firms and individuals that have courteously furnished material for
illustrations.
Willis E. Tower.
Charles H. Smith.
Charles M. Turton.
proofs. Also to Mr. W. H. Collins, Jr., Bowen High School, Chicago, who
supervised the preparation of drawings for the diagrams and figures; and to
many firms and individuals that have courteously furnished material for
illustrations.
Willis E. Tower.
Charles H. Smith.
Charles M. Turton.
Page 9
ON THE STUDY OF PHYSICS
When a pupil begins the study of Physics he has in his possession many bits
of knowledge which are fundamental in the science. He has learned to
throw a ball and can tell how a thrown ball moves. He has drawn out nails
with a claw hammer. He has seen wood float and iron sink. He has sucked
liquids up through straws. In his mother's kitchen, he sees water as ice,
liquid, and steam. On a wintry day he reads the temperature on a
thermometer. He sees sparks fly from car wheels when the brakes are
applied. He has played with a horseshoe magnet, and has found the north by
means of a compass. The telephone, the electric light and the motor he sees,
and perhaps uses, many times a day. He dresses before a mirror, focuses his
camera, watches the images at a moving picture show, and admires the
colors of the rainbow. He has cast stones into water to watch the ripples
spread, has shouted to hear the echo, and perhaps plays some musical
instrument. These, and a thousand other things, are known to the intelligent
and normal boy or girl who has reached the age at which the study of
Physics is properly begun.
To a great extent even the terms used in the science are familiar to the
beginner. He speaks of the horse-power of an engine, reads kilowatt-hours
from the meter in the cellar, and may know that illuminating gas costs one
dollar per thousand "cubic feet." "Ampere" and "volt" are words he
frequently hears and sees.
When he takes up the study of Physics, the attitude of the student toward
these familiar things and words must undergo a change. Casual information
about them must be changed to sound knowledge, purposely acquired. Hazy
notions about the meanings of words must be replaced by exact definitions.
Bits of knowledge must be built into a structure in which each fact finds its
proper place in relation to the others.
The only agent which can accomplish these changes is the student himself.
He must consciously and purposely seek the truth and must reflect upon it
until he sees it in its relation to other truth. Upon him, and upon him alone,
rests the final responsibility for the success or failure of his study.
When a pupil begins the study of Physics he has in his possession many bits
of knowledge which are fundamental in the science. He has learned to
throw a ball and can tell how a thrown ball moves. He has drawn out nails
with a claw hammer. He has seen wood float and iron sink. He has sucked
liquids up through straws. In his mother's kitchen, he sees water as ice,
liquid, and steam. On a wintry day he reads the temperature on a
thermometer. He sees sparks fly from car wheels when the brakes are
applied. He has played with a horseshoe magnet, and has found the north by
means of a compass. The telephone, the electric light and the motor he sees,
and perhaps uses, many times a day. He dresses before a mirror, focuses his
camera, watches the images at a moving picture show, and admires the
colors of the rainbow. He has cast stones into water to watch the ripples
spread, has shouted to hear the echo, and perhaps plays some musical
instrument. These, and a thousand other things, are known to the intelligent
and normal boy or girl who has reached the age at which the study of
Physics is properly begun.
To a great extent even the terms used in the science are familiar to the
beginner. He speaks of the horse-power of an engine, reads kilowatt-hours
from the meter in the cellar, and may know that illuminating gas costs one
dollar per thousand "cubic feet." "Ampere" and "volt" are words he
frequently hears and sees.
When he takes up the study of Physics, the attitude of the student toward
these familiar things and words must undergo a change. Casual information
about them must be changed to sound knowledge, purposely acquired. Hazy
notions about the meanings of words must be replaced by exact definitions.
Bits of knowledge must be built into a structure in which each fact finds its
proper place in relation to the others.
The only agent which can accomplish these changes is the student himself.
He must consciously and purposely seek the truth and must reflect upon it
until he sees it in its relation to other truth. Upon him, and upon him alone,
rests the final responsibility for the success or failure of his study.
Page 10
But the student is not without assistance. In his teacher he finds a guide to
stimulate, to direct, and to aid his efforts, and a critic to point out wherein
his efforts have failed and wherein they have succeeded. Weights, measures,
and other apparatus are furnished to enable him to answer for himself
questions which have arisen in his studies.
In addition to these the student has his text book, his teacher for his hours of
private study. A good text book is an inspiring teacher in print. It directs
attention to things familiar to the student through long experience, and
inspires him to make a closer scrutiny of them. It invites him to observe, to
analyze, to compare, to discover likenesses and differences in behavior. It
questions him at every turn. Its ever repeated challenge reads, "Weigh and
consider." It furnishes him needed information that he cannot otherwise
acquire. It satisfies his desire to know, "By whom, where, when, and how
was this first discovered?"
The student of Physics must never forget that he is studying not pages of
text but the behavior and properties of iron, water, mica, moving balls,
pumps, boiling liquids, compressed air, mirrors, steam engines, magnets,
dynamos, violins, flutes, and a host of other things. His studies should,
whenever possible, be made first hand upon the things themselves. The text
is an aid to study, never a substitute for the thing studied.
It is an excellent plan for each student to select some one thing for special
study, the telephone for example. By observation, experiment, and reading,
he may acquire a large amount of valuable information about such a subject
while pursuing his course in Physics. Every part of the science will be
found to bear some relation to it.
The student who takes up the study of Physics in the way suggested will
find himself at the end of a year of study in possession of much new and
valuable knowledge about the physical world in which he lives. By virtue of
this knowledge he will be better able to enjoy the world, to control it, and to
use it.
Thomas D. Cope.
Philadelphia.
stimulate, to direct, and to aid his efforts, and a critic to point out wherein
his efforts have failed and wherein they have succeeded. Weights, measures,
and other apparatus are furnished to enable him to answer for himself
questions which have arisen in his studies.
In addition to these the student has his text book, his teacher for his hours of
private study. A good text book is an inspiring teacher in print. It directs
attention to things familiar to the student through long experience, and
inspires him to make a closer scrutiny of them. It invites him to observe, to
analyze, to compare, to discover likenesses and differences in behavior. It
questions him at every turn. Its ever repeated challenge reads, "Weigh and
consider." It furnishes him needed information that he cannot otherwise
acquire. It satisfies his desire to know, "By whom, where, when, and how
was this first discovered?"
The student of Physics must never forget that he is studying not pages of
text but the behavior and properties of iron, water, mica, moving balls,
pumps, boiling liquids, compressed air, mirrors, steam engines, magnets,
dynamos, violins, flutes, and a host of other things. His studies should,
whenever possible, be made first hand upon the things themselves. The text
is an aid to study, never a substitute for the thing studied.
It is an excellent plan for each student to select some one thing for special
study, the telephone for example. By observation, experiment, and reading,
he may acquire a large amount of valuable information about such a subject
while pursuing his course in Physics. Every part of the science will be
found to bear some relation to it.
The student who takes up the study of Physics in the way suggested will
find himself at the end of a year of study in possession of much new and
valuable knowledge about the physical world in which he lives. By virtue of
this knowledge he will be better able to enjoy the world, to control it, and to
use it.
Thomas D. Cope.
Philadelphia.
Page 11
Page 12
CONTENTS
Chapter I. Introduction And Measurement. Page
(1) Introduction 1
(2) States of Matter 4
(3) The Metric System 8
Chapter II. Molecular Forces And Motions.
(1) Molecular Motions in Gases 13
(2) Molecular Motions in Liquids 18
(3) Molecular Forces in Liquids 21
(4) Molecular Forces in Liquids and Solids 27
(5) Molecular Forces in Solids 31
Chapter III. Mechanics or Liquids.
(1) Liquid Pressure 36
(2) Transmission of Liquid Pressure 41
(3) Archimedes' Principle 47
(4) Density and Specific Gravity 52
Chapter IV. Mechanics Of Gases.
(1) Weight and Pressure of the Air 55
(2) Compressibility and Expansibility of the Air 62
(3) Pneumatic Appliances 66
Chapter V. Force And Motion.
(1) Force, how Measured and Represented 79
(2) Motion. Newton's Laws 85
(3) Resolution of Forces 96
(4) Moment of Force and Parallel Forces 99
Chapter I. Introduction And Measurement. Page
(1) Introduction 1
(2) States of Matter 4
(3) The Metric System 8
Chapter II. Molecular Forces And Motions.
(1) Molecular Motions in Gases 13
(2) Molecular Motions in Liquids 18
(3) Molecular Forces in Liquids 21
(4) Molecular Forces in Liquids and Solids 27
(5) Molecular Forces in Solids 31
Chapter III. Mechanics or Liquids.
(1) Liquid Pressure 36
(2) Transmission of Liquid Pressure 41
(3) Archimedes' Principle 47
(4) Density and Specific Gravity 52
Chapter IV. Mechanics Of Gases.
(1) Weight and Pressure of the Air 55
(2) Compressibility and Expansibility of the Air 62
(3) Pneumatic Appliances 66
Chapter V. Force And Motion.
(1) Force, how Measured and Represented 79
(2) Motion. Newton's Laws 85
(3) Resolution of Forces 96
(4) Moment of Force and Parallel Forces 99
Page 13
(5) Gravitation and Gravity 103
(6) Falling Bodies 109
(7) The Pendulum 115
Chapter VI. Work And Energy.
(1) Work and Energy 119
(2) Power and Energy 123
(3) The Lever and Simple Machines 129
(4) Wheel and Axle and Pulley 136
(5) Efficiency and the Inclined Plane 142
(6) Friction and its Uses 147
(7) Water Power 152
Chapter VII. Heat, Its Production And Transmission.
(1) Sources and Effects of Heat 159
(2) Temperature and Expansion 162
(3) Expansion of Gases, Liquids and Solids 167
(4) Modes of Transmitting Heat 173
(5) Convection, Heating and Ventilation 179
(6) The Moisture in the Air, Hygrometry 191
(7) Evaporation 196
Chapter VIII. Heat And Work.
(1) Heat Measurement and Specific Heat 200
(2) Heat and Changes of State 205
(3) Heat and Work 212
(4) Heat Engines 222
Chapter IX. Magnetism.
(1) General Properties of Magnets 228
(2) Theory of Magnetism, Magnetic Fields 232
(3) The Earth's Magnetism 238
Chapter XI. Static Electricity.
(6) Falling Bodies 109
(7) The Pendulum 115
Chapter VI. Work And Energy.
(1) Work and Energy 119
(2) Power and Energy 123
(3) The Lever and Simple Machines 129
(4) Wheel and Axle and Pulley 136
(5) Efficiency and the Inclined Plane 142
(6) Friction and its Uses 147
(7) Water Power 152
Chapter VII. Heat, Its Production And Transmission.
(1) Sources and Effects of Heat 159
(2) Temperature and Expansion 162
(3) Expansion of Gases, Liquids and Solids 167
(4) Modes of Transmitting Heat 173
(5) Convection, Heating and Ventilation 179
(6) The Moisture in the Air, Hygrometry 191
(7) Evaporation 196
Chapter VIII. Heat And Work.
(1) Heat Measurement and Specific Heat 200
(2) Heat and Changes of State 205
(3) Heat and Work 212
(4) Heat Engines 222
Chapter IX. Magnetism.
(1) General Properties of Magnets 228
(2) Theory of Magnetism, Magnetic Fields 232
(3) The Earth's Magnetism 238
Chapter XI. Static Electricity.
Page 14
(1) Electrification and Electrical Charges 243
(2) Electric Fields and Electrostatic Induction 247
(3) Electric Theories, Distribution and Electric Charges 252
(4) Potential, Capacity, and the Electric Condenser 257
(5) Electrostatic Generators 262
Chapter XI. Electric Currents Produced By Voltaic Cells.
(1) Electrical Currents and Circuits 267
(2) The Simple Voltaic Cell and its Action 270
(3) Practical Voltaic Cells 274
Chapter XII. Magnetic Effects Of Electric Currents, And Electrical
Measurements.
(1) The Magnetic Effect of Electric Currents 279
(2) Electrical Measurements 289
(3) Ohm's Law and Electrical Circuits 298
(4) Grouping of Cells and Measuring Resistance 302
Chapter XIII. Chemical And Heat Effects Of Electric Currents.
(1) The Chemical Effect of Electric Currents 307
(2) The Storage Battery and Electric Power 312
(3) The Heat Effect of Electric Currents 318
Chapter XIV. Induced Currents.
(1) Electromagnetic Induction 326
(2) The Dynamo and the Motor 335
(3) The Induction Coil and the Transformer 343
(4) The Telephone 349
Chapter XV. Sound.
(1) Sound, Source, Speed, Media 354
(2) Waves and Wave Motion 357
(3) Intensity and Pitch of Sound 363
(2) Electric Fields and Electrostatic Induction 247
(3) Electric Theories, Distribution and Electric Charges 252
(4) Potential, Capacity, and the Electric Condenser 257
(5) Electrostatic Generators 262
Chapter XI. Electric Currents Produced By Voltaic Cells.
(1) Electrical Currents and Circuits 267
(2) The Simple Voltaic Cell and its Action 270
(3) Practical Voltaic Cells 274
Chapter XII. Magnetic Effects Of Electric Currents, And Electrical
Measurements.
(1) The Magnetic Effect of Electric Currents 279
(2) Electrical Measurements 289
(3) Ohm's Law and Electrical Circuits 298
(4) Grouping of Cells and Measuring Resistance 302
Chapter XIII. Chemical And Heat Effects Of Electric Currents.
(1) The Chemical Effect of Electric Currents 307
(2) The Storage Battery and Electric Power 312
(3) The Heat Effect of Electric Currents 318
Chapter XIV. Induced Currents.
(1) Electromagnetic Induction 326
(2) The Dynamo and the Motor 335
(3) The Induction Coil and the Transformer 343
(4) The Telephone 349
Chapter XV. Sound.
(1) Sound, Source, Speed, Media 354
(2) Waves and Wave Motion 357
(3) Intensity and Pitch of Sound 363
Page 15
(4) Musical Scales and Resonance 368
(5) Interference, Beats, Vibration of Strings 374
(6) Tone Quality, Vibrating Plates and Air Columns 384
Chapter XVI. Light.
(1) Rectilinear Propagation of Light 388
(2) Photometry and Law of Reflection 393
(3) Mirrors and Formation of Images 400
(4) Refraction of Light 410
(5) The Formation of Images by Lenses 416
(6) Optical Instruments 423
(7) Color and Spectra 430
(8) Nature of Light 442
Chapter XVII. Invisible Radiations.
(1) Electric waves and Radioactivity 448
Chapter XVIII. Wireless Telephony And Alternating Currents.
(1) Wireless Telephony 460
(2) Alternating Currents 466
Index 487
PHYSICS
(5) Interference, Beats, Vibration of Strings 374
(6) Tone Quality, Vibrating Plates and Air Columns 384
Chapter XVI. Light.
(1) Rectilinear Propagation of Light 388
(2) Photometry and Law of Reflection 393
(3) Mirrors and Formation of Images 400
(4) Refraction of Light 410
(5) The Formation of Images by Lenses 416
(6) Optical Instruments 423
(7) Color and Spectra 430
(8) Nature of Light 442
Chapter XVII. Invisible Radiations.
(1) Electric waves and Radioactivity 448
Chapter XVIII. Wireless Telephony And Alternating Currents.
(1) Wireless Telephony 460
(2) Alternating Currents 466
Index 487
PHYSICS
Page 16
CHAPTER I
INTRODUCTION AND MEASUREMENT
(1) Introduction
1. Physics, an Explanation of Common Things.—Many students take up
the study of physics expecting to see wonderful experiments with the "X"
rays, wireless telegraphy, dynamos, and other interesting devices. Others
are dreading to begin a study that to them seems strange and difficult,
because they fear it deals with ideas and principles that are beyond their
experience and hard to comprehend.
Each of these classes is surprised to learn that physics is mainly an
explanation of common things. It is a study that systematizes our knowledge
of the forces and changes about us; such as the pull of the earth, the
formation of dew, rain and frost, water pressure and pumps, echoes and
music, thermometers and engines, and many other things about us with
which people are more or less familiar. Physics is like other school subjects,
such as mathematics and language, in having its own peculiar vocabulary
and methods of study; these will be acquired as progress is made in the
course.
The most useful habit that the student of physics can form is that of
connecting or relating each new idea or fact that is presented to him to some
observation or experience that will illustrate the new idea. This relating or
connecting of the new ideas to one's own personal experience is not only
one of the best known means of cultivating the memory and power of
association, but it is of especial help in a subject such as physics, which
deals with the systematic study and explanation of the facts of our every-
day experience.
2. Knowledge—Common and Scientific.—This leads to the distinction
between common knowledge and scientific knowledge. We all possess
common knowledge of the things about us, gained from the impressions
received by our senses, from reading, and from the remarks of others.
INTRODUCTION AND MEASUREMENT
(1) Introduction
1. Physics, an Explanation of Common Things.—Many students take up
the study of physics expecting to see wonderful experiments with the "X"
rays, wireless telegraphy, dynamos, and other interesting devices. Others
are dreading to begin a study that to them seems strange and difficult,
because they fear it deals with ideas and principles that are beyond their
experience and hard to comprehend.
Each of these classes is surprised to learn that physics is mainly an
explanation of common things. It is a study that systematizes our knowledge
of the forces and changes about us; such as the pull of the earth, the
formation of dew, rain and frost, water pressure and pumps, echoes and
music, thermometers and engines, and many other things about us with
which people are more or less familiar. Physics is like other school subjects,
such as mathematics and language, in having its own peculiar vocabulary
and methods of study; these will be acquired as progress is made in the
course.
The most useful habit that the student of physics can form is that of
connecting or relating each new idea or fact that is presented to him to some
observation or experience that will illustrate the new idea. This relating or
connecting of the new ideas to one's own personal experience is not only
one of the best known means of cultivating the memory and power of
association, but it is of especial help in a subject such as physics, which
deals with the systematic study and explanation of the facts of our every-
day experience.
2. Knowledge—Common and Scientific.—This leads to the distinction
between common knowledge and scientific knowledge. We all possess
common knowledge of the things about us, gained from the impressions
received by our senses, from reading, and from the remarks of others.
Page 17
Scientific knowledge is attained when the bits of common knowledge are
connected and explained by other information gained through study or
experience. That is, common knowledge becomes scientific, when it is
organized. This leads to the definition: Science is organized knowledge.
Common knowledge of the forces and objects about us becomes scientific
only as we are able to make accurate measurements of these. That is,
science is concerned not only in how things work, but even more in how
much is involved or results from a given activity. For example, a scientific
farmer must be able to compute his costs and results in order to determine
accurately his net profits. The business man who is conducting his business
with efficiency knows accurately his costs of production and distribution.
This book is written in the hope that it will make more scientific the
student's common knowledge of the forces and changes in the world about
him and will give him many ideas and principles that will help him to
acquire the habit of looking from effects to their natural causes and thus
tend to develop what is called the scientific habit of thought.
3. Hypothesis, Theory, and Law.—Three words that are frequently used in
science may be mentioned here: hypothesis, theory, and law. An hypothesis
is a supposition advanced to explain some effect, change, or condition that
has been observed. For example, the Nebular Hypothesis of which many
high-school students have heard, is an attempt to explain the origin of the
sun, the earth, the planets, and other solar systems.
A theory is an hypothesis which has been tested in a variety of ways and
which seems to fit the conditions and results so that it is generally accepted
as giving a satisfactory explanation of the matter in question. The Molecular
Theory of Matter which states that matter of all kinds is composed of very
small particles called molecules (see Art. 6), is a familiar example of a
theory.
A theory becomes a law when it may be definitely proved. Many laws are
expressed in mathematical language, e.g., the law of gravitation. (See Art.
88.) Many of the laws of physics are illustrated by laboratory experiments,
which show in a simple way just what the law means.
Exercises
connected and explained by other information gained through study or
experience. That is, common knowledge becomes scientific, when it is
organized. This leads to the definition: Science is organized knowledge.
Common knowledge of the forces and objects about us becomes scientific
only as we are able to make accurate measurements of these. That is,
science is concerned not only in how things work, but even more in how
much is involved or results from a given activity. For example, a scientific
farmer must be able to compute his costs and results in order to determine
accurately his net profits. The business man who is conducting his business
with efficiency knows accurately his costs of production and distribution.
This book is written in the hope that it will make more scientific the
student's common knowledge of the forces and changes in the world about
him and will give him many ideas and principles that will help him to
acquire the habit of looking from effects to their natural causes and thus
tend to develop what is called the scientific habit of thought.
3. Hypothesis, Theory, and Law.—Three words that are frequently used in
science may be mentioned here: hypothesis, theory, and law. An hypothesis
is a supposition advanced to explain some effect, change, or condition that
has been observed. For example, the Nebular Hypothesis of which many
high-school students have heard, is an attempt to explain the origin of the
sun, the earth, the planets, and other solar systems.
A theory is an hypothesis which has been tested in a variety of ways and
which seems to fit the conditions and results so that it is generally accepted
as giving a satisfactory explanation of the matter in question. The Molecular
Theory of Matter which states that matter of all kinds is composed of very
small particles called molecules (see Art. 6), is a familiar example of a
theory.
A theory becomes a law when it may be definitely proved. Many laws are
expressed in mathematical language, e.g., the law of gravitation. (See Art.
88.) Many of the laws of physics are illustrated by laboratory experiments,
which show in a simple way just what the law means.
Exercises
Page 18
Explain what is meant by the following terms and expressions:
1. Common knowledge.
2. Scientific knowledge.
3. Science.
4. Topics in physics.
5. Scientific habit of thought.
6. Value of relating new ideas to former experiences.
7. Hypothesis.
8. Theory.
9. Law.
(2) The States of Matter
4. Physics Defined.—In the study of any science or field of knowledge, it
is helpful to have a basis for grouping or classifying the facts studied. In
physics we are to study the objects, forces, and changes about us, to
understand them and their relations to one another. Accordingly, physics,
dealing with the material world about us, is often defined as the science of
matter and energy, matter being anything that occupies space and energy
the capacity for doing work. This definition of physics while not strictly
accurate is sufficiently comprehensive for our present purpose.
5. The Three States of Matter.—Our bodies are matter since they occupy
space. Further, they possess energy since they are able to do work. In
beginning the study of physics it will simplify our work if we study one of
these topics before the other. We will therefore begin with matter and
consider first its three states.
Some bodies are solid; as ice, iron, wax. Others are liquid; as water,
mercury, oil. Still others are in the state of gas; as steam, air, and
illuminating gas. Further we notice that the same substance may be found in
any one of the three states. For example water may be either ice, water or
steam; that is, either a solid, a liquid, or a gas.
1. Common knowledge.
2. Scientific knowledge.
3. Science.
4. Topics in physics.
5. Scientific habit of thought.
6. Value of relating new ideas to former experiences.
7. Hypothesis.
8. Theory.
9. Law.
(2) The States of Matter
4. Physics Defined.—In the study of any science or field of knowledge, it
is helpful to have a basis for grouping or classifying the facts studied. In
physics we are to study the objects, forces, and changes about us, to
understand them and their relations to one another. Accordingly, physics,
dealing with the material world about us, is often defined as the science of
matter and energy, matter being anything that occupies space and energy
the capacity for doing work. This definition of physics while not strictly
accurate is sufficiently comprehensive for our present purpose.
5. The Three States of Matter.—Our bodies are matter since they occupy
space. Further, they possess energy since they are able to do work. In
beginning the study of physics it will simplify our work if we study one of
these topics before the other. We will therefore begin with matter and
consider first its three states.
Some bodies are solid; as ice, iron, wax. Others are liquid; as water,
mercury, oil. Still others are in the state of gas; as steam, air, and
illuminating gas. Further we notice that the same substance may be found in
any one of the three states. For example water may be either ice, water or
steam; that is, either a solid, a liquid, or a gas.
Page 19
Most persons have heard of liquid air and possibly some know of ice air,
i.e., air cooled until it not only liquefies, but is solidified. On the other hand,
iron may be melted and, if heated hot enough, may be turned into iron
vapor. In fact most substances by heating or cooling sufficiently may be
changed into any one of the three states.
Before defining the three states, let us consider the structure of matter. This
may help us to answer the question: How is it possible to change a hard
solid, such as ice, into a liquid, water, and then into an invisible gas like
steam? This is explained by the molecular theory of matter.
6. The Molecular Theory of Matter.—It is believed that all bodies are
made up of very small particles called molecules, and that these instead of
being packed tightly together like square packages in a box, are, strange as
it may seem, very loosely packed even in solids and do not permanently
touch their neighbors. The size of these molecules is so minute that it has
been estimated that if a drop of water could be magnified to the size of the
earth, the molecules magnified in the same proportion would be in size
between a baseball and a football. The air and all other gases are believed to
be made up of molecules in rapid motion, striking and rebounding
continually from one another and from any objects in contact with the gas.
7. States of Matter Defined.—These ideas of the structure of matter assist
us in understanding the following definitions: A solid is that state of matter
in which the molecules strongly cling together and tend to keep the same
relative positions. (This of course follows from the tendency of a solid to
retain a definite form.) A liquid is that state of matter in which the
molecules tend to cling together, yet move about freely. Hence a liquid takes
the form of any vessel in which it is placed. A gas is that state of matter in
which the molecules move about freely and tend to separate indefinitely.
Hence a gas will fill any space in which it is placed.
8. Effect of Heat on Matter.—It is further believed that when a body is
heated, that the action really consists in making its molecules move or
vibrate faster and faster as the heating progresses. This increase of motion
causes the molecules to push apart from one another and this separation of
the molecules causes an expansion of the body whether it be solid, liquid, or
gas. Fig. 1 shows the expansion of air in an air thermometer. Fig. 2 shows
the expansion of a solid on heating.
i.e., air cooled until it not only liquefies, but is solidified. On the other hand,
iron may be melted and, if heated hot enough, may be turned into iron
vapor. In fact most substances by heating or cooling sufficiently may be
changed into any one of the three states.
Before defining the three states, let us consider the structure of matter. This
may help us to answer the question: How is it possible to change a hard
solid, such as ice, into a liquid, water, and then into an invisible gas like
steam? This is explained by the molecular theory of matter.
6. The Molecular Theory of Matter.—It is believed that all bodies are
made up of very small particles called molecules, and that these instead of
being packed tightly together like square packages in a box, are, strange as
it may seem, very loosely packed even in solids and do not permanently
touch their neighbors. The size of these molecules is so minute that it has
been estimated that if a drop of water could be magnified to the size of the
earth, the molecules magnified in the same proportion would be in size
between a baseball and a football. The air and all other gases are believed to
be made up of molecules in rapid motion, striking and rebounding
continually from one another and from any objects in contact with the gas.
7. States of Matter Defined.—These ideas of the structure of matter assist
us in understanding the following definitions: A solid is that state of matter
in which the molecules strongly cling together and tend to keep the same
relative positions. (This of course follows from the tendency of a solid to
retain a definite form.) A liquid is that state of matter in which the
molecules tend to cling together, yet move about freely. Hence a liquid takes
the form of any vessel in which it is placed. A gas is that state of matter in
which the molecules move about freely and tend to separate indefinitely.
Hence a gas will fill any space in which it is placed.
8. Effect of Heat on Matter.—It is further believed that when a body is
heated, that the action really consists in making its molecules move or
vibrate faster and faster as the heating progresses. This increase of motion
causes the molecules to push apart from one another and this separation of
the molecules causes an expansion of the body whether it be solid, liquid, or
gas. Fig. 1 shows the expansion of air in an air thermometer. Fig. 2 shows
the expansion of a solid on heating.
Page 20
9. Physical and Chemical Changes. A change of state
such as the freezing or boiling of water is called a physical
change, for this change has not affected the identity of the
substance. It is water even though it has become solid or
gaseous. Heating a platinum wire red hot is also a physical
change for the wire when on cooling is found to be the
same substance as before. Further if salt or sugar be
dissolved in water the act of solution is also a physical
change since the identical substance (salt or sugar) is in
the solution and may be obtained by evaporating the
water.
Fig. 1.—
When the
bulb is
heated, the
air within
expands
forcing down
the water in
the tube.
Fig. 2 (a) represents a straight bar made of a
strip of brass and a strip of iron riveted
together and attached to a handle. Upon
heating the compound bar in a gas flame, the
brass expands faster than the iron causing the
bar to bend toward the latter as in Fig. 2 (b).
such as the freezing or boiling of water is called a physical
change, for this change has not affected the identity of the
substance. It is water even though it has become solid or
gaseous. Heating a platinum wire red hot is also a physical
change for the wire when on cooling is found to be the
same substance as before. Further if salt or sugar be
dissolved in water the act of solution is also a physical
change since the identical substance (salt or sugar) is in
the solution and may be obtained by evaporating the
water.
Fig. 1.—
When the
bulb is
heated, the
air within
expands
forcing down
the water in
the tube.
Fig. 2 (a) represents a straight bar made of a
strip of brass and a strip of iron riveted
together and attached to a handle. Upon
heating the compound bar in a gas flame, the
brass expands faster than the iron causing the
bar to bend toward the latter as in Fig. 2 (b).
Page 21
If some sugar, however, is heated strongly, say in a test-tube, it is found to
blacken, some water is driven off and on cooling some black charcoal is
found in the tube instead of the sugar. This action which has resulted in a
change in the nature of the substance treated is called a chemical change.
To illustrate further, if some magnesium wire is heated strongly in a flame,
it burns, giving off an intense light and when it cools one finds it changed to
a light powdery substance like ashes. Chemical changes, or those that
change the nature of the substance affected, are studied in chemistry. In
physics we have to do only with physical changes, that is, with those
changes that do not affect the nature of the substance.
Important Topics
1. Physics defined.
2. The three states of matter; solid, liquid, gas.
3. Molecular theory of matter.
4. Physical and chemical changes.
Exercises
Write out in your own words your understanding of:
1. The structure of matter.
2. Some of the differences between solids, liquids, and gases.
3. How to change solids to liquids and gases and vice versa.
4. The reason for the changes of size of a body on heating.
5. Why cooling a gas tends to change it to a liquid or a solid.
6. The actual size of molecules.
Which of the following changes are chemical and which physical?
Give reasons.
1. Melting of ice.
2. Burning of a candle.
blacken, some water is driven off and on cooling some black charcoal is
found in the tube instead of the sugar. This action which has resulted in a
change in the nature of the substance treated is called a chemical change.
To illustrate further, if some magnesium wire is heated strongly in a flame,
it burns, giving off an intense light and when it cools one finds it changed to
a light powdery substance like ashes. Chemical changes, or those that
change the nature of the substance affected, are studied in chemistry. In
physics we have to do only with physical changes, that is, with those
changes that do not affect the nature of the substance.
Important Topics
1. Physics defined.
2. The three states of matter; solid, liquid, gas.
3. Molecular theory of matter.
4. Physical and chemical changes.
Exercises
Write out in your own words your understanding of:
1. The structure of matter.
2. Some of the differences between solids, liquids, and gases.
3. How to change solids to liquids and gases and vice versa.
4. The reason for the changes of size of a body on heating.
5. Why cooling a gas tends to change it to a liquid or a solid.
6. The actual size of molecules.
Which of the following changes are chemical and which physical?
Give reasons.
1. Melting of ice.
2. Burning of a candle.
Page 22
3. Production of steam.
4. Falling of a weight.
5. Drying of clothes.
6. Making an iron casting.
7. Decay of vegetables.
8. Sprouting of seeds.
9. Flying an aeroplane.
10. Growth of a plant.
11. Grinding of grain.
12. Sawing a board.
13. Pulverizing stone.
14. Making toast.
15. Sweetening tea or coffee with sugar.
16. Burning wood or gas.
(3) The Metric System
10. The Metric System.—In order to study the three states of matter with
sufficient exactness it is necessary to employ a system of measurement. The
system universally employed by scientists is called The Metric System. In
many respects it is the most convenient for all purposes. Every student
should therefore become familiar with it and learn to use it. At the present
time, not only do scientists everywhere use it, but many countries have
adopted it and use it in common measurements. It was legalized in the
United States in 1866. The metric system was originated by the French
Academy of Sciences during the latter part of the 18th century. There were
so many different systems of weights and measures in use, each country
having a system of its own, that commerce was much hindered. It was
therefore decided to make a system based upon scientific principles. The
length of the earth's quadrant passing from the equator to the pole was
determined by surveying and computation. One-ten-millionth of this
4. Falling of a weight.
5. Drying of clothes.
6. Making an iron casting.
7. Decay of vegetables.
8. Sprouting of seeds.
9. Flying an aeroplane.
10. Growth of a plant.
11. Grinding of grain.
12. Sawing a board.
13. Pulverizing stone.
14. Making toast.
15. Sweetening tea or coffee with sugar.
16. Burning wood or gas.
(3) The Metric System
10. The Metric System.—In order to study the three states of matter with
sufficient exactness it is necessary to employ a system of measurement. The
system universally employed by scientists is called The Metric System. In
many respects it is the most convenient for all purposes. Every student
should therefore become familiar with it and learn to use it. At the present
time, not only do scientists everywhere use it, but many countries have
adopted it and use it in common measurements. It was legalized in the
United States in 1866. The metric system was originated by the French
Academy of Sciences during the latter part of the 18th century. There were
so many different systems of weights and measures in use, each country
having a system of its own, that commerce was much hindered. It was
therefore decided to make a system based upon scientific principles. The
length of the earth's quadrant passing from the equator to the pole was
determined by surveying and computation. One-ten-millionth of this
Page 23
distance was selected as the unit of length and called a meter. Accurate
copies of this meter were made and preserved as standards.
Later surveys have shown that the original determination of the earth's
quadrant was not strictly accurate; so that after all the meter is not exactly
one-ten-millionth of the earth's quadrant.
11. The Standard Meter.—The standard unit of length in the metric system
is the meter. It is the distance, at the temperature of melting ice, between
two transverse parallel lines ruled on a bar of platinum (see Fig. 3), which is
kept in the Palace of the Archives in Paris. Accurate copies of this and other
metric standards are also kept at the Bureau of Standards at Washington, D.
C. Fig. 4 shows the relation between the inch and the centimeter (one-
hundredth of a meter).
12. Units and Tables in the Metric System.—The metric unit of area
commonly used in physics is the square centimeter.
The standard unit of volume or capacity is the liter. It is a
cube one-tenth of a meter on each edge. It is equal to 1.057
quarts. It corresponds, therefore, to the quart in English
measure.
Fig. 3—
The
standard
meter.
Fig. 4.—Centimeter and inch scales.
copies of this meter were made and preserved as standards.
Later surveys have shown that the original determination of the earth's
quadrant was not strictly accurate; so that after all the meter is not exactly
one-ten-millionth of the earth's quadrant.
11. The Standard Meter.—The standard unit of length in the metric system
is the meter. It is the distance, at the temperature of melting ice, between
two transverse parallel lines ruled on a bar of platinum (see Fig. 3), which is
kept in the Palace of the Archives in Paris. Accurate copies of this and other
metric standards are also kept at the Bureau of Standards at Washington, D.
C. Fig. 4 shows the relation between the inch and the centimeter (one-
hundredth of a meter).
12. Units and Tables in the Metric System.—The metric unit of area
commonly used in physics is the square centimeter.
The standard unit of volume or capacity is the liter. It is a
cube one-tenth of a meter on each edge. It is equal to 1.057
quarts. It corresponds, therefore, to the quart in English
measure.
Fig. 3—
The
standard
meter.
Fig. 4.—Centimeter and inch scales.
Page 24
The standard unit of mass is the kilogram. It is the mass of 1 liter of pure
water at the temperature of its greatest density, 4°C. or 39.2°F.
The three principal units of the metric system, the meter, the liter, and the
kilogram, are related to one another in a simple manner, since the liter is a
cube one-tenth of a meter in each dimension and the kilogram is the mass of
a liter of water. (See Fig. 5.)
The metric system is a decimal system that is, one unit is related to another
unit in the ratio of ten or of some power of ten. This is indicated by the
following tables:
Metric Table of Length
10 millimeters (mm.) equal 1 centimeter.
10 centimeters (cm.) equal 1 decimeter.
10 decimeters (dm.) equal 1 meter.
10 meters (m.) equal 1 dekameter.
10 dekameters (Dm.) equal 1 hectometer.
10 hectometers (hm.) equal 1 kilometer.
10 kilometers (km.) equal 1 myriameter.
The measures commonly used are the centimeter, meter and kilometer.
Metric Table of Mass (or Weight)
10 milligrams (mg.) equal 1 centigram.
10 centigrams (cg.) equal 1 decigram.
10 decigrams (dg.) equal 1 gram.
10 grams (g.) equal 1 dekagram.
10 dekagrams (Dg.) equal 1 hectogram.
10 hectograms (hg.) equal 1 kilogram.
10 kilograms (kg.) equal 1 myriagram.
The masses commonly used are the milligram, gram and kilogram.
Notice in these tables the similarity to 10 mills equal 1 cent, 10 cents equal
1 dime, 10 dimes equal 1 dollar, in the table of United States money.
Other tables in the metric system are built upon the same plan. Learn the
prefixes in order thus: milli, centi, deci, deka, hecto, kilo, myria. The first
water at the temperature of its greatest density, 4°C. or 39.2°F.
The three principal units of the metric system, the meter, the liter, and the
kilogram, are related to one another in a simple manner, since the liter is a
cube one-tenth of a meter in each dimension and the kilogram is the mass of
a liter of water. (See Fig. 5.)
The metric system is a decimal system that is, one unit is related to another
unit in the ratio of ten or of some power of ten. This is indicated by the
following tables:
Metric Table of Length
10 millimeters (mm.) equal 1 centimeter.
10 centimeters (cm.) equal 1 decimeter.
10 decimeters (dm.) equal 1 meter.
10 meters (m.) equal 1 dekameter.
10 dekameters (Dm.) equal 1 hectometer.
10 hectometers (hm.) equal 1 kilometer.
10 kilometers (km.) equal 1 myriameter.
The measures commonly used are the centimeter, meter and kilometer.
Metric Table of Mass (or Weight)
10 milligrams (mg.) equal 1 centigram.
10 centigrams (cg.) equal 1 decigram.
10 decigrams (dg.) equal 1 gram.
10 grams (g.) equal 1 dekagram.
10 dekagrams (Dg.) equal 1 hectogram.
10 hectograms (hg.) equal 1 kilogram.
10 kilograms (kg.) equal 1 myriagram.
The masses commonly used are the milligram, gram and kilogram.
Notice in these tables the similarity to 10 mills equal 1 cent, 10 cents equal
1 dime, 10 dimes equal 1 dollar, in the table of United States money.
Other tables in the metric system are built upon the same plan. Learn the
prefixes in order thus: milli, centi, deci, deka, hecto, kilo, myria. The first
Page 25
three prefixes are Latin numerals and represent divisions of the unit. The
last four are Greek numerals and represent multiples. In these tables, milli
means 1/1000, centi means 1/100, deci means 1/10, deka means 10, hecto,
100, kilo, 1000, myria, 10,000. Two other prefixes are sometimes used,
micro which means 1/1,000,000; as microfarad or microvolt, and meg
which means 1,000,000, as megohm meaning 1,000,000 ohms.
13. Advantages of the Metric System.—First, it is a decimal system;
second, the same form and prefixes are used in every table; third, the
standards of length (meter), volume (liter), and mass (kilogram) bear a
simple relation to one another. This simple relation between the three
standard units may be given thus: first, the liter is a cubic decimeter, and
second, the kilogram is the mass of a liter of water. (See Fig. 5) Since the
liter is a cubic decimeter, the length of one side is 10 cm. The liter therefore
holds 1000 ccm. (10 × 10 × 10). Therefore, 1 liter = 1 cu. dm. = 1000 ccm.
and since 1 liter of water has a mass of 1 kg. or 1000 g., then 1000 ccm. of
water has a mass of 1000 g., or 1 ccm. of water has a mass of 1 g.
Fig. 5.—One liter of the water has a mass of
one kilogram.
The following table of equivalents gives the relation between the most
common English and metric units. Those marked (*) should be memorized.
(*) 1 meter = 39.37 inches. 1 cu, in. = 16.387 ccm.
(*) 1 inch = 2.54 cm. 1 cu. ft. = 28315 cm.
1 foot = 30.48 cm. 1 cu. m. = 1.308 cu. yd.
1 mile = 1.609 km. (*) 1 liter = 1.057 qt.
1 sq. in. = 6.45 sq. cm. (*) 1 kg. = 2.204 lbs.
last four are Greek numerals and represent multiples. In these tables, milli
means 1/1000, centi means 1/100, deci means 1/10, deka means 10, hecto,
100, kilo, 1000, myria, 10,000. Two other prefixes are sometimes used,
micro which means 1/1,000,000; as microfarad or microvolt, and meg
which means 1,000,000, as megohm meaning 1,000,000 ohms.
13. Advantages of the Metric System.—First, it is a decimal system;
second, the same form and prefixes are used in every table; third, the
standards of length (meter), volume (liter), and mass (kilogram) bear a
simple relation to one another. This simple relation between the three
standard units may be given thus: first, the liter is a cubic decimeter, and
second, the kilogram is the mass of a liter of water. (See Fig. 5) Since the
liter is a cubic decimeter, the length of one side is 10 cm. The liter therefore
holds 1000 ccm. (10 × 10 × 10). Therefore, 1 liter = 1 cu. dm. = 1000 ccm.
and since 1 liter of water has a mass of 1 kg. or 1000 g., then 1000 ccm. of
water has a mass of 1000 g., or 1 ccm. of water has a mass of 1 g.
Fig. 5.—One liter of the water has a mass of
one kilogram.
The following table of equivalents gives the relation between the most
common English and metric units. Those marked (*) should be memorized.
(*) 1 meter = 39.37 inches. 1 cu, in. = 16.387 ccm.
(*) 1 inch = 2.54 cm. 1 cu. ft. = 28315 cm.
1 foot = 30.48 cm. 1 cu. m. = 1.308 cu. yd.
1 mile = 1.609 km. (*) 1 liter = 1.057 qt.
1 sq. in. = 6.45 sq. cm. (*) 1 kg. = 2.204 lbs.
Page 26
1 sq. cm. = 0.155 sq. in. 1 g. = 15.44 grains.
1 sq. m. = 1.196 sq. yd. 1 lb. = 0.4536 kg.
1 acre = 0.405 ha. 1 oz. = 28.35 g.
1 hectare = 2.45 acres. 1 g. = 0.0353 oz.
The c. g. s. system. Scientists have devised a plan for expressing any
measurement in terms of what are called the three fundamental units of
length, mass, and time. The units used are the centimeter, the gram and the
second. Whenever a measurement has been reduced to its equivalent in
terms of these units, it is said to be expressed in C.G.S. units.
Important Topics
1. The metric system; how originated.
2. Units; meter, liter, kilogram.
3. Metric tables.
4. Advantages of the metric system.
5. Equivalents.
6. The C.G.S. system.
Exercises
1. Which is cheaper, milk at 8 cents a quart or 8 cents a liter? Why?
2. Which is more expensive, cloth at $1.00 a yard or at $1.00 a meter?
Why?
3. Which is a better bargain, sugar at 5 cents a pound or 11 cents a
kilogram? Why?
4. Express in centimeters the height of a boy 5 ft. 6 in. tall.
5. What is the length of this page in centimeters? In inches?
6. What is the mass of a liter of water? Of 500 ccm.? Of 1 ccm.?
7. From Chicago to New York is 940 miles. Express in kilometers.
1 sq. m. = 1.196 sq. yd. 1 lb. = 0.4536 kg.
1 acre = 0.405 ha. 1 oz. = 28.35 g.
1 hectare = 2.45 acres. 1 g. = 0.0353 oz.
The c. g. s. system. Scientists have devised a plan for expressing any
measurement in terms of what are called the three fundamental units of
length, mass, and time. The units used are the centimeter, the gram and the
second. Whenever a measurement has been reduced to its equivalent in
terms of these units, it is said to be expressed in C.G.S. units.
Important Topics
1. The metric system; how originated.
2. Units; meter, liter, kilogram.
3. Metric tables.
4. Advantages of the metric system.
5. Equivalents.
6. The C.G.S. system.
Exercises
1. Which is cheaper, milk at 8 cents a quart or 8 cents a liter? Why?
2. Which is more expensive, cloth at $1.00 a yard or at $1.00 a meter?
Why?
3. Which is a better bargain, sugar at 5 cents a pound or 11 cents a
kilogram? Why?
4. Express in centimeters the height of a boy 5 ft. 6 in. tall.
5. What is the length of this page in centimeters? In inches?
6. What is the mass of a liter of water? Of 500 ccm.? Of 1 ccm.?
7. From Chicago to New York is 940 miles. Express in kilometers.
Page 27
8. A 10-gallon can of milk contains how many liters?
9. What will 100 meters of cloth cost at 10 cents a yard?
10. What will 4 kg. of beef cost at 15 cents a pound?
11. What will 5-1/2 lbs. of mutton cost at 40 cents a kilogram?
12. How can you change the state of a body? Give three methods.
13. Correct the statement 1 ccm. = 1 g.
14. How many liters in 32 quarts?
9. What will 100 meters of cloth cost at 10 cents a yard?
10. What will 4 kg. of beef cost at 15 cents a pound?
11. What will 5-1/2 lbs. of mutton cost at 40 cents a kilogram?
12. How can you change the state of a body? Give three methods.
13. Correct the statement 1 ccm. = 1 g.
14. How many liters in 32 quarts?
Page 28
CHAPTER II
MOLECULAR FORCES AND MOTIONS
(1) Evidences of Molecular Motion in Gases
14. Size of Molecules.—The difference between solids, liquids, and gases
has been explained as due to the different behavior of molecules in the three
states of matter. That is, in solids they cling together, in liquids they move
freely, and in gases they separate. At this time we are to consider the
evidences of molecular motion in gases. It must be kept in mind that
molecules are exceedingly small. It has been said that if a bottle containing
about 1 ccm. of ordinary air has pierced in it a minute opening so that
100,000,000 molecules (a number nearly equal to the population of the
United States) pass out every second, it would take, not minutes or hours,
but nearly 9000 years for all of the molecules to escape. The number of
molecules in 1 ccm. of air at 0°C. and 76 cm. pressure has been calculated
by Professor Rutherford to be 2.7 × 1019. It is evident that such minute
particles cannot be seen or handled as individuals. We must judge of their
size and action by the results obtained from experiments.
15. Diffusion of Gases.—One line of evidence which indicates that a gas
consists of moving particles is the rapidity with which a gas having a strong
odor penetrates to all parts of a room. For example, if illuminating gas is
escaping it soon diffuses and is noticed throughout the room. In fact, the
common experience of the diffusion of gases having a strong odor is such
that we promptly recognize that it is due to motion of some kind. The gas
having the odor consists of little particles that are continually hitting their
neighbors and are being struck and buffeted in turn until the individual
molecules are widely scattered. When cabbage is boiled in the kitchen soon
all in the house know it. Other illustrations of the diffusion of gases will
occur to anyone from personal experience, such for instance as the pleasing
odor from a field of clover in bloom.
The following experiment illustrates the rapid diffusion of gases.
MOLECULAR FORCES AND MOTIONS
(1) Evidences of Molecular Motion in Gases
14. Size of Molecules.—The difference between solids, liquids, and gases
has been explained as due to the different behavior of molecules in the three
states of matter. That is, in solids they cling together, in liquids they move
freely, and in gases they separate. At this time we are to consider the
evidences of molecular motion in gases. It must be kept in mind that
molecules are exceedingly small. It has been said that if a bottle containing
about 1 ccm. of ordinary air has pierced in it a minute opening so that
100,000,000 molecules (a number nearly equal to the population of the
United States) pass out every second, it would take, not minutes or hours,
but nearly 9000 years for all of the molecules to escape. The number of
molecules in 1 ccm. of air at 0°C. and 76 cm. pressure has been calculated
by Professor Rutherford to be 2.7 × 1019. It is evident that such minute
particles cannot be seen or handled as individuals. We must judge of their
size and action by the results obtained from experiments.
15. Diffusion of Gases.—One line of evidence which indicates that a gas
consists of moving particles is the rapidity with which a gas having a strong
odor penetrates to all parts of a room. For example, if illuminating gas is
escaping it soon diffuses and is noticed throughout the room. In fact, the
common experience of the diffusion of gases having a strong odor is such
that we promptly recognize that it is due to motion of some kind. The gas
having the odor consists of little particles that are continually hitting their
neighbors and are being struck and buffeted in turn until the individual
molecules are widely scattered. When cabbage is boiled in the kitchen soon
all in the house know it. Other illustrations of the diffusion of gases will
occur to anyone from personal experience, such for instance as the pleasing
odor from a field of clover in bloom.
The following experiment illustrates the rapid diffusion of gases.
Page 29
Fig. 6a.—Diffusion of gases. Fig. 6b.—Effusion
of gases.
Take two tumblers (see Fig. 6a), wet the inside of one with a few drops of
strong ammonia water and the other with a little hydrochloric acid. Cover
each with a sheet of clean paper. Nothing can now be seen in either tumbler.
Invert the second one over the first with the paper between, placing them so
that the edges will match. On removing the paper it is noticed that both
tumblers are quickly filled with a cloud of finely divided particles, the two
substances having united chemically to form a new substance, ammonium
chloride.
On account of their small size, molecules of air readily pass through porous
solids, cloth, unglazed earthenware, etc. The following experiment shows
this fact strikingly. (See Fig. 6b.)
A flask containing water is closed by a rubber stopper through which pass
the stem of a glass funnel and a bent glass tube that has been drawn out to a
small opening (J). The funnel has cemented in its top an inverted porous
clay jar (C), over the top of the latter is placed a beaker (B). A piece of
flexible rubber tubing (H) leading from a hydrogen generator is brought up
to the top of the space between the jar and the beaker. When hydrogen gas
is allowed to flow into the space between C and B, the level of the water in
W is seen to lower and a stream of water runs out at J spurting up into the
air.
of gases.
Take two tumblers (see Fig. 6a), wet the inside of one with a few drops of
strong ammonia water and the other with a little hydrochloric acid. Cover
each with a sheet of clean paper. Nothing can now be seen in either tumbler.
Invert the second one over the first with the paper between, placing them so
that the edges will match. On removing the paper it is noticed that both
tumblers are quickly filled with a cloud of finely divided particles, the two
substances having united chemically to form a new substance, ammonium
chloride.
On account of their small size, molecules of air readily pass through porous
solids, cloth, unglazed earthenware, etc. The following experiment shows
this fact strikingly. (See Fig. 6b.)
A flask containing water is closed by a rubber stopper through which pass
the stem of a glass funnel and a bent glass tube that has been drawn out to a
small opening (J). The funnel has cemented in its top an inverted porous
clay jar (C), over the top of the latter is placed a beaker (B). A piece of
flexible rubber tubing (H) leading from a hydrogen generator is brought up
to the top of the space between the jar and the beaker. When hydrogen gas
is allowed to flow into the space between C and B, the level of the water in
W is seen to lower and a stream of water runs out at J spurting up into the
air.
Page 30
On stopping the flow of hydrogen and removing B, the water falls rapidly in
J and bubbles of air are seen to enter the water from the tube. (The
foregoing steps may be repeated as often as desired).
This experiment illustrates the fact that the molecules of some gases move
faster than those of some other gases. Hydrogen molecules are found to
move about four times as fast as air molecules. Hence, while both air and
hydrogen molecules are at first going in opposite directions through the
walls of C, the hydrogen goes in much faster than the air comes out. In
consequence it accumulates, creates pressure, and drives down the water in
W and out at J. On removing B, the hydrogen within the porous cup comes
out much faster than the air reënters. This lessens the pressure within, so
that air rushes in through J. This experiment demonstrates not only the fact
of molecular motion in gases but also that molecules of hydrogen move
much faster than those of air. (This experiment will work with illuminating
gas but not so strikingly.)
Careful experiments have shown that the speed of ordinary air molecules is
445 meters or 1460 ft. per second; while hydrogen molecules move at the
rate of 1700 meters or 5575 ft. or more than a mile per second.
16. Expansion of Gases.—Gases also possess the property of indefinite
expansion, that is, if a small quantity of gas is placed in a vacuum, the gas
will expand immediately to fill the entire space uniformly. This is shown by
an experiment with the air pump. On raising the piston the air follows
instantly to fill up the space under it. As the air is removed from the
receiver of an air pump the air remaining is uniformly distributed within.
17. How Gases Exert Pressure.—It is further found that air under ordinary
conditions exerts a pressure of about 15 lbs. to the square inch. In an
automobile tire the pressure may be 90 lbs. and in a steam boiler it may be
200 lbs. or more to the square inch.
How is the pressure produced? The molecules are not packed together
solidly in a gas, for when steam changes to water it shrinks to about 1/1600
of its former volume. Air diminishes to about 1/800 of its volume on
changing to liquid air. The pressure of a gas is not due then to the gas filling
all of the space in which it acts, but is due rather to the motion of the
molecules. The blow of a single molecule is imperceptible, but when
multitudes of molecules strike against a surface their combined effect is
J and bubbles of air are seen to enter the water from the tube. (The
foregoing steps may be repeated as often as desired).
This experiment illustrates the fact that the molecules of some gases move
faster than those of some other gases. Hydrogen molecules are found to
move about four times as fast as air molecules. Hence, while both air and
hydrogen molecules are at first going in opposite directions through the
walls of C, the hydrogen goes in much faster than the air comes out. In
consequence it accumulates, creates pressure, and drives down the water in
W and out at J. On removing B, the hydrogen within the porous cup comes
out much faster than the air reënters. This lessens the pressure within, so
that air rushes in through J. This experiment demonstrates not only the fact
of molecular motion in gases but also that molecules of hydrogen move
much faster than those of air. (This experiment will work with illuminating
gas but not so strikingly.)
Careful experiments have shown that the speed of ordinary air molecules is
445 meters or 1460 ft. per second; while hydrogen molecules move at the
rate of 1700 meters or 5575 ft. or more than a mile per second.
16. Expansion of Gases.—Gases also possess the property of indefinite
expansion, that is, if a small quantity of gas is placed in a vacuum, the gas
will expand immediately to fill the entire space uniformly. This is shown by
an experiment with the air pump. On raising the piston the air follows
instantly to fill up the space under it. As the air is removed from the
receiver of an air pump the air remaining is uniformly distributed within.
17. How Gases Exert Pressure.—It is further found that air under ordinary
conditions exerts a pressure of about 15 lbs. to the square inch. In an
automobile tire the pressure may be 90 lbs. and in a steam boiler it may be
200 lbs. or more to the square inch.
How is the pressure produced? The molecules are not packed together
solidly in a gas, for when steam changes to water it shrinks to about 1/1600
of its former volume. Air diminishes to about 1/800 of its volume on
changing to liquid air. The pressure of a gas is not due then to the gas filling
all of the space in which it acts, but is due rather to the motion of the
molecules. The blow of a single molecule is imperceptible, but when
multitudes of molecules strike against a surface their combined effect is
Page 31
considerable. In fact, this action is known to produce the pressure that a gas
exerts against the walls of a containing vessel. Naturally if we compress
twice as much gas into a given space there will be twice as many molecules
striking in a given time, which will give twice as much pressure.
If gas is heated, it is found that the heat will cause a swifter motion of the
molecules. This will also make the molecules strike harder and hence cause
the gas to expand or exert more pressure.
17a. Brownian Movements.—Direct photographic evidence of the motion
of molecules in gases has been obtained by studying the behavior of minute
drops of oil suspended in stagnant air. Such drops instead of being at rest
are constantly dancing about as if they were continually receiving blows
from many directions. These motions have been called Brownian
Movements (see Fig. 7).
It has been proved that these movements are due to the blows that these
small drops receive from the swiftly moving molecules of the gas about
them. If the drops are made smaller or the gas more dense, the movements
increase in intensity. These effects are especially marked at a pressure of
0.01 of an atmosphere.
Fig. 7.—Photograph of Brownian movement.
This record is prepared by the aid of
Siedentopf's ultra-microscope and a plate
moving uniformly across the field from left to
right.
Important Topics
exerts against the walls of a containing vessel. Naturally if we compress
twice as much gas into a given space there will be twice as many molecules
striking in a given time, which will give twice as much pressure.
If gas is heated, it is found that the heat will cause a swifter motion of the
molecules. This will also make the molecules strike harder and hence cause
the gas to expand or exert more pressure.
17a. Brownian Movements.—Direct photographic evidence of the motion
of molecules in gases has been obtained by studying the behavior of minute
drops of oil suspended in stagnant air. Such drops instead of being at rest
are constantly dancing about as if they were continually receiving blows
from many directions. These motions have been called Brownian
Movements (see Fig. 7).
It has been proved that these movements are due to the blows that these
small drops receive from the swiftly moving molecules of the gas about
them. If the drops are made smaller or the gas more dense, the movements
increase in intensity. These effects are especially marked at a pressure of
0.01 of an atmosphere.
Fig. 7.—Photograph of Brownian movement.
This record is prepared by the aid of
Siedentopf's ultra-microscope and a plate
moving uniformly across the field from left to
right.
Important Topics
Page 32
It is assumed that air and all gases are made up of molecules in rapid
motion; that this motion is dependent upon temperature and pressure.
Evidence of this is shown by (a) diffusion, (b) expansion, (c) pressure.
Brownian Movements.
Questions
1. What is the molecular (kinetic) theory of gases?
2. What three kinds of evidence help to confirm the theory?
3. What have you seen that seems to show that a gas consists of molecules
in motion?
4. How many meters long is a 10-ft. pole?
5. A 50-kg. boy weighs how many pounds?
6. What are three advantages of the metric system?
7. What will 12 qts. of milk cost at 8 cents a liter?
8. A cube 1 meter each way will contain how many cubic centimeters? How
many liters? What will a cubic meter of water weigh?
(2) Molecular Motion in Liquids
18. Diffusion of Liquids.—From the evidence given in Arts. 14-17, (a) of
diffusion of odors, (b) of the continued expansion of air in the air pump, and
(c) of the pressure exerted by a gas in all directions, one may realize
without difficulty that a gas consists of small particles in rapid motion. Let
us now consider some of the evidence of molecular motion in liquids. If a
little vinegar is placed in a pail of water, all of the water will soon taste
sour. A lump of sugar in a cup of tea will sweeten the entire contents. This
action is somewhat similar to the diffusion of gases but it takes place much
more slowly. It is therefore believed that the motion of liquid molecules is
much slower than that of gas molecules.
Again, if a dish of water is left standing in the open air in fine weather,
within a few days the dish will become dry though no one has taken
anything from it. We say the water has evaporated. What was liquid is now
motion; that this motion is dependent upon temperature and pressure.
Evidence of this is shown by (a) diffusion, (b) expansion, (c) pressure.
Brownian Movements.
Questions
1. What is the molecular (kinetic) theory of gases?
2. What three kinds of evidence help to confirm the theory?
3. What have you seen that seems to show that a gas consists of molecules
in motion?
4. How many meters long is a 10-ft. pole?
5. A 50-kg. boy weighs how many pounds?
6. What are three advantages of the metric system?
7. What will 12 qts. of milk cost at 8 cents a liter?
8. A cube 1 meter each way will contain how many cubic centimeters? How
many liters? What will a cubic meter of water weigh?
(2) Molecular Motion in Liquids
18. Diffusion of Liquids.—From the evidence given in Arts. 14-17, (a) of
diffusion of odors, (b) of the continued expansion of air in the air pump, and
(c) of the pressure exerted by a gas in all directions, one may realize
without difficulty that a gas consists of small particles in rapid motion. Let
us now consider some of the evidence of molecular motion in liquids. If a
little vinegar is placed in a pail of water, all of the water will soon taste
sour. A lump of sugar in a cup of tea will sweeten the entire contents. This
action is somewhat similar to the diffusion of gases but it takes place much
more slowly. It is therefore believed that the motion of liquid molecules is
much slower than that of gas molecules.
Again, if a dish of water is left standing in the open air in fine weather,
within a few days the dish will become dry though no one has taken
anything from it. We say the water has evaporated. What was liquid is now
Page 33
vapor. If we were to observe carefully any dish of water we would find that
it continually loses weight on dry days. That is, there is a constant
movement of the molecules of water into the air. This movement of the
molecules is explained as follows. There appear to be in the dish of water
some molecules that by moving back and forth acquire a greater velocity
than their neighbors; when these reach the surface of the liquid, some
vibration or movement sends them flying into the air above. They are now
vapor or gas molecules, flying, striking, and rebounding like the air
molecules. Sometimes on rebounding, the water molecules get back into the
water again. This is especially apt to happen when the air is damp, i.e.,
when it contains many water molecules. Sometimes the air over a dish
becomes saturated, as in the upper part of a corked bottle containing water.
Although molecules are continually leaving the surface of the water they
cannot escape from the bottle, so in time as many molecules must return to
the water from the space above as leave the water in the same time. When
this condition exists, the air above the water is said to be saturated. On very
damp days the air is often saturated. The explanation above shows why wet
clothes dry so slowly on such a day (See Arts. 166-7 on Saturation.)
19. Cooling Effect of Evaporation. We have seen that warming a gas
increases its volume. This expansion is due to the increased motion of the
warmed molecules. Now the molecules that escape from a liquid when it
evaporates are naturally the fastest moving ones, i.e., the hottest ones. The
molecules remaining are the slower moving ones or colder molecules. The
liquid therefore becomes colder as it evaporates, unless it is heated. This
explains why water evaporating on the surface of our bodies cools us. In
evaporating, the water is continually losing its warm, fast moving
molecules. The cooling effect of evaporation is, therefore an evidence of
molecular motion in liquids.
20. Osmosis.—If two liquids are separated by a membrane or porous
partition, they tend to pass through and mix. This action is called osmose, or
osmosis.
Such a movement of liquid molecules in osmosis may be illustrated by
filling a beet or carrot that has had its interior cut out to form a circular
opening (see Fig. 8) with a thick syrup. The opening is then closed at the
top with a rubber stopper through which passes a long glass tube.
it continually loses weight on dry days. That is, there is a constant
movement of the molecules of water into the air. This movement of the
molecules is explained as follows. There appear to be in the dish of water
some molecules that by moving back and forth acquire a greater velocity
than their neighbors; when these reach the surface of the liquid, some
vibration or movement sends them flying into the air above. They are now
vapor or gas molecules, flying, striking, and rebounding like the air
molecules. Sometimes on rebounding, the water molecules get back into the
water again. This is especially apt to happen when the air is damp, i.e.,
when it contains many water molecules. Sometimes the air over a dish
becomes saturated, as in the upper part of a corked bottle containing water.
Although molecules are continually leaving the surface of the water they
cannot escape from the bottle, so in time as many molecules must return to
the water from the space above as leave the water in the same time. When
this condition exists, the air above the water is said to be saturated. On very
damp days the air is often saturated. The explanation above shows why wet
clothes dry so slowly on such a day (See Arts. 166-7 on Saturation.)
19. Cooling Effect of Evaporation. We have seen that warming a gas
increases its volume. This expansion is due to the increased motion of the
warmed molecules. Now the molecules that escape from a liquid when it
evaporates are naturally the fastest moving ones, i.e., the hottest ones. The
molecules remaining are the slower moving ones or colder molecules. The
liquid therefore becomes colder as it evaporates, unless it is heated. This
explains why water evaporating on the surface of our bodies cools us. In
evaporating, the water is continually losing its warm, fast moving
molecules. The cooling effect of evaporation is, therefore an evidence of
molecular motion in liquids.
20. Osmosis.—If two liquids are separated by a membrane or porous
partition, they tend to pass through and mix. This action is called osmose, or
osmosis.
Such a movement of liquid molecules in osmosis may be illustrated by
filling a beet or carrot that has had its interior cut out to form a circular
opening (see Fig. 8) with a thick syrup. The opening is then closed at the
top with a rubber stopper through which passes a long glass tube.
Page 34
If the carrot is immersed in water, as in Fig. 8, a
movement of water through the porous wall to the
interior begins at once. Here, as in the experiment of
the hydrogen and air passing through the porous cup,
the lighter fluid moves faster. The water collecting in
the carrot rises in the tube. This action of liquids
passing through porous partitions and mingling is
called osmosis.
Gases and liquids are alike in that each will flow. Each
is therefore called a fluid. Sometimes there is much
resistance to the flow of a liquid as in molasses. This
resistance is called viscosity. Alcohol and gasoline
have little viscosity. They are limpid or mobile. Air
also has some viscosity. For instance, a stream of air
always drags some of the surrounding air along with
it.
Fig. 8.—Osmosis
Shown by carrot
placed in water.
Important Topics
1. Liquids behave as if they were composed of small particles in motion.
2. This is shown by (1) Diffusion, (2) Solution, (3) Evaporation, (4)
Expansion, (5) Osmosis.
Exercises
movement of water through the porous wall to the
interior begins at once. Here, as in the experiment of
the hydrogen and air passing through the porous cup,
the lighter fluid moves faster. The water collecting in
the carrot rises in the tube. This action of liquids
passing through porous partitions and mingling is
called osmosis.
Gases and liquids are alike in that each will flow. Each
is therefore called a fluid. Sometimes there is much
resistance to the flow of a liquid as in molasses. This
resistance is called viscosity. Alcohol and gasoline
have little viscosity. They are limpid or mobile. Air
also has some viscosity. For instance, a stream of air
always drags some of the surrounding air along with
it.
Fig. 8.—Osmosis
Shown by carrot
placed in water.
Important Topics
1. Liquids behave as if they were composed of small particles in motion.
2. This is shown by (1) Diffusion, (2) Solution, (3) Evaporation, (4)
Expansion, (5) Osmosis.
Exercises
Page 35
1. Give an example or illustration of each of the five evidences of molecular
motion in liquids.
2. When is air saturated? What is the explanation?
3. Why does warming a liquid increase its rate of evaporation?
4. Air molecules are in rapid motion in all directions. Do they enter a liquid
with a surface exposed to the air? Give reason.
5. What are some of the inconveniences of living in a saturated atmosphere?
6. Fish require oxygen. How is it obtained?
(3) Molecular Forces in Liquids
21. Cohesion and Adhesion.—In liquids "the molecules move about freely
yet tend to cling together." This tendency of molecules to cling together
which is not noticeable in gases is characteristic of liquids and especially of
solids. It is the cause of the viscosity mentioned in the previous section and
is readily detected in a variety of ways. For instance, not only do liquid
molecules cling together to form drops and streams, but they cling to the
molecules of solids as well, as is shown by the wet surface of an object that
has been dipped in water. The attraction of like molecules for one another is
called cohesion, while the attraction of unlike molecules is called adhesion,
although the force is the same whether the molecules are alike or unlike. It
is the former that causes drops of water to form and that holds iron, copper,
and other solids so rigidly together. The adhesion of glue to other objects is
well known. Paint also "sticks" well. Sometimes the "joint" where two
boards are glued together is stronger than the board itself. The force of
attraction between molecules has been studied carefully. The attraction acts
only through very short distances. The attraction even in liquids is
considerable and may be measured. The cohesion of water may be shown
by an experiment where the force required to pull a glass plate from the
surface of water is measured.
Take a beam balance and suspend from one arm a circular glass plate, Fig.
9. Weigh the plate and its support. Adjust the glass plate so that it hangs
horizontally and just touches the surface of clean water, the under side
motion in liquids.
2. When is air saturated? What is the explanation?
3. Why does warming a liquid increase its rate of evaporation?
4. Air molecules are in rapid motion in all directions. Do they enter a liquid
with a surface exposed to the air? Give reason.
5. What are some of the inconveniences of living in a saturated atmosphere?
6. Fish require oxygen. How is it obtained?
(3) Molecular Forces in Liquids
21. Cohesion and Adhesion.—In liquids "the molecules move about freely
yet tend to cling together." This tendency of molecules to cling together
which is not noticeable in gases is characteristic of liquids and especially of
solids. It is the cause of the viscosity mentioned in the previous section and
is readily detected in a variety of ways. For instance, not only do liquid
molecules cling together to form drops and streams, but they cling to the
molecules of solids as well, as is shown by the wet surface of an object that
has been dipped in water. The attraction of like molecules for one another is
called cohesion, while the attraction of unlike molecules is called adhesion,
although the force is the same whether the molecules are alike or unlike. It
is the former that causes drops of water to form and that holds iron, copper,
and other solids so rigidly together. The adhesion of glue to other objects is
well known. Paint also "sticks" well. Sometimes the "joint" where two
boards are glued together is stronger than the board itself. The force of
attraction between molecules has been studied carefully. The attraction acts
only through very short distances. The attraction even in liquids is
considerable and may be measured. The cohesion of water may be shown
by an experiment where the force required to pull a glass plate from the
surface of water is measured.
Take a beam balance and suspend from one arm a circular glass plate, Fig.
9. Weigh the plate and its support. Adjust the glass plate so that it hangs
horizontally and just touches the surface of clean water, the under side
Page 36
being completely wet. Now find what additional
weight is required to raise the glass plate from the
water.
Just as the plate comes from the water its under
side is found to be wet. That is, the water was
pulled apart, and the plate was not pulled from the
water. The cohesion of the water to itself is not so
strong as its adhesion to the glass.
The cohesion of liquids is further shown by the
form a drop of liquid tends to take when left to Fig. 9.—The water is
itself. This is readily seen in small drops of liquids. pulled apart.
The spherical shape of drops of water or mercury
is an example. A mixture of alcohol and water in proper proportions will
just support olive oil within it. By carefully dropping olive oil from a
pipette into such a mixture, a drop of the oil, an inch or more in diameter
suspended in the liquid, may be formed. It is best to use a bottle with plane
or flat sides, for if a round bottle is used, the sphere of oil will appear
flattened.
Figs. 10 a and b.—Surface tension of a liquid
film.
22. Surface Tension.—The cohesion of liquids is also indicated by the
tendency of films to assume the smallest possible surface. Soap bubble
weight is required to raise the glass plate from the
water.
Just as the plate comes from the water its under
side is found to be wet. That is, the water was
pulled apart, and the plate was not pulled from the
water. The cohesion of the water to itself is not so
strong as its adhesion to the glass.
The cohesion of liquids is further shown by the
form a drop of liquid tends to take when left to Fig. 9.—The water is
itself. This is readily seen in small drops of liquids. pulled apart.
The spherical shape of drops of water or mercury
is an example. A mixture of alcohol and water in proper proportions will
just support olive oil within it. By carefully dropping olive oil from a
pipette into such a mixture, a drop of the oil, an inch or more in diameter
suspended in the liquid, may be formed. It is best to use a bottle with plane
or flat sides, for if a round bottle is used, the sphere of oil will appear
flattened.
Figs. 10 a and b.—Surface tension of a liquid
film.
22. Surface Tension.—The cohesion of liquids is also indicated by the
tendency of films to assume the smallest possible surface. Soap bubble
Page 37
films show this readily. Fig. 10 a represents a circular wire form holding a
film in which floats a loop of thread. The tension of the film is shown in
Fig. 10 b by the circular form of the loop after the film within it has been
pierced by a hot wire, Fig. 11 shows a rectangular wire form with a "rider."
The tension in the film draws the rider forward.
Fig. 11.—The rider is drawn forward.
Fig. 12.—Surface tension causes the pointed
shape.
A soap bubble takes its spherical shape because this form holds the
confined air within the smallest possible surface. A drop of liquid is
spherical for the same reason. Many illustrations of the tension in films may
be given. Users of water colors notice that a dry camel's-hair brush is bushy.
(Fig. 12 A). When in water it is still bushy. (Fig. 12 B.) But when it is taken
from the water and the excess is shaken from it, it is pointed as in Fig. 12 C.
It is held to the pointed shape by the tension of the liquid film about the
brush.
The surface of water acts as if covered by a film which
coheres more strongly than the water beneath it. This is
shown by the fact that a steel needle or a thin strip of
metal may be floated upon the surface of water. It is
supported by the surface film. (See Fig. 13.) If the film
breaks the needle sinks. This film also supports the little
water bugs seen running over the surface of a quiet Fig. 13.—A
pond in summer. The surface film is stronger in some needle
liquids than in others. This may be shown by taking depresses the
film in which floats a loop of thread. The tension of the film is shown in
Fig. 10 b by the circular form of the loop after the film within it has been
pierced by a hot wire, Fig. 11 shows a rectangular wire form with a "rider."
The tension in the film draws the rider forward.
Fig. 11.—The rider is drawn forward.
Fig. 12.—Surface tension causes the pointed
shape.
A soap bubble takes its spherical shape because this form holds the
confined air within the smallest possible surface. A drop of liquid is
spherical for the same reason. Many illustrations of the tension in films may
be given. Users of water colors notice that a dry camel's-hair brush is bushy.
(Fig. 12 A). When in water it is still bushy. (Fig. 12 B.) But when it is taken
from the water and the excess is shaken from it, it is pointed as in Fig. 12 C.
It is held to the pointed shape by the tension of the liquid film about the
brush.
The surface of water acts as if covered by a film which
coheres more strongly than the water beneath it. This is
shown by the fact that a steel needle or a thin strip of
metal may be floated upon the surface of water. It is
supported by the surface film. (See Fig. 13.) If the film
breaks the needle sinks. This film also supports the little
water bugs seen running over the surface of a quiet Fig. 13.—A
pond in summer. The surface film is stronger in some needle
liquids than in others. This may be shown by taking depresses the
Page 38
water, colored so that it can be seen, placing a thin layer surface when
of it on a white surface and dropping alcohol upon it. floating.
Wherever the alcohol drops, the water is seen to pull
away from it, leaving a bare space over which the alcohol has been spread.
This indicates that the alcohol has the weaker film. The film of greasy
benzine is stronger than the film of the pure material. If one wishes to
remove a grease spot and places pure benzine at the center of the spot, the
stronger film of the greasy liquid will pull away from the pure benzine, and
spread out, making a larger spot than before, while if pure benzine is placed
around the grease spot, the greasy liquid at the center pulls away from the
pure benzine, drawing more and more to the center, where it may be wiped
up and the grease entirely removed.
Fig. 14.—The molecule at A is held differently
from one within the liquid.
23. Explanation of the Surface Film.—Beneath the surface of a liquid
each molecule is attracted by all the other molecules around it. It is attracted
equally in all directions. Consequently the interior molecules move very
easily over each other in any direction. A molecule at the surface, as at A,
Fig. 14, is not attracted upward by other liquid molecules. Its freedom of
motion is thereby hindered with the result that a molecule at the surface
behaves differently from one beneath the surface. The surface molecules act
as if they form an elastic skin or membrane upon the liquid surface.
24. Capillarity.—A striking action of the surface film of a liquid is seen in
the rise of liquids in tubes of small bore when the liquid wets them. If the
liquid does not wet the tube, as when mercury is placed in glass, the liquid
is depressed. It is found in general that: Liquids rise in capillary tubes when
they wet them and are depressed in tubes which they do not wet; the smaller
the diameter of the tube the greater the change of level. (See Fig. 15.) This
of it on a white surface and dropping alcohol upon it. floating.
Wherever the alcohol drops, the water is seen to pull
away from it, leaving a bare space over which the alcohol has been spread.
This indicates that the alcohol has the weaker film. The film of greasy
benzine is stronger than the film of the pure material. If one wishes to
remove a grease spot and places pure benzine at the center of the spot, the
stronger film of the greasy liquid will pull away from the pure benzine, and
spread out, making a larger spot than before, while if pure benzine is placed
around the grease spot, the greasy liquid at the center pulls away from the
pure benzine, drawing more and more to the center, where it may be wiped
up and the grease entirely removed.
Fig. 14.—The molecule at A is held differently
from one within the liquid.
23. Explanation of the Surface Film.—Beneath the surface of a liquid
each molecule is attracted by all the other molecules around it. It is attracted
equally in all directions. Consequently the interior molecules move very
easily over each other in any direction. A molecule at the surface, as at A,
Fig. 14, is not attracted upward by other liquid molecules. Its freedom of
motion is thereby hindered with the result that a molecule at the surface
behaves differently from one beneath the surface. The surface molecules act
as if they form an elastic skin or membrane upon the liquid surface.
24. Capillarity.—A striking action of the surface film of a liquid is seen in
the rise of liquids in tubes of small bore when the liquid wets them. If the
liquid does not wet the tube, as when mercury is placed in glass, the liquid
is depressed. It is found in general that: Liquids rise in capillary tubes when
they wet them and are depressed in tubes which they do not wet; the smaller
the diameter of the tube the greater the change of level. (See Fig. 15.) This
Page 39
action is explained as follows: The molecules of
a liquid have an attraction for each other and
also for the sides of a tube. The former is called
"cohesion for itself," the latter is called
"adhesion for the sides of the containing vessel."
If the cohesion for itself is greater than the
adhesion for the side of the containing vessel,
the liquid is pulled away from the side and is
depressed. If the adhesion is greater, the liquid is
elevated. This action is called "capillary action"
from the Latin word (capillus) signifying hair, Fig. 15.—Capillary
since it shows best in fine hairlike tubes. attraction in tubes.
There are many common illustrations of
capillary action: oil rising in a wick; water rising in a towel or through
clothes; ink in a blotter, etc. The minute spaces between the fibers
composing these objects act as fine tubes. If cloth is treated with a
preparation which prevents water from adhering to its fibers, the material
will not be wet when water is poured upon it, because the water will not run
in between the fibers; a surface film spreads over the cloth so that no water
enters it. Cravenette cloth has been treated in this way and hence is
waterproof.
The action of this film may be shown by the following experiment. Dip a
sieve of fine copper gauze in melted paraffin, thus coating each wire so that
water will not adhere to it. Water may now be poured into the sieve, if a
piece of paper is first laid in it to break the force of the water. On carefully
removing the paper the surface film of the water will prevent the passage of
the water through the sieve.
25. Capillary Action in Soils.—The distribution of moisture in the soil
depends largely upon capillary action. When the soil is compact the minute
spaces between the soil particles act as capillary tubes, thus aiding the water
to rise to the surface. As the water evaporates from the surface more of it
rises by capillary action from the damper soil below. Keeping the soil loose
by cultivation, makes the spaces between the particles too large for much
capillary action, thus the moisture is largely prevented from rising to the
surface.
a liquid have an attraction for each other and
also for the sides of a tube. The former is called
"cohesion for itself," the latter is called
"adhesion for the sides of the containing vessel."
If the cohesion for itself is greater than the
adhesion for the side of the containing vessel,
the liquid is pulled away from the side and is
depressed. If the adhesion is greater, the liquid is
elevated. This action is called "capillary action"
from the Latin word (capillus) signifying hair, Fig. 15.—Capillary
since it shows best in fine hairlike tubes. attraction in tubes.
There are many common illustrations of
capillary action: oil rising in a wick; water rising in a towel or through
clothes; ink in a blotter, etc. The minute spaces between the fibers
composing these objects act as fine tubes. If cloth is treated with a
preparation which prevents water from adhering to its fibers, the material
will not be wet when water is poured upon it, because the water will not run
in between the fibers; a surface film spreads over the cloth so that no water
enters it. Cravenette cloth has been treated in this way and hence is
waterproof.
The action of this film may be shown by the following experiment. Dip a
sieve of fine copper gauze in melted paraffin, thus coating each wire so that
water will not adhere to it. Water may now be poured into the sieve, if a
piece of paper is first laid in it to break the force of the water. On carefully
removing the paper the surface film of the water will prevent the passage of
the water through the sieve.
25. Capillary Action in Soils.—The distribution of moisture in the soil
depends largely upon capillary action. When the soil is compact the minute
spaces between the soil particles act as capillary tubes, thus aiding the water
to rise to the surface. As the water evaporates from the surface more of it
rises by capillary action from the damper soil below. Keeping the soil loose
by cultivation, makes the spaces between the particles too large for much
capillary action, thus the moisture is largely prevented from rising to the
surface.
Page 40
In the semi-arid regions of the West "dry farming" is successfully practised.
This consists in keeping the surface covered with a "dust mulch" produced
by frequent cultivation. In this way the moisture is kept below the surface,
where it can be utilized during the hot dry summer by the roots of growing
plants.
Important Topics
1. Attractive forces between liquid molecules.
2. Cohesion (like molecules); adhesion (unlike molecules).
3. Special effects of this force are classified as (a) capillary action, and (b)
surface tension.
Exercises
1. What evidence of capillary action have you seen outside of the
laboratory?
2. What is the explanation for capillary action?
3. Where are surface films found?
4. What are three common effects of surface films?
5. Explain why cravenette cloth sheds water.
6. If a circular glass disc 10 cm. in diameter requires 50 grams of force to
draw it from the water, what is the cohesion of water per square centimeter?
7. What is the weight in grams of 1 ccm. of water? of a liter of water?
8. Name five examples of adhesion to be found in your home.
9. Under what conditions will a liquid wet a solid and spread over it?
10. When will it form in drops on the surface?
11. Explain the proper procedure for removing a grease spot with benzine.
12. What difference is there between a liquid and a fluid?
13. Why cannot a "soap bubble" be blown from pure water?
This consists in keeping the surface covered with a "dust mulch" produced
by frequent cultivation. In this way the moisture is kept below the surface,
where it can be utilized during the hot dry summer by the roots of growing
plants.
Important Topics
1. Attractive forces between liquid molecules.
2. Cohesion (like molecules); adhesion (unlike molecules).
3. Special effects of this force are classified as (a) capillary action, and (b)
surface tension.
Exercises
1. What evidence of capillary action have you seen outside of the
laboratory?
2. What is the explanation for capillary action?
3. Where are surface films found?
4. What are three common effects of surface films?
5. Explain why cravenette cloth sheds water.
6. If a circular glass disc 10 cm. in diameter requires 50 grams of force to
draw it from the water, what is the cohesion of water per square centimeter?
7. What is the weight in grams of 1 ccm. of water? of a liter of water?
8. Name five examples of adhesion to be found in your home.
9. Under what conditions will a liquid wet a solid and spread over it?
10. When will it form in drops on the surface?
11. Explain the proper procedure for removing a grease spot with benzine.
12. What difference is there between a liquid and a fluid?
13. Why cannot a "soap bubble" be blown from pure water?
Page 41
14. Which are larger, the molecules of steam or those of water? Why?
15. Why is the ground likely to be damp under a stone or board when it is
dry all around?
16. Why does any liquid in falling through the air assume the globule form?
17. Give three examples of capillary attraction found in the home. Three out
of doors.
18. Why does cultivation of the soil prevent rapid evaporation of water
from the ground?
(4) Evidences of Molecular Forces in Liquids and Solids
26. Solutions.—A crystal of potassium permanganate is placed in a liter of
water. It soon dissolves and on shaking the flask each portion of the liquid
is seen to be colored red. The dissolving of the permanganate is an
illustration of the attraction of the molecules of water for the molecules of
the permanganate. We are familiar with this action in the seasoning of food
with salt and sweetening with sugar.
Water will dissolve many substances, but in varying degrees, i.e., of some it
will dissolve much, of others, little, and some not at all. Further, different
liquids have different solvent powers. Alcohol will dissolve resin and
shellac, but it will not dissolve gum arabic, which is soluble in water.
Benzine dissolves grease. Beeswax is not dissolved by water, alcohol or
benzine, but is soluble in turpentine.
It is found that the temperature of the liquid has a marked effect upon the
amount of substance that will dissolve. This is an indication that the
motions of the molecules are effective in solution. It appears that dissolving
a solid is in some respects similar to evaporation, and just as at higher
temperatures more of the liquid evaporates, because more of the molecules
will escape from the liquid into the air above, so at higher temperatures,
more molecules of a solid will detach themselves through greater vibration
and will move into the liquid.
Further, just as an evaporating liquid may saturate the space above it so that
any escape of molecules is balanced by those returning, so with a dissolving
solid, the liquid may become saturated so that the solution of more of the
15. Why is the ground likely to be damp under a stone or board when it is
dry all around?
16. Why does any liquid in falling through the air assume the globule form?
17. Give three examples of capillary attraction found in the home. Three out
of doors.
18. Why does cultivation of the soil prevent rapid evaporation of water
from the ground?
(4) Evidences of Molecular Forces in Liquids and Solids
26. Solutions.—A crystal of potassium permanganate is placed in a liter of
water. It soon dissolves and on shaking the flask each portion of the liquid
is seen to be colored red. The dissolving of the permanganate is an
illustration of the attraction of the molecules of water for the molecules of
the permanganate. We are familiar with this action in the seasoning of food
with salt and sweetening with sugar.
Water will dissolve many substances, but in varying degrees, i.e., of some it
will dissolve much, of others, little, and some not at all. Further, different
liquids have different solvent powers. Alcohol will dissolve resin and
shellac, but it will not dissolve gum arabic, which is soluble in water.
Benzine dissolves grease. Beeswax is not dissolved by water, alcohol or
benzine, but is soluble in turpentine.
It is found that the temperature of the liquid has a marked effect upon the
amount of substance that will dissolve. This is an indication that the
motions of the molecules are effective in solution. It appears that dissolving
a solid is in some respects similar to evaporation, and just as at higher
temperatures more of the liquid evaporates, because more of the molecules
will escape from the liquid into the air above, so at higher temperatures,
more molecules of a solid will detach themselves through greater vibration
and will move into the liquid.
Further, just as an evaporating liquid may saturate the space above it so that
any escape of molecules is balanced by those returning, so with a dissolving
solid, the liquid may become saturated so that the solution of more of the
Page 42
solid is balanced by the return of the molecules from the liquid to the solid
condition.
27. Crystals and Crystallization.—This return from the liquid to the solid
state, of molecules that are in solution, is especially noticeable when the
solution is cooling or evaporating and hence is losing its capacity to hold so
much of the solid. On returning to the solid, the molecules attach
themselves in a definite manner to the solid portion, building up regular
solid forms. These regular forms are crystals. The action that forms them is
called crystallization.
Each substance seems to have its own peculiar form of crystal due to the
manner in which the molecules attach themselves to those previously in
place. The largest and most symmetrical crystals are those in which the
molecules are deposited slowly with no disturbance of the liquid. Beautiful
crystals of alum may be obtained by dissolving 25 g. of alum in 50 ccm. of
hot water, hanging two or three threads in the solution and letting it stand
over night. The thread fibers provide a foundation upon which crystals
grow.
When a solution of a solid evaporates, the molecules of the liquid escape as
a gas, the molecules of the solid remain accumulating as crystals. This
principle has many uses: (a) sea water is purified by evaporating the water
and condensing the vapor, which of course forms pure water. (b) water is
forced down to salt beds where it dissolves the salt. The brine is then raised
and evaporated, leaving the salt in the evaporating pans.
28. Absorption of Gases by Solids and Liquids.—If a piece of heated
charcoal is placed in a test-tube containing ammonia gas, inverted in
mercury, the ammonia is seen to disappear, the mercury rising to take its
place. The ammonia has been absorbed by the charcoal, the gas molecules
clinging closely to the solid. The charcoal being very porous presents a
large surface to the action of the gas.
This experiment indicates that attraction exists between gas molecules and
other molecules. Many porous substances have this power of absorbing
gases. We have all noticed that butter has its flavor affected by substances
placed near it.
condition.
27. Crystals and Crystallization.—This return from the liquid to the solid
state, of molecules that are in solution, is especially noticeable when the
solution is cooling or evaporating and hence is losing its capacity to hold so
much of the solid. On returning to the solid, the molecules attach
themselves in a definite manner to the solid portion, building up regular
solid forms. These regular forms are crystals. The action that forms them is
called crystallization.
Each substance seems to have its own peculiar form of crystal due to the
manner in which the molecules attach themselves to those previously in
place. The largest and most symmetrical crystals are those in which the
molecules are deposited slowly with no disturbance of the liquid. Beautiful
crystals of alum may be obtained by dissolving 25 g. of alum in 50 ccm. of
hot water, hanging two or three threads in the solution and letting it stand
over night. The thread fibers provide a foundation upon which crystals
grow.
When a solution of a solid evaporates, the molecules of the liquid escape as
a gas, the molecules of the solid remain accumulating as crystals. This
principle has many uses: (a) sea water is purified by evaporating the water
and condensing the vapor, which of course forms pure water. (b) water is
forced down to salt beds where it dissolves the salt. The brine is then raised
and evaporated, leaving the salt in the evaporating pans.
28. Absorption of Gases by Solids and Liquids.—If a piece of heated
charcoal is placed in a test-tube containing ammonia gas, inverted in
mercury, the ammonia is seen to disappear, the mercury rising to take its
place. The ammonia has been absorbed by the charcoal, the gas molecules
clinging closely to the solid. The charcoal being very porous presents a
large surface to the action of the gas.
This experiment indicates that attraction exists between gas molecules and
other molecules. Many porous substances have this power of absorbing
gases. We have all noticed that butter has its flavor affected by substances
placed near it.
Page 43
That liquids absorb gases is shown by slowly heating cold water in a
beaker. Small bubbles of air form on the sides and rise before the boiling
point is reached. Ammonia gas is readily absorbed in water, the bubbles
disappearing almost as soon as they escape into the water from the end of
the delivery tube. Household ammonia is simply a solution of ammonia gas
in water. On warming the solution of ammonia the gas begins to pass off;
thus, warming a liquid tends to drive off any gas dissolved in it.
Soda water is made by forcing carbon dioxide gas into water under strong
pressure. When placed in a vessel open to the air the pressure is lessened
and part of the gas escapes. The dissolved gas gives the characteristic taste
to the beverage.
Important Topics
1. The solution of solids is increased by heating.
2. The solution of gases is decreased by heating.
3. Pressure increases the quantity of gas that can be dissolved in a liquid.
4. The attraction (cohesion) of molecules of a dissolved solid for each other
is shown by crystallization.
Exercises
1. How do fish obtain oxygen for breathing?
2. Why does warming water enable it to dissolve more of a salt?
3. Why does warming water lessen the amount of a gas that will stay in
solution?
4. Will water absorb gases of strong odor? How do you know?
5. Name three solvents. Give a use for each.
6. What liquids usually contain gases in solution? Name some uses for these
dissolved gases.
7. What is the weight of a cubic meter of water?
8. Name three substances obtained by crystallization.
beaker. Small bubbles of air form on the sides and rise before the boiling
point is reached. Ammonia gas is readily absorbed in water, the bubbles
disappearing almost as soon as they escape into the water from the end of
the delivery tube. Household ammonia is simply a solution of ammonia gas
in water. On warming the solution of ammonia the gas begins to pass off;
thus, warming a liquid tends to drive off any gas dissolved in it.
Soda water is made by forcing carbon dioxide gas into water under strong
pressure. When placed in a vessel open to the air the pressure is lessened
and part of the gas escapes. The dissolved gas gives the characteristic taste
to the beverage.
Important Topics
1. The solution of solids is increased by heating.
2. The solution of gases is decreased by heating.
3. Pressure increases the quantity of gas that can be dissolved in a liquid.
4. The attraction (cohesion) of molecules of a dissolved solid for each other
is shown by crystallization.
Exercises
1. How do fish obtain oxygen for breathing?
2. Why does warming water enable it to dissolve more of a salt?
3. Why does warming water lessen the amount of a gas that will stay in
solution?
4. Will water absorb gases of strong odor? How do you know?
5. Name three solvents. Give a use for each.
6. What liquids usually contain gases in solution? Name some uses for these
dissolved gases.
7. What is the weight of a cubic meter of water?
8. Name three substances obtained by crystallization.
Page 44
9. How is maple sugar obtained?
10. Name five crystalline substances.
(5) Evidence of Molecular Forces in Solids
29. Differences between Solids and Gases.—In studying gases, it is seen
that they behave as if they were composed of small particles in rapid
motion, continually striking and rebounding, and separating to fill any
space into which they are released. This action indicates that there is
practically no attractive force between such molecules.
Between the molecules of a solid, however, the forces of attraction are
strong, as is shown by the fact that a solid often requires a great force to
pull it apart; some, as steel and iron, show this property in a superlative
degree, a high-grade steel rod 1 cm. in diameter requiring nearly 9 tons to
pull it apart. Tests show that the breaking strengths of such rods are directly
proportional to their areas of cross-section. That is, twice the area has twice
the breaking strength.
30. Elasticity.—Fully as important as a
knowledge of the breaking strengths of
solids, is the knowledge of what happens
when the forces used are not great enough
to break the rods or wires.
Take a wooden rod (as a meter stick) and
clamp one end to the table top, as in Fig.
16. At the other end hang a weight. Fasten Fig. 16.—Elasticity of
a wire to this end so that it projects out in bending.
front of a scale. Add successively several
equal weights and note the position of the wire each time. Remove the
weights in order, noting the positions as before. The rod will probably
return to the first position.
This simple experiment illustrates a characteristic of solids: that of
changing shape when force is applied and of returning to the original shape
when the force is removed. This property is called elasticity.
10. Name five crystalline substances.
(5) Evidence of Molecular Forces in Solids
29. Differences between Solids and Gases.—In studying gases, it is seen
that they behave as if they were composed of small particles in rapid
motion, continually striking and rebounding, and separating to fill any
space into which they are released. This action indicates that there is
practically no attractive force between such molecules.
Between the molecules of a solid, however, the forces of attraction are
strong, as is shown by the fact that a solid often requires a great force to
pull it apart; some, as steel and iron, show this property in a superlative
degree, a high-grade steel rod 1 cm. in diameter requiring nearly 9 tons to
pull it apart. Tests show that the breaking strengths of such rods are directly
proportional to their areas of cross-section. That is, twice the area has twice
the breaking strength.
30. Elasticity.—Fully as important as a
knowledge of the breaking strengths of
solids, is the knowledge of what happens
when the forces used are not great enough
to break the rods or wires.
Take a wooden rod (as a meter stick) and
clamp one end to the table top, as in Fig.
16. At the other end hang a weight. Fasten Fig. 16.—Elasticity of
a wire to this end so that it projects out in bending.
front of a scale. Add successively several
equal weights and note the position of the wire each time. Remove the
weights in order, noting the positions as before. The rod will probably
return to the first position.
This simple experiment illustrates a characteristic of solids: that of
changing shape when force is applied and of returning to the original shape
when the force is removed. This property is called elasticity.
Page 45
Tests of elasticity are made by subjecting wire of different materials but of
the same dimensions to the same tension. The one changing least is said to
have the greatest elastic force or elasticity. If greater forces are applied to
the wire and then removed, one will finally be found that will permanently
stretch the wire so that it will not return exactly to the former length. The
wire has now passed its elastic limit and has been permanently stretched.
Just as there are great differences between the elastic forces of different
substances, so there are great differences in the limits of elasticity. In some
substances the limit is reached with slight distortion, while others are
perfectly elastic even when greatly stretched. India rubber is an example of
a body having perfect elasticity through wide limits. Glass has great elastic
force but its limit of elasticity is soon reached. Substances like India rubber
may be said to have great "stretchability," but little elastic force. In physics,
elasticity refers to the elastic force rather than to ability to endure
stretching.
31. Kinds of Elasticity.—Elasticity may be shown in four ways:
compression, bending or flexure, extension or stretching, twisting or torsion.
The first is illustrated by squeezing a rubber eraser, the second by an
automobile spring, the third by the stretching of a rubber band, the fourth by
the twisting and untwisting of a string by which a weight is suspended.
There are two kinds of elasticity: (1) elasticity of form or shape; (2)
elasticity of volume. Gases and liquids possess elasticity of volume, but not
of shape, while solids may have both kinds. Gases and liquids are perfectly
elastic because no matter how great pressure may be applied, as soon as the
pressure is removed they regain their former volume. No solid possesses
perfect elasticity, because sooner or later the limit of elasticity will be
reached.
32. Hooke's Law.[A]—On examining the successive movements of the end
of the rod in Art. 30, we find that they are approximately equal. Carefully
conducted experiments upon the elasticity of bodies have shown that the
changes in shape are directly proportional to the forces applied, provided
that the limit of elasticity is not reached. This relation, discovered by Robert
Hooke, is sometimes expressed as follows: "Within the limits of perfect
elasticity, all changes of size or shape are directly proportional to the forces
producing them."
the same dimensions to the same tension. The one changing least is said to
have the greatest elastic force or elasticity. If greater forces are applied to
the wire and then removed, one will finally be found that will permanently
stretch the wire so that it will not return exactly to the former length. The
wire has now passed its elastic limit and has been permanently stretched.
Just as there are great differences between the elastic forces of different
substances, so there are great differences in the limits of elasticity. In some
substances the limit is reached with slight distortion, while others are
perfectly elastic even when greatly stretched. India rubber is an example of
a body having perfect elasticity through wide limits. Glass has great elastic
force but its limit of elasticity is soon reached. Substances like India rubber
may be said to have great "stretchability," but little elastic force. In physics,
elasticity refers to the elastic force rather than to ability to endure
stretching.
31. Kinds of Elasticity.—Elasticity may be shown in four ways:
compression, bending or flexure, extension or stretching, twisting or torsion.
The first is illustrated by squeezing a rubber eraser, the second by an
automobile spring, the third by the stretching of a rubber band, the fourth by
the twisting and untwisting of a string by which a weight is suspended.
There are two kinds of elasticity: (1) elasticity of form or shape; (2)
elasticity of volume. Gases and liquids possess elasticity of volume, but not
of shape, while solids may have both kinds. Gases and liquids are perfectly
elastic because no matter how great pressure may be applied, as soon as the
pressure is removed they regain their former volume. No solid possesses
perfect elasticity, because sooner or later the limit of elasticity will be
reached.
32. Hooke's Law.[A]—On examining the successive movements of the end
of the rod in Art. 30, we find that they are approximately equal. Carefully
conducted experiments upon the elasticity of bodies have shown that the
changes in shape are directly proportional to the forces applied, provided
that the limit of elasticity is not reached. This relation, discovered by Robert
Hooke, is sometimes expressed as follows: "Within the limits of perfect
elasticity, all changes of size or shape are directly proportional to the forces
producing them."
Page 46
33. Molecular Forces and Molecular Motions.—If a solid is compressed,
on releasing the pressure the body regains its former shape if it has not been
compressed too far. This indicates that at a given temperature the
"molecules of a solid tend to remain at a fixed distance from each other, and
resist any attempt to decrease or increase this distance." This raises the
question, Why does not the cohesion pull the molecules tightly together so
that compression would be impossible? The reason is that heat affects the
size of solid bodies. On lowering the temperature, bodies do contract, for as
soon as the temperature is lowered the vibration of the molecule is lessened.
On raising the temperature the molecules are pushed farther apart.
The size of a body, then, is the result of a balance of opposing forces. The
attractive force between the molecules pulling them together is cohesion,
while the force which pushes them apart is due to the motions of the
molecules. Raising the temperature and thus increasing the motion causes
expansion; lowering the temperature decreases the molecular motion and so
causes contraction. If an outside force tries to pull the body apart or to
compress it this change of size is resisted by either cohesion or molecular
motion.
34. Properties of Matter.—Many differences in the physical properties of
solids are due to differences between the cohesive force of different kinds
of molecules. In some substances, the attraction is such that they may be
rolled out in very thin sheets. Gold is the best example of this, sheets being
formed 1/300,000 of an inch thick. This property is called malleability. In
other substances the cohesion permits it to be drawn out into fine threads or
wire. Glass and quartz are examples of this. This property is called ductility.
In some, the cohesion makes the substance excessively hard, so that it is
difficult to work or scratch its surface. The diamond is the hardest substance
known. Some substances are tough, others brittle. These are tested by the
ability to withstand sudden shocks as the blow of a hammer.
Important Topics
1. Molecular forces in solids; (a) adhesion, (b) cohesion.
2. Elasticity, Hooke's Law.
3. Contraction on cooling.
on releasing the pressure the body regains its former shape if it has not been
compressed too far. This indicates that at a given temperature the
"molecules of a solid tend to remain at a fixed distance from each other, and
resist any attempt to decrease or increase this distance." This raises the
question, Why does not the cohesion pull the molecules tightly together so
that compression would be impossible? The reason is that heat affects the
size of solid bodies. On lowering the temperature, bodies do contract, for as
soon as the temperature is lowered the vibration of the molecule is lessened.
On raising the temperature the molecules are pushed farther apart.
The size of a body, then, is the result of a balance of opposing forces. The
attractive force between the molecules pulling them together is cohesion,
while the force which pushes them apart is due to the motions of the
molecules. Raising the temperature and thus increasing the motion causes
expansion; lowering the temperature decreases the molecular motion and so
causes contraction. If an outside force tries to pull the body apart or to
compress it this change of size is resisted by either cohesion or molecular
motion.
34. Properties of Matter.—Many differences in the physical properties of
solids are due to differences between the cohesive force of different kinds
of molecules. In some substances, the attraction is such that they may be
rolled out in very thin sheets. Gold is the best example of this, sheets being
formed 1/300,000 of an inch thick. This property is called malleability. In
other substances the cohesion permits it to be drawn out into fine threads or
wire. Glass and quartz are examples of this. This property is called ductility.
In some, the cohesion makes the substance excessively hard, so that it is
difficult to work or scratch its surface. The diamond is the hardest substance
known. Some substances are tough, others brittle. These are tested by the
ability to withstand sudden shocks as the blow of a hammer.
Important Topics
1. Molecular forces in solids; (a) adhesion, (b) cohesion.
2. Elasticity, Hooke's Law.
3. Contraction on cooling.
Page 47
4. Malleability, ductility, hardness, brittleness, etc.
Exercises
1. Give an illustration of Hooke's Law from your own experience.
2. What devices make use of it?
3. Do solids evaporate. Give reasons.
4. When iron is welded, is cohesion or adhesion acting?
5. When a tin basin is soldered, is cohesion or adhesion acting?
6. Sometimes a spring is made more elastic by tempering and made soft by
annealing. Look up the two terms. How is each accomplished?
7. Review the definitions: solid, liquid, and gas. Why do these definitions
mean more to you now than formerly?
8. If a wire is stretched 0.3 cm. on applying 4 kg. of force, what force will
stretch it 0.75 cm? Explain.
9. How long will it take under ordinary conditions for a gas molecule to
cross a room? Give reasons for your answer.
10. What is meant by the elastic limit of a body?
11. Without reaching the elastic limit, if a beam is depressed 4 mm. under a
load of 60 kg., what will be the depression under a load of 400 kg.? Of 600
kg.?
12. Name three substances that possess elasticity of volume.
13. Give three examples of each; elasticity of (1) compression, (2)
stretching, (3) torsion, (4) flexure.
Review Outline: Introduction and Molecules
Physics; definition, topics considered, physical and chemical changes.
Science; hypothesis, theory, law. Knowledge; common, scientific.
Matter; three states, molecular theory. Mass, weight, volume.
Exercises
1. Give an illustration of Hooke's Law from your own experience.
2. What devices make use of it?
3. Do solids evaporate. Give reasons.
4. When iron is welded, is cohesion or adhesion acting?
5. When a tin basin is soldered, is cohesion or adhesion acting?
6. Sometimes a spring is made more elastic by tempering and made soft by
annealing. Look up the two terms. How is each accomplished?
7. Review the definitions: solid, liquid, and gas. Why do these definitions
mean more to you now than formerly?
8. If a wire is stretched 0.3 cm. on applying 4 kg. of force, what force will
stretch it 0.75 cm? Explain.
9. How long will it take under ordinary conditions for a gas molecule to
cross a room? Give reasons for your answer.
10. What is meant by the elastic limit of a body?
11. Without reaching the elastic limit, if a beam is depressed 4 mm. under a
load of 60 kg., what will be the depression under a load of 400 kg.? Of 600
kg.?
12. Name three substances that possess elasticity of volume.
13. Give three examples of each; elasticity of (1) compression, (2)
stretching, (3) torsion, (4) flexure.
Review Outline: Introduction and Molecules
Physics; definition, topics considered, physical and chemical changes.
Science; hypothesis, theory, law. Knowledge; common, scientific.
Matter; three states, molecular theory. Mass, weight, volume.
Page 48
Metric system; units, tables, equivalents, advantages.
Evidences of molecular motions; gases (3), liquids (5), solids (3).
Evidences of molecular forces; liquids (3), solids (many) special properties
such as: elasticity, tenacity, ductility, hardness, etc.
Hooke's law; applications.
Evidences of molecular motions; gases (3), liquids (5), solids (3).
Evidences of molecular forces; liquids (3), solids (many) special properties
such as: elasticity, tenacity, ductility, hardness, etc.
Hooke's law; applications.
Page 49
CHAPTER III
MECHANICS OF LIQUIDS
(1) The Gravity Pressure of Liquids
35. Pressure of Liquids against Surfaces.—The sight of a great ship,
perhaps built of iron and floating on water, causes one to wonder at the
force that supports it. This same force is noticed when one pushes a light
body, as a cork, under water. It is quite evident in such a case that a force
exists sufficient to overcome the weight of the cork so that it tends to rise to
the surface. Even the weight of our bodies is so far supported by water that
many persons can float.
The following experiment provides a means of
testing this force:
If an empty can is pushed down into water, we
feel at once the force of the liquid acting against
the object and tending to push it upward. It may
be noticed also that so long as the can is not
completely submerged the deeper the can is
pushed into the water the greater is the upward
force exerted by the liquid.
Fig. 17.—Water forces
We may test this action in various ways: a
the card against the
chimney. simple way is to take a cylindrical lamp
chimney, press a card against its lower end and
place it in the water in a vertical position. The
force of the water will hold the card firmly against the end of the chimney.
(See Fig. 17.) The amount of force may be tested by dropping shot into the
tube until the card drops off. At greater depths more shot will be required,
showing that the force of the water increases with the depth. Or one may
pour water into the chimney. It will then be found that the card does not
drop until the level of the water inside the chimney is the same as on the
outside. That is, before the card will fall off, the water must stand as high
MECHANICS OF LIQUIDS
(1) The Gravity Pressure of Liquids
35. Pressure of Liquids against Surfaces.—The sight of a great ship,
perhaps built of iron and floating on water, causes one to wonder at the
force that supports it. This same force is noticed when one pushes a light
body, as a cork, under water. It is quite evident in such a case that a force
exists sufficient to overcome the weight of the cork so that it tends to rise to
the surface. Even the weight of our bodies is so far supported by water that
many persons can float.
The following experiment provides a means of
testing this force:
If an empty can is pushed down into water, we
feel at once the force of the liquid acting against
the object and tending to push it upward. It may
be noticed also that so long as the can is not
completely submerged the deeper the can is
pushed into the water the greater is the upward
force exerted by the liquid.
Fig. 17.—Water forces
We may test this action in various ways: a
the card against the
chimney. simple way is to take a cylindrical lamp
chimney, press a card against its lower end and
place it in the water in a vertical position. The
force of the water will hold the card firmly against the end of the chimney.
(See Fig. 17.) The amount of force may be tested by dropping shot into the
tube until the card drops off. At greater depths more shot will be required,
showing that the force of the water increases with the depth. Or one may
pour water into the chimney. It will then be found that the card does not
drop until the level of the water inside the chimney is the same as on the
outside. That is, before the card will fall off, the water must stand as high
Page 50
within the chimney as without no matter to what depth the lower end of the
chimney is thrust below the surface of the water.
36. Law of Liquid Pressure.—As there is twice as much water or shot in
the chimney when it is filled to a depth of 10 cm. as there is when it is filled
to a depth of 5 cm. the force of the water upward on the bottom must be
twice as great at a depth of 10 cm. as at a depth of 5 cm. Since this
reasoning will hold good for a comparison of forces at any two depths, we
have the law: "The pressure exerted by a liquid is directly proportional to
the depth."
The amount of this force may be computed as follows: First, the card stays
on the end of the tube until the weight of water from above equals the force
of the water from below, and second, the card remains until the water is at
the same height inside the tube as it is outside. Now if we find the weight of
water at a given depth in the tube, we can determine the force of the water
from below. If for instance the chimney has an area of cross-section of 12
sq. cm. and is filled with water to a depth of 10 cm., the volume of the
water contained will be 120 ccm. This volume of water will weigh 120 g.
This represents then, not only the weight of the water in the tube, but also
the force of the water against the bottom. In a similar way one may measure
the force of water against any horizontal surface.
37. Force and Pressure.—We should now distinguish between force and
pressure. Pressure refers to the force acting against unit area, while force
refers to the action against the whole surface. Thus for example, the
atmospheric pressure is often given as 15 pounds to the square inch or as
one kilogram to the square centimeter. On the other hand, the air may exert
a force of more than 300 pounds upon each side of the hand of a man; or a
large ship may be supported by the force of thousands of tons exerted by
water against the bottom of the ship.
In the illustration, given in Art. 36, the upward force of the water against the
end of the tube at a depth of 10 cm. is computed as 120 grams. The pressure
at the same depth will be 10 grams per sq. cm. What will be the pressure at
a depth of 20 cm.? at a depth of 50 cm.? of 100 cm.? Compare these
answers with the law of liquid pressure in Art. 36.
38. Density.—If other liquids, as alcohol, mercury, etc., were in the jar, the
chimney would need filling to the same level outside, with the same liquid,
chimney is thrust below the surface of the water.
36. Law of Liquid Pressure.—As there is twice as much water or shot in
the chimney when it is filled to a depth of 10 cm. as there is when it is filled
to a depth of 5 cm. the force of the water upward on the bottom must be
twice as great at a depth of 10 cm. as at a depth of 5 cm. Since this
reasoning will hold good for a comparison of forces at any two depths, we
have the law: "The pressure exerted by a liquid is directly proportional to
the depth."
The amount of this force may be computed as follows: First, the card stays
on the end of the tube until the weight of water from above equals the force
of the water from below, and second, the card remains until the water is at
the same height inside the tube as it is outside. Now if we find the weight of
water at a given depth in the tube, we can determine the force of the water
from below. If for instance the chimney has an area of cross-section of 12
sq. cm. and is filled with water to a depth of 10 cm., the volume of the
water contained will be 120 ccm. This volume of water will weigh 120 g.
This represents then, not only the weight of the water in the tube, but also
the force of the water against the bottom. In a similar way one may measure
the force of water against any horizontal surface.
37. Force and Pressure.—We should now distinguish between force and
pressure. Pressure refers to the force acting against unit area, while force
refers to the action against the whole surface. Thus for example, the
atmospheric pressure is often given as 15 pounds to the square inch or as
one kilogram to the square centimeter. On the other hand, the air may exert
a force of more than 300 pounds upon each side of the hand of a man; or a
large ship may be supported by the force of thousands of tons exerted by
water against the bottom of the ship.
In the illustration, given in Art. 36, the upward force of the water against the
end of the tube at a depth of 10 cm. is computed as 120 grams. The pressure
at the same depth will be 10 grams per sq. cm. What will be the pressure at
a depth of 20 cm.? at a depth of 50 cm.? of 100 cm.? Compare these
answers with the law of liquid pressure in Art. 36.
38. Density.—If other liquids, as alcohol, mercury, etc., were in the jar, the
chimney would need filling to the same level outside, with the same liquid,
Page 51
before the card would fall off. This brings in a factor that was not
considered before, that of the mass[B] of a cubic centimeter of the liquid.
This is called the density of the liquid. Alcohol has a density of 0.8 g. per
cubic centimeter, mercury of 13.6 g. per cubic centimeter, while water has a
density of 1 g. per cubic centimeter.
39. Liquid Force against Any Surface.—To find the force exerted by a
liquid against a surface we must take into consideration the area of the
surface, and the height and the density of the liquid above the surface. The
following law, and the formula representing it, which concisely expresses
the principle by which the force exerted by a liquid against any surface may
be computed, should be memorized:
The force which a liquid exerts against any surface, equals the area of the
surface, times its average depth below the surface of the liquid, times the
weight of unit volume of the liquid.
Or, expressed by a formula, F = Ahd. In this formula, "F" stands for the
force which a liquid exerts against any surface, "A" the area of the surface,
"h," for the average depth (or height) of the liquid pressing on the surface,
and "d", for the weight of unit volume of the liquid. This is the first
illustration in this text, of the use of a formula to represent a law. Observe
how accurately and concisely the law is expressed by the formula. When
the formula is employed, however, we should keep in mind the law
expressed by it.
We must remember that a liquid presses not only downward and upward but
sideways as well, as we see when water spurts out of a hole in the side of a
vessel. Experiments have shown that at a point the pressure in a fluid is the
same in all directions, hence the rule given above may be applied to the
pressure of a liquid against the side of a tank, or boat, or other object,
provided we are accurate in determining the average depth of the liquid;
The following example illustrates the use of the law.
For Example: If the English system is used, the area of the surface should
be expressed in square feet, the depth in feet and the weight of the liquid in
pounds per cubic foot. One cubic foot of water weighs 62.4 lbs.
Suppose that a box 3 ft. square and 4 ft. deep is full of water. What force
will be exerted by the water against the bottom and a side?
considered before, that of the mass[B] of a cubic centimeter of the liquid.
This is called the density of the liquid. Alcohol has a density of 0.8 g. per
cubic centimeter, mercury of 13.6 g. per cubic centimeter, while water has a
density of 1 g. per cubic centimeter.
39. Liquid Force against Any Surface.—To find the force exerted by a
liquid against a surface we must take into consideration the area of the
surface, and the height and the density of the liquid above the surface. The
following law, and the formula representing it, which concisely expresses
the principle by which the force exerted by a liquid against any surface may
be computed, should be memorized:
The force which a liquid exerts against any surface, equals the area of the
surface, times its average depth below the surface of the liquid, times the
weight of unit volume of the liquid.
Or, expressed by a formula, F = Ahd. In this formula, "F" stands for the
force which a liquid exerts against any surface, "A" the area of the surface,
"h," for the average depth (or height) of the liquid pressing on the surface,
and "d", for the weight of unit volume of the liquid. This is the first
illustration in this text, of the use of a formula to represent a law. Observe
how accurately and concisely the law is expressed by the formula. When
the formula is employed, however, we should keep in mind the law
expressed by it.
We must remember that a liquid presses not only downward and upward but
sideways as well, as we see when water spurts out of a hole in the side of a
vessel. Experiments have shown that at a point the pressure in a fluid is the
same in all directions, hence the rule given above may be applied to the
pressure of a liquid against the side of a tank, or boat, or other object,
provided we are accurate in determining the average depth of the liquid;
The following example illustrates the use of the law.
For Example: If the English system is used, the area of the surface should
be expressed in square feet, the depth in feet and the weight of the liquid in
pounds per cubic foot. One cubic foot of water weighs 62.4 lbs.
Suppose that a box 3 ft. square and 4 ft. deep is full of water. What force
will be exerted by the water against the bottom and a side?
Page 52
From the law given above, the force of a liquid against a surface equals the
product of the area of the surface, the depth of the liquid and its weight per
unit volume, or using the formula, F = Ahd. To compute the downward
force against the bottom we have the area, 9, depth, 4, and the weight 62.4
lbs. per cubic foot. 9 × 4 × 62.4 lbs. = 2246.4 lbs. To compute the force
against a side, the area is 12, the average depth of water on the side is 2, the
weight 62.4, 12 × 2 × 62.4 lbs. = 1497.6 lbs.
Important Topics
1. Liquids exert pressure; the greater the depth the greater the pressure.
2. Difference between force and pressure.
3. Rules for finding upward and horizontal force exerted by a liquid. F =
Ahd.
4. Weight, mass, density.
Exercises
1. What is the density of water?
2. What force is pressing upward against the bottom of a flat boat, if it is 60
ft. long, 15 ft. wide and sinks to a depth of 2 ft. in the water? What is the
weight of the boat?
3. If a loaded ship sinks in the water to an average depth of 20 ft., the area
of the bottom being 6000 sq. ft., what is the upward force of the water?
What is the weight of the ship?
4. If this ship sinks only 10 ft. when empty, what is the weight of the ship
alone? What was the weight of the cargo in Problem 3?
5. What is the liquid force against one side of an aquarium 10 ft. long, 4 ft.
deep and full of water?
6. What is the liquid force on one side of a liter cube full of water? Full of
alcohol? Full of mercury? What force is pressing on the bottom in each
case?
product of the area of the surface, the depth of the liquid and its weight per
unit volume, or using the formula, F = Ahd. To compute the downward
force against the bottom we have the area, 9, depth, 4, and the weight 62.4
lbs. per cubic foot. 9 × 4 × 62.4 lbs. = 2246.4 lbs. To compute the force
against a side, the area is 12, the average depth of water on the side is 2, the
weight 62.4, 12 × 2 × 62.4 lbs. = 1497.6 lbs.
Important Topics
1. Liquids exert pressure; the greater the depth the greater the pressure.
2. Difference between force and pressure.
3. Rules for finding upward and horizontal force exerted by a liquid. F =
Ahd.
4. Weight, mass, density.
Exercises
1. What is the density of water?
2. What force is pressing upward against the bottom of a flat boat, if it is 60
ft. long, 15 ft. wide and sinks to a depth of 2 ft. in the water? What is the
weight of the boat?
3. If a loaded ship sinks in the water to an average depth of 20 ft., the area
of the bottom being 6000 sq. ft., what is the upward force of the water?
What is the weight of the ship?
4. If this ship sinks only 10 ft. when empty, what is the weight of the ship
alone? What was the weight of the cargo in Problem 3?
5. What is the liquid force against one side of an aquarium 10 ft. long, 4 ft.
deep and full of water?
6. What is the liquid force on one side of a liter cube full of water? Full of
alcohol? Full of mercury? What force is pressing on the bottom in each
case?
Page 53
7. What depth of water will produce a pressure of 1 g. per square
centimeter? 10 g. per square centimeter? 1000 g. per square centimeter?
8. What depth of water will produce a pressure of 1 lb. per square inch? 10
lbs. per square inch? 100 lbs. per square inch?
9. What will be the force against a vertical dam-breast 30 meters long, the
depth of the water being 10 meters?
10. A trap door with an area of 100 sq. dcm. is set in the bottom of a tank
containing water 5 meters deep. What force does the water exert against the
trap door?
11. What is the force on the bottom of a conical tank, filled with water, the
bottom of which is 3 meters in diameter, the depth 1.5 meters?
12. If alcohol, density 0.8 were used in problem 11, what would be the
force? What would be the depth of alcohol to have the same force on the
bottom as in problem 11?
13. What is the pressure in pounds per square inch at a depth of 1 mile in
sea water, density 1.026 grams per cc.?
14. Find the force on the sides and bottom of a rectangular cistern filled
with water, 20 ft. long, 10 ft. wide, and 10 ft. deep?
15. Find the force on the bottom of a water tank 14 ft. in diameter when the
water is 15 ft. deep, when full of water.
16. Find the force on one side of a cistern 8 ft. deep and 10 ft. square, when
full of water.
17. Find the force on a vertical dam 300 ft. long and 10 ft. high, when full
of water.
18. Find the pressure at the bottom of the dam in question 17.
19. Why are dams made thicker at the bottom than at the top?
20. A ship draws 26 ft. of water, i.e., its keel is 26 ft. under water. What is
the liquid force against a square foot surface of the keel? Find the pressure
on the bottom.
(2) Transmission of Liquid Pressure
centimeter? 10 g. per square centimeter? 1000 g. per square centimeter?
8. What depth of water will produce a pressure of 1 lb. per square inch? 10
lbs. per square inch? 100 lbs. per square inch?
9. What will be the force against a vertical dam-breast 30 meters long, the
depth of the water being 10 meters?
10. A trap door with an area of 100 sq. dcm. is set in the bottom of a tank
containing water 5 meters deep. What force does the water exert against the
trap door?
11. What is the force on the bottom of a conical tank, filled with water, the
bottom of which is 3 meters in diameter, the depth 1.5 meters?
12. If alcohol, density 0.8 were used in problem 11, what would be the
force? What would be the depth of alcohol to have the same force on the
bottom as in problem 11?
13. What is the pressure in pounds per square inch at a depth of 1 mile in
sea water, density 1.026 grams per cc.?
14. Find the force on the sides and bottom of a rectangular cistern filled
with water, 20 ft. long, 10 ft. wide, and 10 ft. deep?
15. Find the force on the bottom of a water tank 14 ft. in diameter when the
water is 15 ft. deep, when full of water.
16. Find the force on one side of a cistern 8 ft. deep and 10 ft. square, when
full of water.
17. Find the force on a vertical dam 300 ft. long and 10 ft. high, when full
of water.
18. Find the pressure at the bottom of the dam in question 17.
19. Why are dams made thicker at the bottom than at the top?
20. A ship draws 26 ft. of water, i.e., its keel is 26 ft. under water. What is
the liquid force against a square foot surface of the keel? Find the pressure
on the bottom.
(2) Transmission of Liquid Pressure
Page 54
40. Pascal's Principle.—Liquids exert pressure not only due to their own
weight, but when confined, may be made to transmit pressure to
considerable distances. This is a matter of common knowledge wherever a
system of waterworks with connections to houses is found, as in cities. The
transmission of liquid pressure has a number of important applications. The
principle underlying each of these was first discovered by Pascal, a French
scientist of the seventeenth century. Pascal's Principle, as it is called, may
be illustrated as follows:
Suppose a vessel of the shape shown in Fig. 18, the upper part of which we
may assume has an area of 1 sq. cm., is filled with water up to the level AB.
A pressure will be exerted upon each square centimeter of area depending
upon the depth. Suppose that the height of AB above CD is 10 cm., then the
force upon 1 sq. cm. of CD is 10 g., or if the area of CD is 16 sq. cm., it
receives a force of 160 g.
If now a cubic centimeter of water be poured upon
AB it will raise the level 1 cm., or the head of water
exerting pressure upon CD becomes 11 cm., or the
total force in CD is 16×11 g., i.e., each square
centimeter of CD receives an additional force of 1 g.
Hence the force exerted on a unit area at AB is
transmitted to every unit area within the vessel.
The usual form in which this law is expressed is as
follows: Pressure applied to any part of a confined
liquid is transmitted unchanged, in all directions, and
adds the same force to all equal surfaces in contact
with the liquid.
Fig. 18.—The
force increases
with the depth.
weight, but when confined, may be made to transmit pressure to
considerable distances. This is a matter of common knowledge wherever a
system of waterworks with connections to houses is found, as in cities. The
transmission of liquid pressure has a number of important applications. The
principle underlying each of these was first discovered by Pascal, a French
scientist of the seventeenth century. Pascal's Principle, as it is called, may
be illustrated as follows:
Suppose a vessel of the shape shown in Fig. 18, the upper part of which we
may assume has an area of 1 sq. cm., is filled with water up to the level AB.
A pressure will be exerted upon each square centimeter of area depending
upon the depth. Suppose that the height of AB above CD is 10 cm., then the
force upon 1 sq. cm. of CD is 10 g., or if the area of CD is 16 sq. cm., it
receives a force of 160 g.
If now a cubic centimeter of water be poured upon
AB it will raise the level 1 cm., or the head of water
exerting pressure upon CD becomes 11 cm., or the
total force in CD is 16×11 g., i.e., each square
centimeter of CD receives an additional force of 1 g.
Hence the force exerted on a unit area at AB is
transmitted to every unit area within the vessel.
The usual form in which this law is expressed is as
follows: Pressure applied to any part of a confined
liquid is transmitted unchanged, in all directions, and
adds the same force to all equal surfaces in contact
with the liquid.
Fig. 18.—The
force increases
with the depth.
Page 55
Fig. 19.—The force is proportional to the area.
The importance of this principle, as Pascal himself pointed out, lies in the
fact that by its aid we are able to exert a great force upon a large area by
applying a small force upon a small area of a confined liquid, both areas
being in contact with the same liquid. Thus in Fig. 19 if the area of the
surface CD is 2000 times the area of the surface AB, then 1 lb. applied to
the liquid on AB will exert or sustain a force of 2000 lbs. on CD.
41. Hydraulic Press.—An important application of Pascal's principle is the
hydraulic press. See Fig. 20. It is used for many purposes where great force
is required, as in pressing paper or cloth, extracting oil from seeds, lifting
heavy objects, etc. Many high school pupils have been seated in a hydraulic
chair used by a dentist or barber. This chair is a modified hydraulic press.
The importance of this principle, as Pascal himself pointed out, lies in the
fact that by its aid we are able to exert a great force upon a large area by
applying a small force upon a small area of a confined liquid, both areas
being in contact with the same liquid. Thus in Fig. 19 if the area of the
surface CD is 2000 times the area of the surface AB, then 1 lb. applied to
the liquid on AB will exert or sustain a force of 2000 lbs. on CD.
41. Hydraulic Press.—An important application of Pascal's principle is the
hydraulic press. See Fig. 20. It is used for many purposes where great force
is required, as in pressing paper or cloth, extracting oil from seeds, lifting
heavy objects, etc. Many high school pupils have been seated in a hydraulic
chair used by a dentist or barber. This chair is a modified hydraulic press.
Page 56
Fig. 20.—Cross-section of a hydraulic press.
The hydraulic press contains two movable pistons, P and p (see Fig. 20).
The larger of these, P, has a cross-sectional area that may be 100 or 1000
times that of the smaller. The smaller one is moved up and down by a lever;
on each upstroke, liquid is drawn in from a reservoir, while each down-
stroke forces some of the liquid into the space about the large piston. Valves
at V and V´ prevent the return of the liquid. If the area of P is 1,000 times
that of p, then the force exerted by P is 1000 times the force employed in
moving p. On the other hand, since the liquid moved by the small piston is
distributed over the area of the large one, the latter will move only 1/1000
as far as does the small piston. The relation between the motions of the two
pistons and the forces exerted by them may be stated concisely as follows:
The motions of the two pistons of the hydraulic press are inversely
proportional to the forces exerted by them. The cross-sectional areas of the
two pistons are, on the other hand, directly proportional to the forces
exerted by them.
An application of Pascal's principle often employed in cities is the hydraulic
elevator. In this device a long plunger or piston extends downward from the
elevator car into a cylinder sunk into the earth, sometimes to a depth of 300
The hydraulic press contains two movable pistons, P and p (see Fig. 20).
The larger of these, P, has a cross-sectional area that may be 100 or 1000
times that of the smaller. The smaller one is moved up and down by a lever;
on each upstroke, liquid is drawn in from a reservoir, while each down-
stroke forces some of the liquid into the space about the large piston. Valves
at V and V´ prevent the return of the liquid. If the area of P is 1,000 times
that of p, then the force exerted by P is 1000 times the force employed in
moving p. On the other hand, since the liquid moved by the small piston is
distributed over the area of the large one, the latter will move only 1/1000
as far as does the small piston. The relation between the motions of the two
pistons and the forces exerted by them may be stated concisely as follows:
The motions of the two pistons of the hydraulic press are inversely
proportional to the forces exerted by them. The cross-sectional areas of the
two pistons are, on the other hand, directly proportional to the forces
exerted by them.
An application of Pascal's principle often employed in cities is the hydraulic
elevator. In this device a long plunger or piston extends downward from the
elevator car into a cylinder sunk into the earth, sometimes to a depth of 300
Page 57
ft. Water forced into this cylinder pushes the piston upward and when the
water is released from the cylinder the piston descends.
Fig. 21 represents another form of hydraulic elevator, where the cylinder
and piston are at one side of the elevator shaft. In this type, to raise the
elevator, water is admitted to the cylinder pushing the piston downward.
42. Artesian Wells.—Sometimes a porous stratum containing water in the
earth's crust is inclined. Then if there are impervious strata (see Fig. 22),
both above and below the water-bearing one, and the latter comes to the
surface so that rain may fill it, a well sunk to the water-bearing stratum at a
point where it is below the surface will usually give an artesian well, that is,
one in which the water rises to or above the surface. Many are found in the
United States.
Fig. 22.—Conditions producing an artesian
well.
water is released from the cylinder the piston descends.
Fig. 21 represents another form of hydraulic elevator, where the cylinder
and piston are at one side of the elevator shaft. In this type, to raise the
elevator, water is admitted to the cylinder pushing the piston downward.
42. Artesian Wells.—Sometimes a porous stratum containing water in the
earth's crust is inclined. Then if there are impervious strata (see Fig. 22),
both above and below the water-bearing one, and the latter comes to the
surface so that rain may fill it, a well sunk to the water-bearing stratum at a
point where it is below the surface will usually give an artesian well, that is,
one in which the water rises to or above the surface. Many are found in the
United States.
Fig. 22.—Conditions producing an artesian
well.
Page 58
Fig. 21.—A hydraulic
freight elevator.
freight elevator.
Page 59
Fig. 23.—A standpipe.
43. Standpipes and Air Cushions.—Many who have lived in cities where
water is pumped into houses under pressure know that the water pressure is
changed when several faucets are opened at the same time. Again, if several
persons are using a hose for sprinkling, the pressure may be lessened so as
to be insufficient to force the water above the first floor. In order to allow
for these changes some flexibility or spring must be introduced somewhere
into the water-pipe system. Water is nearly incompressible and if no means
were employed to take care of the pressure changes, the sudden stopping
and starting of the flow would cause serious jars and start leaks in the pipes.
Two common devices for controlling sudden changes in the water pressure
are the standpipe and the air cushion.
The standpipe is simply a large vertical tube connected to the water mains
from which and into which water readily flows. When many faucets are
43. Standpipes and Air Cushions.—Many who have lived in cities where
water is pumped into houses under pressure know that the water pressure is
changed when several faucets are opened at the same time. Again, if several
persons are using a hose for sprinkling, the pressure may be lessened so as
to be insufficient to force the water above the first floor. In order to allow
for these changes some flexibility or spring must be introduced somewhere
into the water-pipe system. Water is nearly incompressible and if no means
were employed to take care of the pressure changes, the sudden stopping
and starting of the flow would cause serious jars and start leaks in the pipes.
Two common devices for controlling sudden changes in the water pressure
are the standpipe and the air cushion.
The standpipe is simply a large vertical tube connected to the water mains
from which and into which water readily flows. When many faucets are
Page 60
opened the water lowers; when most faucets are closed the water rises,
giving a simple automatic control of the surplus water and a supply of water
for a short time during a shut-down of the pumps. Standpipes are often used
in towns and small cities. Fig. 23 represents the standpipe at Jerome, Idaho.
The air cushion (Fig. 24) is a metal pipe or dome filled with air attached to
a water pipe where sudden changes in pressure are to be controlled. At
many faucets in a city water system such an air cushion is employed. It
contains air; this, unlike water, is easily compressible and the confined air
when the tap is suddenly closed receives and checks gradually the rush of
water in the pipe. Even with an air cushion, the "pound" of the water in the
pipe when a tap is suddenly closed is often heard. If air cushions were not
provided, the "water hammer" would frequently crack or break the pipes.
Fig. 24.—The short
pipe above the
faucet contains air
forming an air
cushion.
Important Topics
1. Pascal's law.
2. Hydraulic press.
3. Artesian wells.
4. Standpipes and air cushions.
Exercises
giving a simple automatic control of the surplus water and a supply of water
for a short time during a shut-down of the pumps. Standpipes are often used
in towns and small cities. Fig. 23 represents the standpipe at Jerome, Idaho.
The air cushion (Fig. 24) is a metal pipe or dome filled with air attached to
a water pipe where sudden changes in pressure are to be controlled. At
many faucets in a city water system such an air cushion is employed. It
contains air; this, unlike water, is easily compressible and the confined air
when the tap is suddenly closed receives and checks gradually the rush of
water in the pipe. Even with an air cushion, the "pound" of the water in the
pipe when a tap is suddenly closed is often heard. If air cushions were not
provided, the "water hammer" would frequently crack or break the pipes.
Fig. 24.—The short
pipe above the
faucet contains air
forming an air
cushion.
Important Topics
1. Pascal's law.
2. Hydraulic press.
3. Artesian wells.
4. Standpipes and air cushions.
Exercises
Page 61
1. Where have you seen an air cushion? Describe it and its use.
2. Where have you seen an hydraulic press? Why and how used?
3. Where have you seen hydraulic elevators? What moves them?
4. Where do you know of liquids under pressure? Three examples.
5. What is the pressure in water at a depth of 1500 cm. Express in grams per
square centimeter and in kilograms per square centimeter.
6. What head[C] of water is required to give a pressure of 200 g. per square
centimeter? 2 kg. per square centimeter?
7. What pressure will be produced by a "head" of water of 20 meters?
8. If 1728 cu. in. of water are placed in a vertical tube 1 sq. in. in cross
section to what height would the water rise? It would give how many feet of
head?
9. What would the water in problem 8 weigh? What pressure would it
produce at the bottom, in pounds per square inch? From this, compute how
many feet of "head" of water will produce a pressure of 1 lb. per square
inch.
10. Using the result in problem 9, what "head" of water will produce a
pressure of 10 lbs. per square inch? 100 lbs. per square inch?
11. From the result in 9, 100 ft. of "head" of water will produce what
pressure? 1000 ft. of "head?"
12. If the diameter of the pump piston in a hydraulic press is 2 cm. and that
of the press piston 50 cm. what will be the force against the latter if the
former is pushed down with a force of 40 kg.?
(3) Archimedes' Principle
44. A Body Supported by a Liquid.—Among the applications of the force
exerted by a liquid upon a surface, Archimedes' Principle is one of the most
important.
Most persons have noted that a body placed in water is partly or wholly
supported by the force of the water upon it. A stone held by a cord and
2. Where have you seen an hydraulic press? Why and how used?
3. Where have you seen hydraulic elevators? What moves them?
4. Where do you know of liquids under pressure? Three examples.
5. What is the pressure in water at a depth of 1500 cm. Express in grams per
square centimeter and in kilograms per square centimeter.
6. What head[C] of water is required to give a pressure of 200 g. per square
centimeter? 2 kg. per square centimeter?
7. What pressure will be produced by a "head" of water of 20 meters?
8. If 1728 cu. in. of water are placed in a vertical tube 1 sq. in. in cross
section to what height would the water rise? It would give how many feet of
head?
9. What would the water in problem 8 weigh? What pressure would it
produce at the bottom, in pounds per square inch? From this, compute how
many feet of "head" of water will produce a pressure of 1 lb. per square
inch.
10. Using the result in problem 9, what "head" of water will produce a
pressure of 10 lbs. per square inch? 100 lbs. per square inch?
11. From the result in 9, 100 ft. of "head" of water will produce what
pressure? 1000 ft. of "head?"
12. If the diameter of the pump piston in a hydraulic press is 2 cm. and that
of the press piston 50 cm. what will be the force against the latter if the
former is pushed down with a force of 40 kg.?
(3) Archimedes' Principle
44. A Body Supported by a Liquid.—Among the applications of the force
exerted by a liquid upon a surface, Archimedes' Principle is one of the most
important.
Most persons have noted that a body placed in water is partly or wholly
supported by the force of the water upon it. A stone held by a cord and
Page 62
lowered into water is felt to have a part of its weight supported, while a
piece of cork or wood is wholly supported and floats.
The human body is almost entirely supported in water, in fact, many people
can easily float in water. It was the consideration of this fact that led the
Greek philosopher Archimedes to discover and state the principle that
describes the supporting of a body in a liquid.
45. Archimedes' Principle.—"A body immersed in
a liquid is pushed up by a force equal to the weight
of the liquid that it displaces." The proof for this
law is simply demonstrated. Suppose a cube, abcd,
is immersed in water (Fig. 25). The upward force
on cd is equal to the weight of a column of water
equal to cdef. (See Art. 39.) The downward force
upon the top of the cube is equal to the weight of
the column of water abef. Then the net upward
force upon the cube, that is, the upward force upon
the bottom less the downward force upon the top,
or the buoyant force exerted by the liquid is exactly
equal to the weight of the displaced water abcd.
Fig. 25.— 46. Law of Floating Bodies.—This same
Theoretical proof of reasoning may be applied to any liquid and to any
Archimedes' body immersed to any depth below the surface of
principle. the liquid. If the body weighs more than the
displaced liquid it will sink. If it weighs less than
the displaced liquid it will float or rise in the water. A block of wood rises
out of the water in which it floats until its own weight just equals the weight
of the water it displaces. From this we have the law of floating bodies.
A floating body displaces its own weight of the liquid in which it floats.
To test the law of floating bodies, take a rod of light wood 1 cm. square and
30 cm. long (Fig. 26). Bore out one end and fill the opening with lead and
seal with paraffin so that the rod will float vertically when placed in water.
Mark upon one side of the rod a centimeter scale, and dip the rod in hot
paraffin to make it waterproof. Now find the weight of the stick in grams
and note the depth to which it sinks in water in centimeters. Compute the
weight of the displaced water. It will equal the weight of the rod.
piece of cork or wood is wholly supported and floats.
The human body is almost entirely supported in water, in fact, many people
can easily float in water. It was the consideration of this fact that led the
Greek philosopher Archimedes to discover and state the principle that
describes the supporting of a body in a liquid.
45. Archimedes' Principle.—"A body immersed in
a liquid is pushed up by a force equal to the weight
of the liquid that it displaces." The proof for this
law is simply demonstrated. Suppose a cube, abcd,
is immersed in water (Fig. 25). The upward force
on cd is equal to the weight of a column of water
equal to cdef. (See Art. 39.) The downward force
upon the top of the cube is equal to the weight of
the column of water abef. Then the net upward
force upon the cube, that is, the upward force upon
the bottom less the downward force upon the top,
or the buoyant force exerted by the liquid is exactly
equal to the weight of the displaced water abcd.
Fig. 25.— 46. Law of Floating Bodies.—This same
Theoretical proof of reasoning may be applied to any liquid and to any
Archimedes' body immersed to any depth below the surface of
principle. the liquid. If the body weighs more than the
displaced liquid it will sink. If it weighs less than
the displaced liquid it will float or rise in the water. A block of wood rises
out of the water in which it floats until its own weight just equals the weight
of the water it displaces. From this we have the law of floating bodies.
A floating body displaces its own weight of the liquid in which it floats.
To test the law of floating bodies, take a rod of light wood 1 cm. square and
30 cm. long (Fig. 26). Bore out one end and fill the opening with lead and
seal with paraffin so that the rod will float vertically when placed in water.
Mark upon one side of the rod a centimeter scale, and dip the rod in hot
paraffin to make it waterproof. Now find the weight of the stick in grams
and note the depth to which it sinks in water in centimeters. Compute the
weight of the displaced water. It will equal the weight of the rod.
Page 63
47. Applications of Archimedes' Principle. There are
numerous applications of Archimedes' Principle and the law
of floating bodies.
(a) To Find the Weight of a Floating Body: Problem.—A
boat 20 ft. long and with an average width of 6 ft. sinks to an
average depth of 3 ft. in the water. Find the weight of the
boat. What weight of cargo will sink it to an average depth
of 5 ft.?
Solution.—The volume of the water displaced is 20 × 6 × 3
cu. ft. = 360 cu. ft. Since 1 cu. ft. of water weighs 62.4 lbs.,
360 × 62.4 lbs. = 22,464 lbs., the weight of water displaced.
By the law of floating bodies this is equal to the weight of Fig. 26.—A
the boat. When loaded the volume of water displaced is 20 floating
ft. × 6 × 5 ft. which equal 600 cu. ft. 600 × 62.4 lbs. = body
37,440 lbs. This is the weight of the water displaced when displaces
loaded. 37,440 lbs. - 22,464 lbs. = 14,976 lbs., the weight of its own
the cargo. weight of
(b) To Find the Volume of an Immersed Solid: Problem. water.
—A stone weighs 187.2 lbs. in air and appears to weigh
124.8 lbs. in water. What is its volume?
Solution.—187.2 lbs. - 124.8 lbs. = 62.4 lbs., the buoyant force of the
water. By Archimedes' Principle, this equals the weight of the displaced
water which has a volume of 1 cu. ft. which is therefore the volume of the
stone.
(c) To Find the Density of a Body: The density of a body is defined as the
mass of unit volume.
We can easily find the mass of a body by weighing it, but the volume is
often impossible to obtain by measurements, especially of irregular solids.
Archimedes' Principle, however, provides a method of finding the volume
of a body accurately by weighing it first in air and then in water (Fig. 27),
the apparent loss in weight being equal to the weight of the displaced water.
One needs only to find the volume of water having the same weight as the
loss of weight to find the volume of the body.
numerous applications of Archimedes' Principle and the law
of floating bodies.
(a) To Find the Weight of a Floating Body: Problem.—A
boat 20 ft. long and with an average width of 6 ft. sinks to an
average depth of 3 ft. in the water. Find the weight of the
boat. What weight of cargo will sink it to an average depth
of 5 ft.?
Solution.—The volume of the water displaced is 20 × 6 × 3
cu. ft. = 360 cu. ft. Since 1 cu. ft. of water weighs 62.4 lbs.,
360 × 62.4 lbs. = 22,464 lbs., the weight of water displaced.
By the law of floating bodies this is equal to the weight of Fig. 26.—A
the boat. When loaded the volume of water displaced is 20 floating
ft. × 6 × 5 ft. which equal 600 cu. ft. 600 × 62.4 lbs. = body
37,440 lbs. This is the weight of the water displaced when displaces
loaded. 37,440 lbs. - 22,464 lbs. = 14,976 lbs., the weight of its own
the cargo. weight of
(b) To Find the Volume of an Immersed Solid: Problem. water.
—A stone weighs 187.2 lbs. in air and appears to weigh
124.8 lbs. in water. What is its volume?
Solution.—187.2 lbs. - 124.8 lbs. = 62.4 lbs., the buoyant force of the
water. By Archimedes' Principle, this equals the weight of the displaced
water which has a volume of 1 cu. ft. which is therefore the volume of the
stone.
(c) To Find the Density of a Body: The density of a body is defined as the
mass of unit volume.
We can easily find the mass of a body by weighing it, but the volume is
often impossible to obtain by measurements, especially of irregular solids.
Archimedes' Principle, however, provides a method of finding the volume
of a body accurately by weighing it first in air and then in water (Fig. 27),
the apparent loss in weight being equal to the weight of the displaced water.
One needs only to find the volume of water having the same weight as the
loss of weight to find the volume of the body.
Page 64
If the metric system is used, 1 ccm. of water weighs 1 g., and the volume is
numerically the same as the loss of weight.
Fig. 27.—A method of
weighing a body
under water.
Important Topics
1. Archimedes' Principle.
2. Law of floating bodies.
3. The applications of Archimedes' Principle are to determine (a) the weight
of a floating body; (b) the volume of an immersed solid, and (c) the density
of a body.
Exercises
1. Look up the story of Archimedes and the crown. Write a brief account of
it.
2. Why is it easier for a fat man to float in water than for a lean one?
3. A fish weighing 1 lb. is placed in a pail full of water. Will the pail and
contents weigh more than before adding the fish? Why?
numerically the same as the loss of weight.
Fig. 27.—A method of
weighing a body
under water.
Important Topics
1. Archimedes' Principle.
2. Law of floating bodies.
3. The applications of Archimedes' Principle are to determine (a) the weight
of a floating body; (b) the volume of an immersed solid, and (c) the density
of a body.
Exercises
1. Look up the story of Archimedes and the crown. Write a brief account of
it.
2. Why is it easier for a fat man to float in water than for a lean one?
3. A fish weighing 1 lb. is placed in a pail full of water. Will the pail and
contents weigh more than before adding the fish? Why?
Page 65
4. Why can a large stone be lifted more easily while under water than when
on the land?
5. Why does the air bubble in a spirit level move as one end of the
instrument is raised or lowered?
6. Why does a dead fish always float?
7. A ship is built for use in fresh water. What will be the effect on its water
line when passing into the ocean?
8. Why can small bugs walk on water while large animals cannot?
9. If an object weighing 62.4 lbs. just floats in water, what weight of water
does it displace? What volume of water is displaced? What is the volume of
the body?
10. What is the volume of a man who just floats in water if he weighs 124.8
lbs.? If he weighs 187.2 lbs.?
11. An object weighing 500 g. just floats in water. What is its volume? How
much water does a floating block of wood displace if it weighs 125 lbs.?
125 g.? 2 kg.? 2000 kg.?
12. A flat boat 10 × 40 ft. in size will sink how much in the water when 10
horses each weighing 1250 lbs. are placed on board?
13. A ship 900 ft. long and 80 ft. average width sinks to an average depth of
25 ft. when empty and 40 ft. when loaded. What is the weight of the ship
and of its load?
14. Will a 1000 cc. block sink or float in water if it weighs 800 g.? If it
weighs 1200 g.? Explain.
15. If a 1000 cc. block of metal weighing 1200 g. is placed in the water in
mid ocean what will become of it?
16. Prove Archimedes' Principle by use of the principles of liquid pressure.
17. An irregular stone, density 2.5 g. per ccm. displaces 2 cu. ft. of water.
What is its weight? Its apparent weight in water?
18. Will the depth to which a vessel sinks in water change as she sails from
Lake Ontario into the Atlantic Ocean? Why?
on the land?
5. Why does the air bubble in a spirit level move as one end of the
instrument is raised or lowered?
6. Why does a dead fish always float?
7. A ship is built for use in fresh water. What will be the effect on its water
line when passing into the ocean?
8. Why can small bugs walk on water while large animals cannot?
9. If an object weighing 62.4 lbs. just floats in water, what weight of water
does it displace? What volume of water is displaced? What is the volume of
the body?
10. What is the volume of a man who just floats in water if he weighs 124.8
lbs.? If he weighs 187.2 lbs.?
11. An object weighing 500 g. just floats in water. What is its volume? How
much water does a floating block of wood displace if it weighs 125 lbs.?
125 g.? 2 kg.? 2000 kg.?
12. A flat boat 10 × 40 ft. in size will sink how much in the water when 10
horses each weighing 1250 lbs. are placed on board?
13. A ship 900 ft. long and 80 ft. average width sinks to an average depth of
25 ft. when empty and 40 ft. when loaded. What is the weight of the ship
and of its load?
14. Will a 1000 cc. block sink or float in water if it weighs 800 g.? If it
weighs 1200 g.? Explain.
15. If a 1000 cc. block of metal weighing 1200 g. is placed in the water in
mid ocean what will become of it?
16. Prove Archimedes' Principle by use of the principles of liquid pressure.
17. An irregular stone, density 2.5 g. per ccm. displaces 2 cu. ft. of water.
What is its weight? Its apparent weight in water?
18. Will the depth to which a vessel sinks in water change as she sails from
Lake Ontario into the Atlantic Ocean? Why?
Page 66
19. If the density of sea water is 1.0269 g. per cubic centimeter and that of
ice 0.918 g. per ccm., what portion of an iceberg is above water?
20. In drawing water from a well by means of a bucket, why is less force
used when it is under water than when entirely above?
21. A stone which weighs 300 lbs. can be lifted under water with a force of
150 lbs. What is the volume of the stone?
22. The average density of the human body is 1.07 grams per c.c. How
much water will a man who weighs 150 lbs. displace when diving? How
much when floating?
(4) Density and Specific Gravity
48. Density.—The density of a substance is often used as a test of its purity.
Archimedes in testing King Hiero's crown to find out if it were made of
pure gold determined first its density. It is by such tests that the purity of
milk, of alcohol, of gold, and a great variety of substances is often
determined.
Knowledge of methods of finding density is of value to everyone and
should be included in the education of every student. The density of a
substance is the mass of unit volume of the substance. In the metric system,
for example, the density of a substance is the mass in grams per 1 ccm.
Taking water, 1 ccm. weighs 1 gr. or its density is therefore 1 g. to the cubic
centimeter. A cubic centimeter of aluminium weighs 2.7 g. Its density
therefore is 2.7 g. per ccm.
49. Specific Gravity.—Specific gravity is the ratio of the weight of any
volume of a substance to the weight of an equal volume of water. Its
meaning is not quite the same as that of density, since specific gravity is
always a ratio, i.e., an abstract number, as 2.7. Density of a substance is a
concrete number, as 2.7 grams per ccm. In the metric system the density of
water is one gram per cubic centimeter, therefore we have:
Density (g. per ccm.) = (numerically) specific gravity.
In the English system, the density of water is 62.4 pounds per cubic foot,
therefore in this system we have:
ice 0.918 g. per ccm., what portion of an iceberg is above water?
20. In drawing water from a well by means of a bucket, why is less force
used when it is under water than when entirely above?
21. A stone which weighs 300 lbs. can be lifted under water with a force of
150 lbs. What is the volume of the stone?
22. The average density of the human body is 1.07 grams per c.c. How
much water will a man who weighs 150 lbs. displace when diving? How
much when floating?
(4) Density and Specific Gravity
48. Density.—The density of a substance is often used as a test of its purity.
Archimedes in testing King Hiero's crown to find out if it were made of
pure gold determined first its density. It is by such tests that the purity of
milk, of alcohol, of gold, and a great variety of substances is often
determined.
Knowledge of methods of finding density is of value to everyone and
should be included in the education of every student. The density of a
substance is the mass of unit volume of the substance. In the metric system,
for example, the density of a substance is the mass in grams per 1 ccm.
Taking water, 1 ccm. weighs 1 gr. or its density is therefore 1 g. to the cubic
centimeter. A cubic centimeter of aluminium weighs 2.7 g. Its density
therefore is 2.7 g. per ccm.
49. Specific Gravity.—Specific gravity is the ratio of the weight of any
volume of a substance to the weight of an equal volume of water. Its
meaning is not quite the same as that of density, since specific gravity is
always a ratio, i.e., an abstract number, as 2.7. Density of a substance is a
concrete number, as 2.7 grams per ccm. In the metric system the density of
water is one gram per cubic centimeter, therefore we have:
Density (g. per ccm.) = (numerically) specific gravity.
In the English system, the density of water is 62.4 pounds per cubic foot,
therefore in this system we have:
Page 67
Density (lbs. per cu. ft.) = (numerically) 62.4 × sp. gr.
50. Methods for Finding Density and Specific Gravity
(a) Regular Solids.—Solids of regular shapes such as cubes, spheres, etc.,
whose volumes may be readily found by measurement, may be weighed.
The mass divided by the volume gives the density, or D = Mμ/v.
(b) Irregular Solids.—with these the volume cannot be found by
measurement but may be obtained by Archimedes' Principle. Weigh the
solid first in the air and then in water. The apparent loss of weight equals
the weight of the equal volume of water displaced. From this the volume
may be found. And then the density equals mass/volume; the specific
gravity =
50. Methods for Finding Density and Specific Gravity
(a) Regular Solids.—Solids of regular shapes such as cubes, spheres, etc.,
whose volumes may be readily found by measurement, may be weighed.
The mass divided by the volume gives the density, or D = Mμ/v.
(b) Irregular Solids.—with these the volume cannot be found by
measurement but may be obtained by Archimedes' Principle. Weigh the
solid first in the air and then in water. The apparent loss of weight equals
the weight of the equal volume of water displaced. From this the volume
may be found. And then the density equals mass/volume; the specific
gravity =
Page 68
wt. in air / wt. of equal volume of water = wt. in air / ((wt. in air) - (wt. in
water))
(c) Solids Lighter than Water.—This will require a sinker to hold the body
under water. Weigh the solid in air (w). Weigh the sinker in water (s). Attach
the sinker to the solid and weigh both in water (w´). The specific gravity
equals
(wt. of solid in air)/(loss in wt. of solid in water) or w/((w + s) - w´)
The apparent loss of weight of the solid is equal to the sum of its weight in
air plus the weight of the sinker in water, less the combined weight of both
in water.
(d) The Density of a Liquid by a Hydrometer.—One may also easily find
the density of any liquid by Archimedes' Principle. If one takes the rod
described in Art. 46, and places it in water, the number of cubic centimeters
of water it displaces indicates its weight in grams. On placing the rod in
another liquid in which it floats, it will of course displace its own weight
and the height to which the liquid rises on the scale gives the volume. By
dividing the weight of the rod as shown by its position in water by the
volume of the liquid displaced we obtain the density of the liquid.
Commercial hydrometers for testing the density of milk, alcohol and other
liquids are made of glass of the form shown in Fig. 28. The long narrow
stem permits small differences in volume to be noticed, hence they are more
accurate than the rod described in the preceding paragraph. For convenience
this rod contains a paper scale, so that when the height of the liquid on the
stem is noted, the density is read at once.
Density of Liquids by Loss of Weight. Weigh a piece of glass in air (Wa),
in water (Ww), and in the liquid to be tested (Wl).
Then (Wa - Ww)gives the weight of the water displaced.
And (Wa - Wl) gives the weight of the liquid displaced.
Hence, (Wa - Wl)/(Wa - Ww) equals the specific gravity of the liquid.
water))
(c) Solids Lighter than Water.—This will require a sinker to hold the body
under water. Weigh the solid in air (w). Weigh the sinker in water (s). Attach
the sinker to the solid and weigh both in water (w´). The specific gravity
equals
(wt. of solid in air)/(loss in wt. of solid in water) or w/((w + s) - w´)
The apparent loss of weight of the solid is equal to the sum of its weight in
air plus the weight of the sinker in water, less the combined weight of both
in water.
(d) The Density of a Liquid by a Hydrometer.—One may also easily find
the density of any liquid by Archimedes' Principle. If one takes the rod
described in Art. 46, and places it in water, the number of cubic centimeters
of water it displaces indicates its weight in grams. On placing the rod in
another liquid in which it floats, it will of course displace its own weight
and the height to which the liquid rises on the scale gives the volume. By
dividing the weight of the rod as shown by its position in water by the
volume of the liquid displaced we obtain the density of the liquid.
Commercial hydrometers for testing the density of milk, alcohol and other
liquids are made of glass of the form shown in Fig. 28. The long narrow
stem permits small differences in volume to be noticed, hence they are more
accurate than the rod described in the preceding paragraph. For convenience
this rod contains a paper scale, so that when the height of the liquid on the
stem is noted, the density is read at once.
Density of Liquids by Loss of Weight. Weigh a piece of glass in air (Wa),
in water (Ww), and in the liquid to be tested (Wl).
Then (Wa - Ww)gives the weight of the water displaced.
And (Wa - Wl) gives the weight of the liquid displaced.
Hence, (Wa - Wl)/(Wa - Ww) equals the specific gravity of the liquid.
Page 69
Fig. 28.—A
hydromete
r used to
find the
density of a
liquid.
Important Topics
1. Definitions of density and specific gravity.
2. Methods of finding density: (a) regular solids; (b) irregular solids; (c)
solids lighter than water; (d) liquids by hydrometer; (e) liquids by loss of
weight.
Exercises
Note.—Consider that 1 cu. ft. of water weighs 62.4 lbs. Consider that 1
ccm. of water weighs 1 g.
1. What is meant by the statement that a block of wood has a specific
gravity of 0.6?
2. Considering that the density of the human body is the same as that of
water, what is the volume of a 125-lb. boy? Of a 250-lb. man? Of a 62.4-lb.
boy? What is the volume of your body?
3. How is the weight of large ships found? Give an example.
hydromete
r used to
find the
density of a
liquid.
Important Topics
1. Definitions of density and specific gravity.
2. Methods of finding density: (a) regular solids; (b) irregular solids; (c)
solids lighter than water; (d) liquids by hydrometer; (e) liquids by loss of
weight.
Exercises
Note.—Consider that 1 cu. ft. of water weighs 62.4 lbs. Consider that 1
ccm. of water weighs 1 g.
1. What is meant by the statement that a block of wood has a specific
gravity of 0.6?
2. Considering that the density of the human body is the same as that of
water, what is the volume of a 125-lb. boy? Of a 250-lb. man? Of a 62.4-lb.
boy? What is the volume of your body?
3. How is the weight of large ships found? Give an example.
Page 70
4. Mention three cases where determinations of density are important.
5. A body weighs 40 g. in air, 15 g. in water, 5 g. in an acid. Find (a) the
density of the body; (b) its volume; (c) density of the acid.
6. If the specific gravity of a horse is 1, what is the volume of a horse
weighing 500 kg.? Of one weighing 1248 lbs.?
7. A weighted wooden box sinks to a depth of 20 cm. in water and 24 cm. in
alcohol, and to a depth of 18 cm. in brine. What is the density of the alcohol
and of the brine?
8. A glass stopper weighs in the air 25 g., in water 15 g., in oil 18 g. Find
the density and volume of the stopper. Find the density of the oil.
9. What would a cubic foot of wood weigh if the specific gravity were 0.5.?
10. The specific gravity of aluminum is 2.7. Find the weight of a cubic foot
of it.
11. A block of wood weighs 40 g. A piece of lead appears to weigh 70 g. in
water. Both together appear to weigh 60 g. in water. Find the density of the
wood.
12. A stone weighs 30 g. in air, 22 g. in water, and 20 g. in salt water. Find
the density of the salt water.
13. Will iron sink in mercury? Why?
14. A submarine boat weighing 200 tons must have what volume in order to
float?
15. Find the weight of 2 cu. ft. of copper from its density.
16. What is the weight in water of a mass whose specific gravity is 3.3 and
whose weight is 50 kg.?
17. A block of granite weighs 1656 lbs.; its volume is 10 cu. ft., what is its
density?
18. If the specific gravity of hard coal is 1.75 how would you determine
how many tons of coal a bin would hold?
19. A hollow copper ball weighs 2 kg. What must be its volume to enable it
to just float in water?
5. A body weighs 40 g. in air, 15 g. in water, 5 g. in an acid. Find (a) the
density of the body; (b) its volume; (c) density of the acid.
6. If the specific gravity of a horse is 1, what is the volume of a horse
weighing 500 kg.? Of one weighing 1248 lbs.?
7. A weighted wooden box sinks to a depth of 20 cm. in water and 24 cm. in
alcohol, and to a depth of 18 cm. in brine. What is the density of the alcohol
and of the brine?
8. A glass stopper weighs in the air 25 g., in water 15 g., in oil 18 g. Find
the density and volume of the stopper. Find the density of the oil.
9. What would a cubic foot of wood weigh if the specific gravity were 0.5.?
10. The specific gravity of aluminum is 2.7. Find the weight of a cubic foot
of it.
11. A block of wood weighs 40 g. A piece of lead appears to weigh 70 g. in
water. Both together appear to weigh 60 g. in water. Find the density of the
wood.
12. A stone weighs 30 g. in air, 22 g. in water, and 20 g. in salt water. Find
the density of the salt water.
13. Will iron sink in mercury? Why?
14. A submarine boat weighing 200 tons must have what volume in order to
float?
15. Find the weight of 2 cu. ft. of copper from its density.
16. What is the weight in water of a mass whose specific gravity is 3.3 and
whose weight is 50 kg.?
17. A block of granite weighs 1656 lbs.; its volume is 10 cu. ft., what is its
density?
18. If the specific gravity of hard coal is 1.75 how would you determine
how many tons of coal a bin would hold?
19. A hollow copper ball weighs 2 kg. What must be its volume to enable it
to just float in water?
Page 71
20. A mass having a volume of 100 ccm. and a specific gravity of 2.67 is
fastened to 200 ccm. of wood, specific gravity 0.55. What will the
combination weigh in water?
21. A block weighing 4 oz. in air is tied to a sinker which appears to weigh
14 oz. in water. Both together appear to weigh 6 oz. in water. What is the
specific gravity of the block?
fastened to 200 ccm. of wood, specific gravity 0.55. What will the
combination weigh in water?
21. A block weighing 4 oz. in air is tied to a sinker which appears to weigh
14 oz. in water. Both together appear to weigh 6 oz. in water. What is the
specific gravity of the block?
Page 72
CHAPTER IV
MECHANICS OF GASES
(1) Weight and Pressure of the Air
51. Weight of Air.—It is said that savages are unaware of the presence of
air. They feel the wind and hear and see it moving the leaves and branches
of the trees, but of air itself they have little conception.
To ordinary observers, it seems to have no weight, and to offer little
resistance to bodies passing through it. That it has weight may be readily
shown as follows: (See Fig. 29.) If a hollow metal sphere, or a glass flask,
provided with tube and stopcock, be weighed when the stopcock is open,
and then after the air has been exhausted from it by an air pump, a definite
loss of weight is noticeable.
If the volume of the sphere is known and it is well
exhausted of air, a fair approximation of the
weight of air may be obtained. Under "standard
conditions," which means at the freezing
temperature and a barometric pressure of 76 cm.,
a liter of air weighs 1.293 g. while 12 cu. ft. of air
weigh approximately 1 lb.
52. Pressure of Air.—Since air has weight it may
be supposed to exert pressure like a liquid. That it
does so may be shown in a variety of ways.
Fig. 29.—Proof that
air has weight. If a plunger fitting tightly in a glass cylinder be
drawn upward, while the lower end of the tube is
under water, the water will rise in the tube (Fig.
30). The common explanation of this is that the water rises because of
"suction." The philosophers of the ancient Greeks explained it by saying
that "nature abhors a vacuum," and therefore the water rises. Neither
explanation is correct. It was found in 1640 that water would not rise in a
MECHANICS OF GASES
(1) Weight and Pressure of the Air
51. Weight of Air.—It is said that savages are unaware of the presence of
air. They feel the wind and hear and see it moving the leaves and branches
of the trees, but of air itself they have little conception.
To ordinary observers, it seems to have no weight, and to offer little
resistance to bodies passing through it. That it has weight may be readily
shown as follows: (See Fig. 29.) If a hollow metal sphere, or a glass flask,
provided with tube and stopcock, be weighed when the stopcock is open,
and then after the air has been exhausted from it by an air pump, a definite
loss of weight is noticeable.
If the volume of the sphere is known and it is well
exhausted of air, a fair approximation of the
weight of air may be obtained. Under "standard
conditions," which means at the freezing
temperature and a barometric pressure of 76 cm.,
a liter of air weighs 1.293 g. while 12 cu. ft. of air
weigh approximately 1 lb.
52. Pressure of Air.—Since air has weight it may
be supposed to exert pressure like a liquid. That it
does so may be shown in a variety of ways.
Fig. 29.—Proof that
air has weight. If a plunger fitting tightly in a glass cylinder be
drawn upward, while the lower end of the tube is
under water, the water will rise in the tube (Fig.
30). The common explanation of this is that the water rises because of
"suction." The philosophers of the ancient Greeks explained it by saying
that "nature abhors a vacuum," and therefore the water rises. Neither
explanation is correct. It was found in 1640 that water would not rise in a
Page 73
pump more than 32 ft. despite the fact that a vacuum was maintained above
the water. Galileo was applied to for an explanation. He said, "evidently
nature's horror of a vacuum does not extend above 32 ft." Galileo began
tests upon "the power of a vacuum" but dying left his pupil Torricelli to
continue the experiment. Torricelli reasoned that if water would rise 32 ft.,
then mercury, which is 13.6 times as dense as water, would rise about 1/13
as much. To test this, he performed the following famous experiment.
53. Torricelli's Experiment (1643).—Take a glass tube
about 3 ft. long, sealed at one end, and fill it with mercury.
Close the end with the finger and invert, placing the end
closed by the finger under mercury in a dish (Fig. 31).
Remove the finger and the mercury sinks until the top of the
mercury is about 30 in. above the level of the mercury in the
dish. Torricelli concluded that the rise of liquids in exhausted
tubes is due to the pressure of the atmosphere acting on the
surface of the mercury in the dish.
To test this, place the tube with its mercury upon the plate of
an air pump and place a tubulated bell jar over the apparatus
so that the tube projects through a tightly fitting stopper. (See Fig. 30.—
Fig. 32.) If the air pressure is the cause of the rise of mercury Air
in the tube, on removing the air from the bell jar the mercury pressure
should fall in the tube. This is seen to happen as soon as the forces the
pump is started. It is difficult to remove all the air from the liquid up
receiver so the mercury rarely falls to the same level in the the tube.
tube as in the dish. A small tube containing mercury is often
attached to air pumps to indicate the degree of exhaustion.
Such tubes are called manometers.
the water. Galileo was applied to for an explanation. He said, "evidently
nature's horror of a vacuum does not extend above 32 ft." Galileo began
tests upon "the power of a vacuum" but dying left his pupil Torricelli to
continue the experiment. Torricelli reasoned that if water would rise 32 ft.,
then mercury, which is 13.6 times as dense as water, would rise about 1/13
as much. To test this, he performed the following famous experiment.
53. Torricelli's Experiment (1643).—Take a glass tube
about 3 ft. long, sealed at one end, and fill it with mercury.
Close the end with the finger and invert, placing the end
closed by the finger under mercury in a dish (Fig. 31).
Remove the finger and the mercury sinks until the top of the
mercury is about 30 in. above the level of the mercury in the
dish. Torricelli concluded that the rise of liquids in exhausted
tubes is due to the pressure of the atmosphere acting on the
surface of the mercury in the dish.
To test this, place the tube with its mercury upon the plate of
an air pump and place a tubulated bell jar over the apparatus
so that the tube projects through a tightly fitting stopper. (See Fig. 30.—
Fig. 32.) If the air pressure is the cause of the rise of mercury Air
in the tube, on removing the air from the bell jar the mercury pressure
should fall in the tube. This is seen to happen as soon as the forces the
pump is started. It is difficult to remove all the air from the liquid up
receiver so the mercury rarely falls to the same level in the the tube.
tube as in the dish. A small tube containing mercury is often
attached to air pumps to indicate the degree of exhaustion.
Such tubes are called manometers.
Page 74
Fig. 31.—Torricelli's experiment.
Fig. 32.—The mercury drops as the air is
removed.
54. The Amount of Atmospheric Pressure.—Torricelli's experiment
enables us to compute readily the pressure of the atmosphere, since it is the
atmospheric pressure that balances the column of mercury in the tube. By
Pascal's Law, the pressure of the atmosphere on the surface of the mercury
in the dish is transmitted as an exactly equal pressure on the mercury
column in the tube at the same level as the mercury outside.
This pressure, due to the air, must balance the weight of the column of
mercury in the tube. It therefore equals the weight of the column of mercury
of unit cross-section. The average height of the column of mercury at sea-
level is 76 cm. Since the weight of 1 cc. of mercury is 13.6 grams, the
pressure inside the tube at the level of the surface of the mercury in the dish
is equal to 1 × 76 × 13.6 or 1033.6 g. per square centimeter. Therefore the
atmospheric pressure on the surface of the mercury in the dish is 1033.6 g.
per square centimeter, approximately 1 kg. per square centimeter or 15 lbs.
per square inch.
55. Pascal's Experiment.—Pascal tested in another way the action of
atmospheric pressure upon the column of mercury by requesting his
brother-in-law, Perrier, who lived near a mountain, to try the experiment on
its top. Perrier found that on ascending 1000 meters the mercury fell 8 cm.
Fig. 32.—The mercury drops as the air is
removed.
54. The Amount of Atmospheric Pressure.—Torricelli's experiment
enables us to compute readily the pressure of the atmosphere, since it is the
atmospheric pressure that balances the column of mercury in the tube. By
Pascal's Law, the pressure of the atmosphere on the surface of the mercury
in the dish is transmitted as an exactly equal pressure on the mercury
column in the tube at the same level as the mercury outside.
This pressure, due to the air, must balance the weight of the column of
mercury in the tube. It therefore equals the weight of the column of mercury
of unit cross-section. The average height of the column of mercury at sea-
level is 76 cm. Since the weight of 1 cc. of mercury is 13.6 grams, the
pressure inside the tube at the level of the surface of the mercury in the dish
is equal to 1 × 76 × 13.6 or 1033.6 g. per square centimeter. Therefore the
atmospheric pressure on the surface of the mercury in the dish is 1033.6 g.
per square centimeter, approximately 1 kg. per square centimeter or 15 lbs.
per square inch.
55. Pascal's Experiment.—Pascal tested in another way the action of
atmospheric pressure upon the column of mercury by requesting his
brother-in-law, Perrier, who lived near a mountain, to try the experiment on
its top. Perrier found that on ascending 1000 meters the mercury fell 8 cm.
Page 75
in the tube. Travelers, surveyors, and aviators frequently determine the
altitude above sea-level by reading the barometer, an ascent of 11 meters
giving a fall of about 1 mm. in the mercury column, or 0.1 in. for every 90
ft. of ascent.
56. The Barometer.—The modern barometer (Fig. 33),
consists of a Torricellian tube properly mounted. Reading a
barometer consists in accurately reading the height of the
mercury column. This height varies from 75 to 76.5 cm. or
29 to 30 in. in localities not far from the sea-level. The
atmospheric pressure varies because of disturbances in the
atmosphere. It is found that these disturbances of the
atmosphere pass across the country from west to east in a
somewhat regular manner, hence a series of readings of the
barometer may give reliable information of the movement of
these disturbances and so assist in forecasting the weather.
The weather Bureau has observations taken at the same
moment at various stations over the country. These
observations form the basis for the daily forecast of the
weather.
Fig. 33.—A
standard
barometer.
altitude above sea-level by reading the barometer, an ascent of 11 meters
giving a fall of about 1 mm. in the mercury column, or 0.1 in. for every 90
ft. of ascent.
56. The Barometer.—The modern barometer (Fig. 33),
consists of a Torricellian tube properly mounted. Reading a
barometer consists in accurately reading the height of the
mercury column. This height varies from 75 to 76.5 cm. or
29 to 30 in. in localities not far from the sea-level. The
atmospheric pressure varies because of disturbances in the
atmosphere. It is found that these disturbances of the
atmosphere pass across the country from west to east in a
somewhat regular manner, hence a series of readings of the
barometer may give reliable information of the movement of
these disturbances and so assist in forecasting the weather.
The weather Bureau has observations taken at the same
moment at various stations over the country. These
observations form the basis for the daily forecast of the
weather.
Fig. 33.—A
standard
barometer.
Page 76
Fig. 34.—An aneroid barometer
Another form of barometer in common use is the Aneroid Barometer (Fig.
34). Its essential parts are a cylindrical air-tight box with an elastic
corrugated cover. Inside the box is a partial vacuum. This makes the cover
very sensitive to slight changes of pressure. The motion of the top of the
box is conveyed by a series of levers to an indicating hand which moves
over a dial. This barometer can be made so sensitive as to indicate the
change of air pressure from a table top to the floor. It is much used by
travelers, explorers, surveying parties and aviators, since the mercurial
barometer is inconvenient to carry.
Important Topics
1. Weight and Pressure of air in English and metric units. How shown.
Evidences.
2. Work of Galileo, Torricelli, and Perrier.
Another form of barometer in common use is the Aneroid Barometer (Fig.
34). Its essential parts are a cylindrical air-tight box with an elastic
corrugated cover. Inside the box is a partial vacuum. This makes the cover
very sensitive to slight changes of pressure. The motion of the top of the
box is conveyed by a series of levers to an indicating hand which moves
over a dial. This barometer can be made so sensitive as to indicate the
change of air pressure from a table top to the floor. It is much used by
travelers, explorers, surveying parties and aviators, since the mercurial
barometer is inconvenient to carry.
Important Topics
1. Weight and Pressure of air in English and metric units. How shown.
Evidences.
2. Work of Galileo, Torricelli, and Perrier.
Page 77
3. Barometer: construction, action, mercurial, aneroid.
Fig. 35.—Air pressure keeps the water In the
tumbler.
Fig. 36.—Cross-section of a modern drinking
fountain.
Exercises
1. Do you think Archimedes' Principle applies to the air? Does Pascal's
Law? Why?
2. Find the downward pressure of the mercury in a barometer tube if the
cross-section is 1 sq. cm. and the height 75 cm. at the level of the mercury
surface in contact with the air. (The density of mercury is 13.6 grams per
cc.)
3. What is the weight of the air in a room if it is 10 × 8 × 4 meters?
4. What weight of air is in a room 10 × 15 × 10 ft.?
5. When smoke rises in a straight line from chimneys, is it an indication of a
high or low barometric pressure? Why?
Fig. 35.—Air pressure keeps the water In the
tumbler.
Fig. 36.—Cross-section of a modern drinking
fountain.
Exercises
1. Do you think Archimedes' Principle applies to the air? Does Pascal's
Law? Why?
2. Find the downward pressure of the mercury in a barometer tube if the
cross-section is 1 sq. cm. and the height 75 cm. at the level of the mercury
surface in contact with the air. (The density of mercury is 13.6 grams per
cc.)
3. What is the weight of the air in a room if it is 10 × 8 × 4 meters?
4. What weight of air is in a room 10 × 15 × 10 ft.?
5. When smoke rises in a straight line from chimneys, is it an indication of a
high or low barometric pressure? Why?
Page 78
6. Why does a tumbler filled with water and inverted in a dish with its rim
under water remain full?
7. If the barometer tube is inclined the mercury remains at the same
horizontal level. How can this be explained?
8. When the mercurial barometer stands at 76 cm., how high would a water
barometer stand? Explain.
9. Explain why it is possible for one to suck soda water through a tube?
10. Fill a tumbler with water. Place a sheet of paper over the top and invert.
The paper clings to the tumbler and prevents the water from escaping.
Explain. (See Fig. 35.)
11. Why must a kerosene oil can have two openings in order to allow the oil
to flow freely?
12. Explain the action of the modern drinking fountain (Fig. 36).
(2) Compressibility and Expansibility of the air
57. Effect of Pressure on Liquids and Gases.—Both classes of fluids,
liquids and gases, have many characteristics in common. Both are
composed of molecules that move freely; hence both flow. At any point
within a fluid the pressure is the same in all directions. Archimedes'
Principle applies, therefore, to both liquids and gases.
We now come to an important difference between liquids and gases. Liquids
are practically incompressible. "So much so, that if water is subjected to a
pressure of 3000 kg. per sq. cm., its volume is reduced only about one-
tenth." Gases show a very different behavior from liquids on being
subjected to pressure. They may readily be compressed to a small fraction
of their volume as is noticed on inflating a pneumatic tire. A gas has also
the ability to spring back to a larger volume as soon as the pressure is
released, as when a cork is driven from a pop gun. Not only is compressed
air able to expand, but air under ordinary conditions will expand if it is
released in a space where the pressure is less.
Hollow bodies, animals and plants, are not crushed by atmospheric
pressure, because the air and gases contained within exert as much force
under water remain full?
7. If the barometer tube is inclined the mercury remains at the same
horizontal level. How can this be explained?
8. When the mercurial barometer stands at 76 cm., how high would a water
barometer stand? Explain.
9. Explain why it is possible for one to suck soda water through a tube?
10. Fill a tumbler with water. Place a sheet of paper over the top and invert.
The paper clings to the tumbler and prevents the water from escaping.
Explain. (See Fig. 35.)
11. Why must a kerosene oil can have two openings in order to allow the oil
to flow freely?
12. Explain the action of the modern drinking fountain (Fig. 36).
(2) Compressibility and Expansibility of the air
57. Effect of Pressure on Liquids and Gases.—Both classes of fluids,
liquids and gases, have many characteristics in common. Both are
composed of molecules that move freely; hence both flow. At any point
within a fluid the pressure is the same in all directions. Archimedes'
Principle applies, therefore, to both liquids and gases.
We now come to an important difference between liquids and gases. Liquids
are practically incompressible. "So much so, that if water is subjected to a
pressure of 3000 kg. per sq. cm., its volume is reduced only about one-
tenth." Gases show a very different behavior from liquids on being
subjected to pressure. They may readily be compressed to a small fraction
of their volume as is noticed on inflating a pneumatic tire. A gas has also
the ability to spring back to a larger volume as soon as the pressure is
released, as when a cork is driven from a pop gun. Not only is compressed
air able to expand, but air under ordinary conditions will expand if it is
released in a space where the pressure is less.
Hollow bodies, animals and plants, are not crushed by atmospheric
pressure, because the air and gases contained within exert as much force
Page 79
outward as the air exerts inward.
58. Boyle's Law.—The relation between the volume and pressure of a gas
was first investigated by Robert Boyle in the seventeenth century. The
experiment by which he first discovered the law or the relation between the
volume and the pressure of a gas is briefly described as follows:
A glass tube is bent in the form of the capital
letter J, the short arm being closed. A little
mercury is poured in to cover the bend. (See
Fig. 37 a.) Since the mercury is at the same level
in both arms, the pressure in (A) is the same as
in (B). Mercury is now poured into (A) until it
stands in the long tube at a height above that in
(B) which is equal to the height of the mercury
column of the barometer. (See Fig. 37 b.) The
air in (BC) is now under a pressure of two
atmospheres (one atmosphere is due to the
mercury column). On measurement the air in
(BC) will be found to have just one-half of its
original volume.
Thus doubling the pressure to which a gas is
subjected reduces its volume to one-half.
Tripling the pressure, reduces the volume to
one-third and so on.
Careful experiments reveal the following law: Figs. 37 a and 37 b.—
The volume of a given mass of gas at constant Boyle's law apparatus.
temperature is inversely proportional to the
pressure to which it is subjected.
This law is often expressed mathematically. P/P´ = V´/V, or PV = P´V´.
Since doubling the pressure reduces the volume one-half, it doubles the
density. Tripling the pressure triples the density. We therefore have P/P´ =
D/D´ or the density of a gas directly proportional to its pressure.
58. Boyle's Law.—The relation between the volume and pressure of a gas
was first investigated by Robert Boyle in the seventeenth century. The
experiment by which he first discovered the law or the relation between the
volume and the pressure of a gas is briefly described as follows:
A glass tube is bent in the form of the capital
letter J, the short arm being closed. A little
mercury is poured in to cover the bend. (See
Fig. 37 a.) Since the mercury is at the same level
in both arms, the pressure in (A) is the same as
in (B). Mercury is now poured into (A) until it
stands in the long tube at a height above that in
(B) which is equal to the height of the mercury
column of the barometer. (See Fig. 37 b.) The
air in (BC) is now under a pressure of two
atmospheres (one atmosphere is due to the
mercury column). On measurement the air in
(BC) will be found to have just one-half of its
original volume.
Thus doubling the pressure to which a gas is
subjected reduces its volume to one-half.
Tripling the pressure, reduces the volume to
one-third and so on.
Careful experiments reveal the following law: Figs. 37 a and 37 b.—
The volume of a given mass of gas at constant Boyle's law apparatus.
temperature is inversely proportional to the
pressure to which it is subjected.
This law is often expressed mathematically. P/P´ = V´/V, or PV = P´V´.
Since doubling the pressure reduces the volume one-half, it doubles the
density. Tripling the pressure triples the density. We therefore have P/P´ =
D/D´ or the density of a gas directly proportional to its pressure.
Page 80
Fig. 38.—Height and density of the air.
59. Height of the Atmosphere.—From its properties of compression and
expansion, the air varies in density and pressure as one ascends in it. At a
height of 3 miles the pressure is reduced to about one-half. This is an
indication that one-half of the air is below this level. Balloonists have gone
to a height of 7 miles, Glaser and Coxwell in England in 1862 and Berson
in France in 1901. The atmosphere has been explored to a height of 30,500
meters (18.95 miles) by sending up self-registering barometers in small
balloons which burst at great altitudes. A parachute protects the instruments
from breakage from too rapid fall. This height of 30,500 meters was
reached by a balloon sent up by William R. Blair, at Huron, South Dakota,
September 1, 1910.
At a height of 35 miles, the density is estimated at 1/30,000 of its value at
sea-level. (See Fig. 38.) It is believed that some rarefied air exists for a
considerable distance above this point, some estimates placing the extent at
100 miles, and others from 200 to 500 miles. Evidences of some air at such
heights are shown by: (a) the height at which meteors first appear, (b) the
59. Height of the Atmosphere.—From its properties of compression and
expansion, the air varies in density and pressure as one ascends in it. At a
height of 3 miles the pressure is reduced to about one-half. This is an
indication that one-half of the air is below this level. Balloonists have gone
to a height of 7 miles, Glaser and Coxwell in England in 1862 and Berson
in France in 1901. The atmosphere has been explored to a height of 30,500
meters (18.95 miles) by sending up self-registering barometers in small
balloons which burst at great altitudes. A parachute protects the instruments
from breakage from too rapid fall. This height of 30,500 meters was
reached by a balloon sent up by William R. Blair, at Huron, South Dakota,
September 1, 1910.
At a height of 35 miles, the density is estimated at 1/30,000 of its value at
sea-level. (See Fig. 38.) It is believed that some rarefied air exists for a
considerable distance above this point, some estimates placing the extent at
100 miles, and others from 200 to 500 miles. Evidences of some air at such
heights are shown by: (a) the height at which meteors first appear, (b) the
Page 81
height of the Aurora Borealis, and (c), the distance that the sun is below the
horizon when the last traces of color disappear from the sky in the evening.
Although the exact limits of the atmosphere are unknown, the weight of a
column of air 1 sq. cm. in cross-section, and extending upward as high as
the atmosphere, may be accurately computed. For this column of air exactly
balances the column of mercury in the tube of the barometer.
Below sea-level, the air increases rapidly in density and it is estimated that
at a depth of 35 miles, the density of the air would be a thousand times that
at the earth's surface, or more than that of water.
Important Topics
1. Evidence of compressibility of gases and incompressibility of liquids.
2. Boyle's Law. Proof, applications.
3. Extent of the atmosphere—three evidences.
Exercises
1. Mention three illustrations of the compressibility and expansibility of air
that you know from your own experience.
2. Increasing the pressure increases the amount of a gas that will be
absorbed by a liquid? Explain this. Have you ever observed this fact?
Where?
3. If a toy balloon containing 2000 ccm. of gas at the earth's surface where
the barometer reading is 76 cm., rises to an elevation where the barometer
reads 54 cm., the balloon will tend to expand to what volume? Explain. Will
it attain this volume?
4. If a gas is compressed, it changes in temperature. How do you explain
this?
5. What change in temperature will occur when compressed air is allowed
to expand? Explain.
6. Air blowing up a mountain side has its pressure lessened as it approaches
the top. How will this affect the temperature? Why? What may result from
this change in temperature? Explain.
horizon when the last traces of color disappear from the sky in the evening.
Although the exact limits of the atmosphere are unknown, the weight of a
column of air 1 sq. cm. in cross-section, and extending upward as high as
the atmosphere, may be accurately computed. For this column of air exactly
balances the column of mercury in the tube of the barometer.
Below sea-level, the air increases rapidly in density and it is estimated that
at a depth of 35 miles, the density of the air would be a thousand times that
at the earth's surface, or more than that of water.
Important Topics
1. Evidence of compressibility of gases and incompressibility of liquids.
2. Boyle's Law. Proof, applications.
3. Extent of the atmosphere—three evidences.
Exercises
1. Mention three illustrations of the compressibility and expansibility of air
that you know from your own experience.
2. Increasing the pressure increases the amount of a gas that will be
absorbed by a liquid? Explain this. Have you ever observed this fact?
Where?
3. If a toy balloon containing 2000 ccm. of gas at the earth's surface where
the barometer reading is 76 cm., rises to an elevation where the barometer
reads 54 cm., the balloon will tend to expand to what volume? Explain. Will
it attain this volume?
4. If a gas is compressed, it changes in temperature. How do you explain
this?
5. What change in temperature will occur when compressed air is allowed
to expand? Explain.
6. Air blowing up a mountain side has its pressure lessened as it approaches
the top. How will this affect the temperature? Why? What may result from
this change in temperature? Explain.
Page 82
7. To what pressure must 500 ccm. of air be subjected to compress it to 300
ccm. the barometer reading at first being 75 cm. Explain.
Fig. 39.—The air pump.
(3) Pneumatic Appliances
60. The Air Pump.—The air pump is used to remove air or other gases
from a closed vessel. It was invented about 1650 by Otto Von Guericke,
burgomaster of Magdeburg, Germany. One form of air pump is shown in
Fig. 39. C is a cylinder within which slides a tightly fitting piston. R is the
vessel from which the air is to be exhausted. r and u are valves opening
upward. The action of the pump is as follows:
On pushing the piston down, the air in C is compressed. This opens valve r
allowing the confined air to escape above the piston. The piston is then
raised making the space in C a partial vacuum. The pressure in R now being
greater than in C, u is pushed up and the air from R rushes into C, until the
pressure is equalized. On pushing down the piston again, valve u closes and
the process is repeated until the pressure in R is no longer able to raise the
valve u. Some air pumps are so constructed that the valves are opened and
closed automatically by the movement of the piston. With these pumps a
higher degree of rarefaction can be obtained.
ccm. the barometer reading at first being 75 cm. Explain.
Fig. 39.—The air pump.
(3) Pneumatic Appliances
60. The Air Pump.—The air pump is used to remove air or other gases
from a closed vessel. It was invented about 1650 by Otto Von Guericke,
burgomaster of Magdeburg, Germany. One form of air pump is shown in
Fig. 39. C is a cylinder within which slides a tightly fitting piston. R is the
vessel from which the air is to be exhausted. r and u are valves opening
upward. The action of the pump is as follows:
On pushing the piston down, the air in C is compressed. This opens valve r
allowing the confined air to escape above the piston. The piston is then
raised making the space in C a partial vacuum. The pressure in R now being
greater than in C, u is pushed up and the air from R rushes into C, until the
pressure is equalized. On pushing down the piston again, valve u closes and
the process is repeated until the pressure in R is no longer able to raise the
valve u. Some air pumps are so constructed that the valves are opened and
closed automatically by the movement of the piston. With these pumps a
higher degree of rarefaction can be obtained.
Page 83
Air is often partially exhausted from receivers or vessels by the use of a
filter pump or aspirator. A stream of water flowing through a constriction
causes a reduced pressure, draws in air and carries it away, and thus
produces a partial vacuum. See Fig. 40 for a section of the device.
61. The Condensing Pump.—This is like the exhaust pump
except that its valves are reversed. It is used in compressing
illuminating gases into cylinders for use in lighting vehicles,
stereopticons, Pintsch lights, gas light buoys, etc., and also
for compressing air to operate air brakes, pneumatic
hammers and drills, and for other uses.
The common condensing pump is the kind used for inflating
tires. (See Fig. 41.) In this, a loosely fitting metal piston is
attached to a disc of leather somewhat larger than the
cylinder. This device is called a cup valve. On raising the
piston, air rushes in from the top past the valve, but on
pushing the piston down, the valve is pressed tightly against
Fig. 40.—
the sides of the cylinder and prevents the escape of any air.
An
The compressed air pushes open a valve on the tire and
aspirator.
enters it. This valve closes as soon as the pressure is lessened
from outside. It is well to notice in all of these pumps that
two valves are used. One holds the air already secured while the other opens
for a new supply. Both valves are never open at the same time.
62. Water Pumps.—The Common Lift Pump. This, the
simplest pump for raising water, consists of a cylinder C
(Fig. 42) connected by a pipe R to a supply of water as a
cistern or well. A valve opening upward is placed at the
bottom of the cylinder over the entrance to the pipe. In the
cylinder is a tightly fitting piston connected by a rod to a
lever for ease in action. The piston contains a valve opening
upward. In operating this pump water is usually first poured
into the cylinder to "prime" it. This helps to close the valves
and prevents air leaking past them. When the piston is
Fig. 41.— lowered the lower valve closes, the air in the cylinder being
Condensin compressed pushes the upper valve open and passes above
g pump the piston. On raising the piston the upper valve closes. This
used in forms a partial vacuum in the cylinder.
filter pump or aspirator. A stream of water flowing through a constriction
causes a reduced pressure, draws in air and carries it away, and thus
produces a partial vacuum. See Fig. 40 for a section of the device.
61. The Condensing Pump.—This is like the exhaust pump
except that its valves are reversed. It is used in compressing
illuminating gases into cylinders for use in lighting vehicles,
stereopticons, Pintsch lights, gas light buoys, etc., and also
for compressing air to operate air brakes, pneumatic
hammers and drills, and for other uses.
The common condensing pump is the kind used for inflating
tires. (See Fig. 41.) In this, a loosely fitting metal piston is
attached to a disc of leather somewhat larger than the
cylinder. This device is called a cup valve. On raising the
piston, air rushes in from the top past the valve, but on
pushing the piston down, the valve is pressed tightly against
Fig. 40.—
the sides of the cylinder and prevents the escape of any air.
An
The compressed air pushes open a valve on the tire and
aspirator.
enters it. This valve closes as soon as the pressure is lessened
from outside. It is well to notice in all of these pumps that
two valves are used. One holds the air already secured while the other opens
for a new supply. Both valves are never open at the same time.
62. Water Pumps.—The Common Lift Pump. This, the
simplest pump for raising water, consists of a cylinder C
(Fig. 42) connected by a pipe R to a supply of water as a
cistern or well. A valve opening upward is placed at the
bottom of the cylinder over the entrance to the pipe. In the
cylinder is a tightly fitting piston connected by a rod to a
lever for ease in action. The piston contains a valve opening
upward. In operating this pump water is usually first poured
into the cylinder to "prime" it. This helps to close the valves
and prevents air leaking past them. When the piston is
Fig. 41.— lowered the lower valve closes, the air in the cylinder being
Condensin compressed pushes the upper valve open and passes above
g pump the piston. On raising the piston the upper valve closes. This
used in forms a partial vacuum in the cylinder.
Page 84
inflating The air pressing on the surface of the water below forces the
tires. water and air that may be in the tube upward through the
lower valve to fill this partial vacuum.
When the cylinder becomes filled with water, this is lifted out on the up-
stroke, whence its name, "lift pump." Since the atmospheric pressure at sea-
level can only support a column of water about 34 ft. high, the lower valve
must be within this distance of the water surface. In actual practice the limit
is about 27 ft. In deeper wells, the cylinder and valves are placed so that
they are within 25 or 27 ft. of the surface of the water in the well, a long
piston rod reaching above the surface of the ground and connected to a
pump handle operates the piston. A discharge pipe extends from the
cylinder to the surface of the ground above.
Fig. 42.—The common lift pump.
Fig. 43.—A force pump with an air chamber
(A).
63. The Force Pump.—The force pump is used to deliver water under
pressure either for spraying or to an elevated reservoir. The piston is solid,
the second valve being placed at the entrance of the discharge pipe. (See
Fig. 43.) The action is the same as that of the lift pump, with this exception;
the piston in its down stroke forces the water out through the discharge
pipe, the velocity depending upon the pressure exerted.
tires. water and air that may be in the tube upward through the
lower valve to fill this partial vacuum.
When the cylinder becomes filled with water, this is lifted out on the up-
stroke, whence its name, "lift pump." Since the atmospheric pressure at sea-
level can only support a column of water about 34 ft. high, the lower valve
must be within this distance of the water surface. In actual practice the limit
is about 27 ft. In deeper wells, the cylinder and valves are placed so that
they are within 25 or 27 ft. of the surface of the water in the well, a long
piston rod reaching above the surface of the ground and connected to a
pump handle operates the piston. A discharge pipe extends from the
cylinder to the surface of the ground above.
Fig. 42.—The common lift pump.
Fig. 43.—A force pump with an air chamber
(A).
63. The Force Pump.—The force pump is used to deliver water under
pressure either for spraying or to an elevated reservoir. The piston is solid,
the second valve being placed at the entrance of the discharge pipe. (See
Fig. 43.) The action is the same as that of the lift pump, with this exception;
the piston in its down stroke forces the water out through the discharge
pipe, the velocity depending upon the pressure exerted.
Page 85
A force pump is usually provided with an air chamber which is connected
with the discharge pipe. On the down stroke of the piston, water is forced
into the air chamber. This compresses the air it contains. The compressed
air reacts and exerts pressure on the water forcing it out in a steady stream.
Force pumps are used in deep wells, being placed at the bottom.
The pumps used in city water works, fire engines, and all steam pumps, are
force pumps. (See Fig. 44.)
Fig. 44.—A steam pump used on a fire engine.
64. The Siphon.—The siphon is a tube used to convey a liquid from one
level over an elevation to a lower level by atmospheric pressure. It is used
to remove liquids from tanks or vessels that have no opening at the bottom.
The siphon cannot be completely understood until one has mastered the
laws of the flow of liquids. The following is offered as an incomplete
explanation of its behavior. Consider the siphon to be full of water and
closed at d (Fig. 45). Atmospheric pressure on a will hold the siphon full if
ab does not exceed 34 feet. If d is opened the water falls out with a speed
equal to that acquired in falling from the level of a to that of d. This speed is
acquired by all the water in the siphon and results in a drop in pressure
throughout it. The pressure at a inside the siphon becomes less than the
pressure at the same level outside as soon as the water starts flowing. The
water in the vessel then flows into the siphon and out at d. This flow
with the discharge pipe. On the down stroke of the piston, water is forced
into the air chamber. This compresses the air it contains. The compressed
air reacts and exerts pressure on the water forcing it out in a steady stream.
Force pumps are used in deep wells, being placed at the bottom.
The pumps used in city water works, fire engines, and all steam pumps, are
force pumps. (See Fig. 44.)
Fig. 44.—A steam pump used on a fire engine.
64. The Siphon.—The siphon is a tube used to convey a liquid from one
level over an elevation to a lower level by atmospheric pressure. It is used
to remove liquids from tanks or vessels that have no opening at the bottom.
The siphon cannot be completely understood until one has mastered the
laws of the flow of liquids. The following is offered as an incomplete
explanation of its behavior. Consider the siphon to be full of water and
closed at d (Fig. 45). Atmospheric pressure on a will hold the siphon full if
ab does not exceed 34 feet. If d is opened the water falls out with a speed
equal to that acquired in falling from the level of a to that of d. This speed is
acquired by all the water in the siphon and results in a drop in pressure
throughout it. The pressure at a inside the siphon becomes less than the
pressure at the same level outside as soon as the water starts flowing. The
water in the vessel then flows into the siphon and out at d. This flow
Page 86
continues as long as there is a fall from the free surface of the water in the
vessel to the outlet at d.
65. The Cartesian Diver.—
This is a device which
illustrates at the same time
transmission of pressure by
liquids, Archimedes'
principle, and compressibility
of gases. It was invented by
Des Cartes (1596-1650). As
ordinarily made, it is a
hollow glass image with a
small opening in the foot. It
contains air and water in such
amounts that the average
Fig. 46.—The density of image and contents
Cartesian diver. is slightly less than that of Fig. 45.—Cross-
water. It is placed in a tall section of a siphon.
glass jar filled with water and covered with tightly
stretched rubber tissue. (See Fig. 46.) By pressing on the rubber cover the
diver may be made to sink, since the air and water transmit the pressure on
the cover which compresses the air inside the figure admitting some water
to it, thus making the diver more dense than water. By varying the pressure
it can be made to sink, rise, or remain stationary at will.[D] A small vial can
be used instead of the image.
66. Hydraulic Ram.—The hydraulic ram (see Fig. 47) is an automatic
device that is much used for raising water from springs to houses located on
higher ground. Water flows through the pipe A through the opening at B.
The pressure closes the valve at B. The increased pressure in the pipe due to
the closing of B opens the valve C and some of the water flows into the air
chamber D. This reduces the pressure against the valve B so that it drops
and allows a little water to escape. Just as this happens, valve C closes. The
pressure in the pipe then closes B and forces water past C. This action being
continually repeated, the air in D becomes so compressed that it has elastic
force enough to raise the water in a steady stream to a height of many feet.
vessel to the outlet at d.
65. The Cartesian Diver.—
This is a device which
illustrates at the same time
transmission of pressure by
liquids, Archimedes'
principle, and compressibility
of gases. It was invented by
Des Cartes (1596-1650). As
ordinarily made, it is a
hollow glass image with a
small opening in the foot. It
contains air and water in such
amounts that the average
Fig. 46.—The density of image and contents
Cartesian diver. is slightly less than that of Fig. 45.—Cross-
water. It is placed in a tall section of a siphon.
glass jar filled with water and covered with tightly
stretched rubber tissue. (See Fig. 46.) By pressing on the rubber cover the
diver may be made to sink, since the air and water transmit the pressure on
the cover which compresses the air inside the figure admitting some water
to it, thus making the diver more dense than water. By varying the pressure
it can be made to sink, rise, or remain stationary at will.[D] A small vial can
be used instead of the image.
66. Hydraulic Ram.—The hydraulic ram (see Fig. 47) is an automatic
device that is much used for raising water from springs to houses located on
higher ground. Water flows through the pipe A through the opening at B.
The pressure closes the valve at B. The increased pressure in the pipe due to
the closing of B opens the valve C and some of the water flows into the air
chamber D. This reduces the pressure against the valve B so that it drops
and allows a little water to escape. Just as this happens, valve C closes. The
pressure in the pipe then closes B and forces water past C. This action being
continually repeated, the air in D becomes so compressed that it has elastic
force enough to raise the water in a steady stream to a height of many feet.
Page 87
67. The Balloon.—Since air is a fluid,
Archimedes' principle applies to it as well as
to liquids. Therefore any object in the air is
lifted up by a force equal to the weight of
the air it displaces. The object will rise, if it
weighs less than this displaced air and will
continue to rise until both weights are equal.
Fig. 47.—Cross-section of
The Balloon (Fig. 48) rises because it
a hydraulic ram.
weighs less than the air it displaces, and
therefore it is pushed up by the heavier air,
the "lifting power" being the difference between its weight and that of the
air displaced. The neck at the bottom is left open to allow for expansion of
the gas. When the aeronaut wishes to descend, he opens a valve at the top
allowing some of the gas to escape.
Archimedes' principle applies to it as well as
to liquids. Therefore any object in the air is
lifted up by a force equal to the weight of
the air it displaces. The object will rise, if it
weighs less than this displaced air and will
continue to rise until both weights are equal.
Fig. 47.—Cross-section of
The Balloon (Fig. 48) rises because it
a hydraulic ram.
weighs less than the air it displaces, and
therefore it is pushed up by the heavier air,
the "lifting power" being the difference between its weight and that of the
air displaced. The neck at the bottom is left open to allow for expansion of
the gas. When the aeronaut wishes to descend, he opens a valve at the top
allowing some of the gas to escape.
Page 88
Fig. 48.—Winner of international
championship race, Paris, 1913.
Hydrogen is the lightest gas, weighing 0.09 kg. per cubic meter, and so
gives the greatest lifting power, but as it is expensive to make, coal gas,
density 0.75 kg. per cubic meter, is ordinarily employed. Helium has
recently been used to fill military balloons because it cannot be set on fire.
The Parachute (Fig. 49) is an umbrella-shaped device for use in descending
from a balloon. After falling a few seconds it opens, the large surface
exposed to the air causing it to descend slowly. The hole in the top keeps
the parachute upright by allowing the air to escape through it, thus relieving
the pressure.
68. The Air Brake.
—Compressed air is
used to do work in
many machines,
such as pneumatic
drills, hammers, and
air brakes. The
Westinghouse air
brake (Fig. 50) uses
air at a pressure of
about 70 lbs. to the Fig. 50.—Cross-section of
square inch. The a Westinghouse air
essential parts as brake.
Fig. 49.—A shown are a
parachute. reservoir R, the brake cylinder C and a triple valve
V, placed under each car with an air pipe P,
leading to the engine. This is connected to R by the triple valve V. When the
pressure in P is reduced by the engineer or by accident, the triple valve
operates so as to admit air from R into the cylinder C pushing the piston H
to the left. H is connected to the brakes by levers which press the brake
shoes strongly against the wheels. When the air pressure in P is restored the
triple valve acts so as to permit the air in C to escape while R is filled again
from P. The hissing sound heard when a train stops is caused by air
escaping from cylinder C. The spring in C keeps the brakes from the wheels
except when the "air is on."
championship race, Paris, 1913.
Hydrogen is the lightest gas, weighing 0.09 kg. per cubic meter, and so
gives the greatest lifting power, but as it is expensive to make, coal gas,
density 0.75 kg. per cubic meter, is ordinarily employed. Helium has
recently been used to fill military balloons because it cannot be set on fire.
The Parachute (Fig. 49) is an umbrella-shaped device for use in descending
from a balloon. After falling a few seconds it opens, the large surface
exposed to the air causing it to descend slowly. The hole in the top keeps
the parachute upright by allowing the air to escape through it, thus relieving
the pressure.
68. The Air Brake.
—Compressed air is
used to do work in
many machines,
such as pneumatic
drills, hammers, and
air brakes. The
Westinghouse air
brake (Fig. 50) uses
air at a pressure of
about 70 lbs. to the Fig. 50.—Cross-section of
square inch. The a Westinghouse air
essential parts as brake.
Fig. 49.—A shown are a
parachute. reservoir R, the brake cylinder C and a triple valve
V, placed under each car with an air pipe P,
leading to the engine. This is connected to R by the triple valve V. When the
pressure in P is reduced by the engineer or by accident, the triple valve
operates so as to admit air from R into the cylinder C pushing the piston H
to the left. H is connected to the brakes by levers which press the brake
shoes strongly against the wheels. When the air pressure in P is restored the
triple valve acts so as to permit the air in C to escape while R is filled again
from P. The hissing sound heard when a train stops is caused by air
escaping from cylinder C. The spring in C keeps the brakes from the wheels
except when the "air is on."
Page 89
69. The Gas Meter.—The gas meter consists of
a box divided into two parts by a vertical
partition (Fig. 51). Two bellows are attached to
this partition, one on each side. The valves that
regulate the flow of gas to and from the bellows
and the chambers A and D are opened and
closed by levers connected with the bellows.
These levers also operate the hands upon the
dials. When the inlet to the bellows B is opened,
the outlet of A is also opened. Gas entering B
opens the bellows and forces the gas in A out
into the house-pipe E. When B is full its inlet
valve closes and its outlet valve opens. The inlet
of A also opens and its outlet closes. Gas now
flows into A, compressing the bellows and B,
and forcing the gas from it into the house-pipe.
At each filling of the bellows B there will be
displaced from A and forced into the house-pipe
as much gas as enters B. It is evident that at each
emptying of B an equal amount of gas enters A. Fig. 51.—Cross-section
Thus we have A and B alternately filling and of a gas meter showing
emptying as long as the gas burner is open. To its construction and
have a continuous flow of gas in the house-pipes action.
two pipes and two chambers are necessary, one
being filled while the other is being emptied.
Fig. 52 represents the dials upon a gas meter showing a reading of 54,600
cu. ft.
70. Centrifugal Pumps. Fluids, such as water
and air, are often put in motion by devices
called centrifugal pumps (see Art. 78). These
pumps contain a revolving part, like a wheel
without a rim, whose spokes are replaced by
thin blades. This revolving part resembles the
Fig. 52.—Dials of a gas paddle wheel of some steam boats and is
meter. enclosed in a case or cover having one
a box divided into two parts by a vertical
partition (Fig. 51). Two bellows are attached to
this partition, one on each side. The valves that
regulate the flow of gas to and from the bellows
and the chambers A and D are opened and
closed by levers connected with the bellows.
These levers also operate the hands upon the
dials. When the inlet to the bellows B is opened,
the outlet of A is also opened. Gas entering B
opens the bellows and forces the gas in A out
into the house-pipe E. When B is full its inlet
valve closes and its outlet valve opens. The inlet
of A also opens and its outlet closes. Gas now
flows into A, compressing the bellows and B,
and forcing the gas from it into the house-pipe.
At each filling of the bellows B there will be
displaced from A and forced into the house-pipe
as much gas as enters B. It is evident that at each
emptying of B an equal amount of gas enters A. Fig. 51.—Cross-section
Thus we have A and B alternately filling and of a gas meter showing
emptying as long as the gas burner is open. To its construction and
have a continuous flow of gas in the house-pipes action.
two pipes and two chambers are necessary, one
being filled while the other is being emptied.
Fig. 52 represents the dials upon a gas meter showing a reading of 54,600
cu. ft.
70. Centrifugal Pumps. Fluids, such as water
and air, are often put in motion by devices
called centrifugal pumps (see Art. 78). These
pumps contain a revolving part, like a wheel
without a rim, whose spokes are replaced by
thin blades. This revolving part resembles the
Fig. 52.—Dials of a gas paddle wheel of some steam boats and is
meter. enclosed in a case or cover having one
Page 90
opening at the rim and another opening on one side about the axle.
Fig. 53.—A vacuum sweeper. (Courtesy of the
Hoover Suction Sweeper Co.)
When the wheel is rapidly revolved, the fluid is driven out with
considerable force through the opening at the rim, while a partial vacuum is
produced at the axle causing a rapid flow into the device at this point.
This is the principle of the action of the vacuum cleaner. Fig. 53 is a section
of a vacuum sweeper showing the revolving wheel and the current of air
passing into the wheel at the lower side and out of the rim of the case at the
rear.
Centrifugal water pumps work on the same principle and furnish a
continuous flow of water, often large in volume and at considerable
pressure.
Important Topics
1. Air pump.
2. Condensing pump.
3. Lift and force pumps.
4. Siphon.
5. Cartesian diver.
6. Hydraulic ram.
7. Balloon.
Fig. 53.—A vacuum sweeper. (Courtesy of the
Hoover Suction Sweeper Co.)
When the wheel is rapidly revolved, the fluid is driven out with
considerable force through the opening at the rim, while a partial vacuum is
produced at the axle causing a rapid flow into the device at this point.
This is the principle of the action of the vacuum cleaner. Fig. 53 is a section
of a vacuum sweeper showing the revolving wheel and the current of air
passing into the wheel at the lower side and out of the rim of the case at the
rear.
Centrifugal water pumps work on the same principle and furnish a
continuous flow of water, often large in volume and at considerable
pressure.
Important Topics
1. Air pump.
2. Condensing pump.
3. Lift and force pumps.
4. Siphon.
5. Cartesian diver.
6. Hydraulic ram.
7. Balloon.
Page 91
8. Air brake.
9. Gas meter.
10. Vacuum cleaner.
Exercises
1. Explain why smoke settles to the ground before storms.
2. Why does the water rise in the suction pipe of a pump?
3. Why is it easier to float in water when the lungs are filled with air than
when they are not filled?
4. Why is it easier to swim in salt water than in fresh water?
5. How are submarines made to sink? to rise to the surface?
6. How can a fish rise or sink in water?
7. Explain why a life preserver made of cork will enable a person to float.
8. Hold the open hand out flat with the fingers together. Place underneath
the fingers a piece of paper. Blow between the first and second fingers
against the paper. As long as you blow hard the paper will not fall but will
stick to the hand. Explain.
9. Why does pressing the bulb of an atomizer force out the liquid in a fine
spray?
10. Why is air that contains a large amount of water vapor lighter than air
that only contains a small amount?
11. How are heights above sea-level ascertained by a barometer?
12. Oil floats on water but sinks in alcohol. Explain.
13. In a balloon the lower end is often open to the air. Why does not the gas
escape and prevent the balloon from rising?
14. How long will a balloon continue to rise?
15. If the pressure against the 8-in. piston of an air brake is 70 lbs. per
square inch, how much force does the piston exert?
9. Gas meter.
10. Vacuum cleaner.
Exercises
1. Explain why smoke settles to the ground before storms.
2. Why does the water rise in the suction pipe of a pump?
3. Why is it easier to float in water when the lungs are filled with air than
when they are not filled?
4. Why is it easier to swim in salt water than in fresh water?
5. How are submarines made to sink? to rise to the surface?
6. How can a fish rise or sink in water?
7. Explain why a life preserver made of cork will enable a person to float.
8. Hold the open hand out flat with the fingers together. Place underneath
the fingers a piece of paper. Blow between the first and second fingers
against the paper. As long as you blow hard the paper will not fall but will
stick to the hand. Explain.
9. Why does pressing the bulb of an atomizer force out the liquid in a fine
spray?
10. Why is air that contains a large amount of water vapor lighter than air
that only contains a small amount?
11. How are heights above sea-level ascertained by a barometer?
12. Oil floats on water but sinks in alcohol. Explain.
13. In a balloon the lower end is often open to the air. Why does not the gas
escape and prevent the balloon from rising?
14. How long will a balloon continue to rise?
15. If the pressure against the 8-in. piston of an air brake is 70 lbs. per
square inch, how much force does the piston exert?
Page 92
16. The capacity of a balloon is 40,000 cu. ft. The weight of the balloon,
car, etc., is 600 lbs.; specific gravity of the gas used is 0.46 that of the air.
Find how much weight the balloon can carry.
17. The so-called Magdeburg hemispheres were invented by Otto von
Guericke of Magdeburg, Germany. When the hemispheres (see Fig. 54) are
placed in contact and the air exhausted it is found very difficult to pull them
apart. Explain.
18. Von Guericke's hemispheres had an inside diameter of 22 in. What force
would be required to pull them apart if all the air were exhausted from
them? (Find the atmospheric force on a circle, 22 in. in diameter.)
19. Von Guericke made a water barometer whose top extended through the
roof of his house. On the top of the water in the tube was placed a wooden
image. In fair weather the image appeared above the roof, but it descended
before a storm. Explain.
20. The balloon "Goodyear" (Fig. 48), which won the International
championship race at Paris in 1913, has a capacity of 80,000 cu. ft. The gas
bag weighs 653 lbs., the net 240 lbs. and the basket 92 lbs. How large a load
can it carry when filled with hydrogen specific gravity 0.069 (compared
with air).
Fig. 54.—
Magdeburg
hemisphere
s.
Review Outline: Liquids and Gases
car, etc., is 600 lbs.; specific gravity of the gas used is 0.46 that of the air.
Find how much weight the balloon can carry.
17. The so-called Magdeburg hemispheres were invented by Otto von
Guericke of Magdeburg, Germany. When the hemispheres (see Fig. 54) are
placed in contact and the air exhausted it is found very difficult to pull them
apart. Explain.
18. Von Guericke's hemispheres had an inside diameter of 22 in. What force
would be required to pull them apart if all the air were exhausted from
them? (Find the atmospheric force on a circle, 22 in. in diameter.)
19. Von Guericke made a water barometer whose top extended through the
roof of his house. On the top of the water in the tube was placed a wooden
image. In fair weather the image appeared above the roof, but it descended
before a storm. Explain.
20. The balloon "Goodyear" (Fig. 48), which won the International
championship race at Paris in 1913, has a capacity of 80,000 cu. ft. The gas
bag weighs 653 lbs., the net 240 lbs. and the basket 92 lbs. How large a load
can it carry when filled with hydrogen specific gravity 0.069 (compared
with air).
Fig. 54.—
Magdeburg
hemisphere
s.
Review Outline: Liquids and Gases
Page 93
Liquids: Force, pressure, and density. Floating and immersed bodies. Laws:
Liquid force, F = A.h.d, Pascal's, Archimedes. Illustrations and
Applications:
Specific gravity, W_{a}/(W_{a} - W_{w}), (W_{a} - W_{l})/(W_{a} -
W_{w}), Boyle's, PV = P´V´
Devices: Hydraulic press, air cushion, barometer—mercurial and aneroid.
Pumps, lift, force, vacuum, compression, centrifugal, balloon, siphon, etc.
Construction and action of each.
Liquid force, F = A.h.d, Pascal's, Archimedes. Illustrations and
Applications:
Specific gravity, W_{a}/(W_{a} - W_{w}), (W_{a} - W_{l})/(W_{a} -
W_{w}), Boyle's, PV = P´V´
Devices: Hydraulic press, air cushion, barometer—mercurial and aneroid.
Pumps, lift, force, vacuum, compression, centrifugal, balloon, siphon, etc.
Construction and action of each.
Page 94
CHAPTER V
FORCE AND MOTION
(1) Force, How Measured and Represented
71. Force.—We have been studying various forces, such as air pressure,
pressure in liquids, and the force of elasticity in solids, and have considered
them simply as pushes or pulls. A more formal study of forces in general
and of devices for representing and measuring them will be helpful at this
point of the course.
A force is that which tends to cause a change in the size or shape of a body
or in its state of motion. In other words a force is a push or a pull. That is,
force tends to produce distortion or change of motion in a body. Force itself
is invisible. We measure it by the effect it produces. Forces are usually
associated with the objects exerting them. Thus we speak of muscular force,
air pressure, liquid pressure, the force of a spring, the force of the earth's
attraction and so on.
Forces are classified in various ways.
I. With respect to the duration and steadiness of the force.
(a) Constant, as the earth's attraction. (b) Impulsive, as the stroke of a bat on
a ball. (c) Variable, as the force of the wind.
II. With respect to the direction of the force.
(a) Attractive, as the earth's attraction. (b) Repulsive, as air pressure, liquid
pressure, etc.
72. Methods of Measuring Force.—Since forces are measured by their
effects which are either distortion or change of motion, either of these
effects may be used to measure them. For example, the force exerted by a
locomotive is sometimes computed by the speed it can develop in a train of
cars in a given time, or the force of the blow of a baseball bat is estimated
by the distance the ball goes before it strikes the ground.
FORCE AND MOTION
(1) Force, How Measured and Represented
71. Force.—We have been studying various forces, such as air pressure,
pressure in liquids, and the force of elasticity in solids, and have considered
them simply as pushes or pulls. A more formal study of forces in general
and of devices for representing and measuring them will be helpful at this
point of the course.
A force is that which tends to cause a change in the size or shape of a body
or in its state of motion. In other words a force is a push or a pull. That is,
force tends to produce distortion or change of motion in a body. Force itself
is invisible. We measure it by the effect it produces. Forces are usually
associated with the objects exerting them. Thus we speak of muscular force,
air pressure, liquid pressure, the force of a spring, the force of the earth's
attraction and so on.
Forces are classified in various ways.
I. With respect to the duration and steadiness of the force.
(a) Constant, as the earth's attraction. (b) Impulsive, as the stroke of a bat on
a ball. (c) Variable, as the force of the wind.
II. With respect to the direction of the force.
(a) Attractive, as the earth's attraction. (b) Repulsive, as air pressure, liquid
pressure, etc.
72. Methods of Measuring Force.—Since forces are measured by their
effects which are either distortion or change of motion, either of these
effects may be used to measure them. For example, the force exerted by a
locomotive is sometimes computed by the speed it can develop in a train of
cars in a given time, or the force of the blow of a baseball bat is estimated
by the distance the ball goes before it strikes the ground.
Page 95
The more common method of measuring force, however, is by distortion,
that is, by measuring the change of shape of a body caused by the force. In
doing this, use is made of Hooke's Law (Art. 32), in which it is stated that
"within the limits of perfect elasticity," changes of size or shape are directly
proportional to the forces employed. That is, twice as great a force will
produce twice as great a change of shape and so on.
A common contrivance using this principle is the spring
balance (Fig. 55), with which all are familiar, as ice scales,
meat scales, postal scales, etc. The object which changes
shape in this device is a coiled spring contained in the case
of the instrument. The balance is so constructed that when
the spring is pulled out as far as possible it has not reached
its limit of elasticity, since, if the spring were stretched so as
to exceed its elastic limit, the index would not return to its
first position on removing the load. (See Arts. 30-32.)
73. Graphic Representation of Forces.—A force is said to
have three elements. These are (a) its point of application,
(b) its direction, and (c) its magnitude. For example, if there
is hung upon the hook of a spring balance a weight of 5 lbs.,
then we have: (a) its point of application on the hook of the
balance, (b) its downward direction and (c) its magnitude, or
5 lbs. These three elements may be represented by a line.
Fig. 55.—A Thus in Fig. 56a, a line AB is drawn as shown, five units
spring long; A represents the point of application; B, the arrow
balance. head, shows the direction; and the length of the line (five
units) shows the magnitude of the force.
This is called a graphic representation since it represents by a line the
quantity in question. If another weight of 5 lbs. were hung from the first
one, the graphic representation of both forces would be as in Fig. 56b. Here
the first force is represented by AB as before, BC representing the second
force applied. The whole line represents the resultant of the two forces or
the result of their combination. If the two weights were hung one at each
end of a short stick AC (Fig. 56c), and the latter suspended at its center their
combined weight or resultant would of course be applied at the center. The
direction would be the same as that of the two weights. The resultant
therefore is represented by ON. In order to exactly balance this resultant
that is, by measuring the change of shape of a body caused by the force. In
doing this, use is made of Hooke's Law (Art. 32), in which it is stated that
"within the limits of perfect elasticity," changes of size or shape are directly
proportional to the forces employed. That is, twice as great a force will
produce twice as great a change of shape and so on.
A common contrivance using this principle is the spring
balance (Fig. 55), with which all are familiar, as ice scales,
meat scales, postal scales, etc. The object which changes
shape in this device is a coiled spring contained in the case
of the instrument. The balance is so constructed that when
the spring is pulled out as far as possible it has not reached
its limit of elasticity, since, if the spring were stretched so as
to exceed its elastic limit, the index would not return to its
first position on removing the load. (See Arts. 30-32.)
73. Graphic Representation of Forces.—A force is said to
have three elements. These are (a) its point of application,
(b) its direction, and (c) its magnitude. For example, if there
is hung upon the hook of a spring balance a weight of 5 lbs.,
then we have: (a) its point of application on the hook of the
balance, (b) its downward direction and (c) its magnitude, or
5 lbs. These three elements may be represented by a line.
Fig. 55.—A Thus in Fig. 56a, a line AB is drawn as shown, five units
spring long; A represents the point of application; B, the arrow
balance. head, shows the direction; and the length of the line (five
units) shows the magnitude of the force.
This is called a graphic representation since it represents by a line the
quantity in question. If another weight of 5 lbs. were hung from the first
one, the graphic representation of both forces would be as in Fig. 56b. Here
the first force is represented by AB as before, BC representing the second
force applied. The whole line represents the resultant of the two forces or
the result of their combination. If the two weights were hung one at each
end of a short stick AC (Fig. 56c), and the latter suspended at its center their
combined weight or resultant would of course be applied at the center. The
direction would be the same as that of the two weights. The resultant
therefore is represented by ON. In order to exactly balance this resultant
Page 96
ON, a force of equal magnitude but opposite in direction must be applied at
the point of application of ON, or O. OM then represents a force that will
just balance or hold in equilibrium the resultant of the two forces AB and
CD. This line OM therefore represents the equilibrant of the weights AB
and CD. The resultant of two forces at an angle with each other is formed
differently, as in Fig. 57 a. Here two forces AB and AC act at an angle with
each other. Lay off at the designated angle the lines AB and AC of such
length as will accurately represent the forces. Lay off BD equal to AC and
CD equal to AB. The figure ABCD is then a parallelogram. Its diagonal AD
represents the resultant of the forces AB and AC acting at the angle BAC. If
BAC equals 90 degrees or is a right angle, AD may be computed thus: AB2
+ BD2 = AD2. Why?
and AD = √([line]AB2 + [line]BD2).
Fig. 56.—Graphic
representation of forces
acting along the same or
parallel lines.
the point of application of ON, or O. OM then represents a force that will
just balance or hold in equilibrium the resultant of the two forces AB and
CD. This line OM therefore represents the equilibrant of the weights AB
and CD. The resultant of two forces at an angle with each other is formed
differently, as in Fig. 57 a. Here two forces AB and AC act at an angle with
each other. Lay off at the designated angle the lines AB and AC of such
length as will accurately represent the forces. Lay off BD equal to AC and
CD equal to AB. The figure ABCD is then a parallelogram. Its diagonal AD
represents the resultant of the forces AB and AC acting at the angle BAC. If
BAC equals 90 degrees or is a right angle, AD may be computed thus: AB2
+ BD2 = AD2. Why?
and AD = √([line]AB2 + [line]BD2).
Fig. 56.—Graphic
representation of forces
acting along the same or
parallel lines.
Page 97
Fig. 57.—Graphic representation of two forces
acting (a) at a right angle, (b) at an acute
angle.
This method of determining the resultant by computation may be used when
the two forces are at right angles. (In any case, AD may be measured using
the same scale that is laid off upon AB and AC, as shown in Fig. 57 b.) The
three cases of combining forces just given may be classified as follows: The
first is that of two forces acting along the same line in the same or opposite
direction, as when two horses are hitched tandem, or in a tug of war. The
second is that of two forces acting along parallel lines, in the same
direction, as when two horses are hitched side by side or abreast. The third
is that of two forces acting at the same point at an angle. It may be
represented by the device shown in Fig. 58, consisting of two spring
balances suspended from nails at the top of the blackboard at A and B. A
cord is attached to both hooks and is passed through a small ring at O from
which is suspended a known weight, W. Lines are drawn on the blackboard
under the stretched cords, from O toward OA, OB, and OW and distances
measured on each from O to correspond to the three forces as read on
balance A and B and the weight W. Let a parallelogram be constructed on
the lines measured off on OA and OB. Its diagonal drawn from O will be
found to be vertical and of the same length as the line measured on OW.
The diagonal is the resultant of the two forces and OW is the equilibrant
which is equal and opposite to the resultant.
Again, the first case may be represented by a boat moving up or down a
stream; the resultant motion being the combined effect of the boat's motion
and that of the stream. The second, may be represented by two horses
attached side by side to the same evener. The resultant force equals the sum
of the two component forces. The third, may be represented by a boat going
acting (a) at a right angle, (b) at an acute
angle.
This method of determining the resultant by computation may be used when
the two forces are at right angles. (In any case, AD may be measured using
the same scale that is laid off upon AB and AC, as shown in Fig. 57 b.) The
three cases of combining forces just given may be classified as follows: The
first is that of two forces acting along the same line in the same or opposite
direction, as when two horses are hitched tandem, or in a tug of war. The
second is that of two forces acting along parallel lines, in the same
direction, as when two horses are hitched side by side or abreast. The third
is that of two forces acting at the same point at an angle. It may be
represented by the device shown in Fig. 58, consisting of two spring
balances suspended from nails at the top of the blackboard at A and B. A
cord is attached to both hooks and is passed through a small ring at O from
which is suspended a known weight, W. Lines are drawn on the blackboard
under the stretched cords, from O toward OA, OB, and OW and distances
measured on each from O to correspond to the three forces as read on
balance A and B and the weight W. Let a parallelogram be constructed on
the lines measured off on OA and OB. Its diagonal drawn from O will be
found to be vertical and of the same length as the line measured on OW.
The diagonal is the resultant of the two forces and OW is the equilibrant
which is equal and opposite to the resultant.
Again, the first case may be represented by a boat moving up or down a
stream; the resultant motion being the combined effect of the boat's motion
and that of the stream. The second, may be represented by two horses
attached side by side to the same evener. The resultant force equals the sum
of the two component forces. The third, may be represented by a boat going
Page 98
across a stream, the resultant motion
being represented by the diagonal of the
parallelogram formed by using the lines
that represent the motion of the stream
and of the boat.
74. Units for Measuring Force.—Force
is commonly measured in units of weight:
in pounds, kilograms, and grams. For
example, we speak of 15 lbs. pressure per
square inch and 1033.6 g. pressure per
square centimeter as representing the air
pressure. It should be noted here that the
words pound, kilogram, and gram are Fig. 58.—Experimental
used not only to represent weight or force proof of parallelogram of
but also the masses of the objects forces.
considered. Thus, one may speak of a
pound-mass meaning the amount of material in the object.
It will help to avoid confusion if we reserve the simple terms "gram" and
"pound" to denote exclusively an amount of matter, that is, a mass, and to
use the full expression "gram of force" or "pound of force" whenever we
have in mind the pull of the earth upon these masses. Or, one may speak of
a pound-weight meaning the amount of attraction exerted by the earth upon
the object. The same is true of gram-mass and gram-weight. The mass of a
body does not change when the body is transferred to another place. The
weight, however, may vary, for on moving a body from the equator toward
the poles of the earth the weight is known to increase.
Important Topics
1. Definition of force.
2. Classification of forces. (a) Duration: constant, impulsive, variable. (b)
Direction: attractive, repulsive.
3. Methods of measuring force. (a) By distortion. (b) By change of motion.
4. Graphic representation of forces: component, resultant, equilibrant.
being represented by the diagonal of the
parallelogram formed by using the lines
that represent the motion of the stream
and of the boat.
74. Units for Measuring Force.—Force
is commonly measured in units of weight:
in pounds, kilograms, and grams. For
example, we speak of 15 lbs. pressure per
square inch and 1033.6 g. pressure per
square centimeter as representing the air
pressure. It should be noted here that the
words pound, kilogram, and gram are Fig. 58.—Experimental
used not only to represent weight or force proof of parallelogram of
but also the masses of the objects forces.
considered. Thus, one may speak of a
pound-mass meaning the amount of material in the object.
It will help to avoid confusion if we reserve the simple terms "gram" and
"pound" to denote exclusively an amount of matter, that is, a mass, and to
use the full expression "gram of force" or "pound of force" whenever we
have in mind the pull of the earth upon these masses. Or, one may speak of
a pound-weight meaning the amount of attraction exerted by the earth upon
the object. The same is true of gram-mass and gram-weight. The mass of a
body does not change when the body is transferred to another place. The
weight, however, may vary, for on moving a body from the equator toward
the poles of the earth the weight is known to increase.
Important Topics
1. Definition of force.
2. Classification of forces. (a) Duration: constant, impulsive, variable. (b)
Direction: attractive, repulsive.
3. Methods of measuring force. (a) By distortion. (b) By change of motion.
4. Graphic representation of forces: component, resultant, equilibrant.
Page 99
5. Three cases of combining forces. (1) Two forces acting on the same line.
(2) Two forces acting in parallel lines. (3) Two forces acting at the same
point at an angle.
6. Units for measuring force, pound, gram.
Exercises
1. Name five natural forces. Which produce a tension? Which a pressure?
2. How much can you lift? Express in pounds and kilograms.
3. Show graphically the resultant of two forces at right angles, one of 12
lbs., the other of 16 lbs. What is the magnitude of this resultant? Then
determine the answer, first by measurement and then by computation.
Which answer is more accurate? Why?
4. Represent by a parallelogram the two forces that support a person sitting
in a hammock and draw the line representing the resultant.
5. Find graphically the resultant of the pull of two forces, one of 500 lbs.
east and one of 600 lbs. northwest.
6. Determine the equilibrant of two forces, one of 800 lbs. south and one of
600 lbs. west.
7. Would the fact that weight varies on going from the equator to either pole
be shown by a spring balance or a beam balance? Explain.
(2) Motion. Newton's Laws of Motion
75. Motion a Change of Position.—Motion is defined as a continuous
change in the position of a body. The position of a body is usually described
as its distance and direction from some fixed point. Thus a man on a boat
may be at rest with respect to the boat and moving with respect to the earth.
Or, if he walks toward the stern as fast as the boat moves forward, he may
keep directly over a rock on the bottom of the lake and hence not be moving
with reference to the rock and yet be in motion with respect to the boat.
Motion and rest, therefore, are relative terms. The earth itself is in motion in
turning on its axis, in moving along its orbit, and in following the sun in its
motion through space. Motions are classified in several ways:
(2) Two forces acting in parallel lines. (3) Two forces acting at the same
point at an angle.
6. Units for measuring force, pound, gram.
Exercises
1. Name five natural forces. Which produce a tension? Which a pressure?
2. How much can you lift? Express in pounds and kilograms.
3. Show graphically the resultant of two forces at right angles, one of 12
lbs., the other of 16 lbs. What is the magnitude of this resultant? Then
determine the answer, first by measurement and then by computation.
Which answer is more accurate? Why?
4. Represent by a parallelogram the two forces that support a person sitting
in a hammock and draw the line representing the resultant.
5. Find graphically the resultant of the pull of two forces, one of 500 lbs.
east and one of 600 lbs. northwest.
6. Determine the equilibrant of two forces, one of 800 lbs. south and one of
600 lbs. west.
7. Would the fact that weight varies on going from the equator to either pole
be shown by a spring balance or a beam balance? Explain.
(2) Motion. Newton's Laws of Motion
75. Motion a Change of Position.—Motion is defined as a continuous
change in the position of a body. The position of a body is usually described
as its distance and direction from some fixed point. Thus a man on a boat
may be at rest with respect to the boat and moving with respect to the earth.
Or, if he walks toward the stern as fast as the boat moves forward, he may
keep directly over a rock on the bottom of the lake and hence not be moving
with reference to the rock and yet be in motion with respect to the boat.
Motion and rest, therefore, are relative terms. The earth itself is in motion in
turning on its axis, in moving along its orbit, and in following the sun in its
motion through space. Motions are classified in several ways:
Page 100
(A) Modes of Motion
1. Translation.—A body is said to have motion of translation when every
line in it keeps the same direction.
2. Rotation.—A body has motion of rotation when it turns upon a fixed axis
within the body, as a wheel upon its axle or the earth upon its axis.
3. Vibration or Oscillation.—A body is said to have vibratory or oscillatory
motion when it returns to the same point at regular intervals by reversals of
motion along a given path, e.g., a pendulum.
(B) Direction of Motion
1. Rectilinear.—A body has rectilinear motion when its path is a straight
line. Absolute rectilinear motion does not exist, although the motion of a
train on a straight stretch of track is nearly rectilinear.
2. Curvilinear.—A body has curvilinear motion when its path is a curved
line, e.g., the path of a thrown ball.
(C) Uniformity of Motion
1. Uniform.—A body has uniform motion when its speed and direction of
motion do not change. Uniform motion for extended periods is rarely
observed. A train may cover, on an average, 40 miles per hour but during
each hour its speed may rise and fall.
2. Variable.—A body has variable motion when its speed or direction of
motion is continually changing. Most bodies have variable motion.
3. Accelerated.—A body has accelerated motion when its speed or direction
of motion continually changes. If the speed changes by the same amount
each second, and the direction of motion does not change the motion is said
to be uniformly accelerated, e.g., a falling body.
Uniformly accelerated motion will be studied further under the topic of
falling bodies.
Velocity is the rate of motion of a body in a given direction. For example, a
bullet may have a velocity of 1300 ft. a second upwards. Acceleration is the
1. Translation.—A body is said to have motion of translation when every
line in it keeps the same direction.
2. Rotation.—A body has motion of rotation when it turns upon a fixed axis
within the body, as a wheel upon its axle or the earth upon its axis.
3. Vibration or Oscillation.—A body is said to have vibratory or oscillatory
motion when it returns to the same point at regular intervals by reversals of
motion along a given path, e.g., a pendulum.
(B) Direction of Motion
1. Rectilinear.—A body has rectilinear motion when its path is a straight
line. Absolute rectilinear motion does not exist, although the motion of a
train on a straight stretch of track is nearly rectilinear.
2. Curvilinear.—A body has curvilinear motion when its path is a curved
line, e.g., the path of a thrown ball.
(C) Uniformity of Motion
1. Uniform.—A body has uniform motion when its speed and direction of
motion do not change. Uniform motion for extended periods is rarely
observed. A train may cover, on an average, 40 miles per hour but during
each hour its speed may rise and fall.
2. Variable.—A body has variable motion when its speed or direction of
motion is continually changing. Most bodies have variable motion.
3. Accelerated.—A body has accelerated motion when its speed or direction
of motion continually changes. If the speed changes by the same amount
each second, and the direction of motion does not change the motion is said
to be uniformly accelerated, e.g., a falling body.
Uniformly accelerated motion will be studied further under the topic of
falling bodies.
Velocity is the rate of motion of a body in a given direction. For example, a
bullet may have a velocity of 1300 ft. a second upwards. Acceleration is the
Page 101
rate of change of velocity in a given direction, or the change of velocity in a
unit of time. A train starting from a station gradually increases its speed.
The gain in velocity during one second is its acceleration. When the
velocity is decreasing, as when a train is slowing down, the acceleration is
opposite in direction to the velocity. A falling body falls faster and faster. It
has downward acceleration. A ball thrown upward goes more and more
slowly. It also has downward acceleration.
76. Momentum.—It is a matter of common observation that a heavy body
is set in motion with more difficulty than a light one, or if the same force is
used for the same length of time upon a light and a heavy body,[E] the light
body will be given a greater velocity. This observation has led to the
calculation of what is called the "quantity of motion" of a body, or its
momentum. It is computed by multiplying the mass by the velocity. If the
C.G.S. system is used we shall have as the momentum of a 12 g. body
moving 25 cm. a second a momentum of 12 × 25 or 300 C.G.S. units of
momentum. This unit has no name and is therefore expressed as indicated
above. The formula for computing momentum is: M = mv.
Newton's Laws of Motion
77. Inertia, First Law of Motion.—One often observes when riding in a
train that if the train moves forward suddenly the passengers do not get into
motion as soon as the train, and apparently are jerked backward. While if
the train is stopped suddenly, the passengers tend to keep in motion. This
tendency of matter to keep moving when in motion and to remain at rest
when at rest is often referred to as the property of inertia. Newton's first law
of motion, often called the law of inertia, describes this property of matter
as follows:
Every body continues in a state of rest or of uniform motion in a straight
line unless it is compelled to change that state by some external force. This
means that if an object like a book is lying on a table it will remain there
until removed by some outside force. No inanimate object can move itself
or stop itself. If a ball is thrown into the air it would move on forever if it
were not for the force of attraction of the earth and the resistance of the air.
unit of time. A train starting from a station gradually increases its speed.
The gain in velocity during one second is its acceleration. When the
velocity is decreasing, as when a train is slowing down, the acceleration is
opposite in direction to the velocity. A falling body falls faster and faster. It
has downward acceleration. A ball thrown upward goes more and more
slowly. It also has downward acceleration.
76. Momentum.—It is a matter of common observation that a heavy body
is set in motion with more difficulty than a light one, or if the same force is
used for the same length of time upon a light and a heavy body,[E] the light
body will be given a greater velocity. This observation has led to the
calculation of what is called the "quantity of motion" of a body, or its
momentum. It is computed by multiplying the mass by the velocity. If the
C.G.S. system is used we shall have as the momentum of a 12 g. body
moving 25 cm. a second a momentum of 12 × 25 or 300 C.G.S. units of
momentum. This unit has no name and is therefore expressed as indicated
above. The formula for computing momentum is: M = mv.
Newton's Laws of Motion
77. Inertia, First Law of Motion.—One often observes when riding in a
train that if the train moves forward suddenly the passengers do not get into
motion as soon as the train, and apparently are jerked backward. While if
the train is stopped suddenly, the passengers tend to keep in motion. This
tendency of matter to keep moving when in motion and to remain at rest
when at rest is often referred to as the property of inertia. Newton's first law
of motion, often called the law of inertia, describes this property of matter
as follows:
Every body continues in a state of rest or of uniform motion in a straight
line unless it is compelled to change that state by some external force. This
means that if an object like a book is lying on a table it will remain there
until removed by some outside force. No inanimate object can move itself
or stop itself. If a ball is thrown into the air it would move on forever if it
were not for the force of attraction of the earth and the resistance of the air.
Page 102
It takes time to put a mass into motion, a heavy object requiring more time
for a change than a light object. As an example of this, note the movements
of passengers in a street car when it starts or stops suddenly. Another
illustration of the law of inertia is the so-called "penny and card"
experiment. Balance a card on the end of a finger. Place on it a coin directly
over the finger, snap the card quickly so as to drive the card from beneath
the coin. The coin will remain on the finger. (See Fig. 59.)
According to Newton's first law of motion a
moving body which could be entirely freed from
the action of all external forces would have
uniform motion, and would describe a perfectly
straight course. The curved path taken by a
baseball when thrown shows that it is acted upon
by an outside force. This force, the attraction of the
earth, is called gravity.
Fig. 59.—The ball
remains when the
card is driven away.
Sir Isaac Newton "By
Permission of the Berlin
Photographic Co., New
for a change than a light object. As an example of this, note the movements
of passengers in a street car when it starts or stops suddenly. Another
illustration of the law of inertia is the so-called "penny and card"
experiment. Balance a card on the end of a finger. Place on it a coin directly
over the finger, snap the card quickly so as to drive the card from beneath
the coin. The coin will remain on the finger. (See Fig. 59.)
According to Newton's first law of motion a
moving body which could be entirely freed from
the action of all external forces would have
uniform motion, and would describe a perfectly
straight course. The curved path taken by a
baseball when thrown shows that it is acted upon
by an outside force. This force, the attraction of the
earth, is called gravity.
Fig. 59.—The ball
remains when the
card is driven away.
Sir Isaac Newton "By
Permission of the Berlin
Photographic Co., New
Page 103
York."
Sir Isaac Newton (1642-
1727) Professor of
mathematics at
Cambridge university;
discovered gravitation;
invented calculus;
announced the laws of
motion; wrote the
Principia; made many
discoveries in light.
Galileo Galilei "By
Permission of the Berlin
Photographic Co., New
York."
Galileo Galilei (1564-
1642). Italian. "Founder
of experimental science";
"Originator of modern
physics"; made the first
thermometer; discovered
the laws of falling bodies
and the laws of the
pendulum; invented
Galilean telescope.
Sir Isaac Newton (1642-
1727) Professor of
mathematics at
Cambridge university;
discovered gravitation;
invented calculus;
announced the laws of
motion; wrote the
Principia; made many
discoveries in light.
Galileo Galilei "By
Permission of the Berlin
Photographic Co., New
York."
Galileo Galilei (1564-
1642). Italian. "Founder
of experimental science";
"Originator of modern
physics"; made the first
thermometer; discovered
the laws of falling bodies
and the laws of the
pendulum; invented
Galilean telescope.
Page 104
Fig. 60.—Cross-section of the DeLaval cream
separator.
78. Curvilinear Motion.—Curvilinear motion occurs when a moving body
is pulled or pushed away from a straight path. The pull or push is called
centripetal (center-seeking) force. A moving stone on the end of a string
when pulled toward the hand moves in a curve. If the string is released the
stone moves in a tangent to the curve. The string pulls the hand. This phase
of the pull is called centrifugal force. The centripetal force is the pull on the
stone. Centripetal and centrifugal force together cause a tension in the
string. Examples of curvilinear motion are very common. The rider and
horse in a circus ring lean inward in order to move in a curve. The curve on
a running track in a gymnasium is "banked" for the same reason. Mud
flying from the wheel of a carriage, the skidding of an automobile when
separator.
78. Curvilinear Motion.—Curvilinear motion occurs when a moving body
is pulled or pushed away from a straight path. The pull or push is called
centripetal (center-seeking) force. A moving stone on the end of a string
when pulled toward the hand moves in a curve. If the string is released the
stone moves in a tangent to the curve. The string pulls the hand. This phase
of the pull is called centrifugal force. The centripetal force is the pull on the
stone. Centripetal and centrifugal force together cause a tension in the
string. Examples of curvilinear motion are very common. The rider and
horse in a circus ring lean inward in order to move in a curve. The curve on
a running track in a gymnasium is "banked" for the same reason. Mud
flying from the wheel of a carriage, the skidding of an automobile when
Page 105
passing rapidly around a corner, and sparks flying from an emery wheel, are
illustrations of the First Law of Motion.
Cream is separated from milk by placing the whole milk in a rapidly
revolving bowl, the cream being lighter collects in the center and is thrown
off at the top. (See Fig. 60.) Clothes in steam laundries are dried by a
centrifugal drier. In amusement parks many devices use this principle. (See
centrifugal pumps, Art. 70.)
79. The Second Law of Motion,
sometimes called the law of momentum,
leads to the measurement of force, by the
momentum or the quantity of motion,
produced by it. The law is stated as
Fig. 61.—The two balls
follows:
reach the floor at the same
time. Change of motion, or momentum, is
proportional to the acting force and takes
place in the direction in which the force acts. In other words, if two or more
forces act at the same instant upon a body each produces the same effect
that it would if acting alone. If a card be supported on two nails driven
horizontally close together into an upright board (see Fig. 61), and two
marbles be so placed on the ends as to balance each other, when one marble
is snapped horizontally by a blow, the other will fall. Both reach the floor at
the same time. The two balls are equally pulled down by the earth's
attraction and strike the ground at the same time, though one is shot
sidewise, and the other is dropped vertically.
As gravity is a constant force, while the blow was only a momentary force,
the actual path or resultant motion will be a curved line.
The constant relation, between the acting force and the change of
momentum it produces in a body, has led to the adoption of a convenient
C.G.S. unit of force called the dyne. The dyne is that force which can impart
to a mass of one gram a change of velocity at the rate of one centimeter per
second every second. This definition assumes that the body acted upon is
free to move without hindrance of any kind, so that the acting force has to
overcome only the inertia of the body. However, the law applies in every
case of application of force, so that each force produces its full effect
illustrations of the First Law of Motion.
Cream is separated from milk by placing the whole milk in a rapidly
revolving bowl, the cream being lighter collects in the center and is thrown
off at the top. (See Fig. 60.) Clothes in steam laundries are dried by a
centrifugal drier. In amusement parks many devices use this principle. (See
centrifugal pumps, Art. 70.)
79. The Second Law of Motion,
sometimes called the law of momentum,
leads to the measurement of force, by the
momentum or the quantity of motion,
produced by it. The law is stated as
Fig. 61.—The two balls
follows:
reach the floor at the same
time. Change of motion, or momentum, is
proportional to the acting force and takes
place in the direction in which the force acts. In other words, if two or more
forces act at the same instant upon a body each produces the same effect
that it would if acting alone. If a card be supported on two nails driven
horizontally close together into an upright board (see Fig. 61), and two
marbles be so placed on the ends as to balance each other, when one marble
is snapped horizontally by a blow, the other will fall. Both reach the floor at
the same time. The two balls are equally pulled down by the earth's
attraction and strike the ground at the same time, though one is shot
sidewise, and the other is dropped vertically.
As gravity is a constant force, while the blow was only a momentary force,
the actual path or resultant motion will be a curved line.
The constant relation, between the acting force and the change of
momentum it produces in a body, has led to the adoption of a convenient
C.G.S. unit of force called the dyne. The dyne is that force which can impart
to a mass of one gram a change of velocity at the rate of one centimeter per
second every second. This definition assumes that the body acted upon is
free to move without hindrance of any kind, so that the acting force has to
overcome only the inertia of the body. However, the law applies in every
case of application of force, so that each force produces its full effect
Page 106
independently of other forces that may be acting at the same time upon the
body.
80. Newton's Third Law.—This law has been experienced by everyone
who has jumped from a rowboat near the shore. The muscular action that
pushes the body forward from the boat also pushes the boat backward, often
with awkward results. The law is stated: To every action, there is always an
opposite and equal reaction, or the mutual actions of any two bodies are
always equal and opposite in direction. Many illustrations of this law are in
every one's mind: a stretched rope pulls with the same force in one direction
as it does in the opposite direction. If a bat hits a ball, the ball hits the bat
with an equal and opposite force. The third law is therefore sometimes
called the law of reaction. When a weight is hung upon a spring balance the
action of the weight pulls down the spring until it has stretched sufficiently
(Hooke's Law) to produce an elastic reaction that equals and hence supports
the weight. When a man stands at the center of a plank supported at its
ends, the action of the man's weight bends the plank until the elastic force
developed in the plank equals the weight applied. Further, when a train or a
wagon is on a bridge the bridge yields until it has developed an elastic
reaction equal to the weight applied. If a person stands in the center of a
room, the floor beams yield until the third law is satisfied. In fact, whenever
a force acts, a contrary equal force always acts.
81. Stress and Strain.—A pair of forces that constitute an action and a
reaction is called a stress. The two forces are two parts of one stress. If the
two forces act away from each other, as in the breaking of a string, the
stress is called a tension, but if they act toward each other as in crushing
anything, the stress is called a pressure. In order for a body to exert force it
must meet with resistance. The force exerted is never greater than the
resistance encountered. Thus one can exert but little force upon a feather
floating in the air or upon other light objects. A fast moving shot exerts no
force unless it encounters some resistance.
Forces, then, are always found in pairs. Thus to break a string, to stretch an
elastic band, to squeeze a lemon, one must exert two equal and opposite
forces. Such a thing as a single force acting alone is unknown. Usually,
however, we give our attention mainly to one of the forces and ignore the
other. When a force acts upon a body the change of shape or size resulting
is called a strain. Hooke's law (Art. 32) is often expressed as follows: "The
body.
80. Newton's Third Law.—This law has been experienced by everyone
who has jumped from a rowboat near the shore. The muscular action that
pushes the body forward from the boat also pushes the boat backward, often
with awkward results. The law is stated: To every action, there is always an
opposite and equal reaction, or the mutual actions of any two bodies are
always equal and opposite in direction. Many illustrations of this law are in
every one's mind: a stretched rope pulls with the same force in one direction
as it does in the opposite direction. If a bat hits a ball, the ball hits the bat
with an equal and opposite force. The third law is therefore sometimes
called the law of reaction. When a weight is hung upon a spring balance the
action of the weight pulls down the spring until it has stretched sufficiently
(Hooke's Law) to produce an elastic reaction that equals and hence supports
the weight. When a man stands at the center of a plank supported at its
ends, the action of the man's weight bends the plank until the elastic force
developed in the plank equals the weight applied. Further, when a train or a
wagon is on a bridge the bridge yields until it has developed an elastic
reaction equal to the weight applied. If a person stands in the center of a
room, the floor beams yield until the third law is satisfied. In fact, whenever
a force acts, a contrary equal force always acts.
81. Stress and Strain.—A pair of forces that constitute an action and a
reaction is called a stress. The two forces are two parts of one stress. If the
two forces act away from each other, as in the breaking of a string, the
stress is called a tension, but if they act toward each other as in crushing
anything, the stress is called a pressure. In order for a body to exert force it
must meet with resistance. The force exerted is never greater than the
resistance encountered. Thus one can exert but little force upon a feather
floating in the air or upon other light objects. A fast moving shot exerts no
force unless it encounters some resistance.
Forces, then, are always found in pairs. Thus to break a string, to stretch an
elastic band, to squeeze a lemon, one must exert two equal and opposite
forces. Such a thing as a single force acting alone is unknown. Usually,
however, we give our attention mainly to one of the forces and ignore the
other. When a force acts upon a body the change of shape or size resulting
is called a strain. Hooke's law (Art. 32) is often expressed as follows: "The
Page 107
strain is proportional to the stress," e.g., the stretch of the spring of a spring
balance is proportional to the load placed upon it.
Important Topics
1. Motion a change of position. Kinds of motion.
2. Newton's laws of motion.
3. Momentum.
4. Inertia. First law of motion. Curvilinear motion.
5. Second law of motion.
6. Third law of motion. Action and reaction, stress and strain.
Exercises
1. Mention three illustrations of the third law, different from those given.
2. A rifle bullet thrown against a board standing upon edge will knock it
down; the same bullet fired at the board will pass through it without
disturbing its position. Explain.
3. A hammer is often driven on to its handle by striking the end of the latter.
Explain.
4. Consider a train moving 60 miles an hour, with a gun on the rear
platform pointing straight backward. If a ball is fired from the gun with a
speed of 60 miles an hour, what will happen to the ball?
5. Could one play ball on the deck of an ocean steamer going 25 miles an
hour without making allowance for the motion of the ship? Explain.
6. On a railroad curve, one rail is always higher. Which? Why?
7. Why can a small boy when chased by a big boy often escape by dodging?
8. Will a stone dropped from a moving train fall in a straight line? Explain.
9. A blast of fine sand driven against a sheet of glass soon gives it a rough
surface. Explain.
balance is proportional to the load placed upon it.
Important Topics
1. Motion a change of position. Kinds of motion.
2. Newton's laws of motion.
3. Momentum.
4. Inertia. First law of motion. Curvilinear motion.
5. Second law of motion.
6. Third law of motion. Action and reaction, stress and strain.
Exercises
1. Mention three illustrations of the third law, different from those given.
2. A rifle bullet thrown against a board standing upon edge will knock it
down; the same bullet fired at the board will pass through it without
disturbing its position. Explain.
3. A hammer is often driven on to its handle by striking the end of the latter.
Explain.
4. Consider a train moving 60 miles an hour, with a gun on the rear
platform pointing straight backward. If a ball is fired from the gun with a
speed of 60 miles an hour, what will happen to the ball?
5. Could one play ball on the deck of an ocean steamer going 25 miles an
hour without making allowance for the motion of the ship? Explain.
6. On a railroad curve, one rail is always higher. Which? Why?
7. Why can a small boy when chased by a big boy often escape by dodging?
8. Will a stone dropped from a moving train fall in a straight line? Explain.
9. A blast of fine sand driven against a sheet of glass soon gives it a rough
surface. Explain.
Page 108
10. Explain the use of fly-wheels in steadying the motion of machinery (for
example, the sewing machine).
11. Is it easier to walk to the front or rear of a passenger train when it is
stopping? Why?
12. Why does lowering the handles of a wheel-barrow on the instant of
striking make it easier to go over a bump?
13. Why should a strong side wind interfere with a game of tennis? How
can it be allowed for?
14. On which side of a railroad track at a curve is it the safer to walk while
a train is passing? Why?
15. Why does a bullet when fired through a window make a clean round
hole in the glass, while a small stone thrown against the window shatters
the glass?
16. A tallow candle can be fired through a pine board. Why?
17. In cyclones, straws are frequently found driven a little distance into
trees; why are the straws not broken and crushed instead of being driven
into the tree unbroken?
18. A bullet weighing one-half oz. is fired from a gun weighing 8 lb. The
bullet has a velocity of 1800 ft. per second. Find the velocity of the "kick"
or recoil of the gun.
18. When football players run into each other which one is thrown the
harder? Why?
20. A railroad train weighing 400 tons has a velocity of 60 miles per hour.
An ocean steamer weighing 20,000 tons has a velocity of one half mile per
hour. How do their momenta compare?
21. Why is a heavy boy preferable to a lighter weight boy for a football
team?
22. Why does a blacksmith when he desires to strike a heavy blow, select a
heavy sledge hammer and swing it over his head?
23. Why does the catcher on a baseball team wear a padded glove?
example, the sewing machine).
11. Is it easier to walk to the front or rear of a passenger train when it is
stopping? Why?
12. Why does lowering the handles of a wheel-barrow on the instant of
striking make it easier to go over a bump?
13. Why should a strong side wind interfere with a game of tennis? How
can it be allowed for?
14. On which side of a railroad track at a curve is it the safer to walk while
a train is passing? Why?
15. Why does a bullet when fired through a window make a clean round
hole in the glass, while a small stone thrown against the window shatters
the glass?
16. A tallow candle can be fired through a pine board. Why?
17. In cyclones, straws are frequently found driven a little distance into
trees; why are the straws not broken and crushed instead of being driven
into the tree unbroken?
18. A bullet weighing one-half oz. is fired from a gun weighing 8 lb. The
bullet has a velocity of 1800 ft. per second. Find the velocity of the "kick"
or recoil of the gun.
18. When football players run into each other which one is thrown the
harder? Why?
20. A railroad train weighing 400 tons has a velocity of 60 miles per hour.
An ocean steamer weighing 20,000 tons has a velocity of one half mile per
hour. How do their momenta compare?
21. Why is a heavy boy preferable to a lighter weight boy for a football
team?
22. Why does a blacksmith when he desires to strike a heavy blow, select a
heavy sledge hammer and swing it over his head?
23. Why does the catcher on a baseball team wear a padded glove?
Page 109
(3) Resolution of Forces
82. Resolution of Forces.—We have been studying the effect of forces in
producing motion and the results of combining forces in many ways; in the
same line, in parallel lines, and in diverging lines. Another case of much
interest and importance is the determination of the effectiveness of a force in
a direction different from the one in which it acts. This case which is called
resolution of forces is frequently used. To illustrate: one needs but to recall
that a sailor uses this principle in a practical way whenever he sails his boat
in any other direction than the one in which the wind is blowing, e.g., when
the wind is blowing, say from the north, the boat may be driven east, west,
or to any point south between the east and west and it is even possible to
beat back against the wind toward the northeast or northwest. Take a sled
drawn by a short rope with the force applied along the line AB (see Fig. 62);
part of this force tends to lift the front of the sled as AC and a part to draw it
forward as AD. Hence not all of the force applied along AB is used in
drawing the sled forward. Its effectiveness is indicated by the relative size
of the component AD compared to AB.
The force of gravity acting upon a sphere
that is resting on an inclined plane may be
readily resolved into two components,
one, the effective component, as OR, and
the other, the non-effective as OS. (See
Fig. 63.) If the angle ACB is 30 degrees,
AB equals 1/2 of AC and OR equals 1/2 of
Fig. 62.—AD is the effective
OG, so that the speed of the sphere down
component.
the plane developed in 1 second is less
than (about one-half of) the speed of a
freely falling body developed in the same time. Why is OS non-effective?
82. Resolution of Forces.—We have been studying the effect of forces in
producing motion and the results of combining forces in many ways; in the
same line, in parallel lines, and in diverging lines. Another case of much
interest and importance is the determination of the effectiveness of a force in
a direction different from the one in which it acts. This case which is called
resolution of forces is frequently used. To illustrate: one needs but to recall
that a sailor uses this principle in a practical way whenever he sails his boat
in any other direction than the one in which the wind is blowing, e.g., when
the wind is blowing, say from the north, the boat may be driven east, west,
or to any point south between the east and west and it is even possible to
beat back against the wind toward the northeast or northwest. Take a sled
drawn by a short rope with the force applied along the line AB (see Fig. 62);
part of this force tends to lift the front of the sled as AC and a part to draw it
forward as AD. Hence not all of the force applied along AB is used in
drawing the sled forward. Its effectiveness is indicated by the relative size
of the component AD compared to AB.
The force of gravity acting upon a sphere
that is resting on an inclined plane may be
readily resolved into two components,
one, the effective component, as OR, and
the other, the non-effective as OS. (See
Fig. 63.) If the angle ACB is 30 degrees,
AB equals 1/2 of AC and OR equals 1/2 of
Fig. 62.—AD is the effective
OG, so that the speed of the sphere down
component.
the plane developed in 1 second is less
than (about one-half of) the speed of a
freely falling body developed in the same time. Why is OS non-effective?
Page 110
Fig. 63.—The effective component is OR.
Fig. 64.—Resolution of the forces acting on an
aeroplane.
83. The Aeroplane.—The aeroplane consists of one or two frames ABCD
(see Fig. 64), over which is stretched cloth or thin sheet metal. It is driven
through the air by a propeller turned by a powerful gasoline motor. This has
the effect of creating a strong breeze coming toward the front of the
aeroplane. As in the case of the sailboat a pressure is created at right angles
to the plane along GF and this may be resolved into two components as GC
and GE, GC acting to lift the aeroplane vertically and GE opposing the
action of the propeller. Fig. 65 represents the Curtis Flying Boat passing
over the Detroit river.
Fig. 65.—The Curtis hydroplane.
Fig. 64.—Resolution of the forces acting on an
aeroplane.
83. The Aeroplane.—The aeroplane consists of one or two frames ABCD
(see Fig. 64), over which is stretched cloth or thin sheet metal. It is driven
through the air by a propeller turned by a powerful gasoline motor. This has
the effect of creating a strong breeze coming toward the front of the
aeroplane. As in the case of the sailboat a pressure is created at right angles
to the plane along GF and this may be resolved into two components as GC
and GE, GC acting to lift the aeroplane vertically and GE opposing the
action of the propeller. Fig. 65 represents the Curtis Flying Boat passing
over the Detroit river.
Fig. 65.—The Curtis hydroplane.
Page 111
Exercises.
1. If a wagon weighing 4000 lbs. is upon a hill which rises 1 ft. in 6, what
force parallel to the hill will just support the load? (Find the effective
component of the weight down the hill.)
2. If a barrel is being rolled up a 16-ft. ladder into a wagon box 3 ft. from
the ground, what force will hold the barrel in place on the ladder, if the
barrel weighs 240 lbs. Show by diagram.
3. Show graphically the components into which a man's push upon the
handle of a lawn mower is resolved.
4. Does a man shooting a flying duck aim at the bird? Explain.
5. What are the three forces that act on a kite when it is "standing" in the
air?
6. What relation does the resultant of any two of the forces in problem five
have to the third?
7. Into what two forces is the weight of a wagon descending a hill resolved?
Explain by use of a diagram.
8. A wind strikes the sail of a boat at an angle of 60 degrees to the
perpendicular with a pressure of 3 lbs. per square foot. What is the effective
pressure, perpendicular to the sail? What would be the effective pressure
when it strikes at 30 degrees?
9. How is the vertical component of the force acting on an aeroplane
affected when the front edge of the plane is elevated? Show by diagram.
(4) Moment of Force and Parallel Forces
84. Moment of Force.—In the study of motion we found that the quantity
of motion is called momentum and is measured by the product of the mass
times the velocity. In the study of parallel forces, especially such as tend to
produce rotation, we consider a similar quantity. It is called a moment of
force, which is the term applied to the effectiveness of a force in producing
change of rotation. It also measured by the product of two quantities; One,
the magnitude of the force itself, and the other, the perpendicular distance
1. If a wagon weighing 4000 lbs. is upon a hill which rises 1 ft. in 6, what
force parallel to the hill will just support the load? (Find the effective
component of the weight down the hill.)
2. If a barrel is being rolled up a 16-ft. ladder into a wagon box 3 ft. from
the ground, what force will hold the barrel in place on the ladder, if the
barrel weighs 240 lbs. Show by diagram.
3. Show graphically the components into which a man's push upon the
handle of a lawn mower is resolved.
4. Does a man shooting a flying duck aim at the bird? Explain.
5. What are the three forces that act on a kite when it is "standing" in the
air?
6. What relation does the resultant of any two of the forces in problem five
have to the third?
7. Into what two forces is the weight of a wagon descending a hill resolved?
Explain by use of a diagram.
8. A wind strikes the sail of a boat at an angle of 60 degrees to the
perpendicular with a pressure of 3 lbs. per square foot. What is the effective
pressure, perpendicular to the sail? What would be the effective pressure
when it strikes at 30 degrees?
9. How is the vertical component of the force acting on an aeroplane
affected when the front edge of the plane is elevated? Show by diagram.
(4) Moment of Force and Parallel Forces
84. Moment of Force.—In the study of motion we found that the quantity
of motion is called momentum and is measured by the product of the mass
times the velocity. In the study of parallel forces, especially such as tend to
produce rotation, we consider a similar quantity. It is called a moment of
force, which is the term applied to the effectiveness of a force in producing
change of rotation. It also measured by the product of two quantities; One,
the magnitude of the force itself, and the other, the perpendicular distance
Page 112
from the axis about which the rotation takes place to the line representing
the direction of the force.
To illustrate: Take a rod, as a meter stick, drill a
hole at S and place through it a screw fastened at
the top of the blackboard. Attach by cords two
spring balances and draw to the right and left, A
and B as in Fig. 66. Draw out the balance B
about half way, hold it steadily, or fasten the
cord at the side of the blackboard, and read both
balances. Note also the distance AS and BS.
Since the rod is at rest, the tendency to rotate to Fig. 66.—The moments
the right and left must be equal. That is, the about S are equal.
moments of the forces at A and B about S are
equal. Since these are computed by the product of the force times the force
arm, multiply B by BS and A by AS and see if the computed moments are
equal. Hence a force that tends to turn or rotate a body to the right can be
balanced by another of equal moment that acts toward the left.
85. Parallel Forces.—Objects are frequently
supported by two or more upward forces acting
at different points and forming in this way a
system of parallel forces; as when two boys
carry a string of fish on a rod between them or
Fig. 67.—Law of when a bridge is supported at its ends. The
parallel forces principle of moments just described aids in
illustrated. determining the magnitude of such forces and of
their resultant. To illustrate this take a wooden
board 4 in. wide and 4 ft. long of uniform dimensions. (See Fig. 67.) Place
several screw hooks on one edge with one set at O where the board will
hang horizontally when the board is suspended there. Weigh the board by a
spring balance hung at O. This will be the resultant in the following tests.
Now hang the board from two spring balances at M and N and read both
balances. Call readings f and f´. To test the forces consider M as a fixed
point (see Fig. 67) and the weight of the board to act at O. Then the moment
of the weight of the board should be equal the moment of the force at N
since the board does not move, or w times OM equals f´ times NM. If N is
considered the fixed point then the moment of the weight of the board and
the direction of the force.
To illustrate: Take a rod, as a meter stick, drill a
hole at S and place through it a screw fastened at
the top of the blackboard. Attach by cords two
spring balances and draw to the right and left, A
and B as in Fig. 66. Draw out the balance B
about half way, hold it steadily, or fasten the
cord at the side of the blackboard, and read both
balances. Note also the distance AS and BS.
Since the rod is at rest, the tendency to rotate to Fig. 66.—The moments
the right and left must be equal. That is, the about S are equal.
moments of the forces at A and B about S are
equal. Since these are computed by the product of the force times the force
arm, multiply B by BS and A by AS and see if the computed moments are
equal. Hence a force that tends to turn or rotate a body to the right can be
balanced by another of equal moment that acts toward the left.
85. Parallel Forces.—Objects are frequently
supported by two or more upward forces acting
at different points and forming in this way a
system of parallel forces; as when two boys
carry a string of fish on a rod between them or
Fig. 67.—Law of when a bridge is supported at its ends. The
parallel forces principle of moments just described aids in
illustrated. determining the magnitude of such forces and of
their resultant. To illustrate this take a wooden
board 4 in. wide and 4 ft. long of uniform dimensions. (See Fig. 67.) Place
several screw hooks on one edge with one set at O where the board will
hang horizontally when the board is suspended there. Weigh the board by a
spring balance hung at O. This will be the resultant in the following tests.
Now hang the board from two spring balances at M and N and read both
balances. Call readings f and f´. To test the forces consider M as a fixed
point (see Fig. 67) and the weight of the board to act at O. Then the moment
of the weight of the board should be equal the moment of the force at N
since the board does not move, or w times OM equals f´ times NM. If N is
considered the fixed point then the moment of the weight of the board and
Page 113
of f with reference to the point N should be equal, or w times ON = f times
NM. Keeping this illustration in mind, the law of parallel forces may be
stated at follows: 1. The resultant of two parallel forces acting in the same
direction at different points in a body is equal to their sum and has the same
direction as the components.
The moment of one of the components about the point of application of the
other is equal and opposite to the moment of the supported weight about the
other.
Problem.—If two boys carry a string of fish weighing 40 lbs. on a rod 8 ft.
long between them, what force must each boy exert if the string is 5 ft. from
the rear boy?
Solution.—The moment of the force F exerted about the opposite end by
the rear boy is F × 8. The moment of the weight about the same point is 40
× (8 - 5) = 120. Therefore F × 8 = 120, or F = 15, the force exerted by the
rear boy. The front boy exerts a force of F whose moment about the other
end of the rod is F × 8. The moment of the weight about the same point is
40 × 5 = 200. Since the moment of F equals this, 200 = F × 8, or F = 25.
Hence the front boy exerts 25 lbs. and the rear boy 15 lbs.
86. The Couple.—If two equal parallel forces
act upon a body along different lines in opposite
directions, as in Fig. 68, they have no single
resultant or there is no one force that will have
the same effect as the two components acting
together. A combination of forces of this kind is
called a couple. Its tendency is to produce
change of rotation in a body. An example is the Fig. 68.—A couple.
action upon a compass needle which is rotated
by a force which urges one end toward the north
and by an equal force which urges the other end toward the south.
Important Topics
1. Moment of force, how measured.
2. Parallel forces.
NM. Keeping this illustration in mind, the law of parallel forces may be
stated at follows: 1. The resultant of two parallel forces acting in the same
direction at different points in a body is equal to their sum and has the same
direction as the components.
The moment of one of the components about the point of application of the
other is equal and opposite to the moment of the supported weight about the
other.
Problem.—If two boys carry a string of fish weighing 40 lbs. on a rod 8 ft.
long between them, what force must each boy exert if the string is 5 ft. from
the rear boy?
Solution.—The moment of the force F exerted about the opposite end by
the rear boy is F × 8. The moment of the weight about the same point is 40
× (8 - 5) = 120. Therefore F × 8 = 120, or F = 15, the force exerted by the
rear boy. The front boy exerts a force of F whose moment about the other
end of the rod is F × 8. The moment of the weight about the same point is
40 × 5 = 200. Since the moment of F equals this, 200 = F × 8, or F = 25.
Hence the front boy exerts 25 lbs. and the rear boy 15 lbs.
86. The Couple.—If two equal parallel forces
act upon a body along different lines in opposite
directions, as in Fig. 68, they have no single
resultant or there is no one force that will have
the same effect as the two components acting
together. A combination of forces of this kind is
called a couple. Its tendency is to produce
change of rotation in a body. An example is the Fig. 68.—A couple.
action upon a compass needle which is rotated
by a force which urges one end toward the north
and by an equal force which urges the other end toward the south.
Important Topics
1. Moment of force, how measured.
2. Parallel forces.
Page 114
3. The two laws of parallel forces.
4. The couple.
Exercises
1. Show by diagram how to arrange a three-horse evener so that each horse
must take one-third of the load.
2. Two boys support a 10-ft. pole on their shoulders with a 40-lb. string of
fish supported from it 4 ft. from the front boy. What load does each boy
carry? Work by principle of moments.
3. If two horses draw a load exerting a combined pull of 300 lbs., what
force must each exert if one is 28 in. and the other is 32 in. from the point
of attachment of the evener to the load?
Fig. 69.—Forces acting upon a stretched rope.
Fig. 70.—A crane with horizontal tie.
4. A weight of 100 lbs. is suspended at the middle of a rope ACB 20 ft. long.
(See Fig. 69.) The ends of the rope are fastened at points A and B at the
same height. Consider D as the center of the line AB. What is the tension of
the rope when CD is 3 ft.? When CD is 1 ft.? When CD is 1 in.?
5. A crane is set up with the tie horizontal. (See Fig. 70.) If 1000 lbs. is to be
lifted, find the tie stress and the boom stress if the boom angle is 30
degrees? If 45 degrees? 60 degrees?
4. The couple.
Exercises
1. Show by diagram how to arrange a three-horse evener so that each horse
must take one-third of the load.
2. Two boys support a 10-ft. pole on their shoulders with a 40-lb. string of
fish supported from it 4 ft. from the front boy. What load does each boy
carry? Work by principle of moments.
3. If two horses draw a load exerting a combined pull of 300 lbs., what
force must each exert if one is 28 in. and the other is 32 in. from the point
of attachment of the evener to the load?
Fig. 69.—Forces acting upon a stretched rope.
Fig. 70.—A crane with horizontal tie.
4. A weight of 100 lbs. is suspended at the middle of a rope ACB 20 ft. long.
(See Fig. 69.) The ends of the rope are fastened at points A and B at the
same height. Consider D as the center of the line AB. What is the tension of
the rope when CD is 3 ft.? When CD is 1 ft.? When CD is 1 in.?
5. A crane is set up with the tie horizontal. (See Fig. 70.) If 1000 lbs. is to be
lifted, find the tie stress and the boom stress if the boom angle is 30
degrees? If 45 degrees? 60 degrees?
Page 115
6. A ball is placed on a plane inclined at an angle of 30 degrees to the
horizontal. What fraction of its weight tends to cause motion down the
plane? What effect does the other component of the weight have? Why?
7. A person weighing 150 lbs. is lying in a hammock. The distance between
the supports is 15 ft. The hammock sags 4 ft. What is the tension in the
supports at each end? What is the tension when the sag is only 1 ft.?
8. A ladder 30 ft. long and weighing 80 lbs. leans against the side of a
building so that it makes an angle of 30 degrees with the building. Find the
direction and magnitude of the component forces on the ground and at the
building.
9. A traveling crane 50 ft. long weighing 10 tons moves from one end of a
shop to the other, at the same time a load of 4000 lbs. moves from end to
end of the crane. Find the pressure of the trucks of the crane on the track
when the load is at a distance of 5, 10, 15, and 25 ft. from either end.
10. Resolve a force of 500 lbs. into two
components at right angles to each other, one of
which shall be four times the other.
11. A truss (see Fig. 71), carries a load of 1000
lbs. at C. Find the forces acting along AC, BC,
and AB. If AC and BC are each 12 ft. and AB 20
ft., which of these forces are tensions and which Fig. 71—A truss.
are pressures?
(5) Gravitation and Gravity
87. Gravitation.—Gravitation is the force of attraction that exists between
all bodies of matter at all distances. This attraction exists not only between
the heavenly bodies, the stars and planets, etc., but is also found between
bodies on the earth. A book attracts all objects in a room and outside of a
room as well, since its weight shows that it is attracted by the earth itself.
The gravitational attraction between ordinary bodies is so slight that it
requires careful experiments to detect it. In fact, it is only when one of the
attracting bodies is large, as for example the earth, that the force becomes
considerable. Careful studies of the motions of the heavenly bodies,
especially of that of the moon in its orbit about the earth, led Sir Isaac
horizontal. What fraction of its weight tends to cause motion down the
plane? What effect does the other component of the weight have? Why?
7. A person weighing 150 lbs. is lying in a hammock. The distance between
the supports is 15 ft. The hammock sags 4 ft. What is the tension in the
supports at each end? What is the tension when the sag is only 1 ft.?
8. A ladder 30 ft. long and weighing 80 lbs. leans against the side of a
building so that it makes an angle of 30 degrees with the building. Find the
direction and magnitude of the component forces on the ground and at the
building.
9. A traveling crane 50 ft. long weighing 10 tons moves from one end of a
shop to the other, at the same time a load of 4000 lbs. moves from end to
end of the crane. Find the pressure of the trucks of the crane on the track
when the load is at a distance of 5, 10, 15, and 25 ft. from either end.
10. Resolve a force of 500 lbs. into two
components at right angles to each other, one of
which shall be four times the other.
11. A truss (see Fig. 71), carries a load of 1000
lbs. at C. Find the forces acting along AC, BC,
and AB. If AC and BC are each 12 ft. and AB 20
ft., which of these forces are tensions and which Fig. 71—A truss.
are pressures?
(5) Gravitation and Gravity
87. Gravitation.—Gravitation is the force of attraction that exists between
all bodies of matter at all distances. This attraction exists not only between
the heavenly bodies, the stars and planets, etc., but is also found between
bodies on the earth. A book attracts all objects in a room and outside of a
room as well, since its weight shows that it is attracted by the earth itself.
The gravitational attraction between ordinary bodies is so slight that it
requires careful experiments to detect it. In fact, it is only when one of the
attracting bodies is large, as for example the earth, that the force becomes
considerable. Careful studies of the motions of the heavenly bodies,
especially of that of the moon in its orbit about the earth, led Sir Isaac
Page 116
Newton to the statement of the law of gravitation which is well expressed in
the following statement:
88. Law of Gravitation.—Every particle of matter in the universe attracts
every other particle with a force that is directly proportional to the product
of their masses and inversely proportional to the square of the distance
between them.
The law may be separated into two parts, one referring to the masses of the
bodies concerned, the other to the effect of the distance between them. The
first part is easily understood since we all know that two quarts of milk will
weigh just twice as much as one quart. To illustrate the second part of the
law, suppose that the moon were removed to twice its present distance from
the earth, then the attraction between the earth and the moon would be one-
fourth its present attraction. If removed to three times its present distance,
the attraction would be one-ninth, etc.
The attraction of the earth for other bodies on or near it is called gravity.
The weight of a body is the measure of the earth's attraction for it; or it is
the force of gravity acting upon it. Newton's third law of motion states that
every action is accompanied by an equal and opposite reaction (Art. 80).
Hence, the attraction of the earth for a book or any other object is
accompanied by an equal attraction of the book for the earth.
89. Weight.—In advanced physics it is proved that a sphere attracts as if it
were concentrated at its center. Thus if the earth's radius be considered as
4000 miles, then a body 4000 miles above the earth's surface would be 8000
miles above the earth's center, or twice as far from the center of the earth as
is a body upon the earth's surface. A body then 4000 miles above the earth's
surface will weigh then but one-fourth as much as it will at the surface of
the earth.
Since the earth is flattened at the poles, the surface at the equator is farther
from the center of the earth than at points north or south. Thus a body
weighing 1 lb. at the equator weighs 1.002 lb. at Chicago, or about 1/500
more. The rotation of the earth also affects the weight of a body upon it so
that at the equator the weight of a body is 1/289 less than at the pole. Both
effects, that of flattening and of rotation, tend to diminish the weight of
bodies at the equator, so that a body at the latter place weighs about 1/192
less than at the poles.
the following statement:
88. Law of Gravitation.—Every particle of matter in the universe attracts
every other particle with a force that is directly proportional to the product
of their masses and inversely proportional to the square of the distance
between them.
The law may be separated into two parts, one referring to the masses of the
bodies concerned, the other to the effect of the distance between them. The
first part is easily understood since we all know that two quarts of milk will
weigh just twice as much as one quart. To illustrate the second part of the
law, suppose that the moon were removed to twice its present distance from
the earth, then the attraction between the earth and the moon would be one-
fourth its present attraction. If removed to three times its present distance,
the attraction would be one-ninth, etc.
The attraction of the earth for other bodies on or near it is called gravity.
The weight of a body is the measure of the earth's attraction for it; or it is
the force of gravity acting upon it. Newton's third law of motion states that
every action is accompanied by an equal and opposite reaction (Art. 80).
Hence, the attraction of the earth for a book or any other object is
accompanied by an equal attraction of the book for the earth.
89. Weight.—In advanced physics it is proved that a sphere attracts as if it
were concentrated at its center. Thus if the earth's radius be considered as
4000 miles, then a body 4000 miles above the earth's surface would be 8000
miles above the earth's center, or twice as far from the center of the earth as
is a body upon the earth's surface. A body then 4000 miles above the earth's
surface will weigh then but one-fourth as much as it will at the surface of
the earth.
Since the earth is flattened at the poles, the surface at the equator is farther
from the center of the earth than at points north or south. Thus a body
weighing 1 lb. at the equator weighs 1.002 lb. at Chicago, or about 1/500
more. The rotation of the earth also affects the weight of a body upon it so
that at the equator the weight of a body is 1/289 less than at the pole. Both
effects, that of flattening and of rotation, tend to diminish the weight of
bodies at the equator, so that a body at the latter place weighs about 1/192
less than at the poles.
Page 117
In studying the effect of the earth's gravity, the following illustration will be
helpful: Imagine an open shaft a mile square extending through the earth.
What would happen to a stone thrown into the shaft? At first it would have
the attraction of the whole earth drawing it and continually increasing its
speed downward. As it descends from the surface, the pull toward the center
grows less and less. Halfway to the center the body has lost half its weight.
When the stone reaches the center, the pull in all directions is the same, or
in other words, it has no weight. It would, however, continue moving
rapidly on account of its inertia, and as it continues on from the center, the
greater part of the earth being left behind, the attraction pulling toward the
center will gradually stop it. It will then fall again toward the center and be
stopped again after passing it, and after repeatedly moving up and down
will finally come to rest at the center of the earth. At this point it will be
found to be a body without weight since it is pulled equally in all directions
by the material of the earth. What force brings the body to rest?
90. Center of Gravity.—A body is composed of a great many particles
each of which is pulled toward the center of the earth by the force of
gravity. A single force that would exactly equal the combined effect of the
pull of the earth for all the particles of a body would be their resultant. The
magnitude of this resultant is the weight of the body. The direction of this
resultant is in a line passing toward the earth's center, while the point of
application of this resultant is called the center of gravity of the body. The
center of gravity of a body may also be briefly defined as the point about
which it may be balanced. As the location of this point depends upon the
distribution of matter in the body, the center of gravity is also sometimes
called the center of mass of the body.
The earth's attraction for a body is considered for the sake of simplicity, not
as a multitude of little forces, but as a single force applied at its center of
gravity. To find the center of gravity of a body find two intersecting lines
along which it balances, see Fig. 72, and the center of gravity will be at the
intersection. A vertical line through this point is sometimes called the line of
direction of the weight.
91. Equilibrium of Bodies.—Equilibrium means equally balanced. A body
at rest or in uniform motion is then in equilibrium. An object is in
equilibrium under gravity when a vertical line through its center of gravity
passes through the point of support. A trunk is an example of a body in
helpful: Imagine an open shaft a mile square extending through the earth.
What would happen to a stone thrown into the shaft? At first it would have
the attraction of the whole earth drawing it and continually increasing its
speed downward. As it descends from the surface, the pull toward the center
grows less and less. Halfway to the center the body has lost half its weight.
When the stone reaches the center, the pull in all directions is the same, or
in other words, it has no weight. It would, however, continue moving
rapidly on account of its inertia, and as it continues on from the center, the
greater part of the earth being left behind, the attraction pulling toward the
center will gradually stop it. It will then fall again toward the center and be
stopped again after passing it, and after repeatedly moving up and down
will finally come to rest at the center of the earth. At this point it will be
found to be a body without weight since it is pulled equally in all directions
by the material of the earth. What force brings the body to rest?
90. Center of Gravity.—A body is composed of a great many particles
each of which is pulled toward the center of the earth by the force of
gravity. A single force that would exactly equal the combined effect of the
pull of the earth for all the particles of a body would be their resultant. The
magnitude of this resultant is the weight of the body. The direction of this
resultant is in a line passing toward the earth's center, while the point of
application of this resultant is called the center of gravity of the body. The
center of gravity of a body may also be briefly defined as the point about
which it may be balanced. As the location of this point depends upon the
distribution of matter in the body, the center of gravity is also sometimes
called the center of mass of the body.
The earth's attraction for a body is considered for the sake of simplicity, not
as a multitude of little forces, but as a single force applied at its center of
gravity. To find the center of gravity of a body find two intersecting lines
along which it balances, see Fig. 72, and the center of gravity will be at the
intersection. A vertical line through this point is sometimes called the line of
direction of the weight.
91. Equilibrium of Bodies.—Equilibrium means equally balanced. A body
at rest or in uniform motion is then in equilibrium. An object is in
equilibrium under gravity when a vertical line through its center of gravity
passes through the point of support. A trunk is an example of a body in
Page 118
equilibrium since a vertical line from its center of
gravity falls within the base formed by the area
upon which it rests. Work will be necessary to tip
the trunk from its position. The amount of work
required will depend upon the weight of the body
and the location of the center of gravity.
92. Kinds of Equilibrium.—(a) Stable.—A body
is in stable equilibrium under gravity if its center
of gravity is raised whenever the body is displaced.
It will return to its first position if allowed to fall
after being slightly displaced. In Fig. 73, a and b if
Fig. 72.—The center slightly tipped will return to their first position.
of gravity is at the They are in stable equilibrium. Other examples are
intersection of the a rocking chair, and the combination shown in Fig.
lines of direction. 74.
Fig. 73.—Stable equilibrium.
(b) Unstable.—A body is in unstable equilibrium under gravity if its center
of gravity is lowered whenever the body is slightly displaced. It will fall
farther from its first position. A pencil balanced on its point or a broom
balanced on the end of the handle are in unstable equilibrium. The slightest
disturbance will make the line of direction of the weight fall outside of
(away from) the point of support (Fig. 75 a).
gravity falls within the base formed by the area
upon which it rests. Work will be necessary to tip
the trunk from its position. The amount of work
required will depend upon the weight of the body
and the location of the center of gravity.
92. Kinds of Equilibrium.—(a) Stable.—A body
is in stable equilibrium under gravity if its center
of gravity is raised whenever the body is displaced.
It will return to its first position if allowed to fall
after being slightly displaced. In Fig. 73, a and b if
Fig. 72.—The center slightly tipped will return to their first position.
of gravity is at the They are in stable equilibrium. Other examples are
intersection of the a rocking chair, and the combination shown in Fig.
lines of direction. 74.
Fig. 73.—Stable equilibrium.
(b) Unstable.—A body is in unstable equilibrium under gravity if its center
of gravity is lowered whenever the body is slightly displaced. It will fall
farther from its first position. A pencil balanced on its point or a broom
balanced on the end of the handle are in unstable equilibrium. The slightest
disturbance will make the line of direction of the weight fall outside of
(away from) the point of support (Fig. 75 a).
Page 119
Fig. 74—An example
of stable equilibrium.
Why?
Fig. 75.—Unstable equilibrium a, neutral
equilibrium b.
(c) Neutral.—A body is in neutral equilibrium if its center of gravity is
neither raised nor lowered whenever the body is moved. Familiar examples
are a ball lying on a table (Fig. 75 b) and a wagon moving on a level street
(referring to its forward motion).
93. Stability.—When a body is in stable equilibrium, effort must be exerted
to overturn it, and the degree of stability is measured by the effort required
to overturn it. To overturn a body, it must be moved so that the vertical line
through its center of gravity will pass outside of its supporting base. This
movement in stable bodies necessitates a raising of the center of gravity.
The higher this center of gravity must be raised in overturning the body, the
more stable it is, e.g., see Fig. 76. Thus a wagon on a hillside will not
overturn until its weight falls outside of its base, as in Fig. 77 B. The
stability of a body depends upon the position of its center of gravity and the
area of its base. The lower the center of gravity and the larger the base, the
of stable equilibrium.
Why?
Fig. 75.—Unstable equilibrium a, neutral
equilibrium b.
(c) Neutral.—A body is in neutral equilibrium if its center of gravity is
neither raised nor lowered whenever the body is moved. Familiar examples
are a ball lying on a table (Fig. 75 b) and a wagon moving on a level street
(referring to its forward motion).
93. Stability.—When a body is in stable equilibrium, effort must be exerted
to overturn it, and the degree of stability is measured by the effort required
to overturn it. To overturn a body, it must be moved so that the vertical line
through its center of gravity will pass outside of its supporting base. This
movement in stable bodies necessitates a raising of the center of gravity.
The higher this center of gravity must be raised in overturning the body, the
more stable it is, e.g., see Fig. 76. Thus a wagon on a hillside will not
overturn until its weight falls outside of its base, as in Fig. 77 B. The
stability of a body depends upon the position of its center of gravity and the
area of its base. The lower the center of gravity and the larger the base, the
Page 120
more stable the body. What means
are employed to give stability to
bodies, in every-day use (such as
clocks, ink-stands, pitchers, vases,
chairs, lamps, etc.)?
Fig. 76.—B is more stable than A.
Fig. 77.—B will overturn; A will not.
Important Topics
1. Gravitation; law of gravitation, gravity, weight.
2. Center of gravity.
3. The three states of equilibrium. Stability.
Exercises
are employed to give stability to
bodies, in every-day use (such as
clocks, ink-stands, pitchers, vases,
chairs, lamps, etc.)?
Fig. 76.—B is more stable than A.
Fig. 77.—B will overturn; A will not.
Important Topics
1. Gravitation; law of gravitation, gravity, weight.
2. Center of gravity.
3. The three states of equilibrium. Stability.
Exercises
Page 121
1. Why is a plumb-line useful in building houses?
2. What is the center of gravity of a body?
3. Explain the action of a rocking chair that has been tipped forward.
4. Is the stability of a box greater when empty or when filled with sand?
Explain.
5. How can you start yourself swinging, in a swing, without touching the
ground?
6. Is the center of gravity of the beam of a balance above, below, or at the
point of a support? How did you find it out?
7. Why are some ink bottles cone shaped with thick bottoms?
8. Would an electric fan in motion on the rear of a light boat move it?
Would it move the boat if revolving under water? Explain.
9. What turns a rotary lawn sprinkler?
10. Why, when you are standing erect against a wall and a coin is placed
between your feet, can you not stoop and pick it up unless you shift your
feet or fall over?
11. What would become of a ball dropped into a large hole bored through
the center of the earth?
12. When an apple falls to the ground, does the earth rise to meet it?
13. How far from the earth does the force of gravity extend?
14. Why in walking up a flight of stairs does the body bend forward?
15. In walking down a steep hill why do people frequently bend backward?
16. Why is it so difficult for a child to learn to walk, while a kitten or a
puppy has no such difficulty?
17. Explain why the use of a cane by old people makes it easier for them to
walk?
(6) Falling Bodies
2. What is the center of gravity of a body?
3. Explain the action of a rocking chair that has been tipped forward.
4. Is the stability of a box greater when empty or when filled with sand?
Explain.
5. How can you start yourself swinging, in a swing, without touching the
ground?
6. Is the center of gravity of the beam of a balance above, below, or at the
point of a support? How did you find it out?
7. Why are some ink bottles cone shaped with thick bottoms?
8. Would an electric fan in motion on the rear of a light boat move it?
Would it move the boat if revolving under water? Explain.
9. What turns a rotary lawn sprinkler?
10. Why, when you are standing erect against a wall and a coin is placed
between your feet, can you not stoop and pick it up unless you shift your
feet or fall over?
11. What would become of a ball dropped into a large hole bored through
the center of the earth?
12. When an apple falls to the ground, does the earth rise to meet it?
13. How far from the earth does the force of gravity extend?
14. Why in walking up a flight of stairs does the body bend forward?
15. In walking down a steep hill why do people frequently bend backward?
16. Why is it so difficult for a child to learn to walk, while a kitten or a
puppy has no such difficulty?
17. Explain why the use of a cane by old people makes it easier for them to
walk?
(6) Falling Bodies
Page 122
94. Falling Bodies.—One of the earliest physical facts learned by a child is
that a body unsupported falls toward the earth. When a child lets go of a
toy, he soon learns to look for it on the floor. It is also of common
observation that light objects, as feathers and paper, fall much slower than a
stone. The information, therefore, that all bodies actually fall at the same
rate in a vacuum or when removed from the retarding influence of the air is
received with surprise.
This fact may be shown by using what is called a coin and feather tube. On
exhausting the air from this tube, the feather and coin within are seen to fall
at the same rate. (See Fig. 78.) when air is again admitted, the feather
flutters along behind.
Fig. 78.—Bodies fall alike in a vacuum.
Fig. 79.—Leaning tower of Pisa.
95. Galileo's Experiment.—The fact that bodies of different weight tend to
fall at the same rate was first experimentally shown by Galileo by dropping
a 1-lb. and a 100-lb. ball from the top of the leaning tower of Pisa in Italy
that a body unsupported falls toward the earth. When a child lets go of a
toy, he soon learns to look for it on the floor. It is also of common
observation that light objects, as feathers and paper, fall much slower than a
stone. The information, therefore, that all bodies actually fall at the same
rate in a vacuum or when removed from the retarding influence of the air is
received with surprise.
This fact may be shown by using what is called a coin and feather tube. On
exhausting the air from this tube, the feather and coin within are seen to fall
at the same rate. (See Fig. 78.) when air is again admitted, the feather
flutters along behind.
Fig. 78.—Bodies fall alike in a vacuum.
Fig. 79.—Leaning tower of Pisa.
95. Galileo's Experiment.—The fact that bodies of different weight tend to
fall at the same rate was first experimentally shown by Galileo by dropping
a 1-lb. and a 100-lb. ball from the top of the leaning tower of Pisa in Italy
Page 123
(represented in Fig. 79). Both starting at the same time struck the ground
together. Galileo inferred from this that feathers and other light objects
would fall at the same rate as iron or lead were it not for the resistance of
the air. After the invention of the air pump this supposition was verified as
just explained.
96. Acceleration Due to Gravity.—If a body falls freely, that is without
meeting a resistance or a retarding influence, its motion will continually
increase. The increase in motion is found to be constant or uniform during
each second. This uniform increase in motion or in velocity of a falling
body gives one of the best illustrations that we have of uniformly
accelerated motion. (Art. 75.) On the other hand, a body thrown upward has
uniformly retarded motion, that is, its acceleration is downward. The
velocity acquired by a falling body in unit time is called its acceleration, or
the acceleration due to gravity, and is equal to 32.16 ft. (980 cm.) per
second, downward, each second of time. In one second, therefore, a falling
body gains a velocity of 32.16 ft. (980 cm.) per second, downward. In two
seconds it gains twice this, and so on.
In formulas, the acceleration of gravity is represented by "g" and the
number of seconds by t, therefore the formula for finding the velocity, V,[F]
of a falling body starting from rest is V = gt. In studying gravity (Art. 89)
we learned that its force varies as one moves toward or away from the
equator. (How?) In latitude 38° the acceleration of gravity is 980 cm. per
second each second of time.
97. Experimental Study of Falling Bodies.—To study falling bodies
experimentally by observing the fall of unobstructed bodies is a difficult
matter. Many devices have been used to reduce the motion so that the action
of a falling body may be observed within the limits of a laboratory or
lecture room. The simplest of these, and in some respects the most
satisfactory, was used by Galileo. It consists of an inclined plane which
reduces the effective component of the force of gravity so that the motion of
a body rolling down the plane may be observed for several seconds. For
illustrating this principle a steel piano wire has been selected as being the
simplest and the most easily understood. This wire is stretched taut across a
room by a turn-buckle so that its slope is about one in sixteen. (See Fig. 80.)
Down this wire a weighted pulley is allowed to run and the distance it
travels in 1, 2, 3, and 4 seconds is observed. From these observations we
together. Galileo inferred from this that feathers and other light objects
would fall at the same rate as iron or lead were it not for the resistance of
the air. After the invention of the air pump this supposition was verified as
just explained.
96. Acceleration Due to Gravity.—If a body falls freely, that is without
meeting a resistance or a retarding influence, its motion will continually
increase. The increase in motion is found to be constant or uniform during
each second. This uniform increase in motion or in velocity of a falling
body gives one of the best illustrations that we have of uniformly
accelerated motion. (Art. 75.) On the other hand, a body thrown upward has
uniformly retarded motion, that is, its acceleration is downward. The
velocity acquired by a falling body in unit time is called its acceleration, or
the acceleration due to gravity, and is equal to 32.16 ft. (980 cm.) per
second, downward, each second of time. In one second, therefore, a falling
body gains a velocity of 32.16 ft. (980 cm.) per second, downward. In two
seconds it gains twice this, and so on.
In formulas, the acceleration of gravity is represented by "g" and the
number of seconds by t, therefore the formula for finding the velocity, V,[F]
of a falling body starting from rest is V = gt. In studying gravity (Art. 89)
we learned that its force varies as one moves toward or away from the
equator. (How?) In latitude 38° the acceleration of gravity is 980 cm. per
second each second of time.
97. Experimental Study of Falling Bodies.—To study falling bodies
experimentally by observing the fall of unobstructed bodies is a difficult
matter. Many devices have been used to reduce the motion so that the action
of a falling body may be observed within the limits of a laboratory or
lecture room. The simplest of these, and in some respects the most
satisfactory, was used by Galileo. It consists of an inclined plane which
reduces the effective component of the force of gravity so that the motion of
a body rolling down the plane may be observed for several seconds. For
illustrating this principle a steel piano wire has been selected as being the
simplest and the most easily understood. This wire is stretched taut across a
room by a turn-buckle so that its slope is about one in sixteen. (See Fig. 80.)
Down this wire a weighted pulley is allowed to run and the distance it
travels in 1, 2, 3, and 4 seconds is observed. From these observations we
Page 124
can compute the distance covered each second and the velocity at the end of
each second.
Fig. 80.—Apparatus to illustrate uniformly
accelerated motion.
In Fig. 63, if OG represents the weight of the body or the pull of gravity,
then the line OR will represent the effective component along the wire, and
OS the non-effective component against the wire. Since the ratio of the
height of the plane to its length is as one to sixteen, then the motion along
the wire in Fig. 80 will be one-sixteenth that of a falling body.
98. Summary of Results.—The following table gives the results that have
been obtained with an apparatus arranged as shown above.
In this table, column 2 is the one which contains the results directly
observed by the use of the apparatus. Columns, 3, 4, and 5 are computed
from preceding columns.
(2) Total
(1) No. of (3) Distance (4) Velocity at (5) Acceleration
distance
seconds each second end of second each second
moved
Per second Per second
1 30 cm. 30 cm. 60 cm. 60 cm.
2 120 cm. 90 cm. 120 cm. 60 cm.
3 270 cm. 150 cm. 180 cm. 60 cm.
4 480 cm. 210 cm. 240 cm. 60 cm.
each second.
Fig. 80.—Apparatus to illustrate uniformly
accelerated motion.
In Fig. 63, if OG represents the weight of the body or the pull of gravity,
then the line OR will represent the effective component along the wire, and
OS the non-effective component against the wire. Since the ratio of the
height of the plane to its length is as one to sixteen, then the motion along
the wire in Fig. 80 will be one-sixteenth that of a falling body.
98. Summary of Results.—The following table gives the results that have
been obtained with an apparatus arranged as shown above.
In this table, column 2 is the one which contains the results directly
observed by the use of the apparatus. Columns, 3, 4, and 5 are computed
from preceding columns.
(2) Total
(1) No. of (3) Distance (4) Velocity at (5) Acceleration
distance
seconds each second end of second each second
moved
Per second Per second
1 30 cm. 30 cm. 60 cm. 60 cm.
2 120 cm. 90 cm. 120 cm. 60 cm.
3 270 cm. 150 cm. 180 cm. 60 cm.
4 480 cm. 210 cm. 240 cm. 60 cm.
Page 125
Column 5 shows that the acceleration is uniform, or the same each second.
Column 4 shows that the velocity increases with the number of seconds or
that V = at. Column 3 shows that the increase in motion from 1 second to
the next is just equal to the acceleration or 60 cm. This is represented by the
following formula: s = 1/2 a(2t - 1).
The results of the second column, it may be seen, increase as 1:4:9:16,
while the number of seconds vary as 1:2:3:4. That is, the total distance
covered is proportional to the square of the number of seconds.
This fact expressed as a formula gives: S = 1/2at2.
Substituting g, the symbol for the acceleration of gravity, for a in the above
formulas, we have: (1) V = gt, (2) S = 1/2gt2, (3) s = 1/2g(2t - 1).
99. Laws of Falling Bodies.—These formulas may be stated as follows for
a body which falls from rest:
1. The velocity of a freely falling body at the end of any second is equal to
32.16 ft. per sec. or 980 cm. per second multiplied by the number of the
second.
2. The distance passed through by a freely falling body during any number
of seconds is equal to the square of the number of seconds multiplied by
16.08 ft. or 490 cm.
3. The distance passed through by a freely falling body during any second is
equal to 16.08 feet or 490 cm. multiplied by one less than twice the number
of the second.
Important Topics
1. Falling bodies.
2. Galileo's experiment.
3. Acceleration due to gravity.
4. Laws of falling bodies.
Exercises
Column 4 shows that the velocity increases with the number of seconds or
that V = at. Column 3 shows that the increase in motion from 1 second to
the next is just equal to the acceleration or 60 cm. This is represented by the
following formula: s = 1/2 a(2t - 1).
The results of the second column, it may be seen, increase as 1:4:9:16,
while the number of seconds vary as 1:2:3:4. That is, the total distance
covered is proportional to the square of the number of seconds.
This fact expressed as a formula gives: S = 1/2at2.
Substituting g, the symbol for the acceleration of gravity, for a in the above
formulas, we have: (1) V = gt, (2) S = 1/2gt2, (3) s = 1/2g(2t - 1).
99. Laws of Falling Bodies.—These formulas may be stated as follows for
a body which falls from rest:
1. The velocity of a freely falling body at the end of any second is equal to
32.16 ft. per sec. or 980 cm. per second multiplied by the number of the
second.
2. The distance passed through by a freely falling body during any number
of seconds is equal to the square of the number of seconds multiplied by
16.08 ft. or 490 cm.
3. The distance passed through by a freely falling body during any second is
equal to 16.08 feet or 490 cm. multiplied by one less than twice the number
of the second.
Important Topics
1. Falling bodies.
2. Galileo's experiment.
3. Acceleration due to gravity.
4. Laws of falling bodies.
Exercises
Page 126
1. How far does a body fall during the first second? Account for the fact
that this distance is numerically equal to half the acceleration.
2. (a) What is the velocity of a falling body at the end of the first second?
(b) How far does it fall during the second second? (c) Account for the
difference between these numbers.
3. What is the velocity of a falling body at the end of the fifth second?
4. How far does a body fall (a) in 5 seconds (b) in 6 seconds (c) during the
sixth second?
5. (a) What is the difference between the average velocity during the sixth
second and the velocity at the beginning of that second?
(b) Is this difference equal to that found in the second problem? Why?
6. A stone dropped from a cliff strikes the foot of it in 5 seconds. What is
the height of the cliff?
7. Why is it that the increased weight of a body when taken to higher
latitudes causes it to fall faster, while at the same place a heavy body falls
no faster than a light one?
8. When a train is leaving a station its acceleration gradually decreases to
zero, although the engine continues to pull. Explain.
9. Would you expect the motion of equally smooth and perfect spheres of
different weight and material to be equally accelerated on the same inclined
plane? Give reason for your answer. Try the experiment.
10. A body is thrown upward with the velocity of 64.32 ft. per sec. How
many seconds will it rise? How far will it rise? How many seconds will it
stay in the air before striking the ground?
11. 32.16 feet = how many centimeters?
12. The acceleration of a freely falling body is constant at any one place.
What does this show about the pull which the earth exerts on the body?
(7) The Pendulum
100. The Simple Pendulum.—Any body suspended so as to swing freely
to and fro is a pendulum, as in Fig. 81. A simple pendulum is defined as a
that this distance is numerically equal to half the acceleration.
2. (a) What is the velocity of a falling body at the end of the first second?
(b) How far does it fall during the second second? (c) Account for the
difference between these numbers.
3. What is the velocity of a falling body at the end of the fifth second?
4. How far does a body fall (a) in 5 seconds (b) in 6 seconds (c) during the
sixth second?
5. (a) What is the difference between the average velocity during the sixth
second and the velocity at the beginning of that second?
(b) Is this difference equal to that found in the second problem? Why?
6. A stone dropped from a cliff strikes the foot of it in 5 seconds. What is
the height of the cliff?
7. Why is it that the increased weight of a body when taken to higher
latitudes causes it to fall faster, while at the same place a heavy body falls
no faster than a light one?
8. When a train is leaving a station its acceleration gradually decreases to
zero, although the engine continues to pull. Explain.
9. Would you expect the motion of equally smooth and perfect spheres of
different weight and material to be equally accelerated on the same inclined
plane? Give reason for your answer. Try the experiment.
10. A body is thrown upward with the velocity of 64.32 ft. per sec. How
many seconds will it rise? How far will it rise? How many seconds will it
stay in the air before striking the ground?
11. 32.16 feet = how many centimeters?
12. The acceleration of a freely falling body is constant at any one place.
What does this show about the pull which the earth exerts on the body?
(7) The Pendulum
100. The Simple Pendulum.—Any body suspended so as to swing freely
to and fro is a pendulum, as in Fig. 81. A simple pendulum is defined as a
Page 127
single particle of matter suspended by a cord without weight. It is of course
impossible to construct such a pendulum. A small metal ball suspended by a
thread is approximately a simple pendulum. When allowed to swing its
vibrations are made in equal times. This feature of the motion of a
pendulum was first noticed by Galileo while watching the slow oscillations
of a bronze chandelier suspended in the Cathedral in Pisa.
101. Definition of Terms. The center of
suspension is the point about which the
pendulum swings. A single vibration is one
swing across the arc. A complete or double
vibration is the swing across the arc and back
again. The time required for a double
vibration is called the period. The length of a
simple pendulum is approximately the
distance from the point of support to the
center of the bob.
A seconds pendulum is one making a single
vibration per second. Its length at sea-level, at
New York is 99.31 cm. or 39.1 in., at the
equator 39.01 in., at the poles 39.22 in.
A compound pendulum is one having an Fig. 81—A simple
appreciable portion of its mass elsewhere than pendulum.
in the small compact body or sphere called a
bob. The ordinary clock pendulum or a meter stick suspended by one end
are examples of compound pendulums.
The amplitude of a vibration is one-half the arc through which it swings, for
example, the arc DC or the angle DAC in Fig. 81.
102. Laws of the Pendulum.—The following laws may be stated:
1. The period of a pendulum is not affected by its mass or the material of
which the pendulum is made.
2. For small amplitudes, the period is not affected by the length of the arc
through which it swings.
3. The period is directly proportional to the square root of the length.
Expressed mathematically, t/t´ = √l/√l´.
impossible to construct such a pendulum. A small metal ball suspended by a
thread is approximately a simple pendulum. When allowed to swing its
vibrations are made in equal times. This feature of the motion of a
pendulum was first noticed by Galileo while watching the slow oscillations
of a bronze chandelier suspended in the Cathedral in Pisa.
101. Definition of Terms. The center of
suspension is the point about which the
pendulum swings. A single vibration is one
swing across the arc. A complete or double
vibration is the swing across the arc and back
again. The time required for a double
vibration is called the period. The length of a
simple pendulum is approximately the
distance from the point of support to the
center of the bob.
A seconds pendulum is one making a single
vibration per second. Its length at sea-level, at
New York is 99.31 cm. or 39.1 in., at the
equator 39.01 in., at the poles 39.22 in.
A compound pendulum is one having an Fig. 81—A simple
appreciable portion of its mass elsewhere than pendulum.
in the small compact body or sphere called a
bob. The ordinary clock pendulum or a meter stick suspended by one end
are examples of compound pendulums.
The amplitude of a vibration is one-half the arc through which it swings, for
example, the arc DC or the angle DAC in Fig. 81.
102. Laws of the Pendulum.—The following laws may be stated:
1. The period of a pendulum is not affected by its mass or the material of
which the pendulum is made.
2. For small amplitudes, the period is not affected by the length of the arc
through which it swings.
3. The period is directly proportional to the square root of the length.
Expressed mathematically, t/t´ = √l/√l´.
Page 128
103. Uses of the Pendulum.—The chief use of the pendulum is to regulate
motion in clocks. The wheels are kept in motion by a spring or a weight and
the regulation is effected by an escapement (Fig. 82). At each vibration of
the pendulum one tooth of the wheel D slips past the prong at one end of
the escapement C, at the same time giving a slight push to the escapement.
This push transmitted to the pendulum keeps it in motion. In this way, the
motion of the wheel work and the hands is controlled. Another use of the
pendulum is in finding the acceleration of gravity, by using the formula, t =
π√(l/g), in which t is the time in seconds of a single vibration and l the
length of the pendulum. If, for example, the length of the seconds pendulum
is 99.31 cm., then 1 = π√(99.31/g); squaring both sides of the equation, we
have 12 = π2(99.31/g), or g = π2 × 99.31/12 = 980.1 cm. per sec., per sec.
From this it follows that, since the force of gravity depends upon the
distance from the center of the earth, the pendulum may be used to
determine the elevation of a place above sea level and also the shape of the
earth.
Important Topics
1. Simple pendulum.
2. Definitions of terms used.
3. Laws of the pendulum.
4. Uses of the pendulum.
Exercises
1. What is the usual shape of the bob of a clock pendulum? Why is this
shape used instead of a sphere?
2. Removing the bob from a clock pendulum has what effect on its motion?
Also on the motion of the hands?
3. How does the expansion of the rod of a pendulum in summer and its
contraction in winter affect the keeping of time by a clock? How can this be
corrected?
motion in clocks. The wheels are kept in motion by a spring or a weight and
the regulation is effected by an escapement (Fig. 82). At each vibration of
the pendulum one tooth of the wheel D slips past the prong at one end of
the escapement C, at the same time giving a slight push to the escapement.
This push transmitted to the pendulum keeps it in motion. In this way, the
motion of the wheel work and the hands is controlled. Another use of the
pendulum is in finding the acceleration of gravity, by using the formula, t =
π√(l/g), in which t is the time in seconds of a single vibration and l the
length of the pendulum. If, for example, the length of the seconds pendulum
is 99.31 cm., then 1 = π√(99.31/g); squaring both sides of the equation, we
have 12 = π2(99.31/g), or g = π2 × 99.31/12 = 980.1 cm. per sec., per sec.
From this it follows that, since the force of gravity depends upon the
distance from the center of the earth, the pendulum may be used to
determine the elevation of a place above sea level and also the shape of the
earth.
Important Topics
1. Simple pendulum.
2. Definitions of terms used.
3. Laws of the pendulum.
4. Uses of the pendulum.
Exercises
1. What is the usual shape of the bob of a clock pendulum? Why is this
shape used instead of a sphere?
2. Removing the bob from a clock pendulum has what effect on its motion?
Also on the motion of the hands?
3. How does the expansion of the rod of a pendulum in summer and its
contraction in winter affect the keeping of time by a clock? How can this be
corrected?
Page 129
4. Master clocks that control the time of a railway system have a cup of
mercury for a bob. This automatically keeps the same rate of vibration
through any changes of temperature. How?
5. How will the length of a seconds pendulum at Denver, 1 mile above sea-
level, compare with one at New York? Why?
6. What is the period of a pendulum 9 in. long? Note.
In problems involving the use of the third law, use the
length of a seconds pendulum for l, and call its period
1.
7. A swing is 20 ft. high, find the time required for one
swing across the arc.
8. A pendulum is 60 cm. long. What is its period?
9. If in a gymnasium a pupil takes 3 sec. to swing once
across while hanging from a ring, how long a
pendulum is formed?
10. A clock pendulum makes four vibrations a second,
what is its length?
Fig. 82—
Escapement and
pendulum of a
clock.
Review Outline: Force and Motion
Force; definition, elements, how measured, units, dyne.
mercury for a bob. This automatically keeps the same rate of vibration
through any changes of temperature. How?
5. How will the length of a seconds pendulum at Denver, 1 mile above sea-
level, compare with one at New York? Why?
6. What is the period of a pendulum 9 in. long? Note.
In problems involving the use of the third law, use the
length of a seconds pendulum for l, and call its period
1.
7. A swing is 20 ft. high, find the time required for one
swing across the arc.
8. A pendulum is 60 cm. long. What is its period?
9. If in a gymnasium a pupil takes 3 sec. to swing once
across while hanging from a ring, how long a
pendulum is formed?
10. A clock pendulum makes four vibrations a second,
what is its length?
Fig. 82—
Escapement and
pendulum of a
clock.
Review Outline: Force and Motion
Force; definition, elements, how measured, units, dyne.
Page 130
Graphic Representation; typical examples of finding a component, a
resultant, or an equilibrant.
Motion; Laws of motion (3), inertia, curvilinear motion, centrifugal force,
momentum, (M = mv), reaction, stress and strain.
Moment of Force; parallel forces, couple, effective and non-effective
component.
Gravitation; law; gravity, center of; weight. Equilibrium 3 forms; stability,
how increased.
Falling Bodies; velocity, acceleration, "g," Laws; V = gt, S = (1/2)gt2 - s =
(1/2)g(2t - 1).
Pendulum; simple, seconds, laws (3), t = π√(l/g).
resultant, or an equilibrant.
Motion; Laws of motion (3), inertia, curvilinear motion, centrifugal force,
momentum, (M = mv), reaction, stress and strain.
Moment of Force; parallel forces, couple, effective and non-effective
component.
Gravitation; law; gravity, center of; weight. Equilibrium 3 forms; stability,
how increased.
Falling Bodies; velocity, acceleration, "g," Laws; V = gt, S = (1/2)gt2 - s =
(1/2)g(2t - 1).
Pendulum; simple, seconds, laws (3), t = π√(l/g).
Page 131
CHAPTER VI
WORK AND ENERGY
104. Work.—"Whenever a force moves a body upon which it acts, it is said
to do work upon that body." For example, if a man pushes a wheelbarrow
along a path, he is doing work on it as long as the wheelbarrow moves, but
if the wheelbarrow strikes a stone and the man continues to push and no
motion results, from a scientific point of view he is then doing no work on
it.
"Work signifies the overcoming of resistance," and unless the resistance is
overcome no work is done. Lifting a weight is doing work on it, supporting
a weight is not, although the latter may be nearly as tiresome as the former.
Work as used in science is a technical term. Do not attach to it meanings
which it has in every-day speech.
105. Measurement of Work.—Work is measured by the product of the
force by the displacement caused in the direction of the force, that is W = fs.
Therefore if a unit of force acts through a unit of space, a unit of work will
be done. There are naturally several units of work depending upon the units
of force and space employed.
English Work Unit.—If the force of one pound acts through the distance of
one foot, a foot-pound of work is done. A foot-pound is defined as the work
done when 1 lb. is lifted 1 ft. against the force of gravity.
Metric Work Unit.—If the force is one kilogram and the distance one meter,
one kilogram-meter of work is done.
Absolute Work Unit.—If the force of one dyne acts through the distance of
one centimeter a dyne-centimeter of work is done. This usually is called an
i. Other work units are sometimes used depending upon the force and
distance units employed. One, the i, is equal to 10,000,000 ergs or 107 ergs.
Problem.—If a load is drawn 2 miles by a team exerting 500 lbs. force,
how much work is done?
WORK AND ENERGY
104. Work.—"Whenever a force moves a body upon which it acts, it is said
to do work upon that body." For example, if a man pushes a wheelbarrow
along a path, he is doing work on it as long as the wheelbarrow moves, but
if the wheelbarrow strikes a stone and the man continues to push and no
motion results, from a scientific point of view he is then doing no work on
it.
"Work signifies the overcoming of resistance," and unless the resistance is
overcome no work is done. Lifting a weight is doing work on it, supporting
a weight is not, although the latter may be nearly as tiresome as the former.
Work as used in science is a technical term. Do not attach to it meanings
which it has in every-day speech.
105. Measurement of Work.—Work is measured by the product of the
force by the displacement caused in the direction of the force, that is W = fs.
Therefore if a unit of force acts through a unit of space, a unit of work will
be done. There are naturally several units of work depending upon the units
of force and space employed.
English Work Unit.—If the force of one pound acts through the distance of
one foot, a foot-pound of work is done. A foot-pound is defined as the work
done when 1 lb. is lifted 1 ft. against the force of gravity.
Metric Work Unit.—If the force is one kilogram and the distance one meter,
one kilogram-meter of work is done.
Absolute Work Unit.—If the force of one dyne acts through the distance of
one centimeter a dyne-centimeter of work is done. This usually is called an
i. Other work units are sometimes used depending upon the force and
distance units employed. One, the i, is equal to 10,000,000 ergs or 107 ergs.
Problem.—If a load is drawn 2 miles by a team exerting 500 lbs. force,
how much work is done?
Page 132
Solution.—Since the force employed is 500 lbs., and the distance is 2 ×
5280 ft., the work done is 500 × 2 × 5280 or 5,280,000 ft.-lbs.
106. Energy.—In the various cases suggested in the paragraphs upon work,
an agent, a man, an animal or a machine, was mentioned as putting forth an
effort in order to do the work. It is also true that in order to perform work an
agent must employ energy, or the energy of a body is its capacity for doing
work. Where an agent does work upon a body, as in winding up a spring or
in lifting a weight, the body upon which the work has been done may
acquire energy by having work done upon it. That is, it may become able to
do work itself upon some other body. For instance, a lifted weight in falling
back to its first position may turn wheels, or drive a post into the ground
against resistance; a coiled spring may run clock work, strike a blow, or
close a door. Hence the energy, or the capacity for doing work, is often
acquired by a body because work has first been done upon that body.
107. Potential Energy.—The wound up spring may do work because work
has first been done upon it. The lifted weight may also do work because
work has first been done in raising it to its elevated position since in falling
it may grind an object to powder, lift another weight or do some other kind
of work. The energy that a body possesses on account of its position or
shape and a stress to which it is subjected is called potential energy. The
potential energy of a body is measured by the work done in lifting it,
changing its shape, or by bringing about the conditions by which it can do
work. Thus if a block of iron weighing 2000 lbs. is lifted 20 ft., it possesses
40,000 ft.-lbs. of potential energy. It is therefore able to do 40,000 ft.-lbs. of
work in falling back to its first position. If the block just mentioned should
fall from its elevated position upon a post, it could drive the post into the
ground because its motion at the instant of striking enables it to do work. To
compute potential energy you compute the work done upon the body. That
is, P.E. = w × h or f × s.
108. Kinetic Energy.—The energy due to the motion of a body is called
kinetic energy. The amount of kinetic energy in a body may be measured by
the amount of work done to put it in motion. It is usually computed,
however, by using its mass and velocity on striking. To illustrate, a 100-lb.
ball is lifted 16 ft. The work done upon it, and hence its potential energy, is
1600 ft.-lbs. On falling to the ground again, this will be changed into kinetic
energy, or there will be 1600 ft.-lbs. of kinetic energy on striking. It will be
5280 ft., the work done is 500 × 2 × 5280 or 5,280,000 ft.-lbs.
106. Energy.—In the various cases suggested in the paragraphs upon work,
an agent, a man, an animal or a machine, was mentioned as putting forth an
effort in order to do the work. It is also true that in order to perform work an
agent must employ energy, or the energy of a body is its capacity for doing
work. Where an agent does work upon a body, as in winding up a spring or
in lifting a weight, the body upon which the work has been done may
acquire energy by having work done upon it. That is, it may become able to
do work itself upon some other body. For instance, a lifted weight in falling
back to its first position may turn wheels, or drive a post into the ground
against resistance; a coiled spring may run clock work, strike a blow, or
close a door. Hence the energy, or the capacity for doing work, is often
acquired by a body because work has first been done upon that body.
107. Potential Energy.—The wound up spring may do work because work
has first been done upon it. The lifted weight may also do work because
work has first been done in raising it to its elevated position since in falling
it may grind an object to powder, lift another weight or do some other kind
of work. The energy that a body possesses on account of its position or
shape and a stress to which it is subjected is called potential energy. The
potential energy of a body is measured by the work done in lifting it,
changing its shape, or by bringing about the conditions by which it can do
work. Thus if a block of iron weighing 2000 lbs. is lifted 20 ft., it possesses
40,000 ft.-lbs. of potential energy. It is therefore able to do 40,000 ft.-lbs. of
work in falling back to its first position. If the block just mentioned should
fall from its elevated position upon a post, it could drive the post into the
ground because its motion at the instant of striking enables it to do work. To
compute potential energy you compute the work done upon the body. That
is, P.E. = w × h or f × s.
108. Kinetic Energy.—The energy due to the motion of a body is called
kinetic energy. The amount of kinetic energy in a body may be measured by
the amount of work done to put it in motion. It is usually computed,
however, by using its mass and velocity on striking. To illustrate, a 100-lb.
ball is lifted 16 ft. The work done upon it, and hence its potential energy, is
1600 ft.-lbs. On falling to the ground again, this will be changed into kinetic
energy, or there will be 1600 ft.-lbs. of kinetic energy on striking. It will be
Page 133
noted that since energy is measured by the work it can do, work units are
always used in measuring energy. To compute the kinetic energy of a falling
body by simply using its mass and velocity one proceeds as follows, in
solving the above problem:
First, find the velocity of the falling body which has fallen 16 ft. A body
falls 16 ft. in one second. In this time it gains a velocity of 32 ft. per second.
Now using the formula for kinetic energy K.E. = wv2/(2g), we have K.E. =
100 × 32 × 32/(2 × 32) = 1600 ft.-lbs. as before. The formula, K.E. =
wv2/(2g), may be derived in the following manner:
The kinetic energy of a falling body equals the work done in giving it its
motion, that is, K.E. = w × S, in which, w = the weight of the body and S =
the distance the body must fall freely in order to acquire its velocity. The
distance fallen by a freely falling body, S, = 1/2gt2 = g2t2/(2g) (Art. 98, p.
111). Now, v = gt and v2 = g2t2.
Substituting for g2t2, its equal v2, we have S = v2/(2g). Substituting this
value of S in the equation K.E. = w × S, we have K.E. = wv2/(2g).
Since the kinetic energy of a moving body depends upon its mass and
velocity and not upon the direction of motion, this formula may be used to
find the kinetic energy of any moving body. Mass and weight in such
problems may be considered numerically equal.
Important Topics
1. Work defined.
2. Work units, foot-pound, kilogram-meter, erg.
3. Energy defined.
4. Kinds of energy, potential and kinetic.
Problems
1. How much work will a 120-lb. boy do climbing a mountain 3000 ft.
high? Should the vertical or slant height be used? Why?
2. In a mine 4000 kg. of coal are lifted 223 meters: how much work is done
upon the coal? What is the kind and amount of energy possessed by the
coal?
always used in measuring energy. To compute the kinetic energy of a falling
body by simply using its mass and velocity one proceeds as follows, in
solving the above problem:
First, find the velocity of the falling body which has fallen 16 ft. A body
falls 16 ft. in one second. In this time it gains a velocity of 32 ft. per second.
Now using the formula for kinetic energy K.E. = wv2/(2g), we have K.E. =
100 × 32 × 32/(2 × 32) = 1600 ft.-lbs. as before. The formula, K.E. =
wv2/(2g), may be derived in the following manner:
The kinetic energy of a falling body equals the work done in giving it its
motion, that is, K.E. = w × S, in which, w = the weight of the body and S =
the distance the body must fall freely in order to acquire its velocity. The
distance fallen by a freely falling body, S, = 1/2gt2 = g2t2/(2g) (Art. 98, p.
111). Now, v = gt and v2 = g2t2.
Substituting for g2t2, its equal v2, we have S = v2/(2g). Substituting this
value of S in the equation K.E. = w × S, we have K.E. = wv2/(2g).
Since the kinetic energy of a moving body depends upon its mass and
velocity and not upon the direction of motion, this formula may be used to
find the kinetic energy of any moving body. Mass and weight in such
problems may be considered numerically equal.
Important Topics
1. Work defined.
2. Work units, foot-pound, kilogram-meter, erg.
3. Energy defined.
4. Kinds of energy, potential and kinetic.
Problems
1. How much work will a 120-lb. boy do climbing a mountain 3000 ft.
high? Should the vertical or slant height be used? Why?
2. In a mine 4000 kg. of coal are lifted 223 meters: how much work is done
upon the coal? What is the kind and amount of energy possessed by the
coal?
Page 134
3. A pile driver weighs 450 lbs. It is lifted 16 ft. How much work has been
done upon it? What kind and amount of energy will it have after falling 16
ft. to the pile?
4. A train weighing 400 tons is moving 30 miles per hour. Compute its
kinetic energy. (Change its weight to pounds and velocity to feet per
second.)
5. What would be the kinetic energy of the train in problem 4 if it were
going 60 miles per hour? If it were going 90 miles per hour? How does
doubling or trebling the speed of an object affect its kinetic energy? How
does it affect its momentum?
6. What is the kinetic energy of a 1600-lb. cannon ball moving 2000 ft. per
second?
7. Mention as many kinds of mechanical work as you can and show how
each satisfies the definition of work.
8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work is done
upon it?
9. If the pile driver in problem 8 is dropped upon the head of a pile which
meets an average resistance of 30,000 lbs., how far will one blow drive it?
10. A 40 kg. stone is placed upon the top of a chimney 50 meters high.
Compute the work done in kilogram-meters and foot-pounds.
(2) Power and Energy
109. Horse-power.—In computing work, no account is taken of the time
required to accomplish it. But since the time needed to perform an
undertaking is of much importance, the rate of work, or the power or
activity of an agent is an important factor. Thus if one machine can do a
piece of work in one-fifth the time required by another machine, it is said to
have five times the power of the other. Therefore the power of a machine is
the rate at which it can do work. James Watt (1736-1819), the inventor of
the steam-engine, in expressing the power of his engine, used as a unit a
horse-power. He considered that a horse could do 33,000 ft.-lbs. of work a
minute. This is equal to 550 ft.-lbs. per second or 76.05 kg.-m. per second.
This is too high a value but it has been used ever since his time. Steam
engines usually have their power rated in horse-power. That is, locomotives
done upon it? What kind and amount of energy will it have after falling 16
ft. to the pile?
4. A train weighing 400 tons is moving 30 miles per hour. Compute its
kinetic energy. (Change its weight to pounds and velocity to feet per
second.)
5. What would be the kinetic energy of the train in problem 4 if it were
going 60 miles per hour? If it were going 90 miles per hour? How does
doubling or trebling the speed of an object affect its kinetic energy? How
does it affect its momentum?
6. What is the kinetic energy of a 1600-lb. cannon ball moving 2000 ft. per
second?
7. Mention as many kinds of mechanical work as you can and show how
each satisfies the definition of work.
8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work is done
upon it?
9. If the pile driver in problem 8 is dropped upon the head of a pile which
meets an average resistance of 30,000 lbs., how far will one blow drive it?
10. A 40 kg. stone is placed upon the top of a chimney 50 meters high.
Compute the work done in kilogram-meters and foot-pounds.
(2) Power and Energy
109. Horse-power.—In computing work, no account is taken of the time
required to accomplish it. But since the time needed to perform an
undertaking is of much importance, the rate of work, or the power or
activity of an agent is an important factor. Thus if one machine can do a
piece of work in one-fifth the time required by another machine, it is said to
have five times the power of the other. Therefore the power of a machine is
the rate at which it can do work. James Watt (1736-1819), the inventor of
the steam-engine, in expressing the power of his engine, used as a unit a
horse-power. He considered that a horse could do 33,000 ft.-lbs. of work a
minute. This is equal to 550 ft.-lbs. per second or 76.05 kg.-m. per second.
This is too high a value but it has been used ever since his time. Steam
engines usually have their power rated in horse-power. That is, locomotives
Page 135
produce from 500 to 1500 horse-power. Some stationary and marine
engines develop as high as 25,000 horse-power. The power of an average
horse is about 3/4 horse-power and of a man about 1/7 horse-power when
working continuously for several hours.
110. The Watt.—In the metric system, the erg as a unit of work would give
as a unit of power 1 erg per second. This amount is so small, however, that
a larger unit is usually employed, the practical unit being 10,000,000 ergs a
second, that is, one joule per second. (See Art. 105.) This practical unit is
called a Watt after James Watt. The power of dynamos is usually expressed
in kilowatts, a kilowatt representing 1000 watts. Steam-engines in modern
practice are often rated in kilowatts instead of horse-power. A horse-power
is equivalent to 746 watts, or is nearly 3/4 of a kilowatt.
111. Energy. Its Transference and Transformation. We have considered
energy as the capacity for doing work, and noted the two kinds, potential
and kinetic, and the facility with which one may change into another. In
fact, the transference of energy from one body to another, and its
transformation from one form to another is one of the most common
processes in nature. Take a pendulum in motion, at the end of a swing, its
energy being entirely due to its elevated position is all potential; at the
lowest point in its path its energy being entirely due to its motion is all
kinetic. The change goes on automatically as long as the pendulum swings.
A motor attached by a belt to a washing machine is started running. The
energy of the motor is transferred by the belt to the washer where it is used
in rubbing and moving the clothes.
The heat used in warming a house is usually obtained by burning coal or
wood. Coal is believed to be formed from the remains of plants that grew in
former geologic times. These plants grew through the help of the radiant
energy of the sun. The following are transformations of energy that have
occurred: The radiant energy of sunlight was transformed into the chemical
energy of the plants. This remained as chemical energy while the plants
were being converted into coal, was mined, brought to the stove or furnace
and burned. The burning transformed the chemical energy into heat energy
in which form we use it for warming rooms. Take the energy used in
running a street car whose electrical energy comes from a waterfall. The
energy of the car itself is mechanical. Its motor, however, receives electrical
energy and transforms it into mechanical. This electrical energy comes
engines develop as high as 25,000 horse-power. The power of an average
horse is about 3/4 horse-power and of a man about 1/7 horse-power when
working continuously for several hours.
110. The Watt.—In the metric system, the erg as a unit of work would give
as a unit of power 1 erg per second. This amount is so small, however, that
a larger unit is usually employed, the practical unit being 10,000,000 ergs a
second, that is, one joule per second. (See Art. 105.) This practical unit is
called a Watt after James Watt. The power of dynamos is usually expressed
in kilowatts, a kilowatt representing 1000 watts. Steam-engines in modern
practice are often rated in kilowatts instead of horse-power. A horse-power
is equivalent to 746 watts, or is nearly 3/4 of a kilowatt.
111. Energy. Its Transference and Transformation. We have considered
energy as the capacity for doing work, and noted the two kinds, potential
and kinetic, and the facility with which one may change into another. In
fact, the transference of energy from one body to another, and its
transformation from one form to another is one of the most common
processes in nature. Take a pendulum in motion, at the end of a swing, its
energy being entirely due to its elevated position is all potential; at the
lowest point in its path its energy being entirely due to its motion is all
kinetic. The change goes on automatically as long as the pendulum swings.
A motor attached by a belt to a washing machine is started running. The
energy of the motor is transferred by the belt to the washer where it is used
in rubbing and moving the clothes.
The heat used in warming a house is usually obtained by burning coal or
wood. Coal is believed to be formed from the remains of plants that grew in
former geologic times. These plants grew through the help of the radiant
energy of the sun. The following are transformations of energy that have
occurred: The radiant energy of sunlight was transformed into the chemical
energy of the plants. This remained as chemical energy while the plants
were being converted into coal, was mined, brought to the stove or furnace
and burned. The burning transformed the chemical energy into heat energy
in which form we use it for warming rooms. Take the energy used in
running a street car whose electrical energy comes from a waterfall. The
energy of the car itself is mechanical. Its motor, however, receives electrical
energy and transforms it into mechanical. This electrical energy comes
Page 136
along a wire from a dynamo at the waterfall, where water-wheels and
generators transform into electrical energy the mechanical energy of the
falling water. The water obtained its energy of position by being evaporated
by the heat of the radiant energy of the sun. The vapor rising into the air is
condensed into clouds and rain, and falling on the mountain side, has, from
its elevated position, potential energy. The order of transformation,
therefore, is in this case, radiant, heat, mechanical, electrical, and
mechanical. Can you trace the energy from the sun step by step to the
energy you are using in reading this page?
112. Forms of Energy.—A steam-engine attached to a train of cars
employs its energy in setting the cars in motion, i.e., in giving them kinetic
energy and in overcoming resistance to motion. But what is the source of
the energy of the engine? It is found in the coal which it carries in its tender.
But of what kind? Surely not kinetic, as no motion is seen. It is therefore
potential. What is the source of the energy of the coal? This question leads
us back to the time of the formation of coal beds, when plants grew in the
sunlight and stored up the energy of the sun's heat and light as chemical
energy. The sun's light brings to the earth the energy of the sun, that central
storehouse of energy, which has supplied nearly all the available energy
upon the earth. Five forms of energy are known, viz., mechanical, heat,
electrical, radiant, and chemical.
113. Energy Recognized by its Effects.—Like force, energy is invisible
and we are aware of the forms only by the effects produced by it.
We recognize heat by warming, by expansion, by pressure.
We recognize light by warming, by its affecting vision.
We recognize electrical energy by its heat, light, motion, or magnetic effect.
We recognize mechanical energy by the motion that it produces. We
recognize chemical energy by knowing that the source of energy does not
belong to any of the foregoing.
A boy or girl is able to do considerable work. They therefore possess
energy. In what form does the energy of the body mainly occur? One can
determine this for himself by applying questions to each form of energy in
turn as in Art. 114.
generators transform into electrical energy the mechanical energy of the
falling water. The water obtained its energy of position by being evaporated
by the heat of the radiant energy of the sun. The vapor rising into the air is
condensed into clouds and rain, and falling on the mountain side, has, from
its elevated position, potential energy. The order of transformation,
therefore, is in this case, radiant, heat, mechanical, electrical, and
mechanical. Can you trace the energy from the sun step by step to the
energy you are using in reading this page?
112. Forms of Energy.—A steam-engine attached to a train of cars
employs its energy in setting the cars in motion, i.e., in giving them kinetic
energy and in overcoming resistance to motion. But what is the source of
the energy of the engine? It is found in the coal which it carries in its tender.
But of what kind? Surely not kinetic, as no motion is seen. It is therefore
potential. What is the source of the energy of the coal? This question leads
us back to the time of the formation of coal beds, when plants grew in the
sunlight and stored up the energy of the sun's heat and light as chemical
energy. The sun's light brings to the earth the energy of the sun, that central
storehouse of energy, which has supplied nearly all the available energy
upon the earth. Five forms of energy are known, viz., mechanical, heat,
electrical, radiant, and chemical.
113. Energy Recognized by its Effects.—Like force, energy is invisible
and we are aware of the forms only by the effects produced by it.
We recognize heat by warming, by expansion, by pressure.
We recognize light by warming, by its affecting vision.
We recognize electrical energy by its heat, light, motion, or magnetic effect.
We recognize mechanical energy by the motion that it produces. We
recognize chemical energy by knowing that the source of energy does not
belong to any of the foregoing.
A boy or girl is able to do considerable work. They therefore possess
energy. In what form does the energy of the body mainly occur? One can
determine this for himself by applying questions to each form of energy in
turn as in Art. 114.
Page 137
114. Source of the Energy of the Human Body.—Is the energy of the human
body mostly heat? No, since we are not very warm. Is it light or electrical?
Evidently not since we are neither luminous nor electrical. Is it mechanical?
No, since we have our energy even when at rest. Is it chemical? It must be
since it is none of the others. Chemical energy is contained within the
molecule.
It is a form of potential energy and it is believed to be due to the position of
the atoms within the molecule. As a tightly coiled watch spring may have
much energy within it, which is set free on allowing the spring to uncoil, so
the chemical energy is released on starting the chemical reaction.
Gunpowder and dynamite are examples of substances containing chemical
energy. On exploding these, heat, light, and motion are produced. Gasoline,
kerosene, and illuminating gas are purchased because of the potential
energy they contain. This energy is set free by burning or exploding them.
The source of the energy of our bodies is of course the food we eat. The
energy contained in the food is also chemical. Vegetables obtain their
energy from the sunlight (radiant energy). This is why plants will not grow
in the dark. The available energy is mostly contained in the form of starch,
sugar and oil. Digestion is employed principally to dissolve these
substances so that the blood may absorb them and carry them to the tissues
of the body where they are needed. The energy is set free by oxidation
(burning), the oxygen needed for this being supplied by breathing.
Breathing also removes the carbon dioxide, which results from the
combustion. It is for its energy that our food is mostly required.
115. Conservation of Energy.—In the study of matter we learned that it is
indestructible. Energy is also believed to be indestructible. This principle
stated concisely teaches that despite the innumerable changes which energy
undergoes the amount in the universe is unchangeable, and while energy
may leave the earth and be lost as far as we are concerned, that it exists
somewhere in some form. The principle which teaches this is called the
"Conservation of Energy." The form into which energy is finally
transformed is believed to be heat.
Important Topics
body mostly heat? No, since we are not very warm. Is it light or electrical?
Evidently not since we are neither luminous nor electrical. Is it mechanical?
No, since we have our energy even when at rest. Is it chemical? It must be
since it is none of the others. Chemical energy is contained within the
molecule.
It is a form of potential energy and it is believed to be due to the position of
the atoms within the molecule. As a tightly coiled watch spring may have
much energy within it, which is set free on allowing the spring to uncoil, so
the chemical energy is released on starting the chemical reaction.
Gunpowder and dynamite are examples of substances containing chemical
energy. On exploding these, heat, light, and motion are produced. Gasoline,
kerosene, and illuminating gas are purchased because of the potential
energy they contain. This energy is set free by burning or exploding them.
The source of the energy of our bodies is of course the food we eat. The
energy contained in the food is also chemical. Vegetables obtain their
energy from the sunlight (radiant energy). This is why plants will not grow
in the dark. The available energy is mostly contained in the form of starch,
sugar and oil. Digestion is employed principally to dissolve these
substances so that the blood may absorb them and carry them to the tissues
of the body where they are needed. The energy is set free by oxidation
(burning), the oxygen needed for this being supplied by breathing.
Breathing also removes the carbon dioxide, which results from the
combustion. It is for its energy that our food is mostly required.
115. Conservation of Energy.—In the study of matter we learned that it is
indestructible. Energy is also believed to be indestructible. This principle
stated concisely teaches that despite the innumerable changes which energy
undergoes the amount in the universe is unchangeable, and while energy
may leave the earth and be lost as far as we are concerned, that it exists
somewhere in some form. The principle which teaches this is called the
"Conservation of Energy." The form into which energy is finally
transformed is believed to be heat.
Important Topics
Page 138
1. Power defined. Units. Horse-power. Watt.
2. Transference and transformations of energy.
3. Forms of energy; heat, electrical, mechanical, radiant, chemical.
4. Effects of the several forms of energy.
5. Energy of the human body.
6. Conservation of energy.
Exercises
1. A boy weighing 110 lbs. ran up a stairs 10 ft. high, in 4 seconds. How
much work was done? What was his rate of work (foot-pounds per
second)? Express also in horse-power.
2. A locomotive drawing a train exerts a draw bar pull of 11,000 lbs. How
much work does it do in moving 3 miles? What is its rate of work if it
moves 3 miles in 5 minutes? Express in horse-power.[G]
3. If 400 kg. are lifted 35 meters in 5 seconds what work is done? What is
the rate of work? Express in horse-power, watts and kilowatts.
4. Trace the energy of a moving railway train back to its source in the sun.
5. Why does turning the propeller of a motor boat cause the boat to move?
6. Does it require more power to go up a flight of stairs in 5 seconds than in
10 seconds? Explain. Is more work done in one case than in the other?
Why?
7. Can 1 man carrying bricks up to a certain elevation for 120 days do as
much work as 120 men carrying up bricks for 1 day?
8. If the 1 man and 120 men of problem 7 do the same amount of work have
they the same power? Explain.
9. If 160 cu. ft. of water flow each second over a dam 15ft. high what is the
available power?
10. What power must an engine have to fill a tank 11 × 8 × 5 ft. with water
120 ft. above the supply, in 5 minutes?
2. Transference and transformations of energy.
3. Forms of energy; heat, electrical, mechanical, radiant, chemical.
4. Effects of the several forms of energy.
5. Energy of the human body.
6. Conservation of energy.
Exercises
1. A boy weighing 110 lbs. ran up a stairs 10 ft. high, in 4 seconds. How
much work was done? What was his rate of work (foot-pounds per
second)? Express also in horse-power.
2. A locomotive drawing a train exerts a draw bar pull of 11,000 lbs. How
much work does it do in moving 3 miles? What is its rate of work if it
moves 3 miles in 5 minutes? Express in horse-power.[G]
3. If 400 kg. are lifted 35 meters in 5 seconds what work is done? What is
the rate of work? Express in horse-power, watts and kilowatts.
4. Trace the energy of a moving railway train back to its source in the sun.
5. Why does turning the propeller of a motor boat cause the boat to move?
6. Does it require more power to go up a flight of stairs in 5 seconds than in
10 seconds? Explain. Is more work done in one case than in the other?
Why?
7. Can 1 man carrying bricks up to a certain elevation for 120 days do as
much work as 120 men carrying up bricks for 1 day?
8. If the 1 man and 120 men of problem 7 do the same amount of work have
they the same power? Explain.
9. If 160 cu. ft. of water flow each second over a dam 15ft. high what is the
available power?
10. What power must an engine have to fill a tank 11 × 8 × 5 ft. with water
120 ft. above the supply, in 5 minutes?
Page 139
11. A hod carrier weighing 150 lbs. carries a load of bricks weighing 100
lbs. up a ladder 30 ft. high. How much work does he do?
12. How much work can a 4-horse-power engine do in 5 minutes?
13. Find the horse-power of a windmill that pumps 6 tons of water from a
well 90 ft. deep in 30 minutes.
14. How many horse-power are there in a waterfall 20 ft. high over which
500 cu. ft. of water pass in a minute?
15. The Chicago drainage canal has a flow of about 6000 cu. ft. a second. If
at the controlling works there is an available fall of 34 ft. how many horse-
power can be developed?
16. How long will it take a 10-horse-power pump to fill a tank of 4000
gallons capacity, standing 300 ft. above the pump?
17. A boy weighing 162 lbs. climbs a stairway a vertical height of 14 ft. in
14.6 seconds. How much power does he exert?
18. The same boy does the same work a second time in 4.2 seconds. How
much power does he exert this time? What causes the difference?
19. What is a horse-power-hour? a kilowatt-hour?
(3) Simple Machines and the Lever
116. Machines and Their Uses.—A man, while standing on the ground,
can draw a flag to the top of a pole, by using a rope passing over a pulley.
A boy can unscrew a tightly fitting nut that he cannot move with his fingers,
by using a wrench.
A woman can sew a long seam by using a sewing machine in much less
time than by hand.
A girl can button her shoes much quicker and easier with a button-hook
than with her fingers.
These illustrations show some of the reasons why machines are used. In fact
it is almost impossible to do any kind of work efficiently without using one
or more machines.
lbs. up a ladder 30 ft. high. How much work does he do?
12. How much work can a 4-horse-power engine do in 5 minutes?
13. Find the horse-power of a windmill that pumps 6 tons of water from a
well 90 ft. deep in 30 minutes.
14. How many horse-power are there in a waterfall 20 ft. high over which
500 cu. ft. of water pass in a minute?
15. The Chicago drainage canal has a flow of about 6000 cu. ft. a second. If
at the controlling works there is an available fall of 34 ft. how many horse-
power can be developed?
16. How long will it take a 10-horse-power pump to fill a tank of 4000
gallons capacity, standing 300 ft. above the pump?
17. A boy weighing 162 lbs. climbs a stairway a vertical height of 14 ft. in
14.6 seconds. How much power does he exert?
18. The same boy does the same work a second time in 4.2 seconds. How
much power does he exert this time? What causes the difference?
19. What is a horse-power-hour? a kilowatt-hour?
(3) Simple Machines and the Lever
116. Machines and Their Uses.—A man, while standing on the ground,
can draw a flag to the top of a pole, by using a rope passing over a pulley.
A boy can unscrew a tightly fitting nut that he cannot move with his fingers,
by using a wrench.
A woman can sew a long seam by using a sewing machine in much less
time than by hand.
A girl can button her shoes much quicker and easier with a button-hook
than with her fingers.
These illustrations show some of the reasons why machines are used. In fact
it is almost impossible to do any kind of work efficiently without using one
or more machines.
Page 140
117. Advantages of Machines.—(a) Many machines make possible an
increased speed as in a sewing machine or a bicycle.
(b) Other machines exert an increased force. A rope and a set of pulleys
may enable a man to lift a heavy object such as a safe or a piano. By the use
of a bar a man can more easily move a large rock. (See Fig. 83.)
increased speed as in a sewing machine or a bicycle.
(b) Other machines exert an increased force. A rope and a set of pulleys
may enable a man to lift a heavy object such as a safe or a piano. By the use
of a bar a man can more easily move a large rock. (See Fig. 83.)
Page 141
(c) The direction of a force may be changed thus
enabling work to be done that could not be readily
accomplished otherwise. As, e.g., the use of a pulley
in raising a flag to the top of a flag pole, or in
raising a bucket of ore from a mine by using a horse
attached to a rope passing over two or more pulleys.
(See Fig. 84.) Fig. 83.—The rock
(d) Other agents than man or animals can be used is easily moved.
such as electricity, water power, the wind, steam,
etc. Fig. 85 represents a windmill often used in pumping water.
A machine is a device for transferring or transforming energy. It is usually
therefore an instrument for doing work. An electric motor is a machine
since it transforms the energy of the electric current into motion or
mechanical energy, and transfers the energy from the wire to the driving
pulley.
Fig. 84.—The horse lifts the bucket of ore.
118. A Machine Cannot Create Energy.—Whatever does work upon a
machine (a man, moving water, wind, etc.) loses energy which is employed
in doing the work of the machine. A pair of shears is a machine since it
transfers energy from the hand to the edges that do the cutting. Our own
bodies are often considered as machines since they both transfer and
transform energy.
enabling work to be done that could not be readily
accomplished otherwise. As, e.g., the use of a pulley
in raising a flag to the top of a flag pole, or in
raising a bucket of ore from a mine by using a horse
attached to a rope passing over two or more pulleys.
(See Fig. 84.) Fig. 83.—The rock
(d) Other agents than man or animals can be used is easily moved.
such as electricity, water power, the wind, steam,
etc. Fig. 85 represents a windmill often used in pumping water.
A machine is a device for transferring or transforming energy. It is usually
therefore an instrument for doing work. An electric motor is a machine
since it transforms the energy of the electric current into motion or
mechanical energy, and transfers the energy from the wire to the driving
pulley.
Fig. 84.—The horse lifts the bucket of ore.
118. A Machine Cannot Create Energy.—Whatever does work upon a
machine (a man, moving water, wind, etc.) loses energy which is employed
in doing the work of the machine. A pair of shears is a machine since it
transfers energy from the hand to the edges that do the cutting. Our own
bodies are often considered as machines since they both transfer and
transform energy.
Page 142
We must keep in mind that a machine cannot create energy. The principle
of "Conservation of Energy" is just as explicit on one side as the other. Just
as energy, cannot be destroyed, so energy cannot be created. A machine can
give out no more energy than is given to it. It acts simply as an agent in
transferring energy from one body to another. Many efforts have been made
to construct machines that when once started will run themselves, giving
out more energy than they receive. Such efforts, called seeking for
perpetual motion, have never succeeded. This fact is strong evidence in
favor of the principle of the conservation of energy.
119. Law of Machines.—When a body receives
energy, work is done upon it. Therefore work is
done upon a machine when it receives energy
and the machine does work upon the body to
which it gives the energy. In the operation of a
machine, therefore, two quantities of work are to
be considered and by the principle of the
conservation of energy, these two must be equal.
The work done by a machine equals the work
done upon it, or the energy given out by a
machine equals the energy received by it. These
two quantities of work must each be composed
of a force factor and a space factor. Therefore
two forces and two spaces are to be considered
in the operation of a machine. The force factor
of the work done on the machine is called the
force or effort. It is the force applied to the
machine. The force factor of the work done by a
machine is called the weight or resistance. It is
the force exerted by the machine in overcoming
the resistance and equals the resistance Fig. 85.—A windmill.
overcome.
If f represents the force or effort, and Df the space it acts through, and w
represents the weight or resistance, and Dw the space it acts through, then
the law of machines may be expressed by an equation, f × Df = w × Dw.
That is, the effort times the distance the effort acts equals the resistance
times the distance the resistance is moved or overcome. When the product
of "Conservation of Energy" is just as explicit on one side as the other. Just
as energy, cannot be destroyed, so energy cannot be created. A machine can
give out no more energy than is given to it. It acts simply as an agent in
transferring energy from one body to another. Many efforts have been made
to construct machines that when once started will run themselves, giving
out more energy than they receive. Such efforts, called seeking for
perpetual motion, have never succeeded. This fact is strong evidence in
favor of the principle of the conservation of energy.
119. Law of Machines.—When a body receives
energy, work is done upon it. Therefore work is
done upon a machine when it receives energy
and the machine does work upon the body to
which it gives the energy. In the operation of a
machine, therefore, two quantities of work are to
be considered and by the principle of the
conservation of energy, these two must be equal.
The work done by a machine equals the work
done upon it, or the energy given out by a
machine equals the energy received by it. These
two quantities of work must each be composed
of a force factor and a space factor. Therefore
two forces and two spaces are to be considered
in the operation of a machine. The force factor
of the work done on the machine is called the
force or effort. It is the force applied to the
machine. The force factor of the work done by a
machine is called the weight or resistance. It is
the force exerted by the machine in overcoming
the resistance and equals the resistance Fig. 85.—A windmill.
overcome.
If f represents the force or effort, and Df the space it acts through, and w
represents the weight or resistance, and Dw the space it acts through, then
the law of machines may be expressed by an equation, f × Df = w × Dw.
That is, the effort times the distance the effort acts equals the resistance
times the distance the resistance is moved or overcome. When the product
Page 143
of two numbers equals the product of two other numbers either pair may be
made the means and the other the extremes of a proportion. The equation
given above may therefore be expressed w: f = Df: Dw. Or the resistance is
to the effort as the effort distance is to the resistance distance. The law of
machines may therefore be expressed in several ways. One should keep in
mind, however, that the same law of machines is expressed even though the
form be different. What two ways of expressing the law are given?
120. The Simple Machines.—There are but six simple machines. All the
varieties of machines known are simply modifications and combinations of
the six simple machines. The six simple machines are more easily
remembered if we separate them into two groups of three each. The first or
lever group consists of those machines in which a part revolves about a
fixed axis. It contains the lever, pulley and wheel and axle. The second or
inclined plane group includes those having a sloping surface. It contains the
inclined plane, the wedge, and the screw.
121. The Lever.—The lever is one of the simple machines most frequently
used, being seen in scissors, broom, coal shovel, whip, wheelbarrow, tongs,
etc. The lever consists of a rigid bar capable of turning about a fixed axis
called the fulcrum. In studying a lever, one wishes to know what weight or
resistance it can overcome when a certain force is applied to it. Diagrams of
levers, therefore, contain the letters w and f. In addition to these, O stands
for the fulcrum on which it turns. By referring to Fig. 86, a, b, c, one may
notice that each of these may occupy the middle position between the other
two. The two forces (other than the one exerted by the fulcrum) acting on a
lever always oppose each other in the matter of changing rotation. They
may be considered as a pair of parallel forces acting on a body, each tending
to produce rotation.
made the means and the other the extremes of a proportion. The equation
given above may therefore be expressed w: f = Df: Dw. Or the resistance is
to the effort as the effort distance is to the resistance distance. The law of
machines may therefore be expressed in several ways. One should keep in
mind, however, that the same law of machines is expressed even though the
form be different. What two ways of expressing the law are given?
120. The Simple Machines.—There are but six simple machines. All the
varieties of machines known are simply modifications and combinations of
the six simple machines. The six simple machines are more easily
remembered if we separate them into two groups of three each. The first or
lever group consists of those machines in which a part revolves about a
fixed axis. It contains the lever, pulley and wheel and axle. The second or
inclined plane group includes those having a sloping surface. It contains the
inclined plane, the wedge, and the screw.
121. The Lever.—The lever is one of the simple machines most frequently
used, being seen in scissors, broom, coal shovel, whip, wheelbarrow, tongs,
etc. The lever consists of a rigid bar capable of turning about a fixed axis
called the fulcrum. In studying a lever, one wishes to know what weight or
resistance it can overcome when a certain force is applied to it. Diagrams of
levers, therefore, contain the letters w and f. In addition to these, O stands
for the fulcrum on which it turns. By referring to Fig. 86, a, b, c, one may
notice that each of these may occupy the middle position between the other
two. The two forces (other than the one exerted by the fulcrum) acting on a
lever always oppose each other in the matter of changing rotation. They
may be considered as a pair of parallel forces acting on a body, each tending
to produce rotation.
Page 144
Fig. 86.—The three classes of levers.
122. Moment of Force.—The effectiveness of each force may therefore be
determined by computing its moment about the fixed axis (see Art. 84), that
is, by multiplying each force by its distance to the fulcrum or axis of
rotation. Let a meter stick have a small hole bored through it at the 50 cm.
mark near one edge, and let it be mounted on a nail driven into a vertical
support and balanced by sliding a bent wire along it. Suspend by a fine wire
or thread a 100 g. weight, 15 cm. from the nail and a 50 g. weight 30 cm.
from the nail, on the other side of the support. These two weights will be
found to balance. When viewed from this side A (Fig. 87) tends to turn the
lever in a clockwise direction (down at right), B in the counter-clockwise
direction (down at left). Since the lever balances, the forces have equal and
opposite effects in changing its rotation as may also be computed by
determining the moment of each force by multiplying each by its distance
from the fulcrum. Therefore the effectiveness of a force in changing rotation
depends upon the distance from it to the axis as well as upon the magnitude
of the force.
From the experiment just described, the
moment of the acting force equals the
moment of the weight or f × Df = w × Dw,
or the effort times the effort arm equals
the weight times the weight arm. This
equation is called the law of the lever. It
corresponds to the general law of
machines and may also be written w: f =
Fig. 87.—The two moments D f: D w .
are equal about C. 100 × 15 =
50 × 30 123. Mechanical Advantage.—A lever
often gives an advantage because by its
use one may lift a stone or weight which the unaided strength of man could
not move. If the lever is used in lifting a stone weighing 500 lbs., the force
available being only 100 lbs., then its mechanical advantage would be 5,
the ratio of w:f. In a similar way, the mechanical advantage of any machine
is found by finding the ratio of the resistance or weight to the effort. What
must be the relative lengths of the effort arm and resistance or weight arm
in the example just mentioned? Since the effort times the effort arm equals
122. Moment of Force.—The effectiveness of each force may therefore be
determined by computing its moment about the fixed axis (see Art. 84), that
is, by multiplying each force by its distance to the fulcrum or axis of
rotation. Let a meter stick have a small hole bored through it at the 50 cm.
mark near one edge, and let it be mounted on a nail driven into a vertical
support and balanced by sliding a bent wire along it. Suspend by a fine wire
or thread a 100 g. weight, 15 cm. from the nail and a 50 g. weight 30 cm.
from the nail, on the other side of the support. These two weights will be
found to balance. When viewed from this side A (Fig. 87) tends to turn the
lever in a clockwise direction (down at right), B in the counter-clockwise
direction (down at left). Since the lever balances, the forces have equal and
opposite effects in changing its rotation as may also be computed by
determining the moment of each force by multiplying each by its distance
from the fulcrum. Therefore the effectiveness of a force in changing rotation
depends upon the distance from it to the axis as well as upon the magnitude
of the force.
From the experiment just described, the
moment of the acting force equals the
moment of the weight or f × Df = w × Dw,
or the effort times the effort arm equals
the weight times the weight arm. This
equation is called the law of the lever. It
corresponds to the general law of
machines and may also be written w: f =
Fig. 87.—The two moments D f: D w .
are equal about C. 100 × 15 =
50 × 30 123. Mechanical Advantage.—A lever
often gives an advantage because by its
use one may lift a stone or weight which the unaided strength of man could
not move. If the lever is used in lifting a stone weighing 500 lbs., the force
available being only 100 lbs., then its mechanical advantage would be 5,
the ratio of w:f. In a similar way, the mechanical advantage of any machine
is found by finding the ratio of the resistance or weight to the effort. What
must be the relative lengths of the effort arm and resistance or weight arm
in the example just mentioned? Since the effort times the effort arm equals
Page 145
the weight times the weight arm, if f × Df = w × Dw, then Df is five times
Dw. Hence the mechanical advantage of a lever is easily found by finding
the ratio of the effort arm to the weight arm.
Important Topics
1. Advantage of machines.
2. Machines cannot create energy.
3. Law of machines.
4. Six simple machines.
5. Lever and principle of moments.
6. Mechanical advantage of a machine.
Exercises
1. Give six examples of levers you use.
2. Fig. 88a represents a pair of paper shears, 88b a pair of tinner's shears.
Which has the greater mechanical advantage? Why? Explain why each has
the most effective shape for its particular work.
Fig. 88.—(a) Paper shears. (b) Tinner's shears.
3. Find examples of levers in a sewing machine.
4. What would result if, in Art. 122, the 100 g. weight were put 25 cm. from
O and the 50 g. weight 45 cm. from O? Why? Explain using principle of
moments.
5. How is the lever principle applied in rowing a boat?
Dw. Hence the mechanical advantage of a lever is easily found by finding
the ratio of the effort arm to the weight arm.
Important Topics
1. Advantage of machines.
2. Machines cannot create energy.
3. Law of machines.
4. Six simple machines.
5. Lever and principle of moments.
6. Mechanical advantage of a machine.
Exercises
1. Give six examples of levers you use.
2. Fig. 88a represents a pair of paper shears, 88b a pair of tinner's shears.
Which has the greater mechanical advantage? Why? Explain why each has
the most effective shape for its particular work.
Fig. 88.—(a) Paper shears. (b) Tinner's shears.
3. Find examples of levers in a sewing machine.
4. What would result if, in Art. 122, the 100 g. weight were put 25 cm. from
O and the 50 g. weight 45 cm. from O? Why? Explain using principle of
moments.
5. How is the lever principle applied in rowing a boat?
Page 146
6. When you cut cardboard with shears, why do you open them wide and
cut near the pivot?
7. In carrying a load on a stick over the shoulder should the pack be carried
near the shoulder or out on the stick? Why?
8. How can two boys on a see-saw start it without touching the ground?
9. In lifting a shovel full of sand do you lift up with one hand as hard as you
push down with the other? Why?
10. Why must the hinges of a gate 3 ft. high and 16
ft. wide be stronger than the hinges of a gate 16 ft.
high and 3 ft. wide?
11. When one sweeps with a broom do the hands
do equal amounts of work? Explain.
12. A bar 6 ft. long is used as a lever to lift a
weight of 500 lbs. If the fulcrum is placed 6 in.
from the weight, what will be the effort required?
Note: two arrangements of weight, fulcrum and
effort are possible.
13. The handle of a hammer is 12 in. long and the
claw that is used in drawing a nail is 2.5 in. long.
(See Fig. 89.) A force of 25 lbs. is required to draw
the nail. What is the resistance of the nail?
14. The effective length of the head of a hammer is
2 in. The handle is 15 in. long and the nail holds in Fig. 89.—The
the wood with a force of 500 lbs. Only 60 lbs. of hammer is a bent
force is available at the end of the handle. What lever. What is its
will be the result? mechanical
15. If an effort of 50 lbs. acting on a machine advantage?
moves 10 ft., how far can it lift a weight of 1000
lbs.?
16. A bar 10 ft. long is to be used as a lever. The weight is kept 2 ft. from
the fulcrum. What different levers can it represent?
cut near the pivot?
7. In carrying a load on a stick over the shoulder should the pack be carried
near the shoulder or out on the stick? Why?
8. How can two boys on a see-saw start it without touching the ground?
9. In lifting a shovel full of sand do you lift up with one hand as hard as you
push down with the other? Why?
10. Why must the hinges of a gate 3 ft. high and 16
ft. wide be stronger than the hinges of a gate 16 ft.
high and 3 ft. wide?
11. When one sweeps with a broom do the hands
do equal amounts of work? Explain.
12. A bar 6 ft. long is used as a lever to lift a
weight of 500 lbs. If the fulcrum is placed 6 in.
from the weight, what will be the effort required?
Note: two arrangements of weight, fulcrum and
effort are possible.
13. The handle of a hammer is 12 in. long and the
claw that is used in drawing a nail is 2.5 in. long.
(See Fig. 89.) A force of 25 lbs. is required to draw
the nail. What is the resistance of the nail?
14. The effective length of the head of a hammer is
2 in. The handle is 15 in. long and the nail holds in Fig. 89.—The
the wood with a force of 500 lbs. Only 60 lbs. of hammer is a bent
force is available at the end of the handle. What lever. What is its
will be the result? mechanical
15. If an effort of 50 lbs. acting on a machine advantage?
moves 10 ft., how far can it lift a weight of 1000
lbs.?
16. A bar 10 ft. long is to be used as a lever. The weight is kept 2 ft. from
the fulcrum. What different levers can it represent?
Page 147
17. The effort arm of a lever is 6 ft., the weight arm 6 in. How long will the
lever be? Give all possible answers.
18. Two boys carry a weight of 100 lbs. on a pole 5 ft. long between them.
Where should the weight be placed in order that one boy may carry one and
one-fourth times as much as the other?
(4) The Wheel and Axle and the Pulley
124. The Wheel and Axle.—1. One of the simple machines most
commonly applied in compound machines is the wheel and axle. It consists
of a wheel H mounted on a cylinder Y so fastened together that both turn on
the same axis. In Fig. 90, ropes are shown attached to the circumferences of
the wheel and axle. Sometimes a hand wheel is used as on the brake of a
freight or street car, or simply a crank and handle is used, as in Fig. 91. The
capstan is used in moving buildings. Sometimes two or three wheels and
axles are geared together as on a derrick or crane as in Fig. 92.
lever be? Give all possible answers.
18. Two boys carry a weight of 100 lbs. on a pole 5 ft. long between them.
Where should the weight be placed in order that one boy may carry one and
one-fourth times as much as the other?
(4) The Wheel and Axle and the Pulley
124. The Wheel and Axle.—1. One of the simple machines most
commonly applied in compound machines is the wheel and axle. It consists
of a wheel H mounted on a cylinder Y so fastened together that both turn on
the same axis. In Fig. 90, ropes are shown attached to the circumferences of
the wheel and axle. Sometimes a hand wheel is used as on the brake of a
freight or street car, or simply a crank and handle is used, as in Fig. 91. The
capstan is used in moving buildings. Sometimes two or three wheels and
axles are geared together as on a derrick or crane as in Fig. 92.
Page 148
Fig. 90.—The wheel and axle.
Fig. 91.—Windlass used in drawing water
from a well.
Fig. 92.—A portable crane.
Fig. 93.—The wheel and axle considered as a
lever.
Fig. 91.—Windlass used in drawing water
from a well.
Fig. 92.—A portable crane.
Fig. 93.—The wheel and axle considered as a
lever.
Page 149
Fig. 94.—View of transmission gears in an
automobile. 1, Drive gear; 2, High and
intermediate gear; 3, Low and reverse gear; 4,
8, Reverse idler gears; 5, 6, 7, Countershaft
gears. (Courtesy of the Automobile Journal.)
Fig. 95.—Reducing gear of a steam turbine.
Fig. 93 is a diagram showing that the wheel and axle acts like a lever. The
axis D is the fulcrum, the effort is applied at F, at the extremity of a radius
of the wheel and the resisting weight W at the extremity of a radius of the
axle. Hence, if Df, the effort distance, is three times Dw, the weight distance,
the weight that can be supported is three times the effort. Here as in the
automobile. 1, Drive gear; 2, High and
intermediate gear; 3, Low and reverse gear; 4,
8, Reverse idler gears; 5, 6, 7, Countershaft
gears. (Courtesy of the Automobile Journal.)
Fig. 95.—Reducing gear of a steam turbine.
Fig. 93 is a diagram showing that the wheel and axle acts like a lever. The
axis D is the fulcrum, the effort is applied at F, at the extremity of a radius
of the wheel and the resisting weight W at the extremity of a radius of the
axle. Hence, if Df, the effort distance, is three times Dw, the weight distance,
the weight that can be supported is three times the effort. Here as in the
Page 150
lever, f × Df = w × Dw, or w:f = Df:Dw, or the ratio of the weight to the
effort equals the ratio of the radius of the wheel to the radius of the axle.
This is therefore the mechanical advantage of the wheel and axle. Since the
diameters or circumferences are in the same ratio as the radii these can be
used instead of the radii. Sometimes, when increased speed instead of
increased force is desired, the radius of the wheel or part to which power is
applied is less than that of the axle. This is seen in the bicycle, buzzsaw, and
blower. Sometimes geared wheels using the principle of the wheel and axle
are used to reduce speed, as in the transmission of an automobile (see Fig.
94), or the reducing gear of a steam turbine. (See Figs. 95 and 293.)
A bevel gear is frequently used to change the direction of the force. (See
Fig. 94.)
effort equals the ratio of the radius of the wheel to the radius of the axle.
This is therefore the mechanical advantage of the wheel and axle. Since the
diameters or circumferences are in the same ratio as the radii these can be
used instead of the radii. Sometimes, when increased speed instead of
increased force is desired, the radius of the wheel or part to which power is
applied is less than that of the axle. This is seen in the bicycle, buzzsaw, and
blower. Sometimes geared wheels using the principle of the wheel and axle
are used to reduce speed, as in the transmission of an automobile (see Fig.
94), or the reducing gear of a steam turbine. (See Figs. 95 and 293.)
A bevel gear is frequently used to change the direction of the force. (See
Fig. 94.)
Page 151
Fig. 96.—A single movable pulley.
Fig. 97.—Block and tackle.
Fig. 98.—The fixed pulley considered as a
lever.
Fig. 99.—The movable pulley considered as a
lever.
125. The Pulley.—The pulley consists of a wheel turning on an axis in a
frame. The wheel is called a sheave and the frame a block. The rim may be
smooth or grooved. The grooved rim is used to hold a cord or rope. One use
of the pulley is to change the direction of the acting force as in Fig. 84,
where pulley B changes a horizontal pull at H to a downward force and
pulley A changes this into an upward force lifting the weight W. These
pulleys are fixed and simply change the direction. Without considering the
loss by friction, the pull at W will equal that at F. Sometimes, a pulley is
attached to the weight and is lifted with it. It is then called a movable pulley.
In Fig. 96 the movable pulley is at P, a fixed pulley is at F. When fixed
pulleys are used, a single cord runs through from the weight to the effort, so
that if a force of 100 lbs. is applied by the effort the same force is received
at the weight. But with movable pulleys several sections of cord may extend
upward from the weight each with the force of the effort upon it. By this
arrangement, a weight several times larger than the effort can be lifted. Fig.
97 represents what is called a block and tackle. If a force of 50 lbs. is
exerted at F, each section of the rope will have the same tension and hence
the six sections of the rope will support 300 lbs. weight. The mechanical
advantage of the pulley or the ratio of the weight to the effort, therefore,
equals the number of sections of cord supporting the weight. The fixed
pulley represents a lever, see Fig. 98, where the effort and weight are equal.
In the movable pulley, the fulcrum (see Fig. 99) is at D; the weight, W, is
applied at the center of the pulley and the effort at F. The weight distance,
Dw, is the radius, and the effort distance, Df, is the diameter of the pulley.
Since W/F = Df / Dw = 2 in a movable pulley, the weight is twice the effort,
or its mechanical advantage is 2.
Important Topics
1. Wheel and Axle, Law of Wheel and Axle.
Fig. 97.—Block and tackle.
Fig. 98.—The fixed pulley considered as a
lever.
Fig. 99.—The movable pulley considered as a
lever.
125. The Pulley.—The pulley consists of a wheel turning on an axis in a
frame. The wheel is called a sheave and the frame a block. The rim may be
smooth or grooved. The grooved rim is used to hold a cord or rope. One use
of the pulley is to change the direction of the acting force as in Fig. 84,
where pulley B changes a horizontal pull at H to a downward force and
pulley A changes this into an upward force lifting the weight W. These
pulleys are fixed and simply change the direction. Without considering the
loss by friction, the pull at W will equal that at F. Sometimes, a pulley is
attached to the weight and is lifted with it. It is then called a movable pulley.
In Fig. 96 the movable pulley is at P, a fixed pulley is at F. When fixed
pulleys are used, a single cord runs through from the weight to the effort, so
that if a force of 100 lbs. is applied by the effort the same force is received
at the weight. But with movable pulleys several sections of cord may extend
upward from the weight each with the force of the effort upon it. By this
arrangement, a weight several times larger than the effort can be lifted. Fig.
97 represents what is called a block and tackle. If a force of 50 lbs. is
exerted at F, each section of the rope will have the same tension and hence
the six sections of the rope will support 300 lbs. weight. The mechanical
advantage of the pulley or the ratio of the weight to the effort, therefore,
equals the number of sections of cord supporting the weight. The fixed
pulley represents a lever, see Fig. 98, where the effort and weight are equal.
In the movable pulley, the fulcrum (see Fig. 99) is at D; the weight, W, is
applied at the center of the pulley and the effort at F. The weight distance,
Dw, is the radius, and the effort distance, Df, is the diameter of the pulley.
Since W/F = Df / Dw = 2 in a movable pulley, the weight is twice the effort,
or its mechanical advantage is 2.
Important Topics
1. Wheel and Axle, Law of Wheel and Axle.
Page 152
2. Pulley, Fixed and Movable, Block and Tackle, Law of Pulley.
Exercises
1. Why do door knobs make it easier to unlatch doors? What simple
machine do they represent? Explain.
2. What combination of pulleys will enable a 160-lb. man to raise a 900-lb.
piano?
3. When you pull a nail with an ordinary claw hammer, what is the effort
arm? the resistance arm?
4. How much work is done by the machine in problem 2 in lifting the piano
20 ft.? How much work must be done upon the machine to do this work?
5. The pilot wheel of a boat has a diameter of 60 in.; the diameter of the
axle is 6 in. If the resistance is 175 lbs., what force must be applied to the
wheel?
6. Four men raise an anchor weighing {1 1/2} tons, with a capstan (see Fig.
110) having a barrel 9 in. in diameter. The circle described by the hand-
spikes is {13 1/2} ft. in diameter. How much force must each man exert?
7. A bicycle has a 28-in. wheel. The rear
sprocket is 3 in. in diameter,[H] the radius of
the pedal crank is 7 in.; 24 lbs. applied to the
pedal gives what force on the rim of the
wheel? What will be the speed of the rim
when the pedal makes one revolution a
second?
8. Measure the diameters of the large and
small pulleys on the sewing-machine at your
home. What mechanical advantage in number
of revolutions does it give? Verify your
computation by turning the wheel and Fig. 100.—The Capstan.
counting the revolutions.
9. What force is required with a single fixed pulley to raise a weight of 200
lbs.? How far will the effort move in raising the weight 10 ft.? What is the
Exercises
1. Why do door knobs make it easier to unlatch doors? What simple
machine do they represent? Explain.
2. What combination of pulleys will enable a 160-lb. man to raise a 900-lb.
piano?
3. When you pull a nail with an ordinary claw hammer, what is the effort
arm? the resistance arm?
4. How much work is done by the machine in problem 2 in lifting the piano
20 ft.? How much work must be done upon the machine to do this work?
5. The pilot wheel of a boat has a diameter of 60 in.; the diameter of the
axle is 6 in. If the resistance is 175 lbs., what force must be applied to the
wheel?
6. Four men raise an anchor weighing {1 1/2} tons, with a capstan (see Fig.
110) having a barrel 9 in. in diameter. The circle described by the hand-
spikes is {13 1/2} ft. in diameter. How much force must each man exert?
7. A bicycle has a 28-in. wheel. The rear
sprocket is 3 in. in diameter,[H] the radius of
the pedal crank is 7 in.; 24 lbs. applied to the
pedal gives what force on the rim of the
wheel? What will be the speed of the rim
when the pedal makes one revolution a
second?
8. Measure the diameters of the large and
small pulleys on the sewing-machine at your
home. What mechanical advantage in number
of revolutions does it give? Verify your
computation by turning the wheel and Fig. 100.—The Capstan.
counting the revolutions.
9. What force is required with a single fixed pulley to raise a weight of 200
lbs.? How far will the effort move in raising the weight 10 ft.? What is the
Page 153
mechanical advantage?
10. In the above problem substitute a single movable pulley for the fixed
pulley and answer the same questions.
11. What is the smallest number of pulleys required to lift a weight of 600
lbs. with a force of 120 lbs.? How should they be arranged?
12. A derrick in lifting a safe weighing 2 tons uses a system of pulleys
employing 3 sections of rope. What is the force required?
13. Name three instances where pulleys are used to do work that otherwise
would be difficult to do.
14. Draw a diagram for a set of pulleys by means of which 100 lbs. can lift
400 lbs.
(5) The Inclined Plane. Efficiency
126. Efficiency.—The general law of machines which states that the work
done by a machine equals the work put into it requires a modification, when
we apply the law in a practical way, for the reason that in using any
machine there is developed more or less friction due to parts of the machine
rubbing on each other and to the resistance of the air as the parts move
through it. Hence the statement of the law that accords with actual working
conditions runs somewhat as follows: The work put into a machine equals
the useful work done by the machine plus the wasted work done by it. The
efficiency of a machine is the ratio of the useful work done by it to the total
work done on the machine. If there were no friction or wasted work, the
efficiency would be perfect, or, as it is usually expressed, would be 100 per
cent. Consider a system of pulleys into which are put 600 ft.-lbs. of work.
With 450 ft.-lbs. of useful work resulting, the efficiency would be 450 ÷
600 = {3/4}, or 75 per cent. In this case 25 per cent. of the work done on
the machine is wasted. In a simple lever the friction is slight so that nearly
100 per cent. efficiency is often secured.
Some forms of the wheel and axle have high efficiencies as in bicycles with
gear wheels. Other forms in which ropes are employed have more friction.
Pulleys have sometimes efficiencies as low as 40 per cent. when heavy
ropes are used.
10. In the above problem substitute a single movable pulley for the fixed
pulley and answer the same questions.
11. What is the smallest number of pulleys required to lift a weight of 600
lbs. with a force of 120 lbs.? How should they be arranged?
12. A derrick in lifting a safe weighing 2 tons uses a system of pulleys
employing 3 sections of rope. What is the force required?
13. Name three instances where pulleys are used to do work that otherwise
would be difficult to do.
14. Draw a diagram for a set of pulleys by means of which 100 lbs. can lift
400 lbs.
(5) The Inclined Plane. Efficiency
126. Efficiency.—The general law of machines which states that the work
done by a machine equals the work put into it requires a modification, when
we apply the law in a practical way, for the reason that in using any
machine there is developed more or less friction due to parts of the machine
rubbing on each other and to the resistance of the air as the parts move
through it. Hence the statement of the law that accords with actual working
conditions runs somewhat as follows: The work put into a machine equals
the useful work done by the machine plus the wasted work done by it. The
efficiency of a machine is the ratio of the useful work done by it to the total
work done on the machine. If there were no friction or wasted work, the
efficiency would be perfect, or, as it is usually expressed, would be 100 per
cent. Consider a system of pulleys into which are put 600 ft.-lbs. of work.
With 450 ft.-lbs. of useful work resulting, the efficiency would be 450 ÷
600 = {3/4}, or 75 per cent. In this case 25 per cent. of the work done on
the machine is wasted. In a simple lever the friction is slight so that nearly
100 per cent. efficiency is often secured.
Some forms of the wheel and axle have high efficiencies as in bicycles with
gear wheels. Other forms in which ropes are employed have more friction.
Pulleys have sometimes efficiencies as low as 40 per cent. when heavy
ropes are used.
Page 154
127. Inclined Plane.—We now come to a type of simple machine of lower
efficiency than those previously mentioned. These belong to the inclined
plane group, which includes the inclined plane (see Fig. 101), the wedge
and the screw. They are extensively used, however, notwithstanding their
low efficiency, on account of often giving a high mechanical advantage.
The relation between these machines may be easily shown, as the wedge is
obviously a double inclined plane. In Art. 82 it is shown that the effort
required to hold a weight upon an inclined plane is to the weight supported
as the height of the plane is to its length.
Fig. 101.—An inclined plane.
Or while the weight is being lifted the vertical height BC, the effort has to
move the length of the plane AC. Since by the law of machines the effort
times its distance equals the weight times its distance, or the weight is to the
effort as the effort distance is to the weight distance, therefore the
mechanical advantage of the inclined plane is the ratio of the length to the
height of the inclined plane.
Inclined planes are used to raise heavy objects short distances, as barrels
into a wagon, and iron safes into a building. Stairways are inclined planes
with steps cut into them.
128. The Wedge.—Wedges are used to separate objects, as in splitting
wood (see Fig. 102), cutting wood, and where great force is to be exerted
for short distances. An axe is a wedge, so is a knife. A fork consists of
several round wedges set in a handle. The edge of any cutting tool is either
efficiency than those previously mentioned. These belong to the inclined
plane group, which includes the inclined plane (see Fig. 101), the wedge
and the screw. They are extensively used, however, notwithstanding their
low efficiency, on account of often giving a high mechanical advantage.
The relation between these machines may be easily shown, as the wedge is
obviously a double inclined plane. In Art. 82 it is shown that the effort
required to hold a weight upon an inclined plane is to the weight supported
as the height of the plane is to its length.
Fig. 101.—An inclined plane.
Or while the weight is being lifted the vertical height BC, the effort has to
move the length of the plane AC. Since by the law of machines the effort
times its distance equals the weight times its distance, or the weight is to the
effort as the effort distance is to the weight distance, therefore the
mechanical advantage of the inclined plane is the ratio of the length to the
height of the inclined plane.
Inclined planes are used to raise heavy objects short distances, as barrels
into a wagon, and iron safes into a building. Stairways are inclined planes
with steps cut into them.
128. The Wedge.—Wedges are used to separate objects, as in splitting
wood (see Fig. 102), cutting wood, and where great force is to be exerted
for short distances. An axe is a wedge, so is a knife. A fork consists of
several round wedges set in a handle. The edge of any cutting tool is either
Page 155
an inclined plane or a wedge. Our front teeth are wedges. Numerous
examples of inclined planes may be seen about us.
No definite statement as to the mechanical advantage of the wedge can be
given as the work done depends largely on friction. The force used is
generally applied by blows on the thick end. In general, the longer the
wedge for a given thickness the greater the mechanical advantage.
129. The Screw.—The screw is a cylinder around whose
circumference winds a spiral groove. (See Fig. 103.) The
raised part between the two adjacent grooves is the thread
of the screw. The screw turns in a block called a nut,
within which is a spiral groove and thread exactly
corresponding to those of the screw. The distance between
two consecutive threads measured parallel to the axis is
called the pitch of the screw. (See Fig. 104.) If the thread
winds around the cylinder ten times in the space of 1 in.,
Fig. 102.—
the screw is said to have ten threads to the inch, the pitch
One use of
being {1/10} in. The screw usually is turned by a lever or
the wedge.
wheel with the effort applied at the end of the lever, or at
the circumference of the wheel. While the effort moves
once about the circumference of the wheel the weight is pushed forward a
distance equal to the distance between two threads (the pitch of the screw).
The work done by the effort therefore equals F × 2πr, r being the radius of
the wheel, and the work done on the weight equals W × s, s being the pitch
of the screw. By the law of machines F × 2πr = W × s or W / F = (2πr) / s.
Therefore the mechanical advantage of the screw equals (2πr) / s. Since the
distance the weight moves is small compared to that the power travels, there
is a great gain in force. The screw is usually employed where great force is
to be exerted through small distances as in the vise (Fig. 105) the jack screw
(Fig. 106), screw clamps, to accurately measure small distances as in the
micrometer (Fig. 107) and spherometer, and to lessen the motion in speed-
reducing devices. The worm gear (Fig. 108) is a modification of the screw
that is sometimes used where a considerable amount of speed reduction is
required.
examples of inclined planes may be seen about us.
No definite statement as to the mechanical advantage of the wedge can be
given as the work done depends largely on friction. The force used is
generally applied by blows on the thick end. In general, the longer the
wedge for a given thickness the greater the mechanical advantage.
129. The Screw.—The screw is a cylinder around whose
circumference winds a spiral groove. (See Fig. 103.) The
raised part between the two adjacent grooves is the thread
of the screw. The screw turns in a block called a nut,
within which is a spiral groove and thread exactly
corresponding to those of the screw. The distance between
two consecutive threads measured parallel to the axis is
called the pitch of the screw. (See Fig. 104.) If the thread
winds around the cylinder ten times in the space of 1 in.,
Fig. 102.—
the screw is said to have ten threads to the inch, the pitch
One use of
being {1/10} in. The screw usually is turned by a lever or
the wedge.
wheel with the effort applied at the end of the lever, or at
the circumference of the wheel. While the effort moves
once about the circumference of the wheel the weight is pushed forward a
distance equal to the distance between two threads (the pitch of the screw).
The work done by the effort therefore equals F × 2πr, r being the radius of
the wheel, and the work done on the weight equals W × s, s being the pitch
of the screw. By the law of machines F × 2πr = W × s or W / F = (2πr) / s.
Therefore the mechanical advantage of the screw equals (2πr) / s. Since the
distance the weight moves is small compared to that the power travels, there
is a great gain in force. The screw is usually employed where great force is
to be exerted through small distances as in the vise (Fig. 105) the jack screw
(Fig. 106), screw clamps, to accurately measure small distances as in the
micrometer (Fig. 107) and spherometer, and to lessen the motion in speed-
reducing devices. The worm gear (Fig. 108) is a modification of the screw
that is sometimes used where a considerable amount of speed reduction is
required.
Page 156
Fig. 103.—The screw is a spiral inclined plane.
Fig. 104.—The pitch is S.
Fig. 104.—The pitch is S.
Page 157
Fig. 105.—A vise.
Fig. 106.—A jack screw.
Fig. 107.—A micrometer screw.
Fig. 108.—This large worm-wheel is a part of
the hoisting mechanism employed for the lock
gates of the Sault Ste. Marie Canal.
Fig. 106.—A jack screw.
Fig. 107.—A micrometer screw.
Fig. 108.—This large worm-wheel is a part of
the hoisting mechanism employed for the lock
gates of the Sault Ste. Marie Canal.
Page 158
Important Topics
1. Efficiency of machines.
2. The inclined plane, wedge and screw. Applications.
Exercises
1. A plank 12 ft. long is used to roll a barrel weighing 200 lbs. into a wagon
3 ft. high. Find the force required parallel to the incline.
2. How long a plank will be needed to roll an iron safe weighing 1-1/2 tons
into a wagon 3 ft. high using a pull of 600 lbs. parallel to the incline.
3. An effort of 50 lbs. acting parallel to the plane prevents a 200-lb. barrel
from rolling down an inclined plane. What is the ratio of the length to the
height of the plane?
4. A man can push with a force of 150 lbs. and wishes to raise a box
weighing 1200 lbs. into a cart 3 ft. high. How long a plank must he use?
5. The radius of the wheel of a letter press is 6 in., the pitch of its screw is
1/4 in. What pressure is produced by a force of 40 lbs.?
6. The pitch of a screw of a vice is 1/4 in., the handle is 1 ft. long. what
pressure can be expected if the force used is 100 lbs.?
7. A jackscrew is used to raise a weight of 2 tons. The bar of the jackscrew
extends 2 ft. from the center of the screw. There are two threads to the inch.
Find the force required.
(6) Friction, Its Uses and Laws
130. Friction.—Although often inconvenient and expensive, requiring
persistent and elaborate efforts to reduce it to a minimum, friction has its
uses, and advantages. Were it not for friction between our shoes and the
floor or sidewalk, we could not keep our footing. Friction is the resistance
that must be overcome when one body moves over another. It is of two
kinds, sliding and rolling. If one draws a block and then a car of equal
weight along a board, the force employed in each case being measured by a
1. Efficiency of machines.
2. The inclined plane, wedge and screw. Applications.
Exercises
1. A plank 12 ft. long is used to roll a barrel weighing 200 lbs. into a wagon
3 ft. high. Find the force required parallel to the incline.
2. How long a plank will be needed to roll an iron safe weighing 1-1/2 tons
into a wagon 3 ft. high using a pull of 600 lbs. parallel to the incline.
3. An effort of 50 lbs. acting parallel to the plane prevents a 200-lb. barrel
from rolling down an inclined plane. What is the ratio of the length to the
height of the plane?
4. A man can push with a force of 150 lbs. and wishes to raise a box
weighing 1200 lbs. into a cart 3 ft. high. How long a plank must he use?
5. The radius of the wheel of a letter press is 6 in., the pitch of its screw is
1/4 in. What pressure is produced by a force of 40 lbs.?
6. The pitch of a screw of a vice is 1/4 in., the handle is 1 ft. long. what
pressure can be expected if the force used is 100 lbs.?
7. A jackscrew is used to raise a weight of 2 tons. The bar of the jackscrew
extends 2 ft. from the center of the screw. There are two threads to the inch.
Find the force required.
(6) Friction, Its Uses and Laws
130. Friction.—Although often inconvenient and expensive, requiring
persistent and elaborate efforts to reduce it to a minimum, friction has its
uses, and advantages. Were it not for friction between our shoes and the
floor or sidewalk, we could not keep our footing. Friction is the resistance
that must be overcome when one body moves over another. It is of two
kinds, sliding and rolling. If one draws a block and then a car of equal
weight along a board, the force employed in each case being measured by a
Page 159
spring balance, a large difference in the force required will be noticed,
showing how much less rolling friction is than sliding friction.
131. Ways of Reducing Friction.—(a) Friction is often caused by the
minute projections of one surface sinking into the depressions of the other
surface as one moves over the other. It follows, therefore, that if these
projections could be made as small as possible that friction would be
lessened. Consequently polishing is one of the best means for reducing
friction. In machines all moving surfaces are made as smooth as possible. In
different kinds of materials these little ridges and depressions are differently
arranged. (b) In Fig. 109 the friction between R and S would be greater than
between R and T. In R and S the surfaces will fit closer together than in R
and T. The use of different materials will reduce friction. The iron axles of
car wheels revolve in bearings of brass. Jewels are used in watches for the
same reason. (c) Another very common method of reducing friction is by
the use of lubricants. The oil or grease used fills up the irregularities of the
bearing surfaces and separates them. Rolling friction is frequently
substituted for sliding friction by the use of ball and roller bearings. These
are used in many machines as in bicycles, automobiles, sewing machines,
etc. (See Fig. 110.)
132. Value of Friction.—Friction always
hinders motion and whenever one body
moves over or through another the energy
used in overcoming the friction is
transformed into heat which is taken up
by surrounding bodies and usually lost.
Fig. 109.—The friction
Friction is therefore the great obstacle to
between R and S is greater
perfect efficiency in machines. Friction,
than between R and T.
however, like most afflictions has its uses.
We would find it hard to get along without
it. Without friction we could neither walk nor run; no machines could be
run by belts; railroad trains, street cars, in fact all ordinary means of travel
would be impossible, since these depend upon friction between the moving
power and the road for propulsion.
showing how much less rolling friction is than sliding friction.
131. Ways of Reducing Friction.—(a) Friction is often caused by the
minute projections of one surface sinking into the depressions of the other
surface as one moves over the other. It follows, therefore, that if these
projections could be made as small as possible that friction would be
lessened. Consequently polishing is one of the best means for reducing
friction. In machines all moving surfaces are made as smooth as possible. In
different kinds of materials these little ridges and depressions are differently
arranged. (b) In Fig. 109 the friction between R and S would be greater than
between R and T. In R and S the surfaces will fit closer together than in R
and T. The use of different materials will reduce friction. The iron axles of
car wheels revolve in bearings of brass. Jewels are used in watches for the
same reason. (c) Another very common method of reducing friction is by
the use of lubricants. The oil or grease used fills up the irregularities of the
bearing surfaces and separates them. Rolling friction is frequently
substituted for sliding friction by the use of ball and roller bearings. These
are used in many machines as in bicycles, automobiles, sewing machines,
etc. (See Fig. 110.)
132. Value of Friction.—Friction always
hinders motion and whenever one body
moves over or through another the energy
used in overcoming the friction is
transformed into heat which is taken up
by surrounding bodies and usually lost.
Fig. 109.—The friction
Friction is therefore the great obstacle to
between R and S is greater
perfect efficiency in machines. Friction,
than between R and T.
however, like most afflictions has its uses.
We would find it hard to get along without
it. Without friction we could neither walk nor run; no machines could be
run by belts; railroad trains, street cars, in fact all ordinary means of travel
would be impossible, since these depend upon friction between the moving
power and the road for propulsion.
Page 160
Fig. 110.—Timken roller bearings. As used in
the front wheel of an automobile.
133. Coefficient of Friction.—The ratio between the friction when motion
is just starting and the force pushing the surfaces together is called the
coefficient of friction.
If the block in Fig. 111 is drawn along the board with uniform motion, the
reading of the spring balances indicates the amount of friction. Suppose the
friction is found to be 500 g., and the weight of the block to be 2000 g.
Then the coefficient of friction for these two substances will be {500/2000}
= {1/4}, or 25 per cent.
134. Laws of Friction, Law I.—The friction when motion is occurring
between two surfaces is proportional to the force holding them together.
Thus if one measures the friction when a brick is drawn along a board, he
will find that it is doubled if a second brick is placed on the first. On brakes
greater pressure causes greater friction. If a rope is drawn through the hands
more pressure makes more friction.
the front wheel of an automobile.
133. Coefficient of Friction.—The ratio between the friction when motion
is just starting and the force pushing the surfaces together is called the
coefficient of friction.
If the block in Fig. 111 is drawn along the board with uniform motion, the
reading of the spring balances indicates the amount of friction. Suppose the
friction is found to be 500 g., and the weight of the block to be 2000 g.
Then the coefficient of friction for these two substances will be {500/2000}
= {1/4}, or 25 per cent.
134. Laws of Friction, Law I.—The friction when motion is occurring
between two surfaces is proportional to the force holding them together.
Thus if one measures the friction when a brick is drawn along a board, he
will find that it is doubled if a second brick is placed on the first. On brakes
greater pressure causes greater friction. If a rope is drawn through the hands
more pressure makes more friction.
Page 161
Fig. 111.—A method for testing the friction
between surfaces.
Law II.—Friction is independent of the extent of surface in contact. Thus a
brick has the same friction drawn on its side as on its edge, since, although
the surface is increased, the weight is unchanged.
Law III.—Friction is greatest at starting, but after starting is practically the
same for all speeds.
135. Fluid Friction.—When a solid moves through a fluid, as when a ship
moves through the water or railroad trains through the air, the resistance
encountered is not the same as with solids but increases with the square of
the velocity for slow speeds and for high speeds at a higher rate. This is the
reason why it costs so much to increase the speed of a fast train, since the
resistance of the air becomes the prominent factor at high speeds. The
resistance to the motion of a ship at high speed is usually considered to
increase as the cube of the velocity so that to double the speed of a boat its
driving force must be eight times as great.
Important Topics
1. Friction: two kinds; sliding and rolling.
2. Four ways of reducing friction.
3. Uses of friction.
4. Coefficient of friction. Three laws of friction.
5. Fluid friction.
Exercises
between surfaces.
Law II.—Friction is independent of the extent of surface in contact. Thus a
brick has the same friction drawn on its side as on its edge, since, although
the surface is increased, the weight is unchanged.
Law III.—Friction is greatest at starting, but after starting is practically the
same for all speeds.
135. Fluid Friction.—When a solid moves through a fluid, as when a ship
moves through the water or railroad trains through the air, the resistance
encountered is not the same as with solids but increases with the square of
the velocity for slow speeds and for high speeds at a higher rate. This is the
reason why it costs so much to increase the speed of a fast train, since the
resistance of the air becomes the prominent factor at high speeds. The
resistance to the motion of a ship at high speed is usually considered to
increase as the cube of the velocity so that to double the speed of a boat its
driving force must be eight times as great.
Important Topics
1. Friction: two kinds; sliding and rolling.
2. Four ways of reducing friction.
3. Uses of friction.
4. Coefficient of friction. Three laws of friction.
5. Fluid friction.
Exercises
Page 162
1. How long must an inclined plane be which is 10 meters high to enable a
car weighing 2000 kg. to be pushed up its length by a force of 100 kg.
parallel to the incline?
2. State how and where friction is of use in the operation of the inclined
plane, the wedge, the screw, the wheel and axle.
3. A wheelbarrow has handles 6 ft. long. If a load of 300 lbs. is placed 18 in.
from the axis of the wheel, what force placed at the end of the handles will
be required to lift it?
4. A jackscrew has 3 threads to the inch, and the lever used to turn it is 4 ft.
long. If the efficiency of the screw is 60 per cent., what force must be
applied to raise a load of 5 tons?
5. In problem 4 how far must the force move in raising the weight 3 in.
Compute the work done upon the weight, the work done by the power and
the efficiency of the machine from these two amounts of work.
6. What simple machines are represented in a jackknife, a sewing-machine,
a screw-driver, a plane, a saw, a table fork?
7. A laborer carries 1500 lbs. of brick to a platform 40 ft. high. How much
useful work does he do?
8. If he weighs 150 lbs. and his hod weighs 10 lbs., how much useless work
does he do in taking 30 trips to carry up the bricks of problem 7? What is
his efficiency?
9. If the laborer hoists the brick of problem 7 in a bucket weighing 50 lbs.,
using a fixed pulley and rope, what is the useless work done if it takes 12
trips to carry up the brick? What is the efficiency of the device?
10. The efficiency of a set of pulleys is 70 per cent. How much force should
be applied if acting through 100 ft. it is to raise a load of 400 lbs. 20 ft.?
11. The spokes of the pilot wheel of a motor-boat are 1 ft. long, the axle
around which the rudder ropes are wound is 3 in. in diameter. What effort
must be applied if the tension in the ropes is 50 lbs.?
12. Why are the elevated railway stations frequently placed at the top of an
incline, the tracks sloping gently away in both directions?
car weighing 2000 kg. to be pushed up its length by a force of 100 kg.
parallel to the incline?
2. State how and where friction is of use in the operation of the inclined
plane, the wedge, the screw, the wheel and axle.
3. A wheelbarrow has handles 6 ft. long. If a load of 300 lbs. is placed 18 in.
from the axis of the wheel, what force placed at the end of the handles will
be required to lift it?
4. A jackscrew has 3 threads to the inch, and the lever used to turn it is 4 ft.
long. If the efficiency of the screw is 60 per cent., what force must be
applied to raise a load of 5 tons?
5. In problem 4 how far must the force move in raising the weight 3 in.
Compute the work done upon the weight, the work done by the power and
the efficiency of the machine from these two amounts of work.
6. What simple machines are represented in a jackknife, a sewing-machine,
a screw-driver, a plane, a saw, a table fork?
7. A laborer carries 1500 lbs. of brick to a platform 40 ft. high. How much
useful work does he do?
8. If he weighs 150 lbs. and his hod weighs 10 lbs., how much useless work
does he do in taking 30 trips to carry up the bricks of problem 7? What is
his efficiency?
9. If the laborer hoists the brick of problem 7 in a bucket weighing 50 lbs.,
using a fixed pulley and rope, what is the useless work done if it takes 12
trips to carry up the brick? What is the efficiency of the device?
10. The efficiency of a set of pulleys is 70 per cent. How much force should
be applied if acting through 100 ft. it is to raise a load of 400 lbs. 20 ft.?
11. The spokes of the pilot wheel of a motor-boat are 1 ft. long, the axle
around which the rudder ropes are wound is 3 in. in diameter. What effort
must be applied if the tension in the ropes is 50 lbs.?
12. Why are the elevated railway stations frequently placed at the top of an
incline, the tracks sloping gently away in both directions?
Page 163
13. The screw of a press has 4 threads to the inch and is worked by a lever
of such length that an effort of 25 lbs. produces a force of 2 tons. What is
the length of the lever?
14. It takes a horizontal force of 10 lbs. to draw a sled weighing 50 lbs.
along a horizontal surface. What is the coefficient of friction?
15. The coefficient of rolling friction of a railroad train on a track is 0.009.
What pull would an engine have to exert to haul a train weighing 1000 tons
along a level track?
16. How heavy a cake of ice can be dragged over a floor by a horizontal
force of 20 lbs., if the coefficient of friction is 0.06?
17. The coefficient of friction of iron on iron is 0.2. What force can a switch
engine weighing 20 tons exert before slipping?
18. Using a system of pulleys with a double movable block a man weighing
200 lbs. is just able to lift 600 lbs. What is the efficiency of the system?
19. What is the horse-power of a pump that can pump out a cellar full of
water 40 ft. × 20 ft. by 10 ft. deep, in 30 minutes?
20. How many tons of coal can a 5 horse-power hoisting engine raise in 30
minutes from a barge to the coal pockets, a height of 50 ft.?
(7) Water Power
136. Energy of Falling Water.—The energy of falling and running water
has been used from the earliest times for developing power and running
machinery. The energy is derived from the action of the moving water in
striking and turning some form of water-wheel, several varieties of which
are described below.
The Overshot Wheel.—The overshot wheel (Fig. 112) is turned by the
weight of the water in the buckets. It was formerly much used in the hilly
and mountainous sections of this country for running sawmills and grist
mills as it is very easily made and requires only a small amount of water. Its
efficiency is high, being from 80 to 90 per cent., the loss being due to
friction and spilling of water from the buckets. To secure this high
of such length that an effort of 25 lbs. produces a force of 2 tons. What is
the length of the lever?
14. It takes a horizontal force of 10 lbs. to draw a sled weighing 50 lbs.
along a horizontal surface. What is the coefficient of friction?
15. The coefficient of rolling friction of a railroad train on a track is 0.009.
What pull would an engine have to exert to haul a train weighing 1000 tons
along a level track?
16. How heavy a cake of ice can be dragged over a floor by a horizontal
force of 20 lbs., if the coefficient of friction is 0.06?
17. The coefficient of friction of iron on iron is 0.2. What force can a switch
engine weighing 20 tons exert before slipping?
18. Using a system of pulleys with a double movable block a man weighing
200 lbs. is just able to lift 600 lbs. What is the efficiency of the system?
19. What is the horse-power of a pump that can pump out a cellar full of
water 40 ft. × 20 ft. by 10 ft. deep, in 30 minutes?
20. How many tons of coal can a 5 horse-power hoisting engine raise in 30
minutes from a barge to the coal pockets, a height of 50 ft.?
(7) Water Power
136. Energy of Falling Water.—The energy of falling and running water
has been used from the earliest times for developing power and running
machinery. The energy is derived from the action of the moving water in
striking and turning some form of water-wheel, several varieties of which
are described below.
The Overshot Wheel.—The overshot wheel (Fig. 112) is turned by the
weight of the water in the buckets. It was formerly much used in the hilly
and mountainous sections of this country for running sawmills and grist
mills as it is very easily made and requires only a small amount of water. Its
efficiency is high, being from 80 to 90 per cent., the loss being due to
friction and spilling of water from the buckets. To secure this high
Page 164
efficiency the overshot wheel must have a diameter equal to the height of
the fall which may be as much as 80 or 90 ft.
Fig. 112.—Overshot
water wheel.
Fig. 113.—Undershot water wheel.
Fig. 114.—Diagram illustrating the principle
of the Pelton wheel.
The Undershot Wheel.—The old style undershot wheel (Fig. 113) is used
in level countries, where there is little fall, often to raise water for irrigation.
Its efficiency is very low, seldom rising more than 25 per cent. The
principle of the undershot wheel, however, is extensively used in the water
motor and the Pelton wheel (Fig. 114). In these the water is delivered from
a nozzle in a jet against the lower buckets of the wheel. They have an
efficiency of about 80 per cent. and are much used in cities for running
the fall which may be as much as 80 or 90 ft.
Fig. 112.—Overshot
water wheel.
Fig. 113.—Undershot water wheel.
Fig. 114.—Diagram illustrating the principle
of the Pelton wheel.
The Undershot Wheel.—The old style undershot wheel (Fig. 113) is used
in level countries, where there is little fall, often to raise water for irrigation.
Its efficiency is very low, seldom rising more than 25 per cent. The
principle of the undershot wheel, however, is extensively used in the water
motor and the Pelton wheel (Fig. 114). In these the water is delivered from
a nozzle in a jet against the lower buckets of the wheel. They have an
efficiency of about 80 per cent. and are much used in cities for running
Page 165
small machines, washing machines, pipe organ blowers, etc., and in
mountainous districts where the head is great.
Fig. 115.—Diagram of a hydro-electric power
house showing a vertical turbine A with
penstock B and tail race C.
mountainous districts where the head is great.
Fig. 115.—Diagram of a hydro-electric power
house showing a vertical turbine A with
penstock B and tail race C.
Page 166
Fig. 116.—The outer case of a turbine showing
the mechanism for controlling the gates.
Fig. 117.—Inner case of a turbine showing the
gates and the lower end of the runner within.
the mechanism for controlling the gates.
Fig. 117.—Inner case of a turbine showing the
gates and the lower end of the runner within.
Page 167
Fig. 118.—The runner of a turbine.
Fig. 119.—Turbine and generator of the
Tacoma hydro-electric power plant.
137. The Turbine.—The turbine is now used more than any other form of
water-wheel. It was invented in 1827 by De Fourneyron in France. It can be
used with a small or large amount of water, the power depending on the
head (the height of the water, in the reservoir above the wheel). It is the
most efficient type of water-wheel, efficiencies of 90 per cent. often being
obtained. The wheel is entirely under water (Fig. 115). It is enclosed in an
outer case (Fig. 116) which is connected with the reservoir by a penstock or
pipe and is always kept full of water. The wheel itself is made in two parts,
a rotating part called the runner (see Fig. 118) and an inner case (Fig. 117)
with gates that regulate the amount of water entering the wheel. This case
Fig. 119.—Turbine and generator of the
Tacoma hydro-electric power plant.
137. The Turbine.—The turbine is now used more than any other form of
water-wheel. It was invented in 1827 by De Fourneyron in France. It can be
used with a small or large amount of water, the power depending on the
head (the height of the water, in the reservoir above the wheel). It is the
most efficient type of water-wheel, efficiencies of 90 per cent. often being
obtained. The wheel is entirely under water (Fig. 115). It is enclosed in an
outer case (Fig. 116) which is connected with the reservoir by a penstock or
pipe and is always kept full of water. The wheel itself is made in two parts,
a rotating part called the runner (see Fig. 118) and an inner case (Fig. 117)
with gates that regulate the amount of water entering the wheel. This case
Page 168
has blades curved so that the water can strike the curved blades of the
rotating part (Fig. 118) at the angle that is best adapted to use the energy of
the water. The water then drops through the central opening into the tail
race below (see Fig. 115). The energy available is the product of the weight
of the water and the head. The turbine is extensively used to furnish power
for generating electricity at places where there is a sufficient fall of water.
The electrical energy thus developed is transmitted from 50 to 200 miles to
cities where it is used in running street cars, electric lighting, etc. Turbines
can be made to revolve about either vertical or horizontal axes. Fig. 119
represents a horizontal water turbine connected to a dynamo. Compare this
with the vertical turbine in Fig. 115.
Exercises
1. Does a person do more work when he goes up a flight of stairs in 5
seconds than when he goes up in 15 seconds? Explain.
2. A motorcycle has a 4 horse-power motor and can go at a rate of 50 miles
per hour. Why cannot 4 horses draw it as fast?
3. What is the efficiency of a motor that is running fast but doing no useful
work?
4. What horse-power can be had from a waterfall, 12 ft. high, if 20 cu. ft. of
water pass over it each second?
5. What is the horse-power of a fire engine if it can throw 600 gallons of
water a minute to a height of 100 ft.?
6. Why are undershot wheels less efficient than the overshot wheel or
turbine?
7. A revolving electric fan is placed on the stern of a boat. Does the boat
move? Why? Place the fan under water. Does the boat now move? Why?
8. Why does an electric fan produce a breeze?
9. Explain the action of the bellows in an organ.
10. At Niagara Falls the turbines are 136 ft. below the surface of the river.
Their average horse-power is 5000 each. 430 cu. ft. of water each second
pass through each turbine. Find the efficiency.
rotating part (Fig. 118) at the angle that is best adapted to use the energy of
the water. The water then drops through the central opening into the tail
race below (see Fig. 115). The energy available is the product of the weight
of the water and the head. The turbine is extensively used to furnish power
for generating electricity at places where there is a sufficient fall of water.
The electrical energy thus developed is transmitted from 50 to 200 miles to
cities where it is used in running street cars, electric lighting, etc. Turbines
can be made to revolve about either vertical or horizontal axes. Fig. 119
represents a horizontal water turbine connected to a dynamo. Compare this
with the vertical turbine in Fig. 115.
Exercises
1. Does a person do more work when he goes up a flight of stairs in 5
seconds than when he goes up in 15 seconds? Explain.
2. A motorcycle has a 4 horse-power motor and can go at a rate of 50 miles
per hour. Why cannot 4 horses draw it as fast?
3. What is the efficiency of a motor that is running fast but doing no useful
work?
4. What horse-power can be had from a waterfall, 12 ft. high, if 20 cu. ft. of
water pass over it each second?
5. What is the horse-power of a fire engine if it can throw 600 gallons of
water a minute to a height of 100 ft.?
6. Why are undershot wheels less efficient than the overshot wheel or
turbine?
7. A revolving electric fan is placed on the stern of a boat. Does the boat
move? Why? Place the fan under water. Does the boat now move? Why?
8. Why does an electric fan produce a breeze?
9. Explain the action of the bellows in an organ.
10. At Niagara Falls the turbines are 136 ft. below the surface of the river.
Their average horse-power is 5000 each. 430 cu. ft. of water each second
pass through each turbine. Find the efficiency.
Page 169
11. At Laxey on the Isle of Man is the largest overshot wheel now in use. It
has a horse-power of 150, a diameter of 72.5 ft., a width of 10 ft., and an
efficiency of 85 per cent. How many cubic feet of water pass over it each
second?
12. The power plant at the Pikes Peak Hydro-electric Company utilizes a
head of 2150 ft., which is equal to a pressure of 935 lbs. per square inch, to
run a Pelton wheel. If the area of the nozzle is 1 sq. in. and the jet has a
velocity of 22,300 ft. per minute, what is the horse-power developed if the
efficiency is 80 per cent.?
13. A test made in 1909 of the turbines at the Centerville power house of the
California Gas and Electric Corporation showed a maximum horse-power
of 9700, speed 400 r.p.m. under a head of 550 ft. The efficiency was 86.25
per cent. How many cubic feet of water passed through the turbines each
second?
14. The turbine in the City of Tacoma Power Plant (see Fig. 120) uses a
head of 415 ft. 145 cu. ft. a second pass through the turbine. Calculate the
horse-power.
15. In problem 14, what is the water pressure per square inch at the turbine?
16. The power plant mentioned in problem 13 develops 6000 kw. What is
the efficiency?
Review Outline: Work and Energy
Work; how measured, units, foot-pound, kilogram meter, erg.
Energy; how measured, units, potential, P.E. = w × h, or f × s. Kinetic =
(wv2)/(2g).
Power; how measured, units, horse power, watt, 5 forms of energy,
conservation. H.p. = (lbs. × ft.)/(550 × sec.).
Machines; 6 simple forms, 2 groups, advantages, uses, Law: W × Dw = F ×
D f.
Lever; moments, mechanical advantage, uses and applications.
Wheel and Axle and Pulley; common applications, mechanical advantage.
has a horse-power of 150, a diameter of 72.5 ft., a width of 10 ft., and an
efficiency of 85 per cent. How many cubic feet of water pass over it each
second?
12. The power plant at the Pikes Peak Hydro-electric Company utilizes a
head of 2150 ft., which is equal to a pressure of 935 lbs. per square inch, to
run a Pelton wheel. If the area of the nozzle is 1 sq. in. and the jet has a
velocity of 22,300 ft. per minute, what is the horse-power developed if the
efficiency is 80 per cent.?
13. A test made in 1909 of the turbines at the Centerville power house of the
California Gas and Electric Corporation showed a maximum horse-power
of 9700, speed 400 r.p.m. under a head of 550 ft. The efficiency was 86.25
per cent. How many cubic feet of water passed through the turbines each
second?
14. The turbine in the City of Tacoma Power Plant (see Fig. 120) uses a
head of 415 ft. 145 cu. ft. a second pass through the turbine. Calculate the
horse-power.
15. In problem 14, what is the water pressure per square inch at the turbine?
16. The power plant mentioned in problem 13 develops 6000 kw. What is
the efficiency?
Review Outline: Work and Energy
Work; how measured, units, foot-pound, kilogram meter, erg.
Energy; how measured, units, potential, P.E. = w × h, or f × s. Kinetic =
(wv2)/(2g).
Power; how measured, units, horse power, watt, 5 forms of energy,
conservation. H.p. = (lbs. × ft.)/(550 × sec.).
Machines; 6 simple forms, 2 groups, advantages, uses, Law: W × Dw = F ×
D f.
Lever; moments, mechanical advantage, uses and applications.
Wheel and Axle and Pulley; common applications, mechanical advantage.
Page 170
Inclined Plane, Wedge, and Screw; mechanical advantage and efficiency.
Friction; uses, how reduced, coefficient of, laws (3).
Water Wheels; types, efficiency, uses.
Friction; uses, how reduced, coefficient of, laws (3).
Water Wheels; types, efficiency, uses.
Page 171
CHAPTER VII
HEAT, ITS PRODUCTION AND TRANSMISSION
(1) Sources and Effects of Heat
138. Importance of the Study of Heat.—Heat is brought to our attention
through the sensations of heat and cold. In winter, we warm our houses and
prevent the escape of heat from them as much as possible. In summer we
endeavor to keep our living rooms cool and our bodies from being
overheated.
A clear understanding of the several sources, effects, and modes of
transferring heat is of importance to everyone living in our complex
civilization, especially when we consider the multitudes of objects that have
as their principal use the production, transfer or utilization of heat.
139. Principal Sources of Heat.—First and most important is the Sun,
which is continually sending to us radiant energy in the form of light and
heat waves. These warm the earth, make plants grow, evaporate water,
besides producing many other important effects.
Second, chemical energy is often transformed into heat. One has but to
think of the heat produced by burning coal, wood, oil, and gas, to recognize
the importance of this source. Chemical energy is also the source of the heat
produced within our bodies. The action of quicklime and water upon each
other produces much heat. This action is sometimes employed during
balloon trips as a means of warming things.
Third, Electrical Energy.—In many cities electric cars are heated by the
electric current. We have all heard of electric toasters and other devices for
heating by electricity. Electric light is produced by the heating of some
material to incandescence by an electric current. The electric furnace has a
wide application in the preparation and refining of metals.
Fourth, heat is also produced whenever mechanical energy of motion is
overcome, whether it be by friction, concussion, or compression. Friction
HEAT, ITS PRODUCTION AND TRANSMISSION
(1) Sources and Effects of Heat
138. Importance of the Study of Heat.—Heat is brought to our attention
through the sensations of heat and cold. In winter, we warm our houses and
prevent the escape of heat from them as much as possible. In summer we
endeavor to keep our living rooms cool and our bodies from being
overheated.
A clear understanding of the several sources, effects, and modes of
transferring heat is of importance to everyone living in our complex
civilization, especially when we consider the multitudes of objects that have
as their principal use the production, transfer or utilization of heat.
139. Principal Sources of Heat.—First and most important is the Sun,
which is continually sending to us radiant energy in the form of light and
heat waves. These warm the earth, make plants grow, evaporate water,
besides producing many other important effects.
Second, chemical energy is often transformed into heat. One has but to
think of the heat produced by burning coal, wood, oil, and gas, to recognize
the importance of this source. Chemical energy is also the source of the heat
produced within our bodies. The action of quicklime and water upon each
other produces much heat. This action is sometimes employed during
balloon trips as a means of warming things.
Third, Electrical Energy.—In many cities electric cars are heated by the
electric current. We have all heard of electric toasters and other devices for
heating by electricity. Electric light is produced by the heating of some
material to incandescence by an electric current. The electric furnace has a
wide application in the preparation and refining of metals.
Fourth, heat is also produced whenever mechanical energy of motion is
overcome, whether it be by friction, concussion, or compression. Friction
Page 172
always results in the production of heat, as when
we warm our hands by rubbing them together.
When friction is excessive, such as in the case
of a heavy bearing not properly oiled, the
bearing may get very hot. This is the cause of
the "hot box" on a railway car. Friction may
produce heat enough to set wood on fire. Some
fires in mills are believed to be due to this cause.
Every boy scout must learn how to produce fire
Fig. 120.—Boy-scout by friction. (See Fig. 120.) Concussion may be
method of making fire illustrated by the heating of a piece of metal by
by friction. hammering it, while the compression of a gas
always makes it warmer, as those who have
used a bicycle pump have observed. The production of heat by compressing
a gas is illustrated by the "fire syringe" (Fig. 121). This consists of a glass
tube with a tightly fitted piston. A sudden compression of the air contained
may ignite a trace of carbon bisulfid vapor.
The interior of the earth is hot, but its heat seldom gets to the surface
except at hot springs and volcanoes.
140. The Effects of Heat.—There are five important changes produced by
heat: (a) change of size, (b) change of temperature, (c) change of state, as
the melting of ice or evaporating of water, (d) chemical change, as the
charring of sugar when it is overheated, and (e) electrical change. This is
illustrated by the production of an electric current, by the heating of the
junction of two different metals. A thermo-electric generator (see Fig. 122)
has been constructed upon this principle and works successfully.
we warm our hands by rubbing them together.
When friction is excessive, such as in the case
of a heavy bearing not properly oiled, the
bearing may get very hot. This is the cause of
the "hot box" on a railway car. Friction may
produce heat enough to set wood on fire. Some
fires in mills are believed to be due to this cause.
Every boy scout must learn how to produce fire
Fig. 120.—Boy-scout by friction. (See Fig. 120.) Concussion may be
method of making fire illustrated by the heating of a piece of metal by
by friction. hammering it, while the compression of a gas
always makes it warmer, as those who have
used a bicycle pump have observed. The production of heat by compressing
a gas is illustrated by the "fire syringe" (Fig. 121). This consists of a glass
tube with a tightly fitted piston. A sudden compression of the air contained
may ignite a trace of carbon bisulfid vapor.
The interior of the earth is hot, but its heat seldom gets to the surface
except at hot springs and volcanoes.
140. The Effects of Heat.—There are five important changes produced by
heat: (a) change of size, (b) change of temperature, (c) change of state, as
the melting of ice or evaporating of water, (d) chemical change, as the
charring of sugar when it is overheated, and (e) electrical change. This is
illustrated by the production of an electric current, by the heating of the
junction of two different metals. A thermo-electric generator (see Fig. 122)
has been constructed upon this principle and works successfully.
Page 173
Fig. 122.—A thermo-electric generator.
Fig.
121.—A
fire
syringe.
Important Topics
1. Importance of a study of heat.
2. Four sources of heat.
3. Five effects of heat.
4. Examples of each.
5. Illustrations of transformation of energy which involve heat.
Exercises
Fig.
121.—A
fire
syringe.
Important Topics
1. Importance of a study of heat.
2. Four sources of heat.
3. Five effects of heat.
4. Examples of each.
5. Illustrations of transformation of energy which involve heat.
Exercises
Page 174
1. Write a list of the sources of heat in the order of their importance to you.
State why each is important to you.
2. Which three of the effects of heat do you make most use of? Explain what
use you make of each of these effects.
3. Which of the forms of energy can be transformed into heat? How in each
case?
4. Into what other forms of energy may heat be transformed? Name the
device or process used in each case.
5. What five different commodities are purchased by people in your
neighborhood for the production of heat? Which of these costs least for the
amount of heat furnished? Which is most expensive? How do you
determine these answers?
6. Why do many people buy heat in an expensive form, as in using an
electric toaster, when they can obtain it in a cheaper form by burning gas or
coal?
7. How many of the five effects of heat have you observed outside of
school?
(2) Temperature and Expansion
141. Heat and Temperature.—We should now clearly distinguish between
the terms, heat and temperature. Heat is a form of energy consisting of
molecular motion. The temperature of a body is its degree of hotness. The
amount of heat present in a body and its temperature are very different
things. The temperature refers to the intensity of the heat in the body. A
quart of water and a red hot iron ball may contain equal amounts of heat,
although the ball has a much higher temperature than the water. A cup of
boiling water will have the same temperature as a tank full of boiling water,
but the tank will contain more heat. Every one knows that it will take longer
to boil a kettle full of water than a cupful. A hot-water bag, holding 2 quarts
of water will give off heat longer than a 1-quart bag, both being filled with
water at the same temperature. To put it in another way, more work is done
in heating a large amount of water, than a small amount through the same
change of temperature.
State why each is important to you.
2. Which three of the effects of heat do you make most use of? Explain what
use you make of each of these effects.
3. Which of the forms of energy can be transformed into heat? How in each
case?
4. Into what other forms of energy may heat be transformed? Name the
device or process used in each case.
5. What five different commodities are purchased by people in your
neighborhood for the production of heat? Which of these costs least for the
amount of heat furnished? Which is most expensive? How do you
determine these answers?
6. Why do many people buy heat in an expensive form, as in using an
electric toaster, when they can obtain it in a cheaper form by burning gas or
coal?
7. How many of the five effects of heat have you observed outside of
school?
(2) Temperature and Expansion
141. Heat and Temperature.—We should now clearly distinguish between
the terms, heat and temperature. Heat is a form of energy consisting of
molecular motion. The temperature of a body is its degree of hotness. The
amount of heat present in a body and its temperature are very different
things. The temperature refers to the intensity of the heat in the body. A
quart of water and a red hot iron ball may contain equal amounts of heat,
although the ball has a much higher temperature than the water. A cup of
boiling water will have the same temperature as a tank full of boiling water,
but the tank will contain more heat. Every one knows that it will take longer
to boil a kettle full of water than a cupful. A hot-water bag, holding 2 quarts
of water will give off heat longer than a 1-quart bag, both being filled with
water at the same temperature. To put it in another way, more work is done
in heating a large amount of water, than a small amount through the same
change of temperature.
Page 175
142. Units of Heat and Temperature.—There are two common units for
measuring heat: the Calorie and the British thermal unit. The calorie is the
amount of heat required to raise the temperature of a gram of water one
centigrade degree. The British thermal unit is the amount of heat required
to raise the temperature of one pound of water one Fahrenheit degree. One
of the units plainly belongs to the metric system, the other to the English.
An instrument for measuring temperature is called a thermometer. Various
scales are placed upon thermometers. The two thermometer scales most
commonly used in this country are the Centigrade and the Fahrenheit. The
Fahrenheit thermometer scale has the temperature of melting ice marked
32°. The boiling point or steam temperature of pure water under standard
conditions of atmospheric pressure is marked 212° and the space between
these two fixed points is divided into 180 parts.
The centigrade thermometer scale has the same fixed points marked 0 and
100 and the space between divided into 100 parts. (See Fig. 123.) The
centigrade scale is the one used by scientists everywhere.
143. Comparison of Thermometer Scales.—It is
often necessary to express in centigrade degrees a
temperature for which the Fahrenheit reading is
given or vice versa. Since there are 180 Fahrenheit
degrees between the "fixed points" and 100
centigrade degrees, the Fahrenheit degrees are
smaller than the centigrade, or 1°F. = 5/9°C. and
1°C. = 9/5°F. One must also take into account the
fact that the melting point of ice on the Fahrenheit
scale is marked 32°. Hence the following rule: To
change a Fahrenheit reading to centigrade subtract
32 and take 5/9 of the remainder, while to change
centigrade to Fahrenheit multiply the centigrade by
9/5 and add 32 to the product. These two rules are
expressed by the following formulas.
(F.° - 32)5/9 = C.°, 9C.°/5 + 32° = F.°
Fig. 123.—
Another method of changing from one
thermometric scale to another is as follows: Comparison of
measuring heat: the Calorie and the British thermal unit. The calorie is the
amount of heat required to raise the temperature of a gram of water one
centigrade degree. The British thermal unit is the amount of heat required
to raise the temperature of one pound of water one Fahrenheit degree. One
of the units plainly belongs to the metric system, the other to the English.
An instrument for measuring temperature is called a thermometer. Various
scales are placed upon thermometers. The two thermometer scales most
commonly used in this country are the Centigrade and the Fahrenheit. The
Fahrenheit thermometer scale has the temperature of melting ice marked
32°. The boiling point or steam temperature of pure water under standard
conditions of atmospheric pressure is marked 212° and the space between
these two fixed points is divided into 180 parts.
The centigrade thermometer scale has the same fixed points marked 0 and
100 and the space between divided into 100 parts. (See Fig. 123.) The
centigrade scale is the one used by scientists everywhere.
143. Comparison of Thermometer Scales.—It is
often necessary to express in centigrade degrees a
temperature for which the Fahrenheit reading is
given or vice versa. Since there are 180 Fahrenheit
degrees between the "fixed points" and 100
centigrade degrees, the Fahrenheit degrees are
smaller than the centigrade, or 1°F. = 5/9°C. and
1°C. = 9/5°F. One must also take into account the
fact that the melting point of ice on the Fahrenheit
scale is marked 32°. Hence the following rule: To
change a Fahrenheit reading to centigrade subtract
32 and take 5/9 of the remainder, while to change
centigrade to Fahrenheit multiply the centigrade by
9/5 and add 32 to the product. These two rules are
expressed by the following formulas.
(F.° - 32)5/9 = C.°, 9C.°/5 + 32° = F.°
Fig. 123.—
Another method of changing from one
thermometric scale to another is as follows: Comparison of
Page 176
A temperature of -40°F. is also represented by centigrade and
-40°C., therefore to change a Fahrenheit reading Fahrenheit scales.
into centigrade, we add 40 to the given reading,
then divide by 1.8 after which subtract 40. To change from a centigrade to
Fahrenheit reading the only difference in this method is to multiply by 1.8
or
C. = (F. + 40)/1.8 - 40 and F. = 1.8(C. + 40) - 40.
144. The Absolute Scale of Temperature.—
One often hears the statement "as cold as ice."
This expresses the incorrect idea that ice cannot
become colder than its freezing temperature.
The fact is that ice may be cooled below
freezing down to the temperature of its
surroundings. If a piece of ice is placed where
the temperature is below the melting point, the
ice, like any other solid, cools to the temperature
of the surrounding space. For example, a piece
of ice out of doors is at 10°F. when the air is at
this temperature. It follows then, that when ice
has been cooled below the freezing temperature
that heat is required to warm the ice up to its
Fig. 124—Comparison melting point; or in other words that ice at its
of absolute, centigrade melting temperature possesses some heat. The
and Fahrenheit scales. temperature at which absolutely no heat exists is
called absolute zero. There has been devised an
absolute scale of temperature. This scale is
based upon the centigrade scale, i.e., with 100° between the two fixed
points; the scale, however, extends down, below the centigrade zero, 273°,
to what is called absolute zero. It follows therefore that upon the absolute
scale, the melting point of ice, and the boiling point of water are 273° and
373° respectively. (See Fig. 124.)
The means employed to find the location of absolute zero are of much
interest. It has been observed that when heated a gas tends to expand. If a
measured volume of air at 0°C. is cooled or heated 1°C., it changes its
volume 1/273, the pressure remaining the same. If it is cooled 10° it loses
10/273, if cooled 100° it loses 100/273 and so on. No matter how far it is
-40°C., therefore to change a Fahrenheit reading Fahrenheit scales.
into centigrade, we add 40 to the given reading,
then divide by 1.8 after which subtract 40. To change from a centigrade to
Fahrenheit reading the only difference in this method is to multiply by 1.8
or
C. = (F. + 40)/1.8 - 40 and F. = 1.8(C. + 40) - 40.
144. The Absolute Scale of Temperature.—
One often hears the statement "as cold as ice."
This expresses the incorrect idea that ice cannot
become colder than its freezing temperature.
The fact is that ice may be cooled below
freezing down to the temperature of its
surroundings. If a piece of ice is placed where
the temperature is below the melting point, the
ice, like any other solid, cools to the temperature
of the surrounding space. For example, a piece
of ice out of doors is at 10°F. when the air is at
this temperature. It follows then, that when ice
has been cooled below the freezing temperature
that heat is required to warm the ice up to its
Fig. 124—Comparison melting point; or in other words that ice at its
of absolute, centigrade melting temperature possesses some heat. The
and Fahrenheit scales. temperature at which absolutely no heat exists is
called absolute zero. There has been devised an
absolute scale of temperature. This scale is
based upon the centigrade scale, i.e., with 100° between the two fixed
points; the scale, however, extends down, below the centigrade zero, 273°,
to what is called absolute zero. It follows therefore that upon the absolute
scale, the melting point of ice, and the boiling point of water are 273° and
373° respectively. (See Fig. 124.)
The means employed to find the location of absolute zero are of much
interest. It has been observed that when heated a gas tends to expand. If a
measured volume of air at 0°C. is cooled or heated 1°C., it changes its
volume 1/273, the pressure remaining the same. If it is cooled 10° it loses
10/273, if cooled 100° it loses 100/273 and so on. No matter how far it is
Page 177
cooled the same rate of reduction continues as long as it remains in the
gaseous state. From these facts it is concluded that if the cooling could be
carried down 273° that the volume would be reduced 273/273 or that the
volume of the gas would be reduced to nothing. This is believed to mean
that the molecular motion constituting heat would cease rather than that the
matter composing the gas would disappear. Scientists have been able to
obtain temperatures of extreme cold far down on the absolute scale. Liquid
air has a temperature of -292°F., or -180°C. or 93°A. The lowest
temperature thus far reported is 1.7°A. or -271.3°C., obtained in 1911, by
evaporating liquid helium.
145. The Law of Charles.—The facts given in the last paragraph mean that
if 273 ccm. of a gas at 0°C. or 273° A. are cooled 100°, or to -100°C., or
173°A., then it will lose 100/273 of its volume or have a volume of 173
ccm. If warmed 100°, or up to 100°C., or 373°A., it will have a volume of
373 ccm. It follows then that in every case the volume will correspond to its
absolute temperature, providing the pressure remains unchanged. The
expression of this fact in scientific language is called the law of Charles. At
a constant pressure the volume of a given mass of gas is proportional to its
absolute temperature.
Expressed mathematically, we have V1/V2 = T1/T2. Compare the statement
and mathematical expression of the laws of Charles and Boyle.
The formulas for the laws of Boyle and Charles are sometimes combined
into one expression as follows:
PV/T = P´V´/T´
or the product of the volume and pressure of a constant mass of gas is
proportional to its absolute temperature.
Important Topics
1. Heat units; calorie, British thermal unit.
2. Three thermometer scales, fixed points on each.
3. Absolute zero, how determined. Its value on each scale.
4. Law of Charles, its meaning. Combination of laws of Boyle and Charles.
gaseous state. From these facts it is concluded that if the cooling could be
carried down 273° that the volume would be reduced 273/273 or that the
volume of the gas would be reduced to nothing. This is believed to mean
that the molecular motion constituting heat would cease rather than that the
matter composing the gas would disappear. Scientists have been able to
obtain temperatures of extreme cold far down on the absolute scale. Liquid
air has a temperature of -292°F., or -180°C. or 93°A. The lowest
temperature thus far reported is 1.7°A. or -271.3°C., obtained in 1911, by
evaporating liquid helium.
145. The Law of Charles.—The facts given in the last paragraph mean that
if 273 ccm. of a gas at 0°C. or 273° A. are cooled 100°, or to -100°C., or
173°A., then it will lose 100/273 of its volume or have a volume of 173
ccm. If warmed 100°, or up to 100°C., or 373°A., it will have a volume of
373 ccm. It follows then that in every case the volume will correspond to its
absolute temperature, providing the pressure remains unchanged. The
expression of this fact in scientific language is called the law of Charles. At
a constant pressure the volume of a given mass of gas is proportional to its
absolute temperature.
Expressed mathematically, we have V1/V2 = T1/T2. Compare the statement
and mathematical expression of the laws of Charles and Boyle.
The formulas for the laws of Boyle and Charles are sometimes combined
into one expression as follows:
PV/T = P´V´/T´
or the product of the volume and pressure of a constant mass of gas is
proportional to its absolute temperature.
Important Topics
1. Heat units; calorie, British thermal unit.
2. Three thermometer scales, fixed points on each.
3. Absolute zero, how determined. Its value on each scale.
4. Law of Charles, its meaning. Combination of laws of Boyle and Charles.
Page 178
Exercises
1. Does ice melt at the same temperature at which water freezes? Express
the temperature of freezing water on the three thermometer scales.
2. A comfortable room temperature is 68°F. What is this temperature on the
centigrade and absolute scales?
3. Change a temperature of 15°C. to F.; 15°F. to C.; -4°C. to F.; -20°F. to C.
4. The temperature of the human body is 98.6°F. What is this temperature
on the absolute and centigrade scales?
5. The temperature of liquid air is -180°C. What is it on the Fahrenheit
scale?
6. Mercury is a solid at -40°F. What is this on the centigrade scale?
7. How much heat will be required to raise the temperature of 8 lbs. of
water 32°F.; 5 lbs. 10°F.?
Fig. 125.—A clinical thermometer used to take
the temperature of the body.
8. How much heat will be required to raise the temperature of 30 g. of water
43°C.; 20 g., 50°C.?
9. Compute the temperature of absolute zero on the Fahrenheit scale.
10. Take three basins of water, one hot, one cold, and one lukewarm. If one
hand be placed in the hot water while the other is placed in the cold and
after a few minutes both are placed in the lukewarm water, this water will
feel cool to one hand and warm to the other. Explain.
11. If 200 ccm. of air at 200° absolute is heated to 300°A. under constant
pressure, what volume will the air occupy at the latter temperature?
12. How does one change a reading on the centigrade scale to a
corresponding reading on the absolute scale?
(3) Expansion of Liquids and Solids
1. Does ice melt at the same temperature at which water freezes? Express
the temperature of freezing water on the three thermometer scales.
2. A comfortable room temperature is 68°F. What is this temperature on the
centigrade and absolute scales?
3. Change a temperature of 15°C. to F.; 15°F. to C.; -4°C. to F.; -20°F. to C.
4. The temperature of the human body is 98.6°F. What is this temperature
on the absolute and centigrade scales?
5. The temperature of liquid air is -180°C. What is it on the Fahrenheit
scale?
6. Mercury is a solid at -40°F. What is this on the centigrade scale?
7. How much heat will be required to raise the temperature of 8 lbs. of
water 32°F.; 5 lbs. 10°F.?
Fig. 125.—A clinical thermometer used to take
the temperature of the body.
8. How much heat will be required to raise the temperature of 30 g. of water
43°C.; 20 g., 50°C.?
9. Compute the temperature of absolute zero on the Fahrenheit scale.
10. Take three basins of water, one hot, one cold, and one lukewarm. If one
hand be placed in the hot water while the other is placed in the cold and
after a few minutes both are placed in the lukewarm water, this water will
feel cool to one hand and warm to the other. Explain.
11. If 200 ccm. of air at 200° absolute is heated to 300°A. under constant
pressure, what volume will the air occupy at the latter temperature?
12. How does one change a reading on the centigrade scale to a
corresponding reading on the absolute scale?
(3) Expansion of Liquids and Solids
Page 179
146. Expansion of Gases.—The law of Charles is found to apply to all
gases. That is, all gases change in volume in proportion to the change of
temperature provided the pressure remains constant. It is for this reason that
we have the gas thermometer (see Fig. 126) which gives in skillful hands
more accurate temperature readings than the best mercurial thermometer.
Galileo devised and used the first air thermometer which consisted of a
hollow bulb blown on a glass tube and inverted in a dish of water. (See Fig.
1.) The water thermometer consists of a glass bulb filled with water which
rises into a tube attached to the bulb. One disadvantage of the water
thermometer is its limited range since it cannot be used below 0° or above
100°. Why?
147. Expansion of Liquids.—The expansion of liquids differs from that of
gases in several important respects:
(a) Liquids have a smaller rate of expansion than gases. The rate of
expansion per degree is called the Coefficient of Expansion. For example,
the coefficient of expansion of a gas under constant pressure at 0°C. is
{1/273} of its volume per degree centigrade.
(b) Different liquids expand at wholly different rates, that is, their
coefficients of expansion differ widely. For example, the coefficient of
expansion of mercury is 0.00018 per degree centigrade, of glycerine 0.0005
per degree centigrade, of petroleum 0.0009 per degree centigrade.
(c) The same liquid often has different coefficients of expansion at different
temperatures. Water between 5°C. and 6°C. has a coefficient expansion of
0.00002 per degree centigrade, between 8° and 50° of 0.0006, between 99°
and 100° of 0.00076. The coefficient of expansion of mercury, however, is
constant for a wide range of temperature and, therefore, it is well adapted
for use in thermometers.
148. Peculiarity in the Expansion of Water.—Water has a peculiar rate of
expansion. This is illustrated by the following experiment:
A test-tube filled with cold water is closed by a stopper containing a small
glass tube, the water extending up into the small tube. (See Fig. 127.) The
test-tube is placed in a freezing mixture of salt and ice contained in a
tumbler. As the water cools, the level of the water in the small tube at first
sinks. But before the water freezes it rises again, showing that after the
gases. That is, all gases change in volume in proportion to the change of
temperature provided the pressure remains constant. It is for this reason that
we have the gas thermometer (see Fig. 126) which gives in skillful hands
more accurate temperature readings than the best mercurial thermometer.
Galileo devised and used the first air thermometer which consisted of a
hollow bulb blown on a glass tube and inverted in a dish of water. (See Fig.
1.) The water thermometer consists of a glass bulb filled with water which
rises into a tube attached to the bulb. One disadvantage of the water
thermometer is its limited range since it cannot be used below 0° or above
100°. Why?
147. Expansion of Liquids.—The expansion of liquids differs from that of
gases in several important respects:
(a) Liquids have a smaller rate of expansion than gases. The rate of
expansion per degree is called the Coefficient of Expansion. For example,
the coefficient of expansion of a gas under constant pressure at 0°C. is
{1/273} of its volume per degree centigrade.
(b) Different liquids expand at wholly different rates, that is, their
coefficients of expansion differ widely. For example, the coefficient of
expansion of mercury is 0.00018 per degree centigrade, of glycerine 0.0005
per degree centigrade, of petroleum 0.0009 per degree centigrade.
(c) The same liquid often has different coefficients of expansion at different
temperatures. Water between 5°C. and 6°C. has a coefficient expansion of
0.00002 per degree centigrade, between 8° and 50° of 0.0006, between 99°
and 100° of 0.00076. The coefficient of expansion of mercury, however, is
constant for a wide range of temperature and, therefore, it is well adapted
for use in thermometers.
148. Peculiarity in the Expansion of Water.—Water has a peculiar rate of
expansion. This is illustrated by the following experiment:
A test-tube filled with cold water is closed by a stopper containing a small
glass tube, the water extending up into the small tube. (See Fig. 127.) The
test-tube is placed in a freezing mixture of salt and ice contained in a
tumbler. As the water cools, the level of the water in the small tube at first
sinks. But before the water freezes it rises again, showing that after the
Page 180
water cools to a certain temperature that expansion of the
water occurs with further cooling.
Careful tests show that the water on cooling contracts until
it reaches 4°C. On cooling below this temperature it
expands. For this reason, when the water of a lake or river
freezes, the coldest water is at the surface. On account of
this the ice forms at the top instead of at the bottom. If
water contracted as it cooled to the freezing temperature
the coldest water would be at the bottom. Freezing would
begin at the bottom instead of at the surface. Lakes and
rivers would freeze solid. In the summer only in shallow
waters would all the ice melt. The result would be that fish
and other aquatic life would be killed. Climate would be
so changed that the earth might become uninhabitable.
Since water is densest at 4°C. all the water in a lake or
river, when it is covered with ice, is at 4°C. except that
near the surface.
Fig. 126.—
Gas 149. The Expansion Of Solids.—Most solids when
thermometer. heated expand less than liquids and gases. Careful
experiments show that expansion is:
(a) Proportional to the change in temperature.
(b) Different in different solids.
Here are a few coefficients of linear (length) expansion.
Brass 0.000018 per degree C.
Glass 0.000009 per degree C.
Ice 0.000052 per degree C.
Iron 0.000012 per degree C.
Platinum 0.000009 per degree C.
Zinc 0.000027 per degree C.
The coefficient of linear expansion is the fraction of its length that a body
expands when heated one degree.
The coefficient of cubical expansion is the fraction of its volume that a body
expands when heated one degree.
water occurs with further cooling.
Careful tests show that the water on cooling contracts until
it reaches 4°C. On cooling below this temperature it
expands. For this reason, when the water of a lake or river
freezes, the coldest water is at the surface. On account of
this the ice forms at the top instead of at the bottom. If
water contracted as it cooled to the freezing temperature
the coldest water would be at the bottom. Freezing would
begin at the bottom instead of at the surface. Lakes and
rivers would freeze solid. In the summer only in shallow
waters would all the ice melt. The result would be that fish
and other aquatic life would be killed. Climate would be
so changed that the earth might become uninhabitable.
Since water is densest at 4°C. all the water in a lake or
river, when it is covered with ice, is at 4°C. except that
near the surface.
Fig. 126.—
Gas 149. The Expansion Of Solids.—Most solids when
thermometer. heated expand less than liquids and gases. Careful
experiments show that expansion is:
(a) Proportional to the change in temperature.
(b) Different in different solids.
Here are a few coefficients of linear (length) expansion.
Brass 0.000018 per degree C.
Glass 0.000009 per degree C.
Ice 0.000052 per degree C.
Iron 0.000012 per degree C.
Platinum 0.000009 per degree C.
Zinc 0.000027 per degree C.
The coefficient of linear expansion is the fraction of its length that a body
expands when heated one degree.
The coefficient of cubical expansion is the fraction of its volume that a body
expands when heated one degree.
Page 181
The expansion of solids is used or allowed for in many cases:
a. Joints between the rails on a railroad allow for the expansion
of the rails in summer.
b. One end of a steel truss bridge is usually supported on rollers
so that it can expand and contract with changing temperatures.
(See Fig. 128.)
Fig. 128.—Truss bridge showing roller
support at one end.
c. Suspension bridges have expansion joints where the ends of
the iron girders can move in or out of an expansion joint thus
making the bridge longer or shorter according to the
temperature.
d. Iron tires are heated, slipped on to wagon wheels and then
cooled, the contraction on cooling setting them tightly in place. Fig. 127.
—
e. Metallic thermometers depend upon the movement due to Apparat
the expansion of a coiled strip of metal which turns a pointer us used
on the dial of the instrument. (See Fig. 129.) in testing
f. The wires that are fused into glass in incandescent light bulbs the
must have the same coefficient of expansion as the glass. expansio
Platinum has therefore been used for this purpose. (See table n of
above.) water.
a. Joints between the rails on a railroad allow for the expansion
of the rails in summer.
b. One end of a steel truss bridge is usually supported on rollers
so that it can expand and contract with changing temperatures.
(See Fig. 128.)
Fig. 128.—Truss bridge showing roller
support at one end.
c. Suspension bridges have expansion joints where the ends of
the iron girders can move in or out of an expansion joint thus
making the bridge longer or shorter according to the
temperature.
d. Iron tires are heated, slipped on to wagon wheels and then
cooled, the contraction on cooling setting them tightly in place. Fig. 127.
—
e. Metallic thermometers depend upon the movement due to Apparat
the expansion of a coiled strip of metal which turns a pointer us used
on the dial of the instrument. (See Fig. 129.) in testing
f. The wires that are fused into glass in incandescent light bulbs the
must have the same coefficient of expansion as the glass. expansio
Platinum has therefore been used for this purpose. (See table n of
above.) water.
Page 182
Fig. 129.—Metallic thermometer.
Important Topics
1. Expansion of Liquids; peculiarities. Anomalous expansion of water and
its results.
2. Expansion of solids; peculiarities, applications.
3. Coefficient of linear expansion.
4. Coefficient of cubical expansion.
Exercises
1. The gas within a partly inflated balloon has a volume of 1000 cu. ft. at a
pressure of 74 cm., and a temperature of 15°C. What will be the volume of
the gas when its pressure is 37 cm. and the temperature is -17°C.?
2. A man taking a full breath on the top of a mountain fourteen thousand
feet high inhales 4 liters of air, the pressure being 40 cm. What volume
would this same mass of air have in a place 600 ft. above sea-level when
the barometer reads 75 cm. and the temperature is the same as on the
mountain top?
Important Topics
1. Expansion of Liquids; peculiarities. Anomalous expansion of water and
its results.
2. Expansion of solids; peculiarities, applications.
3. Coefficient of linear expansion.
4. Coefficient of cubical expansion.
Exercises
1. The gas within a partly inflated balloon has a volume of 1000 cu. ft. at a
pressure of 74 cm., and a temperature of 15°C. What will be the volume of
the gas when its pressure is 37 cm. and the temperature is -17°C.?
2. A man taking a full breath on the top of a mountain fourteen thousand
feet high inhales 4 liters of air, the pressure being 40 cm. What volume
would this same mass of air have in a place 600 ft. above sea-level when
the barometer reads 75 cm. and the temperature is the same as on the
mountain top?
Page 183
3. If the coefficient of linear expansion of iron is 0.000012 per degree C.,
how much will an iron bridge 1000 ft. long change in length in warming
from -20°C. on a winter day to 30°C. upon a summer day.
4. What are some of the results that would follow in freezing weather if
water continually contracted on being cooled to zero instead of beginning to
expand when cooled below 4°C.?
5. Mention two instances that you have noticed of expansion occurring
when a body is heated?
6. Compare the density of air at 30°C. with that at 10°C. at the same
pressure. If both are present in a room, where will each be found? Why?
7. Compare the density of water at 40°C. with that at 10°C. If water at the
two temperatures are in a tank, where will each be found? Why?
8. If water at 0°C. and at 4°C. are both in a tank, where will each be found?
Why?
9. How much heat will be required to raise the temperature of a cubic foot
of water 10°F.?
10. How much heat will be required to raise the temperature of 4 liters of
water 25°C.?
11. How much longer would the cables of the Brooklyn suspension bridge
be on a summer's day when the temperature is 30°C. than in winter at
-20°C., the length of cable between the supports being about 1600 ft.
12. If 25 liters of air at -23°C. is warmed to 77°C. under constant pressure,
what will be the resulting volume of air? Explain.
13. White pig iron melts at about 2000°F. Express this temperature upon the
centigrade and absolute scales.
14. If 200 ccm. of air at 76 cm. pressure and 27°C. temperature be heated to
127°C. at a pressure of 38 cm. what will be the resulting volume?
15. A balloon contains 10,000 cu. ft. of gas at 75.2 cm. pressure and 24°C.
It ascends until the pressure is 18 cm. and the temperature is -10°C. What is
the volume of gas it then contains.
how much will an iron bridge 1000 ft. long change in length in warming
from -20°C. on a winter day to 30°C. upon a summer day.
4. What are some of the results that would follow in freezing weather if
water continually contracted on being cooled to zero instead of beginning to
expand when cooled below 4°C.?
5. Mention two instances that you have noticed of expansion occurring
when a body is heated?
6. Compare the density of air at 30°C. with that at 10°C. at the same
pressure. If both are present in a room, where will each be found? Why?
7. Compare the density of water at 40°C. with that at 10°C. If water at the
two temperatures are in a tank, where will each be found? Why?
8. If water at 0°C. and at 4°C. are both in a tank, where will each be found?
Why?
9. How much heat will be required to raise the temperature of a cubic foot
of water 10°F.?
10. How much heat will be required to raise the temperature of 4 liters of
water 25°C.?
11. How much longer would the cables of the Brooklyn suspension bridge
be on a summer's day when the temperature is 30°C. than in winter at
-20°C., the length of cable between the supports being about 1600 ft.
12. If 25 liters of air at -23°C. is warmed to 77°C. under constant pressure,
what will be the resulting volume of air? Explain.
13. White pig iron melts at about 2000°F. Express this temperature upon the
centigrade and absolute scales.
14. If 200 ccm. of air at 76 cm. pressure and 27°C. temperature be heated to
127°C. at a pressure of 38 cm. what will be the resulting volume?
15. A balloon contains 10,000 cu. ft. of gas at 75.2 cm. pressure and 24°C.
It ascends until the pressure is 18 cm. and the temperature is -10°C. What is
the volume of gas it then contains.
Page 184
16. A gas holder contains 50 "cu. ft." of gas at a pressure of one atmosphere
and 62°F. How much gas will it hold at 10 atmospheres and 32°F.
17. One thousand "cubic feet" of illuminating gas has what volume with 75
lbs. pressure and temperature of 10°C.
18. Define a "cubic foot" of illuminating gas.
150. Methods of Transmitting Heat.—One of the most practical benefits
of the study of heat is clearer understanding of the different methods by
which heat is transferred from one place to another and an intelligent idea
of the means employed to prevent the transfer of heat.
It should be definitely understood at the beginning that cold signifies the
absence of heat, just as darkness implies the absence of light, so when one
speaks of cold getting into a house what is really meant is either the
entrance of cold air by some opening or else the escape of the heat.
There are three distinct methods by which heat energy is transferred from
one place to another, depending upon the medium or substance that
transfers the heat.
a. A solid transmits heat by the method called conduction.
b. A fluid, either a liquid or a gas, transmits heat mainly by the method
called convection.
c. Space transmits the energy of hot objects by the method called radiation.
151. Conduction.—To illustrate conduction, place in a gas flame the ends
of same metal wires supported as in Fig. 130. In a short time the other ends
of the wires become hot enough to burn one's hand. This may be explained
as follows: The hot gas flame contains molecules in violent vibration and
those striking the wire set its molecules rapidly vibrating. Since, in a solid,
the molecules are held in the same relative positions, when one end of a
wire is heated the rapidly vibrating molecules at the hot end set their
neighbors vibrating and these the next in turn and so on until the whole wire
is hot. It is a fortunate circumstance that different substances have different
rates of conductivity for heat. To realize this, suppose that our clothing were
as good a conductor as iron, clothing would then be very uncomfortable
both in hot and in cold weather. The best conductors for heat are metals. It
is interesting to note that, as a rule good conductors of heat are also good
and 62°F. How much gas will it hold at 10 atmospheres and 32°F.
17. One thousand "cubic feet" of illuminating gas has what volume with 75
lbs. pressure and temperature of 10°C.
18. Define a "cubic foot" of illuminating gas.
150. Methods of Transmitting Heat.—One of the most practical benefits
of the study of heat is clearer understanding of the different methods by
which heat is transferred from one place to another and an intelligent idea
of the means employed to prevent the transfer of heat.
It should be definitely understood at the beginning that cold signifies the
absence of heat, just as darkness implies the absence of light, so when one
speaks of cold getting into a house what is really meant is either the
entrance of cold air by some opening or else the escape of the heat.
There are three distinct methods by which heat energy is transferred from
one place to another, depending upon the medium or substance that
transfers the heat.
a. A solid transmits heat by the method called conduction.
b. A fluid, either a liquid or a gas, transmits heat mainly by the method
called convection.
c. Space transmits the energy of hot objects by the method called radiation.
151. Conduction.—To illustrate conduction, place in a gas flame the ends
of same metal wires supported as in Fig. 130. In a short time the other ends
of the wires become hot enough to burn one's hand. This may be explained
as follows: The hot gas flame contains molecules in violent vibration and
those striking the wire set its molecules rapidly vibrating. Since, in a solid,
the molecules are held in the same relative positions, when one end of a
wire is heated the rapidly vibrating molecules at the hot end set their
neighbors vibrating and these the next in turn and so on until the whole wire
is hot. It is a fortunate circumstance that different substances have different
rates of conductivity for heat. To realize this, suppose that our clothing were
as good a conductor as iron, clothing would then be very uncomfortable
both in hot and in cold weather. The best conductors for heat are metals. It
is interesting to note that, as a rule good conductors of heat are also good
Page 185
conductors of electricity, while poor conductors of
heat are also poor electric conductors. Careful
experiments in testing the rate that heat will be
conducted through different substances show the
following rates of conductivity.
These figures are averages
taken mainly from the
Smithsonian Physical
Tables:
Silver 100
Copper 74 Fig. 130.—Solids
Aluminum 35 conduct heat.
Brass 27
Zinc 26
Iron 15
Fig. 131.—Water is a Tin 14.7
poor conductor of German silver 8.4
heat. Mercury 1.7
Granite 0.53
Limestone 0.52
Ice 0.5
Glass 0.2
Water 0.124
Pine, with grain 0.03
Pine, across grain 0.01
Felt 0.008
Air 0.005
To test the conductivity of liquids, take a test-tube nearly full of cold water,
hold the lower end in the hand while the tube is inclined so that the upper
end is heated by a gas flame until the water boils. The lower end will be
found to remain cold. (See Fig. 131.) Careful measurements of the
conductivity of water show that heat is transmitted through it only {1/800}
as rapidly as in silver, while air conducts but {1/25} as rapidly as water.
heat are also poor electric conductors. Careful
experiments in testing the rate that heat will be
conducted through different substances show the
following rates of conductivity.
These figures are averages
taken mainly from the
Smithsonian Physical
Tables:
Silver 100
Copper 74 Fig. 130.—Solids
Aluminum 35 conduct heat.
Brass 27
Zinc 26
Iron 15
Fig. 131.—Water is a Tin 14.7
poor conductor of German silver 8.4
heat. Mercury 1.7
Granite 0.53
Limestone 0.52
Ice 0.5
Glass 0.2
Water 0.124
Pine, with grain 0.03
Pine, across grain 0.01
Felt 0.008
Air 0.005
To test the conductivity of liquids, take a test-tube nearly full of cold water,
hold the lower end in the hand while the tube is inclined so that the upper
end is heated by a gas flame until the water boils. The lower end will be
found to remain cold. (See Fig. 131.) Careful measurements of the
conductivity of water show that heat is transmitted through it only {1/800}
as rapidly as in silver, while air conducts but {1/25} as rapidly as water.
Page 186
Fig. 132.—Wall construction of a refrigerator.
1, Porcelain enamel lining lock joint; 2, inside
wood lining; 3, 3-ply red rope waterproof
paper; 4, wool felt deafening paper; 5,
flaxlinum insulation; 6, dead air space; 7,
flaxlinum insulation; 8, wool felt deafening
paper; 9, 3-ply red rope waterproof paper; 10,
outside wood case.
Fig. 133.—Sectional view of a Thermos bottle.
152. Non-conductors and Their Uses.—Many solids, however, are poor
conductors, as leather, fur, felt, and woolen cloth. These substances owe
their non-conductivity mainly to the fact that they are porous. The air which
fills the minute spaces of these substances is one of the poorest conductors
known and hinders the transfer of heat through these solids. For the same
1, Porcelain enamel lining lock joint; 2, inside
wood lining; 3, 3-ply red rope waterproof
paper; 4, wool felt deafening paper; 5,
flaxlinum insulation; 6, dead air space; 7,
flaxlinum insulation; 8, wool felt deafening
paper; 9, 3-ply red rope waterproof paper; 10,
outside wood case.
Fig. 133.—Sectional view of a Thermos bottle.
152. Non-conductors and Their Uses.—Many solids, however, are poor
conductors, as leather, fur, felt, and woolen cloth. These substances owe
their non-conductivity mainly to the fact that they are porous. The air which
fills the minute spaces of these substances is one of the poorest conductors
known and hinders the transfer of heat through these solids. For the same
Page 187
reason loosely packed snow is a protection to vegetation covered by it
during a period of severe cold in winter. The efficiency of storm sash or
double windows, and of the double and triple walls of ice-houses and
refrigerators (see Fig. 132) in preventing the conduction of heat is also
largely due to the poor conductivity of the air confined in the spaces
between the walls. To prevent the circulation of the air, sawdust, charcoal,
and other porous material is often loosely packed into the space between the
walls of such structure.
Other illustrations of effective non-conductors will occur to every one; such
as woolen clothing, wooden handles for hot objects, and the packing used in
fireless cookers. A Thermos bottle is effective as a non-conductor of heat
because the space between the double walls has the air exhausted from it
(Figs. 133 and 134).
Of several objects in a cold room, some feel much colder to the touch than
others, thus iron, marble, oil cloth, and earthenware will feel colder than
woolen cloth, carpet, feathers, or paper. The first four objects feel cold
because they are conductors, and conduct the heat away from the hand
rapidly. The other substances named are non-conductors and hence remove
heat from the hand less rapidly, and therefore do not feel so cold. In a
similar way, if several hot objects are touched by the hand, the good
conductors are the ones which will burn one most quickly by conducting
heat rapidly to the hand. The non-conductors, however, will rarely burn one.
Why are the handles of hot utensils often made of non-conducting materials
such as wood, cloth, asbestos, etc.?
153. Radiation is the method by which heat comes to us from the sun
across space containing no tangible matter. It is also the method by which
heat gets to us when we stand near a fire. Everyone has noticed that this
heat is cut off by holding an object between the person and the fire. This
fact indicates that radiant heat travels in straight lines.
The radiation of heat is believed to be accomplished by means of waves in
a medium called ether, which is invisible and yet pervades everything.
Three of the most important characteristics of radiation are first, heat is
transferred by radiation with the speed of light, or 186,000 miles per
second. This fact is shown by the cutting off of both the sun's heat and light
at the same instant during an eclipse of the sun. Second, radiant heat[I]
during a period of severe cold in winter. The efficiency of storm sash or
double windows, and of the double and triple walls of ice-houses and
refrigerators (see Fig. 132) in preventing the conduction of heat is also
largely due to the poor conductivity of the air confined in the spaces
between the walls. To prevent the circulation of the air, sawdust, charcoal,
and other porous material is often loosely packed into the space between the
walls of such structure.
Other illustrations of effective non-conductors will occur to every one; such
as woolen clothing, wooden handles for hot objects, and the packing used in
fireless cookers. A Thermos bottle is effective as a non-conductor of heat
because the space between the double walls has the air exhausted from it
(Figs. 133 and 134).
Of several objects in a cold room, some feel much colder to the touch than
others, thus iron, marble, oil cloth, and earthenware will feel colder than
woolen cloth, carpet, feathers, or paper. The first four objects feel cold
because they are conductors, and conduct the heat away from the hand
rapidly. The other substances named are non-conductors and hence remove
heat from the hand less rapidly, and therefore do not feel so cold. In a
similar way, if several hot objects are touched by the hand, the good
conductors are the ones which will burn one most quickly by conducting
heat rapidly to the hand. The non-conductors, however, will rarely burn one.
Why are the handles of hot utensils often made of non-conducting materials
such as wood, cloth, asbestos, etc.?
153. Radiation is the method by which heat comes to us from the sun
across space containing no tangible matter. It is also the method by which
heat gets to us when we stand near a fire. Everyone has noticed that this
heat is cut off by holding an object between the person and the fire. This
fact indicates that radiant heat travels in straight lines.
The radiation of heat is believed to be accomplished by means of waves in
a medium called ether, which is invisible and yet pervades everything.
Three of the most important characteristics of radiation are first, heat is
transferred by radiation with the speed of light, or 186,000 miles per
second. This fact is shown by the cutting off of both the sun's heat and light
at the same instant during an eclipse of the sun. Second, radiant heat[I]
Page 188
travels in straight lines, while other modes of transferring
heat may follow irregular paths. The straight line motion of
radiant heat is shown by its being cut off where a screen is
placed between the source of heat and the object sheltered.
Third, radiant heat may pass through an object without
heating it. This is shown by the coldness of the upper layers
of the atmosphere and also by the fact that a pane of glass
may not be heated appreciably by the heat and light from the
sun which passes through it.
When radiant energy falls upon any object it may be (a)
reflected at the surface of the object, (b) transmitted through
Fig. 134. the substance, (c), absorbed. All three of these effects occur in
—Cross- different degrees with different portions of the radiation. Well-
section of polished surfaces are good reflectors. Rough and blackened
the surfaces are good absorbers. Transparent objects are those
vacuum which transmit light well, but even they absorb some of the
flask in a energy.
Thermos 154. The Radiometer.—Radiant heat may be detected by
bottle. means of the radiometer (Fig. 135). This consists of a glass
bulb from which the air has been nearly exhausted. Within it
is a wheel with four vanes of mica or of aluminum mounted on a vertical
axis. One side of each vane is covered with lampblack, the other being
highly polished. when exposed to radiant heat from any source the vanes
revolve with the bright side in advance.
The bulb is so nearly exhausted of air that a single molecule remaining may
travel from the walls of the bulb to the vanes without coming in contact
with another molecule.
The blackened sides absorb more heat than the highly polished sides. The
air molecules striking these blackened sides receive more heat and so
rebound with greater velocity than from the other side, thus exerting greater
pressure. The blackened sides therefore are driven backward. If the air were
not so rarified the air molecules would hit each other so frequently as to
equalize the pressure and there would be no motion.
Sun's Radiation.—Accurate tests of the amount of the sun's radiation
received upon a square centimeter of the earth's surface perpendicular to the
heat may follow irregular paths. The straight line motion of
radiant heat is shown by its being cut off where a screen is
placed between the source of heat and the object sheltered.
Third, radiant heat may pass through an object without
heating it. This is shown by the coldness of the upper layers
of the atmosphere and also by the fact that a pane of glass
may not be heated appreciably by the heat and light from the
sun which passes through it.
When radiant energy falls upon any object it may be (a)
reflected at the surface of the object, (b) transmitted through
Fig. 134. the substance, (c), absorbed. All three of these effects occur in
—Cross- different degrees with different portions of the radiation. Well-
section of polished surfaces are good reflectors. Rough and blackened
the surfaces are good absorbers. Transparent objects are those
vacuum which transmit light well, but even they absorb some of the
flask in a energy.
Thermos 154. The Radiometer.—Radiant heat may be detected by
bottle. means of the radiometer (Fig. 135). This consists of a glass
bulb from which the air has been nearly exhausted. Within it
is a wheel with four vanes of mica or of aluminum mounted on a vertical
axis. One side of each vane is covered with lampblack, the other being
highly polished. when exposed to radiant heat from any source the vanes
revolve with the bright side in advance.
The bulb is so nearly exhausted of air that a single molecule remaining may
travel from the walls of the bulb to the vanes without coming in contact
with another molecule.
The blackened sides absorb more heat than the highly polished sides. The
air molecules striking these blackened sides receive more heat and so
rebound with greater velocity than from the other side, thus exerting greater
pressure. The blackened sides therefore are driven backward. If the air were
not so rarified the air molecules would hit each other so frequently as to
equalize the pressure and there would be no motion.
Sun's Radiation.—Accurate tests of the amount of the sun's radiation
received upon a square centimeter of the earth's surface perpendicular to the
Page 189
sun's rays were made at Mt. Wilson in 1913. The average
of 690 observations gave a value of 1.933 calories per
minute. These results indicate that the sun's radiation per
square centimeter is sufficient to warm 1 g. of water
1.933°C. each minute. Although the nature of radiation is
not discussed until Art. 408-411 in light, it should be said
here that all bodies are radiating heat waves at all
temperatures, the heat waves from cool bodies being much
longer than those from hot bodies. Glass allows the short
luminous waves to pass through freely but the longer heat
waves from objects at the room temperature pass through
with difficulty. This is the reason why glass is used in the
covering of greenhouses and hot beds. Water also absorbs
many of the longer heat waves. It is therefore used in
Fig. 135.—A stereopticons to prevent delicate lantern slides from being
radiometer. injured by overheating.
Important Topics
1. Conduction in solids, liquids, gases.
2. Non-conductors; uses, best non-conductors.
3. Radiation, three characteristics.
4. The sun's radiation, amount. The radiometer.
Exercises
1. Does clothing ever afford us heat in winter? How then does it keep us
warm?
2. Why are plants often covered with paper on a night when frost is
expected?
3. Will frost form in the fall of the year sooner on a wooden or a cement
sidewalk? Why? On which does ice remain longer? Why?
4. Why in freezing ice-cream do we put the ice in a wooden pail and the
cream in a tin one?
of 690 observations gave a value of 1.933 calories per
minute. These results indicate that the sun's radiation per
square centimeter is sufficient to warm 1 g. of water
1.933°C. each minute. Although the nature of radiation is
not discussed until Art. 408-411 in light, it should be said
here that all bodies are radiating heat waves at all
temperatures, the heat waves from cool bodies being much
longer than those from hot bodies. Glass allows the short
luminous waves to pass through freely but the longer heat
waves from objects at the room temperature pass through
with difficulty. This is the reason why glass is used in the
covering of greenhouses and hot beds. Water also absorbs
many of the longer heat waves. It is therefore used in
Fig. 135.—A stereopticons to prevent delicate lantern slides from being
radiometer. injured by overheating.
Important Topics
1. Conduction in solids, liquids, gases.
2. Non-conductors; uses, best non-conductors.
3. Radiation, three characteristics.
4. The sun's radiation, amount. The radiometer.
Exercises
1. Does clothing ever afford us heat in winter? How then does it keep us
warm?
2. Why are plants often covered with paper on a night when frost is
expected?
3. Will frost form in the fall of the year sooner on a wooden or a cement
sidewalk? Why? On which does ice remain longer? Why?
4. Why in freezing ice-cream do we put the ice in a wooden pail and the
cream in a tin one?
Page 190
5. Is iron better than brick or porcelain as a material for stoves? Explain.
6. Which is better, a good or a poor conductor for keeping a body warm? for
keeping a body cool?
7. Should the bottom of a teakettle be polished? Explain.
8. How are safes made fireproof?
9. Explain the principle of the Thermos bottle.
10. Explain why the coiled wire handles of some objects as stove-lid lifters,
oven doors, etc., do not get hot.
(5) Transmission of Heat in Fluids. Heating and Ventilation
155. Convection.—While fluids are poor conductors, they may transmit
heat more effectively than solids by the mode called convection. To
illustrate: if heat is applied at the top of a test-tube of water, the hot water
being lighter is found at the top, while at the bottom the water remains cold.
On the other hand, if heat is applied at the bottom of the vessel, as soon as
the water at the bottom is warmed (above 4°C.) it expands, becomes lighter
and is pushed up to the top by the colder, denser water about it. This
circulation of water continues as long as heat is applied below, until all of
the water is brought to the boiling temperature. (See Fig. 136.)
When a liquid or a gas is heated in the manner just described, the heat is
said to be transferred by convection. Thus the air in the lower part of a room
may receive heat by conduction from a stove or radiator. As it expands on
being warmed, it is pushed up by the colder denser air about it, which takes
its place, thus creating a circulation of the air in the room. (See Fig. 137.)
The heated currents of air give up their heat to the objects in the room as the
circulation continues. These air currents may be observed readily by using
the smoke from burning "touch paper" (unglazed paper that has been dipped
into a solution of potassium nitrate ["saltpeter"] and dried).
156. Draft of a Chimney.—When a fire is started in a stove or a furnace
the air above the fire becomes heated, expands, and therefore is less dense
than it was before. This warm air and the heated gases which are the
products of the combustion of the fuel weigh less than an equal volume of
the colder air outside. Therefore they are pushed upward by a force equal to
6. Which is better, a good or a poor conductor for keeping a body warm? for
keeping a body cool?
7. Should the bottom of a teakettle be polished? Explain.
8. How are safes made fireproof?
9. Explain the principle of the Thermos bottle.
10. Explain why the coiled wire handles of some objects as stove-lid lifters,
oven doors, etc., do not get hot.
(5) Transmission of Heat in Fluids. Heating and Ventilation
155. Convection.—While fluids are poor conductors, they may transmit
heat more effectively than solids by the mode called convection. To
illustrate: if heat is applied at the top of a test-tube of water, the hot water
being lighter is found at the top, while at the bottom the water remains cold.
On the other hand, if heat is applied at the bottom of the vessel, as soon as
the water at the bottom is warmed (above 4°C.) it expands, becomes lighter
and is pushed up to the top by the colder, denser water about it. This
circulation of water continues as long as heat is applied below, until all of
the water is brought to the boiling temperature. (See Fig. 136.)
When a liquid or a gas is heated in the manner just described, the heat is
said to be transferred by convection. Thus the air in the lower part of a room
may receive heat by conduction from a stove or radiator. As it expands on
being warmed, it is pushed up by the colder denser air about it, which takes
its place, thus creating a circulation of the air in the room. (See Fig. 137.)
The heated currents of air give up their heat to the objects in the room as the
circulation continues. These air currents may be observed readily by using
the smoke from burning "touch paper" (unglazed paper that has been dipped
into a solution of potassium nitrate ["saltpeter"] and dried).
156. Draft of a Chimney.—When a fire is started in a stove or a furnace
the air above the fire becomes heated, expands, and therefore is less dense
than it was before. This warm air and the heated gases which are the
products of the combustion of the fuel weigh less than an equal volume of
the colder air outside. Therefore they are pushed upward by a force equal to
Page 191
the difference between their weight and the
weight of an equal volume of the colder air.
The chimney soon becomes filled with these
heated gases. (See Fig. 138.) These are pushed
upward by the pressure of the colder, denser air,
because this colder air is pulled downward more
strongly by the force of gravity than are the
heated gases in the chimney.
Other things being equal, the taller the chimney,
the greater the draft, because there is a greater
difference between the weight of the gases
inside and the weight of an equal volume of
outside air.
Fig. 136.—Convection
in a liquid.
Fig. 137.—Convection currents in a room.
Fig. 138.—Fire place showing draft of a
chimney.
weight of an equal volume of the colder air.
The chimney soon becomes filled with these
heated gases. (See Fig. 138.) These are pushed
upward by the pressure of the colder, denser air,
because this colder air is pulled downward more
strongly by the force of gravity than are the
heated gases in the chimney.
Other things being equal, the taller the chimney,
the greater the draft, because there is a greater
difference between the weight of the gases
inside and the weight of an equal volume of
outside air.
Fig. 136.—Convection
in a liquid.
Fig. 137.—Convection currents in a room.
Fig. 138.—Fire place showing draft of a
chimney.
Page 192
157. Convection Currents in Nature.—Winds are produced by differences
in the pressure or density of the air, the movement being from places of
high toward places of low pressure. One of the causes of a difference in
density of the air is a difference in temperature. This is illustrated by what
are called the land and sea breezes along the sea shore or large lakes.
During the day, the temperature of the land becomes higher than that of the
sea. The air over the land expands and being lighter is moved back and
upward by the colder, denser air from the sea or lake. This constitutes the
sea breezes (Fig. 139). At night the land becomes cooler much sooner than
the sea and the current is reversed causing the land breeze. (See Fig. 140.)
Fig. 139.—Sea breeze.
Fig. 140.—Land breeze.
The trade winds are convection currents moving toward the hot equatorial
belt from both the north and the south. In the hot belt the air rises and the
upper air flows back to the north and the south. This region of ascending
currents of air is a region of heavy rainfall, since the saturated air rises to
cool altitudes where its moisture is condensed. The ocean currents are also
convection currents. Their motion is due to prevailing winds, differences in
density due to evaporation and freezing, and to the rotation of the earth, as
well as to changes in temperature.
158. The heating and ventilation of buildings and the problems connected
therewith are matters of serious concern to all who live in winter in the
temperate zone. Not only should the air in living rooms be comfortably
heated, but it should be continually changed especially in the crowded
rooms of public buildings, as those of schools, churches, and assembly
halls, so that each person may be supplied with 30 or more cubic feet of
fresh air per minute. In the colonial days, the open fire place afforded the
ordinary means for heating rooms. This heated the room mainly by
radiation. It was wasteful as most of the heat passed up the chimney. This
mode of heating secured ample ventilation. Fire places are sometimes built
in modern homes as an aid to ventilation.
in the pressure or density of the air, the movement being from places of
high toward places of low pressure. One of the causes of a difference in
density of the air is a difference in temperature. This is illustrated by what
are called the land and sea breezes along the sea shore or large lakes.
During the day, the temperature of the land becomes higher than that of the
sea. The air over the land expands and being lighter is moved back and
upward by the colder, denser air from the sea or lake. This constitutes the
sea breezes (Fig. 139). At night the land becomes cooler much sooner than
the sea and the current is reversed causing the land breeze. (See Fig. 140.)
Fig. 139.—Sea breeze.
Fig. 140.—Land breeze.
The trade winds are convection currents moving toward the hot equatorial
belt from both the north and the south. In the hot belt the air rises and the
upper air flows back to the north and the south. This region of ascending
currents of air is a region of heavy rainfall, since the saturated air rises to
cool altitudes where its moisture is condensed. The ocean currents are also
convection currents. Their motion is due to prevailing winds, differences in
density due to evaporation and freezing, and to the rotation of the earth, as
well as to changes in temperature.
158. The heating and ventilation of buildings and the problems connected
therewith are matters of serious concern to all who live in winter in the
temperate zone. Not only should the air in living rooms be comfortably
heated, but it should be continually changed especially in the crowded
rooms of public buildings, as those of schools, churches, and assembly
halls, so that each person may be supplied with 30 or more cubic feet of
fresh air per minute. In the colonial days, the open fire place afforded the
ordinary means for heating rooms. This heated the room mainly by
radiation. It was wasteful as most of the heat passed up the chimney. This
mode of heating secured ample ventilation. Fire places are sometimes built
in modern homes as an aid to ventilation.
Page 193
Benjamin Franklin seeing the waste of heat in the open fire places devised
an iron box to contain the fire. This was placed in the room and provided
heat by conduction, convection, and radiation. It was called Franklin's stove
and in many forms is still commonly used. It saves a large part of the heat
produced by burning the fuel and some ventilation is provided by its draft.
Fig. 141.—Heating and ventilating by means
of a hot-air furnace.
159. Heating by Hot Air.—The presence of stoves in living rooms of
homes is accompanied by the annoyance of scattered fuel, dust, ashes,
smoke, etc. One attempt to remove this inconvenience led to placing a large
stove or fire box in the basement or cellar, surrounding this with a jacket to
provide a space for heating air which is then conducted by pipes to the
rooms above. This device is called the hot-air furnace. (See Fig. 141.) The
heated air rises because it is pushed up by colder, denser air which enters
through the cold-air pipes. The hot-air furnace provides a good circulation
of warm air and also ventilation, provided some cold air is admitted to the
furnace from the outside. One objection to its use is that it may not heat a
building evenly, one part being very hot while another may be cool. To
provide even and sufficient heat throughout a large building, use is made of
hot water or steam heating.
an iron box to contain the fire. This was placed in the room and provided
heat by conduction, convection, and radiation. It was called Franklin's stove
and in many forms is still commonly used. It saves a large part of the heat
produced by burning the fuel and some ventilation is provided by its draft.
Fig. 141.—Heating and ventilating by means
of a hot-air furnace.
159. Heating by Hot Air.—The presence of stoves in living rooms of
homes is accompanied by the annoyance of scattered fuel, dust, ashes,
smoke, etc. One attempt to remove this inconvenience led to placing a large
stove or fire box in the basement or cellar, surrounding this with a jacket to
provide a space for heating air which is then conducted by pipes to the
rooms above. This device is called the hot-air furnace. (See Fig. 141.) The
heated air rises because it is pushed up by colder, denser air which enters
through the cold-air pipes. The hot-air furnace provides a good circulation
of warm air and also ventilation, provided some cold air is admitted to the
furnace from the outside. One objection to its use is that it may not heat a
building evenly, one part being very hot while another may be cool. To
provide even and sufficient heat throughout a large building, use is made of
hot water or steam heating.
Page 194
Fig. 142.—A hot-water system of heating.
Page 195
Fig. 143.—One-pipe system of steam heating.
160. Hot-water Heating.—In hot-water heating a furnace arranged for
heating water is placed in the basement. (See Fig. 142.) Attached to the top
of the heater are pipes leading to the radiators in the various rooms; other
pipes connect the radiators to the bottom of the boiler. The heater, pipes,
and radiators are all filled with water before the fire is started. When the
water is warmed, it expands and is pushed up through the pipes by the
colder water in the return pipe. The circulation continuing brings hot water
to the radiator while the cooled water returns to the heater, the hot radiators
heating the several rooms.
161. Steam Heating.—In steam heating a steam boiler is connected to
radiators by pipes. (See Fig. 143.) The steam drives the air out of the pipes
and radiators and serves as an efficient source of heat. Heating by steam is
quicker than heating with hot water. It is therefore preferred where quick,
efficient heating is required. Hot water is less intense and more economical
in mild weather and is often used in private homes.
162. Direct and Indirect Heating.—In heating by direct radiation (Figs.
142, 143), the steam or hot-water radiators are placed in the rooms to be
heated. With direct radiation, ventilation must be provided by special
means, such as opening windows, doors, and ventilators. Sometimes
radiators are placed in a box or room in the basement. Air from out of doors
is then driven by a fan over and about the hot radiators. The air thus heated
is conducted by pipes to the several rooms. This arrangement is called
160. Hot-water Heating.—In hot-water heating a furnace arranged for
heating water is placed in the basement. (See Fig. 142.) Attached to the top
of the heater are pipes leading to the radiators in the various rooms; other
pipes connect the radiators to the bottom of the boiler. The heater, pipes,
and radiators are all filled with water before the fire is started. When the
water is warmed, it expands and is pushed up through the pipes by the
colder water in the return pipe. The circulation continuing brings hot water
to the radiator while the cooled water returns to the heater, the hot radiators
heating the several rooms.
161. Steam Heating.—In steam heating a steam boiler is connected to
radiators by pipes. (See Fig. 143.) The steam drives the air out of the pipes
and radiators and serves as an efficient source of heat. Heating by steam is
quicker than heating with hot water. It is therefore preferred where quick,
efficient heating is required. Hot water is less intense and more economical
in mild weather and is often used in private homes.
162. Direct and Indirect Heating.—In heating by direct radiation (Figs.
142, 143), the steam or hot-water radiators are placed in the rooms to be
heated. With direct radiation, ventilation must be provided by special
means, such as opening windows, doors, and ventilators. Sometimes
radiators are placed in a box or room in the basement. Air from out of doors
is then driven by a fan over and about the hot radiators. The air thus heated
is conducted by pipes to the several rooms. This arrangement is called
Page 196
indirect heating. (See Fig. 144.)
The latter method, it may be
observed, provides both heat and
ventilation, and hence is often used
in schools, churches, court houses,
and stores. Since heated air,
especially in cold weather, has a
low relative humidity some means
of moistening the air of living
rooms should be provided. Air
when too dry is injurious to the
health and also to furniture and
Fig. 144.—Heating by an indirect
radiator with side-wall register. wood work. The excessive drying
of wood and glue in a piece of
furniture often causes it to fall
apart.
163.
Vacuum
Steam
Heating
.—In
steam
heating,
air
valves
(Fig.
145) are
placed
on the
Fig. 145.—An radiators
automatic air valve. to allow
the air
they contain to escape when the Fig. 146.—An automatic vacuum
steam is turned on. When all the air valve.
is driven out the valve closes.
Automatic vacuum valves (Fig. 146) are sometimes used. When the fire is
low and there is no steam pressure in the radiators the pressure of the air
The latter method, it may be
observed, provides both heat and
ventilation, and hence is often used
in schools, churches, court houses,
and stores. Since heated air,
especially in cold weather, has a
low relative humidity some means
of moistening the air of living
rooms should be provided. Air
when too dry is injurious to the
health and also to furniture and
Fig. 144.—Heating by an indirect
radiator with side-wall register. wood work. The excessive drying
of wood and glue in a piece of
furniture often causes it to fall
apart.
163.
Vacuum
Steam
Heating
.—In
steam
heating,
air
valves
(Fig.
145) are
placed
on the
Fig. 145.—An radiators
automatic air valve. to allow
the air
they contain to escape when the Fig. 146.—An automatic vacuum
steam is turned on. When all the air valve.
is driven out the valve closes.
Automatic vacuum valves (Fig. 146) are sometimes used. When the fire is
low and there is no steam pressure in the radiators the pressure of the air
Page 197
closes the valve, making a partial vacuum inside. The boiling point of water
falls as the pressure upon it is reduced. As water will not boil under
ordinary atmospheric pressure until its temperature is 100°C. (212°F.), it
follows that by the use of vacuum systems, often called vapor systems, of
steam heating, water will be giving off hot vapor even after the fire has
been banked for hours. This results in a considerable saving of fuel.
Fig. 147.—Plenum hot-blast system with
temperature regulation.
164. The Plenum System of Heating.—In the plenum system of heating
(see Fig. 147) fresh air is drawn through a window from outdoors and goes
first through tempering coils where the temperature is raised to about 70°.
The fan then forces some of the air through heating coils, where it is
reheated and raised to a much higher temperature, depending upon the
weather conditions. Both the hot and tempered air are kept under pressure
by the fan in the plenum room and are forced from this room through
galvanized iron ducts to the various rooms to be heated. The foul air is
forced out of the room through vent ducts which lead to the attic where it
escapes through ventilators in the roof.
falls as the pressure upon it is reduced. As water will not boil under
ordinary atmospheric pressure until its temperature is 100°C. (212°F.), it
follows that by the use of vacuum systems, often called vapor systems, of
steam heating, water will be giving off hot vapor even after the fire has
been banked for hours. This results in a considerable saving of fuel.
Fig. 147.—Plenum hot-blast system with
temperature regulation.
164. The Plenum System of Heating.—In the plenum system of heating
(see Fig. 147) fresh air is drawn through a window from outdoors and goes
first through tempering coils where the temperature is raised to about 70°.
The fan then forces some of the air through heating coils, where it is
reheated and raised to a much higher temperature, depending upon the
weather conditions. Both the hot and tempered air are kept under pressure
by the fan in the plenum room and are forced from this room through
galvanized iron ducts to the various rooms to be heated. The foul air is
forced out of the room through vent ducts which lead to the attic where it
escapes through ventilators in the roof.
Page 198
Fig. 148.—A thermostat. (Johnson System.)
A thermostat is placed in the tempered-air part of the plenum room to
maintain the proper temperature of the tempered air. This thermostat
operates the by-pass damper under the tempering coils, and sometimes the
valves on the coils. The mixing dampers at the base of the galvanized-iron
ducts are controlled by their respective room thermostats. Attic-vent, fresh-
air, and return-air dampers are under pneumatic switch control. A
humidifier can be provided readily for this system. This system of heating is
designed particularly for school houses where adequate ventilation is a
necessity.
165. The Thermostat.—One of the many examples of the expansion of
metals is shown in one form of the thermostat (Fig. 148) in which two
pieces of different metals and of unequal rates of expansion, as brass and
iron, are securely fastened together.
The thermostatic strip T moving inward and outward, as affected by the
room temperature, varies the amount of air which can escape through the
small port C. When the port C is completely closed (Fig. 148a) the full air
pressure collects on the diaphragm B which forces down the main valve,
A thermostat is placed in the tempered-air part of the plenum room to
maintain the proper temperature of the tempered air. This thermostat
operates the by-pass damper under the tempering coils, and sometimes the
valves on the coils. The mixing dampers at the base of the galvanized-iron
ducts are controlled by their respective room thermostats. Attic-vent, fresh-
air, and return-air dampers are under pneumatic switch control. A
humidifier can be provided readily for this system. This system of heating is
designed particularly for school houses where adequate ventilation is a
necessity.
165. The Thermostat.—One of the many examples of the expansion of
metals is shown in one form of the thermostat (Fig. 148) in which two
pieces of different metals and of unequal rates of expansion, as brass and
iron, are securely fastened together.
The thermostatic strip T moving inward and outward, as affected by the
room temperature, varies the amount of air which can escape through the
small port C. When the port C is completely closed (Fig. 148a) the full air
pressure collects on the diaphragm B which forces down the main valve,
Page 199
letting the compressed air from the main pass through the chamber D into
chamber E as the valve is forced off its seat. The air from chamber E then
passes into the branch to operate the damper.
When port C is fully open (Fig. 148b) the air pressure on diaphragm B is
relieved, the back pressure in E lifts up the diaphragm and the air from the
branch escapes out through the hollow stem of the main valve, operating the
damper in the opposite direction from that when C is closed.
Important Topics
1. Transmission of heat in fluids.
2. Convection. Drafts of a chimney. Land and sea breezes.
3. Heating and ventilation of buildings.
(a) By hot air.
(b) Hot-water heating.
(c) Steam heating.
(d) Direct and indirect heating.
(e) Vacuum steam heating.
(f) The plenum system.
(g) The thermostat.
Exercises
1. Is a room heated mainly by conduction, convection, or radiation, from (a)
a stove, (b) a hot-air furnace, (c) a steam radiator?
2. Name three natural convection currents.
3. Explain the draft of a chimney. What is it? Why does it occur?
4. Make a cross-section sketch of your living room and indicate the
convection currents by which the room is heated. Explain the heating of the
room.
5. Make a sketch showing how the water in the hot-water tank in the
kitchen or laundry is heated. Explain your sketch, indicating convection
currents.
chamber E as the valve is forced off its seat. The air from chamber E then
passes into the branch to operate the damper.
When port C is fully open (Fig. 148b) the air pressure on diaphragm B is
relieved, the back pressure in E lifts up the diaphragm and the air from the
branch escapes out through the hollow stem of the main valve, operating the
damper in the opposite direction from that when C is closed.
Important Topics
1. Transmission of heat in fluids.
2. Convection. Drafts of a chimney. Land and sea breezes.
3. Heating and ventilation of buildings.
(a) By hot air.
(b) Hot-water heating.
(c) Steam heating.
(d) Direct and indirect heating.
(e) Vacuum steam heating.
(f) The plenum system.
(g) The thermostat.
Exercises
1. Is a room heated mainly by conduction, convection, or radiation, from (a)
a stove, (b) a hot-air furnace, (c) a steam radiator?
2. Name three natural convection currents.
3. Explain the draft of a chimney. What is it? Why does it occur?
4. Make a cross-section sketch of your living room and indicate the
convection currents by which the room is heated. Explain the heating of the
room.
5. Make a sketch showing how the water in the hot-water tank in the
kitchen or laundry is heated. Explain your sketch, indicating convection
currents.
Page 200
6. Is it economical to keep stoves and radiators highly polished? Explain.
7. If you open the door between a warm and a cool room what will be the
direction of the air currents at the top and at the bottom of the door?
Explain.
8. If a hot-water heating system contains 100 cu. ft. of water how much heat
will be required to raise its temperature 150°F.?
9. Why does a tall chimney give a better draft than a short one?
10. Explain how your school room is heated and ventilated.
11. Should a steam or hot-water radiator be placed near the floor or near the
ceiling of a room? Why?
12. In a hot-water heating system an open tank connected with the pipes is
placed in the attic or above the highest radiator. Explain its use.
(6) The Moisture in the Atmosphere, Hygrometry
166. Water Vapor in the Air.—The amount of water vapor present in the
air has a marked effect upon the weather and the climate of a locality. The
study of the moisture conditions of the atmosphere, or hygrometry, is
therefore a matter of general interest and importance. The water vapor in
the atmosphere is entirely due to evaporation from bodies of water, or snow,
or ice. In the discussion of evaporation, it is described as due to the gradual
escape of molecules into the air from the surface of a liquid. This
description fits exactly the conditions found by all careful observers. Since
the air molecules are continually striking the surface of the liquid, many of
them penetrate it and become absorbed. In the same manner many vapor
molecules reenter the liquid, and if enough vapor molecules are present in
the air so that as many vapor molecules reenter the liquid each second as
leave it, the space above the liquid is said to be saturated as previously
described. (See Art. 18.)
167. Conditions for Saturation.—If a liquid is evaporating into a vacuum,
the molecules on leaving find no opposition until they reach the limits of
the vessel containing the vacuum. Evaporation under these conditions goes
on with great rapidity and the space becomes saturated almost instantly. If,
however, air be present at ordinary pressure, many of the ordinary water
7. If you open the door between a warm and a cool room what will be the
direction of the air currents at the top and at the bottom of the door?
Explain.
8. If a hot-water heating system contains 100 cu. ft. of water how much heat
will be required to raise its temperature 150°F.?
9. Why does a tall chimney give a better draft than a short one?
10. Explain how your school room is heated and ventilated.
11. Should a steam or hot-water radiator be placed near the floor or near the
ceiling of a room? Why?
12. In a hot-water heating system an open tank connected with the pipes is
placed in the attic or above the highest radiator. Explain its use.
(6) The Moisture in the Atmosphere, Hygrometry
166. Water Vapor in the Air.—The amount of water vapor present in the
air has a marked effect upon the weather and the climate of a locality. The
study of the moisture conditions of the atmosphere, or hygrometry, is
therefore a matter of general interest and importance. The water vapor in
the atmosphere is entirely due to evaporation from bodies of water, or snow,
or ice. In the discussion of evaporation, it is described as due to the gradual
escape of molecules into the air from the surface of a liquid. This
description fits exactly the conditions found by all careful observers. Since
the air molecules are continually striking the surface of the liquid, many of
them penetrate it and become absorbed. In the same manner many vapor
molecules reenter the liquid, and if enough vapor molecules are present in
the air so that as many vapor molecules reenter the liquid each second as
leave it, the space above the liquid is said to be saturated as previously
described. (See Art. 18.)
167. Conditions for Saturation.—If a liquid is evaporating into a vacuum,
the molecules on leaving find no opposition until they reach the limits of
the vessel containing the vacuum. Evaporation under these conditions goes
on with great rapidity and the space becomes saturated almost instantly. If,
however, air be present at ordinary pressure, many of the ordinary water
Page 201
vapor molecules on leaving are struck and returned to the water by the air
molecules directly above. Those escaping gradually work their way upward
through the air. This explains why it is that our atmosphere is not often
saturated even near large bodies of water, the retarding effect of the air upon
the evaporation preventing more than the layers of air near the water
surface becoming saturated.
Just as the amount of salt that can be held in solution in a liquid is lessened
by cooling the solution (Art. 26), so the amount of water vapor that can be
held in the air is lessened by lowering its temperature. If air not moist
enough to be saturated with water vapor is cooled, it will, as the cooling
continues, finally reach a temperature at which it will be saturated or will
contain all the water vapor it can hold at this temperature. If the air be still
further cooled some of the water vapor will condense and may form fog,
dew, rain, snow, etc., the form it takes depending upon where and how the
cooling takes place.
168. The Formation of Dew.—If the cooling of the atmosphere is at the
surface of some cold object which lowers the temperature of the air below
its saturation point, some of its moisture condenses and collects upon the
cold surface as dew. This may be noticed upon the surface of a pitcher of
ice-water in summer. At night, the temperature of grass and other objects
near or on the ground may fall much faster than that of the atmosphere
owing to the radiation of heat from these objects. If the temperature falls
below the saturation point, dew will be formed. This natural radiation is
hindered when it is cloudy, therefore little dew forms on cloudy nights.
Clear nights help radiation, therefore we have the most dew on nights when
the sky is clear. If the temperature is below freezing, frost forms instead of
dew.
169. Formation of Fog.—If the cooling at night is great enough to cool the
body of air near the earth below the saturation temperature, then not only
may dew be formed, but some moisture is condensed in the air itself,
usually upon fine dust particles suspended in it. This constitutes a fog. If the
cooling of the body of air takes place above the earth's surface as when a
warm moist current of air enters a colder region, e.g., moves over the top of
a cold mountain, or into the upper air, then as this air is cooled below its
saturation point, condensation upon fine suspended dust particles takes
place, and a cloud is formed. If much moisture is present in the cloud, the
molecules directly above. Those escaping gradually work their way upward
through the air. This explains why it is that our atmosphere is not often
saturated even near large bodies of water, the retarding effect of the air upon
the evaporation preventing more than the layers of air near the water
surface becoming saturated.
Just as the amount of salt that can be held in solution in a liquid is lessened
by cooling the solution (Art. 26), so the amount of water vapor that can be
held in the air is lessened by lowering its temperature. If air not moist
enough to be saturated with water vapor is cooled, it will, as the cooling
continues, finally reach a temperature at which it will be saturated or will
contain all the water vapor it can hold at this temperature. If the air be still
further cooled some of the water vapor will condense and may form fog,
dew, rain, snow, etc., the form it takes depending upon where and how the
cooling takes place.
168. The Formation of Dew.—If the cooling of the atmosphere is at the
surface of some cold object which lowers the temperature of the air below
its saturation point, some of its moisture condenses and collects upon the
cold surface as dew. This may be noticed upon the surface of a pitcher of
ice-water in summer. At night, the temperature of grass and other objects
near or on the ground may fall much faster than that of the atmosphere
owing to the radiation of heat from these objects. If the temperature falls
below the saturation point, dew will be formed. This natural radiation is
hindered when it is cloudy, therefore little dew forms on cloudy nights.
Clear nights help radiation, therefore we have the most dew on nights when
the sky is clear. If the temperature is below freezing, frost forms instead of
dew.
169. Formation of Fog.—If the cooling at night is great enough to cool the
body of air near the earth below the saturation temperature, then not only
may dew be formed, but some moisture is condensed in the air itself,
usually upon fine dust particles suspended in it. This constitutes a fog. If the
cooling of the body of air takes place above the earth's surface as when a
warm moist current of air enters a colder region, e.g., moves over the top of
a cold mountain, or into the upper air, then as this air is cooled below its
saturation point, condensation upon fine suspended dust particles takes
place, and a cloud is formed. If much moisture is present in the cloud, the
Page 202
drops of water grow in size until they begin to fall and rain results; or if it is
cold enough, instead of rain, snowflakes will be formed and fall. Sometimes
whirling winds in severe thunderstorms carry the raindrops into colder and
then warmer regions, alternately freezing and moistening the drops or bits
of ice. It is in this way that hail is said to be formed.
170. The Dew Point.—The temperature to which air must be cooled to
saturate it or the temperature at which condensation begins is called the dew
point. This is often determined in the laboratory by partly filling a polished
metal vessel with water and cooling the water by adding ice until a thin film
of moisture is formed upon the outer surface. The temperature of the
surface when the moisture first forms is the dew point.
171. The Humidity of the Atmosphere.—After the dew point has been
obtained, one may compute the relative humidity or degree of saturation of
the atmosphere, from the table given below. This is defined as the ratio of
the amount of water vapor present in the air to the amount that would be
present if the air were saturated at the same temperature.
For example, if the dew point is 5°C. and the temperature of the air is
22°C., we find the densities of the water vapor at the two temperatures, and
find their ratio: 6.8/19.3 = 35 per cent. nearly. Determinations of humidity
may give indication of rain or frost and are regularly made at weather
bureau stations. They are also made in buildings such as greenhouses,
hospitals, and schoolhouses to see if the air is moist enough. For the most
healthful conditions the relative humidity should be from 40 per cent. to 50
per cent.
Weight of Water (w) in Grams Contained in 1 Cubic Meter of Saturated
Air at Various Temperatures (t°)C.
t°C. w
-10 2.1
- 9 2.4
- 8 2.7
- 7 3.0
- 6 3.2
- 5 3.5
- 4 3.8
cold enough, instead of rain, snowflakes will be formed and fall. Sometimes
whirling winds in severe thunderstorms carry the raindrops into colder and
then warmer regions, alternately freezing and moistening the drops or bits
of ice. It is in this way that hail is said to be formed.
170. The Dew Point.—The temperature to which air must be cooled to
saturate it or the temperature at which condensation begins is called the dew
point. This is often determined in the laboratory by partly filling a polished
metal vessel with water and cooling the water by adding ice until a thin film
of moisture is formed upon the outer surface. The temperature of the
surface when the moisture first forms is the dew point.
171. The Humidity of the Atmosphere.—After the dew point has been
obtained, one may compute the relative humidity or degree of saturation of
the atmosphere, from the table given below. This is defined as the ratio of
the amount of water vapor present in the air to the amount that would be
present if the air were saturated at the same temperature.
For example, if the dew point is 5°C. and the temperature of the air is
22°C., we find the densities of the water vapor at the two temperatures, and
find their ratio: 6.8/19.3 = 35 per cent. nearly. Determinations of humidity
may give indication of rain or frost and are regularly made at weather
bureau stations. They are also made in buildings such as greenhouses,
hospitals, and schoolhouses to see if the air is moist enough. For the most
healthful conditions the relative humidity should be from 40 per cent. to 50
per cent.
Weight of Water (w) in Grams Contained in 1 Cubic Meter of Saturated
Air at Various Temperatures (t°)C.
t°C. w
-10 2.1
- 9 2.4
- 8 2.7
- 7 3.0
- 6 3.2
- 5 3.5
- 4 3.8
Page 203
- 3 4.1
- 2 4.4
- 1 4.6
0 4.9
1 5.2
2 5.6
3 6.0
4 6.4
5 6.8
6 7.3
7 7.7
8 8.1
9 8.8
10 9.4
11 10.0
12 10.6
13 11.3
14 12.0
15 12.8
16 13.6
17 14.5
18 15.1
19 16.2
20 17.2
21 18.2
22 19.3
23 20.4
24 21.5
25 22.9
26 24.2
27 25.6
28 27.0
29 28.6
30 30.1
- 2 4.4
- 1 4.6
0 4.9
1 5.2
2 5.6
3 6.0
4 6.4
5 6.8
6 7.3
7 7.7
8 8.1
9 8.8
10 9.4
11 10.0
12 10.6
13 11.3
14 12.0
15 12.8
16 13.6
17 14.5
18 15.1
19 16.2
20 17.2
21 18.2
22 19.3
23 20.4
24 21.5
25 22.9
26 24.2
27 25.6
28 27.0
29 28.6
30 30.1
Page 204
172. Wet and Dry Bulb Hygrometer.—A device for indicating the relative
humidity of the air is called an hygrometer. There are various forms. The
wet and dry bulb hygrometer is shown in Fig. 149. This device consists of
two thermometers, one with its bulb dry and exposed to the air, the other
bulb being kept continually moist by a wick dipping into a vessel of water.
An application of the principle of cooling by evaporation is made in this
instrument. Unless the air is saturated so that evaporation is prevented, the
wet-bulb thermometer shows a lower temperature, the difference depending
upon the amount of moisture in the air, or upon the relative humidity. Most
determinations of relative humidity are made with this kind of instrument. It
is necessary in order to make an accurate determination, to fan or set the air
in motion about the thermometers for some time before reading them. The
relative humidity is then found by using tables giving the relative humidity
that corresponds to any reading of the thermometers.
Fig. 149.—Wet and dry bulb hygrometer.
Fig. 150.—A dial hygrometer.
A form of hygrometer in common use is shown in Fig. 150. In this device, a
thin strip of hygroscopic material (as a piece of goose quill) is formed into a
spiral coil. One end of this is fastened to a post. The other end carried a
hand or pointer. The latter moves over a printed scale and indicates directly
the relative humidity. Its indications should be tested by comparing its
humidity of the air is called an hygrometer. There are various forms. The
wet and dry bulb hygrometer is shown in Fig. 149. This device consists of
two thermometers, one with its bulb dry and exposed to the air, the other
bulb being kept continually moist by a wick dipping into a vessel of water.
An application of the principle of cooling by evaporation is made in this
instrument. Unless the air is saturated so that evaporation is prevented, the
wet-bulb thermometer shows a lower temperature, the difference depending
upon the amount of moisture in the air, or upon the relative humidity. Most
determinations of relative humidity are made with this kind of instrument. It
is necessary in order to make an accurate determination, to fan or set the air
in motion about the thermometers for some time before reading them. The
relative humidity is then found by using tables giving the relative humidity
that corresponds to any reading of the thermometers.
Fig. 149.—Wet and dry bulb hygrometer.
Fig. 150.—A dial hygrometer.
A form of hygrometer in common use is shown in Fig. 150. In this device, a
thin strip of hygroscopic material (as a piece of goose quill) is formed into a
spiral coil. One end of this is fastened to a post. The other end carried a
hand or pointer. The latter moves over a printed scale and indicates directly
the relative humidity. Its indications should be tested by comparing its
Page 205
readings with the results of dew-point determinations. The position of the
pointer may be adjusted by turning the post.
Important Topics
1. Water vapor in the air. Cause and effect.
2. Formation of dew, fog, rain, and snow.
3. Dew point, relative humidity.
4. Use of the dry- and wet-bulb hygrometer. Goose-quill hygrometer.
Exercises
1. How is the relative humidity of the air affected by warming it? Explain.
2. How does the white cloud of steam seen about a locomotive in cold
weather differ from fog? Explain.
3. In cold weather is the relative humidity of air out of doors and indoors
the same? Explain.
4. Compare the relative humidity of air in a desert and near the ocean.
5. Look up the derivation of the term "hygrometer." Give the use of the
instrument.
6. Find the relative humidity of air at 20°C. if its dew point is at 10°C.
7. How may the relative humidity of the air in a home be increased?
8. What is the effect of high humidity in the summer upon human beings?
How do you explain this?
9. Does dew fall? Explain how dew is formed?
10. In what respects is a cloud similar to a fog? In what respects different?
11. Why are icebergs frequently enveloped in fog?
12. Does dew form in the day time? Explain.
(7) Evaporation
pointer may be adjusted by turning the post.
Important Topics
1. Water vapor in the air. Cause and effect.
2. Formation of dew, fog, rain, and snow.
3. Dew point, relative humidity.
4. Use of the dry- and wet-bulb hygrometer. Goose-quill hygrometer.
Exercises
1. How is the relative humidity of the air affected by warming it? Explain.
2. How does the white cloud of steam seen about a locomotive in cold
weather differ from fog? Explain.
3. In cold weather is the relative humidity of air out of doors and indoors
the same? Explain.
4. Compare the relative humidity of air in a desert and near the ocean.
5. Look up the derivation of the term "hygrometer." Give the use of the
instrument.
6. Find the relative humidity of air at 20°C. if its dew point is at 10°C.
7. How may the relative humidity of the air in a home be increased?
8. What is the effect of high humidity in the summer upon human beings?
How do you explain this?
9. Does dew fall? Explain how dew is formed?
10. In what respects is a cloud similar to a fog? In what respects different?
11. Why are icebergs frequently enveloped in fog?
12. Does dew form in the day time? Explain.
(7) Evaporation
Page 206
173. Effects of Evaporation.—In Art. 19 the cooling effect of evaporation
is mentioned and some explanation is made of the cooling effect observed.
Since evaporation is employed in so many ways, and since its action is
simply explained by the study we have made of molecular motions and
molecular forces, it may be well to consider this subject further.
Take three shallow dishes, and place in one a little water, in another some
alcohol, and some ether in the third, the liquids being taken from bottles
that have stood several hours in the room so that all are at the same
temperature. After a short time take the temperature of the three liquids.
Each will be at a lower temperature than at first, but of the three the ether
will be found to be the coolest, alcohol next, and the water nearest its first
temperature. It will be noticed also that the ether has evaporated most in the
same time. Similar effects may be observed by placing a few drops of each
of these three liquids upon the back of one's hand, or by placing a few drops
in turn upon the bulb of a simple air thermometer.
174. Cooling Effect of Evaporation.—The molecules that leave an
evaporating liquid are naturally the swiftest moving ones, that is, the ones
having the highest temperature, so their escape leaves the liquids cooler
than before, and the one whose molecules leave fastest is naturally the one
that becomes coldest, that is, the ether, in the experiment of Art. 173. If no
air pressure were exerted upon the surface of the liquid, the escape of the
molecules would be much increased and the temperature of the liquid
would be lowered rapidly.
To test this, fill a thin watch glass with ether and place it over a thin slip of
glass with a drop of cold water between the two. Now place this apparatus
under the receiver of an air pump and exhaust the air. The rapid evaporation
of the ether so lowers its temperature, that often the drop of water is frozen.
The lowest temperatures are obtained by evaporating liquids at reduced
pressure.
Onnes by evaporating liquid helium at a pressure of about 1.2 mm. reached
the lowest temperature yet attained, -456°F., or -271.3°C.
If four thermometers are taken, the bulbs of three being wetted respectively
with ether, alcohol, and water the fourth being dry, on vigorously fanning
these, the moistened thermometers show that they have been cooled while
the dry one is unaffected.
is mentioned and some explanation is made of the cooling effect observed.
Since evaporation is employed in so many ways, and since its action is
simply explained by the study we have made of molecular motions and
molecular forces, it may be well to consider this subject further.
Take three shallow dishes, and place in one a little water, in another some
alcohol, and some ether in the third, the liquids being taken from bottles
that have stood several hours in the room so that all are at the same
temperature. After a short time take the temperature of the three liquids.
Each will be at a lower temperature than at first, but of the three the ether
will be found to be the coolest, alcohol next, and the water nearest its first
temperature. It will be noticed also that the ether has evaporated most in the
same time. Similar effects may be observed by placing a few drops of each
of these three liquids upon the back of one's hand, or by placing a few drops
in turn upon the bulb of a simple air thermometer.
174. Cooling Effect of Evaporation.—The molecules that leave an
evaporating liquid are naturally the swiftest moving ones, that is, the ones
having the highest temperature, so their escape leaves the liquids cooler
than before, and the one whose molecules leave fastest is naturally the one
that becomes coldest, that is, the ether, in the experiment of Art. 173. If no
air pressure were exerted upon the surface of the liquid, the escape of the
molecules would be much increased and the temperature of the liquid
would be lowered rapidly.
To test this, fill a thin watch glass with ether and place it over a thin slip of
glass with a drop of cold water between the two. Now place this apparatus
under the receiver of an air pump and exhaust the air. The rapid evaporation
of the ether so lowers its temperature, that often the drop of water is frozen.
The lowest temperatures are obtained by evaporating liquids at reduced
pressure.
Onnes by evaporating liquid helium at a pressure of about 1.2 mm. reached
the lowest temperature yet attained, -456°F., or -271.3°C.
If four thermometers are taken, the bulbs of three being wetted respectively
with ether, alcohol, and water the fourth being dry, on vigorously fanning
these, the moistened thermometers show that they have been cooled while
the dry one is unaffected.
Page 207
This indicates that fanning a dry body at the temperature of the air does not
change its temperature. Fanning does increase evaporation by removing the
air containing the evaporated molecules near the surface of the liquid so
that unsaturated air is continually over the liquid. If a pint of water is placed
in a bottle and another pint in a wide pan the latter will become dry much
sooner because of the greater surface over which evaporation can take
place. Application of this is made at salt works where the brine is spread out
in shallow pans.
175. Rate of Evaporation.—The rate of evaporation is affected by several
factors. These have been illustrated in the preceding paragraphs. To briefly
summarize:
The rate of evaporation of a liquid is affected by—
(a) The nature of the liquid.
(b) The temperature of the liquid.
(c) The pressure upon its evaporating surface.
(d) The degree of saturation of the space into which the liquid is
evaporating.
(e) The rate of circulation of air over its surface.
(f) The extent of surface exposed to evaporation.
176. Molecular Motion in Solids.—Evidence of molecular motion in
liquids is given by expansion on heating, evaporation, and diffusion. Do any
of these lines of evidence apply to solids? It is a fact of common experience
that solids do become larger on heating. Spaces are left between the ends of
rails on railroads so that when they expand in summer they will not distort
the track. Iron tires are placed on wheels by heating them until they slip on
easily. Then on cooling, the iron shrinks and presses the wheel tightly.
Many common demonstrations of expansion are found in lecture rooms.
The fact of the evaporation of a solid is often detected by noticing the odor
of a substance. The odor of moth balls is one example. Camphor also
evaporates. Heated tin has a characteristic odor noted by many. Ice and
snow disappear in winter even though the temperature is below freezing.
Wet clothes, "freeze dry," that is, dry after freezing, by evaporation. A few
crystals of iodine placed in a test-tube and gently heated form a vapor easily
change its temperature. Fanning does increase evaporation by removing the
air containing the evaporated molecules near the surface of the liquid so
that unsaturated air is continually over the liquid. If a pint of water is placed
in a bottle and another pint in a wide pan the latter will become dry much
sooner because of the greater surface over which evaporation can take
place. Application of this is made at salt works where the brine is spread out
in shallow pans.
175. Rate of Evaporation.—The rate of evaporation is affected by several
factors. These have been illustrated in the preceding paragraphs. To briefly
summarize:
The rate of evaporation of a liquid is affected by—
(a) The nature of the liquid.
(b) The temperature of the liquid.
(c) The pressure upon its evaporating surface.
(d) The degree of saturation of the space into which the liquid is
evaporating.
(e) The rate of circulation of air over its surface.
(f) The extent of surface exposed to evaporation.
176. Molecular Motion in Solids.—Evidence of molecular motion in
liquids is given by expansion on heating, evaporation, and diffusion. Do any
of these lines of evidence apply to solids? It is a fact of common experience
that solids do become larger on heating. Spaces are left between the ends of
rails on railroads so that when they expand in summer they will not distort
the track. Iron tires are placed on wheels by heating them until they slip on
easily. Then on cooling, the iron shrinks and presses the wheel tightly.
Many common demonstrations of expansion are found in lecture rooms.
The fact of the evaporation of a solid is often detected by noticing the odor
of a substance. The odor of moth balls is one example. Camphor also
evaporates. Heated tin has a characteristic odor noted by many. Ice and
snow disappear in winter even though the temperature is below freezing.
Wet clothes, "freeze dry," that is, dry after freezing, by evaporation. A few
crystals of iodine placed in a test-tube and gently heated form a vapor easily
Page 208
seen, even though none of the iodine melts. Where the vapor strikes the side
of the tube, it condenses back to dark gray crystals of iodine. This change
from solid directly to gas and back again without becoming liquid is called
sublimation. A number of solids are purified by this process.
Important Topics
1. Cooling effect of evaporation, rate of evaporation affected by six
conditions.
2. Effects of molecular motion in solids: (a) Expansion, (b) Evaporation, (c)
Sublimation.
Exercises
1. Does sprinkling the streets or sidewalks cool the air? Why?
2. Give an illustration for each of the factors affecting evaporation.
3. Give an illustration for each of the three evidences of molecular motions
in solids.
4. Since three-quarters of the earth's surface is covered with water, why is
not the air constantly saturated?
5. If the air has the temperature of the body, will fanning the perfectly dry
face cool one? Explain. Will the effect be the same if the face is moist?
Explain.
6. What is the cause of "Cloud Capped" mountains?
7. Why does the exhaust steam from an engine appear to have so much
greater volume on a cold day in winter than on a warm one in summer?
8. What causes an unfrozen pond or lake to "steam" on a very cold day in
winter, or on a very cool morning in summer?
9. As the air on a mountain top settles down the sides to places of greater
pressure, how will its temperature be affected? its relative humidity?
Explain.
of the tube, it condenses back to dark gray crystals of iodine. This change
from solid directly to gas and back again without becoming liquid is called
sublimation. A number of solids are purified by this process.
Important Topics
1. Cooling effect of evaporation, rate of evaporation affected by six
conditions.
2. Effects of molecular motion in solids: (a) Expansion, (b) Evaporation, (c)
Sublimation.
Exercises
1. Does sprinkling the streets or sidewalks cool the air? Why?
2. Give an illustration for each of the factors affecting evaporation.
3. Give an illustration for each of the three evidences of molecular motions
in solids.
4. Since three-quarters of the earth's surface is covered with water, why is
not the air constantly saturated?
5. If the air has the temperature of the body, will fanning the perfectly dry
face cool one? Explain. Will the effect be the same if the face is moist?
Explain.
6. What is the cause of "Cloud Capped" mountains?
7. Why does the exhaust steam from an engine appear to have so much
greater volume on a cold day in winter than on a warm one in summer?
8. What causes an unfrozen pond or lake to "steam" on a very cold day in
winter, or on a very cool morning in summer?
9. As the air on a mountain top settles down the sides to places of greater
pressure, how will its temperature be affected? its relative humidity?
Explain.
Page 209
10. On our Pacific coast, moist winds blow from the west over the
mountains. Where will it rain? Where be dry? Explain.
mountains. Where will it rain? Where be dry? Explain.
Page 210
CHAPTER VIII
HEAT AND WORK
(1) Heat Measurement and Specific Heat
177. Specific Heat.—In the study of density and specific gravity it is made
clear that different substances differ widely in the amount of matter
contained in equal volumes, e.g., lead is much denser than water. The study
of the relative densities of substance is usually considered under the subject
of specific gravity.
Specific heat as distinguished from specific gravity is concerned with the
capacity for heat possessed by different substances. The definition for
specific heat is: The ratio of the amount of heat required to change the
temperature of a given mass of a substance 1 C. degree to the amount of
heat required to change the temperature of the same mass of water 1 C.
degree. By definition, it requires 1 calorie to raise the temperature of the
gram of water 1°C. The specific heat therefore of water is taken as one. The
specific heat of most substances except hydrogen, is less than that of water,
and as a rule, the denser the body the less its specific heat, as may be
observed in the following table:
Specific gravity Specific heat
Gold 19.3 0.032
Mercury 13.6 0.033
Copper 8.9 0.093
Brass 8.4-8.9 0.094
Nickel 8.57 0.11
Iron 7.5+ 0.1125
Aluminum 2.67 0.218
Glass 2.5-3.6 0.19
Ice 0.918 0.504
Air 0.00129 0.237
HEAT AND WORK
(1) Heat Measurement and Specific Heat
177. Specific Heat.—In the study of density and specific gravity it is made
clear that different substances differ widely in the amount of matter
contained in equal volumes, e.g., lead is much denser than water. The study
of the relative densities of substance is usually considered under the subject
of specific gravity.
Specific heat as distinguished from specific gravity is concerned with the
capacity for heat possessed by different substances. The definition for
specific heat is: The ratio of the amount of heat required to change the
temperature of a given mass of a substance 1 C. degree to the amount of
heat required to change the temperature of the same mass of water 1 C.
degree. By definition, it requires 1 calorie to raise the temperature of the
gram of water 1°C. The specific heat therefore of water is taken as one. The
specific heat of most substances except hydrogen, is less than that of water,
and as a rule, the denser the body the less its specific heat, as may be
observed in the following table:
Specific gravity Specific heat
Gold 19.3 0.032
Mercury 13.6 0.033
Copper 8.9 0.093
Brass 8.4-8.9 0.094
Nickel 8.57 0.11
Iron 7.5+ 0.1125
Aluminum 2.67 0.218
Glass 2.5-3.6 0.19
Ice 0.918 0.504
Air 0.00129 0.237
Page 211
Steam 0.00061 0.480
Hydrogen 0.00009 3.409
178. Method of Determining Specific Heat.—The specific heat of a body
is usually determined by what is called the method of mixtures.
Hydrogen 0.00009 3.409
178. Method of Determining Specific Heat.—The specific heat of a body
is usually determined by what is called the method of mixtures.
Page 212
For example, a definite weight of a substance, say a 200-g. iron ball, is
placed in boiling water until it has the temperature of the hot water, 100°C.
Suppose that 300 g. of water at 18°C. be placed in a calorimeter, and that
the hot iron ball on being placed in the water raises its temperature to
23.5°C. The heat received by the water equals 5.5 × 300 = 1650 calories.
This must have come from the heated iron ball. 200 g. of iron then in
cooling 76.5°C. (100°-23.5°) gave out 1650 calories. Then 1 g. of iron in
cooling 76.5°C. Would give out 8.25 calories or 1 g. of iron cooling 1°C.
would yield about 0.11 calorie. The specific heat of the iron is then 0.11.
For accurate determination the heat received by the calorimeter must be
considered.
179. Heat Capacity of Water.—The large capacity for heat shown by
water is useful in regulating the temperature of the air near lakes and the
ocean. In hot weather the water rises slowly in temperature absorbing heat
from the warm winds blowing over it. In winter the large amount of heat
stored in the water is slowly given out to the air above. Thus the climate
near the ocean is made more moderate both in winter and summer by the
large capacity of water for heat. This large heat capacity of water may seem
to be a disadvantage when one is warming it for domestic purposes since it
requires so much heat to warm water to boiling. However, it is this capacity
that makes hot-water bottles and hot-water heating effective.
If one takes a pound of ice at 0°C. in one dish and a pound of water at 0°C.
in another, and warms the dish of ice by a Bunsen flame until the ice is just
melted, and then warms the water in the other dish for the same time, the
water will be found to be hot and at a temperature 80°C., or 176°F.
180. The Heat of Fusion of Ice.—This experiment indicates the large
amount of heat required to change the ice to water without changing its
temperature. As indicated by the experiment, it requires 80 calories to melt
1 g. of ice without changing its temperature or, in other words, if one placed
1 g. of ice at 0°C. in 1 g. of water at 80°C., the ice would be melted and the
water would be cooled to 0°C.
181. Heat Given out by Freezing water.—Just as 80 calories of heat are
required to melt 1 g. of ice, so in freezing 1 g. of water, 80 calories of heat
are given out.
placed in boiling water until it has the temperature of the hot water, 100°C.
Suppose that 300 g. of water at 18°C. be placed in a calorimeter, and that
the hot iron ball on being placed in the water raises its temperature to
23.5°C. The heat received by the water equals 5.5 × 300 = 1650 calories.
This must have come from the heated iron ball. 200 g. of iron then in
cooling 76.5°C. (100°-23.5°) gave out 1650 calories. Then 1 g. of iron in
cooling 76.5°C. Would give out 8.25 calories or 1 g. of iron cooling 1°C.
would yield about 0.11 calorie. The specific heat of the iron is then 0.11.
For accurate determination the heat received by the calorimeter must be
considered.
179. Heat Capacity of Water.—The large capacity for heat shown by
water is useful in regulating the temperature of the air near lakes and the
ocean. In hot weather the water rises slowly in temperature absorbing heat
from the warm winds blowing over it. In winter the large amount of heat
stored in the water is slowly given out to the air above. Thus the climate
near the ocean is made more moderate both in winter and summer by the
large capacity of water for heat. This large heat capacity of water may seem
to be a disadvantage when one is warming it for domestic purposes since it
requires so much heat to warm water to boiling. However, it is this capacity
that makes hot-water bottles and hot-water heating effective.
If one takes a pound of ice at 0°C. in one dish and a pound of water at 0°C.
in another, and warms the dish of ice by a Bunsen flame until the ice is just
melted, and then warms the water in the other dish for the same time, the
water will be found to be hot and at a temperature 80°C., or 176°F.
180. The Heat of Fusion of Ice.—This experiment indicates the large
amount of heat required to change the ice to water without changing its
temperature. As indicated by the experiment, it requires 80 calories to melt
1 g. of ice without changing its temperature or, in other words, if one placed
1 g. of ice at 0°C. in 1 g. of water at 80°C., the ice would be melted and the
water would be cooled to 0°C.
181. Heat Given out by Freezing water.—Just as 80 calories of heat are
required to melt 1 g. of ice, so in freezing 1 g. of water, 80 calories of heat
are given out.
Page 213
The fact that heat is set free or given out when a liquid solidifies may be
strikingly shown by making a strong solution of sodium acetate. On
allowing this to cool quietly it will come to the room temperature and
remain liquid. If now a small crystal of sodium acetate is dropped into the
liquid the latter quickly becomes a solid mass of crystals, at the same time
rising markedly in temperature. The amount of heat now liberated must
enter the sodium acetate when the mass of crystals is melted again.
The large amount of heat that must be liberated before water freezes
accounts for the slowness of the formation of ice. It is also the reason why
the temperature never falls so low in the vicinity of large lakes as it does far
inland, the heat given out by the freezing water warming the surrounding
air.
The heat that disappears on melting and reappears on solidifying is called
the heat of fusion. It is sometimes called latent heat since the heat seems to
become hidden or latent. It is now believed that the heat energy that
disappears when a body melts has been transformed into the potential
energy of partially separated molecules. The heat of fusion therefore
represents the work done in changing a solid to a liquid without a change of
temperature.
182. Melting of Crystalline and Amorphous Substances.—If a piece of
ice is placed in boiling hot water and then removed, the temperature of the
unmelted ice is still 0°C. There is no known means of warming ice under
atmospheric pressure above its melting point and maintaining its solid state.
Ice being composed of ice crystals is called a crystalline body. All
crystalline substances have fixed melting points. For example, ice always
melts at 0°C. The melting points of some common crystalline substances
are given below:
Melting Points of Some Crystalline Substances
1. Aluminum 658 C.
2. Cast iron 1200 C.
3. Copper 1083 C.
4. Ice 0 C.
5. Lead 327 C.
6. Mercury -39 C.
strikingly shown by making a strong solution of sodium acetate. On
allowing this to cool quietly it will come to the room temperature and
remain liquid. If now a small crystal of sodium acetate is dropped into the
liquid the latter quickly becomes a solid mass of crystals, at the same time
rising markedly in temperature. The amount of heat now liberated must
enter the sodium acetate when the mass of crystals is melted again.
The large amount of heat that must be liberated before water freezes
accounts for the slowness of the formation of ice. It is also the reason why
the temperature never falls so low in the vicinity of large lakes as it does far
inland, the heat given out by the freezing water warming the surrounding
air.
The heat that disappears on melting and reappears on solidifying is called
the heat of fusion. It is sometimes called latent heat since the heat seems to
become hidden or latent. It is now believed that the heat energy that
disappears when a body melts has been transformed into the potential
energy of partially separated molecules. The heat of fusion therefore
represents the work done in changing a solid to a liquid without a change of
temperature.
182. Melting of Crystalline and Amorphous Substances.—If a piece of
ice is placed in boiling hot water and then removed, the temperature of the
unmelted ice is still 0°C. There is no known means of warming ice under
atmospheric pressure above its melting point and maintaining its solid state.
Ice being composed of ice crystals is called a crystalline body. All
crystalline substances have fixed melting points. For example, ice always
melts at 0°C. The melting points of some common crystalline substances
are given below:
Melting Points of Some Crystalline Substances
1. Aluminum 658 C.
2. Cast iron 1200 C.
3. Copper 1083 C.
4. Ice 0 C.
5. Lead 327 C.
6. Mercury -39 C.
Page 214
7. Phenol (carbolic acid) 43 C.
8. Platinum 1755 C.
9. Salt (sodium chloride) 795 C.
10. Saltpeter (potassium nitrate) 340 C.
11. Silver 961 C.
12. Sodium hyposulphite (hypo) 47 C.
13. Zinc 419 C.
Non-crystalline or amorphous substances such as glass, tar, glue, etc., do
not have well defined melting points as do crystalline bodies. When heated
they gradually soften and become fluid. For this reason glass can be pressed
and molded.
183. Change of Volume During Solidification.—The fact that ice floats
and that it breaks bottles and pipes in which it freezes shows that water
expands on freezing. How a substance may occupy more space when solid
than when liquid may be understood when we learn that ice consists of
masses of star-shaped crystals. (See Fig. 151.) The formation of these
crystals must leave unoccupied spaces between them in the ice. When
liquefied, however, no spaces are left and the substance occupies less
volume. Most substances contract upon solidifying. Antimony and bismuth,
however, expand on solidifying while iron changes little in volume. Only
those bodies that expand, or else show little change of volume on
solidifying, can make sharp castings, for if they contract they will not
completely fill the mold. For this reason gold and silver coins must be
stamped and not cast. Type metal, an alloy of antimony and lead, expands
on solidifying to form the sharp outlines of good type. Several important
effects of the expansion of water when freezing should be noted. (a) Ice
floats, (b) if it sank as soon as formed, lakes and rivers would freeze solid,
(c) freezing water is one of the active agents in the disintegration of rocks.
8. Platinum 1755 C.
9. Salt (sodium chloride) 795 C.
10. Saltpeter (potassium nitrate) 340 C.
11. Silver 961 C.
12. Sodium hyposulphite (hypo) 47 C.
13. Zinc 419 C.
Non-crystalline or amorphous substances such as glass, tar, glue, etc., do
not have well defined melting points as do crystalline bodies. When heated
they gradually soften and become fluid. For this reason glass can be pressed
and molded.
183. Change of Volume During Solidification.—The fact that ice floats
and that it breaks bottles and pipes in which it freezes shows that water
expands on freezing. How a substance may occupy more space when solid
than when liquid may be understood when we learn that ice consists of
masses of star-shaped crystals. (See Fig. 151.) The formation of these
crystals must leave unoccupied spaces between them in the ice. When
liquefied, however, no spaces are left and the substance occupies less
volume. Most substances contract upon solidifying. Antimony and bismuth,
however, expand on solidifying while iron changes little in volume. Only
those bodies that expand, or else show little change of volume on
solidifying, can make sharp castings, for if they contract they will not
completely fill the mold. For this reason gold and silver coins must be
stamped and not cast. Type metal, an alloy of antimony and lead, expands
on solidifying to form the sharp outlines of good type. Several important
effects of the expansion of water when freezing should be noted. (a) Ice
floats, (b) if it sank as soon as formed, lakes and rivers would freeze solid,
(c) freezing water is one of the active agents in the disintegration of rocks.
Page 215
Fig. 151.—Ice crystals.
Since water expands on freezing,
pressure would on compressing ice at
0°C., tend to turn it into water.
Pressure does lower the melting point
of ice, so that a little ice may melt
when it is subjected to pressure. On
removing the pressure the water
freezes. This may be shown by
placing a loop of fine piano wire (see
Fig. 152) over a piece of ice supported
Fig. 152.—Melting ice by so that a weight may be hung upon the
pressure. wire. The wire will be found to
gradually cut through the ice, the
melted ice refreezing above the wire.
Important Topics
1. Specific heat.
2. Heat of fusion of ice.
3. Crystalline substances have fixed melting points.
4. Expansion on freezing, importance.
Exercises
1. What are two advantages in the high heat of fusion of ice?
Since water expands on freezing,
pressure would on compressing ice at
0°C., tend to turn it into water.
Pressure does lower the melting point
of ice, so that a little ice may melt
when it is subjected to pressure. On
removing the pressure the water
freezes. This may be shown by
placing a loop of fine piano wire (see
Fig. 152) over a piece of ice supported
Fig. 152.—Melting ice by so that a weight may be hung upon the
pressure. wire. The wire will be found to
gradually cut through the ice, the
melted ice refreezing above the wire.
Important Topics
1. Specific heat.
2. Heat of fusion of ice.
3. Crystalline substances have fixed melting points.
4. Expansion on freezing, importance.
Exercises
1. What are two advantages in the high heat of fusion of ice?
Page 216
2. What are two advantages in the expansion of water while freezing?
3. How much heat will be required to melt 1000 g. of ice and warm the
water to 20°C.?
4. How many grams of ice at 0°C. can be melted by 400 g. of water at
55°C.?
5. What are two advantages of the high specific heat of water? Two
disadvantages?
6. If the specific heat of iron is 0.1125, how much ice at 0°C. can be melted
by a 200-g. ball of iron heated to 300°C?
7. What is the temperature of a hot ball of iron weighing 80 g., if when
placed on a piece of ice at 0°C. it melts 90 g. of ice?
8. If 500 g. of copper at 400°C. are placed into 3000 g. of water at 10°C.
what will be the resulting temperature?
9. What weight of water at 90°C. will just melt 10 kg. of ice at 0°C.?
10. If the smooth dry surface of two pieces of ice are pressed together for a
short time the two pieces will be frozen into one piece. Explain.
11. Tubs of hot water are sometimes placed in vegetable cellars to prevent
the vegetables from freezing. Explain.
12. How many B.t.u. are given out when 2 lbs. of water freeze?
(2) Heat and Change of State
3. How much heat will be required to melt 1000 g. of ice and warm the
water to 20°C.?
4. How many grams of ice at 0°C. can be melted by 400 g. of water at
55°C.?
5. What are two advantages of the high specific heat of water? Two
disadvantages?
6. If the specific heat of iron is 0.1125, how much ice at 0°C. can be melted
by a 200-g. ball of iron heated to 300°C?
7. What is the temperature of a hot ball of iron weighing 80 g., if when
placed on a piece of ice at 0°C. it melts 90 g. of ice?
8. If 500 g. of copper at 400°C. are placed into 3000 g. of water at 10°C.
what will be the resulting temperature?
9. What weight of water at 90°C. will just melt 10 kg. of ice at 0°C.?
10. If the smooth dry surface of two pieces of ice are pressed together for a
short time the two pieces will be frozen into one piece. Explain.
11. Tubs of hot water are sometimes placed in vegetable cellars to prevent
the vegetables from freezing. Explain.
12. How many B.t.u. are given out when 2 lbs. of water freeze?
(2) Heat and Change of State
Page 217
Fig. 153.—The black cube in the upper corner
represents one cubic inch of water. The entire
cube represents the space occupied by the
cubic inch of water in the form of steam. The
reduced spaces at the bottom and sides show
how much short the cube is of being one cubic
foot. (American Radiator Co.)
184. Heat of Vaporization.—In our study of evaporation in Art. 174 we
considered the more rapidly moving or vibrating molecules in the liquid
escaping to the air above and the slower moving molecules being left
behind in the liquid; this means that a loss of heat will result upon
evaporation, the liquid remaining becoming cooler as the process continues.
Now just as a ball thrown up in the air loses its kinetic energy as it rises,
and acquires energy of position or potential energy, so molecules escaping
from a liquid lose a certain amount of kinetic energy or heat and acquire a
corresponding amount of energy of position or potential energy. Conversely,
as the ball returns to the ground its potential energy is changed to kinetic
energy. Similarly when vapor molecules return to the liquid condition they
lose their energy of position and acquire kinetic energy. In other words,
when a liquid evaporates a certain amount of heat disappears, or becomes
latent and when the vapor condenses the heat reappears, or becomes
sensible heat. The amount of heat that disappears when 1 g. of a substance
is vaporized is called the heat of vaporization. In the case of water at its
represents one cubic inch of water. The entire
cube represents the space occupied by the
cubic inch of water in the form of steam. The
reduced spaces at the bottom and sides show
how much short the cube is of being one cubic
foot. (American Radiator Co.)
184. Heat of Vaporization.—In our study of evaporation in Art. 174 we
considered the more rapidly moving or vibrating molecules in the liquid
escaping to the air above and the slower moving molecules being left
behind in the liquid; this means that a loss of heat will result upon
evaporation, the liquid remaining becoming cooler as the process continues.
Now just as a ball thrown up in the air loses its kinetic energy as it rises,
and acquires energy of position or potential energy, so molecules escaping
from a liquid lose a certain amount of kinetic energy or heat and acquire a
corresponding amount of energy of position or potential energy. Conversely,
as the ball returns to the ground its potential energy is changed to kinetic
energy. Similarly when vapor molecules return to the liquid condition they
lose their energy of position and acquire kinetic energy. In other words,
when a liquid evaporates a certain amount of heat disappears, or becomes
latent and when the vapor condenses the heat reappears, or becomes
sensible heat. The amount of heat that disappears when 1 g. of a substance
is vaporized is called the heat of vaporization. In the case of water at its
Page 218
boiling point, 536 calories of heat disappear when 1 g. of water turns to
vapor, and this same amount of heat reappears when the vapor condenses.
The change of volume of water on turning to steam is shown in Fig. 153.
Fig. 154.—Effect of pressure on the boiling
point.
185. The Boiling Point.—The boiling temperature depends upon the
pressure. The boiling point may be defined as the temperature at which
bubbles of vapor are formed within the liquid. These bubbles increase the
surface at which evaporation can take place in the liquid, and the principal
reason why rapid application of heat to a liquid does not raise its
temperature above the boiling point is that as more heat is applied more
bubbles form so that the increase of evaporating surface supplies a
correspondingly greater surface for cooling. The variation of the boiling
temperature with changing pressure may be shown by partly filling a strong
7/8-in. test-tube with water. Close the neck with a one-hole rubber stopper
through which passes a glass tube to which is attached a soft rubber tube.
(See Fig. 154.) Support the tube by a holder, heat the water and boil until all
the air is driven from the tube, then close the soft rubber tube with a pinch
cock and hold the tube in an inverted position. On cooling the end of the
tube above the water with cold water or snow, the vapor within is
condensed and the pressure upon the water is reduced. Vigorous boiling
begins at once. By condensing the vapor repeatedly the water may be made
to boil at the room temperature. At the top of Mt. Blanc water boils at 84°C.
While in steam boilers at 225 lbs. pressure to the square inch the boiling
point is nearly 200°C.
vapor, and this same amount of heat reappears when the vapor condenses.
The change of volume of water on turning to steam is shown in Fig. 153.
Fig. 154.—Effect of pressure on the boiling
point.
185. The Boiling Point.—The boiling temperature depends upon the
pressure. The boiling point may be defined as the temperature at which
bubbles of vapor are formed within the liquid. These bubbles increase the
surface at which evaporation can take place in the liquid, and the principal
reason why rapid application of heat to a liquid does not raise its
temperature above the boiling point is that as more heat is applied more
bubbles form so that the increase of evaporating surface supplies a
correspondingly greater surface for cooling. The variation of the boiling
temperature with changing pressure may be shown by partly filling a strong
7/8-in. test-tube with water. Close the neck with a one-hole rubber stopper
through which passes a glass tube to which is attached a soft rubber tube.
(See Fig. 154.) Support the tube by a holder, heat the water and boil until all
the air is driven from the tube, then close the soft rubber tube with a pinch
cock and hold the tube in an inverted position. On cooling the end of the
tube above the water with cold water or snow, the vapor within is
condensed and the pressure upon the water is reduced. Vigorous boiling
begins at once. By condensing the vapor repeatedly the water may be made
to boil at the room temperature. At the top of Mt. Blanc water boils at 84°C.
While in steam boilers at 225 lbs. pressure to the square inch the boiling
point is nearly 200°C.
Page 219
186. Laws of Boiling.—The following statements have been found by
experiments to be true.
1. Every liquid has its own boiling point which under the same conditions
of pressure is always the same.
2. The temperature of the boiling liquid remains at the boiling point until all
the liquid is changed into vapor.
3. The boiling point rises with increased pressure and falls if the pressure is
diminished.
4. A boiling liquid and the vapor formed from it have the same temperature.
On cooling, a vapor will liquefy at the boiling point.
5. The solution of solid substances in a
liquid raises its boiling point, additional
energy being needed to overcome the
adhesion involved in the solution. The
boiling point is also affected by the
character of the vessel containing the
liquid. In glass the boiling point is 101°.
187. Distillation of Water.—Usually
when solids are dissolved in liquids the
vapor coming from the liquid contains
Fig. 155.—Distilling none of the dissolved solid. Thus by
apparatus. evaporating salt sea water, and collecting
and condensing the vapor, pure water is
obtained. Distillation is the process of boiling a liquid and condensing the
vapor formed back again into a liquid. (See Fig. 155.) The liquid to be
distilled is placed in vessel F and boiled. The vapor is conducted into the
tube J which is surrounded by a larger tube containing cold water. The
vapor is condensed on the cold walls of the tube. The resulting liquid is
collected in the vessel R. Distillation is employed for two purposes: (a) To
remove impurities from a liquid (water is purified in this way). (b) Mixtures
of different liquids having different boiling points may be separated by
distillation. The one having the lower boiling point will be vaporized first.
Thus a mixture of alcohol and water, on distillation yields a distillate having
a much larger percentage of alcohol than at first. Repeating this process
experiments to be true.
1. Every liquid has its own boiling point which under the same conditions
of pressure is always the same.
2. The temperature of the boiling liquid remains at the boiling point until all
the liquid is changed into vapor.
3. The boiling point rises with increased pressure and falls if the pressure is
diminished.
4. A boiling liquid and the vapor formed from it have the same temperature.
On cooling, a vapor will liquefy at the boiling point.
5. The solution of solid substances in a
liquid raises its boiling point, additional
energy being needed to overcome the
adhesion involved in the solution. The
boiling point is also affected by the
character of the vessel containing the
liquid. In glass the boiling point is 101°.
187. Distillation of Water.—Usually
when solids are dissolved in liquids the
vapor coming from the liquid contains
Fig. 155.—Distilling none of the dissolved solid. Thus by
apparatus. evaporating salt sea water, and collecting
and condensing the vapor, pure water is
obtained. Distillation is the process of boiling a liquid and condensing the
vapor formed back again into a liquid. (See Fig. 155.) The liquid to be
distilled is placed in vessel F and boiled. The vapor is conducted into the
tube J which is surrounded by a larger tube containing cold water. The
vapor is condensed on the cold walls of the tube. The resulting liquid is
collected in the vessel R. Distillation is employed for two purposes: (a) To
remove impurities from a liquid (water is purified in this way). (b) Mixtures
of different liquids having different boiling points may be separated by
distillation. The one having the lower boiling point will be vaporized first.
Thus a mixture of alcohol and water, on distillation yields a distillate having
a much larger percentage of alcohol than at first. Repeating this process
Page 220
which is called fractional
distillation yields alcohol of
increasing strength of purity.
Distilled liquor such as alcohol,
brandy, and whisky are made by
distilling fermented liquor, alcohol
being made from fermented grains.
Gasoline and kerosene are distilled
from crude petroleum. Sometimes
as in the production of sugar or
evaporated milk the object is to
remove the water by evaporation in
order to obtain the solid material.
Since the two substances named are
injured by heating, the syrup, or
milk is evaporated under reduced
pressure in a vacuum pan, that is in
a boiler from which air and vapor
are removed by an air pump. (See Fig. 156.—A vacuum pan.
Fig. 156.)
188. Artificial Cooling.—The fact has been brought out that when a solid
is melted, a certain amount of heat, called the heat of fusion, is absorbed or
disappears. This absorption of heat is also noticed when a solid is liquefied
by dissolving it in a liquid as well as when it is liquefied by simply applying
heat. Thus if some table salt is placed in a tumbler of water the temperature
of the solution is lowered several degrees below that of the salt and water
used. The liquefaction or solution of the salt has been accompanied by an
absorption or disappearance of heat. This heat has been taken from the salt
and from the water, resulting in a lowered temperature. Sal ammoniac or
ammonium nitrate when dissolved in water produce a much more marked
cooling effect than does table salt. The dissolving of a crystal in a liquid is
something like evaporation, except that the molecules of the liquid attract
the molecules of the solid and thus assist the change of state.
189. Freezing Mixtures.—If one attempts to freeze a solution of salt and
water, ice will not form at 0°C. but several degrees lower. The ice formed
however is pure. Evidently the attraction of the molecules of salt for the
distillation yields alcohol of
increasing strength of purity.
Distilled liquor such as alcohol,
brandy, and whisky are made by
distilling fermented liquor, alcohol
being made from fermented grains.
Gasoline and kerosene are distilled
from crude petroleum. Sometimes
as in the production of sugar or
evaporated milk the object is to
remove the water by evaporation in
order to obtain the solid material.
Since the two substances named are
injured by heating, the syrup, or
milk is evaporated under reduced
pressure in a vacuum pan, that is in
a boiler from which air and vapor
are removed by an air pump. (See Fig. 156.—A vacuum pan.
Fig. 156.)
188. Artificial Cooling.—The fact has been brought out that when a solid
is melted, a certain amount of heat, called the heat of fusion, is absorbed or
disappears. This absorption of heat is also noticed when a solid is liquefied
by dissolving it in a liquid as well as when it is liquefied by simply applying
heat. Thus if some table salt is placed in a tumbler of water the temperature
of the solution is lowered several degrees below that of the salt and water
used. The liquefaction or solution of the salt has been accompanied by an
absorption or disappearance of heat. This heat has been taken from the salt
and from the water, resulting in a lowered temperature. Sal ammoniac or
ammonium nitrate when dissolved in water produce a much more marked
cooling effect than does table salt. The dissolving of a crystal in a liquid is
something like evaporation, except that the molecules of the liquid attract
the molecules of the solid and thus assist the change of state.
189. Freezing Mixtures.—If one attempts to freeze a solution of salt and
water, ice will not form at 0°C. but several degrees lower. The ice formed
however is pure. Evidently the attraction of the molecules of salt for the
Page 221
water molecules prevented the formation of ice until the motions of the
water molecules had been reduced more than is necessary in pure water. As
the temperature of freezing water is that of melting ice, ice in a salt solution
melts at lower temperature than in pure water. In a saturated salt solution
this temperature is -22°C. It is for this reason that the mixture of ice and salt
used in freezing cream is so effective, the salt water in melting the ice,
being cooled to a temperature many degrees below the freezing point of the
cream. The best proportion for a freezing mixture of salt and ice is one part
salt to three parts of finely powdered or shaved ice.
190. Refrigeration by Evaporation.—Intense cold is also produced by
permitting the rapid evaporation of liquids under pressure. Carbon dioxide
under high pressure is a liquid, but when allowed to escape into the air
evaporates so rapidly that a portion of the liquid is frozen into solid carbon
dioxide which has a temperature of -80° C. The evaporation of liquid
ammonia by permitting it to escape into a pipe, under reduced pressure, is
used on a large scale as a means of producing cold in cold storage and
refrigeration plants. (See Fig. 157.)
Fig. 157.—Diagram of a refrigerating system.
The essential parts of the refrigerating system employing ammonia is
represented in Fig. 157. The compressor exhausts ammonia gas from the
coiled pipe in "E" and compresses the gas in "C," where under 150 pounds
pressure and the cooling effect of water it condenses to liquid ammonia.
This is allowed to pass slowly through the regulating valve, whereupon it
evaporates and expands in the long coiled pipe in "E" on its way back to the
compressor. This evaporation and expansion causes a large amount of heat
to be absorbed from the brine, cooling the latter below the freezing point of
pure water and thus permitting the freezing of cans of water suspended in
water molecules had been reduced more than is necessary in pure water. As
the temperature of freezing water is that of melting ice, ice in a salt solution
melts at lower temperature than in pure water. In a saturated salt solution
this temperature is -22°C. It is for this reason that the mixture of ice and salt
used in freezing cream is so effective, the salt water in melting the ice,
being cooled to a temperature many degrees below the freezing point of the
cream. The best proportion for a freezing mixture of salt and ice is one part
salt to three parts of finely powdered or shaved ice.
190. Refrigeration by Evaporation.—Intense cold is also produced by
permitting the rapid evaporation of liquids under pressure. Carbon dioxide
under high pressure is a liquid, but when allowed to escape into the air
evaporates so rapidly that a portion of the liquid is frozen into solid carbon
dioxide which has a temperature of -80° C. The evaporation of liquid
ammonia by permitting it to escape into a pipe, under reduced pressure, is
used on a large scale as a means of producing cold in cold storage and
refrigeration plants. (See Fig. 157.)
Fig. 157.—Diagram of a refrigerating system.
The essential parts of the refrigerating system employing ammonia is
represented in Fig. 157. The compressor exhausts ammonia gas from the
coiled pipe in "E" and compresses the gas in "C," where under 150 pounds
pressure and the cooling effect of water it condenses to liquid ammonia.
This is allowed to pass slowly through the regulating valve, whereupon it
evaporates and expands in the long coiled pipe in "E" on its way back to the
compressor. This evaporation and expansion causes a large amount of heat
to be absorbed from the brine, cooling the latter below the freezing point of
pure water and thus permitting the freezing of cans of water suspended in
Page 222
the brine. The chilled brine may also be sent through pipes in order to cool
storage rooms containing meat or other food products. The ammonia
absorbs heat when it vaporizes and gives up heat when it is compressed and
liquified.
Important Topics
1. Heat of vaporization, of water 536 calories per gram.
2. Boiling point, effect of pressure upon boiling point, laws of boiling.
3. Distillation, artificial cooling, freezing mixtures, refrigeration by
evaporation.
Exercises
1. How much heat is required (a) to melt 1 g. of ice at 0°C., (b) to raise the
temperature of the water resulting to 100°C., (c) to change this water to
steam?
2. If the water leaving a steam radiator is as hot as the steam how is the
room warmed?
3. What is the effect of placing salt upon icy sidewalks in cold weather?
4. Is rain water distilled water? Is it perfectly pure?
5. What are two advantages of the high heat of vaporization of water?
6. If the heat from 1 g. of steam at 100°C. in changing to water and cooling
to 0°C. could be used in melting ice at 0°C. how much ice would be
melted?
(3) Heat and Work
191. Necessity for Heat Energy.—From early times man has been able to
transform motion into heat, and has used this ability in many directions as
in starting fires and warming himself by friction. It took man many
centuries, however, to devise an effective machine for transforming heat
into mechanical energy or to use it in doing work.
storage rooms containing meat or other food products. The ammonia
absorbs heat when it vaporizes and gives up heat when it is compressed and
liquified.
Important Topics
1. Heat of vaporization, of water 536 calories per gram.
2. Boiling point, effect of pressure upon boiling point, laws of boiling.
3. Distillation, artificial cooling, freezing mixtures, refrigeration by
evaporation.
Exercises
1. How much heat is required (a) to melt 1 g. of ice at 0°C., (b) to raise the
temperature of the water resulting to 100°C., (c) to change this water to
steam?
2. If the water leaving a steam radiator is as hot as the steam how is the
room warmed?
3. What is the effect of placing salt upon icy sidewalks in cold weather?
4. Is rain water distilled water? Is it perfectly pure?
5. What are two advantages of the high heat of vaporization of water?
6. If the heat from 1 g. of steam at 100°C. in changing to water and cooling
to 0°C. could be used in melting ice at 0°C. how much ice would be
melted?
(3) Heat and Work
191. Necessity for Heat Energy.—From early times man has been able to
transform motion into heat, and has used this ability in many directions as
in starting fires and warming himself by friction. It took man many
centuries, however, to devise an effective machine for transforming heat
into mechanical energy or to use it in doing work.
Page 223
The power of a man is small and as long as the work of the world had to be
done by man power, progress was retarded. When man began the use of
beasts of burden, he took a long step in advance since one man could then
employ and direct the power of many men in the animals he controlled.
Man also built water-wheels and windmills thus gaining power directly
from the forces of nature and these added much to his working ability. But
he took the greatest step in gaining control over his surroundings when he
learned to use heat energy and to make it drive his machines.
192. Heat Engines.—At the present time there is a great variety of heat
engines in use such as steam, hot air, gas, and gasoline engines, all using
heat energy to produce motion. The expansive power of steam when
confined has been observed for hundreds of years and many different
machines have been invented to use it in doing work.
Fig. 158.—Cross-section view of cylinder and
steam chest of a steam engine.
Fig. 159.—The steam drives the piston to the
left.
Fig. 160.—External view of steam engine.
done by man power, progress was retarded. When man began the use of
beasts of burden, he took a long step in advance since one man could then
employ and direct the power of many men in the animals he controlled.
Man also built water-wheels and windmills thus gaining power directly
from the forces of nature and these added much to his working ability. But
he took the greatest step in gaining control over his surroundings when he
learned to use heat energy and to make it drive his machines.
192. Heat Engines.—At the present time there is a great variety of heat
engines in use such as steam, hot air, gas, and gasoline engines, all using
heat energy to produce motion. The expansive power of steam when
confined has been observed for hundreds of years and many different
machines have been invented to use it in doing work.
Fig. 158.—Cross-section view of cylinder and
steam chest of a steam engine.
Fig. 159.—The steam drives the piston to the
left.
Fig. 160.—External view of steam engine.
Page 224
193. The Steam-engine.—The man who perfected the steam-engine, and
devised its modern form was James Watt (1736-1819). The essential parts
and the action of the steam engine may be readily understood by studying a
diagram. In Fig. 158, S stands for steam chest, C for cylinder, P for piston
and v for slide valve. The first two are hollow iron boxes, the latter are parts
that slide back and forth within them. The action of the steam engine is as
follows: Steam under pressure enters the steam chest, passes into the
cylinder and pushes the piston to the other end. The slide valve is moved to
its position in Fig. 159. Steam now enters the right end of the cylinder,
driving the piston to the left, the "dead" steam in the left end of the cylinder
escaping at E to the air. The slide valve is now shifted to its first position
and the process is repeated. It will assist the student to understand this
action if he makes a cardboard model of these parts, the piston and slide
valve being movable. In practical steam-engines, the piston rod is attached
to a crank rod fastened to a crank which turns a wheel. (See Fig. 160.) The
back and forth, or reciprocating motion of the piston is by this means
transformed into rotary motion, just as in the sewing-machine the back-and-
forth motion of the treadle produces rotary motion of the large wheel. Upon
the shaft of the steam engine is fastened an eccentric (see Fig. 163) which
moves the slide valve. The steam engine acts continuously as long as steam
is supplied to it. Since it shifts the position of the slide valve automatically,
it is called an automatic steam engine. And because the team drives the
piston both ways, it is called a double-acting steam engine. See Fig. 161 for
a length-section of a modern locomotive.
Fig. 161.—Length-section of modern, fast-
passenger locomotive. A, cylinder valve—
piston type valve; B, cylinder—piston at out
end of stroke; C, boiler tubes—flues from fire-
box; D, fire-tube type superheater; E, draught
devised its modern form was James Watt (1736-1819). The essential parts
and the action of the steam engine may be readily understood by studying a
diagram. In Fig. 158, S stands for steam chest, C for cylinder, P for piston
and v for slide valve. The first two are hollow iron boxes, the latter are parts
that slide back and forth within them. The action of the steam engine is as
follows: Steam under pressure enters the steam chest, passes into the
cylinder and pushes the piston to the other end. The slide valve is moved to
its position in Fig. 159. Steam now enters the right end of the cylinder,
driving the piston to the left, the "dead" steam in the left end of the cylinder
escaping at E to the air. The slide valve is now shifted to its first position
and the process is repeated. It will assist the student to understand this
action if he makes a cardboard model of these parts, the piston and slide
valve being movable. In practical steam-engines, the piston rod is attached
to a crank rod fastened to a crank which turns a wheel. (See Fig. 160.) The
back and forth, or reciprocating motion of the piston is by this means
transformed into rotary motion, just as in the sewing-machine the back-and-
forth motion of the treadle produces rotary motion of the large wheel. Upon
the shaft of the steam engine is fastened an eccentric (see Fig. 163) which
moves the slide valve. The steam engine acts continuously as long as steam
is supplied to it. Since it shifts the position of the slide valve automatically,
it is called an automatic steam engine. And because the team drives the
piston both ways, it is called a double-acting steam engine. See Fig. 161 for
a length-section of a modern locomotive.
Fig. 161.—Length-section of modern, fast-
passenger locomotive. A, cylinder valve—
piston type valve; B, cylinder—piston at out
end of stroke; C, boiler tubes—flues from fire-
box; D, fire-tube type superheater; E, draught
Page 225
screen; F-A, fire-brick arch to protect tubes
from direct heat; F-B, firebox; G, grate; H,
exhaust nozzle; I, safety valve nest; T, throttle
lever; R, throttle rod; Y, throttle valve.
194. The Mechanical Equivalent of Heat.—While watching workmen
bore holes in cannon, Count Rumford, 1753-1814, noticed with much
interest the large amount of heat produced in the process. He observed that
the heat developed seemed to have some relation to the work done upon the
drill in boring the holes. Later experiments performed by many men
indicated that a definite relation exists between the heat produced by
friction and the amount of work done in overcoming the friction. This
discovery indicates that in some way heat is related to energy and that heat
is probably a form of energy. Later experiments have confirmed this idea,
and it is now considered well established that heat is a form of energy.
Many attempts have been made to discover the relation between the units of
heat energy and the units of mechanical energy. To illustrate one method
employed, suppose one measures a given length in inches and in
centimeters; on dividing one result by the other, it will be found that a
certain relation exists between the two sets of measurements, and that in
every case that 1 in. equals 2.54 cm. Similarly, when the same amount of
energy is measured both in heat units and in work units a constant relation
is always found between the units employed. One B.T.U. is found
equivalent to 778 ft.-lbs. 1 calorie being equivalent to 42,700 g. cm. (427 g.
m.). This relation is called the mechanical equivalent of heat, or in other
words it represents the number of work units equivalent to one heat unit.
One of the first successful experiments in
determining the relation between work
units and heat units was devised by Joule
in England. (See portrait p. 217.) The
experiment consisted in taking a can of
metal containing water (Fig. 162) in
which was placed a thermometer, and a
rod carrying paddles. The rod was turned
by a cord connected through suitable
apparatus to heavy weights, W and W. The
Fig. 162.—Apparatus for energy represented by the downward
from direct heat; F-B, firebox; G, grate; H,
exhaust nozzle; I, safety valve nest; T, throttle
lever; R, throttle rod; Y, throttle valve.
194. The Mechanical Equivalent of Heat.—While watching workmen
bore holes in cannon, Count Rumford, 1753-1814, noticed with much
interest the large amount of heat produced in the process. He observed that
the heat developed seemed to have some relation to the work done upon the
drill in boring the holes. Later experiments performed by many men
indicated that a definite relation exists between the heat produced by
friction and the amount of work done in overcoming the friction. This
discovery indicates that in some way heat is related to energy and that heat
is probably a form of energy. Later experiments have confirmed this idea,
and it is now considered well established that heat is a form of energy.
Many attempts have been made to discover the relation between the units of
heat energy and the units of mechanical energy. To illustrate one method
employed, suppose one measures a given length in inches and in
centimeters; on dividing one result by the other, it will be found that a
certain relation exists between the two sets of measurements, and that in
every case that 1 in. equals 2.54 cm. Similarly, when the same amount of
energy is measured both in heat units and in work units a constant relation
is always found between the units employed. One B.T.U. is found
equivalent to 778 ft.-lbs. 1 calorie being equivalent to 42,700 g. cm. (427 g.
m.). This relation is called the mechanical equivalent of heat, or in other
words it represents the number of work units equivalent to one heat unit.
One of the first successful experiments in
determining the relation between work
units and heat units was devised by Joule
in England. (See portrait p. 217.) The
experiment consisted in taking a can of
metal containing water (Fig. 162) in
which was placed a thermometer, and a
rod carrying paddles. The rod was turned
by a cord connected through suitable
apparatus to heavy weights, W and W. The
Fig. 162.—Apparatus for energy represented by the downward
Page 226
determining the mechanical motion of the weights through a given
equivalent of heat. distance was compared with the heat
energy
developed in the
water as shown by
its rise in
temperature. Careful
experiments showed
that when 778 ft.-lbs.
of work had been
done by the moving
weights the heat
produced at the same
time would warm
one pound of water 1
Fahrenheit degree. If
the experiment was
performed using
metric units, it was James Prescott Joule
William Gilbert (1540- found that the (1818-1889), England,
1603), "Father of expenditure of determined the
magnetic philosophy." 42,700 gram mechanical equivalent
Especially noted for his centimeters (427 of heat; discovered the
experiments and gram meters) would relation between an
discoveries in result in producing electric current and
magnetism; first to use enough heat to warm the heat produced;
the word "electricity." one gram of water first proved
First man to one centigrade experimentally the
practically emphasize degree. The facts just identity of various
experimental science. given may be forms of energy.
summarized as
Dr. William Gilbert follows: 778 foot- James Prescott Joule
(Popular Science pounds of energy are (Popular Science
Monthly) equivalent to 1 Monthly)
British thermal unit
and 42,700 gram centimeters, or 427 gram
equivalent of heat. distance was compared with the heat
energy
developed in the
water as shown by
its rise in
temperature. Careful
experiments showed
that when 778 ft.-lbs.
of work had been
done by the moving
weights the heat
produced at the same
time would warm
one pound of water 1
Fahrenheit degree. If
the experiment was
performed using
metric units, it was James Prescott Joule
William Gilbert (1540- found that the (1818-1889), England,
1603), "Father of expenditure of determined the
magnetic philosophy." 42,700 gram mechanical equivalent
Especially noted for his centimeters (427 of heat; discovered the
experiments and gram meters) would relation between an
discoveries in result in producing electric current and
magnetism; first to use enough heat to warm the heat produced;
the word "electricity." one gram of water first proved
First man to one centigrade experimentally the
practically emphasize degree. The facts just identity of various
experimental science. given may be forms of energy.
summarized as
Dr. William Gilbert follows: 778 foot- James Prescott Joule
(Popular Science pounds of energy are (Popular Science
Monthly) equivalent to 1 Monthly)
British thermal unit
and 42,700 gram centimeters, or 427 gram
Page 227
meters, of energy are equivalent to 1 calorie. This relation of work units to
heat units is called the mechanical equivalent of heat.
195. The Heat Equivalent of Fuels and Efficiency Tests of Engines.—To
determine the efficiency of a steam engine it is necessary to know not only
the mechanical equivalent of heat but also the heat produced by burning
coal or gas; 1 lb. of average soft coal should produce about 12,600 B.t.u.
Now since 778 ft.-lbs. are equivalent to one B.t.u. the energy produced
when 2 lbs. of average soft coal is burned is 778 × 12,600 × 2 = 19,605,600
ft.-lbs. In actual practice 2 lbs. of average soft coal burned will develop
about 1 horse-power for 1 hour. 1 horse-power-hour = 33,000 ft.-lbs. × 60 =
1,980,000 ft.-lbs. Now efficiency equals (work out)/(work in)
1,980,000/19,605,600 = 1/10 or 10 per cent.. This is the efficiency of a
good steam engine. Ordinary ones require 3 lbs. of coal burned to each
horse-power-hour produced or they are but 2/3 as efficient or have but
about 7 per cent. efficiency.
Heat of Combustion of Various Fuels
Data in this table are taken from U. S. Geological Survey, Bulletin No. 332,
and U. S. Bureau of Mines, Bulletin No. 23.
B.T.U. Calories
per lb. per gram
Alcohol, denatured 11,600 6,450
Coal, anthracite, average 12,600 7,500
Coal, bituminous, average 19,000 7,000
Gasoline 19,000 10,550
Illuminating gas 18,000 10,000
Kerosene 19,990 11,050
Constants for Heat Transmission
Data from "Ideal Fitter," American Radiator Co.
B.t.u. transmitted per square foot per hour per degree (Fahrenheit)
difference in temperature between inside and outside air.
Brick work
heat units is called the mechanical equivalent of heat.
195. The Heat Equivalent of Fuels and Efficiency Tests of Engines.—To
determine the efficiency of a steam engine it is necessary to know not only
the mechanical equivalent of heat but also the heat produced by burning
coal or gas; 1 lb. of average soft coal should produce about 12,600 B.t.u.
Now since 778 ft.-lbs. are equivalent to one B.t.u. the energy produced
when 2 lbs. of average soft coal is burned is 778 × 12,600 × 2 = 19,605,600
ft.-lbs. In actual practice 2 lbs. of average soft coal burned will develop
about 1 horse-power for 1 hour. 1 horse-power-hour = 33,000 ft.-lbs. × 60 =
1,980,000 ft.-lbs. Now efficiency equals (work out)/(work in)
1,980,000/19,605,600 = 1/10 or 10 per cent.. This is the efficiency of a
good steam engine. Ordinary ones require 3 lbs. of coal burned to each
horse-power-hour produced or they are but 2/3 as efficient or have but
about 7 per cent. efficiency.
Heat of Combustion of Various Fuels
Data in this table are taken from U. S. Geological Survey, Bulletin No. 332,
and U. S. Bureau of Mines, Bulletin No. 23.
B.T.U. Calories
per lb. per gram
Alcohol, denatured 11,600 6,450
Coal, anthracite, average 12,600 7,500
Coal, bituminous, average 19,000 7,000
Gasoline 19,000 10,550
Illuminating gas 18,000 10,000
Kerosene 19,990 11,050
Constants for Heat Transmission
Data from "Ideal Fitter," American Radiator Co.
B.t.u. transmitted per square foot per hour per degree (Fahrenheit)
difference in temperature between inside and outside air.
Brick work
Page 228
4 in. thick = 0.68
8 in. thick = 0.46
12 in. thick = 0.33
concrete cement 50 per cent. more than brick.
stone 33-1/3 per cent. more than brick.
Window = 1.090
Wood as wall = 0.220
Double window = 0.560
concrete reinforced 20 per cent. more than brick.
Important Topics
1. Heat a manifestation of energy.
2. Steam-engine and its action.
3. Mechanical equivalent of heat and heat equivalent of fuels and efficiency
of engines.
Exercises
1. Construct a working model of the cylinder and steam chest of a steam
engine and be prepared to explain its action.
2. At $5.00 per ton how many B.T.U.'s should be produced from 1 cent's
worth of bituminous coal?
3. Try the following experiment: Place a quart of water in a teakettle and
place it over the fire for 5 minutes, and note the rise in temperature and
compute the number of B.T.U.'s entering the water. Place another quart of
water at the same temperature in an aluminum or tin dish and heat for 5
minutes, note the rise in temperature and compute the heat used before.
Which of the dishes shows the greater efficiency? How do the efficiencies
of the two dishes compare? How do you account for any differences in the
efficiencies found?
4. How high would 8 cu. ft. of water be lifted if all of the energy produced
by burning 1 lb. of coal were used in raising it?
8 in. thick = 0.46
12 in. thick = 0.33
concrete cement 50 per cent. more than brick.
stone 33-1/3 per cent. more than brick.
Window = 1.090
Wood as wall = 0.220
Double window = 0.560
concrete reinforced 20 per cent. more than brick.
Important Topics
1. Heat a manifestation of energy.
2. Steam-engine and its action.
3. Mechanical equivalent of heat and heat equivalent of fuels and efficiency
of engines.
Exercises
1. Construct a working model of the cylinder and steam chest of a steam
engine and be prepared to explain its action.
2. At $5.00 per ton how many B.T.U.'s should be produced from 1 cent's
worth of bituminous coal?
3. Try the following experiment: Place a quart of water in a teakettle and
place it over the fire for 5 minutes, and note the rise in temperature and
compute the number of B.T.U.'s entering the water. Place another quart of
water at the same temperature in an aluminum or tin dish and heat for 5
minutes, note the rise in temperature and compute the heat used before.
Which of the dishes shows the greater efficiency? How do the efficiencies
of the two dishes compare? How do you account for any differences in the
efficiencies found?
4. How high would 8 cu. ft. of water be lifted if all of the energy produced
by burning 1 lb. of coal were used in raising it?
Page 229
5. What is the mechanical equivalent of a pound of coal expressed in horse-
power hours?
6. If a furnace burns 100 lbs. of coal a day and its efficiency is 50 per cent.
how many B.T.U.'s are used in warming the house?
7. How many B.T.U.'s can be obtained by burning 1/2 ton of bituminous
coal?
8. when a pound of water is heated from 40°F. to 212°F., how many foot-
pounds of energy are absorbed by the water?
9. How many loads of coal each weighing 2 tons, could be lifted 12 ft. by
the energy put into the water in problem 8?
Fig. 163.—An eccentric.
10. When 3 cu. ft. of water are used for a hot bath and the water has been
heated from 50°F. to 112°F., how many B.T.U.'s have been absorbed by the
water?
11. If the average temperature of water at the surface of Lake Michigan is
50°F., how many B.T.U.'s would be given off by each cubic foot of water at
the surface, if the temperature of the water should drop 5°F.?
12. In a cold storage plant carbon dioxide gas is used. The pipe leading
from the compression pump to the expansion valve passes through a
condensing tank of cold water. Why?
13. When the gas is compressed in a cold storage plant, what becomes of
the energy used by the compression pump?
14. An eccentric (Fig. 163), is a round disc mounted a little to one side of its
center, A, on the engine shaft B. A band, C, on the circumference of the disc
is connected by a rod, D, with the slide valve in the steam chest. How is the
power hours?
6. If a furnace burns 100 lbs. of coal a day and its efficiency is 50 per cent.
how many B.T.U.'s are used in warming the house?
7. How many B.T.U.'s can be obtained by burning 1/2 ton of bituminous
coal?
8. when a pound of water is heated from 40°F. to 212°F., how many foot-
pounds of energy are absorbed by the water?
9. How many loads of coal each weighing 2 tons, could be lifted 12 ft. by
the energy put into the water in problem 8?
Fig. 163.—An eccentric.
10. When 3 cu. ft. of water are used for a hot bath and the water has been
heated from 50°F. to 112°F., how many B.T.U.'s have been absorbed by the
water?
11. If the average temperature of water at the surface of Lake Michigan is
50°F., how many B.T.U.'s would be given off by each cubic foot of water at
the surface, if the temperature of the water should drop 5°F.?
12. In a cold storage plant carbon dioxide gas is used. The pipe leading
from the compression pump to the expansion valve passes through a
condensing tank of cold water. Why?
13. When the gas is compressed in a cold storage plant, what becomes of
the energy used by the compression pump?
14. An eccentric (Fig. 163), is a round disc mounted a little to one side of its
center, A, on the engine shaft B. A band, C, on the circumference of the disc
is connected by a rod, D, with the slide valve in the steam chest. How is the
Page 230
rotary motion of the shaft changed into a backward and forward motion of
the slide valve?
(4) Heat Engines
196. The Gas Engine.—One of the heat engines in common use to-day is
the gasoline engine. It is used to propel automobiles and motor boats, to
drive machinery, etc. The construction and action of a gasoline engine may
be understood by studying a working model, or by proper diagrams.
Fig. 164.—Cut away view of a modern
automobile engine, with parts requiring
attention most frequently, indicated. (Courtesy
of the "Automobile Journal")
The common gasoline or gas engine is called a four-cycle (better four-part
cycle) engine (see Fig. 164), since it requires four movements of the piston
to complete one cycle or series of changes. This is illustrated in Fig. 165 1,
which represents a cross-section of the cylinder of the gasoline engine with
the piston moving downward. At the upper end of the cylinder are two ports
or openings. One, the exhaust port, is closed, the inlet port is open and a
mixture of gas and air is entering. Fig. 165 2 shows the piston returning;
both ports are closed and the "charge" of air and gas is being compressed.
the slide valve?
(4) Heat Engines
196. The Gas Engine.—One of the heat engines in common use to-day is
the gasoline engine. It is used to propel automobiles and motor boats, to
drive machinery, etc. The construction and action of a gasoline engine may
be understood by studying a working model, or by proper diagrams.
Fig. 164.—Cut away view of a modern
automobile engine, with parts requiring
attention most frequently, indicated. (Courtesy
of the "Automobile Journal")
The common gasoline or gas engine is called a four-cycle (better four-part
cycle) engine (see Fig. 164), since it requires four movements of the piston
to complete one cycle or series of changes. This is illustrated in Fig. 165 1,
which represents a cross-section of the cylinder of the gasoline engine with
the piston moving downward. At the upper end of the cylinder are two ports
or openings. One, the exhaust port, is closed, the inlet port is open and a
mixture of gas and air is entering. Fig. 165 2 shows the piston returning;
both ports are closed and the "charge" of air and gas is being compressed.
Page 231
As the piston reaches the end of its stroke in compressing the charge, an
electric spark explodes or "fires" the charge of gas and air. The hot burning
gas expands suddenly driving the piston downward with great force (Fig.
165 3). The piston rod is attached to the crank of a heavy fly-wheel and this
is given sufficient energy or momentum to keep it going through the next
three strokes. Fig. 165 4 represents the returning piston pushing out the
burnt "charge" through the open exhaust valve e. On the next downward
motion of the piston the valve e closes. It opens, and new charges of gas
and air enter and the "cycle" is repeated.
In order to make the motion more even
and continuous and also to secure more
power, more than one cylinder is attached
to the same shaft and fly-wheel. Two,
three, four, six, eight and even more
cylinders have been attached to one shaft.
Four or six cylinders are commonly used
in automobile gasoline motors. To lessen
the sound of the "exhaust," the latter is
sent through a "muffler" which often
reduces the noise to a low throbbing. (See
Fig. 166.) The gasoline engine is more
efficient than the steam-engine, since the
fuel, gas, is burned in the cylinder and not
in a separate furnace. The combustion of
the fuel in the cylinders makes some
special cooling device necessary to
prevent their overheating. This usually
consists of a casing about the cylinders.
Between the cylinder and this casing is
water which on being heated passes to a
tank or radiator. In the radiator the water
cools and then returns to the space Fig. 165.—The four strokes
between the cylinders and casing thus of a gas engine cycle.
keeping up the circulation.
electric spark explodes or "fires" the charge of gas and air. The hot burning
gas expands suddenly driving the piston downward with great force (Fig.
165 3). The piston rod is attached to the crank of a heavy fly-wheel and this
is given sufficient energy or momentum to keep it going through the next
three strokes. Fig. 165 4 represents the returning piston pushing out the
burnt "charge" through the open exhaust valve e. On the next downward
motion of the piston the valve e closes. It opens, and new charges of gas
and air enter and the "cycle" is repeated.
In order to make the motion more even
and continuous and also to secure more
power, more than one cylinder is attached
to the same shaft and fly-wheel. Two,
three, four, six, eight and even more
cylinders have been attached to one shaft.
Four or six cylinders are commonly used
in automobile gasoline motors. To lessen
the sound of the "exhaust," the latter is
sent through a "muffler" which often
reduces the noise to a low throbbing. (See
Fig. 166.) The gasoline engine is more
efficient than the steam-engine, since the
fuel, gas, is burned in the cylinder and not
in a separate furnace. The combustion of
the fuel in the cylinders makes some
special cooling device necessary to
prevent their overheating. This usually
consists of a casing about the cylinders.
Between the cylinder and this casing is
water which on being heated passes to a
tank or radiator. In the radiator the water
cools and then returns to the space Fig. 165.—The four strokes
between the cylinders and casing thus of a gas engine cycle.
keeping up the circulation.
Page 232
Fig. 166.—An efficient automobile muffler.
(Courtesy Popular Science Monthly.)
197. Efficiency of Gas Engines.—One may test the efficiency of a gas
engine by determining the amount of power developed and comparing it
with the mechanical equivalent of the fuel burned. Illuminating gas is
sometimes employed to drive gas engines. One cubic foot of illuminating
gas should produce 600 B.T.U. when burned. The efficiency of the gas or
gasoline engines is sometimes as high as 25 per cent. This engine is free
from smoke and is also compact and quickly started. While the fuel, gas or
gasoline, is somewhat expensive it is light and easily carried. Suppose a gas
engine produces 1 horse-power and uses 20 cu. ft. of gas an hour, what is its
efficiency? 1 horse-power-hour = 550 × 60 × 60 = 1,980,000 ft.-lbs. 20 cu.
ft. of gas = 20 × 600 × 778 = 9,336,000 ft.-lbs.
Efficiency = work out/work in = 1,980,000/9,336,000 = 21.2 per cent.
198. The Steam Turbine. One form of the steam-engine that is coming into
general use is the turbine. (See Fig. 167.) This consists of a shaft to which
are attached blades, the shaft and blades being contained in a closed case.
Steam is admitted by nozzles and strikes the blades so as to set them and the
shaft in motion. There are also stationary blades (see Fig. 168), which assist
in directing the steam effectively against the rotating parts. The steam
turbine is used for large power plants. (See Fig. 293.) It is very efficient,
makes very little vibration, and occupies about one-tenth the floor space
that a reciprocating engine of equal power uses. Some large ocean steamers
are now driven by steam turbines.
(Courtesy Popular Science Monthly.)
197. Efficiency of Gas Engines.—One may test the efficiency of a gas
engine by determining the amount of power developed and comparing it
with the mechanical equivalent of the fuel burned. Illuminating gas is
sometimes employed to drive gas engines. One cubic foot of illuminating
gas should produce 600 B.T.U. when burned. The efficiency of the gas or
gasoline engines is sometimes as high as 25 per cent. This engine is free
from smoke and is also compact and quickly started. While the fuel, gas or
gasoline, is somewhat expensive it is light and easily carried. Suppose a gas
engine produces 1 horse-power and uses 20 cu. ft. of gas an hour, what is its
efficiency? 1 horse-power-hour = 550 × 60 × 60 = 1,980,000 ft.-lbs. 20 cu.
ft. of gas = 20 × 600 × 778 = 9,336,000 ft.-lbs.
Efficiency = work out/work in = 1,980,000/9,336,000 = 21.2 per cent.
198. The Steam Turbine. One form of the steam-engine that is coming into
general use is the turbine. (See Fig. 167.) This consists of a shaft to which
are attached blades, the shaft and blades being contained in a closed case.
Steam is admitted by nozzles and strikes the blades so as to set them and the
shaft in motion. There are also stationary blades (see Fig. 168), which assist
in directing the steam effectively against the rotating parts. The steam
turbine is used for large power plants. (See Fig. 293.) It is very efficient,
makes very little vibration, and occupies about one-tenth the floor space
that a reciprocating engine of equal power uses. Some large ocean steamers
are now driven by steam turbines.
Page 233
Fig. 167.—The principle of the
steam turbine.
steam turbine.
Page 234
Fig. 168.—Path of steam in
DeLaval steam turbine. (a) and (c)
movable blades, (b) stationary.
Important Topics
1. The gas engine, its construction, action and efficiency.
2. The steam turbine.
Exercises
1. If coal costs $4.00 a ton, and gas, $0.80 per 1000 cu. ft. what amounts of
heat can be secured from 1 cent's worth of each?
2. What will it cost to heat 30 gallons of water (1 gal. of water weighs about
8-1/3 lbs.) from 40°F. to 190°F. with coal costing $4.00 per ton and yielding
12,000 B.T U. per lb. if the heater has an efficiency of 50 per cent.
DeLaval steam turbine. (a) and (c)
movable blades, (b) stationary.
Important Topics
1. The gas engine, its construction, action and efficiency.
2. The steam turbine.
Exercises
1. If coal costs $4.00 a ton, and gas, $0.80 per 1000 cu. ft. what amounts of
heat can be secured from 1 cent's worth of each?
2. What will it cost to heat 30 gallons of water (1 gal. of water weighs about
8-1/3 lbs.) from 40°F. to 190°F. with coal costing $4.00 per ton and yielding
12,000 B.T U. per lb. if the heater has an efficiency of 50 per cent.
Page 235
3. What will it cost to heat 30 gallons of water from 40°F. to 190°F. with
gas at $0.80 per 1000 cu. ft. if the heating device has an efficiency of 75 per
cent.
4. Construct a cardboard working-model showing the action of the gas
engine and be prepared to explain the action of the various parts.
5. If 500 lbs. of iron should fall 2000 ft. and all of the resulting mechanical
kinetic energy should be transformed into heat, what would be the amount
of heat produced?
6. What are the special advantages of (a) the gasoline engine? (b) the
turbine? (c) the reciprocating steam engine?
7. Do you burn coal or gas in your kitchen stove at home? Which is for you
the more economical? Why?
8. What are the advantages of using a fireless cooker?
9. What is the efficiency of a locomotive that burns 3.2 lbs. of coal per
horse-power-hour?
10. A gas engine developed in a test 0.34 horse-power for 1 minute. and 50
seconds, 0.5 cu. ft. of gas being used. The heat of combustion of the gas
was 600 B.T.U. per cu. ft. Find the efficiency of the engine.
11. Find the horse-power of an engine, the diameter of the piston being 19
in., stroke 26 in.; it uses steam at an average pressure of 200 lbs. per square.
inch and makes 100 strokes a minute.
12. What is the efficiency of an engine and boiler that develops 200 horse-
power, while burning 390 lbs. of soft coal per hour?
13. If a locomotive has an efficiency of 6 per cent. and develops 1700
horse-power how much coal is burned in an hour?
14. If an automobile engine burns 1 gallon of gasoline in an hour and
develops 10 horse-power, what is its efficiency?
15. The A.L.A.M.[J] formula for horse-power is (N B2)/2.5 when the piston
speed is 1000 ft. per minute, N being the number of cylinders and B, their
diameter. Find the horse-power of a 4-cylinder engine, the cylinders having
a diameter of 4 in.
gas at $0.80 per 1000 cu. ft. if the heating device has an efficiency of 75 per
cent.
4. Construct a cardboard working-model showing the action of the gas
engine and be prepared to explain the action of the various parts.
5. If 500 lbs. of iron should fall 2000 ft. and all of the resulting mechanical
kinetic energy should be transformed into heat, what would be the amount
of heat produced?
6. What are the special advantages of (a) the gasoline engine? (b) the
turbine? (c) the reciprocating steam engine?
7. Do you burn coal or gas in your kitchen stove at home? Which is for you
the more economical? Why?
8. What are the advantages of using a fireless cooker?
9. What is the efficiency of a locomotive that burns 3.2 lbs. of coal per
horse-power-hour?
10. A gas engine developed in a test 0.34 horse-power for 1 minute. and 50
seconds, 0.5 cu. ft. of gas being used. The heat of combustion of the gas
was 600 B.T.U. per cu. ft. Find the efficiency of the engine.
11. Find the horse-power of an engine, the diameter of the piston being 19
in., stroke 26 in.; it uses steam at an average pressure of 200 lbs. per square.
inch and makes 100 strokes a minute.
12. What is the efficiency of an engine and boiler that develops 200 horse-
power, while burning 390 lbs. of soft coal per hour?
13. If a locomotive has an efficiency of 6 per cent. and develops 1700
horse-power how much coal is burned in an hour?
14. If an automobile engine burns 1 gallon of gasoline in an hour and
develops 10 horse-power, what is its efficiency?
15. The A.L.A.M.[J] formula for horse-power is (N B2)/2.5 when the piston
speed is 1000 ft. per minute, N being the number of cylinders and B, their
diameter. Find the horse-power of a 4-cylinder engine, the cylinders having
a diameter of 4 in.
Page 236
16. Find the horse-power of a 6-cylinder automobile engine, if the cylinder
diameter is 4.5 in.
17. A 4-cylinder automobile having 4-in. cylinders, uses 1 gallon of
gasoline in 1 hour. Find its efficiency, if its average horse-power developed
is 6.
18. The motor boat Disturber III, has 24 cylinders each with diameter 3.5
in. If the piston speed is 1000 ft. per minute, what is the horse-power? (See
problem 15.)
Review Outline: Heat
Heat; sources (4), effects (5), units (2).
Temperature; thermometer scales (3), absolute temperature, 9C°/5 + 32° =
F°.
Expansion; gases, Law of Charles (V1/V2 = T1/T2), liquids, peculiarity of
water, solids, coefficient of expansion, uses, results.
Heat Transference; conduction, uses of good and poor conductors,
convection, in nature, heating and ventilating systems, radiation, 3
peculiarities, value of sun's radiation.
Heat and Moisture; relative humidity, dew point, formation of dew, fog,
rain, snow, etc., evaporation, effects, conditions.
Heat Measurement; specific heat, heat of fusion, of vaporization,
combustion.
Vaporization; Boiling point, laws of boiling, distillation, artificial cooling.
Heat Engines; steam, gas.—construction, action, efficiency, mechanical
equivalent of heat. Heat equivalent of fuels.
diameter is 4.5 in.
17. A 4-cylinder automobile having 4-in. cylinders, uses 1 gallon of
gasoline in 1 hour. Find its efficiency, if its average horse-power developed
is 6.
18. The motor boat Disturber III, has 24 cylinders each with diameter 3.5
in. If the piston speed is 1000 ft. per minute, what is the horse-power? (See
problem 15.)
Review Outline: Heat
Heat; sources (4), effects (5), units (2).
Temperature; thermometer scales (3), absolute temperature, 9C°/5 + 32° =
F°.
Expansion; gases, Law of Charles (V1/V2 = T1/T2), liquids, peculiarity of
water, solids, coefficient of expansion, uses, results.
Heat Transference; conduction, uses of good and poor conductors,
convection, in nature, heating and ventilating systems, radiation, 3
peculiarities, value of sun's radiation.
Heat and Moisture; relative humidity, dew point, formation of dew, fog,
rain, snow, etc., evaporation, effects, conditions.
Heat Measurement; specific heat, heat of fusion, of vaporization,
combustion.
Vaporization; Boiling point, laws of boiling, distillation, artificial cooling.
Heat Engines; steam, gas.—construction, action, efficiency, mechanical
equivalent of heat. Heat equivalent of fuels.
Page 237
CHAPTER IX
MAGNETISM
(1) General Properties of Magnets
199. Magnets.—Since the times of the early Greek philosophers men have
known of certain stones that have the property of attracting to themselves
objects of iron and steel. Such stones are called natural magnets. It is
thought by many that the name magnet is derived from Magnesia in Asia
Minor, where these stones are abundant, though this is but tradition.
It was also learned long ago that iron and steel objects when rubbed with
natural magnets become magnetized, that is, acquire the properties of
magnets. These are said to be artificial magnets.
Fig. 169.—A bar magnet.
Fig. 170.—A horseshoe magnet.
Some 800 years ago it was discovered that magnets, natural or artificial,
when suspended so as to turn freely, always come to rest in a definite
position pointing approximately north or south. This is especially noticeable
when the magnet is long and narrow. Because of this property of indicating
direction, natural magnets were given the name of lodestone (lode-leading).
Artificial magnets are made by rubbing steel bars with a magnet or by
placing the steel bar in a coil of wire through which a current of electricity
MAGNETISM
(1) General Properties of Magnets
199. Magnets.—Since the times of the early Greek philosophers men have
known of certain stones that have the property of attracting to themselves
objects of iron and steel. Such stones are called natural magnets. It is
thought by many that the name magnet is derived from Magnesia in Asia
Minor, where these stones are abundant, though this is but tradition.
It was also learned long ago that iron and steel objects when rubbed with
natural magnets become magnetized, that is, acquire the properties of
magnets. These are said to be artificial magnets.
Fig. 169.—A bar magnet.
Fig. 170.—A horseshoe magnet.
Some 800 years ago it was discovered that magnets, natural or artificial,
when suspended so as to turn freely, always come to rest in a definite
position pointing approximately north or south. This is especially noticeable
when the magnet is long and narrow. Because of this property of indicating
direction, natural magnets were given the name of lodestone (lode-leading).
Artificial magnets are made by rubbing steel bars with a magnet or by
placing the steel bar in a coil of wire through which a current of electricity
Page 238
is flowing. The magnetized steel bars may have any form, usually they are
either straight or bent into a "U" shape. These forms are known as bar and
horseshoe magnets. (See Figs. 169 and 170.) Magnets retain their strength
best when provided with soft-iron "keepers," as in Fig. 171.
200. Magnetic Poles.—If a magnet is placed in iron
filings and removed, the filings will be found to cling
strongly at places near the ends of the magnet, but for
a portion of its length near the middle no attraction is
found. (See Fig. 172.) These places of greatest
attraction on a magnet are called poles. If a bar
magnet is suspended so as to swing freely about a
vertical axis the magnetic pole at the end pointing
north is called the north-seeking pole; at the other
end, is the south-seeking pole. In most places the
needle does not point to the true north, but somewhat
to the east or west of north. The direction taken by a
magnetic needle is parallel to the magnetic meridian.
201. Law of Magnetic
Action.—The north pole
of a magnet is usually Fig. 170.—A
marked. If a marked bar horseshoe
magnet be held in the magnet.Fig. 171.
Fig. 172.—Iron filings hand and its north- —Bar magnets
attracted to the poles seeking pole be brought with keepers.
of a magnet. near the north-seeking
pole of a freely suspended bar magnet, the two
poles will be found to repel each other, as will also two south-seeking poles,
while a north-seeking and a south-seeking pole attract each other. (See Fig.
173.) This action leads to the statement of the Law of Magnetic Action: Like
poles repel, while unlike poles attract each other. The force of attraction or
repulsion lessens as the distance increases. The force of the action between
magnetic poles is inversely proportional to the square of the distance
between them. Compare this with the law of gravitation (Art. 88).
either straight or bent into a "U" shape. These forms are known as bar and
horseshoe magnets. (See Figs. 169 and 170.) Magnets retain their strength
best when provided with soft-iron "keepers," as in Fig. 171.
200. Magnetic Poles.—If a magnet is placed in iron
filings and removed, the filings will be found to cling
strongly at places near the ends of the magnet, but for
a portion of its length near the middle no attraction is
found. (See Fig. 172.) These places of greatest
attraction on a magnet are called poles. If a bar
magnet is suspended so as to swing freely about a
vertical axis the magnetic pole at the end pointing
north is called the north-seeking pole; at the other
end, is the south-seeking pole. In most places the
needle does not point to the true north, but somewhat
to the east or west of north. The direction taken by a
magnetic needle is parallel to the magnetic meridian.
201. Law of Magnetic
Action.—The north pole
of a magnet is usually Fig. 170.—A
marked. If a marked bar horseshoe
magnet be held in the magnet.Fig. 171.
Fig. 172.—Iron filings hand and its north- —Bar magnets
attracted to the poles seeking pole be brought with keepers.
of a magnet. near the north-seeking
pole of a freely suspended bar magnet, the two
poles will be found to repel each other, as will also two south-seeking poles,
while a north-seeking and a south-seeking pole attract each other. (See Fig.
173.) This action leads to the statement of the Law of Magnetic Action: Like
poles repel, while unlike poles attract each other. The force of attraction or
repulsion lessens as the distance increases. The force of the action between
magnetic poles is inversely proportional to the square of the distance
between them. Compare this with the law of gravitation (Art. 88).
Page 239
Fig. 173.—Like poles of two magnets repel.
Fig. 174.—A magnetoscope.
202. Magnetic Substances and Properties.—It is found that if an iron or
steel magnet is heated red hot that its magnetic properties disappear.
Accordingly one method of demagnetizing a magnet is to raise it to a red
heat. If a magnet that has been heated red hot and then cooled is brought
near a suspended bar magnet, it is found to attract either end, showing that
it has regained magnetic properties even though it has lost its magnetic
polarity. A suspended bar magnet used to test the magnetic properties of a
body is called a magnetoscope. (See Fig. 174.) The needle of a magnetic
compass serves very well as a magnetoscope. Magnetic properties are most
strongly exhibited by iron and steel, though nickel and cobalt show some
magnetic effects. There is a peculiar alloy of copper, aluminum, and
manganese, known as Heusler's Alloy, that is also magnetic. However, of all
substances, iron and steel show the strongest magnetic effects.
203. Magnetic Induction.—Let the north-seeking pole of a bar magnet
support an iron nail by its head. (See Fig. 175.) Test the point of the nail for
polarity. See whether a second nail can be attached by its head to the point
of the first. Test the polarity of the point of this nail. Find by trial how many
nails can be suspended in succession from the magnet. Test in each case for
polarity. Withdraw carefully the magnet from the first nail—the string of
nails will fall apart. Repeat the test with a thickness of paper between the
magnet and the first nail. Results similar to those secured at first will be
found, though probably fewer nails will be supported. The presence of
paper between the magnet and nails simply weakens the action. Test the
action of the magnet upon the nail when there is between them a piece of
glass, one's thumb, thin pieces of wood, copper, zinc, etc. The magnetizing
Fig. 174.—A magnetoscope.
202. Magnetic Substances and Properties.—It is found that if an iron or
steel magnet is heated red hot that its magnetic properties disappear.
Accordingly one method of demagnetizing a magnet is to raise it to a red
heat. If a magnet that has been heated red hot and then cooled is brought
near a suspended bar magnet, it is found to attract either end, showing that
it has regained magnetic properties even though it has lost its magnetic
polarity. A suspended bar magnet used to test the magnetic properties of a
body is called a magnetoscope. (See Fig. 174.) The needle of a magnetic
compass serves very well as a magnetoscope. Magnetic properties are most
strongly exhibited by iron and steel, though nickel and cobalt show some
magnetic effects. There is a peculiar alloy of copper, aluminum, and
manganese, known as Heusler's Alloy, that is also magnetic. However, of all
substances, iron and steel show the strongest magnetic effects.
203. Magnetic Induction.—Let the north-seeking pole of a bar magnet
support an iron nail by its head. (See Fig. 175.) Test the point of the nail for
polarity. See whether a second nail can be attached by its head to the point
of the first. Test the polarity of the point of this nail. Find by trial how many
nails can be suspended in succession from the magnet. Test in each case for
polarity. Withdraw carefully the magnet from the first nail—the string of
nails will fall apart. Repeat the test with a thickness of paper between the
magnet and the first nail. Results similar to those secured at first will be
found, though probably fewer nails will be supported. The presence of
paper between the magnet and nails simply weakens the action. Test the
action of the magnet upon the nail when there is between them a piece of
glass, one's thumb, thin pieces of wood, copper, zinc, etc. The magnetizing
Page 240
of a piece of iron or steel by a magnet near or touching it is called magnetic
induction. This action takes place through all substances except large bodies
of iron or steel hence these substances are often used as magnetic screens.
The pole of the new induced magnet adjacent to the bar magnet is just
opposite to the pole used. Thus the N.-pole of the magnet used will produce
a S.-pole at the near end of the nail and a N.-pole at the end farther away.
(See Fig. 175.) On removing the magnet, the nails are found to retain a part
of their induced magnetism.
204. Retentivity.—In several of the foregoing paragraphs it
has been seen that a piece of iron or steel when once
magnetized does not entirely lose its magnetism when the
magnetizing force is removed. Different pieces of iron and
steel vary greatly in this respect, some remaining strongly
magnetized, others losing much of their magnetism. This
property of retaining magnetism is called retentivity.
Hardened steel has a high degree of retentivity, while soft
iron retains but little magnetism.
Fig. 175.—
Nails
magnetized
by
induction.
Important Topics
1. Magnet; natural, artificial, bar, horseshoe.
2. Magnetic poles; north seeking, south seeking.
3. Law of action, magnetoscope, retentivity, induced magnet.
Exercises
induction. This action takes place through all substances except large bodies
of iron or steel hence these substances are often used as magnetic screens.
The pole of the new induced magnet adjacent to the bar magnet is just
opposite to the pole used. Thus the N.-pole of the magnet used will produce
a S.-pole at the near end of the nail and a N.-pole at the end farther away.
(See Fig. 175.) On removing the magnet, the nails are found to retain a part
of their induced magnetism.
204. Retentivity.—In several of the foregoing paragraphs it
has been seen that a piece of iron or steel when once
magnetized does not entirely lose its magnetism when the
magnetizing force is removed. Different pieces of iron and
steel vary greatly in this respect, some remaining strongly
magnetized, others losing much of their magnetism. This
property of retaining magnetism is called retentivity.
Hardened steel has a high degree of retentivity, while soft
iron retains but little magnetism.
Fig. 175.—
Nails
magnetized
by
induction.
Important Topics
1. Magnet; natural, artificial, bar, horseshoe.
2. Magnetic poles; north seeking, south seeking.
3. Law of action, magnetoscope, retentivity, induced magnet.
Exercises
Page 241
1. Make a summary of the facts of magnetism presented in this lesson.
2. Is magnetism matter, force, or energy? How do you decide? To what
other phenomenon that we have studied is it similar? How?
3. Make a simple magnetoscope for yourself by suspending a thin steel
needle or rod 5 to 10 cm. long, with a light thread or silk fiber at its center,
so that it will hang level. Then magnetize the needle, and keep the
magnetoscope in your book.
4. Name three uses for magnets or magnetism.
5. Mention three uses for a magnetoscope.
6. Are all magnets produced by induction? Explain.
7. In what magnetic devices is a high retentivity desirable?
(2) The Theory of Magnetism and Magnetic Fields
205. The Theory of Magnetism.—If a magnetized watch spring is broken
in two, each part is found to be a magnet. If one of these parts be broken
and this process of breaking be continued as far as possible, the smallest
part obtained has two poles and is in fact a complete magnet. (See Fig.
176.) It is supposed that if the division could be continued far enough that
each of the molecules of the steel spring would be found to have two poles
and to be a magnet. In other words, magnetism is believed to be molecular.
Other evidence supporting this idea is found in the fact that when a magnet
is heated red hot, to a temperature of violent molecular motion, its
magnetism disappears. Also if a long, fine soft iron wire be strongly
magnetized, a light jar causes its magnetism to disappear. This would lead
us to believe that magnetism is not a property of the surface of the body, but
that it depends upon molecular structure or the arrangement of the
molecules.
It is believed also that the molecules of a magnetic substance are magnets at
all times; that before the body is magnetized the molecules are arranged
haphazard (see Fig. 177) but that when a magnet is brought near, the
molecules tend to arrange themselves in line, with their north-seeking poles
pointing in the same direction. (See Fig. 178.) If the magnet is jarred some
2. Is magnetism matter, force, or energy? How do you decide? To what
other phenomenon that we have studied is it similar? How?
3. Make a simple magnetoscope for yourself by suspending a thin steel
needle or rod 5 to 10 cm. long, with a light thread or silk fiber at its center,
so that it will hang level. Then magnetize the needle, and keep the
magnetoscope in your book.
4. Name three uses for magnets or magnetism.
5. Mention three uses for a magnetoscope.
6. Are all magnets produced by induction? Explain.
7. In what magnetic devices is a high retentivity desirable?
(2) The Theory of Magnetism and Magnetic Fields
205. The Theory of Magnetism.—If a magnetized watch spring is broken
in two, each part is found to be a magnet. If one of these parts be broken
and this process of breaking be continued as far as possible, the smallest
part obtained has two poles and is in fact a complete magnet. (See Fig.
176.) It is supposed that if the division could be continued far enough that
each of the molecules of the steel spring would be found to have two poles
and to be a magnet. In other words, magnetism is believed to be molecular.
Other evidence supporting this idea is found in the fact that when a magnet
is heated red hot, to a temperature of violent molecular motion, its
magnetism disappears. Also if a long, fine soft iron wire be strongly
magnetized, a light jar causes its magnetism to disappear. This would lead
us to believe that magnetism is not a property of the surface of the body, but
that it depends upon molecular structure or the arrangement of the
molecules.
It is believed also that the molecules of a magnetic substance are magnets at
all times; that before the body is magnetized the molecules are arranged
haphazard (see Fig. 177) but that when a magnet is brought near, the
molecules tend to arrange themselves in line, with their north-seeking poles
pointing in the same direction. (See Fig. 178.) If the magnet is jarred some
Page 242
o
f
t
h
e
Fig. 177.—Possible arrangement
of molecules in an unmagnetized Fig. 176.—Effect of breaking a
iron bar. magnet.
molecules tend to get out of line,
perhaps to form little closed chains of molecules. (See Fig. 177.)
206. Magnetic Fields and Lines of
Force.—The behavior of magnets is
better understood after observing and
studying the lines of force of a
magnet. The earliest descriptions of
these are by William Gilbert, the first
Englishman to appreciate fully the Fig. 178.—Arrangement of
value of making experimental molecules in a saturated magnet.
observations. He wrote a book in 1600
called De Magnete in which he published his experiments and discoveries
in magnetism. (See p. 217.)
Magnetic lines of force may be observed by placing a magnet upon the
table, then laying upon it a sheet of paper and sprinkling over the latter fine
iron filings. On gently tapping the paper, the filings arrange themselves
along curved lines extending from one end of the magnet to the other. These
are called the magnetic lines of force. (See Fig. 179.) The space about a
magnet in which the magnetic lines are found is called the magnetic field.
(See Fig. 180.)
f
t
h
e
Fig. 177.—Possible arrangement
of molecules in an unmagnetized Fig. 176.—Effect of breaking a
iron bar. magnet.
molecules tend to get out of line,
perhaps to form little closed chains of molecules. (See Fig. 177.)
206. Magnetic Fields and Lines of
Force.—The behavior of magnets is
better understood after observing and
studying the lines of force of a
magnet. The earliest descriptions of
these are by William Gilbert, the first
Englishman to appreciate fully the Fig. 178.—Arrangement of
value of making experimental molecules in a saturated magnet.
observations. He wrote a book in 1600
called De Magnete in which he published his experiments and discoveries
in magnetism. (See p. 217.)
Magnetic lines of force may be observed by placing a magnet upon the
table, then laying upon it a sheet of paper and sprinkling over the latter fine
iron filings. On gently tapping the paper, the filings arrange themselves
along curved lines extending from one end of the magnet to the other. These
are called the magnetic lines of force. (See Fig. 179.) The space about a
magnet in which the magnetic lines are found is called the magnetic field.
(See Fig. 180.)
Page 243
Fig. 179.—Iron filings on paper over a bar
magnet.
Many interesting things have been discovered concerning the lines of force.
Some of the facts of magnetic action are given a simple explanation if we
think of them as due to the magnetic lines of force. A summary of several
discoveries concerning magnetic fields follows:
(A) Magnetic lines of force run side by side and do not cross one another.
(See magnetic fields.)
(B) Magnetic lines of force are believed to form "closed curves" or to be
continuous. The part outside of the magnet is a continuation of the part
within the magnet. (See Fig. 180.)
(C) The attraction of a magnet is strongest
where the magnetic lines are thickest,
hence they are believed to be the means
by which a magnet attracts.
(D) Since like poles repel and unlike poles
attract, it is known that the action along a
line of force is not the same in both
directions. It has therefore been agreed by
physicists to indicate by an arrow head
(Fig. 180), the direction that a north-
seeking pole tends to move along a line of Fig. 180.—Diagram of the
magnet.
Many interesting things have been discovered concerning the lines of force.
Some of the facts of magnetic action are given a simple explanation if we
think of them as due to the magnetic lines of force. A summary of several
discoveries concerning magnetic fields follows:
(A) Magnetic lines of force run side by side and do not cross one another.
(See magnetic fields.)
(B) Magnetic lines of force are believed to form "closed curves" or to be
continuous. The part outside of the magnet is a continuation of the part
within the magnet. (See Fig. 180.)
(C) The attraction of a magnet is strongest
where the magnetic lines are thickest,
hence they are believed to be the means
by which a magnet attracts.
(D) Since like poles repel and unlike poles
attract, it is known that the action along a
line of force is not the same in both
directions. It has therefore been agreed by
physicists to indicate by an arrow head
(Fig. 180), the direction that a north-
seeking pole tends to move along a line of Fig. 180.—Diagram of the
Page 244
force. The lines of force are considered as field of a bar magnet.
leaving the north-seeking pole of a
magnet and entering the south-seeking pole. (See Figs. 181 and 182.)
Fig. 181.—Magnetic field between like poles
showing repulsion.
(E) A freely suspended small magnet in a magnetic field places itself
parallel to the lines of force. (Test this by holding a magnetic compass in
different portions of a magnetic field). Note the position of the needle and
the lines of force. This fact indicates that the compass needle points north
on account of its tendency to turn so as to be parallel to the earth's magnetic
held.
leaving the north-seeking pole of a
magnet and entering the south-seeking pole. (See Figs. 181 and 182.)
Fig. 181.—Magnetic field between like poles
showing repulsion.
(E) A freely suspended small magnet in a magnetic field places itself
parallel to the lines of force. (Test this by holding a magnetic compass in
different portions of a magnetic field). Note the position of the needle and
the lines of force. This fact indicates that the compass needle points north
on account of its tendency to turn so as to be parallel to the earth's magnetic
held.
Page 245
Fig. 182.—Magnetic field between unlike poles
showing attraction.
(F) Each magnet is accompanied by its own magnetic field. When a piece of
iron is brought within the field of a magnet the lines of force passing
through the iron tend to arrange the iron molecules in line or to magnetize
the iron.
207. Magnetic Induction.—The action of magnetic lines of force in
magnetizing iron when they pass through it, is called Magnetic Induction.
This may now be defined as the production of magnetism in a body by
placing it within a magnetic field. Freely suspended magnets place
themselves parallel to the lines of force in a magnetic field, therefore when
an iron rod is placed in a weak field, or one with few lines of force, the iron
is but slightly magnetized; that is, but few molecules are brought into line.
Increasing the strength of the magnetizing field, gives stronger
magnetization to the iron up to a certain point. After this, stronger fields
give no increase in magnetizing effect. When iron exhibits its greatest
magnetization it is said to be saturated.
208. Permeability.—If a piece of iron is placed
between the poles of a horseshoe magnet, the "field"
obtained by sprinkling iron filings upon a sheet of
paper over the magnet resembles that shown in Fig.
183. The lines in the space between the poles of the
magnet seem to crowd in to the piece of iron. The
property of the iron by which it tends to concentrate
and increase the number of lines of force of a
magnetic field is called permeability. Soft iron shows
high permeability. Marked differences in behavior are
shown by different kinds of iron and steel when placed
in a magnetic field. Very pure iron, or soft iron, is Fig. 183.—Effect
strongly magnetized by a magnetic field of medium of a piece of iron
strength. Its magnetism, however, is quickly lost when in a magnetic
the magnetizing field is removed. This indicates that field.
soft-iron molecules are easily swung into line, but also
disarrange themselves as easily when removed from a magnetizing force.
Soft-iron magnets having high permeability quickly lose their magnetism.
They are therefore called temporary magnets. On the other hand a hardened
showing attraction.
(F) Each magnet is accompanied by its own magnetic field. When a piece of
iron is brought within the field of a magnet the lines of force passing
through the iron tend to arrange the iron molecules in line or to magnetize
the iron.
207. Magnetic Induction.—The action of magnetic lines of force in
magnetizing iron when they pass through it, is called Magnetic Induction.
This may now be defined as the production of magnetism in a body by
placing it within a magnetic field. Freely suspended magnets place
themselves parallel to the lines of force in a magnetic field, therefore when
an iron rod is placed in a weak field, or one with few lines of force, the iron
is but slightly magnetized; that is, but few molecules are brought into line.
Increasing the strength of the magnetizing field, gives stronger
magnetization to the iron up to a certain point. After this, stronger fields
give no increase in magnetizing effect. When iron exhibits its greatest
magnetization it is said to be saturated.
208. Permeability.—If a piece of iron is placed
between the poles of a horseshoe magnet, the "field"
obtained by sprinkling iron filings upon a sheet of
paper over the magnet resembles that shown in Fig.
183. The lines in the space between the poles of the
magnet seem to crowd in to the piece of iron. The
property of the iron by which it tends to concentrate
and increase the number of lines of force of a
magnetic field is called permeability. Soft iron shows
high permeability. Marked differences in behavior are
shown by different kinds of iron and steel when placed
in a magnetic field. Very pure iron, or soft iron, is Fig. 183.—Effect
strongly magnetized by a magnetic field of medium of a piece of iron
strength. Its magnetism, however, is quickly lost when in a magnetic
the magnetizing field is removed. This indicates that field.
soft-iron molecules are easily swung into line, but also
disarrange themselves as easily when removed from a magnetizing force.
Soft-iron magnets having high permeability quickly lose their magnetism.
They are therefore called temporary magnets. On the other hand a hardened
Page 246
steel bar is difficult to magnetize, but when once magnetized retains its
magnetism permanently, unless some action weakens the magnet. Such
magnets are called permanent magnets.
Note.—The term "line of force" as used in this text means the same as "line
of induction" as used in more advanced texts.
Important Topics
1. Molecular theory of magnetism, saturation, permeability.
2. Magnetic fields and lines of force.
3. Six facts concerning magnetic fields.
Exercises
1. Name an object whose usefulness depends upon its retentivity. Explain.
2. How do you explain the retentivity of hard steel?
3. Are the molecules of a piece of iron magnetized at all times? Explain.
4. When a piece of iron is magnetized by induction does any magnetism
enter the iron from the magnet? Does the magnet lose as the iron gains
magnetism? Explain.
5. Have all magnets been produced by induction? Explain.
6. Why will tapping a piece of iron when in a magnetic field increase the
amount it will be magnetized?
7. Express in your own words the theory of magnetism.
8. Place two bar magnets in a line 5 cm. apart, unlike poles adjacent; obtain
the magnetic field with iron filings. Sketch it.
9. Repeat Exercise No. 8 using like poles. Describe the appearance of a
field that gives attraction; of a field that gives repulsion.
(3) The Earth's Magnetism
magnetism permanently, unless some action weakens the magnet. Such
magnets are called permanent magnets.
Note.—The term "line of force" as used in this text means the same as "line
of induction" as used in more advanced texts.
Important Topics
1. Molecular theory of magnetism, saturation, permeability.
2. Magnetic fields and lines of force.
3. Six facts concerning magnetic fields.
Exercises
1. Name an object whose usefulness depends upon its retentivity. Explain.
2. How do you explain the retentivity of hard steel?
3. Are the molecules of a piece of iron magnetized at all times? Explain.
4. When a piece of iron is magnetized by induction does any magnetism
enter the iron from the magnet? Does the magnet lose as the iron gains
magnetism? Explain.
5. Have all magnets been produced by induction? Explain.
6. Why will tapping a piece of iron when in a magnetic field increase the
amount it will be magnetized?
7. Express in your own words the theory of magnetism.
8. Place two bar magnets in a line 5 cm. apart, unlike poles adjacent; obtain
the magnetic field with iron filings. Sketch it.
9. Repeat Exercise No. 8 using like poles. Describe the appearance of a
field that gives attraction; of a field that gives repulsion.
(3) The Earth's Magnetism
Page 247
209. The Earth's Magnetic Field.—Dr. William Gilbert's famous book, De
Magnete, contains many helpful and suggestive ideas, none perhaps more
important than his explanation of the behavior of the compass needle. He
assumed that the earth is a magnet, with a south-seeking pole near the
geographical north pole, and with a north-seeking pole near the
geographical south pole. This idea has since been shown to be correct. The
north magnetic (or south-seeking) pole was found in 1831, by Sir James
Ross in Boothia Felix, Canada. Its approximate present location as
determined by Captain Amundsen in 1905 is latitude 70° 5´ N. and
longitude 96° 46´ W. The south magnetic pole is in latitude 72° S.,
longitude 155° 16´ E. The north magnetic pole is continually changing its
position. At present it is moving slowly westward.
Fig. 184.—Magnetic map of the earth for 1910. Isogonic lines ———
Isoclinic lines - - - -
210. Direction of the Earth's Magnetic Field.—Reference has been made
to the fact that the compass does not always point exactly north. This
indicates that the earth's magnetic field varies in its direction. Columbus
discovered this fact upon his first voyage. The discovery alarmed the sailors
since they feared they might come to a place where the compass would be
unreliable. This variation is called declination. It is defined as the angle
between the direction of the needle and the geographical meridian.
Magnete, contains many helpful and suggestive ideas, none perhaps more
important than his explanation of the behavior of the compass needle. He
assumed that the earth is a magnet, with a south-seeking pole near the
geographical north pole, and with a north-seeking pole near the
geographical south pole. This idea has since been shown to be correct. The
north magnetic (or south-seeking) pole was found in 1831, by Sir James
Ross in Boothia Felix, Canada. Its approximate present location as
determined by Captain Amundsen in 1905 is latitude 70° 5´ N. and
longitude 96° 46´ W. The south magnetic pole is in latitude 72° S.,
longitude 155° 16´ E. The north magnetic pole is continually changing its
position. At present it is moving slowly westward.
Fig. 184.—Magnetic map of the earth for 1910. Isogonic lines ———
Isoclinic lines - - - -
210. Direction of the Earth's Magnetic Field.—Reference has been made
to the fact that the compass does not always point exactly north. This
indicates that the earth's magnetic field varies in its direction. Columbus
discovered this fact upon his first voyage. The discovery alarmed the sailors
since they feared they might come to a place where the compass would be
unreliable. This variation is called declination. It is defined as the angle
between the direction of the needle and the geographical meridian.
Page 248
Declination is due to the fact that the geographical and magnetic poles do
not coincide. What is meant by a declination of 90°? Lines drawn upon a
map so as to pass through places of the same declination are called isogonic
lines. The line passing through points where the needle points north,
without declination, is the agonic line. The agonic line is slowly moving
westward. It now passes near Lansing, Michigan; Cincinnati, Ohio; and
Charleston, S. Carolina. (See Fig. 184.) At all points in the United States
and Canada east of the agonic line the declination is west, at points west of
the agonic line the declination is east.
211. The Dipping Needle.—Mount an unmagnetized steel needle on a
horizontal axis so as to be in neutral equilibrium, that is, so as to remain
balanced in any position in which it is left. Upon being magnetized and
placed so that it can swing in a north and south plane, the north-seeking
pole will now be found to be depressed, the needle forming an angle of
nearly 70° with the horizontal. (See Fig. 185.) The position assumed by the
needle indicates that the earth's magnetic field instead of being horizontal in
the United States dips down at an angle of about 70°. Over the magnetic
pole, the dipping needle as it is called, is vertical. At the earth's equator it is
nearly horizontal. The angle between a horizontal plane and the earth's
magnetic lines of force is called the inclination or dip.
212. Inductive Effect of the Earth's Magnetic Field.
—The earth's magnetic lines of force are to be
considered as filling the space above the earth, passing
through all objects on the surface and into and through
the earth's interior. The direction of the earth's field is
shown by the compass and the dipping needle.
Magnetic lines of force tend to crowd into and follow
iron and steel objects on account of their permeability.
Therefore, iron or steel objects, such as posts,
columns, etc., are permeated by the earth's lines of
force, which in the United States enter at the top of
these objects and leave at the bottom. The lines of Fig. 185.—A
force passing through these bodies arrange their dipping needle.
molecules in line or magnetize the bodies. The
inductive effect of the earth's magnetism indicates how lodestones or natural
magnets acquire their magnetized condition. So far as is known, magnetism
not coincide. What is meant by a declination of 90°? Lines drawn upon a
map so as to pass through places of the same declination are called isogonic
lines. The line passing through points where the needle points north,
without declination, is the agonic line. The agonic line is slowly moving
westward. It now passes near Lansing, Michigan; Cincinnati, Ohio; and
Charleston, S. Carolina. (See Fig. 184.) At all points in the United States
and Canada east of the agonic line the declination is west, at points west of
the agonic line the declination is east.
211. The Dipping Needle.—Mount an unmagnetized steel needle on a
horizontal axis so as to be in neutral equilibrium, that is, so as to remain
balanced in any position in which it is left. Upon being magnetized and
placed so that it can swing in a north and south plane, the north-seeking
pole will now be found to be depressed, the needle forming an angle of
nearly 70° with the horizontal. (See Fig. 185.) The position assumed by the
needle indicates that the earth's magnetic field instead of being horizontal in
the United States dips down at an angle of about 70°. Over the magnetic
pole, the dipping needle as it is called, is vertical. At the earth's equator it is
nearly horizontal. The angle between a horizontal plane and the earth's
magnetic lines of force is called the inclination or dip.
212. Inductive Effect of the Earth's Magnetic Field.
—The earth's magnetic lines of force are to be
considered as filling the space above the earth, passing
through all objects on the surface and into and through
the earth's interior. The direction of the earth's field is
shown by the compass and the dipping needle.
Magnetic lines of force tend to crowd into and follow
iron and steel objects on account of their permeability.
Therefore, iron or steel objects, such as posts,
columns, etc., are permeated by the earth's lines of
force, which in the United States enter at the top of
these objects and leave at the bottom. The lines of Fig. 185.—A
force passing through these bodies arrange their dipping needle.
molecules in line or magnetize the bodies. The
inductive effect of the earth's magnetism indicates how lodestones or natural
magnets acquire their magnetized condition. So far as is known, magnetism
Page 249
produces no effect upon the human body. It can therefore be studied only by
observing its effects upon magnets or bodies affected by it.
Important Topics
The earth's magnetic field, dip, declination, agonic line, induction by the
earth's field.
Exercises
1. How would a dipping needle be of assistance in locating the magnetic
poles of the earth?
2. Will a dipping needle weigh more before or after it is magnetized?
Explain.
3. It is said that induction precedes attraction. Using this idea, explain how
a magnet attracts a piece of soft iron.
4. Devise an experiment to show that a piece of iron attracts a magnet just
as a magnet attracts a piece of iron.
5. Give two methods for determining the poles of a magnet.
6. State three of the most important points in the theory of magnetism. What
evidence supports each?
7. Why is a permanent magnet injured when it is dropped?
8. Name two important uses of the earth's magnetic field.
9. What magnetic pole would you find at the top of an iron post that has
stood for some time in the ground? What pole at the bottom? How would
you test this?
observing its effects upon magnets or bodies affected by it.
Important Topics
The earth's magnetic field, dip, declination, agonic line, induction by the
earth's field.
Exercises
1. How would a dipping needle be of assistance in locating the magnetic
poles of the earth?
2. Will a dipping needle weigh more before or after it is magnetized?
Explain.
3. It is said that induction precedes attraction. Using this idea, explain how
a magnet attracts a piece of soft iron.
4. Devise an experiment to show that a piece of iron attracts a magnet just
as a magnet attracts a piece of iron.
5. Give two methods for determining the poles of a magnet.
6. State three of the most important points in the theory of magnetism. What
evidence supports each?
7. Why is a permanent magnet injured when it is dropped?
8. Name two important uses of the earth's magnetic field.
9. What magnetic pole would you find at the top of an iron post that has
stood for some time in the ground? What pole at the bottom? How would
you test this?
Page 250
CHAPTER X
STATIC ELECTRICITY
(1) Electrification and Electrical Charges
213. Electrical Charges.—The ideas gained in the study of magnetism are
of assistance in the study of electricity in giving some fundamental ideas
and principles that will often be referred to as a basis for comparing the
actions of magnetized and electrified bodies. The process of electrifying a
body is very different from that of magnetizing it. Thus if a rubber comb or
rod be rubbed with a woolen cloth the object rubbed is able to attract to
itself light bits of paper, thread, etc. This peculiar attraction was noticed and
recorded by the ancient Greeks, 600 B.C., when it was found that amber
when rubbed would attract light objects to itself. For a long time it was
supposed that amber was the only substance showing this property. Dr.
William Gilbert, however, discovered that the electrified condition could be
produced by rubbing a great variety of substances. He named the result
produced, electrification, after the Greek name for amber (elektron). A body
like hard rubber or amber which will attract light objects when rubbed is
said to be electrified, or to have been given a charge of electricity.
214. Law of Electric Action.—Let a vulcanite rod be electrified by rubbing
with a woolen cloth until it will attract light objects; then place it in a wire
stirrup suspended by a silk thread. If a second vulcanite rod is similarly
electrified and brought near the first, the two will be found to repel. (See
Fig. 186.) If now a glass rod be rubbed with silk and brought near the
suspended rod, the two will attract. This difference in behavior indicates a
difference in the electrification or charge upon the rods. The two charged
vulcanite rods repelling and the charged glass and vulcanite attracting
indicate the law of electric action. Like charges repel each other and unlike
charges attract each other. Extensive experiments with all kinds of
substances indicate that there are but two kinds of electrical charges. The
electrical charge upon glass when rubbed with silk or wool is called
STATIC ELECTRICITY
(1) Electrification and Electrical Charges
213. Electrical Charges.—The ideas gained in the study of magnetism are
of assistance in the study of electricity in giving some fundamental ideas
and principles that will often be referred to as a basis for comparing the
actions of magnetized and electrified bodies. The process of electrifying a
body is very different from that of magnetizing it. Thus if a rubber comb or
rod be rubbed with a woolen cloth the object rubbed is able to attract to
itself light bits of paper, thread, etc. This peculiar attraction was noticed and
recorded by the ancient Greeks, 600 B.C., when it was found that amber
when rubbed would attract light objects to itself. For a long time it was
supposed that amber was the only substance showing this property. Dr.
William Gilbert, however, discovered that the electrified condition could be
produced by rubbing a great variety of substances. He named the result
produced, electrification, after the Greek name for amber (elektron). A body
like hard rubber or amber which will attract light objects when rubbed is
said to be electrified, or to have been given a charge of electricity.
214. Law of Electric Action.—Let a vulcanite rod be electrified by rubbing
with a woolen cloth until it will attract light objects; then place it in a wire
stirrup suspended by a silk thread. If a second vulcanite rod is similarly
electrified and brought near the first, the two will be found to repel. (See
Fig. 186.) If now a glass rod be rubbed with silk and brought near the
suspended rod, the two will attract. This difference in behavior indicates a
difference in the electrification or charge upon the rods. The two charged
vulcanite rods repelling and the charged glass and vulcanite attracting
indicate the law of electric action. Like charges repel each other and unlike
charges attract each other. Extensive experiments with all kinds of
substances indicate that there are but two kinds of electrical charges. The
electrical charge upon glass when rubbed with silk or wool is called
Page 251
positive, and that upon hard rubber or vulcanite when rubbed with wool is
called negative.
Fig. 186.—
Repulsion of
like charges.
Fig. 187.—An aluminum foil electroscope.
Fig. 188.—A proof plane.
215. The Electroscope and its Uses.—An electroscope is a device
employed to test the presence of an electrical charge. The aluminum foil
electroscope consists of a flask closed by a rubber stopper through which
passes a rod which ends at the top in a ball or plate and below is attached
two narrow leaves of thin aluminum-foil. Ordinarily the two leaves hang
close together and parallel but if a charged body is brought near the
electroscope the leaves spread apart at the bottom. (See Fig. 187.) The kind
of charge upon a body may be determined with an electroscope as follows:
Make a proof-plane by sealing a small metal disc on the end of a hard
called negative.
Fig. 186.—
Repulsion of
like charges.
Fig. 187.—An aluminum foil electroscope.
Fig. 188.—A proof plane.
215. The Electroscope and its Uses.—An electroscope is a device
employed to test the presence of an electrical charge. The aluminum foil
electroscope consists of a flask closed by a rubber stopper through which
passes a rod which ends at the top in a ball or plate and below is attached
two narrow leaves of thin aluminum-foil. Ordinarily the two leaves hang
close together and parallel but if a charged body is brought near the
electroscope the leaves spread apart at the bottom. (See Fig. 187.) The kind
of charge upon a body may be determined with an electroscope as follows:
Make a proof-plane by sealing a small metal disc on the end of a hard
Page 252
rubber rod. (See Fig. 188.) Touch the disc of the proof-plane first to a
charged rubber rod and then to the top of the electroscope. The leaves of the
latter will separate showing that the electroscope is charged. This charge
remains after the proof-plane is removed. If the charged vulcanite rod is
brought near the electroscope, the leaves separate further That is, a charge
like that on the electroscope makes the leaves separate further. But if an
unlike charge, as that on a positively charged glass rod, is cautiously
brought near, the leaves will be seen to move together.
216. Two Charges are Produced at the Same
Time.—A closely fitting woolen cover or cap
some 3 in. long is made for the end of a
vulcanite rod. A silk thread attached to the cap
enables one to hold the latter while the rod is
Fig. 189.—Rod with
turned within it. (See Fig. 189.) If the rod woolen cap.
bearing the cap is held near a charged
electroscope little or no effect is noticed. If now
the cap is removed by the silk thread and held near the electroscope, it will
be found to be positively charged while the rod is negatively charged. The
fact that no result is seen when the cap and rod are together, indicates that
one charge neutralizes the other. In other words, the charges must be equal.
This illustrates the truth that when electrification is produced by friction, the
two objects rubbed together acquire equal and opposite charges.
217. Charging by Contact and Conduction.—If a small pith ball is
suspended by a silk thread, a charged rod brought near is at first attracted,
but after contact is repelled (see Fig. 190) showing that the ball has become
charged with the same kind of electrification that is upon the rod. That is, a
charge given to an object by contact with a charged body is of the same
kind as that upon the charged one. The proof-plane in Art. 215 carries the
same kind of charge that is upon the rod it is charged from. Some
substances have the ability to transfer charges of electrification. These are
called conductors, those that do not conduct electrification are insulators.
The conducting power of a body is readily tested by placing one end of a
rod of the material upon the top of an electroscope and the other end upon
an insulated support, as in Fig. 191. If now a charge be put in contact with
the body of a, the electroscope will show by its leaves whether the rod
tested conducts or not. The leaves separate instantly when conducting
charged rubber rod and then to the top of the electroscope. The leaves of the
latter will separate showing that the electroscope is charged. This charge
remains after the proof-plane is removed. If the charged vulcanite rod is
brought near the electroscope, the leaves separate further That is, a charge
like that on the electroscope makes the leaves separate further. But if an
unlike charge, as that on a positively charged glass rod, is cautiously
brought near, the leaves will be seen to move together.
216. Two Charges are Produced at the Same
Time.—A closely fitting woolen cover or cap
some 3 in. long is made for the end of a
vulcanite rod. A silk thread attached to the cap
enables one to hold the latter while the rod is
Fig. 189.—Rod with
turned within it. (See Fig. 189.) If the rod woolen cap.
bearing the cap is held near a charged
electroscope little or no effect is noticed. If now
the cap is removed by the silk thread and held near the electroscope, it will
be found to be positively charged while the rod is negatively charged. The
fact that no result is seen when the cap and rod are together, indicates that
one charge neutralizes the other. In other words, the charges must be equal.
This illustrates the truth that when electrification is produced by friction, the
two objects rubbed together acquire equal and opposite charges.
217. Charging by Contact and Conduction.—If a small pith ball is
suspended by a silk thread, a charged rod brought near is at first attracted,
but after contact is repelled (see Fig. 190) showing that the ball has become
charged with the same kind of electrification that is upon the rod. That is, a
charge given to an object by contact with a charged body is of the same
kind as that upon the charged one. The proof-plane in Art. 215 carries the
same kind of charge that is upon the rod it is charged from. Some
substances have the ability to transfer charges of electrification. These are
called conductors, those that do not conduct electrification are insulators.
The conducting power of a body is readily tested by placing one end of a
rod of the material upon the top of an electroscope and the other end upon
an insulated support, as in Fig. 191. If now a charge be put in contact with
the body of a, the electroscope will show by its leaves whether the rod
tested conducts or not. The leaves separate instantly when conducting
Page 253
substances are tested, while no action results with insulators. In testing
some materials for conductivity the leaves are found to diverge gradually.
Such bodies are said to be poor conductors. All degrees of conductivity are
found. The metals are the best conductors. The best insulators are rubber,
mica, shellac, glass, silk, porcelain, paraffin, and oils.
Fig. 190.—The pith ball charged by contact is
repelled.
Fig. 191.—Testing for conductivity.
Important Topics
1. Positive and negative changes. Law of electric action.
2. Electroscope and its uses.
3. Conductors and insulators.
Exercises
1. Is air a conductor? Give reasons for your answer.
2. Mention two points of likeness and two points of difference between
magnetism and electrification.
3. If you were testing the electrification of a body with a charged pith ball
suspended by a silk thread, would attraction or repulsion be the better test?
Give reasons.
some materials for conductivity the leaves are found to diverge gradually.
Such bodies are said to be poor conductors. All degrees of conductivity are
found. The metals are the best conductors. The best insulators are rubber,
mica, shellac, glass, silk, porcelain, paraffin, and oils.
Fig. 190.—The pith ball charged by contact is
repelled.
Fig. 191.—Testing for conductivity.
Important Topics
1. Positive and negative changes. Law of electric action.
2. Electroscope and its uses.
3. Conductors and insulators.
Exercises
1. Is air a conductor? Give reasons for your answer.
2. Mention two points of likeness and two points of difference between
magnetism and electrification.
3. If you were testing the electrification of a body with a charged pith ball
suspended by a silk thread, would attraction or repulsion be the better test?
Give reasons.
Page 254
4. Have you ever produced electrification by friction outside of a
laboratory? Explain.
5. Are the rods upon which we produce electrification by friction,
conductors or insulators? How do you explain this?
6. Are conductors or insulators of the greater importance in practical
electricity? Explain.
(2) Electric Fields and Electrostatic Induction
Fig. 192.—An electric field about a positively
charged shell.
Fig. 193.—A "detector."
218. Electrical Fields.—In our study of magnetism we learned that a
magnet affects objects about it by its magnetic lines of force. In a similar
way it is assumed that a charged body produces electrical effects upon its
surroundings by electric lines of force. For example, the attraction that a
charged body exerts upon light objects through short distances or the
influence of a charge upon an electroscope several feet away, is said to be
due to the electric field about the charged body. (See Fig. 192.) The
presence of the electric lines of force may be shown by placing a
perforated, slender, diamond-shaped piece of tissue paper upon a light glass
pointer (Fig. 193). When placed in an electric field the tissue paper
"detector" places itself parallel to the lines of force. Electric lines of force
are said to extend from a positive to a negative charge. (See Fig. 194.) The
direction shown by the arrow upon the lines is that along which a small
positive charge tends to move. Electric lines of force unlike those from
laboratory? Explain.
5. Are the rods upon which we produce electrification by friction,
conductors or insulators? How do you explain this?
6. Are conductors or insulators of the greater importance in practical
electricity? Explain.
(2) Electric Fields and Electrostatic Induction
Fig. 192.—An electric field about a positively
charged shell.
Fig. 193.—A "detector."
218. Electrical Fields.—In our study of magnetism we learned that a
magnet affects objects about it by its magnetic lines of force. In a similar
way it is assumed that a charged body produces electrical effects upon its
surroundings by electric lines of force. For example, the attraction that a
charged body exerts upon light objects through short distances or the
influence of a charge upon an electroscope several feet away, is said to be
due to the electric field about the charged body. (See Fig. 192.) The
presence of the electric lines of force may be shown by placing a
perforated, slender, diamond-shaped piece of tissue paper upon a light glass
pointer (Fig. 193). When placed in an electric field the tissue paper
"detector" places itself parallel to the lines of force. Electric lines of force
are said to extend from a positive to a negative charge. (See Fig. 194.) The
direction shown by the arrow upon the lines is that along which a small
positive charge tends to move. Electric lines of force unlike those from
Page 255
magnets are not continuous. They extend from a positive charge to a
negative charge. Therefore each positive charge is connected by lines of
force to a negative charge somewhere. These ideas of electric fields are of
much assistance in explaining many electrical effects. Electrical fields
between oppositely charged shells will be found similar to Fig. 194, while
between shells with like charges, fields are found as in Fig. 195.
2
1
9
.
Fig. 194.—Electric field between
Fig. 195.—Electric field between
unlike charges.
like charges.
Electrostatic Induction.—If a
charged body is brought near an aluminum-foil electroscope, the leaves
separate. (See Fig. 198.) The nearer the charge is brought the wider the
leaves spread, but when the charge is removed, the leaves collapse showing
that nothing was given to the electroscope. It was simply affected by the
charge in its vicinity. This production of an electrified condition in a body
by the influence of a charge near it is called electrostatic induction. Placing
insulators, such as a sheet of glass, between the charge and the electroscope
does not affect the result, which is apparently brought about by the action of
the electric lines of force. These lines of force extend without difficulty
through uncharged insulators and terminate often at the surface of a
conductor, where their influence causes a charge to accumulate. Charged
insulators, however, do affect inductive action. This may be noticed by
using a sensitive electroscope.
negative charge. Therefore each positive charge is connected by lines of
force to a negative charge somewhere. These ideas of electric fields are of
much assistance in explaining many electrical effects. Electrical fields
between oppositely charged shells will be found similar to Fig. 194, while
between shells with like charges, fields are found as in Fig. 195.
2
1
9
.
Fig. 194.—Electric field between
Fig. 195.—Electric field between
unlike charges.
like charges.
Electrostatic Induction.—If a
charged body is brought near an aluminum-foil electroscope, the leaves
separate. (See Fig. 198.) The nearer the charge is brought the wider the
leaves spread, but when the charge is removed, the leaves collapse showing
that nothing was given to the electroscope. It was simply affected by the
charge in its vicinity. This production of an electrified condition in a body
by the influence of a charge near it is called electrostatic induction. Placing
insulators, such as a sheet of glass, between the charge and the electroscope
does not affect the result, which is apparently brought about by the action of
the electric lines of force. These lines of force extend without difficulty
through uncharged insulators and terminate often at the surface of a
conductor, where their influence causes a charge to accumulate. Charged
insulators, however, do affect inductive action. This may be noticed by
using a sensitive electroscope.
Page 256
Fig. 196.—Production of two charges by the
influence of a third charge.
Fig. 197.—The two charges separated.
220. Electrical Separation by Induction.—The action just described may
be illustrated further by taking two insulated, uncharged brass shells, A and
B. (See Fig. 196.) Bring a charged vulcanite rod near shell "A" while the
shells are touching each other. Then remove shell B (Fig. 197) while the rod
remains near A. On testing the shells for electrification, A is found to
possess a positive charge. This action is in some respects similar to
magnetic induction, for if one places a north-seeking pole near a piece of
iron, the iron develops by induction a south-seeking pole at the end nearest
the magnet and a north-seeking at the other end. There is, however, one
striking difference. If the magnetized iron be separated into two parts, each
part is a complete magnet possessing two unlike poles; while if the object
affected by electrostatic induction is separated into two parts one part has a
positive charge and the other a negative charge.
influence of a third charge.
Fig. 197.—The two charges separated.
220. Electrical Separation by Induction.—The action just described may
be illustrated further by taking two insulated, uncharged brass shells, A and
B. (See Fig. 196.) Bring a charged vulcanite rod near shell "A" while the
shells are touching each other. Then remove shell B (Fig. 197) while the rod
remains near A. On testing the shells for electrification, A is found to
possess a positive charge. This action is in some respects similar to
magnetic induction, for if one places a north-seeking pole near a piece of
iron, the iron develops by induction a south-seeking pole at the end nearest
the magnet and a north-seeking at the other end. There is, however, one
striking difference. If the magnetized iron be separated into two parts, each
part is a complete magnet possessing two unlike poles; while if the object
affected by electrostatic induction is separated into two parts one part has a
positive charge and the other a negative charge.
Page 257
Fig. 198.—Effect of a charged rod near an
electroscope.
Fig. 199.—When a finger is touched to the top
of the electroscope, the repelled negative
charge escapes.
Fig. 200.—The electroscope is now positively
charged.
221. Charging a body by induction is easily accomplished. To charge an
aluminum-foil electroscope by induction bring near (say 10 cm.) from the
top of the electroscope a charged rubber rod. (See Fig. 198.) The separated
leaves show the presence of the repelled or negative charge, the positive
charge being on the disc at the top. If while the charged rod is held near, the
metal top of the electroscope is touched by the finger the leaves at once fall
together showing that the repelled negative charge has escaped from the
electroscope (Fig. 199). On removing first the finger and next the charged
rod, the positive charge spreads over the metal parts of the electroscope, as
is shown by the separation of the leaves (Fig. 200). The electroscope is now
charged positively by induction. If the charged rubber rod is brought to
about 30 cm. from the electroscope, its leaves tend to move together. If a
body charged similarly to the electroscope or positively, is moved toward
the electroscope the leaves separate further. This behavior of the
electroscope enables one to determine the kind of charge upon a body.
electroscope.
Fig. 199.—When a finger is touched to the top
of the electroscope, the repelled negative
charge escapes.
Fig. 200.—The electroscope is now positively
charged.
221. Charging a body by induction is easily accomplished. To charge an
aluminum-foil electroscope by induction bring near (say 10 cm.) from the
top of the electroscope a charged rubber rod. (See Fig. 198.) The separated
leaves show the presence of the repelled or negative charge, the positive
charge being on the disc at the top. If while the charged rod is held near, the
metal top of the electroscope is touched by the finger the leaves at once fall
together showing that the repelled negative charge has escaped from the
electroscope (Fig. 199). On removing first the finger and next the charged
rod, the positive charge spreads over the metal parts of the electroscope, as
is shown by the separation of the leaves (Fig. 200). The electroscope is now
charged positively by induction. If the charged rubber rod is brought to
about 30 cm. from the electroscope, its leaves tend to move together. If a
body charged similarly to the electroscope or positively, is moved toward
the electroscope the leaves separate further. This behavior of the
electroscope enables one to determine the kind of charge upon a body.
Page 258
Two principles of electrostatic induction may now be stated: (1) Two equal,
unlike charges are always produced by electrostatic induction.
(2) If the body affected by induction is connected to the earth by a
conductor, the repelled or "free" charge is conducted away from the body
while the "bound" charge is held by the inducing charge.
These principles apply in every case of induction.
Important Topics
1. Electric lines of force. Characteristics (3).
2. Electrostatic induction. Principles (2).
3. Charging by induction. Explanation.
Exercises
1. What are electric lines of force? Where are they found? What does the
arrow mean upon the lines?
2. Name three effects produced by electric fields.
3. Does electrostatic induction occur outside of laboratories? Where?
When?
4. Given a charged rubber rod, how may one charge from it by induction,
insulated brass shells, giving some a positive and some a negative charge?
5. How may the charges upon the shells be tested?
6. In charging an electroscope by induction, why must the finger be
removed before the glass rod?
7. Why is it best to have the rubber and glass rods, used in electrification,
warmer than the air of the room in which the experiments are being
performed?
8. When a sharp metallic point is held near the knob of a charged
electroscope the leaves quickly come together. Explain.
unlike charges are always produced by electrostatic induction.
(2) If the body affected by induction is connected to the earth by a
conductor, the repelled or "free" charge is conducted away from the body
while the "bound" charge is held by the inducing charge.
These principles apply in every case of induction.
Important Topics
1. Electric lines of force. Characteristics (3).
2. Electrostatic induction. Principles (2).
3. Charging by induction. Explanation.
Exercises
1. What are electric lines of force? Where are they found? What does the
arrow mean upon the lines?
2. Name three effects produced by electric fields.
3. Does electrostatic induction occur outside of laboratories? Where?
When?
4. Given a charged rubber rod, how may one charge from it by induction,
insulated brass shells, giving some a positive and some a negative charge?
5. How may the charges upon the shells be tested?
6. In charging an electroscope by induction, why must the finger be
removed before the glass rod?
7. Why is it best to have the rubber and glass rods, used in electrification,
warmer than the air of the room in which the experiments are being
performed?
8. When a sharp metallic point is held near the knob of a charged
electroscope the leaves quickly come together. Explain.
Page 259
9. Might one of the members of your class in physics be charged with
electricity, if he should stand on a board supported by dry glass insulators?
Explain.
10. If a metal can is charged strongly while standing on an insulator, tests
made by means of the proof-plane and electroscope show no charge on the
inside. Explain.
(3) Electrical Theories and Distribution of Charges
222. Franklin's Theory of Electricity.—We have studied the production of
electrification by friction and induction. It will be helpful now to consider
some of the theories of electricity. From the ease with which electrification
moves, along a conductor, many have imagined that electricity is a fluid.
Benjamin Franklin's One Fluid Theory held that a positive charge consisted
in an accumulation or an excess of electricity while a negative charge
implies a deficiency or less than the usual amount. This theory led to
representing positive electrification by a plus (+) sign and negative, by a
minus (-) sign. These signs are in general use to-day. The use and
significance of these signs should be clearly fixed in mind.
223. The Electron Theory.—Various discoveries and experiments made in
recent years indicate, however, that negative electricity consists of little
corpuscles or electrons which may pass readily from one molecule of a
conductor to another while their movement through an insulator is much
retarded if not entirely prevented. This theory, sometimes called the
Electron Theory, holds that each atom of a substance has as a nucleus a
corpuscle of positive electricity, and surrounding it, minute negative
corpuscles or electrons. It is thought that the electrons in the atom are very
much smaller than the positive charges and are revolving about the latter
with great rapidity. Ordinarily, the positive and negative charges are equal
so that the atom is in a neutral or uncharged condition. By the action of
various forces some of the negative corpuscles within a conductor may be
moved from molecule to molecule. Thus if a negatively charged rod is
brought near a conductor, many electrons stream away to the far end
charging it negatively, while the nearer end of the conductor is left with
fewer electrons than usual along with the fixed positive corpuscles. Hence
the near end is positively charged. (See Fig. 198.) On the other hand, if a
electricity, if he should stand on a board supported by dry glass insulators?
Explain.
10. If a metal can is charged strongly while standing on an insulator, tests
made by means of the proof-plane and electroscope show no charge on the
inside. Explain.
(3) Electrical Theories and Distribution of Charges
222. Franklin's Theory of Electricity.—We have studied the production of
electrification by friction and induction. It will be helpful now to consider
some of the theories of electricity. From the ease with which electrification
moves, along a conductor, many have imagined that electricity is a fluid.
Benjamin Franklin's One Fluid Theory held that a positive charge consisted
in an accumulation or an excess of electricity while a negative charge
implies a deficiency or less than the usual amount. This theory led to
representing positive electrification by a plus (+) sign and negative, by a
minus (-) sign. These signs are in general use to-day. The use and
significance of these signs should be clearly fixed in mind.
223. The Electron Theory.—Various discoveries and experiments made in
recent years indicate, however, that negative electricity consists of little
corpuscles or electrons which may pass readily from one molecule of a
conductor to another while their movement through an insulator is much
retarded if not entirely prevented. This theory, sometimes called the
Electron Theory, holds that each atom of a substance has as a nucleus a
corpuscle of positive electricity, and surrounding it, minute negative
corpuscles or electrons. It is thought that the electrons in the atom are very
much smaller than the positive charges and are revolving about the latter
with great rapidity. Ordinarily, the positive and negative charges are equal
so that the atom is in a neutral or uncharged condition. By the action of
various forces some of the negative corpuscles within a conductor may be
moved from molecule to molecule. Thus if a negatively charged rod is
brought near a conductor, many electrons stream away to the far end
charging it negatively, while the nearer end of the conductor is left with
fewer electrons than usual along with the fixed positive corpuscles. Hence
the near end is positively charged. (See Fig. 198.) On the other hand, if a
Page 260
positive charge is used, it attracts the electrons from the far end, leaving the
immovable positive corpuscles there, and that end becomes positively
electrified, while the nearer end with its surplus of electrons is, of course,
negatively electrified.
The Electron Theory is considered well founded since the electrons have (a)
had their mass determined, (b) their speed measured, (c) their electric
charge determined, (d) and their behavior while passing through magnetic
and electric fields observed. These facts and other experimental evidence
have demonstrated the existence of electrons. The positive corpuscle has
not been directly observed but is assumed to exist to account for the effects
observed in induction, charging by friction, etc.
224. Distribution of an Electric Charge upon a Conductor.—We have
applied the electron theory in explaining the phenomenon of electrostatic
induction. Let us now use it in studying the distribution of an electric charge
upon a conductor. Let a cylindrical metal vessel open at the top and
insulated by being placed upon pieces of sealing wax have a charge of
negative electricity given it. (See Fig. 201.) On now taking a proof plane
and attempting to obtain a charge from the interior of the vessel no result is
found, while a charge is readily obtained from the outside of the dish. This
result is explained by considering that the electrons are mutually self-
repellent and in their attempt to separate as widely as possible pass to the
outer surface of the vessel. This same condition is also true of a dish made
of woven wire. If the charged conductor is not spherical in outline, an
uneven distribution of the charge is observed. Thus if an egg-shaped
conductor is insulated and charged (see Fig. 202), a proof plane touched to
the broad end of the body and then to an electroscope causes a certain
divergence of the leaves of the latter. If now a charge be taken from the
pointed end by the proof plane to the uncharged electroscope, a greater
spreading of the leaves than before will be noticed. This indicates that the
electricity may be unevenly distributed over the surface of a body. It is
found that the electric density, as it is called, is greatest where the surface
curves most sharply. At a very sharp curve, as at a point, the electric density
may be so great that a part of the charge escapes into the air. (See Fig. 203.)
For this reason electric conductors on which it is desired to keep an electric
charge have round surfaces and all sharp points and corners are avoided.
While conductors, such as lightning rods, which are designed to facilitate
immovable positive corpuscles there, and that end becomes positively
electrified, while the nearer end with its surplus of electrons is, of course,
negatively electrified.
The Electron Theory is considered well founded since the electrons have (a)
had their mass determined, (b) their speed measured, (c) their electric
charge determined, (d) and their behavior while passing through magnetic
and electric fields observed. These facts and other experimental evidence
have demonstrated the existence of electrons. The positive corpuscle has
not been directly observed but is assumed to exist to account for the effects
observed in induction, charging by friction, etc.
224. Distribution of an Electric Charge upon a Conductor.—We have
applied the electron theory in explaining the phenomenon of electrostatic
induction. Let us now use it in studying the distribution of an electric charge
upon a conductor. Let a cylindrical metal vessel open at the top and
insulated by being placed upon pieces of sealing wax have a charge of
negative electricity given it. (See Fig. 201.) On now taking a proof plane
and attempting to obtain a charge from the interior of the vessel no result is
found, while a charge is readily obtained from the outside of the dish. This
result is explained by considering that the electrons are mutually self-
repellent and in their attempt to separate as widely as possible pass to the
outer surface of the vessel. This same condition is also true of a dish made
of woven wire. If the charged conductor is not spherical in outline, an
uneven distribution of the charge is observed. Thus if an egg-shaped
conductor is insulated and charged (see Fig. 202), a proof plane touched to
the broad end of the body and then to an electroscope causes a certain
divergence of the leaves of the latter. If now a charge be taken from the
pointed end by the proof plane to the uncharged electroscope, a greater
spreading of the leaves than before will be noticed. This indicates that the
electricity may be unevenly distributed over the surface of a body. It is
found that the electric density, as it is called, is greatest where the surface
curves most sharply. At a very sharp curve, as at a point, the electric density
may be so great that a part of the charge escapes into the air. (See Fig. 203.)
For this reason electric conductors on which it is desired to keep an electric
charge have round surfaces and all sharp points and corners are avoided.
While conductors, such as lightning rods, which are designed to facilitate
Page 261
the escape of electric charges, are provided with a number of sharp points at
the end or elsewhere. At such points, air particles are drawn forcibly against
the point and after being charged are driven away strongly, creating the so-
called electrical wind which carries away the charge at a rapid rate. (See
Fig. 203.)
225. Lightning and Electricity.—
The fact that lightning is an electrical
discharge was first shown in 1752 by
Benjamin Franklin, who drew
electric charges from a cloud by
flying a kite in a thunderstorm. With
the electricity which passed down the
kite string he performed a number of
electrical experiments. This
discovery made Franklin famous
among scientific men everywhere. Fig. 202.—
Fig. 201.—No Franklin then suggested the use of More charge
charge is found lightning rods to protect buildings at the pointed
inside a hollow from lightning. These rods act as end.
vessel. conductors for the electric discharge
and thus prevent it from passing through the building,
with the risk of overheating some part and setting the latter on fire. The
points provided at the top of lightning rods are believed to aid in preventing
strokes of lightning by the silent discharge of the so-called electric wind
which tends to quietly unite the charges in the clouds and on the earth
beneath.
Fig. 203.—Electrical wind produced by a
pointed conductor.
the end or elsewhere. At such points, air particles are drawn forcibly against
the point and after being charged are driven away strongly, creating the so-
called electrical wind which carries away the charge at a rapid rate. (See
Fig. 203.)
225. Lightning and Electricity.—
The fact that lightning is an electrical
discharge was first shown in 1752 by
Benjamin Franklin, who drew
electric charges from a cloud by
flying a kite in a thunderstorm. With
the electricity which passed down the
kite string he performed a number of
electrical experiments. This
discovery made Franklin famous
among scientific men everywhere. Fig. 202.—
Fig. 201.—No Franklin then suggested the use of More charge
charge is found lightning rods to protect buildings at the pointed
inside a hollow from lightning. These rods act as end.
vessel. conductors for the electric discharge
and thus prevent it from passing through the building,
with the risk of overheating some part and setting the latter on fire. The
points provided at the top of lightning rods are believed to aid in preventing
strokes of lightning by the silent discharge of the so-called electric wind
which tends to quietly unite the charges in the clouds and on the earth
beneath.
Fig. 203.—Electrical wind produced by a
pointed conductor.
Page 262
Fig. 204.—Electrical whirl. The reaction from
the electrical wind causes it to revolve.
The charge in an electrified cloud acts
inductively upon the earth beneath, attracting an
opposite charge to the objects below. The
discharge from the cloud often passes to the
objects beneath, such as trees or buildings.
Thunder is believed to be due to the sudden
expansion of the air when intensely heated by
the electric discharge and its sudden contraction,
like a slap, as the track instantly cools. Thunder
at a distance is usually followed by rumblings
due to changes in the intensity of the sound
mainly due to reflections of sound waves from
Fig 205. The wire clouds and other reflecting surfaces.
screen protects the
226. An electric screen is a device for cutting
electroscope.
off the influence of an electric charge. Faraday
found that if a sensitive electroscope is
surrounded by a wire mesh screen (see Fig. 205), no evidence of
electrification could be found inside. In other words, a network of
conductors on a building makes the best protection against lightning,
provided it is connected to the earth by good conductors at several places.
Important Topics
1. Electrical theories. Evidences for electron theory.
2. How is the theory used in explaining induction?
3. Charges, and distribution on conductors (effect of shape).
4. Lightning: cause, effects, lightning rods.
Exercises
1. In what respects is Franklin's one-fluid theory like the electron theory? In
what respects different?
the electrical wind causes it to revolve.
The charge in an electrified cloud acts
inductively upon the earth beneath, attracting an
opposite charge to the objects below. The
discharge from the cloud often passes to the
objects beneath, such as trees or buildings.
Thunder is believed to be due to the sudden
expansion of the air when intensely heated by
the electric discharge and its sudden contraction,
like a slap, as the track instantly cools. Thunder
at a distance is usually followed by rumblings
due to changes in the intensity of the sound
mainly due to reflections of sound waves from
Fig 205. The wire clouds and other reflecting surfaces.
screen protects the
226. An electric screen is a device for cutting
electroscope.
off the influence of an electric charge. Faraday
found that if a sensitive electroscope is
surrounded by a wire mesh screen (see Fig. 205), no evidence of
electrification could be found inside. In other words, a network of
conductors on a building makes the best protection against lightning,
provided it is connected to the earth by good conductors at several places.
Important Topics
1. Electrical theories. Evidences for electron theory.
2. How is the theory used in explaining induction?
3. Charges, and distribution on conductors (effect of shape).
4. Lightning: cause, effects, lightning rods.
Exercises
1. In what respects is Franklin's one-fluid theory like the electron theory? In
what respects different?
Page 263
2. Consider two shells charged by induction from an electrified rubber rod,
one positively and one negatively. Explain the process, using the ideas of
the electron theory.
3. Should the metal top of an electroscope have sharp corners? Explain.
4. Would a tall steel tower have the same need of a lightning rod as a brick
chimney of the same height? Explain.
5. Will a solid sphere hold a greater charge of electricity than a hollow one
of the same diameter? Explain.
6. If a positively charged cloud floats over a tree which is a good conductor
of electricity will the tree be charged? Show diagram. Explain.
(4) Potential, Capacity and the Electric Condenser
227. Conditions Causing a Movement of Electricity.—In the study of
conductors and insulators it was observed that an electric charge moved
along the conducting rod to the electroscope. This movement of electricity
along a conductor is a result of great practical importance. We will now
consider the conditions that produce the "flow" or "current" of electricity.
Let two electroscopes stand near each other. Charge one, C´ (Fig. 206),
strongly and charge the other slightly. If now a light stiff wire attached to a
stick of sealing wax be placed so as to connect the tops of the electroscopes,
the leaves of C will partly close while those of D will open slightly, thus
indicating a movement of electricity from C to D along the wire. The
movement was from a place of greater degree of electrification to one of
less.
228. Potential.—The potential of an electrified body is its degree of
electrification. Therefore, it is said that electroscope C mentioned above has
a greater potential than electroscope D. The movement of electricity is from
a place of greater or high potential to one of lesser or low potential. If two
bodies are at the same potential there will be found no movement of
electricity between them. A difference of potential between two points
connected by a conductor is therefore the necessary condition for an electric
current. Just as heat is transmitted along a conductor from a place of high to
one of lower temperature, so electricity is transmitted along a conductor
from a place of high to one of low potential. Thus potential in electricity
one positively and one negatively. Explain the process, using the ideas of
the electron theory.
3. Should the metal top of an electroscope have sharp corners? Explain.
4. Would a tall steel tower have the same need of a lightning rod as a brick
chimney of the same height? Explain.
5. Will a solid sphere hold a greater charge of electricity than a hollow one
of the same diameter? Explain.
6. If a positively charged cloud floats over a tree which is a good conductor
of electricity will the tree be charged? Show diagram. Explain.
(4) Potential, Capacity and the Electric Condenser
227. Conditions Causing a Movement of Electricity.—In the study of
conductors and insulators it was observed that an electric charge moved
along the conducting rod to the electroscope. This movement of electricity
along a conductor is a result of great practical importance. We will now
consider the conditions that produce the "flow" or "current" of electricity.
Let two electroscopes stand near each other. Charge one, C´ (Fig. 206),
strongly and charge the other slightly. If now a light stiff wire attached to a
stick of sealing wax be placed so as to connect the tops of the electroscopes,
the leaves of C will partly close while those of D will open slightly, thus
indicating a movement of electricity from C to D along the wire. The
movement was from a place of greater degree of electrification to one of
less.
228. Potential.—The potential of an electrified body is its degree of
electrification. Therefore, it is said that electroscope C mentioned above has
a greater potential than electroscope D. The movement of electricity is from
a place of greater or high potential to one of lesser or low potential. If two
bodies are at the same potential there will be found no movement of
electricity between them. A difference of potential between two points
connected by a conductor is therefore the necessary condition for an electric
current. Just as heat is transmitted along a conductor from a place of high to
one of lower temperature, so electricity is transmitted along a conductor
from a place of high to one of low potential. Thus potential in electricity
Page 264
corresponds to temperature in heat. One is
the "degree of electrification," the other,
"the degree of hotness."
Fig. 206.—Electricity flows
from high to low potential.
Fig. 207.—Air pressure apparatus to illustrate
electrical pressure.
229. Electrical pressure is a term sometimes used for difference of
potential. To better understand electrical pressure consider three round tanks
(Fig. 207) containing air. A is a tank holding air at 10 lbs. pressure per
the "degree of electrification," the other,
"the degree of hotness."
Fig. 206.—Electricity flows
from high to low potential.
Fig. 207.—Air pressure apparatus to illustrate
electrical pressure.
229. Electrical pressure is a term sometimes used for difference of
potential. To better understand electrical pressure consider three round tanks
(Fig. 207) containing air. A is a tank holding air at 10 lbs. pressure per
Page 265
square inch, above atmospheric pressure, B is open to the air and hence is at
atmospheric pressure while C has a partial vacuum, with 10 lbs. less
pressure than that of the atmosphere. If the valve at D or E is opened a flow
of air sets up until the pressures are equalized. While if the pump at P is
working a difference in pressure is easily maintained. Tank A corresponds
to an insulated body charged to a high positive potential; tank B, open to the
air, a body connected to the earth; while tank C represents a body having a
negative potential. The earth is said to have zero potential.
Now just as compressed air will be pushed into the atmosphere (as from A
to B) while air at atmospheric pressure will if possible be forced itself into a
partial vacuum (as from B to C), so electricity at a positive potential will
tend to move to a place at zero potential, while that at zero potential tends
to move to a place of negative potential. Bodies at the same potential as the
earth, or at zero potential, are also said to be neutral. Those positively
electrified have a positive potential, those negatively electrified have a
negative potential. As in gases, movement always tends from higher
pressure (potential) to lower pressure (potential).
230. Capacity.—If we have a 100-gallon tank and a 10-
gallon tank connected by a pipe both filled with
compressed air, the larger tank will contain ten times as
much air as the smaller at the same pressure since it has
ten times the capacity, or, if the two tanks are separated
and the same amount of air is contained in each, the
pressure of the air contained in the small tank will be ten
times that in the large one.
The electrical capacity of a conductor is in some respects
similar to the capacity of a tank for air. Since, however,
electrical charges are upon the surface of a body, its
capacity depends in part upon the extent of surface. For
example, if a charge is taken from a charged rubber rod by
a proof plane to an electroscope a certain divergence of
the leaves will be noticed. If a circular metal plate several
times the diameter of the top of the electroscope is laid
upon the latter (see Fig. 208), and a charge equal to that
used before is brought to the electroscope, the leaves show Fig. 208.—
less divergence than before, showing that the same charge The metal
atmospheric pressure while C has a partial vacuum, with 10 lbs. less
pressure than that of the atmosphere. If the valve at D or E is opened a flow
of air sets up until the pressures are equalized. While if the pump at P is
working a difference in pressure is easily maintained. Tank A corresponds
to an insulated body charged to a high positive potential; tank B, open to the
air, a body connected to the earth; while tank C represents a body having a
negative potential. The earth is said to have zero potential.
Now just as compressed air will be pushed into the atmosphere (as from A
to B) while air at atmospheric pressure will if possible be forced itself into a
partial vacuum (as from B to C), so electricity at a positive potential will
tend to move to a place at zero potential, while that at zero potential tends
to move to a place of negative potential. Bodies at the same potential as the
earth, or at zero potential, are also said to be neutral. Those positively
electrified have a positive potential, those negatively electrified have a
negative potential. As in gases, movement always tends from higher
pressure (potential) to lower pressure (potential).
230. Capacity.—If we have a 100-gallon tank and a 10-
gallon tank connected by a pipe both filled with
compressed air, the larger tank will contain ten times as
much air as the smaller at the same pressure since it has
ten times the capacity, or, if the two tanks are separated
and the same amount of air is contained in each, the
pressure of the air contained in the small tank will be ten
times that in the large one.
The electrical capacity of a conductor is in some respects
similar to the capacity of a tank for air. Since, however,
electrical charges are upon the surface of a body, its
capacity depends in part upon the extent of surface. For
example, if a charge is taken from a charged rubber rod by
a proof plane to an electroscope a certain divergence of
the leaves will be noticed. If a circular metal plate several
times the diameter of the top of the electroscope is laid
upon the latter (see Fig. 208), and a charge equal to that
used before is brought to the electroscope, the leaves show Fig. 208.—
less divergence than before, showing that the same charge The metal
Page 266
gives a lower potential when placed upon a body of plate gives
greater capacity. the
231. The electric condenser is a device having a large electroscope a
electrical capacity consisting of parallel conductors greater
separated by good insulators. It has been devised to enable surface and
hence greater
one to obtain a large electrical charge upon a body of
convenient size. Such an apparatus is of great practical capacity.
v
a
l
u
e
i
n Fig. 209.—A plate condenser.
Fig. 210.—A condenser of many experiments and operations. Its
several plates. construction involves the principle of
electrostatic induction in which a
charge of one kind attracts and "holds"
strongly a charge of opposite kind near it. In its simplest form it consists of
two parallel conductors separated from each other (Fig. 209). The upper
plate has been charged negatively. This has given the lower plate a positive
charge by induction, since the latter is connected to the earth. These positive
and negative charges hold or "bind" each other so that a large quantity may
be accumulated. To increase the capacity of a condenser, several plates are
used connected as in Fig. 210.
It is a curious fact that the kind of insulator between the charged conductors
of a condenser affects its capacity. Thus if glass, paraffine, or beeswax is
between the plates instead of air, the plates will "hold" more electricity at
the same potential. For this reason condenser plates are often separated by
sheets of glass, paraffined paper, or mica.
232. The Leyden Jar.—A convenient form of condenser, used as long ago
as 1745, is the Leyden jar. It consists of a glass jar (Fig. 211) coated part
way up, inside and out, with tinfoil. The inner coating is connected by a
chain to a knob at the top. The Leyden jar is charged by connecting the
outer coating to the earth while to the inner coating is given a charge of
greater capacity. the
231. The electric condenser is a device having a large electroscope a
electrical capacity consisting of parallel conductors greater
separated by good insulators. It has been devised to enable surface and
hence greater
one to obtain a large electrical charge upon a body of
convenient size. Such an apparatus is of great practical capacity.
v
a
l
u
e
i
n Fig. 209.—A plate condenser.
Fig. 210.—A condenser of many experiments and operations. Its
several plates. construction involves the principle of
electrostatic induction in which a
charge of one kind attracts and "holds"
strongly a charge of opposite kind near it. In its simplest form it consists of
two parallel conductors separated from each other (Fig. 209). The upper
plate has been charged negatively. This has given the lower plate a positive
charge by induction, since the latter is connected to the earth. These positive
and negative charges hold or "bind" each other so that a large quantity may
be accumulated. To increase the capacity of a condenser, several plates are
used connected as in Fig. 210.
It is a curious fact that the kind of insulator between the charged conductors
of a condenser affects its capacity. Thus if glass, paraffine, or beeswax is
between the plates instead of air, the plates will "hold" more electricity at
the same potential. For this reason condenser plates are often separated by
sheets of glass, paraffined paper, or mica.
232. The Leyden Jar.—A convenient form of condenser, used as long ago
as 1745, is the Leyden jar. It consists of a glass jar (Fig. 211) coated part
way up, inside and out, with tinfoil. The inner coating is connected by a
chain to a knob at the top. The Leyden jar is charged by connecting the
outer coating to the earth while to the inner coating is given a charge of
Page 267
either kind of electricity. The other kind of
charge is developed by induction upon the outer
coating, and each charge binds the other. To
discharge a jar, a conductor, as a wire, is
connected first to the outer coating and held
there while the other end is brought to the knob
at the top. A bright spark is produced when the
two charges combine. It is best not to let the
discharge from the jar pass through the body
unless one is certain that only a very small
charge is present.
Fig. 211.—A Leyden
233. Oscillatory Discharge.—The discharge jar and a discharger.
from a Leyden jar is an interesting phenomenon.
The rush of electricity from one coat to the other
does not stop when the two coats are exactly neutralized but continues until
the two plates are charged just oppositely to their condition at first, then a
rush of electricity in the opposite direction occurs. This alternation
continues several times and constitutes what is called the oscillatory
discharge. (See Fig. 414.) This oscillatory discharge sets up waves in the
ether. These are called Hertzian waves in honor of their discoverer,
Heinrich Hertz. They are the ether waves used in wireless telegraphy. A
lightning flash has been shown by photographs and by other means to be
oscillatory. This fact supports the idea that the electrical conditions just
preceding the stroke of lightning reproduce a condenser on a large scale.
The charged cloud is the upper charged plate, the earth beneath, charged by
induction from the cloud, is the lower charged plate, while the air between
is the insulator or dielectric as it is sometimes called.
Important Topics
1. Potential: high, low, zero, positive, negative, similar to temperature and
air pressure.
2. Capacity affected by (1) area, (2) induction.
3. Condensers, Leyden jar, parallel plate.
4. Oscillatory discharge, conditions, results.
charge is developed by induction upon the outer
coating, and each charge binds the other. To
discharge a jar, a conductor, as a wire, is
connected first to the outer coating and held
there while the other end is brought to the knob
at the top. A bright spark is produced when the
two charges combine. It is best not to let the
discharge from the jar pass through the body
unless one is certain that only a very small
charge is present.
Fig. 211.—A Leyden
233. Oscillatory Discharge.—The discharge jar and a discharger.
from a Leyden jar is an interesting phenomenon.
The rush of electricity from one coat to the other
does not stop when the two coats are exactly neutralized but continues until
the two plates are charged just oppositely to their condition at first, then a
rush of electricity in the opposite direction occurs. This alternation
continues several times and constitutes what is called the oscillatory
discharge. (See Fig. 414.) This oscillatory discharge sets up waves in the
ether. These are called Hertzian waves in honor of their discoverer,
Heinrich Hertz. They are the ether waves used in wireless telegraphy. A
lightning flash has been shown by photographs and by other means to be
oscillatory. This fact supports the idea that the electrical conditions just
preceding the stroke of lightning reproduce a condenser on a large scale.
The charged cloud is the upper charged plate, the earth beneath, charged by
induction from the cloud, is the lower charged plate, while the air between
is the insulator or dielectric as it is sometimes called.
Important Topics
1. Potential: high, low, zero, positive, negative, similar to temperature and
air pressure.
2. Capacity affected by (1) area, (2) induction.
3. Condensers, Leyden jar, parallel plate.
4. Oscillatory discharge, conditions, results.
Page 268
Exercises
1. Is the air a conductor? Explain.
2. Can the Leyden jar be strongly charged if the outer coat is insulated?
Explain.
3. Upon what two conditions does the capacity of a body depend? How in
each case?
4. Would a lightning discharge produce wireless waves? Explain.
5. If a sharp tack be dropped point up on the plate of an electroscope the
latter is quickly discharged. Explain.
(5) Electrostatic Generators
234. Static Electric Machines.—Many machines have been invented to
produce larger quantities of static electricity than we have used in the
experiments previously described. One of the earlier of these was the plate
friction machine in which a large circular glass plate was rotated while a
pad of some material was held against it. This machine was capable of
producing powerful effects, but it took much work to turn it, and it has been
abandoned for a more efficient device, the static induction machine.
235. The electrophorus is the simplest static induction generator,
consisting simply of a flat circular plate of some insulating material, as
paraffine, shellac, or rosin contained in a metal pan, and a flat circular metal
disc having an insulating handle.
The electrophorus is used as
follows: The plate is first electrified
by rubbing or beating with fur or a
woolen cloth. The plate will be
found to be charged negatively. The
metal disc is placed upon the plate
by holding the insulating handle. Fig. 212.—An electrophorus.
The upper surface of the charged
body is slightly uneven so that the disc touches but a few high points. The
greater part of the charged surface is separated from the metal disc by air, a
1. Is the air a conductor? Explain.
2. Can the Leyden jar be strongly charged if the outer coat is insulated?
Explain.
3. Upon what two conditions does the capacity of a body depend? How in
each case?
4. Would a lightning discharge produce wireless waves? Explain.
5. If a sharp tack be dropped point up on the plate of an electroscope the
latter is quickly discharged. Explain.
(5) Electrostatic Generators
234. Static Electric Machines.—Many machines have been invented to
produce larger quantities of static electricity than we have used in the
experiments previously described. One of the earlier of these was the plate
friction machine in which a large circular glass plate was rotated while a
pad of some material was held against it. This machine was capable of
producing powerful effects, but it took much work to turn it, and it has been
abandoned for a more efficient device, the static induction machine.
235. The electrophorus is the simplest static induction generator,
consisting simply of a flat circular plate of some insulating material, as
paraffine, shellac, or rosin contained in a metal pan, and a flat circular metal
disc having an insulating handle.
The electrophorus is used as
follows: The plate is first electrified
by rubbing or beating with fur or a
woolen cloth. The plate will be
found to be charged negatively. The
metal disc is placed upon the plate
by holding the insulating handle. Fig. 212.—An electrophorus.
The upper surface of the charged
body is slightly uneven so that the disc touches but a few high points. The
greater part of the charged surface is separated from the metal disc by air, a
Page 269
good insulator. The charge therefore acts inductively upon the disc repelling
negative electricity to the upper surface of the disc, leaving the lower
surface charged positively (Fig. 212). If now the finger is touched to the
disc the repelled negative charge escapes and the whole disc is left
positively charged. The disc is now removed (Fig. 213) and the charge upon
it may be tested or used in any desired manner. The disc may be recharged
many times without rubbing the plate again.
These electrical charges possess
energy. What is the source of this
energy? The answer may be
determined by the following
experiment. Place the disc upon the
charged plate. Touch the disc with
the finger to remove the repelled
charge. Connect an electroscope to
the disc by a fine wire. Nothing
appears on the electroscope, since
Fig. 213.—Electrophorus charged. the disc has been connected to the
earth, and is therefore at zero
potential. If now the disc is lifted slowly, the leaves of the electroscope
gradually separate, showing that a charge of electricity appears when the
disc is being lifted against the force of attraction between the two charges.
Just as potential energy is developed in a weight when it is lifted against the
earth's attraction so electrical energy appears in the disc while it is being
separated from the plate. The electrical energy of the charge is therefore due
to the work done in separating the two charges. This electrical energy
appears as heat and light, when the disc is discharged. It may be employed
to ignite gas, gunpowder, etc.
236. The Toepler-Holtz Induction Machine.—This is a type of induction
or influence machine that is often used for producing a continuous supply
of electricity as in the operation of "X" ray machines, in lecture
demonstrations, etc. This machine (Fig. 214) consists of two discs: one
fixed, the other mounted so as to revolve. Upon the back of the fixed plate
are two sectors of tinfoil which become charged oppositely. Upon the
revolving plate are six metallic discs. These discs act like the discs of the
electrophorus. They become charged by induction from the charges upon
negative electricity to the upper surface of the disc, leaving the lower
surface charged positively (Fig. 212). If now the finger is touched to the
disc the repelled negative charge escapes and the whole disc is left
positively charged. The disc is now removed (Fig. 213) and the charge upon
it may be tested or used in any desired manner. The disc may be recharged
many times without rubbing the plate again.
These electrical charges possess
energy. What is the source of this
energy? The answer may be
determined by the following
experiment. Place the disc upon the
charged plate. Touch the disc with
the finger to remove the repelled
charge. Connect an electroscope to
the disc by a fine wire. Nothing
appears on the electroscope, since
Fig. 213.—Electrophorus charged. the disc has been connected to the
earth, and is therefore at zero
potential. If now the disc is lifted slowly, the leaves of the electroscope
gradually separate, showing that a charge of electricity appears when the
disc is being lifted against the force of attraction between the two charges.
Just as potential energy is developed in a weight when it is lifted against the
earth's attraction so electrical energy appears in the disc while it is being
separated from the plate. The electrical energy of the charge is therefore due
to the work done in separating the two charges. This electrical energy
appears as heat and light, when the disc is discharged. It may be employed
to ignite gas, gunpowder, etc.
236. The Toepler-Holtz Induction Machine.—This is a type of induction
or influence machine that is often used for producing a continuous supply
of electricity as in the operation of "X" ray machines, in lecture
demonstrations, etc. This machine (Fig. 214) consists of two discs: one
fixed, the other mounted so as to revolve. Upon the back of the fixed plate
are two sectors of tinfoil which become charged oppositely. Upon the
revolving plate are six metallic discs. These discs act like the discs of the
electrophorus. They become charged by induction from the charges upon
Page 270
the sectors fastened to the fixed plate. The brushes held by a rod touch the
discs at just the right time to take off the repelled charge. The charges
induced upon the discs are taken off by two metal combs whose points are
held close to the revolving disc. The Leyden jars assist in accumulating a
good strong charge before a spark passes between the terminal knobs. Some
machines are built up of several pairs of plates and give correspondingly
large amounts of electricity.
Fig. 214.—The Toepler-Holtz induction
machine.
Important Topics
Static Electric Generators.—(a) plate friction machine, (b) electrophorus,
(c) induction or influence machine.
Exercises
1. Potential is similar to what other terms that we have studied?
2. What three electrical phenomena are better understood from a study of
the lines of force?
3. How many charges may be produced by an electrophorus before the plate
needs to be electrified again? Explain.
discs at just the right time to take off the repelled charge. The charges
induced upon the discs are taken off by two metal combs whose points are
held close to the revolving disc. The Leyden jars assist in accumulating a
good strong charge before a spark passes between the terminal knobs. Some
machines are built up of several pairs of plates and give correspondingly
large amounts of electricity.
Fig. 214.—The Toepler-Holtz induction
machine.
Important Topics
Static Electric Generators.—(a) plate friction machine, (b) electrophorus,
(c) induction or influence machine.
Exercises
1. Potential is similar to what other terms that we have studied?
2. What three electrical phenomena are better understood from a study of
the lines of force?
3. How many charges may be produced by an electrophorus before the plate
needs to be electrified again? Explain.
Page 271
4. The static induction machine is often called a "continuous
electrophorous." Why?
5. The Leyden jars used with the induction machine cause much brighter
sparks to be produced than without them. Explain.
6. With the Leyden jars removed, would the frequency with which the
sparks pass between the knobs be increased or decreased? Explain.
7. Mention three likenesses and three differences between magnetism and
static electricity.
8. Will you receive a greater shock by touching a knob of a charged Leyden
jar when it is held in the hand or when it is standing on a sheet of glass?
Explain.
9. In what way may an electric charge be divided into three equal parts?
Review Outline: Magnetism and Static Electricity
Comparison between Magnetism and Static Electricity.
Substances
magnetic, non-magnetic. conductors, insulators.
are:
Produced by: induction. friction, or induction.
Theory: molecular. electron. (fluid)
Fields of attraction, repulsion,
Force induction, action of attraction, repulsion, induction.
Explain: compass.
magnetoscope, dip,
electroscope, electron, positive,
declination, pole,
negative, potential, capacity,
Terms: retentivity, permeability,
condenser, electrophorus,
lodestone, magnetic
oscillatory discharge, lightning.
meridian.
Likeness: a—produced by induction, b—attract and repel, c—have
both are: fields of force.
a—electricity can be conducted, magnetism cannot. b—
Differences: electricity in all substances, magnetism in few. c—
magnetism with the compass indicates direction.
electrophorous." Why?
5. The Leyden jars used with the induction machine cause much brighter
sparks to be produced than without them. Explain.
6. With the Leyden jars removed, would the frequency with which the
sparks pass between the knobs be increased or decreased? Explain.
7. Mention three likenesses and three differences between magnetism and
static electricity.
8. Will you receive a greater shock by touching a knob of a charged Leyden
jar when it is held in the hand or when it is standing on a sheet of glass?
Explain.
9. In what way may an electric charge be divided into three equal parts?
Review Outline: Magnetism and Static Electricity
Comparison between Magnetism and Static Electricity.
Substances
magnetic, non-magnetic. conductors, insulators.
are:
Produced by: induction. friction, or induction.
Theory: molecular. electron. (fluid)
Fields of attraction, repulsion,
Force induction, action of attraction, repulsion, induction.
Explain: compass.
magnetoscope, dip,
electroscope, electron, positive,
declination, pole,
negative, potential, capacity,
Terms: retentivity, permeability,
condenser, electrophorus,
lodestone, magnetic
oscillatory discharge, lightning.
meridian.
Likeness: a—produced by induction, b—attract and repel, c—have
both are: fields of force.
a—electricity can be conducted, magnetism cannot. b—
Differences: electricity in all substances, magnetism in few. c—
magnetism with the compass indicates direction.
Page 272
Page 273
CHAPTER XI
CURRENT ELECTRICITY
(1) Electrical Currents and Circuits
237. Sources of Electric Currents.—In studying the production and
distribution of static electricity it was seen that if two bodies at different
potentials are connected by a copper wire a movement of electricity to the
body having the lower potential occurred along the conducting wire. This
movement of electricity is called an electric current (Art. 227). A difference
of potential is therefore often called an electromotive force (E.M.F.), since it
produces the movement of electricity in a conductor. The current between
two oppositely charged bodies lasts for so short a time as to be of little or
no practical value unless some means are found for continually recharging
the bodies. That is, some device must be used to restore the difference in
potential as fast as the conducting wire equalizes it. The continual charging
of the bodies takes work. In other words, it requires a continual expenditure
of some form of energy (which is converted into electrical energy) to
produce the electric current. Two forms of energy are commonly used for
this purpose.
(A) Chemical energy is employed in voltaic cells for producing electric
currents. (B) Mechanical energy is used for the same purpose in the dynamo
and similar devices.
238. The voltaic cell is named after Volta, an Italian physicist, who in 1800
invented it. In its simplest form it consists of a strip of copper and a strip of
zinc placed in dilute sulphuric acid (one part acid to fifteen or twenty of
water) (Fig. 215). By the use of sensitive apparatus, it can be shown that the
copper plate of the voltaic cell has a positive charge and the zinc plate a
negative charge. For example, let a flat plate 10 cm. in diameter be placed
upon the knob of an electroscope and a similar plate, coated with shellac
and provided with an insulating handle, be set upon it to form a condenser.
(See Fig. 216.) If now wires from the two plates of a simple voltaic cell be
CURRENT ELECTRICITY
(1) Electrical Currents and Circuits
237. Sources of Electric Currents.—In studying the production and
distribution of static electricity it was seen that if two bodies at different
potentials are connected by a copper wire a movement of electricity to the
body having the lower potential occurred along the conducting wire. This
movement of electricity is called an electric current (Art. 227). A difference
of potential is therefore often called an electromotive force (E.M.F.), since it
produces the movement of electricity in a conductor. The current between
two oppositely charged bodies lasts for so short a time as to be of little or
no practical value unless some means are found for continually recharging
the bodies. That is, some device must be used to restore the difference in
potential as fast as the conducting wire equalizes it. The continual charging
of the bodies takes work. In other words, it requires a continual expenditure
of some form of energy (which is converted into electrical energy) to
produce the electric current. Two forms of energy are commonly used for
this purpose.
(A) Chemical energy is employed in voltaic cells for producing electric
currents. (B) Mechanical energy is used for the same purpose in the dynamo
and similar devices.
238. The voltaic cell is named after Volta, an Italian physicist, who in 1800
invented it. In its simplest form it consists of a strip of copper and a strip of
zinc placed in dilute sulphuric acid (one part acid to fifteen or twenty of
water) (Fig. 215). By the use of sensitive apparatus, it can be shown that the
copper plate of the voltaic cell has a positive charge and the zinc plate a
negative charge. For example, let a flat plate 10 cm. in diameter be placed
upon the knob of an electroscope and a similar plate, coated with shellac
and provided with an insulating handle, be set upon it to form a condenser.
(See Fig. 216.) If now wires from the two plates of a simple voltaic cell be
Page 274
respectively connected to the plates of the condenser, charges from the
copper and zinc plates will accumulate upon the two condenser plates. Now
remove the wires and lift the upper plate. The "bound" charge upon the
lower plate will spread over the leaves and cause them to separate. Upon
testing, the charge from the zinc plate will be found to be negative and that
from the copper plate, positive. Since a positive charge is found upon the
copper plate it is called the positive electrode; the zinc plate is called the
negative electrode.
Fig. 215.—Cross-section of a simple voltaic
cell.
Fig. 216.—Testing the charges upon the plates
of a simple voltaic cell.
239. Test for an Electric Current.—If the copper and zinc plates of a
voltaic cell are connected by a wire, a current of electricity is set up in the
conductor. Evidence of the current may be obtained by holding the
conducting wire over and parallel to the needle of a magnetoscope. The
needle is deflected by the action of the current parallel to it (Fig. 217). This
magnetic effect of a current is the means usually employed for the detection
and measurement of an electric current. Such a device which detects an
electric current by its magnetic effect is called a galvanoscope, in honor of
Galvani, who in 1786 was the first to discover how to produce an electric
current.
240. The Electric Circuit.—The entire conducting path along which a
current of electricity flows is called an electric circuit. In the case of a
copper and zinc plates will accumulate upon the two condenser plates. Now
remove the wires and lift the upper plate. The "bound" charge upon the
lower plate will spread over the leaves and cause them to separate. Upon
testing, the charge from the zinc plate will be found to be negative and that
from the copper plate, positive. Since a positive charge is found upon the
copper plate it is called the positive electrode; the zinc plate is called the
negative electrode.
Fig. 215.—Cross-section of a simple voltaic
cell.
Fig. 216.—Testing the charges upon the plates
of a simple voltaic cell.
239. Test for an Electric Current.—If the copper and zinc plates of a
voltaic cell are connected by a wire, a current of electricity is set up in the
conductor. Evidence of the current may be obtained by holding the
conducting wire over and parallel to the needle of a magnetoscope. The
needle is deflected by the action of the current parallel to it (Fig. 217). This
magnetic effect of a current is the means usually employed for the detection
and measurement of an electric current. Such a device which detects an
electric current by its magnetic effect is called a galvanoscope, in honor of
Galvani, who in 1786 was the first to discover how to produce an electric
current.
240. The Electric Circuit.—The entire conducting path along which a
current of electricity flows is called an electric circuit. In the case of a
Page 275
voltaic cell, the
circuit includes
not only the
wires
connecting the
plates but also
Fig. 218.—Diagram of an the plates
electric bell circuit. themselves and
the liquid Fig. 217.—The magnetic
between them. When some device or needle is deflected by the
apparatus is to receive current from the cell, it current.
is attached to the plates and wires so that the
device is a part of the electric circuit. Separating the circuit at any point is
called breaking or opening the circuit, while connecting the ends of an open
circuit is called making or closing the circuit. A device for opening and
closing a circuit is called a key or switch. The electric circuit used in ringing
a door bell is familiar to most boys and girls. This circuit is open most of
the time. It is closed by pressing the push-button at the door, and the flow of
current through the electric bell causes the latter to ring. Such a circuit is
represented in Fig. 218. Here C is the voltaic cell, the two lines representing
the plates of the cell. A cross-section view of the push-button (P), shows
how the circuit is closed, (B) is the bell. Wherever current electricity is used
the device in which it is employed forms a part of an electric circuit
extending back to some electric generator. This generator must be able to
continually produce an E.M.F., or a difference of potential between its
terminals, in order that the movement of electricity may be continuous.
Important Topics
(a) Electric generators: (1) voltaic cell uses chemical energy; (2) dynamo
uses mechanical energy.
(b) Electric circuits: (1) open, (2) closed, (3) key and switch.
(c) Voltaic and galvanic electricity (names).
(d) Galvanoscope, uses.
circuit includes
not only the
wires
connecting the
plates but also
Fig. 218.—Diagram of an the plates
electric bell circuit. themselves and
the liquid Fig. 217.—The magnetic
between them. When some device or needle is deflected by the
apparatus is to receive current from the cell, it current.
is attached to the plates and wires so that the
device is a part of the electric circuit. Separating the circuit at any point is
called breaking or opening the circuit, while connecting the ends of an open
circuit is called making or closing the circuit. A device for opening and
closing a circuit is called a key or switch. The electric circuit used in ringing
a door bell is familiar to most boys and girls. This circuit is open most of
the time. It is closed by pressing the push-button at the door, and the flow of
current through the electric bell causes the latter to ring. Such a circuit is
represented in Fig. 218. Here C is the voltaic cell, the two lines representing
the plates of the cell. A cross-section view of the push-button (P), shows
how the circuit is closed, (B) is the bell. Wherever current electricity is used
the device in which it is employed forms a part of an electric circuit
extending back to some electric generator. This generator must be able to
continually produce an E.M.F., or a difference of potential between its
terminals, in order that the movement of electricity may be continuous.
Important Topics
(a) Electric generators: (1) voltaic cell uses chemical energy; (2) dynamo
uses mechanical energy.
(b) Electric circuits: (1) open, (2) closed, (3) key and switch.
(c) Voltaic and galvanic electricity (names).
(d) Galvanoscope, uses.
Page 276
Exercises
1. In what two ways are static and current electricity alike? In what two
different?
2. Draw a diagram of an electric bell circuit at your home. Give the location
of the electric bell, the electric generator and the push-button. Show the
connecting wires, and explain briefly how the circuit is operated.
3. Represent some other electric circuit, naming the generator and other
devices in the circuit.
4. Look up the work of Volta and Galvani and write a statement of the
electrical discoveries and inventions made by them.
(2) The Voltaic Cell and its Action
241. The simple voltaic cell consists of a strip of copper and a strip of zinc
placed in dilute sulphuric acid. (See Fig. 219.) A short time after placing the
plates in the acid, bubbles of a gas (hydrogen) appear on the surface of the
zinc. These bubbles increase in size and some rise to the surface of the
liquid. Nothing appears upon the copper plate. If the tops of the plates are
connected by a wire, an electric current is set up through the wire and the
cell, and bubbles of gas also appear upon the copper as well as on the zinc.
In a short time the surface of the copper becomes coated with bubbles and
the current becomes much weaker. If the plates are left in the acid for some
time the zinc is found to be eaten away, having been dissolved in the acid
through chemical action. The copper, however, remains practically
unaffected.
242. How the Current is Produced.—To maintain the electric current a
continual supply of energy is required. This is furnished by the chemical
action of the acid upon the zinc. The chemical action is in several respects
like combustion or burning, by means of which chemical energy is
transformed into heat energy. In the voltaic cell the chemical action of the
acid upon the zinc transforms chemical energy into electrical energy. The
E.M.F. or difference of potential may be considered as originating at the
surface of the zinc where the chemical action takes place. At this point the
zinc has the lower and the liquid in contact with it the higher potential. The
1. In what two ways are static and current electricity alike? In what two
different?
2. Draw a diagram of an electric bell circuit at your home. Give the location
of the electric bell, the electric generator and the push-button. Show the
connecting wires, and explain briefly how the circuit is operated.
3. Represent some other electric circuit, naming the generator and other
devices in the circuit.
4. Look up the work of Volta and Galvani and write a statement of the
electrical discoveries and inventions made by them.
(2) The Voltaic Cell and its Action
241. The simple voltaic cell consists of a strip of copper and a strip of zinc
placed in dilute sulphuric acid. (See Fig. 219.) A short time after placing the
plates in the acid, bubbles of a gas (hydrogen) appear on the surface of the
zinc. These bubbles increase in size and some rise to the surface of the
liquid. Nothing appears upon the copper plate. If the tops of the plates are
connected by a wire, an electric current is set up through the wire and the
cell, and bubbles of gas also appear upon the copper as well as on the zinc.
In a short time the surface of the copper becomes coated with bubbles and
the current becomes much weaker. If the plates are left in the acid for some
time the zinc is found to be eaten away, having been dissolved in the acid
through chemical action. The copper, however, remains practically
unaffected.
242. How the Current is Produced.—To maintain the electric current a
continual supply of energy is required. This is furnished by the chemical
action of the acid upon the zinc. The chemical action is in several respects
like combustion or burning, by means of which chemical energy is
transformed into heat energy. In the voltaic cell the chemical action of the
acid upon the zinc transforms chemical energy into electrical energy. The
E.M.F. or difference of potential may be considered as originating at the
surface of the zinc where the chemical action takes place. At this point the
zinc has the lower and the liquid in contact with it the higher potential. The
Page 277
molecules of the acid are believed to be
separated or broken up into two parts called
ions; one ion, the SO4 or sulphion, combines
with the zinc forming zinc sulphate, the other, or
hydrogen (H) ion, passes over to the copper
plate, and accumulates on the surface of this
plate giving it a positive charge. It is therefore
called the positive ion. The sulphion ion, or SO4
ion, carries a negative charge to the zinc. It is
therefore called the negative ion.
243. The Direction of the Current.[K]—
Beginning at the surface of the zinc the direction
of the movement of positive electricity may be Fig. 219.—A simple
traced through the liquid to the copper plate, to voltaic cell.
the wire, to the zinc plate, to the starting point,
thus completing the electric circuit. When the circuit is closed it is found
that the movement of electricity starts in all parts of the circuit at practically
the same instant.
244. The production of the current may be
illustrated by describing a device for producing
a continuous circulation of water. Thus let Cu
and Zn represent two pipes connected by two
horizontal tubes, one at V provided with a valve
and one at P with a rotary Pump. (See Fig. 220.)
Suppose the pipes filled to the level of V and the
pump started. The pump will force water from
Zn to Cu, through P, the level falling in Zn and
rising in Cu. If the valve V is open the water will
flow back through V as long as the pump is
working. If V is closed, the level in Cu will rise
Fig. 220.—A as high as the driving force of the pump can
comparison of a voltaic send it. If now V is opened, the pump will
cell and circuit to a maintain the water in circulation from Cu to Zn
water pump and through V. In the illustration, the tubes Cu and
connecting pipes. Zn correspond to the conducting plates of
copper and zinc of a voltaic cell. The pump P
separated or broken up into two parts called
ions; one ion, the SO4 or sulphion, combines
with the zinc forming zinc sulphate, the other, or
hydrogen (H) ion, passes over to the copper
plate, and accumulates on the surface of this
plate giving it a positive charge. It is therefore
called the positive ion. The sulphion ion, or SO4
ion, carries a negative charge to the zinc. It is
therefore called the negative ion.
243. The Direction of the Current.[K]—
Beginning at the surface of the zinc the direction
of the movement of positive electricity may be Fig. 219.—A simple
traced through the liquid to the copper plate, to voltaic cell.
the wire, to the zinc plate, to the starting point,
thus completing the electric circuit. When the circuit is closed it is found
that the movement of electricity starts in all parts of the circuit at practically
the same instant.
244. The production of the current may be
illustrated by describing a device for producing
a continuous circulation of water. Thus let Cu
and Zn represent two pipes connected by two
horizontal tubes, one at V provided with a valve
and one at P with a rotary Pump. (See Fig. 220.)
Suppose the pipes filled to the level of V and the
pump started. The pump will force water from
Zn to Cu, through P, the level falling in Zn and
rising in Cu. If the valve V is open the water will
flow back through V as long as the pump is
working. If V is closed, the level in Cu will rise
Fig. 220.—A as high as the driving force of the pump can
comparison of a voltaic send it. If now V is opened, the pump will
cell and circuit to a maintain the water in circulation from Cu to Zn
water pump and through V. In the illustration, the tubes Cu and
connecting pipes. Zn correspond to the conducting plates of
copper and zinc of a voltaic cell. The pump P
Page 278
represents the chemical action which produces the electrical pressure. The
upper pipe represents the part of the circuit outside of the cell, the valve V
corresponds to an electric key or switch which is used to open and close the
electric circuit.
245. Polarization.—In the simple voltaic cell, after the circuit is closed,
bubbles of hydrogen collect upon the copper plate. This accumulation of
hydrogen gas is called polarization. It acts as a non-conducting layer upon
the surface of the plate and seriously interferes with the movement of
electricity from the liquid to the copper plate not only in the simple voltaic
cell but in many others as well. Some voltaic cells are made entirely free
from this defect, either (a) by the removal of the hydrogen as fast as it is
formed, or (b) by the use of such chemicals that no hydrogen is produced.
246. Local Action.—It is noticed that when a strip of zinc is placed in
dilute acid that bubbles appear upon the surface of the zinc. The appearance
of these bubbles indicates that some of the hydrogen ions carrying positive
electricity have moved to the zinc plate. Careful examination of the plate
after it has been in acid shows numerous black spots upon it. These are bits
of carbon. They are always found in ordinary zinc. Small electric currents
are set up which run from molecules of pure zinc into the liquid and back to
the carbon particles, thus forming small closed circuits. (See Fig. 221.) The
formation of these circuits from and to the zinc is called local action. This
action is a defect in voltaic cells since a part of the current is thus kept from
passing through the main outside circuit, and the zinc may be consumed
even when no outside current is flowing.
upper pipe represents the part of the circuit outside of the cell, the valve V
corresponds to an electric key or switch which is used to open and close the
electric circuit.
245. Polarization.—In the simple voltaic cell, after the circuit is closed,
bubbles of hydrogen collect upon the copper plate. This accumulation of
hydrogen gas is called polarization. It acts as a non-conducting layer upon
the surface of the plate and seriously interferes with the movement of
electricity from the liquid to the copper plate not only in the simple voltaic
cell but in many others as well. Some voltaic cells are made entirely free
from this defect, either (a) by the removal of the hydrogen as fast as it is
formed, or (b) by the use of such chemicals that no hydrogen is produced.
246. Local Action.—It is noticed that when a strip of zinc is placed in
dilute acid that bubbles appear upon the surface of the zinc. The appearance
of these bubbles indicates that some of the hydrogen ions carrying positive
electricity have moved to the zinc plate. Careful examination of the plate
after it has been in acid shows numerous black spots upon it. These are bits
of carbon. They are always found in ordinary zinc. Small electric currents
are set up which run from molecules of pure zinc into the liquid and back to
the carbon particles, thus forming small closed circuits. (See Fig. 221.) The
formation of these circuits from and to the zinc is called local action. This
action is a defect in voltaic cells since a part of the current is thus kept from
passing through the main outside circuit, and the zinc may be consumed
even when no outside current is flowing.
Page 279
247. Amalgamation.—Local action is prevented by coating the zinc
with mercury. This process is called amalgamation. The mercury
covers the entire surface of the plate in the acid. Its action is to
dissolve pure zinc and bring it to the outer surface where it is acted
upon by the acid. The carbon particles are kept covered so that no local
currents can be formed as long as the bits of carbon are below the
surface. Amalgamation therefore prevents local action.
Fig.
221.—
Local
action.
Important Topics
The Simple Voltaic Cell
1. Two plates: zinc, copper; electrolyte, dilute sulphuric acid.
2. Ions: hydrogen, positive: sulphion, negative.
3. Current, where and how produced, direction, illustration.
4. Polarization: cure, local action, cure.
Exercises
1. Write in your own words an account of the production of an electric current by
the simple voltaic cell. Use sketches.
2. Which plate has the higher potential? How is it produced?
3. Would you expect to get an E.M.F. by forming a cell of two copper plates?
Why?
(3) Practical Voltaic Cells
248. Advantages of Voltaic Cells.—Many forms of voltaic cells have been
devised. Several of the more common of these will be described and their electro-
chemical action explained.
with mercury. This process is called amalgamation. The mercury
covers the entire surface of the plate in the acid. Its action is to
dissolve pure zinc and bring it to the outer surface where it is acted
upon by the acid. The carbon particles are kept covered so that no local
currents can be formed as long as the bits of carbon are below the
surface. Amalgamation therefore prevents local action.
Fig.
221.—
Local
action.
Important Topics
The Simple Voltaic Cell
1. Two plates: zinc, copper; electrolyte, dilute sulphuric acid.
2. Ions: hydrogen, positive: sulphion, negative.
3. Current, where and how produced, direction, illustration.
4. Polarization: cure, local action, cure.
Exercises
1. Write in your own words an account of the production of an electric current by
the simple voltaic cell. Use sketches.
2. Which plate has the higher potential? How is it produced?
3. Would you expect to get an E.M.F. by forming a cell of two copper plates?
Why?
(3) Practical Voltaic Cells
248. Advantages of Voltaic Cells.—Many forms of voltaic cells have been
devised. Several of the more common of these will be described and their electro-
chemical action explained.
Page 280
At the present time voltaic cells are employed only where small currents are
needed, such as for electric bells and induction coils. Where more than a small
amount of current is required, the dynamo and the storage battery have generally
taken their place as sources of electric current.
The advantages of voltaic cells as electric generators are: (a) they are inexpensive,
(b) they are easily taken from place to place, (c) they may be ready for instant use.
The most desirable voltaic cell would be one having the following qualities: (a)
High electromotive force, (b) no polarization or local action, (c) very low internal
resistance, (d) small expense, both as to first cost and upkeep.
249. The Leclanché cell is the one commonly used
for ringing door bells. It has two plates: one of zinc
and the other of carbon. These are placed in a solution
of sal ammoniac (Fig. 222). Take up the desirable
qualities mentioned at the end of the preceding
paragraph. (a) It may be shown that this cell has a
good E.M.F. about 1.5 volts. (b) It polarizes easily yet
it recovers well when left upon open circuit. Usually a
substance called manganese dioxide is mixed with the
Fig. 222.—The carbon. This acts as a depolarizer, that is, it combines
Leclanché cell, "wet" with the hydrogen to form water. (c) Its resistance
type. varies and is often considerable. (d) The expense for
upkeep is small, since a 5-cent rod of zinc, and a 5-
cent charge of sal ammoniac will keep the cell in action on a bell circuit from six
months to a year or more. It is well suited for use on open circuits that is, where
the circuit is open the greater part of the time and is closed only occasionally; as
in ringing door bells, operating telephones, and other devices whose circuits are
usually open.
250. The Dry Cell.—Many forms of Leclanché cells are made. One of these is
called the dry cell (See Fig. 223.) In this cell the zinc plate is made into a jar or
can and contains the other materials. At the center of the cell is a rod of carbon
and manganese dioxide. The space between the carbon and zinc is filled with a
porous material such as sawdust or plaster of Paris. A strong solution of sal
ammoniac fills the porous material. The top of the cell is sealed with pitch or wax
to prevent evaporation. The great advantage of this cell is that it may be used or
carried in any position without danger of spilling its contents. Dry cells are often
used to operate the spark coils of gas and gasoline engines. The Leclanché cell
described in Art. 249 is commonly known as the "wet cell."
needed, such as for electric bells and induction coils. Where more than a small
amount of current is required, the dynamo and the storage battery have generally
taken their place as sources of electric current.
The advantages of voltaic cells as electric generators are: (a) they are inexpensive,
(b) they are easily taken from place to place, (c) they may be ready for instant use.
The most desirable voltaic cell would be one having the following qualities: (a)
High electromotive force, (b) no polarization or local action, (c) very low internal
resistance, (d) small expense, both as to first cost and upkeep.
249. The Leclanché cell is the one commonly used
for ringing door bells. It has two plates: one of zinc
and the other of carbon. These are placed in a solution
of sal ammoniac (Fig. 222). Take up the desirable
qualities mentioned at the end of the preceding
paragraph. (a) It may be shown that this cell has a
good E.M.F. about 1.5 volts. (b) It polarizes easily yet
it recovers well when left upon open circuit. Usually a
substance called manganese dioxide is mixed with the
Fig. 222.—The carbon. This acts as a depolarizer, that is, it combines
Leclanché cell, "wet" with the hydrogen to form water. (c) Its resistance
type. varies and is often considerable. (d) The expense for
upkeep is small, since a 5-cent rod of zinc, and a 5-
cent charge of sal ammoniac will keep the cell in action on a bell circuit from six
months to a year or more. It is well suited for use on open circuits that is, where
the circuit is open the greater part of the time and is closed only occasionally; as
in ringing door bells, operating telephones, and other devices whose circuits are
usually open.
250. The Dry Cell.—Many forms of Leclanché cells are made. One of these is
called the dry cell (See Fig. 223.) In this cell the zinc plate is made into a jar or
can and contains the other materials. At the center of the cell is a rod of carbon
and manganese dioxide. The space between the carbon and zinc is filled with a
porous material such as sawdust or plaster of Paris. A strong solution of sal
ammoniac fills the porous material. The top of the cell is sealed with pitch or wax
to prevent evaporation. The great advantage of this cell is that it may be used or
carried in any position without danger of spilling its contents. Dry cells are often
used to operate the spark coils of gas and gasoline engines. The Leclanché cell
described in Art. 249 is commonly known as the "wet cell."
Page 281
251. The Daniell
Cell.—This cell is
often used in
laboratories, and on
closed circuits such as
those connected with
fire and burglar
alarms and telegraph
lines. It has two plates
of zinc and copper
placed in two
Fig. 224.—The Daniell cell.
different liquids
Fig. 223.—The which are kept
Leclanché cell, "dry" separated by a porous clay cup (Fig. 224). The zinc
type. rod is kept in a solution of zinc sulphate contained in
the porous cup. The copper plate is in a solution of
copper sulphate filling the rest of the glass jar. Unlike the Leclanché cell, this one
must be kept upon a closed circuit to do its best work, as the two liquids mix
when the circuit is open. Taking its qualities in order, (a) its E.M.F. is about one
volt, (b) it has no polarization since copper instead of hydrogen is deposited upon
the copper plate. Therefore a uniform E.M.F. may be obtained from it, making it
especially useful in laboratory experiments and tests. (c) Its resistance is
considerable and (d) it is more expensive to operate than the Leclanché. It is
sometimes used upon closed circuits outside of laboratories as in burglar and fire
alarms, although in recent years, the storage battery is taking its place for these
purposes.
252. The Gravity Cell.—Fig. 225 is like the Daniell cell in most respects, except
that in this cell, the zinc plate is held at the top of the jar in a solution of zinc
sulphate while the copper plate is at the bottom, surrounded by a solution of
copper sulphate. The solutions mix but slowly as the copper sulphate solution is
denser and remains at the bottom. This cell like the Daniell must also be kept
upon closed circuit. On account of its simplicity and economy it is often used to
operate telegraph instruments. Its qualities are similar to those of the Daniell cell.
253. Symbol for Voltaic Cells.—In electrical diagrams, the symbol employed to
represent a voltaic cell is a short thick line near to and parallel to a longer thin
one. As in Fig. 226. If several cells are to be represented the conventional symbol
of the combination is represented as in Fig. 227. A single cell and a group of cells
are each frequently called a battery.
Cell.—This cell is
often used in
laboratories, and on
closed circuits such as
those connected with
fire and burglar
alarms and telegraph
lines. It has two plates
of zinc and copper
placed in two
Fig. 224.—The Daniell cell.
different liquids
Fig. 223.—The which are kept
Leclanché cell, "dry" separated by a porous clay cup (Fig. 224). The zinc
type. rod is kept in a solution of zinc sulphate contained in
the porous cup. The copper plate is in a solution of
copper sulphate filling the rest of the glass jar. Unlike the Leclanché cell, this one
must be kept upon a closed circuit to do its best work, as the two liquids mix
when the circuit is open. Taking its qualities in order, (a) its E.M.F. is about one
volt, (b) it has no polarization since copper instead of hydrogen is deposited upon
the copper plate. Therefore a uniform E.M.F. may be obtained from it, making it
especially useful in laboratory experiments and tests. (c) Its resistance is
considerable and (d) it is more expensive to operate than the Leclanché. It is
sometimes used upon closed circuits outside of laboratories as in burglar and fire
alarms, although in recent years, the storage battery is taking its place for these
purposes.
252. The Gravity Cell.—Fig. 225 is like the Daniell cell in most respects, except
that in this cell, the zinc plate is held at the top of the jar in a solution of zinc
sulphate while the copper plate is at the bottom, surrounded by a solution of
copper sulphate. The solutions mix but slowly as the copper sulphate solution is
denser and remains at the bottom. This cell like the Daniell must also be kept
upon closed circuit. On account of its simplicity and economy it is often used to
operate telegraph instruments. Its qualities are similar to those of the Daniell cell.
253. Symbol for Voltaic Cells.—In electrical diagrams, the symbol employed to
represent a voltaic cell is a short thick line near to and parallel to a longer thin
one. As in Fig. 226. If several cells are to be represented the conventional symbol
of the combination is represented as in Fig. 227. A single cell and a group of cells
are each frequently called a battery.
Page 282
Fig. 225.—The
gravity cell.
Fig. 226.—Diagram of a single cell.
Fig. 227.—Diagram of a group of cells.
254. Effects of Electric Currents.—Having studied some of the devices for
producing an electric current, let us now consider some of the effects caused by it.
These effects will be studied under three heads: (a) Magnetic, (b) Chemical, and
(c) Heat effects. Devices or articles showing these effects known to most high
school students are respectively: (a) the electromagnet (b) electro-plated silver
ware and (c) electric heaters, such as electric flat irons, electric toasters, etc. The
magnetic effect of an electric current was first detected by Oersted at the
University of Copenhagen in 1819. It may be observed by holding a wire carrying
a current from a voltaic cell above and parallel to the needle of a magnetoscope.
The needle is at once deflected (Fig. 228). If the current is reversed in direction
the magnetoscope needle is deflected in the reverse direction. This simple device
is the most common means for detecting an electric current. It therefore
constitutes a galvanoscope. (See Art. 239.)
gravity cell.
Fig. 226.—Diagram of a single cell.
Fig. 227.—Diagram of a group of cells.
254. Effects of Electric Currents.—Having studied some of the devices for
producing an electric current, let us now consider some of the effects caused by it.
These effects will be studied under three heads: (a) Magnetic, (b) Chemical, and
(c) Heat effects. Devices or articles showing these effects known to most high
school students are respectively: (a) the electromagnet (b) electro-plated silver
ware and (c) electric heaters, such as electric flat irons, electric toasters, etc. The
magnetic effect of an electric current was first detected by Oersted at the
University of Copenhagen in 1819. It may be observed by holding a wire carrying
a current from a voltaic cell above and parallel to the needle of a magnetoscope.
The needle is at once deflected (Fig. 228). If the current is reversed in direction
the magnetoscope needle is deflected in the reverse direction. This simple device
is the most common means for detecting an electric current. It therefore
constitutes a galvanoscope. (See Art. 239.)
Page 283
Fig. 227.—
Diagram of a
group of
cells.Fig. 228.—A
galvanoscope.
Important Topics
1. Leclanché cells, (a), wet, (b), dry, construction, advantages, uses.
2. Daniell and gravity cells, construction, advantages, uses.
3. Three effects of electric currents, illustrations.
4. The galvanoscope, uses.
Exercises
1. Explain how the direction of current in a wire can be determined by a compass.
2. Would you expect to obtain a current from a zinc and copper cell containing a
solution of common salt? Perform the experiment.
3. What conditions in a voltaic cell will give a steady electromotive force.
4. What conditions in a voltaic cell will give a strong electromotive force.
5. Name three different electric circuits that you know exist. Which are open and
which are closed circuits?
6. Are voltaic cells used in your home? If so, for what purpose are they used? On
open or closed circuits? Have you seen them? what kind are they?
Diagram of a
group of
cells.Fig. 228.—A
galvanoscope.
Important Topics
1. Leclanché cells, (a), wet, (b), dry, construction, advantages, uses.
2. Daniell and gravity cells, construction, advantages, uses.
3. Three effects of electric currents, illustrations.
4. The galvanoscope, uses.
Exercises
1. Explain how the direction of current in a wire can be determined by a compass.
2. Would you expect to obtain a current from a zinc and copper cell containing a
solution of common salt? Perform the experiment.
3. What conditions in a voltaic cell will give a steady electromotive force.
4. What conditions in a voltaic cell will give a strong electromotive force.
5. Name three different electric circuits that you know exist. Which are open and
which are closed circuits?
6. Are voltaic cells used in your home? If so, for what purpose are they used? On
open or closed circuits? Have you seen them? what kind are they?
Page 284
CHAPTER XII
THE MAGNETIC EFFECT OF ELECTRIC CURRENTS. ELECTRICAL
MEASUREMENTS
(1) The Magnetic Effect of Electric Currents
255. The Magnetic Effect.—Of all the effects of electric currents, it is generally
conceded that the magnetic effect is the one of greatest practical importance, and
it is also the one most extensively used. An experiment illustrating this effect has
been described in Art. 239. This experiment shows that an electric current, if
parallel to a magnetic needle, and near it will deflect the north-seeking pole of
the needle to the right or left depending upon the direction of the current flow.
This deflection of the magnetic needle is due to the fact that surrounding every
electric current are magnetic lines of force. It is this magnetic field of the current
that causes the needle to turn. The position taken by the needle is the resultant of
the forces of two magnetic fields; one, the earth's field, the other, that of the
current.
256. Right-hand Rule for a Conductor.—To show the presence of the magnetic
field about a current, pass a thick copper wire vertically through a sheet of paper,
and connect the ends of the wire to a source of current. While the current (this
should be as much as 10 amperes if possible) is flowing, sprinkle iron filings upon
the paper and tap gently. The filings will arrange themselves in circles about the
wire showing the magnetic field. (See Fig. 229.) The needle of a magnetoscope
tends to place itself parallel to the lines of force of this field and from this action
or tendency the direction of the magnetic lines about a current may be
determined. The following rule is helpful and should be memorized: Grasp the
conductor with the right hand with the outstretched thumb in the direction that the
current is flowing. The fingers will then encircle the wire in the direction of the
lines of force. This rule may be reversed, for, if the fingers of the right hand grasp
the wire so as to point with the magnetic field, then the current flows in the
direction in which the thumb points. (See Fig. 230.)
THE MAGNETIC EFFECT OF ELECTRIC CURRENTS. ELECTRICAL
MEASUREMENTS
(1) The Magnetic Effect of Electric Currents
255. The Magnetic Effect.—Of all the effects of electric currents, it is generally
conceded that the magnetic effect is the one of greatest practical importance, and
it is also the one most extensively used. An experiment illustrating this effect has
been described in Art. 239. This experiment shows that an electric current, if
parallel to a magnetic needle, and near it will deflect the north-seeking pole of
the needle to the right or left depending upon the direction of the current flow.
This deflection of the magnetic needle is due to the fact that surrounding every
electric current are magnetic lines of force. It is this magnetic field of the current
that causes the needle to turn. The position taken by the needle is the resultant of
the forces of two magnetic fields; one, the earth's field, the other, that of the
current.
256. Right-hand Rule for a Conductor.—To show the presence of the magnetic
field about a current, pass a thick copper wire vertically through a sheet of paper,
and connect the ends of the wire to a source of current. While the current (this
should be as much as 10 amperes if possible) is flowing, sprinkle iron filings upon
the paper and tap gently. The filings will arrange themselves in circles about the
wire showing the magnetic field. (See Fig. 229.) The needle of a magnetoscope
tends to place itself parallel to the lines of force of this field and from this action
or tendency the direction of the magnetic lines about a current may be
determined. The following rule is helpful and should be memorized: Grasp the
conductor with the right hand with the outstretched thumb in the direction that the
current is flowing. The fingers will then encircle the wire in the direction of the
lines of force. This rule may be reversed, for, if the fingers of the right hand grasp
the wire so as to point with the magnetic field, then the current flows in the
direction in which the thumb points. (See Fig. 230.)
Page 285
Fig. 229.—Magnetic field about a wire
carrying an electric current.
Fig. 230.—Right-hand rule for the magnetic
field of a current.
257. Magnetic Field of a Helix.—If a wire be wound about a cylinder to form a
cylindrical coil with parallel turns, it forms a helix or solenoid. The shape of the
magnetic field about a current depends upon the form of the conductor. If the
latter is in the form of a helix its magnetic field resembles that of a straight bar
magnet. (See Fig. 231). In fact the helix has the properties of a magnet with
north- and south-seeking poles while a current is flowing through it. If such a coil
is suspended so as to turn freely, it tends to turn until the field within it is parallel
to the earth's magnetic field. Such a suspended helix may therefore be used as a
compass. In order to strengthen the magnetic field of a helix or solenoid, the
space within its turns is filled with iron, often in the form of small soft-iron wires.
This bundle of iron wire is called the core of the helix. The core becomes strongly
magnetized by the field of the helix while the current is flowing and quickly loses
its magnetic force when the current is stopped. The direction of the current in a
helix (Fig. 232) or the polarity of its core may be determined by another right-
hand rule. If the helix is grasped with the right hand so that the fingers point in
the direction in which the current is flowing, the extended thumb will point in the
direction of the north pole of the helix. On the other hand, if the poles of the helix
are known, then, when the helix is grasped with the right hand so that the thumb
points to the north-seeking pole, the current is flowing in the wires in the direction
that the fingers point.
carrying an electric current.
Fig. 230.—Right-hand rule for the magnetic
field of a current.
257. Magnetic Field of a Helix.—If a wire be wound about a cylinder to form a
cylindrical coil with parallel turns, it forms a helix or solenoid. The shape of the
magnetic field about a current depends upon the form of the conductor. If the
latter is in the form of a helix its magnetic field resembles that of a straight bar
magnet. (See Fig. 231). In fact the helix has the properties of a magnet with
north- and south-seeking poles while a current is flowing through it. If such a coil
is suspended so as to turn freely, it tends to turn until the field within it is parallel
to the earth's magnetic field. Such a suspended helix may therefore be used as a
compass. In order to strengthen the magnetic field of a helix or solenoid, the
space within its turns is filled with iron, often in the form of small soft-iron wires.
This bundle of iron wire is called the core of the helix. The core becomes strongly
magnetized by the field of the helix while the current is flowing and quickly loses
its magnetic force when the current is stopped. The direction of the current in a
helix (Fig. 232) or the polarity of its core may be determined by another right-
hand rule. If the helix is grasped with the right hand so that the fingers point in
the direction in which the current is flowing, the extended thumb will point in the
direction of the north pole of the helix. On the other hand, if the poles of the helix
are known, then, when the helix is grasped with the right hand so that the thumb
points to the north-seeking pole, the current is flowing in the wires in the direction
that the fingers point.
Page 286
Fig. 231.—The magnetic field of a helix.
Fig. 232.—Right-hand rule for a helix.
258. The Electromagnet.—These "right-hand" rules are applied in many
different devices. Among these, perhaps the most important is the electromagnet,
which is used in the electric bell, the telegraph, the telephone, the dynamo, the
motor, and many other electric contrivances.
The electromagnet is defined as a mass of iron around which is placed a helix for
conducting an electric current. On account of its large permeability, the iron core
of the helix adds greatly to the effectiveness of the electromagnet, since the
magnetism of the iron is added to that of the current in the helix. The magnetism
remaining in the iron after the current stops is called the residual magnetism. The
residual magnetism is small when the core is made of small wires or thin plates,
but is larger when the iron core is solid. Like artificial steel magnets,
electromagnets are usually of two forms, bar and horseshoe. (See Figs. 233 and
234.) For most purposes the horseshoe form is the more effective since it permits
a complete iron circuit for the magnetic lines of force. (See Fig. 235.) This is the
form used in the electric bell, in the telegraph sounder, and in lifting magnets.
(See Fig. 236.)
Fig. 233.—A bar electromagnet.
Fig. 234.—A horseshoe electromagnet.
Fig. 232.—Right-hand rule for a helix.
258. The Electromagnet.—These "right-hand" rules are applied in many
different devices. Among these, perhaps the most important is the electromagnet,
which is used in the electric bell, the telegraph, the telephone, the dynamo, the
motor, and many other electric contrivances.
The electromagnet is defined as a mass of iron around which is placed a helix for
conducting an electric current. On account of its large permeability, the iron core
of the helix adds greatly to the effectiveness of the electromagnet, since the
magnetism of the iron is added to that of the current in the helix. The magnetism
remaining in the iron after the current stops is called the residual magnetism. The
residual magnetism is small when the core is made of small wires or thin plates,
but is larger when the iron core is solid. Like artificial steel magnets,
electromagnets are usually of two forms, bar and horseshoe. (See Figs. 233 and
234.) For most purposes the horseshoe form is the more effective since it permits
a complete iron circuit for the magnetic lines of force. (See Fig. 235.) This is the
form used in the electric bell, in the telegraph sounder, and in lifting magnets.
(See Fig. 236.)
Fig. 233.—A bar electromagnet.
Fig. 234.—A horseshoe electromagnet.
Page 287
Fig. 235.—A horseshoe electromagnet may
have a complete iron circuit for its lines of
force.
Fig. 236.—A lifting magnet.
259. Effective Electromagnets.—The magnetic effect of a current in a helix is
small, hence the force usually is increased by inserting a core of iron. When at
first man tried to signal with electromagnets at a distance it was found that the
current would not work the electromagnet. An American by the name of Joseph
Henry discovered the remedy for this condition. He found that if the copper wire
was insulated by wrapping silk thread about it, and then many layers of the silk
insulated wire were wound upon a spool with an iron core, that the magnet would
work at a great distance from the source of current. If the current is increased, the
magnet is stronger than at first. Thus an electromagnet may be made stronger by
(a) increasing the number of turns of wire in its coils and by (b) sending a
stronger current through it.
260. The Telegraph.—The invention of an
effective electromagnet by Henry made possible
the electric telegraph. In its simplest form it
consists of a battery, C, a key, K, and a sounder,
S, with connecting wires. (See Fig. 237.) The
sounder (Fig. 238) contains a horseshoe
electromagnet and a bar of soft iron across its
poles called an armature, A, attached to a lever Fig. 237.—A simple
L. When the key is closed, the electromagnet telegraph circuit.
draws down the armature and lever until the
latter hits a stop O, making a click. When the key is raised, the magnet releases
the armature which is raised by the action of a spring at S until the lever hits a
stop at T making another click. Closing and opening the circuit at K will start and
stop the current which operates S which may be 100 miles or more from K. One
voltaic cell will work a sounder in the same room. But if many miles of wire are
in the circuit, the E.M.F. of a single cell will not force sufficient current through
the long wire to operate the sounder.
have a complete iron circuit for its lines of
force.
Fig. 236.—A lifting magnet.
259. Effective Electromagnets.—The magnetic effect of a current in a helix is
small, hence the force usually is increased by inserting a core of iron. When at
first man tried to signal with electromagnets at a distance it was found that the
current would not work the electromagnet. An American by the name of Joseph
Henry discovered the remedy for this condition. He found that if the copper wire
was insulated by wrapping silk thread about it, and then many layers of the silk
insulated wire were wound upon a spool with an iron core, that the magnet would
work at a great distance from the source of current. If the current is increased, the
magnet is stronger than at first. Thus an electromagnet may be made stronger by
(a) increasing the number of turns of wire in its coils and by (b) sending a
stronger current through it.
260. The Telegraph.—The invention of an
effective electromagnet by Henry made possible
the electric telegraph. In its simplest form it
consists of a battery, C, a key, K, and a sounder,
S, with connecting wires. (See Fig. 237.) The
sounder (Fig. 238) contains a horseshoe
electromagnet and a bar of soft iron across its
poles called an armature, A, attached to a lever Fig. 237.—A simple
L. When the key is closed, the electromagnet telegraph circuit.
draws down the armature and lever until the
latter hits a stop O, making a click. When the key is raised, the magnet releases
the armature which is raised by the action of a spring at S until the lever hits a
stop at T making another click. Closing and opening the circuit at K will start and
stop the current which operates S which may be 100 miles or more from K. One
voltaic cell will work a sounder in the same room. But if many miles of wire are
in the circuit, the E.M.F. of a single cell will not force sufficient current through
the long wire to operate the sounder.
Page 288
Fig. 238.—A telegraph sounder.
Fig. 239.—A telegraph relay.
Fig. 240.—How the relay is used.
A battery of several cells is then required. Even a large battery is insufficient to
operate a long line containing many sounders in circuit. Recourse is therefore
usually made to a more sensitive device called a relay. (See Fig. 239.) In the relay
a very small current will magnetize its electromagnet enough to draw toward it
the delicately hung armature thereby closing a second circuit which contains a
sounder and a battery. (See Fig. 240.) when the current in the main circuit is
stopped, the armature of the relay is drawn back by a light spring. This opens the
local circuit. Thus the local circuit is closed and opened by the relay just in time
with the starting and stopping of the current in the main line. It is thus possible for
a small current in the main line by the use of a relay, to close and open a second
local circuit containing a local battery and sounder. Modern telegraph lines are
operated in this manner.
261. The electric bell (see Fig. 241), consists of an electromagnet, M, a soft iron
armature, A, attached to the tapper, T, and a post, R. When no current is flowing a
Fig. 239.—A telegraph relay.
Fig. 240.—How the relay is used.
A battery of several cells is then required. Even a large battery is insufficient to
operate a long line containing many sounders in circuit. Recourse is therefore
usually made to a more sensitive device called a relay. (See Fig. 239.) In the relay
a very small current will magnetize its electromagnet enough to draw toward it
the delicately hung armature thereby closing a second circuit which contains a
sounder and a battery. (See Fig. 240.) when the current in the main circuit is
stopped, the armature of the relay is drawn back by a light spring. This opens the
local circuit. Thus the local circuit is closed and opened by the relay just in time
with the starting and stopping of the current in the main line. It is thus possible for
a small current in the main line by the use of a relay, to close and open a second
local circuit containing a local battery and sounder. Modern telegraph lines are
operated in this manner.
261. The electric bell (see Fig. 241), consists of an electromagnet, M, a soft iron
armature, A, attached to the tapper, T, and a post, R. When no current is flowing a
Page 289
spring at S holds the
armature against the post
R. When current flows
through the helix, its core
becomes magnetized and
attracts the armature,
drawing it away from the
post, R, and causing the
tapper to hit the bell.
Drawing A away from the
post, however, breaks the
circuit at R and the current
stops. The magnetism in
the core disappears
releasing the armature,
which is then pulled back
by the spring S against the
Samuel F. B. Morse post R. This completes the Thomas A. Edison,
(1791-1872). Inventor circuit and the process Orange, New Jersey.
of the electromagnetic repeats itself several times Invented the
recording telegraph a second as long as the incandescent lamp;
and of the dot and current flows. phonograph; moving
dash alphabet. picture; most noted
262. Static and Current
Electricity Compared.— inventor of electrical
Samuel F. B. Morse appliances of the
"From Appleton's The likeness between a
discharge of static present day.
Cyclopedia of
American Biography, electricity and an electric Thomas A. Edison
Copyright 1888 by D. current may be shown by "Copyright,
Appleton & Co." winding a coil of insulated
wire about a glass tube Photographische
which contains a steel Gessellschaft," and
needle. If a Leyden jar (see Fig. 242) is discharged "By Permission of the
through the coil the steel needle is usually found to be Berlin Photographic
magnetized, showing that the discharge of the static Co., New York."
electricity has a magnetic effect similar to that of an
electric current. Sometimes a given end of the needle has a north pole and at other
times a south pole. This is believed to indicate that the charge of the Leyden jar is
oscillatory, and that in different discharges sometimes a surge in one direction and
at other times a surge in the reverse direction has been most effective in
magnetizing the needle. Compare this action with that described in Art. 233.
armature against the post
R. When current flows
through the helix, its core
becomes magnetized and
attracts the armature,
drawing it away from the
post, R, and causing the
tapper to hit the bell.
Drawing A away from the
post, however, breaks the
circuit at R and the current
stops. The magnetism in
the core disappears
releasing the armature,
which is then pulled back
by the spring S against the
Samuel F. B. Morse post R. This completes the Thomas A. Edison,
(1791-1872). Inventor circuit and the process Orange, New Jersey.
of the electromagnetic repeats itself several times Invented the
recording telegraph a second as long as the incandescent lamp;
and of the dot and current flows. phonograph; moving
dash alphabet. picture; most noted
262. Static and Current
Electricity Compared.— inventor of electrical
Samuel F. B. Morse appliances of the
"From Appleton's The likeness between a
discharge of static present day.
Cyclopedia of
American Biography, electricity and an electric Thomas A. Edison
Copyright 1888 by D. current may be shown by "Copyright,
Appleton & Co." winding a coil of insulated
wire about a glass tube Photographische
which contains a steel Gessellschaft," and
needle. If a Leyden jar (see Fig. 242) is discharged "By Permission of the
through the coil the steel needle is usually found to be Berlin Photographic
magnetized, showing that the discharge of the static Co., New York."
electricity has a magnetic effect similar to that of an
electric current. Sometimes a given end of the needle has a north pole and at other
times a south pole. This is believed to indicate that the charge of the Leyden jar is
oscillatory, and that in different discharges sometimes a surge in one direction and
at other times a surge in the reverse direction has been most effective in
magnetizing the needle. Compare this action with that described in Art. 233.
Page 290
Fig. 241.—An electric
bell and its circuit.
Fig. 242.—Magnetizing by
the discharge of a Leyden
jar.
Important Topics
1. Right-hand rules, for conductor, for helix.
2. The electromagnet, two forms, where used?
3. Likeness between static and current electricity.
4. The electric bell, parts, action.
5. The telegraph, key, sounder, relay.
Exercises
1. What is the difference between an electric charge and a current?
2. How can a magnetic effect be produced from an electric charge?
3. What is a magnetic field? Give two evidences of a magnetic field about a
current in a wire?
4. A current is flowing north in trolley wire, what is the direction of the magnetic
field under the wire? Explain.
5. What would be the result if a hard steel core were placed in the electromagnet?
Explain.
6. If the north-seeking pole of a helix is facing you, does the current in the coils
before you move in a clockwise or in a counter-clockwise direction? Explain.
bell and its circuit.
Fig. 242.—Magnetizing by
the discharge of a Leyden
jar.
Important Topics
1. Right-hand rules, for conductor, for helix.
2. The electromagnet, two forms, where used?
3. Likeness between static and current electricity.
4. The electric bell, parts, action.
5. The telegraph, key, sounder, relay.
Exercises
1. What is the difference between an electric charge and a current?
2. How can a magnetic effect be produced from an electric charge?
3. What is a magnetic field? Give two evidences of a magnetic field about a
current in a wire?
4. A current is flowing north in trolley wire, what is the direction of the magnetic
field under the wire? Explain.
5. What would be the result if a hard steel core were placed in the electromagnet?
Explain.
6. If the north-seeking pole of a helix is facing you, does the current in the coils
before you move in a clockwise or in a counter-clockwise direction? Explain.
Page 291
7. A helix is placed horizontally with its north-seeking pole toward the north.
Does the current in the wire at the top of the helix move east or west? Explain.
8. State at least six conditions any one of which will put an electric bell circuit out
of commission.
9. If one desires to insert a battery into a telegraph circuit already in operation,
how will he determine the direction of the current in the wire?
10. If a boy who had magnetized his knife blade in a physics laboratory, pointed
end south-seeking, should lose his way in the woods on a cloudy day, how could
he determine his way out?
11. At a certain point the earth's field acts north, that of an electric current, east.
The magnetoscope needle points exactly northeast when placed at that point. How
do the two magnetic fields compare?
(2) Electrical Measurements
263. Galvanometers.—In using electric currents it is often necessary or desirable
to be able to know not only that a given current is weak or strong, but precisely
what its strength is. We can determine the relative strengths of two currents by the
use of a galvanometer.
Fig. 243.—The magnet is at the center of the
coil.
Fig. 244.—A moving-magnet (tangent)
galvanometer.
The older or moving-magnet type of galvanometer is similar to the galvanoscope
mentioned in Art. 239. It consists of a magnetic needle mounted at the center of a
coil of wire. The coil is placed facing east and west, so that the needle will be held
by the earth's magnetic field parallel to the plane of the coil. When a current is
Does the current in the wire at the top of the helix move east or west? Explain.
8. State at least six conditions any one of which will put an electric bell circuit out
of commission.
9. If one desires to insert a battery into a telegraph circuit already in operation,
how will he determine the direction of the current in the wire?
10. If a boy who had magnetized his knife blade in a physics laboratory, pointed
end south-seeking, should lose his way in the woods on a cloudy day, how could
he determine his way out?
11. At a certain point the earth's field acts north, that of an electric current, east.
The magnetoscope needle points exactly northeast when placed at that point. How
do the two magnetic fields compare?
(2) Electrical Measurements
263. Galvanometers.—In using electric currents it is often necessary or desirable
to be able to know not only that a given current is weak or strong, but precisely
what its strength is. We can determine the relative strengths of two currents by the
use of a galvanometer.
Fig. 243.—The magnet is at the center of the
coil.
Fig. 244.—A moving-magnet (tangent)
galvanometer.
The older or moving-magnet type of galvanometer is similar to the galvanoscope
mentioned in Art. 239. It consists of a magnetic needle mounted at the center of a
coil of wire. The coil is placed facing east and west, so that the needle will be held
by the earth's magnetic field parallel to the plane of the coil. When a current is
Page 292
sent through the coil a magnetic field is produced within it. This deflects the
needle, its north end turning east or west depending upon the direction of the
current. (See Fig. 243.) The coils of a moving-magnet or tangent galvanometer
(see Fig. 244) are large and firmly fastened to the base, while the magnet is small.
The moving-coil type of galvanometer (see Fig. 245) consists of a large magnet
fastened to the frame of the device. The magnet usually has a horseshoe form to
produce as strong a field as possible. The coil is wound on a light rectangular
frame and is suspended between the two poles of the magnet. To concentrate the
magnetic field, a cylinder of soft iron is usually placed within the coil. Fig. 246
represents a common form of moving-coil galvanometer.
Fig. 245.—To illustrate the principle of the
moving-coil galvanometer.
Fig. 246.—A moving-coil (D'Arsonval)
galvanometer.
264. Measurement of Electric Currents.—A galvanometer enables one to
compare electric currents. To measure electric currents it is necessary to employ a
unit of electrical quantity, just as in measuring the quantity of water delivered by a
pipe, a unit of liquid measure is employed; thus, e.g., the current delivered by a
given pipe may be 2 gallons of water per second, so in measuring the flow of an
electric current one may speak of two coulombs per second. The coulomb is the
unit quantity of electricity just as the unit of quantity of water is the gallon.
For most practical purposes, however, we are more interested in the rate or
intensity of flow of current than in the actual quantity delivered. The unit of rate
of flow or current is called the ampere.
needle, its north end turning east or west depending upon the direction of the
current. (See Fig. 243.) The coils of a moving-magnet or tangent galvanometer
(see Fig. 244) are large and firmly fastened to the base, while the magnet is small.
The moving-coil type of galvanometer (see Fig. 245) consists of a large magnet
fastened to the frame of the device. The magnet usually has a horseshoe form to
produce as strong a field as possible. The coil is wound on a light rectangular
frame and is suspended between the two poles of the magnet. To concentrate the
magnetic field, a cylinder of soft iron is usually placed within the coil. Fig. 246
represents a common form of moving-coil galvanometer.
Fig. 245.—To illustrate the principle of the
moving-coil galvanometer.
Fig. 246.—A moving-coil (D'Arsonval)
galvanometer.
264. Measurement of Electric Currents.—A galvanometer enables one to
compare electric currents. To measure electric currents it is necessary to employ a
unit of electrical quantity, just as in measuring the quantity of water delivered by a
pipe, a unit of liquid measure is employed; thus, e.g., the current delivered by a
given pipe may be 2 gallons of water per second, so in measuring the flow of an
electric current one may speak of two coulombs per second. The coulomb is the
unit quantity of electricity just as the unit of quantity of water is the gallon.
For most practical purposes, however, we are more interested in the rate or
intensity of flow of current than in the actual quantity delivered. The unit of rate
of flow or current is called the ampere.
Page 293
In determining the exact quantity of an electric current, physicists make use of a
device called a coulomb meter. (See Fig. 247.) This contains a solution of silver
nitrate in which are placed two silver plates. The current to be measured is sent
through the solution, in at one plate and out at the other. The plate where the
current goes in, the anode, A (Fig. 247), loses in weight since some of the silver is
dissolved. The plate where the current goes out, the cathode, C, increases in
weight since some of the silver is deposited. By an international agreement, the
intensity of the current which deposits silver at the rate of 0.001118 g. per second
is 1 ampere. This is equal to 4.025 g. per hour.
The coulomb is defined as the quantity of electricity
delivered by a current of one ampere during one
second.
A 40-watt-incandescent lamp takes about 0.4
ampere of current. An arc lamp takes from 6 to 15
amperes. A new dry cell may send 20 amperes
through a testing meter. A street car may take from
50 to 100 amperes.
265. The Ammeter.—The method described above
is not used ordinarily for measuring current
strengths on account of its inconvenience. The usual
device employed is an ammeter. This instrument is
a moving-coil galvanometer. It contains, wound on
a light form, a coil of fine copper wire. The form is
mounted on jewel bearings between the poles of a
strong permanent horseshoe magnet. (See Fig. 248.) Fig. 247.—A coulomb
As in other moving-coil galvanometers, a soft iron meter, the anode A is
cylinder within the form concentrates the field of separated from the
the magnet. The form and its coil is held in balance cathode C by a porous
by two spiral springs which also conduct current cup.
into and out of the coil.
Only a small part of the whole current measured, in some cases only 0.0001
passes through the coil, the larger part of the current passing through a metal wire
or strip called a shunt[L] (see Fig. 248) connecting the binding posts of the
instrument. A fixed fraction of the whole current flows through the coil. Its field
crossing the field of the horseshoe magnet, tends to turn until its turning force is
balanced by the spiral springs. As the coil turns it moves a pointer attached to it
across a scale graduated to indicate the number of amperes in the whole current.
device called a coulomb meter. (See Fig. 247.) This contains a solution of silver
nitrate in which are placed two silver plates. The current to be measured is sent
through the solution, in at one plate and out at the other. The plate where the
current goes in, the anode, A (Fig. 247), loses in weight since some of the silver is
dissolved. The plate where the current goes out, the cathode, C, increases in
weight since some of the silver is deposited. By an international agreement, the
intensity of the current which deposits silver at the rate of 0.001118 g. per second
is 1 ampere. This is equal to 4.025 g. per hour.
The coulomb is defined as the quantity of electricity
delivered by a current of one ampere during one
second.
A 40-watt-incandescent lamp takes about 0.4
ampere of current. An arc lamp takes from 6 to 15
amperes. A new dry cell may send 20 amperes
through a testing meter. A street car may take from
50 to 100 amperes.
265. The Ammeter.—The method described above
is not used ordinarily for measuring current
strengths on account of its inconvenience. The usual
device employed is an ammeter. This instrument is
a moving-coil galvanometer. It contains, wound on
a light form, a coil of fine copper wire. The form is
mounted on jewel bearings between the poles of a
strong permanent horseshoe magnet. (See Fig. 248.) Fig. 247.—A coulomb
As in other moving-coil galvanometers, a soft iron meter, the anode A is
cylinder within the form concentrates the field of separated from the
the magnet. The form and its coil is held in balance cathode C by a porous
by two spiral springs which also conduct current cup.
into and out of the coil.
Only a small part of the whole current measured, in some cases only 0.0001
passes through the coil, the larger part of the current passing through a metal wire
or strip called a shunt[L] (see Fig. 248) connecting the binding posts of the
instrument. A fixed fraction of the whole current flows through the coil. Its field
crossing the field of the horseshoe magnet, tends to turn until its turning force is
balanced by the spiral springs. As the coil turns it moves a pointer attached to it
across a scale graduated to indicate the number of amperes in the whole current.
Page 294
It should be noted that while all of the
current measured passed through the
ammeter, but a small part goes through the
coil.
266. Resistance of Conductors.—With an
ammeter one may study the change
produced in the amount of current flowing
in a wire when a change is made in the wire
conducting the current. For example, if one
measures with an ammeter the current
flowing from a dry cell through a long and
then through a short piece of fine copper
wire, it will be seen that less current flows
when the long piece is used. That is, the
Fig. 248.—Diagram of a long wire seems to hinder or to resist the
commercial ammeter. S is the passing of the current more than the short
shunt. piece. In other words, the long wire is said
to have more resistance.
The resistance of a conducting body is affected by several conditions.
(a) It is directly proportional to the length of the conductor, one hundred feet of
wire having twice the resistance of fifty feet.
(b) It is inversely proportional to the square of the diameter; a wire 0.1 inch in
diameter has four times the resistance of a wire 0.2 inch in diameter.
(c) It differs with different substances, iron having about six times as much as
copper.
(d) It varies with the temperature, metals having greater resistance at a higher
temperature.
Since silver is the best conductor known, the resistances of other substances are
compared with it as a standard.
The ratio of the resistance of a wire of any substance as compared to the
resistance of a silver wire of exactly the same diameter and length is called its
relative resistance.
Purified substances arranged in order of increasing resistance for the same length
and sectional area (Ayrton-Mather) are given on p. 294.
Silver annealed 1.00
current measured passed through the
ammeter, but a small part goes through the
coil.
266. Resistance of Conductors.—With an
ammeter one may study the change
produced in the amount of current flowing
in a wire when a change is made in the wire
conducting the current. For example, if one
measures with an ammeter the current
flowing from a dry cell through a long and
then through a short piece of fine copper
wire, it will be seen that less current flows
when the long piece is used. That is, the
Fig. 248.—Diagram of a long wire seems to hinder or to resist the
commercial ammeter. S is the passing of the current more than the short
shunt. piece. In other words, the long wire is said
to have more resistance.
The resistance of a conducting body is affected by several conditions.
(a) It is directly proportional to the length of the conductor, one hundred feet of
wire having twice the resistance of fifty feet.
(b) It is inversely proportional to the square of the diameter; a wire 0.1 inch in
diameter has four times the resistance of a wire 0.2 inch in diameter.
(c) It differs with different substances, iron having about six times as much as
copper.
(d) It varies with the temperature, metals having greater resistance at a higher
temperature.
Since silver is the best conductor known, the resistances of other substances are
compared with it as a standard.
The ratio of the resistance of a wire of any substance as compared to the
resistance of a silver wire of exactly the same diameter and length is called its
relative resistance.
Purified substances arranged in order of increasing resistance for the same length
and sectional area (Ayrton-Mather) are given on p. 294.
Silver annealed 1.00
Page 295
Copper annealed from 1.04
(Copper annealed) to 1.09
Aluminum annealed 1.64
Nickel annealed 4.69
Platinum annealed 6.09
Iron annealed 6.56
German Silver from 12.80
(German Silver) to 20.20
Mercury 63.30
Nichrome 67.50
Carbon from 2700.00
(Carbon) to 6700.00
267. The ohm, the unit of resistance, is defined by international agreement as
follows: An ohm is the resistance of a column of pure mercury, 106.3 cm. long
with a cross-section of a square millimeter and at a temperature of 0°C.
It should be noted that each of the four conditions affecting resistance is
mentioned in the definition, viz., length, cross-section, material, and temperature.
Since it is inconvenient to handle mercury, standard resistance coils, made of an
alloy of high resistance are used in comparing and measuring resistances.
A piece of copper wire No. 22 (diameter 0.644 mm.) 60. 5 ft. long has a resistance
of 1 ohm. See table p. 296.
The resistance of some telephone receivers is 75 ohms, of a telegraph sounder, 4
ohms, of a relay 200 ohms.
268. Resistance of Circuits.—Every part of an electrical circuit possesses
resistance. In an electric-bell circuit, for instance, the wires, the bell, the push-
button, and the cell itself, each offers a definite resistance to the passage of the
current. The resistance within the cell is termed internal resistance, while the
resistance of the parts outside of the electric generator is called external
resistance.
269. Electromotive Force.—In order to set in motion anything, some force must
be applied. This is as true of electricity as of solids, liquids, or gases. By analogy
that which is exerted by a battery or by a dynamo in causing current to flow is
called an electromotive force. The unit of electromotive force, the volt, may be
defined as the electromotive force that will drive a current of 1 ampere through
the resistance of 1 ohm. The electromotive force of a dry cell is about 1.5 volts, of
a Daniell cell 1.08 volts. Most electric light circuits in buildings carry current at
(Copper annealed) to 1.09
Aluminum annealed 1.64
Nickel annealed 4.69
Platinum annealed 6.09
Iron annealed 6.56
German Silver from 12.80
(German Silver) to 20.20
Mercury 63.30
Nichrome 67.50
Carbon from 2700.00
(Carbon) to 6700.00
267. The ohm, the unit of resistance, is defined by international agreement as
follows: An ohm is the resistance of a column of pure mercury, 106.3 cm. long
with a cross-section of a square millimeter and at a temperature of 0°C.
It should be noted that each of the four conditions affecting resistance is
mentioned in the definition, viz., length, cross-section, material, and temperature.
Since it is inconvenient to handle mercury, standard resistance coils, made of an
alloy of high resistance are used in comparing and measuring resistances.
A piece of copper wire No. 22 (diameter 0.644 mm.) 60. 5 ft. long has a resistance
of 1 ohm. See table p. 296.
The resistance of some telephone receivers is 75 ohms, of a telegraph sounder, 4
ohms, of a relay 200 ohms.
268. Resistance of Circuits.—Every part of an electrical circuit possesses
resistance. In an electric-bell circuit, for instance, the wires, the bell, the push-
button, and the cell itself, each offers a definite resistance to the passage of the
current. The resistance within the cell is termed internal resistance, while the
resistance of the parts outside of the electric generator is called external
resistance.
269. Electromotive Force.—In order to set in motion anything, some force must
be applied. This is as true of electricity as of solids, liquids, or gases. By analogy
that which is exerted by a battery or by a dynamo in causing current to flow is
called an electromotive force. The unit of electromotive force, the volt, may be
defined as the electromotive force that will drive a current of 1 ampere through
the resistance of 1 ohm. The electromotive force of a dry cell is about 1.5 volts, of
a Daniell cell 1.08 volts. Most electric light circuits in buildings carry current at
Page 296
110 or 220 volts pressure. Currents for street cars have an electromotive force of
from 550 to 660 volts.
270. The Voltmeter.—An
instrument for measuring the
electromotive force of
electric currents is called a
voltmeter (Fig. 249). It is
usually a moving-coil
galvanometer, and is always
of high resistance. It is like
an ammeter in construction
and appearance. In fact, a
voltmeter is an ammeter
which has had its shunt
removed or disconnected. In
place of a shunt, the
voltmeter uses a coil of wire
of high resistance (see R, Fig.
249) in series with the
galvanometer coil. The high
resistance of the voltmeter
permits but a very small
current to flow through it.
Hence a voltmeter must be
placed across a circuit and Fig. 249.—Diagram of a commercial
not in it. In other words a voltmeter.
voltmeter is connected in
shunt, while an ammeter is in series with the circuit as is shown in Fig. 250.
Dimensions and Functions of Copper Wires
Weight
Diameter and
Sectional Resistance
B. & S. length, Capacity
Circular area in at 24°C.,
gauge Density = in
mils square feet per
number 8.9, feet amperes
Mils Millimeters millimeters ohm
per
pound
0000 460.000 11.684 211,600.00 107.219 1.56 19,929.700 312.0
000 409.640 10.405167,805.00 85.028 1.97 15,804.900 262.0
from 550 to 660 volts.
270. The Voltmeter.—An
instrument for measuring the
electromotive force of
electric currents is called a
voltmeter (Fig. 249). It is
usually a moving-coil
galvanometer, and is always
of high resistance. It is like
an ammeter in construction
and appearance. In fact, a
voltmeter is an ammeter
which has had its shunt
removed or disconnected. In
place of a shunt, the
voltmeter uses a coil of wire
of high resistance (see R, Fig.
249) in series with the
galvanometer coil. The high
resistance of the voltmeter
permits but a very small
current to flow through it.
Hence a voltmeter must be
placed across a circuit and Fig. 249.—Diagram of a commercial
not in it. In other words a voltmeter.
voltmeter is connected in
shunt, while an ammeter is in series with the circuit as is shown in Fig. 250.
Dimensions and Functions of Copper Wires
Weight
Diameter and
Sectional Resistance
B. & S. length, Capacity
Circular area in at 24°C.,
gauge Density = in
mils square feet per
number 8.9, feet amperes
Mils Millimeters millimeters ohm
per
pound
0000 460.000 11.684 211,600.00 107.219 1.56 19,929.700 312.0
000 409.640 10.405167,805.00 85.028 1.97 15,804.900 262.0
Page 297
00 364.800 9.266133,079.40 67.431 2.49 12,534.200 220.0
0 324.950 8.254105,592.50 53.470 3.13 9,945.300 185.0
2 257.630 6.544 66,373.00 33.631 4.99 6,251.400 131.0
4 204.310 5.189 41,742.00 21.151 7.93 3,931.600 92.3
6 162.020 4.115 26,250.50 13.301 12.61 2,472.400 65.2
8 128.490 3.264 16,509.00 8.366 20.05 1,555.000 46.1
10 101.890 2.588 10,381.00 5.260 31.38 977.800 32.5
12 80.808 2.053 6,529.90 3.309 50.69 615.020 23.0
14 64.084 1.628 4,106.80 2.081 80.59 386.800 16.2
16 50.820 1.291 2,582.90 1.309 128.14 243.250 11.5
18 40.303 1.024 1,624.30 0.823 203.76 152.990 8.1
20 31.961 0.812 1,021.50 0.5176 324.00 96.210 5.7
22 25.347 0.644 642.70 0.3255 515.15 60.510 4.0
24 20.100 0.511 504.01 0.2047 819.21 38.050 2.8
26 15.940 0.405 254.01 0.1288 1,302.61 23.930 2.0
28 12.641 0.321 159.79 0.08097 2,071.22 15.050 1.4
30 10.025 0.255 100.50 0.05092 3,293.97 9.466 1.0
32 7.950 0.202 63.20 0.03203 5,236.66 5.952 0.70
34 6.304 0.160 39.74 0.02014 8,328.30 3.743 0.50
36 5.000 0.127 25.00 0.01267 13,238.83 2.355 0.35
38 3.965 0.101 15.72 0.00797 20,854.65 1.481 0.25
40 3.144 0.080 9.89 0.00501 33,175.94 0.931 0.17
Important Topics
(1) Galvanometers: (1) moving magnet, fixed coil; (2) moving coil, fixed magnet,
ammeter, voltmeter.
(2) Unit of quantity, coulomb.
(3) Unit of current, ampere.
(4) Unit of resistance, ohm.
(5) Unit of electromotive force, volt.
Exercises
0 324.950 8.254105,592.50 53.470 3.13 9,945.300 185.0
2 257.630 6.544 66,373.00 33.631 4.99 6,251.400 131.0
4 204.310 5.189 41,742.00 21.151 7.93 3,931.600 92.3
6 162.020 4.115 26,250.50 13.301 12.61 2,472.400 65.2
8 128.490 3.264 16,509.00 8.366 20.05 1,555.000 46.1
10 101.890 2.588 10,381.00 5.260 31.38 977.800 32.5
12 80.808 2.053 6,529.90 3.309 50.69 615.020 23.0
14 64.084 1.628 4,106.80 2.081 80.59 386.800 16.2
16 50.820 1.291 2,582.90 1.309 128.14 243.250 11.5
18 40.303 1.024 1,624.30 0.823 203.76 152.990 8.1
20 31.961 0.812 1,021.50 0.5176 324.00 96.210 5.7
22 25.347 0.644 642.70 0.3255 515.15 60.510 4.0
24 20.100 0.511 504.01 0.2047 819.21 38.050 2.8
26 15.940 0.405 254.01 0.1288 1,302.61 23.930 2.0
28 12.641 0.321 159.79 0.08097 2,071.22 15.050 1.4
30 10.025 0.255 100.50 0.05092 3,293.97 9.466 1.0
32 7.950 0.202 63.20 0.03203 5,236.66 5.952 0.70
34 6.304 0.160 39.74 0.02014 8,328.30 3.743 0.50
36 5.000 0.127 25.00 0.01267 13,238.83 2.355 0.35
38 3.965 0.101 15.72 0.00797 20,854.65 1.481 0.25
40 3.144 0.080 9.89 0.00501 33,175.94 0.931 0.17
Important Topics
(1) Galvanometers: (1) moving magnet, fixed coil; (2) moving coil, fixed magnet,
ammeter, voltmeter.
(2) Unit of quantity, coulomb.
(3) Unit of current, ampere.
(4) Unit of resistance, ohm.
(5) Unit of electromotive force, volt.
Exercises
Page 298
1. How will the resistance of 20 ft. of No. 22 German silver wire compare with
that of 10 ft. of No. 22 copper wire? Explain.
2. Where in a circuit is copper wire desirable? Where should German silver wire
be used?
3. Explain the action of the ammeter. Why does not the needle or coil swing the
full distance with a small current?
4. Why is a telegraph sounder more apt to work on a short line than upon a long
one?
Fig. 250.—The ammeter is connected in series
and the voltmeter in shunt.
5. Find the resistance of 15 miles of copper telephone wire No. 12. (See table p.
296.)
6. What will be the weight and resistance of 1,000 feet of No. 20 copper wire?
7. A storage battery sends 4 amperes of current through a plating solution. How
much silver will it deposit in 2 hours?
8. (a) Compare the diameters of No. 22 and No. 16 copper wire.
(b) Compare the lengths of the same wires giving 1 ohm resistance.
(c) What relation exists between (a) and (b)?
9. Why is an electric bell circuit usually open while a telegraph line circuit is
usually closed?
10. A copper wire and an iron wire of the same length are found to have the same
resistance. Which is thicker? Why?
11. Why are electric bells usually arranged in parallel instead of in series?
12. What would happen if a voltmeter were put in series in a line?
that of 10 ft. of No. 22 copper wire? Explain.
2. Where in a circuit is copper wire desirable? Where should German silver wire
be used?
3. Explain the action of the ammeter. Why does not the needle or coil swing the
full distance with a small current?
4. Why is a telegraph sounder more apt to work on a short line than upon a long
one?
Fig. 250.—The ammeter is connected in series
and the voltmeter in shunt.
5. Find the resistance of 15 miles of copper telephone wire No. 12. (See table p.
296.)
6. What will be the weight and resistance of 1,000 feet of No. 20 copper wire?
7. A storage battery sends 4 amperes of current through a plating solution. How
much silver will it deposit in 2 hours?
8. (a) Compare the diameters of No. 22 and No. 16 copper wire.
(b) Compare the lengths of the same wires giving 1 ohm resistance.
(c) What relation exists between (a) and (b)?
9. Why is an electric bell circuit usually open while a telegraph line circuit is
usually closed?
10. A copper wire and an iron wire of the same length are found to have the same
resistance. Which is thicker? Why?
11. Why are electric bells usually arranged in parallel instead of in series?
12. What would happen if a voltmeter were put in series in a line?
Page 299
(3) Ohm's Law and Electrical Circuits
271. Conditions Affecting Current Flow.—Sometimes over a long circuit one
cell will not work a telegraph sounder. In such a case, two, three, or more cells are
connected so that the zinc of one is joined to the copper plate of the other. When
connected in this way the cells are said to be in series (Fig. 251). In the figure A
represents a voltmeter. It is found that when cells are in series the E.M.F. of the
battery is the sum of the electromotive forces of the cells. An ammeter in the
circuit shows increased current as the cells are added. Hence if the resistance of
the circuit remains unchanged, the greater the E.M.F. the greater is the current
strength. In this respect, the movement of electricity in a circuit is similar to the
flow of water in a small pipe under pressure, as in the latter the flow of water
increases as the pressure becomes greater. The current in a circuit may also be
increased by lessening the resistance, since the current through a long wire is less
than that through a short one, just as the flow of water will be greater through a
short pipe than through a long one. To increase the current flowing in an electric
circuit, one may therefore either increase the E.M.F. or decrease the resistance.
272. Ohm's Law.—The relation between the
electromotive force applied to a circuit, its resistance,
and the current produced was discovered in 1827 by
George Ohm. Ohm's law, one of the most important
laws of electricity, states that, in any circuit, the
current in amperes equals the electromotive force in
volts divided by the resistance in ohms.
This principle is usually expressed thus:
Current intensity = electromotive force/resistance or
Fig. 251.—Diagram of
cells connected in Amperes = volts/ohms or I = E/R
series. 273. Resistance of
Conductors in
Series.—A study of the resistance of conductors
when alone and when grouped in various ways
is of importance since, the current flow through
any circuit is dependent upon its resistance. The Fig. 252.—The street cars
two most common methods of combining are connected in parallel
several conductors in a circuit are in series and with each other.
in parallel. Conductors are in series when all of
the current passes through each of the
271. Conditions Affecting Current Flow.—Sometimes over a long circuit one
cell will not work a telegraph sounder. In such a case, two, three, or more cells are
connected so that the zinc of one is joined to the copper plate of the other. When
connected in this way the cells are said to be in series (Fig. 251). In the figure A
represents a voltmeter. It is found that when cells are in series the E.M.F. of the
battery is the sum of the electromotive forces of the cells. An ammeter in the
circuit shows increased current as the cells are added. Hence if the resistance of
the circuit remains unchanged, the greater the E.M.F. the greater is the current
strength. In this respect, the movement of electricity in a circuit is similar to the
flow of water in a small pipe under pressure, as in the latter the flow of water
increases as the pressure becomes greater. The current in a circuit may also be
increased by lessening the resistance, since the current through a long wire is less
than that through a short one, just as the flow of water will be greater through a
short pipe than through a long one. To increase the current flowing in an electric
circuit, one may therefore either increase the E.M.F. or decrease the resistance.
272. Ohm's Law.—The relation between the
electromotive force applied to a circuit, its resistance,
and the current produced was discovered in 1827 by
George Ohm. Ohm's law, one of the most important
laws of electricity, states that, in any circuit, the
current in amperes equals the electromotive force in
volts divided by the resistance in ohms.
This principle is usually expressed thus:
Current intensity = electromotive force/resistance or
Fig. 251.—Diagram of
cells connected in Amperes = volts/ohms or I = E/R
series. 273. Resistance of
Conductors in
Series.—A study of the resistance of conductors
when alone and when grouped in various ways
is of importance since, the current flow through
any circuit is dependent upon its resistance. The Fig. 252.—The street cars
two most common methods of combining are connected in parallel
several conductors in a circuit are in series and with each other.
in parallel. Conductors are in series when all of
the current passes through each of the
Page 300
conductors in turn (Fig. 218), thus the cell, push-button, wires, and electric bell in
an electric-bell circuit are in series. Conductors are in parallel when they are so
connected that they are side by side and a part of the whole current goes through
each. None of the current that passes through one conductor can go through the
conductors in parallel with it. Thus the electric street cars are in parallel with each
other. (See Fig. 252.) It is easily seen that none of the current passing through one
car can go through any of the others. When the conductors are in series the
combined resistance is the sum of the several resistances. Thus in an electric-bell
circuit if the battery has a resistance of 1 ohm, the bell of 2 ohms, and the wire 1
ohm, the total resistance in the circuit is 4 ohms. When conductors are in parallel
the combined resistance is always less than the separate resistances. Just as a
crowd of people meets less resistance in leaving a building through several exits,
so electricity finds less resistance in moving from one point to another along
several parallel lines, than along one of the lines.
274. Resistance of Conductors in Parallel.—If three conductors of equal
resistance are in parallel, the combined resistance is just one-third the resistance
of each separately (Fig. 253). The rule that states the relation between the
combined resistance of conductors in parallel and the separate resistances is as
follows:The combined resistance of conductors in parallel is the reciprocal of the
sum of the reciprocals of the several resistances. For example, find the combined
resistance of three unequal resistances in parallel; the first being 4 ohms, the
second, 6 ohms, and third 3 ohms. The reciprocals of the three resistances are 1/4,
1/6, and 1/3. Their sum equals 6/24 + 4/24 + 8/24 = 18/24. The reciprocal of this
is 24/18 which equals 1-1/3 ohms, the combined resistance.
This rule may be understood better if we
consider the conductance of the conductors in
parallel. Since the conductance of a two ohm
wire is just one-half that of a one-ohm wire, we
say that the conductance of a body is inversely
as the resistance, or that it is the reciprocal of
the resistance. The conductance of the 4-, 6-,
and 3-ohm coils will therefore be respectively
1/4, 1/6, and 1/3, and since the combined
conductance is the sum of the several
Fig. 253.—The three conductances, the total conductance is 18/24.
conductors are connected in Also since this is the reciprocal of the total
parallel. resistance, the latter is 24/18 or 1-1/3 ohms.
When two or more conductors are connected in
parallel each one is said to be a shunt of the others. Many circuits are connected in
an electric-bell circuit are in series. Conductors are in parallel when they are so
connected that they are side by side and a part of the whole current goes through
each. None of the current that passes through one conductor can go through the
conductors in parallel with it. Thus the electric street cars are in parallel with each
other. (See Fig. 252.) It is easily seen that none of the current passing through one
car can go through any of the others. When the conductors are in series the
combined resistance is the sum of the several resistances. Thus in an electric-bell
circuit if the battery has a resistance of 1 ohm, the bell of 2 ohms, and the wire 1
ohm, the total resistance in the circuit is 4 ohms. When conductors are in parallel
the combined resistance is always less than the separate resistances. Just as a
crowd of people meets less resistance in leaving a building through several exits,
so electricity finds less resistance in moving from one point to another along
several parallel lines, than along one of the lines.
274. Resistance of Conductors in Parallel.—If three conductors of equal
resistance are in parallel, the combined resistance is just one-third the resistance
of each separately (Fig. 253). The rule that states the relation between the
combined resistance of conductors in parallel and the separate resistances is as
follows:The combined resistance of conductors in parallel is the reciprocal of the
sum of the reciprocals of the several resistances. For example, find the combined
resistance of three unequal resistances in parallel; the first being 4 ohms, the
second, 6 ohms, and third 3 ohms. The reciprocals of the three resistances are 1/4,
1/6, and 1/3. Their sum equals 6/24 + 4/24 + 8/24 = 18/24. The reciprocal of this
is 24/18 which equals 1-1/3 ohms, the combined resistance.
This rule may be understood better if we
consider the conductance of the conductors in
parallel. Since the conductance of a two ohm
wire is just one-half that of a one-ohm wire, we
say that the conductance of a body is inversely
as the resistance, or that it is the reciprocal of
the resistance. The conductance of the 4-, 6-,
and 3-ohm coils will therefore be respectively
1/4, 1/6, and 1/3, and since the combined
conductance is the sum of the several
Fig. 253.—The three conductances, the total conductance is 18/24.
conductors are connected in Also since this is the reciprocal of the total
parallel. resistance, the latter is 24/18 or 1-1/3 ohms.
When two or more conductors are connected in
parallel each one is said to be a shunt of the others. Many circuits are connected in
Page 301
shunt or in parallel. Fig. 254 represents four lamps in parallel. Incandescent lamps
in buildings are usually connected in parallel, while arc lamps are usually
connected in series. Fig. 255 represents four lamps in series.
Important Topics
1. Conditions affecting current flow, (a) E.M.F., (b) resistance.
2. Ohm's law, three forms for formula.
3. Resistance of conductors: (a) in series, (b) in parallel; how computed,
illustrations.
Fig. 255.—The four lamps are connected in
series.
Fig. 254.—The four lamps are connected in
parallel.
Exercises
1. What current flows through a circuit if its E.M.F. is 110 volts and the resistance
is 220 ohms?
2. A circuit contains four conductors in series with resistances of 10, 15, 6, and 9
ohms respectively. What current will flow through this circuit at 110 volts
pressure? What will be the resistance of these four conductors in parallel?
3. What is the combined resistance of 8 conductors in parallel if each is 220
ohms? What current will flow through these 8 conductors at 110 volts pressure?
4. What is the resistance of a circuit carrying 22 amperes, if the E.M.F. is 20
volts?
5. What E.M.F. will send 8 amperes of current through a circuit of 75 ohms
resistance?
6. How does the voltmeter differ from the ammeter?
7. How can one determine the resistance of a conductor?
in buildings are usually connected in parallel, while arc lamps are usually
connected in series. Fig. 255 represents four lamps in series.
Important Topics
1. Conditions affecting current flow, (a) E.M.F., (b) resistance.
2. Ohm's law, three forms for formula.
3. Resistance of conductors: (a) in series, (b) in parallel; how computed,
illustrations.
Fig. 255.—The four lamps are connected in
series.
Fig. 254.—The four lamps are connected in
parallel.
Exercises
1. What current flows through a circuit if its E.M.F. is 110 volts and the resistance
is 220 ohms?
2. A circuit contains four conductors in series with resistances of 10, 15, 6, and 9
ohms respectively. What current will flow through this circuit at 110 volts
pressure? What will be the resistance of these four conductors in parallel?
3. What is the combined resistance of 8 conductors in parallel if each is 220
ohms? What current will flow through these 8 conductors at 110 volts pressure?
4. What is the resistance of a circuit carrying 22 amperes, if the E.M.F. is 20
volts?
5. What E.M.F. will send 8 amperes of current through a circuit of 75 ohms
resistance?
6. How does the voltmeter differ from the ammeter?
7. How can one determine the resistance of a conductor?
Page 302
8. The resistance of a hot incandescent lamp is 100 ohms. The current used is 1.1
amperes. Find the E.M.F. applied.
9. What is the resistance of the wires in an electric heater if the current used is 10
amperes, the voltage being 110?
10. The resistance of 1000 ft. of No. 36 copper wire is 424 ohms. How many feet
should be used in winding a 200 ohms relay?
11. The resistance of No. 00 trolley wire is 0.80 ohm per 1000 ft. What is the
resistance of a line 1 mile long?
12. A wire has a resistance of 20 ohms. It is joined in parallel with another wire of
6 ohms, find their combined resistance.
13. The separate resistances of two incandescent lamps are 200 ohms and 70
ohms. What is their combined resistance when joined in parallel? When joined in
series?
(4) Methods of Grouping Cells and Measuring Resistance
275. Internal Resistance of a Voltaic Cell.—The current produced by a voltaic
cell is affected by the resistance that the current meets in passing from one plate
to another through the liquid of the cell. This is called the internal resistance of
the cell. A Daniell cell has several (1-5) ohms internal resistance. The resistance
of dry cells varies from less than 0.1 of an ohm when new to several ohms when
old. If cells are joined together their combined internal resistance depends upon
the method of grouping the cells.
276. Cells Grouped in Series and in Parallel.—When in series the copper or
carbon plate of one cell is joined to the zinc of another and so on. (See Fig. 251.)
The effect of connecting, say four cells, in series may be illustrated by taking four
cans of water, placed one above another. (See Fig. 256.) The combined water
pressure of the series is the sum of the several pressures of the cans of water,
while the opposition offered to the movement of a quantity of water through the
group of cans is the sum of the several resistances of the cans. In applying this
illustration to the voltaic cell, we make use of Ohm's law. Let E represent the
e.m.f. of a single cell, r the internal resistance of the cell, and R the external
resistance or the resistance of the rest of the circuit. Consider a group of cells in
series. If n represents the number of cells in series, then Ohm's law becomes
I = nE/(nr + R).
amperes. Find the E.M.F. applied.
9. What is the resistance of the wires in an electric heater if the current used is 10
amperes, the voltage being 110?
10. The resistance of 1000 ft. of No. 36 copper wire is 424 ohms. How many feet
should be used in winding a 200 ohms relay?
11. The resistance of No. 00 trolley wire is 0.80 ohm per 1000 ft. What is the
resistance of a line 1 mile long?
12. A wire has a resistance of 20 ohms. It is joined in parallel with another wire of
6 ohms, find their combined resistance.
13. The separate resistances of two incandescent lamps are 200 ohms and 70
ohms. What is their combined resistance when joined in parallel? When joined in
series?
(4) Methods of Grouping Cells and Measuring Resistance
275. Internal Resistance of a Voltaic Cell.—The current produced by a voltaic
cell is affected by the resistance that the current meets in passing from one plate
to another through the liquid of the cell. This is called the internal resistance of
the cell. A Daniell cell has several (1-5) ohms internal resistance. The resistance
of dry cells varies from less than 0.1 of an ohm when new to several ohms when
old. If cells are joined together their combined internal resistance depends upon
the method of grouping the cells.
276. Cells Grouped in Series and in Parallel.—When in series the copper or
carbon plate of one cell is joined to the zinc of another and so on. (See Fig. 251.)
The effect of connecting, say four cells, in series may be illustrated by taking four
cans of water, placed one above another. (See Fig. 256.) The combined water
pressure of the series is the sum of the several pressures of the cans of water,
while the opposition offered to the movement of a quantity of water through the
group of cans is the sum of the several resistances of the cans. In applying this
illustration to the voltaic cell, we make use of Ohm's law. Let E represent the
e.m.f. of a single cell, r the internal resistance of the cell, and R the external
resistance or the resistance of the rest of the circuit. Consider a group of cells in
series. If n represents the number of cells in series, then Ohm's law becomes
I = nE/(nr + R).
Page 303
Cells are grouped in series when large E.M.F. is required to
force a current through a large external resistance such as
through a long telegraph line. Cells are connected in parallel
when it is desired to send a large current through a small
external resistance. To connect cells in parallel all the copper
plates are joined and also all the zinc plates. (See Fig. 257.) To
illustrate the effect of this mode of grouping cells, suppose
several cans of water are placed side by side (Fig. 258). It is
easily seen that the pressure of the group is the same as that of a
single cell, while the resistance to the flow is less than that of a
single cell. Applying this reasoning to the electric circuit we
have by Ohm's law the formula for the current flow of a group
of
n cells arranged in parallel I = E/((r/n) + R).
Fig. 256.—
The four cans
exert four
times the
water
pressure that
one can will
exert.
force a current through a large external resistance such as
through a long telegraph line. Cells are connected in parallel
when it is desired to send a large current through a small
external resistance. To connect cells in parallel all the copper
plates are joined and also all the zinc plates. (See Fig. 257.) To
illustrate the effect of this mode of grouping cells, suppose
several cans of water are placed side by side (Fig. 258). It is
easily seen that the pressure of the group is the same as that of a
single cell, while the resistance to the flow is less than that of a
single cell. Applying this reasoning to the electric circuit we
have by Ohm's law the formula for the current flow of a group
of
n cells arranged in parallel I = E/((r/n) + R).
Fig. 256.—
The four cans
exert four
times the
water
pressure that
one can will
exert.
Page 304
Fig. 257.—Four cells connected in parallel.
Fig. 258.—The water pressure of the group in
parallel is the same as that of one.
277. Illustrative Problems.—Suppose that four cells are grouped in parallel,
each with an E.M.F. of 1.5 volts and an internal resistance of 2 ohms. What
current will flow in the circuit if the external resistance is 2.5 ohms? Substitute in
the formula for cells in parallel the values given above, and we have I = 1.5/(0.5 +
2.5) = 1.5/3 = 0.5 ampere. Suppose again that these four cells were grouped in
series with the same external resistance, substituting the values in the formula for
cells in series we have I = 4(1.5)/(4 × 2 + 2.5) = 6/10.5 = 0.57 ampere.
278. Volt-ammeter Method for Finding Resistance.—Measurements of the
resistance of conductors are often made. One of these methods depends upon an
application of Ohm's law. It is called the volt-ammeter method since it employs
both a voltmeter and an ammeter. If the conductor whose resistance is to be
measured is made a part of an electric circuit, being connected in series with the
ammeter and in shunt with the voltmeter, the resistance may easily be determined,
since R = E/I. (See Fig. 250.) If, for example, the difference in E.M.F., or as it is
often called, the fall of potential between the ends of the wire as read on the
voltmeter is 2 volts, and the current is 0.5 ampere, then the resistance of the wire
is 4 ohms. This method may be readily applied to find the resistance of any wire
that is a part of an electric circuit.
279. The Wheatstone Bridge.—To find the resistance of a separate wire or of an
electrical device another method devised by an Englishman named Wheatstone is
commonly employed. This method requires that three known resistances, a, b, c,
in addition to the unknown resistance x be taken. These four resistances are
arranged in the form of a parallelogram. (See Fig. 259.) A voltaic cell is joined to
the parallelogram at the extremities of one diagonal while a moving-coil
galvanometer is connected across the extremities of the other diagonal. The
known resistances are changed until when on pressing the keys at E and K no
current flows through the galvanometer. when this condition is reached, the four
resistances form a true proportion, thus a: b = c: x.
Since the values of a, b, and c are known, x is readily computed. Thus if a = 10, b
= 100, and c = 1.8 ohms, then x, the unknown resistance, equals 18 ohms, since
10: 100 = 1.8: 18. This method devised by Wheatstone may be employed to find
the resistance of a great variety of objects. It is the one most commonly employed
by scientists and practical electricians.
Fig. 258.—The water pressure of the group in
parallel is the same as that of one.
277. Illustrative Problems.—Suppose that four cells are grouped in parallel,
each with an E.M.F. of 1.5 volts and an internal resistance of 2 ohms. What
current will flow in the circuit if the external resistance is 2.5 ohms? Substitute in
the formula for cells in parallel the values given above, and we have I = 1.5/(0.5 +
2.5) = 1.5/3 = 0.5 ampere. Suppose again that these four cells were grouped in
series with the same external resistance, substituting the values in the formula for
cells in series we have I = 4(1.5)/(4 × 2 + 2.5) = 6/10.5 = 0.57 ampere.
278. Volt-ammeter Method for Finding Resistance.—Measurements of the
resistance of conductors are often made. One of these methods depends upon an
application of Ohm's law. It is called the volt-ammeter method since it employs
both a voltmeter and an ammeter. If the conductor whose resistance is to be
measured is made a part of an electric circuit, being connected in series with the
ammeter and in shunt with the voltmeter, the resistance may easily be determined,
since R = E/I. (See Fig. 250.) If, for example, the difference in E.M.F., or as it is
often called, the fall of potential between the ends of the wire as read on the
voltmeter is 2 volts, and the current is 0.5 ampere, then the resistance of the wire
is 4 ohms. This method may be readily applied to find the resistance of any wire
that is a part of an electric circuit.
279. The Wheatstone Bridge.—To find the resistance of a separate wire or of an
electrical device another method devised by an Englishman named Wheatstone is
commonly employed. This method requires that three known resistances, a, b, c,
in addition to the unknown resistance x be taken. These four resistances are
arranged in the form of a parallelogram. (See Fig. 259.) A voltaic cell is joined to
the parallelogram at the extremities of one diagonal while a moving-coil
galvanometer is connected across the extremities of the other diagonal. The
known resistances are changed until when on pressing the keys at E and K no
current flows through the galvanometer. when this condition is reached, the four
resistances form a true proportion, thus a: b = c: x.
Since the values of a, b, and c are known, x is readily computed. Thus if a = 10, b
= 100, and c = 1.8 ohms, then x, the unknown resistance, equals 18 ohms, since
10: 100 = 1.8: 18. This method devised by Wheatstone may be employed to find
the resistance of a great variety of objects. It is the one most commonly employed
by scientists and practical electricians.
Page 305
Fig. 259.—Diagram of
a Wheatstone bridge.
Important Topics
1. The internal resistance of voltaic cells.
2. Ohm's law applied to groups of cells. (a) Cells in series, (b) cells in parallel.
3. Measurement of resistance: (a) volt-ammeter method, (b) Wheatstone bridge
method.
Exercises
1. What is the resistance of an electric bell circuit where the E.M.F. is 3 volts and
the current is 0.6 ampere?
2. A telegraph wire is broken somewhere, the ends lying upon damp ground. If an
E.M.F. of 30 volts is applied from the ground to the wire and a current of 0.1 of an
ampere flows, what is the resistance of the part connected to the ammeter. (The
earth which completes the circuit from the end of the wire has very small
resistance.) Why?
3. How far away is the break in the wire if the latter has a resistance of 80 ohms to
the mile? Diagram.
4. What current will flow through a bell circuit of 8 ohms resistance if it contains
three cells in series each with an E.M.F. of 1.5 volts and an internal resistance of
1/3 ohm?
5. If the same three cells are connected in parallel on the same circuit what current
flows? Is the current in problem 4 or 5 the larger? Why?
a Wheatstone bridge.
Important Topics
1. The internal resistance of voltaic cells.
2. Ohm's law applied to groups of cells. (a) Cells in series, (b) cells in parallel.
3. Measurement of resistance: (a) volt-ammeter method, (b) Wheatstone bridge
method.
Exercises
1. What is the resistance of an electric bell circuit where the E.M.F. is 3 volts and
the current is 0.6 ampere?
2. A telegraph wire is broken somewhere, the ends lying upon damp ground. If an
E.M.F. of 30 volts is applied from the ground to the wire and a current of 0.1 of an
ampere flows, what is the resistance of the part connected to the ammeter. (The
earth which completes the circuit from the end of the wire has very small
resistance.) Why?
3. How far away is the break in the wire if the latter has a resistance of 80 ohms to
the mile? Diagram.
4. What current will flow through a bell circuit of 8 ohms resistance if it contains
three cells in series each with an E.M.F. of 1.5 volts and an internal resistance of
1/3 ohm?
5. If the same three cells are connected in parallel on the same circuit what current
flows? Is the current in problem 4 or 5 the larger? Why?
Page 306
6. If four cells each with 1.5 volts E.M.F. and an internal resistance of 0.4 ohm are
connected with a circuit having an external resistance of 0.8 ohm, what current
will the parallel connection give? The series connection? Which gives the larger
current? Why?
7. Four Daniell cells each having 1 volt E.M.F. and 3 ohms internal resistance are
connected in series with 2 telegraph sounders of 4 ohms each. The connecting
wires have 6 ohms resistance. Find the current intensity.
8. A battery of 2 cells arranged in series is used to ring a door bell. The E.M.F. of
each cell is 1.5 volts, internal resistance 0.3 ohm, and the resistance of the bell is
4 ohms. What is the current in amperes?
9. In the above problem find the current if the cells are connected in parallel.
connected with a circuit having an external resistance of 0.8 ohm, what current
will the parallel connection give? The series connection? Which gives the larger
current? Why?
7. Four Daniell cells each having 1 volt E.M.F. and 3 ohms internal resistance are
connected in series with 2 telegraph sounders of 4 ohms each. The connecting
wires have 6 ohms resistance. Find the current intensity.
8. A battery of 2 cells arranged in series is used to ring a door bell. The E.M.F. of
each cell is 1.5 volts, internal resistance 0.3 ohm, and the resistance of the bell is
4 ohms. What is the current in amperes?
9. In the above problem find the current if the cells are connected in parallel.
Page 307
CHAPTER XIII
THE CHEMICAL AND HEAT EFFECTS OF ELECTRIC CURRENTS
(1) The Chemical Effect of an Electric Current
280. Electroplating.—If two carbon rods (electric light carbons answer very
well) are placed in a solution of copper sulphate (Fig. 260) and then connected by
wires to the binding posts of an electric battery, one of the rods soon becomes
covered with a coating of metallic copper while bubbles of gas may be seen upon
the other carbon. If a solution of lead acetate is used in the same way a deposit of
metallic lead is secured, while a solution of silver nitrate gives silver.
Fig. 260.—Two carbons placed in a solution of
copper sulphate.
Fig. 261.—An electroplating bath.
This process of depositing metals upon the surface of solids by an electric current
is called electroplating. Everyone has seen electroplated articles such as silver
plated knives, forks, and spoons, and nickel-plated rods, handles, etc. Copper
electrotype plates such as are used in printing school books are made by this
process. In practical electroplating a solution of the metal to be deposited is
placed in a tank; across the top of this tank are placed copper rods to act as
conducting supports. From one of these rods, the cathode, objects to be plated are
hung so as to be immersed in the liquid. From other rods, the anodes, are hung
plates of the metal to be deposited. These are dissolved as the current deposits a
THE CHEMICAL AND HEAT EFFECTS OF ELECTRIC CURRENTS
(1) The Chemical Effect of an Electric Current
280. Electroplating.—If two carbon rods (electric light carbons answer very
well) are placed in a solution of copper sulphate (Fig. 260) and then connected by
wires to the binding posts of an electric battery, one of the rods soon becomes
covered with a coating of metallic copper while bubbles of gas may be seen upon
the other carbon. If a solution of lead acetate is used in the same way a deposit of
metallic lead is secured, while a solution of silver nitrate gives silver.
Fig. 260.—Two carbons placed in a solution of
copper sulphate.
Fig. 261.—An electroplating bath.
This process of depositing metals upon the surface of solids by an electric current
is called electroplating. Everyone has seen electroplated articles such as silver
plated knives, forks, and spoons, and nickel-plated rods, handles, etc. Copper
electrotype plates such as are used in printing school books are made by this
process. In practical electroplating a solution of the metal to be deposited is
placed in a tank; across the top of this tank are placed copper rods to act as
conducting supports. From one of these rods, the cathode, objects to be plated are
hung so as to be immersed in the liquid. From other rods, the anodes, are hung
plates of the metal to be deposited. These are dissolved as the current deposits a
Page 308
coating upon the articles, thus keeping the solution up to its proper strength. (See
Fig. 261.)
281. Electrolysis.—A solution from which a deposit is
made by an electric current is called an electrolyte.
The plates or other objects by which the current enters
or leaves the electrolyte are called the electrodes. The
electrode by which the current enters is called the
anode (an = in) while the electrode by which it leaves
is the cathode (cath = away). The process by which an
electric current decomposes a solution and deposits a
substance upon an electrode is called electrolysis. The
current always flows within the cell from anode to the
cathode. (See Fig. 262.) The metal goes with the
current and is found deposited upon the cathode.
282. Theory of Electrolysis.—The action going on in
an electrolytic cell has been carefully studied. The
theory of electrolysis, which is supported by much
experimental evidence, supposes that many of the
Fig. 262.—The current
molecules in a dilute solution of a substance "split up"
is carried through the
into two parts called "ions," one ion having a positive,
solution by ions.
the other a negative charge. In a dilute solution of
sulphuric acid, the positive ion is of hydrogen, while
the negative ion is the (SO4) or sulphion. These ions bearing electric charges are
believed to be the carriers of the electric current through the electrolyte.
The positive ions move with the current from the anode to the cathode, while the
negative ions apparently are repelled by the cathode and appear upon the anode.
Evidence of the accumulation of the two kinds of ions at the two electrodes is
furnished by the electrolysis of water, described below.
283. Electrolysis of Water.—Two glass tubes (Fig. 263), H and O, are attached at
the bottom to a horizontal glass tube. To the latter is also connected an upright
tube T. At the lower ends of H and O are inserted, fused in the glass, platinum
wires, A and C. The tubes are filled with a weak solution of sulphuric acid. The
tops of H and O are closed with stopcocks, T being open; a current of electricity is
sent in at A and out at C. A movement of the ions at once begins, the positive
hydrogen ions appearing at C. These accumulate as bubbles of hydrogen which
rise to the top of H and displace the liquid. At the same time bubbles of oxygen
appear at A. These rise in O and also displace the liquid which rises in T. After the
action has continued some time it may be noticed that the volume of hydrogen is
Fig. 261.)
281. Electrolysis.—A solution from which a deposit is
made by an electric current is called an electrolyte.
The plates or other objects by which the current enters
or leaves the electrolyte are called the electrodes. The
electrode by which the current enters is called the
anode (an = in) while the electrode by which it leaves
is the cathode (cath = away). The process by which an
electric current decomposes a solution and deposits a
substance upon an electrode is called electrolysis. The
current always flows within the cell from anode to the
cathode. (See Fig. 262.) The metal goes with the
current and is found deposited upon the cathode.
282. Theory of Electrolysis.—The action going on in
an electrolytic cell has been carefully studied. The
theory of electrolysis, which is supported by much
experimental evidence, supposes that many of the
Fig. 262.—The current
molecules in a dilute solution of a substance "split up"
is carried through the
into two parts called "ions," one ion having a positive,
solution by ions.
the other a negative charge. In a dilute solution of
sulphuric acid, the positive ion is of hydrogen, while
the negative ion is the (SO4) or sulphion. These ions bearing electric charges are
believed to be the carriers of the electric current through the electrolyte.
The positive ions move with the current from the anode to the cathode, while the
negative ions apparently are repelled by the cathode and appear upon the anode.
Evidence of the accumulation of the two kinds of ions at the two electrodes is
furnished by the electrolysis of water, described below.
283. Electrolysis of Water.—Two glass tubes (Fig. 263), H and O, are attached at
the bottom to a horizontal glass tube. To the latter is also connected an upright
tube T. At the lower ends of H and O are inserted, fused in the glass, platinum
wires, A and C. The tubes are filled with a weak solution of sulphuric acid. The
tops of H and O are closed with stopcocks, T being open; a current of electricity is
sent in at A and out at C. A movement of the ions at once begins, the positive
hydrogen ions appearing at C. These accumulate as bubbles of hydrogen which
rise to the top of H and displace the liquid. At the same time bubbles of oxygen
appear at A. These rise in O and also displace the liquid which rises in T. After the
action has continued some time it may be noticed that the volume of hydrogen is
Page 309
just twice that of the oxygen. This was to have been expected since the formula
for water is H2O. The nature of the gas in H or O may be tested by opening the
stopcock and allowing the gas to escape slowly. The hydrogen gas can be lighted
by a flame while the oxygen gas will cause a spark upon a piece of wood to glow
brightly, but does not burn itself.
284. Evidence that ions are necessary to conduct a
current in a liquid is furnished by the following
experiment. A quart jar is carefully cleaned, and half
filled with distilled water. Two pieces of zinc 5 cm.
square are soldered to pieces of rubber-insulated No. 14
copper wire. The zincs are placed in the distilled water
(Fig. 264) and the wires are connected to a 110 volt
circuit with a 16 candle-power incandescent lamp in
series with the cell, as in the figure. If the zincs have
been carefully cleansed and the water is pure, no current
flows as is shown by the lamp remaining dark. If a
minute quantity of sulphuric acid or of common salt is
placed in the water the lamp at once begins to glow. Ions
are now present in the liquid and conduct the current.
That some substances in solution do not form ions may
be shown by adding to another jar of pure water some
glycerine and some cane sugar, substances resembling
the acid and salt in external appearance but which do not
ionize when dissolved as is shown by the lamp remaining Fig. 263.-Electrolysis
dark after adding the glycerine and sugar. The acid and of water; oxygen
salt are of mineral origin while the glycerine and sugar collects in O,
are vegetable products. This experiment illustrates the hydrogen in H.
principle that the water will conduct only when it
contains ions.
285. Laws of Electrolysis.—These were discovered by
Faraday in 1833, and may be stated as follows: I. The
mass of a substance deposited by an electric current
from an electrolyte is proportional to the intensity of
current which passes through it.
II. The mass of any substance deposited by a current of
uniform intensity is directly proportional to the time the
current flows.
Fig. 264.—The
for water is H2O. The nature of the gas in H or O may be tested by opening the
stopcock and allowing the gas to escape slowly. The hydrogen gas can be lighted
by a flame while the oxygen gas will cause a spark upon a piece of wood to glow
brightly, but does not burn itself.
284. Evidence that ions are necessary to conduct a
current in a liquid is furnished by the following
experiment. A quart jar is carefully cleaned, and half
filled with distilled water. Two pieces of zinc 5 cm.
square are soldered to pieces of rubber-insulated No. 14
copper wire. The zincs are placed in the distilled water
(Fig. 264) and the wires are connected to a 110 volt
circuit with a 16 candle-power incandescent lamp in
series with the cell, as in the figure. If the zincs have
been carefully cleansed and the water is pure, no current
flows as is shown by the lamp remaining dark. If a
minute quantity of sulphuric acid or of common salt is
placed in the water the lamp at once begins to glow. Ions
are now present in the liquid and conduct the current.
That some substances in solution do not form ions may
be shown by adding to another jar of pure water some
glycerine and some cane sugar, substances resembling
the acid and salt in external appearance but which do not
ionize when dissolved as is shown by the lamp remaining Fig. 263.-Electrolysis
dark after adding the glycerine and sugar. The acid and of water; oxygen
salt are of mineral origin while the glycerine and sugar collects in O,
are vegetable products. This experiment illustrates the hydrogen in H.
principle that the water will conduct only when it
contains ions.
285. Laws of Electrolysis.—These were discovered by
Faraday in 1833, and may be stated as follows: I. The
mass of a substance deposited by an electric current
from an electrolyte is proportional to the intensity of
current which passes through it.
II. The mass of any substance deposited by a current of
uniform intensity is directly proportional to the time the
current flows.
Fig. 264.—The
Page 310
current passes only These laws have been used as a basis for defining and
when ions are measuring the unit of current flow, the ampere. (See Art.
present in the liquid. 264.)
286. Instances of Electrolysis.—(a) Medicines,
especially those containing a mineral substance, are sometimes introduced into
the human body by electrolysis. (b) Water and gas pipes are sometimes much
weakened by the effects of electric currents in the earth, especially return currents
from street railways. Such currents use the metal pipes as a conductor. At the
place where the current leaves the metal and enters the ground, it removes
metallic ions from the pipe. This process continuing, the pipe becomes weakened
and at length breaks. (c) Copper is purified by the use of electric currents that
remove the copper from ore or from other metals and deposit it upon electrodes.
Electrolytic copper is the purest known. (d) Aluminum is obtained by the use of
large currents of electricity that first heat the material used until it melts and then
deposit the metal from the fluid material by electrolysis. These results are called
chemical effects of the current since by the use of electric currents substances are
changed chemically, that is, they are separated into different chemical substances.
Important Topics
1. Electrolysis, electroplating, anode, cathode, ion.
2. Theory of electrolysis—evidence: (a) electrolysis of water; (b) conductivity of
acid and water.
3. Laws of electrolysis.
4. Practical use of electrolysis.
Exercises
1. A dynamo has an E.M.F. of 10 volts. What is the resistance in the circuit when
20 amperes are flowing?
2. How much silver will be deposited in an hour by this current?
3. Name five objects outside of the laboratory that have been acted upon by
electrolysis. How in each case?
4. Why is table ware silver plated? Why are many iron objects nickel plated?
5. How is the electrolysis of water pipes prevented?
when ions are measuring the unit of current flow, the ampere. (See Art.
present in the liquid. 264.)
286. Instances of Electrolysis.—(a) Medicines,
especially those containing a mineral substance, are sometimes introduced into
the human body by electrolysis. (b) Water and gas pipes are sometimes much
weakened by the effects of electric currents in the earth, especially return currents
from street railways. Such currents use the metal pipes as a conductor. At the
place where the current leaves the metal and enters the ground, it removes
metallic ions from the pipe. This process continuing, the pipe becomes weakened
and at length breaks. (c) Copper is purified by the use of electric currents that
remove the copper from ore or from other metals and deposit it upon electrodes.
Electrolytic copper is the purest known. (d) Aluminum is obtained by the use of
large currents of electricity that first heat the material used until it melts and then
deposit the metal from the fluid material by electrolysis. These results are called
chemical effects of the current since by the use of electric currents substances are
changed chemically, that is, they are separated into different chemical substances.
Important Topics
1. Electrolysis, electroplating, anode, cathode, ion.
2. Theory of electrolysis—evidence: (a) electrolysis of water; (b) conductivity of
acid and water.
3. Laws of electrolysis.
4. Practical use of electrolysis.
Exercises
1. A dynamo has an E.M.F. of 10 volts. What is the resistance in the circuit when
20 amperes are flowing?
2. How much silver will be deposited in an hour by this current?
3. Name five objects outside of the laboratory that have been acted upon by
electrolysis. How in each case?
4. Why is table ware silver plated? Why are many iron objects nickel plated?
5. How is the electrolysis of water pipes prevented?
Page 311
6. Two grams of silver are to be deposited on a spoon by a current of 1 ampere.
Find the time required.
7. How long will it take to deposit 20 g. of silver in an electroplating bath if a
current of 20 amperes is used?
8. If 1000 g. of silver are deposited on the cathode of an electrolytic reduction
plant in 10 minutes, what is the current intensity employed?
(2) The Storage Battery and Electric Power
287. Differences Between Voltaic and Storage Cells. Voltaic cells in which
electric currents are produced by the chemical action between metal plates and an
electrolyte are often called primary batteries. In voltaic cells one or both plates
and the electrolyte are used up or lose their chemical energy in producing the
current and after a time need to be replaced by new material, the chemical energy
of the electrolyte and of one of the plates having been transformed into electrical
energy.
A different proceeding obtains with another type of cell. This is called a storage
battery, or an accumulator. In these cells, the same plates and electrolyte are used
without change for extended periods, sometimes for a number of years. For this
reason storage batteries have displaced many other types of cells, and they are
now used (a) to operate many telephone, telegraph, and fire-alarm circuits, (b) to
work the spark coils of gas and gasoline engines, (c) to help carry the "peak" load
upon lighting and power circuits and (d) to furnish power for electric automobiles.
Since a storage battery can deliver an electric current only after an electric current
from an outside source has first been sent through it, they are often called
secondary batteries.
288. Construction and Action of a Storage Cell.—The common type of storage
cells consists of a number of perforated plates made of an alloy of lead and a little
antimony. (See Figs. 265, 266, 267.) Into the perforations is pressed a paste of red
lead and litharge mixed with sulphuric acid. The plates are placed in a strong
solution (20 to 25 per cent.) of sulphuric acid. The plates are now ready to be
charged. This is accomplished by sending a direct current from an electric
generator through the cell. The hydrogen ions are moved by the current to one set
of plates and change the paste to spongy metallic lead. The sulphions move to the
other set of plates and change the paste to lead oxide. This electrolytic action
causes the two plates to become quite different chemically so that when the cell is
fully charged it is like a voltaic cell, in having plates that are different chemically.
It has, when fully charged, an E.M.F. of about 2.2 volts. The several plates of a
Find the time required.
7. How long will it take to deposit 20 g. of silver in an electroplating bath if a
current of 20 amperes is used?
8. If 1000 g. of silver are deposited on the cathode of an electrolytic reduction
plant in 10 minutes, what is the current intensity employed?
(2) The Storage Battery and Electric Power
287. Differences Between Voltaic and Storage Cells. Voltaic cells in which
electric currents are produced by the chemical action between metal plates and an
electrolyte are often called primary batteries. In voltaic cells one or both plates
and the electrolyte are used up or lose their chemical energy in producing the
current and after a time need to be replaced by new material, the chemical energy
of the electrolyte and of one of the plates having been transformed into electrical
energy.
A different proceeding obtains with another type of cell. This is called a storage
battery, or an accumulator. In these cells, the same plates and electrolyte are used
without change for extended periods, sometimes for a number of years. For this
reason storage batteries have displaced many other types of cells, and they are
now used (a) to operate many telephone, telegraph, and fire-alarm circuits, (b) to
work the spark coils of gas and gasoline engines, (c) to help carry the "peak" load
upon lighting and power circuits and (d) to furnish power for electric automobiles.
Since a storage battery can deliver an electric current only after an electric current
from an outside source has first been sent through it, they are often called
secondary batteries.
288. Construction and Action of a Storage Cell.—The common type of storage
cells consists of a number of perforated plates made of an alloy of lead and a little
antimony. (See Figs. 265, 266, 267.) Into the perforations is pressed a paste of red
lead and litharge mixed with sulphuric acid. The plates are placed in a strong
solution (20 to 25 per cent.) of sulphuric acid. The plates are now ready to be
charged. This is accomplished by sending a direct current from an electric
generator through the cell. The hydrogen ions are moved by the current to one set
of plates and change the paste to spongy metallic lead. The sulphions move to the
other set of plates and change the paste to lead oxide. This electrolytic action
causes the two plates to become quite different chemically so that when the cell is
fully charged it is like a voltaic cell, in having plates that are different chemically.
It has, when fully charged, an E.M.F. of about 2.2 volts. The several plates of a
Page 312
cell being in parallel and close together, the cell has but small internal resistance.
Consequently a large current is available.
Fig. 265.—The positive plate of a storage cell.
Fig. 266.—The negative plate of a storage cell.
Fig. 267.—A complete storage cell.
Fig. 268.
About 75 per cent. of the energy put into the storage cell in charging can be
obtained upon discharging. Therefore the efficiency of a good storage cell is about
75 per cent. Fig. 268 represents a storage battery connected to charging and
discharging circuits. The lower is the charging circuit. It contains a dynamo and a
resistance (neither of which are shown in the figure) to control the current sent
into the cell. The charging current enters the positive pole and leaves by the
negative pole. The current produced by the cell, however, flows in the opposite
direction through it, that is, out from the positive and in at the negative pole. This
current may be controlled by a suitable resistance and measured by an ammeter.
Storage cells have several advantages: (a) They can be charged and discharged a
great many times before the material placed in the perforations in the plates falls
out. (b) The electrical energy used in charging the plates costs less than the plates
and electrolyte of voltaic cells. (c) Charging storage cells takes much less labor
Consequently a large current is available.
Fig. 265.—The positive plate of a storage cell.
Fig. 266.—The negative plate of a storage cell.
Fig. 267.—A complete storage cell.
Fig. 268.
About 75 per cent. of the energy put into the storage cell in charging can be
obtained upon discharging. Therefore the efficiency of a good storage cell is about
75 per cent. Fig. 268 represents a storage battery connected to charging and
discharging circuits. The lower is the charging circuit. It contains a dynamo and a
resistance (neither of which are shown in the figure) to control the current sent
into the cell. The charging current enters the positive pole and leaves by the
negative pole. The current produced by the cell, however, flows in the opposite
direction through it, that is, out from the positive and in at the negative pole. This
current may be controlled by a suitable resistance and measured by an ammeter.
Storage cells have several advantages: (a) They can be charged and discharged a
great many times before the material placed in the perforations in the plates falls
out. (b) The electrical energy used in charging the plates costs less than the plates
and electrolyte of voltaic cells. (c) Charging storage cells takes much less labor
Page 313
than replacing the electrolyte and plates of voltaic cells. (d) Storage cells produce
larger currents than voltaic cells. The two principal disadvantages of storage cells
are that (a) they are very heavy, and (b) their initial cost is considerable.
Fig. 269.—The Edison storage cell.
Fig. 270.—The plates of the Edison storage
cell.
289. The Edison storage cell (Figs. 269 and 270) has plates of iron and nickel
oxide. The electrolyte is a strong solution of potassium hydroxide. These cells are
lighter than lead cells of the same capacity and they are claimed to have a longer
life.
290. Energy and Power of a Storage Cell.—In a storage cell, the electrical
energy of the charging current is transformed into chemical energy by the action
of electrolysis. It is this chemical energy that is transformed into the energy of the
electric current when the cell is discharged. The capacity of storage cells is rated
in "ampere hours," a 40 ampere hour cell being capable of producing a current of
1 ampere for 40 hours, or 5 amperes for 8 hours, etc. The production and
extensive use of electric currents have made necessary accurate methods for
measuring the energy and power of these currents. To illustrate how this is
accomplished, let us imagine an electric circuit as represented in Fig. 268. Here
four storage cells in series have an E.M.F. of 8 volts and in accordance with
larger currents than voltaic cells. The two principal disadvantages of storage cells
are that (a) they are very heavy, and (b) their initial cost is considerable.
Fig. 269.—The Edison storage cell.
Fig. 270.—The plates of the Edison storage
cell.
289. The Edison storage cell (Figs. 269 and 270) has plates of iron and nickel
oxide. The electrolyte is a strong solution of potassium hydroxide. These cells are
lighter than lead cells of the same capacity and they are claimed to have a longer
life.
290. Energy and Power of a Storage Cell.—In a storage cell, the electrical
energy of the charging current is transformed into chemical energy by the action
of electrolysis. It is this chemical energy that is transformed into the energy of the
electric current when the cell is discharged. The capacity of storage cells is rated
in "ampere hours," a 40 ampere hour cell being capable of producing a current of
1 ampere for 40 hours, or 5 amperes for 8 hours, etc. The production and
extensive use of electric currents have made necessary accurate methods for
measuring the energy and power of these currents. To illustrate how this is
accomplished, let us imagine an electric circuit as represented in Fig. 268. Here
four storage cells in series have an E.M.F. of 8 volts and in accordance with
Page 314
Ohm's law produce a current of 2 amperes through a resistance in the circuit of 4
ohms. Now the work done or energy expended by the current in passing through
the resistance between the points M and N depends upon three factors (1) the
E.M.F. or potential difference; (2) the current intensity and (3) the time. The
energy is measured by their product. That is, electrical energy = potential
difference × current intensity × time. This represents the electrical energy in
joules, or
Joules = volts × amperes × seconds, or
j = E × I × t.
In the circuit represented in Fig. 268 the energy expended between the points M
and N in 1 minute (60 seconds) is 8 × 2 × 60 = 960 joules.
291. Electric Power.—Since power refers to the time rate at which work is done
or energy expended, it may be computed by dividing the electrical energy by the
time, or the electrical power = volts × amperes. The power of 1 joule per second
is called a watt. Therefore,
Watts = volts × amperes, or
Watts = E × I.
Other units of power are the kilowatt = 1000 watts and the horse-power = 746
watts. In the example given in Art. 290 the power of the current is 8 × 2 = 16
watts, or if the energy of the current expended between the joints M and N were
converted into mechanical horse-power it would equal 16/746 of a horse-power.
Electrical energy is usually sold by the kilowatt-hour, or the amount of electrical
energy that would exert a power of 1000 watts for one hour, or of 100 watts for 10
hours, or of 50 watts for 20 hours, etc.
Important Topics
1. The storage battery, its construction, electrolyte, action, uses, advantages,
disadvantages.
2. Electric energy, unit value, how computed?
3. Electric power, three units, value, how computed, how sold?
Exercises
1. In what three respects are voltaic and storage cells alike? In what two ways
different?
ohms. Now the work done or energy expended by the current in passing through
the resistance between the points M and N depends upon three factors (1) the
E.M.F. or potential difference; (2) the current intensity and (3) the time. The
energy is measured by their product. That is, electrical energy = potential
difference × current intensity × time. This represents the electrical energy in
joules, or
Joules = volts × amperes × seconds, or
j = E × I × t.
In the circuit represented in Fig. 268 the energy expended between the points M
and N in 1 minute (60 seconds) is 8 × 2 × 60 = 960 joules.
291. Electric Power.—Since power refers to the time rate at which work is done
or energy expended, it may be computed by dividing the electrical energy by the
time, or the electrical power = volts × amperes. The power of 1 joule per second
is called a watt. Therefore,
Watts = volts × amperes, or
Watts = E × I.
Other units of power are the kilowatt = 1000 watts and the horse-power = 746
watts. In the example given in Art. 290 the power of the current is 8 × 2 = 16
watts, or if the energy of the current expended between the joints M and N were
converted into mechanical horse-power it would equal 16/746 of a horse-power.
Electrical energy is usually sold by the kilowatt-hour, or the amount of electrical
energy that would exert a power of 1000 watts for one hour, or of 100 watts for 10
hours, or of 50 watts for 20 hours, etc.
Important Topics
1. The storage battery, its construction, electrolyte, action, uses, advantages,
disadvantages.
2. Electric energy, unit value, how computed?
3. Electric power, three units, value, how computed, how sold?
Exercises
1. In what three respects are voltaic and storage cells alike? In what two ways
different?
Page 315
2. Name the four advantages of storage cells in the order of their importance.
Give your reasons for choosing this order.
3. Why are dry cells more suitable for operating a door-bell circuit, than a storage
battery? Give two reasons.
4. The current for a city telephone system is provided by a storage battery. Why is
this better than dry cells at each telephone?
5. An incandescent lamp takes 0.5 ampere at 110 volts. What power is required to
operate it? How much energy will it transform in 1 minute?
6. How long would it take for this lamp to use a kilowatt hour of energy?
7. A street car used 100 amperes at 600 volts pressure. What power was delivered
to it? Express also in kilowatts and horse-power.
8. An electric toaster takes 5 amperes at 110 volts. If it toasts a slice of bread in 2
minutes, what is the cost at 10 cents a kilowatt hour?
9. An electric flat iron takes 5 amperes at 110 volts. Find the cost of using it for 2
hours at 12 cents a kilowatt hour.
10. A 1/4 kilowatt motor is used to run a washing-machine for 5 hours. What is
the expense for this power at 10 cents a kilowatt hour?
11. What is the efficiency of a motor that takes 7390 watts and develops 9 horse-
power?
12. How many horse-power are there in a water-fall 212 ft. high over which flows
800 cu. ft. of water per second? Express this power in kilowatts.
13. What horse-power must be applied to a dynamo having an efficiency of go per
cent. if it is to light 20 arc lamps in series, each taking 10 amperes at 60 volts?
(3) The Heat Effect of Electric Currents
292. The Production of Heat by an Electric Current.—When no chemical or
mechanical work is done by an electric current its energy is employed in
overcoming the resistance of the conducting circuit and is transformed into heat.
This effect has many practical applications and some disadvantages. Many
devices employ the heating effect of electric currents, (a) the electric furnace, (b)
electric lights, (c) heating coils for street cars, (d) devices about the home, as flat
irons, toasters, etc. Sometimes the heat produced by an electric current in the
wires of a device such as a transformer is so large in amount that especial means
of cooling are employed. Unusually heavy currents have been known to melt the
Give your reasons for choosing this order.
3. Why are dry cells more suitable for operating a door-bell circuit, than a storage
battery? Give two reasons.
4. The current for a city telephone system is provided by a storage battery. Why is
this better than dry cells at each telephone?
5. An incandescent lamp takes 0.5 ampere at 110 volts. What power is required to
operate it? How much energy will it transform in 1 minute?
6. How long would it take for this lamp to use a kilowatt hour of energy?
7. A street car used 100 amperes at 600 volts pressure. What power was delivered
to it? Express also in kilowatts and horse-power.
8. An electric toaster takes 5 amperes at 110 volts. If it toasts a slice of bread in 2
minutes, what is the cost at 10 cents a kilowatt hour?
9. An electric flat iron takes 5 amperes at 110 volts. Find the cost of using it for 2
hours at 12 cents a kilowatt hour.
10. A 1/4 kilowatt motor is used to run a washing-machine for 5 hours. What is
the expense for this power at 10 cents a kilowatt hour?
11. What is the efficiency of a motor that takes 7390 watts and develops 9 horse-
power?
12. How many horse-power are there in a water-fall 212 ft. high over which flows
800 cu. ft. of water per second? Express this power in kilowatts.
13. What horse-power must be applied to a dynamo having an efficiency of go per
cent. if it is to light 20 arc lamps in series, each taking 10 amperes at 60 volts?
(3) The Heat Effect of Electric Currents
292. The Production of Heat by an Electric Current.—When no chemical or
mechanical work is done by an electric current its energy is employed in
overcoming the resistance of the conducting circuit and is transformed into heat.
This effect has many practical applications and some disadvantages. Many
devices employ the heating effect of electric currents, (a) the electric furnace, (b)
electric lights, (c) heating coils for street cars, (d) devices about the home, as flat
irons, toasters, etc. Sometimes the heat produced by an electric current in the
wires of a device such as a transformer is so large in amount that especial means
of cooling are employed. Unusually heavy currents have been known to melt the
Page 316
conducting wires of circuits and electrical devices. Hence all circuits for electric
power as well as many others that ordinarily carry small currents are protected by
fuses. An electric fuse is a short piece of wire that will melt and break the circuit
if the current exceeds a determined value. The fuse wire is usually enclosed in an
incombustible holder. Fuse wire is frequently made of lead or of an alloy of lead
and other easily fusible metals. (See Figs. 271 and 272.)
Fig. 271.—A type of enclosed fuse.
Fig. 272.—A link fuse (above); plug fuses
(below).
293. Heat Developed in a Conductor.—A rule for computing the amount of heat
produced in an electric circuit by a given current has been accurately determined
by experiment. It has been found that 1 calorie of heat (Art. 142), is produced by
an expenditure of 4.2 joules of electrical (or other) energy. In other words, 1 joule
will produce 1/4.2 or 0.24 calorie. Now the number of joules of electrical energy
in an electric circuit is expressed by the following formula:
Joules = volts × amperes × seconds, or since 1 joule = 0.24 calorie,
Calories = volts × amperes × seconds × 0.24 or
H = EI × t × 0.24 (1)
By Ohm's law, I = E/R or E = I × R, substituting in equation (1) IR for its equal E
we have
H = I2R × t × 0.24 (2)
Also since I = E/R substitute E/R for I in equation (1) and we have
H = E2/R t × 0.24 (3)
To illustrate the use of these formulas by a problem suppose that a current of 10
amperes is flowing in a circuit having a resistance of 11 ohms, for 1 minute. The
heat produced will be by formula (2) = (10)2 × 11 × 60 × 0.24 equals 15,840
calories.
power as well as many others that ordinarily carry small currents are protected by
fuses. An electric fuse is a short piece of wire that will melt and break the circuit
if the current exceeds a determined value. The fuse wire is usually enclosed in an
incombustible holder. Fuse wire is frequently made of lead or of an alloy of lead
and other easily fusible metals. (See Figs. 271 and 272.)
Fig. 271.—A type of enclosed fuse.
Fig. 272.—A link fuse (above); plug fuses
(below).
293. Heat Developed in a Conductor.—A rule for computing the amount of heat
produced in an electric circuit by a given current has been accurately determined
by experiment. It has been found that 1 calorie of heat (Art. 142), is produced by
an expenditure of 4.2 joules of electrical (or other) energy. In other words, 1 joule
will produce 1/4.2 or 0.24 calorie. Now the number of joules of electrical energy
in an electric circuit is expressed by the following formula:
Joules = volts × amperes × seconds, or since 1 joule = 0.24 calorie,
Calories = volts × amperes × seconds × 0.24 or
H = EI × t × 0.24 (1)
By Ohm's law, I = E/R or E = I × R, substituting in equation (1) IR for its equal E
we have
H = I2R × t × 0.24 (2)
Also since I = E/R substitute E/R for I in equation (1) and we have
H = E2/R t × 0.24 (3)
To illustrate the use of these formulas by a problem suppose that a current of 10
amperes is flowing in a circuit having a resistance of 11 ohms, for 1 minute. The
heat produced will be by formula (2) = (10)2 × 11 × 60 × 0.24 equals 15,840
calories.
Page 317
Fig. 273.—A carbon filament incandescent
lamp.
Fig. 274.—A tungsten lamp.
294. The Incandescent Lamp.—One of the most common devices employing the
heat effect of an electric current is the incandescent lamp. (See Fig. 273.) In this
lamp the current is sent through a carbon filament, which is heated to
incandescence. In order to keep the filament from burning as well as to prevent
loss of heat by convection, it is placed in a glass bulb from which the air is
exhausted. Two platinum wires fused in the glass connect the carbon filament
with the grooved rim and the end piece of the base. The end piece and rim
connect with the socket so that an electric current may flow through the filament
of the lamp. The carbon incandescent lamp has a low efficiency. It takes 0.5
ampere of current at 110 volts or in other words it requires 55 watts to cause a 16-
candle-power lamp to glow brightly, hence 1 candle power in this lamp takes
55/16 = 3.43 watts.
The efficiency of electric lamps is measured by the number of watts per candle
power. This is a peculiar use of the term efficiency, as the larger the number the
less efficient is the lamp. More efficient lamps have been devised with filaments
of the metals tantalum and tungsten (Fig. 274). These give a whiter light than do
carbon lamps, and consume but about 1.25 watts per candle power.
Comparative "Efficiency" of Electric Lamps
Watts per candle Watts per candle
Name of lamp Name of lamp
power power
Carbon filament 3 to 4 Arc lamp 0.5 to 0.8
lamp.
Fig. 274.—A tungsten lamp.
294. The Incandescent Lamp.—One of the most common devices employing the
heat effect of an electric current is the incandescent lamp. (See Fig. 273.) In this
lamp the current is sent through a carbon filament, which is heated to
incandescence. In order to keep the filament from burning as well as to prevent
loss of heat by convection, it is placed in a glass bulb from which the air is
exhausted. Two platinum wires fused in the glass connect the carbon filament
with the grooved rim and the end piece of the base. The end piece and rim
connect with the socket so that an electric current may flow through the filament
of the lamp. The carbon incandescent lamp has a low efficiency. It takes 0.5
ampere of current at 110 volts or in other words it requires 55 watts to cause a 16-
candle-power lamp to glow brightly, hence 1 candle power in this lamp takes
55/16 = 3.43 watts.
The efficiency of electric lamps is measured by the number of watts per candle
power. This is a peculiar use of the term efficiency, as the larger the number the
less efficient is the lamp. More efficient lamps have been devised with filaments
of the metals tantalum and tungsten (Fig. 274). These give a whiter light than do
carbon lamps, and consume but about 1.25 watts per candle power.
Comparative "Efficiency" of Electric Lamps
Watts per candle Watts per candle
Name of lamp Name of lamp
power power
Carbon filament 3 to 4 Arc lamp 0.5 to 0.8
Page 318
Metallized
2.5 Mercury arc 0.6
carbon
Tantalum 2.0 Flaming arc 0.4
Nitrogen-filled
Tungsten 1.0 to 1.5 0.6 to 0.7
tungsten
Incandescent lamps are connected in parallel (see Fig. 254) to wires that are kept
at a constant difference of potential of 110 or 115 volts. It is customary to place
not more than twelve lamps upon one circuit, each circuit being protected by a
fuse and controlled by one or more switches.
295. The Arc Light.—The electric arc light (see Fig. 275) is extensively used for
lighting large rooms, also in stereopticons and motion picture machines. The light
is intense, varying from 500 to 1700 candle power. The so-called mean spherical
candle power of the arc light is about 510. The candle power in the direction of
greatest intensity is about 1200. It is produced at an expenditure of about 500
watts. It is therefore more efficient than the incandescent lamp, often taking less
than 0.5 watt per candle power produced. The arc light was first devised by Sir
Humphrey Davy in 1809, who used two pieces of charcoal connected to 2000
voltaic cells. The arc light requires so much power that its production by voltaic
cells is very expensive. Consequently it did not come into common use until the
dynamo had been perfected. Fig. 276 shows the appearance of the two carbons in
an arc light. If a direct current is used the positive carbon is heated more intensely,
and gives out the greater part of the light. The positive carbon is consumed about
twice as fast as the negative and its end is concave, the negative remaining
pointed.
2.5 Mercury arc 0.6
carbon
Tantalum 2.0 Flaming arc 0.4
Nitrogen-filled
Tungsten 1.0 to 1.5 0.6 to 0.7
tungsten
Incandescent lamps are connected in parallel (see Fig. 254) to wires that are kept
at a constant difference of potential of 110 or 115 volts. It is customary to place
not more than twelve lamps upon one circuit, each circuit being protected by a
fuse and controlled by one or more switches.
295. The Arc Light.—The electric arc light (see Fig. 275) is extensively used for
lighting large rooms, also in stereopticons and motion picture machines. The light
is intense, varying from 500 to 1700 candle power. The so-called mean spherical
candle power of the arc light is about 510. The candle power in the direction of
greatest intensity is about 1200. It is produced at an expenditure of about 500
watts. It is therefore more efficient than the incandescent lamp, often taking less
than 0.5 watt per candle power produced. The arc light was first devised by Sir
Humphrey Davy in 1809, who used two pieces of charcoal connected to 2000
voltaic cells. The arc light requires so much power that its production by voltaic
cells is very expensive. Consequently it did not come into common use until the
dynamo had been perfected. Fig. 276 shows the appearance of the two carbons in
an arc light. If a direct current is used the positive carbon is heated more intensely,
and gives out the greater part of the light. The positive carbon is consumed about
twice as fast as the negative and its end is concave, the negative remaining
pointed.
Page 319
Fig. 275.—An electric arc light.
Fig. 276.—The appearance of a pair of used
carbons.
With alternating currents, the rods are equally consumed and produce equal
amounts of light. In the stereopticon, the carbons are usually placed at right angles
as in Fig. 277. In the stereopticon as well as in outdoor lighting the direct current
is more effective, although the alternating current is often used, since the latter
can be produced and distributed more cheaply than can direct currents. In arc
lamps, placing an inner glass globe (Fig. 278) about the carbons, decreases the
consumption of the carbons materially. The carbon rods of enclosed arc lamps
often last 60 to 100 hours.
Fig. 277.—A right-angle electric arc lamp for a
stereopticon.
Fig. 278.—An enclosed arc lamp.
Fig. 276.—The appearance of a pair of used
carbons.
With alternating currents, the rods are equally consumed and produce equal
amounts of light. In the stereopticon, the carbons are usually placed at right angles
as in Fig. 277. In the stereopticon as well as in outdoor lighting the direct current
is more effective, although the alternating current is often used, since the latter
can be produced and distributed more cheaply than can direct currents. In arc
lamps, placing an inner glass globe (Fig. 278) about the carbons, decreases the
consumption of the carbons materially. The carbon rods of enclosed arc lamps
often last 60 to 100 hours.
Fig. 277.—A right-angle electric arc lamp for a
stereopticon.
Fig. 278.—An enclosed arc lamp.
Page 320
The reason why an open arc lamp needs to be "retrimmed" oftener than the
enclosed lamp, that is, have new carbons placed in it, is because the carbons
"burn" freely, that is unite with the oxygen of the air. In the enclosed arc lamp, the
supply of oxygen in the inner globe is limited and is soon consumed, therefore the
carbons last many times longer in such lamps.
Some carbon rods have soft cores containing calcium salts. These vaporize in the
arc producing the flaming arc light of a bright yellow color, and give more light
than the ordinary lamp.
Important Topics
1. Heat effects of electric currents, uses and applications.
2. Computation of the heat developed in a circuit. Three formulas.
3. Electric lamps; incandescent and arc; construction, uses, efficiency.
Exercises
1. Sketch a circuit containing 10 incandescent lamps in parallel. If each lamp
when hot has a resistance of 220 ohms, and the E.M.F. is 100 volts, what current
will flow?
2. What will it cost to use these lights for 3 hours a day for 30 days at 10 cents a
kilowatt hour?
3. How much heat will these lamps produce per minute?
4. How could you connect 110-volt lamps to a street car circuit of 660 volts?
Explain this arrangement and draw a diagram.
5. A certain arc lamp required 10 amperes of current at 45 volts pressure. What
would it cost at 10 cents per kilowatt hour if used 3 hours a day for 30 days?
6. Show a diagram of 3 arc lamps in series. If each takes 45 volts and 10 amperes,
how much E.M.F. and current will they require?
7. If an electric toaster uses 5 amperes at 115 volts, how much heat will this
develop in half an hour?
9. How much heat is developed in an electric toaster in 2 minutes, if it uses 5
amperes at 100 volts?
enclosed lamp, that is, have new carbons placed in it, is because the carbons
"burn" freely, that is unite with the oxygen of the air. In the enclosed arc lamp, the
supply of oxygen in the inner globe is limited and is soon consumed, therefore the
carbons last many times longer in such lamps.
Some carbon rods have soft cores containing calcium salts. These vaporize in the
arc producing the flaming arc light of a bright yellow color, and give more light
than the ordinary lamp.
Important Topics
1. Heat effects of electric currents, uses and applications.
2. Computation of the heat developed in a circuit. Three formulas.
3. Electric lamps; incandescent and arc; construction, uses, efficiency.
Exercises
1. Sketch a circuit containing 10 incandescent lamps in parallel. If each lamp
when hot has a resistance of 220 ohms, and the E.M.F. is 100 volts, what current
will flow?
2. What will it cost to use these lights for 3 hours a day for 30 days at 10 cents a
kilowatt hour?
3. How much heat will these lamps produce per minute?
4. How could you connect 110-volt lamps to a street car circuit of 660 volts?
Explain this arrangement and draw a diagram.
5. A certain arc lamp required 10 amperes of current at 45 volts pressure. What
would it cost at 10 cents per kilowatt hour if used 3 hours a day for 30 days?
6. Show a diagram of 3 arc lamps in series. If each takes 45 volts and 10 amperes,
how much E.M.F. and current will they require?
7. If an electric toaster uses 5 amperes at 115 volts, how much heat will this
develop in half an hour?
9. How much heat is developed in an electric toaster in 2 minutes, if it uses 5
amperes at 100 volts?
Page 321
10. How many B.t.u.'s are given off in an electric oven that takes 10 amperes at
110 volts for 1 hour? (1 B.t.u. equals 252 calories.)
11. An electric heater supplies heat at the rate of 700 B.t.u.'s an hour. How much
power does it require?
12. How many watts are required to operate 120 incandescent lamps in parallel if
each takes 0.5 amperes at 110 volts?
13. An electric lamp takes 12 amperes at a P.D. of 110 volts. How many B.t.u.'s
are radiated from it each second? How many calories?
14. If a 110-volt incandescent lamp is submerged for 10 minutes in 400 gr. of cold
water while a current of 0.5 amperes is flowing, how many degrees centigrade
will the water be warmed?
15. In an electric furnace a current of 3000 amperes is used at a P.D. of 10 volts.
Find the heat developed in 1 minute.
16. How many candle power should a 20-watt tungsten lamp give if its efficiency
is one watt per candle power?
17. What is the "efficiency" of a 40-watt tungsten lamp if it gives 34 candle
power?
Review Outline: Current Electricity
Produced by—Chemical action; voltaic and storage cells.
Magnetic, electromagnet, uses and applications.
Three Principal Effects: Chemical, electrolysis, applications.
Heat, lighting and heating devices.
Theories: (a) of voltaic cells, (b) of electrolysis.
Units: Ampere, ohm, volt, watt, joule, kilowatt, horse power.
Measurement:
(a) magnetic effect; galvanometer, ammeter, voltmeter, wattmeter,
Wheatstone bridge, construction and use.
(b) chemical effect; voltameter.
Laws:
(a) Right hand rules, for conductor and helix.
110 volts for 1 hour? (1 B.t.u. equals 252 calories.)
11. An electric heater supplies heat at the rate of 700 B.t.u.'s an hour. How much
power does it require?
12. How many watts are required to operate 120 incandescent lamps in parallel if
each takes 0.5 amperes at 110 volts?
13. An electric lamp takes 12 amperes at a P.D. of 110 volts. How many B.t.u.'s
are radiated from it each second? How many calories?
14. If a 110-volt incandescent lamp is submerged for 10 minutes in 400 gr. of cold
water while a current of 0.5 amperes is flowing, how many degrees centigrade
will the water be warmed?
15. In an electric furnace a current of 3000 amperes is used at a P.D. of 10 volts.
Find the heat developed in 1 minute.
16. How many candle power should a 20-watt tungsten lamp give if its efficiency
is one watt per candle power?
17. What is the "efficiency" of a 40-watt tungsten lamp if it gives 34 candle
power?
Review Outline: Current Electricity
Produced by—Chemical action; voltaic and storage cells.
Magnetic, electromagnet, uses and applications.
Three Principal Effects: Chemical, electrolysis, applications.
Heat, lighting and heating devices.
Theories: (a) of voltaic cells, (b) of electrolysis.
Units: Ampere, ohm, volt, watt, joule, kilowatt, horse power.
Measurement:
(a) magnetic effect; galvanometer, ammeter, voltmeter, wattmeter,
Wheatstone bridge, construction and use.
(b) chemical effect; voltameter.
Laws:
(a) Right hand rules, for conductor and helix.
Page 322
(b) Resistance, Conductors in series and parallel.
(c) Ohm's law, heat law, power law, 3 forms for each.
(d) Cells in parallel and series.
Problems: Upon applications of the laws and formulas studied.
Voltaic cells; wet, dry, and Daniell.
Electrolysis and the storage battery.
Devices and Instruments:
Measuring instruments, electric bell, sounder,
Heating and lighting devices.
Terms: Anode, cathode, electrolyte, ion, circuit switch, current, e.m.f., resistance,
potential.
(c) Ohm's law, heat law, power law, 3 forms for each.
(d) Cells in parallel and series.
Problems: Upon applications of the laws and formulas studied.
Voltaic cells; wet, dry, and Daniell.
Electrolysis and the storage battery.
Devices and Instruments:
Measuring instruments, electric bell, sounder,
Heating and lighting devices.
Terms: Anode, cathode, electrolyte, ion, circuit switch, current, e.m.f., resistance,
potential.
Page 323
CHAPTER XIV
INDUCED CURRENTS
(1) Electromagnetic Induction
296. Current Induced by a Magnet.—The discovery in 1819 that a current in a
conductor can deflect a magnetic needle or that it has a magnetic effect, led to
many attempts to produce an electric current by means of a magnet. It was not
until about 1831, however, that Joseph Henry in America and Michael Faraday in
England, independently discovered how to accomplish this important result.
At the present time, voltaic cells produce but a very small part of the current
electricity used. Practically all that is employed for power, light, heat, and
electrolysis is produced by the use of magnetic fields, or by electromagnetic
induction.
297. Laws of Induced Currents.[M]—To illustrate how a current can be
produced by electromagnetic induction:
Connect a coil of 400 or more turns of No. 22 insulated copper wire to a sensitive
galvanometer. (See Fig. 279.) Now insert a bar magnet in the coil. A sudden
movement of the galvanometer will be noticed, indicating the production of a
current. When the magnet stops moving, however, the current stops, and the coil
of the galvanometer returns to its first position. If now the magnet is removed, a
movement of the galvanometer coil in the opposite direction is noticed. This
action may be repeated as often as desired with similar results.
Careful experiments have shown that it is the magnetic field of the magnet that
produces the action, and that only when the number of lines of force in the coil is
changing do we find a current produced in the coil. These facts lead to Law I. Any
change in the number of magnetic lines of force passing through or cut by a coil
will produce an electromotive force in the coil. In the account of the experiment
just given, electric currents are produced, while in Law I, electromotive forces are
mentioned. This difference is due to the fact that an E.M.F. is always produced in
a coil when the magnetic field within it is changed, while a current is found only
when the coil is part of a closed circuit. The inductive action of the earth's
magnetic field (see Fig. 280), may be shown by means of a coil of 400 to 500
turns a foot in diameter.
INDUCED CURRENTS
(1) Electromagnetic Induction
296. Current Induced by a Magnet.—The discovery in 1819 that a current in a
conductor can deflect a magnetic needle or that it has a magnetic effect, led to
many attempts to produce an electric current by means of a magnet. It was not
until about 1831, however, that Joseph Henry in America and Michael Faraday in
England, independently discovered how to accomplish this important result.
At the present time, voltaic cells produce but a very small part of the current
electricity used. Practically all that is employed for power, light, heat, and
electrolysis is produced by the use of magnetic fields, or by electromagnetic
induction.
297. Laws of Induced Currents.[M]—To illustrate how a current can be
produced by electromagnetic induction:
Connect a coil of 400 or more turns of No. 22 insulated copper wire to a sensitive
galvanometer. (See Fig. 279.) Now insert a bar magnet in the coil. A sudden
movement of the galvanometer will be noticed, indicating the production of a
current. When the magnet stops moving, however, the current stops, and the coil
of the galvanometer returns to its first position. If now the magnet is removed, a
movement of the galvanometer coil in the opposite direction is noticed. This
action may be repeated as often as desired with similar results.
Careful experiments have shown that it is the magnetic field of the magnet that
produces the action, and that only when the number of lines of force in the coil is
changing do we find a current produced in the coil. These facts lead to Law I. Any
change in the number of magnetic lines of force passing through or cut by a coil
will produce an electromotive force in the coil. In the account of the experiment
just given, electric currents are produced, while in Law I, electromotive forces are
mentioned. This difference is due to the fact that an E.M.F. is always produced in
a coil when the magnetic field within it is changed, while a current is found only
when the coil is part of a closed circuit. The inductive action of the earth's
magnetic field (see Fig. 280), may be shown by means of a coil of 400 to 500
turns a foot in diameter.
Page 324
Fig. 279.—The moving magnet induces a
current in the coil.
Fig. 280.—A current may be induced by
turning the coil in the earth's magnetic field.
Connect its ends to a sensitive galvanometer and hold it at right angles to the
earth's field. Then quickly revolve the coil through 180 degrees and note the
movement of the galvanometer. Reverse the coil and the galvanometer swings in
the opposite direction.
If the magnet in Fig. 279 is moved in and out of the coil at first slowly and later
swiftly, small and large deflections of the galvanometer coil are noticed. The
quicker the movement of the magnetic field the greater are the galvanometer
deflections produced. This leads to Law II. The electromotive forces produced are
proportional to the number of lines of force cut per second.
298. The magneto is a device that illustrates the laws of induced currents stated
in Art. 297. The magneto (see Fig. 281), consists of several permanent, "U"-
shaped magnets placed side by side. Between the poles of these magnets is placed
a slotted iron cylinder having a coil of many turns of fine insulated copper wire
wound in the slot as in Fig. 282. The cylinder and coil form what is called an
armature. The armature is mounted so as to be revolved between the poles of the
"U"-shaped magnets by means of a handle. As the armature revolves, the lines of
force from the magnets pass through the coil first in one direction and then in the
other. This repeated change in the lines of force passing through the coil produces
an E.M.F. which may be felt by holding in the hands the two wires leading from
the armature coil. On turning the armature faster the current is felt much stronger,
showing that the E.M.F. in the coil increases as the rate of cutting the magnetic
lines of force by the coils increases.
current in the coil.
Fig. 280.—A current may be induced by
turning the coil in the earth's magnetic field.
Connect its ends to a sensitive galvanometer and hold it at right angles to the
earth's field. Then quickly revolve the coil through 180 degrees and note the
movement of the galvanometer. Reverse the coil and the galvanometer swings in
the opposite direction.
If the magnet in Fig. 279 is moved in and out of the coil at first slowly and later
swiftly, small and large deflections of the galvanometer coil are noticed. The
quicker the movement of the magnetic field the greater are the galvanometer
deflections produced. This leads to Law II. The electromotive forces produced are
proportional to the number of lines of force cut per second.
298. The magneto is a device that illustrates the laws of induced currents stated
in Art. 297. The magneto (see Fig. 281), consists of several permanent, "U"-
shaped magnets placed side by side. Between the poles of these magnets is placed
a slotted iron cylinder having a coil of many turns of fine insulated copper wire
wound in the slot as in Fig. 282. The cylinder and coil form what is called an
armature. The armature is mounted so as to be revolved between the poles of the
"U"-shaped magnets by means of a handle. As the armature revolves, the lines of
force from the magnets pass through the coil first in one direction and then in the
other. This repeated change in the lines of force passing through the coil produces
an E.M.F. which may be felt by holding in the hands the two wires leading from
the armature coil. On turning the armature faster the current is felt much stronger,
showing that the E.M.F. in the coil increases as the rate of cutting the magnetic
lines of force by the coils increases.
Page 325
Fig. 281.—A magneto.
Fig. 282.—A shuttle armature.
Fig. 283.—The induced current has a field
which opposes the motion of the magnet. The
heavy line represents the direction of the
induced current.
299. Lenz's Law.—While one is turning the armature of a magneto if the two
wires leading from its coil are connected, forming what is called a "short circuit,"
the difficulty of turning the armature is at once increased. If now the circuit is
broken, the armature turns as easily as at first. The increased difficulty in turning
the armature is due to the current produced in the coil. This current sets up a
magnetic field of its own that opposes the field from the steel magnets. This
opposition makes it necessary for work to be done to keep up the motion of the
coil when a current is passing through it. This fact is called Lenz's Law. It may be
expressed as follows: Whenever a current is induced by the relative motion of a
magnetic field and a conductor, the direction of the induced current is always
such as to set up a magnetic field that opposes the motion. Lenz's Law follows
from the principle of conservation of energy, that energy can be produced only
from an expenditure of other energy. Now since an electric current possesses
energy, such a current can be produced only by doing mechanical work or by
expending some other form of energy. To illustrate Lenz's Law, suppose that the
Fig. 282.—A shuttle armature.
Fig. 283.—The induced current has a field
which opposes the motion of the magnet. The
heavy line represents the direction of the
induced current.
299. Lenz's Law.—While one is turning the armature of a magneto if the two
wires leading from its coil are connected, forming what is called a "short circuit,"
the difficulty of turning the armature is at once increased. If now the circuit is
broken, the armature turns as easily as at first. The increased difficulty in turning
the armature is due to the current produced in the coil. This current sets up a
magnetic field of its own that opposes the field from the steel magnets. This
opposition makes it necessary for work to be done to keep up the motion of the
coil when a current is passing through it. This fact is called Lenz's Law. It may be
expressed as follows: Whenever a current is induced by the relative motion of a
magnetic field and a conductor, the direction of the induced current is always
such as to set up a magnetic field that opposes the motion. Lenz's Law follows
from the principle of conservation of energy, that energy can be produced only
from an expenditure of other energy. Now since an electric current possesses
energy, such a current can be produced only by doing mechanical work or by
expending some other form of energy. To illustrate Lenz's Law, suppose that the
Page 326
north-seeking pole of a bar magnet be inserted in a closed coil of wire. (See Fig.
283.) The current induced in the coil has a direction such that its lines of force
will pass within the coil so as to oppose the field of the bar magnet, when the
north pole of the magnet is inserted so as to point to the left. That is, the north
pole of the helix is at the right. Applying the right-hand rule to the coil, its current
will then be counter clockwise. On withdrawing the magnet, the current reverses,
becoming clockwise with its field passing to the left within the coil.
A striking illustration of the opposition offered by the field of the induced current
to that of the inducing field is afforded by taking a strong electromagnet (see Fig.
284) and suspending a sheet of copper so as to swing freely between the poles.
When no current flows through the magnet the sheet swings easily for some time.
When, however, the coils are magnetized, the copper sheet has induced within it,
currents that set up magnetic fields strongly opposing the motion, the swinging
being stopped almost instantly. The principle is applied in good ammeters and
voltmeters to prevent the swinging of the needle when deflected. The current
induced in the metal form on which is wound the galvanometer coil is sufficient
to make the needle practically "dead beat."
300. The Magneto and the Dynamo.—Magnetos are used to
develop small currents, such as are used for telephone signals,
and for operating the sparking devices of gasoline engines. They
are therefore found in automobiles containing gasoline motors.
The most important device for producing electric currents by
electromagnetic induction, however, is the dynamo. It is
employed whenever large currents are desired. The principle of
this device is similar to that of the magneto except that it
contains an electromagnet for producing the magnetic field.
Since the electromagnet can develop a much stronger field than
a permanent magnet, the dynamo can produce a higher E.M.F.
and a much larger current than the magneto.
Fig. 284.—
301. The Magnetic Fields of Generators.—In the magneto, the
The magnetic
magnetic field is produced by permanent steel magnets. In
field stops the
dynamos powerful electromagnets are used. The latter are
swinging of
sometimes excited by currents from some other source, but
the sheet of
usually current from the armature is sent around the field coils to
copper.
produce the magnetic fields. Dynamos are classified according
to the manner in which the current is sent to their field coils.
283.) The current induced in the coil has a direction such that its lines of force
will pass within the coil so as to oppose the field of the bar magnet, when the
north pole of the magnet is inserted so as to point to the left. That is, the north
pole of the helix is at the right. Applying the right-hand rule to the coil, its current
will then be counter clockwise. On withdrawing the magnet, the current reverses,
becoming clockwise with its field passing to the left within the coil.
A striking illustration of the opposition offered by the field of the induced current
to that of the inducing field is afforded by taking a strong electromagnet (see Fig.
284) and suspending a sheet of copper so as to swing freely between the poles.
When no current flows through the magnet the sheet swings easily for some time.
When, however, the coils are magnetized, the copper sheet has induced within it,
currents that set up magnetic fields strongly opposing the motion, the swinging
being stopped almost instantly. The principle is applied in good ammeters and
voltmeters to prevent the swinging of the needle when deflected. The current
induced in the metal form on which is wound the galvanometer coil is sufficient
to make the needle practically "dead beat."
300. The Magneto and the Dynamo.—Magnetos are used to
develop small currents, such as are used for telephone signals,
and for operating the sparking devices of gasoline engines. They
are therefore found in automobiles containing gasoline motors.
The most important device for producing electric currents by
electromagnetic induction, however, is the dynamo. It is
employed whenever large currents are desired. The principle of
this device is similar to that of the magneto except that it
contains an electromagnet for producing the magnetic field.
Since the electromagnet can develop a much stronger field than
a permanent magnet, the dynamo can produce a higher E.M.F.
and a much larger current than the magneto.
Fig. 284.—
301. The Magnetic Fields of Generators.—In the magneto, the
The magnetic
magnetic field is produced by permanent steel magnets. In
field stops the
dynamos powerful electromagnets are used. The latter are
swinging of
sometimes excited by currents from some other source, but
the sheet of
usually current from the armature is sent around the field coils to
copper.
produce the magnetic fields. Dynamos are classified according
to the manner in which the current is sent to their field coils.
Page 327
Lord Kelvin Michael Faraday
"By Permission of the "By Permission of the
Berlin Photographic Berlin Photographic
Co., New York." Co., New York."
Lord Kelvin (Sir Michael Faraday
William Thomson), (1791-1867). Famous
(1824-1907). Professor English Physicist.
of Physics, Glasgow Made many discoveries
University. Invented in electricity and
the absolute scale of magnetism; "Greatest
temperature: also experimentalist of the
many practical nineteenth century."
electrical measuring
instruments. The
foremost physicist of
the latter part of the
nineteenth century.
"By Permission of the "By Permission of the
Berlin Photographic Berlin Photographic
Co., New York." Co., New York."
Lord Kelvin (Sir Michael Faraday
William Thomson), (1791-1867). Famous
(1824-1907). Professor English Physicist.
of Physics, Glasgow Made many discoveries
University. Invented in electricity and
the absolute scale of magnetism; "Greatest
temperature: also experimentalist of the
many practical nineteenth century."
electrical measuring
instruments. The
foremost physicist of
the latter part of the
nineteenth century.
Page 328
Fig. 285.—A series-wound dynamo.
Fig. 286.—A shunt-wound dynamo.
Fig. 287.—A compound-wound dynamo.
A. The series wound dynamo (see Fig. 285) is arranged so that all of the current
produced by the armature is sent through coils of coarse wire upon the fields, after
flowing through the external circuit.
B. The shunt wound dynamo (see Fig. 286) sends a part only of the current
produced through the field coils. The latter are of many turns of fine wire so as to
use as little current as possible. The greater part of the current goes to the main
circuit. If the number of lamps or motors connected to the main circuit is
increased, the voltage is lessened which weakens the current in the field coils,
causing a weaker field and still lower voltage, producing a fluctuating E.M.F.
which is unsatisfactory for many purposes. This fault is overcome by
C. the compound wound dynamo. This dynamo has both shunt and series coils
upon its fields. (See Fig. 287.) If more current is drawn into the main circuit with
this dynamo, the series coils produce a stronger field compensating for the weaker
field of the shunt coils, so that uniform voltage is maintained. The compound
wound generator is therefore the one most commonly employed.
Important Topics
1. Laws of electromagnetic induction (a) conditions, (b) E.M.F., (c) direction.
2. Devices, (a) magneto, (b) dynamo: series, shunt, compound.
3. Illustrations of the laws.
Exercises
1. Under what conditions may an electric current be produced by a magnet?
Fig. 286.—A shunt-wound dynamo.
Fig. 287.—A compound-wound dynamo.
A. The series wound dynamo (see Fig. 285) is arranged so that all of the current
produced by the armature is sent through coils of coarse wire upon the fields, after
flowing through the external circuit.
B. The shunt wound dynamo (see Fig. 286) sends a part only of the current
produced through the field coils. The latter are of many turns of fine wire so as to
use as little current as possible. The greater part of the current goes to the main
circuit. If the number of lamps or motors connected to the main circuit is
increased, the voltage is lessened which weakens the current in the field coils,
causing a weaker field and still lower voltage, producing a fluctuating E.M.F.
which is unsatisfactory for many purposes. This fault is overcome by
C. the compound wound dynamo. This dynamo has both shunt and series coils
upon its fields. (See Fig. 287.) If more current is drawn into the main circuit with
this dynamo, the series coils produce a stronger field compensating for the weaker
field of the shunt coils, so that uniform voltage is maintained. The compound
wound generator is therefore the one most commonly employed.
Important Topics
1. Laws of electromagnetic induction (a) conditions, (b) E.M.F., (c) direction.
2. Devices, (a) magneto, (b) dynamo: series, shunt, compound.
3. Illustrations of the laws.
Exercises
1. Under what conditions may an electric current be produced by a magnet?
Page 329
2. Show how Lenz's Law, follows from the principle of conservation of energy.
3. A bar magnet is fixed upright with its north-seeking pole upward. A coil is
thrust down over the magnet. What is the direction of the current induced in the
coil? Explain.
4. In what two ways may a current be induced in a closed coil?
5. What method is employed in the magneto? In the dynamo?
6. What is the nature of the current produced in the armature coil of a magneto,
that is, is it direct or alternating? Why?
7. What is the resistance of a 20-watt tungsten lamp if the E.M.F. is 115 volts?
8. Find the resistance of a 40-watt tungsten lamp when the voltage is 115? How
much heat will it produce per minute?
9. An Edison storage battery cell on a test gave a discharge of 30 amperes. The
average voltage was 1.19. What was the resistance of the cell?
10. Eight storage cells are connected in series. Each has an E.M.F. of 1.2 volts and
an internal resistance of 0.03 ohms. What will be the current flowing through a
voltmeter having 500 ohms resistance in circuit with them?
(2) The Dynamo and the Motor
302. The Dynamo may be defined as a machine for transforming mechanical
energy into the energy of electric currents by electromagnetic induction. Although
electromagnetic induction was discovered in 1821, practical dynamos were not
built for about 40 years or until between 1860 and 1870. The great development
in the production and use of electric currents has come since the latter date. The
principle parts of the dynamo are (a) the field magnet, (b) the armature, (c) the
commutator or collecting rings, (d) the brushes. Fig. 288 shows several common
methods of arranging the field coils and the armature.
Fig. 288.—Several methods of arranging the
field coils and the armature of a dynamo.
3. A bar magnet is fixed upright with its north-seeking pole upward. A coil is
thrust down over the magnet. What is the direction of the current induced in the
coil? Explain.
4. In what two ways may a current be induced in a closed coil?
5. What method is employed in the magneto? In the dynamo?
6. What is the nature of the current produced in the armature coil of a magneto,
that is, is it direct or alternating? Why?
7. What is the resistance of a 20-watt tungsten lamp if the E.M.F. is 115 volts?
8. Find the resistance of a 40-watt tungsten lamp when the voltage is 115? How
much heat will it produce per minute?
9. An Edison storage battery cell on a test gave a discharge of 30 amperes. The
average voltage was 1.19. What was the resistance of the cell?
10. Eight storage cells are connected in series. Each has an E.M.F. of 1.2 volts and
an internal resistance of 0.03 ohms. What will be the current flowing through a
voltmeter having 500 ohms resistance in circuit with them?
(2) The Dynamo and the Motor
302. The Dynamo may be defined as a machine for transforming mechanical
energy into the energy of electric currents by electromagnetic induction. Although
electromagnetic induction was discovered in 1821, practical dynamos were not
built for about 40 years or until between 1860 and 1870. The great development
in the production and use of electric currents has come since the latter date. The
principle parts of the dynamo are (a) the field magnet, (b) the armature, (c) the
commutator or collecting rings, (d) the brushes. Fig. 288 shows several common
methods of arranging the field coils and the armature.
Fig. 288.—Several methods of arranging the
field coils and the armature of a dynamo.
Page 330
The field coils vary in number and position. The
purpose of their construction is always to send
the largest possible number of lines of force
through the armature. Some dynamos are
bipolar, or have two poles, others are multipolar
or have more than two. In Fig. 288 No. 4 has
four poles. The armature of a dynamo differs
from a magneto armature in that it consists of a Fig. 289.—A drum
armature.
series of coils of insulated copper wire wound in
numerous slots cut in the surface of a cylindrical
piece of iron. Fig. 289 shows a side view of the iron core of such an armature.
Iron is used to form the body of the armature since the magnetic lines of force
flow easily through the iron. The iron by its permeability also concentrates and
increases the magnetic flux. The best armatures are made of many thin sheets of
soft iron. These are called laminated armatures. An armature made of a solid
piece of iron becomes hot when revolving in a magnetic field. This is due to
electric currents induced in the iron itself. This heating is largely reduced by
laminating the armature. Why?
Fig. 290.—Armature connected to slip rings
producing an alternating current.
303. Methods of Collecting Current from the Armature.—The electric currents
produced in the armature are conducted away by special sliding contacts. The
stationary part of the sliding contact is called a brush. The moving part is a slip
ring or a commutator. Fig. 290 shows an armature coil connected to slip rings. As
the armature revolves, the coils and slip rings revolve with it. The two ends of the
armature coils are connected to the two rings respectively. Now as the armature
revolves it cuts the lines of force first in one direction and then in the other. This
produces in the coils an E.M.F. first one way and then the other. This E.M.F. sets
up a current which is conducted to the outside circuits through the slip rings and
brushes. Such a current which repeatedly reverses its direction is called an
alternating current. Fig. 291 (1) indicates graphically how the current moves
alternately one way and then the other. Alternating currents are extensively used
purpose of their construction is always to send
the largest possible number of lines of force
through the armature. Some dynamos are
bipolar, or have two poles, others are multipolar
or have more than two. In Fig. 288 No. 4 has
four poles. The armature of a dynamo differs
from a magneto armature in that it consists of a Fig. 289.—A drum
armature.
series of coils of insulated copper wire wound in
numerous slots cut in the surface of a cylindrical
piece of iron. Fig. 289 shows a side view of the iron core of such an armature.
Iron is used to form the body of the armature since the magnetic lines of force
flow easily through the iron. The iron by its permeability also concentrates and
increases the magnetic flux. The best armatures are made of many thin sheets of
soft iron. These are called laminated armatures. An armature made of a solid
piece of iron becomes hot when revolving in a magnetic field. This is due to
electric currents induced in the iron itself. This heating is largely reduced by
laminating the armature. Why?
Fig. 290.—Armature connected to slip rings
producing an alternating current.
303. Methods of Collecting Current from the Armature.—The electric currents
produced in the armature are conducted away by special sliding contacts. The
stationary part of the sliding contact is called a brush. The moving part is a slip
ring or a commutator. Fig. 290 shows an armature coil connected to slip rings. As
the armature revolves, the coils and slip rings revolve with it. The two ends of the
armature coils are connected to the two rings respectively. Now as the armature
revolves it cuts the lines of force first in one direction and then in the other. This
produces in the coils an E.M.F. first one way and then the other. This E.M.F. sets
up a current which is conducted to the outside circuits through the slip rings and
brushes. Such a current which repeatedly reverses its direction is called an
alternating current. Fig. 291 (1) indicates graphically how the current moves
alternately one way and then the other. Alternating currents are extensively used
Page 331
for electric light, heat, and power. Direct currents or those going continuously in
one direction are however in much demand especially for street car service, for
electrolysis, and for charging storage batteries.
304. The Commutator.—For a dynamo to deliver a direct current it must carry
upon the shaft of the armature a commutator. The commutator is used to reverse
the connections of the ends of the armature coils at the instant that the current
changes its direction in the armature. This reversal of connection when the
direction of current changes, keeps the current in the outside circuit flowing in the
same direction. Fig. 291 is a diagram of an armature with a commutator. The
commutator is a split ring, having as many parts or segments as there are coils
upon the armature. The brushes touch opposite points upon the commutator as
they slide over the surface of the latter. Suppose that the armature viewed from
the commutator end rotates in a counter-clockwise direction, also that the currents
from the upper part move toward the commutator and out the top brush.
As the armature revolves, its coils soon
begin to cut the force lines in the opposite
direction. This change in the direction of
cutting the lines of force causes the
current to reverse in the coils of the
armature. At the instant the current
changes in direction, what was the upper
segment of the commutator slips over into
contact with the lower brush, and the Fig. 291.—The armature coils are
other segment swings over to touch the connected to a commutator
upper brush. Since the current has producing a direct current.
reversed in the coils it continues to flow
out of the upper brush. This change in
connection at the brushes takes place at each half turn of the armature, just as the
current changes in direction in the coils. This is the manner in which the
commutator of a dynamo changes the alternating current produced in the armature
coils, into a direct current in the external circuit. Fig. 292 (1) represents
graphically an alternating current, (2) of the same figure shows current taken from
the brushes of the commutator of a dynamo with one coil on the armature.
A practical dynamo, however, has many coils upon its armature with a
corresponding number of segments upon the commutator. (See Figs. 289 and
293.) As each coil and commutator segment passes a brush, it contributes an
impulse to the current with the result that armatures with many coils produce
currents that flow quite evenly. (See Fig. 292, 3.)
one direction are however in much demand especially for street car service, for
electrolysis, and for charging storage batteries.
304. The Commutator.—For a dynamo to deliver a direct current it must carry
upon the shaft of the armature a commutator. The commutator is used to reverse
the connections of the ends of the armature coils at the instant that the current
changes its direction in the armature. This reversal of connection when the
direction of current changes, keeps the current in the outside circuit flowing in the
same direction. Fig. 291 is a diagram of an armature with a commutator. The
commutator is a split ring, having as many parts or segments as there are coils
upon the armature. The brushes touch opposite points upon the commutator as
they slide over the surface of the latter. Suppose that the armature viewed from
the commutator end rotates in a counter-clockwise direction, also that the currents
from the upper part move toward the commutator and out the top brush.
As the armature revolves, its coils soon
begin to cut the force lines in the opposite
direction. This change in the direction of
cutting the lines of force causes the
current to reverse in the coils of the
armature. At the instant the current
changes in direction, what was the upper
segment of the commutator slips over into
contact with the lower brush, and the Fig. 291.—The armature coils are
other segment swings over to touch the connected to a commutator
upper brush. Since the current has producing a direct current.
reversed in the coils it continues to flow
out of the upper brush. This change in
connection at the brushes takes place at each half turn of the armature, just as the
current changes in direction in the coils. This is the manner in which the
commutator of a dynamo changes the alternating current produced in the armature
coils, into a direct current in the external circuit. Fig. 292 (1) represents
graphically an alternating current, (2) of the same figure shows current taken from
the brushes of the commutator of a dynamo with one coil on the armature.
A practical dynamo, however, has many coils upon its armature with a
corresponding number of segments upon the commutator. (See Figs. 289 and
293.) As each coil and commutator segment passes a brush, it contributes an
impulse to the current with the result that armatures with many coils produce
currents that flow quite evenly. (See Fig. 292, 3.)
Page 332
T
he
cu
rr
en
t
re
pr
es
en
Fig. 292.—Graphic te
representation of (1) an d
alternating current; (2) in
a pulsating current; (3) Fi Fig. 293.—DeLaval multi-stage turbine and
a continuous current. g. gear driving 750-kw., 750-r.p.m., 600-volt
2 direct-current generator.
92 (2) is called a pulsating
current.
Fig. 294.—A wire carrying a current across a
magnetic field is pushed sideways by the field.
305. The electric motor is a machine which transforms the energy of an electric
current into mechanical energy or motion. The direct current motor consists of the
same essential parts as a direct current dynamo, viz., the field magnet, armature,
commutator and brushes. Its operation is readily comprehended after one
understands the following experiment:
Set up two bar electromagnets with unlike poles facing each other about an inch
apart. A wire connected to a source of current is hung loosely between the poles
as in Fig. 294. The circuit through the wire should contain a key or switch. If a
he
cu
rr
en
t
re
pr
es
en
Fig. 292.—Graphic te
representation of (1) an d
alternating current; (2) in
a pulsating current; (3) Fi Fig. 293.—DeLaval multi-stage turbine and
a continuous current. g. gear driving 750-kw., 750-r.p.m., 600-volt
2 direct-current generator.
92 (2) is called a pulsating
current.
Fig. 294.—A wire carrying a current across a
magnetic field is pushed sideways by the field.
305. The electric motor is a machine which transforms the energy of an electric
current into mechanical energy or motion. The direct current motor consists of the
same essential parts as a direct current dynamo, viz., the field magnet, armature,
commutator and brushes. Its operation is readily comprehended after one
understands the following experiment:
Set up two bar electromagnets with unlike poles facing each other about an inch
apart. A wire connected to a source of current is hung loosely between the poles
as in Fig. 294. The circuit through the wire should contain a key or switch. If a
Page 333
current is sent through the electromagnets and then another is sent through the
wire, the latter will be found to be pushed either up or down, while if the current
is reversed through the wire it is pushed in the opposite direction. These results
may be explained as follows:
Consider the magnetic field about a wire carrying a current (See Fig. 295.) If such
a wire is placed in the magnetic field between two opposite poles of an
electromagnet (Fig. 296), the wire will be moved either up or down. The reason
for this is shown by the diagram in Fig. 297. Here a wire carrying a current and
therefore surrounded by a magnetic field passes across another magnetic field.
The two fields affect each other causing a crowding of the force lines either above
or below the wire. The wire at once tends to move sideways across the field away
from the crowded side. In the figure, the wire tends to move downward.
Fig. 295.—The magnetic field about a wire
carrying a current.
Fig. 296.—The magnetic field between two
unlike poles.
In a practical motor, the wires upon the armature are
so connected that those upon one side (see Fig.
298), carry currents that pass in, while on the other
side they pass out. To represent the direction of the
current in the wires, the following device is
employed; a circle with a cross (to represent the
feather in the tail of an arrow) indicates a current
going away from the observer, while a circle with a
dot at its center (to represent the tip of an arrow) Fig. 297.—The crowding
indicates a current coming toward the observer. of the lines of force above
the wire, pushes it
In Fig. 298 the north pole is at the left and the south downward.
pole at the right. The field of the magnets therefore
passes from left to right as indicated in the figure. Now in the armature the
currents in the wires on the left half of the armature are coming toward the
wire, the latter will be found to be pushed either up or down, while if the current
is reversed through the wire it is pushed in the opposite direction. These results
may be explained as follows:
Consider the magnetic field about a wire carrying a current (See Fig. 295.) If such
a wire is placed in the magnetic field between two opposite poles of an
electromagnet (Fig. 296), the wire will be moved either up or down. The reason
for this is shown by the diagram in Fig. 297. Here a wire carrying a current and
therefore surrounded by a magnetic field passes across another magnetic field.
The two fields affect each other causing a crowding of the force lines either above
or below the wire. The wire at once tends to move sideways across the field away
from the crowded side. In the figure, the wire tends to move downward.
Fig. 295.—The magnetic field about a wire
carrying a current.
Fig. 296.—The magnetic field between two
unlike poles.
In a practical motor, the wires upon the armature are
so connected that those upon one side (see Fig.
298), carry currents that pass in, while on the other
side they pass out. To represent the direction of the
current in the wires, the following device is
employed; a circle with a cross (to represent the
feather in the tail of an arrow) indicates a current
going away from the observer, while a circle with a
dot at its center (to represent the tip of an arrow) Fig. 297.—The crowding
indicates a current coming toward the observer. of the lines of force above
the wire, pushes it
In Fig. 298 the north pole is at the left and the south downward.
pole at the right. The field of the magnets therefore
passes from left to right as indicated in the figure. Now in the armature the
currents in the wires on the left half of the armature are coming toward the
Page 334
observer while those on the right move away.
Applying the right-hand rule, the magnetic lines
will crowd under the wires on the left side of
the armature while they will crowd over the
wires on the right side. This will cause a rotation
up on the left side and down on the right, or in a
clockwise direction.
Fig. 298.—The crowding of
If the current in the armature is reversed (in on
the lines of force causes the
the left and out on the right), the lines of force
armature to revolve in a
will crowd the armature around in the opposite
clockwise direction.
direction or counter clockwise. The rotation of
the armature will also be reversed if, while the
current in the armature is unchanged in
direction, the poles of the magnet are changed
thus reversing the magnetic field.
The motorman of a street car reverses the
motion of his car by reversing the direction of
the current in the armature of the motor.
Fig. 299.—View of a one-half
horse-power motor.
Applying the right-hand rule, the magnetic lines
will crowd under the wires on the left side of
the armature while they will crowd over the
wires on the right side. This will cause a rotation
up on the left side and down on the right, or in a
clockwise direction.
Fig. 298.—The crowding of
If the current in the armature is reversed (in on
the lines of force causes the
the left and out on the right), the lines of force
armature to revolve in a
will crowd the armature around in the opposite
clockwise direction.
direction or counter clockwise. The rotation of
the armature will also be reversed if, while the
current in the armature is unchanged in
direction, the poles of the magnet are changed
thus reversing the magnetic field.
The motorman of a street car reverses the
motion of his car by reversing the direction of
the current in the armature of the motor.
Fig. 299.—View of a one-half
horse-power motor.
Page 335
Fig. 300.—The frame and electromagnet (at
left), front bracket and brush holder (at right)
of the motor shown in Fig. 299.
Fig. 301.—The armature of a motor.
306. Practical motors have many coils upon the armature with a corresponding
number of segments upon the commutator. A large number of coils and
commutator segments enables some one of the coils to exert its greatest efficiency
at each instant, hence a steady force is provided for turning the armature which
causes it to run smoothly. Fig. 299 represents a 1/2 horse-power motor ready for
use while Fig. 300 shows the frame and poles and the front bracket and brush
holder, and Fig. 301 represents the armature.
Important Topics
1. The dynamo, four essential parts, action (a) for alternating currents, (b) for
direct currents.
2. The electric motor: (a) essential parts, (b) action.
Exercises
1. Why is an alternating current produced in the armature of a dynamo?
left), front bracket and brush holder (at right)
of the motor shown in Fig. 299.
Fig. 301.—The armature of a motor.
306. Practical motors have many coils upon the armature with a corresponding
number of segments upon the commutator. A large number of coils and
commutator segments enables some one of the coils to exert its greatest efficiency
at each instant, hence a steady force is provided for turning the armature which
causes it to run smoothly. Fig. 299 represents a 1/2 horse-power motor ready for
use while Fig. 300 shows the frame and poles and the front bracket and brush
holder, and Fig. 301 represents the armature.
Important Topics
1. The dynamo, four essential parts, action (a) for alternating currents, (b) for
direct currents.
2. The electric motor: (a) essential parts, (b) action.
Exercises
1. Why is an alternating current produced in the armature of a dynamo?
Page 336
2. How is this current produced? Give careful explanations.
3. What is the result of Lenz's law as applied to the dynamo?
4. Apply the first two laws of electromagnetic induction to the dynamo.
5. What is the power of a dynamo if it produces 40 amperes of current at 110
volts?
6. How much power must be applied to this dynamo if its efficiency is 90 per
cent.?
7. A motor takes 10 amperes of current at 220 volts; what is the power of the
current in watts? If this motor has an efficiency of 95 per cent., how many horse-
power of mechanical energy can it develop?
8. Explain why reversing the current in the armature of a motor reverses the
direction of rotation.
9. Find the cost of running a washing machine using a 1/2-horsepower motor 2
hours if the cost of the electricity is 10 cents a kilowatt hour.
10. A 1/8-horse-power motor is used to run a sewing machine. If used for 3 hours
what will be the cost at 11 cents a kilowatt hour?
(3) The Induction Coil and the Transformer
307. The Induction Coil.—Practically all electric currents are produced either by
voltaic cells or by dynamos. It is frequently found, however, that it is desirable to
change the E.M.F. of the current used, either for purposes of effectiveness,
convenience, or economy. The induction coil and the transformer, devices for
changing the E.M.F. of electric currents, are therefore in common use. The
induction coil (see Fig. 302) consists of a primary coil of coarse wire P (Fig. 303)
wound upon a core of soft iron wire, and a secondary coil, S, of several thousand
turns of fine wire. In circuit with the primary coil is a battery, B, and a current
interrupter, K, which works like the interrupter upon an electric bell. The ends of
the secondary coil are brought to binding posts or spark points as at D.
3. What is the result of Lenz's law as applied to the dynamo?
4. Apply the first two laws of electromagnetic induction to the dynamo.
5. What is the power of a dynamo if it produces 40 amperes of current at 110
volts?
6. How much power must be applied to this dynamo if its efficiency is 90 per
cent.?
7. A motor takes 10 amperes of current at 220 volts; what is the power of the
current in watts? If this motor has an efficiency of 95 per cent., how many horse-
power of mechanical energy can it develop?
8. Explain why reversing the current in the armature of a motor reverses the
direction of rotation.
9. Find the cost of running a washing machine using a 1/2-horsepower motor 2
hours if the cost of the electricity is 10 cents a kilowatt hour.
10. A 1/8-horse-power motor is used to run a sewing machine. If used for 3 hours
what will be the cost at 11 cents a kilowatt hour?
(3) The Induction Coil and the Transformer
307. The Induction Coil.—Practically all electric currents are produced either by
voltaic cells or by dynamos. It is frequently found, however, that it is desirable to
change the E.M.F. of the current used, either for purposes of effectiveness,
convenience, or economy. The induction coil and the transformer, devices for
changing the E.M.F. of electric currents, are therefore in common use. The
induction coil (see Fig. 302) consists of a primary coil of coarse wire P (Fig. 303)
wound upon a core of soft iron wire, and a secondary coil, S, of several thousand
turns of fine wire. In circuit with the primary coil is a battery, B, and a current
interrupter, K, which works like the interrupter upon an electric bell. The ends of
the secondary coil are brought to binding posts or spark points as at D.
Page 337
The current from the battery flows through
the primary coil magnetizing the iron core.
The magnetism in the core attracts the soft-
iron end of the interrupter, drawing the latter
over and breaking the circuit at the screw
contact, K. This abruptly stops the current and
at once the core loses its magnetism. The
Fig. 302.—An induction spring support of the interrupter now draws
coil. the latter back to the contact, T, again
completing the circuit. The whole operation is
repeated, the interrupter vibrating rapidly
continually opening and closing the circuit.
308. The Production of Induced
Currents in the Secondary Coil.—
When the current flows through the
primary it sets up a magnetic field in
the core. When the current is
interrupted, the field disappears. The
increase and decrease in the field of
the core induces an E.M.F. in the
secondary coil, in accordance with the
first law of electromagnetic induction.
The E.M.F. produced depends upon
(a) the number of turns in the Fig. 303.—Diagram showing the
secondary, (b) the strength of the parts of an induction coil.
magnetic field and (c) the rate of
change of the field. The rate of change in the field is more rapid at the break
than at the make. When the circuit is closed it takes perhaps 1/10 of a
second for the current to build up to its full strength while at a break the
current stops in perhaps 0.00001 of a second, so that the induced E.M.F. is
perhaps 10,000 times as great at "break" as at make. To increase the
suddenness of the "make" and "break," a condenser is often connected in
the primary circuit, in parallel, with the interrupter. (See Fig. 303, C.) This
condenser provides a place to hold the rush of current at the instant that the
interrupter breaks the circuit. This stored up charge reinforces the current at
the make producing a much more sudden change in the magnetic field with
the primary coil magnetizing the iron core.
The magnetism in the core attracts the soft-
iron end of the interrupter, drawing the latter
over and breaking the circuit at the screw
contact, K. This abruptly stops the current and
at once the core loses its magnetism. The
Fig. 302.—An induction spring support of the interrupter now draws
coil. the latter back to the contact, T, again
completing the circuit. The whole operation is
repeated, the interrupter vibrating rapidly
continually opening and closing the circuit.
308. The Production of Induced
Currents in the Secondary Coil.—
When the current flows through the
primary it sets up a magnetic field in
the core. When the current is
interrupted, the field disappears. The
increase and decrease in the field of
the core induces an E.M.F. in the
secondary coil, in accordance with the
first law of electromagnetic induction.
The E.M.F. produced depends upon
(a) the number of turns in the Fig. 303.—Diagram showing the
secondary, (b) the strength of the parts of an induction coil.
magnetic field and (c) the rate of
change of the field. The rate of change in the field is more rapid at the break
than at the make. When the circuit is closed it takes perhaps 1/10 of a
second for the current to build up to its full strength while at a break the
current stops in perhaps 0.00001 of a second, so that the induced E.M.F. is
perhaps 10,000 times as great at "break" as at make. To increase the
suddenness of the "make" and "break," a condenser is often connected in
the primary circuit, in parallel, with the interrupter. (See Fig. 303, C.) This
condenser provides a place to hold the rush of current at the instant that the
interrupter breaks the circuit. This stored up charge reinforces the current at
the make producing a much more sudden change in the magnetic field with
Page 338
a corresponding increase in the E.M.F. The induced currents from induction
coils are sometimes called faradic currents in honor of Faraday who
discovered electromagnetic induction. They are used to operate sparking
devices upon gas and gasoline engines and in many devices and
experiments in which high-tension electricity is employed.
Fig. 304.—The transformer has a closed core;
the induction coil, an open core.
Fig. 305.—The laminated iron core of a
transformer.
Fig. 306.—Cross-section of the transformer
shown in Fig. 305 showing the magnetic field
around the primary and secondary coils.
309. The Transformer.—This is like the induction coil in that it uses a
primary and a secondary coil, and an iron core to carry the magnetic field.
(See Fig. 304.) They differ in that the transformer has a closed core or one
forming a continuous iron circuit, while the induction coil has an open core,
or one in which the magnetic field must travel in air from the north to the
south poles of the core. The transformer must always be used with an
alternating current while the induction coil may use either a direct or an
coils are sometimes called faradic currents in honor of Faraday who
discovered electromagnetic induction. They are used to operate sparking
devices upon gas and gasoline engines and in many devices and
experiments in which high-tension electricity is employed.
Fig. 304.—The transformer has a closed core;
the induction coil, an open core.
Fig. 305.—The laminated iron core of a
transformer.
Fig. 306.—Cross-section of the transformer
shown in Fig. 305 showing the magnetic field
around the primary and secondary coils.
309. The Transformer.—This is like the induction coil in that it uses a
primary and a secondary coil, and an iron core to carry the magnetic field.
(See Fig. 304.) They differ in that the transformer has a closed core or one
forming a continuous iron circuit, while the induction coil has an open core,
or one in which the magnetic field must travel in air from the north to the
south poles of the core. The transformer must always be used with an
alternating current while the induction coil may use either a direct or an
Page 339
alternating current. Further, the induction coil always produces a higher
E.M.F. while the transformer may produce an E.M.F. in its secondary coil
that is either higher or lower than the one in the primary. The former is
called "step-up" while the latter is a "step-down" transformer. The
alternating current in the primary coil of the transformer produces an
alternating magnetic flux in the iron core. This iron core is laminated (see
Fig. 305) to prevent the heating that would result if a solid core were used.
The alternating magnetic flux induces in the secondary coil an E.M.F. in
accordance with the following rule. The ratio of the number of turns in the
primary to the number of the turns in the secondary coil equals the ratio of
the electromotive forces in these respective coils. If the secondary coil has 8
turns while the primary has 4, the E.M.F. of the secondary will be just twice
that of the primary. Or, if in the primary coil of the transformer Fig. 306 is
an E.M.F. of 110 volts, in the secondary will be found an E.M.F. of 220
volts.
310. Uses of Transformers.—In electric lighting systems,
dynamos often produce alternating currents at 1000 to
12,000 volts pressure. It is very dangerous to admit currents
at this pressure into dwellings and business houses, so that
transformers are installed just outside of buildings to "step-
down" the high voltage currents to 110 or 220 volts. The
lighting current that enters a house does not come directly
from a dynamo. It is an induced current produced by a
transformer placed near the house. (See Fig. 307.) In a Fig. 307.—
perfect transformer the efficiency would be 100 per cent. A
This signifies that the energy that is sent into the primary commercial
coil of the transformer exactly equals the energy in the transforme
secondary coil. The best transformers actually show r.
efficiencies better than 97 per cent. The lost energy appears
as heat in the transformer. "The transfer of great power in a large
transformer from one circuit to another circuit entirely separate and distinct,
without any motion or noise and almost without loss, is one of the most
wonderful phenomena under the control of man."
311. The mercury arc rectifier is a device for changing an alternating
current into a direct current. It is frequently used for charging storage
batteries where only alternating current is supplied by the electric power
E.M.F. while the transformer may produce an E.M.F. in its secondary coil
that is either higher or lower than the one in the primary. The former is
called "step-up" while the latter is a "step-down" transformer. The
alternating current in the primary coil of the transformer produces an
alternating magnetic flux in the iron core. This iron core is laminated (see
Fig. 305) to prevent the heating that would result if a solid core were used.
The alternating magnetic flux induces in the secondary coil an E.M.F. in
accordance with the following rule. The ratio of the number of turns in the
primary to the number of the turns in the secondary coil equals the ratio of
the electromotive forces in these respective coils. If the secondary coil has 8
turns while the primary has 4, the E.M.F. of the secondary will be just twice
that of the primary. Or, if in the primary coil of the transformer Fig. 306 is
an E.M.F. of 110 volts, in the secondary will be found an E.M.F. of 220
volts.
310. Uses of Transformers.—In electric lighting systems,
dynamos often produce alternating currents at 1000 to
12,000 volts pressure. It is very dangerous to admit currents
at this pressure into dwellings and business houses, so that
transformers are installed just outside of buildings to "step-
down" the high voltage currents to 110 or 220 volts. The
lighting current that enters a house does not come directly
from a dynamo. It is an induced current produced by a
transformer placed near the house. (See Fig. 307.) In a Fig. 307.—
perfect transformer the efficiency would be 100 per cent. A
This signifies that the energy that is sent into the primary commercial
coil of the transformer exactly equals the energy in the transforme
secondary coil. The best transformers actually show r.
efficiencies better than 97 per cent. The lost energy appears
as heat in the transformer. "The transfer of great power in a large
transformer from one circuit to another circuit entirely separate and distinct,
without any motion or noise and almost without loss, is one of the most
wonderful phenomena under the control of man."
311. The mercury arc rectifier is a device for changing an alternating
current into a direct current. It is frequently used for charging storage
batteries where only alternating current is supplied by the electric power
Page 340
company. It consists of an exhausted bulb containing two carbon or graphite
electrodes marked G in Fig. 308 and a mercury electrode marked M. It is
found that current will pass through such a bulb only from the graphite to
the mercury but not in the reverse direction. In operating the device, the
secondary terminals of an alternating current transformer T are connected to
the graphite terminals of the rectifier. A wire connected to the center of the
secondary of the transformer at C is attached to the negative terminal of the
storage battery SB. The positive terminal of the battery is connected to the
mercury electrode of the rectifier tube through a reactance or choke coil R.
This coil serves to sustain the arc between the alternations. Sw is a starting
switch, used only in striking the arc. It is opened immediately after the tube
begins to glow.
Fig. 308.—Diagram of a
mercury arc rectifier.
Important Topics
Transformer, induction coil, mercury arc rectifier, construction, action; uses
of each.
Exercises
electrodes marked G in Fig. 308 and a mercury electrode marked M. It is
found that current will pass through such a bulb only from the graphite to
the mercury but not in the reverse direction. In operating the device, the
secondary terminals of an alternating current transformer T are connected to
the graphite terminals of the rectifier. A wire connected to the center of the
secondary of the transformer at C is attached to the negative terminal of the
storage battery SB. The positive terminal of the battery is connected to the
mercury electrode of the rectifier tube through a reactance or choke coil R.
This coil serves to sustain the arc between the alternations. Sw is a starting
switch, used only in striking the arc. It is opened immediately after the tube
begins to glow.
Fig. 308.—Diagram of a
mercury arc rectifier.
Important Topics
Transformer, induction coil, mercury arc rectifier, construction, action; uses
of each.
Exercises
Page 341
1. Does the spark of an induction coil occur at "make" or at "break?" Why?
2. What must be the relative number of turns upon the primary and
secondary coils of a transformer if it receives current at 220 volts and
delivers current at 110? Also show by diagram.
3. Would the transformer work upon a direct current? Why?
4. Explain why the interrupter is a necessary part of the induction coil and
not of the transformer.
5. If a building used eighty 110-volt incandescent lamps, what would be
necessary to light them if they were joined in series? Why would this not be
practical?
6. If a 16-candle-power lamp requires 0.5 ampere upon a 110-volt circuit
what current and voltage will be needed to operate 12 such lamps in
parallel?
7. What will it cost to run these lamps 4 hours a night for 30 days at 10
cents per kilowatt hour?
8. If a mercury arc rectifier uses 5 amperes of current at 110 volts
alternating current to produce 5 amperes of direct current at 70 volts, what
is the efficiency of the rectifier?
9. Compute the heat produced in a 40 watt tungsten lamp in 1 minute.
10. Compute the heat produced in a 60 watt carbon incandescent lamp in 1
hour.
(4) The Telephone
312. The Electric Telephone.—This is an instrument for reproducing the
human voice at a distance by an electric current. The modern electric
telephone consists of at least four distinct parts (see Fig. 312); viz., a
transmitter, an induction coil, an electric battery, and a receiver. The first
three of these are concerned in sending, or transmitting over the connecting
wires a fluctuating electric current, which has been modified by the waves
of a human voice. The receiver, is affected by the fluctuating current and
reproduces the voice. It will be considered first, in our study.
2. What must be the relative number of turns upon the primary and
secondary coils of a transformer if it receives current at 220 volts and
delivers current at 110? Also show by diagram.
3. Would the transformer work upon a direct current? Why?
4. Explain why the interrupter is a necessary part of the induction coil and
not of the transformer.
5. If a building used eighty 110-volt incandescent lamps, what would be
necessary to light them if they were joined in series? Why would this not be
practical?
6. If a 16-candle-power lamp requires 0.5 ampere upon a 110-volt circuit
what current and voltage will be needed to operate 12 such lamps in
parallel?
7. What will it cost to run these lamps 4 hours a night for 30 days at 10
cents per kilowatt hour?
8. If a mercury arc rectifier uses 5 amperes of current at 110 volts
alternating current to produce 5 amperes of direct current at 70 volts, what
is the efficiency of the rectifier?
9. Compute the heat produced in a 40 watt tungsten lamp in 1 minute.
10. Compute the heat produced in a 60 watt carbon incandescent lamp in 1
hour.
(4) The Telephone
312. The Electric Telephone.—This is an instrument for reproducing the
human voice at a distance by an electric current. The modern electric
telephone consists of at least four distinct parts (see Fig. 312); viz., a
transmitter, an induction coil, an electric battery, and a receiver. The first
three of these are concerned in sending, or transmitting over the connecting
wires a fluctuating electric current, which has been modified by the waves
of a human voice. The receiver, is affected by the fluctuating current and
reproduces the voice. It will be considered first, in our study.
Page 342
313. The telephone receiver was invented in 1876 by Alexander Graham
Bell. It consists of a permanent steel magnet, U shaped, with a coil of fine
insulated copper wire about each pole. (See Fig. 310.) A disc of thin sheet
iron is supported so that its center does not quite touch the poles of the
magnet. A hard rubber cap or ear piece with an opening at its center is
screwed on so as to hold the iron disc firmly in place.
The action of the receiver may be understood
from the following explanation: The electric
current sent to the receiver, comes from the
secondary coil of the induction coil; it is an
alternating current, fluctuating back and forth
just in time with the waves of the voice
affecting it at the transmitter. This alternating
current flows around the coils on the poles of
Fig. 309.—The simplest
the permanent magnet. When this current
telephone system. It
flows in one direction, its magnetic field
consists of two telephone
assists the field of the permanent magnet,
receivers connected in
strengthening it. This stronger magnetic field
series on a circuit. It will draws the thin iron disc in front of the poles
work, but not of the magnet a little closer to them. When the
satisfactorily. current in the coils flows the other way, its
magnetic field weakens the field of the steel
magnet, and the disc is drawn back by the force of its own elasticity. Thus
the disc of the receiver vibrates with the alternations of the current, and
reproduces the same sounds that were spoken into the transmitter.
314. The Telephone Transmitter.—The telephone
receiver just described has great sensitiveness in
reproducing sound, but it is not satisfactory as a
transmitter or sending apparatus. The transmitter
commonly used is represented in cross-section in
Fig. 311. In this figure, back of the mouthpiece, is
a thin carbon disc, D. Back of this disc is a circular
compartment containing granular carbon, g. The
wires of the circuit are connected to the carbon Fig. 310.—A
disc and to the back of the case containing granular telephone receiver.
carbon. The circuit through the transmitter also This receiver has a
Bell. It consists of a permanent steel magnet, U shaped, with a coil of fine
insulated copper wire about each pole. (See Fig. 310.) A disc of thin sheet
iron is supported so that its center does not quite touch the poles of the
magnet. A hard rubber cap or ear piece with an opening at its center is
screwed on so as to hold the iron disc firmly in place.
The action of the receiver may be understood
from the following explanation: The electric
current sent to the receiver, comes from the
secondary coil of the induction coil; it is an
alternating current, fluctuating back and forth
just in time with the waves of the voice
affecting it at the transmitter. This alternating
current flows around the coils on the poles of
Fig. 309.—The simplest
the permanent magnet. When this current
telephone system. It
flows in one direction, its magnetic field
consists of two telephone
assists the field of the permanent magnet,
receivers connected in
strengthening it. This stronger magnetic field
series on a circuit. It will draws the thin iron disc in front of the poles
work, but not of the magnet a little closer to them. When the
satisfactorily. current in the coils flows the other way, its
magnetic field weakens the field of the steel
magnet, and the disc is drawn back by the force of its own elasticity. Thus
the disc of the receiver vibrates with the alternations of the current, and
reproduces the same sounds that were spoken into the transmitter.
314. The Telephone Transmitter.—The telephone
receiver just described has great sensitiveness in
reproducing sound, but it is not satisfactory as a
transmitter or sending apparatus. The transmitter
commonly used is represented in cross-section in
Fig. 311. In this figure, back of the mouthpiece, is
a thin carbon disc, D. Back of this disc is a circular
compartment containing granular carbon, g. The
wires of the circuit are connected to the carbon Fig. 310.—A
disc and to the back of the case containing granular telephone receiver.
carbon. The circuit through the transmitter also This receiver has a
Page 343
includes a voltaic or storage cell and the primary permanent
coil of an induction coil. (See Fig. 312.) horseshoe magnet
with a coil about
each pole.
Fig. 311.—A telephone transmitter.
Fig. 312.—Telephone instruments at one end
of a talking circuit.
315. The action of the transmitter is explained as follows: When the
sound waves of the voice strike upon the carbon disc, the latter vibrates,
alternately increasing and decreasing the pressure upon the granular carbon.
When the pressure increases, the electrical resistance of the granular carbon
is lessened, and when the pressure upon it is decreased, its resistance
increases. This changing resistance causes fluctuations in the electric
current that correspond exactly with the sound waves of the voice affecting
it.
316. A complete telephone system operating with a local battery is shown
in Fig. 312. A person speaking into the transmitter causes a fluctuation in
the electric current in the transmitter as described in Art. 315. This
fluctuating current passes through the primary coil of the induction coil Ic.
This fluctuating current produces a fluctuating magnetic field in its core.
This fluctuating field induces an alternating current in the secondary coil
which alternates just as the primary current fluctuates, but with a much
higher E.M.F. than the latter. The alternating current passes to the receiver
which reproduces the speech as described in Art. 313. The line circuit
includes the secondary of the induction coil, the receiving instrument and
the receiver of the sending instrument so that the voice is reproduced in
both receivers. An electric bell is placed at each station to call the attention
of parties wanted. The movement of the receiver hook when the receiver is
coil of an induction coil. (See Fig. 312.) horseshoe magnet
with a coil about
each pole.
Fig. 311.—A telephone transmitter.
Fig. 312.—Telephone instruments at one end
of a talking circuit.
315. The action of the transmitter is explained as follows: When the
sound waves of the voice strike upon the carbon disc, the latter vibrates,
alternately increasing and decreasing the pressure upon the granular carbon.
When the pressure increases, the electrical resistance of the granular carbon
is lessened, and when the pressure upon it is decreased, its resistance
increases. This changing resistance causes fluctuations in the electric
current that correspond exactly with the sound waves of the voice affecting
it.
316. A complete telephone system operating with a local battery is shown
in Fig. 312. A person speaking into the transmitter causes a fluctuation in
the electric current in the transmitter as described in Art. 315. This
fluctuating current passes through the primary coil of the induction coil Ic.
This fluctuating current produces a fluctuating magnetic field in its core.
This fluctuating field induces an alternating current in the secondary coil
which alternates just as the primary current fluctuates, but with a much
higher E.M.F. than the latter. The alternating current passes to the receiver
which reproduces the speech as described in Art. 313. The line circuit
includes the secondary of the induction coil, the receiving instrument and
the receiver of the sending instrument so that the voice is reproduced in
both receivers. An electric bell is placed at each station to call the attention
of parties wanted. The movement of the receiver hook when the receiver is
Page 344
lifted, disconnects the bell and closes the talking circuit. The latter is
opened and the bell connected when the receiver is hung up again.
Fig. 313.—Diagram of a telephone system as
used in a large exchange.
In cities and towns, the telephone system in use differs from the one
described in usually having one large battery placed in the central exchange,
instead of dry cells at each instrument. (See Fig. 313.) Also the operator at
central is called by simply taking the receiver from the hook instead of
being "rung up" by the subscriber. The operations of the transmitter,
induction coil and receiver, however, are the same in all telephones.
Important Topics
1. Receiver: parts, action.
2. Transmitter: parts, action.
3. Induction coil, bell, line wires, etc.
4. Action of the whole device.
Exercises
1. State three important electrical laws or principles that are employed in
the operation of the telephone. What is the application of each?
2. Connect the binding posts of a telephone receiver with a sensitive
galvanometer and press on the diaphragm of the receiver; a deflection of the
galvanometer will be noticed. Release the diaphragm and a reflection in the
opposite direction is seen. Explain.
3. Is the current passing through the transmitter the one going to the
receiver of the instrument? Explain.
opened and the bell connected when the receiver is hung up again.
Fig. 313.—Diagram of a telephone system as
used in a large exchange.
In cities and towns, the telephone system in use differs from the one
described in usually having one large battery placed in the central exchange,
instead of dry cells at each instrument. (See Fig. 313.) Also the operator at
central is called by simply taking the receiver from the hook instead of
being "rung up" by the subscriber. The operations of the transmitter,
induction coil and receiver, however, are the same in all telephones.
Important Topics
1. Receiver: parts, action.
2. Transmitter: parts, action.
3. Induction coil, bell, line wires, etc.
4. Action of the whole device.
Exercises
1. State three important electrical laws or principles that are employed in
the operation of the telephone. What is the application of each?
2. Connect the binding posts of a telephone receiver with a sensitive
galvanometer and press on the diaphragm of the receiver; a deflection of the
galvanometer will be noticed. Release the diaphragm and a reflection in the
opposite direction is seen. Explain.
3. Is the current passing through the transmitter the one going to the
receiver of the instrument? Explain.
Page 345
4. Does the receiver at the telephone used by a person repeat the speech of
the person? Explain.
5. How many 0.5 ampere lamps can be used with a 6 ampere fuse?
6. Why is it necessary to have a rheostat connected in series with a
stereopticon or moving picture machine while a rheostat is not used with
arc lights out doors?
7. How many candle power should a 60 watt carbon incandescent lamp
give, if its efficiency is 3.4 watts per candle power?
8. Three incandescent lamps having resistances of 100, 150, and 240 ohms,
respectively, are connected in parallel. What is their combined resistance?
Review Outline: Induced Currents
Induced currents; 3 laws, illustrations.
Construction, action, and uses of—magneto, dynamo, induction coil,
transformer, motor, telephone. Mercury arc rectifier.
Terms—primary, secondary, for coils and currents, armature, commutator,
slip ring, brush, rectifier, open core, series, shunt, and compound
connections for dynamos.
the person? Explain.
5. How many 0.5 ampere lamps can be used with a 6 ampere fuse?
6. Why is it necessary to have a rheostat connected in series with a
stereopticon or moving picture machine while a rheostat is not used with
arc lights out doors?
7. How many candle power should a 60 watt carbon incandescent lamp
give, if its efficiency is 3.4 watts per candle power?
8. Three incandescent lamps having resistances of 100, 150, and 240 ohms,
respectively, are connected in parallel. What is their combined resistance?
Review Outline: Induced Currents
Induced currents; 3 laws, illustrations.
Construction, action, and uses of—magneto, dynamo, induction coil,
transformer, motor, telephone. Mercury arc rectifier.
Terms—primary, secondary, for coils and currents, armature, commutator,
slip ring, brush, rectifier, open core, series, shunt, and compound
connections for dynamos.
Page 346
CHAPTER XV
SOUND
(1) Sound and Wave Motion
317. What is a Sound?—This question has two answers, which may be
illustrated as follows: Suppose that an alarm clock is set so that it will strike
in one week and that it is placed upon a barren rock in the Pacific Ocean by
sailors who immediately sail away. If when the tapper strikes the bell at the
end of the week no ear is within a hundred miles, is any sound produced?
The two view-points are now made evident, for some will answer "no"
others "yes." Those answering "no" hold that sound is a sensation which
would not be produced if no ear were at hand to be affected. Those
answering "yes" understand, by the term sound, a mode of motion capable
of affecting the auditory nerves, and that sound exists wherever such
motions are present. This latter point of view is called the physical and is
the one we are to use in this study.
318. Source of Sound.—If we trace any sound to its
source, it will be found to originate in a body in rapid
motion usually in what is called a state of vibration. To
illustrate, take a tuning fork, strike it to set it in vibration
and place its stem firmly against a thin piece of wood; the
sound will be strengthened materially by the vibration of
the wood. If now the vibrating fork is placed with the tips
of the prongs in water, the vibration is plainly shown by
the spattering of the water (Fig. 314). When one speaks,
the vibrating body is in the larynx at the top of the
windpipe. Its vibration may be plainly felt by the hand
placed upon the throat while speaking.
319. Sound Media.—Usually sounds reach the ear
through the air. The air is then said to be a medium for
Fig. 314.— sound. Other substances may serve as a sound medium,
SOUND
(1) Sound and Wave Motion
317. What is a Sound?—This question has two answers, which may be
illustrated as follows: Suppose that an alarm clock is set so that it will strike
in one week and that it is placed upon a barren rock in the Pacific Ocean by
sailors who immediately sail away. If when the tapper strikes the bell at the
end of the week no ear is within a hundred miles, is any sound produced?
The two view-points are now made evident, for some will answer "no"
others "yes." Those answering "no" hold that sound is a sensation which
would not be produced if no ear were at hand to be affected. Those
answering "yes" understand, by the term sound, a mode of motion capable
of affecting the auditory nerves, and that sound exists wherever such
motions are present. This latter point of view is called the physical and is
the one we are to use in this study.
318. Source of Sound.—If we trace any sound to its
source, it will be found to originate in a body in rapid
motion usually in what is called a state of vibration. To
illustrate, take a tuning fork, strike it to set it in vibration
and place its stem firmly against a thin piece of wood; the
sound will be strengthened materially by the vibration of
the wood. If now the vibrating fork is placed with the tips
of the prongs in water, the vibration is plainly shown by
the spattering of the water (Fig. 314). When one speaks,
the vibrating body is in the larynx at the top of the
windpipe. Its vibration may be plainly felt by the hand
placed upon the throat while speaking.
319. Sound Media.—Usually sounds reach the ear
through the air. The air is then said to be a medium for
Fig. 314.— sound. Other substances may serve as a sound medium,
Page 347
The tuning for if the head is under water and two stones, also under
fork is water, are struck together a sharp sound is heard. Also if
vibrating. one end of a wooden rod is held at the ear and the other
end of the rod is scratched by a pin, the sound is more
plainly perceived through the wood than through the air. Think of some
illustration from your own experience of a solid acting as medium for
sound. If an electric bell is placed in a bell jar attached to an air pump, as in
Fig. 315, on exhausting the air the loudness of the sound is found to
diminish, indicating that in a perfect vacuum no sound would be
transmitted. This effect of a vacuum upon the transmission of sound is very
different from its effect upon radiation of heat and light. Both heat and light
are known to pass through a vacuum since both come to the earth from the
sun through space that so far as we know contains no air or other matter.
Sound differs from this in that it is always transmitted by some material
body and cannot exist in a vacuum.
320. Speed of Sound.—Everyone has noticed that it takes
time for sound to travel from one place to another. If we see
a gun fired at a distance, the report is heard a few seconds
after the smoke or flash is seen. The time elapsing between a
flash of lightning and the thunder shows that sound takes
time to move from one place to another. Careful experiments
to determine the speed of sound have been made. One
method measures accurately the time required for the sound
of a gun to pass between two stations several miles apart. A
Fig. 315.—
gun or cannon is placed at each station. These are fired
Sound does
alternately, first the one at one station and then the one at the
not travel
other so as to avoid an error in computation due to the
in a
motion of wind. This mode of determining the speed of
vacuum.
sound is not accurate. Other methods, more refined than the
one just described have given accurate values for the speed
of sound. The results of a number of experiments show that, at the freezing
temperature, 0°C., the speed of sound in air is 332 meters or 1090 ft. a
second. The speed of sound in air is affected by the temperature, increasing
2 ft. or 0.6 meter per second for each degree that the temperature rises
above 0°C. The speed decreases the same amount for each degree C. that
the air is cooled below the freezing point. The speed of sound in various
substances has been carefully determined. It is greater in most of them than
fork is water, are struck together a sharp sound is heard. Also if
vibrating. one end of a wooden rod is held at the ear and the other
end of the rod is scratched by a pin, the sound is more
plainly perceived through the wood than through the air. Think of some
illustration from your own experience of a solid acting as medium for
sound. If an electric bell is placed in a bell jar attached to an air pump, as in
Fig. 315, on exhausting the air the loudness of the sound is found to
diminish, indicating that in a perfect vacuum no sound would be
transmitted. This effect of a vacuum upon the transmission of sound is very
different from its effect upon radiation of heat and light. Both heat and light
are known to pass through a vacuum since both come to the earth from the
sun through space that so far as we know contains no air or other matter.
Sound differs from this in that it is always transmitted by some material
body and cannot exist in a vacuum.
320. Speed of Sound.—Everyone has noticed that it takes
time for sound to travel from one place to another. If we see
a gun fired at a distance, the report is heard a few seconds
after the smoke or flash is seen. The time elapsing between a
flash of lightning and the thunder shows that sound takes
time to move from one place to another. Careful experiments
to determine the speed of sound have been made. One
method measures accurately the time required for the sound
of a gun to pass between two stations several miles apart. A
Fig. 315.—
gun or cannon is placed at each station. These are fired
Sound does
alternately, first the one at one station and then the one at the
not travel
other so as to avoid an error in computation due to the
in a
motion of wind. This mode of determining the speed of
vacuum.
sound is not accurate. Other methods, more refined than the
one just described have given accurate values for the speed
of sound. The results of a number of experiments show that, at the freezing
temperature, 0°C., the speed of sound in air is 332 meters or 1090 ft. a
second. The speed of sound in air is affected by the temperature, increasing
2 ft. or 0.6 meter per second for each degree that the temperature rises
above 0°C. The speed decreases the same amount for each degree C. that
the air is cooled below the freezing point. The speed of sound in various
substances has been carefully determined. It is greater in most of them than
Page 348
in air. In water the speed is about 1400 meters a second; in wood, while its
speed varies with different kinds, it averages about 4000 meters a second; in
brass the speed is about 3500 meters; while in iron it is about 5100 meters a
second.
321. The Nature of Sound.—We have observed that sound originates at a
vibrating body, that it requires a medium in order to be transmitted from
one place to another, and that it travels at a definite speed in a given
substance. Nothing has been said, however, of the mode of transmission, or
of the nature of sound. Sounds continue to come from an alarm clock even
though it is placed under a bell jar. It is certain that nothing material can
pass through the glass of the jar. If, however, we consider that sound is
transmitted by waves through substances the whole matter can be given a
simple explanation. In order to better understand the nature of sound a study
of waves and wave motion will be taken up in the next section.
Important Topics
Sound: two definitions, source, medium, speed, nature.
Exercises
1. Give two illustrations from outside the laboratory of the fact that sound is
transmitted by other materials than air.
2. Name the vibrating part that is the source of the sound in three different
musical instruments.
3. Is sound transmitted more strongly in solids, liquids or gases? How do
you explain this?
4. How far away is a steamboat if the sound of its whistle is heard 10
seconds after the steam is seen, the temperature being 20°C.? Compute in
feet and in meters.
5. How many miles away is lightning if the thunder is heard 12 seconds
after the flash in seen, the temperature being 25°C.?
6. Four seconds after a flash of lightning is seen the thunder clap is heard.
The temperature is 90°F. How far away was the discharge?
speed varies with different kinds, it averages about 4000 meters a second; in
brass the speed is about 3500 meters; while in iron it is about 5100 meters a
second.
321. The Nature of Sound.—We have observed that sound originates at a
vibrating body, that it requires a medium in order to be transmitted from
one place to another, and that it travels at a definite speed in a given
substance. Nothing has been said, however, of the mode of transmission, or
of the nature of sound. Sounds continue to come from an alarm clock even
though it is placed under a bell jar. It is certain that nothing material can
pass through the glass of the jar. If, however, we consider that sound is
transmitted by waves through substances the whole matter can be given a
simple explanation. In order to better understand the nature of sound a study
of waves and wave motion will be taken up in the next section.
Important Topics
Sound: two definitions, source, medium, speed, nature.
Exercises
1. Give two illustrations from outside the laboratory of the fact that sound is
transmitted by other materials than air.
2. Name the vibrating part that is the source of the sound in three different
musical instruments.
3. Is sound transmitted more strongly in solids, liquids or gases? How do
you explain this?
4. How far away is a steamboat if the sound of its whistle is heard 10
seconds after the steam is seen, the temperature being 20°C.? Compute in
feet and in meters.
5. How many miles away is lightning if the thunder is heard 12 seconds
after the flash in seen, the temperature being 25°C.?
6. Four seconds after a flash of lightning is seen the thunder clap is heard.
The temperature is 90°F. How far away was the discharge?
Page 349
7. The report of a gun is heard 3 seconds after the puff of smoke is seen.
How far away is the gun if the temperature is 20°C.?
8. An explosion takes place 10 miles away. How long will it take the sound
to reach you, the temperature being 80°F?. How long at 0°F.?
9. How long after a whistle is sounded will it be heard if the distance away
is 1/4 mile, the temperature being 90°F.?
10. The report of an explosion of dynamite is heard 2 minutes after the puff
of smoke is seen. How far away is the explosion the temperature being
77°F.?
(2) Waves[N] and Wave Motion
322. Visible Waves.—It is best to begin the study of wave motion by
considering some waves which are familiar to most persons. Take for
example the waves that move over the surface of water (Fig. 316). These
have an onward motion, yet boards or chips upon the surface simply rise
and fall as the waves pass them. They are not carried onward by the waves.
The water surface simply rises and falls as the waves pass by. Consider also
the waves that may be seen to move across a field of tall grass or grain.
Such waves are produced by the bending and rising of the stalks as the wind
passes over them. Again, waves may be produced in a rope fastened at one
end, by suddenly moving the other end up and down. These waves move to
the end of the rope where they are reflected and return. The three types of
waves just mentioned are illustrations of transverse waves, the ideal case
being that in which the particles move at right angles to the path or course
of the wave. Such waves are therefore called transverse waves.
323. Longitudinal waves.—Another kind of wave is
found in bodies that are elastic and compressible and
have inertia, such as gases and coiled wire springs.
Such waves may be studied by considering a wire
Fig. 316.—Water spring as the medium through which the waves pass.
waves. (See Fig. 318.)
If the end of the wire spring shown in Fig. 317 is
struck the first few turns of the spring will be compressed. Since the spring
How far away is the gun if the temperature is 20°C.?
8. An explosion takes place 10 miles away. How long will it take the sound
to reach you, the temperature being 80°F?. How long at 0°F.?
9. How long after a whistle is sounded will it be heard if the distance away
is 1/4 mile, the temperature being 90°F.?
10. The report of an explosion of dynamite is heard 2 minutes after the puff
of smoke is seen. How far away is the explosion the temperature being
77°F.?
(2) Waves[N] and Wave Motion
322. Visible Waves.—It is best to begin the study of wave motion by
considering some waves which are familiar to most persons. Take for
example the waves that move over the surface of water (Fig. 316). These
have an onward motion, yet boards or chips upon the surface simply rise
and fall as the waves pass them. They are not carried onward by the waves.
The water surface simply rises and falls as the waves pass by. Consider also
the waves that may be seen to move across a field of tall grass or grain.
Such waves are produced by the bending and rising of the stalks as the wind
passes over them. Again, waves may be produced in a rope fastened at one
end, by suddenly moving the other end up and down. These waves move to
the end of the rope where they are reflected and return. The three types of
waves just mentioned are illustrations of transverse waves, the ideal case
being that in which the particles move at right angles to the path or course
of the wave. Such waves are therefore called transverse waves.
323. Longitudinal waves.—Another kind of wave is
found in bodies that are elastic and compressible and
have inertia, such as gases and coiled wire springs.
Such waves may be studied by considering a wire
Fig. 316.—Water spring as the medium through which the waves pass.
waves. (See Fig. 318.)
If the end of the wire spring shown in Fig. 317 is
struck the first few turns of the spring will be compressed. Since the spring
Page 350
possesses elasticity, the turns will move
forward a little and compress those ahead,
these will press the next in turn and so on.
Thus a compression wave will move to
the end of the spring, where it will be
reflected and return. Consider the turns of Fig. 317.—The compression
the spring as they move toward the end. wave travels through the
On account of their inertia they will spring.
continue moving until they have separated
from each other more than at first, before returning to their usual position.
This condition of a greater separation of the turns of the spring than usual is
called a rarefaction. It moves along the spring following the wave of
compression. The condensation and rarefaction are considered as together
forming a complete wave. Since the turns of wire move back and forth in a
direction parallel to that in which the wave is traveling, these waves are
called longitudinal.
Fig. 318.—Longitudinal waves (1) in a spring,
(2) in air, and (3) graphic representation
showing wave length, condensations, and
rarefactions.
324. The transmission of a sound by the air may be understood by
comparing it with the process by which a wave is transmitted by a wire
spring. Consider a light spring (Fig. 318, 1) attached at the end of a
vibrating tuning fork, K, and also to a diaphragm, D. Each vibration of the
fork will first compress and then separate the coils of the spring. These
impulses will be transmitted by the spring as described in Art. 315, and
cause the diaphragm to vibrate at the same rate as the tuning fork. The
forward a little and compress those ahead,
these will press the next in turn and so on.
Thus a compression wave will move to
the end of the spring, where it will be
reflected and return. Consider the turns of Fig. 317.—The compression
the spring as they move toward the end. wave travels through the
On account of their inertia they will spring.
continue moving until they have separated
from each other more than at first, before returning to their usual position.
This condition of a greater separation of the turns of the spring than usual is
called a rarefaction. It moves along the spring following the wave of
compression. The condensation and rarefaction are considered as together
forming a complete wave. Since the turns of wire move back and forth in a
direction parallel to that in which the wave is traveling, these waves are
called longitudinal.
Fig. 318.—Longitudinal waves (1) in a spring,
(2) in air, and (3) graphic representation
showing wave length, condensations, and
rarefactions.
324. The transmission of a sound by the air may be understood by
comparing it with the process by which a wave is transmitted by a wire
spring. Consider a light spring (Fig. 318, 1) attached at the end of a
vibrating tuning fork, K, and also to a diaphragm, D. Each vibration of the
fork will first compress and then separate the coils of the spring. These
impulses will be transmitted by the spring as described in Art. 315, and
cause the diaphragm to vibrate at the same rate as the tuning fork. The
Page 351
diaphragm will then give out a sound similar to that of the tuning fork.
Suppose that the spring is replaced by air, and the diaphragm, by the ear of
a person, E, (Fig. 318, 2.) when the prong of the fork moves toward the ear
it starts a compression and when it moves back a rarefaction. The fork
continues vibrating and these impulses move onward like those in the
spring at a speed of about 1120 ft. in a second. They strike the diaphragm of
the ear causing it to move back and forth or to vibrate at the same rate as the
tuning fork, just as in the case of the diaphragm attached to the spring.
325. Graphic Representation of Sound waves.—It is frequently desirable
to represent sound waves graphically. The usual method is to use a curve
like that in (Fig. 318, 3). This curve is considered as representing a train of
waves moving in the same direction as those in Fig. 318 1 and 2, and also
having the same length. The part of the wave A-B represents a condensation
of the sound wave and the part B-C represents a rarefaction. A complete
wave consisting of a condensation and a rarefaction is represented by that
portion of the curve A-C. The portion of the curve B-D also represents a full
wave length as the latter is defined as the distance between two
corresponding parts of the adjacent waves. The curve, Fig. (318, 3)
represents not only the wave length, but also the height of the wave or the
amount of movement of the particles along the wave. This is called the
amplitude and is indicated by the distance A-b. Since the loudness or
intensity of a sound is found to depend upon the amount of movement of
the particles along the wave, the amplitude of the curve is used to indicate
the loudness of the sound represented. All of the characteristics of a sound
wave may be graphically represented by curves. Such curves will be used
frequently as an aid in explaining the phenomena of wave motion both in
sound and in light.
326. Reflections of Sound.—It is found that a wave moving along a wire
spring is reflected when it reaches the end and returns along the spring.
Similarly a sound wave in air is reflected upon striking the surface of a
body. If the wave strikes perpendicularly it returns along the line from
which it comes, if, however, it strikes at some other angle it does not return
along the same line, but as in other cases of reflected motion, the direction
of the reflected wave is described by the Law of Reflected Motion as
follows: The angle of reflection is always equal to the angle of incidence.
This law is illustrated in Fig. 319. Suppose that a series of waves coming
Suppose that the spring is replaced by air, and the diaphragm, by the ear of
a person, E, (Fig. 318, 2.) when the prong of the fork moves toward the ear
it starts a compression and when it moves back a rarefaction. The fork
continues vibrating and these impulses move onward like those in the
spring at a speed of about 1120 ft. in a second. They strike the diaphragm of
the ear causing it to move back and forth or to vibrate at the same rate as the
tuning fork, just as in the case of the diaphragm attached to the spring.
325. Graphic Representation of Sound waves.—It is frequently desirable
to represent sound waves graphically. The usual method is to use a curve
like that in (Fig. 318, 3). This curve is considered as representing a train of
waves moving in the same direction as those in Fig. 318 1 and 2, and also
having the same length. The part of the wave A-B represents a condensation
of the sound wave and the part B-C represents a rarefaction. A complete
wave consisting of a condensation and a rarefaction is represented by that
portion of the curve A-C. The portion of the curve B-D also represents a full
wave length as the latter is defined as the distance between two
corresponding parts of the adjacent waves. The curve, Fig. (318, 3)
represents not only the wave length, but also the height of the wave or the
amount of movement of the particles along the wave. This is called the
amplitude and is indicated by the distance A-b. Since the loudness or
intensity of a sound is found to depend upon the amount of movement of
the particles along the wave, the amplitude of the curve is used to indicate
the loudness of the sound represented. All of the characteristics of a sound
wave may be graphically represented by curves. Such curves will be used
frequently as an aid in explaining the phenomena of wave motion both in
sound and in light.
326. Reflections of Sound.—It is found that a wave moving along a wire
spring is reflected when it reaches the end and returns along the spring.
Similarly a sound wave in air is reflected upon striking the surface of a
body. If the wave strikes perpendicularly it returns along the line from
which it comes, if, however, it strikes at some other angle it does not return
along the same line, but as in other cases of reflected motion, the direction
of the reflected wave is described by the Law of Reflected Motion as
follows: The angle of reflection is always equal to the angle of incidence.
This law is illustrated in Fig. 319. Suppose that a series of waves coming
Page 352
from a source of sound move from H to O. After striking the surface IJ the
waves are reflected and move toward L along the line OL. Let PO be
perpendicular to the surface IJ at O. Then HOP is the angle of incidence
and LOP is the angle of reflection. By the law of reflected motion these
angles are equal. In an ordinary room when a person speaks the sound
waves reflected from the smooth walls reinforce the sound waves moving
directly to the hearers. It is for this reason that it is usually easier to speak in
at room than in the open air. Other illustrations of the reinforcement of
sound by reflection are often seen. Thus an ear trumpet (Fig. 320), uses the
principle of reflection and concentration of sound. So-called sounding
boards are sometimes placed back of speakers in large halls to reflect sound
waves to the audience.
Fig. 319.—Law of reflection.
Fig. 320.—An ear trumpet.
327. Echoes.—An echo is the repetition of a sound caused by its reflection
from some distant surface such as that of a building, cliff, clouds, trees, etc.
The interval of time between the production of a sound and the perception
of its echo is the time that the sound takes to travel from its source to the
reflecting body and back to the listener. Experiments have shown that the
sensation of a sound persists about one-tenth of a second. Since the velocity
of sound at 20°C. is about 1130 ft. per second, during one-tenth of a second
the sound wave will travel some 113 ft. If the reflecting surface is about 56
ft. distant a short sound will be followed immediately by its echo as it is
heard one-tenth of a second after the original sound. The reflected sound
tends to strengthen the original one if the reflecting surface is less than 56
ft. away. If the distance of the reflecting surface is much more than 56 ft.
however, the reflected sound does not blend with the original one but forms
a distinct echo. The echoes in large halls especially those with large smooth
walls may very seriously affect the clear perception of the sound. Such
waves are reflected and move toward L along the line OL. Let PO be
perpendicular to the surface IJ at O. Then HOP is the angle of incidence
and LOP is the angle of reflection. By the law of reflected motion these
angles are equal. In an ordinary room when a person speaks the sound
waves reflected from the smooth walls reinforce the sound waves moving
directly to the hearers. It is for this reason that it is usually easier to speak in
at room than in the open air. Other illustrations of the reinforcement of
sound by reflection are often seen. Thus an ear trumpet (Fig. 320), uses the
principle of reflection and concentration of sound. So-called sounding
boards are sometimes placed back of speakers in large halls to reflect sound
waves to the audience.
Fig. 319.—Law of reflection.
Fig. 320.—An ear trumpet.
327. Echoes.—An echo is the repetition of a sound caused by its reflection
from some distant surface such as that of a building, cliff, clouds, trees, etc.
The interval of time between the production of a sound and the perception
of its echo is the time that the sound takes to travel from its source to the
reflecting body and back to the listener. Experiments have shown that the
sensation of a sound persists about one-tenth of a second. Since the velocity
of sound at 20°C. is about 1130 ft. per second, during one-tenth of a second
the sound wave will travel some 113 ft. If the reflecting surface is about 56
ft. distant a short sound will be followed immediately by its echo as it is
heard one-tenth of a second after the original sound. The reflected sound
tends to strengthen the original one if the reflecting surface is less than 56
ft. away. If the distance of the reflecting surface is much more than 56 ft.
however, the reflected sound does not blend with the original one but forms
a distinct echo. The echoes in large halls especially those with large smooth
walls may very seriously affect the clear perception of the sound. Such
Page 353
rooms are said to have poor acoustic properties. Furniture, drapery, and
carpets help to deaden the echo because of diffused reflection. The Mormon
Tabernacle at Salt Lake City, Utah, is a fine example of a building in which
the reflecting surfaces of the walls and ceiling are of such shape and
material that its acoustic properties are remarkable, a pin dropped at one
end being plainly heard at the other end about 200 ft. away.
Important Topics
1. Waves: transverse, longitudinal; wave length, condensation, rarefaction.
2. Wave motion: in coiled spring, in air, on water.
3. Reflection of waves: law, echoes.
Exercises
1. A hunter hears an echo in 8 seconds after firing his gun. How far is the
reflecting surface if the temperature is 20°C.?
2. How far is the reflecting surface of a building if the echo of one's
footsteps returns in 1 second at 10°C.?
3. Why is it easier to speak or sing in a room than out of doors?
4. Draw a curve that represents wave motion. Make it exactly three full
wave lengths, and state why your curve shows this length. Indicate the parts
of the curve that correspond to a condensation and to a rarefaction.
5. How long does it take the sound of the "pin drop" to reach a person at the
farther end of the building mentioned at the end of Art. 327?
6. An echo is heard after 6 seconds. How far away is the reflecting surface,
the temperature being 70°F.?
7. Why are outdoor band-stands generally made with the back curving over
the band?
8. A man near a forest calls to a friend. In 4 seconds the echo comes back.
How far away is he from the forest?
carpets help to deaden the echo because of diffused reflection. The Mormon
Tabernacle at Salt Lake City, Utah, is a fine example of a building in which
the reflecting surfaces of the walls and ceiling are of such shape and
material that its acoustic properties are remarkable, a pin dropped at one
end being plainly heard at the other end about 200 ft. away.
Important Topics
1. Waves: transverse, longitudinal; wave length, condensation, rarefaction.
2. Wave motion: in coiled spring, in air, on water.
3. Reflection of waves: law, echoes.
Exercises
1. A hunter hears an echo in 8 seconds after firing his gun. How far is the
reflecting surface if the temperature is 20°C.?
2. How far is the reflecting surface of a building if the echo of one's
footsteps returns in 1 second at 10°C.?
3. Why is it easier to speak or sing in a room than out of doors?
4. Draw a curve that represents wave motion. Make it exactly three full
wave lengths, and state why your curve shows this length. Indicate the parts
of the curve that correspond to a condensation and to a rarefaction.
5. How long does it take the sound of the "pin drop" to reach a person at the
farther end of the building mentioned at the end of Art. 327?
6. An echo is heard after 6 seconds. How far away is the reflecting surface,
the temperature being 70°F.?
7. Why are outdoor band-stands generally made with the back curving over
the band?
8. A man near a forest calls to a friend. In 4 seconds the echo comes back.
How far away is he from the forest?
Page 354
9. Would it be possible for us ever to hear a great explosion upon the moon?
Explain.
10. If a sunset gun was fired exactly at 6:00 P.M. at a fort, at what time was
the report heard by a man 25 miles away, if the temperature was 10°C.?
(3) Intensity and Pitch of Sounds
Fig. 321.—Graphic representations of (a) a
noise, (b) a musical sound.
328. Musical Sounds and Noises Distinguished.—The question is
sometimes raised, what is the difference between a noise and a musical
sound? The latter has been found to be produced by an even and regular
vibration such as that of a tuning fork or of a piano string. A noise on the
other hand is characterized by sudden or irregular vibrations such as those
produced by a wagon bumping over a stony street. These differences may
be represented graphically as in Fig. 321, (a) represents a noise, (b) a
musical tone.
329. Characteristics of Musical Sounds.—
Musical tones differ from one another in three
ways or are said to have three characteristics,
viz., intensity, pitch, and quality. Thus two
sounds may differ only in intensity or
Fig. 322.—Curve b
loudness, that is, be alike in all other respects
represents a tone of
except this one, as when a string of a piano is
greater intensity.
struck at first gently, and again harder. The
second sound is recognized as being louder.
The difference is due to the greater amplitude of vibration caused by more
energy being used. Fig. 322 shows these differences graphically. Curve b
represents the tone of greater intensity or loudness, since its amplitude of
vibration is represented as being greater.
Explain.
10. If a sunset gun was fired exactly at 6:00 P.M. at a fort, at what time was
the report heard by a man 25 miles away, if the temperature was 10°C.?
(3) Intensity and Pitch of Sounds
Fig. 321.—Graphic representations of (a) a
noise, (b) a musical sound.
328. Musical Sounds and Noises Distinguished.—The question is
sometimes raised, what is the difference between a noise and a musical
sound? The latter has been found to be produced by an even and regular
vibration such as that of a tuning fork or of a piano string. A noise on the
other hand is characterized by sudden or irregular vibrations such as those
produced by a wagon bumping over a stony street. These differences may
be represented graphically as in Fig. 321, (a) represents a noise, (b) a
musical tone.
329. Characteristics of Musical Sounds.—
Musical tones differ from one another in three
ways or are said to have three characteristics,
viz., intensity, pitch, and quality. Thus two
sounds may differ only in intensity or
Fig. 322.—Curve b
loudness, that is, be alike in all other respects
represents a tone of
except this one, as when a string of a piano is
greater intensity.
struck at first gently, and again harder. The
second sound is recognized as being louder.
The difference is due to the greater amplitude of vibration caused by more
energy being used. Fig. 322 shows these differences graphically. Curve b
represents the tone of greater intensity or loudness, since its amplitude of
vibration is represented as being greater.
Page 355
330. Conditions Affecting the Intensity of Sound.—The intensity of
sounds is also affected by the area of the vibrating body. This is shown by
setting a tuning fork in vibration. The area of the vibrating part being small,
the sound is heard but a short distance from the fork. If, however, the stem
of the vibrating fork is pressed against the panel of a door or the top of a
box, the sound may be heard throughout a room. The stem of the fork has
communicated its vibrations to the wood. The vibrating area, being greater,
the sound is thereby much increased in intensity, producing a wave of
greater amplitude. The same principle is employed in the sounding boards
of musical instruments as in the piano, violin, etc. It is a common
observation that sounds decrease in loudness as the distance from the source
increases. This is due to the increase of the surface of the spherical sound
waves spreading in all directions from the source. Careful experiments have
shown that in a uniform medium the intensity of a sound is inversely
proportional to the square of the distance from its source. If a sound is
confined so that it cannot spread, such as the sound moving through a
speaking tube, it maintains its intensity for a considerable distance. An ear
trumpet (see Fig. 320) also applies this principle. It is constructed so that
sound from a given area is concentrated by reflection to a much smaller
area with a corresponding increase in intensity. The megaphone (Fig. 323),
and the speaking trumpet start the sound waves of the voice in one direction
so that they are kept from spreading widely, consequently by its use the
voice may be heard several times the usual distance. The intensity of a
sound is also affected by the density of the transmitting medium. Thus a
sound produced on a mountain top is fainter and thinner than one produced
in a valley. The sound of a bell in the receiver of an air pump becomes
weaker as the air is exhausted from the latter. Four factors thus influence
the intensity of a sound, the area of the vibrating body, its amplitude of
vibration, the distance of the source and the density of the transmitting
medium. It is well to fix in mind the precise effect of each of these factors.
331. Pitch.—The most characteristic difference between musical sounds is
that of pitch. Some sounds have a high pitch, such as those produced by
many insects and birds. Others have a low pitch as the notes of a bass drum
or the sound of thunder. How notes of different pitch are produced may be
shown by the siren (Fig. 324). This is a disc mounted so as to be rotated on
an axis. Several rows of holes are drilled in it in concentric circles. The
number of holes in successive rows increases from within outward. If when
sounds is also affected by the area of the vibrating body. This is shown by
setting a tuning fork in vibration. The area of the vibrating part being small,
the sound is heard but a short distance from the fork. If, however, the stem
of the vibrating fork is pressed against the panel of a door or the top of a
box, the sound may be heard throughout a room. The stem of the fork has
communicated its vibrations to the wood. The vibrating area, being greater,
the sound is thereby much increased in intensity, producing a wave of
greater amplitude. The same principle is employed in the sounding boards
of musical instruments as in the piano, violin, etc. It is a common
observation that sounds decrease in loudness as the distance from the source
increases. This is due to the increase of the surface of the spherical sound
waves spreading in all directions from the source. Careful experiments have
shown that in a uniform medium the intensity of a sound is inversely
proportional to the square of the distance from its source. If a sound is
confined so that it cannot spread, such as the sound moving through a
speaking tube, it maintains its intensity for a considerable distance. An ear
trumpet (see Fig. 320) also applies this principle. It is constructed so that
sound from a given area is concentrated by reflection to a much smaller
area with a corresponding increase in intensity. The megaphone (Fig. 323),
and the speaking trumpet start the sound waves of the voice in one direction
so that they are kept from spreading widely, consequently by its use the
voice may be heard several times the usual distance. The intensity of a
sound is also affected by the density of the transmitting medium. Thus a
sound produced on a mountain top is fainter and thinner than one produced
in a valley. The sound of a bell in the receiver of an air pump becomes
weaker as the air is exhausted from the latter. Four factors thus influence
the intensity of a sound, the area of the vibrating body, its amplitude of
vibration, the distance of the source and the density of the transmitting
medium. It is well to fix in mind the precise effect of each of these factors.
331. Pitch.—The most characteristic difference between musical sounds is
that of pitch. Some sounds have a high pitch, such as those produced by
many insects and birds. Others have a low pitch as the notes of a bass drum
or the sound of thunder. How notes of different pitch are produced may be
shown by the siren (Fig. 324). This is a disc mounted so as to be rotated on
an axis. Several rows of holes are drilled in it in concentric circles. The
number of holes in successive rows increases from within outward. If when
Page 356
the siren is rapidly rotated air is blown
through a tube against a row of holes a clear
musical tone is heard. The tone is due to the
succession of pulses in the air produced by
the row of holes in the rotating disc
alternately cutting off and permitting the air
blast to pass through at very short intervals. If
the blast is directed against a row of holes Fig. 323.—The
nearer the circumference the pitch is higher, if megaphone.
against a row nearer the center the pitch is
lower. Or if the blast is sent against the same row of holes the pitch rises
when the speed increases and lowers when the speed lessens. These facts
indicate that the pitch of a tone is due to the number of pulses or vibrations
that strike the ear each second; also that the greater the rate of vibration,
the higher the pitch.
332. The Major Scale.—If a siren is made with
eight rows of holes, it may indicate the relation
between the notes of a major scale. To accomplish
this, the number of holes in the successive rows
should be 24, 27, 30, 32, 36, 40, 45, 48. If a disc so
constructed is rapidly rotated at a uniform rate, a
blast of air sent against all of the rows in
succession produces the tones of the scale. These
facts indicate that the relative vibration numbers of
the notes of any major scale have the same relation
Fig. 324.—A siren. as the numbers 24, 27, 30, 32, 36, 40, 45, 48.
The note called middle C is considered by
physicists as having 256 vibrations a second. This would give the following
actual vibration numbers to the remaining notes of the major scale that
begins with "Middle C" D.-288, E.-320, F.-341.3, G.-384, A.-426.6, B.-480,
C'.-512. Musicians, however, usually make use of a scale of slightly higher
pitch. The international standard of pitch in this country and in Europe is
that in which "A" has 435 vibrations per second. This corresponds to 261
vibrations for middle C.
333. The Relation between Speed, Wave Length, and Number of
Vibrations per Second.—Since the notes from the various musical
through a tube against a row of holes a clear
musical tone is heard. The tone is due to the
succession of pulses in the air produced by
the row of holes in the rotating disc
alternately cutting off and permitting the air
blast to pass through at very short intervals. If
the blast is directed against a row of holes Fig. 323.—The
nearer the circumference the pitch is higher, if megaphone.
against a row nearer the center the pitch is
lower. Or if the blast is sent against the same row of holes the pitch rises
when the speed increases and lowers when the speed lessens. These facts
indicate that the pitch of a tone is due to the number of pulses or vibrations
that strike the ear each second; also that the greater the rate of vibration,
the higher the pitch.
332. The Major Scale.—If a siren is made with
eight rows of holes, it may indicate the relation
between the notes of a major scale. To accomplish
this, the number of holes in the successive rows
should be 24, 27, 30, 32, 36, 40, 45, 48. If a disc so
constructed is rapidly rotated at a uniform rate, a
blast of air sent against all of the rows in
succession produces the tones of the scale. These
facts indicate that the relative vibration numbers of
the notes of any major scale have the same relation
Fig. 324.—A siren. as the numbers 24, 27, 30, 32, 36, 40, 45, 48.
The note called middle C is considered by
physicists as having 256 vibrations a second. This would give the following
actual vibration numbers to the remaining notes of the major scale that
begins with "Middle C" D.-288, E.-320, F.-341.3, G.-384, A.-426.6, B.-480,
C'.-512. Musicians, however, usually make use of a scale of slightly higher
pitch. The international standard of pitch in this country and in Europe is
that in which "A" has 435 vibrations per second. This corresponds to 261
vibrations for middle C.
333. The Relation between Speed, Wave Length, and Number of
Vibrations per Second.—Since the notes from the various musical
Page 357
instruments of an orchestra are noticed to harmonize as well at a distance as
at the place produced, it is evident that notes of all pitches travel at the same
rate, or have the same speed. Notes of high pitch, having a high vibration
rate produce more waves in a second than notes of low pitch, consequently
the former are shorter than the latter. The following formula gives the
relation between the speed (v), wave length (l), and number of vibrations
per sec. (n):
v = l × n, or l = v/n
that is, the speed of a sound wave is equal to the number of vibrations per
second times the wave length, or the wave length is equal to the speed
divided by the number of vibrations per second. This formula may also be
employed to find the number of vibrations when the wave length and speed
are given.
Important Topics
1. Difference between noise and music.
2. Factors affecting intensity: area, amplitude, density, distance.
3. Pitch, major scale, relative vibration numbers.
4. Relation between speed, wave length and vibration rate.
Exercises
1. Give an illustration from your own experience of each of the factors
affecting intensity.
2. Write the relative vibration numbers of a major scale in which do has 120
vibrations.
3. What is the wave length of the "A" of international concert pitch at
25°C.? Compute in feet and centimeters.
4. At what temperature will sound waves in air in unison with "Middle C"
be exactly 4 ft. long?
5. Explain the use of a megaphone.
at the place produced, it is evident that notes of all pitches travel at the same
rate, or have the same speed. Notes of high pitch, having a high vibration
rate produce more waves in a second than notes of low pitch, consequently
the former are shorter than the latter. The following formula gives the
relation between the speed (v), wave length (l), and number of vibrations
per sec. (n):
v = l × n, or l = v/n
that is, the speed of a sound wave is equal to the number of vibrations per
second times the wave length, or the wave length is equal to the speed
divided by the number of vibrations per second. This formula may also be
employed to find the number of vibrations when the wave length and speed
are given.
Important Topics
1. Difference between noise and music.
2. Factors affecting intensity: area, amplitude, density, distance.
3. Pitch, major scale, relative vibration numbers.
4. Relation between speed, wave length and vibration rate.
Exercises
1. Give an illustration from your own experience of each of the factors
affecting intensity.
2. Write the relative vibration numbers of a major scale in which do has 120
vibrations.
3. What is the wave length of the "A" of international concert pitch at
25°C.? Compute in feet and centimeters.
4. At what temperature will sound waves in air in unison with "Middle C"
be exactly 4 ft. long?
5. Explain the use of a megaphone.
Page 358
6. What tone has waves 3 ft. long at 25°C.?
7. What is the purpose of the "sounding board" of a piano?
8. Two men are distant 1000 and 3000 ft. respectively from a fog horn.
What is the relative intensity of the sounds heard by the two men?
9. The speaking tone of the average man's voice has 160 vibrations per
second. How long are the waves produced by him at 20°C.?
(4) Musical Scales and Resonance
334. A musical interval refers to the ratio between the pitches[O] of two
notes as indicated by the results of the siren experiment. The simplest
interval, or ratio between two notes is the octave, C':C, or 2:1 (48:24). Other
important intervals with the corresponding ratios are the fifth, G:C, or 3:2
(36:24); the sixth, A:C, or 5:3 (40:24); the fourth, F:C, 4:3 (32:24); the
major third, E:C, or 5:4 (30:24); and the minor third, G:E, 6:5. The interval
between any two notes may be determined by finding the ratio between the
vibration numbers of the two notes. Thus, if one note is produced by 600
vibrations a second and another by 400, the interval is 3:2, or a fifth, and
this would be recognized by a musician who heard the notes sounded
together or one after the other. Below is a table of musical nomenclatures,
showing various relations between the notes of the major scale.
Table of Musical Nomenclatures
Name of note C D E F G A B C´
Frequency in terms of "do" n 9/8n 5/4n 4/3n 3/2n 5/3n 15/8n 2n
Intervals 9/8 10/9 16/15 9/8 10/9 9/8 16/15
Name of note in vocal music do re mi fa sol la ti do
Treble clef.
[Music]
Bass clef.
[Music]
International pitch of treble
261293.6326.3 348. 391.5435 489.4 522
clef
Scientific scale 256288 320 341.3384 426.6480 512
7. What is the purpose of the "sounding board" of a piano?
8. Two men are distant 1000 and 3000 ft. respectively from a fog horn.
What is the relative intensity of the sounds heard by the two men?
9. The speaking tone of the average man's voice has 160 vibrations per
second. How long are the waves produced by him at 20°C.?
(4) Musical Scales and Resonance
334. A musical interval refers to the ratio between the pitches[O] of two
notes as indicated by the results of the siren experiment. The simplest
interval, or ratio between two notes is the octave, C':C, or 2:1 (48:24). Other
important intervals with the corresponding ratios are the fifth, G:C, or 3:2
(36:24); the sixth, A:C, or 5:3 (40:24); the fourth, F:C, 4:3 (32:24); the
major third, E:C, or 5:4 (30:24); and the minor third, G:E, 6:5. The interval
between any two notes may be determined by finding the ratio between the
vibration numbers of the two notes. Thus, if one note is produced by 600
vibrations a second and another by 400, the interval is 3:2, or a fifth, and
this would be recognized by a musician who heard the notes sounded
together or one after the other. Below is a table of musical nomenclatures,
showing various relations between the notes of the major scale.
Table of Musical Nomenclatures
Name of note C D E F G A B C´
Frequency in terms of "do" n 9/8n 5/4n 4/3n 3/2n 5/3n 15/8n 2n
Intervals 9/8 10/9 16/15 9/8 10/9 9/8 16/15
Name of note in vocal music do re mi fa sol la ti do
Treble clef.
[Music]
Bass clef.
[Music]
International pitch of treble
261293.6326.3 348. 391.5435 489.4 522
clef
Scientific scale 256288 320 341.3384 426.6480 512
Page 359
Relative vibration numbers 24 27 30 32 36 40 45 48
335. Major and Minor Triads.—The notes C, E, G (do, mi, sol) form what
is called a major triad. The relative vibration numbers corresponding are
24, 30, 36. These in simplest terms have ratios of 4:5:6. Any three other
tones with vibration ratios of 4:5:6 will also form a major triad. If the
octave of the lower tone is added, the four make a major chord. Thus: F, A,
C´ (fa, la, do), 32:40:48, or 4:5:6, also form a major triad as do G, B, D´
(sol, ti, re), 36:45:54, or 4:5:6. Inspection will show that these three major
triads comprise all of the tones of the major scale D´ being the octave of D.
It is, therefore, said that the major scale is based, or built, upon these three
major triads. The examples just given indicate the mathematical basis for
harmony in music. Three notes having vibration ratios of 10:12:15 are
called minor triads. These produce a less pleasing effect than those having
ratios of 4:5:6.
336. The Need for Sharps and Flats.—We have considered the key of C.
This is represented upon the piano or organ by white keys only (Fig. 325).
Now in order (a) to give variety to instrumental selections, and (b) to
accommodate instruments to the range of the human voice, it has been
335. Major and Minor Triads.—The notes C, E, G (do, mi, sol) form what
is called a major triad. The relative vibration numbers corresponding are
24, 30, 36. These in simplest terms have ratios of 4:5:6. Any three other
tones with vibration ratios of 4:5:6 will also form a major triad. If the
octave of the lower tone is added, the four make a major chord. Thus: F, A,
C´ (fa, la, do), 32:40:48, or 4:5:6, also form a major triad as do G, B, D´
(sol, ti, re), 36:45:54, or 4:5:6. Inspection will show that these three major
triads comprise all of the tones of the major scale D´ being the octave of D.
It is, therefore, said that the major scale is based, or built, upon these three
major triads. The examples just given indicate the mathematical basis for
harmony in music. Three notes having vibration ratios of 10:12:15 are
called minor triads. These produce a less pleasing effect than those having
ratios of 4:5:6.
336. The Need for Sharps and Flats.—We have considered the key of C.
This is represented upon the piano or organ by white keys only (Fig. 325).
Now in order (a) to give variety to instrumental selections, and (b) to
accommodate instruments to the range of the human voice, it has been
Page 360
necessary to introduce other notes in musical instruments. These are
represented by the black keys upon the piano and organ and are known as
sharps and flats. To illustrate the necessity for these additional notes take
the major scale starting with B. This will give vibration frequencies of 240,
270, 300, 320, 360, 400, 450, and 480. The only white keys that may be
used with this scale are E 320 and B 480 vibrations. Since the second note
on this scale requires 270 vibrations about halfway between C and D the
black key C sharp is inserted. Other notes must be inserted between D and
E (D sharp), between F and G (F sharp), also G and A sharps.
Fig. 325.—Section of a piano keyboard.
337. Tempered Scales.—In musical instruments with fixed notes, such as
the harp, organ, or piano, complications were early recognized when an
attempt was made to adapt these instruments so that they could be played in
all keys. For the vibration numbers that would give a perfect major scale
starting at C are not the same as will give a perfect major scale beginning
with any other key. In using the various notes as the keynote for a major
scale, 72 different notes in the octave would be required. This would make
it more difficult for such instruments as the piano to be played. To avoid
these complications as much as possible, it has been found necessary to
abandon the simple ratios between successive notes and to substitute
another ratio in order that the vibration ratio between any two successive
notes will be equal in every case. The differences between semitones are
abolished so that, for example, C sharp and D flat become the same tone
instead of two different tones. Such a scale is called a tempered scale. The
tempered scale has 13 notes to the octave, with 12 equal intervals, the ratio
between two successive notes being the ¹²√2 or 1.059. That is, any vibration
rate on the tempered scale may be computed by multiplying the vibration
rate of the preceding note by 1.059. While this is a necessary arrangement,
there is some loss in perfect harmony. It is for this reason that a quartette or
chorus of voices singing without accompaniment is often more harmonious
represented by the black keys upon the piano and organ and are known as
sharps and flats. To illustrate the necessity for these additional notes take
the major scale starting with B. This will give vibration frequencies of 240,
270, 300, 320, 360, 400, 450, and 480. The only white keys that may be
used with this scale are E 320 and B 480 vibrations. Since the second note
on this scale requires 270 vibrations about halfway between C and D the
black key C sharp is inserted. Other notes must be inserted between D and
E (D sharp), between F and G (F sharp), also G and A sharps.
Fig. 325.—Section of a piano keyboard.
337. Tempered Scales.—In musical instruments with fixed notes, such as
the harp, organ, or piano, complications were early recognized when an
attempt was made to adapt these instruments so that they could be played in
all keys. For the vibration numbers that would give a perfect major scale
starting at C are not the same as will give a perfect major scale beginning
with any other key. In using the various notes as the keynote for a major
scale, 72 different notes in the octave would be required. This would make
it more difficult for such instruments as the piano to be played. To avoid
these complications as much as possible, it has been found necessary to
abandon the simple ratios between successive notes and to substitute
another ratio in order that the vibration ratio between any two successive
notes will be equal in every case. The differences between semitones are
abolished so that, for example, C sharp and D flat become the same tone
instead of two different tones. Such a scale is called a tempered scale. The
tempered scale has 13 notes to the octave, with 12 equal intervals, the ratio
between two successive notes being the ¹²√2 or 1.059. That is, any vibration
rate on the tempered scale may be computed by multiplying the vibration
rate of the preceding note by 1.059. While this is a necessary arrangement,
there is some loss in perfect harmony. It is for this reason that a quartette or
chorus of voices singing without accompaniment is often more harmonious
Page 361
and satisfactory than when accompanied with an instrument of fixed notes
as the piano, since the simple harmonious ratios may be employed when the
voices are alone. The imperfection introduced by equal temperament tuning
is illustrated by the following table:
C D E F G A B C
Perfect Scale of C 256.0 288.0320.0 341.3384.0426.6480.0512.0
Tempered Scale 256.0 287.3322.5 341.7383.6430.5483.3512.0
338. Resonance.—If two tuning forks of the same pitch are placed near
each other, and one is set vibrating, the other will soon be found to be in
vibration. This result is said to be due to sympathetic vibration, and is an
example of resonance (Fig. 326). If water is poured into a glass tube while a
vibrating tuning fork is held over its top, when the air column has a certain
length it will start vibrating, reinforcing strongly the sound of the tuning
fork. (See Fig. 327.) This is also an example of resonance. These and other
similar facts indicate that sound waves started by a vibrating body will
cause another body near it to start vibrating if the two have the same rate of
vibration. Most persons will recall illustrations of this effect from their own
experience.
Fig. 326.—One tuning fork will vibrate in
sympathy with the other, if they have exactly
equal rates of vibration.
Fig. 327.—An air column of the proper length
reinforces the sound of the tuning fork.
as the piano, since the simple harmonious ratios may be employed when the
voices are alone. The imperfection introduced by equal temperament tuning
is illustrated by the following table:
C D E F G A B C
Perfect Scale of C 256.0 288.0320.0 341.3384.0426.6480.0512.0
Tempered Scale 256.0 287.3322.5 341.7383.6430.5483.3512.0
338. Resonance.—If two tuning forks of the same pitch are placed near
each other, and one is set vibrating, the other will soon be found to be in
vibration. This result is said to be due to sympathetic vibration, and is an
example of resonance (Fig. 326). If water is poured into a glass tube while a
vibrating tuning fork is held over its top, when the air column has a certain
length it will start vibrating, reinforcing strongly the sound of the tuning
fork. (See Fig. 327.) This is also an example of resonance. These and other
similar facts indicate that sound waves started by a vibrating body will
cause another body near it to start vibrating if the two have the same rate of
vibration. Most persons will recall illustrations of this effect from their own
experience.
Fig. 326.—One tuning fork will vibrate in
sympathy with the other, if they have exactly
equal rates of vibration.
Fig. 327.—An air column of the proper length
reinforces the sound of the tuning fork.
Page 362
339. Sympathetic vibration is explained as follows: Sound waves produce
very slight motions in objects affected by them; if the vibration of a given
body is exactly in time with the vibrations of a given sound each impulse of
the sound wave will strike the body so as to increase the vibratory motion
of the latter. This action continuing, the body soon acquires a motion
sufficient to produce audible waves. A good illustration of sympathetic
vibration is furnished by the bell ringer, who times his pulls upon the bell
rope with the vibration rate of the swing of the bell. In the case of the
resonant air column over which is held a vibrating tuning fork (see Fig.
328), when the prong of the fork starts downward from 1 to 2, a
condensation wave moves down to the water surface and back just in time
to join the condensation wave above the fork as the prong begins to move
from 2 to 1; also when the prong starts upward from 2 to 1, the rarefaction
produced under it moves to the bottom of the air column and back so as to
join the rarefaction above the fork as the prong returns. While the prong is
making a single movement, up or down, it is plain that the air wave moves
twice the length of the open tube. During a complete vibration of the fork,
therefore, the sound wave moves four times the length of the air column. In
free air, the sound progresses a wave length during a complete vibration,
hence the resonant air column is one-fourth the length of the sound wave to
which it responds. Experiments with tubes cf different lengths show that the
diameter of the air column has some effect upon the length giving best
resonance. About 25 per cent. of the diameter of the tube must be added to
the length of the air column to make it just one-fourth the wave length. The
sound heard in seashells and in other hollow bodies is due to resonance.
Vibrations in the air too feeble to affect the ear are intensified by
sympathetic vibration until they can be heard. A tuning fork is often
mounted upon a box called a resonator, which contains an air column of
such dimensions that it reinforces the sound of the fork's sympathetic
vibration.
very slight motions in objects affected by them; if the vibration of a given
body is exactly in time with the vibrations of a given sound each impulse of
the sound wave will strike the body so as to increase the vibratory motion
of the latter. This action continuing, the body soon acquires a motion
sufficient to produce audible waves. A good illustration of sympathetic
vibration is furnished by the bell ringer, who times his pulls upon the bell
rope with the vibration rate of the swing of the bell. In the case of the
resonant air column over which is held a vibrating tuning fork (see Fig.
328), when the prong of the fork starts downward from 1 to 2, a
condensation wave moves down to the water surface and back just in time
to join the condensation wave above the fork as the prong begins to move
from 2 to 1; also when the prong starts upward from 2 to 1, the rarefaction
produced under it moves to the bottom of the air column and back so as to
join the rarefaction above the fork as the prong returns. While the prong is
making a single movement, up or down, it is plain that the air wave moves
twice the length of the open tube. During a complete vibration of the fork,
therefore, the sound wave moves four times the length of the air column. In
free air, the sound progresses a wave length during a complete vibration,
hence the resonant air column is one-fourth the length of the sound wave to
which it responds. Experiments with tubes cf different lengths show that the
diameter of the air column has some effect upon the length giving best
resonance. About 25 per cent. of the diameter of the tube must be added to
the length of the air column to make it just one-fourth the wave length. The
sound heard in seashells and in other hollow bodies is due to resonance.
Vibrations in the air too feeble to affect the ear are intensified by
sympathetic vibration until they can be heard. A tuning fork is often
mounted upon a box called a resonator, which contains an air column of
such dimensions that it reinforces the sound of the fork's sympathetic
vibration.
Page 363
Fig. 328.—
Explanation of
resonance.
Important Topics
1. Musical intervals: octave, sixth, fifth, fourth, third.
2. Major chord, 4:5:6.
3. Use of sharps and flats. Tempered scale.
4. Resonance, sympathetic vibration, explanation, examples.
Exercises
1. What is a major scale? Why is a major scale said to be built upon three
triads?
2. Why are sharps and flats necessary in music?
3. What is the tempered scale and why is it used? What instruments need
not use it? Why?
4. Mention two examples of resonance or sympathetic vibration from your
own experience out of school.
Explanation of
resonance.
Important Topics
1. Musical intervals: octave, sixth, fifth, fourth, third.
2. Major chord, 4:5:6.
3. Use of sharps and flats. Tempered scale.
4. Resonance, sympathetic vibration, explanation, examples.
Exercises
1. What is a major scale? Why is a major scale said to be built upon three
triads?
2. Why are sharps and flats necessary in music?
3. What is the tempered scale and why is it used? What instruments need
not use it? Why?
4. Mention two examples of resonance or sympathetic vibration from your
own experience out of school.
Page 364
5. An air column 2 ft. long closed at one end is resonant to what wave
length? What number of vibrations will this sound have per second at
25°C.?
6. At 24°C. What length of air column closed at one end will be resonant to
a sound having 27 vibrations a second?
7. A given note has 300 vibrations a second. What will be the number of
vibrations of its (a) octave, (b) fifth, (c) sixth, (d) major third?
8. In the violin or guitar what takes the place of the sounding board of the
piano?
9. Can you explain why the pitch of the bell on a locomotive rises as you
rapidly approach it and falls as you recede from it?
10. Do notes of high or low pitch travel faster? Explain.
11. An "A" tuning fork on the "international" scale makes 435 vibrations
per second. What is the length of the sound waves produced?
(5) Wave Interference, Beats, Vibration of Strings
340. Interference of waves.—The possibility of two trains of waves
combining so as to produce a reduced motion or a complete destruction of
motion may be shown graphically. Suppose two trains of waves of equal
wave length and amplitude as in Fig. 329 meet in opposite phases. That is,
the parts corresponding to the crests of A coincide with the troughs of B,
also the troughs of A with the crests of B; when this condition obtains, the
result is that shown at C, the union of the two waves resulting in complete
destruction of motion. The more or less complete destruction of one train of
waves by another similar train is an illustration of interference. If two sets
of water waves so unite as to entirely destroy each other the result is a level
water surface. If two trains of sound waves combine they may so interfere
that silence results. The conditions for securing interference of sound waves
may readily be secured by using a tuning fork and a resonating air column.
If the tuning fork is set vibrating and placed over the open end of the
resonating air column (see Fig. 328), an increase in the sound through
resonance may be heard. If the fork is rotated about its axis, in some
positions no sound is heard while in other positions the sound is strongly
length? What number of vibrations will this sound have per second at
25°C.?
6. At 24°C. What length of air column closed at one end will be resonant to
a sound having 27 vibrations a second?
7. A given note has 300 vibrations a second. What will be the number of
vibrations of its (a) octave, (b) fifth, (c) sixth, (d) major third?
8. In the violin or guitar what takes the place of the sounding board of the
piano?
9. Can you explain why the pitch of the bell on a locomotive rises as you
rapidly approach it and falls as you recede from it?
10. Do notes of high or low pitch travel faster? Explain.
11. An "A" tuning fork on the "international" scale makes 435 vibrations
per second. What is the length of the sound waves produced?
(5) Wave Interference, Beats, Vibration of Strings
340. Interference of waves.—The possibility of two trains of waves
combining so as to produce a reduced motion or a complete destruction of
motion may be shown graphically. Suppose two trains of waves of equal
wave length and amplitude as in Fig. 329 meet in opposite phases. That is,
the parts corresponding to the crests of A coincide with the troughs of B,
also the troughs of A with the crests of B; when this condition obtains, the
result is that shown at C, the union of the two waves resulting in complete
destruction of motion. The more or less complete destruction of one train of
waves by another similar train is an illustration of interference. If two sets
of water waves so unite as to entirely destroy each other the result is a level
water surface. If two trains of sound waves combine they may so interfere
that silence results. The conditions for securing interference of sound waves
may readily be secured by using a tuning fork and a resonating air column.
If the tuning fork is set vibrating and placed over the open end of the
resonating air column (see Fig. 328), an increase in the sound through
resonance may be heard. If the fork is rotated about its axis, in some
positions no sound is heard while in other positions the sound is strongly
Page 365
reinforced. Similar effects may be perceived by holding a vibrating fork
near the ear and slowly rotating as before. In some positions interference
results while in other positions the sound is plainly heard. The explanation
of interference may be made clear by the use of a diagram. (See Fig. 330.)
Let us imagine that we are looking at the two square ends of a tuning fork.
When the fork is vibrating the two prongs approach each other and then
recede. As they approach, a condensation is produced at 2 and rarefactions
at 1 and 3. As they separate, a rarefaction is produced at 2 and
condensations at 1 and 3. Now along the lines at which the simultaneously
produced rarefactions and condensations meet there is more or less
complete interference. (See Fig. 331.) These positions have been indicated
by dotted lines extending through the ends of the prongs. As indicated
above, these positions may be easily found by rotating a vibrating fork over
a resonant air column, or near the ear.
Fig. 329.—Interference of sound waves.
Fig. 330.—At 2 is a condensation; at 1 and 3
are rarefactions.
Fig. 331.—The condensations and rarefactions
meet along the dotted lines producing silence.
near the ear and slowly rotating as before. In some positions interference
results while in other positions the sound is plainly heard. The explanation
of interference may be made clear by the use of a diagram. (See Fig. 330.)
Let us imagine that we are looking at the two square ends of a tuning fork.
When the fork is vibrating the two prongs approach each other and then
recede. As they approach, a condensation is produced at 2 and rarefactions
at 1 and 3. As they separate, a rarefaction is produced at 2 and
condensations at 1 and 3. Now along the lines at which the simultaneously
produced rarefactions and condensations meet there is more or less
complete interference. (See Fig. 331.) These positions have been indicated
by dotted lines extending through the ends of the prongs. As indicated
above, these positions may be easily found by rotating a vibrating fork over
a resonant air column, or near the ear.
Fig. 329.—Interference of sound waves.
Fig. 330.—At 2 is a condensation; at 1 and 3
are rarefactions.
Fig. 331.—The condensations and rarefactions
meet along the dotted lines producing silence.
Page 366
Fig. 332.—Diagram illustrating the formations
of beats.
341. Beats.—If two tuning forks of slightly different pitch are set vibrating
and placed over resonating air columns or with the stem of each fork upon a
sounding board, so that the sounds may be intensified, a peculiar pulsation
of the sound may be noticed. This phenomenon is known as beats. Its
production may be easily understood by considering a diagram (Fig. 332).
Let the curve A represent the sound wave sent out by one tuning fork and B,
that sent out by the other. C represents the effect produced by the
combination of these waves. At R the two sound waves meet in the same
phase and reinforce each other. This results in a louder sound than either
produces alone. Now since the sounds are of slightly different pitch, one
fork sends out a few more vibrations per second than the other. The waves
from the first fork are therefore a little shorter than those from the other.
Consequently, although the two waves are at one time in the same phase,
they must soon be in opposite phases as at I. Here interference occurs, and
silence results. Immediately the waves reinforce, producing a louder sound
and so on alternately. The resulting rise and fall of the sound are known as
beats. The number of beats per second must, of course, be the same as the
difference between the numbers of vibrations per second of the two sounds.
One effect of beats is discord. This is especially noticeable when the
number of beats per second is between 30 and 120. Strike the two lowest
notes on a piano at the same time. The beats are very noticeable.
of beats.
341. Beats.—If two tuning forks of slightly different pitch are set vibrating
and placed over resonating air columns or with the stem of each fork upon a
sounding board, so that the sounds may be intensified, a peculiar pulsation
of the sound may be noticed. This phenomenon is known as beats. Its
production may be easily understood by considering a diagram (Fig. 332).
Let the curve A represent the sound wave sent out by one tuning fork and B,
that sent out by the other. C represents the effect produced by the
combination of these waves. At R the two sound waves meet in the same
phase and reinforce each other. This results in a louder sound than either
produces alone. Now since the sounds are of slightly different pitch, one
fork sends out a few more vibrations per second than the other. The waves
from the first fork are therefore a little shorter than those from the other.
Consequently, although the two waves are at one time in the same phase,
they must soon be in opposite phases as at I. Here interference occurs, and
silence results. Immediately the waves reinforce, producing a louder sound
and so on alternately. The resulting rise and fall of the sound are known as
beats. The number of beats per second must, of course, be the same as the
difference between the numbers of vibrations per second of the two sounds.
One effect of beats is discord. This is especially noticeable when the
number of beats per second is between 30 and 120. Strike the two lowest
notes on a piano at the same time. The beats are very noticeable.
Page 367
Fig. 333.—Turkish cymbals.
Fig. 334.—The cornet.
342. Three Classes of Musical Instruments.—There are three classes or
groups of musical instruments, if we consider the vibrating body that
produces the sound in each: (A) Those in which the sound is produced by a
vibrating plate or membrane, as the drum, cymbals (Fig. 333), etc.; (B)
those with vibrating air columns, as the flute, pipe organ, and cornet (Fig.
334), and (C) with vibrating wires or strings, as the piano, violin, and guitar.
It is worth while to consider some of these carefully. We will begin with a
consideration of vibrating wires and strings, these often producing tones of
rich quality.
Let us consider the strings of a piano. (If possible, look at the strings in
some instrument.) The range of the piano is 7-1/3 octaves. Its lowest note,
A4, has about 27 vibrations per second. Its highest, C4, about 4176. This
great range in vibration rate is secured by varying the length, the tension,
and the diameter of the strings.
343. The Laws of Vibrating Strings.—The relations between the vibration
rate, the length, the tension and the diameter, of vibrating strings have been
carefully studied with an instrument called a sonometer (Fig. 335). By this
device it is found that the pitch of a vibrating string is raised one octave
when its vibrating length is reduced to one-half. By determining the
vibration rate of many lengths, the following law has been derived: (Law I)
The rate of vibration of a string is inversely proportional to its length.
Fig. 334.—The cornet.
342. Three Classes of Musical Instruments.—There are three classes or
groups of musical instruments, if we consider the vibrating body that
produces the sound in each: (A) Those in which the sound is produced by a
vibrating plate or membrane, as the drum, cymbals (Fig. 333), etc.; (B)
those with vibrating air columns, as the flute, pipe organ, and cornet (Fig.
334), and (C) with vibrating wires or strings, as the piano, violin, and guitar.
It is worth while to consider some of these carefully. We will begin with a
consideration of vibrating wires and strings, these often producing tones of
rich quality.
Let us consider the strings of a piano. (If possible, look at the strings in
some instrument.) The range of the piano is 7-1/3 octaves. Its lowest note,
A4, has about 27 vibrations per second. Its highest, C4, about 4176. This
great range in vibration rate is secured by varying the length, the tension,
and the diameter of the strings.
343. The Laws of Vibrating Strings.—The relations between the vibration
rate, the length, the tension and the diameter, of vibrating strings have been
carefully studied with an instrument called a sonometer (Fig. 335). By this
device it is found that the pitch of a vibrating string is raised one octave
when its vibrating length is reduced to one-half. By determining the
vibration rate of many lengths, the following law has been derived: (Law I)
The rate of vibration of a string is inversely proportional to its length.
Page 368
Fig. 335.—A sonometer.
Careful tests upon the change of vibration rate produced by a change of
tension or pull upon the strings show that if the pull is increased four times
its vibrations rate is doubled, and if it is increased nine times its rate is
tripled, that is: (Law II) The vibration rates of strings are directly
proportional to the square roots of their tensions.
Tests of the effects of diameter are made by taking wires of equal length
and tension and of the same material but of different diameter. Suppose one
is twice as thick as the other. This string has a tone an octave lower or
vibrates one-half as fast as the first. Therefore: (Law III) The vibration rates
of strings are inversely proportional to the diameters. These laws may be
expressed by a formula n ∝√(t)/dl.
The vibration of a string is rarely a simple matter. It usually vibrates in parts
at the same time that it is vibrating as a whole. The tone produced by a
string vibrating as a whole is called its fundamental. The vibrating parts of a
string are called loops or segments (see Fig. 336), while the points of least
or no vibration are nodes. Segments are often called antinodes.
Fig. 336.—A string yielding its fundamental
and its first overtone.
344. Overtones.—The quality of the tone produced by a vibrating string is
affected by its vibration in parts when it is also vibrating as a whole. (See
Fig. 336.) The tones produced by the vibration in parts are called overtones
or partial tones. The presence of these overtones may often be detected by
the sympathetic vibration of other wires near-by. What is called the first
overtone is produced by a string vibrating in two parts, the second overtone
by a string vibrating in three parts, the third overtone by its vibration in
four parts and so on. In any overtone, the number of the parts or vibrating
segments of the string is one more than the number of the overtone. For
example, gently press down the key of middle C of a piano. This will leave
the string free to vibrate. Now strongly strike the C an octave lower and
then remove the finger from this key. The middle C string will be heard
Careful tests upon the change of vibration rate produced by a change of
tension or pull upon the strings show that if the pull is increased four times
its vibrations rate is doubled, and if it is increased nine times its rate is
tripled, that is: (Law II) The vibration rates of strings are directly
proportional to the square roots of their tensions.
Tests of the effects of diameter are made by taking wires of equal length
and tension and of the same material but of different diameter. Suppose one
is twice as thick as the other. This string has a tone an octave lower or
vibrates one-half as fast as the first. Therefore: (Law III) The vibration rates
of strings are inversely proportional to the diameters. These laws may be
expressed by a formula n ∝√(t)/dl.
The vibration of a string is rarely a simple matter. It usually vibrates in parts
at the same time that it is vibrating as a whole. The tone produced by a
string vibrating as a whole is called its fundamental. The vibrating parts of a
string are called loops or segments (see Fig. 336), while the points of least
or no vibration are nodes. Segments are often called antinodes.
Fig. 336.—A string yielding its fundamental
and its first overtone.
344. Overtones.—The quality of the tone produced by a vibrating string is
affected by its vibration in parts when it is also vibrating as a whole. (See
Fig. 336.) The tones produced by the vibration in parts are called overtones
or partial tones. The presence of these overtones may often be detected by
the sympathetic vibration of other wires near-by. What is called the first
overtone is produced by a string vibrating in two parts, the second overtone
by a string vibrating in three parts, the third overtone by its vibration in
four parts and so on. In any overtone, the number of the parts or vibrating
segments of the string is one more than the number of the overtone. For
example, gently press down the key of middle C of a piano. This will leave
the string free to vibrate. Now strongly strike the C an octave lower and
then remove the finger from this key. The middle C string will be heard
Page 369
giving its tone. In like manner try E1 and G1, with C. This experiment
shows that the sound of the C string contains these tones as overtones. It
also illustrates sympathetic vibration.
Important Topics
1. Interference, beats, production, effects.
2. Vibration of strings, three laws.
3. Three classes of musical instruments.
4. Fundamental and overtones, nodes, segments, how produced? Results.
Exercises
1. What different means are employed to produce variation of the pitch of
piano strings? For violin strings?
2. How many beats per second will be produced by two tuning forks having
512 and 509 vibrations per second respectively?
3. A wire 180 cm. long produces middle C. Show by a diagram, using
numbers, where a bridge would have to be placed to cause the string to emit
each tone of the major scale.
4. How can a violinist play a tune on a single string?
5. What are the frequencies of the first 5 overtones of a string whose
fundamental gives 256 vibrations per second?
6. One person takes 112 steps a minute and another 116. How many times a
minute will the two walkers be in step? How many times a minute will one
be advancing the left foot just when the other advances the right?
7. Why is it necessary to have a standard pitch?
8. How can the pitch of the sounds given by a phonograph be lowered?
9. How many beats per second will occur when two tuning forks having
frequencies of 512 and 515 respectively, are sounded together?
10. Which wires of a piano give the highest pitch? Why?
shows that the sound of the C string contains these tones as overtones. It
also illustrates sympathetic vibration.
Important Topics
1. Interference, beats, production, effects.
2. Vibration of strings, three laws.
3. Three classes of musical instruments.
4. Fundamental and overtones, nodes, segments, how produced? Results.
Exercises
1. What different means are employed to produce variation of the pitch of
piano strings? For violin strings?
2. How many beats per second will be produced by two tuning forks having
512 and 509 vibrations per second respectively?
3. A wire 180 cm. long produces middle C. Show by a diagram, using
numbers, where a bridge would have to be placed to cause the string to emit
each tone of the major scale.
4. How can a violinist play a tune on a single string?
5. What are the frequencies of the first 5 overtones of a string whose
fundamental gives 256 vibrations per second?
6. One person takes 112 steps a minute and another 116. How many times a
minute will the two walkers be in step? How many times a minute will one
be advancing the left foot just when the other advances the right?
7. Why is it necessary to have a standard pitch?
8. How can the pitch of the sounds given by a phonograph be lowered?
9. How many beats per second will occur when two tuning forks having
frequencies of 512 and 515 respectively, are sounded together?
10. Which wires of a piano give the highest pitch? Why?
Page 370
(6) Tone Quality, Vibrating Air Columns, Plates
345. Quality.—The reason for the differences in tone quality between notes
of the same pitch and intensity as produced, e.g., by a violin and a piano,
was long a matter of conjecture. Helmholtz, a German physicist (see p. 397)
first definitely proved that tone quality is due to the various overtones
present along with the fundamental and their relative intensities. If a tuning
fork is first set vibrating by drawing a bow across it and then by striking it
with a hard object, a difference in the quality of the tones produced is
noticeable. It is thus evident that the manner of setting a body in vibration
affects the overtones produced and thus the quality. Piano strings are struck
by felt hammers at a point about one-seventh of the length of the string
from one end. This point has been selected by experiment, it having been
found to yield the best combination of overtones as shown by the quality of
the tone resulting.
Fig. 337.—Chladni's
plate.
345. Quality.—The reason for the differences in tone quality between notes
of the same pitch and intensity as produced, e.g., by a violin and a piano,
was long a matter of conjecture. Helmholtz, a German physicist (see p. 397)
first definitely proved that tone quality is due to the various overtones
present along with the fundamental and their relative intensities. If a tuning
fork is first set vibrating by drawing a bow across it and then by striking it
with a hard object, a difference in the quality of the tones produced is
noticeable. It is thus evident that the manner of setting a body in vibration
affects the overtones produced and thus the quality. Piano strings are struck
by felt hammers at a point about one-seventh of the length of the string
from one end. This point has been selected by experiment, it having been
found to yield the best combination of overtones as shown by the quality of
the tone resulting.
Fig. 337.—Chladni's
plate.
Page 371
Fig. 338.—Chladni's figures.
346. Chladni's Plate.—The fact that vibrating bodies are capable of many
modes of vibration is well illustrated by what is known as Chladni's plate.
This consists of a circular or square sheet of brass attached to a stand at its
center so as to be held horizontally. (See Fig. 337.) Fine sand is sprinkled
over its surface and the disc is set vibrating by drawing a violin bow across
its edge. The mode of vibration of the disc is indicated by the sand
accumulating along the lines of least vibration, called nodal lines. A variety
of nodal lines each accompanied by its characteristic tone may be obtained
by changing the position of the bow and by touching the fingers at different
points at the edge of the disc. They are known as Chladni's figures. (See
Fig. 338.)
Fig. 339.—Manometric flame apparatus.
347. Manometric Flames.—The actual presence of overtones along with
the fundamental may be made visible by the manometric flame apparatus.
This consists of a wooden box, C, mounted upon a stand. (See Fig. 339.)
346. Chladni's Plate.—The fact that vibrating bodies are capable of many
modes of vibration is well illustrated by what is known as Chladni's plate.
This consists of a circular or square sheet of brass attached to a stand at its
center so as to be held horizontally. (See Fig. 337.) Fine sand is sprinkled
over its surface and the disc is set vibrating by drawing a violin bow across
its edge. The mode of vibration of the disc is indicated by the sand
accumulating along the lines of least vibration, called nodal lines. A variety
of nodal lines each accompanied by its characteristic tone may be obtained
by changing the position of the bow and by touching the fingers at different
points at the edge of the disc. They are known as Chladni's figures. (See
Fig. 338.)
Fig. 339.—Manometric flame apparatus.
347. Manometric Flames.—The actual presence of overtones along with
the fundamental may be made visible by the manometric flame apparatus.
This consists of a wooden box, C, mounted upon a stand. (See Fig. 339.)
Page 372
The box is divided vertically by a flexible partition or diaphragm. Two
outlets are provided on one side of the partition, one, C, leads to a gas pipe,
the other is a glass tube, D. On the other side of the partition a tube, E, leads
to a mouthpiece. A mirror, M, is mounted so as to be rotated upon a vertical
axis in front of F and near it. Gas is now turned on and lighted at F. The
sound of the voice produced at the mouthpiece sends sound waves through
the tube and against the diaphragm which vibrates back and forth as the
sound waves strike it. This action affects the flame which rises and falls. If
now the mirror is rotated, the image of the flame seen in the mirror rises
and falls, showing not only the fundamental or principal vibrations but also
the overtones. If the different vowel sounds are uttered in succession in the
mouthpiece, each is found to be accompanied by its characteristic wave
form (Fig. 340). In some, the fundamental is strongly prominent, while in
others, the overtones produce marked modifications. Other devices have
been invented which make possible the accurate analysis of sounds into
their component vibrations, while still others unite simple tones to produce
any complex tone desired.
348. The Phonograph.—The graphophone or phonograph provides a
mechanism for cutting upon a disc or cylinder a groove that reproduces, in
the varying form or depth of the tracing, every peculiarity of the sound
waves affecting it. The reproducer consists of a sensitive diaphragm to
which is attached a needle. The disc or cylinder is rotated under the
reproducing needle. The irregularities of the bottom of the tracing cause
corresponding movements of the needle and the attached diaphragm, which
start waves that reproduce the sounds that previously affected the recorder.
The construction of the phonograph has reached such perfection that very
accurate reproduction of a great variety of sounds is secured.
349. Wind Instruments.—In many musical instruments as the cornet,
pipe-organ, flute, etc., and also in whistles, the vibrating body that serves as
a source of sound is a column of air, usually enclosed in a tube. Unlike
vibrating strings, this vibrating source of sound changes but little in tension
or density, hence changes in the pitch of air columns is secured by changing
their length. The law being similar to that with strings, the vibration rates of
air columns are inversely proportional to their lengths.
outlets are provided on one side of the partition, one, C, leads to a gas pipe,
the other is a glass tube, D. On the other side of the partition a tube, E, leads
to a mouthpiece. A mirror, M, is mounted so as to be rotated upon a vertical
axis in front of F and near it. Gas is now turned on and lighted at F. The
sound of the voice produced at the mouthpiece sends sound waves through
the tube and against the diaphragm which vibrates back and forth as the
sound waves strike it. This action affects the flame which rises and falls. If
now the mirror is rotated, the image of the flame seen in the mirror rises
and falls, showing not only the fundamental or principal vibrations but also
the overtones. If the different vowel sounds are uttered in succession in the
mouthpiece, each is found to be accompanied by its characteristic wave
form (Fig. 340). In some, the fundamental is strongly prominent, while in
others, the overtones produce marked modifications. Other devices have
been invented which make possible the accurate analysis of sounds into
their component vibrations, while still others unite simple tones to produce
any complex tone desired.
348. The Phonograph.—The graphophone or phonograph provides a
mechanism for cutting upon a disc or cylinder a groove that reproduces, in
the varying form or depth of the tracing, every peculiarity of the sound
waves affecting it. The reproducer consists of a sensitive diaphragm to
which is attached a needle. The disc or cylinder is rotated under the
reproducing needle. The irregularities of the bottom of the tracing cause
corresponding movements of the needle and the attached diaphragm, which
start waves that reproduce the sounds that previously affected the recorder.
The construction of the phonograph has reached such perfection that very
accurate reproduction of a great variety of sounds is secured.
349. Wind Instruments.—In many musical instruments as the cornet,
pipe-organ, flute, etc., and also in whistles, the vibrating body that serves as
a source of sound is a column of air, usually enclosed in a tube. Unlike
vibrating strings, this vibrating source of sound changes but little in tension
or density, hence changes in the pitch of air columns is secured by changing
their length. The law being similar to that with strings, the vibration rates of
air columns are inversely proportional to their lengths.
Page 373
Fig. 340.—
Characteristic forms
of manometric
flames.
Fig. 341.—(R) Cross-section of an organ pipe
showing action of tongue at C. (a) The
fundamental tone in a closed pipe has a wave
Characteristic forms
of manometric
flames.
Fig. 341.—(R) Cross-section of an organ pipe
showing action of tongue at C. (a) The
fundamental tone in a closed pipe has a wave
Page 374
length four times the length of the pipe; (b)
and (c) how the first and second overtones are
formed in a closed pipe; (d) the fundamental
tone of an open pipe has a wave length equal
to twice the length of the pipe; (e) and (f) first
and second overtones of open pipe.
If an open organ pipe be sounded by blowing gently through it, a tone of
definite pitch is heard. Now if one end is closed, on being sounded again
the pitch is found to be an octave lower. Therefore, the pitch of a closed
pipe is an octave lower than that of an open one of the same length.
350. Nodes in Organ Pipes.—Fig. 341, R represents a cross-section of a
wooden organ pipe. Air is blown through A, and strikes against a thin
tongue of wood C. This starts the jet of air vibrating thus setting the column
of air in vibration so that the sound is kept up as long as air is blown
through A. To understand the mode of vibration of the air column a study of
the curve that represents wave motion (Fig. 342) is helpful Let AB represent
such a curve, in this 2, 4 and 6 represent nodes or points of least vibration,
while 1, 3 and 5 are antinodes or places of greatest motion. A full wave
length extends from 1-5, or 2-6. Now in the open organ pipe (Fig. 341d),
the end of the air column d is a place of great vibration or is an antinode. At
the other end also occurs another place of great vibration or an antinode;
between these two antinodes must be a place of least vibration or a node.
The open air column therefore extends from antinode to antinode (or from
1-3) or is one-half a wave length. The closed air column (Fig. 341a) extends
from a place of great vibration at a to a place of no vibration at the closed
end. The distance from an antinode to a node is that from 1-2 on the curve
and is one-fourth a wave length.
W
he
n
a
pi
Fig. 343.—A clarinet.
Fig. 342.—Graphic pe
representation of is
sound waves. blown strongly it yields overtones. The bugle is
a musical instrument in which notes of different
and (c) how the first and second overtones are
formed in a closed pipe; (d) the fundamental
tone of an open pipe has a wave length equal
to twice the length of the pipe; (e) and (f) first
and second overtones of open pipe.
If an open organ pipe be sounded by blowing gently through it, a tone of
definite pitch is heard. Now if one end is closed, on being sounded again
the pitch is found to be an octave lower. Therefore, the pitch of a closed
pipe is an octave lower than that of an open one of the same length.
350. Nodes in Organ Pipes.—Fig. 341, R represents a cross-section of a
wooden organ pipe. Air is blown through A, and strikes against a thin
tongue of wood C. This starts the jet of air vibrating thus setting the column
of air in vibration so that the sound is kept up as long as air is blown
through A. To understand the mode of vibration of the air column a study of
the curve that represents wave motion (Fig. 342) is helpful Let AB represent
such a curve, in this 2, 4 and 6 represent nodes or points of least vibration,
while 1, 3 and 5 are antinodes or places of greatest motion. A full wave
length extends from 1-5, or 2-6. Now in the open organ pipe (Fig. 341d),
the end of the air column d is a place of great vibration or is an antinode. At
the other end also occurs another place of great vibration or an antinode;
between these two antinodes must be a place of least vibration or a node.
The open air column therefore extends from antinode to antinode (or from
1-3) or is one-half a wave length. The closed air column (Fig. 341a) extends
from a place of great vibration at a to a place of no vibration at the closed
end. The distance from an antinode to a node is that from 1-2 on the curve
and is one-fourth a wave length.
W
he
n
a
pi
Fig. 343.—A clarinet.
Fig. 342.—Graphic pe
representation of is
sound waves. blown strongly it yields overtones. The bugle is
a musical instrument in which notes of different
Page 375
pitch are produced by differences in blowing. (See Fig. 341.) (d), (e), (f). In
playing the cornet different pitches are produced by differences in blowing,
and by valves which change the length of the vibrating air column. (See
Fig. 334.) The clarinet has a mouthpiece containing a reed similar to that
made by cutting a tongue on a straw or quill. The length of the vibrating air
column in the clarinet is changed by opening holes in the sides of the tube.
(See Fig. 343.)
351. How we Hear.—Our hearing apparatus is arranged in three parts. (See
Fig. 344.) The external ear leads to the tympanum. The middle ear contains
three bones that convey the vibrations of the tympanum to the internal ear.
The latter is filled with a liquid which conveys the vibrations to a part
having a coiled shell-like structure called the Cochlea. Stretched across
within the cochlea are some 3000 fibers or strings. It is believed that each is
sensitive to a particular vibration rate and that each is also attached to a
nerve fiber. The sound waves of the air transmitted by the tympanum, the
ear bones and the liquid of the internal ear start sympathetic vibrations in
the strings of the cochlea which affect the auditory nerve and we hear. The
highest tones perceptible by the human ear are produced by from 24,000 to
40,000 vibrations per second. The average person cannot hear sounds
produced by more than about 28,000 vibrations. The usual range of hearing
is about 11 octaves. The tones produced by higher vibrations than about
4100 per second are shrill and displeasing. In music the range is 7-1/3
octaves, the lowest tone being produced by 27.5 vibrations, the highest by
about 4100 per second.
The tones produced by men are lower than those of women and boys. In
men the vocal cords are about 18 mm. long; in women they are 12 mm.
long.
The compass of the human voice is about two octaves, although some noted
singers have a range of two and one-half octaves. In ordinary conversation
the wave length of sounds produced by a man's voice is from 8 to 12 ft. and
that of a woman's voice is from 2 to 4 ft.
playing the cornet different pitches are produced by differences in blowing,
and by valves which change the length of the vibrating air column. (See
Fig. 334.) The clarinet has a mouthpiece containing a reed similar to that
made by cutting a tongue on a straw or quill. The length of the vibrating air
column in the clarinet is changed by opening holes in the sides of the tube.
(See Fig. 343.)
351. How we Hear.—Our hearing apparatus is arranged in three parts. (See
Fig. 344.) The external ear leads to the tympanum. The middle ear contains
three bones that convey the vibrations of the tympanum to the internal ear.
The latter is filled with a liquid which conveys the vibrations to a part
having a coiled shell-like structure called the Cochlea. Stretched across
within the cochlea are some 3000 fibers or strings. It is believed that each is
sensitive to a particular vibration rate and that each is also attached to a
nerve fiber. The sound waves of the air transmitted by the tympanum, the
ear bones and the liquid of the internal ear start sympathetic vibrations in
the strings of the cochlea which affect the auditory nerve and we hear. The
highest tones perceptible by the human ear are produced by from 24,000 to
40,000 vibrations per second. The average person cannot hear sounds
produced by more than about 28,000 vibrations. The usual range of hearing
is about 11 octaves. The tones produced by higher vibrations than about
4100 per second are shrill and displeasing. In music the range is 7-1/3
octaves, the lowest tone being produced by 27.5 vibrations, the highest by
about 4100 per second.
The tones produced by men are lower than those of women and boys. In
men the vocal cords are about 18 mm. long; in women they are 12 mm.
long.
The compass of the human voice is about two octaves, although some noted
singers have a range of two and one-half octaves. In ordinary conversation
the wave length of sounds produced by a man's voice is from 8 to 12 ft. and
that of a woman's voice is from 2 to 4 ft.
Page 376
Fig. 344.—The
human ear.
Important Topics
1. Tone quality. Fundamental and overtones. Chladni's plate.
2. Manometric flame apparatus.
3. Phonograph recorder and reproducer.
4. Air columns and wind instruments.
5. How we hear.
Exercises
1. What determines the pitch of the note of a toy whistle?
2. The lowest note of the organ has a wave length of about 64 ft. What is the
length of a closed pipe giving this note? Of an open pipe?
3. What is the first overtone of C? What are the second and third overtones?
Give vibration numbers and pitch names or letters.
4. Why is the music of a band just as harmonious at a distance of 400 ft. as
at 100 ft.?
5. A resonant air column 60 cm. long closed at one end will respond to what
rate of vibration at 10°C.?
human ear.
Important Topics
1. Tone quality. Fundamental and overtones. Chladni's plate.
2. Manometric flame apparatus.
3. Phonograph recorder and reproducer.
4. Air columns and wind instruments.
5. How we hear.
Exercises
1. What determines the pitch of the note of a toy whistle?
2. The lowest note of the organ has a wave length of about 64 ft. What is the
length of a closed pipe giving this note? Of an open pipe?
3. What is the first overtone of C? What are the second and third overtones?
Give vibration numbers and pitch names or letters.
4. Why is the music of a band just as harmonious at a distance of 400 ft. as
at 100 ft.?
5. A resonant air column 60 cm. long closed at one end will respond to what
rate of vibration at 10°C.?
Page 377
6. Can you find out how the valves on a cornet operate to change the pitch
of the tone?
7. How is the trombone operated to produce tones of different pitch?
8. The lowest note on an organ has a wave length of about 64 ft. What must
be the length of a closed pipe giving this note?
9. What is the approximate length of an open organ pipe which sends out
waves 4 ft. long?
Review Outline: Sound
Sound—definition, source, medium, speed, nature.
Waves—longitudinal, transverse, illustrations.
intensity—area, amplitude, density, distance.
Characteristics of
pitch—scales; major, tempered, triads, N = V/L
Musical Sounds:
quality—fundamental and overtones.
Sympathetic Vibrations—resonance, interference, beats, discord.
Musical Instruments—string, air column, membrane or plate.
Laws of; (a) vibrating strings (3), (b) vibrating air columns (2).
of the tone?
7. How is the trombone operated to produce tones of different pitch?
8. The lowest note on an organ has a wave length of about 64 ft. What must
be the length of a closed pipe giving this note?
9. What is the approximate length of an open organ pipe which sends out
waves 4 ft. long?
Review Outline: Sound
Sound—definition, source, medium, speed, nature.
Waves—longitudinal, transverse, illustrations.
intensity—area, amplitude, density, distance.
Characteristics of
pitch—scales; major, tempered, triads, N = V/L
Musical Sounds:
quality—fundamental and overtones.
Sympathetic Vibrations—resonance, interference, beats, discord.
Musical Instruments—string, air column, membrane or plate.
Laws of; (a) vibrating strings (3), (b) vibrating air columns (2).
Page 378
CHAPTER XVI
LIGHT
(1) Light, Its Rectilinear Propagation, Shadows
352. A Comparison of Sound and Light.—Light from the standpoint of
physics is considered much as is sound, as a mode of motion; one affecting
the ear, the other producing the result called vision. There are other
differences also worth considering. (a) While sound travels as vibrations of
some material medium, light travels only as vibrations of the ether; solids,
liquids, and gases act so as to hinder rather than to assist in its movement.
That is, light travels best in a vacuum or in a space devoid of ordinary
matter. (b) The speed of light is so great that at ordinary distances on the
earth its motion is practically instantaneous. Experiments have shown that
its speed is about 186,000 miles to 300,000 kilometers a second.
353. Luminous and Illuminated Bodies.—If we consider the objects
within a room, some of them, as books and furniture, would be invisible if
all light from external sources were excluded. On the other hand, some
other objects, such as a lighted lamp, a burning coal, or a red hot iron,
would be seen if no outside light were present. Such bodies are said to be
luminous. Most luminous bodies are hot and become non-luminous on
cooling. There are, however, some bodies that are luminous at ordinary
room temperatures, as the firefly and some phosphorescent paints. When
light emitted by a luminous body strikes an object, a portion of it is always
reflected. It is this reflected light that makes the illuminated object visible.
If the object is a sheet of glass, some of the light is transmitted. If a
substance is so clear that objects can be seen through it, the substance is
transparent, but if objects cannot be seen through it, the substance is said to
be translucent. Objects transmitting no light are opaque. Some of the light
falling upon a body is neither reflected nor transmitted, but is absorbed and
tends to warm the body. The light falling upon a body is therefore either
reflected, transmitted, or absorbed. Thus Fig. 345 represents light coming
from S to a piece of glass GL. A portion of the light represented by R is
LIGHT
(1) Light, Its Rectilinear Propagation, Shadows
352. A Comparison of Sound and Light.—Light from the standpoint of
physics is considered much as is sound, as a mode of motion; one affecting
the ear, the other producing the result called vision. There are other
differences also worth considering. (a) While sound travels as vibrations of
some material medium, light travels only as vibrations of the ether; solids,
liquids, and gases act so as to hinder rather than to assist in its movement.
That is, light travels best in a vacuum or in a space devoid of ordinary
matter. (b) The speed of light is so great that at ordinary distances on the
earth its motion is practically instantaneous. Experiments have shown that
its speed is about 186,000 miles to 300,000 kilometers a second.
353. Luminous and Illuminated Bodies.—If we consider the objects
within a room, some of them, as books and furniture, would be invisible if
all light from external sources were excluded. On the other hand, some
other objects, such as a lighted lamp, a burning coal, or a red hot iron,
would be seen if no outside light were present. Such bodies are said to be
luminous. Most luminous bodies are hot and become non-luminous on
cooling. There are, however, some bodies that are luminous at ordinary
room temperatures, as the firefly and some phosphorescent paints. When
light emitted by a luminous body strikes an object, a portion of it is always
reflected. It is this reflected light that makes the illuminated object visible.
If the object is a sheet of glass, some of the light is transmitted. If a
substance is so clear that objects can be seen through it, the substance is
transparent, but if objects cannot be seen through it, the substance is said to
be translucent. Objects transmitting no light are opaque. Some of the light
falling upon a body is neither reflected nor transmitted, but is absorbed and
tends to warm the body. The light falling upon a body is therefore either
reflected, transmitted, or absorbed. Thus Fig. 345 represents light coming
from S to a piece of glass GL. A portion of the light represented by R is
Page 379
reflected. Another part A is absorbed and disappears, while still another part
T is transmitted and passes on.
There is no sharply drawn line between transparent
and opaque bodies. Very thin sheets of gold
transmit a greenish light, and experiments have
shown that substances as transparent as clear water
absorb enough light so that at considerable depths
in an ocean or lake little or no light is ever found.
All light whether from luminous bodies or
reflected from non-luminous objects shows certain
properties which will now be considered.
354. The Rectilinear Propagation of Light.—If a
beam of light passes through a hole in a window
shade into a darkened room, it is seen to follow a
perfectly straight course. If a person while
coughing holds a book before the face, the sound
passes around the book and is heard at any point in
the room while the face is hidden by the book. In Fig. 345.—The light
other words, light ordinarily does not pass around is transmitted (T),
corners as sound does, but travels in straight lines. reflected (R), or
This fact is made use of when one aims a gun or absorbed (A).
merely looks at an object. So well established in
our minds is the idea that an object is in the direction from which we see the
light coming to us from it, that we are sometimes deceived as to the real
position of an object, when the course of the light from it has been changed
by a mirror or some other reflecting surface. Many illusions are produced in
this way, of which the mirage of the desert is one example. (See Art. 381.)
355. Shadows.—A shadow is the
space from which light is cut off by
an opaque body. Thus if a book (see
Fig. 346) is held between a screen,
N, and a small source of light, L, a
shadow is produced which extends
from the book to the screen. Notice
that the shadow is a space and not
Fig. 346.—Shadow from a small an area. If a large gas flame (see
T is transmitted and passes on.
There is no sharply drawn line between transparent
and opaque bodies. Very thin sheets of gold
transmit a greenish light, and experiments have
shown that substances as transparent as clear water
absorb enough light so that at considerable depths
in an ocean or lake little or no light is ever found.
All light whether from luminous bodies or
reflected from non-luminous objects shows certain
properties which will now be considered.
354. The Rectilinear Propagation of Light.—If a
beam of light passes through a hole in a window
shade into a darkened room, it is seen to follow a
perfectly straight course. If a person while
coughing holds a book before the face, the sound
passes around the book and is heard at any point in
the room while the face is hidden by the book. In Fig. 345.—The light
other words, light ordinarily does not pass around is transmitted (T),
corners as sound does, but travels in straight lines. reflected (R), or
This fact is made use of when one aims a gun or absorbed (A).
merely looks at an object. So well established in
our minds is the idea that an object is in the direction from which we see the
light coming to us from it, that we are sometimes deceived as to the real
position of an object, when the course of the light from it has been changed
by a mirror or some other reflecting surface. Many illusions are produced in
this way, of which the mirage of the desert is one example. (See Art. 381.)
355. Shadows.—A shadow is the
space from which light is cut off by
an opaque body. Thus if a book (see
Fig. 346) is held between a screen,
N, and a small source of light, L, a
shadow is produced which extends
from the book to the screen. Notice
that the shadow is a space and not
Fig. 346.—Shadow from a small an area. If a large gas flame (see
Page 380
source of light. Fig. 347) is used as the source of
light, the shadow of the book is no
longer clear cut at the edges as before,
but has a darker central part with a
lighter fringe of partial shadow at the
edges. The dark portion within the
shadow has all the light excluded from
it and is called the umbra. The lighter
portion of the shadow at the edges has Fig. 347.—Shadow when source
only a part of the light from the flame of light is large.
cut off. This portion is called the
penumbra. when one stands in
sunlight his shadow extends from his body to the ground or object on which
the shadow falls. At night we are in the earth's shadow, which extends out
into space beyond the earth.
356. Eclipses.—Since the sun is a very
large object the shadow cast by the earth
contains both umbra and penumbra. (See
Fig. 348.) When the moon passes into the
shadow of the earth, there is said to be an
eclipse of the moon, while if the moon's
shadow falls upon the earth, the portion of
Fig. 348.—Character of the the earth cut off from the sun's light has
earth's shadow. an eclipse of the sun.
357. Images by Small Apertures.—The
straight line movement of light makes possible the pin-hole camera, by
which satisfactory photographs have been made. The action of this device
may be illustrated by placing a luminous body, a lighted candle, an
incandescent lamp, or a gas flame, in front of a piece of cardboard, S, which
has a small opening in it. Light from the object (see Fig. 349) falls upon a
screen, S2, so as to produce an inverted image. Other applications of this
principle will be given later.
In Fig. 349 let PQ represent a gas flame, then light from point P at the top
of the flame will pass in a straight line through the opening or aperture of
the cardboard and strike at P2 at the bottom of the illuminated spot upon the
light, the shadow of the book is no
longer clear cut at the edges as before,
but has a darker central part with a
lighter fringe of partial shadow at the
edges. The dark portion within the
shadow has all the light excluded from
it and is called the umbra. The lighter
portion of the shadow at the edges has Fig. 347.—Shadow when source
only a part of the light from the flame of light is large.
cut off. This portion is called the
penumbra. when one stands in
sunlight his shadow extends from his body to the ground or object on which
the shadow falls. At night we are in the earth's shadow, which extends out
into space beyond the earth.
356. Eclipses.—Since the sun is a very
large object the shadow cast by the earth
contains both umbra and penumbra. (See
Fig. 348.) When the moon passes into the
shadow of the earth, there is said to be an
eclipse of the moon, while if the moon's
shadow falls upon the earth, the portion of
Fig. 348.—Character of the the earth cut off from the sun's light has
earth's shadow. an eclipse of the sun.
357. Images by Small Apertures.—The
straight line movement of light makes possible the pin-hole camera, by
which satisfactory photographs have been made. The action of this device
may be illustrated by placing a luminous body, a lighted candle, an
incandescent lamp, or a gas flame, in front of a piece of cardboard, S, which
has a small opening in it. Light from the object (see Fig. 349) falls upon a
screen, S2, so as to produce an inverted image. Other applications of this
principle will be given later.
In Fig. 349 let PQ represent a gas flame, then light from point P at the top
of the flame will pass in a straight line through the opening or aperture of
the cardboard and strike at P2 at the bottom of the illuminated spot upon the
Page 381
screen. Light from Q passing in straight lines through the aperture will
strike at Q2 at the top of the lighted space. This spot of light will have the
same outlines as the luminous body PQ and being formed as just described
will be inverted.
Fig. 349.—Image formed by a small aperture
is inverted.
This spot of light, resembling in its outlines the flame, is called an image.
An image is defined as an optical counterpart of an object. Images are
formed in a variety of devices, such as apertures, mirrors, and lenses. The
pin-hole camera is simply a light-tight box with a small aperture in one
side. Light passing through this aperture forms an image upon the opposite
side of the interior of the box, of whatever object is in front of the camera.
Light entering a room through a large aperture such as a window produces
a multitude of overlapping images which blend to form a somewhat evenly
illuminated surface.
Important Topics
1. Light contrasted with sound (three differences).
2. Bodies: transparent, translucent, opaque.
3. Light: reflected, transmitted, absorbed.
4. Light travels in straight lines, evidence, shadows, umbra, penumbra.
5. Formation of images by small apertures.
strike at Q2 at the top of the lighted space. This spot of light will have the
same outlines as the luminous body PQ and being formed as just described
will be inverted.
Fig. 349.—Image formed by a small aperture
is inverted.
This spot of light, resembling in its outlines the flame, is called an image.
An image is defined as an optical counterpart of an object. Images are
formed in a variety of devices, such as apertures, mirrors, and lenses. The
pin-hole camera is simply a light-tight box with a small aperture in one
side. Light passing through this aperture forms an image upon the opposite
side of the interior of the box, of whatever object is in front of the camera.
Light entering a room through a large aperture such as a window produces
a multitude of overlapping images which blend to form a somewhat evenly
illuminated surface.
Important Topics
1. Light contrasted with sound (three differences).
2. Bodies: transparent, translucent, opaque.
3. Light: reflected, transmitted, absorbed.
4. Light travels in straight lines, evidence, shadows, umbra, penumbra.
5. Formation of images by small apertures.
Page 382
Exercises
1. Consider the circumference of the earth as 25,000 miles. How many
times would the speed of light cover this distance in a second?
2. How soon after any great disturbance takes place on the sun, 93,000,000
miles distant, can it be seen upon the earth?
3. Construct a diagram of the moon's shadow. How much of the sun can one
see when in the moon's umbra? When in its penumbra? Have you ever been
in either? When? Have you ever been in the earth's umbra? In its
penumbra?
4. Explain, using a diagram, the formation of an inverted image by a small
aperture.
5. If the sun is 45 degrees above the horizon, what is the height of a pole
casting a shadow 60 ft. long?
6. If a shadow 6 ft. long is cast by a 10-ft. pole standing vertically upon a
walk, how tall is the tree whose shadow is 42 ft. long, both measurements
being made at the same time?
7. Why are the shadows caused by an electric arc lamp so sharply defined?
8. Why should schoolroom windows be all on one side and reach to the
ceiling?
9. What is the relation between the size of an image and its distance from
the aperture forming it? Can you prove this by geometry?
10. What are silhouettes and how are they produced?
(2) Photometry and the Law of Reflection
358. Photometry.—It is desirable at times to compare the intensities of
illumination produced by light from different sources. This is done to
determine the relative cost or effectiveness of various illuminants such as
candles, kerosene and gas lamps, and electric lights The process of
determining the relative intensity of lights or lamps is called photometry.
(Photos = light.)
1. Consider the circumference of the earth as 25,000 miles. How many
times would the speed of light cover this distance in a second?
2. How soon after any great disturbance takes place on the sun, 93,000,000
miles distant, can it be seen upon the earth?
3. Construct a diagram of the moon's shadow. How much of the sun can one
see when in the moon's umbra? When in its penumbra? Have you ever been
in either? When? Have you ever been in the earth's umbra? In its
penumbra?
4. Explain, using a diagram, the formation of an inverted image by a small
aperture.
5. If the sun is 45 degrees above the horizon, what is the height of a pole
casting a shadow 60 ft. long?
6. If a shadow 6 ft. long is cast by a 10-ft. pole standing vertically upon a
walk, how tall is the tree whose shadow is 42 ft. long, both measurements
being made at the same time?
7. Why are the shadows caused by an electric arc lamp so sharply defined?
8. Why should schoolroom windows be all on one side and reach to the
ceiling?
9. What is the relation between the size of an image and its distance from
the aperture forming it? Can you prove this by geometry?
10. What are silhouettes and how are they produced?
(2) Photometry and the Law of Reflection
358. Photometry.—It is desirable at times to compare the intensities of
illumination produced by light from different sources. This is done to
determine the relative cost or effectiveness of various illuminants such as
candles, kerosene and gas lamps, and electric lights The process of
determining the relative intensity of lights or lamps is called photometry.
(Photos = light.)
Page 383
The unit for measuring the power of light is called a candle power. It is the
light produced by a sperm candle burning 120 grains per hour. An ordinary
gas light burns 5 or more cubic feet of gas per hour and yields from 15 to 25
candle power. A Welsbach gas lamp, consuming 3 cu. ft. per hour, produces
50 to 100 candle power.
Instead of using candles, for practical photometry, incandescent lamps
standardized by the Bureau of Standards are used for testing or calibration
purposes.
It is necessary to distinguish between the intensity of a luminous body, i.e.,
as a source of light, and the intensity of illumination upon some surface
produced by a light. It is considered that two sources of light are of equal
intensity if they produce equal illumination at equal distances.
359. Law of Intensity of Light.—A device for measuring the candle power
of a light is called a photometer. Its use is based upon the law of intensity of
light. The intensity of illumination of a surface is inversely proportional to
the square of its distance from the source of light. This relation is similar to
that existing between the intensity of a sound and the distance from its
source. The following device illustrates the truth of this law in a simple
manner.
Fig. 350.—The light spreads over four times
the area at twice the distance.
Cut a hole 1 in. square in a large sheet of cardboard (K) and place the card
in an upright position 1 meter from an arc light or other point source of
light (L). Now rule inch squares upon another card (M) and place it parallel
to the first card and 2 meters from it. (See Fig. 350.) The light that passed
through the hole of 1 sq. in. at a distance of 1 meter is spread over 4 sq. in.
at a distance of 2 meters. Therefore, the intensity of illumination on each
square inch of M is one-fourth that upon the surface of K. If M is placed 3
light produced by a sperm candle burning 120 grains per hour. An ordinary
gas light burns 5 or more cubic feet of gas per hour and yields from 15 to 25
candle power. A Welsbach gas lamp, consuming 3 cu. ft. per hour, produces
50 to 100 candle power.
Instead of using candles, for practical photometry, incandescent lamps
standardized by the Bureau of Standards are used for testing or calibration
purposes.
It is necessary to distinguish between the intensity of a luminous body, i.e.,
as a source of light, and the intensity of illumination upon some surface
produced by a light. It is considered that two sources of light are of equal
intensity if they produce equal illumination at equal distances.
359. Law of Intensity of Light.—A device for measuring the candle power
of a light is called a photometer. Its use is based upon the law of intensity of
light. The intensity of illumination of a surface is inversely proportional to
the square of its distance from the source of light. This relation is similar to
that existing between the intensity of a sound and the distance from its
source. The following device illustrates the truth of this law in a simple
manner.
Fig. 350.—The light spreads over four times
the area at twice the distance.
Cut a hole 1 in. square in a large sheet of cardboard (K) and place the card
in an upright position 1 meter from an arc light or other point source of
light (L). Now rule inch squares upon another card (M) and place it parallel
to the first card and 2 meters from it. (See Fig. 350.) The light that passed
through the hole of 1 sq. in. at a distance of 1 meter is spread over 4 sq. in.
at a distance of 2 meters. Therefore, the intensity of illumination on each
square inch of M is one-fourth that upon the surface of K. If M is placed 3
Page 384
meters from the light, 9 sq. in. are illuminated, or the intensity is one-ninth
that at 1 meter distance.
Fig. 351.—The Bunsen photometer.
These relations show that the intensity of illumination is inversely
proportional to the square of the distance from the source of light. An
application of the law of intensity is made in using a simple (Bunsen)
photometer. This consists of a card containing a spot soaked with oil or
melted wax. (See Fig. 351.) The lights whose intensities are to be compared
are placed upon opposite sides of the card. The card is then adjusted so that
the spot appears the same on both sides. The illumination is now equal on
both sides of the card and the candle powers of the two lights are
proportional to the squares of their distances from the card. The simple
device just described will give approximate results only. For accurate
results more elaborate apparatus is required.
360. Measurement of the Intensity of Illumination.—A standard candle
(Art. 358) produces when lighted 1 candle power. The illumination caused
by this upon a surface 1 ft. away and at right angles to the light rays is
called a foot-candle. It is the unit of intensity of illumination. A 4-candle-
power lamp, at a distance of 1 ft., produces 4 foot-candles. A 16-candle-
power lamp at a distance of 2 ft. also produces 4 foot-candles—(16 ÷ 22).
The intensity of illumination required for a good light for seeing varies with
the conditions. Thus, for stage and store lighting about 4 foot-candles are
needed, while homes and churches may require but 1 foot-candle.
Too great an intensity of illumination is as harmful as not enough. Exposed
lights having an intensity of more than 5 candle power per square inch are
often a cause of eye trouble. Such lights should be protected by frosted
globes.
that at 1 meter distance.
Fig. 351.—The Bunsen photometer.
These relations show that the intensity of illumination is inversely
proportional to the square of the distance from the source of light. An
application of the law of intensity is made in using a simple (Bunsen)
photometer. This consists of a card containing a spot soaked with oil or
melted wax. (See Fig. 351.) The lights whose intensities are to be compared
are placed upon opposite sides of the card. The card is then adjusted so that
the spot appears the same on both sides. The illumination is now equal on
both sides of the card and the candle powers of the two lights are
proportional to the squares of their distances from the card. The simple
device just described will give approximate results only. For accurate
results more elaborate apparatus is required.
360. Measurement of the Intensity of Illumination.—A standard candle
(Art. 358) produces when lighted 1 candle power. The illumination caused
by this upon a surface 1 ft. away and at right angles to the light rays is
called a foot-candle. It is the unit of intensity of illumination. A 4-candle-
power lamp, at a distance of 1 ft., produces 4 foot-candles. A 16-candle-
power lamp at a distance of 2 ft. also produces 4 foot-candles—(16 ÷ 22).
The intensity of illumination required for a good light for seeing varies with
the conditions. Thus, for stage and store lighting about 4 foot-candles are
needed, while homes and churches may require but 1 foot-candle.
Too great an intensity of illumination is as harmful as not enough. Exposed
lights having an intensity of more than 5 candle power per square inch are
often a cause of eye trouble. Such lights should be protected by frosted
globes.
Page 385
A pleasing form of lighting for large halls and public buildings is the
indirect system. In this, the lamps are hidden by reflectors which throw the
light upon the ceiling from which it is diffused over the room. This form of
lighting is more expensive than other systems since but a part of the light is
reflected. Its cost therefore is an important factor when considering its use.
361. The Reflection of Light.—The light reflected from the surfaces of
bodies about us gives us information concerning our surroundings. A
knowledge of the behavior of light undergoing reflection is not usually
gained from ordinary observation. The law of reflection of light may be
shown, however, by an experiment.
Fig. 352.—B´ is as
far back of the
mirror as B is in
front of it.
Christian Huygens
(Popular Science
Monthly)
Christian Huygens
(1629-1695). Dutch
physicist; invented the
pendulum clock
(1656); developed the
wave theory of light;
indirect system. In this, the lamps are hidden by reflectors which throw the
light upon the ceiling from which it is diffused over the room. This form of
lighting is more expensive than other systems since but a part of the light is
reflected. Its cost therefore is an important factor when considering its use.
361. The Reflection of Light.—The light reflected from the surfaces of
bodies about us gives us information concerning our surroundings. A
knowledge of the behavior of light undergoing reflection is not usually
gained from ordinary observation. The law of reflection of light may be
shown, however, by an experiment.
Fig. 352.—B´ is as
far back of the
mirror as B is in
front of it.
Christian Huygens
(Popular Science
Monthly)
Christian Huygens
(1629-1695). Dutch
physicist; invented the
pendulum clock
(1656); developed the
wave theory of light;
Page 386
discovered polarization
of light (1690).
H. V. Helmholtz
"By Permission of the
Berlin Photographic
Co., New York."
Hermann von
Helmholtz (1821-1894)
Germany. Established
the doctrine of
conservation of energy;
made many discoveries
in sound; invented the
ophthalmoscope;
established the
physical basis of tone
quality.
A plane mirror, M, is held in a vertical position resting upon a sheet of
paper. (See Fig. 352.) Pins are set upright in the paper at A and B. On
placing the eye along the line AC and looking toward the mirror an image
of light (1690).
H. V. Helmholtz
"By Permission of the
Berlin Photographic
Co., New York."
Hermann von
Helmholtz (1821-1894)
Germany. Established
the doctrine of
conservation of energy;
made many discoveries
in sound; invented the
ophthalmoscope;
established the
physical basis of tone
quality.
A plane mirror, M, is held in a vertical position resting upon a sheet of
paper. (See Fig. 352.) Pins are set upright in the paper at A and B. On
placing the eye along the line AC and looking toward the mirror an image
Page 387
of B may be seen in the mirror due to the light reflected from its surface.
Pins C and D are now set in the paper so that when one looks along the line
BD toward the mirror one may see all four pins apparently in one line. This
indicates that the light from A and C passing along CA toward O is reflected
back along the light CBD. By means of a ruler, draw lines through BD and
AC till they intersect at O. Also draw PO perpendicular to the mirror at O.
Then the angles AOP and BOP will be found equal. These are called the
angles of incidence and reflection respectively. The law of reflection is
therefore stated: The angle of reflection is equal to the angle of incidence.
These angles are in the same plane, that of the paper. This law applies in all
cases of reflection of light. It is similar to the law of reflection of sound
(Art. 326.)
Important Topics
1. Photometry, law of intensity, candle power, foot-candle.
2. Intensity of illumination.
3. Reflected light and law of reflection.
Exercises
1. Both sides of a card are equally illuminated when two lights are on
opposite sides of it and 10 and 30 cm. respectively from it. what are their
relative intensities?
2. What are the relative intensities of illumination from a gas light upon a
book 6 ft. and 2 ft. respectively from the light?
3. Which is more expensive per candle power? How many times as
expensive? A 50-watt 16-candle-power incandescent lamp at 10 cents per
kilowatt-hour or a 100-candle-power Welsbach light burning 5 cu. ft. of gas
per hour at 80 cents per 1000 cu. ft. of gas. (Find cost of each per hour, and
then the cost of 1 candle power hour for each.)
4. Why are not ordinary shadows perfectly dark?
Pins C and D are now set in the paper so that when one looks along the line
BD toward the mirror one may see all four pins apparently in one line. This
indicates that the light from A and C passing along CA toward O is reflected
back along the light CBD. By means of a ruler, draw lines through BD and
AC till they intersect at O. Also draw PO perpendicular to the mirror at O.
Then the angles AOP and BOP will be found equal. These are called the
angles of incidence and reflection respectively. The law of reflection is
therefore stated: The angle of reflection is equal to the angle of incidence.
These angles are in the same plane, that of the paper. This law applies in all
cases of reflection of light. It is similar to the law of reflection of sound
(Art. 326.)
Important Topics
1. Photometry, law of intensity, candle power, foot-candle.
2. Intensity of illumination.
3. Reflected light and law of reflection.
Exercises
1. Both sides of a card are equally illuminated when two lights are on
opposite sides of it and 10 and 30 cm. respectively from it. what are their
relative intensities?
2. What are the relative intensities of illumination from a gas light upon a
book 6 ft. and 2 ft. respectively from the light?
3. Which is more expensive per candle power? How many times as
expensive? A 50-watt 16-candle-power incandescent lamp at 10 cents per
kilowatt-hour or a 100-candle-power Welsbach light burning 5 cu. ft. of gas
per hour at 80 cents per 1000 cu. ft. of gas. (Find cost of each per hour, and
then the cost of 1 candle power hour for each.)
4. Why are not ordinary shadows perfectly dark?
Page 388
5. At what distance will a 16-candle-power lamp give the same illumination
as a single candle at 10 in.?
6. If the sun is at an elevation of 30 degrees what is the angle of incidence
at which it strikes the surface of water? What is the angle between the
incident and the reflected rays?
7. What is the difference between the phenomena of reflection of light from
a white sheet of writing paper and from a piece of clear window glass?
8. A horizontal ray of light, traveling due east, strikes a vertical mirror so
that after reflection it is traveling due north. If the mirror be now turned 10
degrees about a vertical axis, the north edge moving east, what will be the
direction of the reflected ray?
9. The necessary illumination for reading is about 2 foot-candles. How far
away may an 8-candle-power lamp be placed?
10. What is the illumination in foot-candles upon a surface 20 ft. from an
arc lamp having an intensity of 1000 candle power?
11. How far from a 100-candle-power Welsbach light would the
illumination be 2 foot-candles?
(3) Mirrors and the Formation of Images
Fig. 353.—Reflection of light, (a) diffused, (b)
regular.
362. Mirrors.—The many purposes served by mirrors in our every-day life
has made their use familiar to everyone. Yet without study and experiment
few understand their properties and action. Any smooth surface may serve
as a mirror, as that of glass, water, polished wood, or metal. Most objects,
as a single candle at 10 in.?
6. If the sun is at an elevation of 30 degrees what is the angle of incidence
at which it strikes the surface of water? What is the angle between the
incident and the reflected rays?
7. What is the difference between the phenomena of reflection of light from
a white sheet of writing paper and from a piece of clear window glass?
8. A horizontal ray of light, traveling due east, strikes a vertical mirror so
that after reflection it is traveling due north. If the mirror be now turned 10
degrees about a vertical axis, the north edge moving east, what will be the
direction of the reflected ray?
9. The necessary illumination for reading is about 2 foot-candles. How far
away may an 8-candle-power lamp be placed?
10. What is the illumination in foot-candles upon a surface 20 ft. from an
arc lamp having an intensity of 1000 candle power?
11. How far from a 100-candle-power Welsbach light would the
illumination be 2 foot-candles?
(3) Mirrors and the Formation of Images
Fig. 353.—Reflection of light, (a) diffused, (b)
regular.
362. Mirrors.—The many purposes served by mirrors in our every-day life
has made their use familiar to everyone. Yet without study and experiment
few understand their properties and action. Any smooth surface may serve
as a mirror, as that of glass, water, polished wood, or metal. Most objects,
Page 389
unlike mirrors, have irregular surfaces; these scatter or diffuse the light that
falls upon them. (See Fig. 353a.) This is called diffused or irregular
reflection. The reflection of light from the smooth surface of a mirror is
regular. (See Fig. 353b.) In every case of reflected light, however, the angle
of reflection equals the angle of incidence, diffusion being due to the
irregularity of the surface. It is by means of the light "diffused" from the
surface of illuminated bodies, such as plants, animals, food, and
manufactured articles, that we "see" the various objects about us, and it is
this light that enables us to judge of their distance, size, form, color, etc.
The moon is seen by the sunlight reflected from its surface. Moonlight is
therefore sunlight diffused by reflection. The new moon is that phase or
condition of the moon when only a narrow strip of the moon's illuminated
surface is turned toward the earth. At the time of the full moon the whole
illuminated surface is seen.
363. Images Formed by a Plane Mirror.—The most common use of
mirrors is in the formation of images. The way in which images are formed
by a plane mirror may be illustrated by diagrams. Thus in Fig. 354, let L
represent a luminous body and E and E´ two positions of the observer's eye.
Take any line or ray as LO along which the light from L strikes the mirror
O-O´. It will be reflected so that angle LOP equals angle POE. Similarly
with any other ray, as LO´, the reflected ray O´E´ has a direction such as
that angle L´O´E´ equals angle P´O´E´. Any other rays will be reflected in a
similar manner, each of the reflected rays appearing to the eye to come from
a point L´ behind the mirror.
364. Light Waves and Wave Diagrams.—Just as a stick continually
moved at the surface of a body of water sets up a series of waves spreading
in all directions, so one may imagine a train of waves sent out by a
luminous body L (as in Fig. 355) to the mirror MN. These waves will be
reflected from the mirror as if the source of light were at L´. It is much
simpler and more convenient to locate the position of the image of a point
by the use of lines or "rays" (as in Fig. 354) than by the wave diagram (as in
Fig. 355). In all ray diagrams, however, it should be kept in mind that the
so-called ray is a symbol used to represent the direction taken by a part of a
light wave. Thus in Fig. 354, the light from L moving toward O is reflected
to E along the line OE, the heavy lines representing rays.
falls upon them. (See Fig. 353a.) This is called diffused or irregular
reflection. The reflection of light from the smooth surface of a mirror is
regular. (See Fig. 353b.) In every case of reflected light, however, the angle
of reflection equals the angle of incidence, diffusion being due to the
irregularity of the surface. It is by means of the light "diffused" from the
surface of illuminated bodies, such as plants, animals, food, and
manufactured articles, that we "see" the various objects about us, and it is
this light that enables us to judge of their distance, size, form, color, etc.
The moon is seen by the sunlight reflected from its surface. Moonlight is
therefore sunlight diffused by reflection. The new moon is that phase or
condition of the moon when only a narrow strip of the moon's illuminated
surface is turned toward the earth. At the time of the full moon the whole
illuminated surface is seen.
363. Images Formed by a Plane Mirror.—The most common use of
mirrors is in the formation of images. The way in which images are formed
by a plane mirror may be illustrated by diagrams. Thus in Fig. 354, let L
represent a luminous body and E and E´ two positions of the observer's eye.
Take any line or ray as LO along which the light from L strikes the mirror
O-O´. It will be reflected so that angle LOP equals angle POE. Similarly
with any other ray, as LO´, the reflected ray O´E´ has a direction such as
that angle L´O´E´ equals angle P´O´E´. Any other rays will be reflected in a
similar manner, each of the reflected rays appearing to the eye to come from
a point L´ behind the mirror.
364. Light Waves and Wave Diagrams.—Just as a stick continually
moved at the surface of a body of water sets up a series of waves spreading
in all directions, so one may imagine a train of waves sent out by a
luminous body L (as in Fig. 355) to the mirror MN. These waves will be
reflected from the mirror as if the source of light were at L´. It is much
simpler and more convenient to locate the position of the image of a point
by the use of lines or "rays" (as in Fig. 354) than by the wave diagram (as in
Fig. 355). In all ray diagrams, however, it should be kept in mind that the
so-called ray is a symbol used to represent the direction taken by a part of a
light wave. Thus in Fig. 354, the light from L moving toward O is reflected
to E along the line OE, the heavy lines representing rays.
Page 390
Fig. 354.—The virtual
image of a fixed object
as seen in a plane
mirror, has the same
location from every
position of the
observer's eye.
Fig. 355.—Wave diagram of image formed in
a plane mirror.
365. To locate the image of an object formed by a plane mirror requires
simply an application of the law of reflection. Thus in Fig. 356 let AB
represent an object and MN a plane mirror. Let AA´ be a ray from A striking
image of a fixed object
as seen in a plane
mirror, has the same
location from every
position of the
observer's eye.
Fig. 355.—Wave diagram of image formed in
a plane mirror.
365. To locate the image of an object formed by a plane mirror requires
simply an application of the law of reflection. Thus in Fig. 356 let AB
represent an object and MN a plane mirror. Let AA´ be a ray from A striking
Page 391
the mirror perpendicularly. It is therefore reflected back along the same line
toward A. Let AO represent any other ray from A. It will be reflected along
OE so that angle r equals i. The intersection of AC and OE at A´ behind the
mirror locates the image of the point A, as seen by reflection from the
mirror. The triangles ACO and A´CO may be proved equal by geometry.
Therefore A´C equals AC. This indicates that the image of a point formed by
a plane mirror is the same distance back of the mirror as the point itself is
in front of it. This principle may be used in locating the image of point B at
B´. Locating the position of the end points of an image determines the
position of the whole image as A´B´.
Fig. 356.—The image A´B´ is as far back of the
mirror M N as the object A B is in front of the
mirror.
366. How the Image is Seen.—Suppose the eye to be placed at E. It will
receive light from A by reflection as if it came from A´. Similarly light
starting from B reaches the eye from the direction of B´. There is nothing
back of the mirror in reality that affects our sight, the light traveling only in
the space in front of the mirror. Yet the action of the reflected light is such
that it produces the same effect as if it came from behind the mirror. Images
such as are seen in plane mirrors are called virtual to distinguish them from
real images, in which light actually comes to the eye from the various parts
of the visible image, as from the real image formed by a projecting lantern
upon a screen, or by an aperture as in the pin-hole camera. Real images
therefore are those that can be obtained upon a screen while virtual images
cannot.
toward A. Let AO represent any other ray from A. It will be reflected along
OE so that angle r equals i. The intersection of AC and OE at A´ behind the
mirror locates the image of the point A, as seen by reflection from the
mirror. The triangles ACO and A´CO may be proved equal by geometry.
Therefore A´C equals AC. This indicates that the image of a point formed by
a plane mirror is the same distance back of the mirror as the point itself is
in front of it. This principle may be used in locating the image of point B at
B´. Locating the position of the end points of an image determines the
position of the whole image as A´B´.
Fig. 356.—The image A´B´ is as far back of the
mirror M N as the object A B is in front of the
mirror.
366. How the Image is Seen.—Suppose the eye to be placed at E. It will
receive light from A by reflection as if it came from A´. Similarly light
starting from B reaches the eye from the direction of B´. There is nothing
back of the mirror in reality that affects our sight, the light traveling only in
the space in front of the mirror. Yet the action of the reflected light is such
that it produces the same effect as if it came from behind the mirror. Images
such as are seen in plane mirrors are called virtual to distinguish them from
real images, in which light actually comes to the eye from the various parts
of the visible image, as from the real image formed by a projecting lantern
upon a screen, or by an aperture as in the pin-hole camera. Real images
therefore are those that can be obtained upon a screen while virtual images
cannot.
Page 392
367. Multiple Reflection.—If the light from an object is reflected by two
or more mirrors various effects may be produced, as may be illustrated by
the kaleidoscope. This consists of three plane mirrors so arranged that a
cross-section of the three forms an equilateral triangle. The mirrors are
placed in a tube across the end of which is a compartment with a translucent
cover containing pieces of colored glass. On looking through the tube, the
reflections from the several surfaces produce beautiful hexagonal designs.
Fig. 357.—Perspective view of "Pepper's
ghost."
Fig. 358.—Diagram of the "Pepper Ghost"
illusion.
368. Optical Illusions by a Plane Mirror.—The illusion called Pepper's
Ghost is typical of many illusions produced by reflection. It may be
illustrated by taking a piece of plate glass, M-N, a tumbler of water, W, and
a lighted candle, C, placed in a box, B, having one side open and arranged
as shown in perspective in Fig. 357, and in section in Fig. 358. If the effect
is produced in a darkened room, the observer at E sees a virtual image of
the lighted candle as if it were in the glass of water, the water being seen by
transmitted light through the plate glass, the latter forming a virtual image
of the candle by reflection. Some of the illusions produced by this means
are: (a) the figure suspended in mid air; (b) the bust of a person without a
trunk; (c) the stage ghost; (d) the disappearing bouquet.
369. Concave Mirrors.—Another useful piece of physical apparatus is the
concave spherical mirror. It is frequently made from plano-convex lenses by
silvering the convex surface of the lens, thus making a concave reflecting
surface from the inner surface of the silvered part; they are also made by
or more mirrors various effects may be produced, as may be illustrated by
the kaleidoscope. This consists of three plane mirrors so arranged that a
cross-section of the three forms an equilateral triangle. The mirrors are
placed in a tube across the end of which is a compartment with a translucent
cover containing pieces of colored glass. On looking through the tube, the
reflections from the several surfaces produce beautiful hexagonal designs.
Fig. 357.—Perspective view of "Pepper's
ghost."
Fig. 358.—Diagram of the "Pepper Ghost"
illusion.
368. Optical Illusions by a Plane Mirror.—The illusion called Pepper's
Ghost is typical of many illusions produced by reflection. It may be
illustrated by taking a piece of plate glass, M-N, a tumbler of water, W, and
a lighted candle, C, placed in a box, B, having one side open and arranged
as shown in perspective in Fig. 357, and in section in Fig. 358. If the effect
is produced in a darkened room, the observer at E sees a virtual image of
the lighted candle as if it were in the glass of water, the water being seen by
transmitted light through the plate glass, the latter forming a virtual image
of the candle by reflection. Some of the illusions produced by this means
are: (a) the figure suspended in mid air; (b) the bust of a person without a
trunk; (c) the stage ghost; (d) the disappearing bouquet.
369. Concave Mirrors.—Another useful piece of physical apparatus is the
concave spherical mirror. It is frequently made from plano-convex lenses by
silvering the convex surface of the lens, thus making a concave reflecting
surface from the inner surface of the silvered part; they are also made by
Page 393
polishing the inner surfaces of
metallic spherical shells. The
concave mirror is represented in
section in Fig. 359 by the curve
MN; C is the center of curvature or
the center of the surface of which
this mirror MN is a part; the line VC
through the center V of the mirror is
called the principal axis; while any Fig. 359.—Action of a concave
other line passing through C is mirror on parallel rays of light.
called a secondary axis. The point
midway between the vertex V and
center of curvature C is called the
principal focus, F. It is the point
through which parallel incident rays
pass after reflection. The angle
MCN which the curve of the mirror
subtends at the center is called the
aperture of the mirror. We learned
in Art. 361, the angle of reflection
Fig. 360.—Real image formed by a of a ray of light is always equal to
concave mirror. the angle of incidence no matter
what the nature of the reflecting
surface may be. If the reflecting surface is a regular concave surface, like
the inner surface of a sphere, the rays of light coming from a point source
may after reflection come to a focus, forming a real image. The two
extreme points of an object should be selected for locating its image; Fig.
360 shows the construction. The real images formed by concave mirrors are
always inverted. The principal focus of a concave mirror may be observed
by holding the mirror in a beam of sunlight entering a darkened room. The
sun's rays after reflection converge to form a small, round, intense spot of
light, which is a real image of the sun, located at the principal focus of the
mirror. The distance of the principal focus from the mirror is the least
distance that a real image can be formed in front of a concave mirror.
370. Virtual Images by Concave Mirrors.—When light comes from a
small point situated between a concave mirror and its principal focus, the
metallic spherical shells. The
concave mirror is represented in
section in Fig. 359 by the curve
MN; C is the center of curvature or
the center of the surface of which
this mirror MN is a part; the line VC
through the center V of the mirror is
called the principal axis; while any Fig. 359.—Action of a concave
other line passing through C is mirror on parallel rays of light.
called a secondary axis. The point
midway between the vertex V and
center of curvature C is called the
principal focus, F. It is the point
through which parallel incident rays
pass after reflection. The angle
MCN which the curve of the mirror
subtends at the center is called the
aperture of the mirror. We learned
in Art. 361, the angle of reflection
Fig. 360.—Real image formed by a of a ray of light is always equal to
concave mirror. the angle of incidence no matter
what the nature of the reflecting
surface may be. If the reflecting surface is a regular concave surface, like
the inner surface of a sphere, the rays of light coming from a point source
may after reflection come to a focus, forming a real image. The two
extreme points of an object should be selected for locating its image; Fig.
360 shows the construction. The real images formed by concave mirrors are
always inverted. The principal focus of a concave mirror may be observed
by holding the mirror in a beam of sunlight entering a darkened room. The
sun's rays after reflection converge to form a small, round, intense spot of
light, which is a real image of the sun, located at the principal focus of the
mirror. The distance of the principal focus from the mirror is the least
distance that a real image can be formed in front of a concave mirror.
370. Virtual Images by Concave Mirrors.—When light comes from a
small point situated between a concave mirror and its principal focus, the
Page 394
reflected rays are divergent and hence no real image of the object can be
found in front of the mirror. But if the rays are extended behind the mirror
they will meet in a point called the virtual focus. This is the point from
which they appear to come. Any image of an object situated between the
principal focus and a concave mirror is therefore a virtual image, erect and
larger than the object. (See Fig. 361.)
371. Construction of Real Images.—There are
five positions at which an object may be situated
in front of a concave mirror, namely: (1) beyond
C; (2) at C; (3) between C and F; (4) at F and
(5) between F and V. There are two ways by
means of which the image formed at each of
these positions may be located, namely; (1)
experimentally, by allowing the rays of light
from a luminous body to focus on a screen and
(2) diagrammatically. By the latter method the
Fig. 361.—Virtual two rays of light are considered the course of
image formed by a each of which may easily be determined; first,
concave mirror. the ray which strikes the mirror parallel to its
principal axis and which after reflection passes
through the principal focus; second, the ray
which passing through the center of curvature strikes the mirror at right
angles and therefore after reflection must pass directly back along its
incident path. Where these two reflected rays intersect is located the real
image of the object. Whenever these two rays of light do actually intersect,
as in Fig. 360, a real image (ab) is formed of the object AB.
The points A and a, B and b and others similarly situated on an axis
extending through the center of curvature C are called conjugate foci, for
they are so related that an object being at either one, its image will be found
at the other.
372. The Convex Mirror.—There are few practical uses to which convex
mirrors can be put. They are sometimes used to give the chauffeur of an
automobile a view of the road behind him. It is then attached to the wind
shield by a short rod. The reflected rays coming from a Convex mirror are
always divergent (see Fig. 362), hence the image is always virtual and
located behind the reflecting surface. The method of construction for
found in front of the mirror. But if the rays are extended behind the mirror
they will meet in a point called the virtual focus. This is the point from
which they appear to come. Any image of an object situated between the
principal focus and a concave mirror is therefore a virtual image, erect and
larger than the object. (See Fig. 361.)
371. Construction of Real Images.—There are
five positions at which an object may be situated
in front of a concave mirror, namely: (1) beyond
C; (2) at C; (3) between C and F; (4) at F and
(5) between F and V. There are two ways by
means of which the image formed at each of
these positions may be located, namely; (1)
experimentally, by allowing the rays of light
from a luminous body to focus on a screen and
(2) diagrammatically. By the latter method the
Fig. 361.—Virtual two rays of light are considered the course of
image formed by a each of which may easily be determined; first,
concave mirror. the ray which strikes the mirror parallel to its
principal axis and which after reflection passes
through the principal focus; second, the ray
which passing through the center of curvature strikes the mirror at right
angles and therefore after reflection must pass directly back along its
incident path. Where these two reflected rays intersect is located the real
image of the object. Whenever these two rays of light do actually intersect,
as in Fig. 360, a real image (ab) is formed of the object AB.
The points A and a, B and b and others similarly situated on an axis
extending through the center of curvature C are called conjugate foci, for
they are so related that an object being at either one, its image will be found
at the other.
372. The Convex Mirror.—There are few practical uses to which convex
mirrors can be put. They are sometimes used to give the chauffeur of an
automobile a view of the road behind him. It is then attached to the wind
shield by a short rod. The reflected rays coming from a Convex mirror are
always divergent (see Fig. 362), hence the image is always virtual and
located behind the reflecting surface. The method of construction for
Page 395
images formed by a convex mirror is similar to
that for concave mirrors. (See Fig. 363.) The
center of curvature and principal focus are
behind the mirror and consequently the reflected
rays have to be produced backward until they
meet. The images are always virtual, erect and
smaller than the object.
373. Spherical
Aberration. Fig. 362.—Action of a
Sometimes in a convex mirror upon
concave mirror when parallel rays of light.
the aperture MCN (Fig.
364) is large the
images are blurred
or indistinct. This
is due to the fact
Fig. 363.— that the incident
Construction of an rays near the outer
image by a convex edge of the mirror
mirror. do not focus after
reflection at the
same point as those which pass into the
mirror near the vertex, but cross the
principal axis at points between the mirror
and principal focus as is shown in Fig. 364;
this result is called spherical aberration.
The larger the aperture of the mirror the
more the image is blurred. Concave mirrors
in practical use do not have an aperture Fig 364.—Illustrations of
much greater than 10 degrees. This non- Spherical Aberration.
focusing of the rays of light by curved
reflecting surfaces may be noticed in many
places, as when light is reflected from the inside of a cup that contains milk
or from the inside of a wide gold ring placed on top of a piece of white
paper. The pupil will note other instances. This curve of light observed is
called the caustic by reflection.
that for concave mirrors. (See Fig. 363.) The
center of curvature and principal focus are
behind the mirror and consequently the reflected
rays have to be produced backward until they
meet. The images are always virtual, erect and
smaller than the object.
373. Spherical
Aberration. Fig. 362.—Action of a
Sometimes in a convex mirror upon
concave mirror when parallel rays of light.
the aperture MCN (Fig.
364) is large the
images are blurred
or indistinct. This
is due to the fact
Fig. 363.— that the incident
Construction of an rays near the outer
image by a convex edge of the mirror
mirror. do not focus after
reflection at the
same point as those which pass into the
mirror near the vertex, but cross the
principal axis at points between the mirror
and principal focus as is shown in Fig. 364;
this result is called spherical aberration.
The larger the aperture of the mirror the
more the image is blurred. Concave mirrors
in practical use do not have an aperture Fig 364.—Illustrations of
much greater than 10 degrees. This non- Spherical Aberration.
focusing of the rays of light by curved
reflecting surfaces may be noticed in many
places, as when light is reflected from the inside of a cup that contains milk
or from the inside of a wide gold ring placed on top of a piece of white
paper. The pupil will note other instances. This curve of light observed is
called the caustic by reflection.
Page 396
374. Parabolic Mirrors.—The best possible surface to give to concave
mirrors is parabolic. This is a curve which may be generated by moving a
point so that its distance from a fixed point and a fixed line are always
equal. If a source of light is placed at F the rays after reflection are rendered
parallel. See Fig. 365. This reflector is used in automobile lamps, headlights
of locomotives, search-lights, etc. It is also used in large reflecting
astronomical telescopes to collect as large an amount of light as possible
from distant stars and bring it to a focus. Such mirrors may be made
exceedingly accurate.
Fig. 365.—Parabolic
mirror.
Important Topics
1. Reflection: regular, diffused; plane mirrors; laws of reflection.
2. Formation and location of images by plane mirrors. Wave and ray
diagrams.
3. Multiple reflection, illusions.
4. Curved mirrors, uses; concave, convex, parabolic.
Exercises
1. Distinguish between regular and diffused reflection. By means of which
do we see non-luminous bodies?
mirrors is parabolic. This is a curve which may be generated by moving a
point so that its distance from a fixed point and a fixed line are always
equal. If a source of light is placed at F the rays after reflection are rendered
parallel. See Fig. 365. This reflector is used in automobile lamps, headlights
of locomotives, search-lights, etc. It is also used in large reflecting
astronomical telescopes to collect as large an amount of light as possible
from distant stars and bring it to a focus. Such mirrors may be made
exceedingly accurate.
Fig. 365.—Parabolic
mirror.
Important Topics
1. Reflection: regular, diffused; plane mirrors; laws of reflection.
2. Formation and location of images by plane mirrors. Wave and ray
diagrams.
3. Multiple reflection, illusions.
4. Curved mirrors, uses; concave, convex, parabolic.
Exercises
1. Distinguish between regular and diffused reflection. By means of which
do we see non-luminous bodies?
Page 397
2. Could a perfect reflecting surface be seen? Explain.
3. A pencil is stood upright in front of a plane mirror set at an angle of 45
degrees to the vertical. Shown by a diagram the location and position of the
image.
4. Show by diagrams the position and location of the images of a pencil (a)
when standing erect and in front of a vertical mirror. (b) when standing
upon a horizontal mirror.
5. What is the difference between a real and a virtual image?
6. A standard candle and a lamp give equal illuminations to a screen that is
1 ft. from the candle and 6 ft. from the lamp. What is the candle power of
the lamp? Explain.
7. Why are walls finished in rough plaster or painted with soft tones without
gloss better for schoolrooms than glossy paints or smooth white plaster?
8. Try to read a printed page by looking at its image in a mirror. write your
name backward on a sheet of paper, and then look at the image of the
writing in a mirror. What effect is produced by the mirror in each case?
9. If the point of a pencil is held to the surface of a piece of plate-glass
mirror two or more images may be seen in the mirror. Explain.
10. Given a small lighted candle, a concave mirror, a meter stick, and a
white screen, how would you prove the statements made in Arts. 369 and
370 concerning the location of images formed by concave mirrors? Make
the diagram in each case.
11. Why do images seen in a quiet pond of water appear inverted? Explain
by a diagram.
(4) Refraction of Light
375. Common Examples of Refraction.—Everyone has noticed the
apparent bending of an oar, of a stick, or of a spoon when placed in water
(see Fig. 366), while many have observed that the bottom of a pond or
stream looks nearer to the surface than it really is. These and similar
illusions are due to the refraction or bending of light rays as they pass from
one medium to another. The principles of refraction are among the most
3. A pencil is stood upright in front of a plane mirror set at an angle of 45
degrees to the vertical. Shown by a diagram the location and position of the
image.
4. Show by diagrams the position and location of the images of a pencil (a)
when standing erect and in front of a vertical mirror. (b) when standing
upon a horizontal mirror.
5. What is the difference between a real and a virtual image?
6. A standard candle and a lamp give equal illuminations to a screen that is
1 ft. from the candle and 6 ft. from the lamp. What is the candle power of
the lamp? Explain.
7. Why are walls finished in rough plaster or painted with soft tones without
gloss better for schoolrooms than glossy paints or smooth white plaster?
8. Try to read a printed page by looking at its image in a mirror. write your
name backward on a sheet of paper, and then look at the image of the
writing in a mirror. What effect is produced by the mirror in each case?
9. If the point of a pencil is held to the surface of a piece of plate-glass
mirror two or more images may be seen in the mirror. Explain.
10. Given a small lighted candle, a concave mirror, a meter stick, and a
white screen, how would you prove the statements made in Arts. 369 and
370 concerning the location of images formed by concave mirrors? Make
the diagram in each case.
11. Why do images seen in a quiet pond of water appear inverted? Explain
by a diagram.
(4) Refraction of Light
375. Common Examples of Refraction.—Everyone has noticed the
apparent bending of an oar, of a stick, or of a spoon when placed in water
(see Fig. 366), while many have observed that the bottom of a pond or
stream looks nearer to the surface than it really is. These and similar
illusions are due to the refraction or bending of light rays as they pass from
one medium to another. The principles of refraction are among the most
Page 398
useful found in the study of light since application is made of them in the
construction and use of important optical instruments, such as the camera,
microscope, telescope, and the eye.
376. Action of Light Undergoing Refraction.—If
a beam of sunlight be admitted to a darkened room
and reflected by a mirror so that it strikes the
surface of water in a glass jar, a part of the beam
may be seen to be reflected while another portion
is transmitted through the water (Fig. 367). The
reflected beam follows the law of reflection while
the transmitted beam is seen to be refracted, or to
have its courses slightly changed in direction upon
Fig. 366.—The stick entering the water. If the mirror is turned so that
appears to be bent the angle at which the light strikes the water is
on account of changed, the amount of refraction or change of
refraction. course of the light is varied. When the light strikes
the water perpendicularly there is no refraction. On
the other hand, the greater the angle at which the
light strikes the water the greater the bending.
377.
Laws of
Refracti
on. The
action of
light on
entering,
passing
through,
Fig. 368.—Illustrating and
the laws of refraction leaving
of light. a great
variety
of substances has been carefully
studied. A summary of the results of
these observations is given in the Fig. 367.—Part of the ray is
following laws of refraction: I.
construction and use of important optical instruments, such as the camera,
microscope, telescope, and the eye.
376. Action of Light Undergoing Refraction.—If
a beam of sunlight be admitted to a darkened room
and reflected by a mirror so that it strikes the
surface of water in a glass jar, a part of the beam
may be seen to be reflected while another portion
is transmitted through the water (Fig. 367). The
reflected beam follows the law of reflection while
the transmitted beam is seen to be refracted, or to
have its courses slightly changed in direction upon
Fig. 366.—The stick entering the water. If the mirror is turned so that
appears to be bent the angle at which the light strikes the water is
on account of changed, the amount of refraction or change of
refraction. course of the light is varied. When the light strikes
the water perpendicularly there is no refraction. On
the other hand, the greater the angle at which the
light strikes the water the greater the bending.
377.
Laws of
Refracti
on. The
action of
light on
entering,
passing
through,
Fig. 368.—Illustrating and
the laws of refraction leaving
of light. a great
variety
of substances has been carefully
studied. A summary of the results of
these observations is given in the Fig. 367.—Part of the ray is
following laws of refraction: I.
Page 399
When light enters a transparent reflected and part passes into the
body, perpendicularly, it passes on water and is refracted.
without changing its direction. II.
When light enters a denser transparent body obliquely, it is bent toward the
perpendicular; when light enters a less dense body obliquely, it is bent
away from the perpendicular. (See Fig. 368.)
378. The cause of refraction may be illustrated by considering a line of
men moving across a field and occupying at equal time intervals the
successive positions 1, 2, 3, etc., indicated in Fig. 369. Suppose that the
upper and lower parts of the field have a smooth hard surface, while at the
center is a strip of newly ploughed ground. The line will move more slowly
over the ploughed field than over the hard field. This will result in a
retardation of the end of the line first striking the soft ground with a
resulting change of direction of the line, toward the perpendicular to the
edge of the field (on entering the place of more difficult travel), and away
from the perpendicular on moving into a place where increased speed
results.
body, perpendicularly, it passes on water and is refracted.
without changing its direction. II.
When light enters a denser transparent body obliquely, it is bent toward the
perpendicular; when light enters a less dense body obliquely, it is bent
away from the perpendicular. (See Fig. 368.)
378. The cause of refraction may be illustrated by considering a line of
men moving across a field and occupying at equal time intervals the
successive positions 1, 2, 3, etc., indicated in Fig. 369. Suppose that the
upper and lower parts of the field have a smooth hard surface, while at the
center is a strip of newly ploughed ground. The line will move more slowly
over the ploughed field than over the hard field. This will result in a
retardation of the end of the line first striking the soft ground with a
resulting change of direction of the line, toward the perpendicular to the
edge of the field (on entering the place of more difficult travel), and away
from the perpendicular on moving into a place where increased speed
results.
Page 400
379. Index of Refraction.—By studying the
change of direction of the marching men as
shown in Fig. 369 it is evident first that it is due
to a difference in speed in the two media. It is
not easy to measure the speed of light in a
medium. However, the amount of refraction
may be determined easily and from this the
relative speed may be computed. The number
that expresses the ratio of the speed of light in
air to its speed in another medium is called the
index of refraction of that medium. The relative
speeds of light, or the indices of refraction for
some substances, are: water, 1.33, crown glass,
Fig. 369.—Diagram 1.51, flint glass, 1.61, diamond, 2.47, carbon
illustrating the cause of bisulphide, 1.64.
refraction.
380. Plates, Prisms,
Lenses.—The
refraction of light is usually observed when it is
passing through a plate, a prism, or a lens. The
important differences between the effects of
each in refracting light are illustrated in Figs.
370, 371 and 372. In Fig. 370 it is seen that the
refraction of the ray on entering the glass is
counteracted by the refraction away from the
perpendicular upon leaving it. So that the
entering and emergent rays are parallel. In Fig.
371 the refraction at the two surfaces of the Fig. 370.—The
prism results in a change of direction of the ray, incident ray and the
the course being bent toward the thicker part of emergent rays are
the prism. In Fig. 372 it may be noticed that the parallel.
convex lens resembles two prisms with their
bases together. Since all parts of the lens refract light toward the thicker
part, the center, the effect of the convex lens is to bring the rays of light to a
focus, at F.
change of direction of the marching men as
shown in Fig. 369 it is evident first that it is due
to a difference in speed in the two media. It is
not easy to measure the speed of light in a
medium. However, the amount of refraction
may be determined easily and from this the
relative speed may be computed. The number
that expresses the ratio of the speed of light in
air to its speed in another medium is called the
index of refraction of that medium. The relative
speeds of light, or the indices of refraction for
some substances, are: water, 1.33, crown glass,
Fig. 369.—Diagram 1.51, flint glass, 1.61, diamond, 2.47, carbon
illustrating the cause of bisulphide, 1.64.
refraction.
380. Plates, Prisms,
Lenses.—The
refraction of light is usually observed when it is
passing through a plate, a prism, or a lens. The
important differences between the effects of
each in refracting light are illustrated in Figs.
370, 371 and 372. In Fig. 370 it is seen that the
refraction of the ray on entering the glass is
counteracted by the refraction away from the
perpendicular upon leaving it. So that the
entering and emergent rays are parallel. In Fig.
371 the refraction at the two surfaces of the Fig. 370.—The
prism results in a change of direction of the ray, incident ray and the
the course being bent toward the thicker part of emergent rays are
the prism. In Fig. 372 it may be noticed that the parallel.
convex lens resembles two prisms with their
bases together. Since all parts of the lens refract light toward the thicker
part, the center, the effect of the convex lens is to bring the rays of light to a
focus, at F.
Page 401
Fig. 371.—Effect of a prism upon a ray of
light.
Fig. 372.—The convex lens brings the rays of
light to a focus.
381. Total Reflection.—It has been shown that when light passes from a
denser to a lighter medium, as from glass or water to air, that the beam is
refracted away from the perpendicular. This is illustrated in Fig. 373. The
diagram represents the change in the course of a ray of light that passes
through water to a surface with air above it. A ray striking perpendicularly
passes through without refraction. Other rays show increasing refraction
with increasing angle of incidence. For one ray the angle of refraction is so
large that the refracted ray is parallel to the surface. When this condition is
reached, the angle of incidence is called the critical angle. Any increase in
the angle of incidence causes all of the light to be reflected as is the beam E.
This action is called total reflection, the course of the reflected ray being
according to the law of reflection. A right-angle prism (see Fig. 374) is
often used where a mirror would ordinarily be employed, the total reflection
occurring within the prism giving more satisfactory results than a mirror.
See Art. 398 for a description of the Zeiss binocular field-glass for an
example of this use of total reflection.
Fig. 373.—An example of total reflection.
Fig. 374.—Total reflection in a right-angle
prism.
light.
Fig. 372.—The convex lens brings the rays of
light to a focus.
381. Total Reflection.—It has been shown that when light passes from a
denser to a lighter medium, as from glass or water to air, that the beam is
refracted away from the perpendicular. This is illustrated in Fig. 373. The
diagram represents the change in the course of a ray of light that passes
through water to a surface with air above it. A ray striking perpendicularly
passes through without refraction. Other rays show increasing refraction
with increasing angle of incidence. For one ray the angle of refraction is so
large that the refracted ray is parallel to the surface. When this condition is
reached, the angle of incidence is called the critical angle. Any increase in
the angle of incidence causes all of the light to be reflected as is the beam E.
This action is called total reflection, the course of the reflected ray being
according to the law of reflection. A right-angle prism (see Fig. 374) is
often used where a mirror would ordinarily be employed, the total reflection
occurring within the prism giving more satisfactory results than a mirror.
See Art. 398 for a description of the Zeiss binocular field-glass for an
example of this use of total reflection.
Fig. 373.—An example of total reflection.
Fig. 374.—Total reflection in a right-angle
prism.
Page 402
The mirage (see Fig. 375) is an optical illusion by which distant objects,
below the horizon, are sometimes plainly seen. This phenomenon is most
frequently observed in hot, desert regions, when the air conditions are such
that the lower strata near the ground are very much hotter than those above.
These lower strata, having expanded the most, are less dense than the cooler
ones above. Hence a ray of light traveling obliquely downward is refracted
more and more until total reflection takes place. The images seen are
inverted giving a representation of trees or other objects reflected on the
surface of still water. The mirage is also frequently seen at sea, ships being
observed, sometimes erect, sometimes inverted, apparently sailing in the
clouds near the horizon. Over the Great Lakes, trees, boats, and towns on
the opposite shore, sixty or seventy miles away, can sometimes be plainly
seen, apparently but a few miles out. In this case the images are erect, the
total reflection being from warm, still layers of air over colder layers near
the water.
Fig. 375.—Diagram of a mirage.
Important Topics
(A) Refraction: cause, illustration, two principles.
(B) Index of refraction, meaning.
(C) Plates, prisms, lenses, action of each.
(D) Total reflection, uses.
Exercises
below the horizon, are sometimes plainly seen. This phenomenon is most
frequently observed in hot, desert regions, when the air conditions are such
that the lower strata near the ground are very much hotter than those above.
These lower strata, having expanded the most, are less dense than the cooler
ones above. Hence a ray of light traveling obliquely downward is refracted
more and more until total reflection takes place. The images seen are
inverted giving a representation of trees or other objects reflected on the
surface of still water. The mirage is also frequently seen at sea, ships being
observed, sometimes erect, sometimes inverted, apparently sailing in the
clouds near the horizon. Over the Great Lakes, trees, boats, and towns on
the opposite shore, sixty or seventy miles away, can sometimes be plainly
seen, apparently but a few miles out. In this case the images are erect, the
total reflection being from warm, still layers of air over colder layers near
the water.
Fig. 375.—Diagram of a mirage.
Important Topics
(A) Refraction: cause, illustration, two principles.
(B) Index of refraction, meaning.
(C) Plates, prisms, lenses, action of each.
(D) Total reflection, uses.
Exercises
Page 403
1. Compute the speed of light in water, the index of refraction being 1.33.
2. If one wished to shoot a fish under water, should he aim at the apparent
location of the fish as viewed from the air? Explain, using a diagram.
3. Define refraction. Mention two illustrations of this action that you have
observed out of school.
4. Why does the moon look larger near the horizon?
5. Is your reflection seen in a pool of water upside down? Why?
6. Why does it whiten molasses candy to pull it?
7. When looking at a building through the ordinary glass of a window why
do straight lines of the building appear to be so distorted? What makes them
appear to move as you move your head slightly?
8. Explain the phenomenon which one observes when looking at an object
through the air arising from a hot stove or radiator.
9. Frequently the horizontal diameter of the setting sun appears to be greater
than the vertical. Explain.
10. Explain why one observes several images of a luminous body like a
lighted candle when the reflected light from a thick glass mirror enters the
eye, the angle of reflection being large.
(5) The Formation of Images by Lenses
382. Uses of Lenses in Optical Instruments.—The use of instruments that
employ lenses in their operation, such as spectacles, reading and opera
glasses, and the camera, microscope, and telescope, is familiar to most
students of physics. The part played by the lenses, however, is not generally
understood. Consequently the study of the formation of images by lenses is
of general interest and importance.
383. Forms of Lenses.—While a lens may be formed from any transparent
solid it is commonly made of glass. It may have two curved surfaces or one
curved and one plane surface. Most lenses are spherical lenses, since their
curved surfaces form a part of the surface of a sphere. Fig. 376 represents a
spherical lens with a curved surface coinciding with that of a sphere whose
2. If one wished to shoot a fish under water, should he aim at the apparent
location of the fish as viewed from the air? Explain, using a diagram.
3. Define refraction. Mention two illustrations of this action that you have
observed out of school.
4. Why does the moon look larger near the horizon?
5. Is your reflection seen in a pool of water upside down? Why?
6. Why does it whiten molasses candy to pull it?
7. When looking at a building through the ordinary glass of a window why
do straight lines of the building appear to be so distorted? What makes them
appear to move as you move your head slightly?
8. Explain the phenomenon which one observes when looking at an object
through the air arising from a hot stove or radiator.
9. Frequently the horizontal diameter of the setting sun appears to be greater
than the vertical. Explain.
10. Explain why one observes several images of a luminous body like a
lighted candle when the reflected light from a thick glass mirror enters the
eye, the angle of reflection being large.
(5) The Formation of Images by Lenses
382. Uses of Lenses in Optical Instruments.—The use of instruments that
employ lenses in their operation, such as spectacles, reading and opera
glasses, and the camera, microscope, and telescope, is familiar to most
students of physics. The part played by the lenses, however, is not generally
understood. Consequently the study of the formation of images by lenses is
of general interest and importance.
383. Forms of Lenses.—While a lens may be formed from any transparent
solid it is commonly made of glass. It may have two curved surfaces or one
curved and one plane surface. Most lenses are spherical lenses, since their
curved surfaces form a part of the surface of a sphere. Fig. 376 represents a
spherical lens with a curved surface coinciding with that of a sphere whose
Page 404
center is at C. This center is called the center of curvature, while the radius
of the sphere R, is the radius of curvature.
There are two classes of lenses: those thick in the
middle are called convex, while those thick at the
edges are concave. The mode of constructing the
six forms of spherical lenses is shown in Fig. 377.
These are named as follows: (1) double convex,
(2) plano convex, (3) concavo-convex, (4) double
concave, (5) plano concave, (6) convexo-concave.
Fig. 376.—
Formation of a
spherical lens.
Fig. 377.—Forms of Lenses. 1. double convex;
2. plano convex; 3. concavo convex; 4. double
concave; 5. plano concave; 6. convexo concave.
Fig. 378.—The action of a burning glass.
of the sphere R, is the radius of curvature.
There are two classes of lenses: those thick in the
middle are called convex, while those thick at the
edges are concave. The mode of constructing the
six forms of spherical lenses is shown in Fig. 377.
These are named as follows: (1) double convex,
(2) plano convex, (3) concavo-convex, (4) double
concave, (5) plano concave, (6) convexo-concave.
Fig. 376.—
Formation of a
spherical lens.
Fig. 377.—Forms of Lenses. 1. double convex;
2. plano convex; 3. concavo convex; 4. double
concave; 5. plano concave; 6. convexo concave.
Fig. 378.—The action of a burning glass.
Page 405
384. Effect of Lenses upon Light.—The most important characteristic of a
lens is its effect upon a beam of light. Most persons have seen a "burning
glass," a double convex lens, used to bring to a point, or focus, a beam of
sunlight. To show the action of a burning glass send a beam of light into a
darkened room, and place in its path a double convex lens. (See Fig. 378.)
If two blackboard erasers are struck together near the lens, the chalk
particles in the path of the light are strongly illuminated, showing that the
light after passing through the lens it brought to a focus and that it spreads
out beyond this point. This point to which the cone of light rays converges
after passing through the convex lens is called the principal focus of the
lens. The distance from the principal focus to the center of the lens is the
focal length or principal focal distance of the lens. The focal length of
double convex lenses of crown glass is about the same as the radius of
curvature of either surface. The action of a convex or converging lens upon
light may be better understood by studying Fig. 379 in which light is
passing from S to F. The successive positions and shape of the advancing
light waves are indicated by lines drawn across the beam. The light being
retarded more in the thicker part of the lens, the light waves on leaving the
lens have a concave front. Since light waves tend to move at right angles to
the front of the wave, the light is brought to a focus. After passing the focus
the waves have a convex front, forming a diverging cone.
385. Concave Lenses.—When sunlight
passes through a concave lens a diverging
cone of light is formed. (See Fig. 380.)
This is caused by the edges of the wave
being retarded more than the center,
producing a convex wave front. This
diverging cone of light acts as if it had
proceeded from a luminous point at F.
Fig. 379.—Wave diagram of This point is called a virtual focus and is
light passing through a nearly at the center of the curvature of the
convex lens. nearer surface.
lens is its effect upon a beam of light. Most persons have seen a "burning
glass," a double convex lens, used to bring to a point, or focus, a beam of
sunlight. To show the action of a burning glass send a beam of light into a
darkened room, and place in its path a double convex lens. (See Fig. 378.)
If two blackboard erasers are struck together near the lens, the chalk
particles in the path of the light are strongly illuminated, showing that the
light after passing through the lens it brought to a focus and that it spreads
out beyond this point. This point to which the cone of light rays converges
after passing through the convex lens is called the principal focus of the
lens. The distance from the principal focus to the center of the lens is the
focal length or principal focal distance of the lens. The focal length of
double convex lenses of crown glass is about the same as the radius of
curvature of either surface. The action of a convex or converging lens upon
light may be better understood by studying Fig. 379 in which light is
passing from S to F. The successive positions and shape of the advancing
light waves are indicated by lines drawn across the beam. The light being
retarded more in the thicker part of the lens, the light waves on leaving the
lens have a concave front. Since light waves tend to move at right angles to
the front of the wave, the light is brought to a focus. After passing the focus
the waves have a convex front, forming a diverging cone.
385. Concave Lenses.—When sunlight
passes through a concave lens a diverging
cone of light is formed. (See Fig. 380.)
This is caused by the edges of the wave
being retarded more than the center,
producing a convex wave front. This
diverging cone of light acts as if it had
proceeded from a luminous point at F.
Fig. 379.—Wave diagram of This point is called a virtual focus and is
light passing through a nearly at the center of the curvature of the
convex lens. nearer surface.
Page 406
Fig. 380.—Wave diagram of light passing
through a concave lens.
386. The Formation of Images by Lenses.—If a beam composed of
parallel rays of light, as sunlight, is sent in turn through three convex lenses
of the same diameter but of different thickness, it is found that the thicker
the lens the greater is its converging power, or the shorter is its focal length.
(See Fig. 381.) Now if a luminous body, such as a lighted candle, be placed
near the convex lens but beyond its focal length, the light will be brought to
a focus upon the other side of the lens and an image of the candle may be
clearly seen upon the screen placed at this point. (See Fig. 382.) The two
points so situated on opposite sides of a lens that an object at one will form
an image at the other are called conjugate foci.
Fig. 381.—The thicker
through a concave lens.
386. The Formation of Images by Lenses.—If a beam composed of
parallel rays of light, as sunlight, is sent in turn through three convex lenses
of the same diameter but of different thickness, it is found that the thicker
the lens the greater is its converging power, or the shorter is its focal length.
(See Fig. 381.) Now if a luminous body, such as a lighted candle, be placed
near the convex lens but beyond its focal length, the light will be brought to
a focus upon the other side of the lens and an image of the candle may be
clearly seen upon the screen placed at this point. (See Fig. 382.) The two
points so situated on opposite sides of a lens that an object at one will form
an image at the other are called conjugate foci.
Fig. 381.—The thicker
Page 407
the lens, the shorter is
its focal length.
Fig. 382.—C and S are at conjugate foci.
It will be helpful to compare the images formed of a candle by an aperture
and by a convex lens. Rays of light from each point of the luminous body
pass through the aperture in straight lines and produce upon the screen a
lighted space of the same shape as the candle. This image is rather hazy in
outline. Each cone of rays from luminous points of the flame is brought by
the lens to a focus on the screen, producing a sharp image. It is the
converging power of convex lenses that enables them to produce clear
images.
Fig. 383.—Construction of a real image by a
convex lens.
387. The Construction of Diagrams to Represent the Formation of
Images by Lenses.—Just as the earth has an axis at right angles to its
equator to which are referred positions and distances, so a lens has a
principal axis at right angles to its greatest diameter and along this axis are
certain definite positions as shown in Fig. 383. Let MN be the principal axis
its focal length.
Fig. 382.—C and S are at conjugate foci.
It will be helpful to compare the images formed of a candle by an aperture
and by a convex lens. Rays of light from each point of the luminous body
pass through the aperture in straight lines and produce upon the screen a
lighted space of the same shape as the candle. This image is rather hazy in
outline. Each cone of rays from luminous points of the flame is brought by
the lens to a focus on the screen, producing a sharp image. It is the
converging power of convex lenses that enables them to produce clear
images.
Fig. 383.—Construction of a real image by a
convex lens.
387. The Construction of Diagrams to Represent the Formation of
Images by Lenses.—Just as the earth has an axis at right angles to its
equator to which are referred positions and distances, so a lens has a
principal axis at right angles to its greatest diameter and along this axis are
certain definite positions as shown in Fig. 383. Let MN be the principal axis
Page 408
of a convex lens, P and P´ are principal foci on either side of the lens, S and
S´ are secondary foci. These are at points on the principal axis that are twice
as far from O, the center of the lens, as are the principal foci. In the
formation of images by a convex lens, several distinct cases may be
noticed:
(A) If a luminous body is at a great distance at the left, its light is brought
to a focus at P, or its image is formed at P. (B) As the object approaches the
lens the image gradually recedes until the object and image are at S and S´,
equally distant from O and of equal size (as in Fig. 383). The object and
image are now said to be at the secondary foci of the lens. (C) As the object
moves from S to P the image recedes, rapidly increasing in size until (D)
when the object is at P the rays become parallel and no image is formed.
(E) When the object is between P and the lens, the rays appear to proceed
from points back of the object, thus forming an erect, larger, virtual image
of the object. (See Fig. 384.) This last arrangement illustrates the simple
microscope.
With a concave lens but one case is possible, that corresponding to the one
last mentioned with convex lenses; since the rays from a body are divergent
after passing through a concave lens they appear to proceed from points
nearer the lens than the object and hence a virtual, erect, smaller image of
the object is formed. This virtual image may be seen by looking through the
lens toward the object. (See Fig. 385.)
Fig. 384.—Construction of a virtual image by
a convex lens.
S´ are secondary foci. These are at points on the principal axis that are twice
as far from O, the center of the lens, as are the principal foci. In the
formation of images by a convex lens, several distinct cases may be
noticed:
(A) If a luminous body is at a great distance at the left, its light is brought
to a focus at P, or its image is formed at P. (B) As the object approaches the
lens the image gradually recedes until the object and image are at S and S´,
equally distant from O and of equal size (as in Fig. 383). The object and
image are now said to be at the secondary foci of the lens. (C) As the object
moves from S to P the image recedes, rapidly increasing in size until (D)
when the object is at P the rays become parallel and no image is formed.
(E) When the object is between P and the lens, the rays appear to proceed
from points back of the object, thus forming an erect, larger, virtual image
of the object. (See Fig. 384.) This last arrangement illustrates the simple
microscope.
With a concave lens but one case is possible, that corresponding to the one
last mentioned with convex lenses; since the rays from a body are divergent
after passing through a concave lens they appear to proceed from points
nearer the lens than the object and hence a virtual, erect, smaller image of
the object is formed. This virtual image may be seen by looking through the
lens toward the object. (See Fig. 385.)
Fig. 384.—Construction of a virtual image by
a convex lens.
Page 409
Fig. 385.—Construction of a virtual image by
a concave lens.
388. The Lens Equation.—The location of either the object or of the image
upon the principal axis of the lens may be calculated if the position of one
of these and the focal length are known. This is accomplished by the use of
a formula 1/F = 1/D0 + 1/D1 in which F represents the focal length and D0
and D1 the distance from the lens of the object and the image respectively.
Thus if an object is placed 30 cm. from a lens of 10 cm. focal length, where
will the image be formed? Thus: 1/10 = 1/30 + 1/D and 3D1 = D1 + 30, or
2D1 = 30 D1 = 15. This result indicates that a real image will be 15 cm.
from the lens. A minus value would indicate a virtual image.
Important Topics
(A) Lenses: convex, concave, six forms, center and radius of curvature.
(B) Principal focus, focal length, virtual focus, conjugate foci.
(C) Principal axis, images formed when object is in various locations.
(D) Computation of location of images.
Exercises
1. Why is an image of a candle formed by an aperture, not sharply defined?
2. When a photographer takes your picture and moves the camera nearer
you, must he move the ground glass screen toward the lens or away from it?
a concave lens.
388. The Lens Equation.—The location of either the object or of the image
upon the principal axis of the lens may be calculated if the position of one
of these and the focal length are known. This is accomplished by the use of
a formula 1/F = 1/D0 + 1/D1 in which F represents the focal length and D0
and D1 the distance from the lens of the object and the image respectively.
Thus if an object is placed 30 cm. from a lens of 10 cm. focal length, where
will the image be formed? Thus: 1/10 = 1/30 + 1/D and 3D1 = D1 + 30, or
2D1 = 30 D1 = 15. This result indicates that a real image will be 15 cm.
from the lens. A minus value would indicate a virtual image.
Important Topics
(A) Lenses: convex, concave, six forms, center and radius of curvature.
(B) Principal focus, focal length, virtual focus, conjugate foci.
(C) Principal axis, images formed when object is in various locations.
(D) Computation of location of images.
Exercises
1. Why is an image of a candle formed by an aperture, not sharply defined?
2. When a photographer takes your picture and moves the camera nearer
you, must he move the ground glass screen toward the lens or away from it?
Page 410
Explain.
3. How can you find the principal focal length of a lens.
4. How can you test a spectacle lens to see whether it is convex concave?
5. When will a convex lens produce a virtual image? Have you ever seen
one? Where?
6. When a photographer wishes to obtain a full length view of a person,
where does he place the camera?
7. The focal length of the lens is 24 cm. How far from the lens must an
object be placed in order that a real image may be three times as long as the
object?
8. There is a perfect image of an object on the ground glass of a camera.
The center of the lens is 20 cm. in front of the image and the object 75 cm.
from the lens. What is the focal length of the lens?
9. An object is 60 cm. from the lens, the image 120 cm. from it. Find the
focal length.
10. How can you find experimentally the principal focal length of a lens?
11. A lens is used to project an enlarged image of a candle upon a screen.
Which is farther from the lens, the candle or the image? Explain.
(6) Optical Instruments
389. The Eye.—The most common optical instrument is the eye. While the
structure of the eye is complicated, the principle of it is simple, involving
the formation of an image by a double convex lens. (See Fig. 386, in which
is shown a front to back, vertical cross-section of the eye.) The eye appears
to be made of portions of two spheres, one of which, smaller than the other,
is placed in front. This projecting part is transparent, but refracts the light
which strikes it obliquely, so as to turn it into the eye. This enables us to see
objects at the side when looking straight ahead. Test this by looking directly
in front of you and see how far back on each side of the head you can notice
a movement of the forefinger of each hand.
390. Action of the Eye in Vision.—When we look at an object, a small,
real, inverted image is formed upon the retina at the back of the interior of
3. How can you find the principal focal length of a lens.
4. How can you test a spectacle lens to see whether it is convex concave?
5. When will a convex lens produce a virtual image? Have you ever seen
one? Where?
6. When a photographer wishes to obtain a full length view of a person,
where does he place the camera?
7. The focal length of the lens is 24 cm. How far from the lens must an
object be placed in order that a real image may be three times as long as the
object?
8. There is a perfect image of an object on the ground glass of a camera.
The center of the lens is 20 cm. in front of the image and the object 75 cm.
from the lens. What is the focal length of the lens?
9. An object is 60 cm. from the lens, the image 120 cm. from it. Find the
focal length.
10. How can you find experimentally the principal focal length of a lens?
11. A lens is used to project an enlarged image of a candle upon a screen.
Which is farther from the lens, the candle or the image? Explain.
(6) Optical Instruments
389. The Eye.—The most common optical instrument is the eye. While the
structure of the eye is complicated, the principle of it is simple, involving
the formation of an image by a double convex lens. (See Fig. 386, in which
is shown a front to back, vertical cross-section of the eye.) The eye appears
to be made of portions of two spheres, one of which, smaller than the other,
is placed in front. This projecting part is transparent, but refracts the light
which strikes it obliquely, so as to turn it into the eye. This enables us to see
objects at the side when looking straight ahead. Test this by looking directly
in front of you and see how far back on each side of the head you can notice
a movement of the forefinger of each hand.
390. Action of the Eye in Vision.—When we look at an object, a small,
real, inverted image is formed upon the retina at the back of the interior of
Page 411
the eye. The retina is an expansion of the optic
nerve and covers the inner surface at the back of
the eyeball. Seeing is due to the action of light
in forming images upon the retina. Our eyes are
so constructed that when they are relaxed the
lens is adjusted to form clear images of distant
objects upon the retina. If we look from distant
to near objects without changing the shape of
the eye lens, a sharp image of the latter cannot
be formed and we get a blurred impression. It is
difficult, however, to look at objects without Fig. 386.—Cross-
automatically adjusting the eye lens so that it section of the eye.
will make a sharp image. Test this by looking
out of a window at a distant object, then without moving the head or eyes
look at the glass of the window; you will notice a slight change of some sort
in the eye itself as the vision is adjusted. This adjustment is made by
muscles that pull or compress the eye lens so as to make it thicker for near
objects and thinner for distant ones. The eye ordinarily does not see objects
nearer than 10 in. clearly. This means that the greatest possible thickening
of lens will not form clear images upon the retina if the object is nearer than
10 in. (25 cm.).
391. The Visual Angle.—To examine objects
carefully we usually bring them as close to
the eye as possible, for the nearer to the eye
the object is brought, the larger is the visual
angle formed by it (see Fig. 387), and the
larger is its image upon the retina. The visual
angle of an object is the angle at the eye lens
Fig. 387.—The visual between the rays that have come from the
angle, AOB is greater at ends of the object. Consequently the more
AB than at A´B´. distant the object, the smaller is its visual
angle. Now if we wish to examine small
objects with great care, we frequently find that it is necessary to bring them
close to the eye so that they have a visual angle of adequate size. If they
must be brought closer than 10 in. a double convex lens is placed in front of
the eye. This assists the eye lens in converging the light so that a clear
image may be formed when the object is close, say an inch or so from the
nerve and covers the inner surface at the back of
the eyeball. Seeing is due to the action of light
in forming images upon the retina. Our eyes are
so constructed that when they are relaxed the
lens is adjusted to form clear images of distant
objects upon the retina. If we look from distant
to near objects without changing the shape of
the eye lens, a sharp image of the latter cannot
be formed and we get a blurred impression. It is
difficult, however, to look at objects without Fig. 386.—Cross-
automatically adjusting the eye lens so that it section of the eye.
will make a sharp image. Test this by looking
out of a window at a distant object, then without moving the head or eyes
look at the glass of the window; you will notice a slight change of some sort
in the eye itself as the vision is adjusted. This adjustment is made by
muscles that pull or compress the eye lens so as to make it thicker for near
objects and thinner for distant ones. The eye ordinarily does not see objects
nearer than 10 in. clearly. This means that the greatest possible thickening
of lens will not form clear images upon the retina if the object is nearer than
10 in. (25 cm.).
391. The Visual Angle.—To examine objects
carefully we usually bring them as close to
the eye as possible, for the nearer to the eye
the object is brought, the larger is the visual
angle formed by it (see Fig. 387), and the
larger is its image upon the retina. The visual
angle of an object is the angle at the eye lens
Fig. 387.—The visual between the rays that have come from the
angle, AOB is greater at ends of the object. Consequently the more
AB than at A´B´. distant the object, the smaller is its visual
angle. Now if we wish to examine small
objects with great care, we frequently find that it is necessary to bring them
close to the eye so that they have a visual angle of adequate size. If they
must be brought closer than 10 in. a double convex lens is placed in front of
the eye. This assists the eye lens in converging the light so that a clear
image may be formed when the object is close, say an inch or so from the
Page 412
eye. This is the principle of the magnifying glass used by watch-makers and
of the simple microscope. The action of the latter is illustrated by Fig. 388.
The convex lens forms a virtual, enlarged image "A´-B´" of the object "A-B"
which it observed instead of the object itself.
392. Defects of
Vision.—There
are several
defects of
vision that may
be corrected by
spectacles or
eye-glasses.
Fig. 389.—"Near One of these is
sightedness", or myopia. "near- Fig. 388.—Action of the
Parallel rays come to a sightedness." It simple microscope.
focus at F; emerging rays is due either to
focus at A, the far point. an eyeball that is elongated, or to an eye lens
that is too convex, or to both conditions. This
condition brings light from distant objects to a focus too soon (as shown in
Fig. 389). Only light from near objects will focus upon the retina in such
cases. With normal vision light from distant or near objects may be focused
without unusual effort upon the retina, see Fig. 390. The remedy for near-
sightedness is to use concave lenses which will assist in properly refracting
the light so the focus will be formed on the retina (Fig. 391). "Far-
sightedness" is the reverse of near-sightedness; the eyeball is either too
short, or the lens too flat, or both conditions obtain, so that the light entering
the eye is brought to a focus behind the eyeball (Fig. 392). The remedy is
convex lenses which will assist in properly converging the light, see Fig.
393. A third defect is called astigmatism. This is caused by some
irregularity or lack of symmetry in the eye. It is corrected by a cylindrical
lens that compensates for this defect of the eye. A diagram similar to Fig.
394 is used as a test for astigmatism. If the lines appear with unequal
distinctness, some irregularity of refraction (astigmatism) is indicated.
of the simple microscope. The action of the latter is illustrated by Fig. 388.
The convex lens forms a virtual, enlarged image "A´-B´" of the object "A-B"
which it observed instead of the object itself.
392. Defects of
Vision.—There
are several
defects of
vision that may
be corrected by
spectacles or
eye-glasses.
Fig. 389.—"Near One of these is
sightedness", or myopia. "near- Fig. 388.—Action of the
Parallel rays come to a sightedness." It simple microscope.
focus at F; emerging rays is due either to
focus at A, the far point. an eyeball that is elongated, or to an eye lens
that is too convex, or to both conditions. This
condition brings light from distant objects to a focus too soon (as shown in
Fig. 389). Only light from near objects will focus upon the retina in such
cases. With normal vision light from distant or near objects may be focused
without unusual effort upon the retina, see Fig. 390. The remedy for near-
sightedness is to use concave lenses which will assist in properly refracting
the light so the focus will be formed on the retina (Fig. 391). "Far-
sightedness" is the reverse of near-sightedness; the eyeball is either too
short, or the lens too flat, or both conditions obtain, so that the light entering
the eye is brought to a focus behind the eyeball (Fig. 392). The remedy is
convex lenses which will assist in properly converging the light, see Fig.
393. A third defect is called astigmatism. This is caused by some
irregularity or lack of symmetry in the eye. It is corrected by a cylindrical
lens that compensates for this defect of the eye. A diagram similar to Fig.
394 is used as a test for astigmatism. If the lines appear with unequal
distinctness, some irregularity of refraction (astigmatism) is indicated.
Page 413
Fig. 390.—The normal eye. The parallel rays
A B focus without accommodative effort at C.
Fig. 391.—Correction of near-sightedness by
concave lens.
Fig. 392.—Far-sightedness or hyperopia.
Parallel rays focused behind the retina.
Fig. 393.—Correction of far-sightedness by a
convex lens.
Fig. 394.—Test card for astigmatism.
393. The Photographic Camera.—This is a light-tight box, provided with
a convex lens in front, covering an aperture and a ground glass screen at the
back. The distance between the lens and the screen is adjusted until a sharp
image is obtained upon the latter, which is then replaced by a sensitive plate
or film. The sensitized surface of the plate or film contains a salt of silver
A B focus without accommodative effort at C.
Fig. 391.—Correction of near-sightedness by
concave lens.
Fig. 392.—Far-sightedness or hyperopia.
Parallel rays focused behind the retina.
Fig. 393.—Correction of far-sightedness by a
convex lens.
Fig. 394.—Test card for astigmatism.
393. The Photographic Camera.—This is a light-tight box, provided with
a convex lens in front, covering an aperture and a ground glass screen at the
back. The distance between the lens and the screen is adjusted until a sharp
image is obtained upon the latter, which is then replaced by a sensitive plate
or film. The sensitized surface of the plate or film contains a salt of silver
Page 414
which is changed by the action of light. After the plate has been "exposed"
to the action of light, it is "developed" by the use of chemicals producing a
negative image. From "negative," by the use of sensitized paper, "positive"
prints may be secured which resemble the object photographed.
Fig. 395.—Diagram of the projecting lantern.
394. The projecting lantern (see Fig. 395) employs a strong source of
light, as an electric arc lamp L, to strongly illuminate a transparent picture,
or lantern slide, S, a real image (I) of which is formed upon a large screen.
Two large plano-convex lenses (C), called condensing lenses, are placed
near the lamp to concentrate the light upon the "slide" S. The convex lens
forming the image is called the "objective" (O).
395. The compound microscope consists of two lenses. One called the
objective is placed near the object to be viewed. This lens has a short focal
length usually less than a centimeter. It forms a real image of the object. A´-
B´. The other lens, the eyepiece forms a virtual image of this real image. A
´´-B´´. (See Fig. 396.)
396. The telescope consists of two lenses, the eyepiece and the objective.
As in the compound microscope, the objective of the telescope forms a real
image of the distant object, the eyepiece forming an enlarged virtual image
of the real image. It is the virtual image that is viewed by the observer. (See
Fig. 397.) In order to collect sufficient light from distant stars the objective
is made large, sometimes 50 in. in diameter.
to the action of light, it is "developed" by the use of chemicals producing a
negative image. From "negative," by the use of sensitized paper, "positive"
prints may be secured which resemble the object photographed.
Fig. 395.—Diagram of the projecting lantern.
394. The projecting lantern (see Fig. 395) employs a strong source of
light, as an electric arc lamp L, to strongly illuminate a transparent picture,
or lantern slide, S, a real image (I) of which is formed upon a large screen.
Two large plano-convex lenses (C), called condensing lenses, are placed
near the lamp to concentrate the light upon the "slide" S. The convex lens
forming the image is called the "objective" (O).
395. The compound microscope consists of two lenses. One called the
objective is placed near the object to be viewed. This lens has a short focal
length usually less than a centimeter. It forms a real image of the object. A´-
B´. The other lens, the eyepiece forms a virtual image of this real image. A
´´-B´´. (See Fig. 396.)
396. The telescope consists of two lenses, the eyepiece and the objective.
As in the compound microscope, the objective of the telescope forms a real
image of the distant object, the eyepiece forming an enlarged virtual image
of the real image. It is the virtual image that is viewed by the observer. (See
Fig. 397.) In order to collect sufficient light from distant stars the objective
is made large, sometimes 50 in. in diameter.
Page 415
Fig. 396.—Formation of an image by a
microscope. A-B is the object. B´-A´ the real
image formed by the "objective." B´´-A´´ is the
virtual image formed by the eyepiece. The eye
sees the virtual image.
The length of the telescope tube depends upon the focal length of the
objective, since the distance between the two lenses must equal the sum of
their focal lengths.
Fig. 397.—Formation of an image by a
telescope. b-a is the real image; d-c is the
virtual image seen by the observer.
397. The opera glass consists of a convex lens as objective and a concave
lens as an eyepiece. The former tends to form a real image but the latter
diverges the rays before a real image can be formed, the action of the two
lenses producing an enlarged virtual image (as in Fig. 398) which is viewed
by the one using the glass. The compact size of the opera glass is due to the
fact that the distance between the two lenses is the difference of the focal
lengths.
microscope. A-B is the object. B´-A´ the real
image formed by the "objective." B´´-A´´ is the
virtual image formed by the eyepiece. The eye
sees the virtual image.
The length of the telescope tube depends upon the focal length of the
objective, since the distance between the two lenses must equal the sum of
their focal lengths.
Fig. 397.—Formation of an image by a
telescope. b-a is the real image; d-c is the
virtual image seen by the observer.
397. The opera glass consists of a convex lens as objective and a concave
lens as an eyepiece. The former tends to form a real image but the latter
diverges the rays before a real image can be formed, the action of the two
lenses producing an enlarged virtual image (as in Fig. 398) which is viewed
by the one using the glass. The compact size of the opera glass is due to the
fact that the distance between the two lenses is the difference of the focal
lengths.
Page 416
Fig. 398.—Formation of an image by an
opera-glass. a-b is the virtual image.
Fig. 399.—Diagram of the Zeiss binocular or
prism field glass.
398. The Prism Field Glass or Binocular.—This instrument. has come
into use in recent years. It possesses the wide field of view of the spy glass
but is as compact as the opera glass. This compact form is secured by
causing the light to pass back and forth between two right-angle prisms (as
shown in Fig. 399). This device permits the use of an objective lens with a
focal length three times that of the tube, securing much greater magnifying
power than the short instrument would otherwise possess. A further
advantage is secured by the total reflection from the two prisms, one of
which is placed so as to reverse the image right for left and the other inverts
it, so that when viewed in the eyepiece it is in its proper position.
Important Topics
1. The eye: parts, formation of image, kind, how, where.
opera-glass. a-b is the virtual image.
Fig. 399.—Diagram of the Zeiss binocular or
prism field glass.
398. The Prism Field Glass or Binocular.—This instrument. has come
into use in recent years. It possesses the wide field of view of the spy glass
but is as compact as the opera glass. This compact form is secured by
causing the light to pass back and forth between two right-angle prisms (as
shown in Fig. 399). This device permits the use of an objective lens with a
focal length three times that of the tube, securing much greater magnifying
power than the short instrument would otherwise possess. A further
advantage is secured by the total reflection from the two prisms, one of
which is placed so as to reverse the image right for left and the other inverts
it, so that when viewed in the eyepiece it is in its proper position.
Important Topics
1. The eye: parts, formation of image, kind, how, where.
Page 417
2. Eye defects, how remedied. Visual angle.
3. Simple microscope, camera; images, kind, how formed.
4. Compound microscope, telescope and opera glass; images, action of each
lens.
Exercises
1. Name three instruments in which lenses form virtual images and three in
which real images are formed.
2. In what direction is an oar in water apparently bent? Explain by a
diagram.
3. What optical instruments have you used? Is the visible image formed by
each of these real or virtual?
4. The focal length of a copying camera lens is 14 in. Where must a
drawing be placed so that an image of the same size may be formed upon
the ground glass screen? What must be the distance of the screen from the
lens?
5. What are two methods by which you can determine the focal lengths of
the lens of a photographic camera?
6. The critical angle for water is 48-1/2 degrees. Show by a diagram how
much of the sky can be seen by a diver who looks upward through the
water.
7. How is near-sightedness caused? How is it corrected? Illustrate by a
diagram.
8. How is the eye accommodated (focused) as an object gradually
approaches it?
9. Explain why a simple microscope assists in looking at the parts of a
flower or insect.
10. Why do people who have good eyesight when young require glasses as
they grow old?
(7) Color and Spectra
3. Simple microscope, camera; images, kind, how formed.
4. Compound microscope, telescope and opera glass; images, action of each
lens.
Exercises
1. Name three instruments in which lenses form virtual images and three in
which real images are formed.
2. In what direction is an oar in water apparently bent? Explain by a
diagram.
3. What optical instruments have you used? Is the visible image formed by
each of these real or virtual?
4. The focal length of a copying camera lens is 14 in. Where must a
drawing be placed so that an image of the same size may be formed upon
the ground glass screen? What must be the distance of the screen from the
lens?
5. What are two methods by which you can determine the focal lengths of
the lens of a photographic camera?
6. The critical angle for water is 48-1/2 degrees. Show by a diagram how
much of the sky can be seen by a diver who looks upward through the
water.
7. How is near-sightedness caused? How is it corrected? Illustrate by a
diagram.
8. How is the eye accommodated (focused) as an object gradually
approaches it?
9. Explain why a simple microscope assists in looking at the parts of a
flower or insect.
10. Why do people who have good eyesight when young require glasses as
they grow old?
(7) Color and Spectra
Page 418
399. Color.—Much
of the pleasure
experienced in
gazing at beautiful
objects is due to the
color shown by
them. The blue sky,
the green grass, and
the varied tints of
flowers, and of the
rainbow all excite
our admiration The
study of color begins
naturally with the
production of the
spectrum, the many-
Guglielmo Marconi colored image upon
a screen produced by Alexander Graham
passing a beam of Bell
"Copyright by
Underwood & light through a
prism. The spectrum "Copyright by
Underwood, N. Y." Underwood &
Guglielmo Marconi is best shown when
the light enters by a Underwood, N. Y."
(Italy). Inventor of Alexander Graham
wireless telegraphy. narrow slit (Fig.
400). The spectrum Bell, Washington, D. C.
was first produced Inventor of the
by Sir Isaac Newton in 1675 by the means just telephone.
described. The names usually given to the more
prominent colors of the spectrum are violet, indigo, blue, green, yellow,
orange, and red. The initials of these names, combined, spell vibgyor, a
word without meaning except to assist in remembering the order of the
colors in a spectrum. If the light that has passed through a prism is sent
through a second prism placed in reverse position (see Fig. 401), the light
passing through both prisms is found to be white. This experiment indicates
that white light is composed of light of all colors.
of the pleasure
experienced in
gazing at beautiful
objects is due to the
color shown by
them. The blue sky,
the green grass, and
the varied tints of
flowers, and of the
rainbow all excite
our admiration The
study of color begins
naturally with the
production of the
spectrum, the many-
Guglielmo Marconi colored image upon
a screen produced by Alexander Graham
passing a beam of Bell
"Copyright by
Underwood & light through a
prism. The spectrum "Copyright by
Underwood, N. Y." Underwood &
Guglielmo Marconi is best shown when
the light enters by a Underwood, N. Y."
(Italy). Inventor of Alexander Graham
wireless telegraphy. narrow slit (Fig.
400). The spectrum Bell, Washington, D. C.
was first produced Inventor of the
by Sir Isaac Newton in 1675 by the means just telephone.
described. The names usually given to the more
prominent colors of the spectrum are violet, indigo, blue, green, yellow,
orange, and red. The initials of these names, combined, spell vibgyor, a
word without meaning except to assist in remembering the order of the
colors in a spectrum. If the light that has passed through a prism is sent
through a second prism placed in reverse position (see Fig. 401), the light
passing through both prisms is found to be white. This experiment indicates
that white light is composed of light of all colors.
Page 419
Fig. 400.—Formation of the spectrum by a
prism.
400. Dispersion.—The separation of the colors
by a prism is called dispersion. In experimenting
to find a reason for dispersion, it has been
learned that lights of different colors are of
different wave lengths. Color in light is
therefore analogous to pitch in sound. We hear
through many octaves, but we see through about
one octave. That is, the shortest visible waves of
Fig. 401.—The colors violet light are about 0.000038 cm. in length
of the spectrum while the longest visible red rays are 0.000076
recombine to form cm., or the longest visible light waves are about
white light. twice the length of the shortest visible ones. It
appears from the evidence of experiments upon
dispersion that light waves of different lengths are refracted differently. This
causes the images formed by refraction through simple glass lenses to be
fringed with color and to lose some of their sharpness and definiteness of
outline, since the violet light is brought to a focus sooner than the red. (See
Fig. 402.) This seriously affects the value of such lenses for optical
purposes. Fortunately it is found that different kinds of glass have a different
rate of dispersion for the same amount of refraction.
401. The Achromatic Lens.—The existence of these different kinds of
glass makes possible a combination of lenses in which dispersion is entirely
overcome with the loss of only about one-half of the refraction. Such a
prism.
400. Dispersion.—The separation of the colors
by a prism is called dispersion. In experimenting
to find a reason for dispersion, it has been
learned that lights of different colors are of
different wave lengths. Color in light is
therefore analogous to pitch in sound. We hear
through many octaves, but we see through about
one octave. That is, the shortest visible waves of
Fig. 401.—The colors violet light are about 0.000038 cm. in length
of the spectrum while the longest visible red rays are 0.000076
recombine to form cm., or the longest visible light waves are about
white light. twice the length of the shortest visible ones. It
appears from the evidence of experiments upon
dispersion that light waves of different lengths are refracted differently. This
causes the images formed by refraction through simple glass lenses to be
fringed with color and to lose some of their sharpness and definiteness of
outline, since the violet light is brought to a focus sooner than the red. (See
Fig. 402.) This seriously affects the value of such lenses for optical
purposes. Fortunately it is found that different kinds of glass have a different
rate of dispersion for the same amount of refraction.
401. The Achromatic Lens.—The existence of these different kinds of
glass makes possible a combination of lenses in which dispersion is entirely
overcome with the loss of only about one-half of the refraction. Such a
Page 420
combination is shown in Fig. 403. It is
called an achromatic lens, since
images formed by it are not colored
but white (a = without, chroma =
color). The achromatic lens consists of
a double convex lens of crown glass
combined with a plano-concave lens
of flint glass. Achromatic lenses are
used in all high-grade optical
instruments such as telescopes and
microscopes. The colored images that
are sometimes seen in cheap opera
glasses show the result of not using Fig. 402.—Violet light comes to
achromatic lenses. a focus sooner than red.
Fig. 403.—An achromatic lens. C is of crown
glass; F, of flint glass.
402. The Color of Bodies.—Project the spectrum of sunlight upon a white
surface in a darkened room.
Now place in different parts of the spectrum objects of various colors. Red
objects will show brilliant red when at the red end of the spectrum but look
black at the blue end, while blue objects appear blue only at the blue end.
These facts indicate that the color of an object depends upon two things: (a)
the light that falls upon it and (b) the light which it sends to the eye. A black
surface absorbs all color while a white one reflects all wave lengths to the
eye in the same proportion that they come to it. A white object will appear
red in red light, and blue in blue light since it reflects both of these. A
colored object reflects light of its own color but absorbs all others. The
color then of a body is due to the light which it does not absorb, but which
comes from it to the eye.
called an achromatic lens, since
images formed by it are not colored
but white (a = without, chroma =
color). The achromatic lens consists of
a double convex lens of crown glass
combined with a plano-concave lens
of flint glass. Achromatic lenses are
used in all high-grade optical
instruments such as telescopes and
microscopes. The colored images that
are sometimes seen in cheap opera
glasses show the result of not using Fig. 402.—Violet light comes to
achromatic lenses. a focus sooner than red.
Fig. 403.—An achromatic lens. C is of crown
glass; F, of flint glass.
402. The Color of Bodies.—Project the spectrum of sunlight upon a white
surface in a darkened room.
Now place in different parts of the spectrum objects of various colors. Red
objects will show brilliant red when at the red end of the spectrum but look
black at the blue end, while blue objects appear blue only at the blue end.
These facts indicate that the color of an object depends upon two things: (a)
the light that falls upon it and (b) the light which it sends to the eye. A black
surface absorbs all color while a white one reflects all wave lengths to the
eye in the same proportion that they come to it. A white object will appear
red in red light, and blue in blue light since it reflects both of these. A
colored object reflects light of its own color but absorbs all others. The
color then of a body is due to the light which it does not absorb, but which
comes from it to the eye.
Page 421
403. The color of transparent bodies, such as colored glass, is due to the
presence of a dye or pigment contained in the body. This pigment absorbs a
part of the light, the part transmitted giving the color. This may be shown by
holding a sheet of colored glass in a beam of light either before or after it
has passed through a prism. Some colors, as red, may be found to be nearly
pure, only the red passing through, while green glass often transmits in
addition to the green some yellow and some red light.
404. Complementary Colors.—If two prisms are placed in reversed
position near each other (see Fig. 401), a beam of light dispersed by one is
recombined into white light by the other. If now a card is held between the
two prisms so as to cut off some of the colored light, say the red, the
remaining light will be found to form a greenish blue. If the card is
removed, the light becomes white again. That is, red and peacock blue light
together form white. Any two colors that together form white light are
called complementary. Other complementary colors are light yellow and
blue, green and crimson, orange and greenish blue, violet and greenish
yellow. We must not confuse the combining of colors (light) and the
combining of pigments, the latter consisting of bodies that absorb light.
Yellow pigment absorbs all but yellow and some green, while blue pigment
absorbs all but blue and some green. Mixing these two pigments causes the
absorption of all colors but green. Blue and yellow paint mixed produce
green, while blue and yellow light give white.
405. The solar spectrum, as the spectrum of sunlight is called, may be
observed in the rainbow. The latter is produced through the dispersion of
light by spherical raindrops. Its formation may be imitated by sending a
small circular beam of light through a screen against a round glass flask
filled with water. (See Fig. 404.) The light passes through the water and is
dispersed when it enters and when it leaves, producing a color upon the
screen at R-V. The course of the light within the drop is indicated in Fig.
405. The violet ray comes to the eye more nearly horizontal and is therefore
below red, as we look at the rainbow.
406. Fraunhofer Lines.—Some of the most important features of the solar
spectrum are not seen in the rainbow or in the band of light usually
observed upon a screen. By the use of a narrow slit and a convex lens to
carefully focus the slit upon a white screen it is seen that the solar spectrum
is crossed by many dark lines. These are called Fraunhofer lines, to honor
presence of a dye or pigment contained in the body. This pigment absorbs a
part of the light, the part transmitted giving the color. This may be shown by
holding a sheet of colored glass in a beam of light either before or after it
has passed through a prism. Some colors, as red, may be found to be nearly
pure, only the red passing through, while green glass often transmits in
addition to the green some yellow and some red light.
404. Complementary Colors.—If two prisms are placed in reversed
position near each other (see Fig. 401), a beam of light dispersed by one is
recombined into white light by the other. If now a card is held between the
two prisms so as to cut off some of the colored light, say the red, the
remaining light will be found to form a greenish blue. If the card is
removed, the light becomes white again. That is, red and peacock blue light
together form white. Any two colors that together form white light are
called complementary. Other complementary colors are light yellow and
blue, green and crimson, orange and greenish blue, violet and greenish
yellow. We must not confuse the combining of colors (light) and the
combining of pigments, the latter consisting of bodies that absorb light.
Yellow pigment absorbs all but yellow and some green, while blue pigment
absorbs all but blue and some green. Mixing these two pigments causes the
absorption of all colors but green. Blue and yellow paint mixed produce
green, while blue and yellow light give white.
405. The solar spectrum, as the spectrum of sunlight is called, may be
observed in the rainbow. The latter is produced through the dispersion of
light by spherical raindrops. Its formation may be imitated by sending a
small circular beam of light through a screen against a round glass flask
filled with water. (See Fig. 404.) The light passes through the water and is
dispersed when it enters and when it leaves, producing a color upon the
screen at R-V. The course of the light within the drop is indicated in Fig.
405. The violet ray comes to the eye more nearly horizontal and is therefore
below red, as we look at the rainbow.
406. Fraunhofer Lines.—Some of the most important features of the solar
spectrum are not seen in the rainbow or in the band of light usually
observed upon a screen. By the use of a narrow slit and a convex lens to
carefully focus the slit upon a white screen it is seen that the solar spectrum
is crossed by many dark lines. These are called Fraunhofer lines, to honor
Page 422
the German scientist who in 1814 first accurately determined their position.
Two experiments with a spectroscope will help to make clear the meaning
of the Fraunhofer lines.
Fig. 404.—A rainbow formed by a beam of
light striking a flask of water.
Fig. 405.—The course of a beam of light
within a drop of water.
407. The Spectroscope and Its Uses.—The spectroscope (Fig. 406) is an
instrument for observing spectra. It consists of a prism, a slit, and a convex
lens T for focusing an image of the slit accurately upon a screen (Fig. 407)
where the spectrum is observed through the eyepiece E.
(A) A Bunsen flame is placed in front of the slit and a heated platinum wire
which has been dipped in common salt or some sodium compound placed
in the Bunsen flame; the latter becomes yellow and a vivid yellow line is
Two experiments with a spectroscope will help to make clear the meaning
of the Fraunhofer lines.
Fig. 404.—A rainbow formed by a beam of
light striking a flask of water.
Fig. 405.—The course of a beam of light
within a drop of water.
407. The Spectroscope and Its Uses.—The spectroscope (Fig. 406) is an
instrument for observing spectra. It consists of a prism, a slit, and a convex
lens T for focusing an image of the slit accurately upon a screen (Fig. 407)
where the spectrum is observed through the eyepiece E.
(A) A Bunsen flame is placed in front of the slit and a heated platinum wire
which has been dipped in common salt or some sodium compound placed
in the Bunsen flame; the latter becomes yellow and a vivid yellow line is
Page 423
observed on the screen in the
spectroscope. Other substances,
as barium and strontium salts,
when heated to incandescence
in the Bunsen flame, give
characteristic bright lines. In
fact each element has been
found to have its own
characteristic set of colored
lines. This fact is made use of in
spectrum analysis, by which the
presence of certain elements in
a substance can be definitely
proved upon the appearance of
its particular lines in the
spectrum.
Fig. 406.—The spectroscope.
Fig. 407.—Diagram of a
spectroscope.
spectroscope. Other substances,
as barium and strontium salts,
when heated to incandescence
in the Bunsen flame, give
characteristic bright lines. In
fact each element has been
found to have its own
characteristic set of colored
lines. This fact is made use of in
spectrum analysis, by which the
presence of certain elements in
a substance can be definitely
proved upon the appearance of
its particular lines in the
spectrum.
Fig. 406.—The spectroscope.
Fig. 407.—Diagram of a
spectroscope.
Page 424
Fig. 408.—The bright line spectrum of iron
and its coincidences with some of the dark
lines of the solar spectrum.
(B) If light from, for example, an arc light is sent over a gas flame
containing sodium vapor, a dark line appears in the spectrum—in the exact
position in which the yellow sodium line appeared. It seems that the sodium
vapor removes from white light the same wave lengths that it itself
produces. This absorption is supposed to be due to sympathetic vibration;
just as a tuning fork is set in vibration by the waves of another fork in
unison with it, at the same time absorbing the wave energy, so in the gas
flame the sodium particles absorb the wave motion of the same vibration
rate as that emitted by them. The fact that the spectrum of sunlight contains
a great many dark lines is believed to indicate that the sun is surrounded by
clouds formed by the vaporization of the various substances in the sun
itself. By comparing the dark lines of the solar spectrum with the bright-line
spectra of various substances found in the earth, such an exact
correspondence of the lines is found that the presence of the vapor of these
substances about the sun is considered proved. (See Fig. 408 which shows
the exact correspondence between the bright-line spectrum of iron vapor
and the dark lines appearing in a portion of the sun's spectrum.) The spectra
of the stars also contain certain dark lines. Thus the presence of the
corresponding substances in distant stars is considered as determined.
408. Theory of Color Vision.—By combining light of the three colors red,
green and blue-violet in proper proportions, it has been found possible to
produce any color effect, even white. This leads to the conclusion that in the
retina of the eye are three different kinds or sets of sensitive nerve endings,
sensitive respectively to red, to green, and to blue light. This idea is given
corroboration by some facts of color blindness. Thus some persons have no
and its coincidences with some of the dark
lines of the solar spectrum.
(B) If light from, for example, an arc light is sent over a gas flame
containing sodium vapor, a dark line appears in the spectrum—in the exact
position in which the yellow sodium line appeared. It seems that the sodium
vapor removes from white light the same wave lengths that it itself
produces. This absorption is supposed to be due to sympathetic vibration;
just as a tuning fork is set in vibration by the waves of another fork in
unison with it, at the same time absorbing the wave energy, so in the gas
flame the sodium particles absorb the wave motion of the same vibration
rate as that emitted by them. The fact that the spectrum of sunlight contains
a great many dark lines is believed to indicate that the sun is surrounded by
clouds formed by the vaporization of the various substances in the sun
itself. By comparing the dark lines of the solar spectrum with the bright-line
spectra of various substances found in the earth, such an exact
correspondence of the lines is found that the presence of the vapor of these
substances about the sun is considered proved. (See Fig. 408 which shows
the exact correspondence between the bright-line spectrum of iron vapor
and the dark lines appearing in a portion of the sun's spectrum.) The spectra
of the stars also contain certain dark lines. Thus the presence of the
corresponding substances in distant stars is considered as determined.
408. Theory of Color Vision.—By combining light of the three colors red,
green and blue-violet in proper proportions, it has been found possible to
produce any color effect, even white. This leads to the conclusion that in the
retina of the eye are three different kinds or sets of sensitive nerve endings,
sensitive respectively to red, to green, and to blue light. This idea is given
corroboration by some facts of color blindness. Thus some persons have no
Page 425
sensation of red, this color not being distinguished from green. Others are
color blind to green or blue. It is supposed that in color blind persons one of
the sets of nerve endings sensitive to one of these three colors is lacking.
409. Three-color Printing.—Since all colors may be produced by mixing
the three colors, light red, green, and blue-violet, these are called the three
primary colors. The so-called primary pigments or paints are simply the
complements of the three primary colors. They are, in order, peacock blue,
crimson, and light yellow. The three pigments when mixed yield black,
since combined they absorb all kinds of visible light. The process of three-
color printing, now so generally employed in printing colored pictures for
books, calendars, etc., consists in combining upon white paper three colored
impressions, using successively the three primary pigments (yellow,
crimson and blue) from plates prepared as follows:
Three photographs of a given colored object are taken, each through a
different sheet of gelatine called a filter, stained the color of one of the
primary colors. From these photographs half-tone blocks are made in the
usual way. The colored picture is made by carefully superposing
impressions from these blocks, using in each case an ink whose color is the
complement of the "filter" through which the original picture was taken. An
illustration of the process is given upon the plate in the frontispiece of this
book.
Important Topics
1. Color, due to wave length; dispersion by prism, sphere in rainbow,
complementary colors, color of opaque and transparent bodies.
2. Spectra, solar; formation of rainbow; bright-line spectra, how formed,
how used; dark-line, how formed, used.
3. Theory of color vision. Three color printing.
Exercises
1. How does a white flower look when viewed through a blue glass?
Through a red glass? Through a red and blue glass at the same time?
color blind to green or blue. It is supposed that in color blind persons one of
the sets of nerve endings sensitive to one of these three colors is lacking.
409. Three-color Printing.—Since all colors may be produced by mixing
the three colors, light red, green, and blue-violet, these are called the three
primary colors. The so-called primary pigments or paints are simply the
complements of the three primary colors. They are, in order, peacock blue,
crimson, and light yellow. The three pigments when mixed yield black,
since combined they absorb all kinds of visible light. The process of three-
color printing, now so generally employed in printing colored pictures for
books, calendars, etc., consists in combining upon white paper three colored
impressions, using successively the three primary pigments (yellow,
crimson and blue) from plates prepared as follows:
Three photographs of a given colored object are taken, each through a
different sheet of gelatine called a filter, stained the color of one of the
primary colors. From these photographs half-tone blocks are made in the
usual way. The colored picture is made by carefully superposing
impressions from these blocks, using in each case an ink whose color is the
complement of the "filter" through which the original picture was taken. An
illustration of the process is given upon the plate in the frontispiece of this
book.
Important Topics
1. Color, due to wave length; dispersion by prism, sphere in rainbow,
complementary colors, color of opaque and transparent bodies.
2. Spectra, solar; formation of rainbow; bright-line spectra, how formed,
how used; dark-line, how formed, used.
3. Theory of color vision. Three color printing.
Exercises
1. How does a white flower look when viewed through a blue glass?
Through a red glass? Through a red and blue glass at the same time?
Page 426
2. Why does a red ribbon appear black when seen by blue light and red
when seen by red light?
3. In what part of the sky must you look to see a rainbow in the morning? In
the afternoon? Explain.
4. How would you arrange two similar prisms so as to produce double the
deviation produced by one?
5. The color of an object depends upon what two things?
6. What kind of a spectrum should moonlight give? Why?
7. A mixture of green and red lights gives a sensation of yellow. Can you
suggest why a mixture of blue and yellow lights gives the sensation of
white?
(8) Nature of Light, Interference, Polarization
410. The Corpuscular Theory.—The theory of the nature of light that was
most generally accepted until about the year 1800, held that light consists of
streams of minute particles, called corpuscles, moving at enormous
velocities. This corpuscular theory was in accord with the facts of reflection
and the rectilinear motion of light, but was abandoned after the discovery
of the interference of light, as it could not account for the latter
phenomenon.
411. The Wave Theory of Light.—The theory that light is a form of wave
motion was first advanced by Huygens, a Dutch physicist, in the
seventeenth century. This theory was opposed at the start since (A) no
medium was known to exist which would convey wave motion through
space, as from the sun to the earth, and (B) the rectilinear motion of light
was unlike that of any other form of known wave motions, such as that of
water or of sound waves which are able to bend around corners. In answer
to the first objection, Huygens assumed the presence of a medium which he
named ether, while the second objection has been completely overcome
during the past century by the discovery that light may deviate from a
straight line. It is now known that the excessive shortness of light waves is
the reason for its straight-line motion. Further, long ether waves, as those of
when seen by red light?
3. In what part of the sky must you look to see a rainbow in the morning? In
the afternoon? Explain.
4. How would you arrange two similar prisms so as to produce double the
deviation produced by one?
5. The color of an object depends upon what two things?
6. What kind of a spectrum should moonlight give? Why?
7. A mixture of green and red lights gives a sensation of yellow. Can you
suggest why a mixture of blue and yellow lights gives the sensation of
white?
(8) Nature of Light, Interference, Polarization
410. The Corpuscular Theory.—The theory of the nature of light that was
most generally accepted until about the year 1800, held that light consists of
streams of minute particles, called corpuscles, moving at enormous
velocities. This corpuscular theory was in accord with the facts of reflection
and the rectilinear motion of light, but was abandoned after the discovery
of the interference of light, as it could not account for the latter
phenomenon.
411. The Wave Theory of Light.—The theory that light is a form of wave
motion was first advanced by Huygens, a Dutch physicist, in the
seventeenth century. This theory was opposed at the start since (A) no
medium was known to exist which would convey wave motion through
space, as from the sun to the earth, and (B) the rectilinear motion of light
was unlike that of any other form of known wave motions, such as that of
water or of sound waves which are able to bend around corners. In answer
to the first objection, Huygens assumed the presence of a medium which he
named ether, while the second objection has been completely overcome
during the past century by the discovery that light may deviate from a
straight line. It is now known that the excessive shortness of light waves is
the reason for its straight-line motion. Further, long ether waves, as those of
Page 427
wireless telegraphy, are found to bend around obstacles in a manner similar
to those of water or sound.
Fig. 409.—Two plates pressed together by a
screw clamp.
Fig. 410.—Illustrating the interference of light
by a thin film of air.
412. The interference of light is one of the phenomena for which the wave
theory offers the only satisfactory explanation. Interference of light may be
shown by taking two pieces of plate glass and forcibly pressing them
together by a screw clamp, as shown in Fig. 409. After a certain pressure
has been reached, colored rings will appear about the compressed spot
when viewed by light reflected from the upper surface of the glass. If light
of one color, such as that transmitted by red glass, falls upon the apparatus,
the rings are seen to be alternately red and dark bands. The explanation of
this phenomenon according to the wave theory is as follows: The two sheets
of glass, although tightly pressed together, are separated in most places by a
thin wedge of air (see Fig. 410), which represents in an exaggerated form
the bending of the plates when pressed by the clamp. Several waves are
represented as coming from the right and entering the glass. Now the wave
moving from R to the plates has some of its light reflected from each glass
surface. Consider the two portions of the wave reflected at each of the
surfaces between the plates, i.e., from the two surfaces of the wedge of air.
If the portion of the wave reflected from the second surface of the air wedge
combines with that reflected from the first surface, in the same phase as at
C, the two reflected waves strengthen each other. While if the two reflected
portions of the wave meet in opposite phases as at A and B, a decrease or a
to those of water or sound.
Fig. 409.—Two plates pressed together by a
screw clamp.
Fig. 410.—Illustrating the interference of light
by a thin film of air.
412. The interference of light is one of the phenomena for which the wave
theory offers the only satisfactory explanation. Interference of light may be
shown by taking two pieces of plate glass and forcibly pressing them
together by a screw clamp, as shown in Fig. 409. After a certain pressure
has been reached, colored rings will appear about the compressed spot
when viewed by light reflected from the upper surface of the glass. If light
of one color, such as that transmitted by red glass, falls upon the apparatus,
the rings are seen to be alternately red and dark bands. The explanation of
this phenomenon according to the wave theory is as follows: The two sheets
of glass, although tightly pressed together, are separated in most places by a
thin wedge of air (see Fig. 410), which represents in an exaggerated form
the bending of the plates when pressed by the clamp. Several waves are
represented as coming from the right and entering the glass. Now the wave
moving from R to the plates has some of its light reflected from each glass
surface. Consider the two portions of the wave reflected at each of the
surfaces between the plates, i.e., from the two surfaces of the wedge of air.
If the portion of the wave reflected from the second surface of the air wedge
combines with that reflected from the first surface, in the same phase as at
C, the two reflected waves strengthen each other. While if the two reflected
portions of the wave meet in opposite phases as at A and B, a decrease or a
Page 428
complete extinction of the light results. This is called interference. If light
of one wave length is used, as red light, the regions of reinforcement and
interference are shown by red and dark rings, while if white light is used,
the ring where red light interferes, yields its complementary color, greenish
blue. Where interference of greenish blue occurs, red is found, etc. Many
phenomena are due to interference, such as (A) the color of thin films of oil
on water, where the portions of light reflected from the two surfaces of the
oil film interfere resulting in the production of color; (B) the color of soap
bubbles. When first formed, soap-bubble films are not thin enough to show
interference well, but as the bubbles increase in size or become thinner on
standing, the conditions for interference are reached and, as the film
becomes thinner, a regular succession of colors is noticed.
413. Differences Between Light and Sound.—Among the important
differences between light and sound that have been considered are the
following: the former are (a) waves in the ether, (b) of very short wave
length, and (c) their motion is in straight lines. Another difference (d) is in
the mode of vibration.
Sound waves are longitudinal, while light waves are transverse. Light
waves consist of vibrations of the ether at right angles to the line of motion.
To illustrate the reasoning that has led to this conclusion, suppose a rope to
be passed through two vertical gratings. (See Fig. 411, 1.) If the rope be set
in transverse vibration by a hand, the waves produced will readily pass
through to the gratings P and Q and continue in the part extending beyond
Q. If, however, Q is at right angles to P, no motion will be found beyond Q.
Now if a stretched coiled spring with longitudinal vibrations should take the
place of the rope, it is evident that the crossed position of the two gratings
would offer no obstacles to the movement of the vibration. In other words,
crossed gratings offer no obstruction to longitudinal vibrations, while they
may completely stop transverse vibrations.
of one wave length is used, as red light, the regions of reinforcement and
interference are shown by red and dark rings, while if white light is used,
the ring where red light interferes, yields its complementary color, greenish
blue. Where interference of greenish blue occurs, red is found, etc. Many
phenomena are due to interference, such as (A) the color of thin films of oil
on water, where the portions of light reflected from the two surfaces of the
oil film interfere resulting in the production of color; (B) the color of soap
bubbles. When first formed, soap-bubble films are not thin enough to show
interference well, but as the bubbles increase in size or become thinner on
standing, the conditions for interference are reached and, as the film
becomes thinner, a regular succession of colors is noticed.
413. Differences Between Light and Sound.—Among the important
differences between light and sound that have been considered are the
following: the former are (a) waves in the ether, (b) of very short wave
length, and (c) their motion is in straight lines. Another difference (d) is in
the mode of vibration.
Sound waves are longitudinal, while light waves are transverse. Light
waves consist of vibrations of the ether at right angles to the line of motion.
To illustrate the reasoning that has led to this conclusion, suppose a rope to
be passed through two vertical gratings. (See Fig. 411, 1.) If the rope be set
in transverse vibration by a hand, the waves produced will readily pass
through to the gratings P and Q and continue in the part extending beyond
Q. If, however, Q is at right angles to P, no motion will be found beyond Q.
Now if a stretched coiled spring with longitudinal vibrations should take the
place of the rope, it is evident that the crossed position of the two gratings
would offer no obstacles to the movement of the vibration. In other words,
crossed gratings offer no obstruction to longitudinal vibrations, while they
may completely stop transverse vibrations.
Page 429
Fig. 411.—Transverse waves will pass through
both gratings in (1) where the openings in the
two gratings are at right angles. The waves
passing P are stopped by Q (2).Fig. 411.—
Transverse waves will pass through both
gratings in (1) where the openings in the two
gratings are at right angles. The waves passing
P are stopped by Q (2).
Fig. 412.—Effect of tourmaline crystals on
light.
414. Polarization of Light.—It is found that two crystals of tourmaline
behave toward light just as the two gratings behave with respect to the
transverse waves of the rope. Thus, if a small opening in a screen is covered
with a tourmaline crystal, light comes through but slightly diminished in
intensity. If a second crystal is placed over the first one so that the two axes
are in the same direction as in Fig. 412P, light is as freely transmitted
through the second crystal as through the first, but if the crystals are crossed
(Fig. 412S) no light passes the second crystal. This experiment shows that
the light which has passed through one tourmaline crystal will pass through
another only when the latter is held in a certain position, hence it is believed
that a tourmaline crystal is capable of transmitting light that is vibrating in
both gratings in (1) where the openings in the
two gratings are at right angles. The waves
passing P are stopped by Q (2).Fig. 411.—
Transverse waves will pass through both
gratings in (1) where the openings in the two
gratings are at right angles. The waves passing
P are stopped by Q (2).
Fig. 412.—Effect of tourmaline crystals on
light.
414. Polarization of Light.—It is found that two crystals of tourmaline
behave toward light just as the two gratings behave with respect to the
transverse waves of the rope. Thus, if a small opening in a screen is covered
with a tourmaline crystal, light comes through but slightly diminished in
intensity. If a second crystal is placed over the first one so that the two axes
are in the same direction as in Fig. 412P, light is as freely transmitted
through the second crystal as through the first, but if the crystals are crossed
(Fig. 412S) no light passes the second crystal. This experiment shows that
the light which has passed through one tourmaline crystal will pass through
another only when the latter is held in a certain position, hence it is believed
that a tourmaline crystal is capable of transmitting light that is vibrating in
Page 430
one particular plane. The direct conclusion from this is that light waves are
transverse rather than longitudinal. The experiment just described
illustrates what is called polarization of light. The beam that after passing
through a (Fig. 412) is unable to pass through b, if the two axes are crossed,
is called a polarized beam. The conclusion that light waves are transverse is
therefore based upon the phenomenon of the polarization of light. This was
first discovered by Huygens in 1690.
Important Topics
1. Interference of light: evidence, reasoning involved, illustration.
2. Polarization of light: evidence, reasoning involved.
3. Nature of light, differences between sound and light.
Exercises
1. Make a list of the differences between sound and light and state briefly
the evidence upon which the knowledge of these differences is based.
2. Why will a thickness of film that will produce interference of red light be
different from that producing interference for green or blue?
3. Using the formula n = v/l compute the vibration rate for violet light if its
wave length is considered as 0.00004 cm.
4. Explain how the fact of polarization affects the wave theory of light.
5. Show how it is possible by comparing the spectrum of the sun with that
of a star to tell whether the star is approaching or receding from the earth.
Review Outline: Light
Light; speed, source, medium.
Straight Line Motion; shadow, umbra, penumbra, eclipse, image.
Photometry; Law of intensity, candle power, foot-candle.
transverse rather than longitudinal. The experiment just described
illustrates what is called polarization of light. The beam that after passing
through a (Fig. 412) is unable to pass through b, if the two axes are crossed,
is called a polarized beam. The conclusion that light waves are transverse is
therefore based upon the phenomenon of the polarization of light. This was
first discovered by Huygens in 1690.
Important Topics
1. Interference of light: evidence, reasoning involved, illustration.
2. Polarization of light: evidence, reasoning involved.
3. Nature of light, differences between sound and light.
Exercises
1. Make a list of the differences between sound and light and state briefly
the evidence upon which the knowledge of these differences is based.
2. Why will a thickness of film that will produce interference of red light be
different from that producing interference for green or blue?
3. Using the formula n = v/l compute the vibration rate for violet light if its
wave length is considered as 0.00004 cm.
4. Explain how the fact of polarization affects the wave theory of light.
5. Show how it is possible by comparing the spectrum of the sun with that
of a star to tell whether the star is approaching or receding from the earth.
Review Outline: Light
Light; speed, source, medium.
Straight Line Motion; shadow, umbra, penumbra, eclipse, image.
Photometry; Law of intensity, candle power, foot-candle.
Page 431
Mirrors; Law of reflection; image—real, virtual; plane, curved, parabolic,
mirrors.
Refraction; cause and effects; plate, prism, lens; total reflection.
Lenses; six forms, principal focus, center, lens equation, 1/F = 1/Do + 1/Di.
Optical instruments; eye, defects and correction, camera, microscope, etc.
Spectra; 3 kinds, dispersion, production of color effects, spectroscope, uses.
Nature of Light; wave theory, interference, polarization, significance.
mirrors.
Refraction; cause and effects; plate, prism, lens; total reflection.
Lenses; six forms, principal focus, center, lens equation, 1/F = 1/Do + 1/Di.
Optical instruments; eye, defects and correction, camera, microscope, etc.
Spectra; 3 kinds, dispersion, production of color effects, spectroscope, uses.
Nature of Light; wave theory, interference, polarization, significance.
Page 432
CHAPTER XVII
INVISIBLE RADIATIONS
(1) Electric Waves and Radio-activity
415. Oscillatory Nature of the Spark from a Leyden Jar.—In studying
sound (Art. 339), the sympathetic vibration of two tuning forks having the
same rate of vibration was given as an illustration of resonance. The
conditions for obtaining electrical resonance by the use of two Leyden jars
are given in the following experiment.
Join the two coats of a Leyden jar (Fig. 413) to a loop of wire L, the sliding
crosspiece M being arranged so that the length of the loop may be changed
as desired. Also place a strip of tinfoil in contact with the inner coating and
bring it over to within about a millimeter of the outer coating as indicated at
G. Now join the outer coating of another exactly similar jar A to a wire loop
of fixed length, the end of the loop being separated from the knob
connected to the inner coating, a short distance at P. Place the jars near each
other with the wire loops parallel and connect coatings of A to the terminals
of a static machine or an induction coil. At each discharge between the
knobs at P, a spark will appear in the other jar at G, if the crosspiece M is so
adjusted that the areas of the two loops are exactly equal. When the wire M
is moved so as to make the areas of the two loops quite unequal, the spark
at G disappears.
The experiment just described shows that two electrical circuits can be
tuned by adjusting their lengths, just as two tuning forks may be made
sympathetic by adjusting their lengths. This fact indicates that the discharge
of the Leyden jar is oscillatory, since resonance can plainly not be secured
except between bodies having natural periods of vibration. This same fact is
also shown by examining the discharge of a Leyden jar as it appears when
viewed in a rapidly revolving mirror. (See Fig. 414.) The appearance in the
mirror shows that the discharge is made up of a number of sparks, often a
dozen or more, vibrating back and forth until they finally come to rest. The
INVISIBLE RADIATIONS
(1) Electric Waves and Radio-activity
415. Oscillatory Nature of the Spark from a Leyden Jar.—In studying
sound (Art. 339), the sympathetic vibration of two tuning forks having the
same rate of vibration was given as an illustration of resonance. The
conditions for obtaining electrical resonance by the use of two Leyden jars
are given in the following experiment.
Join the two coats of a Leyden jar (Fig. 413) to a loop of wire L, the sliding
crosspiece M being arranged so that the length of the loop may be changed
as desired. Also place a strip of tinfoil in contact with the inner coating and
bring it over to within about a millimeter of the outer coating as indicated at
G. Now join the outer coating of another exactly similar jar A to a wire loop
of fixed length, the end of the loop being separated from the knob
connected to the inner coating, a short distance at P. Place the jars near each
other with the wire loops parallel and connect coatings of A to the terminals
of a static machine or an induction coil. At each discharge between the
knobs at P, a spark will appear in the other jar at G, if the crosspiece M is so
adjusted that the areas of the two loops are exactly equal. When the wire M
is moved so as to make the areas of the two loops quite unequal, the spark
at G disappears.
The experiment just described shows that two electrical circuits can be
tuned by adjusting their lengths, just as two tuning forks may be made
sympathetic by adjusting their lengths. This fact indicates that the discharge
of the Leyden jar is oscillatory, since resonance can plainly not be secured
except between bodies having natural periods of vibration. This same fact is
also shown by examining the discharge of a Leyden jar as it appears when
viewed in a rapidly revolving mirror. (See Fig. 414.) The appearance in the
mirror shows that the discharge is made up of a number of sparks, often a
dozen or more, vibrating back and forth until they finally come to rest. The
Page 433
time of one vibration varies from one
millionth to one hundred millionth of a
second, depending on the space between
the discharging balls and the size of the
jars.
The
dischar
ge of a
Leyden
Fig. 413. jar or
of
another condenser sets up ether waves
that have the speed of light. Heinrich
Fig. 414.—Photograph of the
Hertz in Germany first proved this in
oscillatory discharge of a
1888. These waves are now known as
Leyden jar.
Hertzian waves. The length of these
varies from 3 cm. to several miles,
depending upon the size and conditions of the discharging circuit.
416. The Coherer.—The coherer is a
device for detecting electric waves. It
consists of a glass tube with metal filings
loosely packed between two metal plugs
that fit the tube closely. (See Fig. 415.)
Fig. 415.—A coherer. These filings offer a high resistance to the
passage of an electric current, but when
electric waves pass through the filings these cohere and allow a weak
current to pass through. This current may be strong enough to operate a
relay connected with a sounder or bell that gives audible signals. If the tube
be tapped the filings will be disturbed and the resistance again made so high
that no current can pass through.
417. Wireless Telegraphy.—In 1894 Marconi, then a young man of twenty,
while making some experiments with electrical discharges discovered that
the coherer would detect electrical waves at a considerable distance from
their source and that by the use of a telegraph key the "dots and dashes" of
the telegraph code could be reproduced by a sounder attached to a relay. At
present the coherer is used principally in laboratory apparatus, as much
millionth to one hundred millionth of a
second, depending on the space between
the discharging balls and the size of the
jars.
The
dischar
ge of a
Leyden
Fig. 413. jar or
of
another condenser sets up ether waves
that have the speed of light. Heinrich
Fig. 414.—Photograph of the
Hertz in Germany first proved this in
oscillatory discharge of a
1888. These waves are now known as
Leyden jar.
Hertzian waves. The length of these
varies from 3 cm. to several miles,
depending upon the size and conditions of the discharging circuit.
416. The Coherer.—The coherer is a
device for detecting electric waves. It
consists of a glass tube with metal filings
loosely packed between two metal plugs
that fit the tube closely. (See Fig. 415.)
Fig. 415.—A coherer. These filings offer a high resistance to the
passage of an electric current, but when
electric waves pass through the filings these cohere and allow a weak
current to pass through. This current may be strong enough to operate a
relay connected with a sounder or bell that gives audible signals. If the tube
be tapped the filings will be disturbed and the resistance again made so high
that no current can pass through.
417. Wireless Telegraphy.—In 1894 Marconi, then a young man of twenty,
while making some experiments with electrical discharges discovered that
the coherer would detect electrical waves at a considerable distance from
their source and that by the use of a telegraph key the "dots and dashes" of
the telegraph code could be reproduced by a sounder attached to a relay. At
present the coherer is used principally in laboratory apparatus, as much
Page 434
more sensitive detectors are now available for commercial work. The
essential parts of a modern wireless telegraph apparatus as used in many
commercial stations are shown in Fig. 416.
Alternating current at 110 volts is sent into the primary, P, of a transformer,
the secondary, S, of which produces a potential of 5000 to 20,000 volts. The
secondary charges a condenser until its potential becomes high enough to
produce a discharge across a spark gap, SG. This discharge is oscillatory,
the frequency being at the rate of about one million a second, depending
upon the capacity of the condenser and the induction of the circuit.
These oscillations pass through the primary of the oscillation transformer,
inducing in the secondary, electric oscillations which surge back and forth
through the antennæ, or aerial wires, A. These oscillations set up the
"wireless waves." The production of these waves is explained as follows:
An electric current in a wire sets up a magnetic field spreading out about
the conductor; when the current stops the field returns to the conductor and
disappears. The oscillations in the antennæ, however, have such a high
frequency, of the order of a million a second, that when one surge of
electricity sets up a magnetic field, the reverse surge immediately following
sets up an opposite magnetic field before the first field can return to the
wire. Under these conditions a succession of oppositely directed magnetic
fields are produced which move out from the antennæ with the speed of
light and induce electric oscillations in any conductors cut by them.
Fig. 416.—Diagram of a commercial wireless
telegraph apparatus.
essential parts of a modern wireless telegraph apparatus as used in many
commercial stations are shown in Fig. 416.
Alternating current at 110 volts is sent into the primary, P, of a transformer,
the secondary, S, of which produces a potential of 5000 to 20,000 volts. The
secondary charges a condenser until its potential becomes high enough to
produce a discharge across a spark gap, SG. This discharge is oscillatory,
the frequency being at the rate of about one million a second, depending
upon the capacity of the condenser and the induction of the circuit.
These oscillations pass through the primary of the oscillation transformer,
inducing in the secondary, electric oscillations which surge back and forth
through the antennæ, or aerial wires, A. These oscillations set up the
"wireless waves." The production of these waves is explained as follows:
An electric current in a wire sets up a magnetic field spreading out about
the conductor; when the current stops the field returns to the conductor and
disappears. The oscillations in the antennæ, however, have such a high
frequency, of the order of a million a second, that when one surge of
electricity sets up a magnetic field, the reverse surge immediately following
sets up an opposite magnetic field before the first field can return to the
wire. Under these conditions a succession of oppositely directed magnetic
fields are produced which move out from the antennæ with the speed of
light and induce electric oscillations in any conductors cut by them.
Fig. 416.—Diagram of a commercial wireless
telegraph apparatus.
Page 435
While the electric waves are radiated in all directions from the aerial, the
length of the waves set up is approximately four times the combined length
of the aerial wires and the "lead in" connection to the oscillation
transformer.
The electric waves induce effective electrical oscillations in the aerial of the
receiving station, even at distances of hundreds of miles, provided the
receiving transformer, RT, is "tuned" in resonance with the transmitting
apparatus by adjustments of the variable condenser, VC, and the loading
coil, L. The detector of these oscillations in the receiving transformer is
simply a crystal of silicon or carborundum, D, in series with two telephone
receivers, Ph. The crystal detector permits the electric oscillations to pass
through it in one direction only. If the crystal did not possess this property,
the telephone could not be used as a receiver as it cannot respond to high
frequency oscillations. While one spark passes at SG, an intermittent current
passes through the receiver in one direction. Since some 300 to 1200 sparks
pass each second at SG while the key, K, is closed, the operator at Ph hears
a musical note of this frequency as long as K is depressed. Short and long
tones then correspond to the dots and dashes of ordinary telegraphy. In
order to maintain a uniform tone a rotary spark gap, as shown, is often
used. This insures a tone of fixed pitch by making uniform the rate of
producing sparks.
The Continental instead of the Morse code of signals is generally employed
in wireless telegraphy, since the former employs only dots and dashes. The
latter code employs, in addition to dots and dashes, spaces which have
sometimes caused confusion in receiving wireless messages. The United
States government has adopted the regulations of the International Radio
Congress which directs that commercial companies shall use wave lengths
between 300 and 600 or above 1600 meters. Amateurs may use wave
lengths less than 200 meters and no others, while the government reserves
the right to wave lengths of 600 to 1600 meters. See p. 459 for Continental
telegraph code.
418. Discharges in Rarefied Air.—Fig. 417 represents a glass tube 60 or
more centimeters long, attached to an air pump. Connect the ends of the
tube to the terminals of a static machine or of an induction coil, a-b. At first
no sparks will pass between a and f, because of the high resistance of the air
in the tube. Upon exhausting the air in the tube, however, the discharge
length of the waves set up is approximately four times the combined length
of the aerial wires and the "lead in" connection to the oscillation
transformer.
The electric waves induce effective electrical oscillations in the aerial of the
receiving station, even at distances of hundreds of miles, provided the
receiving transformer, RT, is "tuned" in resonance with the transmitting
apparatus by adjustments of the variable condenser, VC, and the loading
coil, L. The detector of these oscillations in the receiving transformer is
simply a crystal of silicon or carborundum, D, in series with two telephone
receivers, Ph. The crystal detector permits the electric oscillations to pass
through it in one direction only. If the crystal did not possess this property,
the telephone could not be used as a receiver as it cannot respond to high
frequency oscillations. While one spark passes at SG, an intermittent current
passes through the receiver in one direction. Since some 300 to 1200 sparks
pass each second at SG while the key, K, is closed, the operator at Ph hears
a musical note of this frequency as long as K is depressed. Short and long
tones then correspond to the dots and dashes of ordinary telegraphy. In
order to maintain a uniform tone a rotary spark gap, as shown, is often
used. This insures a tone of fixed pitch by making uniform the rate of
producing sparks.
The Continental instead of the Morse code of signals is generally employed
in wireless telegraphy, since the former employs only dots and dashes. The
latter code employs, in addition to dots and dashes, spaces which have
sometimes caused confusion in receiving wireless messages. The United
States government has adopted the regulations of the International Radio
Congress which directs that commercial companies shall use wave lengths
between 300 and 600 or above 1600 meters. Amateurs may use wave
lengths less than 200 meters and no others, while the government reserves
the right to wave lengths of 600 to 1600 meters. See p. 459 for Continental
telegraph code.
418. Discharges in Rarefied Air.—Fig. 417 represents a glass tube 60 or
more centimeters long, attached to an air pump. Connect the ends of the
tube to the terminals of a static machine or of an induction coil, a-b. At first
no sparks will pass between a and f, because of the high resistance of the air
in the tube. Upon exhausting the air in the tube, however, the discharge
Page 436
begins to pass through it instead of between a and b. This shows that an
electrical discharge will pass more readily through a partial vacuum than
through air at ordinary pressure. As the air becomes more and more
exhausted, the character of the discharge changes. At first it is a faint spark,
gradually changing until it becomes a glow extending from one terminal to
the other and nearly filling the tube.
Geissler tubes are tubes like the above.
They are usually made of different kinds
of glass twisted into various shapes to
produce beautiful color effects. The
aurora borealis or northern light is
supposed to be electric discharges through
rarefied air at the height of from 60 to 100
miles above the earth's magnetic poles. Fig. 417.—An Aurora tube.
(See Fig. 418.)
Fig. 418.—Aurora Borealis.
419. Cathode Rays.—When the tube in Art. 420 is exhausted to a pressure
of 0.001 mm., or a little less than one millionth of an atmosphere, the
character of the discharge is entirely changed. The tube becomes filled with
a yellowish green phosphorescent light. This is produced by what are called
cathode rays striking the glass walls of the tube. These rays are called
cathode rays because they come from the cathode of the tube. They are
invisible and that they travel in straight lines is shown by the shadow
obtained by using a tube with a screen (Fig. 419).
electrical discharge will pass more readily through a partial vacuum than
through air at ordinary pressure. As the air becomes more and more
exhausted, the character of the discharge changes. At first it is a faint spark,
gradually changing until it becomes a glow extending from one terminal to
the other and nearly filling the tube.
Geissler tubes are tubes like the above.
They are usually made of different kinds
of glass twisted into various shapes to
produce beautiful color effects. The
aurora borealis or northern light is
supposed to be electric discharges through
rarefied air at the height of from 60 to 100
miles above the earth's magnetic poles. Fig. 417.—An Aurora tube.
(See Fig. 418.)
Fig. 418.—Aurora Borealis.
419. Cathode Rays.—When the tube in Art. 420 is exhausted to a pressure
of 0.001 mm., or a little less than one millionth of an atmosphere, the
character of the discharge is entirely changed. The tube becomes filled with
a yellowish green phosphorescent light. This is produced by what are called
cathode rays striking the glass walls of the tube. These rays are called
cathode rays because they come from the cathode of the tube. They are
invisible and that they travel in straight lines is shown by the shadow
obtained by using a tube with a screen (Fig. 419).
Page 437
420. "X" Rays.—In 1895, Professor Röntgen of
Wurtzburg, Germany, discovered that when the
cathode rays strike the walls of the tube or any
solid within it they excite a form of invisible
radiation. This radiation is called Röntgen rays, or
more commonly, "X" rays. Careful experiments
show that they travel in straight lines, and that they
can not be reflected or refracted as light waves are.
They pass through glass and opaque objects such
Fig. 419.—A cathode as flesh, cardboard, cloth, leather, etc., but not
ray tube. through metallic substances. The tube in Fig. 420
has a screen covered with crystals which become
luminous when struck by the cathode rays. On bringing a magnet near the
tube the luminous line is raised or lowered showing that the magnetic field
affects the stream of cathode rays, attracting it when in one position but
repelling it when in the reverse direction. The cathode rays which cause the
bright line possess a negative charge of electricity. They are now believed to
be electrons shot off from the surface of the cathode with speeds that may
reach 100,000 miles a second. "X" rays possess no electrical charge
whatever and cannot be deflected by a magnet. They produce the same
effect on a photograph plate as light does, only more slowly. Hence, they
can be used in taking "X" ray photographs. Certain crystals, like barium
platinum cyanide, fluoresce when struck by the "X" rays. The fluoroscope is
the name given to a light-tight box closed at one end by a cardboard
covered with these crystals (Fig. 421). On looking into the fluoroscope with
an opaque object such as the hand placed between the screen and the "X"
ray tube, a shadow of the bones of the hand can be seen upon the screen of
the fluoroscope. (See Fig. 422.)
Wurtzburg, Germany, discovered that when the
cathode rays strike the walls of the tube or any
solid within it they excite a form of invisible
radiation. This radiation is called Röntgen rays, or
more commonly, "X" rays. Careful experiments
show that they travel in straight lines, and that they
can not be reflected or refracted as light waves are.
They pass through glass and opaque objects such
Fig. 419.—A cathode as flesh, cardboard, cloth, leather, etc., but not
ray tube. through metallic substances. The tube in Fig. 420
has a screen covered with crystals which become
luminous when struck by the cathode rays. On bringing a magnet near the
tube the luminous line is raised or lowered showing that the magnetic field
affects the stream of cathode rays, attracting it when in one position but
repelling it when in the reverse direction. The cathode rays which cause the
bright line possess a negative charge of electricity. They are now believed to
be electrons shot off from the surface of the cathode with speeds that may
reach 100,000 miles a second. "X" rays possess no electrical charge
whatever and cannot be deflected by a magnet. They produce the same
effect on a photograph plate as light does, only more slowly. Hence, they
can be used in taking "X" ray photographs. Certain crystals, like barium
platinum cyanide, fluoresce when struck by the "X" rays. The fluoroscope is
the name given to a light-tight box closed at one end by a cardboard
covered with these crystals (Fig. 421). On looking into the fluoroscope with
an opaque object such as the hand placed between the screen and the "X"
ray tube, a shadow of the bones of the hand can be seen upon the screen of
the fluoroscope. (See Fig. 422.)
Page 438
Fig. 420.—The stream of cathode rays is
deflected by a magnet.
Fig. 421.—A fluoroscope.
Fig. 422.—A view of the "shadow" of a hand
as seen in a fluoroscope.
A special form of the tube is used. (See Fig. 423.) In this tube a platinum
disc is placed at the focus of the concave cathode. This concentrates the "X"
rays in one direction. It is now generally believed that "X" rays are waves in
the ether set up by the sudden stoppage of the cathode rays at the platinum
anode.
421. The Electromagnetic Theory of Light.—The study of electric waves
has shown that they are similar to light waves in many respects: (a) they
deflected by a magnet.
Fig. 421.—A fluoroscope.
Fig. 422.—A view of the "shadow" of a hand
as seen in a fluoroscope.
A special form of the tube is used. (See Fig. 423.) In this tube a platinum
disc is placed at the focus of the concave cathode. This concentrates the "X"
rays in one direction. It is now generally believed that "X" rays are waves in
the ether set up by the sudden stoppage of the cathode rays at the platinum
anode.
421. The Electromagnetic Theory of Light.—The study of electric waves
has shown that they are similar to light waves in many respects: (a) they
Page 439
have the same velocity; (b) they can be reflected
and refracted. The main difference is in their
length, light waves being very much shorter. In
1864 James Clerk Maxwell, an English
physicist, proposed the theory that ether waves
could be produced by electrical means and that
light waves are electromagnetic. In 1888 Hertz
proved by his experiments that ether waves
having the same velocity as light could be
produced in this way. It is now the general belief
Fig. 423.—An "X" ray
that light waves are ether waves produced by the
tube.
vibrations of the electrons within the atoms and
that they consist of electromagnetic waves in the
ether.
422. Radio-activity.—In 1896 Henri Becquerel of Paris discovered that
uranium and its compounds emit a form of radiation that produces an effect
upon a photographic plate that is similar to that resulting from the action of
"X" rays. These rays are often called Becquerel rays in honor of their
discoverer. The property of emitting such rays is called radio-activity, and
the substances producing them are called radio-active.
In 1898, Professor and Mme. Curie after an investigation of all the elements
found that thorium, one of the chief constituents of incandescent gas
mantles, together with its compounds, was also radio-active. This may be
shown by the following experiment:
Place a flattened gas mantle upon a photographic plate and leave in a light
tight-box for several days. Upon developing the plate in the usual way a
distinct image of the mantle will be found upon the plate.
423. Radium.—Mme. Curie discovered also that pitch-blende possessed
much greater radio-active power than either thorium or uranium. After
prolonged chemical experiments she obtained from several tons of the ore a
few milligrams of a substance more than a million times as active as
thorium or uranium. She called this new substance radium. Radium is
continually being decomposed, this decomposition being accompanied by
the production of a great deal of heat. It has been calculated that it will take
about 300 years for a particle of radium to be entirely decomposed and
and refracted. The main difference is in their
length, light waves being very much shorter. In
1864 James Clerk Maxwell, an English
physicist, proposed the theory that ether waves
could be produced by electrical means and that
light waves are electromagnetic. In 1888 Hertz
proved by his experiments that ether waves
having the same velocity as light could be
produced in this way. It is now the general belief
Fig. 423.—An "X" ray
that light waves are ether waves produced by the
tube.
vibrations of the electrons within the atoms and
that they consist of electromagnetic waves in the
ether.
422. Radio-activity.—In 1896 Henri Becquerel of Paris discovered that
uranium and its compounds emit a form of radiation that produces an effect
upon a photographic plate that is similar to that resulting from the action of
"X" rays. These rays are often called Becquerel rays in honor of their
discoverer. The property of emitting such rays is called radio-activity, and
the substances producing them are called radio-active.
In 1898, Professor and Mme. Curie after an investigation of all the elements
found that thorium, one of the chief constituents of incandescent gas
mantles, together with its compounds, was also radio-active. This may be
shown by the following experiment:
Place a flattened gas mantle upon a photographic plate and leave in a light
tight-box for several days. Upon developing the plate in the usual way a
distinct image of the mantle will be found upon the plate.
423. Radium.—Mme. Curie discovered also that pitch-blende possessed
much greater radio-active power than either thorium or uranium. After
prolonged chemical experiments she obtained from several tons of the ore a
few milligrams of a substance more than a million times as active as
thorium or uranium. She called this new substance radium. Radium is
continually being decomposed, this decomposition being accompanied by
the production of a great deal of heat. It has been calculated that it will take
about 300 years for a particle of radium to be entirely decomposed and
Page 440
separated into other substances. It is also believed that radium itself is the
product of the decomposition of uranium, atomic weight 238, and that the
final product of successive decompositions may be some inert metal, like
lead, atomic weight 207.
The radiation given off by radio-active substances consists of three kinds:
(A) Positively charged particles of helium called alpha rays: (B) negatively
charged particles called beta rays: (C) gamma rays.
The alpha rays have little penetrating power, a sheet of paper or a sheet of
aluminum 0.05 mm. stopping them. Upon losing their charges they become
atoms of helium. Their velocity is about 1/10 of that of light or 18,000 miles
a second. The spinthariscope is a little instrument devised by Sir Williams
Crookes in 1903 to show direct evidence that particles are continually being
shot off from radium. In this instrument (Fig. 424), a speck of radium R is
placed on the under side of a wire placed a few millimeters above a screen S
covered with crystals of zinc sulphide. Looking in the dark at this screen
through the lens L, a continuous succession of sparks is seen like a swarm
of fireflies on a warm summer night. Each flash is due to an alpha particle
striking the screen. The beta rays are supposed to be cathode rays or
electrons with velocities of from 40,000 to 170,000 miles a second. The
gamma rays are supposed to be "X" rays produced by the beta rays striking
solid objects.
424. The discovery of radio-activity has revolutionized
the ideas of the constitution of matter. Further, the results
of experiments upon radio-active materials reveals the
presence of immense quantities of sub-atomic energy. If
man ever discovers a means of utilizing this, he will enter
a storehouse of energy of far greater extent and value than
any of which he has as yet made use. A consideration of
this unexplored region gives zest to the work of those who
day by day are striving to understand and control forces of
Fig. 424.—A nature.
spinthariscop
e.
Important Topics
product of the decomposition of uranium, atomic weight 238, and that the
final product of successive decompositions may be some inert metal, like
lead, atomic weight 207.
The radiation given off by radio-active substances consists of three kinds:
(A) Positively charged particles of helium called alpha rays: (B) negatively
charged particles called beta rays: (C) gamma rays.
The alpha rays have little penetrating power, a sheet of paper or a sheet of
aluminum 0.05 mm. stopping them. Upon losing their charges they become
atoms of helium. Their velocity is about 1/10 of that of light or 18,000 miles
a second. The spinthariscope is a little instrument devised by Sir Williams
Crookes in 1903 to show direct evidence that particles are continually being
shot off from radium. In this instrument (Fig. 424), a speck of radium R is
placed on the under side of a wire placed a few millimeters above a screen S
covered with crystals of zinc sulphide. Looking in the dark at this screen
through the lens L, a continuous succession of sparks is seen like a swarm
of fireflies on a warm summer night. Each flash is due to an alpha particle
striking the screen. The beta rays are supposed to be cathode rays or
electrons with velocities of from 40,000 to 170,000 miles a second. The
gamma rays are supposed to be "X" rays produced by the beta rays striking
solid objects.
424. The discovery of radio-activity has revolutionized
the ideas of the constitution of matter. Further, the results
of experiments upon radio-active materials reveals the
presence of immense quantities of sub-atomic energy. If
man ever discovers a means of utilizing this, he will enter
a storehouse of energy of far greater extent and value than
any of which he has as yet made use. A consideration of
this unexplored region gives zest to the work of those who
day by day are striving to understand and control forces of
Fig. 424.—A nature.
spinthariscop
e.
Important Topics
Page 441
1. Oscillatory nature of discharge of Leyden jar. Proofs.
2. Wireless telegraphy and telephony.
3. Electrical discharges in rarefied gases.
4. Cathode and "X" rays.
5. Electromagnetic theory of light.
6. Radio activity and radium.
CONTINENTAL TELEGRAPH CODE
A.-J.---S...
B-...K-.-T-
C-.-.L.-..U..-
D-..M--V...-
E.N-.W.--
F..-.O---X-..-
G - - . P .- - . Y - . - -
H....Q--.-Z--..
I..R.-.
Period Interrogation Exclamation
........--..--..--
1.----2..---3...--
2. Wireless telegraphy and telephony.
3. Electrical discharges in rarefied gases.
4. Cathode and "X" rays.
5. Electromagnetic theory of light.
6. Radio activity and radium.
CONTINENTAL TELEGRAPH CODE
A.-J.---S...
B-...K-.-T-
C-.-.L.-..U..-
D-..M--V...-
E.N-.W.--
F..-.O---X-..-
G - - . P .- - . Y - . - -
H....Q--.-Z--..
I..R.-.
Period Interrogation Exclamation
........--..--..--
1.----2..---3...--
Page 442
4....-5.....6-....7--...
8---..9----.0-----
8---..9----.0-----
Page 443
CHAPTER XVIII
WIRELESS TELEPHONY AND ALTERNATING CURRENTS
The developments in wireless communication have been so rapid during
recent years that a more extended account, than that given in Art. 417 of the
apparatus and methods used at the present time, seems desirable. The study
of Alternating Currents is also included with the idea that it will make the
text more complete and of wider usefulness.
Wireless Telephony
425. The Wireless Telephone.—One of the most important developments
in wireless communication in recent years has been in wireless telephony.
We realize its possibilities, when we hear of the achievements of talking
across an ocean or between airplanes and the ground.
The wireless telephone can be best understood by comparing it with the
common telephone. When the latter is in use, a direct current flows
continually through the instrument. (See Arts. 312-316.) When a person
speaks into the transmitter, the sound waves of the voice cause the
diaphragm to vibrate, this action causes rapid changes in the resistance of
the transmitter, which in turn causes the direct current to fluctuate just in
step with the pulses of the voice waves. This fluctuating direct current
passes through the primary of an induction coil, producing in the secondary
an intensified alternating current. This passes over the line wires to the
receiver where it produces variations in the magnetic field affecting the
receiver diaphragm, causing the latter to reproduce the voice of the person
speaking in the transmitter. Now to make the comparison clear, two facts
must be noted with regard to the wire telephone: first, there must be an
action in the transmitter which causes variations in a current through the
instrument; second, this fluctuating current produces a more intense
alternating current which flows over the line and affects the receiver
diaphragm, producing there sound vibrations of greater intensity than those
used at the transmitter. This added energy comes from the current flowing
WIRELESS TELEPHONY AND ALTERNATING CURRENTS
The developments in wireless communication have been so rapid during
recent years that a more extended account, than that given in Art. 417 of the
apparatus and methods used at the present time, seems desirable. The study
of Alternating Currents is also included with the idea that it will make the
text more complete and of wider usefulness.
Wireless Telephony
425. The Wireless Telephone.—One of the most important developments
in wireless communication in recent years has been in wireless telephony.
We realize its possibilities, when we hear of the achievements of talking
across an ocean or between airplanes and the ground.
The wireless telephone can be best understood by comparing it with the
common telephone. When the latter is in use, a direct current flows
continually through the instrument. (See Arts. 312-316.) When a person
speaks into the transmitter, the sound waves of the voice cause the
diaphragm to vibrate, this action causes rapid changes in the resistance of
the transmitter, which in turn causes the direct current to fluctuate just in
step with the pulses of the voice waves. This fluctuating direct current
passes through the primary of an induction coil, producing in the secondary
an intensified alternating current. This passes over the line wires to the
receiver where it produces variations in the magnetic field affecting the
receiver diaphragm, causing the latter to reproduce the voice of the person
speaking in the transmitter. Now to make the comparison clear, two facts
must be noted with regard to the wire telephone: first, there must be an
action in the transmitter which causes variations in a current through the
instrument; second, this fluctuating current produces a more intense
alternating current which flows over the line and affects the receiver
diaphragm, producing there sound vibrations of greater intensity than those
used at the transmitter. This added energy comes from the current flowing
Page 444
through the transmitter. The case is analogous to that of an electric bell. The
armature of the bell vibrates with greater energy than is required to push the
button, the extra energy being derived from the battery.
426. The Action of the Wireless Telephone.—In the wireless telephone we
have a continuous stream of electric waves of high frequency. (See Fig.
425A.) This stream of electric waves corresponds to the current that flows
through the transmitter in the wire telephone. These waves are of such high
frequency that even though we had a receiver diaphragm vibrating in step
with the waves, we could not hear the sound because the human ear cannot
hear a sound which consists of more than about 40,000 vibrations per
second. The sound waves act upon this stream of waves very much, as in
the wire telephone, the transmitter acts to modify the line current. The
impulses caused by the voice are much slower than the electric waves first
mentioned and these slower impulses are reproduced in the receiver. Not
only are these slower impulses reproduced but they are amplified, that is,
produced with greater energy than the impulses impressed on the stream of
waves. Fig. 425A represents as nearly as is possible in a diagram the
continuous stream of electric waves. Fig. 426B, represents the impulses
produced by the sound alone, and Fig. 426C, shows how these voice
impulses are impressed on the stream of waves.
armature of the bell vibrates with greater energy than is required to push the
button, the extra energy being derived from the battery.
426. The Action of the Wireless Telephone.—In the wireless telephone we
have a continuous stream of electric waves of high frequency. (See Fig.
425A.) This stream of electric waves corresponds to the current that flows
through the transmitter in the wire telephone. These waves are of such high
frequency that even though we had a receiver diaphragm vibrating in step
with the waves, we could not hear the sound because the human ear cannot
hear a sound which consists of more than about 40,000 vibrations per
second. The sound waves act upon this stream of waves very much, as in
the wire telephone, the transmitter acts to modify the line current. The
impulses caused by the voice are much slower than the electric waves first
mentioned and these slower impulses are reproduced in the receiver. Not
only are these slower impulses reproduced but they are amplified, that is,
produced with greater energy than the impulses impressed on the stream of
waves. Fig. 425A represents as nearly as is possible in a diagram the
continuous stream of electric waves. Fig. 426B, represents the impulses
produced by the sound alone, and Fig. 426C, shows how these voice
impulses are impressed on the stream of waves.
Page 445
Fig. 425.—A, unmodified high frequency
waves; B, waves of voice frequency; C, high
frequency waves modified by waves of voice
frequency.
waves; B, waves of voice frequency; C, high
frequency waves modified by waves of voice
frequency.
Page 446
Fig. 426.—Vacuum tube, transmitting type.
(Western Electric Co.)
Fig. 427.—Vacuum tube, receiving type.
(Western Electric Co.)
Fig. 428.—Diagram of wireless telephone
transmitting set.
427. The Vacuum Tube or Audion.—The device by which all of this is
accomplished is the vacuum tube. (See Fig. 426.) This tube contains three
(Western Electric Co.)
Fig. 427.—Vacuum tube, receiving type.
(Western Electric Co.)
Fig. 428.—Diagram of wireless telephone
transmitting set.
427. The Vacuum Tube or Audion.—The device by which all of this is
accomplished is the vacuum tube. (See Fig. 426.) This tube contains three
Page 447
electrodes. First, a filament (F, in Fig. 428) which is heated by a current
from a battery (B1, Fig. 428) and because it is heated, sends out a stream of
electrons. Second, the plate which forms the anode of the circuit from
battery, B2. This plate receives the electrons which are thrown off by the
heated filament, hence a current flows through the circuit of B2; the
discharge through the tube depending on the e.m.f. between the filament
and the plate. Third, a grid is placed between the filament and the plate and
is connected to the secondary of the induction coil, the primary of which is
connected to the transmitter. When the transmitter diaphragm is vibrating,
the e.m.f. induced in the secondary of the induction coil causes a variation
in the potential of the grid. This means a variation in the electric field
between the filament and the plate. (See Fig. 428.) The changing electric
field causes a variation in the discharge of electrons through the tube; the
variation corresponds to the vibrations of the transmitter diaphragm. This
produces a surging current of the frequency of the sound waves in the
primary of the transformer (T, Fig. 428). The secondary of this transformer
is connected to the antennæ (A) and the earth (E). By means of the
transformer, rapid surgings are set up in the antennæ and these surgings
produce a continuous stream of electromagnetic waves which goes out in
space. (Like Fig. 426C.) These electromagnetic waves produce oscillations
in the antennæ of a receiving station. The antennæ transmit the impulses to
a tube (Fig. 427) which acts as a detector, and makes possible the
reproduction of the sound by an ordinary telephone receiver.
from a battery (B1, Fig. 428) and because it is heated, sends out a stream of
electrons. Second, the plate which forms the anode of the circuit from
battery, B2. This plate receives the electrons which are thrown off by the
heated filament, hence a current flows through the circuit of B2; the
discharge through the tube depending on the e.m.f. between the filament
and the plate. Third, a grid is placed between the filament and the plate and
is connected to the secondary of the induction coil, the primary of which is
connected to the transmitter. When the transmitter diaphragm is vibrating,
the e.m.f. induced in the secondary of the induction coil causes a variation
in the potential of the grid. This means a variation in the electric field
between the filament and the plate. (See Fig. 428.) The changing electric
field causes a variation in the discharge of electrons through the tube; the
variation corresponds to the vibrations of the transmitter diaphragm. This
produces a surging current of the frequency of the sound waves in the
primary of the transformer (T, Fig. 428). The secondary of this transformer
is connected to the antennæ (A) and the earth (E). By means of the
transformer, rapid surgings are set up in the antennæ and these surgings
produce a continuous stream of electromagnetic waves which goes out in
space. (Like Fig. 426C.) These electromagnetic waves produce oscillations
in the antennæ of a receiving station. The antennæ transmit the impulses to
a tube (Fig. 427) which acts as a detector, and makes possible the
reproduction of the sound by an ordinary telephone receiver.
Page 448
Fig. 429.—View of wireless telephone set.
The vacuum tube in the transmitting circuit also amplifies the impulses, that
is, the energy of the waves given out is greater than that of the impulses
which produce them, the additional energy being derived from the battery
sending current through the plate and filament. In operation, the filament
and the plate are connected to a battery with a condenser (VC) and an
inductance coil (I) in the circuit, as shown in Fig. 428. Photograph of a
complete modern wireless telephone set is shown in Fig. 429.
Alternating Currents
428. Alternating currents are of interest to us because of their general
commercial use. To understand the reason for the extensive application of
alternating currents it is necessary to learn the fundamental principles which
pertain to them. The production of such currents has already been explained
in Arts. 300-304. It should be remembered that the current developed in the
armature of a dynamo is alternating. A dynamo may deliver a direct or an
alternating current, depending on the method of collecting the current from
the armature. If a commutator is used, the machine delivers direct current, if
slip rings are employed, an alternating current is delivered.
The vacuum tube in the transmitting circuit also amplifies the impulses, that
is, the energy of the waves given out is greater than that of the impulses
which produce them, the additional energy being derived from the battery
sending current through the plate and filament. In operation, the filament
and the plate are connected to a battery with a condenser (VC) and an
inductance coil (I) in the circuit, as shown in Fig. 428. Photograph of a
complete modern wireless telephone set is shown in Fig. 429.
Alternating Currents
428. Alternating currents are of interest to us because of their general
commercial use. To understand the reason for the extensive application of
alternating currents it is necessary to learn the fundamental principles which
pertain to them. The production of such currents has already been explained
in Arts. 300-304. It should be remembered that the current developed in the
armature of a dynamo is alternating. A dynamo may deliver a direct or an
alternating current, depending on the method of collecting the current from
the armature. If a commutator is used, the machine delivers direct current, if
slip rings are employed, an alternating current is delivered.
Page 449
429. The Magnetic Field of an Alternating Current.—The magnetic field
of a direct current has been considered in Arts. 255-256. It has been shown
to be arranged in circles about the conductor, according to the Right Hand
Rule. (See Figs. 229 and 230.) These facts will help one to understand the
following experiment:
If a number of magnetic compasses be arranged in a circle about a straight
vertical wire carrying a direct current, the compass needles will point out a
circle about the wire. (See Fig. 430, A.) If now the current be reversed the
compass needles will reverse themselves and point in a direction just
opposite to that taken at first. (See Fig. 430, B.) This will be clear if you
imagine yourself walking around the wire in the direction the compass
needles pointed at first, and then walking around the wire in the reverse
direction. This illustrates what happens in the field of an alternating current.
The field reverses each time the current reverses.
The magnetic field of an alternating current not only rapidly reverses itself,
but also continually changes in intensity. At the instant when the current
reverses, the force of the magnetic field is zero since the current at that
instant is zero. As the current begins flowing and increases to its maximum
intensity, the magnetic field appears and increases in intensity; and as the
current decreases to zero, the magnetic field changes in a similar manner.
The field as it grows in strength extends farther and farther from the wire,
as it decreases in strength it contracts or draws closer to the wire. Thus the
magnetic field may be said to expand and contract. We may picture the lines
of force as continually moving. In a typical a.-c. circuit, the complete series
of changes takes place in a small fraction of a second, and is repeated many
times over in a second. Contrast this with the magnetic field of a constant
direct current. Here the magnetic field has the same direction as long as the
current flows and does not change in strength. This comparison is important
because most of the differences between direct and alternating currents
depend on differences in the action of their magnetic fields.
of a direct current has been considered in Arts. 255-256. It has been shown
to be arranged in circles about the conductor, according to the Right Hand
Rule. (See Figs. 229 and 230.) These facts will help one to understand the
following experiment:
If a number of magnetic compasses be arranged in a circle about a straight
vertical wire carrying a direct current, the compass needles will point out a
circle about the wire. (See Fig. 430, A.) If now the current be reversed the
compass needles will reverse themselves and point in a direction just
opposite to that taken at first. (See Fig. 430, B.) This will be clear if you
imagine yourself walking around the wire in the direction the compass
needles pointed at first, and then walking around the wire in the reverse
direction. This illustrates what happens in the field of an alternating current.
The field reverses each time the current reverses.
The magnetic field of an alternating current not only rapidly reverses itself,
but also continually changes in intensity. At the instant when the current
reverses, the force of the magnetic field is zero since the current at that
instant is zero. As the current begins flowing and increases to its maximum
intensity, the magnetic field appears and increases in intensity; and as the
current decreases to zero, the magnetic field changes in a similar manner.
The field as it grows in strength extends farther and farther from the wire,
as it decreases in strength it contracts or draws closer to the wire. Thus the
magnetic field may be said to expand and contract. We may picture the lines
of force as continually moving. In a typical a.-c. circuit, the complete series
of changes takes place in a small fraction of a second, and is repeated many
times over in a second. Contrast this with the magnetic field of a constant
direct current. Here the magnetic field has the same direction as long as the
current flows and does not change in strength. This comparison is important
because most of the differences between direct and alternating currents
depend on differences in the action of their magnetic fields.
Page 450
Fig. 430.—Arrangement of compasses about a
wire carrying an alternating current.
430. Transformers.—The transformer has been described in Arts. 309-310.
The principle of the transformer may be illustrated by the following
experiment:
A coil having several hundred turns of No. 18 d.c.c. copper wire is placed
over one arm of a "U" shaped iron core (see Fig. 431) and then connected to
a 110 volt a.-c. lighting circuit. Another coil (S) having about 50 turns of
No. 22 d.c.c. copper wire is connected to an electric bell or buzzer, or a low
voltage electric light bulb. When the small coil is held over the other arm of
the "U" shaped iron core, the bell rings or the bulb glows. It is evident that
the electromotive force developed in the small coil (S) is due to the
alternating magnetic field surging back and forth through the iron core. In
Fig. 431 the core is "open" since the magnetic field must pass through the
air from one end of the core to the other. A typical transformer has a closed
core to provide a closed magnetic circuit. To secure this, take a suitable bar
of iron and lay across the end of the "U" shaped core, and notice any change
in the induced current produced in the small coil, due to increased
movement of magnetism through the closed iron core.
wire carrying an alternating current.
430. Transformers.—The transformer has been described in Arts. 309-310.
The principle of the transformer may be illustrated by the following
experiment:
A coil having several hundred turns of No. 18 d.c.c. copper wire is placed
over one arm of a "U" shaped iron core (see Fig. 431) and then connected to
a 110 volt a.-c. lighting circuit. Another coil (S) having about 50 turns of
No. 22 d.c.c. copper wire is connected to an electric bell or buzzer, or a low
voltage electric light bulb. When the small coil is held over the other arm of
the "U" shaped iron core, the bell rings or the bulb glows. It is evident that
the electromotive force developed in the small coil (S) is due to the
alternating magnetic field surging back and forth through the iron core. In
Fig. 431 the core is "open" since the magnetic field must pass through the
air from one end of the core to the other. A typical transformer has a closed
core to provide a closed magnetic circuit. To secure this, take a suitable bar
of iron and lay across the end of the "U" shaped core, and notice any change
in the induced current produced in the small coil, due to increased
movement of magnetism through the closed iron core.
Page 451
Fig. 431.—Diagram of a transformer.
This experiment illustrates the construction and action of a transformer. In a
commercial transformer, the two windings are on a closed magnetic circuit.
(See Figs. 304 and 305, p. 346.) To keep the coils insulated, the transformer
is placed in an iron "housing" and covered with oil. These "housings," or
transformer cases are generally attached to poles near buildings in which
alternating current is used.
431. Voltage Relation in a Transformer.—In the experiment described
above, a bell was rung by an induced current produced in the secondary
coil. The induced e.m.f. was less than the voltage of the primary coil partly
because there was some magnetic leakage, but mainly because there were
fewer turns of wire on the secondary. In a commercial transformer the
magnetic leakage is practically zero. In such a case, the ratio of the number
of turns on the primary coil to the number on the secondary equals the ratio
of the e.m.f. induced in the primary to the e.m.f. induced in the secondary.
Suppose, for example, we wish to make a bell ringing transformer to use on
a 110 volt lighting circuit, 10 volts being required for the bell; the
secondary will then need one-eleventh of the number of turns of the
primary. So that if 550 turns are on the primary, then 50 turns will be
needed for the secondary. This will be a "step-down" transformer. On the
other hand, suppose we wish to "step-up" the voltage as is done in a certain
power station where the voltage of the generators is 6000 volts, the voltage
This experiment illustrates the construction and action of a transformer. In a
commercial transformer, the two windings are on a closed magnetic circuit.
(See Figs. 304 and 305, p. 346.) To keep the coils insulated, the transformer
is placed in an iron "housing" and covered with oil. These "housings," or
transformer cases are generally attached to poles near buildings in which
alternating current is used.
431. Voltage Relation in a Transformer.—In the experiment described
above, a bell was rung by an induced current produced in the secondary
coil. The induced e.m.f. was less than the voltage of the primary coil partly
because there was some magnetic leakage, but mainly because there were
fewer turns of wire on the secondary. In a commercial transformer the
magnetic leakage is practically zero. In such a case, the ratio of the number
of turns on the primary coil to the number on the secondary equals the ratio
of the e.m.f. induced in the primary to the e.m.f. induced in the secondary.
Suppose, for example, we wish to make a bell ringing transformer to use on
a 110 volt lighting circuit, 10 volts being required for the bell; the
secondary will then need one-eleventh of the number of turns of the
primary. So that if 550 turns are on the primary, then 50 turns will be
needed for the secondary. This will be a "step-down" transformer. On the
other hand, suppose we wish to "step-up" the voltage as is done in a certain
power station where the voltage of the generators is 6000 volts, the voltage
Page 452
being stepped up to 44,000 by means of large transformers. This means that
the secondary coils have approximately 7-1/3 times as many turns as the
primary.
432. Power Loss in a Transformer.—When the voltage is "stepped up" in
a transformer, do we gain power? To answer this question we must
remember that electric power does not depend on voltage alone but on the
product of e.m.f. and current intensity. (See Art. 291.) By tests with a.-c.
voltmeters and ammeters, we find that when the secondary e.m.f. is greater
than the primary e.m.f., the secondary current intensity is less than that in
the primary. It is also found that the power developed is less than the power
received by the transformer, i.e., the "output" is less than the "input" as we
would expect from the law of machines. The power loss is mainly due to
the work required to reverse the magnetism, that is, to continually reverse
the position of the iron molecules. (See Art. 205.) The energy lost in this
manner is known as "core loss" since it occurs in the iron core. The lost
energy appears as heat. So much heat is developed in large transformers
that special means of cooling are provided. In order to make the heat
developed as small as possible, the cores are "laminated" (see Fig. 305, p.
346), that is, built up of thin sheets of iron, because if the iron cores were
solid, the changing magnetic fields would induce electric currents in the
iron cores, which would produce an excessive amount of heat with a
correspondingly large power loss.
Fig. 432.—Diagram of "bell-ringing"
transformer.
the secondary coils have approximately 7-1/3 times as many turns as the
primary.
432. Power Loss in a Transformer.—When the voltage is "stepped up" in
a transformer, do we gain power? To answer this question we must
remember that electric power does not depend on voltage alone but on the
product of e.m.f. and current intensity. (See Art. 291.) By tests with a.-c.
voltmeters and ammeters, we find that when the secondary e.m.f. is greater
than the primary e.m.f., the secondary current intensity is less than that in
the primary. It is also found that the power developed is less than the power
received by the transformer, i.e., the "output" is less than the "input" as we
would expect from the law of machines. The power loss is mainly due to
the work required to reverse the magnetism, that is, to continually reverse
the position of the iron molecules. (See Art. 205.) The energy lost in this
manner is known as "core loss" since it occurs in the iron core. The lost
energy appears as heat. So much heat is developed in large transformers
that special means of cooling are provided. In order to make the heat
developed as small as possible, the cores are "laminated" (see Fig. 305, p.
346), that is, built up of thin sheets of iron, because if the iron cores were
solid, the changing magnetic fields would induce electric currents in the
iron cores, which would produce an excessive amount of heat with a
correspondingly large power loss.
Fig. 432.—Diagram of "bell-ringing"
transformer.
Page 453
433. Choke Coils and Inductance.—If we refer to Fig. 432 we see that the
primary winding of the bell ringing transformer is connected across the line.
This winding forms a closed circuit whether the bell is ringing or not. The
resistance of this winding is small. Let us assume it to be one ohm. With a
one ohm resistance connected across a 110 volt line we might expect a
current of 110 amperes. This is certainly what we should get if we were to
connect a one ohm resistance across a line having 110 volts direct. The
primary would form a short circuit if the current were direct. But the fact is
that practically no current flows through the primary winding when the bell
is not ringing. Herein lies one of the important differences between
alternating and direct currents. With an alternating current the primary
winding of our transformer acts as a choke coil and "chokes" down the
current almost to zero. Let us see how this is done.
Let Fig. 433 represent a choke
coil. Since alternating current is
used, the magnetic field is
continually changing. Each turn
of wire has its own magnetic
field. The lines of force of turn
number 1 expand and contract
and as they do so they move
across turns 2, 3 and so on. In
Fig. 433.—A circuit containing a like manner the lines of force
choke coil. from each turn of wire move
across the other turns. In other
words the coil is cutting its own lines of force. Now whenever an electric
conductor cuts magnetic lines of force an electromotive force is induced in
the conductor. There is then an e.m.f. induced in the coil by its own
magnetic field. This induced e.m.f. on the whole opposes the applied e.m.f.;
in the primary of our bell ringing transformer the induced e.m.f. opposes the
e.m.f. of the line to such an extent as to reduce the current almost to zero.
Inductance is the action of an alternating current in inducing an opposing
e.m.f. in the coil in which the current is flowing. Since this opposing e.m.f.
is induced in the coil by its own magnetic field this action is also called self-
induction. In a transformer the action of the field of the primary upon the
secondary is mutual induction; while the action of the field of the primary
in choking the current in the primary itself is self-induction or inductance. A
primary winding of the bell ringing transformer is connected across the line.
This winding forms a closed circuit whether the bell is ringing or not. The
resistance of this winding is small. Let us assume it to be one ohm. With a
one ohm resistance connected across a 110 volt line we might expect a
current of 110 amperes. This is certainly what we should get if we were to
connect a one ohm resistance across a line having 110 volts direct. The
primary would form a short circuit if the current were direct. But the fact is
that practically no current flows through the primary winding when the bell
is not ringing. Herein lies one of the important differences between
alternating and direct currents. With an alternating current the primary
winding of our transformer acts as a choke coil and "chokes" down the
current almost to zero. Let us see how this is done.
Let Fig. 433 represent a choke
coil. Since alternating current is
used, the magnetic field is
continually changing. Each turn
of wire has its own magnetic
field. The lines of force of turn
number 1 expand and contract
and as they do so they move
across turns 2, 3 and so on. In
Fig. 433.—A circuit containing a like manner the lines of force
choke coil. from each turn of wire move
across the other turns. In other
words the coil is cutting its own lines of force. Now whenever an electric
conductor cuts magnetic lines of force an electromotive force is induced in
the conductor. There is then an e.m.f. induced in the coil by its own
magnetic field. This induced e.m.f. on the whole opposes the applied e.m.f.;
in the primary of our bell ringing transformer the induced e.m.f. opposes the
e.m.f. of the line to such an extent as to reduce the current almost to zero.
Inductance is the action of an alternating current in inducing an opposing
e.m.f. in the coil in which the current is flowing. Since this opposing e.m.f.
is induced in the coil by its own magnetic field this action is also called self-
induction. In a transformer the action of the field of the primary upon the
secondary is mutual induction; while the action of the field of the primary
in choking the current in the primary itself is self-induction or inductance. A
Page 454
coil having a single winding and used to introduce inductance in a circuit is
called a choke coil. A choke coil inserted in a lamp circuit in series with the
lamps dims the lamps because it reduces the intensity of the current.
Fig. 434.—Diagram showing graphically an
alternating current with a "lag" of 30° behind
its electromotive force.
Self-induction causes the current to lag, that is, the current does not quite
reach its maximum at the instant the voltage reaches its maximum. Fig. 434
shows graphically an e.m.f. and a lagging current. In this figure the
maximum current is shown following the maximum voltage at an interval
of 30 degrees. In other words the armature in a two-pole field must turn 30
degrees from the position of maximum voltage before the current in the
coil, where the self-induction occurs, reaches its maximum.
434. Reactance and Impedance.—A choke coil has resistance as well as
inductance. Its resistance can be found by the voltmeter-ammeter method,
using a direct current. (See Art. 278.) Let us take for example the primary
winding of a bell ringing transformer. Using a direct current and testing the
coil with a voltmeter and ammeter we find its resistance to be, let us say,
one ohm. If we connect the same coil across a 110 volt a.-c. line we find the
current to be very small, say 0.05 ampere. The coil now has resistance and
reactance. Reactance is the effect of self-induction in hindering the flow of
current. It is measured in ohms. The combined effect of resistance and
reactance is called impedance. In the example above, the coil has 110
(volts)/0.05 (ampere) = 2200 ohms of impedance. In applying Ohm's law to
an alternating current circuit, impedance must be substituted for resistance.
called a choke coil. A choke coil inserted in a lamp circuit in series with the
lamps dims the lamps because it reduces the intensity of the current.
Fig. 434.—Diagram showing graphically an
alternating current with a "lag" of 30° behind
its electromotive force.
Self-induction causes the current to lag, that is, the current does not quite
reach its maximum at the instant the voltage reaches its maximum. Fig. 434
shows graphically an e.m.f. and a lagging current. In this figure the
maximum current is shown following the maximum voltage at an interval
of 30 degrees. In other words the armature in a two-pole field must turn 30
degrees from the position of maximum voltage before the current in the
coil, where the self-induction occurs, reaches its maximum.
434. Reactance and Impedance.—A choke coil has resistance as well as
inductance. Its resistance can be found by the voltmeter-ammeter method,
using a direct current. (See Art. 278.) Let us take for example the primary
winding of a bell ringing transformer. Using a direct current and testing the
coil with a voltmeter and ammeter we find its resistance to be, let us say,
one ohm. If we connect the same coil across a 110 volt a.-c. line we find the
current to be very small, say 0.05 ampere. The coil now has resistance and
reactance. Reactance is the effect of self-induction in hindering the flow of
current. It is measured in ohms. The combined effect of resistance and
reactance is called impedance. In the example above, the coil has 110
(volts)/0.05 (ampere) = 2200 ohms of impedance. In applying Ohm's law to
an alternating current circuit, impedance must be substituted for resistance.
Page 455
Ohm's law as applied to an a-c. circuit should be stated: "Current intensity
equals e.m.f. divided by impedance", or I = E/Z. (Z = impedance.)
Fig. 435.—The relation between resistance,
reactance and impedance.
Impedance, however, does not equal the sum of resistance and reactance.
The relation between these three quantities is similar to that between the
three sides of a right triangle, in which the impedance represents the
hypotenuse, and the resistance and reactance the other two sides. See Fig.
435 which indicates that Resistance2 + Reactance2 = Impedance2, or (R2 +
X2 = Z2). (X = reactance.) To illustrate this relation; suppose the primary of
a transformer has 10 ohms impedance and 8 ohms resistance, then the
reactance equals 102 - 82 = 62, or the reactance is 6 ohms.
Exercises
1. Find the reactance of a choke coil having a resistance of 10 ohms, when
its impedance is 50 ohms. How great a current flows through this coil if the
terminal voltage is 110 volts?
2. When the bell is ringing, the primary of a bell ringing transformer has an
appreciable current. Suppose this current is 0.2 ampere. What is the
impedance if the voltage of the line is 115 volts? What is the reactance if
the resistance is 1 ohm?
3. The primary of a large transformer has a terminal voltage of 6000 volts
and a current of 600 amperes. What is the impedance? If the resistance is 6
ohms, what is the reactance?
equals e.m.f. divided by impedance", or I = E/Z. (Z = impedance.)
Fig. 435.—The relation between resistance,
reactance and impedance.
Impedance, however, does not equal the sum of resistance and reactance.
The relation between these three quantities is similar to that between the
three sides of a right triangle, in which the impedance represents the
hypotenuse, and the resistance and reactance the other two sides. See Fig.
435 which indicates that Resistance2 + Reactance2 = Impedance2, or (R2 +
X2 = Z2). (X = reactance.) To illustrate this relation; suppose the primary of
a transformer has 10 ohms impedance and 8 ohms resistance, then the
reactance equals 102 - 82 = 62, or the reactance is 6 ohms.
Exercises
1. Find the reactance of a choke coil having a resistance of 10 ohms, when
its impedance is 50 ohms. How great a current flows through this coil if the
terminal voltage is 110 volts?
2. When the bell is ringing, the primary of a bell ringing transformer has an
appreciable current. Suppose this current is 0.2 ampere. What is the
impedance if the voltage of the line is 115 volts? What is the reactance if
the resistance is 1 ohm?
3. The primary of a large transformer has a terminal voltage of 6000 volts
and a current of 600 amperes. What is the impedance? If the resistance is 6
ohms, what is the reactance?
Page 456
Fig. 436.—A telephone set showing a
condenser used in the circuit of the "ringer."
435.—The electric condenser (see Art. 231) is a very useful device in a.-c.
circuits; e.g., in telephone sets used in cities, a condenser is used in the
ringing circuit, as shown in Fig. 436. Alternating current is required to ring
such a bell and a condenser permits an a.-c. current to act through it,
although it entirely prevents the flow of a direct current. This peculiar
action will now be explained.
436. The action of a condenser in an alternating current circuit may be
illustrated by the following experiment. Connect twelve, 1 m.f. (microfarad)
condensers, in parallel, and then attach them to a 110 volt a.-c. line so that
an incandescent lamp is in circuit as shown in Fig. 437. The lamp will be
found to glow brightly, although there is no electrical connection between
the two sets of condenser plates. If the same arrangement is connected to a
110 volt direct current circuit, the lamp does not glow because it is really an
open circuit. The lamp glows on an a.-c. circuit because, although no
electricity flows through the condenser, it does flow into and out of the
condenser, surging back and forth through the lamp with sufficient intensity
to cause it to glow brightly. When the a.-c. current moves one way in the
circuit, one set of plates of the condensers becomes charged positively, the
other, negatively. When the a.-c. current reverses, the charges on the
condenser plates reverse. In the ordinary lighting circuit 120 reversals take
place each second, so that electricity rapidly flows into and out of the
condensers. On removing one condenser after another from the circuit, the
lamp is found to glow less and less, till when but one condenser is left, no
condenser used in the circuit of the "ringer."
435.—The electric condenser (see Art. 231) is a very useful device in a.-c.
circuits; e.g., in telephone sets used in cities, a condenser is used in the
ringing circuit, as shown in Fig. 436. Alternating current is required to ring
such a bell and a condenser permits an a.-c. current to act through it,
although it entirely prevents the flow of a direct current. This peculiar
action will now be explained.
436. The action of a condenser in an alternating current circuit may be
illustrated by the following experiment. Connect twelve, 1 m.f. (microfarad)
condensers, in parallel, and then attach them to a 110 volt a.-c. line so that
an incandescent lamp is in circuit as shown in Fig. 437. The lamp will be
found to glow brightly, although there is no electrical connection between
the two sets of condenser plates. If the same arrangement is connected to a
110 volt direct current circuit, the lamp does not glow because it is really an
open circuit. The lamp glows on an a.-c. circuit because, although no
electricity flows through the condenser, it does flow into and out of the
condenser, surging back and forth through the lamp with sufficient intensity
to cause it to glow brightly. When the a.-c. current moves one way in the
circuit, one set of plates of the condensers becomes charged positively, the
other, negatively. When the a.-c. current reverses, the charges on the
condenser plates reverse. In the ordinary lighting circuit 120 reversals take
place each second, so that electricity rapidly flows into and out of the
condensers. On removing one condenser after another from the circuit, the
lamp is found to glow less and less, till when but one condenser is left, no
Page 457
glowing is observed, since one small condenser does not have sufficient
capacity.
Fig. 437.—Twelve condensers in circuit with
an incandescent lamp.
The unit of capacity is the Farad. Capacity is defined as the quantity of
electricity per second that flows into a condenser when the voltage at the
terminals changes at the rate of one volt per second. If a change of one volt
per second causes one coulomb to flow per second, that is, a current of one
ampere, the capacity is one farad. The condensers used in the above
experiment have a capacity of one microfarad, or one millionth of a farad.
A condenser, on account of its capacity, causes an a.-c. current to lead the
voltage, that is the current reaches its maximum value before the voltage
does. In this respect a condenser has an effect opposite to that of the self-
induction of a choke coil (the latter causing the current to "lag"). (See Fig.
435.)
437. Transmission of Electric Power.—A field of peculiar usefulness for
a.-c. currents is in the economical transmission of electric power. This fact
is due to the following reasons: (a) The loss of electrical power in a
transmission line is due to the production of heat; the heat produced being
proportional to I2R, or to the square of the current intensity. Any lessening
of the current flow required to transmit a given power will therefore
increase the efficiency of transmission. (b) In order to employ a small
current in transmitting a large amount of power, we must use a very high
e.m.f. Such high electromotive forces, say from 60,000 to 100,000 volts,
can be obtained only by the use of a.-c. transformers, since it is not
practicable to build a direct current generator capable of producing 60,000
volts. In large power transmission systems, a.-c. generators are used to
produce powerful alternating currents. The e.m.f. is then stepped up to a
suitable voltage (2300-100,000) by transformers and sent over transmission
lines to the various places where the power is to be used; at these places
capacity.
Fig. 437.—Twelve condensers in circuit with
an incandescent lamp.
The unit of capacity is the Farad. Capacity is defined as the quantity of
electricity per second that flows into a condenser when the voltage at the
terminals changes at the rate of one volt per second. If a change of one volt
per second causes one coulomb to flow per second, that is, a current of one
ampere, the capacity is one farad. The condensers used in the above
experiment have a capacity of one microfarad, or one millionth of a farad.
A condenser, on account of its capacity, causes an a.-c. current to lead the
voltage, that is the current reaches its maximum value before the voltage
does. In this respect a condenser has an effect opposite to that of the self-
induction of a choke coil (the latter causing the current to "lag"). (See Fig.
435.)
437. Transmission of Electric Power.—A field of peculiar usefulness for
a.-c. currents is in the economical transmission of electric power. This fact
is due to the following reasons: (a) The loss of electrical power in a
transmission line is due to the production of heat; the heat produced being
proportional to I2R, or to the square of the current intensity. Any lessening
of the current flow required to transmit a given power will therefore
increase the efficiency of transmission. (b) In order to employ a small
current in transmitting a large amount of power, we must use a very high
e.m.f. Such high electromotive forces, say from 60,000 to 100,000 volts,
can be obtained only by the use of a.-c. transformers, since it is not
practicable to build a direct current generator capable of producing 60,000
volts. In large power transmission systems, a.-c. generators are used to
produce powerful alternating currents. The e.m.f. is then stepped up to a
suitable voltage (2300-100,000) by transformers and sent over transmission
lines to the various places where the power is to be used; at these places
Page 458
suitable transformers "step-down" the e.m.f. to a convenient or safe voltage
for use. (See Fig. 442 of a transmission line and Fig. 438 of a large power
transmission system, and Fig. 439 of an a.-c. generator and power plant.)
Fig. 438.—Diagram of an alternating current
high tension power system. (A) Alternator,
(Tu) water turbine, direct connected to
alternator, (E) exciter, (T1) step-up
transformers in power station, (T2) step-down
transformers in substation, (M) motor, (L)
lamps, single-phase, three-wire system, (T3)
step-down transformers delivering three-
phase current to rotary converter (R) which
delivers direct current to the trolley line.
438. Power Factor.—The power factor is a matter of interest and
importance in the use of a.-c. machines. Its meaning and use may be learned
from the following explanation: In a direct current circuit, watts equals
volts times amperes. In an alternating current circuit, this equation is true
only when the current is "in step" with the voltage, that is, only when there
is no inductance or capacity in the circuit. If current and voltage are out of
step, i.e., if there is lag or lead (see Fig. 434), the product of volts and
amperes gives only the apparent power, the ratio between true and apparent
power depending on the amount of lag or lead. This ratio is called the
power factor. In an a.-c. circuit, then, the power equation is: watts = volts ×
amperes × power factor, or power factor = true power/apparent power. The
for use. (See Fig. 442 of a transmission line and Fig. 438 of a large power
transmission system, and Fig. 439 of an a.-c. generator and power plant.)
Fig. 438.—Diagram of an alternating current
high tension power system. (A) Alternator,
(Tu) water turbine, direct connected to
alternator, (E) exciter, (T1) step-up
transformers in power station, (T2) step-down
transformers in substation, (M) motor, (L)
lamps, single-phase, three-wire system, (T3)
step-down transformers delivering three-
phase current to rotary converter (R) which
delivers direct current to the trolley line.
438. Power Factor.—The power factor is a matter of interest and
importance in the use of a.-c. machines. Its meaning and use may be learned
from the following explanation: In a direct current circuit, watts equals
volts times amperes. In an alternating current circuit, this equation is true
only when the current is "in step" with the voltage, that is, only when there
is no inductance or capacity in the circuit. If current and voltage are out of
step, i.e., if there is lag or lead (see Fig. 434), the product of volts and
amperes gives only the apparent power, the ratio between true and apparent
power depending on the amount of lag or lead. This ratio is called the
power factor. In an a.-c. circuit, then, the power equation is: watts = volts ×
amperes × power factor, or power factor = true power/apparent power. The
Page 459
product of volts and amperes is the apparent power and is called volt-
amperes in distinction from the true power or watts. Therefore the following
is true: power factor = true watts/volt-amperes.
Fig. 439.—Power house showing alternators,
direct connected to horizontal hydraulic
turbines. Note the direct current "exciter" on
end of shaft of alternator. (Courtesy of General
Electric Co.)
439. Single-phase Currents.—There are several kinds of a.-c. currents.
One of the most common is the single-phase. It is simply the common a.-c.
current used for light and power in the average home, and uses a two-wire
circuit around which the current is rapidly alternating. Fig. 440 illustrates
the changes of e.m.f. in an a.-c. single-phase current. It may be produced by
a single coil rotating in a magnetic field. The curve of Fig. 440 represents
one cycle, that is, one complete series of changes in the electromotive
forces. At the end of the cycle the armature is in the same condition as at the
beginning so far as the magnetic field is concerned. It then begins a new
cycle. The ordinary commercial alternating current has a frequency of 60,
that is 60 cycles per second. One rotation produces as many cycles as there
are pairs of poles. For example, if there are 48 poles in the generator field,
one rotation produces 24 cycles.
amperes in distinction from the true power or watts. Therefore the following
is true: power factor = true watts/volt-amperes.
Fig. 439.—Power house showing alternators,
direct connected to horizontal hydraulic
turbines. Note the direct current "exciter" on
end of shaft of alternator. (Courtesy of General
Electric Co.)
439. Single-phase Currents.—There are several kinds of a.-c. currents.
One of the most common is the single-phase. It is simply the common a.-c.
current used for light and power in the average home, and uses a two-wire
circuit around which the current is rapidly alternating. Fig. 440 illustrates
the changes of e.m.f. in an a.-c. single-phase current. It may be produced by
a single coil rotating in a magnetic field. The curve of Fig. 440 represents
one cycle, that is, one complete series of changes in the electromotive
forces. At the end of the cycle the armature is in the same condition as at the
beginning so far as the magnetic field is concerned. It then begins a new
cycle. The ordinary commercial alternating current has a frequency of 60,
that is 60 cycles per second. One rotation produces as many cycles as there
are pairs of poles. For example, if there are 48 poles in the generator field,
one rotation produces 24 cycles.
Page 460
Fig. 440.—Graph showing the e.m.f. changes
of a single-phase current for one "cycle."
440. Three-phase Currents.—Now suppose we have three coils as in Fig.
441, the coils being evenly spaced, or 120 degrees apart, at A, B, and C. If
the coils are rotated in a magnetic field, each will produce an electromotive
force. The result produced by three such coils is called a three-phase
current. Ordinarily six wires, or three circuits, would be required to carry
the current produced by three separate coils; for when coil "C" is in the 90
degree position, where its e.m.f. is a maximum, coil "B" is 120 degrees past
its maximum, and coil "A" is 240 degrees past its maximum. The graph
(Fig. 441) shows the maximum points of the three e.m.f's. separated by
intervals of 120 degrees. In practice, however, it is found possible to use
three wires instead of six, as explained in Art. 441.
of a single-phase current for one "cycle."
440. Three-phase Currents.—Now suppose we have three coils as in Fig.
441, the coils being evenly spaced, or 120 degrees apart, at A, B, and C. If
the coils are rotated in a magnetic field, each will produce an electromotive
force. The result produced by three such coils is called a three-phase
current. Ordinarily six wires, or three circuits, would be required to carry
the current produced by three separate coils; for when coil "C" is in the 90
degree position, where its e.m.f. is a maximum, coil "B" is 120 degrees past
its maximum, and coil "A" is 240 degrees past its maximum. The graph
(Fig. 441) shows the maximum points of the three e.m.f's. separated by
intervals of 120 degrees. In practice, however, it is found possible to use
three wires instead of six, as explained in Art. 441.
Page 461
Fig. 441.—Graph showing the e.m.f. changes
of a three-phase current for one "cycle."
441. Three-wire Transmission.—The currents produced in the three coils
just described undergo precisely the same changes as those represented in
the graph (Fig. 441) for the three electromotive forces. Careful examination
of the graph will show that at any point the sum of the plus e.m.f's. equals
the sum of the minus e.m.f's. In other words the algebraic sum of the three
e.m.f's. is zero. Therefore if we properly connect a transmission line of
three wires to the generator, the sum of the currents leaving the generator
will equal the sum of the currents returning to it. Since the algebraic sum of
the currents produced by the three coil combination described in Art. 440 is
always zero, it is possible to use three wires on three-phase transmission
lines. Fig. 442 shows a "tower" carrying three, three-wire transmission
lines. Long distance, high tension transmission lines are generally three-
wire lines carrying three-phase a.-c. currents.
Fig. 442.—A "tower" supporting three, three-
phase circuits of a high tension transmission
line.
of a three-phase current for one "cycle."
441. Three-wire Transmission.—The currents produced in the three coils
just described undergo precisely the same changes as those represented in
the graph (Fig. 441) for the three electromotive forces. Careful examination
of the graph will show that at any point the sum of the plus e.m.f's. equals
the sum of the minus e.m.f's. In other words the algebraic sum of the three
e.m.f's. is zero. Therefore if we properly connect a transmission line of
three wires to the generator, the sum of the currents leaving the generator
will equal the sum of the currents returning to it. Since the algebraic sum of
the currents produced by the three coil combination described in Art. 440 is
always zero, it is possible to use three wires on three-phase transmission
lines. Fig. 442 shows a "tower" carrying three, three-wire transmission
lines. Long distance, high tension transmission lines are generally three-
wire lines carrying three-phase a.-c. currents.
Fig. 442.—A "tower" supporting three, three-
phase circuits of a high tension transmission
line.
Page 462
442. Alternators.—A dynamo which delivers alternating current is known
as an alternator. Commercial alternators have many pairs of poles in the
field and as a rule the field rotates while the armature is stationary. The field
must be supplied with direct current for the polarity of each coil in the field
must remain unchanged. Usually a separate "exciter" is used, which is a
small direct current generator. The current from this exciter is fed into the
rotating field by means of slip rings. Fig. 439 shows a d.-c. (direct current)
exciter on the end of the armature shaft of the large alternator.
443. The A.-C. Series Motors.—
The only type of motor that will run
on either alternating or direct
current is the series motor. The
"universal" motor used in
household appliances such as
electric fans, vacuum cleaners, etc.,
is a series motor. The reason a
series motor will run on either
direct or alternating current is
because the direction of rotation of
the armature of a motor depends on
(a) the direction of the current in
the armature, and (b) the polarity of
the field. Reversing either of these
alone, reverses the direction of
rotation of the armature, while
Fig. 443.—Diagram of a "Series reversing both at the same instant
Motor." leaves the direction of rotation
unchanged. Fig. 443 is a diagram of
a series motor since the field coils
and armature are connected in series. On an a.-c. line, both field and
armature current must therefore reverse at the same instant. In a shunt
motor (similar to Fig. 286) we have a divided circuit, and the greater self-
induction of the field coils causes an a.-c. current through these coils to lag
behind that flowing in the armature so that the two currents do not reverse
at the same instant.
as an alternator. Commercial alternators have many pairs of poles in the
field and as a rule the field rotates while the armature is stationary. The field
must be supplied with direct current for the polarity of each coil in the field
must remain unchanged. Usually a separate "exciter" is used, which is a
small direct current generator. The current from this exciter is fed into the
rotating field by means of slip rings. Fig. 439 shows a d.-c. (direct current)
exciter on the end of the armature shaft of the large alternator.
443. The A.-C. Series Motors.—
The only type of motor that will run
on either alternating or direct
current is the series motor. The
"universal" motor used in
household appliances such as
electric fans, vacuum cleaners, etc.,
is a series motor. The reason a
series motor will run on either
direct or alternating current is
because the direction of rotation of
the armature of a motor depends on
(a) the direction of the current in
the armature, and (b) the polarity of
the field. Reversing either of these
alone, reverses the direction of
rotation of the armature, while
Fig. 443.—Diagram of a "Series reversing both at the same instant
Motor." leaves the direction of rotation
unchanged. Fig. 443 is a diagram of
a series motor since the field coils
and armature are connected in series. On an a.-c. line, both field and
armature current must therefore reverse at the same instant. In a shunt
motor (similar to Fig. 286) we have a divided circuit, and the greater self-
induction of the field coils causes an a.-c. current through these coils to lag
behind that flowing in the armature so that the two currents do not reverse
at the same instant.
Page 463
Fig. 444.—Diagram of a gramme ring. It is
shown connected to a single-phase current so
as to produce a rotating magnetic field, similar
to that obtained with a three-phase current.
(Ahrens, Harley and Burns.)
Fig. 445.—The "stator" of an induction motor.
444. The Induction Motor.—Another common type of a.-c. motor is the
induction motor. Its advantage lies in its simplicity. It has neither
shown connected to a single-phase current so
as to produce a rotating magnetic field, similar
to that obtained with a three-phase current.
(Ahrens, Harley and Burns.)
Fig. 445.—The "stator" of an induction motor.
444. The Induction Motor.—Another common type of a.-c. motor is the
induction motor. Its advantage lies in its simplicity. It has neither
Page 464
commutator nor brushes, the armature having no connection with an
external circuit. If the wires of a three-phase line be connected to a coil
wound in the form of a gramme ring, the connections being 120 degrees
apart as in Fig. 444, the magnetic field within this coil will change in the
same manner as if a magnet were spinning upon a pivot at the center of the
coil. Suppose the N pole at one instant is at A, in one-third of a cycle it
moves to B, in another third to C, and in one cycle it makes a complete
revolution. Thus we have a rotating magnetic field. If a cup of some non-
magnetic metal such as aluminium or copper be placed on a pivot in the
center of this coil, the cup is cut by the moving lines of force and currents
are induced in it. Because of these currents, the cup has a magnetic field of
its own, and the action of the two magnetic fields is such as to pull the cup
around and cause it to rotate in the same direction as that in which the field
of the coil rotates. The coil represents the stationary part, the stator (Fig.
445) and the cup the rotating part, the rotor, of an induction motor. While
the cup rotates in the same direction, it does not rotate so rapidly as the
magnetic field. If it should it is plain that it would not cut the lines of force.
The difference between the rate of rotation of the rotor and that of the
magnetic field is called the "slip." The rotating part in small induction
motors is frequently made in a single casting. In large motors, it is built up
of heavy copper bars. Thus, from its appearance the common form of rotor
is known as the "squirrel cage" rotor. (See Fig. 446.)
Fig. 446.—The "rotor" of an induction motor.
external circuit. If the wires of a three-phase line be connected to a coil
wound in the form of a gramme ring, the connections being 120 degrees
apart as in Fig. 444, the magnetic field within this coil will change in the
same manner as if a magnet were spinning upon a pivot at the center of the
coil. Suppose the N pole at one instant is at A, in one-third of a cycle it
moves to B, in another third to C, and in one cycle it makes a complete
revolution. Thus we have a rotating magnetic field. If a cup of some non-
magnetic metal such as aluminium or copper be placed on a pivot in the
center of this coil, the cup is cut by the moving lines of force and currents
are induced in it. Because of these currents, the cup has a magnetic field of
its own, and the action of the two magnetic fields is such as to pull the cup
around and cause it to rotate in the same direction as that in which the field
of the coil rotates. The coil represents the stationary part, the stator (Fig.
445) and the cup the rotating part, the rotor, of an induction motor. While
the cup rotates in the same direction, it does not rotate so rapidly as the
magnetic field. If it should it is plain that it would not cut the lines of force.
The difference between the rate of rotation of the rotor and that of the
magnetic field is called the "slip." The rotating part in small induction
motors is frequently made in a single casting. In large motors, it is built up
of heavy copper bars. Thus, from its appearance the common form of rotor
is known as the "squirrel cage" rotor. (See Fig. 446.)
Fig. 446.—The "rotor" of an induction motor.
Page 465
Fig. 447.—Diagram illustrating the principle
of the synchronous motor. The armature coil
passes the position shown in the figure at the
instant the current in the line reverses. Thus
the armature keeps with the line current,
making one revolution with each "cycle."
445. A synchronous motor is one that keeps step with the alterations of an
alternating current. The line current is fed into the armature by means of
two slip rings and brushes. The principle of the synchronous motor is
illustrated in Fig. 447. This shows a motor having a two-pole field. The
armature current must be reversed twice in each revolution. The reversal
must take place when the armature winding is perpendicular to the lines of
force of the field. In a direct current motor this reversal is brought about by
the commutator. In a synchronous motor the armature reaches the 90 degree
position at the exact instant at which the current reverses in the line. Thus in
the case of a two-pole motor the armature must make exactly one revolution
for each cycle; it is, therefore, a constant speed motor. Such motors are
frequently employed in converter stations where alternating current is
converted into direct current by what are called rotary converters.
In practice the synchronous motor has a number of pairs of field poles. It is
essentially an alternating current generator running as a motor. One of the
principal uses of the synchronous motor is that of a converter, receiving
alternating current and delivering direct current. Synchronous motors are
also used in transmission lines to aid in maintaining constant voltage.
Important Topics
of the synchronous motor. The armature coil
passes the position shown in the figure at the
instant the current in the line reverses. Thus
the armature keeps with the line current,
making one revolution with each "cycle."
445. A synchronous motor is one that keeps step with the alterations of an
alternating current. The line current is fed into the armature by means of
two slip rings and brushes. The principle of the synchronous motor is
illustrated in Fig. 447. This shows a motor having a two-pole field. The
armature current must be reversed twice in each revolution. The reversal
must take place when the armature winding is perpendicular to the lines of
force of the field. In a direct current motor this reversal is brought about by
the commutator. In a synchronous motor the armature reaches the 90 degree
position at the exact instant at which the current reverses in the line. Thus in
the case of a two-pole motor the armature must make exactly one revolution
for each cycle; it is, therefore, a constant speed motor. Such motors are
frequently employed in converter stations where alternating current is
converted into direct current by what are called rotary converters.
In practice the synchronous motor has a number of pairs of field poles. It is
essentially an alternating current generator running as a motor. One of the
principal uses of the synchronous motor is that of a converter, receiving
alternating current and delivering direct current. Synchronous motors are
also used in transmission lines to aid in maintaining constant voltage.
Important Topics
Page 466
The wireless telephone, essential parts, action, arrangement.
Alternating currents, alternating fields.
Transformers, voltage relation of coils, power and core losses.
Self-induction, inductance, and coke coils, uses, applications.
Impedance, reactance, and resistance; relation and effects.
Condensers, uses and applications with a-c. circuits.
Alternating current power transmission; uses, advantages.
Power factor, lag, lead, volt-amperes, true watts.
Single- and three-phase currents; uses and nature of each.
Three-wire transmission systems, alternators, construction, and action.
A-c. motors, series, induction, synchronous.
Alternating currents, alternating fields.
Transformers, voltage relation of coils, power and core losses.
Self-induction, inductance, and coke coils, uses, applications.
Impedance, reactance, and resistance; relation and effects.
Condensers, uses and applications with a-c. circuits.
Alternating current power transmission; uses, advantages.
Power factor, lag, lead, volt-amperes, true watts.
Single- and three-phase currents; uses and nature of each.
Three-wire transmission systems, alternators, construction, and action.
A-c. motors, series, induction, synchronous.
Page 467
INDEX
Aberration, spherical, 408
Absolute scale of temperature, 164
Absorptions of gases by solids and liquids, 29
Accelerated motion, 86
Acceleration, 87
Adhesion, 21
Aeroplane, 97
Air, aspirator, 67
brake, 74
cushion, 46
height (of atmosphere), 64
pressure, 56
pump, 66
weight, 56
Alternators, 481
Alternating current, 337, 466
Amalgamation, 273
Ammeter, 291
Ampere, 291
Archimedes' principle, 48
Arc light, 321
Armature, 335
Artesian wells, 44
Audion, 463
Aurora borealis, 453
Balloon, 72
Barometer, 59
Beats, 376
Boiling, laws, 208
point, 207
Boyle's Law, 63
Aberration, spherical, 408
Absolute scale of temperature, 164
Absorptions of gases by solids and liquids, 29
Accelerated motion, 86
Acceleration, 87
Adhesion, 21
Aeroplane, 97
Air, aspirator, 67
brake, 74
cushion, 46
height (of atmosphere), 64
pressure, 56
pump, 66
weight, 56
Alternators, 481
Alternating current, 337, 466
Amalgamation, 273
Ammeter, 291
Ampere, 291
Archimedes' principle, 48
Arc light, 321
Armature, 335
Artesian wells, 44
Audion, 463
Aurora borealis, 453
Balloon, 72
Barometer, 59
Beats, 376
Boiling, laws, 208
point, 207
Boyle's Law, 63
Page 468
Breezes, land and sea, 181
British thermal unit, 162
Brownian movements, 16
Calorie, defined, 162
Camera, 426
Candlepower, 394
Capillary action, 25
Cartesian diver, 71
Cathode rays, 453
Centrifugal force, 91
Charles' Law, 165
Chladni's figures, 381
Choke coils, 470
Coefficient of expansion, definitions, 170
gases, 167
liquids, 168
solids, 169
Coherer, 449
Cohesion, 21, 33
Color, 435
bodies, 435
complementary, 436
primary, 440
prismatic, 433
theory of color vision, 440
three-color printing, 440
Commutator, 335, 336
Compass, 230, 240
Concave lens, 418
Condenser, 260, 474
Conductors, 246
Conservation of energy, 127
Continental code, 459
compared with the Morse, 452
Convection, 179
currents in nature, 181
British thermal unit, 162
Brownian movements, 16
Calorie, defined, 162
Camera, 426
Candlepower, 394
Capillary action, 25
Cartesian diver, 71
Cathode rays, 453
Centrifugal force, 91
Charles' Law, 165
Chladni's figures, 381
Choke coils, 470
Coefficient of expansion, definitions, 170
gases, 167
liquids, 168
solids, 169
Coherer, 449
Cohesion, 21, 33
Color, 435
bodies, 435
complementary, 436
primary, 440
prismatic, 433
theory of color vision, 440
three-color printing, 440
Commutator, 335, 336
Compass, 230, 240
Concave lens, 418
Condenser, 260, 474
Conductors, 246
Conservation of energy, 127
Continental code, 459
compared with the Morse, 452
Convection, 179
currents in nature, 181
Page 469
draft of a chimney, 180
Convex lens, 416
Cooling, artificial, 210
Corpuscular theory, 442
Coulomb, 290
meter, 291
Couple, 101
Critical angle, 414
Crookes' tube, 456
Crystallization, 28
melting point of some crystalline substances, 203
Daniel cell, 276
Declination, 240
Density, 38, 52
methods for finding, 53
Dew, 192
Dew point, 193
Diffusion of gases, 13
Dipping needle, 240
Direct Current, 337
Dispersion, 433
Distillation, 208
Draft of a chimney, 180
Dry cell, 275
Dynamo, 330, 333
Dyne, 93
Eye, the, 423
action of, in vision, 423
defects of, 425
Ear, the, 386
trumpet, 361
Earth's magnetism, 238
Echoes, 362
Eclipses, 391
Efficiency, 142
Convex lens, 416
Cooling, artificial, 210
Corpuscular theory, 442
Coulomb, 290
meter, 291
Couple, 101
Critical angle, 414
Crookes' tube, 456
Crystallization, 28
melting point of some crystalline substances, 203
Daniel cell, 276
Declination, 240
Density, 38, 52
methods for finding, 53
Dew, 192
Dew point, 193
Diffusion of gases, 13
Dipping needle, 240
Direct Current, 337
Dispersion, 433
Distillation, 208
Draft of a chimney, 180
Dry cell, 275
Dynamo, 330, 333
Dyne, 93
Eye, the, 423
action of, in vision, 423
defects of, 425
Ear, the, 386
trumpet, 361
Earth's magnetism, 238
Echoes, 362
Eclipses, 391
Efficiency, 142
Page 470
engines (tests), 219
machines, 142
Elasticity, 31
Electric bell, 269, 287
charge, distribution of, upon a conductor, 253
circuit, 269
currents, 267
single phase, 479
three phase, 479
effects, 277
induced, 326
discharge in rarefied air, 452
motor, 339
screen, 256
Electrical capacity, 259
fields, 247
Electrification, 243
Electrolysis, 308
laws, 311
practical uses, 311
Electromagnet, 281
Electromagnetic theory of light, 456
Electromotive force, 267
unit of, 295
Electron theory, 252
Electrophorus, 263
Electroplating, 307
Electroscope, 244
Electrostatic induction, 248
Energy, 120
conservation, 127
falling water, 152
forms, 125
human body, 126
Energy, kinetic, 121
potential, 120
transference and transformation, 124
machines, 142
Elasticity, 31
Electric bell, 269, 287
charge, distribution of, upon a conductor, 253
circuit, 269
currents, 267
single phase, 479
three phase, 479
effects, 277
induced, 326
discharge in rarefied air, 452
motor, 339
screen, 256
Electrical capacity, 259
fields, 247
Electrification, 243
Electrolysis, 308
laws, 311
practical uses, 311
Electromagnet, 281
Electromagnetic theory of light, 456
Electromotive force, 267
unit of, 295
Electron theory, 252
Electrophorus, 263
Electroplating, 307
Electroscope, 244
Electrostatic induction, 248
Energy, 120
conservation, 127
falling water, 152
forms, 125
human body, 126
Energy, kinetic, 121
potential, 120
transference and transformation, 124
Page 471
Engines, 213
Engines, gas, 222
steam, 213
turbine, 225
Equilibrant, 81
Equilibrium, 106
neutral, 107
stable, 106
stability, 108
unstable, 107
Erg, 119
Ether, 177
Evaporation, 18
cooling effect, 19, 197
rate, 198
Expansion, coefficient, 168
gases, 167
liquids, 168
peculiarity, in water, 168
solids, 169
water, on turning to steam, 206
Falling bodies, 109
experimental study, 111
laws, 113
Floating bodies, 48
Fluoroscope, 455
Foot candle, 396
Force, 79
dyne, 93
effectiveness, 134
graphic representation, 80
liquid, against any surface, 38
measuring, 79
moment, 99
parallel, 100
resolution, 96
Engines, gas, 222
steam, 213
turbine, 225
Equilibrant, 81
Equilibrium, 106
neutral, 107
stable, 106
stability, 108
unstable, 107
Erg, 119
Ether, 177
Evaporation, 18
cooling effect, 19, 197
rate, 198
Expansion, coefficient, 168
gases, 167
liquids, 168
peculiarity, in water, 168
solids, 169
water, on turning to steam, 206
Falling bodies, 109
experimental study, 111
laws, 113
Floating bodies, 48
Fluoroscope, 455
Foot candle, 396
Force, 79
dyne, 93
effectiveness, 134
graphic representation, 80
liquid, against any surface, 38
measuring, 79
moment, 99
parallel, 100
resolution, 96
Page 472
units, 83
Forces, parallel, 100
Franklin's theory of electricity, 252
Fraunhofer lines, 439
Freezing, evaporation, 197, 199
mixtures, 210
Friction, 147,
coefficient, 149
fluid, 150
kinds, 147
Friction, laws, 150
reducing, 148
uses, 149
Galvanometers, 289
Galvanoscope, 269
Gas engine, 222
efficiency of, 224
Gas meter, 75
Geissler tubes, 453
Gravitation, 103
law, 104
Gravity, 88, 104
acceleration due to, 111
cell, 277
center of, 105
Hail, 193
Hearing, 386
Heat, capacity for water, 201
conduction, 173
constants for transmission, 220
convection, 179
effects, 161
engines, 213, 222
equivalent of fuels, 219
fusion, 201
Forces, parallel, 100
Franklin's theory of electricity, 252
Fraunhofer lines, 439
Freezing, evaporation, 197, 199
mixtures, 210
Friction, 147,
coefficient, 149
fluid, 150
kinds, 147
Friction, laws, 150
reducing, 148
uses, 149
Galvanometers, 289
Galvanoscope, 269
Gas engine, 222
efficiency of, 224
Gas meter, 75
Geissler tubes, 453
Gravitation, 103
law, 104
Gravity, 88, 104
acceleration due to, 111
cell, 277
center of, 105
Hail, 193
Hearing, 386
Heat, capacity for water, 201
conduction, 173
constants for transmission, 220
convection, 179
effects, 161
engines, 213, 222
equivalent of fuels, 219
fusion, 201
Page 473
measurement, 200
methods of transmitting, 173
produced by electric current, 318
radiation, 176
sources, 159
units, 162
vaporization, 205
work, 212
Heating of buildings, 182
direct and indirect radiation, 186
hot air, 183
water, 186
plenum system, 187
steam, 186
vacuum steam, 187
vapor steam, 187
Hertzian waves, 262, 449
Hooke's law, 33
Horse power, 123
electric equivalent of, 123
Humidity, 194
Hydraulic press, 42
elevator, 44
ram, 72
Hygrometers, 194
Hygrometry, 191
conditions for saturation, 192
dew point, 193
fog, 193
formation, of dew, 192
humidity, 194
hygrometers, 194
importance, 191
Hypothesis, 3
Images, concave mirrors, 405
construction, 405
methods of transmitting, 173
produced by electric current, 318
radiation, 176
sources, 159
units, 162
vaporization, 205
work, 212
Heating of buildings, 182
direct and indirect radiation, 186
hot air, 183
water, 186
plenum system, 187
steam, 186
vacuum steam, 187
vapor steam, 187
Hertzian waves, 262, 449
Hooke's law, 33
Horse power, 123
electric equivalent of, 123
Humidity, 194
Hydraulic press, 42
elevator, 44
ram, 72
Hygrometers, 194
Hygrometry, 191
conditions for saturation, 192
dew point, 193
fog, 193
formation, of dew, 192
humidity, 194
hygrometers, 194
importance, 191
Hypothesis, 3
Images, concave mirrors, 405
construction, 405
Page 474
definition, 392
plain mirror, 401
small apertures, 391
Impedance, 472
Incandescent lamp, 320
Inclined plane, 143
Inductance, 471
Induction coil, 343
Inertia, 87
Insulators, 246
Intensity of sound, 363
Interference, light, 442
sound, 374
Joule, 120, 319
Laws, boiling, 208
Boyle's 63
Charles', 165
electric action, 243
falling bodies, 113
floating bodies, 48
gravitation, 104
Hooke's, 33
induced currents, 326
intensity of light, 394
Lenz's, 328
liquid pressure, 37
machines, 131
magnetic action, 229
motion, 87
Ohm's, 298
pendulum, 116
reflection, 399
refraction of light, 411
vibration of strings, 378
Lenses, achromatic, 434
plain mirror, 401
small apertures, 391
Impedance, 472
Incandescent lamp, 320
Inclined plane, 143
Inductance, 471
Induction coil, 343
Inertia, 87
Insulators, 246
Intensity of sound, 363
Interference, light, 442
sound, 374
Joule, 120, 319
Laws, boiling, 208
Boyle's 63
Charles', 165
electric action, 243
falling bodies, 113
floating bodies, 48
gravitation, 104
Hooke's, 33
induced currents, 326
intensity of light, 394
Lenz's, 328
liquid pressure, 37
machines, 131
magnetic action, 229
motion, 87
Ohm's, 298
pendulum, 116
reflection, 399
refraction of light, 411
vibration of strings, 378
Lenses, achromatic, 434
Page 475
effect on light, 417
equation, 421
formation of images, 418
forms, 416
Leclanché cell, 275
Lever, 132
Leyden jar, 261
oscillatory nature of the discharge, 448
Light, compared with sound, 388, 444
electromagnetic theory, 456
intensity, 394
interference, 442
polarization, 445
rectilinear propagation, 389
reflection, 396
total reflection, 413
Lightning, 254
Lines, of force, 233
agonic, 240
isogonic, 240
Liquids, pressure, 36
Local action, 273
Luminous and illuminated bodies, 388
Machines, 129
advantages, 129
cannot create energy, 130
efficiency, 142
law, 131
mechanical advantage, 134
the six simple, 132
uses, 129
Magnetic action, 229
fields, 233, 466
induction, 231, 236
permeability, 237
poles, 229
equation, 421
formation of images, 418
forms, 416
Leclanché cell, 275
Lever, 132
Leyden jar, 261
oscillatory nature of the discharge, 448
Light, compared with sound, 388, 444
electromagnetic theory, 456
intensity, 394
interference, 442
polarization, 445
rectilinear propagation, 389
reflection, 396
total reflection, 413
Lightning, 254
Lines, of force, 233
agonic, 240
isogonic, 240
Liquids, pressure, 36
Local action, 273
Luminous and illuminated bodies, 388
Machines, 129
advantages, 129
cannot create energy, 130
efficiency, 142
law, 131
mechanical advantage, 134
the six simple, 132
uses, 129
Magnetic action, 229
fields, 233, 466
induction, 231, 236
permeability, 237
poles, 229
Page 476
properties, 230
retentivity, 231
substances, 230
effect of electric current, 279
Magnetism, 228
Magnetism, theory, 232
Major and minor triads, 369
Magneto, 328
Magnetoscope, 230
Magnets, 228
poles, 229
Major scale, 366
Manometric flames, 382
Matter, 4
effect of heat, 5
molecular theory, 5
properties, 34
states of, 4
states of, defined, 5
Mechanical advantage, 134
Megaphone, 365
Melting points, 203
Mercury arc rectifier, 347
Metric system, 8
Microscope, 427
Mirage, 414
Mirrors, 400
concave, 405
convex, 407
parabolic, 409
plane, 401
Molecular motion in liquids, 18
in gases, 13
in liquids and solids, 27
in solids, 31
Molecules, motion, 16
size, 13
retentivity, 231
substances, 230
effect of electric current, 279
Magnetism, 228
Magnetism, theory, 232
Major and minor triads, 369
Magneto, 328
Magnetoscope, 230
Magnets, 228
poles, 229
Major scale, 366
Manometric flames, 382
Matter, 4
effect of heat, 5
molecular theory, 5
properties, 34
states of, 4
states of, defined, 5
Mechanical advantage, 134
Megaphone, 365
Melting points, 203
Mercury arc rectifier, 347
Metric system, 8
Microscope, 427
Mirage, 414
Mirrors, 400
concave, 405
convex, 407
parabolic, 409
plane, 401
Molecular motion in liquids, 18
in gases, 13
in liquids and solids, 27
in solids, 31
Molecules, motion, 16
size, 13
Page 477
Moment of force, 99, 133
Momentum, 87
law of, 92
Motion, 85
accelerated, 86
curvilinear, 88
direction, 86
first law, 87
modes, 85
second law, 92
third law, 93
uniformity, 86
Motor (electric), 339
A. C. series, 482
induction, 483
synchronous, 485
Muffler, 224
Musical instruments, 377
interval, 368
nomenclatures, table, 369
Musical sounds, characteristics 364
Newton's Laws of motion, 87
Nodes, in pipes, 384
in strings, 379
Noise and music, 363
Ohm, 294
Ohm's Law, 298
Opera glass, 428
Optical illusions, 390, 404
instruments, 423
camera, 426
eye, 423
microscope, 427
opera glass, 428
prism field glass, 429
Momentum, 87
law of, 92
Motion, 85
accelerated, 86
curvilinear, 88
direction, 86
first law, 87
modes, 85
second law, 92
third law, 93
uniformity, 86
Motor (electric), 339
A. C. series, 482
induction, 483
synchronous, 485
Muffler, 224
Musical instruments, 377
interval, 368
nomenclatures, table, 369
Musical sounds, characteristics 364
Newton's Laws of motion, 87
Nodes, in pipes, 384
in strings, 379
Noise and music, 363
Ohm, 294
Ohm's Law, 298
Opera glass, 428
Optical illusions, 390, 404
instruments, 423
camera, 426
eye, 423
microscope, 427
opera glass, 428
prism field glass, 429
Page 478
projecting lantern, 427
telescope, 428
Organ pipes, closed, 384
nodes, 384
open, 384
Oscillatory discharge, 448
Osmosis, 19
Outline Review,
current electricity, 325
force and motion, 118
heat, 227
induced currents, 353
light, 446
magnetism and static electricity, 266
sound, 387
work and energy, 158
Overtones, 379
Pascal's principle, 41
Pendulum, compound, 115
laws, 116
simple, 115
uses, 116
Pepper's ghost, 404
Permeability, 237
Phonograph, 383
Physics, definition, 4
Photometer, 394
Photometry, 393
Pitch, 365
Polarization, of light, 445
of voltaic cells, 273
Portraits,
Bell, 431
Edison, 285
Faraday, 331
Galileo, 89
telescope, 428
Organ pipes, closed, 384
nodes, 384
open, 384
Oscillatory discharge, 448
Osmosis, 19
Outline Review,
current electricity, 325
force and motion, 118
heat, 227
induced currents, 353
light, 446
magnetism and static electricity, 266
sound, 387
work and energy, 158
Overtones, 379
Pascal's principle, 41
Pendulum, compound, 115
laws, 116
simple, 115
uses, 116
Pepper's ghost, 404
Permeability, 237
Phonograph, 383
Physics, definition, 4
Photometer, 394
Photometry, 393
Pitch, 365
Polarization, of light, 445
of voltaic cells, 273
Portraits,
Bell, 431
Edison, 285
Faraday, 331
Galileo, 89
Page 479
Gilbert, 217
Helmholtz, 397
Huygens, 397
Joule, 217
Kelvin, 331
Marconi, 431
Morse, 285
Newton, 89
Potential, 257
Power, 123
electric, 316
power factor, 476
transmission of electric, 476
water, 152
Pressure, air, 56
atmospheric, 58
Pressure, definition, 37
effect on liquids and gases, 62
law of liquid, 37
Prism field glass, 429
Projecting lantern, 427
Proof-plane, 244
Pulley, 139
Pumps, air, 66
condensing, 67
water (lift, 68, force, 69)
Quality of musical tones, 380
Radiation, 176
sun's, 178
Radio-activity, 457
Radiometer, 177
Radium, 457
Rainbow, 436
Reactance, 472
Reflection, light, 396
Helmholtz, 397
Huygens, 397
Joule, 217
Kelvin, 331
Marconi, 431
Morse, 285
Newton, 89
Potential, 257
Power, 123
electric, 316
power factor, 476
transmission of electric, 476
water, 152
Pressure, air, 56
atmospheric, 58
Pressure, definition, 37
effect on liquids and gases, 62
law of liquid, 37
Prism field glass, 429
Projecting lantern, 427
Proof-plane, 244
Pulley, 139
Pumps, air, 66
condensing, 67
water (lift, 68, force, 69)
Quality of musical tones, 380
Radiation, 176
sun's, 178
Radio-activity, 457
Radiometer, 177
Radium, 457
Rainbow, 436
Reactance, 472
Reflection, light, 396
Page 480
multiple, 404
sound, 360
total of light, 413
Refraction, 410
cause, 412
index, 412
light, 410
in plates, prisms, and lenses, 413
Resolution of forces, 96
Resistance, cells in series, and parallel, 302
conductors, 293
in series and parallel, 299, 300
unit, 294
volt-ammeter method for finding, 304
Resonance, 371
Resonator, 373
Resultant, 81
Retentivity, 231
Right hand rule, 279
Rotary converter, 486
Science, definition, 2
Screw, 144
Shadows, 390
Single phase currents, 479
Siphon, 70
Siren, 366
Solidification, change of volume during, 203
Solutions, 27
Sound, compared with light, 388
interference, 374
media, 355
nature, 356
reflection, 360
rule for finding velocity, 367
source, 354
speed, 355
sound, 360
total of light, 413
Refraction, 410
cause, 412
index, 412
light, 410
in plates, prisms, and lenses, 413
Resolution of forces, 96
Resistance, cells in series, and parallel, 302
conductors, 293
in series and parallel, 299, 300
unit, 294
volt-ammeter method for finding, 304
Resonance, 371
Resonator, 373
Resultant, 81
Retentivity, 231
Right hand rule, 279
Rotary converter, 486
Science, definition, 2
Screw, 144
Shadows, 390
Single phase currents, 479
Siphon, 70
Siren, 366
Solidification, change of volume during, 203
Solutions, 27
Sound, compared with light, 388
interference, 374
media, 355
nature, 356
reflection, 360
rule for finding velocity, 367
source, 354
speed, 355
Page 481
transmission in air, 359
Specific heat, 200
method of determining, 201
Spectroscope, 438
Spectrum, 433
Spherical aberration, 408
Spinthariscope, 458
Stability, 108
Standpipe, 46
Static and current electricity compared, 287
electrical machines, 262
Steam engine, 213
turbine, 225
Storage battery, 312
Stress and strain, 94
Sublimation, 199
Surface tension, 22
Sympathetic vibration, 372
Telegraph, 283
wireless, 450
Telephone, 349
receiver, 349
transmitter, 350
wireless, 460
Telescope, 428
Temperature, 162
absolute scale, 164
Tempered scale, 370
Theory, 3
Thermometer, air, 167
centigrade, Fahrenheit, 163
gas, 167
Thermos bottle, 176
Thermostat, 188
Three-color printing, 440
Three-phase currents, 479
Specific heat, 200
method of determining, 201
Spectroscope, 438
Spectrum, 433
Spherical aberration, 408
Spinthariscope, 458
Stability, 108
Standpipe, 46
Static and current electricity compared, 287
electrical machines, 262
Steam engine, 213
turbine, 225
Storage battery, 312
Stress and strain, 94
Sublimation, 199
Surface tension, 22
Sympathetic vibration, 372
Telegraph, 283
wireless, 450
Telephone, 349
receiver, 349
transmitter, 350
wireless, 460
Telescope, 428
Temperature, 162
absolute scale, 164
Tempered scale, 370
Theory, 3
Thermometer, air, 167
centigrade, Fahrenheit, 163
gas, 167
Thermos bottle, 176
Thermostat, 188
Three-color printing, 440
Three-phase currents, 479
Page 482
Three wire transmission, 480
Torricelli's experiment, 57
Trade winds, 182
Transformer, 345, 467
uses, 347
Turbine, steam, 225
water, 154
Vacuum cleaner, 76
pan, 210
Velocity, 86
Vibration strings, 378
sympathetic, 372
Visual angle, 424
Viscosity, 20
Volt, 295
Voltaic cell, 270
advantages, 274
amalgamation, 273
local action, 273
polarization, 273
simple, 270
Voltmeter, 295
Water wheels, 152
overshot, 152
turbine, 154
undershot, 153
Watt, 123, 317
Wave theory, of light, 442
Waves, beats, 376
interference, 374
longitudinal, 358
sound, 358
transverse, 358
visible, 357
Wedge, 144
Torricelli's experiment, 57
Trade winds, 182
Transformer, 345, 467
uses, 347
Turbine, steam, 225
water, 154
Vacuum cleaner, 76
pan, 210
Velocity, 86
Vibration strings, 378
sympathetic, 372
Visual angle, 424
Viscosity, 20
Volt, 295
Voltaic cell, 270
advantages, 274
amalgamation, 273
local action, 273
polarization, 273
simple, 270
Voltmeter, 295
Water wheels, 152
overshot, 152
turbine, 154
undershot, 153
Watt, 123, 317
Wave theory, of light, 442
Waves, beats, 376
interference, 374
longitudinal, 358
sound, 358
transverse, 358
visible, 357
Wedge, 144
Page 483
Weight, 104
Wheatstone bridge, 304
Wheel and axle, 136
Wind instruments, 383
Wireless telegraphy, 450
telephony, 460
Work, 119
units, 119
"X" rays 454
FOOTNOTES:
Wheatstone bridge, 304
Wheel and axle, 136
Wind instruments, 383
Wireless telegraphy, 450
telephony, 460
Work, 119
units, 119
"X" rays 454
FOOTNOTES:
Page 484
[A] A law is a statement of a constant mode of behavior. It is often expressed in
mathematical language.
[B] The mass of a body is the amount of matter in it, the weight is the pull of the
earth upon it.
[C] "Head" is a term used to express the vertical height of water in pipes.
[D] The position of a submarine in or under water is controlled in a similar
manner.
[E] By a light body is meant one of small mass, a heavy body possessing much
greater mass.
[F] V represents the velocity of a falling body at the end of t seconds.
[G] The following formula is of assistance in computing horse-power in
problems: H. p. = (lbs. × ft.)/(550 × sec.).
[H] Consider the diameter of the front sprocket as 6 inches.
[I] Radiant heat is really radiant energy and becomes heat when it is absorbed by
a body.
[J] American League of Automobile Manufacturers.
[K] Many scientists consider that current in a conductor consists of negative
electrons flowing in a direction opposite to that described in Art. 243. This is
called the electron current, as distinguished from the electric current described
above.
[L] A shunt is a conductor or coil connected in parallel with another conductor or
circuit. It carries a part of the current.
[M] An induced current is one produced by changing the number of magnetic
lines of force passing through a coil.
[N] A wave is a disturbance in a substance or medium that is transmitted through
it.
[O] Pitch as used here, means vibration rate.
Transcriber's note:
This book uses B.T.U. and B.t.u., electrophorous and electrophorus, e.m.f. and E.M.F.
and this has been left as written.
Hyphenation is also left as written, e.g. electro-plated and electroplated.
On page 324, Exercise number 8 was not used in the original. The exercises have not
been renumbered.
mathematical language.
[B] The mass of a body is the amount of matter in it, the weight is the pull of the
earth upon it.
[C] "Head" is a term used to express the vertical height of water in pipes.
[D] The position of a submarine in or under water is controlled in a similar
manner.
[E] By a light body is meant one of small mass, a heavy body possessing much
greater mass.
[F] V represents the velocity of a falling body at the end of t seconds.
[G] The following formula is of assistance in computing horse-power in
problems: H. p. = (lbs. × ft.)/(550 × sec.).
[H] Consider the diameter of the front sprocket as 6 inches.
[I] Radiant heat is really radiant energy and becomes heat when it is absorbed by
a body.
[J] American League of Automobile Manufacturers.
[K] Many scientists consider that current in a conductor consists of negative
electrons flowing in a direction opposite to that described in Art. 243. This is
called the electron current, as distinguished from the electric current described
above.
[L] A shunt is a conductor or coil connected in parallel with another conductor or
circuit. It carries a part of the current.
[M] An induced current is one produced by changing the number of magnetic
lines of force passing through a coil.
[N] A wave is a disturbance in a substance or medium that is transmitted through
it.
[O] Pitch as used here, means vibration rate.
Transcriber's note:
This book uses B.T.U. and B.t.u., electrophorous and electrophorus, e.m.f. and E.M.F.
and this has been left as written.
Hyphenation is also left as written, e.g. electro-plated and electroplated.
On page 324, Exercise number 8 was not used in the original. The exercises have not
been renumbered.
Page 485
*** END OF THE PROJECT GUTENBERG EBOOK PHYSICS ***
Updated editions will replace the previous one—the old editions will be
renamed.
Creating the works from print editions not protected by U.S. copyright law
means that no one owns a United States copyright in these works, so the
Foundation (and you!) can copy and distribute it in the United States
without permission and without paying copyright royalties. Special rules,
set forth in the General Terms of Use part of this license, apply to copying
and distributing Project Gutenberg™ electronic works to protect the
PROJECT GUTENBERG™ concept and trademark. Project Gutenberg is a
registered trademark, and may not be used if you charge for an eBook,
except by following the terms of the trademark license, including paying
royalties for use of the Project Gutenberg trademark. If you do not charge
anything for copies of this eBook, complying with the trademark license is
very easy. You may use this eBook for nearly any purpose such as creation
of derivative works, reports, performances and research. Project Gutenberg
eBooks may be modified and printed and given away—you may do
practically ANYTHING in the United States with eBooks not protected by
U.S. copyright law. Redistribution is subject to the trademark license,
especially commercial redistribution.
START: FULL LICENSE
Updated editions will replace the previous one—the old editions will be
renamed.
Creating the works from print editions not protected by U.S. copyright law
means that no one owns a United States copyright in these works, so the
Foundation (and you!) can copy and distribute it in the United States
without permission and without paying copyright royalties. Special rules,
set forth in the General Terms of Use part of this license, apply to copying
and distributing Project Gutenberg™ electronic works to protect the
PROJECT GUTENBERG™ concept and trademark. Project Gutenberg is a
registered trademark, and may not be used if you charge for an eBook,
except by following the terms of the trademark license, including paying
royalties for use of the Project Gutenberg trademark. If you do not charge
anything for copies of this eBook, complying with the trademark license is
very easy. You may use this eBook for nearly any purpose such as creation
of derivative works, reports, performances and research. Project Gutenberg
eBooks may be modified and printed and given away—you may do
practically ANYTHING in the United States with eBooks not protected by
U.S. copyright law. Redistribution is subject to the trademark license,
especially commercial redistribution.
START: FULL LICENSE
Page 486
THE FULL PROJECT GUTENBERG™ LICENSE
PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK
To protect the Project Gutenberg™ mission of promoting the free
distribution of electronic works, by using or distributing this work (or any
other work associated in any way with the phrase “Project Gutenberg”), you
agree to comply with all the terms of the Full Project Gutenberg License
available with this file or online at www.gutenberg.org/license.
Section 1. General Terms of Use and Redistributing
Project Gutenberg electronic works
1.A. By reading or using any part of this Project Gutenberg electronic work,
you indicate that you have read, understand, agree to and accept all the
terms of this license and intellectual property (trademark/copyright)
agreement. If you do not agree to abide by all the terms of this agreement,
you must cease using and return or destroy all copies of Project Gutenberg
electronic works in your possession. If you paid a fee for obtaining a copy
of or access to a Project Gutenberg electronic work and you do not agree to
be bound by the terms of this agreement, you may obtain a refund from the
person or entity to whom you paid the fee as set forth in paragraph 1.E.8.
1.B. “Project Gutenberg” is a registered trademark. It may only be used on
or associated in any way with an electronic work by people who agree to be
bound by the terms of this agreement. There are a few things that you can
do with most Project Gutenberg electronic works even without complying
with the full terms of this agreement. See paragraph 1.C below. There are a
lot of things you can do with Project Gutenberg electronic works if you
follow the terms of this agreement and help preserve free future access to
Project Gutenberg electronic works. See paragraph 1.E below.
1.C. The Project Gutenberg Literary Archive Foundation (“the Foundation”
or PGLAF), owns a compilation copyright in the collection of Project
Gutenberg electronic works. Nearly all the individual works in the
collection are in the public domain in the United States. If an individual
work is unprotected by copyright law in the United States and you are
PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK
To protect the Project Gutenberg™ mission of promoting the free
distribution of electronic works, by using or distributing this work (or any
other work associated in any way with the phrase “Project Gutenberg”), you
agree to comply with all the terms of the Full Project Gutenberg License
available with this file or online at www.gutenberg.org/license.
Section 1. General Terms of Use and Redistributing
Project Gutenberg electronic works
1.A. By reading or using any part of this Project Gutenberg electronic work,
you indicate that you have read, understand, agree to and accept all the
terms of this license and intellectual property (trademark/copyright)
agreement. If you do not agree to abide by all the terms of this agreement,
you must cease using and return or destroy all copies of Project Gutenberg
electronic works in your possession. If you paid a fee for obtaining a copy
of or access to a Project Gutenberg electronic work and you do not agree to
be bound by the terms of this agreement, you may obtain a refund from the
person or entity to whom you paid the fee as set forth in paragraph 1.E.8.
1.B. “Project Gutenberg” is a registered trademark. It may only be used on
or associated in any way with an electronic work by people who agree to be
bound by the terms of this agreement. There are a few things that you can
do with most Project Gutenberg electronic works even without complying
with the full terms of this agreement. See paragraph 1.C below. There are a
lot of things you can do with Project Gutenberg electronic works if you
follow the terms of this agreement and help preserve free future access to
Project Gutenberg electronic works. See paragraph 1.E below.
1.C. The Project Gutenberg Literary Archive Foundation (“the Foundation”
or PGLAF), owns a compilation copyright in the collection of Project
Gutenberg electronic works. Nearly all the individual works in the
collection are in the public domain in the United States. If an individual
work is unprotected by copyright law in the United States and you are
Page 487
located in the United States, we do not claim a right to prevent you from
copying, distributing, performing, displaying or creating derivative works
based on the work as long as all references to Project Gutenberg are
removed. Of course, we hope that you will support the Project Gutenberg
mission of promoting free access to electronic works by freely sharing
Project Gutenberg works in compliance with the terms of this agreement for
keeping the Project Gutenberg name associated with the work. You can
easily comply with the terms of this agreement by keeping this work in the
same format with its attached full Project Gutenberg License when you
share it without charge with others.
1.D. The copyright laws of the place where you are located also govern
what you can do with this work. Copyright laws in most countries are in a
constant state of change. If you are outside the United States, check the
laws of your country in addition to the terms of this agreement before
downloading, copying, displaying, performing, distributing or creating
derivative works based on this work or any other Project Gutenberg work.
The Foundation makes no representations concerning the copyright status
of any work in any country other than the United States.
1.E. Unless you have removed all references to Project Gutenberg:
1.E.1. The following sentence, with active links to, or other immediate
access to, the full Project Gutenberg License must appear prominently
whenever any copy of a Project Gutenberg work (any work on which the
phrase “Project Gutenberg” appears, or with which the phrase “Project
Gutenberg” is associated) is accessed, displayed, performed, viewed, copied
or distributed:
This eBook is for the use of anyone anywhere in the United States
and most other parts of the world at no cost and with almost no
restrictions whatsoever. You may copy it, give it away or re-use it
under the terms of the Project Gutenberg™ License included with
this eBook or online at www.gutenberg.org. If you are not located in
the United States, you will have to check the laws of the country
where you are located before using this eBook.
copying, distributing, performing, displaying or creating derivative works
based on the work as long as all references to Project Gutenberg are
removed. Of course, we hope that you will support the Project Gutenberg
mission of promoting free access to electronic works by freely sharing
Project Gutenberg works in compliance with the terms of this agreement for
keeping the Project Gutenberg name associated with the work. You can
easily comply with the terms of this agreement by keeping this work in the
same format with its attached full Project Gutenberg License when you
share it without charge with others.
1.D. The copyright laws of the place where you are located also govern
what you can do with this work. Copyright laws in most countries are in a
constant state of change. If you are outside the United States, check the
laws of your country in addition to the terms of this agreement before
downloading, copying, displaying, performing, distributing or creating
derivative works based on this work or any other Project Gutenberg work.
The Foundation makes no representations concerning the copyright status
of any work in any country other than the United States.
1.E. Unless you have removed all references to Project Gutenberg:
1.E.1. The following sentence, with active links to, or other immediate
access to, the full Project Gutenberg License must appear prominently
whenever any copy of a Project Gutenberg work (any work on which the
phrase “Project Gutenberg” appears, or with which the phrase “Project
Gutenberg” is associated) is accessed, displayed, performed, viewed, copied
or distributed:
This eBook is for the use of anyone anywhere in the United States
and most other parts of the world at no cost and with almost no
restrictions whatsoever. You may copy it, give it away or re-use it
under the terms of the Project Gutenberg™ License included with
this eBook or online at www.gutenberg.org. If you are not located in
the United States, you will have to check the laws of the country
where you are located before using this eBook.
Page 488
1.E.2. If an individual Project Gutenberg electronic work is derived from
texts not protected by U.S. copyright law (does not contain a notice
indicating that it is posted with permission of the copyright holder), the
work can be copied and distributed to anyone in the United States without
paying any fees or charges. If you are redistributing or providing access to a
work with the phrase “Project Gutenberg” associated with or appearing on
the work, you must comply either with the requirements of paragraphs
1.E.1 through 1.E.7 or obtain permission for the use of the work and the
Project Gutenberg trademark as set forth in paragraphs 1.E.8 or 1.E.9.
1.E.3. If an individual Project Gutenberg electronic work is posted with the
permission of the copyright holder, your use and distribution must comply
with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed
by the copyright holder. Additional terms will be linked to the Project
Gutenberg License for all works posted with the permission of the
copyright holder found at the beginning of this work.
1.E.4. Do not unlink or detach or remove the full Project Gutenberg License
terms from this work, or any files containing a part of this work or any
other work associated with Project Gutenberg.
1.E.5. Do not copy, display, perform, distribute or redistribute this
electronic work, or any part of this electronic work, without prominently
displaying the sentence set forth in paragraph 1.E.1 with active links or
immediate access to the full terms of the Project Gutenberg License.
1.E.6. You may convert to and distribute this work in any binary,
compressed, marked up, nonproprietary or proprietary form, including any
word processing or hypertext form. However, if you provide access to or
distribute copies of a Project Gutenberg work in a format other than “Plain
Vanilla ASCII” or other format used in the official version posted on the
official Project Gutenberg website (www.gutenberg.org), you must, at no
additional cost, fee or expense to the user, provide a copy, a means of
exporting a copy, or a means of obtaining a copy upon request, of the work
in its original “Plain Vanilla ASCII” or other form. Any alternate format
must include the full Project Gutenberg License as specified in paragraph
1.E.1.
texts not protected by U.S. copyright law (does not contain a notice
indicating that it is posted with permission of the copyright holder), the
work can be copied and distributed to anyone in the United States without
paying any fees or charges. If you are redistributing or providing access to a
work with the phrase “Project Gutenberg” associated with or appearing on
the work, you must comply either with the requirements of paragraphs
1.E.1 through 1.E.7 or obtain permission for the use of the work and the
Project Gutenberg trademark as set forth in paragraphs 1.E.8 or 1.E.9.
1.E.3. If an individual Project Gutenberg electronic work is posted with the
permission of the copyright holder, your use and distribution must comply
with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed
by the copyright holder. Additional terms will be linked to the Project
Gutenberg License for all works posted with the permission of the
copyright holder found at the beginning of this work.
1.E.4. Do not unlink or detach or remove the full Project Gutenberg License
terms from this work, or any files containing a part of this work or any
other work associated with Project Gutenberg.
1.E.5. Do not copy, display, perform, distribute or redistribute this
electronic work, or any part of this electronic work, without prominently
displaying the sentence set forth in paragraph 1.E.1 with active links or
immediate access to the full terms of the Project Gutenberg License.
1.E.6. You may convert to and distribute this work in any binary,
compressed, marked up, nonproprietary or proprietary form, including any
word processing or hypertext form. However, if you provide access to or
distribute copies of a Project Gutenberg work in a format other than “Plain
Vanilla ASCII” or other format used in the official version posted on the
official Project Gutenberg website (www.gutenberg.org), you must, at no
additional cost, fee or expense to the user, provide a copy, a means of
exporting a copy, or a means of obtaining a copy upon request, of the work
in its original “Plain Vanilla ASCII” or other form. Any alternate format
must include the full Project Gutenberg License as specified in paragraph
1.E.1.
Page 489
1.E.7. Do not charge a fee for access to, viewing, displaying, performing,
copying or distributing any Project Gutenberg works unless you comply
with paragraph 1.E.8 or 1.E.9.
1.E.8. You may charge a reasonable fee for copies of or providing access to
or distributing Project Gutenberg electronic works provided that:
• You pay a royalty fee of 20% of the gross profits you derive from the
use of Project Gutenberg works calculated using the method you
already use to calculate your applicable taxes. The fee is owed to the
owner of the Project Gutenberg trademark, but he has agreed to donate
royalties under this paragraph to the Project Gutenberg Literary
Archive Foundation. Royalty payments must be paid within 60 days
following each date on which you prepare (or are legally required to
prepare) your periodic tax returns. Royalty payments should be clearly
marked as such and sent to the Project Gutenberg Literary Archive
Foundation at the address specified in Section 4, “Information about
donations to the Project Gutenberg Literary Archive Foundation.”
• You provide a full refund of any money paid by a user who notifies
you in writing (or by e-mail) within 30 days of receipt that s/he does
not agree to the terms of the full Project Gutenberg™ License. You
must require such a user to return or destroy all copies of the works
possessed in a physical medium and discontinue all use of and all
access to other copies of Project Gutenberg™ works.
• You provide, in accordance with paragraph 1.F.3, a full refund of any
money paid for a work or a replacement copy, if a defect in the
electronic work is discovered and reported to you within 90 days of
receipt of the work.
• You comply with all other terms of this agreement for free distribution
of Project Gutenberg™ works.
1.E.9. If you wish to charge a fee or distribute a Project Gutenberg™
electronic work or group of works on different terms than are set forth in
this agreement, you must obtain permission in writing from the Project
Gutenberg Literary Archive Foundation, the manager of the Project
copying or distributing any Project Gutenberg works unless you comply
with paragraph 1.E.8 or 1.E.9.
1.E.8. You may charge a reasonable fee for copies of or providing access to
or distributing Project Gutenberg electronic works provided that:
• You pay a royalty fee of 20% of the gross profits you derive from the
use of Project Gutenberg works calculated using the method you
already use to calculate your applicable taxes. The fee is owed to the
owner of the Project Gutenberg trademark, but he has agreed to donate
royalties under this paragraph to the Project Gutenberg Literary
Archive Foundation. Royalty payments must be paid within 60 days
following each date on which you prepare (or are legally required to
prepare) your periodic tax returns. Royalty payments should be clearly
marked as such and sent to the Project Gutenberg Literary Archive
Foundation at the address specified in Section 4, “Information about
donations to the Project Gutenberg Literary Archive Foundation.”
• You provide a full refund of any money paid by a user who notifies
you in writing (or by e-mail) within 30 days of receipt that s/he does
not agree to the terms of the full Project Gutenberg™ License. You
must require such a user to return or destroy all copies of the works
possessed in a physical medium and discontinue all use of and all
access to other copies of Project Gutenberg™ works.
• You provide, in accordance with paragraph 1.F.3, a full refund of any
money paid for a work or a replacement copy, if a defect in the
electronic work is discovered and reported to you within 90 days of
receipt of the work.
• You comply with all other terms of this agreement for free distribution
of Project Gutenberg™ works.
1.E.9. If you wish to charge a fee or distribute a Project Gutenberg™
electronic work or group of works on different terms than are set forth in
this agreement, you must obtain permission in writing from the Project
Gutenberg Literary Archive Foundation, the manager of the Project
Page 490
Gutenberg™ trademark. Contact the Foundation as set forth in Section 3
below.
1.F.
1.F.1. Project Gutenberg volunteers and employees expend considerable
effort to identify, do copyright research on, transcribe and proofread works
not protected by U.S. copyright law in creating the Project Gutenberg™
collection. Despite these efforts, Project Gutenberg™ electronic works, and
the medium on which they may be stored, may contain “Defects,” such as,
but not limited to, incomplete, inaccurate or corrupt data, transcription
errors, a copyright or other intellectual property infringement, a defective or
damaged disk or other medium, a computer virus, or computer codes that
damage or cannot be read by your equipment.
1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except
for the “Right of Replacement or Refund” described in paragraph 1.F.3, the
Project Gutenberg Literary Archive Foundation, the owner of the Project
Gutenberg™ trademark, and any other party distributing a Project
Gutenberg™ electronic work under this agreement, disclaim all liability to
you for damages, costs and expenses, including legal fees. YOU AGREE
THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT
EXCEPT THOSE PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE
THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY
DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE
TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL,
PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE
NOTICE OF THE POSSIBILITY OF SUCH DAMAGE.
1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you
discover a defect in this electronic work within 90 days of receiving it, you
can receive a refund of the money (if any) you paid for it by sending a
written explanation to the person you received the work from. If you
received the work on a physical medium, you must return the medium with
your written explanation. The person or entity that provided you with the
defective work may elect to provide a replacement copy in lieu of a refund.
If you received the work electronically, the person or entity providing it to
below.
1.F.
1.F.1. Project Gutenberg volunteers and employees expend considerable
effort to identify, do copyright research on, transcribe and proofread works
not protected by U.S. copyright law in creating the Project Gutenberg™
collection. Despite these efforts, Project Gutenberg™ electronic works, and
the medium on which they may be stored, may contain “Defects,” such as,
but not limited to, incomplete, inaccurate or corrupt data, transcription
errors, a copyright or other intellectual property infringement, a defective or
damaged disk or other medium, a computer virus, or computer codes that
damage or cannot be read by your equipment.
1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except
for the “Right of Replacement or Refund” described in paragraph 1.F.3, the
Project Gutenberg Literary Archive Foundation, the owner of the Project
Gutenberg™ trademark, and any other party distributing a Project
Gutenberg™ electronic work under this agreement, disclaim all liability to
you for damages, costs and expenses, including legal fees. YOU AGREE
THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT
EXCEPT THOSE PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE
THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY
DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE
TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL,
PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE
NOTICE OF THE POSSIBILITY OF SUCH DAMAGE.
1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you
discover a defect in this electronic work within 90 days of receiving it, you
can receive a refund of the money (if any) you paid for it by sending a
written explanation to the person you received the work from. If you
received the work on a physical medium, you must return the medium with
your written explanation. The person or entity that provided you with the
defective work may elect to provide a replacement copy in lieu of a refund.
If you received the work electronically, the person or entity providing it to
Page 491
you may choose to give you a second opportunity to receive the work
electronically in lieu of a refund. If the second copy is also defective, you
may demand a refund in writing without further opportunities to fix the
problem.
1.F.4. Except for the limited right of replacement or refund set forth in
paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO OTHER
WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR
FITNESS FOR ANY PURPOSE.
1.F.5. Some states do not allow disclaimers of certain implied warranties or
the exclusion or limitation of certain types of damages. If any disclaimer or
limitation set forth in this agreement violates the law of the state applicable
to this agreement, the agreement shall be interpreted to make the maximum
disclaimer or limitation permitted by the applicable state law. The invalidity
or unenforceability of any provision of this agreement shall not void the
remaining provisions.
1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
trademark owner, any agent or employee of the Foundation, anyone
providing copies of Project Gutenberg™ electronic works in accordance
with this agreement, and any volunteers associated with the production,
promotion and distribution of Project Gutenberg™ electronic works,
harmless from all liability, costs and expenses, including legal fees, that
arise directly or indirectly from any of the following which you do or cause
to occur: (a) distribution of this or any Project Gutenberg work, (b)
alteration, modification, or additions or deletions to any Project Gutenberg
work, and (c) any Defect you cause.
Section 2. Information about the Mission of Project
Gutenberg
Project Gutenberg is synonymous with the free distribution of electronic
works in formats readable by the widest variety of computers including
obsolete, old, middle-aged and new computers. It exists because of the
electronically in lieu of a refund. If the second copy is also defective, you
may demand a refund in writing without further opportunities to fix the
problem.
1.F.4. Except for the limited right of replacement or refund set forth in
paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO OTHER
WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR
FITNESS FOR ANY PURPOSE.
1.F.5. Some states do not allow disclaimers of certain implied warranties or
the exclusion or limitation of certain types of damages. If any disclaimer or
limitation set forth in this agreement violates the law of the state applicable
to this agreement, the agreement shall be interpreted to make the maximum
disclaimer or limitation permitted by the applicable state law. The invalidity
or unenforceability of any provision of this agreement shall not void the
remaining provisions.
1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
trademark owner, any agent or employee of the Foundation, anyone
providing copies of Project Gutenberg™ electronic works in accordance
with this agreement, and any volunteers associated with the production,
promotion and distribution of Project Gutenberg™ electronic works,
harmless from all liability, costs and expenses, including legal fees, that
arise directly or indirectly from any of the following which you do or cause
to occur: (a) distribution of this or any Project Gutenberg work, (b)
alteration, modification, or additions or deletions to any Project Gutenberg
work, and (c) any Defect you cause.
Section 2. Information about the Mission of Project
Gutenberg
Project Gutenberg is synonymous with the free distribution of electronic
works in formats readable by the widest variety of computers including
obsolete, old, middle-aged and new computers. It exists because of the
Page 492
efforts of hundreds of volunteers and donations from people in all walks of
life.
Volunteers and financial support to provide volunteers with the assistance
they need are critical to reaching Project Gutenberg’s goals and ensuring
that the Project Gutenberg collection will remain freely available for
generations to come. In 2001, the Project Gutenberg Literary Archive
Foundation was created to provide a secure and permanent future for
Project Gutenberg and future generations. To learn more about the Project
Gutenberg Literary Archive Foundation and how your efforts and donations
can help, see Sections 3 and 4 and the Foundation information page at
www.gutenberg.org.
Section 3. Information about the Project Gutenberg
Literary Archive Foundation
The Project Gutenberg Literary Archive Foundation is a non-profit 501(c)
(3) educational corporation organized under the laws of the state of
Mississippi and granted tax exempt status by the Internal Revenue Service.
The Foundation’s EIN or federal tax identification number is 64-6221541.
Contributions to the Project Gutenberg Literary Archive Foundation are tax
deductible to the full extent permitted by U.S. federal laws and your state’s
laws.
The Foundation’s business office is located at 41 Watchung Plaza #516,
Montclair NJ 07042, USA, +1 (862) 621-9288. Email contact links and up
to date contact information can be found at the Foundation’s website and
official page at www.gutenberg.org/contact
Section 4. Information about Donations to the Project
Gutenberg Literary Archive Foundation
Project Gutenberg™ depends upon and cannot survive without widespread
public support and donations to carry out its mission of increasing the
number of public domain and licensed works that can be freely distributed
in machine-readable form accessible by the widest array of equipment
life.
Volunteers and financial support to provide volunteers with the assistance
they need are critical to reaching Project Gutenberg’s goals and ensuring
that the Project Gutenberg collection will remain freely available for
generations to come. In 2001, the Project Gutenberg Literary Archive
Foundation was created to provide a secure and permanent future for
Project Gutenberg and future generations. To learn more about the Project
Gutenberg Literary Archive Foundation and how your efforts and donations
can help, see Sections 3 and 4 and the Foundation information page at
www.gutenberg.org.
Section 3. Information about the Project Gutenberg
Literary Archive Foundation
The Project Gutenberg Literary Archive Foundation is a non-profit 501(c)
(3) educational corporation organized under the laws of the state of
Mississippi and granted tax exempt status by the Internal Revenue Service.
The Foundation’s EIN or federal tax identification number is 64-6221541.
Contributions to the Project Gutenberg Literary Archive Foundation are tax
deductible to the full extent permitted by U.S. federal laws and your state’s
laws.
The Foundation’s business office is located at 41 Watchung Plaza #516,
Montclair NJ 07042, USA, +1 (862) 621-9288. Email contact links and up
to date contact information can be found at the Foundation’s website and
official page at www.gutenberg.org/contact
Section 4. Information about Donations to the Project
Gutenberg Literary Archive Foundation
Project Gutenberg™ depends upon and cannot survive without widespread
public support and donations to carry out its mission of increasing the
number of public domain and licensed works that can be freely distributed
in machine-readable form accessible by the widest array of equipment
Page 493
including outdated equipment. Many small donations ($1 to $5,000) are
particularly important to maintaining tax exempt status with the IRS.
The Foundation is committed to complying with the laws regulating
charities and charitable donations in all 50 states of the United States.
Compliance requirements are not uniform and it takes a considerable effort,
much paperwork and many fees to meet and keep up with these
requirements. We do not solicit donations in locations where we have not
received written confirmation of compliance. To SEND DONATIONS or
determine the status of compliance for any particular state visit
www.gutenberg.org/donate.
While we cannot and do not solicit contributions from states where we have
not met the solicitation requirements, we know of no prohibition against
accepting unsolicited donations from donors in such states who approach us
with offers to donate.
International donations are gratefully accepted, but we cannot make any
statements concerning tax treatment of donations received from outside the
United States. U.S. laws alone swamp our small staff.
Please check the Project Gutenberg web pages for current donation methods
and addresses. Donations are accepted in a number of other ways including
checks, online payments and credit card donations. To donate, please visit:
www.gutenberg.org/donate.
Section 5. General Information About Project Gutenberg
electronic works
Professor Michael S. Hart was the originator of the Project Gutenberg
concept of a library of electronic works that could be freely shared with
anyone. For forty years, he produced and distributed Project Gutenberg
eBooks with only a loose network of volunteer support.
Project Gutenberg eBooks are often created from several printed editions,
all of which are confirmed as not protected by copyright in the U.S. unless a
particularly important to maintaining tax exempt status with the IRS.
The Foundation is committed to complying with the laws regulating
charities and charitable donations in all 50 states of the United States.
Compliance requirements are not uniform and it takes a considerable effort,
much paperwork and many fees to meet and keep up with these
requirements. We do not solicit donations in locations where we have not
received written confirmation of compliance. To SEND DONATIONS or
determine the status of compliance for any particular state visit
www.gutenberg.org/donate.
While we cannot and do not solicit contributions from states where we have
not met the solicitation requirements, we know of no prohibition against
accepting unsolicited donations from donors in such states who approach us
with offers to donate.
International donations are gratefully accepted, but we cannot make any
statements concerning tax treatment of donations received from outside the
United States. U.S. laws alone swamp our small staff.
Please check the Project Gutenberg web pages for current donation methods
and addresses. Donations are accepted in a number of other ways including
checks, online payments and credit card donations. To donate, please visit:
www.gutenberg.org/donate.
Section 5. General Information About Project Gutenberg
electronic works
Professor Michael S. Hart was the originator of the Project Gutenberg
concept of a library of electronic works that could be freely shared with
anyone. For forty years, he produced and distributed Project Gutenberg
eBooks with only a loose network of volunteer support.
Project Gutenberg eBooks are often created from several printed editions,
all of which are confirmed as not protected by copyright in the U.S. unless a
Page 494
copyright notice is included. Thus, we do not necessarily keep eBooks in
compliance with any particular paper edition.
Most people start at our website which has the main PG search facility:
www.gutenberg.org.
This website includes information about Project Gutenberg, including how
to make donations to the Project Gutenberg Literary Archive Foundation,
how to help produce our new eBooks, and how to subscribe to our email
newsletter to hear about new eBooks.
compliance with any particular paper edition.
Most people start at our website which has the main PG search facility:
www.gutenberg.org.
This website includes information about Project Gutenberg, including how
to make donations to the Project Gutenberg Literary Archive Foundation,
how to help produce our new eBooks, and how to subscribe to our email
newsletter to hear about new eBooks.
Page 495
back
Page 496
back
Page 497
back
Page 498
back
Page 499
back
Page 500
back