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Title: The Practical Astronomer

Author: Thomas Dick

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Language: English

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*** START OF THE PROJECT GUTENBERG EBOOK THE
PRACTICAL ASTRONOMER ***

THE AUTHOR’S OBSERVATORY.

THE
PRACTICAL ASTRONOMER,
COMPRISING
ILLUSTRATIONS OF LIGHT AND COLOURS—PRACTICAL
DESCRIPTIONS OF ALL KINDS OF TELESCOPES—THE
USE OF THE EQUATORIAL-TRANSIT—CIRCULAR,
AND OTHER ASTRONOMICAL
INSTRUMENTS,

A PARTICULAR ACCOUNT OF THE

EARL OF ROSSE’S LARGE TELESCOPES,

AND OTHER TOPICS CONNECTED WITH ASTRONOMY.

BY THOMAS DICK, LL.D.
AUTHOR OF THE “CHRISTIAN PHILOSOPHER,” “CELESTIAL SCENERY,”
“THE SIDEREAL HEAVENS,” &C. &C.

Illustrated with One hundred Engravings.

SEELEY, BURNSIDE, AND SEELEY,
FLEET-STREET, LONDON.
MDCCCXLV.

PRINTED BY L. SEELEY.

PREFACE.
The following work was announced several years ago in the preface to the
volume on “The Sidereal Heavens;” since which time numerous enquiries
have been made after it by correspondents in England, the West Indies, and
America. It was nearly ready for publication three years ago; but
circumstances over which the Author had no controul, prevented its
appearance at that period. This delay, however, has enabled him to
introduce descriptions of certain instruments and inventions which were
partly unknown at the time to which he refers.

The title “Practical Astronomer” has been fixed upon, as the shortest that
could be selected, although the volume does not comprise a variety of
topics and discussions generally comprehended in this department of
astronomy. The work is intended for the information of general readers,
especially for those who have acquired a relish for astronomical pursuits,
and who wish to become acquainted with the instruments by which celestial
observations are made, and to apply their mechanical skill to the
construction of some of those which they may wish to possess. With this
view the Author has entered into a variety of minute details, in reference to
the construction and practical application of all kinds of telescopes, &c.
which are not to be found in general treatises on Optics and Astronomy.

As Light is the foundation of astronomical science, and of all the
instruments used for celestial observation, a brief description is given of the
general properties of light—of the laws by which it is refracted and
reflected when passing through different mediums—and of the effects it
produces in the system of nature—in order to prepare the way for a clear
understanding of the principles on which optical instruments are
constructed, and the effects they produce.

As this, as well as every other physical subject, forms a part of the
arrangements of the Creator throughout the material system—the Author

has occasionally taken an opportunity of directing the attention of the reader
to the Wisdom and Beneficence of the Great First Cause, and of introducing
those moral reflections which naturally flow from the subject.

The present is the ninth volume which the Author has presented to the
public, and he indulges the hope that it will meet with the same favourable
reception which his former publications have uniformly experienced. It was
originally intended to conclude the volume with a few remarks on the utility
of astronomical studies, and their moral and religious tendency, but this has
been prevented, for the present, in consequence of the work having swelled
to a greater size than was anticipated. Should he again appear before the
public as an author, the subject of discussion and illustration will have a
more direct bearing than the present on the great objects of religion and a
future world.

Broughty Ferry, near Dundee, August, 1845.

CONTENTS.

PART I.
ON LIGHT.

INTRODUCTION.
Necessity of light to the knowledge and happiness of all sentient beings
—Its beautiful and enlivening effects—An emblem of the Deity—
Provision made for its universal diffusion
page 1-7.

CHAPTER I.

General Properties of Light.
Interesting nature of this study—Different hypotheses which have been
formed respecting the nature of light—It radiates in straight lines—
Moves with amazing velocity—Flows in all directions from
luminous bodies—Duration of its impressions on the eye—
Supposed to have a certain degree of force or momentum—
Experiments in relation to this point—Its intensity diminished in
proportion to the square of the distance—Its reflection from opake
bodies renders objects visible—Intensity of reflected light—Subject
to the law of attraction—Forms a constituent part of certain bodies
—Solar phosphori, and the phenomena they exhibit—Produces
certain effects on planets and flowers, exemplified in a variety of
instances—Supposed to have an influence on the propagation of
sound
page 8-37

Reflections on the nature of light, and the multifarious effects it produces
throughout the universe—A representation of the Divinity—
Wisdom and Goodness of God displayed in its formation
page 37-40.

CHAPTER II.

On the Refraction of Light.
Nature of refraction—Illustrated by experiments—Angle of refraction—
Familiar experiments illustrative of refraction—Refraction explains
the causes of many curious and interesting phenomena—Its effect
on the heavenly bodies—On the twilight—Illustrated by figures
page 41-53.

EXTRAORDINARY CASES OF REFRACTION IN RELATION TO
TERRESTRIAL OBJECTS.
Extraordinary appearance of the coast of France from Hastings—
Appearance of a ship seen by Captain Colby, beyond the coast of
Caithness—Scoresby’s view of his father’s ship when beyond the
horizon—Phenomenon near the Himalaya mountains—Bell Rock
light-house—Summary statement of the diversified effects of
refraction—Reflections on the beneficent and diversified effects
produced by the law of refraction—It increases the length of the
day, particularly in the polar regions—Is the cause of that splendour
which appears in the objects around us—Quantity of refraction in
respect to terrestrial objects, and its utility—Its effects may be more
diversified in other worlds
page 53-63.

CHAPTER III.

On the Refraction of Light through Spherical Transparent
Substances, or Lenses.
Refraction the foundation of optical instruments—Various forms of
lenses—Parallel, converging, and diverging rays—Illustrated by

diagrams—Concave lenses, their effects, and how to find their focal
distances—Images formed by convex lenses—Illustrated by
experiments—Principles in relation to images formed by lenses—
Their magnifying powers, &c.
page 63-75.

REFLECTIONS DEDUCED FROM THE PRECEDING SUBJECT.
Property of the rays of light in forming images of objects—Wonderful
results and discoveries which have flowed from this property—in
relation to our knowledge of the scenery of the heavens and the
minute parts of nature—and of our views of the attributes of Deity
page 75-80.

CHAPTER IV.

On the Reflection of Light.
Nature of reflection—Plane, convex, and concave speculums—Angle of
reflection—Reflection of objects from plane mirrors, illustrated by
figures—Reflection by Convex and Concave mirrors—Properties of
convex mirrors, and the purposes to which they are applied.
Properties of concave speculums, and their utility—Of the images
formed by concave speculums—Illustrated by a variety of figures
and experiments—Their power of magnifying and burning—
Amusing deceptions produced by—Resemblance between the
properties of convex lenses, and concave mirrors—Quantity of light
reflected by polished surfaces
page 81-106.

UNCOMMON APPEARANCES OF NATURE PRODUCED BY THE
COMBINED INFLUENCE OF REFLECTION AND REFRACTION.
Fata Morgana—The Mirage—Inverted images of ships seen in the
horizon—Appearance of Dover castle at Ramsgate—Spectre of the
Brocken—Scenes in the Highlands of Scotland—Large cross seen
at Migné in France—Dr. Wollaston’s illustrations of such
phenomena—Utility of science in dissipating superstitious fears
page 106-118.

REMARKS AND REFLECTIONS IN REFERENCE TO THE
PHENOMENA DESCRIBED ABOVE.
Light, the beauty of the universe, and a symbol of the Divinity—In other
worlds it may produce an infinite variety of sublime scenery
page 118-122.

CHAPTER V.

Sect. 1.—On the Colours of Light.
Colours, the beauty of nature—Opinions which were formerly
entertained respecting their cause—Sir I. Newton’s experiments
with the Prism—Colours and phenomena produced by the prism—
Imperfection of optic lenses—Various illustrations—Differently
coloured rays have not the same illuminating power—Heating and
chemical properties of some of the rays of the solar spectrum—
property of communicating the Magnetic power—Fraunhofer, and
his discoveries in reference to the spectrum—Experiments on white
and coloured light
page 123-137.

Sect. 2.—on the colours of natural objects.
Colours not in the objects themselves, but in the light which falls upon
them—Illustrations of this position—Atmosphere the source of a
variety of colours—Various natural phenomena, in relation to
colour, explained
page 137-143.

Sect. 3.—phenomena of the rainbow.
Rainbow described—Experiments to illustrate its cause—Descriptions of
its various phenomena, and optical explanations of their causes—
Rainbows exhibiting complete circles—Their appearance in
different countries—Summary view of the principal facts respecting
the rainbow—Lunar rainbows—Scriptural allusions to the rainbow
—Whether there was any rainbow before the deluge
page 144-157.

Sect. 4.—reflections on the beauty and utility of colours.
Beauty and variety derived from colours in the scenery of nature—
Colours produced by the atmosphere in different countries—What
would be the aspect of nature, in heaven and on earth, were there
only one colour—How it would affect the common intercourse and
employments of society—Wisdom and Beneficence of the Creator
displayed in the diversity of colours—Throughout all the systems of
the universe, a diversity of colours prevails—This subject has a
tendency to inspire us with gratitude
page 158-168.

PART II.
ON TELESCOPES.

CHAPTER I.

History of the Invention of Telescopes.
The telescope a noble instrument—Effects it produces—Whether known
to the ancients—Friar Bacon’s ideas respecting telescopes—First
constructed in Holland—The invention claimed by different
persons—Galileo’s account of the construction of his telescope—
Discoveries which he made with this instrument—How his
discoveries were received by the learned—Specimens of learned
nonsense brought forward by pretended philosophers—Supposed
length of Galileo’s telescope—Various claimants to the invention of
this instrument
page 169-183.

CHAPTER II.

Of the Camera Obscura.

Appearance of objects in a camera obscura—The dark chamber—This
instrument serves to explain the nature of a refracting telescope—
Particulars to be attended to, in exhibiting objects with the Camera
—It illustrates the nature of vision—Revolving camera obscura—
Portable camera
page 184-196.

The Daguerreotype.
An important discovery for fixing the images produced by the camera—
Description of the Daguerreotype process—Preparation of the plate,
fixing the impression, &c.—Preparation of photogenic paper—
Beneficial effects which this art may produce—Representations of
objects in the heavens, &c.
page 196-205.

CHAPTER III.

On the Optical Angle, and the Apparent Magnitude of Objects.
Various illustrations of the apparent magnitude of objects—Fallacies in
relation to apparent magnitudes—Apparent magnitudes in the
heavens—Difference between absolute and apparent magnitudes
page 206-213.

CHAPTER IV.

On the Different Kinds of Refracting Telescopes.

Sect. 1.—The Galilean Telescope.
Construction and peculiar properties of this instrument
page 214-217.

Sect. 2.—The Common Astronomical Refracting Telescope.
Description of its nature and construction—How its magnifying power is
determined. Table of the linear aperture, magnifying powers, &c.,

of astronomical telescopes from 1 to 120 feet in length—Summary
view of the properties of this telescope
page 218-224.

Sect. 3.—The Aerial Telescope.
This telescope is used without a tube—Description of the apparatus
connected with it, illustrated with figures—Huygens’ Hartsocker’s
and Cassini’s large telescopes
page 224-228.

Sect. 4.—The Common Refracting Telescope for Terrestrial
Objects.
Arrangement of its lenses—Magnifying power—Manner in which the
rays of light are refracted through the telescopes now described
page 228-231.

Sect. 5.—Telescope Formed by a Single Lens.
Various experiments in relation to this point—Experiments with a lens
26 focal distance, and 11½ inches diameter
page 232-235.

Sect. 6.—The Achromatic Telescope.
Imperfections of common refracting telescopes—Dollond’s discovery—
Newton’s error—Explanation of the principle of achromatic
telescopes—Combination of lenses—Difficulties in the
construction of such instruments—Difficulty in procuring large
disks of flint glass—Guinaud’s experiments
page 235-248.

NOTICES OF SOME LARGE ACHROMATIC TELESCOPES ON
THE CONTINENT, AND IN GREAT BRITAIN.
The Dorpat telescope—Sir J. South’s telescope—Captain Smyth’s—Rev.
Dr. Pearson’s—Mr. Lawson’s—Mr. Cooper’s—Mr. Bridges’, &c.,
—Achromatics in Cambridge and Paris observatories
pages 248-254.

ACHROMATIC TELESCOPES OF A MODERATE SIZE, WITH
THEIR PRICES, AS SOLD BY LONDON OPTICIANS.
The 2½ feet Achromatic—The 3½ feet—The powers applied to it—and
the views it gives of the heavenly bodies—The 5 feet achromatic—
Stands for telescopes, illustrated by engravings
page 254-264.

PROPORTIONS OR CURVATURE OF THE LENSES WHICH
FORM AN ACHROMATIC OBJECT-GLASS.
Various tables and explanations
page 265-269.

ACHROMATIC TELESCOPES COMPOSED OF FLUID LENSES.
Blair’s fluid telescope, with an account of its performance—Barlow’s
large refracting telescope with a fluid concave lens—Its
construction, and the effect it produces on double stars, &c.—
Rogers’ achromatic telescope on a new plan—Wilson’s telescope,
&c.
page 269-283.

CHAPTER V.

On Reflecting Telescopes.

Sect. 1.—History of the Invention, and a General Description of
the Construction of These Instruments.

Gregory’s Reflector—Newtonian Reflector—Cassegrainian Reflector—
Magnifying powers of reflectors—Short’s Reflectors—Their
powers and prices—General remarks on Gregorian reflectors—
Apertures and magnifying powers of Newtonian telescopes—Prices
of Reflecting telescopes
page 284-301.

Sect. 2.—The Herschelian Telescope.

Description of Sir W. Herschel’s 40 feet telescope, with its machinery,
apparatus, and the discoveries made by it—Sir J. Herschel’s 20 feet
reflector
page 301-308.

Sect. 3.—Ramage’s Large Reflecting Telescope.
page 308-311.

Sect. 4.—The Aerial Reflector—constructed by the Author.
Construction of this telescope, and the manner of using it—Illustrated by
figures—Its properties and advantages—Tube not necessary in
reflecting telescopes—How a large reflector might be constructed
without a tube—How the form of a telescope may be used for
viewing perspectives
page 311-325.

Sect. 4.—Earl of Rosse’s Reflecting Telescopes.
His mode of forming a large speculum, &c., see also, Appendix
page 325-328.

Sect. 5.—Reflecting Telescopes With Glass Specula.
Various experiments on this subject, with their results
page 329-331.

Sect. 6.—A Reflecting Telescope With a Single Mirror and No
Eye-piece.
Experiments illustrative of this construction
page 332-334.

ON THE EYE-PIECES OF TELESCOPES. ASTRONOMICAL
EYE-PIECES.
Huygenian eye-piece—Ramsden’s eye-piece—Aberration of lenses—
Celestial eye-pieces with variable powers. Diagonal eye-pieces—
Various forms of them described—Various aspects in which objects
may be viewed by them
page 335-347.

TERRESTRIAL EYE-PIECES.
Eye-pieces with four lenses—Proportions of the focal lengths of these
lenses—Dimensions and powers of several eye-pieces stated
page 347-353.

DESCRIPTION OF AN EYE-PIECE, &C., OF AN OLD DUTCH
ACHROMATIC TELESCOPE.
This telescope supposed to have been invented in Holland before
Dollond’s discovery was known—Peculiarity of its eye-piece
page 354-357.

DESCRIPTION OF THE PANCRATIC EYE-TUBE.
page 357-360.

CHAPTER VI.

Miscellaneous Remarks in Relation to Telescopes.
1. Adjustments requisite to be attended to in the use of telescopes—2.
State of the atmosphere most proper for observing terrestrial and
celestial objects—Average number of hours in the year fit for
celestial observations.—3. On the magnifying powers requisite for
observing the phenomena of the different planets—Comets—
Double stars, &c.—Illustrated at large from p. 369-380.—4. Mode
of exhibiting the solar spots—Eye-pieces best adapted for this
purpose—How they may be exhibited to a large company—Mode
in which their dimensions may be determined.—5. On the space-
penetrating power of telescopes—Herschel’s observations on
space-penetrating powers—Comparison of achromatic and
Gregorian reflectors.—6. On choosing telescopes, and ascertaining
their properties—Various modes of ascertaining the goodness of
telescopes—General remarks and cautions on this point—A
circumstance which requires to be attended to in using achromatics.
—7. On the mode of determining the magnifying power of
telescopes—Various experiments in relation to this point.—8. On
cleaning the lenses of telescopes

page 361-407.

ON MEGALASCOPES, OR TELESCOPES FOR VIEWING VERY
NEAR OBJECTS.
Mode of adapting a telescope for this purpose—objects to which they
may be applied
page 407-411.

REFLECTIONS ON LIGHT AND VISION, AND ON THE NATURE
AND UTILITY OF TELESCOPES.
Wonderful and mysterious nature of light—The organ of vision, and its
expansive range—Wonderful nature of the telescope, and the
objects it has disclosed to view—No boundaries should be set to the
discoveries of science and the improvement of art—The telescope
is a machine which virtually transports us to the distant regions of
space—It enlarges our views of the sublime scenes of creation—It
has tended to amplify our conceptions of the empire and the
attributes of the Deity—Various uses of this instrument in relation
to science and common life
page 411-431.

CHAPTER VII.

On the Method of Grinding and Polishing Optical Lenses and
Specula.
1. Directions for grinding lenses for eye-glasses, microscopes, &c.—2.
Method of casting and grinding the specula of reflecting telescopes
—Compositions for speculum metal—To try the figure of the metal
—To adjust the eye-hole of Gregorian reflectors—To center the
specula—To center lenses.
page 432-442.

PART III.
ON VARIOUS ASTRONOMICAL

INSTRUMENTS.

CHAPTER I.

On Micrometers.
Various descriptions of micrometers—Cavallo’s micrometer described—
To ascertain the value of its divisions—Practical uses of this
micrometer—Problems which may be solved by it—Tables for
facilitating its use
page 443-452.

CHAPTER II.

On the Equatorial Telescope, or Portable Observatory.
History of equatorials—Description of one of the simplest construction
of these instruments—To adjust the equatorial for observation—To
adjust the line of sight—Description of the nonius—To find the
meridian line by one observation—Manner of observing stars and
planets in the day-time
page 453-464.

OBSERVATIONS, BY THE AUTHOR, ON THE FIXED STARS
AND PLANETS, MADE IN THE DAY-TIME, BY THE
EQUATORIAL.
Object of these observations—stars of the first and second magnitudes—
General deductions from these observations
page 464-469.

OBSERVATIONS ON THE PLANETS IN THE DAY-TIME.
Series of observations on Venus, when near the sun—Seen at the time of
her superior conjunction in 1843—Conclusions deduced from these
observations—phenomena observed during these observations—
Remarkable phenomenon during an eclipse of the sun
page 469-480.

OBSERVATIONS ON JUPITER AND OTHER PLANETS.
General conclusions, &c.
page 480-485.

UTILITY OF CELESTIAL DAY OBSERVATIONS.
page 485-491.

ON THE ASTRONOMICAL QUADRANT.
page 492-496.

THE ASTRONOMICAL CIRCLE.
page 496-502.

THE TRANSIT INSTRUMENT.
page 502-505.

CHAPTER III.

On Observatories.
Leading features of a spot adapted for celestial observations—Public and
private observatories—Greenwich observatory—Instruments with
which an observatory should be furnished—The Author’s private
observatory—Revolving domes for observatories—Cautions to be
attended to in celestial observations
page 506-516.

CHAPTER IV.

On Orreries or Planetariums.
History of such machines—Sphere of Archimedes and Posidonius—Dr.
Long’s Uranium—Wheel-work of the common Planetarium—
Figure representing this machine—Problems which may be
performed by it
page 517-527.

DR. HENDERSON’S PLANETARIUM.
Section of its wheel-work—Number of teeth in the wheels and pinions
which move the different planets—Extreme accuracy of these
movements.
page 527-538.

ON THE VARIOUS OPINIONS WHICH WERE ORIGINALLY
FORMED OF SATURN’S RING, ILLUSTRATED WITH 13 VIEWS.
When and by whom its true figure was discovered.
page 538-543.

ON THE SUPPOSED DIVISION OF THE EXTERIOR RING OF
SATURN.
Kater’s, Short’s, Quetelet’s and Decuppis’s observations
page 543-547.

APPENDIX.

1. Description of the Earl of Rosse’s Largest Telescope.
Composition of the speculum, and the process of casting it—Mode of
grinding and polishing it—Manner in which it is filled up—
Expenses incurred in its construction—Results of observations
which have been made with it—Two views representing this
instrument and the buildings connected with it—Sir J. South’s
remarks and anticipations
page 548-562.

2. Hints to amateurs in astronomy respecting the
construction of telescopes.
page 563.

LIST OF ENGRAVINGS.
Figure Page
1. Representation of the diminution of the intensity of
22
light.
2. Illustrative of the refraction of light. 43
3. Representing the angles of incidence and refraction. 44
4. The refraction of the atmosphere. 51
5. Various forms of lenses. 65
6, 7, 8. Parallel, converging, and diverging rays. 66
9, 10, 11. Passage of parallel, diverging, and
67
converging rays through convex lenses.
12. Passage of parallel rays through concave lenses. 69
13. Images formed by convex lenses. 71
14. Angle of incidence and reflection. 83
15. Images as reflected from a plane mirror. 84
16. Illustrative of reflections from a plane mirror. 85
17. Shewing how the image in a plane mirror is twice the
86
length of the object.
18. Reflection from concave mirrors. 87
19. Reflection from convex mirrors. 89
20. Parallel rays as reflected from concave mirrors. 91
21. Diverging rays as reflected from concave mirrors. 91
22. Images formed before concave mirrors. 93
23. Images formed behind concave mirrors. 96
24. Illustrating the magnifying power of concave
97
mirrors.
25. Inverted images formed in the front of concave
98
mirrors.
26. Illustrative of deceptions produced by concave
100
mirrors.

27, 28. Experiment with a bottle half filled with water. 101
29. Effect of extraordinary refraction on ships at sea. 109
30. Experiment for illustrating the causes of uncommon
117
refraction.
31. Prismatic spectrum. 127
32. Different foci of coloured rays in convex lenses. 129
33. Experiment to show the different foci of red and
129
violet rays.
34. Illustrative of the prismatic colours. 136
35. Explanatory of refraction and reflection from drops
147
of rain.
36. Explanatory of the rainbow. 149
37. Images of objects formed in a dark chamber. 187
38. The revolving Camera Obscura. 194
39, 40. The portable Camera Obscura. 195, 196
40,* 41, 42. Illustrative of the angle of vision, and the 206, 207,
apparent magnitude of objects. 208
43. The Galilean telescope. 215
44. The astronomical telescope. 218
45, 46. The aerial refracting telescope. 226
47. The common refracting telescope. 228
48, 49, 50. Manner in which the rays of light are
231
refracted in telescopes.
51. Telescope with a single lens. 234
52. Illustrative of spherical aberration. 236
53. Illustrative of the principle of achromatic telescopes. 241
54, 55. Double and treble achromatic object-glass. 242
57. Common stand for achromatic telescopes. 260
58. Equatorial stand for achromatic telescopes. 262
59. Dollond’s stand for achromatic telescopes. 264
60. Blair’s fluid achromatic object-glass. 271
61. Barlow’s fluid telescope. 274
62, 63, 64, 65, 66. Various forms of reflecting telescopes. 288
67. Gregorian reflecting telescope. 293
69. The aerial reflector. 313

70. Front view of the aerial reflector. 314
71. Construction of large reflecting telescope. 322
72. Reflecting telescope with a single mirror. 332
73. Huygenian eye-piece. 336
74. Ramsden’s eye-piece. 339
75, 76. Combination of lenses for achromatic eye-pieces. 340
77, 78. Diagonal eye-pieces. 344, 345
79. Terrestrial eye-piece with four lenses. 349
80. Eye-piece of an old Dutch achromatic telescope. 356
81. Pancratic eye-piece. 359
82. Manner of exhibiting the solar spots. 384
84. Mode of measuring distances from one station. 430
85. Cavallo’s micrometer. 446
86. The equatorial telescope, or portable observatory. 455
87. Figure to illustrate the principle of the quadrant. 491
88. The astronomical quadrant. 493
89. The astronomical circle. 496
90. The transit instrument. 502
91. Plan of a private observatory. 511
92. Rotatory dome for an observatory. 513
93. Wheel-work of a planetarium. 521
94. Perspective view of a planetarium. 522
95. Apparatus for exhibiting the retrograde motions of
525
the planets.
96. Section of the wheel-work of Dr. Henderson’s
528
planetarium.
97. Thirteen views of the supposed form of Saturn’s ring. 539
98. Earl of Rosse’s Great Telescope. 559
99. Section of the machinery connected with the
560
telescope.
100. Perspective view of the author’s observatory—to
front the title.

THE

PRACTICAL ASTRONOMER.

PART I.
ON LIGHT.

INTRODUCTION.

Light is that invisible etherial matter which renders objects perceptible by
the visual organs. It appears to be distributed throughout the immensity of
the universe, and is essentially requisite to the enjoyment of every rank of
perceptive existence. It is by the agency of this mysterious substance, that
we become acquainted with the beauties and sublimities of the universe,
and the wonderful operations of the Almighty Creator. Without its universal
influence, an impenetrable veil would be thrown over the distant scenes of
creation; the sun, the moon, the planets, and the starry orbs, would be
shrouded in the deepest darkness, and the variegated surface of the globe on
which we dwell, would be almost unnoticed and unknown. Creation would
disappear, a mysterious gloom would surround the mind of every
intelligence, all around would appear a dismal waste, and an
undistinguished chaos. To whatever quarter we might turn, no form nor
comeliness would be seen, and scarcely a trace of the perfections and
agency of an All Wise and Almighty Being could be perceived throughout
the universal gloom. In short, without the influence of light, no world could
be inhabited, no animated being could subsist in the manner it now does, no
knowledge could be acquired of the works of God, and happiness, even in
the lowest degree, could scarcely be enjoyed by any organized intelligence.

We have never yet known what it is to live in a world deprived of this
delightful visitant; for in the darkest night we enjoy a share of its beneficial
agency, and even in the deepest dungeon its influence is not altogether
unfelt.1 The blind, indeed, do not directly enjoy the advantages of light, but
its influence is reflected upon them, and their knowledge is promoted
through the medium of those who enjoy the use of their visual organs. Were
all the inhabitants of the world deprived of their eye-sight, neither
knowledge nor happiness, such as we now possess, could possibly be
enjoyed.

There is nothing which so strikingly displays the beneficial and enlivening
effects of light, as the dawn of a mild morning after a night of darkness and
tempest. All appears gloom and desolation, in our terrestrial abode, till a

faint light begins to whiten the eastern horizon. Every succeeding moment
brings along with it something new and enlivening. The crescent of light
towards the east, now expands its dimensions and rises upwards towards the
cope of heaven; and objects, which a little before were immersed in the
deepest gloom, begin to be clearly distinguished. At length the sun arises,
and all nature is animated by his appearance; the magnificent scene of
creation, which a little before was involved in obscurity, opens gradually to
view, and every object around excites sentiments of wonder, delight, and
adoration. The radiance which emanates from this luminary, displays before
us a world strewed with blessings and embellished with the most beautiful
attire. It unveils the lofty mountains and the forests with which they are
crowned—the fruitful fields with the crops that cover them—the meadows,
with the rivers which water and refresh them—the plains adorned with
verdure, the placid lake and the expansive ocean. It removes the curtain of
darkness from the abodes of men, and shows us the cities, towns and
villages, the lofty domes, the glittering spires, and the palaces and temples
with which the landscape is adorned. The flowers expand their buds and put
forth their colours, the birds awake to melody, man goes forth to his labour,
the sounds of human voices are heard, and all appears life and activity, as if
a new world had emerged from the darkness of Chaos.

The whole of this splendid scene, which light produces, may be considered
as a new creation, no less grand and beneficent than the first creation, when
the command was issued, “Let there be light, and light was.” The aurora
and the rising sun cause the earth and all the objects which adorn its
surface, to arise out of that profound darkness and apparent desolation
which deprived us of the view of them, as if they had been no more. It may
be affirmed, in full accordance with truth, that the efflux of light in the
dawn of the morning, after a dark and cloudy night, is even more
magnificent and exhilarating than at the first moment of its creation. At that
period, there were no spectators on earth to admire its glorious effects; and
no objects, such as we now behold, to be embellished with its radiance. The
earth was a shapeless chaos, where no beauty or order could be perceived;
the mountains had not reared their heads; the seas were not collected into
their channels; no rivers rolled through the valleys, no verdure adorned the
plains; the atmosphere was not raised on high to reflect the radiance, and no
animated beings existed to diversify and enliven the scene. But now, when

the dawning of the morning scatters the darkness of the night, it opens to
view a scene of beauty and magnificence. The heavens are adorned with
azure, the clouds are tinged with the most lively colours, the mountains and
plains are clothed with verdure, and the whole of this lower creation stands
forth arrayed with diversified scenes of beneficence and grandeur, while the
contemplative eye looks round and wonders.

Such, then, are the important and beneficent effects of that light which
every moment diffuses its blessings around us. It may justly be considered
as one of the most essential substances connected with the system of the
material universe, and which gives efficiency to all the other principles and
arrangements of nature. Hence we are informed, in the sacred history, that
light was the first production of the Almighty Creator, and the first born of
created beings; for without it the universe would have presented nothing but
an immense blank to all sentient existences. Hence, likewise, the Divine
Being is metaphorically represented under the idea of light, as being the
source of knowledge and felicity to all subordinate intelligences: “God is
light, and in Him is no darkness at all;” and he is exhibited as “dwelling in
light unapproachable and full of glory, whom no man hath seen or can see.”
In allusion to these circumstances, Milton, in his Paradise Lost, introduces
the following beautiful apostrophe:—

‘Hail holy light! offspring of heaven first born,
Or of the eternal co-eternal beam!
May I express thee unblam’d? since God is light,
And never but in unapproached light
Dwelt from eternity; dwelt then in thee,
Bright effluence of bright essence increate.
----Before the sun
Before the heavens thou wert, and at the voice
Of God, as with a mantle, did’st invest
The rising world of waters dark and deep
Won from the void and formless infinite.’

As light is an element of so much importance and utility in the system of
nature, so we find that arrangements have been made for its universal

diffusion throughout all the worlds in the universe. The sun is one of the
principal sources of light to this earth on which we dwell, and to all the
other planetary bodies. And, in order that it may be equally distributed over
every portion of the surfaces of these globes, to suit the exigencies of their
inhabitants, they are endowed with a motion of rotation, by which every
part of their surfaces is alternately turned towards the source of light; and
when one hemisphere is deprived of the direct influence of the solar rays,
its inhabitants derive a portion of light from luminaries in more distant
regions, and have their views directed to other suns and systems dispersed,
in countless numbers, throughout the remote spaces of the universe. Around
several of the planets, satellites, or moons, have been arranged for the
purpose of throwing light on their surfaces in the absence of the sun, while
at the same time the primary planets themselves reflect an effulgence of
light upon their satellites. All the stars which our unassisted vision can
discern in the midnight sky, and the millions more which the telescope
alone enables us to descry, must be considered as so many fountains of
light, not merely to illuminate the voids of immensity, but to irradiate with
their beams surrounding worlds with which they are more immediately
connected, and to diffuse a general lustre throughout the amplitudes of
infinite space. And, therefore, we have every reason to believe, that, could
we fly, for thousands of years, with the swiftness of a seraph, through the
spaces of immensity, we should never approach a region of absolute
darkness, but should find ourselves, every moment encompassed with the
emanations of light, and cheered with its benign influences. That Almighty
Being who inhabiteth immensity and “dwells in light inaccessible,”
evidently appears to have diffused light over the remotest spaces of his
creation, and to have thrown a radiance upon all the provinces of his wide
and eternal empire, so that every intellectual being, wherever existing, may
feel its beneficent effects, and be enabled, through its agency, to trace his
wonderful operations, and the glorious attributes with which he is invested.

As the science of astronomy depends solely on the influence of light upon
the organ of vision, which is the most noble and extensive of all our senses;
and as the construction of telescopes and other astronomical instruments is
founded upon our knowledge of the nature of light and the laws by which it
operates—it is essentially requisite, before proceeding to a description of
such instruments, to take a cursory view of its nature and properties, in so

far as they have been ascertained, and the effects it produces when
obstructed by certain bodies, or when passing through different mediums.

CHAPTER I.

GENERAL PROPERTIES OF LIGHT.

It is not my intention to discuss the subject of light in minute detail—a
subject which is of considerable extent, and which would require a separate
treatise to illustrate it in all its aspects and bearings. All that I propose is to
offer a few illustrations of its general properties, and the laws by which it is
refracted and reflected, so as to prepare the way for explaining the nature
and construction of telescopes, and other optical instruments.

There is no branch of natural science more deserving of our study and
investigation than that which relates to light—whether we consider its
beautiful and extensive effects—the magnificence and grandeur of the
objects it unfolds to view—the numerous and diversified phenomena it
exhibits—the optical instruments which a knowledge of its properties has
enabled us to construct—or the daily advantages we derive, as social
beings, from its universal diffusion. If air, which serves as the medium of
sound, and the vehicle of speech, enables us to carry on an interchange of
thought and affection with our fellow-men; how much more extensively is
that intercourse increased by light, which presents the images of our friends
and other objects as it were immediately before us, in all their interesting
forms and aspects—the speaking eye—the rosy cheeks—the benevolent
smile, and the intellectual forehead! The eye, more susceptible of
multifarious impressions than the other senses, ‘takes in at once the
landscape of the world,’ and enables us to distinguish, in a moment, the
shapes and forms of all its objects, their relative positions, the colours that
adorn them, their diversified aspect, and the motions by which they are
transported from one portion of space to another. Light, through the
medium of the eye, not only unfolds to us the persons of others, in all their
minute modifications and peculiarities, but exhibits us to ourselves. It
presents to our own vision a faithful portrait of our peculiar features behind
reflecting substances, without which property we should remain entirely

ignorant of those traits of countenance which characterize us in the eyes of
others.

But, what is the nature of this substance we call light, which thus unfolds to
us the scenes of creation? On this subject two leading opinions have
prevailed in the philosophical world. One of those opinions is, that the
whole sphere of the universe is filled with a subtle matter, which receives
from luminous bodies an agitation which is incessantly continued, and
which, by its vibratory motion, enables us to perceive luminous bodies.
According to this opinion, light may be considered as analogous to sound,
which is conveyed to the ear by the vibratory motions of the air. This was
the hypothesis of Descartes, which was adopted, with some modifications,
by the celebrated Euler, Huygens, Franklin, and other philosophers, and has
been admitted by several scientific gentlemen of the present day. The other
opinion is, that light consists of the emission or emanation of the particles
of luminous bodies, thrown out incessantly on all sides, in consequence of
the continued agitation it experiences. This is the hypothesis of the
illustrious Newton, and has been most generally adopted by British
philosophers.

To the first hypothesis, it is objected that, if true, ‘light would not only
spread itself in a direct line, but its motion would be transmitted in every
direction like that of sound, and would convey the impression of luminous
bodies in the regions of space beyond the obstacles that intervene to stop its
progress.’ No wall or other opaque body could obstruct its course, if it
undulated in every direction like sound; and it would be a necessary
consequence, that we should have no night, nor any such phenomena as
eclipses of the sun or moon, or of the satellites of Jupiter and Saturn. This
objection has never been very satisfactorily answered. On the other hand,
Euler brings forward the following objections against the Newtonian
doctrine of emanation. 1. That, were the sun emitting continually, and in all
directions, such floods of luminous matter with a velocity so prodigious, he
must speedily be exhausted, or at least, some alteration must, after the lapse
of so many ages, be perceptible. 2. That the sun is not the only body that
emits rays, but that all the stars have the same quality; and as every where
the rays of the sun must be crossing the rays of the stars, their collision

must be violent in the extreme, and that their direction must be changed by
such a collision.2

To the first of these objections it is answered—that so vast is the tenuity of
light, that it utterly exceeds the power of conception: the most delicate
instrument having never been certainly put in motion by the impulse of the
accumulated sun-beams. It has been calculated that in the space of
385,130,000 Egyptian years, (of 360 days,) the sun would lose only the
1
/1,217,420th of his bulk from the continual efflux of his light. And, therefore, if
in 385 millions of years the sun’s diminution would be so extremely small,
it would be altogether insensible during the comparatively short period of
five or six thousand years. To the second objection it is replied—that the
particles of light are so extremely rare that their distance from one another
is incomparably greater than their diameters—that all objections of this
kind vanish when we attend to the continuation of the impression upon the
retina, and to the small number of luminous particles which are on that
account necessary for producing constant vision. For it appears, from the
accurate experiments of M. D’Arcy, that the impression of light upon the
retina continues eight thirds, and as a particle of light would move through
26,000 miles in that time, constant vision would be maintained by a
succession of luminous particles twenty-six thousand miles distant from
each other.

Without attempting to decide on the merits of these two hypotheses, I shall
leave the reader to adopt that opinion which he may judge to be attended
with the fewest difficulties, and proceed to illustrate some of the properties
of light:—and in the discussion of this subject, I shall generally adhere to
the terms employed by those who have adopted the hypothesis of the
emanation of light.

1. Light emanates or radiates from luminous bodies in a straight line. This
property is proved by the impossibility of seeing light through bent tubes, or
small holes pierced in metallic plates placed one behind another, except the
holes be placed in a straight line. If we endeavour to look at the sun or a
candle through the bore of a bended pipe, we cannot perceive the object,
nor any light proceeding from it, but through a straight pipe the object may
be perceived. This is likewise evident from the form of the rays of light that

penetrate a dark room, which proceed straight forward in lines proceeding
from the luminous body; and from the form of the shadows which bodies
project, which are bounded by right lines passing from the luminous body,
and meeting the lines which terminate the interposing body. This property
may be demonstrated to the eye, by causing light to pass through small
holes into a dark room filled with smoke or dust. It is to be understood,
however, that in this case, the rays of light are considered as passing
through the same medium; for when they pass from air into water, glass, or
other media, they are bent at the point where they enter a different medium,
as we shall afterwards have occasion to explain.

2. Light moves with amazing velocity. The ancients believed that it was
propagated from the sun and other luminous bodies instantaneously; but the
observations of modern astronomers have demonstrated that this is an
erroneous hypothesis, and that light, like other projectiles, occupies a
certain time in passing from one part of space to another. Its velocity,
however, is prodigious, and exceeds that of any other body with which we
are acquainted. It flies across the earth’s orbit—a space 190 millions of
miles in extent, in the course of sixteen and a half minutes, which is at the
rate of 192,000 miles every second, and more than a million of times
swifter than a cannon ball flying with its greatest velocity. It appears from
the discoveries of Dr. Bradley, respecting the aberration of the stars, that
light flies from those bodies, with a velocity similar, if not exactly the same;
so that the light of the sun, the planets, the stars, and every luminous body
in the universe is propagated with uniform velocity.3 But, if the velocity of
light be so very great, it may be asked, how does it not strike against all
objects with a force equal to its velocity? If the finest sand were thrown
against our bodies with the hundredth part of this velocity, each grain would
pierce us as certainly as the sharpest and swiftest arrows from a bow. It is a
principle in mechanics that the force with which all bodies strike, is in
proportion to the size of these bodies, or the quantity of matter they contain,
multiplied by the velocity with which they move. Therefore if the particles
of light were not almost infinitely small, they would, of necessity prove
destructive in the highest degree. If a particle of light were equal in size to
the twelve hundred thousandth part of a small grain of sand,—supposing
light to be material—we should be no more able to withstand its force than
we should that of sand shot point blank from the mouth of a cannon. Every

object would be battered and perforated by such celestial artillery, till our
world were laid in ruins, and every living being destroyed. And herein are
the wisdom and benevolence of the Creator displayed in making the
particles of light so extremely small as to render them in some degree
proportionate to the greatness of the force with which they are impelled;
otherwise, all nature would have been thrown into ruin and confusion, and
the great globes of the universe shattered to atoms.

We have many proofs, besides the above, that the particles of light are next
to infinitely small. We find that they penetrate with facility the hardest
substances, such as crystal, glass, various kinds of precious stones, and even
the diamond itself, though among the hardest of stones; for such bodies
could not be transparent, unless light found an easy passage through their
pores. When a candle is lighted in an elevated situation, in the space of a
second or two, it will fill a cubical space (if there be no interruption) of two
miles around it, in every direction, with luminous particles, before the least
sensible part of its substance is lost by the candle:—that is, it will in a short
instant, fill a sphere four miles in diameter, twelve and a half miles in
circumference, and containing thirty-three and a half cubical miles with
particles of light; for an eye placed in any part of this cubical space would
perceive the light emitted by the candle. It has been calculated that the
number of particles of light contained in such a space cannot be less than
four hundred septillions—a number which is six billions of times greater
than the number of grains of sand which could be contained in the whole
earth considered as a solid globe, and supposing each cubic inch of it to
contain ten hundred thousand grains. Such is the inconceivable tenuity of
that substance which emanates from all luminous bodies, and which gives
beauty and splendour to the universe! This may also be evinced by the
following experiment. Make a small pin-hole in a piece of black paper, and
hold the paper upright facing a row of candles placed near each other, and at
a little distance behind the black paper, place a piece of white pasteboard.
On this pasteboard the rays which flow from all the candles through the
small hole in the black paper, will form as many specks of light as there are
candles, each speck being as clear and distinct as if there were only one
speck from a single candle. This experiment shows that the streams of light
from the different candles pass through the small hole without confusion,
and consequently, that the particles of light are exceedingly small. For the

same reason we can easily see through a small hole not more than 1/100th of
an inch in diameter, the sky, the trees, houses, and nearly all the objects in
an extensive landscape, occupying nearly an entire hemisphere, the light of
all which may pass through this small aperture.

3. Light is sent forth in all directions from every visible point of luminous
bodies. If we hold a sheet of paper before a candle, or the sun, or any other
source of light, we shall find that the paper is illuminated in whatever
position we hold it, provided the light is not obstructed by its edge or by
any other body. Hence, wherever a spectator is placed with regard to a
luminous body, every point of that part of its surface which is toward him
will be visible, when no intervening object intercepts the passage of the
light. Hence, likewise, it follows, that the sun illuminates, not only an
immense plane extending along the paths of the planets, from the one side
of the orbit of Uranus to the other, but the whole of that sphere, or solid
space, of which the distance of Uranus is the radius. The diameter of this
sphere is three thousand six hundred millions of miles, and it, consequently,
contains about 24,000,000,000,000,000,000,000,000,000, or twenty-four
thousand quartillions of cubical miles,—every point of which immense
space is filled with the solar beams. Not only so, but the whole cubical
space which intervenes between the sun and the nearest fixed stars is more
or less illuminated by his rays. For, at the distance of Sirius, or any other of
the nearest stars, the sun would be visible, though only as a small twinkling
orb; and consequently, his rays must be diffused, however faint, throughout
the most distant spaces whence he is visible. The diameter of this immense
sphere of light cannot be less than forty billions of miles, and its solid
contents 33,500,000,000,000,000,000,000,000,000,000,000,000,000 or,
thirty-three thousand, five hundred sextillions of cubical miles. All this
immense, and incomprehensible space is filled with the radiations of the
solar orb; for were an eye placed in any one point of it, where no extraneous
body interposed, the sun would be visible either as a large luminous orb, or
as a small twinkling star. But he can be visible only by the rays he emits,
and which enter the organs of vision. How inconceivably immense, then,
must be the quantity of rays which are thrown off in all directions from that
luminary which is the source of our day! Every star must likewise be
considered as emitting innumerable streams of radiance over a space
equally extensive, so that no point in the universe can be conceived where

absolute darkness prevails, unless in the interior regions of planetary
bodies.

4. The effect of light upon the eye is not instantaneous, but continues for a
short space of time. This may be proved and illustrated by the following
examples:—If a stick—or a ball connected with a string—be whirled round
in a circle, and a certain degree of velocity given it, the object will appear to
fill the whole circle it describes. If a lighted firebrand be whirled round in
the same rapid manner, a complete circle of light will be exhibited. This
experiment obviously shows that the impression made on the eye by the
light from the ball or the firebrand—when in any given point of the circle—
is sufficiently lasting to remain till it has described the whole circle, and
again renews its effect, as often as the circular motion is continued. The
same is proved by the following considerations:—We are continually
shutting our eyes, or winking; and, during the time our eyes are shut, on
such occasions, we should lose the view of surrounding objects, if the
impression of light did not continue a certain time while the eye-lid covers
the pupil; but experience proves that during such vibrations of the eye-lids,
the light from surrounding objects is not sensibly intercepted. If we look for
some time steadily at the light of a candle, and particularly, if we look
directly at the sun, without any interposing medium, or if we look for any
considerable time at this luminary, through a telescope with a coloured
glass interposed—in all these cases, if we shut our eyes immediately after
viewing such objects, we shall still perceive a faint image of the object, by
the impression which its light has made upon our eyes.

‘With respect to the duration of the impression of light, it has been
observed that the teeth of a cog-wheel in a clock were still visible in
succession, when the velocity of rotation brought 246 teeth through a given
fixed point in a second. In this case it is clear that if the impression made on
the eye by the light reflected from any tooth, had lasted without sensible
diminution for the 246th part of a second, the teeth would have formed one
unbroken line, because a new tooth would have continually arrived in the
place of the interior one before its image could have disappeared. If a live
coal be whirled round, it is observed that the luminous circle is complete,
when the rotation is performed in the (8½)/60th of a second. In this instance
we see that the impression was much more durable than the former. Lastly,

if an observer sitting in a room direct his sight through a window, to any
particular object out of doors, for about half a minute, and then shut his
eyes and cover them with his hands, he will still continue to see the
window, together with the outline of the terrestrial objects bordering on the
sky. This appearance will remain for near a minute, though occasionally
vanishing and changing colour in a manner that brevity forbids our
minutely describing. From these facts we are authorized to conclude, that
all impressions of light on the eye, last a considerable time, that the
brightest objects make the most lasting impressions; and that, if the object
be very bright, or the eye weak, the impression may remain for a time so
strong, as to mix with and confuse the subsequent impressions made by
other objects. In the last case the eye is said to be dazzled by the light.’4

The following experiment has likewise been suggested as a proof of the
impression which light makes upon the eye. If a card, on both sides of
which a figure is drawn, for example, a bird and a cage, be made to revolve
rapidly on the straight line which divides it symmetrically, the eye will
perceive both figures at the same time, provided they return successively to
the same place. M. D’Arcy found by various experiments, that, in general,
the impression which light produces on the eye, lasts about the eighth of a
second. M. Plateau, of Brussels, found that the impression of different
colours lasted the following periods; the numbers here stated being the
decimal parts of a second. Flame, 0.242. or nearly one fourth of a second;
Burning coal, 0.229; White, 0.182, or, a little more than one sixth of a
second; Blue, 0.186; Yellow, 0.173; Red, 0.184.

5. Light, though extremely minute, is supposed to have a certain degree of
force or momentum. In order to prove this, the late ingenious Mr. Mitchell
contrived the following experiment. He constructed a small vane in the
form of a common weather-cock, of a very thin plate of copper, about an
inch square, and attached to one of the finest harpsicord wires, about ten
inches long, and nicely balanced at the other end of the wire, by a grain of
very small shot. The instrument had also fixed to it in the middle, at right
angles to the length of the wire, and in an horizontal direction, a small bit of
a very slender sewing needle, about half an inch long, which was made
magnetical. In this state the whole instrument might weigh about ten grains.
The vane was supported in the manner of the needle in the mariner’s

compass, so that it could turn with the greatest ease; and to prevent its being
affected by the vibrations of the air, it was enclosed in a glass case or box.
The rays of the sun were then thrown upon the broad part of the vane or
copper plate, from a concave mirror of about two feet diameter, which,
passing through the front glass of the box, were collected into the focus of
the mirror upon the copper plate. In consequence of this the plate began to
move with a slow motion of about an inch in a second of time, till it had
moved through a space of about two inches and a half, when it struck
against the back of the box. The mirror being removed, the instrument
returned to its former situation, and the rays of the sun being again thrown
upon it, it again began to move, and struck against the back of the box as
before. This was repeated three or four times with the same success.

On the above experiment, the following calculation has been founded: If we
impute the motion produced in this experiment to the impulse of the rays of
light, and suppose that the instrument weighed ten grains, and acquired a
velocity of one inch in a second, we shall find that the quantity of matter
contained in the rays falling upon the instrument in that time amounted to
no more than one twelve hundred-millionth part of a grain, the velocity of
light exceeding the velocity of one inch in a second in the proportion of
about 12,000,000,000 to 1. The light in this experiment was collected from
a surface of about three square feet, which reflecting only about half what
falls upon it, the quantity of matter contained in the rays of the sun incident
upon a foot and a half of surface in one second of time, ought to be no more
than the twelve hundred-millionth part of a grain. But the density of the
rays of light at the surface of the sun is greater than that at the earth in the
proportion of 45,000 to 1; there ought therefore to issue from one square
foot of the sun’s surface in one second of time, in order to supply the waste
by light 1/45,000th part of a grain of matter, that is, a little more than two grains
a day, or about 4,752,000 grains, or 670 pounds avoirdupoise, nearly, in
6,000 years, a quantity which would have shortened the sun’s diameter no
more than about ten feet, if it were formed of the density of water only.

If the above experiment be considered as having been accurately performed,
and if the calculations founded upon it be correct, it appears that there can
be no grounds for apprehension that the sun can ever be sensibly
diminished by the immense and incessant radiations proceeding from his

body on the supposition that light is a material emanation. For the diameter
of the sun is no less than 880,000 miles; and, before this diameter could be
shortened, by the emission of light, one English mile, it would require three
millions, one hundred and sixty-eight thousand years, at the rate now stated;
and, before it could be shortened ten miles, it would require a period of
above thirty-one millions of years. And although the sun were thus actually
diminished, it would produce no sensible effect or derangement throughout
the planetary system. We have no reason to believe that the system, in its
present state and arrangements, was intended to endure for ever, and before
that luminary could be so far reduced, during the revolutions of eternity, as
to produce any irregularities in the system, new arrangements and
modifications might be introduced by the hand of the All Wise and
Omnipotent Creator. Besides, it is not improbable that a system of means is
established by which the sun and all the luminaries in the universe receive
back again a portion of the light which they are continually emitting, either
from the planets from whose surfaces it is reflected, or from the millions of
stars whose rays are continually traversing the immense spaces of creation,
or from some other sources to us unknown.

6. The intensity of light is diminished in proportion to the square of the
distance from the luminous body. Thus, a person at two feet distance from a
candle, has only the fourth part of the light he would have at one foot, at
three feet distance the ninth part, at four feet the sixteenth part, at five feet
the twenty fifth part, and so on for other distances. Hence the light received
by the planets of the Solar system decreases in proportion to the squares of
the distances of these bodies from the sun. This may be illustrated by the
following figure,

Figure 1.

Suppose the light which flows from a point A, and passes through a square
hole B, is received upon a plane C, parallel to the plane of the hole—or, let
the figure C be considered as the shadow of the plane B. When the distance
of C is double of B, the length and breadth of the shadow C will be each
double of the length and breadth of the plane B, and treble when AD is
treble of AB, and so on, which may be easily examined by the light of a
candle placed at A. Therefore the surface of the shadow C, at the distance
AC—double of AB, is divisible into four squares, and at a treble distance,
into nine squares, severally equal to the square B, as represented in the
figure. The light, then, which falls upon the plane B being suffered to pass
to double that distance, will be uniformly spread over four times the space,
and consequently will be four times thinner in every part of that space. And
at a treble distance it will be nine times thinner, and at a quadruple distance
sixteen times thinner than it was at first. Consequently the quantities of this
rarified light received upon a surface of any given size and shape when
removed successively to these several distances, will be but one-fourth,
one-ninth, one-sixteenth, of the whole quantity received by it at the first
distance AB.

In conformity with this law, the relative quantities of light on the surfaces of
the planets may be easily determined, when their distances from the sun are
known. Thus, the distance of Uranus from the sun is 1,800,000,000 miles,
which is about nineteen times greater than the distance of the earth from the
same luminary. The square of 19 is 361; consequently the earth enjoys 361
times the intensity of light when compared with that of Uranus; in other

words, this distant planet enjoys only the 1/361 part of the quantity of light
which falls upon the earth. This quantity, however, is equivalent to the light
we should enjoy from the combined effulgence of 348 full moons; and if
the pupils of the eyes of the inhabitants of this planet be much larger than
ours, and the retina of the eye be endued with a much greater degree of
nervous sensibility, they may perceive objects with as great a degree of
splendour as we perceive on the objects which surround us in this world.
Following out the same principle, we find that the quantity of light enjoyed
by the planet Mercury is nearly seven times greater than that of the Earth,
and that of Venus nearly double of what we enjoy—that Mars has less than
the one half—Jupiter the one twenty-seventh part—and Saturn only the one
ninetieth part of the light which falls upon the Earth. That the light of these
distant planets, however, is not so weak as we might at first imagine
appears from the brilliancy they exhibit, when viewed in our nocturnal sky,
either with the telescope or with the unassisted eye—and likewise from the
circumstance that a very small portion of the Sun—such as the one fortieth
or one fiftieth part diffuses a quantity of light sufficient for most of the
purposes of life, as is found in the case of total eclipses of the Sun, when his
western limb begins to be visible, only like a fine luminous thread, for his
light is then sufficient to render distinctly visible all the parts of the
surrounding landscape.

7. It is by light reflected from opake bodies that most of the objects around
us are rendered visible. When a lighted candle is brought into a dark room,
not only the candle but all other bodies in the room become visible. Rays of
the sun passing into a dark room render luminous a sheet of paper on which
they fall, and this sheet in its turn enlightens, to a certain extent, the whole
apartment, and renders objects in it visible, so long as it receives the rays of
the sun. In like manner, the moon and the planets are opake bodies, but the
light of the sun falling upon them, and being reflected from their surfaces,
renders them visible. Were no light to fall on them from the sun, or were
they not endued with a power of reflecting it, they would be altogether
invisible to our sight. When the moon comes between us and the sun, as in a
total eclipse of that luminary, as no solar light is reflected from the surface
next the earth, she is invisible—only the curve or outline of her figure being
distinguished by her shadow. In this case, however, there is a certain portion
of reflected light on the lunar hemisphere next the earth, though not

distinguishable during a solar eclipse. The earth is enlightened by the sun,
and a portion of the rays which fall upon it is reflected upon the dark
hemisphere of the moon which is then towards the earth. This reflected light
from the earth is distinctly perceptible, when the moon appears as a slender
crescent, two or three days after new moon—when the earth reflects its
light back on the moon, in the same manner as the full moon reflects her
light on the earth. Hence, even at this period of the moon, her whole face
becomes visible to us, but its light is not uniform or of equal intensity. The
thin crescent on which the full blaze of the solar light falls, is very brilliant
and distinctly seen, while the other part, on which falls only a
comparatively feeble light from the earth, appears very faint, and is little
more than visible to the naked eye, but with a telescope of moderate power,
—if the atmosphere be very clear—it appears beautifully distinct, so that
the relative positions of many of the lunar spots may be distinguished.

The intensity of reflected light is very small, when compared with that
which proceeds directly from luminous bodies. M. Bouguer, a French
philosopher, who made a variety of experiments to ascertain the proportion
of light emitted by the heavenly bodies, concluded from these experiments,
that the light transmitted from the sun to the earth is at least 300,000 times
as great as that which descends to us from the full moon—and that, of
300,000 rays which the moon receives, from 170,000 to 200,000 are
absorbed. Hence we find that, however brilliant the moon may appear at
night—in the day time she appears as obscure as a small portion of dusky
cloud to which she happens to be adjacent, and reflects no more light than a
portion of whitish cloud of the same size. And as the full moon fills only the
ninety thousandth part of the sky, it would require at least ninety thousand
moons to produce as much light as we enjoy in the day-time under a cloudy
sky.

As the moon and the planets are rendered visible to us only by light
reflected from their surfaces, so it is in the same way that the images of
most of the objects around us are conveyed to our organs of vision. We
behold all the objects which compose an extensive landscape,—the hills
and vales, the woods and lawns, the lakes and rivers, and the habitations of
man—in consequence of the capacity with which they are endued of
sending forth reflected rays to the eye, from every point of their surfaces

and in all directions. In connection with the reflection of light, the following
curious observation may be stated. Baron Funk, visiting some silver mines
in Sweden, observed, that, ‘in a clear day, it was as dark as pitch
underground in the eye of a pit, at sixty or seventy fathoms deep; whereas,
in a cloudy or rainy day, he could see to read even at 106 fathoms deep.
Enquiring of the miners, he was informed that this is always the case; and
reflecting upon it, he imagined it arose from this circumstance, that when
the atmosphere is full of clouds, light is reflected from them into the pit in
all directions, and that thereby a considerable proportion of the rays are
reflected perpendicularly upon the earth: whereas when the atmosphere is
clear, there are no opaque bodies to reflect the light in this manner, at least
in a sufficient quantity; and rays from the sun himself can never fall
perpendicularly in that country.’—The reason here assigned is, in all
probability, the true cause of the phenomenon now described.

8. It is supposed by some philosophers that light is subject to the same laws
of attraction that govern all other material substances—and that it is
imbibed and forms a constituent part of certain bodies. This has been
inferred from the phenomena of the Bolognian stone, and what are
generally called the solar phosphori. The Bolognian stone was first
discovered about the year 1680, by Leascariolo, a shoe-maker of Bologna.
Having collected together some stones of a shining appearance at the
bottom of Monte Paterno, and being in quest of some alchemical secret, he
put them into a crucible to calcine them—that is, to reduce them to the state
of cinders. Having taken them out of the crucible, and exposed them to the
light of the sun, he afterwards happened to carry them into a dark place,
when to his surprise, he observed that they possessed a self-illuminating
power, and continued to emit faint rays of light for some hours afterwards.
In consequence of this discovery, the Bolognian spar came into
considerable demand among natural philosophers and the curious in
general; and the best way of preparing it seems to have been hit upon by the
family of Zagoni, who supplied all Europe with Bolognian phosphorus, till
the discovery of more powerful phosphoric substances put an end to their
monopoly.—In the year 1677, Baldwin, a native of Misnia, observed that
chalk dissolved in aqua-fortis exactly resembled the Bolognian stone in its
property of imbibing light, and emitting it after it was brought into the dark
; and hence it has obtained the name of Baldwin’s phosphorus.

In 1730 M. du Fay directed his attention to this subject, and observed that
all earthy substances susceptible of calcination, either by mere fire, or when
assisted by the previous action of nitrous acid, possessed the property of
becoming more or less luminous, when calcined and exposed for a short
time in the light—that the most perfect of these phosphori were limestones,
and other kinds of carbonated lime, gypsum, and particularly the topaz, and
that some diamonds were also observed to be luminous by simple exposure
to the sun’s rays. Sometime afterwards, Beccaria discovered that a great
variety of other bodies were convertible into phosphori by exposure to the
mere light of the sun, such as, organic animal remains, most compound
salts, nitre and borax—all the farinaceous and oily seeds of vegetable
substances, all the gums and several of the resins—the white woods and
vegetable fibre, either in the form of paper or linen; also starch and loaf-
sugar proved to be good phosphori, after being made thoroughly dry, and
exposed to the direct rays of the sun. Certain animal substances by a similar
treatment were also converted into phosphori; particularly bone, sinew,
glue, hair, horn, hoof, feathers, and fish-shells. The same property was
communicated to rock crystal and some other of the gems, by rubbing them
against each other so as to roughen their surfaces, and then placing them for
some minutes in the focus of a lens, by which the rays of light were
concentrated upon them, at the same time that they were also moderately
heated.

In the year 1768 Mr. Canton contributed some important facts in relation to
solar phosphori, and communicated a method of preparing a very powerful
one, which, after the inventor, is usually called Canton’s phosphorus. He
affirms that his phosphorus, enclosed in a glass flask, and hermetically
sealed, retains its property of becoming luminous for at least four years,
without any apparent decrease of activity. It has also been found that, if a
common box smoothing-iron, heated in the usual manner, be placed for half
a minute on a sheet of dry, white paper, and the paper be then exposed to
the light, and afterwards examined in a dark closet, it will be found that the
whole paper will be luminous, that part, however, on which the iron had
stood being much more shining than the rest.

From the above facts it would seem that certain bodies have the power of
imbibing light and again emitting it, in certain circumstances, and that this

power may remain for a considerable length of time. It is observed that the
light which such bodies emit bears an analogy to that which they have
imbibed. In general, the illuminated phosphorus is reddish; but when a
weak light only has been admitted to it, or when it has been received
through pieces of white paper, the emitted light is pale or whitish.—Mr.
Morgan, in the seventy-fifth volume of the Philosophical Transactions,
treats the subject of light at considerable length; and as a foundation for his
reasoning, he assumes the following data:—1. That light is a body, and like
all others, subject to the laws of attraction. 2. That light is a heterogeneous
body; and that the same attractive power operates with different degrees of
force on its different parts. To the principle of attraction, likewise, Sir Isaac
Newton has referred the most extraordinary phenomena of light, Refraction
and Inflection. He has also endeavoured to show that light is not only
subject to the law of attraction but of repulsion also, since it is repelled or
reflected from certain bodies. If such principles be admitted, then, it is
highly probable that the phosphorescent bodies to which we have adverted
have a power of attracting or imbibing the substance of light, and of
retaining or giving it out under certain circumstances, and that the matter of
light is incorporated at least with the surface of such bodies. But on this
subject, as on many others, there is a difference of opinion among
philosophers.5

9. Light is found to produce a remarkable effect on Plants and Flowers, and
other vegetable productions. Of all the phenomena which living vegetables
exhibit there are few that appear more extraordinary than the energy and
constancy with which their stems incline toward the light. Most of the
discous flowers follow the sun in his course. They attend him to his evening
retreat, and meet his rising lustre in the morning with the same unerring
law. They unfold their flowers on the approach of this luminary; they follow
his course by turning on their stems, and close them as soon as he
disappears. If a plant, also, is shut up in a dark room, and a small hole
afterwards opened by which the light of the sun may enter, the plant will
turn towards that hole, and even alter its own shape in order to get near it;
so that though it was straight before, it will in time become crooked, that it
may get near the light. Vegetables placed in rooms where they receive light
only in one direction, always extend themselves in that direction. If they
receive light in two directions, they direct their course towards that which is

strongest. It is not the heat but the light of the sun which the plant thus
covets; for, though a fire be kept in the room, capable of giving a much
stronger heat than the sun, the plant will turn away from the fire in order to
enjoy the solar light. Trees growing in thick forests, where they only receive
light from above, direct their shoots almost invariably upwards, and
therefore become much taller and less spreading than such as stand single.

The green colour of plants is likewise found to depend on the sun’s light
being allowed to shine on them; for without the influence of the solar light,
they are always of a white colour. It is found by experiment that, if a plant
which has been reared in darkness be exposed to the light of day, in two or
three days it will acquire a green colour perceptibly similar to that of plants
which have grown in open day-light. If we expose to the light one part of
the plant, whether leaf or branch, this part alone will become green. If we
cover any part of a leaf with an opake substance, this place will remain
white, while the rest becomes green. The whiteness of the inner leaves of
cabbages is a partial effect of the same cause, and many other examples of
the same kind might easily be produced. M. Decandolle, who seems to have
paid particular attention to this subject, has the following remarks: ‘It is
certain, that between the white state of plants vegetating in darkness, and
complete verdure, every possible intermediate degree exists, determined by
the intensity of the light. Of this any one may easily satisfy himself by
attending to the colour of a plant exposed to the full day-light; it exhibits in
succession all the degrees of verdure. I had already seen the same
phenomenon, in a particular manner, by exposing plants reared in darkness
to the light of lamps. In these experiments, I not only saw the colour come
on gradually, according to the continuance of the exposure to light; but I
satisfied myself, that a certain intensity of permanent light never gives to a
plant more than a certain degree of colour. The same fact readily shows
itself in nature, when we examine the plants that grow under shelter or in
forests, or when we examine in succession the state of the leaves that form
the heads of cabbages.’6

It is likewise found that the perspiration of vegetables is increased or
diminished, in a certain measure by the degree of light which falls upon
them. The experiments of Mr. P. Miller and others, prove that plants
uniformly perspire most in the forenoon, though the temperature of the air

in which they are placed should be unvaried. M. Guettard likewise informs
us that a plant exposed to the rays of the sun, has its perspiration increased
to a much greater degree than if it had been exposed to the same heat under
the shade. Vegetables are likewise found to be indebted to light for their
smell, taste, combustibility, maturity, and the resinous principle, which
equally depend upon this fluid. The aromatic substances, resins, and volatile
oil are the productions of southern climates, where the light is more pure,
constant, and intense. In fine, another remarkable property of light on the
vegetable kingdom is that, when vegetables are exposed to open day-light,
or to the sun’s rays, they emit oxygen gas or vital air. It has been proved
that, in the production of this effect, the sun does not act as a body that
heats. The emission of the gas is determined by the light: pure air is
therefore separated by the action of light, and the operation is stronger as
the light is more vivid. By this continual emission of vital air, the Almighty
incessantly purifies the atmosphere, and repairs the loss of pure air
occasioned by respiration, combustion, fermentation, putrefaction, and
numerous other processes which have a tendency to contaminate this fluid
so essential to the vigor and comfort of animal life; so that, in this way, by
the agency of light, a due equilibrium is always maintained between the
constituent parts of the atmosphere.

In connection with this subject the following curious phenomenon may be
stated, as related by M. Haggern, a Lecturer on Natural History in Sweden.
One evening he perceived a faint flash of light repeatedly dart from a
marigold. Surprised at such an uncommon appearance, he resolved to
examine it with attention; and, to be assured it was no deception of the eye,
he placed a man near him, with orders to make a signal at the moment when
he observed the light. They both saw it constantly at the same moment. The
light was most brilliant on marigolds of an orange or flame colour, but
scarcely visible on pale ones. The flash was frequently seen on the same
flower two or three times in quick succession; but more commonly at
intervals of several minutes; and when several flowers in the same place
emitted their light together, it could be observed at a considerable distance.
The phenomenon was remarked in the months of July and August at sun-
set, and for half an hour when the atmosphere was clear; but after a rainy
day, or when the air was loaded with vapours, nothing of it was seen. The
following flowers emitted flashes more or less vivid, in this order:—1. The

Marigold, 2. Monk’s hood, 3. The Orange Lily, 4. The Indian Pink. As to
the cause of this phenomenon, different opinions may be entertained. From
the rapidity of the flash and other circumstances, it may be conjectured that
electricity is concerned in producing this appearance. M. Haggern, after
having observed the flash from the orange lily, the antheræ of which are at
considerable distance from the petals, found that the light proceeded from
the petals only; whence he concludes, that this electrical light is caused by
the pollen which, in flying off, is scattered on the petals. But, perhaps, the
true cause of it still remains to be ascertained.

10. Light has been supposed to produce a certain degree of influence on the
PROPAGATION OF SOUND?—M. Parolette, in a long paper in the ‘Journal de
Physique,’ vol. 68, which is copied into ‘Nicholson’s Philosophical
Journal,’ vol. 25, pp. 28-39,—has offered a variety of remarks, and detailed
a number of experiments on this subject. The author states the following
circumstances as having suggested the connection between light and sound.
‘In 1803, I lived in Paris, and being accustomed to rise before day to finish
a work on which I had long been employed, I found myself frequently
disturbed by the sound of carriages, as my windows looked into one of the
most frequented streets in that city. This circumstance which disturbed me
in my studies every morning, led me to remark, that the appearance of day-
break peculiarly affected the propagation of the sound: from dull and deep,
which it was before day, it seemed to me to acquire a more sonorous
sharpness in the period that succeeded the dissipation of darkness. The
rolling of the wheels seemed to announce the friction of some substances
grown more elastic; and my ear on attending to it perceived this difference
diminish, in proportion as the sound of wheels was confounded with those
excited by the tumult of objects quitting their nocturnal silence. Struck with
this observation, I attempted to discover whether any particular causes had
deceived my ears. I rose several times before day for this purpose alone,
and was every time confirmed in my suspicion, that light must have a
peculiar influence on the propagation of sound. This variation, however, in
the manner in which the air gave sounds might be the effect of the agitation
of the atmosphere produced by the rarefaction the presence of the sun
occasioned; but the situation of my windows, and the usual direction of the
morning breeze, militated against this argument.’

The author then proceeds to give a description of a very delicate instrument,
and various apparatus for measuring the propagation and intensity of sound,
and the various experiments both in the dark, and in day-light, and likewise
under different changes of the atmosphere, which were made with his
apparatus—all of which tended to prove that light had a sensible influence
in the propagation of sound. But the detail of these experiments and their
several results would be too tedious to be here transcribed.—The night has
generally been considered as more favourable than the day for the
transmission of sound. ‘That this is the case (says Parolette) with respect to
our ears cannot be doubted; but this argues nothing against my opinion. We
hear further by night on account of the silence, and this always contributes
to it, while the noise of a wind favourable to the propagation of a sound,
may prevent the sound from being heard.’ In reference to the cause which
produces the effect now stated, he proposes the following queries. ‘Is the
atmospheric air more dense on the appearance of light than in darkness? Is
this greater density of the air or of the elastic fluid that is subservient to the
propagation of sound, the effect of aeriform substances kept in this state
through the medium of light?’ He is disposed, on the whole, to conclude,
that the effect in question is owing to the action of light upon the oxygen of
the atmosphere, since oxygen gas is found by experiment to be best adapted
to the transmission of sound.

Our author concludes his communication with the following remarks:
—‘Light has a velocity 900,000 times as rapid as that of sound. Whether it
emanate from the sun and reach to our earth, or act by means of vibrations
agitating the particles of a fluid of a peculiar nature—the particles of this
fluid must be extremely light, elastic and active. Nor does it appear to me
unreasonable, to ascribe to the mechanical action of these particles set in
motion by the sun, the effects its presence occasions in the vibrations that
proceed from sonorous bodies. The more deeply we investigate the theory
of light, the more we must perceive, that the powers by which the universe
is moved reside in the imperceptible particles of bodies; and that the grand
results of nature are but an assemblage of an order of actions that take place
in its infinitely small parts; consequently, we cannot institute a series of
experiments more interesting than those which tend to develope the
properties of light. Our organs of sense are so immediately connected with
the fluid that enlightens us, that the notion of having acquired an idea of the

mode of action of this fluid presents itself to our minds, as the hope of a
striking advance in the knowledge of what composes the organic
mechanism of our life, and of that of beings which closely follow the rank
assigned to the human species.’

Such is a brief description of some of the leading properties of light. Of all
the objects that present themselves to the philosophic and contemplative
mind, light is one of the noblest and most interesting. The action it exerts on
all the combinations of matter, its extreme divisibility, the rapidity of its
propagation, the sublime wonders it reveals, and the office it performs in
what constitutes the life of organic beings, lead us to consider it as a
substance acting the first part in the economy of nature. The magic power
which this emanation from the heavens exerts on our organs of vision, in
exhibiting to our view the sublime spectacle of the universe, cannot be
sufficiently admired. Nor is its power confined to the organs of sight; all our
senses are, in a greater or less degree, subjected to the action of light, and
all the objects in this lower creation—whether in the animal, the vegetable,
or the mineral kingdoms—are, to a certain extent, susceptible of its
influence. Our globe appears to be little more than an accumulation of
terrestrial materials introduced into the boundless ocean of the solar light,
as a theatre on which it may display its exhaustless power and energy, and
give animation, beauty and sublimity to every surrounding scene—and to
regulate all the powers of nature, and render them subservient to the
purposes for which they were ordained. This elementary substance appears
to be universal in its movements, and in its influence. It descends to us from
the solar orb. It wings its way through the voids of space, along a course of
ninety-five millions of miles, till it arrives at the outskirts of our globe; it
passes freely through the surrounding atmosphere, it strikes upon the clouds
and is reflected by them; it irradiates the mountains, the vales, the forests,
the rivers, the seas, and all the productions of the vegetable kingdom, and
adorns them with a countless assemblage of colours. It scatters and
disperses its rays from one end of creation to another, diffusing itself
throughout every sphere of the universe. It flies without intermission from
star to star, and from suns to planets, throughout the boundless sphere of

immensity, forming a connecting chain and a medium of communication
among all the worlds and beings within the wide empire of Omnipotence.

When the sun is said “to rule over the day,” it is intimated that he acts as the
vicegerent of the Almighty, who has invested him with a mechanical power
of giving light, life and motion to all the beings susceptible of receiving
impressions from his radiance. As the servant of his creator he distributes
blessings without number among all the tribes of sentient and intelligent
existence. When his rays illumine the eastern sky in the morning, all nature
is enlivened with his presence. When he sinks beneath the western horizon,
the flowers droop, the birds retire to their nests, and a mantle of darkness is
spread over the landscape of the world. When he approaches the equinox in
spring, the animal and vegetable tribes revive, and nature puts on a new and
a smiling aspect. When he declines towards the winter solstice, dreariness
and desolation ensue, and a temporary death takes place among the tribes of
the vegetable world.—This splendid luminary, whose light embellishes the
whole of this lower creation, forms the most lively representation of Him
who is the source and the centre of all beauty and perfection. “God is a
sun,” the sun of the moral and spiritual universe, from whom all the
emanations of knowledge, love and felicity descend. “He covereth himself
with light as with a garment.” and “dwells in light inaccessible and full of
glory.” The felicity and enjoyments of the future world are adumbrated
under the ideas of light and glory. “The glory of God enlightens the
celestial city,” its inhabitants are represented as “the saints in light,” it is
declared that “their sun shall no more go down,” and that “the Lord God is
their everlasting light.” So that light not only cheers and enlivens all beings
throughout the material creation, but is the emblem of the Eternal Mind,
and of all that is delightful and transporting in the scenes of a blessed
immortality.

In the formation of light, and the beneficent effects it produces, the wisdom
and goodness of the Almighty are conspicuously displayed. Without the
beams of the sun and the influence of light, what were all the realms of this
world, but an undistinguished chaos and so many dungeons of darkness? In
vain should we roll our eyes around to behold, amidst the universal gloom,
the flowery fields, the verdant plains, the flowing streams, the expansive
ocean, the moon walking in brightness, the planets in their courses, or the

innumerable host of stars. All would be lost to the eye of man, and the
“blackness of darkness” would surround him for ever. And with how much
wisdom has every thing been arranged in relation to the motion and
minuteness of light? Were it capable of being transformed into a solid
substance, and retain its present velocity, it would form the most dreadful
and appalling element in nature, and produce universal terror and
destruction throughout the universe. That this is not impossible, and could
easily be effected by the hand of Omnipotence, appears from such
substances as phosphorus, where light is supposed to be concentrated in a
solid state. But in all its operations and effects, as it is now directed by
unerring wisdom and beneficence, it exhibits itself as the most benign and
delightful element connected with the constitution of the material system,
diffusing splendour and felicity wherever its influence extends.

CHAPTER II.

ON THE REFRACTION OF LIGHT.

Refraction is the turning or bending of the rays of light out of their natural
course.

Light, when proceeding from a luminous body—without being reflected
from any opake substance or inflected by passing near one—is invariably
found to proceed in straight lines without the least deviation. But if it
happens to pass obliquely from one medium to another, it always leaves the
direction it had before and assumes a new one. This change of direction, or
bending of the rays of light, is what is called Refraction—a term which
probably had its origin from the broken appearance which a staff or a long
pole exhibits, when a portion of it is immersed in water—the word, derived
from the Latin frango, literally signifying breaking or bending.

When light is thus refracted, or has taken a new direction, it then proceeds
invariably in a straight line till it meets with a different medium,7 when it is
again turned out of its course. It must be observed, however, that though we
may by this means cause the rays of light to make any number of angles in
their course, it is impossible for us to make them describe a curve, except in
one single case, namely, where they pass through a medium, the density of
which either uniformly increases or diminishes. This is the case with the
light of the celestial bodies, which passes downwards through our
atmosphere, and likewise with that which is reflected upwards through it by
terrestrial objects. In both these cases it describes a curve of the hyperbolic
kind; but at all other times, it proceeds in straight lines, or in what may be
taken for straight lines without any sensible error.

There are two circumstances essential to refraction. 1. That the rays of light
shall pass out of one medium into another of a different density, or of a
greater or less degree of resistance. 2. That they pass in an oblique
direction. The denser the refracting medium, or that into which the ray
enters, the greater will be its refracting power; and of two refracting

mediums of the same density, that which is of an oily or inflammable nature
will have a greater refracting power than the other. The nature of refraction
may be more particularly explained and illustrated by the following figure
and description.

Let ADHI fig. 2, be a body of water, AD its surface, C a point in which a
ray of light BC enters from the air into the water. This ray, by the greater
density of the water, instead of passing straight forward in its first direction
to K, will be bent at the point C, and pass along in the direction CE, which
is called the refracted ray. Let the line FG be drawn perpendicular to the
surface of the water in C, then it is evident that the ray BC, in passing out of
air, a rare medium, into a dense medium, as water, is refracted into a ray CE
which is nearer to the perpendicular CG than the incident ray BC, and on
the contrary, the ray EC passing out of a denser medium into a rarer will be
refracted into CB, which is farther from the perpendicular.

figure 2.

The same thing may be otherwise illustrated as follows:—suppose a hole
made in one of the sides of the vessel as at a, and a lighted candle placed
within two or three feet of it, when empty, so that its flame may be at L, a
ray of light proceeding from it will pass through the hole a in a straight line
LBCK till it reach the bottom of the vessel at K, where it will form a small
circle of light. Having put a mark at the point K, pour water into the vessel
till it rise to the height AD, and the round spot that was formerly at K, will
appear at E; that is, the ray which went straight forward, when the vessel
was empty, to K, has been bent at the point C, where it falls into the the
water, into the line CE. In this experiment it is necessary that the front of
the vessel should be of glass, in order that the course of the ray may be
seen; and if a little soap be mixed with the water so as to give it a little
mistiness, the ray CE will be distinctly perceived. If, in place of fresh water
we pour in salt water, it will be found that the ray BC is more bent at C. In
like manner alcohol will refract the ray BC more than salt water, and oil
more than alcohol, and a piece of solid glass, of the shape of the water,
would refract the light still more than the oil.

The angle of refraction depends on the obliquity of the rays falling on the
refracting surface being always such, that the sine of the incident angle is to
the sine of the refracted angle, in a given proportion. The incident angle is
the angle made by a ray of light and a line drawn perpendicular to the
refracting surface, at the point where the light enters the surface. The
refracted angle is the angle made by the ray in the refracting medium with
the same perpendicular produced. The sine of the angle is a line which
serves to measure the angle, being drawn from a point in one leg
perpendicular to the other. The following figure (fig. 3.) will tend to
illustrate these definitions.

figure 3.

In this figure BC is the incident ray, CE the refracted ray, DG the
perpendicular, AD the sine of the angle of incidence ACD, and HR the sine
of the angle of refraction GCE. Now, it is a proposition in optics that,—the
sine AD of the angle of incidence BCD is either accurately or very nearly in
a given proportion to the sine HR of the angle of refraction GCE. This ratio
of the sines is as four to three, when the refraction is made out of air into
water, that is AD is to HR as four to three. When the refraction is out of air
into glass, the proportion is about as thirty-one to twenty, or nearly as three
to two. If the refraction be out of air into diamond it is as five to two, that is
AD : HR :: 5 : 2. The denser the medium is, the less is the angle and sine of
refraction. If a ray of light MC, were to pass from air into water, or from
empty space into air, in the direction MC perpendicular to the plane NO
which separates the two mediums, it would suffer no refraction, because
one of the essentials to that effect is wanting, namely, the obliquity of the
incidence.

It may be also proper to remark, that a ray of light cannot pass out of a
denser medium into a rarer, if the angle of incidence exceed a certain limit.
Thus a ray of light will not pass out of glass into air, if the angle of
incidence exceed 40° 11´; or out of glass into water, if the angle of
incidence exceed 59° 20´. In such cases refraction will be changed into
reflection.

The following common experiments, which are easily performed, will
illustrate the doctrine of refraction. Put a shilling or any other small object
which is easily distinguished, into a bason or any other similar vessel, and
then retire to such a distance as that the edge of the vessel shall just hide it
from your sight. If then you cause another person to fill the vessel with
water, you will then find that the shilling is rendered perfectly visible,
although you have not in the slightest degree changed your position. The
reason of this is, that the rays of light, by which it is rendered visible, are
bent out of their course. Thus, suppose the shilling to have been placed in
the bottom of the bason at E, (fig. 2.) the ray of light BC which passes
obliquely from the air into water at C, instead of continuing its course to K,
takes the direction CE, and consequently an object at E would be rendered
visible by rays proceeding in that direction, when they would not have
touched it had they proceeded in their direct course.

The same principle is illustrated by the following experiment. Place a bason
or square box on a table, and a candle at a small distance from it; lay a
small rod or stick across the sides of the bason, and mark the place where
the extremity of the shadow falls, by placing a shilling or other object at the
point; then let water be poured into the bason, and the shadow will then fall
much nearer to the side next the candle than before. This experiment may
likewise be performed by simply observing the change produced on the
shadow of the side of the bason itself. Again, put a long stick obliquely into
deep water, and the stick will seem to be broken at the point where it
appears at the surface of the water—the part which is immersed in the water
appearing to be bent upwards. Hence every one must have observed that, in
rowing a boat, the ends of the oars appear bent or broken every time they
are immersed in the water, and their appearance at such times is a
representation of the course of the refracted rays. Again, fill a pretty deep
jar with water, and you will observe the bottom of the jar considerably

elevated, so that it appears much shallower than it did before the water was
poured in, in the proportion of nearly a third of its depth, which is owing to
the same cause as that which makes the end of a stick immersed in water
appear more elevated than it would do if there were no refraction. Another
experiment may be just mentioned. Put a sixpence in a wine-glass, and pour
upon it a little water. When viewed in a certain position, two sixpences will
appear in the glass—one image of the sixpence from below, which comes
directly to the eye, and another which appears considerably raised above the
other, in consequence of the rays of light rising through the water, and being
refracted. In this experiment the wine-glass should not be more than half
filled with water.

The refraction of light explains the causes of many curious and interesting
phenomena both in the heavens and on the earth. When we stand on the
banks of a river, and look obliquely through the waters to its bottom, we are
apt to think it is much shallower than it really is. If it be eight feet deep in
reality, it will appear from the bank to be only six feet; if it be five feet and
a half deep, it will appear only about four feet. This is owing to the effects
of refraction, by which the bottom of the river is apparently raised by the
refraction of the light passing through the water into air, so as to make the
bottom appear higher than it really is, as in the experiment with the jar of
water. This is a circumstance of some importance to be known and attended
to in order to personal safety. For many school-boys and other young
persons have lost their lives by attempting to ford a river, the bottom of
which appeared to be within their reach, when they viewed it from its
banks: and even adult travellers on horseback have sometimes fallen
victims to this optical deception; and this is not the only case in which a
knowledge of the laws of nature may be useful in guarding us against
dangers and fatal accidents.

It is likewise owing to this refractive power in water, that a skilful
marksman who wishes to shoot fish under water, is obliged to take aim
considerably below the fish as it appears, because it seems much nearer the
top of the water than it really is. An acquaintance with this property of light
is particularly useful to divers, for, in any of their movements or operations,
should they aim directly at the object, they would arrive at a point
considerably beyond it; whereas, by having some idea of the depth of the

water, and the angle which a line drawn from the eye to the object makes
with its surface, the point at the bottom of the water, between the eye and
the object at which the aim is to be taken, may be easily determined. For the
same reason, a person below water does not see objects distinctly. For, as
the aqueous humour of the eye has the same refractive power as water, the
rays of light from any object under water will undergo no refraction in
passing through the cornea, and aqueous humour, and will therefore meet in
a point far behind the retina. But if any person accustomed to go below
water should use a pair of spectacles, consisting of two convex lenses, the
radius of whose surface is three tenths of an inch—which is nearly the
radius of the convexity of the cornea—he will see objects as distinctly
below water as above it.

It is owing to refraction, that we cannot judge so accurately of magnitudes
and distances in water as in air. A fish looks considerably larger in water
than when taken out of it. An object plunged vertically into water always
appears contracted, and the more so as its upper extremity approaches
nearer the surface of the water. Every thing remaining in the same situation,
if we take the object gradually out of the water, and it be of a slender form,
we shall see it become larger and larger, by a rapid developement, as it
were, of all its parts. The distortion of objects, seen through a crooked pane
of glass in a window, likewise arises from its unequal refraction of the rays
that pass through it. It has been calculated that in looking through the
common glass of a window, objects appear about the one thirtieth of an inch
out of their real place, by means of the refraction.

Refraction likewise produces an effect upon the heavenly bodies, so that
their apparent positions are generally different from their real. By the
refractive power of the atmosphere, the sun is seen before he comes to the
horizon in the morning, and after he sinks beneath it in the evening; and
hence this luminary is never seen in the place in which it really is, except
when it passes the zenith at noon, to places within the torrid zone. The sun
is visible, when actually thirty-two minutes of a degree below the horizon,
and when the opake rotundity of the earth is interposed between our eye and
that orb, just on the same principle as, in the experiment with the shilling
and basin of water, the shilling was seen when the edge of the basin
interposed between it and the sight. The refractive power of the atmosphere

has been found to be much greater, in certain cases, than what has been now
stated. In the year 1595 a company of Dutch sailors having been wrecked
on the shores of Nova Zembla, and having been obliged to remain in that
desolate region during a night of more than three months—beheld the sun
make his appearance in the horizon about sixteen days before the time in
which he should have risen according to calculation, and when his body
was actually more than four degrees below the horizon; which circumstance
has been attributed to the great refractive power of the atmosphere in those
intensely cold regions. This refraction of the atmosphere, which renders the
apparent rising and setting of the sun both earlier and later than the real,
produces at least one important beneficial effect. It procures for us the
benefit of a much longer day, at all seasons of the year, than we should
enjoy, did not this property of the atmosphere produce this effect. It is
owing to the same cause that the disks of the sun and moon appear elliptical
or oval, when seen in the horizon, their horizontal diameters appearing
longer than their vertical—which is caused by the greater refraction of the
rays coming from the lower limb, which is immersed in the densest part of
the atmosphere.

The illumination of the heavens which precedes the rising of the sun, and
continues sometime after he is set—or, what is commonly called the
morning and evening twilight—is likewise produced by the atmospherical
refraction—which circumstance forms a very pleasing and beneficial
arrangement in the system of nature. It not only prolongs to us the influence
of the solar light, and adds nearly two hours to the length of our day, but
prevents us from being transported all at once from the darkness of
midnight to the splendour of noon-day, and from the effulgence of day to
the gloom and horrors of the night—which would bewilder the traveller and
navigator in their journeys by sea or land, and strike the living world with
terror and amazement.

The following figure will illustrate the position now stated, and the manner
in which the refraction of the atmosphere produces these effects. Let A a C,
fig. 4, represent one half of our globe, and the dark space between that
curve and B r D, the atmosphere. A person standing on the earth’s surface at
a would see the sun rise at b, when that luminary was in reality only at c—
more than half a degree below the horizon. When the rays of the sun, after

having proceeded in a straight line through empty space, strike the upper
part of the atmosphere at the point d, they are bent out of their right-lined
course, by the refraction of the atmosphere, into the direction d a, so that
the body of the sun, though actually intercepted by the curve of the earth’s
convexity consisting of a dense mass of land or water, is actually beheld by
the spectator at a. The refractive power of the atmosphere gradually
diminishes from the horizon to the zenith, and increases from the zenith to
the horizon, in proportion to the density of its different strata, being densest
at its lower extremity next the earth, and more rare towards its higher
regions. If a person at a had the sun, e, in his zenith, he would see him
where he really is; for his rays coming perpendicularly through the
atmosphere, would be equally attracted in all directions, and would
therefore suffer no inflection. But, about two in the afternoon, he would see
the sun at i, though, in reality, he was at k, thirty-three seconds lower than
his apparent situation. At about four in the afternoon he would see him at m,
when he is at n, one minute and thirty-eight seconds from his apparent
situation. But at six o’clock, when we shall suppose he sets, he will be seen
at o, though he is at that time at p, more than thirty-two minutes below the
horizon. These phenomena arise from the different refractive powers of the
atmosphere at different elevations, and from the obliquity with which the
rays of light fall upon it; for we see every object along that line in which the
rays from it are directed by the last medium through which they passed.

figure 4.

The same phenomena happen in relation to the moon, the planets, the
comets, the stars, and every other celestial body, all of which appear more
elevated, especially when near the horizon, than their true places. The
variable and increasing refraction from the zenith to the horizon, is a source
of considerable trouble and difficulty in making astronomical observations,
and in nautical calculations. For, in order to determine the real altitudes of
the heavenly bodies, the exact degree of refraction, at the observed
elevation, must be taken into account. To the same cause we are to ascribe a
phenomenon that has sometimes occurred—namely, that the moon has been
seen rising totally eclipsed, while the sun was still visible in the opposite
quarter of the horizon. At the middle of a total eclipse of the moon, the sun
and moon are in opposition, or 180 degrees asunder; and, therefore, were no
atmosphere surrounding the earth, these luminaries, in such a position,
could never be seen above the horizon at the same time. But, by the
refraction of the atmosphere near the horizon, the bodies of the sun and
moon are raised more than 32 minutes above their true places, which is

equal, and sometimes more than equal to the apparent diameters of these
bodies.

Extraordinary cases of refraction in relation to terrestrial objects.

In consequence of the accidental condensation of certain strata of the
atmosphere, some very singular effects have been produced in the apparent
elevation of terrestrial objects to a position much beyond that in which they
usually appear. The following instance is worthy of notice. It is taken from
the Philosophical Transactions of London for 1798, and was communicated
by W. Latham, Esq., F.R.S., who observed the phenomenon from Hastings,
on the south coast of England:—‘On July 26, 1797, about five o’clock in
the afternoon, as I was sitting in my dining-room in this place, which is
situated upon the Parade, close to the sea-shore, nearly fronting the south,
my attention was excited by a number of people running down to the sea-
side. Upon inquiring the reason, I was informed, that the coast of France
was plainly to be distinguished by the naked eye. I immediately went down
to the shore, and was surprised to find that, even without the assistance of a
telescope, I could very plainly see the cliffs on the opposite coast, which, at
the nearest part, are between forty and fifty miles distant, and are not to be
discerned from that low situation by the aid of the best glasses. They
appeared to be only a few miles off, and seemed to extend for some leagues
along the coast. I pursued my walk along the shore eastward, close to the
water’s edge, conversing with the sailors and fishermen upon the subject.
They at first would not be persuaded of the reality of the appearance; but
they soon became so thoroughly convinced by the cliffs gradually appearing
more elevated, and approaching nearer, as it were, that they pointed out and
named to me the different places they had been accustomed to visit, such as
the Bay, the Old Head, or Man, the Windmill, &c. at Boulogne, St. Vallery,
and other places on the coast of Picardy, which they afterwards confirmed,
when they viewed them through their telescopes. Their observations were,
that the places appeared as near as if they were sailing, at a small distance,
into the harbours. The day on which this phenomenon was seen was
extremely hot; it was high water at Hastings about two o’clock, P.M., and not
a breath of wind was stirring the whole day.’ From the summit of an
adjacent hill, a most beautiful scene is said to have presented itself. At one

glance the spectators could see Dungeness, Dover Cliffs, and the French
coast, all along from Calais to St. Vallery, and, as some affirmed, as far to
the westward as Dieppe, which could not be much less than eighty or ninety
miles. By the telescope, the French fishing-boats were plainly seen at
anchor, and the different colours of the land on the heights, with the
buildings, were perfectly discernible.

This singular phenomenon was doubtless occasioned by an extraordinary
refraction produced either by an unusual expansion, or condensation of the
lower strata of the atmosphere, arising from circumstances connected with
the extreme heat of the season. The objects seem to have been apparently
raised far above their natural positions; for, from the beach at Hastings, a
straight line drawn across towards the French coast, would have been
intercepted by the curve of the waters. They seem also to have been
magnified by the refraction, and brought apparently four or five times
nearer the eye than in the ordinary state of the atmosphere.

The following are likewise instances of unusual refraction:—When Captain
Colby was ranging over the coast of Caithness, with the telescope of his
great Theodolite, on the 21st of June, 1819, at eight o’clock, P.M. from
Corryhabbie Hill, near Mortlich, in Banffshire, he observed a brig over the
land of Caithness, sailing to the westward in the Pentland Frith, between the
Dunnet and Duncansby heads. Having satisfied himself as to the fact, he
requested his assistants, Lieutenants Robe and Dawson, to look through the
telescope, which they immediately did, and observed the brig likewise. It
was very distinctly visible for several minutes, while the party continued to
look at it, and to satisfy themselves as to its position. The brig could not
have been less than from ninety to one hundred miles distant; and, as the
station on Corryhabbie is not above 850 yards above the sea, the
phenomenon is interesting. The thermometer was at 44°. The night and day
preceding the sight of the brig had been continually rainy and misty, and it
was not till 7 o’clock of the evening of the 21st that the clouds cleared off
the hill.8

Captain Scoresby relates a singular phenomenon of this kind, which
occurred while he was traversing the Polar seas. His ship had been
separated by the ice from that of his father for a considerable time, and he

was looking out for her every day, with great anxiety. At length, one
evening, to his utter astonishment, he saw her suspended in the air, in an
inverted position, traced on the horizon in the clearest colours, and with the
most distinct and perfect representation. He sailed in the direction in which
he saw this visionary phenomenon, and actually found his father’s vessel by
its indication. He was divided from him by immense masses of icebergs,
and at such a distance, that it was quite impossible to have seen the ship in
her actual situation, or to have seen her at all, if her spectrum had not been
thus raised several degrees above the horizon into the sky by this
extraordinary refraction. She was reckoned to be seventeen miles beyond
the visible horizon, and thirty miles distant.

Mrs. Somerville states, that a friend of her’s, while standing on the plains of
Hindostan, saw the whole upper chain of the Himalaya mountains start into
view, from a sudden change in the density of the air, occasioned by a heavy
shower, after a long course of dry and hot weather. In looking at distant
objects through a telescope, over the top of a ridge of hills, about two miles
distant, I have several times observed, that some of the more distant objects
which are sometimes hid by the interposition of a ridge of hills, are, at other
times, distinctly visible above them. I have sometimes observed, that
objects near the middle of the field of view of a telescope, which was in a
fixed position, have suddenly appeared to descend to the lower part, or
ascend to the upper part of the field, while the telescope remained
unaltered. I have likewise seen, with a powerful telescope, the Bell Rock
Lighthouse, at the distance of about twenty miles, to appear as if contracted
to less than two-thirds of its usual apparent height, while every part of it
was quite distinct and well-defined, and in the course of an hour or less, it
appeared to shoot up to its usual apparent elevation—all which phenomena
are evidently produced by the same cause to which we have been adverting.

Such are some of the striking effects produced by the refraction of light. It
enables us to see objects in a direction where they are not; it raises,
apparently, the bottoms of lakes and rivers: it magnifies objects when their
light passes through dense mediums: it makes the sun appear above the
horizon, when he is actually below it, and thus increases the length of our
day: it produces the Aurora and the evening twilight, which forms, in many
instances, the most delightful part of a summer day: it prevents us from

being involved in total darkness, the moment after the sun has descended
beneath the horizon: it modifies the appearances of the celestial bodies, and
the directions in which they are beheld: it tinges the sun, moon, and stars, as
well as the clouds, with a ruddy hue, when near the horizon: it elevates the
appearance of terrestrial objects, and, in certain extraordinary cases, brings
them nearer to our view, and enables us to behold them when beyond the
line of our visible horizon. In combination with the power of reflection, it
creates visionary landscapes, and a variety of grotesque and extraordinary
appearances, which delight and astonish, and sometimes appal the
beholders. In short,—as we shall afterwards see more particularly—the
refraction of light through glasses of different figures, forms the principle
on which telescopes and microscopes are constructed, by which both the
remote and the minute wonders of creation have been disclosed to view. So
that had there been no bodies capable of refracting the rays of light, we
should have remained for ever ignorant of many sublime and august objects
in the remote regions of the universe, and of the admirable mechanism and
the countless variety of minute objects which lie beyond the range of the
unassisted eye in our lower creation, all of which are calculated to direct
our views, and to enlarge our conceptions of the Almighty Creator.

In the operation of the law of refraction in these and numerous other
instances, we have a specimen of the diversified and beneficent effects
which the Almighty can produce by the agency of a single principle in
nature. By the influence of the simple law of gravitation, the planets are
retained in their orbits, the moon directed in her course around the earth,
and the whole of the bodies connected with the sun preserved in one
harmonious system. By the same law the mountains of our globe rest on a
solid basis, the rivers flow through the plains toward the seas, the ocean is
confined to its prescribed boundaries, and the inhabitants of the earth are
retained to its surface and prevented from flying upwards through the voids
of space. In like manner the law by which light is refracted produces a
variety of beneficial effects essential to the present constitution of our world
and the comfort of its inhabitants. When a ray of light enters obliquely into
the atmosphere, instead of passing directly through, it bends a little
downwards, so that the greater portion of the rays which thus enter the
atmospheric mass, descend by inflection to the earth. We then enjoy the
benefit of that light which would otherwise have been totally lost. We

perceive the light of day an hour before the solar orb makes its appearance,
and a portion of its light is still retained when it has descended nearly
eighteen degrees below our horizon. We thus enjoy, throughout the year,
seven hundred and thirty hours of light which would have been lost, had it
not been refracted down upon us from the upper regions of the atmosphere.
To the inhabitants of the polar regions this effect is still more interesting
and beneficial. Were it not for their twilight, they would be involved, for a
much longer period than they now are, in perpetual darkness; but by the
powerful refraction of light which takes place in the frigid zones, the day
sooner makes its appearance towards spring, and their long winter nights
are, in certain cases, shortened by a period of thirty days. Under the poles,
where the darkness of night would continue six months without
intermission, if there were no refraction, total darkness does not prevail
during the one half of this period. When the sun sets, at the North pole
about the 23rd of September, the inhabitants (if any) enjoy a perpetual
aurora, till he has descended 18 degrees below the horizon. In his course
through the ecliptic the sun is two months before he can reach this point,
during which time there is a perpetual twilight. In two months more he
arrives again at the same point, namely 18 degrees below the horizon, when
a new twilight commences, which is continually increasing in brilliancy, for
other two months, at the end of which the body of this luminary is seen
rising in all its glory. So that, in this region, the light of day is enjoyed, in a
greater or less degree, for ten months without interruption, by the effects of
atmospheric refraction; and, during the two months when the influence of
the solar light is entirely withdrawn, the moon is shining above the horizon
for two half months without intermission; and thus it happens, that no more
than two separate fortnights are passed in absolute darkness; and this
darkness is alleviated by the light of the stars and the frequent coruscations
of the Aurora Borealis. Hence, it appears, that there are no portions of our
globe that enjoy, throughout the year, so large a portion of the solar light, as
these northern regions, which is chiefly owing to the refraction of the
atmosphere.

The refraction of light by the atmosphere, combined with its power of
reflecting it, is likewise the cause of that universal light and splendour
which appears on all the objects around us. Were the earth disrobed of its
atmosphere, and exposed naked to the solar beams—in this case, we might

see the sun without having day, strictly so called. His rising would not be
preceded by any twilight as it now is. The most intense darkness would
cover us till the very moment of his rising; he would then suddenly break
out from under the horizon with the same splendour he would exhibit at the
highest part of his course, and would not change his brightness till the very
moment of his setting, when in an instant all would be black as the darkest
night. At noon day we should see the sun like an intensely brilliant globe
shining in a sky as black as ebony, like a clear fire in the night seen in the
midst of an extensive field, and his rays would show us the adjacent objects
immediately around us; but the rays which fall on the objects remote from
us would be for ever lost in the expanse of the heavens. Instead of the
beautiful azure of the sky, and the colours which distinguish the face of
nature by day, we should see nothing but an abyss of darkness, and the stars
shining from a vault as dark as chaos. Thus there would be no day, such as
we now enjoy, without the atmosphere: since it is by the refraction and
reflections connected with this aerial fluid that light is so modified and
directed, as to produce all that beauty, splendour and harmony, which
appear on the concave of the sky, and on the objects which diversify our
terrestrial abode.

The effect of refraction, in respect to terrestrial objects, is likewise of a
beneficial nature. The quantity of this refraction is estimated by Dr.
Maskelyne at one-tenth of the distance of the object observed, expressed in
degrees of a great circle. Hence, if the distance be 10,000 fathoms, its tenth
part 1000 fathoms, is the sixtieth part of a degree, or one minute, which is
the refraction in altitude. Le Gendre estimates it at one fourteenth; De
Lambre at one eleventh; and others at a twelfth of the distance; but it must
be supposed to vary at different times and places according to the varying
state of the atmosphere. This refraction, as it makes objects appear to be
raised higher than they really are, enlarges the extent of our landscapes, and
enables us to perceive distant objects which would otherwise have been
invisible. It is particularly useful to the navigator at sea. It is one important
object of the mariner when traversing his course, to look out for capes and
headlands, rocks and islands, so as to descry them as soon as they are
within the reach of his eye. Now, by means of refraction, the tops of hills
and the elevated parts of coasts, are apparently raised into the air, so that
they may be discovered several leagues further off on the sea than they

would be, did no such refractive power exist. This circumstance is therefore
a considerable benefit to the science of navigation, in enabling the mariner
to steer his course aright, and to give him the most early warning of the
track he ought to take, or of the dangers to which he may be exposed.

In short, the effects produced by the refraction and reflection of light on the
scenery connected with our globe, teach us that these principles, in the hand
of the Almighty, might be so modified and directed, as to produce the most
picturesque, the most glorious and wonderful phenomena, such as mortal
eyes have never yet seen, and of which human imagination can form no
conception; and in other worlds, more resplendent and magnificent than
ours, such scenes may be fully realized, in combination with the operation
of physical principles and agents, with which we are at present
unacquainted. From what we already know of the effects of the reflection
and the refraction of light, it is not beyond the bounds of probability to
suppose, that in certain regions of the universe, light may be reflected and
refracted through different mediums, in such a manner, as to present to the
view of their inhabitants the prominent scenes connected with distant
systems and worlds, and to an extent, as shall infinitely surpass the effects
produced by our most powerful telescopes.

CHAPTER III.

ON THE REFRACTION OF LIGHT THROUGH SPHERICAL
TRANSPARENT SUBSTANCES, OR LENSES.

It is to the refraction of light that we are indebted for the use of lenses or
artificial glasses to aid the powers of vision. It lays the foundation of
telescopes, microscopes, camera obscuras, phantasmagorias, and other
optical instruments, by which so many beautiful, useful, and wonderful
effects have been produced. In order therefore to illustrate the principles on
which such instruments are constructed, it is necessary to explain the
manner in which the rays of light are refracted and modified, when passing
through spherical mediums of different forms. I do not intend however to
enter into the minutiæ of this subject, nor into any abstract mathematical
demonstrations, but shall simply offer a few explanations of general
principles, and several experimental illustrations, which may enable the
general reader to understand the construction of the optical instruments to
be afterwards described.

A lens is a transparent substance of a different density from the surrounding
medium, and terminating in two surfaces, either both spherical, or one
spherical and the other plain. It is usually made of glass, but may also be
formed of any other transparent substance, as ice, crystal, diamond, pebbles,
or by fluids of different densities and refractive powers, enclosed between
concave glasses. Lenses are ground into various forms, according to the
purpose they are intended to serve. They may be generally distinguished as
being either convex or concave. A convex glass is thickest in the middle,
and thinner towards the edges. A concave glass is thin in the middle, and
thicker towards the extremities. Of these there are various forms, which are
represented in fig. 5. A, is a plano-convex lens, which has one side plane,
and the other spherical or convex. B, is a plano-concave, which is plane on
the one side and concave on the other. C, is a double-convex, or one which
is spherical on both sides. D, a double-concave, or concave on both sides.
E, is called a meniscus, which is convex on one side and concave on the

other. F, is a concavo-convex, the convex side of which is of a smaller
sphere than the concave. In regard to the degree of convexity or concavity
in lenses, it is evident that there may be almost an infinite variety. For every
convex surface is to be considered as the segment of a circle, the diameter
and radius of which may vary to almost any extent. Hence, lenses have been
formed by opticians, varying from one-fiftieth of an inch in radius, to two
hundred feet. When we speak of the length of the radius of a lens,—as for
instance, when we say that a lens is two inches or forty inches radius, we
mean, that the convex surface of the glass is the part of a circle the radius of
which, or half the diameter is two inches or forty inches; or in other words,
were the portion of the sphere on which it is ground formed into a globe of
corresponding convexity, it would be four inches or eighty inches in
diameter.

figure 5.

figure 6.

figure 7.

figure 8.

The axis of a lens is a straight line drawn through the center of its spherical
surface; and as the spherical sides of every lens are arches of circles the axis
of the lens would pass through the centre of that circle of which its sides are
segments. Rays are those emanations of light which proceed from a
luminous body, or from a body that is illuminated. The Radiant is that body
or object which emits the rays of light—whether it be a self-luminous body,
or one that only reflects the rays of light. Rays may proceed from a Radiant
in different directions. They may be either parallel, converging, or
diverging. Parallel rays are those which proceed equally distant from each
other through their whole course. Rays proceeding from the sun, the
planets, the stars, and distant terrestrial objects are considered as parallel, as
in fig. 6. Converging rays are such as, proceeding from a body, approach
nearer and nearer in their progress, tending to a certain point where they all
unite. Thus, the rays proceeding from the object AB, (fig. 7.) to the point F,
are said to converge towards that point. All convex glasses cause parallel
rays, which fall upon them to converge in a greater or less degree; and they
render converging rays still more convergent. If AB, fig. 7. represent a
convex lens, and H G I parallel rays falling upon it, they will be refracted
and converge towards the point F, which is called the focus, or burning
point; because, when the sun’s rays are thus converged to a point by a large
lens, they set on fire combustible substances. In this point the rays meet and

intersect each other. Diverging rays are those which, proceeding from any
point as A, fig. 8, continually recede from each other as they pass along in
their course towards BC. All the rays which proceed from near objects as a
window in a room, or an adjacent house or garden are more or less
divergent. The following figures show the effects of parallel, converging
and diverging rays in passing through a double convex lens.

figure 11. figure 9. figure 10.

Fig. 9, shows the effects of parallel rays, KA, DE, LB, falling on a convex
glass AB. The rays which fall near the extremities at A and B, are bent or
refracted towards CF, the focus, and centre of convexity. It will be
observed, that they are less refracted as they approach the center of the lens,
and the central ray DEC, which is called the axis of the lens, and which
passes through its center, suffers no refraction. Fig. 10, exhibits the course

of converging rays, when passing through a similar lens. In this case the
rays converge to a focus nearer to the lens than the center; for a convex lens
uniformly increases the convergence of converging rays. The converging
rays here represented, may be conceived as having been refracted by
another convex lens of a longer focus, and, passing on towards a point of
convergence, were intercepted by the lens AB. The point D is the place
where the rays would have converged to a focus, had they not been thus
intercepted. Fig. 11, represents the course of diverging rays when falling on
a double convex glass. In this case the rays D B, D A, &c., after passing
through the lens, converge to a focus at a point considerably farther from
the lens than its centre, as at F. Such rays must be considered as proceeding
from near objects, and the fact may be illustrated by the following
experiment. Take a common reading-glass, and hold it in the rays of the
sun, opposite a sheet of writing-paper or a white wall, and observe at what
distance from the glass the rays on the paper converge to a small distinct
white spot. This distance gives the focal length of the lens by parallel rays.
If now, we hold the glass within a few feet of a window, or a burning
candle, and receive its image on the paper, the focal distance of the image
from the glass will be found to be longer. If, in the former case, the focal
distance was twelve inches,—in the latter case it will be thirteen, fifteen, or
sixteen inches, according to the distance of the window or the candle from
the glass.

If the lens A B, fig. 9, on which parallel rays are represented as falling, were
a plano-convex, as represented at A, fig, 5, the rays would converge to a
point P, at double the radius, or the whole diameter of the sphere of which it
is a segment. If the thickness of a plano-convex be considered, and if it be
exposed on its convex side to parallel rays, as those of the sun, the focus
will be at the distance of twice the radius, wanting two-thirds of the
thickness of the lens. But if the same lens be exposed with its plane side to
parallel rays, the focus will then be precisely at the distance of twice the
radius from the glass.

The effects of concave lenses are directly opposite to those of convex.
Parallel rays, striking one of those glasses, instead of converging towards a
point, are made to diverge. Rays already divergent are rendered more so,
and convergent rays are made less convergent. Hence objects seen through

concave glasses appear considerably smaller and more distant than they
really are. The following diagram, fig. 12, represents the course of parallel
rays through a double concave lens, where the parallel rays T A, D E, I B,
&c., when passing through the concave glass A B, diverge into the rays G L,
E C, H P, &c., as if they proceeded from F, a point before the lens, which is
the principal focus of the lens.

figure 12.

The principal focal distance E F, is the same as in convex lenses. Concave
glasses are used to correct the imperfect vision of short-sighted persons. As
the form of the eye of such persons is too convex, the rays are made to
converge before they reach the optic nerve; and therefore a concave glass,
causing a little divergency, assists this defect of vision, by diminishing the
effect produced by the too great convexity of the eye, and lengthening its
focus. These glasses are seldom used, in modern times, in the construction
of optical instruments, except as eye-glasses for small pocket perspectives,
and opera glasses.

To find the focal distance of a concave glass. Take a piece of paste-board or
card paper, and cut a round hole in it, not larger than the diameter of the
lens; and, on another piece of paste-board, describe a circle whose diameter
is just double the diameter of the hole. Then apply the piece with the hole in
it to the lens, and hold them in the sun-beams, with the other piece at such a
distance behind, that the light proceeding from the hole may spread or
diverge so as precisely to fill the circle; then the distance of the circle from
the lens is equal to its virtual focus, or to its radius, if it be a double
concave, and to its diameter, if a plano-concave. Let d, e, (fig. 12,) represent

the diameter of the hole, and g, i, the diameter of the circle, then the
distance C, I, is the virtual focus of the lens.9

The meniscus represented at E, fig. 5, is like the crystal of a common watch,
and as the convexity is the same as the concavity, it neither magnifies nor
diminishes. Sometimes, however, it is made in the form of a crescent, as at
F, fig. 5, and is called a concavo-convex lens; and, when the convexity is
greater than the concavity, or, when it is thickest in the middle, it acts nearly
in the same way as a double or plano-convex lens of the same focal
distance.

Of the IMAGES formed by convex lenses.

It is a remarkable circumstance, and which would naturally excite
admiration, were it not so common and well known, that when the rays of
light from any object are refracted through a convex lens, they paint a
distinct and accurate picture of the object before it, in all its colours,
shades, and proportions. Previous to experience, we could have had no
conception that light, when passing through such substances, and
converging to a point, could have produced so admirable an effect,—an
effect on which the construction and utility of all our optical instruments
depend. The following figure will illustrate this position. Let L, N, represent
a double convex lens, A, C, a, its axis, and OB, an object perpendicular to
it. A ray passing from the extremity of the object at O, after being refracted
by the lens at F, will pass on in the direction FI, and form an image of that
part of the object at I. This ray will be the axis of all the rays which fall on
the lens from the point O, and I will be the focus where they will all be
collected. In like manner BCM, is the axis of that parcel of rays which
proceed from the extremity of the object B, and their focus will be at M;
and since all the points in the object between O, and B, must necessarily
have their foci between I and M, a complete picture of the points from
which they come will be depicted, and consequently an image of the whole
object OB.

figure 13.

It is obvious, from the figure, that the image of the object is formed in the
focus of the lens, in an inverted position. It must necessarily be in this
position, as the rays cross at C, the centre of the lens; and as it is impossible
that the rays from the upper part of the object O, can be carried by
refraction to the upper end of the image at M. This is a universal principle
in relation to convex lenses of every description, and requires to be attended
to in the construction and use of all kinds of telescopes and microscopes. It
is easily illustrated by experiment. Take a convex lens of eight, twelve, or
fifteen inches focal distance, such as a reading glass, or the glass belonging
to a pair of spectacles, and holding it, at its focal distance from a white wall,
in a line with a burning candle, the flame of the candle will be seen depicted
on the wall in an inverted position, or turned upside down. The same
experiment may be performed with a window-sash, or any other bright
object. But, the most beautiful exhibition of the images of objects formed
by convex lenses, is made by darkening a room, and placing a convex lens
of a long focal distance in a hole cut out of the window-shutter; when a
beautiful inverted landscape, or picture of all the objects before the window,
will be painted on a white paper or screen placed in the focus of the glass.
The image thus formed exhibits not only the proportions and colours, but
also the motions of all the objects opposite the lens, forming as it were a

living landscape. This property of lenses lays the foundation of the camera
obscura, an instrument to be afterwards described.

The following principles in relation to images formed by convex lenses may
be stated. 1. That the image subtends the same angle at the centre of the
glass as the object itself does. Were an eye placed at C, the centre of the
lens LN, fig. 13, it would see the object OB, and the image IM under the
same optical angle, or, in other words, they would appear equally large. For,
whenever right lines intersect each other, as OI and BM, the opposite angles
are always equal, that is, the angle MCI is equal to the angle OCB. 2. The
length of the image formed by a convex lens, is to the length of the object,
as the distance of the image is to the distance of the object from the lens:
that is, MI is to OB :: as Ca to CA. Suppose the distance of the object CA
from the lens, to be forty-eight inches, the length of the object OB = sixteen
inches, and the distance of the image from the lens, six inches, then the
length of the image will be found by the following proportion, 48 : 16 :: 6 :
2, that is, the length of the image, in such a case, is two inches. 3. If the
object be at an infinite distance, the image will be formed exactly in the
focus. 4. If the object be at the same distance from the lens as its focus, the
image is removed to an infinite distance on the opposite side; in other
words, the rays will proceed in a parallel direction. On this principle, lamps
on the streets are sometimes directed to throw a bright light along a foot-
path where it is wanted, when a large convex glass is placed at its focal
distance from the burner; and on the same principle, light is thrown to a
great distance from lighthouses, either by a very large convex lens of a short
focal distance, or by a concave reflector. 5. If the object be at double the
distance of the focus from the glass, the image will also be at double the
distance of the focus from the glass. Thus, if a lens of six inches focal
distance be held at twelve inches distance from a candle, the image of the
candle will be formed at twelve inches from the glass on the other side. 6. If
the object be a little further from the lens than its focal distance, an image
will be formed, at a distance from the object, which will be greater or
smaller in proportion to the distance. For example, if a lens five inches
focus, be held at a little more than five inches from a candle, and a wall or
screen at five feet six inches distant, receive the image, a large and inverted
image of the candle will be depicted, which will be magnified in proportion
as the distance of the wall from the candle exceeds the distance of the lens

from the candle. Suppose the distance of the lens to be five and a half
inches, then the distance of the wall where the image is formed, being
twelve times greater, the image of the candle will be magnified twelve
times. If MI (fig. 13.) be considered as the object, then OB will represent
the magnified image on the wall. On this principle the image of the object is
formed by the small object glass of a compound microscope. On the same
principle the large pictures are formed by the Magic Lantern and the
Phantasmagoria; and in the same way small objects are represented in a
magnified form, on a sheet or wall by the Solar microscope. 7. All convex
lenses magnify the objects seen through them, in a greater or less degree.
The shorter the focal distance of the lens, the greater is the magnifying
power. A lens four inches focal distance, will magnify objects placed in the
focus, two times in length and breadth; a lens two inches focus will magnify
four times, a lens one inch focus eight times; a lens half an inch focus
sixteen times, &c. supposing eight inches to be the least distance at which
we see near objects distinctly. In viewing objects with small lenses, the
object to be magnified should be placed exactly at the focal distance of the
lens, and the eye at about the same distance on the other side of the lens.
When we speak of magnifying power, as, for example, that a lens one inch
focal distance magnifies objects eight times, it is to be understood of the
lineal dimensions of the object. But as every object at which we look has
breadth as well as length, the surface of the object is in reality magnified
sixty-four times, or the square of its lineal dimensions; and for the same
reason a lens half an inch focal distance magnifies the surfaces of objects
256 times.

Reflections deduced from the preceding subject.

Such are some of the leading principles which require to be recognised in
the construction of refracting telescopes, microscopes, and other dioptric
instruments whose performance chiefly depends on the refraction of light.
—It is worthy of particular notice that all the phenomena of optical lenses
now described, depend upon that peculiar property which the Creator has
impressed upon the rays of light, that, when they are refracted to a focus by
a convex transparent substance, they depict an accurate image of the
objects whence they proceed. This, however common, and however much

overlooked by the bulk of mankind, is indeed a very wonderful property
with which light has been endued. Previous to experience we could have
had no conception that such an effect would be produced; and, in the first
instance, we could not possibly have traced it to all its consequences. All
the objects in creation might have been illuminated as they now are, for
aught we know, without sending forth either direct or reflected rays with the
property of forming exact representations of the objects whence they
proceeded. But this we find to be a universal law in regard to light of every
description, whether as emanating directly from the sun, or as reflected
from the objects he illuminates, or as proceeding from bodies artificially
enlightened. It is a law or a property of light not only in our own system,
but throughout all the systems of the universe to which mortal eyes have yet
penetrated. The rays from the most distant star which astronomers have
descried, are endued with this property, otherwise they could never have
been perceived by means of our optical instruments; for it is by the pictures
or images formed in these instruments that such distant objects are brought
to view. Without this property of light, therefore, we should have had no
telescopes, and consequently we could not have surveyed, as we can now
do, the hills and vales, the deep caverns, the extensive plains, the circular
ranges of mountains, and many other novel scenes which diversify the
surface of our moon. We should have known nothing of the stupendous
spots which appear on the surface of the sun—of the phases of Venus—of
the satellites and belts of Jupiter—of the majestic rings of Saturn—of the
existence of Uranus and his six moons,—or of the planets Vesta, Juno,
Ceres, and Pallas, nor could the exact bulks of any of these bodies have
been accurately determined. But, above all, we should have been entirely
ignorant of the wonderful phenomena of double stars—which demonstrate
that suns revolve around suns—of the thousands and millions of stars which
crowd the profundities of the Milky Way and other regions of the heavens
—of the thousands of Nebulæ or starry systems which are dispersed
throughout the immensity of the firmament, and many other objects of
sublimity and grandeur, which fill the contemplative mind with admiration
and awe, and raise its faculties to higher conceptions than it could otherwise
have formed of the omnipotence and grandeur of the Almighty Creator.

Without this property of the rays of light we should likewise have wanted
the use of the microscope—an instrument which has disclosed a world

invisible to common eyes, and has opened to our view the most astonishing
exhibitions of Divine mechanism, and of the wisdom and intelligence of the
Eternal Mind. We should have been ignorant of those tribes of living
beings, invisible to the unassisted eye, which are found in water, vinegar,
and many other fluids—many of which are twenty thousand times smaller
than the least visible point, and yet display the same admirable skill and
contrivance in their construction, as are manifested in the formation of the
larger animals. We should never have beheld the purple tide of life, and
even the globules of the blood rolling with swiftness through veins and
arteries smaller than the finest hair; or had the least conception that
numberless species of animated beings, so minute that a million of them are
less than a grain of sand, could have been rendered visible to human eyes,
or that such a number of vessels, fluids, movements, diversified organs of
sensation, and such a profusion of the richest ornaments and the gayest
colours could have been concentrated in a single point. We should never
have conceived that even the atmosphere is replenished with invisible
animation, that the waters abound with countless myriads of sensitive
existence, that the whole earth is full of life, and that there is scarcely a tree,
plant, or flower, but affords food and shelter to a species of inhabitants
peculiar to itself, which enjoy the pleasures of existence and share in the
bounty of the Creator. We could have formed no conception of the beauties
and the varieties of mechanism which are displayed in the scenery of that
invisible world to which the microscope introduces us—beauties and
varieties, in point of ornament and delicate contrivance, which even surpass
what is beheld in the visible operations and aspect of nature around us. We
find joints, muscles, a heart, stomach, entrails, veins, arteries, a variety of
motions, a diversity of forms, and a multiplicity of parts and functions—in
breathing atoms. We behold in a small fibre of a peacock’s feather, not more
than one-eighth of an inch in length, a profusion of beauties no less
admirable than is presented by the whole feather to the naked eye—a stem
sending out multitudes of lateral branches, each of which emits numbers of
little sprigs, which consist of a multitude of bright shining globular parts,
adorned with a rich variety of colours. In the sections of plants, we see
thousands and ten thousands of tubes and pores, and other vessels for the
conveyance of air and juices for the sustenance of the plant; in some
instances, more than ten hundred thousand of these being compressed
within the space of a quarter of an inch in diameter, and presenting to the

eye the most beautiful configurations. There is not a weed, nor a moss, nor
the most insignificant vegetable, which does not show a multiplicity of
vessels disposed in the most curious manner for the circulation of sap for its
nourishment, and which is not adorned with innumerable graces for its
embellishment. All these and ten thousands of other wonders which lie
beyond the limits of natural vision, in this new and unexplored region of the
universe, would have been for ever concealed from our view, had not the
Creator endued the rays of light with the power of depicting the images of
objects, when refracted by convex transparent substances.

In this instance, as well as in many others, we behold a specimen of the
admirable and diversified effects, which the Creator can produce from the
agency of a single principle in nature. By means of optical instruments, we
are now enabled to take a more minute and expansive view of the amazing
operations of nature, both in heaven and on earth, than former generations
could have surmised. These views tend to raise our conceptions of the
attributes of that Almighty Being, who presides over all the arrangements of
the material system, and to present them to our contemplation in a new, a
more elevated, and expansive point of view. There is, therefore, a
connection which may be traced between the apparently accidental
principle of the rays of light forming images of objects, and the
comprehensive views we are now enabled to take of the character and
perfections of the Divinity. Without the existence of the law or principle
alluded to, we could not, in the present state, have formed precisely the
same conceptions either of the Omnipotence, or of the wisdom and
intelligence of the Almighty. Had no microscope ever been invented, the
idea never could have entered into the mind of man, that worlds of living
beings exist beyond the range of natural vision, that organized beings
possessed of animation exist, whose whole bulk is less than the ten hundred
thousandth part of the smallest grain of sand; that, descending from a
visible point to thousands of degrees beyond it, an invisible world exists,
peopled with tribes of every form and size, the extent of which, and how far
it verges towards infinity downwards, mortals have never yet explored, and
perhaps will never be able to comprehend. This circumstance alone presents
before us the perfections of the divinity in a new aspect, and plainly
intimates that it is the will and the intention of the Deity, that we should
explore his works, and investigate the laws by which the material world is

regulated, that we may acquire more expansive views of his character and
operations. The inventions of man in relation to art and science, are not
therefore to be considered as mere accidental occurrences, but as special
arrangements in the divine government, for the purpose of carrying forward
the human mind to more clear and ample views of the scenes of the
universe, and of the attributes and the agency of Him “who is wonderful in
counsel and excellent in working.”

CHAPTER IV.

ON THE REFLECTION OF LIGHT.

The reflection of the rays of light is that property by which—after
approaching the surfaces of bodies, they are thrown back, or repelled. It is
in consequence of this property that all the objects around us, and all the
diversified landscapes on our globe, are rendered visible. It is by light
reflected from their surfaces that we perceive the planetary bodies and their
satellites, the belts of Jupiter, the rings of Saturn, the various objects which
diversify the surface of the Moon, and all the bodies in the universe which
have no light of their own. When the rays of light fall upon rough and
uneven surfaces, they are reflected very irregularly and scattered in all
directions, in consequence of which thousands of eyes, at the same time,
may perceive the same objects, in all their peculiar colours, aspects, and
relations. But, when they fall upon certain smooth and polished surfaces,
they are reflected with regularity, and according to certain laws. Such
surfaces, when highly polished, are called Mirrors or Speculums; and it is to
the reflection of light from such surfaces, and the effects it produces, that I
am now to direct the attention of the reader.

Mirrors or Specula, may be distinguished into three kinds, plane, concave,
and convex, according as they are bounded by plane or spherical surfaces.
These are made either of metal or of glass, and have their surfaces highly
polished for the purpose of reflecting the greatest number of rays. Those
made of glass are foliated or quicksilvered on one side; and the metallic
specula are generally formed of a composition of different metallic
substances, which, when accurately polished, is found to reflect the greatest
quantity of light. I shall, in the first place, illustrate the phenomena of
reflection produced by plane-mirrors.

When light impinges, or falls, upon a polished flat surface, rather more than
the half of it is reflected, or thrown back in a direction similar to that of its
approach; that is to say, if it fall perpendicularly on the polished surface, it
will be perpendicularly reflected; but if it fall obliquely, it will be reflected

with the same obliquity. Hence, the following fundamental law, regarding
the reflection of light, has been deduced both from experiment and
mathematical demonstration, namely, that the angle of reflection is, in all
cases, exactly equal to the angle of incidence. This is a law which is
universal in all cases of reflection, whether it be from plane or spherical
surfaces, or whether these surfaces be concave or convex, and which
requires to be recognized in the construction of all instruments which
depend on the reflection of the rays of light. The following figure (fig. 14)
will illustrate the position now stated.

Let AB represent a plane mirror, and CD a line or ray of light perpendicular
to it. Let FD represent the incident ray from any object, then DE will be the
reflected ray, thrown back in the direction from D to E, and it will make
with the perpendicular CD the same angle which the incident ray FD did
with the same perpendicular, that is, the angle FDC will be equal to the
angle EDC, in all cases of obliquity. The incident ray of light may be
considered as rebounding from the mirror, like a tennis ball from a marble
pavement, or the wall of a court.

figure 14.

In viewing objects by reflection we see them in a different direction from
that in which they really are, namely, along the line in which the rays come
to us last. Thus, if AB (fig. 15) represent a plane mirror, the image of an
object C appears to the eye at E behind the mirror, in the direction EG, and
always in the intersection G of the perpendicular CG, and the reflected ray
EG—and consequently at G as far behind the mirror, as the object C is
before it. We therefore see the image in the line EG, the direction in which
the reflected rays proceed. A plane mirror does not alter the figure or size of
objects; but the whole image is equal and similar to the whole object, and
has a like situation with respect to one side of the plane, that the object has
with respect to the other.

figure 15.

Mr. Walker illustrates the manner in which we see our faces in a mirror by
the following figure (16). AB represents a mirror, and OC, a person looking
into it. If we conceive a ray proceeding from the forehead CE, it will be sent
to the eye at O, agreeably to the angle of incidence and reflection. But the
mind puts CEO into one line, and the forehead is seen at H, as if the lines CEO
had turned on a hinge at E.—It seems a wonderful faculty of the mind to put
the two oblique lines CE and OE into one straight line OH, yet it is seen every
time we look at a mirror. For the ray has really travelled from C to E, and

from E to O, and it is that journey which determines the distance of the
object; and hence we see ourselves as far beyond the mirror as we stand
from it. Though a ray is here taken only from one part of the face, it may be
easily conceived that rays from every other part of the face must produce a
similar effect.

figure 16.

In every plain mirror, the image is always equal to the object, at what
distance soever it may be placed; and as the mirror is only at half the
distance of the image from the eye, it will completely receive an image of
twice its own length. Hence a man six feet high may view himself
completely in a looking glass of three feet in length, and half his own
breadth; and this will be the case at whatever distance he may stand from
the glass. Thus, the man AC (fig. 17) will see the whole of his own image in
the glass AB, which is but one half as large as himself. The rays from the
head pass to the mirror in the line Aa, perpendicular to the mirror, and are

returned to the eye in the same line; consequently, having travelled twice
the length Aa, the man must see his head at B. From his feet C rays will be
sent to the bottom of the mirror at B; these will be reflected at an equal
angle to the eye in the direction BA, as if they had proceeded in the direction
DbA, so that the man will see his foot at D, and consequently his whole
figure at BD.

figure 17.

A person when looking into a mirror, will always see his own image as far
beyond the mirror as he is before it, and as he moves to or from it, the
image will, at the same time, move towards or from him on the other side;
but apparently with a double velocity, because the two motions are equal
and contrary. In like manner, if while the spectator is at rest, an object be in
motion, its image behind the mirror will be seen to move at the same time.
And if the spectator moves, the images of objects that are at rest will appear
to approach, or recede from him, after the same manner as when he moves
towards real objects; plane mirrors reflecting not only the object, but the
distance also, and that exactly in its natural dimensions—The following
principle is sufficient for explaining most of the phenomena seen in a plane
mirror, namely;—That the image of an object seen in a plane mirror, is
always in a perpendicular to the mirror joining the object and the image,
and that the image is as much on one side the mirror, as the object is on the
other.

Reflection by Convex and Concave Mirrors.

Both convex and concave mirrors are formed of portions of a sphere. A
convex speculum is ground and polished in a concave dish or tool which is
a portion of a sphere, and a concave speculum is ground upon a convex
tool. The inner surface of a sphere brings parallel rays to a focus at one
fourth of its diameter, as represented in the following figure, where C is the
centre of the sphere on which the concave speculum AB is formed, and F
the focus where parallel rays from a distant object would be united, after
reflection, that is, at one half the radius, or one fourth of the diameter from
the surface of the speculum. Were a speculum of this kind presented to the
sun, F would be the point where the reflected rays would be converged to a
focus, and set fire to combustible substances if the speculum be of a large
diameter, and of a short focal distance. Were a candle placed in that focus,
its light would be reflected parallel as represented in the figure. These are
properties of concave specula which require to be particularly attended to in
the construction of reflecting telescopes. It follows, from what has been
now stated, that if we intend to form a speculum of a certain focal distance,
—for example, two feet, it is necessary that it should be ground upon a tool
whose radius is double that distance, or four feet.

figure 18.

Properties of Convex Mirrors.

From a convex surface, parallel rays when reflected are made to diverge;
convergent rays are reflected less convergent; and divergent rays are
rendered more divergent. It is the nature of all convex mirrors and surfaces
to scatter or disperse the rays of light, and in every instance to impede their
convergence. The following figure shows the course of parallel rays as
reflected from a convex mirror. AEB is the convex surface of the mirror;
and KA, IE, LB, parallel rays falling upon it. These rays, when they strike
the mirror, are made to diverge in the direction AG, BH, &c. and both the
parallel and divergent rays are here represented as they appear in a dark
chamber, when a convex mirror is presented to the solar rays. The dotted
lines denote only the course or tendency of the reflected rays, towards the

virtual focus F, were they not intercepted by the mirror. This virtual focus is
just equal to half the radius CE.

figure 19.

The following are some of the properties of convex mirrors: 1. The image
appears always erect, and behind the reflecting surface. 2. The image is
always smaller than the object, and the diminution is greater in proportion
as the object is further from the mirror, but if the object touch the mirror,
the image at the point of contact is of the same size as the object. 3. The
image does not appear so far behind the reflecting surface as in a plain
mirror. 4. The image of a straight object, placed either parallel or oblique to
the mirror is seen curved in the mirror; because the different points of the
object are not all at an equal distance from the surface of the mirror. 5.
Concave mirrors have a real focus where an image is actually formed; but
convex specula have only a virtual focus, and this focus is behind the
mirror; no image of any object being formed before it.

The following are some of the purposes to which convex mirrors are
applied. They are frequently employed by painters for reducing the
proportions of the objects they wish to represent, as the images of objects
diminish in proportion to the smallness of the radius of convexity, and to
the distances of objects from the surface of the mirror. They form a
fashionable part of modern furniture, as they exhibit a large company

assembled in a room, with all the furniture it contains, in a very small
compass, so that a large hall with all its objects, and even an extensive
landscape, being reduced in size, may be seen from one point of view. They
are likewise used as the small specula of those reflecting telescopes which
are fitted up on the Cassegrainian plan, and in the construction of Smith’s
Reflecting Microscope. But on the whole, they are very little used in the
construction of optical instruments.

Properties of Concave speculums.

Concave specula have properties very different from those which are
convex; they are of more importance in the construction of reflecting
telescopes and other optical instruments; and therefore require more minute
description and illustration. Concave mirrors cause parallel rays to
converge; they increase the convergence of rays that are already
converging; they diminish the divergence of diverging rays; and, in some
cases, render them parallel and even convergent; which effects are all in
proportion to the concavity of the mirror. The following figures show the
course of diverging and parallel rays as reflected from concave mirrors.

Fig. 20 represents the course of parallel rays, and AB, the concave mirror
on which they fall. In this case, they are reflected so as to unite at F, which
point is distant from its surface one fourth of the diameter of the sphere of
the mirror. This point is called the focus of parallel rays, or the true focus of
the mirror. And, since the sun beams are parallel among themselves, if they
are received on a concave mirror, they will all be reflected to that point, and
there burn in proportion to the quantity of rays collected by the mirror. Fig.
21. shows the direction of diverging rays, or those which proceed from a
near object. These rays proceeding from an object further from the mirror
than the true focal point, as from D to A and to B, are reflected converging
and meet at a point F, further from the mirror than the focal point of parallel
rays. If the distance of the radiant, or object D, be equal to the radius CE,
then will the focal distance be likewise equal to the radius: That is, if an
object be placed in the center of a concave speculum, the image will be
reflected upon the object, or they will seem to meet and embrace each other
in the centre. If the distance of the radiant be equal to half the radius, its
image will be reflected to an infinite distance, for the rays will then be

parallel. If, therefore, a luminous body be placed at half the radius from a
concave speculum, it will enlighten places directly before it at great
distances. Hence their use when placed behind a candle in a common
lantern; hence their utility in throwing light upon objects in the Magic
Lantern and Phantasmagoria, and hence the vast importance of very large
mirrors of this description, as now used in most of our Light Houses, for
throwing a brilliant light to great distances at sea to guide the mariner when
directing his course under the cloud of night.

figure 20.

figure 21.

When converging rays fall upon a concave mirror, they are reflected more
converging and unite at a point between the focus of parallel rays and the
mirror; that is, nearer the mirror than one half the radius; and their precise
degree of convergency will be greater than that wherein they converged
before reflection.

Of the images formed by Concave Mirrors.

If rays proceeding from a distant object fall upon a concave speculum, they
will paint an image or representation of the object on its focus before the
mirror. This image will be inverted, because the rays cross at the points
where the image is formed. We have already seen that a convex glass forms
an image of an object behind it; the rays of light from objects pass through
the glass, and the picture is formed on the side farthest from the object. But
in concave mirrors the images of distant objects—and of all objects that are
farther from its surface than its principal focus—are formed before the
mirror, or on the same side as the object. In almost every other respect,
however, the effect of a concave mirror is the same as that of a convex lens,
in regard to the formation of images, and the course pursued by the rays of
light, except that the effect is produced in the one case by refraction, and in
the other by reflection. The following figure represents the manner in which
images are formed by concave mirrors. GF represents the reflecting surface
of the mirror; OAB, the object; and IAM, the image formed by the mirror.

The rays proceeding from O, will be carried to the mirror, in the direction
OG, and according to the law that the angle of incidence is equal to the
angle of reflection, will be reflected to I, in the direction GI. In like manner
the rays from B, will be reflected from F to M, the rays from A, will be
reflected to a, and so of all the intermediate rays, so that an inverted image
of the object OB, will be formed at IM. If the rays proceeded from objects
at a very great distance the image would be formed in the real focus of the
mirror, or at one-fourth the diameter of the sphere from its surface; but near
objects, which send forth diverging rays, will have their images formed a
little farther from the surface of the mirror.

figure 22.

If we suppose a real object placed at IM, then OB will represent its
magnified image, which will be larger than the object, in proportion to its
distance from the mirror. This may be experimentally illustrated by a
concave mirror and a candle. Suppose a concave mirror whose focal
distance is five inches, and that a candle is placed before it, at a little
beyond its focus, (as at IM)—suppose at five and a half inches,—and that a
wall or white screen receives the image, at the distance of five feet six

inches from the mirror, an image of the candle will be formed on the wall
which will be twelve times longer and broader than the candle itself. In this
way concave mirrors may be made to magnify the images of objects to an
indefinite extent. This experiment is an exact counterpart of what is effected
in similar circumstances by a convex lens, as described p. 74; the mirror
performing the same thing by reflection, as the lens did by refraction.

From what has been stated in relation to concave mirrors it will be easily
understood how they make such powerful burning-glasses. Suppose the
focal distance of a concave mirror to be twelve inches, and its diameter or
breadth twelve inches. When the sun’s rays fall on such a mirror, they form
an image of the sun at the focal point whose diameter is found to be about
one-tenth of an inch. All the rays which fall upon the mirror are converged
into this small point; and consequently their intensity is in proportion as the
square of the surface of the mirror is to the square of the image. The squares
of these diameters are as 14,400 to 1; and consequently the density of the
sun’s rays, in the focus, is to their density on the surface of the mirror as
14,400 to 1. That is, the heat of the solar rays in the focus of such a mirror
will be fourteen thousand four hundred times greater than before—a heat
which is capable of producing very powerful effects in melting and setting
fire to substances of almost every description.

Were we desirous of forming an image by a concave speculum which shall
be exactly equal to the object, the object must be placed exactly in the
centre; and, by an experiment of this kind, the centre of the concavity of a
mirror may be found.

In the cases now stated, the images of objects are all formed in the front of
the mirror, or between it and the object. But there is a case in which the
image is formed behind the mirror. This happens when the object is placed
between the mirror and the focus of parallel rays, and then the image is
larger than the object. In fig. 23, GF is a concave mirror, whose focus of
parallel rays is at E. If an object OB be placed a little within this focus, as at
A, a large image IM will be seen behind the mirror, somewhat curved and
erect, which will be seen by an eye looking directly into the front of the
mirror. Here the image appears at a greater distance behind the mirror than
the object is before it, and the object appears magnified in proportion to its

distance from the focus and the mirror. If the mirror be one inch focal
distance, and the object be placed eight-tenths of an inch from its surface,
the image would be five times as large as the object in length and breadth,
and consequently twenty-five times larger in surface. In this way small
objects may be magnified by reflection, as such objects are magnified by
refraction, in the case of deep convex lenses. When such mirrors are large,
for example six inches diameter, and eight or ten inches focal distance, they
exhibit the human face as of an enormous bulk. This is illustrated by the
following figure. Let C N, Fig. 24, represent the surface of a concave mirror,
and A a human face looking into it, the face will appear magnified as
represented by the image behind the mirror D Q. Suppose a ray A C
proceeding from the forehead, and another M N from the chin; these rays are
reflected to the person’s eye at O, which consequently sees the image in the
lines of reflection O D, O Q, and in the angle D O Q, and consequently
magnified much beyond the natural size, and at a small distance behind the
mirror.

figure 23.

figure 24.

If we suppose the side T U to represent a convex mirror, and the figure D Q a
head of an ordinary size, then the figure A will represent the diminished
appearance which a person’s face exhibits, when viewed in such a mirror. It
will not only appear reduced, but somewhat distorted; because from the
form of the mirror, one part of the object is nearer to it than another, and
consequently will be reflected under a different angle.

The effect we have now mentioned as produced by concave mirrors, will
only take place when the eye is nearer the mirror than its principal focus. If
the spectator retire beyond this focus—suppose to the distance of five or six
feet, he will not see the image behind the mirror; but he will see his image
in a diminished form, hanging upside down, and suspended in the air, in a
line between his eye and the mirror. In this case, his image is formed before
the mirror as represented at IM fig. 22. In this situation, if you hold out your
hand towards the mirror, the hand of the image will come out towards your
hand, and, when at the centre of concavity, it will be of an equal size with it,
and you may shake hands with this aerial image. If you move your hand
farther, you will find the hand of the image pass by your hand, and come
between it and your body. If you move your hand towards either side, the
hand of the image will move towards the other side; the image moving

always in a contrary direction to the object. All this while the by-standers, if
any, see nothing of the image, because none of the reflected rays that form it
can enter their eyes.—The following figure represents a phenomenon
produced in the same manner. A B is a concave mirror of a large size; C
represents a hand presented before the mirror, at a point farther distant than
its focus. In this case, an inverted image of the hand is formed which is seen
hanging in the air at M. The rays C and D go diverging from the two opposite
points of the object, and by the action of the mirror, they are again made to
converge to points at O and S where they cross, form an image, and again
proceed divergent to the eye.10

figure 25.

In consequence of the properties of concave mirrors, now described, many
curious experiments and optical deceptions have been exhibited. The
appearance of images in the air, suspended between the mirror and the
object, have sometimes been displayed with such dexterity and an air of
mystery, as to have struck with astonishment those who were ignorant of
the cause. In this way birds, flying angels, spectres and other objects have
been exhibited, and when the hand attempts to lay hold on them, it finds
them to be nothing, and they seem to vanish into air. An apple or a beautiful
flower is presented, and when a spectator attempts to touch it, it instantly

vanishes, and a death’s head immediately appears, and seems to snap at his
fingers. A person with a drawn sword appears before him, in an attitude as
if about to run him through, or one terrific phantom starts up after another,
or sometimes the resemblances of deceased persons are made to appear, as
if, by the art of conjuration, they had been forced to return from the world
of spirits. In all such exhibitions, a very large concave mirror is requisite, a
brilliant light must be thrown upon the objects, and every arrangement is
made, by means of partitions, &c., to prevent either the light, the mirror, or
the object from being seen by the spectators. The following representation
(fig. 26.) shows one of the methods by which this is effected: A is a large
concave mirror, either of metal or of glass, placed on the back part of a dark
box, D is the performer, concealed from the spectators by the cross partition
C; E is a strong light, which is likewise concealed by the partition I, which is
thrown upon the actor D, or upon any thing he may hold in his hand. If he
hold a book, as represented in the figure, the light reflected from it will pass
between the partitions C and I to the mirror, and will be reflected from
thence to Z, where the image of the book will appear so distinct and
tangible, that a spectator looking through the opening at X, will imagine
that it is in his power to take hold of it. In like manner, the person situated
at D, may exhibit his own head or body—a portrait, a painting, a spectre, a
landscape, or any object or device which he can strongly illuminate.

figure 26.

figure 27.

figure 28.

There is another experiment, made with a concave mirror, which has
somewhat puzzled philosophers to account for the phenomena. Take a glass
bottle AC, (fig. 27) and fill it with water to the point B; leave the upper part
BC empty, and cork it in the common manner. Place this bottle opposite a
concave mirror, and beyond its focus, that it may appear reversed, and,
before the mirror place yourself still further distant from the bottle, and it
will appear in the situation A B C. Now, it is remarkable in this apparent
bottle, that the water, which, according to the laws of catoptrics, should
appear at A B, appears on the contrary at B C, and consequently, the part A B
appears empty. If the bottle be inverted and placed before the mirror, its
image will appear in its natural erect position, and the water which is in
reality at BC (fig. 28) is seen at A B. If while the bottle is inverted, it be
uncorked, and the water run gently out, it will appear, that, while the part
BC is emptying, that of A B in the image is filling, and, what is remarkable,
as soon as the bottle is empty, the illusion ceases, the image also appearing
entirely empty.—The remarkable circumstances in this experiment are, first,
not only to see the object where it is not, but also where its image is not;
and secondly, that of two objects which are really in the same place, as the
surface of the bottle and the water it contains, the one is seen at one place,
and the other at another; and to see the bottle in the place of its image, and
the water where neither it nor its image are.

The following experiments are stated by Mr. Ferguson in his “Lectures on
select Subjects,” &c. “If a fire be made in a large room, and a smooth
mahogany table be placed at a good distance near the wall, before a large
concave mirror, so placed that the light of the fire may be reflected from the

mirror to its focus upon the table; if a person stand by the table, he will see
nothing upon it but a longish beam of light: but if he stand at a distance
toward the fire, not directly between the fire and mirror, he will see an
image of the fire upon the table, large and erect. And if another person who
knows nothing of the matter beforehand should chance to come into the
room, and should look from the fire toward the table, he would be startled
at the appearance; for the table would seem to be on fire, and by being near
the wainscot, to endanger the whole house. In this experiment there should
be no light in the room but what proceeds from the fire; and the mirror
ought to be at least fifteen inches in diameter. If the fire be darkened by a
screen, and a large candle be placed at the back of the screen, a person
standing by the candle will see the appearance of a very fine large star, or
rather planet, upon the table, as bright as Venus or Jupiter. And if a small
wax taper—whose flame is much less than the flame of the candle—be
placed near the candle, a satellite to the planet will appear on the table; and
if the taper be moved round the candle, the satellite will go round the
planet.”

Many other illustrations of the effects of concave specula might have been
given, but I shall conclude this department by briefly stating some of the
general properties of speculums.

1. There is a great resemblance between the properties of convex lenses and
concave mirrors. They both form an inverted focal image of any remote
object, by the convergence of the pencil of rays. In those instruments whose
performances are the effects of reflection, as reflecting telescopes, the
concave mirror is substituted in the place of the convex lens. The whole
effect of these instruments, in bringing to view remote objects in heaven
and on earth, entirely depends on the property of a concave mirror in
forming images of objects in its focus. 2. The image of an object placed
beyond the centre, is less than the object; if the object be placed between
the principal focus and the centre, the image is greater than the object. In
both cases the image is inverted. 3. When the object is placed between the
focus and the mirror, the image situated behind the mirror is greater than the
object, and it has the same direction: in proportion as the object approaches
the focus, the image becomes larger and more distant. These and similar
results are proved by placing a lighted candle at different distances from a

concave mirror. 4. An eye cannot see an image in the air except it be placed
in the diverging rays; but if the image be received on a piece of white paper,
it may be seen in any position of the eye, as the rays are then reflected in
every direction. 5. If a picture drawn according to the rules of perspective,
be placed before a large concave speculum, a little nearer than its principal
focus, the image of the picture will appear extremely natural, and very
nearly like the real objects whence it was taken. Not only are the objects
considerably magnified, so as to approach to their natural size, but they
have also different apparent distances, as in nature, so that the view of the
inside of a church appears very like what it is in reality, and representations
of landscapes appear very nearly, as they do from the spot whence they
were taken. In this respect a large concave speculum may be made to serve
nearly the same purpose, as the Optical Diagonal Machine, in viewing
perspective prints. 6. The concave speculum is that alone which is used as
the great mirror which forms the first image in reflecting telescopes; and it
is likewise the only kind of speculum used as the small mirror, in that
construction of the instrument called the Gregorian Reflector.

Quantity of light reflected by polished surfaces.

As this is a circumstance connected with the construction of reflecting
telescopes, it may not be improper, in this place, to state some of the results
of the accurate experiments of M. Bonguer on this subject. This philosopher
ascertained that of the light reflected from mercury, or quicksilver, more
than one-fourth is lost, though it is probable that no substances reflect more
light than this. The rays were received at an angle of eleven and a half
degrees of incidence, measured from the surface of the reflecting body, and
not from the perpendicular. The reflection from water was found to be
almost as great as that of quicksilver; so that in very small angles it reflects
nearly three-fourths of the direct light. This is the reason why so strong a
reflection appears on water, when one walks, in still weather, on the brink
of a lake opposite to the sun. The direct light of the sun diminishes
gradually as it approaches the horizon, while the reflected light at the same
time grows stronger; so that there is a certain elevation of the sun in which
the united force of the direct and reflected light will be the greatest possible,
and this is when he is twelve or thirteen degrees in altitude. On the other
hand, light reflected from water at great angles of incidence is extremely

small. When the light was perpendicular, it reflected no more than the
thirty-seventh part which mercury does in the same circumstances, and only
the fifty-fifth part of what fell upon it in this case.

Using a smooth piece of glass, one line in thickness, he found that, when it
was placed at an angle of fifteen degrees with the incident rays, it reflected
628 parts of 1000 which fell upon it; at the same time, a metallic mirror
which he tried in the same circumstances, reflected only 561 of them. At a
less angle of incidence much more light was reflected; so that at an angle of
three degrees, the glass reflected 700 parts, and the metal something less, as
in the former case. The most striking observations made by this
experimenter relate to the very great difference in the quantity of light
reflected at different angles of incidence. He found that for 1000 incident
rays, the reflected rays, at different angles of incidence, were as follows.

Angles of incidence Rays reflected by water Rays reflected by glass
5° 501 549
10 333 412
15 211 299
30 65 112
50 22 34
70 18 25
90 18 25

With regard to such mirrors as the specula of reflecting telescopes, it will be
found, in general, that they reflect little more than the one half of the rays
which fall upon them.

Uncommon appearances in nature produced by the combined influences of
Reflection and Refraction.

The reflection and refraction of the rays of light frequently produce
phenomena which astonish the beholders, and which have been regarded by
the ignorant and the superstitious, as the effects of supernatural agency. Of
these phenomena I shall state a few examples.

One of the most striking appearances of this kind is what has been termed
the Fata Morgana, or optical appearances of figures in the sea and the air,
as seen in the Faro of Messina. The following account is translated from a
work of Minasi, who witnessed the phenomenon, and wrote a dissertation
on the subject. “When the rising sun shines from that point whence its
incident ray forms an angle of about forty-five degrees to the sea of Riggio,
and the bright surface of the water in the bay is not disturbed either by the
wind or the current, the spectator being placed on an eminence of the city,
with his back to the sun and his face to the sea;—on a sudden there appear
on the water, as in a catoptric theatre, various multiplied objects, that is to
say, numberless series of pilasters, arches, castles well delineated, regular
columns, lofty towers, superb palaces, with balconies and windows,
extended alleys of trees, delightful plains with herds and flocks, armies of
men on foot and horseback, and many other strange images, in their natural
colours and proper actions, passing rapidly in succession along the surface
of the sea, during the whole of the short period of time, while the above
mentioned causes remain.—But, if in addition to the circumstances now
described, the atmosphere be highly impregnated with vapour and dense
exhalations, not previously dispersed by the winds or the sun, it then
happens that, in this vapour, as in a curtain extended along the channel, at
the height of about thirty palms, and nearly down to the sea, the observer
will behold the scene of the same objects, not only reflected from the
surface of the sea, but likewise in the air, though not so distant or well
defined, as the former objects from the sea.—Lastly, if the air be slightly
hazy or opake, and at the same time dewy and adapted to form the iris, the
then above-mentioned objects will appear only at the surface of the sea, as
in the first case, but all vividly coloured or fringed with red, green, blue and
other prismatic colours.”11

It is somewhat difficult to account for all the appearances here described;
but, in all probability, they are produced by a calm sea, and one or more
strata of superincumbent air differing in refractive and consequently in
reflective power. At any rate reflection and refraction are some of the
essential causes which operate in the production of the phenomena.

The Mirage, seen in the deserts of Africa, is a phenomenon, in all
probability produced by a similar cause. M. Monge, who accompanied the

French army to Egypt, relates that, when in the desert between Alexandria
and Cairo, the mirage of the blue sky was inverted, and so mingled with the
sand below, as to give to the desolate and arid wilderness an appearance of
the most rich and beautiful country. They saw, in all directions, green
islands, surrounded with extensive lakes of pure, transparent water. Nothing
could be conceived more lovely and picturesque than the landscape. In the
tranquil surface of the lakes, the trees and houses with which the islands
were covered, were strongly reflected with vivid and varied hues, and the
party hastened forward to enjoy the cool refreshments of shade and stream
which these populous villages proffered to them. When they arrived, the
lake on whose bosom they floated, the trees among whose foliage they were
embowered, and the people who stood on the shore inviting their approach,
had all vanished, and nothing remained but an uniform and irksome desert
of sand and sky, with a few naked huts and ragged Arabs. Had they not been
undeceived by their nearer approach, there was not a man in the French
army who would not have sworn that the visionary trees and lakes had a
real existence in the midst of the desert.

Dr. Clark observed precisely the same appearances at Rosetta. The city
seemed surrounded with a beautiful sheet of water; and so certain was his
Greek interpreter—who was unacquainted with the country—of this fact,
that he was quite indignant at an Arab who attempted to explain to him that
it was a mere optical delusion. At length they reached Rosetta in about two
hours, without meeting with any water; and on looking back on the sand
they had just crossed, it seemed to them as if they had waded through a vast
blue lake.

figure 29.

On the 1st of August, 1798, Dr. Vince observed at Ramsgate a ship which
appeared as at A, (fig. 29.) the topmast being the only part of it that was
seen above the horizon. An inverted image of it was seen at B, immediately
above the real ship A, and an erect image at C, both of them being complete
and well defined. The sea was distinctly seen between them, as at V W. As
the ship rose to the horizon the image C gradually disappeared, and while
this was going on, the image B descended, but the mainmast of B did not
meet the mainmast of A. The two images BC were perfectly visible when the
whole ship was actually below the horizon. Dr. Vince then directed his
telescope to another ship whose hull was just in the horizon, and he
observed a complete inverted image of it, the mainmast of which just
touched the mainmast of the ship itself. He saw at the same time several
other ships whose images appeared in nearly a similar manner, in one of

which the two images were visible when the whole ship was beneath the
horizon. These phenomena must have been produced by the same causes
which operated in the case formerly mentioned, in relation to Captain
Scoresby, when he saw the figure of his father’s ship inverted in the distant
horizon. Such cases are, perhaps not uncommon, especially in calm and
sultry weather, but they are seldom observed, except when a person’s
attention is accidentally directed to the phenomenon, and, unless he use a
telescope, it will not be so distinctly perceived.

The following phenomenon, of a description nearly related to the above, has
been supposed to be chiefly owing to reflection. On the 18th of November,
1804, Dr. Buchan, when watching the rising sun, about a mile to the east of
Brighton, just as the solar disk emerged from the surface of the water, saw
the face of the cliff on which he was standing, a windmill, his own figure
and the figure of his friend, distinctly represented, precisely opposite, at
some distance from the ocean. This appearance lasted about ten minutes, till
the sun had risen nearly his own diameter above the sea. The whole then
seemed to be elevated into the air and successively disappeared. The surface
of the sun was covered with a dense fog of many yards in height, which
gradually receded from the rays of the sun as he ascended from the horizon.

The following appearance most probably arose chiefly from the refraction
of the atmosphere. It was beheld at Ramsgate, by Dr. Vince of Cambridge
and another gentleman. It is well known that the four turrets of Dover castle
are seen at Ramsgate, over a hill which intervenes between a full prospect
of the whole. On the 2nd of August, 1806, not only were the four turrets
visible, but the castle itself appeared as though situated on that side of the
hill nearest Ramsgate, and so striking was the appearance, that for a long
time the Doctor thought it an illusion; but at last, by accurate observation,
was convinced that it was an actual image of the castle. He, with another
individual, observed it attentively for twenty minutes, but were prevented
by rain from making further observations. Between the observers and the
land from which the hill rises, there were about six miles of sea, and from
thence to the top of the hill there was about the same distance, their own
height above the surface of the water was about seventy feet.—The cause of
this phenomenon was, undoubtedly, unequal refraction. The air being more
dense near the ground and above the sea than at greater heights, reached the

eye of the observer, not in straight but in curvilinear lines. If the rays from
the castle had in their path struck an eye at a much greater distance than
Ramsgate, the probability is, that the image of the castle would have been
inverted in the air; but in the present case,the rays from the turret and the
base of the castle had not crossed each other.

To similar causes as those now alluded to are to be attributed such
phenomena as the following:

The Spectre of the Brocken. This is a wonderful and, at first sight, a terrific
phenomenon, which is sometimes seen from the summit of one of the Hartz
mountains in Hanover, which is about 3,300 feet above the level of the sea,
and overlooks all the country fifteen miles round. From this mountain the
most gigantic and terrific spectres have been seen, which have terrified the
credulous, and gratified the curious, in a very high degree. M. Hawé who
witnessed this phenomenon, says, the sun rose about four o’clock, after he
had ascended to the summit, in a serene sky, free of clouds; and about a
quarter past five, when looking round to see if the sky continued clear, he
suddenly beheld at a little distance, a human figure of a monstrous size
turned towards him, and glaring at him. While gazing on this gigantic
spectre, with a mixture of awe and apprehension, a sudden gust of wind
nearly carried off his hat, and he clapt his hand to his head to detain it, when
to his great delight, the colossal spectre did the same. He changed his body
into a variety of attitudes,all which the spectre exactly imitated, and then
suddenly vanished without any apparent cause, and, in a short time as
suddenly appeared. Being joined by another spectator, after the first visions
had disappeared, they kept steadily looking for the aërial spectres, when
two gigantic monsters suddenly appeared. These spectres had been long
considered as preternatural, by the inhabitants of the adjacent districts, and
the whole country had been filled with awe and terror. Some of the lakes of
Ireland are found to be susceptible of producing illusions, particularly the
lake of Killarney. This romantic sheet of water is bounded on one side, by a
semicircle of rugged mountains, and on the other by a flat morass; and the
vapours generated in the marsh, and broken by the mountains, continually
represent the most fantastic objects. Frequently men riding along the shore
are seen as if they were moving across the lake, which is supposed to have

given rise to the legend of O’Donougho, a magician who is said to be
visible on the lake every May morning.

There can be little doubt that most of those visionary appearances which
have been frequently seen in the sky and in mountainous regions, are
phantoms produced by the cause to which I am adverting, such as armies of
footmen and horsemen, which some have asserted to have been seen in the
air near the horizon. A well authenticated instance of this kind occurred in
the Highlands of Scotland:—Mr. Wren of Wetton Hall, and D. Stricket his
servant, in the year 1744, were sitting at the door of the house in a summer
evening, when they were surprised to see opposite to them on the side of
Sonterfell hill—a place so extremely steep, that scarce a horse could walk
slowly along it—the figure of a man with a dog pursuing several horses, all
running at a most rapid pace. Onwards they passed till at last they
disappeared at the lower end of the Fell. In expectation of finding the man
dashed to pieces by so tremendous a fall, they went early next morning and
made a search, but no trace of man or horse, or the prints of their feet on the
turf could be found. Sometime afterwards, about seven in the evening, on
the same spot, they beheld a troop of horsemen advancing in close ranks
and at a brisk pace. The inmates of every cottage for a mile round beheld
the wondrous scene, though they had formerly ridiculed the story told by
Mr. Wren and his servant, and were struck with surprise and fear. The
figures were seen for upwards of two hours, till the approach of darkness
rendered them invisible. The various evolutions and changes through which
the troops passed were distinctly visible, and were marked by all the
observers. It is not improbable that these aërial troopers were produced by
the same cause which made the castle of Dover to appear on the side of the
hill next to Ramsgate, and it is supposed that they were the images of a
body of rebels, on the other side of the hill, exercising themselves previous
to the rebellion in 1745.12

I shall mention only another instance of this description which lately
occurred in France, and for a time caused a powerful sensation among all
ranks. On Sunday the 17th of December, 1826, the clergy in the parish of
Migné, in the vicinity of Poictiers, were engaged in the exercises of the
Jubilee which preceded the festival of Christmas, and a number of persons
to the amount of 3000 souls assisted in the service. They had planted as part

of the ceremony, a large cross, twenty-five feet high, and painted red, in the
open air beside the church. While one of the preachers, about five in the
evening, was addressing the multitude, he reminded them of the miraculous
cross which appeared in the sky to Constantine and his army, and the effect
it produced—when suddenly a similar celestial cross appeared in the
heavens just before the porch of the church about 200 feet above the
horizon, and 140 feet in length, and its breadth from three to four feet, of a
bright silver colour tinged with red. The curate and congregation fixed their
wondering gaze upon this extraordinary phenomenon, and the effect
produced on the minds of the assembly was strong and solemn: they
spontaneously threw themselves on their knees; and many, who had been
remiss in their religious duties, humbly confessed their sins, and made vows
of penance and reformation. A commission was appointed to investigate the
truth of this extraordinary appearance, and a memorial stating the above and
other facts was subscribed by more than forty persons of rank and
intelligence, so that no doubt was entertained as to the reality of the
phenomenon. By many it was considered as strictly miraculous, as having
happened at the time and in the circumstances mentioned. But it is evident,
from what we have already stated, that it may be accounted for on physical
principles. The large cross of wood painted red was doubtless the real
object which produced the magnified image. The state of the atmosphere,
according to the descriptions given in the memorial, must have been
favourable for the production of such images. The spectrum of the wooden
cross must have been cast on the concave surface of some atmospheric
mirror, and so reflected back to the eyes of the spectators, from an opposite
place—retaining exactly the same shape and proportions, but dilated in size;
and what is worthy of attention, it was tinged with red, the very colour of
the object of which it was the reflected image.

Such phenomena as we have now described, and the causes of them which
science is able to unfold, are worthy of consideration, in order to divest the
mind of superstitious terrors, and enable it clearly to perceive the laws by
which the Almighty directs the movements of the material system. When
any appearance in nature, exactly the reverse of every thing we could have
previously conceived—presents itself to view, and when we know of no
material cause by which it could be produced, the mind must feel a certain
degree of awe and terror, and will naturally resort to supernatural agency as

acting either in opposition to the established laws of the universe, or beyond
the range to which they are confined. Besides the fears and apprehensions
to which such erroneous conceptions give rise, they tend to convey false
and distorted impressions of the attributes of the Deity and of his moral
government. Science, therefore, performs an invaluable service to man, by
removing the cause of superstitious alarms, by investigating the laws and
principles which operate in the physical system, and by assigning reasons
for those occasional phenomena, which at first sight appeared beyond the
range of the operation of natural causes.

The late ingenious Dr. Wollaston illustrated the causes of some of the
phenomena we have described, in the following manner. He looked along
the side of a red hot poker at a word or object ten or twelve feet distant; and
at a distance less than three eights of an inch from the line of the poker, an
inverted image was seen, and within and without that image, an erect
image, in consequence of the change produced, by the heat of the poker, in
the density of the air. He also suggested the following experiment as
another illustration of the same principle, namely, viewing an object
through a stratum of spirit of wine lying above water, or a stratum of water
laid above one of syrup. He poured into a square phial a small quantity of
clear syrup, and above this he poured an equal quantity of water which
gradually combined with the syrup, as seen at A. fig. 30. The word ‘Syrup,’
on a card held behind the bottle, appeared erect when seen through the pure
spirit, but inverted, when seen through the mixture of water and syrup. He
afterwards put nearly the same quantity of rectified spirits of wine above
the water, as seen at B, and he saw the appearance as represented, namely,
the true place of the word ‘Spirit,’ and the inverted and erect images below.
These substances, by their gradual incorporation, produce refracting power,
diminishing from the spirit of wine to the water, or from the syrup to the
water; so that by looking through the mixed stratum, an inverted image of
any object is seen behind the bottle. These experiments show that the
mirage and several other atmospherical phenomena may be produced by
variations in the refractive power of different strata of the atmosphere.

figure 30.

It is not unlikely that phenomena of a new and different description from
any we have hitherto observed, may be produced from the same causes to
which we have adverted. A certain optical writer remarks—‘If the variation
of the refractive power of the air takes place in a horizontal line
perpendicular to the line of vision, that is, from right to left, then we may
have a lateral Mirage, that is, an image of a ship may be seen on the right or
left hand of the real ship, or on both, if the variation of refractive power is
the same on each side of the line of vision, and a fact of this kind was once
observed on the Lake of Geneva. If there should happen at the same time,
both a vertical and a lateral variation of refractive power in the air, and if
the variation should be such as to expand or elongate the object in both
directions, then the object would be magnified as if seen through a
telescope, and might be seen and recognized at a distance at which it would

not otherwise have been visible. If the refracting power, on the contrary,
varied, so as to construct the object in both directions, the image of it would
be diminished as if seen through a concave lens.’

Remarks and Reflections, in reference to the phenomena described above.

Such, then, are some of the striking and interesting effects produced by the
refraction and the reflection of the rays of light. As the formation of the
images of objects by convex lenses, lays the foundation of the construction
of refracting telescopes and microscopes, and of all the discoveries they
have brought to light, so the property of concave specula, in forming
similar images, is that on which the construction of Reflecting telescopes
entirely depends. To this circumstance Herschel was indebted for the
powerful telescopes he was enabled to construct—which were all formed
on the principle of reflection—and for all the discoveries they enabled him
to make in the planetary system, and in the sidereal heavens. The same
principles which operate in optical instruments, under the agency of man,
we have reason to believe, frequently act on a more expansive scale in
various parts of the system of nature. The magnificent Cross which
astonished the preacher and the immense congregation assembled at Migné,
was, in all probability, formed by a vast atmospherical speculum formed by
the hand of nature, and representing its objects on a scale far superior to that
of human art; and probably, to the same cause is to be attributed the singular
phenomenon of the coast of France having been made to appear within two
or three miles of the town of Hastings, as formerly described, (see p. 53.)
Many other phenomena which we have never witnessed, and of which we
can form no conception, may be produced by the same cause operating in
an infinity of modes.

The facts we have stated above, and the variety of modes by which light
may be refracted and reflected by different substances in nature, lead us to
form some conceptions of the magnificent and diversified scenes which
light may produce in other systems and worlds, under the arrangements of
the all-wise and Beneficent Creator. Light, in all its modifications and
varieties of colour and reflection, may be considered as the beauty and
glory of the universe, and the source of unnumbered enjoyments to all its
inhabitants. It is a symbol of the Divinity himself; for “God is Light, and in

Him is no darkness at all.” It is a representative of Him who is exhibited in
the Sacred oracles, as “The Sun of Righteousness,” and “the Light of the
world.” It is an emblem of the glories and felicities of that future world,
where knowledge shall be perfected, and happiness complete; for its
inhabitants are designated “the saints in light;” and it is declared in Sacred
history, to have been the first born of created beings. In our lower world, its
effects on the objects which surround us, and its influences upon all
sensitive beings, are multifarious and highly admirable. While passing from
infinitude to infinitude, it reveals the depth and immensity of the heavens,
the glory of the sun, the beauty of the stars, the arrangements of the planets,
the rainbow encompassing the sky with its glorious circle, the embroidery
of flowers, the rich clothing of the meadows, the valleys standing thick with
corn, “the cattle on a thousand hills,” the rivers rolling through the plains,
and the wide expanse of the ocean. But in other worlds the scenes it creates
may be far more resplendent and magnificent. This may depend upon the
refractive and reflective powers with which the Creator has endowed the
atmospheres of other planets, and the peculiar constitution of the various
objects with which they are connected. It is evident, from what we already
know of the reflection of light, that very slight modifications of certain
physical principles, and very slight additions to the arrangements of our
terrestrial system, might produce scenes of beauty, magnificence and
splendour of which, at present, we can form no conception. And, it is not
unlikely that by such diversities of arrangement, in other worlds, an infinite
variety of natural scenery is produced throughout the universe.

In the arrangements connected with the planet Saturn, and the immense
rings with which it is encompassed, and in the various positions which its
satellites daily assume with regard to one another, to the planet itself, and to
these rings—there is, in all probability, a combination of refractions,
reflections, light, and shadows, which produce scenes wonderfully
diversified, and surpassing in grandeur what we can now distinctly
conceive. In the remote regions of the heavens, there are certain bodies
composed of immense masses of luminous matter, not yet formed into any
regular system, and which are known by the name of Nebulæ. What should
hinder us from supposing that certain exterior portions of those masses form
speculums of enormous size, as some parts of our atmosphere are
sometimes found to do? Such specula may be conceived to be hundreds and

even thousands of miles in diameter, and that they may form images of the
most distant objects in the heavens, on a scale of immense magnitude and
extent, and which may be reflected, in all their grandeur, to the eyes of
intelligences at a vast distance. And, if the organs of vision of such beings,
be far superior to ours in acuteness and penetrating power, they may thus be
enabled to take a survey of an immense sphere of vision, and to descry
magnificent objects at distances the most remote from the sphere they
occupy. Whatever grounds there may be for such suppositions, it must be
admitted, that all the knowledge we have hitherto acquired respecting the
operation of light, and the splendid effects it is capable of producing, is
small indeed, and limited to a narrow circle, compared with the immensity
of its range, the infinite modifications it may undergo, and the wondrous
scenes it may create in regions of creation to which human eyes have never
yet penetrated,—and which may present to view objects of brilliancy and
magnificence such as, “Eye hath not yet seen, nor ear heard, nor hath it
entered into the heart of man to conceive.”

CHAPTER V.

SECT. I.—ON THE COLOURS OF LIGHT.

We have hitherto considered light chiefly as a simple homogeneous
substance, as if all its rays were white, and as if they were all refracted in
the same manner by the different lenses on which they fall. Investigations
however, into the nature of this wonderful fluid, have demonstrated that this
is not the case, and that it is possessed of certain additional properties, of
the utmost importance in the system of nature. Had every ray of light been a
pure white, and incapable of being separated into any other colours, the
scene of the universe would have exhibited a very different aspect from
what we now behold. One uniform hue would have appeared over the
whole face of nature, and one object could scarcely have been distinguished
from another. The different shades of verdure which now diversify every
landscape, the brilliant colouring of the flowery fields, and almost all the
beauties and sublimities which adorn this lower creation would have been
withdrawn. But it is now ascertained that every ray of white light is
composed of an assemblage of colours, whence proceed that infinite variety
of shade and colour with which the whole of our terrestrial habitation is
arrayed. Those colours are found not to be in the objects themselves, but in
the rays of light which fall upon them, without which they would either be
invisible, or wear an uniform aspect. In reference to this point, Goldsmith
has well observed: ‘The blushing beauties of the rose, the modest blue of
the violet, are not in the flowers themselves, but in the light that adorns
them. Odour, softness, and beauty of figure are their own; but it is light
alone that dresses them up in those robes which shame the monarch’s
glory.’

Many strange opinions and hypotheses were entertained respecting colours,
by the ancients, and even by many modern writers, prior to the time of Sir
Isaac Newton. The Pythagoreans called colour the superficies of bodies;
Plato said that it was a flame issuing from them. According to Zeno it is the
first configuration of matter, and according to Aristotle, it is that which

moves bodies actually transparent. Among the moderns, Des Cartes
imagined that the difference of colour proceeds from the prevalence of the
direct or rotatory motions of the particles of light. Grimaldi, Dechales, and
others, thought the differences of colour depended upon the quick or slow
vibrations of a certain elastic medium filling the whole universe. Rohault
imagined that the different colours were made by the rays of light entering
the eye at different angles with respect to the optic axis; and Dr. Hook
conceived that colour is caused by the sensation of the oblique or uneven
pulse of light; and this being capable of no more than two varieties, he
concluded that there could be no more than two primary colours. Such were
some of the crude opinions which prevailed before the era of the illustrious
Newton, by whose enlightened investigations the true theory of colours was
at last discovered. In the year 1666 this philosopher began to investigate the
subject; and finding the coloured image of the sun, formed by a glass prism,
to be of an oblong and not of a circular form, as according to the laws of
refraction it ought to be, he was surprised at the great disproportion between
its length and breadth, the former being five times the length of the latter;
and he began to conjecture that light is not homogeneal, but that it consists
of rays some of which are much more refrangible than others. Prior to this
period, philosophers supposed that all light, in passing out of one medium
into another of different density was equally refracted in the same or like
circumstances; but Newton discovered that this is not the fact; but that there
are different species of light, and that each species is disposed both to suffer
a different degree of refrangibility in passing out of one medium into
another,—and to excite in us the idea of a different colour from the rest; and
that bodies appear of that colour which arises from the peculiar rays they
are disposed to reflect. It is now, therefore, universally acknowledged, that
the light of the sun, which to us seems perfectly homogeneal and white, is
composed of no fewer than seven different colours, namely Red, Orange,
Yellow, Green, Blue, Indigo and Violet. A body which appears of a red
colour has the property of reflecting the red rays more powerfully than any
of the others; a body of a green colour reflects the green rays more
copiously than rays of any other colour, and so of the orange, yellow, blue,
purple and violet. A body which is of a black colour, instead of reflecting—
absorbs all, or the greater part of the rays that fall upon it; and, on the
contrary, a body that appears white reflects the greater part of the rays
indiscriminately without separating the one from the other.

Before proceeding to describe the experiments by which the above results
were obtained, it may be proper to give some idea of the form and effects of
the Prism by which such experiments are made. This instrument is
triangular and straight, and generally about three or four inches long. It is
commonly made of white glass, as free as possible from veins and bubbles,
and other similar defects, and is solid throughout. Its lateral faces, or sides,
should be perfectly plane and of a fine polish. The angle formed by the two
faces, one receiving the ray of light that is refracted in the instrument, and
the other affording it an issue on its returning into the air, is called the
refracting angle of the prism, as ACB, (fig. 31.) The manner in which
Newton performed his experiments, and established the discovery to which
we have alluded, is as follows.

In the window-shutter EG, (fig. 31.) of a dark room, a hole F, was made, of
about one third of an inch diameter, and behind it was placed a glass prism
ACB, so that the beam of light, SF, proceeding directly from the sun was
made to pass through the prism. Before the interposition of the prism, the
beam proceeded in a straight line towards T, where it formed a round white
spot; but being now bent out of its course by the prism, it formed an oblong
image OP, upon the white pasteboard, or screen LM, containing the seven
colours marked in the figure—the red being the least, and the violet the
most refracted from the original direction of the solar beam, ST. This
oblong image is called the prismatic spectrum. If the refracting angle of the
prism ACB, be 64 degrees, and the distance of the pasteboard from the
prism about 18 feet, the length of the image OP will be about 10 inches, and
the breadth 2 inches. The sides of the spectrum are right lines distinctly
bounded, and the ends are semicircular. From this circumstance it is evident
that it is still the image of the sun, but elongated by the refractive power of
the prism. It is evident from the figure, that since some part of the beam,
RO, is refracted much further out of its natural course WT, than some other
part of the beam, as WP, the rays towards RO have a much greater
disposition to be refracted than those toward WP; and that this disposition
arises from the naturally different qualities of those rays, is evident from
this consideration, that the refracting angle or power of the prism is the
same in regard to the superior part of the beam as to the inferior.

figure 31.

By making a hole in the screen LM opposite any one of the colours of the
spectrum, so as to allow that colour alone to pass—and by letting the colour
thus separated fall upon a second prism—Newton found that the light of
each of the colours was alike refrangible, because the second prism could
not separate them into an oblong image, or into any other colour. Hence he
called all the seven colours simple or homogeneous, in opposition to white
light, which he called compound or heterogeneous. With the prism which
this philosopher used he found the lengths of the colours and spaces of the
spectrum to be as follows: Red, 45; Orange, 27; Yellow, 40; Green, 60;
Blue, 60; Indigo, 48; Violet, 80: or 360 in all. But these spaces vary a little
with prisms formed of different substances, and as they are not separated by
distinct limits, it is difficult to obtain any thing like an accurate measure of
their relative extents. Newton examined the ratio between the sines of
incidence and refraction of these decompounded rays (see p. 30,) and found
that each of the seven primary colour-making rays, had certain limits within
which they were confined. Thus let the sine of incidence in glass be divided
into 50 equal parts, the sine of refraction into air of the least refrangible,
and the most refrangible rays will contain respectively 77 and 78 such parts.
The sines of refraction of all the degrees of red will have the intermediate
degrees of magnitude, from 77 to 77 one-eighth; Orange from 77 one-
eighth to 77 one-fifth; Yellow from 77 one-fifth to 77 one-third; Green from
77 one-third to 77 one-half; Blue from 77 one-half to 77 two-thirds; Indigo
from 77 two-thirds to 77 seven-ninths; and Violet from 77 seven-ninths to
78.

From what has been now stated, it is evident that, in proportion as any part
of an optic glass bears a resemblance to the form of a prism, the component
rays that pass through it must be necessarily separated, and will
consequently paint or tinge the object with colours. The edges of every
convex lens approach to this form, and it is on this account that the
extremities of objects when viewed through them are found to be tinged
with the prismatic colours. In such a glass, therefore, those different
coloured rays will have different foci, and will form their respective images
at different distances from the lens. Thus, suppose LN (fig. 32.) to represent
a double convex-lens, and OB an object at some distance from it. If the
object OB was of a pure red colour, the rays proceeding from it would form
a red image at Rr; if the object was of a violet colour, an image of that
colour would be formed at Vv, nearer the lens; and if the object was white
or any other combination of the colour-making rays, those rays would have
their respective foci at different distances from the lens, and form a
succession of images, in the order of the prismatic colours, between the
space Rr and Vv.

figure 32.

figure 33.

This may be illustrated by experiment in the following manner. Take a card
or slip of white pasteboard, as ABEF, (fig. 33.) and paint one half ABCD
red, the other half CF, violet or indigo; and tying black threads across it, set
it near the flame of a candle G, then take a lens HI, and holding a sheet of
white paper behind it, move it backwards and forwards upon the edge of a
graduated ruler, till you see the black threads most distinctly in the image,
and you will find the focus of the violet FE, much nearer than that of the red
AC, which plainly shows that bodies of different colours can never be
depicted by convex-lenses, without some degree of confusion.

The quantity of dispersion of the coloured rays in convex lenses depends
upon the focal length of the glass; the space which the coloured images
occupy being about the twenty-eighth part. Thus if the lens be twenty-eight
inches focal distance, the space between Rr and Vv (fig 32) will be about
one inch; if it be twenty-eight feet focus, the same space will be about one
foot, and so on in proportion. Now, when such a succession of images
formed by the different coloured rays, is viewed through an eye-glass, it
will seem to form but one image, and consequently very indistinct, and
tinged with various colours, and as the red figure Rr is largest, or seen
under the greatest angle—the extreme parts of this confused image will be
red, and a succession of the prismatic colours will be formed within this red
fringe, as is generally found in common refracting-telescopes, constructed
with a single object-glass. It is owing to this circumstance that the common
refracting telescope cannot be much improved without having recourse to
lenses of a very long focal distance; and hence, about 150 years ago, such
telescopes were constructed of 80, and 100, and 120 feet in length. But still
the image was not formed so distinctly as was desired, and the aperture of
the object-glass was obliged to be limited. This is a defect which was long
regarded as without a remedy; and even Newton himself despaired of

discovering any means by which the defects of refracting telescopes might
be removed and their improvement effected. This, however, was
accomplished by Dollond to an extent far surpassing what could have been
expected, of which a particular account will be given in the sequel.

It was originally remarked by Newton, and the fact has since been
confirmed by the experiments of Sir W. Herschel, that the different-coloured
rays have not the same illuminating power. The violet rays appear to have
the least illuminating effect; the indigo more, and the effect increases in the
order of the colours,—the green being very great; between the green and the
yellow the greatest of all; the yellow the same as the green; but the red less
than the yellow. Herschel also endeavoured to determine whether the power
of the differently-coloured rays to heat bodies, varied with their power to
illuminate them. He introduced a beam of light into a dark room, which was
decomposed by a prism, and then exposed a very sensible thermometer to
all the rays in succession, and observed the heights to which it rose in a
given time. He found that their heating power increased from the violet to
the red. The mercury in the thermometer rose higher when its bulb was
placed in the Indigo than when it was placed in the violet, still higher in
blue, and highest of all at red. Upon placing the bulb of the thermometer
below the red, quite out of the spectrum, he was surprised to find that the
mercury rose highest of all; and concluded that rays proceed from the sun,
which have the power of HEATING, but not of illuminating bodies. These rays
have been called invisible solar rays. They were about half an inch from the
commencement of the red rays; at a greater distance from this point the heat
began to diminish, but was very perceptible even at the distance of 1½ inch.
He determined that the heating power of the red to that of the green rays,
was 2¾ to 1, and 3½ to 1, in red to violet. He afterwards made experiments
to collect those invisible calorific rays, and caused them to act
independently of the light, from which he concluded that they are sufficient
to account for all the effects produced by the solar rays in exciting heat; that
they are capable of passing through glass, and of being refracted and
reflected, after they have been finally detached from the solar beam.

M. Ritter of Jena, Wollaston, Beckman and others, have found that the rays
of the spectrum are possessed of certain chemical properties—that beyond
the least brilliant extremity, namely, a little beyond the violet ray, there are

invisible rays which act chemically, while they have neither the power of
heating nor illuminating bodies. Muriate of silver exposed to the action of
the red rays becomes blackish; a greater effect is produced by the yellow: a
still greater by the violet, and the greatest of all by the invisible rays beyond
the violet. When phosphorus is exposed to the action of the invisible rays
beyond the red, it emits white fumes; but the invisible rays beyond the
violet extinguish them. The influence of these rays is daily seen in the
change produced upon vegetable colours, which fade, when frequently
exposed to the direct influence of the sum. What object they are destined to
accomplish in the general economy of nature, is not yet distinctly known;
we cannot however doubt that they are essentially requisite to various
processes going forward in the material system. And we know that, not only
the comfort of all the tribes of the living world, but the very existence of the
animal and vegetable creation depends upon the unremitting agency of the
Calorific rays.

It has likewise been lately discovered that certain rays of the spectrum,
particularly the violet, possesses the property of communicating the
magnetic power. Dr. Morichini, of Rome, appears to have been the first
who found that the violet rays of the spectrum had this property. The result
of his experiments, however, was involved in doubt, till it was established
by a series of experiments instituted by Mrs. Somerville, whose name is so
well known in the scientific world. This lady having covered half of a
sewing-needle, about an inch long, with paper, she exposed the other half
for two hours, to the violet rays. The needle had then acquired North
polarity. The indigo rays produced nearly the same effect; and the blue and
green rays produced it in a still less degree. In the yellow, orange, red and
invisible rays, no magnetic influence was exhibited, even though the
experiment was continued for three successive days. The same effects were
produced by enclosing the needle in blue or green glass, or wrapping it in
blue and green ribbands one half of the needle being always covered with
paper.

One of the most curious discoveries of modern times, in reference to the
solar spectrum, is that of Fraunhofer of Munich—one of the most
distinguished artists and opticians on the Continent.13 He discovered that the
spectrum is covered with dark and coloured lines, parallel to one another,

and perpendicular to the length of the spectrum; and he counted no less than
590 of these lines. In order to observe these lines, it is necessary to use
prisms of the most perfect construction, of very pure glass, free of veins—
to exclude all extraneous light, and even to stop those rays which form the
coloured spaces, which we are not examining. It is necessary also to use a
magnifying instrument, and the light must enter and emerge from the prism
at equal angles. One of the important practical results of this discovery is,
that those lines are fixed points in the spectrum, or rather, that they have
always the same position in the coloured spaces in which they are found.
Fraunhofer likewise discovered in the spectrum produced by the light of
Venus, the same streaks, as in the solar spectrum; in the spectrum of the
light of Sirius, he perceived three large streaks which, according to
appearance, had no resemblance to those of the light of the sun; one of them
was in the green, two in the blue. The stars appear to differ from one
another in their streaks. The electric light differs very much from the light
of the sun and that of a lamp, in regard to the streaks of the spectrum
—‘This experiment may also be made, though in an imperfect manner, by
viewing a narrow slit between two nearly closed window-shutters, through
a very excellent glass prism held close to the eye, with the refracting angle
parallel to the line of light. When the spectrum is formed by the sun’s rays,
either direct or indirect, as from the sky, clouds, rainbow, moon, or planets,
the black bands are always found to be in the same parts of the spectrum,
and under all circumstances to maintain the same relative position, breadth
and intensities.’

From what has been stated in reference to the solar spectrum it will
evidently appear, that white light is nothing else than a compound of all the
prismatic colours; and this may be still farther illustrated by shewing, that
the seven primary colours, when again put together, recompose white light.
This may be rudely proved for the purpose of illustration, by mixing
together seven different powders, having the colours and proportion of the
spectrum; but the best mode, on the whole, is the following. Let two circles
be drawn on a smooth round board, covered with white paper, as in fig. 34:
Let the outermost be divided into 360 equal parts; then draw seven right
lines as A,B,C, &c., from the center to the outermost circle, making the
lines A and B include 80 degrees of that circle. The lines B and C, 40
degrees; C and D, 60; D and E, 60; E and F, 48; F and G, 27; G and A, 45.

Then between these two circles paint the space AG red, inclining to orange
near G; GF orange, inclining to yellow near F; FE yellow, inclining to green
near E; ED green, inclining to blue near D; DC blue, inclining to indigo
near C; CB indigo, inclining to violet near B; and BA violet, inclining to a
soft red near A. This done, paint all that part of the board black which lies
within the inner circle; and putting an axis through the centre of the board,
let it be turned swiftly round that axis, so that the rays proceeding from the
above colours, may be all blended and mixed together in coming to the eye.
Then the whole coloured part will appear like a white ring a little grayish—
not perfectly white, because no art can prepare or lay on perfect colours, in
all their delicate shades, as found in the real spectrum.

figure 34.

That all the colours of light, when blended together in their proper
proportions, produce a pure white is rendered certain by the following
experiment. Take a large convex glass, and place it in the room of the paper
or screen on which the solar spectrum was depicted (LM fig. 31), the glass
will unite all the rays which come from the prism, if a paper is placed to
receive them, and you will see a circular spot of a pure lively white. The
rays will cross each other in the focus of the glass, and, if the paper be
removed a little further from that point, you will see the prismatic colours
again displayed, but in an inverted order, owing to the crossing of the rays.

SECT. 2.—ON THE COLOURS OF NATURAL OBJECTS.

From what has been stated above we may learn the true cause of those
diversified hues exhibited by natural and artificial objects, and the
variegated colouring which appears on the face of nature. It is owing to the
surfaces of bodies being disposed to reflect one colour rather than another.
When this disposition is such that the body reflects every kind of ray, in the
mixed state in which it receives them, that body appears white to us—
which, properly speaking, is no colour, but rather the assemblage of all
colours. If the body has a fitness to reflect one sort of rays more abundantly
than others, by absorbing all the others, it will appear of the colour
belonging to that species of rays. Thus, the grass is green, because it
absorbs all the rays except the green. It is these green rays only which the
grass, the trees, the shrubs, and all the other verdant parts of the landscape
reflect to our sight, and which make them appear green. In the same manner
the different flowers reflect their respective colours; the rose, the red rays;
the violet, the blue; the jonquil, the yellow; the marigold, the orange, and
every object, whether natural or artificial, appears of that colour which its
peculiar texture is fitted to reflect. A great number of bodies are fitted to
reflect at once several kinds of rays, and of consequence they appear under
mixed colours. It may even happen, that of two bodies which should be
green, for example, one may reflect the pure green of light, and the other
the mixture of yellow and blue. This quality, which varies to infinity,
occasions the different kinds of rays to unite in every possible manner, and
every possible proportion; and hence the inexhaustible variety of shades
and hues which nature has diffused over the landscape of the world. When a

body absorbs nearly all the light which reaches it, that body appears black.
It transmits to the eye so few reflected rays that it is scarcely perceptible in
itself, and its presence and form make no impression upon us, unless as it
interrupts the brightness of the surrounding space. Black is, therefore, the
absence of all the coloured rays.

It is evident, then, that all the various assemblages of colours which we see
in the objects around us, are not in the bodies themselves, but in the light
which falls upon them. There is no colour inherent in the grass, the trees,
the fruits, and the flowers, nor even in the most splendid and variegated
dress that adorns a lady. All such objects are as destitute of colour, in
themselves, as bodies which are placed in the centre of the earth, or as the
chaotic materials out of which our globe was formed, before light was
created. For where there is no light, there is no colour. Every object is
black, or without colour, in the dark, and it only appears coloured as soon as
light renders it visible. This is further evident from the following
experiment. If we place a coloured body in one of the colours of the
spectrum which is formed by the prism, it appears of the colour of the rays
in which it is placed. Take, for example, a red rose, and expose it first to the
red rays, and it will appear of a more brilliant ruddy hue. Hold it in the blue
rays, and it appears no longer red, but of a dingy blue colour, and in like
manner its colour will appear different, when placed in all the other
differently coloured rays. This is the reason why the colours of objects are
essentially altered by the nature of the light in which they are seen. The
colours of ribbons and various pieces of silk or woollen stuff are not the
same when viewed by candle-light as in the day time. In the light of a
candle or a lamp, blue often appears green, and yellow objects assume a
whitish aspect. The reason is that the light of a candle is not so pure a white
as that of the sun, but has a yellowish tinge, and therefore, when refracted
by the prism, the yellowish rays are found to predominate, and the
superabundance of yellow rays gives to blue objects a greenish hue.

The doctrine we are now illustrating is one which a great many persons,
especially among the fair sex, find it difficult to admit. They cannot
conceive it possible that there is no colour really inherent in their splendid
attire, and no tints of beauty in their countenances. ‘What,’ said a certain
lady, ‘are there no colours in my shawl, and in the ribbons that adorn my

head-dress—and, are we all as black as negroes in the dark; I should almost
shudder to think of it.’ Such persons, however, need be in no alarm at the
idea; but may console themselves with the reflection, that, when they are
stripped of all their coloured ornaments in the dark, they are certain that
they will never be seen by any one in that state; and therefore, there is no
reason to regret the temporary loss of those beauties which light creates—
when they themselves and all surrounding objects are invisible. But, to give
a still more palpable proof of this position, the following popular
experiments may be stated.

Take a pint of common spirit, and pour it into a soup dish, and then set it on
fire; as it begins to blaze, throw a handful of salt into the burning spirit, and
keep stirring it with a spoon. Several handfuls may thus be successively
thrown in, and then the spectators, standing around the flame, will see each
other frightfully changed, their colours being altered into a ghastly
blackness, in consequence of the nature of the light which falls upon them
—which produces colours very different from those of the solar light. The
following experiment, as described by Sir D. Brewster, illustrates the same
principle. ‘Having obtained the means of illuminating any apartment with
yellow light, let the exhibition be made in a room with furniture of various
bright colours, and with oil or water coloured paintings on the wall. The
party which is to witness the experiment should be dressed in a diversity of
the gayest colours; and the brightest coloured flowers, and highly coloured
drawings should be placed on the tables. The room being at first lighted
with ordinary lights, the bright and gay colours of every thing that it
contains will be finely displayed. If the white lights are now suddenly
extinguished, and the yellow lamps lighted, the most appalling
metamorphosis will be exhibited. The astonished individuals will no longer
be able to recognise each other. All the furniture of the room, and all the
objects it contains, will exhibit only one colour. The flowers will lose their
hues; the paintings and drawings will appear as if they were executed in
China ink, and the gayest dresses, the brightest scarlets, the purest lilacs, the
richest blues and the most vivid greens, will all be converted into one
monotonous yellow. The complexions of the parties, too, will suffer a
corresponding change. One pallid deathlike yellow, will envelope the young
and the old, and the sallow face will alone escape from the metamorphosis.

Each individual derives merriment from the cadaverous appearance of his
neighbour, without being sensible that he is one of the ghastly assemblage.’

——Like the unnatural hue
Which autumn paints upon the perished leaf,

From such experiments as these we might conclude, that were the solar rays
of a very different description from what they are now found to be, the
colours which embellish the face of nature, and the whole scene of our
sublunary creation would assume a new aspect, and appear very different
from what we now behold around us in every landscape. We find that the
stars display great diversity of colour; which is doubtless owing to the
different kinds of light which are emitted from those bodies; and hence we
may conclude, that the colouring thrown upon the various objects of the
universe is different in every different system, and that thus, along with
other arrangements, an infinite variety of colouring and of scenery is
distributed throughout the immensity of creation.

The atmosphere, in consequence of its different refractive and reflective
powers, is the source of a variety of colours which frequently embellish and
diversify the aspect of our sky. The air reflects the blue rays most
plentifully, and must therefore transmit the red, orange, and yellow, more
copiously than the other rays. When the sun and other heavenly bodies are
at a high elevation, their light is transmitted without any perceptible change,
but when they are near the horizon, their light must pass through a long and
dense track of air, and must therefore be considerably modified before it
reach the eye of the observer. The momentum of the red rays being greater
than that of the violet, will force their way through the resisting medium,
while the violet rays will be either reflected or absorbed. If the light of the
setting sun, by thus passing through a long track of air, be divested of the
green, blue, indigo, and violet rays, the remaining rays which are
transmitted through the atmosphere, will illuminate the western clouds, first
with an orange colour; and then, as the sun gradually sinks into the horizon,
the track through which the rays must pass becoming longer, the yellow and
orange are reflected, and the clouds grow more deeply red, till at length the
disappearance of the sun leaves them of a leaden hue by the reflection of
the blue light through the air. Similar changes of colour are sometimes seen
on the eastern and western fronts of white buildings. St. Paul’s Church, in
London, is frequently seen at sun-set, tinged with a very considerable

degree of redness; and the same cause occasions the moon to assume a
ruddy colour, by the light transmitted through the atmosphere. From such
atmospherical refractions and reflections are produced those rich and
beautiful hues with which our sky is gilded by the setting sun, and the
glowing red which tinges the morning and evening clouds, till their ruddy
glare is tempered by the purple of twilight, and the reflected azure of the
sky.

When a direct spectrum is thrown on colours darker than itself, it mixes
with them: as the yellow spectrum of the setting sun, thrown on the green
grass, becomes a greener yellow. But when a direct spectrum is thrown on
colours brighter than itself, it becomes instantly changed into the reverse
spectrum, which mixes with those brighter colours. Thus the yellow
spectrum of the setting sun thrown on the luminous sky, becomes blue, and
changes with the colour or brightness of the clouds on which it appears. The
red part of light being capable of struggling through thick and resisting
mediums which intercept all other colours—is likewise the cause why the
sun appears red when seen through a fog,—why distant light, though
transmitted through blue or green glass, appears red—why lamps at a
distance, seen through the smoke of a long street, are red, while those that
are near, are white. To the same cause it is owing that a diver at the bottom
of the sea is surrounded with the red light which has pierced through the
superincumbent fluid, and that the blue rays are reflected from the surface
of the ocean. Hence, Dr. Halley informs us that, when he was in a diving
bell, at the bottom of the sea, his hand always appeared red in the water.

The blue rays, as already noticed, being unable to resist the obstructions
they meet with in their course through the atmosphere, are either reflected
or absorbed in their passage. It is to this cause, that most philosophers
ascribe the blue colour of the sky, the faintness and obscurity of distant
objects, and the bright azure which tinges the mountains of a distant
landscape.

SECT. 3.—PHENOMENA OF THE RAINBOW.

Since the rays of light are found to be decomposed by refracting surfaces,
and reflected in an infinite variety of modes and shades of colour, we need

not be surprised at the changes produced in any scene or object by the
intervention of another, and by the numerous modifications of which the
primary colours of nature are susceptible. The vivid colours which gild the
rising and the setting sun, must necessarily differ from those which adorn
its noon-day splendour. Variety of atmospheric scenery will thus necessarily
be produced, greater than the most lively fancy can well imagine. The
clouds will sometimes assume the most fantastic forms, and at other times
will be irradiated with beams of light, or, covered with the darkest hues,
will assume a lowering aspect, prognostive of the thunder’s roar and the
lightning’s flash—all in accordance with the different rays that are reflected
to our eyes, or the quantity absorbed by the vapours which float in the
atmosphere.

Light, which embellishes with so much magnificence a pure and serene sky,
by means of innumerable bright starry orbs which are spread over it,
sometimes, in a dark and cloudy sky, exhibits an ornament which, by its
pomp, splendour and variety of colours, attracts the attention of every eye
that has an opportunity of beholding it. At certain times, when there is a
shower either around us, or at a distance from us in an opposite quarter to
that of the sun, a species of arch or bow is seen in the sky, adorned with all
the seven primary colours of light. This phenomenon, which is one of the
most beautiful meteors in nature, has obtained the name of the Rainbow.
The rainbow was, for ages, considered as an inexplicable mystery, and by
some nations it was adored as a deity. Even after the dawn of true
philosophy, it was a considerable time before any discovery of importance
was made, as to the true causes which operate in the production of this
phenomenon. About the year 1571, M. Fletcher of Breslau, made a certain
approximation to the discovery of the true cause, by endeavouring to
account for the colours of the rainbow by means of a double refraction and
one reflection. A nearer approximation was made by Antonio de Dominis,
bishop of Spalatro, about 1601. He maintained that the double refraction of
Fletcher, with an intervening reflection, was sufficient to produce the
colours of the bow, and also to bring the rays that formed them to the eye of
the spectator, without any subsequent reflection. To verify this hypothesis,
he procured a small globe of solid glass, and viewing it when it was
exposed to the rays of the sun—with his back to that luminary—in the same
manner as he had supposed the drops of rain were situated with respect to

them, he observed the same colours which he had seen in the rainbow, and
in the same order. But he could give no good reason why the bow should be
coloured, and much less any satisfactory account of the order in which the
colours appear. It was not till Sir I. Newton discovered the different
refrangibility of the rays of light, that a complete and satisfactory
explanation could be given of all the circumstances connected with this
phenomenon.

As the full elucidation of this subject involves a variety of optical and
mathematical investigations, I shall do little more than explain the general
principle on which the prominent phenomena of the rainbow may be
accounted for, and some of the facts and results which theory and
observation have deduced.

We have just now alluded to an experiment with a glass globe:—If, then,
we take either a solid glass globe, or a hollow globe filled with water, and
suspend it so high in the solar rays above the eye, that the spectator, with
his back to the sun, can see the globe red;—if it be lowered slowly, he will
see it orange, then yellow, then green, then blue, then indigo, and then
violet; so that the drop at different heights, shall present to the eye the seven
primitive colours in succession. In this case, the globe, from its form, will
act in some measure like a prism, and the ray will be separated into its
component parts. The following figure will more particularly illustrate this
point. Suppose A (fig. 35.) to represent a drop of rain—which may be
considered as a globe of glass in miniature, and will produce the same effect
on the rays of light—and let Sd represent a ray from the sun falling upon
the upper part of the drop at D. At the point of entering the drop, it will
suffer a refraction, and instead of going forward to C, it will be bent to N.
From N a part of the light will be reflected to Q—some part of it will, of
course, pass through the drop. By the obliquity with which it falls on the
side of the drop at Q, that part becomes a kind of prism, and separates the
ray into its primitive colours. It is found by computation that, after a ray has
suffered two refractions and one reflection, as here represented, the least
refrangible part of it, namely the red ray, will make an angle with the
incident solar ray of 42° 2´, as Sfq; and the violet, or greatest refrangible
ray will make with the solar ray, an angle of 40° 17´, as Scq; and thus all
the particles of water within the difference of those two angles, namely 1°

45´—(supposing the ray to proceed merely from the centre of the sun)—
will exhibit severally the colours of the prism, and constitute the interior
bow of the cloud. This holds good at whatever height the sun may chance to
be in a shower of rain. If he be at a high altitude, the rainbow will be low; if
he be at a low elevation, the rainbow must be high; and if a shower happen
in a vale, when the spectator is on a mountain, he will sometimes see the
bow in the form of a complete circle below him. We have at present
described the phenomena only of a single drop; but it is to be considered
that in a shower of rain there are drops at all heights and at all distances;
and therefore the eye situated at G will see all the different colours. All
those drops that are in a certain position with respect to the spectator will
reflect the red rays, all those in the next station the orange, those in the next
the green, and so on with regard to all the other colours.

figure 35.

It appears, then, that the first or primary bow is formed by two refractions
and one reflection; but there is frequently a second bow, on the outside of
the other, which is considerably fainter. This is produced by drops of rain
above the drop we have supposed at A. If B (fig. 35.) represent one of these
drops, the ray to be sent to the eye enters the drop near the bottom, and
suffers two refractions and two reflections, by which means the colours
become reversed, that is, the violet is lowest in the exterior bow, and the red
is lowest in the interior one, and the other colours are reversed accordingly.
The ray T is refracted at R: a part of it is reflected from S to T, and at T it
suffers another reflection from T to U. At the points S and T part of the ray
passes through the drop on account of its transparency, towards W and X,
and therefore we say that part only of the ray is reflected. By these losses
and reflections the exterior bow becomes faint and ill-defined in

comparison of the interior or primary bow. In this case the upper part of the
secondary bow will not be seen when the sun is above 54° 10´ above the
horizon; and the lower part of the bow will not be seen when the sun is 60°
58´ above the horizon.

figure 36.

For the further illustrations of this subject, we may introduce the following
section of a bow, (fig. 36.) and, in order to prevent confusion in attempting
to represent all the different colours—let us suppose only three drops of
rain, and three different colours, as shown in the figure. The spectator O
being in the centre of the two bows, here represented,—the planes of which
must be considered as perpendicular to his view—the drops A,B, and C

produce part of the interior bow by two refractions and one reflection as
stated above, and the drops D,E,F will produce the exterior bow by two
refractions and two reflections, the sun’s rays being represented by 3,3. It is
evident that the angle COP is less than the angle BOP, and that the angle
AOP is the greatest of the three. The largest angle, then, is formed by the
red rays, the middle one consists of the green, and the smallest the purple or
violet. All the drops of rain, therefore, that happen to be in a certain position
with respect to the spectator’s eye, will reflect the red rays, and form a band
or semicircle of red, and so of the other colours from drops in other
positions. If the spectator alters his station, he will see a bow, but not the
same as before; and if there be many spectators, they will each see a
different bow, though it appears to be the same.

The rainbow assumes a semicircular appearance, because it is only at
certain angles that the refracted rays are visible to our eyes, as is evident
from the experiment of the glass globe formerly alluded to, which will
refract the rays only in a certain position. We have already stated that the
red rays make an angle of 42° 2´, and the violet an angle of 40° 17´. Now, if
a line be drawn horizontally from the spectator’s eye, it is evident that
angles formed with this line, of a certain dimension, in every direction, will
produce a circle, as will appear by attaching a cord of a given length to a
certain point, round which it may turn as round its axis; and, in every point
will describe an angle with the horizontal line of a certain and determinate
extent.

Sometimes it happens that three or more bows are visible, though with
different degrees of distinctness. I have more than once observed this
phenomenon, particularly in Edinburgh, in the month of August, 1825,
when three rainbows were distinctly seen in the same quarter of the sky;
and, if I recollect right, a fragment of a fourth made its appearance. This
happens when the rays suffer a third or fourth reflection; but, on account of
the light lost by so many reflections, such bows are, for the most part,
altogether imperceptible.

If there were no ground to intercept the rain and the view of the observer,
the rainbow would form a complete circle, the centre of which is
diametrically opposite to the sun. Such circles are sometimes seen in the

spray of the sea or of a cascade, or from the tops of lofty mountains, when
the showers happen in the vales below. Rainbows of various descriptions
are frequently observed rising amidst the spray and exhalations of
waterfalls, and among the waves of the sea whose tops are blown by the
wind into small drops. There is one regularly seen, when the sun is shining,
and the spectator in a proper position, at the fall of Staubbach, in the bosom
of the Alps; one near Schaffhausen; one at the cascade of Lauffen; and one
at the cataract of Niagara in North America. A still more beautiful one is
said to be seen at Terni, where the whole current of the river Velino, rushing
from a steep precipice of nearly 200 feet high, presents to the spectator
below, a variegated circle, over-arching the fall, and two other bows
suddenly reflected on the right and left. Don Ulloa, in the account of his
journeys in South America, relates that circular rainbows are frequently
seen on the mountains above Quito in Peru. It is said that a rainbow was
once seen near London, caused by the exhalations of that city, after the sun
had been below the horizon more than twenty minutes.14 A naval friend,
says Mr. Bucke, informed me, that, as he was one day watching the sun’s
effect upon the exhalations near Juan Fernandez, he saw upwards of five-
and-twenty ires marinæ animate the sea at the same time. In these marine
bows the concave sides were turned upwards, the drops of water rising from
below, and not falling from above, as in the instances of the aerial arches.
Rainbows are also occasionally seen on the grass, in the morning dew, and
likewise when the hoar-frost is descending. Dr. Langwith once saw a bow
lying on the ground, the colours of which were almost as lively as those of a
common rainbow. It was not round but oblong, and was extended several
hundred yards. The colours took up less space, and were much more lively
in those parts of the bow which were near him than in those which were at a
distance. When M. Labillardiere was on Mount Teneriffe, he saw the
contours of his body traced on the clouds beneath him in all the colours of
the solar bow. He had previously witnessed this phenomenon on the
Kesrouan in Asia Minor. The rainbows of Greenland are said to be
frequently of a pale white, fringed with a brownish yellow, arising from the
rays of the sun being reflected from a frozen cloud.

The following is a summary view of the principal facts which have been
ascertained respecting the rainbow:—1. The rainbow can only be seen when
it rains, and in that point of the heavens which is opposite to the sun. 2.

Both the primary and secondary bows are variegated with all the prismatic
colours—the red being the highest colour in the primary, or brightest bow,
and the violet the highest in the exterior. 3. The primary rainbow can never
be a greater arc than a semicircle; and when the sun is set, no bow, in
ordinary circumstances, can be seen. 4. The breadth of the inner or primary
bow—supposing the sun but a point—is 1° 45´; and the breadth of the
exterior bow 3° 12´, which is nearly twice as great as that of the other; and
the distance between the bows is 8° 55´. But since the body of the sun
subtends an angle of about half a degree, by so much will each bow be
increased, and their distance diminished; and therefore the breadth of the
interior bow will be 2° 15´, and that of the exterior, 3° 42´, and their
distance 8° 25´. The greatest semidiameter of the interior bow, on the same
grounds, will be 42° 17´, and the least of the exterior bow 50° 43´. 5. When
the sun is in the horizon, either in the morning or evening, the bows will
appear complete semicircles. On the other hand, when the sun’s altitude is
equal to 42° 2´ or to 54° 10´, the summits of the bows will be depressed
below the horizon. Hence, during the days of summer, within a certain
interval each day, no visible rainbows can be formed, on account of the
sun’s high altitude above the horizon. 6. The altitude of the bows above the
horizon, or surface of the earth, varies, according to the elevation of the sun.
The altitude, at any time, may be taken by a common quadrant, or other
angular instrument; but, if the sun’s altitude at any particular time be
known, the height of the summit of any of the bows may be found, by
subtracting the sun’s altitude from 42° 2´ for the inner bow, and from 54° 10
´, for the outer. Thus, if the sun’s altitude were 26°, the height of the
primary bow would 16° 2´, and of the secondary, 28° 10´. It follows, that
the height and the size of the bows diminish as the altitude of the sun
increases. 7. If the sun’s altitude is more than 42 degrees, and less than 54°,
the exterior bow may be seen though the interior bow is invisible. 8.
Sometimes only a portion of an arch will be visible while all the other parts
of the bow are invisible. This happens when the rain does not occupy a
space of sufficient extent to complete the bow; and the appearance of this
position, and even of the bow itself, will be various, according to the nature
of the situation, and the space occupied by the rain.

The appearance of the rainbow may be produced by artificial means, at any
time when the sun is shining and not too highly elevated above the horizon.

This is effected by means of artificial fountains or Jet d’eaus, which are
intended to throw up streams of water to a great height. These streams,
when they spread very wide, and blend together in their upper parts, form,
when falling, a shower of artificial rain. If, then, when the fountain is
playing, we move between it and the sun, at a proper distance from the
fountain, till our shadow point directly towards it, and look at the shower,—
we shall observe the colours of the rainbow, strong and vivid; and, what is
particularly worthy of notice, the bow appears, notwithstanding the
nearness of the shower, to be as large, and as far off, as the rainbow which
we see in a natural shower of rain. The same experiment may be made by
candle-light, and with any instrument that will form an artificial shower.

Lunar Rainbows.—A lunar bow is sometimes formed at night by the rays of
the moon striking on a rain-cloud, especially when she is about the full. But
such a phenomenon is very rare. Aristotle is said to have considered himself
the first who had seen a lunar rainbow. For more than a hundred years prior
to the middle of the last century, we find only two or three instances
recorded in which such phenomena are described with accuracy. In the
philosophical transactions for 1783, however, we have an account of three
having been seen in one year, and all in the same place, but they are by no
means common phenomena. I have had an opportunity within the last
twenty years of witnessing two phenomena of this description—one of
which was seen at Perth, on a sabbath evening, in the autumn of 1825, and
the other at Edinburgh, on Wednesday, the 9th of September 1840, about
eight o’clock in the evening—of both which I gave a detailed description in
some of the public journals. The Moon, in both cases, was within a day or
two of the full; the arches were seen in the northern quarter of the heavens,
and extended nearly from east to west, the moon being not far from the
southern meridian. The bows appeared distinct and well defined, but no
distinct traces of the prismatic colours could be perceived on any of them.
That which appeared in 1825 was the most distinctly formed, and continued
visible for more than an hour. The other was much fainter, and lasted little
more than half an hour, dark clouds having obscured the face of the moon.
These bows bore a certain resemblance to some of the luminous arches
which sometimes accompany the Aurora Borealis, and this latter
phenomenon has not unfrequently been mistaken for a Lunar rainbow; but
they may be always distinguished by attending to the phases and position of

the moon. If the moon be not visible above the horizon, if she be in her first
or last quarter, or if any observed phenomenon be not in a direction
opposite to the moon, we may conclude with certainty that, whatever
appearance is presented, there is no lunar rainbow.

The rainbow is an object which has engaged universal attention, and its
beautiful colours and form have excited universal admiration. The poets
have embellished their writings with many beautiful allusions to this
splendid meteor; and the playful school-boy, while viewing the ‘bright
enchantment,’ has frequently run ‘to catch the falling glory.’ When its arch
rests on the opposite sides of a narrow valley, or on the summits of two
adjacent mountains, its appearance is both beautiful and grand. In all
probability, its figure first suggested the idea of arches, which are now
found of so much utility in forming aqueducts and bridges, and for adorning
the architecture of palaces and temples. It is scarcely possible seriously to
contemplate this splendid phenomenon, without feeling admiration and
gratitude towards that wise and beneficent Being, whose hands have bent it
into so graceful and majestic a form, and decked it with all the pride of
colours. “Look upon the rainbow,” says the son of Sirach,15 and praise Him
that made it: very beautiful it is in the brightness thereof. It compasseth the
heaven about with a glorious circle, and the hands of the Most High have
bended it." To this grand etherial bow, the inspired writers frequently allude
as one of the emblems of the majesty and splendour of the Almighty. In the
prophecies of Ezekiel, the throne of Deity is represented as adorned with a
brightness “like the appearance of the bow that is in the cloud in the day of
rain—the appearance of the likeness of the glory of Jehovah.” And, in the
visions recorded in the Book of the Revelations, where the Most High is
represented as sitting upon a throne; “there was a rainbow round about the
throne, in sight like unto an emerald,” as an emblem of his propitious
character and of his faithfulness and mercy. After the deluge, this bow was
appointed as a sign and memorial of the covenant which God made with
Noah and his sons, that a flood of waters should never again be permitted to
deluge the earth and its inhabitants;—and as a pledge of inviolable fidelity
and Divine benignity. When, therefore, we at any time behold “the bow in
the cloud,” we have not only a beautiful and sublime phenomenon
presented to the eye of sense, but also a memorial exhibited to the mental
eye, assuring us, that, “While the earth remaineth, seed-time and harvest,

and cold and heat, and summer and winter, and day and night, shall not
cease.”16

——On the broad sky is seen
“A dewy cloud, and in the cloud a bow
Conspicuous, with seven listed colours gay
Betokening peace with God and covenant new.—
He gives a promise never to destroy
The earth again by flood, nor let the sea
Surpass his bounds, nor rain to drown the world.”
Milton. Par. Lost, Book XI.

SECT. 4.—REFLECTIONS ON THE BEAUTY AND UTILITY OF
COLOURS.

Colour is one of the properties of light which constitutes, chiefly, the beauty
and sublimity of the universe. It is colour, in all its diversified shades,
which presents to our view that almost infinite variety of aspect which
appears on the scene of nature, which gives delight to the eye and the
imagination, and which adds a fresh pleasure to every new landscape we
behold. Every flower which decks our fields and gardens is compounded of
different hues; every plain is covered with shrubs and trees of different
degrees of verdure; and almost every mountain is clothed with herbs and
grass of different shade from those which appear on the hills and landscape
with which it is surrounded. In the country, during summer, nature is every
day, and almost every hour, varying her appearance, by the multitude and
variety of her hues and decorations, so that the eye wanders with pleasure
over objects continually diversified, and extending as far as the sight can
reach. In the flowers with which every landscape is adorned, what a lovely
assemblage of colours, and what a wonderful art in the disposition of their
shades! Here, a light pencil seems to have laid on the delicate tints; there,
they are blended according to the nicest rules of art. Although green is the
general colour which prevails over the scene of sublunary nature, yet it is
diversified by a thousand different shades, so that every species of tree,
shrub and herb, is clothed with its own peculiar verdure. The dark green of

the forests is thus easily distinguished from the lighter shades of cornfields
and the verdure of the lawns. The system of animated nature likewise,
displays a diversified assemblage of beautiful colours. The plumage of
birds, the brilliant feathers of the peacock, the ruby and emerald hues which
adorn the little humming-bird, and the various embellishments of many
species of the insect tribe, present to the eye, in every region of the globe, a
scene of diversified beauty and embellishment. Nor is the mineral kingdom
destitute of such embellishments. For some of the darkest and most
unshapely stones and pebbles, when polished by the hand of art, display a
mixture of the most delicate and variegated colours. All which beauties and
varieties in the scene around us are entirely owing to that property, in every
ray of light, by which it is capable of being separated into the primitive
colours.

To the same cause, likewise, are to be ascribed those beautiful and
diversified appearances, which frequently adorn the face of the sky,—the
yellow, orange and ruby hues which embellish the firmament at the rising of
the sun, and when he is about to descend below the western horizon; and
those aerial landscapes, so frequently beheld in tropical climes, where
rivers, castles and mountains, are depicted rolling over each other along the
circle of the horizon. The clouds, especially in some countries, reflect
almost every colour in nature. Sometimes they wear the modest blush of the
rose; sometimes they appear like stripes of deep vermillion, and sometimes
as large brilliant masses tinged with various hues; now they are white as
ivory, and now as yellow as native gold. In some tropical countries,
according to St. Pierre, the clouds roll themselves up into enormous masses
as white as snow, and are piled upon each other, like the Cordeliers of Peru,
and are moulded into the shape of mountains, of caverns and of rocks.
When the sun sets behind this magnificent aërial net-work, a multitude of
luminous rays are transmitted through each particular interstice, which
produce such an effect, that the two sides of the lozenge illuminated by
them, have the appearance of being begirt with a fillet of gold; and the other
two which are in the shade, seem tinged with a superb ruddy orange. Four
or five divergent streams of light, emanating from the setting sun up to the
zenith, clothe with fringes of gold the undeterminate summits of this
celestial barrier, and proceed to strike with the reflexes of their fires the
pyramids of the collateral aerial mountains, which then appear to consist of

silver and vermilion.—In short, colour diversifies every sublunary scene,
whether on the earth or in the atmosphere, it imparts a beauty to the
phenomena of falling stars, of luminous arches, and the coruscations of the
Aurora Borealis, and gives a splendour and sublimity to the spacious vault
of heaven.

Let us now consider for a moment, what would be the aspect of nature, if,
instead of the beautiful variety of embellishments which now appear on
every landscape, and on the concave of the sky,—one uniform colour had
been thrown over the scenery of the universe. Let us conceive the whole of
terrestrial nature to be covered with snow, so that not an object on earth
should appear with any other hue, and that the vast expanse of the
firmament presented precisely the same uniform aspect. What would be the
consequence? The light of the sun would be strongly reflected from all the
objects within the bounds of our horizon, and would produce a lustre which
would dazzle every eye. The day would acquire a greater brightness than it
now exhibits, and our eyes might, after some time, be enabled freely to
expatiate over the surrounding landscape; but every thing, though
enlightened, would appear confused, and particular objects would scarcely
be distinguishable. A tree, a house or a church, near at hand, might possibly
be distinguished, on account of its elevation above the general surface of
the ground, and the bed of a river by reason of its being depressed below it.
But we should be obliged rather to guess, and to form a conjecture as to the
particular object we wished to distinguish, than to arrive at any certain
conclusion respecting it; and if it lay at a considerable distance, it would be
impossible, with any degree of probability, to discriminate any one object
from another. Notwithstanding the universal brightness of the scene, the
uniformity of colour thrown on every object, would most certainly prevent
us from distinguishing a church from a palace, a cottage from a knoll or a
heap of rubbish, a splendid mansion from rugged rocks, the trees from the
hills on which they grow, or a barren desert from rich and fertile plains. In
such a case, human beings would be confounded, and even friends and
neighbours be at a loss to recognize one another.

The vault of heaven, too, would wear a uniform aspect. Neither planets nor
comets would be visible to any eye, nor those millions of stars which now
shine forth with so much brilliancy, and diversify the nocturnal sky. For, it

is by the contrast produced by the deep azure of the heavens and the white
radiance of the stars, that those bodies are rendered visible. Were they
depicted on a pure white ground, they would not be distinguished from that
ground, and would consequently be invisible, unless any of them
occasionally assumed a different colour. Of course, all that beautiful variety
of aspect which now appears on the face of sublunary nature—the rich
verdure of the fields, the stately port of the forest, the rivers meandering
through the valleys, the splendid hues that diversify and adorn our gardens
and meadows, the gay colouring of the morning and evening clouds, and all
that variety which distinguishes the different seasons, would entirely
disappear. As every landscape would exhibit nearly the same aspect, there
would be no inducement to the poet and the philosopher to visit distant
countries to investigate the scenes of nature, and journeyings from one
region to another would scarcely be productive of enjoyment. Were any
other single colour to prevail, nearly the same results would ensue. Were a
deep ruddy hue to be uniformly spread over the scene of creation, it would
not only be offensive to the eye, but would likewise prevent all distinction
of objects. Were a dark blue or a deep violet to prevail, it would produce a
similar effect, and at the same time, present the scene of nature as covered
with a dismal gloom. Even if creation were arrayed in a robe of green,
which is a more pleasant colour to the eye—were it not diversified with the
different shades it now exhibits, every object would be equally
undistinguishable.

Such would have been the aspect of creation, and the inconveniences to
which we should have been subjected, had the Creator afforded us light
without that intermixture of colours which now appears over all nature, and
which serves to discriminate one object from another. Even our very
apartments would have been tame and insipid, incapable of the least degree
of ornament, and the articles with which they are furnished, almost
undistinguishable, so that in discriminating one object from another, we
should have been as much indebted to the sense of touch as to the sense of
vision. Our friends and fellow men would have presented no objects of
interest in our daily associations. The sparkling eye, the benignant smile,
the modest blush, the blended hues of white and vermillion in the human
face, and the beauty of the female countenance, would all have vanished,
and we should have appeared to one another as so many moving marble

statues cast nearly in the same mould. But, what would have been worst of
all, the numerous delays, uncertainties and perplexities to which we should
have been subjected, had we been under the necessity, every moment, of
distinguishing objects by trains of reasoning, and by circumstances of time,
place, and relative position? An artist, when commencing his work in the
morning, with a hundred tools of nearly the same size and shape around
him, would have spent a considerable portion of his time before he could
have selected those proper for his purpose, or the objects to which they
were to be applied; and in every department of society, and in all our
excursions from one place to another, similar difficulties and perplexities
would have occurred. The one half of our time must thus have been
employed in uncertain guesses, and perplexing reasonings, respecting the
real nature and individuality of objects, rather than in a regular train of
thinking and of employment; and after all our perplexities and conjectures,
we must have remained in the utmost uncertainty, as to the thousands of
scenes and objects, which are now obvious to us, through the
instrumentality of colours, as soon as we open our eyes.

In short, without colour, we could have had no books nor writings: we
could neither have corresponded with our friends by letters, nor have
known any thing with certainty, of the events which happened in former
ages. No written revelation of the will of God, and of his character, such as
we now enjoy, could have been handed down to us from remote periods and
generations. The discoveries of science, and the improvements of art, would
have remained unrecorded. Universal ignorance would have prevailed
throughout the world, and the human mind have remained in a state of
demoralization and debasement. All these, and many other inconveniences
and evils would have inevitably followed, had not God painted the rays of
light with a diversity of colours, And hence we may learn, that the most
important scenes and events in the universe, may depend upon the existence
of a single principle in nature, and even upon the most minute
circumstances, which we may be apt to overlook, in the arrangements of the
material world.

In the existing state of things in the visible creation, we cannot but admire
the Wisdom and Beneficence of the Deity, in thus enabling us to distinguish
objects by so easy and expeditious a mode as that of colour, which in a

moment, discriminates every object and its several relations. We rise in the
morning to our respective employments, and our food, our drink, our tools,
our books, and whatever is requisite for our comfort, are at once
discriminated. Without the least hesitation or uncertainty, and without any
perplexing process of reasoning, we can lay our hands on whatever articles
we require. Colour clothes every object with its peculiar livery, and
infallibly directs the hand in its movements, and the eye in its surveys and
contemplations. But, this is not the only end which the Divine Being had in
view, in impressing on the rays of light a diversity of colours. It is evident,
that he likewise intended to minister to our pleasures, as well as to our
wants. To every man of taste, and almost to every human being, the
combination of colours in flowers, the delicate tints with which they are
painted, the diversified shades of green with which the hills and dales, the
mountains and the vales are arrayed; and that beautiful variety which
appears in a bright summer day, on all the objects of this lower creation—
are sources of the purest enjoyment and delight. It is colour, too, as well as
magnitude, that adds to the sublimity of objects. Were the canopy of heaven
of one uniform hue, it would fail in producing those lofty conceptions, and
those delightful and transporting emotions, which a contemplation of its
august scenery is calculated to inspire. Colours are likewise of considerable
utility in the intercourse of general society. They serve both for ornaments,
and for distinguishing the different ranks and conditions of the community:
they add to the beauty and gracefulness of our furniture and clothing. At a
glance, they enable us at once to distinguish the noble from the ignoble, the
prince from his subjects, the master from his servant, and the widow
clothed with sable weeds from the bride adorned with her nuptial
ornaments.

Since colours, then, are of so much value and importance, they may be
reckoned as holding a rank among the noblest natural gifts of the Creator.
As they are of such essential service to the inhabitants of our globe, there
can be no doubt that they serve similar or analogous purposes throughout
all the worlds in the universe. The colours displayed in the solar beams are
common to all the globes which compose the planetary system, and must
necessarily be reflected, in all their diversified hues, from objects on their
surfaces. The light which radiates from the fixed stars displays a similar
diversity of colours. Some of the double stars are found to emit light of

different hues;—the larger star exhibiting light of a ruddy or orange hue,
and the smaller one a radiance which approaches to blue or green. There is
therefore reason to conclude, that the objects connected with the planets
which revolve round such stars—being occasionally enlightened by suns of
different hues—will display a more variegated and splendid scenery of
colouring than is ever beheld in the world on which we dwell; and that one
of the distinguishing characteristics of different worlds, in regard to their
embellishments, may consist in the splendour and variety of colours with
which the objects on their surfaces are adorned. In the metaphorical
description of the glories of the New Jerusalem, recorded in the Book of
Revelation, one of the chief characteristics of that city is said to consist in
the splendour and diversity of hues with which it is adorned. It is
represented as “coming down from heaven, prepared as a bride adorned for
her husband,” and as reflecting all the beautiful and variegated colours
which the finest gems on earth can exhibit; evidently indicating, that
splendour and variety of colouring are some of the grandest features of
celestial scenery.

On the whole, the subject of colours, when seriously considered, is
calculated to excite us to the adoration of the goodness and intelligence of
that Almighty Being whose wisdom planned all the arrangements of the
universe, and to inspire us with gratitude for the numerous conveniences
and pleasures we derive from those properties and laws he has impressed on
the material system. He might have afforded us light, and even splendid
illumination, without the pleasures and advantages which diversified
colours now produce, and man and other animated beings might have
existed in such a state. But, what a very different scene would the world
have presented from what it now exhibits! Of how many thousands of
pleasures should we have been deprived! and to what numerous
inconveniences and perplexities should we have been subjected! The
sublimity and glories of the firmament, and the endless beauties and
varieties which now embellish our terrestrial system, would have been for
ever unknown, and man could have had little or no incitement to study and
investigate the works of his Creator. In this, as well as in many other
arrangements in nature, we have a sensible proof of the presence and
agency of that Almighty Intelligence “in whom we live, and move, and
have our being.” None but an infinitely Wise and Beneficent Being,

intimately present in all places, could thus so regularly create in us by
means of colour, those exquisite sensations which afford so much delight,
and which unite us, as it were, with every thing around us. In the diversity
of hues spread over the face of creation, we have as real a display of the
Divine presence as Moses enjoyed at the burning bush. The only difference
is, that the one was out of the common order of Divine procedure, and the
other in accordance with those permanent laws which regulate the economy
of the universe. In every colour, then, which we contemplate, we have a
sensible memorial of the presence of that Being “whose Spirit garnished the
heavens and laid the foundations of the earth,” and whose “merciful
visitation” sustains us every moment in existence. But the revelation of God
to our senses, through the various objects of the material world, has become
so familiar, that we are apt to forget the Author of all our enjoyments, even
at the moment when we are investigating his works and participating of his
benefits. “O that men would praise Jehovah for his goodness, and for his
wonderful works towards the children of men.”

PART II.
ON TELESCOPES.

CHAPTER I.

HISTORY OF THE INVENTION OF TELESCOPES.

The telescope is an optical instrument for viewing objects at a distance. Its
name is compounded of two Greek words,—τηλε, which signifies, at a
distance, or far off, and σχοπειν, to view, or to contemplate. By means of
telescopes, remote objects are represented as if they were near, small
apparent magnitudes are enlarged, confused objects are rendered distinct,
and the invisible and obscure parts of very distant scenes are rendered
perceptible and clear to the organ of vision. The telescope is justly
considered as a grand and noble instrument. It is not a little surprising that it
should be in the power of man to invent and construct an instrument by
which objects, too remote for the unassisted eye to distinguish, should be
brought within the range of distinct vision, as if they were only a few yards
from our eye, and that thousands of august objects in the heavens, which
had been concealed from mortals for numerous ages, should be brought
within the limits of our contemplation, and be as distinctly perceived, as if
we had been transported many millions of miles from the space we occupy,
through the celestial regions. The celebrated Huygens remarks, in reference
to this instrument, that, in his opinion, ‘the wit and industry of man has not
produced any thing so noble and so worthy of his faculties as this sort of
knowledge; (namely of the telescope) insomuch that if any particular person
had been so diligent and sagacious as to invent this instrument from the
principles of nature and geometry,—for my part, I should have thought his
abilities were more than human; but the case is so far from this, that the
most learned men have not yet been able sufficiently to explain the reason
of the effects of this casual invention.’

The persons who constructed the first telescopes, and the exact period when
they were first invented, are involved in some degree of obscurity. It does
not certainly appear that such instruments were known to the ancients,
although we ought not to be perfectly decisive on this point. The cabinets of
the curious contain some very ancient gems, of admirable workmanship, the

figures on which are so small, that they appear beautiful through a
magnifying glass, but altogether confused and indistinct to the naked eye:
and, therefore, it may be asked, if they cannot be viewed, how could they be
wrought, without the assistance of glasses? And as some of the ancients
have declared that the moon has a form like that of the earth, and has plains,
hills, and valleys in it,—how could they know this—unless by mere
conjecture, without the use of a telescope? And how could they have known
that the Milky Way is formed by the combined rays of an infinite number of
stars? For Ovid states, in reference to this zone, ‘its ground-work is of
stars.’ But whatever knowledge the ancients may have possessed of the
telescope or other optical glasses, it is quite evident that they never had
telescopes of such size and power as those which we now possess; and that
no discoveries in the heavens, such as are now brought to light, were made
by any of the ancient astronomers; otherwise some allusions to them must
have been found in their writings.

Among the moderns, the illustrious Friar Bacon appears to have acquired
some rude ideas respecting the construction of telescopes. ‘Lenses and
specula’ says he, ‘may be so figured that one object may be multiplied into
many, that those which are situated at a great distance may be made to
appear very near, that those which are small may be made to appear very
large, and those which are obscure very plain; and we can make stars to
appear wherever we will.’ From these expressions, it appears highly
probable, that this philosopher was acquainted with the general principle
both of telescopes and microscopes, and that he may have constructed
telescopes of small magnifying power, for his own observation and
amusement, although they never came into general use. He was a man of
extensive learning, and made so rapid a progress in the sciences, when
attending the university of Paris, that he was esteemed the glory of that seat
of learning. He prosecuted his favourite study of experimental philosophy
with unremitting ardour; and in this pursuit, in the course of twenty years,
he expended no less than £2000 in experiments, instruments, and in
procuring scarce books. In consequence of such extraordinary talents, and
such astonishing progress in the sciences, in that ignorant age, he was
represented, by the envy of his illiterate fraternity, as having dealings with
the devil; and, under this pretence, he was restrained from reading lectures,
and at length, in 1278, when sixty-four years of age, he was imprisoned in

his cell, where he remained in confinement for ten years. He shone like a
single bright star in a dark hemisphere—the glory of our country—and died
at Oxford, in the year 1294, in the eightieth year of his age. ‘Friar Bacon,’
says the Rev. Mr. Jones, ‘may be considered as the first of English
philosophers; his profound skill in mechanics, optics, astronomy, and
chemistry, would make an honourable figure in the present age. But he is
entitled to further praise, as he made all his studies subservient to theology,
and directed all his writings, as much as could be, to the glory of God. He
had the highest regard for the sacred scriptures, and was persuaded they
contain the principles of all true science.’

The next person who is supposed to have acquired a knowledge of
telescopes, was Joannes Baptista Porta, of Naples, who flourished in the
sixteenth century. He discovered the Camera Obscura—the knowledge of
which might naturally have led to the invention of the telescope; but it does
not appear that he ever constructed such an instrument. Des Cartes
considers James Metius, a Dutchman, as the first constructor of a telescope,
and says, that ‘as he was amusing himself with making mirrors and
burning-glasses, he casually thought of looking through two of his lenses at
a time, and found that distant objects appeared very large and distinct.’
Others say that this great discovery was first made by John Lippersheim, a
maker of spectacles at Middleburg, or rather by his children, who were
diverting themselves with looking through two glasses at a time, and
placing them at different distances from each other. But Borellus, who
wrote a book ‘on the invention of the telescope,’ gives this honour to
Zacharias Jansen, another spectacle-maker in the same town, who, he says,
made the first telescope in 1590. Jansen was a diligent inquirer into nature,
and, being engaged in such pursuits, he was trying what use could be made
of lenses for those purposes, when he fortunately hit upon the construction.
Having found the arrangement of glasses which produced the effect desired,
he enclosed them in a tube, and ran with his instrument to prince Maurice,
who, immediately conceiving that it might be of use to him in his wars,
desired the author to keep it a secret. Such are the rude conceptions and
selfish views of princely warriors, who would apply every invention in
their power for the destruction of mankind. But the telescope was soon
destined to more noble and honourable achievements. Jansen, it is said,
directed his instrument towards celestial objects, and distinctly saw the

spots on the surface of the moon, and discovered many new stars,
particularly seven pretty considerable ones in the Great Bear. His son
Joannes is said to have noted the lucid circle near the lower limb of the
moon, now named Tycho, from whence several bright rays seem to dart in
different directions. In viewing Jupiter, he perceived two, sometimes three,
and at the most four small stars, a little above or below him, and thought
that they performed revolutions around him. This was, probably, the first
observation of the satellites of Jupiter, though the person who made it was
not aware of the importance of his discovery.17

It is not improbable that different persons about Middleburgh hit upon the
invention, in different modes, about the same time. Lippersheim seems to
have made his first rude telescope by adjusting two glasses on a board, and
supporting them on brass circles.18 Other workmen, particularly Metius and
Jansen, in emulation of each other, seem to have made use of that discovery,
and by the new form they gave it, made all the honour of it their own. One
of them, considering the effects of light as injurious to distinctness, placed
the glasses in a tube blackened within. The other, still more cautious, placed
the same glasses within tubes capable of sliding one in another, both to vary
the prospects, by lengthening the instrument, according to the pleasure of
the observer, and to render it portable and commodious. Thus, it is probable
that different persons had a share in the invention, and jointly contributed to
its improvement. At any rate, it is undoubtedly to the Dutch that we owe the
original invention. The first telescope made by Jansen, did not exceed
fifteen or sixteen inches in length, and therefore its magnifying power could
not have been very great.

The famous Galileo has frequently been supposed to have been the inventor
of the telescope, but he acknowledges that he had not the honour of being
the original inventor, having first learned from a German, that such an
instrument had already been made; although, from his own account, it
appears that he had actually re-invented this instrument. The following is
the account, in his own words, of the circumstances which led him to
construct a telescope. ‘Nearly ten months ago (namely in April or May
1609) it was reported that a certain Dutchman had made a perspective
through which many distant objects appeared distinct as if they were near:
several effects of this wonderful instrument were reported, which some

believed and others denied: but, having it confirmed to me a few days after
by a letter from the noble John Badoverie, at Paris, I applied myself to
consider the reason of it, and by what means I might contrive a similar
instrument, which I afterwards attained to by the doctrine of refractions.
And, first, I prepared a leaden tube, to whose extremities I fitted two
spectacle-glasses, both of them plain on one side, and on the other side, one
of them was spherically convex, and the other concave. Then applying my
eye to the concave, I saw objects appear pretty large and pretty near me.
They appeared three times nearer and nine times larger in surface than to
the naked eye: and soon after I made another, which represented objects
about sixty times larger, and eight times nearer; and, at last, having spared
no labour nor expense, I made an instrument so excellent, as to show things
almost a thousand times larger, and above thirty times nearer, than to the
naked eye.’ In another part of his writings, Galileo informs us that ‘he was
at Venice when he heard of Prince Maurice’s instrument, but nothing of its
construction; that the first night, after he returned to Padua, he solved the
problem, and made his instrument the next day; and soon after, presented it
to the Doge at Venice, who, to do him honour for his grand invention, gave
him the ducal letters which settled him for life in his lectureship at Padua;
and the Republic, on the twenty-fifth of August in the same year (1610)
more than tripled his salary as professor.’

The following is the account which this philosopher gives of the process of
reasoning, which led him to the construction of a telescope:—‘I argued in
the following manner. The contrivance consists either of one glass or more
—one is not sufficient, since it must be either convex, concave, or plane;
the last does not produce any sensible alteration in objects, the concave
diminishes them; it is true that the convex magnifies, but it renders them
confused and indistinct; consequently one glass is insufficient to produce
the desired effect. Proceeding to consider two glasses, and bearing in mind
that the plane glass causes no change, I determined that the instrument
could not consist of the combination of a plane glass with either of the other
two. I therefore applied myself to make experiments on combinations of the
two other kinds; and thus obtained that of which I was in search.’ If the true
inventor is the person who makes the discovery by reasoning and reflection,
by tracing facts and principles to their consequences, and by applying his
invention to important purposes, then, Galileo may be considered as the real

inventor of the telescope. No sooner had he constructed this instrument—
before he had seen any similar one—than he directed his tube to the
celestial regions, and his unwearied diligence and ardour were soon
rewarded by a series of new and splendid discoveries. He descried the four
satellites of Jupiter, and marked the periods of their revolutions; he
discovered the phases of Venus, and thus was enabled to adduce a new
proof of the Copernican system, and to remove an objection that had been
brought against it. He traced on the lunar orb, a resemblance to the structure
of the earth, and plainly perceived the outlines of mountains and vales,
casting their shadows over different parts of its surface. He observed, that
when Mars was in quadrature, his figure varied slightly from a perfect
circle; and that Saturn consisted of a triple body, having a small globe on
each side—which deception was owing to the imperfect power of his
telescope, which was insufficient to show him that the phenomenon was in
reality a ring. In viewing the sun, he discovered large dark spots on the
surface of that luminary, by which he ascertained that that mighty orb
performed a revolution round its axis. He brought to view multitudes of
stars imperceptible to the naked eye, and ascertained that those nebulous
appearances in the heavens which constitute the Milky Way, consist of a
vast collection of minute stars, too closely compacted together to produce
an impression on our unassisted vision.

The results of Galileo’s observations were given to the world in a small
work, entitled ‘Nuncius Sidereus,’ or, ‘News from the starry regions,’ which
produced an extraordinary sensation among the learned. These discoveries
soon spread throughout Europe, and were incessantly talked of, and were
the cause of much speculation and debate among the circles of
philosophers. Many doubted; many positively refused to believe so novel
and unlooked-for announcements, because they ran counter to the
philosophy of Aristotle, and all the preconceived notions which then
prevailed in the learned world. It is curious, and may be instructive, to
consider to what a length of absurdity, ignorance and prejudice carried
many of those who made pretensions to learning and science. Some tried to
reason against the facts alleged to be discovered, others contented
themselves, and endeavoured to satisfy others, with the simple assertion
that such things were not, and could not possibly be; and the manner in
which they supported themselves in their incredulity was truly ridiculous.

‘O my dear Kepler,’ says Galileo in a letter to that astronomer, ‘how I wish
we could have one hearty laugh together. Here at Padua is the principal
professor of philosophy, whom I have repeatedly and urgently requested to
look at the moon and planets through my glass, which he pertinaciously
refuses to do, lest his opinions should be overturned. Why are you not here?
what shouts of laughter we should have at this glorious folly! and to hear
the professor of philosophy at Pisa labouring with the Grand Duke with
logical arguments, as if with magical incantations, to charm the new planets
out of the sky.’ Another opponent of Galileo, one Christmann, says in a
book he published, ‘We are not to think that Jupiter has four satellites given
him by nature, in order, by revolving round him, to immortalize the Medici
who first had notice of the observation. These are the dreams of idle men,
who love ludicrous ideas better than our laborious and industrious
correction of the heavens. Nature abhors so horrible a chaos; and to the
truly wise, such vanity is detestable.’ One Martin Horky, a would-be
philosopher, declared to Kepler, ‘I will never concede his four new planets
to that Italian from Padua, though I should die for it;’ and he followed up
this declaration, by publishing a book against Galileo, in which he examines
four principal questions respecting the alleged planets; 1. Whether they
exist? 2. What they are? 3. What they are like? 4. Why they are? The first
question is soon disposed of by declaring positively that he has examined
the heavens with Galileo’s own glass, and that no such thing as a satellite
about Jupiter exists. To the second, he declares solemnly that he does not
more surely know, that he has a soul in his body than that reflected rays are
the sole cause of Galileo’s erroneous observations. In regard to the third
question, he says, that these planets are like the smallest fly compared to an
elephant; and finally, concludes on the fourth, that the only use of them is to
gratify Galileo’s ‘thirst of gold,’ and to afford himself a subject of
discussion. Kepler, in a letter to Galileo, when alluding to Horky, says, ‘He
begged so hard to be forgiven, that I have taken him again into favour upon
this preliminary condition—that I am to show him Jupiter’s satellites, AND
HE IS TO SEE THEM, and own that they are there.’

The following is a specimen of the reasoning of certain pretended
philosophers of that age against the discoveries of Galileo. Sizzi, a
Florentine astronomer, reasons in this strain: ‘There are seven windows
given to animals in the domicile of the head, through which the air is

admitted to the rest of the tabernacle of the body to enlighten, to warm and
to nourish it; two nostrils, two eyes, two ears, and a mouth; so in the
heavens, or the great world, there are two favourable stars, two
unpropitious, two luminaries, and Mercury alone undecided and indifferent.
From which and many other similar phenomena in nature, such as the seven
metals, &c., we gather that the number of planets is necessarily seven.
Moreover, the satellites are invisible to the naked eye, and therefore can
exert no influence on the earth, and therefore would be useless, and
therefore do not exist. Besides, as well the Jews as other ancient nations
have adopted the division of the week into seven days, and have named
them from the seven planets. Now, if we increase the number of the planets,
this whole system falls to the ground.’ The opinions which then prevailed in
regard to Galileo’s observations on the moon, were such as the following:—
Some thought that the dark shades on the moon’s surface arose from the
interposition of opaque bodies floating between her and the sun, which
prevent his light from reaching those parts; others imagined that, on account
of her vicinity to the earth, she was partly tainted with the imperfections of
our terrestrial and elementary nature, and was not of that entirely pure and
refined substance of which the more remote heavens consist: and a third
party looked on her as a vast mirror, and maintained that the dark parts of
her surface were the reflected images of our earthly forests and mountains.

Such learned nonsense is a disgrace to our species, and to the rational
faculties with which man is endowed, and exhibits, in a most ludicrous
manner, the imbecility and prejudice of those who made bold pretensions to
erudition and philosophy. The statement of such facts, however, may be
instructive, if they tend to guard us against those prejudices and pre-
conceived opinions, which prevent the mind from the cordial reception of
truth, and from the admission of improvements in society which run counter
to long-established customs. For the same principles and prejudices, though
in a different form, still operate in society and retard the improvement of the
social state, the march of science, and the progress of Christianity. How
ridiculous is it for a man, calling himself a philosopher, to be afraid to look
through a glass to an existing object in the heavens, lest it should endanger
his previous opinions! And how foolish is it to resist any improvement or
reformation in society, because it does not exactly accord with existing
opinions, and with ‘the wisdom of our ancestors.’

It is not a little surprising, that Galileo should have first hit on that
construction of a telescope which goes by his name, and which was formed
with a concave glass next the eye. This construction of a telescope is more
difficult to be understood, in theory, than one which is composed solely of
convex glasses; and its field of view is comparatively very small, so that it
is almost useless when attempted to be made of a great length. In the
present day, we cannot help wondering that Galileo and other astronomers,
should have made such discoveries as they did with such an instrument, the
use of which must have required a great degree of patience and address.
Galileo’s best telescope, which he constructed ‘with great trouble and
expense,’ magnified the diameters of objects only thirty-three times; but its
length is not stated—which would depend upon the focal distance of the
concave eye-glass. If the eye-glass was two inches focus, the length of the
instrument would be five feet four inches; if it was only one inch, the length
would be two feet eight inches, which is the least we can allow to it—the
object-glass being thirty-three inches focus, and the eye-glass placed an
inch within this focus. With this telescope, Galileo discovered the satellites
of Jupiter, the crescent of Venus, and the other celestial objects to which we
have already alluded. The telescopes made in Holland, are supposed to have
been constructed solely of convex glasses, on the principle of the
astronomical telescope; and, if so, Galileo’s telescope was in reality a new
invention.

Certain other claimants of the invention of the telescope, have appeared,
besides those already mentioned. Francis Fontana, in his ‘celestial
observations,’ says, that he was assured by a Mr. Hardy, advocate of the
parliament of Paris, a person of great learning and undoubted integrity, that
on the death of his father, there was found among his things an old tube, by
which distant objects were distinctly seen, and that it was of a date long
prior to the telescope lately invented, and had been kept by him as a secret.
Mr. Leonard Digges, a gentleman who lived near Bristol, in the seventeenth
century, and was possessed of great and various knowledge, positively
asserts in his ‘Stratoticos,’ and in another work, that his father, a military
gentleman, had an instrument which he used in the field, by which he could
bring distant objects near, and could know a man at the distance of three
miles. Mr. Thomas Digges, in the preface to his ‘Pantometria,’ published in
1591, declares, “My father, by his continual painful practices, assisted by

demonstrations mathematical, was able, and sundry times hath by
proportional glasses, duly situate in convenient angles, not only discovered
things far off, read letters, numbered pieces of money, with the very coin
and superscription thereof, cast by some of his friends of purpose, upon
downs in open fields, but also, seven miles off, declared what hath been
done that instant, in private places. He hath also, sundry times, by the sun-
beams, fired powder and discharged ordnance half a mile and more distant,
and many other matters far more strange and rare, of which there are yet
living divers witnesses.”

It is by no means unlikely, that persons accustomed to reflection, and
imbued with a certain degree of curiosity, when handling spectacle-glasses,
and amusing themselves with their magnifying powers and other properties,
might sometimes hit upon the construction of a telescope; as it only requires
two lenses of different focal distances to be held at a certain distance from
each other, in order to show distant objects magnified. Nay, even one lens,
of a long focal distance, is sufficient to constitute a telescope of a moderate
magnifying power, as I shall show in the sequel. But such instruments,
when they happened to be constructed accidentally, appear to have been
kept as secrets, and confined to the cabinets of the curious, so that they
never came into general use; and as their magnifying power would probably
be comparatively small, the appearance of the heavenly bodies would not
be much enlarged by such instruments—nor is it likely that they would be
often directed to the heavens. On the whole, therefore, we may conclude
that the period when instruments of this description came into general use,
and were applied to useful purposes, was when Galileo constructed his first
telescopes.

CHAPTER II.

OF THE CAMERA OBSCURA.

Before proceeding to a particular description of the different kinds of
telescopes, I shall first give a brief description of the Camera Obscura, as
the phenomena exhibited by this instrument tend to illustrate the principle
of a refracting telescope.

The term Camera Obscura literally signifies a darkened vault or roof; and
hence it came to denote a chamber, or box, or any other place made dark for
the purpose of optical experiments. The camera obscura, though a simple, is
yet a very curious and noble contrivance; as it naturally and clearly explains
the manner in which vision is performed, and the principle of the telescope,
and entertains the spectator with a most exquisite picture of surrounding
objects, painted in the most accurate proportions and colours by the hand of
nature. The manner of exhibiting the pictures of objects in a dark room is as
follows:—In one of the window-shutters of a room which commands a
good prospect of objects not very distant, a circular hole should be cut of
four or five inches diameter. In this hole an instrument should be placed,
called a Scioptric ball, which has three parts, a frame, a ball, and a lens. The
ball has a circular hole cut through the middle, in which the lens is fixed,
and its use is, to turn every way so as to take in a view of objects on every
side. The chamber should be made perfectly dark; and a white screen, or a
large sheet of elephant paper, should be placed opposite to the lens, and in
its focus, to receive the image. If then, the objects without be strongly
enlightened by the sun, there will be a beautiful living picture of the scene
delineated on the white screen, where every object is beheld in its
proportions, and with its colours even more vivid than life; green objects
appear in the picture more intensely green, and yellow, blue, red or white
flowers appear much more beautiful in the picture than in nature; if the lens
be a good one, and the room perfectly dark, the perspective is seen in
perfection. The lights and shadows are not only perfectly just, but also
greatly heightened; and, what is peculiar to this delineation, and which no

other picture or painting can exhibit—the motions of all the objects are
exactly expressed in the picture; the boughs of the trees wave, the leaves
quiver, the smoke ascends in a waving form, the people walk, the children
at their sports leap and run, the horse and cart move along, the ships sail,
the clouds soar and shift their aspects, and all as natural as in the real
objects; the motions being somewhat quicker, as they are performed in a
more contracted scene.

These are the inimitable perfections of a picture, drawn by the rays of light
as the only pencil in nature’s hand, and which are finished in a moment; for
no sensible interval elapses before the painting is completed, when the
ground on which it is painted is prepared and adjusted. In comparison of
such a picture, the finest productions of the most celebrated artists, the
proportions of Raphael, the natural tints and colouring of Titian, and the
shadowing of the Venetians, are but coarse and sorry daubings, when set in
competition with what nature can exhibit by the rays of light passing
through a single lens. The Camera obscura is at the same time the painter’s
assistant, and the painter’s reproach. From the picture it forms he receives
his best instructions, and is shown what he should endeavour to attain; and
hence, too, he learns the imperfections of his art, and what it is impossible
for him to imitate. As a proof of this, the picture formed in the dark
chamber will bear to be magnified to a great extent, without defacing its
beauty, or injuring the fineness of its parts; but the finest painted landscape,
if viewed through a high magnifier will appear only as a coarse daubing.

The following scheme will illustrate what has been now stated respecting
the dark chamber. EF represents a darkened room, in the side of which, IK,
is made the circular hole V, in which, on the inside, is fixed the scioptric
ball. At some considerable distance from this hole is exhibited a landscape
of houses, trees, and other objects, ABCD, which are opposite to the
window. The rays which flow from the different objects which compose this
landscape, to the lens at V, and which pass through it, are converged to their
respective foci, on the opposite wall of the chamber HG or on a white
moveable screen placed in the focus of the lens, where they all combine to
paint a lively and beautiful picture of the range of objects directly opposite,
and on each side, so far as the lens can take in.

Though I have said, that a scioptric ball and socket are expedient to be used
in the above experiment, yet where such an instrument is not at hand, the
lens may be placed in a short tube made of pasteboard or any other material,
and fixed in the hole made in the window shutter. The only imperfection
attending this method is, that the lens can exhibit those objects only which
lie directly opposite the window.

figure 37.

Some may be disposed to consider it as an imperfection in this picture, that
all the objects appear in an inverted position; as they must necessarily do,
according to what we formerly stated respecting the properties of convex
lenses, (p. 72). There are, however, different modes of viewing the picture
as if it were erect. For, if we stand before the picture, and hold a common
mirror against our breast at an acute angle with the picture, and look down
upon it, we shall see all the images of the objects as if restored to their erect
position; and by the reflection of the mirror, the picture will receive such a
lustre as will make it still more delightful. Or, if a large concave mirror
were placed before the picture at such a distance, that its image may appear

before the mirror, it will then appear erect and pendulous in the air in the
front of the mirror. Or, if the image be received on a frame of paper, we
may stand behind the frame, with our face towards the window, and look
down upon the objects, when they will appear as if erect.

The experiment of the Camera Obscura may serve to explain and illustrate
the nature of a common refracting telescope. Let us suppose, that the lens in
the window-shutter represents the object-glass of a refracting telescope.
This glass forms an image in its focus, which is in every respect an exact
picture or representation of the objects before it; and consequently the same
idea is formed in the mind, of the nature, form, magnitude, and colour of
the object—whether the eye at the centre of the glass views the object itself,
or the image formed in its focus. For, as formerly stated, the object and its
image are both seen under the same angles by the eye placed at the centre of
the lens. Without such an image as is formed in the camera obscura—
depicted either in the tube of a telescope or in the eye itself—no telescope
could possibly be formed. If we now suppose that, behind the image formed
in the dark chamber, we apply a convex lens of a short focal distance to
view that image, then the image will be seen distinctly, in the same manner
as we view common objects, such as a leaf or a flower, with a magnifying
glass; consequently, the object itself will be seen distinct and magnified.
And, as the same image is nearer to one lens than the other, it will subtend a
larger angle at the nearest lens, and of course, will appear larger than
through the other, and consequently the object will be seen magnified in
proportion. For example, let us suppose the lens in the camera obscura, or
the object lens of a telescope, to be five feet, or sixty inches focal distance,
at this distance from the glass, an image of the distant objects opposite to it
will be formed. If now, we place a small lens two inches focal distance
beyond this point, or five feet two inches from the object-glass, the objects,
when viewed through the small lens, will appear considerably magnified,
and apparently much nearer than to the naked eye. The degree of
magnifying power is in proportion to the focal distances of the two glasses;
that is, in the present case, in the proportion of two inches, the focus of the
small lens, to sixty inches, the focus of the object lens. Divide sixty by two,
the quotient is thirty, which gives the magnifying power of such a telescope,
that is, it represents objects thirty times nearer, or under an angle thirty
times larger than to the naked eye. If the eye-glass, instead of being two

inches, were only one and a half inch focus, the magnifying power would
be in the proportion of one and a half to sixty, or forty times. If the eye-
glass were three inches focus, the magnifying power would be twenty
times; and so on, with regard to other proportions. In all cases, where a
telescope is composed of only two convex lenses, the magnifying power is
determined, by dividing the focal distance of the object-glass, by the focal
distance of the eye-glass, and the quotient expresses the number of times
the object is magnified, in length and breadth. This and various other
particulars, will be more fully illustrated in the sequel.

In performing experiments with the camera obscura in a darkened chamber,
it is requisite that the following particulars be attended to:—1. That the lens
be well figured, and free from any veins or blemishes that might distort the
picture. 2. That it be placed directly against the object whose image we
wish to see distinctly delineated. 3. The lens should be of a proper size both
as to its breadth and focal distance. It should not be less than three or four
feet focal distance, otherwise the picture will be too small, and the parts of
objects too minute to be distinctly perceived; nor should it exceed fifteen or
eighteen feet, as in this case the picture will be faint, and of course not so
pleasing. The best medium as to focal distance, is from five to eight or ten
feet. The aperture, too, or breadth of the glass, should not be too small,
otherwise the image will be obscure, and the minute parts of it invisible for
want of a sufficient quantity of light. A lens of six feet focal distance, for
example, will require an aperture of at least two inches. Lenses of a shorter
focal distance require less apertures, and those of a longer focal distance
larger. But if the aperture be too large, the image will be confused, and
indistinct, by the admission of too much light. 4. We should never attempt
to exhibit the images of objects, unless when the sun is shining and strongly
illuminating the objects, except in the case of very near objects placed in a
good light. As one of the greatest beauties, in the phenomena of the dark
chamber, consists in the exquisite appearance and contrast of light and
shadows, nothing of this kind can be perceived but from objects directly
illuminated by the sun. 5. A south window should never be used in the
forenoon, as the sun cannot then enlighten the north side of an object; and
besides, his rays would be apt to shine upon the lens, which would make the
picture appear with a confused lustre. An east window is best in the
afternoon, and a western in the morning; but a north window is in most

cases to be preferred, especially in the forenoon, when the sun is shining
with his greatest strength and splendour. In general, that window ought to
be used which looks to the quarter opposite to that in which the sun is
shining.

The picture should be received upon a very white surface, as the finest and
whitest paper, or a painted cloth, bordered with black; as white bodies
reflect most copiously the incident rays, while black surfaces absorb them.
If the screen could be bent into the concave segment of a sphere, of which
the focal distance of the double convex lens which is used, is the radius, the
parts of the picture adjacent to the extremities would appear most distinct.
Sir D. Brewster informs us that, having tried a number of white substances
of different degrees of smoothness, and several metallic surfaces, on which
to receive the image, he happened to receive the picture on the silvered
back of a looking-glass, and was surprised at the brilliancy and distinctness
with which external objects were represented. To remove the spherical
protuberances of the tin foil, he ground the surface very carefully with a bed
of hones which he had used for working the plane specula of Newtonian
telescopes. By this operation, which may be performed without injuring the
other side of the mirror, he obtained a surface finely adapted for the
reception of images. The minute parts of the landscape were formed with so
much precision, and the brilliancy of colouring was so uncommonly fine, as
to equal, if not exceed the images that are formed in the air by means of
concave specula.

The following additional circumstances may be stated respecting the
phenomena exhibited in the dark chamber. A more critical idea may be
formed of any movement in the picture here presented than from observing
the motion of the object itself. For instance, a man walking in a picture
appears to have an undulating motion, or to rise up and down every step he
takes, and the hands seem to move almost exactly like a pendulum; whereas
scarcely any thing of this kind is observed in the man himself, as viewed by
the naked eye. Again, if an object be placed just twice the focal distance
from the lens without the room, the image will be formed at the same
distance from the lens within the room, and consequently will be equal in
magnitude to the object itself. The recognition of this principle may be of
use to those concerned in drawing, and who may wish, at any time, to form

a picture of the exact size of the object. If the object be placed further from
the lens than twice its focal length, the image will be less than the object. If
it be placed nearer, the image will be greater than the life. In regard to
immoveable objects, such as houses, gardens, trees, &c., we may form the
images of so many different sizes, by means of different lenses, the shorter
focus making the lesser picture, and the longer focal distance the largest.

The experiments with the camera obscura, may likewise serve to illustrate
the nature of vision, and the functions of the human eye. The frame or
socket of the scioptric ball may represent the orbit of the natural eye. The
ball, which turns every way, resembles the globe of the eye, moveable in its
orbit. The hole in the ball may represent the pupil of the eye; the convex
lens corresponds to the crystalline humour, which is shaped like a lens, and
contributes to form the images of objects on the inner part of the eye. The
dark chamber itself, is somewhat similar to the internal part of the eye,
which is lined all around, and under the retina, with a membrane, over
which is spread a mucous of a very black colour. The white wall or frame of
white paper to receive the picture of objects, is a fair representation of the
retina of the eye, on which all the images of external objects are depicted.
Such are some of the general points of resemblance between the apparatus
connected with the dark chamber, and the organ of vision; but the human
eye is an organ of such exquisite construction, and composed of such a
number and variety of delicate parts, that it cannot be adequately
represented by any artificial contrivance.

The darkened chamber is frequently exhibited in a manner somewhat
different from what we have above described, as in the following scheme,
(fig. 38) which is termed the revolving camera obscura. In this
construction, KH represents a plane mirror or metallic reflector, placed at
half a right angle to the convex lens HI, by which, rays proceeding from
objects situated in the direction O are reflected to the lens, which forms an
image of the objects on a round white table at T, around which several
spectators may stand, and view the picture, as delineated on a horizontal
plane. The reflector, along with its case, is capable of being turned round,
by means of a simple apparatus connected with it, so as to take in, in
succession, all the objects which compose the surrounding scene. But as the
image here is received on a flat surface, the rays fm, en, will have to diverge

farther than the central rays dc; and hence the representation of the object,
near the sides, will be somewhat distorted; to remedy which, the image
should be received on a concave surface, as ab or PS. This is the general
plan of those Camera Obscuras, fitted up in large wooden tents, which are
frequently exhibited in our large cities, and removed occasionally from one
town to another. Were an instrument of this kind fitted up on a small scale, a
hole might be made in one of the sides, as at E, where the eye could be
applied to view the picture. The focal distances of the lenses used in large
instruments of this kind, are generally from eight to twelve feet, in which
case they produce a telescopic effect upon distant objects, so as to make
them appear nearer than when viewed with the naked eye.

figure 38.

figure 39.

The camera obscura is frequently constructed in a portable form, so as to be
carried about for the purpose of delineating landscapes. The following is a
brief description of the instrument in this form. AC is a convex lens placed
near the end of a tube or drawer, which is moveable in the side of a square
box, within which is a plane mirror DE, reclining backward in an angle of
forty-five degrees from the perpendicular pn. The pencils of rays flowing
from the object OB, and passing through the convex lens—instead of
proceeding forward and forming the image HI, are reflected upward by the
mirror, and meet in points as FG, at the same distance at which they would
have met at H and I, if they had not been intercepted by the mirror. At FG,
the image of the object OB is received either on a piece of oiled paper, or
more frequently on a plane unpolished glass, placed in the horizontal
situation FG, which receives the images of all objects, opposite to the lens,
and on which, or on an oiled paper placed upon it, their outlines may be
traced by a pencil. The moveable tube on which the lens is fixed, serves to
adjust the focus for near and distant objects, till their images appear
distinctly painted on the horizontal glass at FG. Above is shown the most
common form of the box of this kind of Camera Obscura. A is the position
of the lens, BC, the position of the mirror, D, the plane unpolished glass on
which the images are depicted, GH a moveable top or screen to prevent the
light from injuring the picture, and EF, the moveable tube.

figure 40.

The Daguerreotype.—An important, and somewhat surprising discovery
has lately been made, in relation to the picture formed by the Camera
Obscura. It is found, that the images formed by this instrument are capable
of being indelibly fixed on certain surfaces previously prepared for the
purpose, so that the picture is rendered permanent. When a Camera is
presented to any object or landscape strongly illuminated by the sun, and
the prepared ground for receiving the image is adjusted, and a certain time
allowed to elapse till the rays of light produce their due effect, in a few
minutes or even seconds, a picture of the objects opposite to the lens is
indelibly impressed upon the prepared plate, in all the accurate proportions
and perspective, which distinguish the images formed in a dark chamber—
which representations may be hung up in apartments, along with other
paintings and engravings; and will likely retain their beauty and lustre for
many years. These are pictures of nature’s own workmanship finished in an
extremely short space of time, and with the most exquisite delicacy and
accuracy. The effect is evidently owing to certain chemical properties in the
rays of light; and opens a new field for experiment and investigation to the
philosopher. The only defect in the picture is, that it is not coloured; but, in
the progress of experiments on this subject, it is not unlikely that even this
object may be accomplished, in which case, we should be able to obtain the
most accurate landscapes and representations of all objects, which can
possibly be formed. This art or discovery goes by the name of the
Daguerreotype from M. Daguerre, a Frenchman, who is supposed to have

been the first discoverer, and who received a large premium from the
French government for disclosing the process, and making the discovery
public. Several improvements and modifications, in reference to the
preparation of the plates, have been made since the discovery was first
announced, about the beginning of 1839; and the pictures formed on this
principle, are frequently distinguished by the name of Photogenic drawings;
and are now exhibited at most of our public scientific institutions.

This new science or art, has been distinguished by different names. It was
first called Photography, from two Greek words, signifying writing by
light: it was afterwards called the art of Photogenic Drawing, or drawing
produced by light. M. Daguerre gave it the name of Heliography, or writing
by the sun, all which appellatives are derived from the Greek, and are
expressive, in some degree, of the nature of the process. We shall, however,
make use of the term Daguerreotype, derived from the name of the inventor.

As it does not fall within our plan to give any minute descriptions of the
Daguerreotype process, we shall just give a few general hints in reference to
it, referring those who wish for particular details, to the separate treatises
which have been published respecting it. The first thing necessary to be
attended to in this art is, the preparation of the plate on which the drawing is
to be made. The plate consists of a thin leaf of copper, plated with silver;
both metals together, not being thicker than a card. The object of the copper
is simply to support the silver, which must be the purest that can be
procured. But though the copper should be no thicker than to serve the
purpose of support, it is necessary that it should be so thick as to prevent the
plate from being warped, which would produce a distortion of the images
traced upon it. This plate must be polished;—and for this purpose, the
following articles are required—a phial of olive oil—some very fine cotton
—pumice-powder, ground till it is almost impalpable, and tied up in a piece
of fine muslin, thin enough to let the powder pass through without touching
the plate when the bag is shaken. A little nitric acid diluted with sixteen
times, by measure, its own quantity of water—a frame of wire on which to
place the plate, when being heated—a spirit lamp to make the plate hot—a
small box with inclined sides within, and having a lid to shut it up close—
and a square board large enough to hold the drawing, and having catches at
the side to keep it steady.

To the above prerequisites, a good Camera Obscura is, of course,
essentially necessary. This instrument should be large enough to admit the
plate of the largest drawing intended to be taken. The lens which forms the
image of the object, should, if possible, be achromatic, and of a
considerable diameter. In an excellent instrument of this description, now
before me, the lens is an achromatic, about 3 inches diameter, but capable
of being contracted to a smaller aperture. Its focal distance is about 17
inches; and the box, exclusive of the tube which contains the lens, is 15
inches long, 13½ inches broad, and 11 inches deep. It forms a beautiful and
well-defined picture of every well-enlightened object to which it is directed.

Before the plate is placed in the camera, there are certain operations to be
performed. 1. The surface of the plate should be made perfectly smooth, or
highly polished. For this purpose, it must be laid flat, with the silver side
upwards, upon several folds of paper for a bedding; and having been well
polished in the usual way, the surface must be powdered equally and
carefully with fine pumice enclosed in the muslin bag. Then taking a little
cotton wool, dipped in olive oil, it must be rubbed over the plate with
rounding strokes, and then crossing them by others which commence at
right angles with the first. This process must be repeated frequently,
changing the cotton, and renewing the pumice powder every time. A small
portion of cotton must now be moistened with the diluted nitric acid, and
applied equally to the whole surface. The next thing to be done is to make
the plate thoroughly and equally hot, by holding the plate with a pair of
pincers, by the corner, over a charcoal fire, and when the plate is
sufficiently hot, a white coating will be observed on the silver, which
indicates that that part of the operation is finished. An even cold surface is
next wanted, such as a metallic plate cooled almost to the freezing point by
muriate of soda, and to this the heated plate must be suddenly transferred.

2. The next operation is to give the plate a coating of Iodine. This is
accomplished by fixing the plate upon a board, and then putting it into a
box containing a little dish with iodine divided into small pieces, with its
face downward, and supported with small brackets at the corners. In this
position, the plate must remain till it assume a full gold colour, through the
condensation of the iodine on its surface—which process should be
conducted in a darkened apartment. The requisite time for the condensation

of the iodine varies from five minutes to half an hour. When this process is
satisfactorily accomplished, the plate should be immediately fixed in a
frame with catches and bands, and placed in the Camera; and the
transference from one receptacle to another should be made as quickly as
possible, and with only so much light as will enable the operator to see what
he is doing.

3. The next operation is to obtain the drawing. Having placed the Camera in
front of the scene to be represented, and the lens being adjusted to the
proper focus, the ground-glass of the Camera is withdrawn, and the
prepared plate is substituted for it; and the whole is left till the natural
images are drawn by the natural light from the object. The time necessary to
leave the plate for a complete delineation of the objects, depends upon the
intensity of the light. Objects in the shade will require more time for their
delineation than those in the broad light. The full clear light of the south of
Europe, Spain, Italy, and particularly, the more glowing brilliancy of
tropical countries, will effect the object much more speedily than the duller
luminosity of a northern clime. Some hours of the day are likewise more
favourable than others. Daguerre states, that ‘the most favourable, is from 7
A.M. to 3 o’clock P.M., and that a drawing could be effected in Paris in 3 or 4
minutes, in June and July, which would require 5 or 6, in May and August,
and 7 or 8 in April and September.’ In the progress of this art, at the present
time, portraits and other objects are frequently delineated in the course of a
few seconds.

4. Immediately after removing the plate from the Camera, it is next placed
over the vapour of mercury, which is placed in a cup at the bottom of a box,
and a spirit lamp applied to its bottom, till the temperature rise to 140 of
Fahrenheit. This process is intended to bring out the image, which is not
visible when withdrawn from the Camera; but in the course of a few
minutes a faint tracery will begin to appear, and in a very short time the
figure will be clearly developed.

5. The next operation is to fix the impression. In order to this, the coating on
which the design was impressed must be removed, to preserve it from being
decomposed by the rays of light. For this purpose, the plate is placed in a
trough containing common water, plunging, and withdrawing it

immediately, and then plunging it into a solution of salt and water, till the
yellow coating has disappeared.

Such is a very brief sketch of the photogenic processes of Daguerre. Other
substances, however, more easily prepared, have been recommended by Mr.
Talbot, F.R.S., who appears, about the same time, to have invented a
process somewhat similar to that of Daguerre. The following are his
directions for the preparation of Photogenic Paper.

The paper is to be dipped into a solution of salt in water, in the proportion
of half an ounce of salt to half a pint of water. Let the superfluous moisture
drain off, and then, laying the paper upon a clean cloth, dab it gently with a
napkin, so as to prevent the salt collecting in one spot more than another.
The paper is then to be pinned down by two of its corners on a drawing
board, by means of common pins, and one side washed or wetted with the
Photogenic fluid, using the brush prepared for that purpose, and taking care
to distribute it equally. Next dry the paper as rapidly as you can at the fire,
and it will be fit for use for most purposes. If, when the paper is exposed to
the sun’s rays, it should assume an irregular tint, a very thin extra wash of
the fluid will render the colour uniform, and at the same time somewhat
darker. Should it be required to make a more sensitive description of paper,
after the first application of the fluid, the solution of salt should be applied,
and the paper dried at the fire. Apply a second wash of the fluid, and dry it
at the fire again: employ the salt a third time, dry it,—and one application
more of the fluid will, when dried, have made the paper extremely sensitive.
When slips of such papers, differently prepared, are exposed to the action of
day light, those which are soonest affected by the light, by becoming dark,
are the best prepared.

When photogenic drawings are finished in a perfect way, the designs then
taken on the plate or paper are exceedingly beautiful and correct, and will
bear to be inspected with a considerable magnifying power, so that the most
minute portions of the objects delineated may be distinctly perceived. We
have seen portraits, finished in this way by a London artist, with an
accuracy which the best miniature painter could never attempt—every
feature being so distinct, as to bear being viewed with a deep magnifier.
And in landscapes and buildings, such is the delicacy and accuracy of such

representations, that the marks of the chisel and the crevices in the stones
may frequently be seen by applying a magnifying lens to the picture; so that
we may justly exclaim, in the words of the Poet: ‘Who can paint like
nature!.’ That LIGHT—which is the first-born of Deity, which pervades all
space, and illuminates all worlds—in the twinkling of an eye, and with an
accuracy which no art can imitate, depicts every object in its exact form and
proportions, superior to every thing that human genius can produce.

The Photogenic art, in its progress, will doubtless be productive of many
highly interesting and beneficial effects. It affords us the power of
representing, by an accurate and rapid process, all the grand and beautiful
objects connected with our globe—the landscapes peculiar to every country
—the lofty ranges of mountains which distinguish Alpine regions—the
noble edifices which art has reared—the monumental remains of antiquity
—and every other object which it would be interesting for human beings to
contemplate; so that in the course of time, the general scenery of our world,
in its prominent parts, might be exhibited to almost every eye. The
commission of the French Chambers, when referring to this art, has the
following remark, ‘To copy the millions upon millions of hieroglyphics
which cover even the exterior of the great monuments of Thebes and
Memphis, of Carnac, &c., would require scores of years and legions of
designers. By the assistance of the Daguerreotype, a single man could finish
that immense work.’—This instrument lays down objects, which the visual
organs of man would overlook, or might be unable to perceive, with the
same minuteness and nicety, that it delineates the most prominent features
of a landscape. The time-stained excrescences on a tree, the blades of grass,
the leaf of a rose, the neglected weed, the moss on the summit of a lofty
tower, and similar objects, are traced with the same accuracy as the larger
objects in the surrounding scene.

It is not improbable, likewise, that this art (still in its infancy) when it
approximates to perfection, may enable us to take representations of the
sublime objects in the heavens. The sun affords sufficient light for this
purpose; and there appears no insurmountable obstacle in taking, in this
way, a highly magnified picture of that luminary, which shall be capable of
being again magnified by a powerful microscope. It is by no means
improbable, from experiments that have hitherto been made, that we may

obtain an accurate delineation of the lunar world from the moon herself.
The plated disks prepared by Daguerre receive impressions from the action
of the lunar rays to such an extent as permits the hope that photographic
charts of the moon may soon be obtained; and, if so, they will excel in
accuracy all the delineations of this orb that have hitherto been obtained;
and if they should bear a microscopic power, objects may be perceived on
the lunar surface which have hitherto been invisible. Nor is it impossible
that the planets Venus, Mars, Jupiter and Saturn, may be delineated in this
way, and objects discovered which cannot be descried by means of the
telescope. It might perhaps be considered as beyond the bounds of
probability to expect that even distant Nebulæ, might thus be fixed, and a
delineation of their objects produced which shall be capable of being
magnified by microscopes. But we ought to consider that the art is yet only
in its infancy—that plates of a more delicate nature than those hitherto used,
may yet be prepared, and that other properties of light may yet be
discovered, which shall facilitate such designs. For, we ought now to set no
boundaries to the discoveries of science, and to the practical applications of
scientific discovery which genius and art may accomplish.

In short, this invention leads to the conclusion, that we have not yet
discovered all the wonderful properties of that Luminous Agent which
pervades the universe, and which unveils to us its beauties and sublimities
—and that thousands of admirable objects and agencies may yet be
disclosed to our view through the medium of light, as philosophical
investigators advance in their researches and discoveries. In the present
instance, as well as in many others, it evidently appears, that the Creator
intends, in the course of his providence, by means of scientific researches,
gradually to open to the view of the inhabitants of our world the wonders,
the beauties and the sublimities of his vast creation, to manifest his infinite
wisdom, and his superabundant goodness, and to raise our souls to the
contemplation and the love of Him who is the original source of all that is
glorious and beneficent in the scene of nature.

CHAPTER III.

ON THE OPTICAL ANGLE, AND THE APPARENT MAGNITUDE OF
OBJECTS.

In order to understand the principle on which telescopes represent distant
objects as magnified, it may be expedient to explain what is meant by the
angle of vision, and the apparent magnitudes under which different objects
appear, and the same object, when placed at different distances.

figure 40*.

The optical angle is the angle contained under two right lines drawn from
the extreme points of an object to the eye. Thus AEB or CED (fig. 40*.) is
the optical or visual angle, or the angle under which the object AB or CD,
appears to the eye at E. These two objects, being at different distances, are
seen under the same angle, although CD is evidently larger than AB. On the
retina of the eye, their images are exactly of the same size, and so is the still
larger object FG.

figure 41.

The apparent magnitude of objects denotes their magnitude as they appear
to us, in contradistinction from their real or true magnitude, and it is
measured by the visual angle; for whatever objects are seen under the same
or equal angles appear equal, however different their real magnitudes. If a
half-crown or half-dollar be placed at about 120 yards from the eye, it is
just perceptible as a visible point, and its apparent magnitude, or the angle
under which it is seen, is very small. At the distance of thirty or forty yards,
its bulk appears sensibly increased, and we perceive it to be a round body;
at the distance of six or eight yards, we can see the king or queen’s head
engraved upon it; and at the distance of eight or ten inches from the eye it
will appear so large, that it will seem to cover a large building placed within
the distance of a quarter of a mile, in other words, the apparent magnitude
of the half-crown held at such a distance, will more than equal that of such
a building, in the picture on the retina, owing to the increase of the optical
angle. If we suppose A (fig. 41.) to represent the apparent size of the half-
crown at nine yards distance, then we say it is seen under the small angle
FED. B will represent its apparent magnitude at 4½ yards distant under the
angle HEG, and the circle C, its apparent magnitude at 3 yards distant,
under the large angle KEI.

figure 42.

This may be otherwise illustrated by the following figure. Let AB (fig. 42.)
be an object viewed directly by the eye QR. From each extremity A and B
draw the lines AN,BM, intersecting each other in the crystalline humour in
I: then is AIB the optical angle which is the measure of the apparent
magnitude or length of the object AB. From an inspection of this figure, it
will evidently appear that the apparent magnitudes of objects will vary
according to their distances. Thus AB, CD, EF, the real magnitudes of
which are unequal, may be situated at such distances from the eye, as to
have their apparent magnitudes all equal, and occupying the same space on
the retina MN, as here represented. In like manner, objects of equal
magnitude, placed at unequal distances, will appear unequal. The objects
AB and GH which are equal, being situated at different distances from the
eye, GH will appear under the large angle TIV, or as large as an object TV,
situated at the same place as the object AB, while AB appears under the
smaller angle AIB. Therefore the object GH is apparently greater than the
object AB, though it is only equal to it. Hence it appears that we have no
certain standard of the true magnitude of objects, by our visual perception
abstractly considered, but only of the proportions of magnitude.

In reference to apparent magnitudes, we scarcely ever judge any object to
be so great or so small as it appears to be, or that there is so great a disparity
in the visible magnitude of two equal bodies at different distances from the
eye. Thus, for example, suppose two men, each six feet 3 inches high, to
stand directly before us, one at the distance of a pole, or 5½ yards, and the

other at the distance of 100 poles, or 550 yards—we should observe a
considerable difference in their apparent size, but we should scarcely
suppose, at first sight, that the one nearest the eye appeared a hundred times
greater than the other, or that, while the nearest one appeared 6 feet 3 inches
high, the remote one appeared only about three fourths of an inch. Yet such
is in reality the case; and not only so, but the visible bulk or area of the one
is to that of the other, as the square of these numbers, namely as 10,000 to
1; the man nearest us presenting to the eye a magnitude or surface ten
thousand times greater than that of the other. Again, suppose two chairs
standing in a large room, the one 21 feet distance from us, and the other 3
feet—the one nearest us will appear 7 times larger both in length and
breadth, than the more distant one, and consequently, its visible area 49
times greater. If I hold up my finger at 9 inches distant from my eye, it
seems to cover a large town a mile and a half in extent, situated at 3 miles
distant; consequently, the apparent magnitude of my finger, at 9 inches
distant from the organ of vision, is greater than that of the large town at 3
miles distance, and forms a larger picture on the retina of the eye. When I
stand at the distance of a foot from my window, and look through one of the
panes to a village less than a quarter of a mile distant, I see, through that
pane, nearly the whole extent of the village, comprehending two or three
hundred houses; consequently, the apparent magnitude of the pane is equal
to nearly the extent of the village, and all the buildings it contains do not
appear larger than the pane of glass in the window, otherwise, the houses
and other objects which compose the village could not be seen through that
single pane. For, if we suppose a line drawn from one end of the village,
passing through the one side of the pane, and another line drawn from the
other end, and passing through the other side of the pane to the eye, these
lines would form the optical angle under which the pane of glass and the
village appears. If the pane of glass be fourteen inches broad, and the length
of the village 2640 yards, or half a mile—this last lineal extent is 6,788
times greater than the other, and yet they have the same apparent magnitude
in the case supposed.

Hence we may learn the absurdity and futility of attempting to describe the
extent of spaces in the heavens, by saying, that a certain phenomenon was
two or three feet or yards distant from another, or that the tail of a comet
appeared several yards in length. Such representations can convey no

definite ideas in relation to such magnitudes, unless it be specified at what
distance from the eye, the foot or yard is supposed to be placed. If a rod, a
yard in length, be held at nine inches from the eye, it will subtend an angle,
or cover a space in the heavens, equal to more than one fourth of the
circumference of the sky, or about one hundred degrees. If it be eighteen
inches from the eye, it will cover a space equal to fifty degrees; if at three
feet, twenty-five degrees, and so on in proportion to the distance from the
eye; so that we can form no correct conceptions of apparent spaces or
distances in the heavens, when we are merely told that two stars, for
example, appear to be three yards distant from each other. The only definite
measure we can use, in such cases, is that of degrees. The sun and moon are
about half a degree in apparent diameter, and the distance between the
extreme stars in Orion’s belt, three degrees, which measures being made
familiar to the eye, may be applied to other spaces of the heavens, and an
approximate idea conveyed of the relative distances of objects in the sky.

From what has been stated above, it is evident that the magnitude of objects
may be considered in different points of view. The true dimensions of an
object, considered in itself, give what is called its real or absolute
magnitude; and the opening of the visual angle determines the apparent
magnitude. The real magnitude, therefore, is a constant quantity; but the
apparent magnitude varies continually with the distance, real or imaginary;
and therefore, if we always judged of the dimensions of an object from its
apparent magnitude, every thing around us would, in this respect, be
undergoing very sensible variations, which might lead us into strange and
serious mistakes. A fly, near enough to the eye, might appear under an angle
as great as an elephant at the distance of twenty feet, and the one be
mistaken for the other. A giant eight feet high, seen at the distance of
twenty-four feet, would not appear taller than a child two feet in height, at
the distance of six feet; for both would be seen nearly under the same angle.
But our experience generally prevents us from being deceived by such
illusions. By the help of touch, and by making allowance for the different
distances at which we see particular objects, we learn to correct the ideas
we might otherwise form from attending to the optical angle alone,
especially in the case of objects that are near us. By the sense of touch we
acquire an impression of the distance of an object; this impression combines
itself with that of the apparent magnitude, so that the impression which

represents to us the real magnitude is the product of these two elements.
When the objects, however, are at a great distance, it is more difficult to
form a correct estimate of their true magnitudes. The visual angles are so
small, that they prevent comparison; and the estimated bulks of the objects
depend in a great measure upon the apparent magnitudes; and thus an
object situated at a great distance, appears to us much smaller than it is in
reality. We also estimate objects to be nearer or farther distant according as
they are more or less clear, and our perception of them more or less distinct
and well defined; and likewise, when several objects intervene between us
and the object we are particularly observing. We make a sort of addition of
all the estimated distances of intermediate objects, in order to form a total
distance of the remote object, which in this case appears to be farther off
than if the intervening space were unoccupied. It is generally estimated that
no terrestrial object can be distinctly perceived, if the visual angle it
subtends be less than one minute of a degree; and that most objects become
indistinct, when the angle they subtend at the pupil of the eye is less than
six minutes.

We have deemed it expedient to introduce the above remarks on the
apparent magnitude of objects, because the principal use of a telescope is to
increase the angle of vision, or to represent objects under a larger angle than
that under which they appear to the naked eye, so as to render the view of
distant objects more distinct, and to exhibit to the organ of vision those
objects which would otherwise be invisible. A telescope may be said to
enlarge an object just as many times as the angle under which the
instrument represents it, is greater than that under which it appears to the
unassisted eye. Thus the moon appears to the naked eye under an angle of
about half a degree; consequently a telescope magnifies 60 times if it
represents that orb under an angle of 30 degrees; and if it magnified 180
times, it would exhibit the moon under an angle of 90 degrees, which would
make her appear to fill half of the visible heavens, or the space which
intervenes from the horizon to the zenith.

CHAPTER IV.

ON THE DIFFERENT KINDS OF REFRACTING TELESCOPES.

There are two kinds of telescopes, corresponding to two modes of vision,
namely, those which perform their office by refraction through lenses, and
those which magnify distant objects by reflection from mirrors. The
telescope which is constructed with lenses, produces its effects solely by
refracted light, and is called a Dioptric, or refracting telescope. The other
kind of telescope produces its effects partly by reflection, and partly by
refraction, and is composed both of mirrors and lenses; but the mirrors form
the principal part of the telescope; and therefore such instruments are
denominated reflecting telescopes. In this chapter I shall describe the
various kinds of refracting telescopes.

SECT 1.—THE GALILEAN TELESCOPE.

This telescope is named after the celebrated Galileo, who first constructed,
and probably invented it in the year 1609. It consists of only two glasses, a
convex glass next the object, and a concave next the eye. The convex is
called the object-glass, and the concave to which the eye is applied, is
called the eye-glass. Let C (fig. 43.) represent the convex object-glass,
presented to any object in the direction DEI, so that the rays fall parallel
upon it;—if these rays, after passing through it, were not intercepted by the
concave lens K, they would pass on, and cross each other in the focus F,
where an inverted image of the object would be formed. But the concave
lens K, the virtual focus of which is at F, being interposed, the rays are not
suffered to converge to that point, but are made less convergent,19 and enter
the pupil almost parallel, as GH, and are converged by the humours of the
eye to their proper foci on the retina. The object, through this telescope, is
seen upright, or in its natural position, because the rays are not suffered to
come to a focus, so as to form an inverted picture. The concave eye-glass is
placed as far within the focus of the object-glass, as is equal to its own
virtual focus; and the magnifying power is as the focal length of the object-

glass to that of the eye-glass, that is, as CF to BF. Thus, suppose the focus
of the object-glass to be 10 inches, and the focus of the eye-glass to be 1
inch, the magnifying power will be 10 times—which is always found by
dividing the focal length of the object-glass by that of the eye-glass. The
interval between the two glasses, in this case, will be 9 inches, which is the
length of the telescope, and the objects seen through it will appear under an
angle ten times greater than they do to the naked eye. These propositions
might be proved mathematically; but the process is somewhat tedious and
intricate, and might not fully be understood by general readers. I shall
therefore only mention some of the general properties of this telescope,
which is now seldom used, except for the purpose of opera-glasses.

figure 43

1. The focal distance of the object-glass must be greater than that of the
eye-glass, otherwise it would not magnify an object: if the focal distance of
the eye-glass were greater than that of the object-glass, it would diminish
objects, instead of magnifying them. 2. The visible area of the object is
greater, the nearer the eye is to the glass; and it depends on the diameter of
the pupil of the eye, and on the breadth of the object-glass; consequently the
field of view in this telescope is very small. 3. The distinctness of vision in
this construction of a telescope exceeds that of almost any other. This arises
from the rays of light proceeding from the object directly through the
lenses, without crossing or intersecting each other; whereas in the
combination of convex lenses, they intersect one another to form an image
in the focus of the object-glass, and this image is magnified by the eye-glass
with all its imperfections and distortions. The thinness of the centre of the
concave lens also contributes to distinctness. 4. Although the field of view
in this telescope is very small, yet where no other telescope can be

procured, it might be made of such a length as to show the spots on the Sun,
the crescent of Venus, the satellites of Jupiter, and the ring of Saturn; and,
requiring only two glasses, it is the cheapest of all telescopes. It has been
found that an object-lens 5 feet focal distance, will bear a concave eye-glass
of only 1 inch focal distance, and will consequently magnify the diameters
of the planets 60 times, and their surfaces 3600 times, which is sufficient to
show the phenomena now stated. And, although only a small portion of the
sun and moon can be seen at once, yet Jupiter and all his satellites may
sometimes be seen at one view; but there is some difficulty in finding
objects with such telescopes. 5. Opera-glasses, which are always of this
construction, have the object-lens generally about 6 inches focus and 1 inch
diameter, with a concave eye-glass of about 2 inches focus. These glasses
magnify about 3 times in diameter, have a pretty large field, and produce
very distinct vision. When adjusted to the eye, they are about 4 inches in
length. To the object end of an opera-glass there is sometimes attached a
plane mirror, placed at an angle of 45 degrees, for the purpose of viewing
objects on either side of us. By this means, in a theatre or assembly, we can
take a view of any person without his having the least suspicion of it, as the
glass is directed in quite a different direction. The instrument with this
appendage is sometimes called a Polemoscope.

SECT. 2.—THE COMMON ASTRONOMICAL REFRACTING
TELESCOPE.

The astronomical telescope is the most simple construction of a telescope,
composed of convex lenses only, of which there are but two essentially
necessary, though a third is sometimes added to the eye-piece for the
purpose of enlarging the field of view. Its construction will be easily
understood from a description of the following figure. Its two essential parts
are, an object-glass AD, and an eye-glass EY, so combined in a tube that the
focus F of the object-glass is exactly coincident with the focus of the eye-
glass. Let OB (fig. 44.) represent a distant object, from which rays nearly
parallel proceed to the object-lens AD. The rays passing through this lens
will cross at F, and form an image of the object at IM. This image forms as
it were an object to the eye-glass EY, which is of a short focal distance, and
the eye is thus enabled to contemplate the object as if it were brought much

nearer than it is in reality. For the rays, which after crossing proceed in a
divergent state, fall upon the lens EY, as if they proceeded from a real
object situated at F. All that is effected therefore, by such a telescope is, to
form an image of a distant object by means of the object-lens, and then to
give the eye such assistance as is necessary for viewing that image as near
as possible, so that the angle it shall subtend at the eye shall be very large
compared with the angle which the object itself would subtend in the same
situation.

figure 44.

Here it may be expedient to explain, 1. how this arrangement of glasses
shows distant objects distinctly, and 2. the reason why objects appear
magnified when seen through it. As to the first particular, it may be proved
as follows:—The rays OA and BD, which are parallel before they fall upon
the object-glass, are by this glass refracted and united at its focus: In order,
then, to distinct vision, the eye-glass must re-establish the parallelism of the
rays,—which is effected by placing the eye-glass so that its focus may be at
F, and consequently the rays will proceed from it parallel to each other and
fall upon the eye in that direction. For distinct vision is produced by
parallel rays. 2. The reason why the object appears magnified will appear, if
we consider that, if the eye viewed the object from the centre of the object-
glass, it would see it under the angle OCB; let OC and BC then be produced
to the focus of the glass, they will then limit the image IM formed in the
focus. If then, two parallel rays are supposed to proceed to the eye-glass EY,
they will be converged to its focus H, and the eye will see the image under
the angle EHY. The apparent magnitude of the object, therefore, as seen by
the naked eye, is to the magnitude of the image as seen through the
telescope, as OCB to EHY, or as the distance CF to the distance FG, in
other words, as the focal length of the object-glass to that of the eye-glass.

It is obvious from the figure, that, through this telescope, all objects will
appear inverted; since the object OB is depicted by the object-glass in an
inverted position at IM, and in this position is viewed by the eye-glass EY;
and, therefore this kind of telescope is not well adapted for viewing
terrestrial objects, since it exhibits the tops of trees, houses, and other
objects as undermost, and the heads of people as pointing downwards. But
this circumstance is of no consequence with respect to the heavenly bodies,
since they are round, and it can make little difference to an observer which
side of a globular body appears uppermost or undermost. All astronomical
refracting telescopes invert objects; but they are preferred to any other
telescopes, because they have few glasses, and consequently more light.
This telescope however, can be transformed into a common day telescope
for land objects, by the addition of two other eye-glasses, as we shall
afterwards explain; but in this case a quantity of light is lost by refraction at
each lens; for there is scarcely any transparent substance that transmits all
the rays of light that fall upon it.

The magnifying power of this telescope is found by dividing the focal
distance of the object-glass by the focal distance of the eye-glass: the
quotient gives the magnifying power, or the number of times that the object
seen through the telescope, appears larger or nearer than to the naked eye.
Thus, for example, if the focal distance of the object-glass be 28 inches, and
the focal distance of the eye-glass 1 inch, the magnifying power will be 28
times. If we would enlarge the telescope and select an object-glass 10 feet,
or 120 inches focus, an eye-glass of 2 inches focal length might be applied,
and then the diameter of objects would be magnified 60 times, and their
surfaces 3600 times. If we would use an object-glass of 100 feet, it would
be necessary to select an eye-glass about 6 inches focus, and the magnifying
power would be 200 times, equal to 1200 inches divided by 6. Since, then,
the power of magnifying depends on the proportion of the focal length of
the object and eye-glasses, and this proportion may be varied to any degree,
it may seem strange to some that a short telescope of this kind will not
answer that purpose as well as a long one. For instance, it may be asked
why an object-glass of 10 feet focus, may not be made to magnify as much,
as one of 100 feet focal length, by using an eye-glass of half an inch focus,
in which case, the magnifying power would be 240 times? But it is to be
considered, that if the power of magnifying be increased, while the length

of the telescope remains the same, it is necessary to diminish the focal
length of the eye-glass in the same proportion, and this cannot be done on
account of the great distortion and colouring which would then appear in
the image, arising both from the deep convexity of the lens and the different
refrangibility of the rays of light. It is found that the length of common
refracting telescopes must be increased in proportion to the square of the
increase of their magnifying power; so that in order to magnify twice as
much as before, with the same light and distinctness, the telescope must be
lengthened four times; to magnify 3 times as much, 9 times; and to magnify
four times as much, sixteen times; that is—suppose a telescope of 3 feet to
magnify 33 times,—in order to procure a power four times as great, or 132
times, we must extend the telescope to the length of 48 feet, or 16 times the
length of the other. Much likewise depends upon the breadth or aperture of
the object-glass. If it be too small, there will not be sufficient light to
illuminate the object; and if it be too large, the redundance of light will
produce confusion in the image.

The following table, constructed originally by Huygens, and which I have
re-calculated and corrected, shows the linear aperture, the focal distance of
the eye-glass, and the magnifying power of astronomical telescopes of
different lengths, which may serve as a guide to those who wish to construct
telescopes of this description.

Focal distance
Linear aperture of Focal distance of Magnifying
of the object-
the object-glass. the eye-glass. power.
glass.

Feet. Inch. Dec. Inch. Dec.
1 0. 545 0. 605 20
2 0. 76 0. 84 20.5
3 0. 94 1. 04 34.6
4 1. 08 1. 18 40
5 1. 21 1. 33 45
6 1. 32 1. 45 50
7 1. 43 1. 58 53

8 1. 53 1. 69 56.8
9 1. 62 1. 78 60.6
10 1. 71 1. 88 63.8
15 2. 10 2. 30 78
20 2. 43 2. 68 89.5
30 3. 00 3. 28 109
40 3. 43 3. 76 127
50 3. 84 4. 20 142
60 4. 20 4. 60 156
70 4. 55 5. 00 168
80 4. 83 5. 35 179
90 5. 15 5. 65 190
100 5. 40 5. 95 200
120 5. 90 6. 52 220

In the above table, the first column expresses the focal length of the object-
glass in feet; the second column, the diameter of the aperture20 of the object-
glass, the third column, the focal distance of the eye-glass, and the fourth,
the magnifying power, which is found by reducing the feet in the first
column to inches, and dividing by the numbers in the third column. From
this table it appears that, in order to obtain a magnifying power of 168
times, by this kind of telescope, it is requisite to have an object-glass of 70
feet focal distance, and an eye-glass five inches focus, and that the aperture
of the object-glass ought not to be more than about 4½ inches diameter. To
obtain a power of 220 times requires a length of 120 feet.

The following is a summary view of the properties of this telescope. 1. The
object is always inverted. 2. The magnifying power is always in the
proportion of the focal distance of the object-glass to the eye-glass. 3. As
the rays emerging from the eye-glass, should be rendered parallel for every
eye, there is a small sliding tube next the eye, which should be pushed out
or in till the object appears distinct. When objects are pretty near, this tube
requires to be pulled out a little. These circumstances require to be attended
to in all telescopes. 4. The apparent magnitude of an object is the same
wherever the eye be placed, but the visible area, or field of view, is the
greatest when the eye is nearly at the focal distance of the eye-glass. 5. The

visual angle depends on the breadth of the eye-glass; for it is equal to the
angle which the eye-glass subtends at the object-glass; but the breadth of
the eye-glass cannot be increased beyond a certain limit, without producing
colouring and distortion.

If the general principles on which this telescope is constructed be
thoroughly understood, it will be quite easy for the reader to understand the
construction of all the other kinds of telescopes, whether refracting or
reflecting. A small astronomical telescope can be constructed in a few
moments, provided one has at hand the following lenses:—1. A common
reading-glass, eight or ten inches focal distance; 2. A common magnifying
lens, such as watchmakers or botanists use, of about 1½ or 2 inches focus.
Hold the reading-glass—suppose of ten inches focus—in the left hand
opposite any object, and the magnifying lens of two inches focus, in the
right hand near the eye, at twelve inches distance from the other in a direct
line, and a telescope is formed which magnifies five times. I have
frequently used this plan, when travelling, when no other telescope was at
hand.

SECT. 3.—THE AERIAL TELESCOPE.

The Aerial is a refracting telescope of the kind we have now described,
intended to be used without a tube in a dark night; for the use of a tube is
not only to direct the glasses, but to make the place dark where the images
are formed. It appears from the preceding table inserted above, that we
cannot obtain a high magnifying power, with the common astronomical
telescope, without making it of an extreme length, in which case the glasses
are not manageable in tubes—which are either too slight and apt to bend, or
too heavy and unwieldy if made of wood, iron or other strong materials.
The astronomers of the seventeenth century, feeling such inconveniences in
making celestial observations with long tubes, contrived a method of using
the glasses without tubes. Hartsocker, an eminent optician, contrived to fix
them at the top of a tree, a high wall, or the roof of a house; but the
celebrated Huygens, who was not only an astronomer, but also an excellent
mechanic, made considerable improvements in the method of using an
object-glass without a tube. He placed it at the top of a very long pole,
having previously enclosed it in a short tube, which was made to turn in all

directions by means of a ball and socket. The axis of this tube he could
command with a fine silken string, so as to bring it into a line with the axis
of another short tube which he held in his hand, and which contained the
eye-glass. The following is a more particular description of one of these
telescopes. On the top of a long pole or mast ab (fig. 45), is fixed a board
moveable up and down in the channel cd: e is a perpendicular arm fixed to
it, and ff is a transverse board that supports the object glass enclosed in the
tube i, which is raised or lowered by means of the silk cord rl; gg is an
endless rope with a weight h, by which the apparatus of the object-glass is
counterpoised; kl is a stick fastened to the tube i; m the ball and socket, by
means of which the object-glass is moveable every way: and to keep it
steady, there is a weight n suspended by a wire; l is a short wire to which
the thread rl is tied; o is the tube which holds the eye-glass; q the stick fixed
to this tube, s a leaden bullet, and t a spool to wind the thread on; u is pins
for the thread to pass through; x the rest for the observer to lean upon, and y
the lantern. Fig. 46 is an apparatus contrived by M. de la Hire for managing
the object-glass; but which it would be too tedious particularly to describe.
To keep off the dew from the object-glass, it was sometimes included in a
pasteboard tube, made of spongy paper, to absorb the humidity of the air.
And to find an object more readily, a broad annulus of white pasteboard
was put over the tube that carried the eye-glass; upon which the image of
the object being painted, an assistant who perceived it, might direct the tube
of the eye-glass into its place.

figure 45.

fig 46.

Such was the construction of the telescopes with which Hevelius, Huygens,
Cassini, and other eminent astronomers of the seventeenth century made
their principal discoveries. With such telescopes, Huygens discovered the
fourth satellite of Saturn, and determined that this planet was surrounded
with a ring; and with the same kind of instrument Cassini detected the first,
second, third, and fifth, satellites of Saturn, and made his other discoveries.
When the night was very dark, they were obliged to make the object-glass
visible, by means of a lantern so constructed as to throw the rays of light up
to it in a parallel direction. In making such observations, they must have

taken incredible pains, endured much cold and fatigue, and subjected
themselves to very great labour and expense—which almost makes us
wonder at the discoveries they were instrumental in bringing to light—and
should make modern philosophers sensible of the obligations they are under
to such men as Newton and Dollond, through whose inventions such
unwieldy instruments are no longer necessary. Telescopes of the description
now stated were made of all sizes, from 30 to above 120 feet in length.
Divini at Rome, and Campani at Bologna, were famed as makers of the
object-glasses of the long focal distance to which we have alluded, who sold
them for a great price, and took every method to keep the art of making them
a secret. It was with telescopes made by Campani, that Cassini made his
discoveries. They were made by the express order of Louis XIV, and were of
86, 100, and 136 Paris feet in focal length. M. Auzout made one object-glass
of 600 feet focus; but he was never able to manage it, so as to make any
practical observations with it. Hartsocker is said to have made some of a still
greater focal length. The famous aerial telescope of Huygens was 123 feet in
focal length, with six inches of aperture. At his death, he bequeathed it to the
Royal Society of London, in whose possession it still remains. It required a
pole of more than a hundred feet high, on which to place the object-glass for
general observations. It was with this glass, that Dr. Derham made the
observations to which he alludes in his preface to his ‘Astro-Theology.’
When this glass was in the possession of Mr. Cavendish, it was compared
with one of Mr. Dollond’s forty-six inch treble object-glass Achromatics,
and the gentlemen who were present at the trial, said that ‘the Dwarf was
fairly a match for the Giant.’ It magnified 218 times, and the trouble of
managing it, was said to be extremely tiresome and laborious.

SECT. 4.—THE COMMON REFRACTING TELESCOPE FOR
TERRESTRIAL OBJECTS.

figure 47.

This telescope is constructed on the same principle as the astronomical
telescope already described, with the addition of two or three glasses. In fig.
47, OB represents a distant object, LN, the object glass, which forms the
image IM in its focus, which is, of course, in an inverted position, and, if the
eye were applied at the lens EE, the object would appear, exactly as through
the astronomical telescope, every object being apparently turned upside
down. To remedy this inconvenience, there are added two other glasses FF
and GG, by which a second image is formed from the first, in the same
position as the object. In order to effect this, the first of these two glasses,
namely FF, is placed at twice its focal distance from the former glass EE,
and the other lens GG, next the eye, is placed at the same distance from FF.
For all the three glasses are supposed to be of the same focal distance. Now,
the lens FF, being placed at twice the focal distance for parallel rays from
EE, receives the pencils of parallel rays after they have crossed each other at
X, and forms an image at i m similar to that at IM and equal to it, but
contrary in position, and consequently erect; which last image is viewed by
the lens GG, in the same manner as the first image IM would be viewed by
the lens EE. In this case, the image IM is considered as an object to the lens
FF of which it forms a picture in its focus, in a reverse position from that of
the first image, and of course, in the same position as the object.

The magnifying power of this telescope is determined precisely in the same
way as that of the astronomical telescope. Suppose the object-glass to be
thirty inches focal distance, and each of the eye-glasses 1½ inch focal
distance, the magnifying power is in the proportion of 30 to 1½, or 20 times,
and the instrument is, of course, considerably longer than an astronomical
telescope of the same power. The distance, in this case, between the object-
glass and the first eye-glass EE is 31½ inches; the distance between EE, and
the second glass FF, is 3 inches, and the distance between FF and the glass
GG next the eye, 3 inches; in all 37½ inches, the whole length of the
telescope. Although it is usual to make use of three eye-glasses in this
telescope, yet two will cause the object to appear erect, and of the same
magnitude. For suppose the middle lens FF taken away, if the first lens EE
be placed at X, which is double its focal distance from the image IM, it will
at the same distance X m, on the other side, form a secondary image i m
equal to the primary image IM, and also in a contrary position. But such a
combination of eye-glasses produces a great degree of colouring in the
image, and therefore is seldom used. Even the combination now described,

consisting of three lenses of equal focal distances, is now almost obsolete,
and has given place to a much better arrangement consisting of four glasses,
of different focal distances—which shall be afterwards described.

The following figures, 48, 49, 50 represent the manner in which the rays of
light are refracted through the glasses of the telescopes we have now
described. Fig. 48 represents the rays of light as they pass from the object to
the eye in the Galilean telescope. After passing in a parallel direction to the
object-glass, they are refracted by that glass, and undergo a slight
convergence in passing towards the concave eye-glass, where they enter the
eye in a parallel direction, but no image is formed previous to their entering
the eye, till they arrive at the retina. Fig. 49 represents the rays as they pass
through the glasses of the astronomical telescope. The rays, after entering
the object-glass, proceed in a converging direction, till they arrive at its
focus, about A, where an image of the object is formed; they then proceed
diverging to the eye-glass, where they are rendered parallel, and enter the
eye in that direction. Fig. 50 represents the rays as they converge and
diverge in passing through the four glasses of the common day-telescope
described above. After passing through the object-glass, they converge
towards B, where the first image is formed. They then diverge towards the
first eye-glass where they are rendered parallel; and passing through the
second eye-glass, they again converge and form a second image at C; from
which point they again diverge, and passing through the first eye-glass enter
the eye in a parallel direction. If the glasses of these telescopes were fixed
on long pieces of wood, at their proper distances from each other, and placed
in a darkened room, when the sun is shining, the beam of the sun’s light
would pass through them in the same manner as here represented.

fig. 48. fig. 49. fig. 50.

SECT. 5.—TELESCOPE FORMED BY A SINGLE LENS.

This is a species of telescope altogether unnoticed by optical writers, so far
as I know; nor has the property of a single lens in magnifying distant objects
been generally adverted to or recognised. It may not therefore be inexpedient
to state a few experiments which I have made in relation to this point. When
we hold a spectacle-glass of a pretty long focal distance—say, from 20 to 24
inches—close to the eye, and direct it to distant objects, they do not appear
sensibly magnified. But if we hold the glass about 12 or 16 inches from our
eye, we shall perceive a sensible degree of magnifying power, as if distant
objects were seen at less than half the distance at which they are placed. This
property of a spectacle-glass I happened to notice when a boy, and, on
different occasions since that period have made several experiments on the
subject, some of which I shall here relate.

With the object-glass of a common refracting telescope 4½ feet focal
distance, and 2½ inches diameter, I looked at distant objects—my eye being
at about 3½ feet from the lens, or about 10 or 12 inches within its focus—
and it produced nearly the same effect as a telescope which magnifies the
diameters of objects 5 or 6 times. With another lens 11 feet focal distance
and 4 inches diameter—standing from it at the distance of about 10 feet, I
obtain a magnifying power of about 12 or 14 times, which enables me to
read the letters on the sign-posts of a village half a mile distant. Having
some time ago procured a very large lens 26 feet focal distance, and 11½
inches diameter, I have tried with it various experiments of this kind upon
different objects. Standing at the distance of about 25 feet from it, I can see
distant objects through it magnified about 26 times in diameter, and
consequently 676 times in surface, and remarkably clear and distinct, so that
I can distinguish the hour and minute hands of a public clock in a village
two miles distant. This single lens, therefore answers the purpose of an
ordinary telescope with a power of 26 times. In making such experiments
our eye must always be within the focus of the lens, at least 8 or 10 inches.
The object will, indeed, be seen at any distance from the glass within this
limit; but the magnifying power is diminished in proportion as we approach
nearer to the glass. Different eyes, too, will require to place themselves at
different distances, so as to obtain the greatest degree of magnifying power
with distinctness, according as individuals are long or short-sighted.

This kind of telescope stands in no need of a tube, but only of a small
pedestal on which it may be placed on a table, nearly at the height of the eye,
and that it be capable of a motion in a perpendicular or parallel direction, to
bring it in a line with the eye and the object. The principle on which the
magnifying power, in this case, is produced, is materially the same as that on
which the performance of the Galilean telescope depends. The eye of the
observer serves instead of the concave lens in that instrument; and as the
concave lens is placed as much within the focus of the object-glass, as is
equal to its own focal distance, so the eye, in these experiments, must be
placed at least its focal distance within the focus of the lens with which we
are experimenting; and the magnifying power will be nearly in the
proportion of the focal distance of the lens to the focal distance of the eye.
If, for example, the focal distance of the eye, or the distance at which we see
to read distinctly, be 10 inches, and the focal distance of the lens, 11 feet, the
magnifying power will be as 11 feet, or 132 inches to 10, that is, about 13

times. Let A (fig. 51.) represent the lens placed on a pedestal; the rays of
light passing through this lens from distant objects will converge towards a
focus at F. If a person then, place his eye at E, a certain distance within the
focal point, he will see distant objects magnified nearly in the proportion of
the focal distance of the lens to that of the eye; and when the lens is very
broad—such as the 26 feet lens mentioned above—two or three persons may
look through it at once, though they will not all see the same object. I have
alluded above to a lens made by M. Azout of 600 feet focal distance. Were it
possible to use such a lens for distant objects, it might represent them as
magnified 5 or 600 times, without the application of any eye-glass. In this
way the aerial telescope of Huygens would magnify objects above 100
times, which is about half the magnifying power it produced with its eye-
piece. Suppose Azout’s lens had been fitted up as a telescope, it would not
have magnified above 480 times, as it would have required an eye-glass of
14 or 15 inches focal distance, whereas, without an eye-glass, it would have
magnified objects considerably above 500 times. It is not unlikely that the
species of telescope to which I have now adverted, constituted one of those
instruments for magnifying distant objects which were said to have been in
the possession of certain persons long before their invention in Holland, and
by Galileo in Italy—to which I have referred in p. 182. Were this kind of
telescope to be applied to the celestial bodies, it would require to be elevated
upon a pole in the manner represented, fig. 45, p. 226.

figure 51.

SECT. 6.—THE ACHROMATIC TELESCOPE.

This telescope constitutes the most important and useful improvement ever
made upon telescopic instruments; and, it is probable, it will, ere long,
supersede the use of all other telescopes. Its importance and utility will at
once appear when we consider, that a good achromatic telescope of only 4 or
5 feet in length will bear a magnifying power as great, as that of a common
astronomical telescope 100 feet long, and even with a greater degree of
distinctness, so that they are now come into general use both for terrestrial
and celestial observations. There are, indeed, certain obstructions which
prevent their being made of a very large size; but from the improvement in
the manufacture of achromatic glass which is now going forward, it is to be
hoped that the difficulties which have hitherto impeded the progress of
opticians will soon be removed. In order to understand the nature of this
telescope, it will be necessary to advert a little to the imperfections
connected with common refracting telescopes.

figure 52.

The first imperfection to which I allude is this, that spherical surfaces do not
refract the rays of light accurately to a point; and hence the image formed
by a single convex lens is not perfectly accurate and distinct. The rays which
pass near the extremities of such a lens meet in foci nearer to the lens than
those which pass nearly through the centre, which may be illustrated by the
following figure. Let PP (fig. 52) be a convex lens and Ee an object, the
point E of which corresponds with the axis, and sends forth the rays EM,
EN, EA, &c., all of which reach the surface of the glass, but in different

parts. It is manifest that the ray EA which passes through the middle of the
glass, suffers no refraction. The rays EM, EM, likewise, which pass through
near to EA, will be converged to a focus at F, which we generally consider
as the focus of the lens. But the rays EN, EN, which are nearer to the edge of
the glass will be differently refracted, and will meet about G, nearer to the
lens, where they will form another image Gg. Hence, it is evident, that the
first image Ff, is formed only by the union of those rays which pass very
near the centre of the lens; but as the rays of light proceeding from every
point of an object are very numerous, there is a succession of images
formed, according to the parts of the lens where they penetrate, which
necessarily produces indistinctness and confusion. This is the imperfection
which is distinguished by the name of spherical aberration, or the error
arising from the spherical form of lenses.

The second and most important imperfection of single lenses, when used for
the object-glasses of telescopes, is, that the rays of compounded light being
differently refrangible, come to their respective foci at different distances
from the glass; the more refrangible rays, as the violet, converging sooner
than those which are less refrangible, as the red. I have had occasion to
illustrate this circumstance, when treating on the colours produced by the
prism, (see p. 128, and figures 32 and 33,) and it is confirmed by the
experiment of a paper painted red, throwing its image, by means of a lens, at
a greater distance than another paper painted blue. From such facts and
experiments, it appears, that the image of a white object consists of an
indefinite number of coloured images, the violet being nearest, and the red
farthest from the lens, and the images of intermediate colours at intermediate
distances. The aggregate, or image itself, must therefore be in some degree
confused; and this confusion being much increased by the magnifying
power, it is found necessary to use an eye glass of a certain limited
convexity to a given object glass. Thus, an object glass of 34 inches focal
length will bear an eye-glass of only 1 inch focus, and will magnify the
diameters of objects 34 times; one of 50 feet focal distance will require an
eye-glass of 4½ inches focus, and will magnify only 142 times; whereas,
could we apply to it an eye-glass of only 1 inch focus, as in the former case,
it would magnify no less than 600 times. And were we to construct an
object-glass of 100 feet focal length, we should require to apply an eye-
glass, not less than 6 inches focus, which would produce a power of about

200 times; so that there is no possibility of producing a great power by
single lenses, without extending the telescope to an immoderate length.

Sir Isaac Newton, after having made his discoveries respecting the colours
of light, considered the circumstance we have now stated as an insuperable
barrier to the improvement of refracting telescopes; and therefore turned his
attention to the improvement of telescopes by reflection. In the telescopes
which he constructed and partly invented, the images of objects are formed
by reflection from speculums or mirrors; and being free from the irregular
convergency of the various coloured rays of light, will admit of a much
larger aperture and the application of a much greater degree of magnifying
power. The reflector which Newton constructed was only 6 inches long, but
it was capable of bearing a power equal to that of a 6 feet refractor. It was a
long time, however, after the invention of these telescopes before they were
made of a size fitted for making celestial observations. After reflecting
telescopes had been some time in use, Dollond made his famous discovery
of the principle which led him to the construction of the achromatic
telescope. This invention consists of a compound object glass formed of two
different kinds of glass, by which both the spherical aberration and the errors
arising from the different refrangibility of the rays of light are, in a great
measure corrected. For the explanation of the nature of this compound object
glass and of the effects it produces; it may be expedient to offer the
following remarks respecting the dispersion of light and its refraction by
different substances.

The dispersion of light is estimated by the variable angle formed by the red
and violet rays which bound the solar spectrum;—or rather, it is the excess
of the refraction of the most refrangible ray above that of the least
refrangible ray. The dispersion is not proportional to the refraction—that is,
the substances which have an equal mean refraction, do not disperse light in
the same ratio. For example, if we make a prism with plates of glass, and fill
it with oil of Cassia, and adjust its refracting angle ACB, (fig. 31, p. 127,) so
that the middle of the spectrum which it forms falls exactly at the same place
where the green rays of a spectrum formed by a glass prism would fall—
then we shall find that the spectrum formed by the oil of Cassia prism will
be two or three times longer than that of the glass prism. The oil of Cassia,
therefore, is said to disperse the rays of light more than the glass, that is, to
separate the extreme red and violet rays at O and P more than the mean ray

at green, and to have a greater dispersive power. Sir I. Newton appears to
have made use of prisms composed of different substances, yet, strange to
tell, he never observed that they formed spectrums, whose lengths were
different, when the refraction of the green ray was the same; but thought that
the dispersion was proportional to the refraction. This error continued to be
overlooked by philosophers for a considerable time, and was the cause of
retarding the invention of the achromatic telescope for more than 50 years.

Dollond was among the first who detected this error. By his experiments it
appears, that the different kinds of glass differ extremely with respect to the
divergency of colours produced by equal refractions. He found that two
prisms, one of white flint glass, whose refracting angle was about 25
degrees, and another of crown glass whose refracting angle was about 29
degrees, refracted the beam of light nearly alike; but that the divergency of
colour in the white flint was considerably more than in the crown glass; so
that when they were applied together, to refract contrary ways, and a beam
of light transmitted through them, though the emergent continued parallel to
the incident part, it was, notwithstanding, separated into component colours.
From this he inferred, that, in order to render the emergent beam white, it is
necessary that the refracting angle of the prism of crown glass should be
increased, and by repeated experiments he discovered the exact quantity. By
these means he obtained a theory in which refraction was performed without
any separation or divergency of colour; and thus the way was prepared for
applying the principle he had ascertained to the construction of the object
glasses of refracting telescopes. For the edges of a convex and concave lens,
when placed in contact with each other, may be considered as two prisms
which refract contrary ways; and if the excess of refraction in the one be
such as precisely to destroy the divergency of colour in the other, a
colourless image will be formed. Thus, if two lenses are made of the same
focal length, the one of flint glass and the other of crown, the length or
diameter of the coloured image in the first will be to that produced by the
crown glass, as 3 to 2 nearly. Now, if we make the focal lengths of the lenses
in this proportion, that is, as 3 to 2, the coloured spectrum produced by each
will be equal. But if the flint lens be concave, and the crown convex—when
placed in contact—they will mutually correct each other, and a pencil of
white light refracted by the compound lens will remain colourless.

figure 53.

The following figure may perhaps illustrate what has been now stated. Let
LL (fig. 53.) represent a convex lens of crown glass, and ll a concave lens of
flint glass. A ray of the sun S, falls at F on the convex lens which will refract
it exactly as the prism ABC, whose faces touch the two surfaces of the lens
at the points where the ray enters and quits it. The solar ray, SF, thus
refracted by the lens LL, or prism ABC, would have formed a spectrum PT
on the wall, had there been no other lens, the violet ray F crossing the axis of
the lens at V, and going to the upper end P of the spectrum; and the red ray
FR, going to the lower end T. But as the flint-glass lens ll, or the prism AaC
which receives the rays FV, FR, at the same points, is interposed, these rays
will be united at f, and form a small circle of white light; the ray SF of the
sun being now refracted without colour from its primitive direction SFY into
the new direction Ff. In like manner the corresponding ray SM will be
refracted to f, and a white and colourless image of the sun will be there
formed by the two lenses. In this combination of lenses it is obvious that the
spherical aberration of the flint lens corrects to a considerable degree that of
the crown-glass, and by a proper adjustment of the radii of the surfaces, it
may be almost wholly removed. This error is still more completely corrected
in the triple achromatic object-glass, which consists of three lenses—a
concave flint lens placed between convexes of crown glass. Fig. 54 shows
the double achromatic lens, and fig. 55, the triple object-glass, as they are
fitted up in their cells, and placed at the object end of the telescope. In
consequence of their producing a focal image free of colour they will bear a
much larger aperture and a much greater magnifying power than common

refracting telescopes of the same length. While a common telescope whose
object-glass is 3½ feet focal distance will bear an aperture of scarcely 1 inch,
the 3½ feet Achromatic will bear an aperture of 3¼ inches, and consequently
transmits 10½ times the quantity of light. While the one can bear a
magnifying power of only about 36 times, the other will bear a magnifying
power for celestial objects of more than 200 times.
figure 54. figure 55.

The theory of the achromatic telescope is somewhat complicated and
abstruse, and would require a more lengthened investigation than my limits
will permit. But what has been already stated may serve to give the reader a
general idea of the principle on which it is constructed, which is all I
intended. The term achromatic by which such instruments are now
distinguished was first given to them by Dr. Bevis. It is compounded of two
Greek words which signify, ‘free of colour.’ And, were it not that even
philosophers are not altogether free of that pedantry which induces us to
select Greek words which are unintelligible to the mass of mankind, they
might have been contented with selecting the plain English word colourless,
which is as significant and expressive as the Greek word achromatic. The
crown-glass, of which the convex lenses of this telescope are made, is the

same as good common window-glass; and the flint-glass is that species of
glass of which wine-glasses, tumblers, decanters and similar articles are
formed, and is sometimes distinguished by the name of crystal-glass. Some
opticians have occasionally formed the concave lens of an achromatic
object-glass from the bottom of a broken tumbler.

This telescope was invented and constructed by Mr. John Dollond, about the
year 1758. When he began his researches into this subject, he was a silk
weaver in Spitalfields, London. The attempt of the celebrated Euler to form
a colourless telescope, by including water between two meniscus glasses,
attracted his attention, and, in the year 1753, he addressed a letter to Mr.
Short, the optician, which was published in the Philosophical Transactions of
London, ‘concerning a mistake in Euler’s theorem for correcting the
aberrations in the object glasses of refracting telescopes.’ After a great
variety of experiments on the refractive and dispersive powers of different
substances, he at last constructed a telescope in which an exact balance of
the opposite dispersive powers of the crown and flint lenses made the
colours disappear, while the predominating refraction of the crown lens
disposed the achromatic rays to meet at a distant focus. In constructing such
object glasses, however, he had several difficulties to encounter. In the first
place, the focal distance as well as the particular surfaces must be very
nicely proportioned to the densities or refractive powers of the glasses,
which are very apt to vary in the same sort of glass made at different times.
In the next place, the centers of the two glasses must be placed truly in the
common axis of the telescope, otherwise the desired effect will be in a great
measure destroyed. To these difficulties is to be added—that there are four
surfaces (even in double achromatic object glasses) to be wrought perfectly
spherical; and every person practised in optical operations will allow, that
there must be the greatest accuracy throughout the whole work. But these
and other difficulties were at length overcome by the judgment and
perseverance of this ingenious artist.

It appears, however, that Dollond was not the only person who had the merit
of making this discovery—a private gentleman, Mr. Chest, of Chest-hall, a
considerable number of years before, having made a similar discovery, and
applied it to the same purpose. This fact was ascertained in the course of a
process raised against Dollond at the instance of Watkins, optician at
Charing-cross, when applying for a patent. But as the other gentleman had

kept his invention a secret, and Dollond had brought it forth for the benefit
of the public, the decision was given in his favour. There was no evidence
that Dollond borrowed the idea from his competitor, and both were, to a
certain extent, entitled to the merits of the invention.

One of the greatest obstructions to the construction of large achromatic
telescopes is, the difficulty of procuring large discs of flint glass of an
uniform refractive density—of good colour, and free from veins. It is said
that, fortunately for Mr. Dollond, this kind of glass was procurable when he
began to make achromatic telescopes, though the attempts of ingenious
chemists have since been exerted to make it without much success. It is also
said, that the glass employed by Dollond in the fabrication of his best
telescopes, was of the same melting, or made at the same time, and that,
excepting this particular treasure, casually obtained, good dense glass for
achromatic purposes, was always as difficult to be procured as it is now. The
dispersion of the flint glass, too, is so variable, that, in forming an
achromatic lens, trials on each specimen require to be made before the
absolute proportional dispersion of the substances can be ascertained. It is
owing, in a great measure, to these circumstances, that a large and good
achromatic telescope cannot be procured unless at a very high price. Mr.
Tulley of Islington—who has been long distinguished as a maker of
excellent achromatic instruments—showed me, about six years ago, a rude
piece of flint glass about five inches diameter, intended for the concave lens
of an achromatic object glass, for which he paid eight guineas. This was
before the piece of glass was either figured or polished, and, consequently,
he had still to perform the delicate operation of figuring, polishing, and
adjusting this concave to the convex lenses with which it was to be
combined; and during the process some veins or irregularities might be
detected in the flint glass which did not then appear. Some years before, he
procured a disc of glass from the continent about seven or eight inches
diameter, for which he paid about thirty guineas, with which an excellent
telescope, twelve feet focal length, was constructed for the Astronomical
Society of London. It is obvious therefore, that large achromatic telescopes
must be charged at a pretty high price.

In order to stimulate ingenious chemists and opticians to make experiments
on this subject, the Board of Longitude, more than half a century ago,
offered a considerable reward for bringing the art of making good flint glass

for optical purposes to the requisite perfection. But considerable difficulties
arise in attempting improvements of this kind; as the experiments must all be
tried on a very large scale, and are necessarily attended with a heavy
expence. And although government has been extremely liberal in voting
money for warlike purposes, and in bestowing pensions on those who stood
in no need of them, it has hitherto thrown an obstruction in the way of such
experiments, by the heavy duty of excise, which is rigorously exacted,
whether the glass be manufactured into saleable articles or not; and has thus
been instrumental in retarding the progress of improvement and discovery. It
would appear that experiments of this kind have been attended with more
success in France, Germany, and other places on the continent, than in
Britain; as several very large achromatic telescopes have been constructed in
those countries by means of flint glass which was cast for the purpose in
different manufactories, and to which British artists have been considerably
indebted; as the London opticians frequently purchase their largest discs of
flint glass from Parisian agents. Guinaud, a continental experimenter, and
who was originally a cabinet maker, appears to have had his labours in this
department of art crowned with great success. Many years were employed in
his experiments, and he too frequently, notwithstanding all his attention,
discovered his metal to be vitiated by striæ, spects or grains, with cometic
tails. He constructed a furnace capable of melting two cwt of glass in one
mass, which he sawed vertically, and polished one of the sections, in order to
observe what had taken place during the fusion. From time to time, as he
obtained blocks, including portions of good glass, his practice was to
separate them by sawing the blocks into horizontal sections, or
perpendicular to their axes. A fortunate accident conducted him to a better
process. While his men were one day carrying a block of this glass, on a
hand-barrow, to a saw mill which he had erected at the Fall of the Doubs, the
mass slipped from its bearers, and, rolling to the bottom of a steep and rocky
declivity, was broken to pieces. Guinaud having selected those fragments
which appeared perfectly homogeneous, softened them in circular moulds,
in such a manner, that on cooling, he obtained discs that were afterwards fit
for working. To this method he adhered, and contrived a way for clearing his
glass while cooling, so that the fractures should follow the most faulty parts.
When flaws occurred in the large masses, they were removed by cleaving
the pieces with wedges; then smelting them again in moulds, which give
them the form of discs. The Astronomical Society of London have made trial

of discs made by Guinaud, and have found them entirely homogeneous and
free from fault. Of this ingenious artist’s flint glass, some of the largest
achromatic telescopes on the continent have been constructed. But, it is
more than twenty years since this experimenter took his flight from this
terrestrial scene, and it is uncertain whether his process be still carried on
with equal success.

Notices of some large Achromatic telescopes on the Continent and in Great
Britain.

1. The Dorpat Telescope.—This is one of the largest and most expensive
Refracting telescopes ever constructed. It was made by the celebrated
Fraunhofer of Munich for the observatory of the Imperial University of
Dorpat, and was received into the observatory by Professor Struve in the
year 1825. The aperture of the object glass of this telescope is 9½ English
inches, and its solar focal length about fourteen feet, the main tube being
thirteen French feet exclusive of the tube which holds the eye pieces. The
smallest of the four magnifying powers it possesses, is 175, and the largest
700, which, in favourable weather, is said to present the object with the
utmost precision. ‘This instrument,’ says Struve, ‘was sold to us by Privy-
Counsellor Von Utzchneider, the chief of the optical establishment at
Munich, for 10,500 florins, (about £950 sterling), a price which only covers
the expenses which the establishment incurred in making it.’ The frame
work of the stand of this telescope is of oak inlaid with pieces of mahogany
in an ornamental manner, and the tube is of deal veneered with mahogany
and highly polished. The whole weight of the telescope and its counterpoises
is supported at one point, at the common center of gravity of all its parts; and
though these weigh 3000 Russian pounds, yet, we are told that this
enormous telescope may be turned in every direction towards the heavens
with more ease and certainty than any other hitherto in use. When the object
end of the telescope is elevated to the zenith, it is sixteen feet four inches,
Paris measure, above the floor, and its eye end in this position is two feet
nine inches high. This instrument is mounted on an Equatorial stand, and
clock work is applied to the Equatorial axis, which gives it a smooth and
regular sidereal motion, which, it is said, keeps a star in the exact center of
the field of view, and produces the appearance of a state of rest in the starry
regions, which motion can be made solar, or even lunar, by a little change

given to the place of a pointer, that is placed as an index on the dial plate.
Professor Struve considers the optical powers of this telescope superior to
those of Schröeter’s twenty-five feet reflector, from having observed σ
Orionis with fifteen companions, though Schröeter observed only twelve,
that he could count with certainty. Nay, he seems disposed to place it in
competition with the late Sir W. Herschel’s forty feet reflector. The finder of
this telescope has a focal distance of 30 French inches, and 2-42 aperture.

2. Sir James South’s Telescope.—About the year 1829, Sir J. South,
President of the London Astronomical Society, procured of M. Cauchoix of
Paris, an achromatic object glass of 112/10 inches, clear aperture, and of 19
feet focal length. The flint glass employed in its construction was the
manufacture of the late Guinaud le Pere, and was found to be absolutely
perfect. The first observation was made with this telescope, while on a
temporary stand, on Feb. 13, 1830, when Sir J. Herschel discovered with it a
sixth star in the trapezium in the nebula of Orion, whose brightness was
about one third of that of the fifth star discovered by Struve, which is as
distinctly seen as the companion to Polaris is in a five feet achromatic. Sir
James gives the following notices of the performance of this instrument on
the morning of May 14, 1830. ‘At half past two, placed the 20 feet
achromatic on the Georgium Sidus, saw it with a power of 346, a beautiful
planetary disc; not the slightest suspicion of any ring, either perpendicular or
horizontal; but the planet three hours east of the meridian, and the moon
within three degrees of the planet.’ At a quarter before three, viewed Jupiter
with 252 and 346, literally covered with belts, and the diameters of his
satellites might have been as easily measured as himself. One came from
behind the body, and the contrast of the colour with that of the planet’s limb
was striking. At three o’clock viewed Mars. The contrast of light in the
vicinity of the poles very decided. Several spots on his body well and
strongly marked—that about the south pole seems to overtake the body of
the planet, and gives an appearance not unlike that afforded by the new
moon, familiarly known as ‘the old moon in the new moon’s arms.’ Saturn
has been repeatedly seen with powers from 130 to 928 under circumstances
the most favourable; but not any thing anomalous about the planet or its ring
could even be suspected. This telescope is erected on an Equatorial stand at
Sir J. South’s observatory, Kensington.

3. Captain Smyth’s Telescope in his private observatory at Bedford.—This
Achromatic telescope is 8½ feet focal length, with a clear aperture of 59/10
inches worked by the late Mr. Tulley, Senior, from a disk purchased by Sir
James South at Paris. It is considered by Captain Smyth to be the finest
specimen of that eminent optician’s skill, and, it is said, will bear with
distinctness, a magnifying power of 1200. Its distinctness has been proved
by the clear vision it gives of the obscure nebulæ, and of the companions of
Polaris, Rigel, α Lyræ, and the most minute double stars—-the lunar
mountains, cavities and shadows under all powers—the lucid polar regions
of Mars—the sharpness of the double ring of Saturn—the gibbous aspect of
Venus—the shadows of Jupiter’s satellites across his body, and the splendid
contrast of colours in α Hercules, γ Andromedæ and other superb double
stars.

Other large Achromatics.—Besides the above, the following, belonging to
public observatories and private individuals, may be mentioned. In the Royal
observatory at Greenwich, there is an Achromatic of 10 feet focal distance,
having a double object glass 5 inches diameter, which was made by Mr.
Peter Dollond, and the only one of that size he ever constructed. There is
also a 46 inch achromatic, with a triple object glass 3¾ inches aperture,
which is said to be the most perfect instrument of the kind ever produced. It
was the favourite instrument of Dr. Maskelyne, late Astronomer Royal, who
had a small room fitted up in the observatory for this telescope. The
observatory, some years ago erected near Cambridge, is perhaps the most
splendid structure of the kind in Great Britain. It is furnished with several
very large achromatic telescopes on Equatorial machinery: but the
Achromatic telescope, lately presented to it by the Duke of Northumberland,
is undoubtedly the largest instrument of this description which is to be found
in this country. The object glass is said to be 25 feet focal distance, and of a
corresponding diameter, but as there was no access to this instrument at the
time I visited this observatory, nearly six years ago, I am unable to give a
particular description of it. In the Royal Observatory at Paris, which I visited
in 1837, I noticed, among other instruments, two very large Achromatic
telescopes which, measuring them rudely by the eye—I estimated to be from
15 to 18 feet long, and the aperture at the object end, from 12 to 15 inches
diameter. They were the largest achromatics I had previously seen; but I
could find no person in the observatory at that time, who could give me any

information as to their history, or to their exact dimensions, or powers of
magnifying.21

The Rev. Dr. Pearson, Treasurer to the Astronomical Society of London, is in
possession of the telescope formerly alluded to, made by Mr. Tulley, of
twelve feet focal distance and seven inches aperture, which is said to be a
very fine one. The small star which accompanies the pole star, with a power
of a 100, appears through this telescope, as distinct and steady as one of
Jupiter’s satellites. With a single lens of 6 inches focus, which produced a
power of 24 times, according to the testimony of an observer who noticed it
—the small star appeared as it does in an achromatic of 3 inches aperture,
which shows the great effect of illuminating power in such instruments. Mr.
Lawson, a diligent astronomical observer in Hereford, possesses a most
beautiful achromatic telescope of about 7 inches aperture, and 12 feet focal
distance, which was made by one of the Dollonds, who considered it as his
chief d’oeuvre. It is said to bear powers as high as 1100 or 1400; and has
been fitted up with mechanism devised by Mr. Lawson himself, so as to be
perfectly easy and manageable to the observer, and which displays this
gentleman’s inventive talent. In several of his observations with this
instrument, he is said to have had a view of some of the more minute
subdivisions of the ring of Saturn. A very excellent achromatic telescope was
fitted up some years ago by my worthy friend William Bridges, Esq.,
Blackheath. Its object glass is 5½ inches diameter, and about 5½ feet focal
length. It is erected upon Equatorial machinery, and placed in a circular
observatory which moves round with a slight touch of the hand. The object
glass of this instrument cost about 200 Guineas, the equatorial machinery on
which it is mounted cost 150 Guineas, and the circular observatory in which
it is placed about 100 Guineas; in all 450 Guineas. Its powers vary from 50
to 300 times.22

Achromatic telescopes of a moderate size.

Such telescopes as I have alluded to above, are among the largest which
have yet been made on the achromatic principle; they are, of course,
comparatively rare, and can be afforded only at a very high price. Few of the
object glasses in the telescopes to which I have referred, would be valued at
less than 200 Guineas, independently of the tubes, eye pieces and other

apparatus with which they are fitted up. It is so difficult to procure large
discs of flint glass for optical purposes, to produce the requisite curves of the
different lenses, and to combine them together with that extreme accuracy
which is requisite, that when a good compound lens of this description is
found perfectly achromatic, the optician must necessarily set a high value
upon it; since it may happen that he may have finished half a dozen before
he has got one that is nearly perfect. The more common sizes of achromatic
telescopes for astronomical purposes, which are regularly sold by the
London opticians, are the following:—

1. The 2½ feet Achromatic.—This telescope has an object glass 30 inches in
focal length, and 2 inches clear aperture. It is generally furnished with two
eye pieces, one for terrestrial objects, magnifying about 30 or 35 times, and
one for celestial objects with a power of 70 or 75 times. It might be
furnished with an additional astronomical eye-piece—if the object glass be a
good one, so as to produce a power of 90 or 95 times. With such a telescope,
the belts and satellites of Jupiter, the phases of Venus and the ring of Saturn
may be perceived; but not to so much advantage as with larger telescopes. It
is generally fitted up either with a mahogany or a brass tube, and is placed
upon a tripod brass stand, with a universal joint which produces a horizontal
and vertical motion. It is packed, along with the eye-pieces, and whatever
else belongs to it, in a neat mahogany box. Its price varies, according as it is
furnished with an elevating rack or other apparatus.

The following are the prices of this instrument as marked in the catalogue of
Mr. Tulley, Terrett’s Court, Islington, London.

£ s. d.
2½ feet telescopes, brass mounted on plain pillar and claw
stand, with one eye piece for astronomical purposes, and
one for land objects, to vary the magnifying power,
packed in a mahogany box 10 10 0
Ditto, ditto, brass mounted on pillar and claw stand, with
elevating rack, 1 eye piece for astronomical purposes,
and 1 for land objects, to vary the magnifying power,
packed in a mahogany box 12 12 0

The following prices of the same kind of telescope are from the catalogue of
Messrs. W. and, S. Jones, 30, Lower Holborn, London.

£ s. d.
The improved 2½ feet achromatic refractor, on a brass stand,
mahogany tube, with three eye pieces, two magnifying
about 40 and 50 times for terrestrial objects, and the
other about 75 times for astronomical purposes, in a
mahogany case 10 10 0
Ditto, ditto, the tube all brass, with three eye pieces 11 11 0
Ditto, ditto, with vertical and horizontal rack work
motions 15 15 0

2. The 3½ feet Achromatic Telescope.—The object glass of this telescope is
from 44 to 46 inches focal length, and 2¾ inches diameter. It is generally
furnished with four eye-pieces, two for terrestrial and two for celestial
objects. The lowest power for land objects is generally about 45, which
affords a large field of view, and exhibits the objects with great brilliance.
The other terrestrial power is usually from 65 to 70. The astronomical
powers are about 80 and 130; but such a telescope should always have
another eye-piece, to produce a power of 180 or 200 times, which it will
bear with distinctness, in a serene state of the atmosphere, if the object glass
be truly achromatic. The illuminating power in this telescope is nearly
double that of the 2½ feet telescope, or in the proportion of 7, 56 to 4; and
therefore it will bear about double the magnifying power with nearly equal
distinctness. This telescope is fitted up in a manner somewhat similar to the
former, with a tripod stand which is placed upon a table. Sometimes,
however, it is mounted on a long mahogany stand which rests upon the floor,
(as in fig. 58.), and is fitted with an equatorial motion; and has generally a
small telescope fixed near the eye end of the large tube, called a finder,
which serves to direct the telescope to a particular object in the heavens
when the higher powers are applied. It is likewise eligible that it should have
an elevating rack and sliding tubes, for supporting the eye end of the
instrument, to keep it steady during astronomical observations, and it would
be an advantage, for various purposes which shall be afterwards described,
to have fitted to it a Diagonal Eye Piece magnifying 40 times or upwards.

The prices of this instrument, as marked in Mr. Tulley’s Catalogue, are as
follows:—

£ s. d.
The 3½ feet achromatic telescope 2¾ inches aperture, on plain
pillar and claw stand, 2 eye pieces for astronomical
purposes, and 1 for land objects to vary the magnifying
power, packed in a mahogany box 21 0 0
Ditto, ditto, with elevating rack and achromatic finder, 2 eye
pieces for astronomical purposes, and 1 for day objects to
vary the magnifying power, packed in a mahogany box 26 5 0

The following are the prices as marked in Messrs. W. and S. Jones’
Catalogue.

£ s. d.
The 3½ feet achromatic, plain mahogany tube 18 18 0
Ditto, ditto, brass tube 21 0 0
Ditto, all in brass, with rack work motions, &c. 26 5 0
Ditto, the object glass of the largest aperture, and the from
rack motions on an improved principle 37l. 16s.
to 42 0 0
Ditto, fitted up with Equatorial motion, framed
mahogany stand, divided altitude, and azimuth
arches, or declination and right ascension circles, from 60l
&c. &c. to 80 0 0

This is the telescope which I would particularly recommend to astronomical
amateurs, whose pecuniary resources do not permit them to purchase more
expensive instruments. When fitted up with the eye pieces and powers
already mentioned, and with a finder and elevating rack,—price 25 guineas
—it will serve all the purposes of general observation. By this telescope,
satisfactory views may be obtained of most of the interesting phenomena of
the heavens, such as the spots of the sun—the mountains, vales, and caverns
on the lunar surface—the phases of Mercury and Venus—the spots on Mars

—the satellites and belts of Jupiter—the ring of Saturn—many of the more
interesting nebulæ, and most of the double stars of the second and third
classes. When the object glass of this telescope is accurately figured and
perfectly achromatic, a power of from 200 to 230 maybe put upon it, by
which the division of Saturn’s ring might occasionally be perceived. It is
more easily managed and represents objects considerably brighter than
reflecting telescopes of the same price and magnifying power, and it is not
so apt to be deranged as reflectors generally are. A telescope of a less size
would not in general be found satisfactory for viewing the objects I have
now specified, and for general astronomical purposes. It may not be
improper for the information of some readers, to explain what is meant in
Mr. Tulley’s catalogue, when it is stated that this instrument has ‘one eye
piece for day objects, to vary the magnifying power.’ The eye piece alluded
to is so constructed, that by drawing out a tube next the eye, you may
increase the power at pleasure, and make it to vary, say from 40 to 80 or 100
times; so that such a construction of the terrestrial eye piece (to be
afterwards explained) serves in a great measure, the purpose of separate eye-
pieces. The whole length of the 3½ feet telescope, when the terrestrial eye
piece is applied, is about 4½ feet from the object glass to the first eye glass.

When the aperture of the object glass of this telescope exceeds 2¾ inches its
price rapidly advances.

The following is Mr. Tulley’s scale of prices, proportionate to the increase of
aperture:—

£ s. d.
3½ feet telescopes 3¼ inches aperture, with vertical and
horizontal rack work motions, achromatic finder, 3 eye
pieces for astronomical purposes, and one for day objects
to vary the magnifying power, packed in a mahogany box 42 0 0
Ditto, ditto, 3¾ inches diameter, mounted as above 68 5 0
Ditto, with universal Equatorial, instead of pillar and
claw stand 84 0 0

Here, in the one case, the increase of half an inch in the diameter of the
object-glass, adds about £16. to the expense; and in the other case no less
than £26. 5s. The proportion of light in those two telescopes, compared with
that of 2¾ inches aperture, is as follows:—The square of the 2¾ object-glass
is 7.56; that of 3¼, 10.56, and that of the 3¾, 14.06; so that the light
admitted by the 3¼ compared with the 2¾ aperture, is nearly as 10 to 7; and
the light admitted by the 3¾ object-glass is nearly double that of the 2¾
aperture, and will bear nearly a proportional increase of magnifying power.

3. The 5 feet Achromatic telescope. The focal length of the object-glass of
this telescope is 5 feet 3 inches, and the diameter of its aperture 38/10 inches.
The usual magnifying powers applied to it are, for land objects 65 times; and
for celestial objects, 110, 190, 250, and sometimes one or two higher
powers. The quantity of light it possesses is not much larger than that of the
3½ feet telescope, with 3¾ inches aperture; but the larger focal length of this
telescope is considered to be an advantage; since the longer the focus of the
object-glass, the less will be its chromatic and spherical aberrations, and the
larger may be the eye-glasses, and the flatter the field of view.

The following are the prices of these telescopes as marked in Mr. Tulley’s
catalogue.

£ s. d.
5 feet telescopes 3¾ inches aperture, on an universal
equatorial stand, with achromatic finder, 4 eye pieces
for astronomical purposes, and 1 for day objects to vary
the magnifying power, packed in a mahogany box 100
guineas to 157 10 0
7 feet ditto, 5 inches aperture, on a newly improved
universal equatorial stand, 6 eye pieces for astronomical
purposes, and 1 for day objects to vary the magnifying
power, with achromatic finder, and Troughton’s
Micrometer 207 5 0

The above are all the kinds of achromatic telescopes generally made by the
London opticians. Those of the larger kind, as 5 and 7 feet telescopes, and

the 3½ feet with 3¾ inches aperture, are generally made to order, and are not
always to be procured. But the 2½ and 3½ feet achromatics of 2¾ inches
aperture, are generally to be found ready-made at most of the optician’s
shops in the metropolis. The prices of these instruments are nearly the same
in most of the optician’s shops in London. Some of them demand a higher
price, but few of them are ever sold lower than what has been stated above,
unless in certain cases, where a discount is allowed.

figure 57.

The stands for these telescopes, and the manner in which they are fitted up
for observation are represented in figures 57, 58, and 59. Fig. 57 represents
either the 2½ or the 3½ feet telescopes mounted on a plain brass stand, to be
placed on a table. A is the long eye-piece for land objects, and B the small

eye-piece for astronomical observation, which is composed of two lenses,
and represents the object in an inverted position. These eye-pieces are
screwed on, as occasion requires, at E, the eye-end of the telescope. The
shorter of the two astronomical eye-tubes which accompany this telescope,
produces the highest magnifying power. For adjusting the telescope to
distinct vision, there is a brass knob or button at a, which moves a piece of
rack-work connected with the eye-tube, which must be turned either one
way or the other till the object appears distinctly; and different eyes
frequently require a different adjustment.

Fig. 58, represents a 5 feet telescope fitted up for astronomical observations.
It is mounted on a mahogany stand, the three legs of which are made to close
up together by means of the brass frame aaa, which is composed of three
bars, connected with three joints in the centre, and three other joints,
connected with the three mahogany bars. It is furnished with an apparatus
for equatorial motions. The brass pin is made to move round in the brass
socket b, and may be tightened by means of the finger screw d, when the
telescope is directed nearly to the object intended to be viewed. This socket
may be set perpendicular to the horizon, or to any other required angle; and
the quantity of the angle is ascertained by the divided arc, and the instrument
made fast in that position by the screw e. If this socket be set to the latitude
of the place of observation, and the plane of this arc be turned so as to be in
the plane of the meridian, the socket b being fixed to the inclination of the
pole of the earth, the telescope when turned in this socket, will have an
equatorial motion, so that celestial objects may be always kept in view, when
this equatorial motion is performed. The two handles at k are connected with
rack-work, intended to move the telescope in any required direction. The
two sets of brass sliding rods ii are intended to render the telescope as steady
as possible, and to elevate and depress it at pleasure, and are so constructed
as to slide into each other with the utmost ease.

figure 58.

The Finder is placed at AE, either on the top or the left side of the tube of
the telescope. When high magnifying powers are applied to any telescope, it
is sometimes difficult, on account of the smallness of the field of view, to
direct the main tube of the telescope to the object. But the Finder, which is a
telescope with a small power, and consequently has a large field of view—
when directed to any object, it is easily found, and being brought to the
centre of the field, where two cross hairs intersect each other, it will then be
seen in the larger telescope. B is the eye-tube for terrestrial objects,
containing 4 glasses, and C, one of the astronomical eye-pieces. A socket is
represented at g, containing a stained glass, which is screwed to any of the
eye-pieces, to protect the eye from the glare of light, when viewing the spots
of the sun. The brass nut above f, is intended for the adjustment of the eye-
piece to distinct vision. The 3½ feet telescope is sometimes mounted in this
form.

Fig. 59, represents a 5 or 6 feet telescope, mounted on a stand of a new
construction by Dollond. It possesses the advantage of supporting the
telescope in two places, which renders it extremely steady—a property of
great importance when viewing celestial objects with high magnifying
powers. It possesses likewise, the advantage of enabling the observer to
continue seated at the same height from the floor, although the telescope be
raised to any altitude—the elevation being entirely at the object end,
although it may be changed from the horizon to the zenith. The frame-work
is composed of bars of mahogany, and rests on three castors, two of which
are made fast to their respective legs in the usual way, and the third stands
under the middle of the lower horizontal bar that connects the two opposite
legs, so that the frame has all the advantages of a tripod. As it becomes very
inconvenient to stoop to the eye end of a telescope, when the altitude of an
object is considerable, and the centre of motion at the middle of the tube,
this construction of a stand serves to remedy such inconvenience.

figure 59.

Proportions of curvature of the lenses which form an achromatic object-
glass.

As some ingenious mechanics may feel a desire to attempt the construction
of a compound achromatic object-glass, I shall here state some of the
proportions of curvature of the concave and convex lenses, which serve to
guide opticians in their construction of achromatic instruments. These
proportions are various; and even when demonstrated to be mathematically
correct, it is sometimes difficult to reduce them to practice, on account of the
different powers of refraction and dispersion possessed by different discs of
crown and flint-glass, and of the difficulty of producing by mechanical
means, the exact curves which theory requires. The following table shows
the radii of curvature of the different surfaces of the lenses necessary to form
a double achromatic object-glass—it being supposed that the sine of

refraction in the crown-glass is as 1.528 to 1, and in the flint as 1.5735 to 1;
the ratio of their dispersive powers being as 1 to 1.524. It is also assumed
that the curvatures of the concave lens are as 1 to 2, that is, that the one side
of this lens is ground on a tool, the radius of which is double that of the
other. The 1st column expresses the compound focus of the object-glass in
inches; the 2nd column states the radius of the anterior surface of the crown,
and column 3rd, its posterior side. Column 4th expresses the radius of the
anterior surface of the concave lens, and column 5th its posterior surface,
which, it will be observed, is exactly double that of the other.

Radius of Radius of
Radius of Radius of
Focus in anterior anterior
posterior posterior
inches. surface, surface,
surface. surface.
convex. concave.
Inc. Dec. Inc. Dec. Inc. Dec. Inc. Dec.
12 3 4. 652 4. 171 8. 342
24 6 9. 304 8. 342 16. 684
30 7. 5 11. 063 10. 428 20. 856
36 9 13. 956 12. 513 25. 027
48 12 18. 608 16. 684 33. 369
60 15 23. 260 20. 856 41. 712
120 30 46. 520 41. 712 83. 424

From the above table it will be seen, that to construct, for example, a 30 inch
compound object-glass, the radius of the anterior side of the crown must be
7½ inches, and that of the posterior side 11.63 inches; the radius of the
anterior surface of the concave 10.428, and that of the posterior 20.856
inches. It may be proper to observe, that in these computations, the radius of
the anterior surface of the concave is less than the posterior side of the
convex, and consequently admits of its approach, without touching in the
centre—a circumstance which always requires to be guarded against in the
combination of achromatic glasses. The following table shows the radii of
curvature of the lenses of a triple object-glass, calculated from formula
deduced by Dr. Robison of Edinburgh.

Focal Convex lens of Concave lens of Convex lens of
length. crown glass. flint glass. crown glass.
Inches Inc. Dec. Inc. Dec. Inc. Dec. Inc. Dec. Inc. Dec. Inc. Dec.
6 4. 54 3. 03 3. 03 6. 36 6. 36 0. 64
9 6. 83 4. 56 4. 56 9. 54 9. 54 0. 92
12 9. 25 6. 17 6. 17 12. 75 12. 75 1. 28
18 13. 67 9. 12 9. 12 19. 08 19. 08 1. 92
24 18. 33 12. 25 12. 25 25. 50 25. 50 2. 56
30 22. 71 15. 16 15. 16 31. 79 31. 79 3. 20
36 27. 33 18. 25 18. 25 38. 17 38. 17 3. 84
42 31. 87 21. 28 21. 28 44. 53 44. 53 4. 48
48 36. 42 24. 33 24. 33 50. 92 50. 92 5. 12
54 40. 96 27. 36 27. 36 57. 28 57. 28 5. 76
60 45. 42 30. 33 30. 33 63. 58 63. 58 6. 40

The following table contains the proportions of curvature, said to be
employed by the London opticians.

Radius of both
Focal Convex lens of the surfaces of Convex lens of
length. crown glass. the concave of crown glass.
flint glass.
Inches Inc. Dec. Inc. Dec. Inc. Dec. Inc. Dec. Inc. Dec.
6 3. 77 4. 49 3. 47 3. 77 4. 49
9 5. 65 6. 74 5. 21 5. 65 6. 74
12 7. 54 8. 99 6. 95 7. 54 8. 99
18 11. 30 13. 48 10. 42 11. 30 13. 48
24 15. 08 17. 98 13. 90 15. 08 17. 98
36 22. 61 26. 96 20. 84 22. 61 26. 96
42 26. 38 31. 45 24. 31 26. 38 31. 45
48 30. 16 35. 96 27. 80 30. 16 35. 96
54 33. 91 40. 45 31. 27 33. 91 40. 45
60 37. 68 44. 94 34. 74 37. 68 44. 94

From this table it appears, that the two convex lenses, have the same radii of
their respective sides and that the concave flint lens has its two surfaces
equally concave, so that a triple object-glass formed according to these
proportions, would require only three pair of grinding tools. The following
are the curves of the lenses of one of the best of Dollond’s achromatic
telescopes, the focal length of the compound object-glass being 46 inches.
Reckoning from the surface next the object—the radii of the crown-glass
were 28 and 40 inches: the concave lens 20.9 inches, and the inner crown-
glass lens, 28.4 and 28.4 inches. This telescope carried magnifying powers
of from 100 to 200 times.

Although I have inserted the above tables, which might in some measure
guide an ingenious artist, yet on the whole, a private amateur has little
chance in succeeding in such attempts. The diversity of glasses, and the
uncertainty of an unpractised workman’s producing the precise curvatures he
intends, is so great, that the object-glass, for the most part, turns out different
from his expectations. The great difficulty in the construction is to find the
exact proportion of the dispersive powers of the crown and flint glass. The
crown is pretty constant, but there are hardly two pots of flint glass which
have the same dispersive power. Even if constant, it is difficult to measure it
accurately; and an error in this greatly affects the instrument; because the
focal distances of the lenses must be nearly as their dispersive powers. In the
two preceding tables, the sine of incidence, in the crown glass, is supposed
to be to the sine of refraction as 1.526 to 1; and in the flint glass, as 1.604 to
1. Opticians who make great numbers of lenses both of flint and crown
glass, acquire, in time, a pretty good guess of the nature of the errors which
may remain after they have finished an object-glass; and having many lenses
intended to be of the same form, but unavoidably differing a little from it,
they try several of the concaves with the two convexes, and finding one
better than the rest, they make use of it to complete the set. In this way some
of the best achromatic telescopes are frequently formed. I have sometimes
found, when supplying a concave flint glass to a telescope where it
happened to be wanting, that, of four or five concave lenses which appeared
to be the same as to curvature and other properties, only one was found to
produce a distinct and colourless image. Should any one, however, wish to
attempt the construction of an achromatic lens, the best way for preventing
disappointments in the result is, to procure a variety of tables of the
respective curvatures founded on different conditions, and which, of course,

require the surfaces of the several lenses to be of different curves. Having
lenses of different radii at his command, and having glass of different
refractive or dispersive powers, when one combination does not exactly suit,
he may try another, and ultimately may succeed in constructing a good
achromatic telescope; for, in many cases, it has been found that chance, or a
happy combination of lenses by trial, has led to the formation of an excellent
object-glass.

Achromatic telescopes composed of fluid lenses.

The best achromatic telescopes, when minutely examined, are found to be in
some respects defective, on account of that slight degree of colour which, by
the aberration of the rays, they give to objects, unless the object-glass be of
small diameter. When we examine with attention a good achromatic
telescope we find that it does not show white or luminous objects perfectly
free from colour, their edges being tinged on one side with a claret-coloured
fringe, and on the other with a green fringe. This telescope, therefore,
required farther improvement, to get rid of these secondary colours, and
Father Boscovich, to whom every branch of optics is much indebted,
displayed much ingenuity in his attempts to attain this object. But it is to Dr.
Blair, professor of astronomy in Edinburgh, that we are chiefly indebted for
the first successful experiments by which this end was accomplished. By a
judicious set of experiments, he proved that the quality of dispersing the rays
in a greater degree than crown-glass, is not confined to a few mediums; but
is possessed by a great variety of fluids, and by some of these in a most
extraordinary degree. Having observed that when the extreme red and violet
rays were perfectly united, the green were left out, he conceived the idea of
making an achromatic concave lens which should refract the green less than
the united red and violet, and an achromatic convex lens which should do
the same, and as the concave lens refracted the outstanding green to the axis,
while the concave one refracted them from the axis, it followed, that, by a
combination of these two opposite effects, the green would be united with
the red and violet.

By means of an ingenious prismatic apparatus, he examined the optical
properties of a great variety of fluids. The solutions of metals and semi-
metals proved in all cases more dispersive than crown glass. Some of the

salts, such as sal-ammoniac, greatly increased the dispersive power of water.
The marine acid disperses very considerably, and this quality increases with
its strength. The most dispersive fluids were accordingly found to be those
in which this acid and the metals were combined. The chemical preparation
called causticum antimoniale, or butter of antimony, in its most concentrated
state, when it has just attracted sufficient humidity to render it fluid,
possesses the quality of dispersing the rays in an astonishing degree. The
great quantity of the semi-metal retained in solution, and the highly
concentrated state of the marine acid, are considered as the cause of this
striking effect. Corrosive sublimate of mercury, added to a solution of sal-
ammoniacum in water, possesses the next place to the butter of antimony
among the dispersive fluids, which Dr. Blair examined. The essential oils
were found to hold the next rank to metallic solutions, among fluids which
possess the dispersive quality, particularly those obtained from bituminous
minerals, as native petrolea, pit coal, and amber. The dispersive power of the
essential oil of sassafras, and the essential oil of lemons, when genuine, were
found to be not much inferior to any of these. But of all the fluids fitted for
optical purposes, Dr. Blair found that the muriatic acid mixed with a metallic
solution, or, in other words, a fluid in which the marine acid and metalline
particles, hold a due proportion, most accurately suited his purpose. In a
spectrum formed by this fluid the green were among the most refrangible
rays, and when its dispersion was corrected by that of glass, there was
produced an inverted secondary spectrum, that is, one in which the green
was above, when it would have been below with a common medium. He
therefore placed a concave lens of muriatic acid with a metallic solution
between the two lenses, as in fig. 60, where AB is the concave fluid lens, CF
a plano-convex lens, with its plane side next the object, and ED, a meniscus.
With this object-glass the rays of different colours were bent from their
rectilineal course with the same equality and regularity as in reflection.

figure 60.

Telescopes constructed with such object-glasses were examined by the late
Dr. Robison and professor Playfair. The focal distance of the object-glass of
one of these did not exceed 17 inches, and yet it bore an aperture of 3½
inches. They viewed some single and double stars and some common
objects with this telescope; and found, that, in magnifying power, brightness,
and distinctness, it was manifestly superior to one of Mr. Dollond of 42
inches focal length. They had most distinct vision of a star, when using an
erecting eye-piece, which made this telescope magnify more than a 100
times; and they found the field of vision as uniformly distinct as with
Dollond’s 42 inch telescope magnifying 46 times; and were led to admire the
nice figuring and centering of the very deep eye-glasses which were
necessary for this amplification. They saw double stars with a degree of
perfection which astonished them. These telescopes, however, have never
yet come into general use; and one reason perhaps, is, that they are much
more apt to be deranged, than telescopes constructed of object-glasses which
are solid. If any species of glass, or other solid transparent substance could
be found with the same optical properties, instruments might perhaps be
constructed of a larger size, and considerably superior to our best achromatic
telescopes.23 It is said that Mr. Blair, the son of Dr. Blair, some years ago,
was engaged in prosecuting his father’s views, but I have not heard any
thing respecting the result of his investigations.

Barlow’s refracting telescope with a fluid concave lens.

Professor Barlow, not many years ago, suggested a new fluid telescope,
which is deserving of attention; and, about the year 1829 constructed one of
pretty large dimensions. The fluid he employs for this purpose is the
sulphuret of Carbon, which he found to be a substance which possessed
every requisite he could desire. Its index is nearly the same as that of the
best flint glass, with a dispersive power more than double. It is perfectly
colourless, beautifully transparent, and although very expansible, possesses
the same, or very nearly the same optical properties under all circumstances
to which it is likely to be exposed in astronomical observations—except
perhaps, direct observations on the solar disc, which will probably be found
inadmissible. Mr. Barlow first constructed an object-glass with this fluid of 3
inches aperture, with which he could see the small star in Polaris with a
power of 46, and with the higher powers several stars which are considered
to require a good telescope, for example 70, ρ Ophinchi, 39 Bootis, the
quadruple star ε Lyræ, ζ Aquarii, α Herculis, &c. He next constructed a 6
inch object-glass. With this instrument the small star in Polaris is so distinct
and brilliant, with a power of 143, that its transit might be taken with the
utmost certainty. As the mode of constructing these telescopes is somewhat
novel, it may be expedient to enter somewhat into detail.

In the usual construction of achromatic telescopes, the two or three lenses
composing the object-glass are brought into immediate contact; and in the
fluid telescope of Dr. Blair, the construction was the same, the fluid having
been enclosed in the object-glass itself. But in Mr. Barlow’s telescope, the
fluid correcting lens is placed at a distance from the plate lens equal to half
its focal length; and it might be carried still farther back, and yet possess
dispersive power to render the object-glass achromatic. By this means the
fluid lens—which is the most difficult part of the construction—is reduced
to one half or to less than one half of the size of the plate lens; consequently,
to construct a telescope of 10 or 12 inches aperture involves no greater
difficulty in the manipulation, than in making a telescope of the usual
description of 5 or 6 inches aperture, except in the simple plate lens itself;
and, hence, a telescope of this kind, of 10 or 12 feet length, will be
equivalent in its focal power to one of 16 or 20 feet. By this means, the tube
may be shortened several feet and yet possess a focal power more
considerable than could be conveniently given to it on the usual principle of

construction. This will be better understood from the annexed diagram. (fig.
61.)

figure 61.

In this figure ABCD represent the tube of the 6 inch telescope, CD, the plate
object-glass, F the first focus of rays, de the fluid concave lens, distant from
the former 24 inches. The focal length MF being 48, and consequently, as 48
: 6 :: 24 : 3 inches, the diameter of the fluid lens. The resulting compound
focus is 62.5 inches. It is obvious, therefore, that the rays df, ef, arrive at the
focus under the same convergency, and with the same light as if they
proceeded from a lens of 6 inches diameter, placed at a distance beyond the
object-glass CD (as GH,) determined by producing those rays till they meet
the sides of the tube in GH, namely at 62.5 inches beyond the fluid lens.

Hence, it is obvious, the rays will converge as they would do from an object-
glass GH of the usual kind with a focus of 10 feet 5 inches. We have thus,
therefore, shortened the tube 38.5 inches, or have at least the advantage of a
focus 38.5 inches longer than our tube; and the same principle may be
carried much farther, so as to reduce the usual length of refracting telescopes
nearly one half without increasing the aberration in the first glass beyond the
least that can possibly belong to a telescope of the usual kind of the whole
length. It should likewise be observed that the adjustment for focus may be
made either in the usual way, or by a slight movement of the fluid lens, as in
the Gregorian Reflectors, by means of the small speculum.

Mr. Barlow afterwards constructed another and a larger telescope on the
same principle, the clear aperture of which is 7.8 inches. Its tube is 11 feet,
which, together with the eye-piece, makes the whole length 12 feet, but its
effective focus is on the principle stated above, 18 feet. It carries a power of
700 on the closest double stars in South’s and Herschel’s catalogue, and the
stars are, with that power, round and defined, although the field is not then
so bright as could be desired. The telescope is mounted on a revolving stand,
which works with considerable accuracy as an azimuth and altitude
instrument. To give steadiness to the stand it has been made substantial and
heavy; its weight by estimation being 400 pounds, and that of the telescope
130 pounds, yet its motions are so smooth, and the power so arranged, that it
may be managed by one person with the greatest ease, the star being
followed by a slight touch, scarcely exceeding that of the keys of a piano-
forte. The focal length of the plate lens is 78 inches, and of the fluid lens
59.8 inches—which at the distance of 40 inches produce a focal length of
104 inches, a total length of 12 feet, and an equivalent focus of 18 feet. The
curves of the parallel meniscus checks for containing the fluid are—30
inches, and 144 inches, the latter towards the eye. The curves for the plate
lens are 56.4 and 144. There is an interior tube 5 inches diameter, and 3 feet
6 inches long, which carries the cell in which the fluid is enclosed, and an
apparatus by which it may be moved backwards and forwards, so that the
proper adjustment may be made for colour, in the first instance, and
afterwards the focus is obtained by the usual rack-work motion. The
following is the mode by which the fluid was enclosed. After the best
position has been determined practically for the checks forming the fluid
lens, these, with the ring between them ground and polished accurately to
the same curves, are applied together, and taken into an artificial high

temperature, exceeding the greatest at which the telescope is ever expected
to be used. After remaining here with the fluid some time, the space between
the glasses is completely filled, immediately closed, cooled down by
evaporation, and removed into a lower temperature. By this means a sudden
condensation takes place, an external pressure is brought on the checks, and
a bubble formed inside, which is of course filled with the vapour of the
fluid; the excess of the atmospheric pressure beyond that of the vapour being
afterwards always acting externally to prevent contact. The extreme edges
are then sealed with the serum of human blood, or by strong fish-glue, and
some thin pliable metal surface. By this process, Mr. Barlow says, ‘I have
every reason to believe the lens becomes as durable as any lens of solid
glass. At all events I have the satisfaction of stating, that my first 3 inch
telescope has now been completed more than fifteen months, and that no
change whatever has taken place in its performance, nor the least perceptible
alteration either in the quantity or the quality of the fluid.’

The following are some of the observations which have been made with this
telescope, and the tests to which it has been subjected. The very small star
which accompanies the pole-star is generally one of the first tests applied to
telescopes. This small point of light appeared brilliant and distinct; it was
best seen with a power of 120, but was visible with a power of 700. The
small star in Aldebaran was very distinct with a power of 120. The small star
α Lyræ was distinctly visible with the same power. The small star called by
Sir J. Herschel Debilissima, between 4 ε and 5 Lyræ, whose existence, he
says, could not be suspected in either the 5 or 7 feet equatorial, and invisible
also with the 7 and 10 feet reflectors of six and 9 inches aperture, but seen
double with the 20 feet reflector, is seen very satisfactorily double with this
telescope. η Persei, marked as double in South and Herschel’s catalogue, at
the distance of 28´´, with another small star at the distance of 3´ 67´´, is seen
distinctly sixfold, four of the small stars being within a considerably less
distance than the remote one of η marked in the catalogue. And, rejecting the
remote star, the principal, and the four other stars, form a miniature
representation of Jupiter and his satellites, three of them being nearly in a
line on one side, and the other on the opposite. Castor, is distinctly double
with 120, and well opened and stars perfectly round with 360 and 700: γ
Leonis and α Piscium are seen with the same powers equally round and
distinct. In ε Bootis, the small star is well separated from the larger, and its
blue colour well marked with a power of 360. η Coronæ Borealis is seen

double with a power of 360 and 700. 52 Orionis, ζ Orionis, and others of the
same class are also well defined with the same powers. In regard to the
planets which happened to be visible—Venus appeared beautifully white and
well defined with a power of 120, but showed some colour with 360. Saturn
with the 120 power, is a very brilliant object, the double ring and belts being
well and satisfactorily defined, and with the 360 power, it is still very fine.
The moon also is remarkably beautiful, the edges and the shadows being
well marked, while the quantity of light is such as to bring to view every
minute distinction of figure and shade.

The principal objections that may be made to this construction of a telescope
are such as these:—Can the fluid be permanently secured? Will it preserve
its transparency and other optical properties? Will it not act upon the surface
of the glass and partially destroy it? &c. To such enquiries Mr. Barlow
replies, that experience is the only test we have; our spirit levels, spirit
thermometers, &c., show that some fluids at least may be preserved for
many years, without experiencing any change, and without producing any in
the appearance of the glass tubes containing them. But should any of these
happen, except the last, nothing can be more simple than to supply the
means of replacing the fluid at any time, and by any person, without
disturbing the adjustment of the telescope. He expresses his hope that,
should these experiments be prosecuted, an achromatic telescope may
ultimately be produced which shall exceed in aperture and power, any
instruments of the kind hitherto attempted. If the prejudice against the use of
fluids could be removed, he feels convinced that well-directed practice
would soon lead to the construction of the most perfect instruments, on this
principle, at a comparatively small expense. ‘I am convinced,’ he says,
‘judging from what has been paid for large object-glasses, that my telescope,
telescope stand, and the building for observation, with every other requisite
convenience, have been constructed for a less sum than would be demanded
for the object-glass only, if one could be produced of the same diameter of
plate and flint-glass; and this is a consideration which should have some
weight, and encourage a perseverance in the principle of construction.’24

ROGERS’ ACHROMATIC TELESCOPE ON A NEW PLAN.

The object of this construction is to render a small disc of flint-glass
available to perform the office of compensation to a much larger one of
crown-glass, and thus to render possible the construction of telescopes of
much larger aperture than are now common, without hindrance from the
difficulty at present experienced in procuring large discs of flint-glass. It is
well known to those who are acquainted with telescopes, that in the
construction of an ordinary achromatic object-glass, in which a single crown
lens is compensated by a single one of flint, the two lenses admit of being
separated only by an interval too small to afford any material advantage, in
diminishing the diameter of the flint lens, by placing it in a narrower part of
the cone of rays—the actual amount of their difference in point of dispersive
power being such as to render the correction of the chromatic aberration
impossible, when their mutual distance exceeds a certain limit. This
inconvenience Mr. Rogers proposes to obviate, by employing, as a
correcting lens—not a single lens of flint, but a compound one consisting of
a convex crown and concave flint, whose foci are such as to cause their
combination to act as a plain glass on the mean refrangible rays. Then it is
evident, that by means of the greater dispersive power of flint than of crown
glass, this will act as a concave on the violet, and as a convex on the red
rays, and that the more powerfully, according as the lenses separately have
greater powers or curvature. If then, such a compound lens be interposed
between the object-glass of a telescope—supposed to be a single lens of
plate or crown-glass—and its focus, it will cause no alteration in the focus
for mean rays, while it will lengthen the focus for violet, and shorten it for
red rays. Now this is precisely what is wanted to produce an achromatic
union of all the rays in the focus; and as nothing in this construction limits
the powers of the individual correcting lenses, they may therefore be applied
any where that convenience may dictate; and thus, theoretically speaking, a
disc of flint-glass, however small, may be made to correct the colour of one
of crown however large.

This construction, likewise, possesses other and very remarkable
advantages. For, first, when the correcting lens is approximately constructed
on a calculation founded on its intended aperture, and on the refractive and
dispersive indices of its materials, the final and complete dispersion of
colour may be effected, not by altering the lenses by grinding them anew,
but by shifting the combination nearer to, or farther from, the object-glass,
as occasion may require, along the tube of a telescope, by a screw motion,

till the condition of achromaticity is satisfied in the best manner possible.
And secondly, the spherical aberration may in like manner be finally
corrected, by slightly separating the lenses of the correcting glass, whose
surfaces should for this purpose be figured to curvatures previously
determined by calculation, to admit of this mode of correction—a condition
which Mr. Rogers finds to be always possible. The following is the rule he
lays down for the determination of the foci of the lenses of the correcting
glass:—‘The focal length of either lens of the correcting lens is to that of the
object-glass, in a ratio compounded of the ratio of the square of the aperture
of the correcting lens to that of the object-glass, and of the ratio of the
difference of the dispersive indices of the crown and flint glass, to the
dispersive index of crown.’ For example, to correct the colour of a lens of
crown or plate glass of 9 inches aperture, and 14 feet focal length (the
dimensions of the telescope of Fraunhofer at Dorpat) by a disc of flint glass
3 inches in diameter, the focus of either lens of the correcting lens will
require to be about 9 inches. To correct it by a 4 inch disc will require a
focus of about 16 inches each.

Mr. Rogers remarks, that it is not indispensable to make the correcting glass
act as a plane lens. It is sufficient if it be so adjusted as to have a shorter
focus for red rays than for violet. If, preserving this condition, it be made to
act as a concave lens, the advantage procured by Mr. Barlow’s construction
of reducing the length of the telescope with the same focal power, is secured,
and he considers, moreover, that by a proper adaptation of the distances,
foci, &c., of the lenses, we might hope to combine with all these advantages
that of the destruction of the secondary spectrum, and thus obtain a perfect
telescope.

The above is an abstract of a paper read to the ‘Astronomical Society of
London’ in April 1828, by A. Rogers, Esq.

The reader will easily perceive that the principle on which Mr. Rogers
proposes to construct his telescope is very nearly similar to that of professor
Barlow, described above, with this difference, that the correcting lens of the
Professor’s telescope is composed of a transparent fluid, while that of Mr.
Rogers is a solid lens consisting of a convex crown and concave flint. The
general object intended to be accomplished by both is the same, namely, to
make a correcting lens of a comparatively small diameter serve the purpose

of a large disc of flint glass, which has hitherto been very expensive, and
very difficult to be procured; and likewise to reduce the length of the
telescope while the advantage of a long focal power is secured.—A
telescope, on this principle, was constructed 7 or 8 years ago by Mr. Wilson,
lecturer on Philosophy and Chemistry, Glasgow, before he was aware that
Mr. Rogers had proposed a similar plan. I have had an opportunity of
particularly inspecting Mr. Wilson’s telescope, and trying its effects on
terrestrial objects with high powers, and was on the whole highly pleased
with its performance. It appeared to be almost perfectly achromatic, and
produced a distinct and well-defined image of minute distant objects, such as
small letters on sign-posts, at 2, 3 and 4 miles distant. But I had no
opportunity of trying its effects on double stars or any other celestial objects.
The instrument is above 6 feet long; the object lens is a plano-convex of
crown glass 4 feet focal distance, and 4 inches diameter, the plain side next
the object.

At 26 inches distant from the object lens is the compound lens of 2 inches in
diameter; and the two lenses of which it is composed are both ground to a
radius of 3¾ inches. That made of crown glass is plano-convex, the other,
made of flint glass, is plano-concave, and are placed close together, the
convex side being next the object, and the concave side next the eye. The
greater refractive power of the flint glass renders the compound one slightly
concave in its effect (although the radius of curvature is similar in both), and
lengthens the focus to 6 feet from the object-glass; and this is consequently
the length of the instrument. The compound corrector so placed intercepts all
those rays which go to form the image in the field of view, producing there
an achromatic image. The concave power of the corrector renders the image
larger than if directly produced by a convex lens of the same focus. The
concavity of the corrector is valuable also in this respect, that a very slight
alteration in its distance from the object-glass, changes the focal distance
much more than if it were plain, and enables us to adjust the instrument to
perfect achromatism with great precision.

CHAPTER V.

ON REFLECTING TELESCOPES.

SECT. 1.—HISTORY OF THE INVENTION, AND A GENERAL
DESCRIPTION OF THE CONSTRUCTION OF THESE
INSTRUMENTS.

Reflecting telescopes are those which represent the images of distant objects
by reflection, chiefly from concave mirrors.

Before the achromatic telescope was invented, there were two glaring
imperfections in refracting telescopes, which the astronomers of the 17th
century were anxious to correct. The first was its very great length when a
high power was to be applied, which rendered it very unwieldy and difficult
to use. The second imperfection was the incorrectness of the image as
formed by a single lens. Mathematicians had demonstrated that a pencil of
rays could not be collected in a single point by a spherical lens, and also that
the image transmitted by such a lens would be in some degree incurvated.
After several attempts had been made to correct this imperfection by
grinding lenses to the figure of one of the conic sections, Sir I. Newton
happened to commence an examination of the colours formed by a prism;
and having, by the means of this simple instrument, discovered the different
refrangibility of the rays of light—to which we have several times adverted
in the preceding descriptions—he then perceived that the errors of
telescopes, arising from that cause alone, were some hundred times greater
than such as were occasioned by the spherical figure of lenses; which
induced this illustrious philosopher to turn his attention to the improvement
of telescopes by reflection.

It is generally supposed that Mr. James Gregory—a son of the Rev. John
Gregory, minister of Drumoak in the county of Aberdeen—was the first who
suggested the construction of a reflecting telescope. He was a young man of
uncommon genius, and an eminent mathematician; and in the year 1663, at
the age of only 24, he published in London, his treatise entitled ‘Optica

Promota,’ in which he explained the theory of that species of reflecting
telescope which still bears his name, and which he stated as being his own
invention. But as Gregory, according to his own account, was endowed with
no mechanical dexterity, and could find no workman capable of realizing his
invention—after some fruitless attempts to form proper specula, he was
obliged to give up the pursuit; so that this telescope remained for a
considerable time neglected. It was several years after Gregory suggested
the construction of reflecting telescopes, till Newton directed his attention
fully to the subject. In a letter addressed to the secretary of the Royal
Society, dated in February, 1672, he says, ‘Finding reflections to be regular,
so that the angle of reflection of all sorts of rays was equal to the angle of
incidence, I understood that, by their mediation, optic instruments might be
brought to any degree of perfection imaginable, providing a reflecting
substance could be found which would polish as finely as glass, and reflect
as much light as glass transmits, and the art of communicating to it a
parabolic figure be also obtained. Amidst these thoughts I was forced from
Cambridge by the intervening plague, and it was more than two years before
I proceeded further.’

It was towards the end of 1668, or in the beginning of the following year,
when Newton, being obliged to have recourse to reflectors, and not relying
on any artificer for making the specula, set about the work himself, and early
in the year 1672, completed two small reflecting telescopes. In these he
ground the great speculum into a spherical concave, although he approved of
the parabolic form, but found himself unable to accomplish it. These
telescopes were of a construction somewhat different from what Gregory
had suggested, and though only 6 inches long, were considered as equal to a
6 feet common refracting telescope. It is not a little singular, however, that
we hear no more about the construction of reflectors till more than half a
century afterwards. It was not till the year 1723, that any reflectors were
known to have been made, adapted to celestial observations. In that year,
Mr. Hadley, the inventor of the reflecting quadrant, which goes by his name,
published in No. 376 of the Philosophical Transactions, an account of a large
reflector on Newton’s plan, which he had just then constructed, the
performance of which left no room to doubt that this invention would remain
any longer in obscurity. The large speculum of this instrument was 62⅝
inches focal distance and 5 inches diameter, was furnished with magnifying
powers of from 190 to 230 times, and equalled in performance the famous

aerial telescope of Huygens of 123 feet in length.25 Since this period, the
reflecting telescope has been in general use among astronomers in most
countries of Europe, and has received numerous improvements, under the
direction of Short, Mudge, Edwards and Herschel—the last of whom
constructed reflectors of 7, 10, 20, and even 40 feet in focal length, which
far surpassed, in brightness and magnifying power, all the instruments of this
description, which had previously been attempted.

I shall now proceed to give a brief sketch of the nature of a reflecting
telescope, and the different forms in which they have been proposed to be
constructed.

Fig. 62 represents the reflecting telescope as originally proposed by Gregory.
ABEF represents a tube open at AF towards the object; at the other end is
placed a concave speculum BE, with a hole CD in its centre, the focus of
which is at e. A little beyond this focus, towards the object end of the
telescope AF, is placed another small concave mirror G, having its polished
face turned towards the great speculum, and is supported by an arm GH
fastened to a slider connected with the tube. At the end of the great tube BE
is screwed in a small tube CDKI, containing a small plano-convex lens IK.
Such are the essential parts of this instrument and their relative positions. It
will be recollected in our description of the properties of concave mirrors
(see page 92), that, when rays proceed from a distant object, and fall upon a
concave-speculum, they paint an image or representation of the object in its
focus before the speculum. Now suppose two parallel rays ab falling on the
speculum BE, in cd; they are reflected to its focus e where an inverted image
of the object is formed. This image is formed at a little more than the focal
distance of the small speculum from its surface, and serves as it were for an
object on which the small mirror may act. By the action of this mirror this
first image is reflected to a point about f, where a second image is formed
very large and erect. This image is magnified in the proportion of fG to eG,
the rays from which are transmitted to the eye glass IK, through which the
eye perceives the object clear and distinct, after the proper adjustments have
been made.
figure 66.

fig. 62.

fig. 63.

fig. 64.

fig. 65.

Suppose the focal distance of the great mirror was 9 inches, and the focal
distance of the small mirror 1½ inch—were we to remove the eye piece of
this telescope, and look through the hole of the great mirror, we should see
the image of the object depicted upon the face of the small speculum, and
magnified, in the proportion of 9 to 1½, or, 6 times, on the same principle as
a common convex object glass 9 inches focal length, with an eye glass
whose focus is 1½ inch magnifies 6 times. This may be regarded as the first
part of the magnifying power. If now, we suppose the small speculum placed
a little more than 1½ inch from the image formed by the great speculum, a
second image is formed about f, as much exceeding the first in its
dimensions as it exceeds it in distance from the small speculum, on the
principle on which the object glass of a compound microscope forms a large
image near the eye glass. Suppose this distance to be 9 times greater, then
the whole magnifying power will be compounded of 6 multiplied by 9, or 54
times. As a telescope it magnifies 6 times, and in the microscope part 9
times.—Such is a general idea of the Gregorian telescope, the minute

particulars and structure of which can only be clearly perceived by a direct
inspection of the instrument.

The Newtonian Reflector.—This instrument is somewhat different both in its
form and in its mode of operation from that of Gregory. It is represented in
fig. 63, where BAEF is the tube, and BE, the object concave mirror, which
reflects the parallel rays ab to a plane speculum G, placed 45°, or half a right
angle to the axis of the concave speculum. This small plane reflector must be
of an oval form, the length of the oval should be to the breadth as 7 to 5, on
account of the obliquity of its position. It is supported on an arm fixed to the
side of the tube; an eye-glass is placed in a small tube, moveable in the
larger tube, so as to be perpendicular to the axis of the large reflector, the
perpendicular line passing through the centre of the small mirror. The small
mirror is situated between the large mirror and its focus, that its distance
from this focal point may be equal to the distance from the centre of the
mirror to the focus of the eye-glass. When the rays ab from a distant object
fall upon the large speculum at cd, they are reflected towards a focus at h;
but being intercepted by the plane mirror G, they are reflected
perpendicularly to the eye-glass at I, in the side of the tube, and the image
formed near that position at e is viewed through a small plano-convex lens.
The magnifying power of this telescope is in the proportion of the focal
distance of the speculum to that of the eye-glass. Thus, if the focal distance
of the speculum be 36 inches, and that of the eye-glass 1/3 of an inch, the
magnifying power will be 108 times. It was this form of the reflecting
telescope, that Newton invented, which Sir. W. Herschel adopted, and with
which he made most of his observations and discoveries.

The Cassegrainian Reflector.—This mode of the reflecting telescope,
suggested by M. Cassegrain, a Frenchman, is represented in fig. 64. It is
constructed in the same way as the Gregorian, with the exception of a small
convex speculum G being substituted in the room of the small concave in
Gregory’s construction. As the focus of a convex mirror is negative, it is
placed at a distance from the large speculum equal to the difference of their
foci, that is, if the focal length of the large speculum be 18 inches, and that
of the small convex 2 inches, they are placed at 16 inches distant from each
other, on a principle similar to that of the Galilean telescope, in which the
concave eye-glass is placed within the focus of the object-glass by a space
equal to the focal length of the eye-glass. In this telescope, likewise, instead

of two there is only one image formed, namely that in the focus of the eye-
glass; and, on this account some are of opinion that the distinctness is
considerably greater than in the Gregorian. Mr. Ramsden was of opinion that
this construction is preferable to either of the former reflectors, because the
aberrations of the two metals have a tendency to correct each other, whereas
in the Gregorian both the metals being concave, any error in the specula will
be doubled. It is his opinion that the aberrations in the Cassegrainian
construction to that of the Gregorian is as 3 to 5. The length of this telescope
is shorter than that of a Gregorian of equal focal length, by twice the focal
length of the small mirror, and it shows every thing in an inverted position,
and consequently is not adapted for viewing terrestrial objects.

Dr. Hook’s Reflector.—Before the reflecting telescope was much known, Dr.
Hook contrived one, the form of which is represented, fig. 65, which differs
in little or nothing from the Gregorian, except that the eye-glass I is placed
in the hole of the great speculum BE.

Martin’s Reflector.—Mr. Bengamin Martin, a distinguished writer on optical
and philosophical science, about a century ago, described a new form of the
reflecting telescope, approximating to the Newtonian structure, which he
contrived for his own use. It is represented in fig. 66. ABEF is the tube, in
which there is an opening or aperture OP, in the upper part. Against this hole
within the tube is placed a large plane speculum GH, at half a right angle
with the axis or sides of the tubes, with a hole CD perforated through its
middle. The parallel rays a b falling on the inclined plane GH are reflected
perpendicularly and parallel on the great speculum BE in the bottom of the
tube. From thence they are reflected converging to a focus e through the hole
of the plane mirror CD, which being also the focus of the eye-glass IK, the
eye will perceive the object magnified and distinct.

In the figures referred to in the above descriptions, only one eye-glass is
represented to avoid complexity; but in most reflecting telescopes, the eye-
piece consists of a combination of two plano-convex glasses, as in fig. 67,
which produces a more correct and a larger field of view than a single lens.
This combination is generally known by the name of the Huygenian eye-
piece which shall be described in the section on the eye-pieces of telescopes.

The following rule has been given for finding the magnifying power of the
Gregorian telescope:—Multiply the focal distance of the great mirror by the
distance of the small mirror from the image next the eye; and multiply the
focal distance of the small mirror by the focal distance of the eye-glass; then
divide the product of the former multiplication by the product of the latter,
and the quotient will express the magnifying power. The following are the
dimensions of one of the reflecting telescopes constructed by Mr. Short—
who was long distinguished as the most eminent maker of such instruments,
on a large scale, and whose large reflectors are still to be found in various
observatories throughout Europe.

The focal distance of the great mirror 9.6 inches; or P m, fig. 67, its breadth
FD 2.3; the focal distance of the small mirror L n 1.5—or 1½ inch—its
breadth g h 0.6—or 6/10 of an inch; the breadth of the hole in the great mirror
UV, 0.5—or half an inch—the distance between the small mirror and the
next eye-glass LR, 14.2; the distance between the two eye-glasses SR, 2.4;
the focal distance of the eye-glass next the metal, 3.8.; and the focal distance
of the eye-glass next the eye, S a 1.1, or one inch and one tenth. The
magnifying power of this telescope was about 60 times. Taking this
telescope as a standard, the following table of the dimensions and
magnifying powers of Gregorian reflecting telescopes, as constructed by Mr.
Short, has been computed.

figure 67.

INDEX:
A: Focal distance of the great mirror.
B: Breadth of the great mirror.
C: Focus of the small speculum.
D: Breadth of the hole in the great speculum.

E: Distance between the small speculum and the first eye-glass.
F: Focal distance of the glass next the metals.
G: Focal distance of the glass next the eye.
H: Distance between the plain sides of the two glasses.
I: Magnifying power.
J: Distance between the second glass and the small eye-hole.

A. B. C. D. E.

P m D F L n U V L R
In. Dec. In. Dec. In. Dec. In. Dec. In. Dec.
5. 65 1. 54 1. 10 0. 31 8. 54
9. 60 2. 30 1. 50 0. 39 14. 61
15. 50 3. 30 2. 14 0. 50 23. 81
36. 00 6. 26 3. 43 0. 65 41. 16
60. 00 9. 21 5. 00 0. 85 68. 17

F. G. H. I. J.

R S R S
In. Dec. In. Dec. In. Dec. In.
2. 44 0. 81 1. 68 39 0. 41
3. 13 1. 04 2. 09 39 0. 53
3. 94 1. 31 2. 63 86 0. 66
5. 12 1. 71 3. 41 165 0. 85
6. 43 2. 14 4. 28 243 1. 07

Mr. Short—who was born in Edinburgh in 1710, and died near London,
1768—was considered as the most accurate constructor of reflecting
telescopes, during the period which intervened from 1732, to 1768. In 1743,
he constructed a reflector for Lord Thomas Spencer, of 12 feet focal length,
for which he received 600 guineas. He made several other telescopes of the
same focal distance, with greater improvements and higher magnifiers; and
in 1752, finished one for the king of Spain, for which, with its whole
apparatus, he received £1200. This was considered the noblest instrument of
its kind that had then been constructed, and perhaps it was never surpassed,