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Title: On the Connexion of the Physical Sciences

Author: Mary Somerville

Release date: August 21, 2016 [eBook #52869]
Most recently updated: October 23, 2024

Language: English

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Transcriber’s Note

This book uses some unusual characters, such as
those representing the constellation Aries (♈) and Libra
( ♎ ). These characters may fail to display correctly if
the font you are using does not support them.
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of the text.

MARY SOMERVILLE
J. COOPER Sc.

ON

THE CONNEXION

OF

THE PHYSICAL SCIENCES.
By MARY SOMERVILLE,

AUTHORESS OF ‘MECHANISM OF THE HEAVENS,’ AND
‘PHYSICAL GEOGRAPHY.’

“No natural phenomenon can be adequately studied in itself alone—but,
to be understood, it must be considered as it stands connected with all
Nature.”—Bacon.

Ninth Edition, completely Revised.

LONDON:
JOHN MURRAY, ALBEMARLE STREET.
1858.

The right of Translation is reserved.

LONDON: PRINTED BY W. CLOWES AND SONS, DUKE STREET,
STAMFORD STREET,
AND CHARING CROSS.

This Book is Dedicated

TO

HER DEAR CHILDREN,

BY THEIR AFFECTIONATE MOTHER,
MARY SOMERVILLE.
Florence, Nov. 1, 1858.

CONTENTS.

Introduction
Page 1

SECTION I.
Attraction of a Sphere—Form of Celestial Bodies—Terrestrial Gravitation
retains the Moon in her Orbit—The Heavenly Bodies move in Conic
Sections—Gravitation Proportional to Mass—Gravitation of the Particles
of Matter—Figure of the Planets—How it affects the Motions of their
Satellites—Rotation and Translation impressed by the same Impulse—
Motion of the Sun and Solar System
4

SECTION II.
Elliptical Motion—Mean and True Motion—Equinoctial—Ecliptic—
Equinoxes—Mean and True Longitude—Equation of Centre—Inclination
of the Orbits of Planets—Celestial Latitude—Nodes—Elements of an
Orbit—Undisturbed or Elliptical Orbits—Great Inclination of the Orbits
of the New Planets—Universal Gravitation the Cause of Perturbations in
the Motions of the Heavenly Bodies—Problem of the Three Bodies—
Stability of Solar System depends upon the Primitive Momentum of the
Bodies
8

SECTION III.

Perturbations, Periodic and Secular—Disturbing Action equivalent to three
Partial Forces—Tangential Force the cause of the Periodic Inequalities in
Longitude, and Secular Inequalities in the Form and Position of the Orbit
in its own Plane—Radial Force the cause of Variations in the Planet’s
Distance from the Sun—It combines with the Tangential Force to produce
the Secular Variations in the Form and Position of the Orbit in its own
Plane—Perpendicular Force the cause of Periodic Perturbations in
Latitude, and Secular Variations in the Position of the Orbit with regard to
the Plane of the Ecliptic—Mean Motion and Major Axis Invariable—
Stability of System—Effects of a Resisting Medium—Invariable Plane of
the Solar System and of the Universe—Great Inequality of Jupiter and
Saturn
13

SECTION IV.
Theory of Jupiter’s Satellites—Effects of the Figure of Jupiter upon his
Satellites—Position of their Orbits—Singular Laws among the Motions
of the first Three Satellites—Eclipses of the Satellites—Velocity of Light
—Aberration—Ethereal Medium—Satellites of Saturn and Uranus
27

SECTION V.
Lunar Theory—Periodic Perturbations of the Moon—Equation of Centre—
Evection—Variation—Annual Equation—Direct and Indirect Action of
Planets—The Moon’s Action on the Earth disturbs her own Motion—
Excentricity and Inclination of Lunar Orbit invariable—Acceleration—
Secular Variation in Nodes and Perigee—Motion of Nodes and Perigee
inseparably connected with the Acceleration—Nutation of Lunar Orbit—
Form and Internal Structure of the Earth determined from it—Lunar,
Solar, and Planetary Eclipses—Occultations and Lunar Distances—Mean
Distance of the Sun from the Earth obtained from Lunar Theory—
Absolute Distances of the Planets, how found
34

SECTION VI.
Form of the Earth and Planets—Figure of a Homogeneous Spheroid in
Rotation—Figure of a Spheroid of variable Density—Figure of the Earth,
supposing it to be an Ellipsoid of Revolution—Mensuration of a Degree
of the Meridian—Compression and Size of the Earth from Degrees of
Meridian—Figure of Earth from the Pendulum
44

SECTION VII.
Parallax—Lunar Parallax found from Direct Observation—Solar Parallax
deduced from the Transit of Venus—Distance of the Sun from the Earth
—Annual Parallax—Distance of the Fixed Stars
52

SECTION VIII.
Masses of Planets that have no Satellites determined from their
Perturbations—Masses of the others obtained from the Motions of their
Satellites—Masses of the Sun, the Earth, of Jupiter and of the Jovial
System—Mass of the Moon—Real Diameters of Planets, how obtained—
Size of Sun, Densities of the Heavenly Bodies—Formation of
Astronomical Tables—Requisite Data and Means of obtaining them
55

SECTION IX.
Rotation of the Sun and Planets—Saturn’s Rings—Periods of the Rotation
of the Moon and other Satellites equal to the Periods of their Revolutions
—Form of Lunar Spheroid—Libration, Aspect, and Constitution of the
Moon—Rotation of Jupiter’s Satellites
65

SECTION X.

Rotation of the Earth invariable—Decrease in the Earth’s mean
Temperature—Earth originally in a state of Fusion—Length of Day
constant—Decrease of Temperature ascribed by Sir John Herschel to the
variation in the Excentricity of the Terrestrial Orbit—Difference in the
Temperature of the two Hemispheres erroneously ascribed to the Excess
in the Length of Spring and Summer in the Southern Hemisphere;
attributed by Sir Charles Lyell to the Operation of existing Causes—
Three principal Axes of Rotation—Position of the Axis of Rotation on the
Surface of the Earth invariable—Ocean not sufficient to restore the
Equilibrium of the Earth if deranged—Its Density and mean Depth—
Internal Structure of the Earth
71

SECTION XI.
Precession and Nutation—Their Effects on the Apparent Places of the Fixed
Stars
79

SECTION XII.
Mean and Apparent Sidereal Time—Mean and Apparent Solar Time—
Equation of Time—English and French Subdivisions of Time—Leap Year
—Christian Era—Equinoctial Time—Remarkable Eras depending upon
the Position of the Solar Perigee—Inequality of the Lengths of the
Seasons in the two Hemispheres—Application of Astronomy to
Chronology—English and French Standards of Weights and Measures
83

SECTION XIII.
Tides—Forces that produce them—Origin and Course of Tidal Wave—Its
Speed—Three kinds of Oscillations in the Ocean—The Semidiurnal
Tides—Equinoctial Tides—Effects of the Declination of the Sun and
Moon—Theory insufficient without Observation—Direction of the Tidal
Wave—Height of Tides—Mass of Moon obtained from her Action on the

Tides—Interference of Undulations—Impossibility of a Universal
Inundation—Currents
91

SECTION XIV.
Molecular Forces—Permanency of the ultimate Particles of Matter—
Interstices—Mossotti’s Theory—Rankin’s Theory of Molecular Vortices
—Gases reduced to Liquids by Pressure—Gravitation of Particles—
Cohesion—Crystallization—Cleavage—Isomorphism—Minuteness of
the Particles—Height of Atmosphere—Chemical Affinity—Definite
Proportions and Relative Weights of Atoms—Faraday’s Discovery with
regard to Affinity—Capillary Attraction
102

SECTION XV.
Analysis of the Atmosphere—Its pressure—Law of Decrease in Density—
Law of Decrease in Temperature—Measurement of Heights by the
Barometer—Extent of the Atmosphere—Barometrical Variations—
Oscillations—Trade-Winds—Cloud-Ring—Monsoons—Rotation of
Winds—Laws of Hurricanes
117

SECTION XVI.
Sound—Propagation of Sound illustrated by a Field of Standing Corn—
Nature of Waves—Propagation of Sound through the Atmosphere—
Intensity—Noises—A Musical Sound—Quality—Pitch—Extent of
Human Hearing—Velocity of Sound in Air, Water, and Solids—Causes of
the Obstruction of Sound—Law of its Intensity—Reflection of Sound—
Echoes—Thunder—Refraction of Sound—Interference of Sounds
129

SECTION XVII.

Vibration of Musical Strings—Harmonic Sounds—Nodes—Vibration of
Air in Wind-Instruments—Vibration of Solids—Vibrating Plates—Bells
—Harmony—Sounding Boards—Forced Vibrations—Resonance—
Speaking Machines
140

SECTION XVIII.
Refraction—Astronomical Refraction and its Laws—Formation of Tables
of Refraction—Terrestrial Refraction—Its Quantity—Instances of
Extraordinary Refraction—Reflection—Instances of Extraordinary
Reflection—Loss of Light by the Absorbing Power of the Atmosphere—
Apparent Magnitude of Sun and Moon in the Horizon
153

SECTION XIX.
Constitution of Light according to Sir Isaac Newton—Absorption of Light
—Colours of Bodies—Constitution of Light according to Sir David
Brewster—New Colours—Fraunhofer’s Dark Lines—Dispersion of Light
—The Achromatic Telescope—Homogeneous Light—Accidental and
Complementary Colours—M. Plateau’s Experiments and Theory of
Accidental Colours
159

SECTION XX.
Interference of Light—Undulatory Theory of Light—Propagation of Light
—Newton’s Rings—Measurement of the Length of the Waves of Light,
and of the Frequency of the Vibrations of Ether for each Colour—
Newton’s Scale of Colours—Diffraction of Light—Sir John Herschel’s
Theory of the Absorption of Light—Refraction and Reflection of Light
167

SECTION XXI.

Polarization of Light—Defined—Polarization by Refraction—Properties of
the Tourmaline—Double Refraction—All doubly Refracted Light is
Polarized—Properties of Iceland Spar—Tourmaline absorbs one of the
two Refracted Rays—Undulations of Natural Light—Undulations of
Polarized Light—The Optic Axes of Crystals—M. Fresnel’s Discoveries
on the Rays passing along the Optic Axis—Polarization by Reflection
179

SECTION XXII.
Phenomena exhibited by the Passage of Polarized Light through Mica and
Sulphate of Lime—The Coloured Images produced by Polarized Light
passing through Crystals having one and two Optic Axes—Circular
Polarization—Elliptical Polarization—Discoveries of MM. Biot, Fresnel,
and Professor Airy—Coloured Images produced by the Interference of
Polarized Rays—Fluorescence
186

SECTION XXIII.
Objections to the Undulatory Theory, from a difference in the Action of
Sound and Light under the same circumstances, removed—The
Dispersion of Light according to the Undulatory Theory—Arago’s final
proof that the Undulatory Theory is the Law of Nature
199

SECTION XXIV.
Chemical or Photographic Rays of Solar Spectrum—Scheele, Ritter, and
Wollaston’s Discoveries—Wedgwood’s and Sir Humphry Davy’s
Photographic Pictures—The Calotype—The Daguerreotype—The
Chromatype—The Cyanotype—Collodion—Sir John Herschel’s
Discoveries in the Chemical Spectrum—M. Becquerel’s Discoveries of
Inactive Lines in ditto—Thermic Spectrum—Phosphoric Spectrum—
Electrical Properties—Parathermic Rays—Moser and Hunt’s Experiments

—General Structure and antagonist Properties of Solar Spectrum—
Defracted Spectrum
203

SECTION XXV.
Size and Constitution of the Sun—The Solar Spots—Intensity of the Sun’s
Light and Heat—The Sun’s Atmosphere—His influence on the Planets—
Atmospheres of the Planets—The Moon has none—Lunar heat—The
Differential Telescope—Temperature of Space—Internal Heat of the
Earth—Zone of constant Temperature—Increase of Heat with the Depth
—Central Heat—Volcanic Action—Quantity of Heat received from the
Sun—Isogeothermal Lines—Line of Perpetual Congelation—Climate—
Isothermal Lines—Same quantity of Heat annually received and radiated
by the Earth
224

SECTION XXVI.
Influence of Temperature on Vegetation—Vegetation varies with the
Latitude and Height above the Sea—Geographical Distribution of Land
Plants—Distribution of Marine Plants—Corallines, Shell-fish, Reptiles,
Insects, Birds, and Quadrupeds—Varieties of Mankind, yet identity of
Species
248

SECTION XXVII.
Terrestrial Heat—Radiation—Transmission—Melloni’s experiments—Heat
in Solar Spectrum—Polarization of Heat—Nature of Heat—Absorptions
—Dew—Rain—Combustion—Expansion—Compensation Pendulum—
Transmission through Crystals—Propagation—Dynamic Theory of Heat
—Mechanical equivalent of Heat—Latent Heat is the Force of Expansion
—Steam—Work performed by Heat—Conservation of Force—
Mechanical Power in the Tides—Dynamical Power of Light—Analogy
between Light, Heat, and Sound

257

SECTION XXVIII.
Common or Static Electricity, or Electricity of Tension—A Dual Power—
Methods of exciting it—Attraction and Repulsion—Conduction—
Electrics and Non-electrics—Induction—Dielectrics—Tension—Law of
the Electric Force—Distribution—Laws of Distribution—Heat of
Electricity—Electrical Light and its Spectrum—Velocity—Atmospheric
Electricity—Its cause—Electric Clouds—Violent effects of Lightning—
Back Stroke—Electric Glow—Phosphorescence
282

SECTION XXIX.
Voltaic Electricity—The Voltaic Battery—Intensity—Quantity—Static
Electricity, and Electricity in Motion—Luminous Effects—Mr. Grove on
the Electric Arc and Light—Decomposition of Water—Formation of
Crystals by Voltaic Electricity—Photo-galvanic Engraving—Conduction
—Heat of Voltaic Electricity—Electric Fish
297

SECTION XXX.
Discovery of Electro-magnetism—Deflection of the Magnetic Needle by a
Current of Electricity—Direction of the Force—Rotatory Motion by
Electricity—Rotation of a Wire and a Magnet—Rotation of a Magnet
about its Axis—Of Mercury and Water—Electro-Magnetic Cylinder or
Helix—Suspension of a Needle in a Helix—Electro-Magnetic Induction
—Temporary Magnets—The Galvanometer
312

SECTION XXXI.
Electro-Dynamics—Reciprocal Action of Electric Currents—Identity of
Electro-Dynamic Cylinders and Magnets—Differences between the

Action of Voltaic Electricity and Electricity of Tension—Effects of a
Voltaic Current—Ampère’s Theory—Dr. Faraday’s Experiment of
Electrifying and Magnetising a Ray of Light
316

SECTION XXXII.
Magneto-Electricity—Volta-Electric Induction—Magneto-Electric
Induction—Identity in the Action of Electricity and Magnetism—
Description of a Magneto-Electric Apparatus and its Effects—Identity of
Magnetism and Electricity—The Submarine Telegraph
322

SECTION XXXIII.
Electricity produced by Rotation—Direction of the Currents—Electricity
from the Rotation of a Magnet—M. Arago’s Experiment explained—
Rotation of a Plate of Iron between the Poles of a Magnet—Relation of
Substances to Magnets of three Kinds—Thermo-Electricity
330

SECTION XXXIV.
Magnetism a Dual Power—Antithetic Character of Paramagnetism and
Diamagnetism—The Earth Paramagnetic—Properties of Paramagnetic
Bodies—Polarity—Induction—Lines of Magnetic Force—Currents of
Electricity induced by them—Proved to be Closed Curves—Analogy and
Identity of Electricity and Magnetism—Terrestrial Magnetism—Mean
Values of the Three Magnetic Elements—Their Variations in Double
Progression proved to consist of Two Superposed Variations—Discovery
of the Periodicity of the Magnetic Storms—The Decennial Period of the
Magnetic Elements the same with that of the Solar Spots—Magnetism of
the Atmosphere—Diamagnetism—Action of Electro-Magnetism on
Paramagnetic, Diamagnetic Bodies, and on Copper, very different—Proof
of Diamagnetic Polarity and Induction—Magnecrystallic Action—Effects
of Compression, Heat, and Cleavage on Magnetic Bodies—Mutual

Dependence of Light, Heat, Electricity, &c. &c.—The Conservation of
Force and the Permanency of Matter Primary Laws of Nature—Definition
of Gravity not according to that Law—Gravity only the Residual Force of
a Universal Power—Magnetism of the Ethereal Medium
335

SECTION XXXV.
Ethereal Medium—Comets—Do not disturb the Solar System—Their
Orbits and Disturbances—M. Faye’s Comet probably the same with
Lexel’s—Periods of other three known—Acceleration in the mean
Motions of Encke’s and Biela’s Comets—The Shock of a Comet—
Disturbing Action of the Earth and Planets on Encke’s and Biela’s
Comets—Velocity of Comets—The Comet of 1264—The great Comet of
1343—Physical Constitution—Shine by borrowed Light—Estimation of
their Number
358

SECTION XXXVI.
The Fixed Stars—Their Number—The Milky Way—Double Stars—Binary
Systems—Their Orbits and Periodic Times—Colours of the Stars—Stars
that have vanished—Variable Stars—Variation in Sun’s Light—Parallax
and Distances of the Fixed Stars—Masses of the Stars—Comparative
Light of the Stars—Proper Motions of the Stars—Apparent Motions of
the Stars—Motion and Velocity of the Sun and Solar System—The
Nebulæ—Their Number—Catalogue of them—Consist of Two Classes—
Diffuse Nebulæ—Definitely formed Nebulæ—Globular Clusters—
Splendour of Milky Way—Distribution of the Nebulæ—The Magellanic
Clouds—Nebulæ round η Argûs—Constitution of Nebulæ, and the
Forces that maintain them—Meteorites and Shooting Stars
384

SECTION XXXVII.

Diffusion of Matter through Space—Gravitation—Its Velocity—Simplicity
of its Laws—Gravitation independent of the Magnitude and Distances of
the Bodies—Not impeded by the intervention of any Substance—Its
Intensity invariable—General Laws—Recapitulation and Conclusion
424

Notes
429

Index
479

THE CONNECTION
OF

THE PHYSICAL SCIENCES.

INTRODUCTION.

Science, regarded as the pursuit of truth, must ever afford occupation of
consummate interest, and subject of elevated meditation. The contemplation
of the works of creation elevates the mind to the admiration of whatever is
great and noble; accomplishing the object of all study, which, in the
eloquent language of Sir James Mackintosh, “is to inspire the love of truth,
of wisdom, of beauty—especially of goodness, the highest beauty—and of
that supreme and eternal Mind, which contains all truth and wisdom, all
beauty and goodness. By the love or delightful contemplation and pursuit of
these transcendent aims, for their own sake only, the mind of man is raised
from low and perishable objects, and prepared for those high destinies
which are appointed for all those who are capable of them.”
Astronomy affords the most extensive example of the connection of the
physical sciences. In it are combined the sciences of number and quantity,
of rest and motion. In it we perceive the operation of a force which is mixed
up with everything that exists in the heavens or on earth; which pervades
every atom, rules the motions of animate and inanimate beings, and is as
sensible in the descent of a rain-drop as in the falls of Niagara; in the weight
of the air, as in the periods of the moon. Gravitation not only binds satellites
to their planet, and planets to the sun, but it connects sun with sun
throughout the wide extent of creation, and is the cause of the disturbances,
as well as of the order of nature; since every tremor it excites in any one
planet is immediately transmitted to the farthest limits of the system, in
oscillations which correspond in their periods with the cause producing
them, like sympathetic notes in music, or vibrations from the deep tones of
an organ.
The heavens afford the most sublime subject of study which can be
derived from science. The magnitude and splendour of the objects, the
inconceivable rapidity with which they move, and the enormous distances
between them, impress the mind with some notion of the energy that

maintains them in their motions, with a durability to which we can see no
limit. Equally conspicuous is the goodness of the great First Cause, in
having endowed man with faculties, by which he can not only appreciate
the magnificence of His works, but trace, with precision, the operation of
His laws, use the globe he inhabits as a base wherewith to measure the
magnitude and distance of the sun and planets, and make the diameter (Note
1) of the earth’s orbit the first step of a scale by which he may ascend to the
starry firmament. Such pursuits, while they ennoble the mind, at the same
time inculcate humility, by showing that there is a barrier which no energy,
mental or physical, can ever enable us to pass: that, however profoundly we
may penetrate the depths of space, there still remain innumerable systems,
compared with which, those apparently so vast must dwindle into
insignificance, or even become invisible; and that not only man, but the
globe he inhabits—nay, the whole system of which it forms so small a part
—might be annihilated, and its extinction be unperceived in the immensity
of creation.
A complete acquaintance with physical astronomy can be attained by
those only who are well versed in the higher branches of mathematical and
mechanical science (N. 2), and they alone can appreciate the extreme
beauty of the results, and of the means by which these results are obtained.
It is nevertheless true, that a sufficient skill in analysis (N. 3) to follow the
general outline—to see the mutual dependence of the different parts of the
system, and to comprehend by what means the most extraordinary
conclusions have been arrived at,—is within the reach of many who shrink
from the task, appalled by difficulties, not more formidable than those
incident to the study of the elements of every branch of knowledge. There is
a wide distinction between the degree of mathematical acquirement
necessary for making discoveries, and that which is requisite for
understanding what others have done.
Our knowledge of external objects is founded upon experience, which
furnishes facts; the comparison of these facts establishes relations, from
which the belief that like causes will produce like effects leads to general
laws. Thus, experience teaches that bodies fall at the surface of the earth
with an accelerated velocity, and with a force proportional to their masses.
By comparison, Newton proved that the force which occasions the fall of
bodies at the earth’s surface is identical with that which retains the moon in
her orbit; and he concluded, that, as the moon is kept in her orbit by the

attraction of the earth, so the planets might be retained in their orbits by the
attraction of the sun. By such steps he was led to the discovery of one of
those powers with which the Creator has ordained that matter should
reciprocally act upon matter.
Physical astronomy is the science which compares and identifies the laws
of motion observed on earth with the motions that take place in the heavens:
and which traces, by an uninterrupted chain of deduction from the great
principle that governs the universe, the revolutions and rotations of the
planets, and the oscillations (N. 4) of the fluids at their surfaces; and which
estimates the changes the system has hitherto undergone, or may hereafter
experience—changes which require millions of years for their
accomplishment.
The accumulated efforts of astronomers, from the earliest dawn of
civilization, have been necessary to establish the mechanical theory of
astronomy. The courses of the planets have been observed for ages, with a
degree of perseverance that is astonishing, if we consider the imperfection
and even the want of instruments. The real motions of the earth have been
separated from the apparent motions of the planets; the laws of the
planetary revolutions have been discovered; and the discovery of these laws
has led to the knowledge of the gravitation (N. 5) of matter. On the other
hand, descending from the principle of gravitation, every motion in the
solar system has been so completely explained, that the laws of any
astronomical phenomena that may hereafter occur are already determined.

SECTION I.

Attraction of a Sphere—Form of Celestial Bodies—Terrestrial Gravitation
retains the Moon in her Orbit—The Heavenly Bodies move in Conic
Sections—Gravitation Proportional to Mass—Gravitation of the Particles
of Matter—Figure of the Planets—How it affects the Motions of their
Satellites—Rotation and Translation impressed by the same Impulse—
Motion of the Sun and Solar System.

It has been proved by Newton, that a particle of matter (N. 6) placed
without the surface of a hollow sphere (N. 7) is attracted by it in the same
manner as if the mass of the hollow sphere, or the whole matter it contains,
were collected into one dense particle in its centre. The same is therefore
true of a solid sphere, which may be supposed to consist of an infinite
number of concentric hollow spheres (N. 8). This, however, is not the case
with a spheroid (N. 9); but the celestial bodies are so nearly spherical, and
at such remote distances from one another, that they attract and are attracted
as if each were condensed into a single particle situate in its centre of
gravity (N. 10)—a circumstance which greatly facilitates the investigation
of their motions.
Newton has shown that the force which retains the moon in her orbit is
the same with that which causes heavy substances to fall at the surface of
the earth. If the earth were a sphere, and at rest, a body would be equally
attracted, that is, it would have the same weight at every point of its surface,
because the surface of a sphere is everywhere equally distant from its
centre. But, as our planet is flattened at the poles (N. 11), and bulges at the
equator, the weight of the same body gradually decreases from the poles,
where it is greatest, to the equator, where it is least. There is, however, a
certain mean (N. 12) latitude (N. 13), or part of the earth intermediate
between the pole and the equator, where the attraction of the earth on bodies

at its surface is the same as if it were a sphere; and experience shows that
bodies there fall through 16·0697 feet in a second. The mean distance
(N. 14) of the moon from the earth is about sixty times the mean radius
(N. 15) of the earth. When the number 16·0697 is diminished in the ratio
(N. 16) of 1 to 3600, which is the square of the moon’s distance (N. 17)
from the earth’s centre, estimated in terrestrial radii, it is found to be exactly
the space the moon would fall through in the first second of her descent to
the earth, were she not prevented by the centrifugal force (N. 18) arising
from the velocity with which she moves in her orbit. The moon is thus
retained in her orbit by a force having the same origin, and regulated by the
same law, with that which causes a stone to fall at the earth’s surface. The
earth may, therefore, be regarded as the centre of a force which extends to
the moon; and, as experience shows that the action and reaction of matter
are equal and contrary (N. 19), the moon must attract the earth with an
equal and contrary force.
Newton also ascertained that a body projected (N. 20) in space (N. 21)
will move in a conic section (N. 22), if attracted by a force proceeding from
a fixed point, with an intensity inversely as the square of the distance
(N. 23); but that any deviation from that law will cause it to move in a curve
of a different nature. Kepler found, by direct observation, that the planets
describe ellipses (N. 24), or oval paths, round the sun. Later observations
show that comets also move in conic sections. It consequently follows that
the sun attracts all the planets and comets inversely as the square of their
distances from its centre; the sun, therefore, is the centre of a force
extending indefinitely in space, and including all the bodies of the system in
its action.
Kepler also deduced from observation that the squares of the periodic
times (N. 25) of the planets, or the times of their revolutions round the sun,
are proportional to the cubes of their mean distances from its centre (N. 26).
Hence the intensity of gravitation of all the bodies towards the sun is the
same at equal distances. Consequently, gravitation is proportional to the
masses (N. 27); for, if the planets and comets were at equal distances from
the sun, and left to the effects of gravity, they would arrive at his surface at
the same time (N. 28). The satellites also gravitate to their primaries (N. 29)
according to the same law that their primaries do to the sun. Thus, by the
law of action and reaction, each body is itself the centre of an attractive
force extending indefinitely in space, causing all the mutual disturbances

which render the celestial motions so complicated, and their investigation
so difficult.
The gravitation of matter directed to a centre, and attracting directly as
the mass and inversely as the square of the distance, does not belong to it
when considered in mass only; particle acts on particle according to the
same law when at sensible distances from each other. If the sun acted on the
centre of the earth, without attracting each of its particles, the tides would
be very much greater than they now are, and would also, in other respects,
be very different. The gravitation of the earth to the sun results from the
gravitation of all its particles, which, in their turn, attract the sun in the ratio
of their respective masses. There is a reciprocal action likewise between the
earth and every particle at its surface. The earth and a feather mutually
attract each other in the proportion of the mass of the earth to the mass of
the feather. Were this not the case, and were any portion of the earth,
however small, to attract another portion, and not be itself attracted, the
centre of gravity of the earth would be moved in space by this action, which
is impossible.
The forms of the planets result from the reciprocal attraction of their
component particles. A detached fluid mass, if at rest, would assume the
form of a sphere, from the reciprocal attraction of its particles. But if the
mass revolve about an axis, it becomes flattened at the poles and bulges at
the equator (N. 11), in consequence of the centrifugal force arising from the
velocity of rotation (N. 30); for the centrifugal force diminishes the gravity
of the particles at the equator, and equilibrium can only exist where these
two forces are balanced by an increase of gravity. Therefore, as the
attractive force is the same on all particles at equal distances from the centre
of a sphere, the equatorial particles would recede from the centre, till their
increase in number balance the centrifugal force by their attraction.
Consequently, the sphere would become an oblate or flattened spheroid, and
a fluid, partially or entirely covering a solid, as the ocean and atmosphere
cover the earth, must assume that form in order to remain in equilibrio. The
surface of the sea is, therefore, spheroidal, and the surface of the earth only
deviates from that figure where it rises above or sinks below the level of the
sea. But the deviation is so small, that it is unimportant when compared
with the magnitude of the earth; for the mighty chain of the Andes, and the
yet more lofty Himalaya, bear about the same proportion to the earth that a
grain of sand does to a globe three feet in diameter. Such is the form of the

earth and planets. The compression (N. 31) or flattening at their poles is,
however, so small, that even Jupiter, whose rotation is the most rapid, and
therefore the most elliptical of the planets, may, from his great distance, be
regarded as spherical. Although the planets attract each other as if they were
spheres, on account of their distances, yet the satellites (N. 32) are near
enough to be sensibly affected in their motions by the forms of their
primaries. The moon, for example, is so near the earth, that the reciprocal
attraction between each of her particles, and each of the particles in the
prominent mass at the terrestrial equator, occasions considerable
disturbances in the motions of both bodies; for the action of the moon on
the matter at the earth’s equator produces a nutation (N. 33) in the axis
(N. 34) of rotation, and the reaction of that matter on the moon is the cause
of a corresponding nutation in the lunar orbit (N. 35).
If a sphere at rest in space receive an impulse passing through its centre
of gravity, all its parts will move with an equal velocity in a straight line;
but, if the impulse does not pass through the centre of gravity, its particles,
having unequal velocities, will have a rotatory or revolving motion, at the
same time that it is translated (N. 36) in space. These motions are
independent of one another; so that a contrary impulse, passing through its
centre of gravity, will impede its progress, without interfering with its
rotation. The sun rotates about an axis, and modern observations show that
an impulse in a contrary direction has not been given to his centre of
gravity, for he moves in space, accompanied by all those bodies which
compose the solar system—a circumstance which in no way interferes with
their relative motions; for, in consequence of the principle that force is
proportional to velocity (N. 37), the reciprocal attractions of a system
remain the same whether its centre of gravity be at rest, or moving
uniformly in space. It is computed that, had the earth received its motion
from a single impulse, that impulse must have passed through a point about
twenty-five miles from its centre.
Since the motions of rotation and translation of the planets are
independent of each other, though probably communicated by the same
impulse, they form separate subjects of investigation.

SECTION II.

Elliptical Motion—Mean and True Motion—Equinoctial—Ecliptic—
Equinoxes—Mean and True Longitude—Equation of Centre—Inclination
of the Orbits of Planets—Celestial Latitude—Nodes—Elements of an
Orbit—Undisturbed or Elliptical Orbits—Great Inclination of the Orbits
of the New Planets—Universal Gravitation the Cause of Perturbations in
the Motions of the Heavenly Bodies—Problem of the Three Bodies—
Stability of Solar System depends upon the Primitive Momentum of the
Bodies.

A planet moves in its elliptical orbit with a velocity varying every instant,
in consequence of two forces, one tending to the centre of the sun, and the
other in the direction of a tangent (N. 38) to its orbit, arising from the
primitive impulse given at the time when it was launched into space. Should
the force in the tangent cease, the planet would fall to the sun by its gravity.
Were the sun not to attract it, the planet would fly off in the tangent. Thus,
when the planet is at the point of its orbit farthest from the sun, his action
overcomes the planet’s velocity, and brings it towards him with such an
accelerated motion, that at last it overcomes the sun’s attraction, and,
shooting past him, gradually decreases in velocity until it arrives at the most
distant point, where the sun’s attraction again prevails (N. 39). In this
motion the radii vectores (N. 40), or imaginary lines joining the centres of
the sun and the planets, pass over equal areas or spaces in equal times
(N. 41).
The mean distance of a planet from the sun is equal to half the major axis
(N. 42) of its orbit: if, therefore, the planet described a circle (N. 43) round
the sun at its mean distance, the motion would be uniform, and the periodic
time unaltered, because the planet would arrive at the extremities of the
major axis at the same instant, and would have the same velocity, whether it

moved in the circular or elliptical orbit, since the curves coincide in these
points. But in every other part the elliptical, or true motion (N. 44), would
either be faster or slower than the circular or mean motion (N. 45). As it is
necessary to have some fixed point in the heavens from whence to estimate
these motions, the vernal equinox (N. 46) at a given epoch has been chosen.
The equinoctial, which is a great circle traced in the starry heavens by the
imaginary extension of the plane of the terrestrial equator, is intersected by
the ecliptic, or apparent path of the sun, in two points diametrically opposite
to one another, called the vernal and autumnal equinoxes. The vernal
equinox is the point through which the sun passes in going from the
southern to the northern hemisphere; and the autumnal, that in which he
crosses from the northern to the southern. The mean or circular motion of a
body, estimated from the vernal equinox, is its mean longitude; and its
elliptical, or true motion, reckoned from that point, is its true longitude
(N. 47): both being estimated from west to east, the direction in which the
bodies move. The difference between the two is called the equation of the
centre (N. 48); which consequently vanishes at the apsides (N. 49), or
extremities of the major axis, and is at its maximum ninety degrees (N. 50)
distant from these points, or in quadratures (N. 51), where it measures the
excentricity (N. 52) of the orbit; so that the place of the planet in its
elliptical orbit is obtained by adding or subtracting the equation of the
centre to or from its mean longitude.
The orbits of the principal planets have a very small obliquity or
inclination (N. 53) to the plane of the ecliptic in which the earth moves;
and, on that account, astronomers refer their motions to this plane at a given
epoch as a known and fixed position. The angular distance of a planet from
the plane of the ecliptic is its latitude (N. 54), which is south or north
according as the planet is south or north of that plane. When the planet is in
the plane of the ecliptic, its latitude is zero; it is then said to be in its nodes
(N. 55). The ascending node is that point in the ecliptic through which the
planet passes in going from the southern to the northern hemisphere. The
descending node is a corresponding point in the plane of the ecliptic
diametrically opposite to the other, through which the planet descends in
going from the northern to the southern hemisphere. The longitude and
latitude of a planet cannot be obtained by direct observation, but are
deduced from observations made at the surface of the earth by a very simple
computation. These two quantities, however, will not give the place of a

planet in space. Its distance from the sun (N. 56) must also be known; and,
for the complete determination of its elliptical motion, the nature and
position of its orbit must be ascertained by observation. This depends upon
seven quantities, called the elements of the orbit (N. 57). These are, the
length of the major axis, and the excentricity, which determine the form of
the orbit; the longitude of the planet when at its least distance from the sun,
called the longitude of the perihelion; the inclination of the orbit to the
plane of the ecliptic, and the longitude of its ascending node: these give the
position of the orbit in space; but the periodic time, and the longitude of the
planet at a given instant, called the longitude of the epoch, are necessary for
finding the place of the body in its orbit at all times. A perfect knowledge of
these seven elements is requisite for ascertaining all the circumstances of
undisturbed elliptical motion. By such means it is found that the paths of
the planets, when their mutual disturbances are omitted, are ellipses nearly
approaching to circles, whose planes, slightly inclined to the ecliptic, cut it
in straight lines, passing through the centre of the sun (N. 58). The orbits of
the recently-discovered planets deviate more from the ecliptic than those of
the ancient planets: that of Pallas, for instance, has an inclination of 34° 42ʹ
29·8ʺ to it; on which account it is more difficult to determine their motions.
Were the planets attracted by the sun only, they would always move in
ellipses, invariable in form and position; and because his action is
proportional to his mass, which is much larger than that of all the planets
put together, the elliptical is the nearest approximation to their true motions.
The true motions of the planets are extremely complicated, in consequence
of their mutual attraction, so that they do not move in any known or
symmetrical curve, but in paths now approaching to, now receding from,
the elliptical form; and their radii vectores do not describe areas or spaces
exactly proportional to the time, so that the areas become a test of
disturbing forces.
To determine the motion of each body, when disturbed by all the rest, is
beyond the power of analysis. It is therefore necessary to estimate the
disturbing action of one planet at a time, whence the celebrated problem of
the three bodies, originally applied to the moon, the earth, and the sun—
namely, the masses being given of three bodies projected from three given
points, with velocities given both in quantity and direction; and supposing
the bodies to gravitate to one another with forces that are directly as their
masses, and inversely as the squares of the distances, to find the lines

described by these bodies, and their positions at any given instant; or, in
other words, to determine the path of a celestial body when attracted by a
second body, and disturbed in its motion round the second body by a third
—a problem equally applicable to planets, satellites, and comets.
By this problem the motions of translation of the celestial bodies are
determined. It is an extremely difficult one, and would be infinitely more so
if the disturbing action were not very small when compared with the central
force; that is, if the action of the planets on one another were not very small
when compared with that of the sun. As the disturbing influence of each
body may be found separately, it is assumed that the action of the whole
system, in disturbing any one planet, is equal to the sum of all the particular
disturbances it experiences, on the general mechanical principle, that the
sum of any number of small oscillations is nearly equal to their
simultaneous and joint effect.
On account of the reciprocal action of matter, the stability of the system
depends upon the intensity of the primitive momentum (N. 59) of the
planets, and the ratio of their masses to that of the sun; for the nature of the
conic sections in which the celestial bodies move depends upon the velocity
with which they were first propelled in space. Had that velocity been such
as to make the planets move in orbits of unstable equilibrium (N. 60), their
mutual attractions might have changed them into parabolas, or even
hyperbolas (N. 22); so that the earth and planets might, ages ago, have been
sweeping far from our sun through the abyss of space. But as the orbits
differ very little from circles, the momentum of the planets, when projected,
must have been exactly sufficient to ensure the permanency and stability of
the system. Besides, the mass of the sun is vastly greater than that of any
planet; and as their inequalities bear the same ratio to their elliptical
motions that their masses do to that of the sun, their mutual disturbances
only increase or diminish the excentricities of their orbits by very minute
quantities; consequently the magnitude of the sun’s mass is the principal
cause of the stability of the system. There is not in the physical world a
more splendid example of the adaptation of means to the accomplishment
of an end than is exhibited in the nice adjustment of these forces, at once
the cause of the variety and of the order of Nature.

SECTION III.

Perturbations, Periodic and Secular—Disturbing Action equivalent to three
Partial Forces—Tangential Force the cause of the Periodic Inequalities in
Longitude, and Secular Inequalities in the Form and Position of the Orbit
in its own Plane—Radial Force the cause of Variations in the Planet’s
Distance from the Sun—It combines with the Tangential Force to produce
the Secular Variations in the Form and Position of the Orbit in its own
Plane—Perpendicular Force the cause of Periodic Perturbations in
Latitude, and Secular Variations in the Position of the Orbit with regard to
the Plane of the Ecliptic—Mean Motion and Major Axis Invariable—
Stability of System—Effects of a Resisting Medium—Invariable Plane of
the Solar System and of the Universe—Great Inequality of Jupiter and
Saturn.

The planets are subject to disturbances of two kinds, both resulting from the
constant operation of their reciprocal attraction: one kind, depending upon
their positions with regard to each other, begins from zero, increases to a
maximum, decreases, and becomes zero again, when the planets return to
the same relative positions. In consequence of these, the disturbed planet is
sometimes drawn away from the sun, sometimes brought nearer to him:
sometimes it is accelerated in its motion, and sometimes retarded. At one
time it is drawn above the plane of its orbit, at another time below it,
according to the position of the disturbing body. All such changes, being
accomplished in short periods, some in a few months, others in years, or in
hundreds of years, are denominated periodic inequalities. The inequalities
of the other kind, though occasioned likewise by the disturbing energy of
the planets, are entirely independent of their relative positions. They depend
upon the relative positions of the orbits alone, whose forms and places in
space are altered by very minute quantities, in immense periods of time, and
are therefore called secular inequalities.

The periodical perturbations are compensated when the bodies return to
the same relative positions with regard to one another and to the sun: the
secular inequalities are compensated when the orbits return to the same
positions relatively to one another and to the plane of the ecliptic.
Planetary motion, including both these kinds of disturbance, may be
represented by a body revolving in an ellipse, and making small and
transient deviations, now on one side of its path, and now on the other,
whilst the ellipse itself is slowly, but perpetually, changing both in form and
position.
The periodic inequalities are merely transient deviations of a planet from
its path, the most remarkable of which only lasts about 918 years; but, in
consequence of the secular disturbances, the apsides, or extremities of the
major axes of all the orbits, have a direct but variable motion in space,
excepting those of the orbit of Venus, which are retrograde (N. 61), and the
lines of the nodes move with a variable velocity in a contrary direction.
Besides these, the inclination and excentricity of every orbit are in a state of
perpetual but slow change. These effects result from the disturbing action of
all the planets on each. But, as it is only necessary to estimate the disturbing
influence of one body at a time, what follows may convey some idea of the
manner in which one planet disturbs the elliptical motion of another.
Suppose two planets moving in ellipses round the sun; if one of them
attracted the other and the sun with equal intensity, and in parallel directions
(N. 62), it would have no effect in disturbing the elliptical motion. The
inequality of this attraction is the sole cause of perturbation, and the
difference between the disturbing planet’s action on the sun and on the
disturbed planet constitutes the disturbing force, which consequently varies
in intensity and direction with every change in the relative positions of the
three bodies. Although both the sun and planet are under the influence of
the disturbing force, the motion of the disturbed planet is referred to the
centre of the sun as a fixed point, for convenience. The whole force (N. 63)
which disturbs a planet is equivalent to three partial forces. One of these
acts on the disturbed planet, in the direction of a tangent to its orbit, and is
called the tangential force: it occasions secular inequalities in the form and
position of the orbit in its own plane, and is the sole cause of the periodical
perturbations in the planet’s longitude. Another acts upon the same body in
the direction of its radius vector, that is, in the line joining the centres of the
sun and planet, and is called the radial force: it produces periodical changes

in the distance of the planet from the sun, and affects the form and position
of the orbit in its own plane. The third, which may be called the
perpendicular force, acts at right angles to the plane of the orbit, occasions
the periodic inequalities in the planet’s latitude, and affects the position of
the orbit with regard to the plane of the ecliptic.
It has been observed, that the radius vector of a planet, moving in a
perfectly elliptical orbit, passes over equal spaces or areas in equal times; a
circumstance which is independent of the law of the force, and would be the
same whether it varied inversely as the square of the distance, or not,
provided only that it be directed to the centre of the sun. Hence the
tangential force, not being directed to the centre, occasions an unequable
description of areas, or, what is the same thing, it disturbs the motion of the
planet in longitude. The tangential force sometimes accelerates the planet’s
motion, sometimes retards it, and occasionally has no effect at all. Were the
orbits of both planets circular, a complete compensation would take place at
each revolution of the two planets, because the arcs in which the
accelerations and retardations take place would be symmetrical on each side
of the disturbing force. For it is clear, that if the motion be accelerated
through a certain space, and then retarded through as much, the motion at
the end of the time will be the same as if no change had taken place. But, as
the orbits of the planets are ellipses, this symmetry does not hold: for, as the
planet moves unequably in its orbit, it is in some positions more directly,
and for a longer time, under the influence of the disturbing force than in
others. And, although multitudes of variations do compensate each other in
short periods, there are others, depending on peculiar relations among the
periodic times of the planets, which do not compensate each other till after
one, or even till after many revolutions of both bodies. A periodical
inequality of this kind in the motions of Jupiter and Saturn has a period of
no less than 918 years.
The radial force, or that part of the disturbing force which acts in the
direction of the line joining the centres of the sun and disturbed planet, has
no effect on the areas, but is the cause of periodical changes of small extent
in the distance of the planet from the sun. It has already been shown, that
the force producing perfectly elliptical motion varies inversely as the square
of the distance, and that a force following any other law would cause the
body to move in a curve of a very different kind. Now, the radial disturbing
force varies directly as the distance; and, as it sometimes combines with and

increases the intensity of the sun’s attraction for the disturbed body, and at
other times opposes and consequently diminishes it, in both cases it causes
the sun’s attraction to deviate from the exact law of gravity, and the whole
action of this compound central force on the disturbed body is either greater
or less than what is requisite for perfectly elliptical motion. When greater,
the curvature of the disturbed planet’s path, on leaving its perihelion
(N. 64), or point nearest the sun, is greater than it would be in the ellipse,
which brings the planet to its aphelion (N. 65), or point farthest from the
sun, before it has passed through 180°, as it would do if undisturbed. So that
in this case the apsides, or extremities of the major axis, advance in space.
When the central force is less than the law of gravity requires, the curvature
of the planet’s path is less than the curvature of the ellipse. So that the
planet, on leaving its perihelion, would pass through more than 180° before
arriving at its aphelion, which causes the apsides to recede in space (N. 66).
Cases both of advance and recess occur during a revolution of the two
planets; but those in which the apsides advance preponderate. This,
however, is not the full amount of the motion of the apsides; part arises also
from the tangential force (N. 63), which alternately accelerates and retards
the velocity of the disturbed planet. An increase in the planet’s tangential
velocity diminishes the curvature of its orbit, and is equivalent to a decrease
of central force. On the contrary, a decrease of the tangential velocity,
which increases the curvature of the orbit, is equivalent to an increase of
central force. These fluctuations, owing to the tangential force, occasion an
alternate recess and advance of the apsides, after the manner already
explained (N. 66). An uncompensated portion of the direct motion, arising
from this cause, conspires with that already impressed by the radial force,
and in some cases even nearly doubles the direct motion of these points.
The motion of the apsides may be represented by supposing a planet to
move in an ellipse, while the ellipse itself is slowly revolving about the sun
in the same plane (N. 67). This motion of the major axis, which is direct in
all the orbits except that of the planet Venus, is irregular, and so slow that it
requires more than 109,830 years for the major axis of the earth’s orbit to
accomplish a sidereal revolution (N. 68), that is, to return to the same stars;
and 20,984 years to complete its tropical revolution (N. 69), or to return to
the same equinox. The difference between these two periods arises from a
retrograde motion in the equinoctial point, which meets the advancing axis
before it has completed its revolution with regard to the stars. The major

axis of Jupiter’s orbit requires no less than 200,610 years to perform its
sidereal revolution, and 22,748 years to accomplish its tropical revolution
from the disturbing action of Saturn alone.
A variation in the excentricity of the disturbed planet’s orbit is an
immediate consequence of the deviation from elliptical curvature, caused
by the action of the disturbing force. When the path of the body, in
proceeding from its perihelion to its aphelion, is more curved than it ought
to be from the effect of the disturbing forces, it falls within the elliptical
orbit, the excentricity is diminished, and the orbit becomes more nearly
circular; when that curvature is less than it ought to be, the path of the
planet falls without its elliptical orbit (N. 66), and the excentricity is
increased; during these changes, the length of the major axis is not altered,
the orbit only bulges out, or becomes more flat (N. 70). Thus the variation
in the excentricity arises from the same cause that occasions the motion of
the apsides (N. 67). There is an inseparable connection between these two
elements: they vary simultaneously, and have the same period; so that,
whilst the major axis revolves in an immense period of time, the
excentricity increases and decreases by very small quantities, and at length
returns to its original magnitude at each revolution of the apsides. The
terrestrial excentricity is decreasing at the rate of about 40 miles annually;
and, if it were to decrease equably, it would be 39,861 years before the
earth’s orbit became a circle. The mutual action of Jupiter and Saturn
occasions variations in the excentricity of both orbits, the greatest
excentricity of Jupiter’s orbit corresponding to the least of Saturn’s. The
period in which these vicissitudes are accomplished is 70,414 years,
estimating the action of these two planets alone; but, if the action of all the
planets were estimated, the cycle would extend to millions of years.
That part of the disturbing force is now to be considered which acts
perpendicularly to the plane of the orbit, causing periodic perturbations in
latitude, secular variations in the inclination of the orbit, and a retrograde
motion to its nodes on the true plane of the ecliptic (N. 71). This force tends
to pull the disturbed body above, or push (N. 72) it below, the plane of its
orbit, according to the relative positions of the two planets with regard to
the sun, considered to be fixed. By this action, it sometimes makes the
plane of the orbit of the disturbed body tend to coincide with the plane of
the ecliptic, and sometimes increases its inclination to that plane. In
consequence of which, its nodes alternately recede or advance on the

ecliptic (N. 73). When the disturbing planet is in the line of the disturbed
planet’s nodes (N. 74), it neither affects these points, the latitude, nor the
inclination, because both planets are then in the same plane. When it is at
right angles to the line of the nodes, and the orbit symmetrical on each side
of the disturbing force, the average motion of these points, after a
revolution of the disturbed body, is retrograde, and comparatively rapid:
but, when the disturbing planet is so situated that the orbit of the disturbed
planet is not symmetrical on each side of the disturbing force, which is most
frequently the case, every possible variety of action takes place.
Consequently, the nodes are perpetually advancing or receding with
unequal velocity; but, as a compensation is not effected, their motion is, on
the whole, retrograde.
With regard to the variations in the inclination, it is clear, that, when the
orbit is symmetrical on each side of the disturbing force, all its variations
are compensated after a revolution of the disturbed body, and are merely
periodical perturbations in the planet’s latitude; and no secular change is
induced in the inclination of the orbit. When, on the contrary, that orbit is
not symmetrical on each side of the disturbing force, although many of the
variations in latitude are transient or periodical, still, after a complete
revolution of the disturbed body, a portion remains uncompensated, which
forms a secular change in the inclination of the orbit to the plane of the
ecliptic. It is true, part of this secular change in the inclination is
compensated by the revolution of the disturbing body, whose motion has
not hitherto been taken into the account, so that perturbation compensates
perturbation; but still a comparatively permanent change is effected in the
inclination, which is not compensated till the nodes have accomplished a
complete revolution.
The changes in the inclination are extremely minute (N. 75), compared
with the motion of the nodes, and there is the same kind of inseparable
connection between their secular changes that there is between the variation
of the excentricity and the motion of the major axis. The nodes and
inclinations vary simultaneously; their periods are the same, and very great.
The nodes of Jupiter’s orbit, from the action of Saturn alone, require 36,261
years to accomplish even a tropical revolution. In what precedes, the
influence of only one disturbing body has been considered; but, when the
action and reaction of the whole system are taken into account, every planet
is acted upon, and does itself act, in this manner, on all the others; and the

joint effect keeps the inclinations and excentricities in a state of perpetual
variation. It makes the major axes of all the orbits continually revolve, and
causes, on an average, a retrograde motion of the nodes of each orbit upon
every other. The ecliptic (N. 71) itself is in motion from the mutual action
of the earth and planets, so that the whole is a compound phenomenon of
great complexity, extending through unknown ages. At the present time the
inclinations of all the orbits are decreasing, but so slowly, that the
inclination of Jupiter’s orbit is only about six minutes less than it was in the
age of Ptolemy.
But, in the midst of all these vicissitudes, the length of the major axes
and the mean motions of the planets remain permanently independent of
secular changes. They are so connected by Kepler’s law, of the squares of
the periodic times being proportional to the cubes of the mean distances of
the planets from the sun, that one cannot vary without affecting the other.
And it is proved, that any variations which do take place are transient, and
depend only on the relative positions of the bodies.
It is true that, according to theory, the radial disturbing force should
permanently alter the dimensions of all the orbits, and the periodic times of
all the planets, to a certain degree. For example, the masses of all the
planets revolving within the orbit of any one, such as Mars, by adding to the
interior mass, increase the attracting force of the sun, which, therefore, must
contract the dimensions of the orbit of that planet, and diminish its periodic
time; whilst the planets exterior to Mars’s orbit must have the contrary
effect. But the mass of the whole of the planets and satellites taken together
is so small, when compared with that of the sun, that these effects are quite
insensible, and could only have been discovered by theory. And, as it is
certain that the length of the major axes and the mean motions are not
permanently changed by any other power whatever, it may be concluded
that they are invariable.
With the exception of these two elements, it appears that all the bodies
are in motion, and every orbit in a state of perpetual change. Minute as
these changes are, they might be supposed to accumulate in the course of
ages, sufficiently to derange the whole order of nature, to alter the relative
positions of the planets, to put an end to the vicissitudes of the seasons, and
to bring about collisions which would involve our whole system, now so
harmonious, in chaotic confusion. It is natural to inquire, what proof exists
that nature will be preserved from such a catastrophe? Nothing can be

known from observation, since the existence of the human race has
occupied comparatively but a point in duration, while these vicissitudes
embrace myriads of ages. The proof is simple and conclusive. All the
variations of the solar system, secular as well as periodic, are expressed
analytically by the sines and cosines of circular arcs (N. 76), which increase
with the time; and, as a sine or cosine can never exceed the radius, but must
oscillate between zero and unity, however much the time may increase, it
follows that when the variations have accumulated to a maximum by slow
changes, in however long a time, they decrease, by the same slow degrees,
till they arrive at their smallest value, again to begin a new course; thus for
ever oscillating about a mean value. This circumstance, however, would be
insufficient, were it not for the small excentricities of the planetary orbits,
their minute inclinations to the plane of the ecliptic, and the revolutions of
all the bodies, as well planets as satellites, in the same direction. These
secure the perpetual stability of the solar system (N. 77). However, at the
time that the stability was proved by La Grange and La Place, the telescopic
planets between Mars and Jupiter had not been discovered; but La Grange,
having investigated the subject under a very general point of view, showed
that, if a planetary system be composed of very unequal masses, the whole
of the larger would maintain an unalterable stability with regard to the form
and position of their orbits, while the orbits of the lesser might undergo
unlimited changes. M. Le Verrier has applied this to the solar system, and
has found that the orbits of all the larger planets will for ever maintain an
unalterable stability in form and position; for, though liable to mutations of
very long periods, they return again exactly to what they originally were,
oscillating between very narrow limits; but he found a zone of instability
between the orbit of Mars, and twice the mean distance of the earth from
the sun,[1] or between 1·5 and 2·00; therefore the position and form of the
orbits of such of the telescopic planets as revolve within that zone will be
subject to unlimited variations. But the orbits of those more remote from the
sun than Flora, or beyond 2·20, will be stable, so that their excentricities
and inclinations must always have been, and will always remain, very great,
since they must have depended upon the primitive conditions that prevailed
when these planetary atoms were launched into space. The 51st of these
small bodies, which was discovered, and the elements of its orbit
determined, by M. Valz, at Nimes, has a mean distance of 1·88; so it
revolves within the zone of instability. It has a shorter periodic time than

any of those previously discovered, and a greater excentricity, with the
exception of Nysa. Its orbit cuts that of Mars, and comes nearer to the earth
than the orbits of either Mars or Venus, a circumstance which would be
favourable for correcting the parallax of the sun, or confirming its accuracy.
The telescopic planets, numerous as they are, have no influence on the
motions of the larger planets, for Jupiter has a diameter of 90,734 miles,
while that of Pallas, his nearest neighbour, is only 97 miles, little more than
the distance from London to Bath. The diameter of Mars, on the other side
of the small planets, is 4546 miles, and that of the earth 79251⁄2 miles, so
that the telescopic group are too minute to disturb the others. M. Le Verrier
found another zone of instability between Venus and the sun, on the border
of which Mercury is revolving, the inclination of whose orbit to the plane of
the ecliptic is about 7°, which is more than that of any of the large planets.
Neptune’s orbit is, no doubt, as stable as that of any other of the large
planets, as the inclination is very small, but he will have periodical
variations of very long duration from the reciprocal attraction between him
and Uranus, one especially of an enormous duration, similar to those of
Jupiter and Saturn, and, like them, depending on the time of his revolution
round the sun, being nearly twice as long as that of Saturn. Mr. Adams has
computed that Neptune produces a periodical perturbation in the motion of
Uranus, whose duration is about 6800 years.
The equilibrium of the system, however, would be deranged if the planets
moved in a resisting medium (N. 78) sufficiently dense to diminish their
tangential velocity, for then both the excentricities and the major axes of the
orbits would vary with the time, so that the stability of the system would be
ultimately destroyed. The existence of an ethereal medium is now proved;
and, although it is so extremely rare that hitherto its effects on the motions
of the planets have been altogether insensible, there can be no doubt that, in
the immensity of time, it will modify the forms of the planetary orbits, and
may at last even cause the destruction of our system, which in itself
contains no principle of decay, unless a rotatory motion from west to east
has been given to this medium by the bodies of the solar system, which
have all been revolving about the sun in that direction for unknown ages.
This rotation, which seems to be highly probable, may even have been
coeval with its creation. Such a vortex would have no effect on bodies
moving with it, but it would influence the motions of those revolving in a
contrary direction. It is possible that the disturbances experienced by

comets, which have already revealed the existence of this medium, may
also, in time, disclose its rotatory motion.
The form and position of the planetary orbits, and the motion of the
bodies in the same direction, together with the periodicity of the terms in
which the inequalities are expressed, assure us that the variations of the
system are confined within very narrow limits, and that, although we do not
know the extent of the limits, nor the period of that grand cycle which
probably embraces millions of years, yet they never will exceed what is
requisite for the stability and harmony of the whole; for the preservation of
which every circumstance is so beautifully and wonderfully adapted.
The plane of the ecliptic itself, though assumed to be fixed at a given
epoch for the convenience of astronomical computation, is subject to a
minute secular variation of 45ʺ·7, occasioned by the reciprocal action of the
planets. But, as this is also periodical, and cannot exceed 2° 42ʹ, the
terrestrial equator, which is inclined to it at an angle[2] of 23° 27ʹ 28ʺ·29,
will never coincide with the plane of the ecliptic: so there never can be
perpetual spring (N. 79). The rotation of the earth is uniform; therefore day
and night, summer and winter, will continue their vicissitudes while the
system endures, or is undisturbed by foreign causes.
Yonder starry sphere
Of planets and of fix’d, in all her wheels,
Resembles nearest mazes intricate,
Eccentric, intervolved, yet regular,
Then most, when most irregular they seem.

The stability of our system was established by La Grange: “a discovery,”
says Professor Playfair, “that must render the name for ever memorable in
science, and revered by those who delight in the contemplation of whatever
is excellent and sublime.” After Newton’s discovery of the mechanical laws
of the elliptical orbits of the planets, that of their periodical inequalities, by
La Grange, is, without doubt, the noblest truth in the mechanism of the
heavens; and, in respect of the doctrine of final causes, it may be regarded
as the greatest of all.
Notwithstanding the permanency of our system, the secular variations in
the planetary orbits would have been extremely embarrassing to
astronomers when it became necessary to compare observations separated

by long periods. The difficulty was in part obviated, and the principle for
accomplishing it established, by La Place, and has since been extended by
M. Poinsot. It appears that there exists an invariable plane (N. 80), passing
through the centre of gravity of the system, about which the whole
oscillates within very narrow limits, and that this plane will always remain
parallel to itself, whatever changes time may induce in the orbits of the
planets, in the plane of the ecliptic, or even in the law of gravitation;
provided only that our system remains unconnected with any other. The
position of the plane is determined by this property—that, if each particle in
the system be multiplied by the area described upon this plane in a given
time, by the projection of its radius vector about the common centre of
gravity of the whole, the sum of all these products will be a maximum
(N. 81). La Place found that the plane in question is inclined to the ecliptic
at an angle of nearly 1° 34ʹ 15ʺ, and that, in passing through the sun, and
about midway between the orbits of Jupiter and Saturn, it may be regarded
as the equator of the solar system, dividing it into two parts, which balance
one another in all their motions. This plane of greatest inertia, by no means
peculiar to the solar system, but existing in every system of bodies
submitted to their mutual attractions only, always maintains a fixed
position, whence the oscillations of the system may be estimated through
unlimited time. Future astronomers will know, from its immutability or
variation, whether the sun and his attendants are connected or not with the
other systems of the universe. Should there be no link between them, it may
be inferred, from the rotation of the sun, that the centre of gravity (N. 82) of
the system situate within his mass describes a straight line in this invariable
plane or great equator of the solar system, which, unaffected by the changes
of time, will maintain its stability through endless ages. But, if the fixed
stars, comets, or any unknown and unseen bodies, affect our sun and
planets, the nodes of this plane will slowly recede on the plane of that
immense orbit which the sun may describe about some most distant centre,
in a period which it transcends the power of man to determine. There is
every reason to believe that this is the case; for it is more than probable that,
remote as the fixed stars are, they in some degree influence our system, and
that even the invariability of this plane is relative, only appearing fixed to
creatures incapable of estimating its minute and slow changes during the
small extent of time and space granted to the human race. “The
development of such changes,” as M. Poinsot justly observes, “is similar to

an enormous curve, of which we see so small an arc that we imagine it to be
a straight line.” If we raise our views to the whole extent of the universe,
and consider the stars, together with the sun, to be wandering bodies,
revolving about the common centre of creation, we may then recognise in
the equatorial plane passing through the centre of gravity of the universe the
only instance of absolute and eternal repose.
All the periodic and secular inequalities deduced from the law of
gravitation are so perfectly confirmed by observation, that analysis has
become one of the most certain means of discovering the planetary
irregularities, either when they are too small, or too long in their periods, to
be detected by other methods. Jupiter and Saturn, however, exhibit
inequalities which for a long time seemed discordant with that law. All
observations, from those of the Chinese and Arabs down to the present day,
prove that for ages the mean motions of Jupiter and Saturn have been
affected by a great inequality of a very long period, forming an apparent
anomaly in the theory of the planets. It was long known by observation that
five times the mean motion of Saturn is nearly equal to twice that of Jupiter;
a relation which the sagacity of La Place perceived to be the cause of a
periodic irregularity in the mean motion of each of these planets, which
completes its period in nearly 918 years, the one being retarded while the
other is accelerated; but both the magnitude and period of these quantities
vary, in consequence of the secular variations in the elements of the orbits.
Suppose the two planets to be on the same side of the sun, and all three in
the same straight line, they are then said to be in conjunction (N. 83). Now,
if they begin to move at the same time, one making exactly five revolutions
in its orbit while the other only accomplishes two, it is clear that Saturn, the
slow-moving body, will only have got through a part of its orbit during the
time that Jupiter has made one whole revolution and part of another, before
they be again in conjunction. It is found that during this time their mutual
action is such as to produce a great many perturbations which compensate
each other, but that there still remains a portion outstanding, owing to the
length of time during which the forces act in the same manner; and, if the
conjunction always happened in the same point of the orbit, this
uncompensated inequality in the mean motion would go on increasing till
the periodic times and forms of the orbits were completely and permanently
changed: a case that would actually take place if Jupiter accomplished
exactly five revolutions in the time Saturn performed two. These

revolutions are, however, not exactly commensurable; the points in which
the conjunctions take place are in advance each time as much as 8°·37; so
that the conjunctions do not happen exactly in the same points of the orbits
till after a period of 850 years; and, in consequence of this small advance,
the planets are brought into such relative positions, that the inequality,
which seemed to threaten the stability of the system, is completely
compensated, and the bodies, having returned to the same relative positions
with regard to one another and the sun, begin a new course. The secular
variations in the elements of the orbit increase the period of the inequality
to 918 years (N. 84). As any perturbation which affects the mean motion
affects also the major axis, the disturbing forces tend to diminish the major
axis of Jupiter’s orbit, and increase that of Saturn’s, during one half of the
period, and the contrary during the other half. This inequality is strictly
periodical, since it depends upon the configuration (N. 85) of the two
planets; and theory is confirmed by observation, which shows that, in the
course of twenty centuries, Jupiter’s mean motion has been accelerated by
about 3° 23ʹ, and Saturn’s retarded by 5° 13ʹ. Several instances of
perturbations of this kind occur in the solar system. One, in the mean
motions of the Earth and Venus, only amounting to a few seconds, has been
recently worked out with immense labour by Professor Airy. It
accomplishes its changes in 240 years, and arises from the circumstance of
thirteen times the periodic time of Venus being nearly equal to eight times
that of the Earth. Small as it is, it is sensible in the motions of the Earth.
It might be imagined that the reciprocal action of such planets as have
satellites would be different from the influence of those that have none. But
the distances of the satellites from their primaries are incomparably less
than the distances of the planets from the sun, and from one another. So that
the system of a planet and its satellites moves nearly as if all these bodies
were united in their common centre of gravity. The action of the sun,
however, in some degree disturbs the motion of the satellites about their
primary.

SECTION IV.

Theory of Jupiter’s Satellites—Effects of the Figure of Jupiter upon his
Satellites—Position of their Orbits—Singular Laws among the Motions
of the first Three Satellites—Eclipses of the Satellites—Velocity of Light
—Aberration—Ethereal Medium—Satellites of Saturn and Uranus.

The changes which take place in the planetary system are exhibited on a
smaller scale by Jupiter and his satellites; and, as the period requisite for the
development of the inequalities of these moons only extends to a few
centuries, it may be regarded as an epitome of that grand cycle which will
not be accomplished by the planets in myriads of ages. The revolutions of
the satellites about Jupiter are precisely similar to those of the planets about
the sun; it is true they are disturbed by the sun, but his distance is so great,
that their motions are nearly the same as if they were not under his
influence. The satellites, like the planets, were probably projected in
elliptical orbits: but, as the masses of the satellites are nearly 100,000 times
less than that of Jupiter; and as the compression of Jupiter’s spheroid is so
great, in consequence of his rapid rotation, that his equatorial diameter
exceeds his polar diameter by no less than 6000 miles; the immense
quantity of prominent matter at his equator must soon have given the
circular form observed in the orbits of the first and second satellites, which
its superior attraction will always maintain. The third and fourth satellites,
being farther removed from its influence, revolve in orbits with a very small
excentricity. And, although the first two sensibly move in circles, their
orbits acquire a small ellipticity, from the disturbances they experience
(N. 86).
It has been stated, that the attraction of a sphere on an exterior body is the
same as if its mass were united in one particle in its centre of gravity, and
therefore inversely as the square of the distance. In a spheroid, however,

there is an additional force arising from the bulging mass at its equator,
which, not following the exact law of gravity, acts as a disturbing force.
One effect of this disturbing force in the spheroid of Jupiter is to occasion a
direct motion in the greater axes of the orbits of all his satellites, which is
more rapid the nearer the satellite is to the planet, and very much greater
than that part of their motion which arises from the disturbing action of the
sun. The same cause occasions the orbits of the satellites to remain nearly in
the plane of Jupiter’s equator (N. 87), on account of which the satellites are
always seen nearly in the same line (N. 88); and the powerful action of that
quantity of prominent matter is the reason why the motions of the nodes of
these small bodies are so much more rapid than those of the planet. The
nodes of the fourth satellite accomplish a tropical revolution in 531 years,
while those of Jupiter’s orbit require no less than 36,261 years;—a proof of
the reciprocal attraction between each particle of Jupiter’s equator and of
the satellites. In fact, if the satellites moved exactly in the plane of Jupiter’s
equator, they would not be pulled out of that plane, because his attraction
would be equal on both sides of it. But, as their orbits have a small
inclination to the plane of the planet’s equator, there is a want of symmetry,
and the action of the protuberant matter tends to make the nodes regress by
pulling the satellites above or below the planes of their orbits; an action
which is so great on the interior satellites, that the motions of their nodes
are nearly the same as if no other disturbing force existed.
The orbits of the satellites do not retain a permanent inclination, either to
the plane of Jupiter’s equator, or to that of his orbit, but to certain planes
passing between the two, and through their intersection. These have a
greater inclination to his equator the farther the satellite is removed, owing
to the influence of Jupiter’s compression; and they have a slow motion
corresponding to secular variations in the planes of Jupiter’s orbit and
equator.
The satellites are not only subject to periodic and secular inequalities
from their mutual attraction, similar to those which affect the motions and
orbits of the planets, but also to others peculiar to themselves. Of the
periodic inequalities arising from their mutual attraction the most
remarkable take place in the angular motions (N. 89) of the three nearest to
Jupiter, the second of which receives from the first a perturbation similar to
that which it produces in the third; and it experiences from the third a
perturbation similar to that which it communicates to the first. In the

eclipses these two inequalities are combined into one, whose period is
437·659 days. The variations peculiar to the satellites arise from the secular
inequalities occasioned by the action of the planets in the form and position
of Jupiter’s orbit, and from the displacement of his equator. It is obvious
that whatever alters the relative positions of the sun, Jupiter, and his
satellites, must occasion a change in the directions and intensities of the
forces, which will affect the motions and orbits of the satellites. For this
reason the secular variations in the excentricity of Jupiter’s orbit occasion
secular inequalities in the mean motions of the satellites, and in the motions
of the nodes and apsides of their orbits. The displacement of the orbit of
Jupiter, and the variation in the position of his equator, also affect these
small bodies (N. 90). The plane of Jupiter’s equator is inclined to the plane
of his orbit at an angle of 3° 5ʹ 30ʺ, so that the action of the sun and of the
satellites themselves produces a nutation and precession (N. 91) in his
equator, precisely similar to that which takes place in the rotation of the
earth, from the action of the sun and moon. Hence the protuberant matter at
Jupiter’s equator is continually changing its position with regard to the
satellites, and produces corresponding mutations in their motions. And, as
the cause must be proportional to the effect, these inequalities afford the
means, not only of ascertaining the compression of Jupiter’s spheroid, but
they prove that his mass is not homogeneous. Although the apparent
diameters of the satellites are too small to be measured, yet their
perturbations give the values of their masses with considerable accuracy—a
striking proof of the power of analysis.
A singular law obtains among the mean motions and mean longitudes of
the first three satellites. It appears from observation that the mean motion of
the first satellite, plus twice that of the third, is equal to three times that of
the second; and that the mean longitude of the first satellite, minus three
times that of the second, plus twice that of the third, is always equal to two
right angles. It is proved by theory, that, if these relations had only been
approximate when the satellites were first launched into space, their mutual
attractions would have established and maintained them, notwithstanding
the secular inequalities to which they are liable. They extend to the synodic
motions (N. 92) of the satellites; consequently they affect their eclipses, and
have a very great influence on their whole theory. The satellites move so
nearly in the plane of Jupiter’s equator, which has a very small inclination
to his orbit, that the first three are eclipsed at each revolution by the shadow

of the planet, which is much larger than the shadow of the moon: the fourth
satellite is not eclipsed so frequently as the others. The eclipses take place
close to the disc of Jupiter when he is near opposition (N. 93); but at times
his shadow is so projected with regard to the earth, that the third and fourth
satellites vanish and reappear on the same side of the disc (N. 94). These
eclipses are in all respects similar to those of the moon: but, occasionally,
the satellites eclipse Jupiter, sometimes passing like obscure spots across
his surface, resembling annular eclipses of the sun, and sometimes like a
bright spot traversing one of his dark belts. Before opposition, the shadow
of the satellite, like a round black spot, precedes its passage over the disc of
the planet; and, after opposition, the shadow follows the satellite.
In consequence of the relations already mentioned in the mean motions
and mean longitudes of the first three satellites, they never can be all
eclipsed at the same time: for, when the second and third are in one
direction, the first is in the opposite direction; consequently, when the first
is eclipsed, the other two must be between the sun and Jupiter. The instant
of the beginning or end of an eclipse of a satellite marks the same instant of
absolute time to all the inhabitants of the earth; therefore, the time of these
eclipses observed by a traveller, when compared with the time of the eclipse
computed for Greenwich, or any other fixed meridian (N. 95), gives the
difference of the meridians in time, and, consequently, the longitude of the
place of observation. The longitude is determined with extreme precision
whenever it is possible to convey the time instantaneously by means of
electricity from one place to another, since it obviates the errors of clocks
and chronometers. The eclipses of Jupiter’s satellites have been the means
of a discovery which, though not so immediately applicable to the wants of
man, unfolds one of the properties of light—that medium without whose
cheering influence all the beauties of the creation would have been to us a
blank. It is observed, that those eclipses of the first satellite which happen
when Jupiter is near conjunction (N. 96), are later by 16ʹ 26ʺ·6 than those
which take place when the planet is in opposition. As Jupiter is nearer to us
when in opposition by the whole breadth of the earth’s orbit than when in
conjunction, this circumstance is to be attributed to the time employed by
the rays of light in crossing the earth’s orbit, a distance of about
190,000,000 of miles; whence it is estimated that light travels at the rate of
192,000 miles in one second. Such is its velocity, that the earth, moving at
the rate of nineteen miles in a second, would take two months to pass

through a distance which a ray of light would dart over in eight minutes.
The subsequent discovery of the aberration of light has fully confirmed this
astonishing result.
Objects appear to be situate in the direction of the rays which proceed
from them. Were light propagated instantaneously, every object, whether at
rest or in motion, would appear in the direction of these rays; but, as light
takes some time to travel, we see Jupiter in conjunction, by means of rays
that left him 16m 26s·6 before; but, during that time, we have changed our
position, in consequence of the motion of the earth in its orbit: we therefore
refer Jupiter to a place in which he is not. His true position is in the
diagonal (N. 97) of the parallelogram, whose sides are in the ratio of the
velocity of light to the velocity of the earth in its orbit, which is as 192,000
to 19, or nearly as 10,000 to 1. In consequence of the aberration of light, the
heavenly bodies seem to be in places in which they are not. In fact, if the
earth were at rest, rays from a star would pass along the axis of a telescope
directed to it; but, if the earth were to begin to move in its orbit with its
usual velocity, these rays would strike against the side of the tube; it would,
therefore, be necessary to incline the telescope a little, in order to see the
star. The angle contained between the axis of the telescope and a line drawn
to the true place of the star is its aberration, which varies in quantity and
direction in different parts of the earth’s orbit; but, as it is only 20ʺ·481, it is
insensible in ordinary cases (N. 98).
The velocity of light deduced from the observed aberration of the fixed
stars perfectly corresponds with that given by the eclipses of the first
satellite. The same result, obtained from sources so different, leaves not a
doubt of its truth. Many such beautiful coincidences, derived from
circumstances apparently the most unpromising and dissimilar, occur in
physical astronomy, and prove connections which we might otherwise be
unable to trace. The identity of the velocity of light, at the distance of
Jupiter, and on the earth’s surface, shows that its velocity is uniform; and as
light consists in the vibrations of an elastic medium or ether filling space,
the uniformity of its velocity shows that the density of the medium
throughout the whole extent of the solar system must be proportional to its
elasticity (N. 99). Among the fortunate conjectures which have been
confirmed by subsequent experience, that of Bacon is not the least
remarkable, “It produces in me,” says the restorer of true philosophy, “a
doubt whether the face of the serene and starry heavens be seen at the

instant it really exists, or not till some time later: and whether there be not,
with respect to the heavenly bodies, a true time and an apparent time, no
less than a true place and an apparent place, as astronomers say, on account
of parallax. For it seems incredible that the species or rays of the celestial
bodies can pass through the immense interval between them and us in an
instant, or that they do not even require some considerable portion of time.”
Great discoveries generally lead to a variety of conclusions: the
aberration of light affords a direct proof of the motion of the earth in its
orbit; and its rotation is proved by the theory of falling bodies, since the
centrifugal force it induces retards the oscillations of the pendulum (N. 100)
in going from the pole to the equator. Thus a high degree of scientific
knowledge has been requisite to dispel the errors of the senses (N. 237).
The little that is known of the theories of the satellites of Saturn and
Uranus is, in all respects, similar to that of Jupiter. Saturn is accompanied
by eight satellites. The seventh is about the size of Mars, and the eighth was
simultaneously discovered by Mr. Bond in America, and that distinguished
astronomer Mr. Lassell, of Liverpool. The orbits of the two last have a
sensible inclination to the plane of the ring; but the great compression of
Saturn occasions the other satellites to move nearly in the plane of his
equator. So many circumstances must concur to render the two interior
satellites visible, that they have very rarely been seen. They move exactly at
the edge of the ring, and their orbits never deviate from its plane. In 1789
Sir William Herschel saw them like beads, threading the slender line of
light which the ring is reduced to when seen edgewise from the earth. And
for a short time he perceived them advancing off it at each end, when
turning round in their orbits. The eclipses of the exterior satellites only take
place when the ring is in this position. Mr. Lassell, with a powerful
telescope, made by himself, has seen Iapetus, the nearest of the two, on
several occasions, even when the opening of the ring was very wide, which
made it extremely difficult to see so minute an object. Of the situation of
the equator of Uranus we know nothing, nor of his compression; but the
orbits of his satellites are nearly perpendicular to the plane of the ecliptic;
and, by analogy, they ought to be in the plane of his equator. Uranus is so
remote that he has more the appearance of a planetary nebula than a planet,
which renders it extremely difficult to distinguish the satellites at all; and
quite hopeless without such a telescope as is rarely to be met with even in
observatories. Sir William Herschel discovered the two that are farthest

from the planet, and ascertained their approximate periods, which his son
afterwards determined to be 13d 11h 7m 12s·6 and 8d 16h 56m 28s·6
respectively. The orbits of both seem to have an inclination of about 101°·2
to the plane of the ecliptic. The two interior satellites are so faint and small,
and so near the edge of the planet, that they can with difficulty be seen even
under the most favourable circumstances: however, Mr. Lassell has
ascertained that the more distant of the two revolves about Uranus in 4
days, and that nearest to the planet in 21⁄2 days, and from a long and minute
examination he is convinced that the system only consists of four satellites.
Soon after Neptune was seen Mr. Lassell discovered the only satellite
known to belong to that planet. The satellites of Uranus and Neptune, the
two planets on the remotest verge of the solar system, offer the singular and
only instance of a revolution from east to west, while all the planets and all
the other satellites revolve from west to east. Retrograde motion is
occasionally met with in the comets and double stars.

SECTION V.

Lunar Theory—Periodic Perturbations of the Moon—Equation of Centre—
Evection—Variation—Annual Equation—Direct and Indirect Action of
Planets—The Moon’s Action on the Earth disturbs her own Motion—
Excentricity and Inclination of Lunar Orbit invariable—Acceleration—
Secular Variation in Nodes and Perigee—Motion of Nodes and Perigee
inseparably connected with the Acceleration—Nutation of Lunar Orbit—
Form and Internal Structure of the Earth determined from it—Lunar,
Solar, and Planetary Eclipses—Occultations and Lunar Distances—Mean
Distance of the Sun from the Earth obtained from Lunar Theory—
Absolute Distances of the Planets, how found.

Our constant companion, the moon, next claims our attention. Several
circumstances concur to render her motions the most interesting, and at the
same time the most difficult to investigate, of all the bodies of our system.
In the solar system, planet troubles planet; but, in the lunar theory, the sun is
the great disturbing cause, his vast distance being compensated by his
enormous magnitude, so that the motions of the moon are more irregular
than those of the planets; and, on account of the great ellipticity of her orbit,
and the size of the sun, the approximations to her motions are tedious and
difficult, beyond what those unaccustomed to such investigations could
imagine. The average distance of the moon from the centre of the earth is
only 238,793 miles, so that her motion among the stars is perceptible in a
few hours. She completes a circuit of the heavens in 27d 7h 43m 11s·5,
moving in an orbit whose excentricity is about 12,985 miles. The moon is
about four hundred times nearer to the earth than the sun. The proximity of
the moon to the earth keeps them together. For so great is the attraction of
the sun, that, if the moon were farther from the earth, she would leave it
altogether, and would revolve as an independent planet about the sun.

The disturbing action (N. 101) of the sun on the moon is equivalent to
three forces. The first, acting in the direction of the line joining the moon
and earth, increases or diminishes her gravity to the earth. The second,
acting in the direction of a tangent to her orbit, disturbs her motion in
longitude. And the third, acting perpendicularly to the plane of her orbit,
disturbs her motion in latitude; that is, it brings her nearer to, or removes
her farther from, the plane of the ecliptic than she would otherwise be. The
periodic perturbations in the moon, arising from these forces, are perfectly
similar to the periodic perturbations of the planets. But they are much
greater and more numerous; because the sun is so large, that many
inequalities which are quite insensible in the motions of the planets, are of
great magnitude in those of the moon. Among the innumerable periodic
inequalities to which the moon’s motion in longitude is liable, the most
remarkable are, the Equation of the Centre, which is the difference between
the moon’s mean and true longitude, the Evection, the Variation, and the
Annual Equation. The disturbing force which acts in the line joining the
moon and earth produces the Evection: it diminishes the excentricity of the
lunar orbit in conjunction and opposition, thereby making it more circular,
and augments it in quadrature, which consequently renders it more
elliptical. The period of this inequality is less than thirty-two days. Were the
increase and diminution always the same, the Evection would only depend
upon the distance of the moon from the sun; but its absolute value also
varies with her distance from the perigee (N. 102) of her orbit. Ancient
astronomers, who observed the moon solely with a view to the prediction of
eclipses, which can only happen in conjunction and opposition, where the
excentricity is diminished by the Evection, assigned too small a value to the
ellipticity of her orbit (N. 103). The Evection was discovered by Ptolemy
from observation, about A.D. 140. The Variation produced by the tangential
disturbing force, which is at its maximum when the moon is 45° distant
from the sun, vanishes when that distance amounts to a quadrant, and also
when the moon is in conjunction and opposition; consequently, that
inequality never could have been discovered from the eclipses: its period is
half a lunar month (N. 104). The Annual Equation depends upon the sun’s
distance from the earth: it arises from the moon’s motion being accelerated
when that of the earth is retarded, and vice versâ—for, when the earth is in
its perihelion, the lunar orbit is enlarged by the action of the sun; therefore,
the moon requires more time to perform her revolution. But, as the earth

approaches its aphelion, the moon’s orbit contracts, and less time is
necessary to accomplish her motion—its period, consequently, depends
upon the time of the year. In the eclipses the Annual Equation combines
with the Equation of the Centre of the terrestrial orbit, so that ancient
astronomers imagined the earth’s orbit to have a greater excentricity than
modern astronomers assign to it.
The planets disturb the motion of the moon both directly and indirectly;
their action on the earth alters its relative position with regard to the sun and
moon, and occasions inequalities in the moon’s motion, which are more
considerable than those arising from their direct action; for the same reason
the moon, by disturbing the earth, indirectly disturbs her own motion.
Neither the excentricity of the lunar orbit, nor its mean inclination to the
plane of the ecliptic, have experienced any changes from secular
inequalities; for, although the mean action of the sun on the moon depends
upon the inclination of the lunar orbit to the ecliptic, and the position of the
ecliptic is subject to a secular inequality, yet analysis shows that it does not
occasion a secular variation in the inclination of the lunar orbit, because the
action of the sun constantly brings the moon’s orbit to the same inclination
to the ecliptic. The mean motion, the nodes, and the perigee, however, are
subject to very remarkable variations.
From the eclipse observed at Babylon, on the 19th of March, seven
hundred and twenty-one years before the Christian era, the place of the
moon is known from that of the sun at the instant of opposition (N. 83),
whence her mean longitude may be found. But the comparison of this mean
longitude with another mean longitude, computed back for the instant of the
eclipse from modern observations, shows that the moon performs her
revolution round the earth more rapidly and in a shorter time now than she
did formerly, and that the acceleration in her mean motion has been
increasing from age to age as the square of the time (N. 105). All ancient
and intermediate eclipses confirm this result. As the mean motions of the
planets have no secular inequalities, this seemed to be an unaccountable
anomaly. It was at one time attributed to the resistance of an ethereal
medium pervading space, and at another to the successive transmission of
the gravitating force. But, as La Place proved that neither of these causes,
even if they exist, have any influence on the motions of the lunar perigee
(N. 102) or nodes, they could not affect the mean motion; a variation in the
mean motion from such causes being inseparably connected with variations

in the motions of the perigee and nodes. That great mathematician, in
studying the theory of Jupiter’s satellites, perceived that the secular
variation in the elements of Jupiter’s orbit, from the action of the planets,
occasions corresponding changes in the motions of the satellites, which led
him to suspect that the acceleration in the mean motion of the moon might
be connected with the secular variation in the excentricity of the terrestrial
orbit. Analysis has shown that he assigned the true cause of the
acceleration.
It is proved that the greater the excentricity of the terrestrial orbit, the
greater is the disturbing action of the sun on the moon. Now, as the
excentricity has been decreasing for ages, the effect of the sun in disturbing
the moon has been diminishing during that time. Consequently the
attraction of the earth has had a more and more powerful effect on the
moon, and has been continually diminishing the size of the lunar orbit. So
that the moon’s velocity has been gradually augmenting for many centuries
to balance the increase of the earth’s attraction. This secular increase in the
moon’s velocity is called the Acceleration, a name peculiarly appropriate at
present, and which will continue to be so for a vast number of ages;
because, as long as the earth’s excentricity diminishes, the moon’s mean
motion will be accelerated; but when the excentricity has passed its
minimum, and begins to increase, the mean motion will be retarded from
age to age. The secular acceleration is now about 11ʺ·9, but its effect on the
moon’s place increases as the square of the time (N. 106). It is remarkable
that the action of the planets, thus reflected by the sun to the moon, is much
more sensible than their direct action either on the earth or moon. The
secular diminution in the excentricity, which has not altered the equation of
the centre of the sun by eight minutes since the earliest recorded eclipses,
has produced a variation of about 1° 48ʹ in the moon’s longitude, and of 7°
12ʹ in her mean anomaly (N. 107).
The action of the sun occasions a rapid but variable motion in the nodes
and perigee of the lunar orbit. Though the nodes recede during the greater
part of the moon’s revolution, and advance during the smaller, they perform
their sidereal revolution in 6793d 9h 23m 9s·3, or about 186⁄10 years; and the
perigee accomplishes a revolution, called of the moon’s apsides, in 3232d
13h 48m 29s·6, or a little more than nine years, notwithstanding its motion is
sometimes retrograde and sometimes direct: but such is the difference
between the disturbing energy of the sun and that of all the planets put

together, that it requires no less than 109,830 years for the greater axis of
the terrestrial orbit to do the same, moving at the rate of 11ʺ·8 annually. The
form of the earth has no sensible effect either on the lunar nodes or apsides.
It is evident that the same secular variation which changes the sun’s
distance from the earth, and occasions the acceleration in the moon’s mean
motion, must affect the nodes and perigee. It consequently appears, from
theory as well as observation, that both these elements are subject to a
secular inequality, arising from the variation in the excentricity of the
earth’s orbit, which connects them with the Acceleration, so that both are
retarded when the mean motion is anticipated. The secular variations in
these three elements are in the ratio of the numbers 3, 0·735, and 1; whence
the three motions of the moon, with regard to the sun, to her perigee, and to
her nodes, are continually accelerated, and their secular equations are as the
numbers 1, 4·702, and 0·612. A comparison of ancient eclipses observed by
the Arabs, Greeks, and Chaldeans, imperfect as they are, with modern
observations, confirms these results of analysis. Future ages will develop
these great inequalities, which at some most distant period will amount to
many circumferences (N. 108). They are, indeed, periodic; but who shall
tell their period? Millions of years must elapse before that great cycle is
accomplished.
The moon is so near, that the excess of matter at the earth’s equator
occasions periodic variations in her longitude, and also that remarkable
inequality in her latitude, already mentioned as a nutation in the lunar orbit,
which diminishes its inclination to the ecliptic when the moon’s ascending
node coincides with the equinox of spring, and augments it when that node
coincides with the equinox of autumn. As the cause must be proportional to
the effect, a comparison of these inequalities, computed from theory, with
the same given by observation, shows that the compression of the terrestrial
spheroid, or the ratio of the difference between the polar and the equatorial
diameters, to the diameter of the equator, is 1⁄305·05. It is proved analytically,
that, if a fluid mass of homogeneous matter, whose particles attract each
other inversely as the squares of the distance, were to revolve about an axis
as the earth does, it would assume the form of a spheroid whose
compression is 1⁄230. Since that is not the case, the earth cannot be
homogeneous, but must decrease in density from its centre to its
circumference. Thus the moon’s eclipses show the earth to be round; and
her inequalities not only determine the form, but even the internal structure

of our planet; results of analysis which could not have been anticipated.
Similar inequalities in the motions of Jupiter’s satellites prove that his mass
is not homogeneous, and that his compression is 1⁄13·8. His equatorial
diameter exceeds his polar diameter by about 6000 miles.
The phases (N. 109) of the moon, which vary from a slender silvery
crescent soon after conjunction, to a complete circular disc of light in
opposition, decrease by the same degrees till the moon is again enveloped
in the morning beams of the sun. These changes regulate the returns of the
eclipses. Those of the sun can only happen in conjunction, when the moon,
coming between the earth and the sun, intercepts his light. Those of the
moon are occasioned by the earth intervening between the sun and moon
when in opposition. As the earth is opaque and nearly spherical, it throws a
conical shadow on the side of the moon opposite to the sun, the axis of
which passes through the centres of the sun and earth (N. 110). The length
of the shadow terminates at the point where the apparent diameters (N. 111)
of the sun and earth would be the same. When the moon is in opposition,
and at her mean distance, the diameter of the sun would be seen from her
centre under an angle of 1918ʺ·1. That of the earth would appear under an
angle of 6908ʺ·3. So that the length of the shadow is at least three times and
a half greater than the distance of the moon from the earth, and the breadth
of the shadow, where it is traversed by the moon, is about eight-thirds of the
lunar diameter. Hence the moon would be eclipsed every time she is in
opposition, were it not for the inclination of her orbit to the plane of the
ecliptic, in consequence of which the moon, when in opposition, is either
above or below the cone of the earth’s shadow, except when in or near her
nodes. Her position with regard to them occasions all the varieties in the
lunar eclipses. Every point of the moon’s surface successively loses the
light of different parts of the sun’s disc before being eclipsed. Her
brightness therefore gradually diminishes before she plunges into the earth’s
shadow. The breadth of the space occupied by the penumbra (N. 112) is
equal to the apparent diameter of the sun, as seen from the centre of the
moon. The mean duration of a revolution of the sun, with regard to the node
of the lunar orbit, is to the duration of a synodic revolution (N. 113) of the
moon as 223 to 19. So that, after a period of 223 lunar months, the sun and
moon would return to the same relative position with regard to the node of
the moon’s orbit, and therefore the eclipses would recur in the same order
were not the periods altered by irregularities in the motions of the sun and

moon. In lunar eclipses, our atmosphere bends the sun’s rays which pass
through it all round into the cone of the earth’s shadow. And as the
horizontal refraction (N. 114) or bending of the rays surpasses half the sum
of the semidiameters of the sun and moon, divided by their mutual distance,
the centre of the lunar disc, supposed to be in the axis of the shadow, would
receive the rays from the same point of the sun, round all sides of the earth;
so that it would be more illuminated than in full moon, if the greater portion
of the light were not stopped or absorbed by the atmosphere. Instances are
recorded where this feeble light has been entirely absorbed, so that the
moon has altogether disappeared in her eclipses.
The sun is eclipsed when the moon intercepts his rays (N. 115). The
moon, though incomparably smaller than the sun, is so much nearer the
earth, that her apparent diameter differs but little from his, but both are
liable to such variations that they alternately surpass one another. Were the
eye of a spectator in the same straight line with the centres of the sun and
moon, he would see the sun eclipsed. If the apparent diameter of the moon
surpassed that of the sun, the eclipse would be total. If it were less, the
observer would see a ring of light round the disc of the moon, and the
eclipse would be annular, as it was on the 17th of May, 1836, and on the
15th of March, 1858. If the centre of the moon should not be in the straight
line joining the centres of the sun and the eye of the observer, the moon
might only eclipse a part of the sun. The variation, therefore, in the
distances of the sun and moon from the centre of the earth, and of the moon
from her node at the instant of conjunction, occasions great varieties in the
solar eclipses. Besides, the height of the moon above the horizon changes
her apparent diameter, and may augment or diminish the apparent distances
of the centres of the sun and moon, so that an eclipse of the sun may occur
to the inhabitants of one country, and not to those of another. In this respect
the solar eclipses differ from the lunar, which are the same for every part of
the earth where the moon is above the horizon. In solar eclipses, the light
reflected by the atmosphere diminishes the obscurity they produce. Even in
total eclipses the higher part of the atmosphere is enlightened by a part of
the sun’s disc, and reflects its rays to the earth. The whole disc of the new
moon is frequently visible from atmospheric reflection. During the eclipse
of the 19th of March, 1849, the spots on the lunar disc were distinctly
visible, and during that of 1856 the moon was like a beautiful rose-coloured

ball floating in the ether: the colour is owing to the refraction of the sun’s
light passing through the earth’s atmosphere.
In total solar eclipses the slender luminous arc that is visible for a few
seconds before the sun vanishes and also before he reappears, resembles a
string of pearls surrounding the dark edge of the moon; it is occasioned by
the sun’s rays passing between the tops of the lunar mountains: it occurs
likewise in annular eclipses.
A phenomenon altogether unprecedented was seen during the total
eclipse of the sun which happened on the 8th of July, 1842. The moon was
like a black patch on the sky surrounded by a faint whitish light or corona
about the eighth of the moon’s diameter in breadth, which is supposed to be
the solar atmosphere rendered visible by the intervention of the moon. In
this whitish corona there appeared three rose-coloured flames like the teeth
of a saw. Similar flames were also seen in the white corona of the total
eclipse which took place in 1851, and a long rose-coloured chain of what
appeared to be jagged mountains or sierras united at the base by a red band
seemed to be raised into the corona by mirage; but there is no doubt that the
corona and red phenomena belong to the sun. This red chain was so bright
that Mr. Airy saw it illuminate the northern horizon through an azimuth of
90° with red light. M. Faye attributes the rose-coloured protuberances to the
constitution of the sun, which, like Sir William Herschel, he conceives to be
an incandescent globe, consisting of two concentric parts of very unequal
density, the internal part being a dark spherical mass, the external a very
extensive atmosphere, at a certain height in which there is a stratum of
luminous clouds which constitutes the photosphere of the sun; above this
rises his real atmosphere, so rare as to be only visible as a white aureola or
corona during total and annular eclipses. M. Faye conceives that from the
central mass gaseous eruptions issue, which form the spots by dissipating
and partly extinguishing the luminous clouds, and then rising into the rare
atmosphere above that they appear as rose-coloured protuberances during
annular eclipses. He estimates that the volume of these vapours sometimes
surpasses that of the earth a thousand or even two thousand times. Sir
William Herschel attributed the spots to occasional openings in the
luminous coating, which seems to be always in motion; but whatever the
cause of the spots may be, it is certainly periodical. The white corona and
beads were seen during the eclipse of the 15th March, 1858, but there were

no rose-coloured appearances, in England at least; but the sky was clouded,
so that the eclipse was only visible at intervals.
Planets sometimes eclipse one another. On the 17th of May, 1737,
Mercury was eclipsed by Venus near their inferior conjunction; Mars passed
over Jupiter on the 9th of January, 1591; and on the 30th of October, 1825,
the moon eclipsed Saturn. These phenomena, however, happen very
seldom, because all the planets, or even a part of them, are very rarely seen
in conjunction at once; that is, in the same part of the heavens at the same
time. More than 2500 years before our era the five great planets were in
conjunction. On the 15th of September, 1186, a similar assemblage took
place between the constellations of Virgo and Libra; and in 1801 the Moon,
Jupiter, Saturn, and Venus were united in the heart of the Lion. These
conjunctions are so rare, that Lalande has computed that more than
seventeen millions of millions of years separate the epochs of the
contemporaneous conjunctions of the six great planets.
The motions of the moon have now become of more importance to the
navigator and geographer than those of any other heavenly body, from the
precision with which terrestrial longitude is determined by occultations of
stars, and by lunar distances. In consequence of the retrograde motion of the
nodes of the lunar orbit, at the rate of 3ʹ 10ʺ·64 daily, these points make a
tour of the heavens in a little more than eighteen years and a half. This
causes the moon to move round the earth in a kind of spiral, so that her disc
at different times passes over every point in a zone of the heavens extending
rather more than 5° 9ʹ on each side of the ecliptic. It is therefore evident that
at one time or other she must eclipse every star and planet she meets with in
this space. Therefore the occultation of a star by the moon is a phenomenon
of frequent occurrence. The moon seems to pass over the star, which almost
instantaneously vanishes at one side of her disc, and after a short time as
suddenly reappears on the other. A lunar distance is the observed distance of
the moon from the sun, or from a particular star or planet, at any instant.
The lunar theory is brought to such perfection, that the times of these
phenomena, observed under any meridian, when compared with those
computed for that of Greenwich, and given in the Nautical Almanac, furnish
the longitude of the observer within a few miles (N. 95.)
From the lunar theory, the mean distance of the sun from the earth, and
thence the whole dimensions of the solar system, are known; for the forces
which retain the earth and moon in their orbits are respectively proportional

to the radii vectores of the earth and moon, each being divided by the
square of its periodic time. And, as the lunar theory gives the ratio of the
forces, the ratio of the distances of the sun and moon from the earth is
obtained. Hence it appears that the sun’s mean distance from the earth is
399·7 or nearly 400 times greater than that of the moon. The method of
finding the absolute distances of the celestial bodies, in miles, is in fact the
same with that employed in measuring the distances of terrestrial objects.
From the extremities of a known base (N. 116), the angles which the visual
rays from the object form with it are measured; their sum subtracted from
two right angles gives the angle opposite the base; therefore, by
trigonometry, all the angles and sides of the triangle may be computed—
consequently the distance of the object is found. The angle under which the
base of the triangle is seen from the object is the parallax of that object. It
evidently increases and decreases with the distance. Therefore the base
must be very great indeed to be visible from the celestial bodies. The globe
itself, whose dimensions are obtained by actual admeasurement, furnishes a
standard of measures with which we compare the distances, masses,
densities, and volumes of the sun and planets.

SECTION VI.

Form of the Earth and Planets—Figure of a Homogeneous Spheroid in
Rotation—Figure of a Spheroid of variable Density—Figure of the Earth,
supposing it to be an Ellipsoid of Revolution—Mensuration of a Degree
of the Meridian—Compression and Size of the Earth from Degrees of
Meridian—Figure of Earth from the Pendulum.

The theoretical investigation of the figure of the earth and planets is so
complicated, that neither the geometry of Newton, nor the refined analysis
of La Place, has attained more than an approximation. The solution of that
difficult problem has been accomplished by our distinguished countryman
Mr. Ivory. The investigation has been conducted by successive steps,
beginning with a simple case, and then proceeding to the more difficult.
But, in all, the forces which occasion the revolutions of the earth and
planets are omitted, because, by acting equally upon all the particles, they
do not disturb their mutual relations. A fluid mass of uniform density,
whose particles mutually gravitate to each other, will assume the form of a
sphere when at rest. But, if the sphere begins to revolve, every particle will
describe a circle (N. 117), having its centre in the axis of revolution. The
planes of all these circles will be parallel to one another and perpendicular
to the axis, and the particles will have a tendency to fly from that axis in
consequence of the centrifugal force arising from the velocity of rotation.
The force of gravity is everywhere perpendicular to the surface (N. 118),
and tends to the interior of the fluid mass; whereas the centrifugal force acts
perpendicularly to the axis of rotation, and is directed to the exterior. And,
as its intensity diminishes with the distance from the axis of rotation, it
decreases from the equator to the poles, where it ceases. Now it is clear that
these two forces are in direct opposition to each other in the equator alone,
and that gravity is there diminished by the whole effect of the centrifugal
force, whereas, in every other part of the fluid, the centrifugal force is

resolved into two parts, one of which, being perpendicular to the surface,
diminishes the force of gravity; but the other, being at a tangent to the
surface, urges the particles towards the equator, where they accumulate till
their numbers compensate the diminution of gravity, which makes the mass
bulge at the equator, and become flattened at the poles. It appears, then, that
the influence of the centrifugal force is most powerful at the equator, not
only because it is actually greater there than elsewhere, but because its
whole effect is employed in diminishing gravity, whereas, in every other
point of the fluid mass, it is only a part that is so employed. For both these
reasons, it gradually decreases towards the poles, where it ceases. On the
contrary, gravity is least at the equator, because the particles are farther
from the centre of the mass, and increases towards the poles, where it is
greatest. It is evident, therefore, that, as the centrifugal force is much less
than the force of gravity—gravitation, which is the difference between the
two, is least at the equator, and continually increases towards the poles,
where it is a maximum. On these principles Sir Isaac Newton proved that a
homogeneous fluid (N. 119) mass in rotation assumes the form of an
ellipsoid of revolution (N. 120), whose compression is 1⁄230. Such, however,
cannot be the form of the earth, because the strata increase in density
towards the centre. The lunar inequalities also prove the earth to be so
constructed; it was requisite, therefore, to consider the fluid mass to be of
variable density. Including this condition, it has been found that the mass,
when in rotation, would still assume the form of an ellipsoid of revolution
(N. 120); that the particles of equal density would arrange themselves in
concentric elliptical strata (N. 121), the most dense being in the centre; but
that the compression or flattening would be less than in the case of the
homogeneous fluid. The compression is still less when the mass is
considered to be, as it actually is, a solid nucleus, decreasing regularly in
density from the centre to the surface, and partially covered by the ocean,
because the solid parts, by their cohesion, nearly destroy that part of the
centrifugal force which gives the particles a tendency to accumulate at the
equator, though not altogether; otherwise the sea, by the superior mobility
of its particles, would flow towards the equator and leave the poles dry.
Besides, it is well known that the continents at the equator are more
elevated than they are in higher latitudes. It is also necessary for the
equilibrium of the ocean that its density should be less than the mean
density of the earth, otherwise the continents would be perpetually liable to

inundations from storms and other causes. On the whole, it appears from
theory, that a horizontal line passing round the earth through both poles
must be nearly an ellipse, having its major axis in the plane of the equator,
and its minor axis coincident with the axis of the earth’s rotation (N. 122). It
is easy to show, in a spheroid whose strata are elliptical, that the increase in
the length of the radii (N. 123), the decrease of gravitation, and the increase
in the length of the arcs of the meridian, corresponding to angles of one
degree, from the poles to the equator, are all proportional to the square of
the cosine of the latitude (N. 124). These quantities are so connected with
the ellipticity of the spheroid, that the total increase in the length of the radii
is equal to the compression or flattening, and the total diminution in the
length of the arcs is equal to the compression, multiplied by three times the
length of an arc of one degree at the equator. Hence, by measuring the
meridian curvature of the earth, the compression, and consequently its
figure, become known. This, indeed, is assuming the earth to be an ellipsoid
of revolution; but the actual measurement of the globe will show how far it
corresponds with that solid in figure and constitution.
The courses of the great rivers, which are in general navigable to a
considerable extent, prove that the curvature of the land differs but little
from that of the ocean; and, as the heights of the mountains and continents
are inconsiderable when compared with the magnitude of the earth, its
figure is understood to be determined by a surface at every point
perpendicular to the direction of gravitation, or of the plumb-line, and is the
same which the sea would have if it were continued all round the earth
beneath the continents. Such is the figure that has been measured in the
following manner:—
A terrestrial meridian is a line passing through both poles, all the points
of which have their noon contemporaneously. Were the lengths and
curvatures of different meridians known, the figure of the earth might be
determined. But the length of one degree is sufficient to give the figure of
the earth, if it be measured on different meridians, and in a variety of
latitudes. For, if the earth were a sphere, all degrees would be of the same
length; but, if not, the lengths of the degrees would be greater, exactly in
proportion as the curvature is less. A comparison of the length of a degree in
different parts of the earth’s surface will therefore determine its size and
form.

An arc of the meridian may be measured by determining the latitude of
its extreme points by astronomical observations (N. 125), and then
measuring the distance between them in feet or fathoms. The distance thus
determined on the surface of the earth, divided by the degrees and parts of a
degree contained in the difference of the latitudes, will give the exact length
of one degree, the difference of the latitudes being the angle contained
between the verticals at the extremities of the arc. This would be easily
accomplished were the distance unobstructed and on a level with the sea.
But, on account of the innumerable obstacles on the surface of the earth, it
is necessary to connect the extreme points of the arc by a series of triangles
(N. 126), the sides and angles of which are either measured or computed, so
that the length of the arc is ascertained with much laborious calculation. In
consequence of the irregularities of the surface each triangle is in a different
plane. They must therefore be reduced by computation to what they would
have been had they been measured on the surface of the sea. And, as the
earth may in this case be esteemed spherical, they require a correction to
reduce them to spherical triangles. The officers who conducted the
trigonometrical survey, in measuring 500 feet of a base in Ireland twice
over, found that the difference in the two measurements did not amount to
the 800th part of an inch; and in the General Survey of Great Britain, five
bases were measured from 5 to 7 miles long, and some of them 400 miles
apart, yet, when connected by series of triangles, the measured and
computed lengths did not differ by more than 3 inches, an unparalleled
degree of accuracy; but such is the accuracy with which these operations
are conducted.
Arcs of the meridian have been measured in a variety of latitudes in both
hemispheres, as well as arcs perpendicular to the meridian. From these
measurements it appears that the length of the degrees increases from the
equator to the poles, nearly in proportion to the square of the sine of the
latitude (N. 127). Consequently, the convexity of the earth diminishes from
the equator to the poles.
Were the earth an ellipsoid of revolution, the meridians would be ellipses
whose lesser axes would coincide with the axis of rotation, and all the
degrees measured between the pole and the equator would give the same
compression when combined two and two. That, however, is far from being
the case. Scarcely any of the measurements give exactly the same results,
chiefly on account of local attractions, which cause the plumb-line to

deviate from the vertical. The vicinity of mountains produces that effect.
One of the most remarkable anomalies of this kind has been observed in
certain localities of northern Italy, where the action of some dense
subterraneous matter causes the plumb-line to deviate seven or eight times
more than it did from the attraction of Chimborazo, in the observations of
Bouguer, while measuring a degree of the meridian at the equator. In
consequence of this local attraction, the degrees of the meridian in that part
of Italy seem to increase towards the equator through a small space, instead
of decreasing, as if the earth was drawn out at the poles, instead of being
flattened.
Many other discrepancies occur, but from the mean of the five principal
measurements of arcs in Peru, India, France, England, and Lapland, Mr.
Ivory has deduced that the figure which most nearly follows this law is an
ellipsoid of revolution whose equatorial radius is 3962·824 miles, and the
polar radius 3949·585 miles. The difference, or 13·239 miles, divided by
the equatorial radius, is 1⁄299 nearly[3] (N. 128). This fraction is called the
compression of the earth, and does not differ much from that given by the
lunar inequalities. Since the preceding quantities were determined, arcs of
the meridian have been measured in various parts of the globe, of which the
most extensive are the Russian arc of 25° 20ʹ between the Glacial Sea and
the Danube, conducted under the superintendence of M. Struve, and the
Indian arc extended to 21° 21ʹ, by Colonel Everest. The compression
deduced by Bessel from the sum of ten arcs is 2983⁄4, the equatorial radius
3962·802, and the polar 3949·554 miles, whilst Mr. Airy arrives at an
almost identical result (3962·824, 3949·585, and 29883⁄100) from a
consideration of all the arcs, measured up to 1831, including the great
Indian and Russian ones. If we assume the earth to be a sphere, the length
of a degree of the meridian is 6914⁄100 English miles. Therefore 360 degrees,
or the whole equatorial circumference of the globe, is 24,899 English miles.
Eratosthenes, who died 194 years before the Christian era, was the first to
give an approximate value of the earth’s circumference, by the
measurement of an arc between Alexandria and Syene.
There is another method of finding the figure of the earth, totally
different from the preceding, solely depending upon the increase of
gravitation from the equator to the poles. The force of gravitation at any
place is measured by the descent of a heavy body during the first second of

its fall. And the intensity of the centrifugal force is measured by the
deflection of any point from the tangent in a second. For, since the
centrifugal force balances the attraction of the earth, it is an exact measure
of the gravitating force. Were the attraction to cease, a body on the surface
of the earth would fly off in the tangent by the centrifugal force, instead of
bending round in the circle of rotation. Therefore, the deflection of the
circle from the tangent in a second measures the intensity of the earth’s
attraction, and is equal to the versed sine of the arc described during that
time, a quantity easily determined from the known velocity of the earth’s
rotation. Whence it has been found that at the equator the centrifugal force
is equal to the 289th part of gravity. Now, it is proved by analysis that,
whatever the constitution of the earth and planets may be, if the intensity of
gravitation at the equator be taken equal to unity, the sum of the
compression of the ellipsoid, and the whole increase of gravitation from the
equator to the pole, is equal to five halves of the ratio of the centrifugal
force to gravitation at the equator. This quantity with regard to the earth is
5
⁄2 of 1⁄289 or 1⁄115·2. Consequently, the compression of the earth is equal to
1
⁄115·2 diminished by the whole increase of gravitation. So that its form will
be known, if the whole increase of gravitation from the equator to the pole
can be determined by experiment. This has been accomplished by a method
founded upon the following considerations:—If the earth were a
homogeneous sphere without rotation, its attraction on bodies at its surface
would be everywhere the same. If it be elliptical and of variable density, the
force of gravity, theoretically, ought to increase from the equator to the
pole, as unity plus a constant quantity multiplied into the square of the sine
of the latitude (N. 127). But for a spheroid in rotation the centrifugal force
varies, by the laws of mechanics, as the square of the sine of the latitude,
from the equator, where it is greatest, to the pole, where it vanishes. And, as
it tends to make bodies fly off the surface, it diminishes the force of gravity
by a small quantity. Hence, by gravitation, which is the difference of these
two forces, the fall of bodies ought to be accelerated from the equator to the
poles proportionably to the square of the sine of the latitude; and the weight
of the same body ought to increase in that ratio. This is directly proved by
the oscillations of the pendulum (N. 129), which, in fact, is a falling body;
for, if the fall of bodies be accelerated, the oscillations will be more rapid:
in order, therefore, that they may always be performed in the same time, the
length of the pendulum must be altered. By numerous and careful

experiments it is proved that a pendulum, which oscillates 86,400 times in a
mean day at the equator, will do the same at every point of the earth’s
surface, if its length be increased progressively to the pole, as the square of
the sine of the latitude.
From the mean of these it appears that the whole decrease of gravitation
from the poles to the equator is 0·0051449, which, subtracted from 1⁄115·2,
shows that the compression of the terrestrial spheroid is about 1⁄285·26. This
value has been deduced by the late Mr. Baily, president of the Astronomical
Society, who devoted much attention to this subject; at the same time, it
may be observed that no two sets of pendulum experiments give the same
result, probably from local attractions. The compression obtained by this
method does not differ much from that given by the lunar inequalities, nor
from the arcs in the direction of the meridian, and those perpendicular to it.
The near coincidence of these three values, deduced by methods so entirely
independent of each other, shows that the mutual tendencies of the centres
of the celestial bodies to one another, and the attraction of the earth for
bodies at its surface, result from the reciprocal attraction of all their
particles. Another proof may be added. The nutation of the earth’s axis and
the precession of the equinoxes (N. 146) are occasioned by the action of the
sun and moon on the protuberant matter at the earth’s equator. And,
although these inequalities do not give the absolute value of the terrestrial
compression, they show that the fraction expressing it is comprised between
the limits 1⁄279 and 1⁄573.
It might be expected that the same compression should result from each,
if the different methods of observation could be made without error. This,
however, is not the case; for after allowance has been made for every cause
of error, such discrepancies are found, both in the degrees of the meridian
and in the length of the pendulum, as show that the figure of the earth is
very complicated. But they are so small, when compared with the general
results, that they may be disregarded. The compression deduced from the
mean of the whole appears not to differ much from 1⁄300; that given by the
lunar theory has the advantage of being independent of the irregularities of
the earth’s surface and of local attractions. The regularity with which the
observed variation in the length of the pendulum follows the law of the
square of the sine of the latitude proves the strata to be elliptical, and
symmetrically disposed round the centre of gravity of the earth, which

affords a strong presumption in favour of its original fluidity. It is
remarkable how little influence the sea has on the variation of the lengths of
the arcs of the meridian, or on gravitation; neither does it much affect the
lunar inequalities, from its density being only about a fifth of the mean
density of the earth. For, if the earth were to become fluid, after being
stripped of the ocean, it would assume the form of an ellipsoid of revolution
whose compression is 1⁄304·8, which differs very little from that determined
by observation, and proves, not only that the density of the ocean is
inconsiderable, but that its mean depth is very small. There are profound
cavities in the bottom of the sea, but its mean depth probably does not much
exceed the mean height of the continents and islands above its level. On this
account, immense tracts of land may be deserted or overwhelmed by the
ocean, as appears really to have been the case, without any great change in
the form of the terrestrial spheroid. The variation in the length of the
pendulum was first remarked by Richter in 1672, while observing transits
of the fixed stars across the meridian at Cayenne, about five degrees north
of the equator. He found that his clock lost at the rate of 2m 28s daily, which
induced him to determine the length of a pendulum beating seconds in that
latitude; and, repeating the experiments on his return to Europe, he found
the seconds’ pendulum at Paris to be more than the twelfth of an inch longer
than that at Cayenne. The form and size of the earth being determined, a
standard of measure is furnished with which the dimensions of the solar
system may be compared.

SECTION VII.

Parallax—Lunar Parallax found from Direct Observation—Solar Parallax
deduced from the Transit of Venus—Distance of the Sun from the Earth
—Annual Parallax—Distance of the Fixed Stars.

The parallax of a celestial body is the angle under which the radius of the
earth would be seen if viewed from the centre of that body; it affords the
means of ascertaining the distances of the sun, moon, and planets (N. 130).
When the moon is in the horizon at the instant of rising or setting, suppose
lines to be drawn from her centre to the spectator and to the centre of the
earth: these would form a right-angled triangle with the terrestrial radius,
which is of a known length; and, as the parallax or angle at the moon can be
measured, all the angles and one side are given; whence the distance of the
moon from the centre of the earth may be computed. The parallax of an
object may be found, if two observers under the same meridian, but at a
very great distance from one another, observe its zenith distances on the
same day at the time of its passage over the meridian. By such
contemporaneous observations at the Cape of Good Hope and at Berlin, the
mean horizontal parallax of the moon was found to be 3459ʺ, whence the
mean distance of the moon is about sixty times the greatest terrestrial
radius, or 237,608 miles nearly.[4] Since the parallax is equal to the radius of
the earth divided by the distance of the moon, it varies with the distance of
the moon from the earth under the same parallel of latitude, and proves the
ellipticity of the lunar orbit. When the moon is at her mean distance, it
varies with the terrestrial radii, thus showing that the earth is not a sphere
(N. 131).
Although the method described is sufficiently accurate for finding the
parallax of an object as near as the moon, it will not answer for the sun,
which is so remote that the smallest error in observation would lead to a

false result. But that difficulty is obviated by the transits of Venus. When
that planet is in her nodes (N. 132), or within 11⁄4° of them, that is, in, or
nearly in, the plane of the ecliptic, she is occasionally seen to pass over the
sun like a black spot. If we could imagine that the sun and Venus had no
parallax, the line described by the planet on his disc, and the duration of the
transit, would be the same to all the inhabitants of the earth. But, as the
semi-diameter of the earth has a sensible magnitude when viewed from the
centre of the sun, the line described by the planet in its passage over his disc
appears to be nearer to his centre, or farther from it, according to the
position of the observer; so that the duration of the transit varies with the
different points of the earth’s surface at which it is observed (N. 133). This
difference of time, being entirely the effect of parallax, furnishes the means
of computing it from the known motions of the earth and Venus, by the
same method as for the eclipses of the sun. In fact, the ratio of the distances
of Venus and the sun from the earth at the time of the transit is known from
the theory of their elliptical motion. Consequently the ratio of the parallaxes
of these two bodies, being inversely as their distances, is given; and as the
transit gives the difference of the parallaxes, that of the sun is obtained. In
1769 the parallax of the sun was determined by observations of a transit of
Venus made at Wardhus in Lapland, and at Tahiti in the South Sea. The
latter observation was the object of Cook’s first voyage. The transit lasted
about six hours at Tahiti, and the difference in duration at these two stations
was eight minutes; whence the sun’s horizontal parallax was found to be
8ʺ·72. But by other considerations it has been reduced by Professor Encke
to 8ʺ·5776; from which the mean distance of the sun appears to be about
ninety-five millions of miles. This is confirmed by an inequality in the
motion of the moon, which depends upon the parallax of the sun, and
which, when compared with observation, gives 8ʺ·6 for the sun’s parallax.
The transits of Venus in 1874 and 1882 will be unfavourable for
ascertaining the accuracy of the solar parallax, and no other transit of that
planet will take place till the twenty-first century; but in the mean time
recourse may be had to the oppositions of Mars.
The parallax of Venus is determined by her transits; that of Mars by
direct observation, and it is found to be nearly double that of the sun, when
the planet is in opposition. The distance of these two planets from the earth
is therefore known in terrestrial radii, consequently their mean distances
from the sun may be computed; and as the ratios of the distances of the

planets from the sun are known by Kepler’s law, of the squares of the
periodic times of any two planets being as the cubes of their mean distances
from the sun, their absolute distances in miles are easily found (N. 134).
This law is very remarkable, in thus uniting all the bodies of the system,
and extending to the satellites as well as the planets.
Far as the earth seems to be from the sun, Uranus is no less than nineteen,
and Neptune thirty times farther. Situate on the verge of the system, the sun
must appear from Uranus not much larger than Venus does to us, and from
Neptune as a star of the fifth magnitude. The earth cannot even be visible as
a telescopic object to a body so remote as either Uranus or Neptune. Yet
man, the inhabitant of the earth, soars beyond the vast dimensions of the
system to which his planet belongs, and assumes the diameter of its orbit as
the base of a triangle whose apex extends to the stars.
Sublime as the idea is, this assumption proves ineffectual, except in a
very few cases; for the apparent places of the fixed stars are not sensibly
changed by the earth’s annual revolution. With the aid derived from the
refinements of modern astronomy, and of the most perfect instruments, a
sensible parallax has been detected only in a very few of these remote suns.
α Centauri has a parallax of one second of space, therefore it is the nearest
known star, and yet it is more than two hundred thousand times farther from
us than the sun is. At such a distance not only the terrestrial orbit shrinks to
a point, but the whole solar system, seen in the focus of the most powerful
telescope, might be eclipsed by the thickness of a spider’s thread. Light,
flying at the rate of 190,000 miles in a second, would take more than three
years to travel over that space. One of the nearest stars may therefore have
been kindled or extinguished more than three years before we could have
been aware of so mighty an event. But this distance must be small when
compared with that of the most remote of the bodies which are visible in the
heavens. The fixed stars are undoubtedly luminous like the sun: it is
therefore probable that they are not nearer to one another than the sun is to
the nearest of them. In the milky way and the other starry nebulæ, some of
the stars that seem to us to be close to others may be far behind them in the
boundless depth of space; nay, may be rationally supposed to be situate
many thousand times farther off. Light would therefore require thousands of
years to come to the earth from those myriads of suns of which our own is
but “the remote companion.”

SECTION VIII.

Masses of Planets that have no Satellites determined from their
Perturbations—Masses of the others obtained from the Motions of their
Satellites—Masses of the Sun, the Earth, of Jupiter and of the Jovial
System—Mass of the Moon—Real Diameters of Planets, how obtained—
Size of Sun, Densities of the Heavenly Bodies—Formation of
Astronomical Tables—Requisite Data and Means of obtaining them.

The masses of such planets as have no satellites are known by comparing
the inequalities they produce in the motions of the earth and of each other,
determined theoretically, with the same inequalities given by observation;
for the disturbing cause must necessarily be proportional to the effect it
produces. The masses of the satellites themselves may also be compared
with that of the sun by their perturbations. Thus, it is found, from the
comparison of a vast number of observations with La Place’s theory of
Jupiter’s satellites, that the mass of the sun is no less than 65,000,000 times
greater than the least of these moons. But, as the quantities of matter in any
two primary planets are directly as the cubes of the mean distances at which
their satellites revolve, and inversely as the squares of their periodic times
(N. 135), the mass of the sun and of any planets which have satellites may
be compared with the mass of the earth. In this manner it is computed that
the mass of the sun is 354,936 times that of the earth; whence the great
perturbations of the moon, and the rapid motion of the perigee and nodes of
her orbit (N. 136). Even Jupiter, the largest of the planets, has been found
by Professor Airy to be 1047·871 times less than the sun; and, indeed, the
mass of the whole Jovial system is not more than the 1054·4th part of that
of the sun. So that the mass of the satellites bears a very small proportion to
that of their primary. The mass of the moon is determined from several
sources—from her action on the terrestrial equator, which occasions the
nutation in the axis of rotation; from her horizontal parallax; from an

inequality she produces in the sun’s longitude; and from her action on the
tides. The three first quantities, computed from theory and compared with
their observed values, give her mass respectively equal to the 1⁄71, 1⁄74·2, and
1
⁄69·2, part of that of the earth, which do not differ much from each other. Dr.
Brinkley has found it to be 1⁄80 from the constant of lunar nutation: but,
from the moon’s action in raising the tides, her mass appears to be about the
1
⁄75 part of that of the earth—a value that cannot differ much from the truth.
The apparent diameters of the sun, moon, and planets are determined by
measurement; therefore their real diameters may be compared with that of
the earth; for the real diameter of a planet is to the real diameter of the
earth, or 7926 miles, as the apparent diameter of the planet to the apparent
diameter of the earth as seen from the planet, that is, to twice the parallax of
the planet. According to Bessel, the mean apparent diameter of the sun is
1923ʺ·64, and with the solar parallax 8ʺ·5776, it will be found that the
diameter of the sun is about 886,877 miles. Therefore, if the centre of the
sun were to coincide with the centre of the earth, his volume would not only
include the orbit of the moon, but would extend nearly as far again; for the
moon’s mean distance from the earth is about sixty times the earth’s
equatorial radius, or 238,793 miles: so that twice the distance of the moon is
477,586 miles, which differs but little from the solar radius; his equatorial
radius is probably not much less than the major axis of the lunar orbit. The
diameter of the moon is only 2160 miles; and Jupiter’s diameter of 88,200
miles is very much less than that of the sun; the diameter of Pallas does not
much exceed 79 miles, so that an inhabitant of that planet, in one of our
steam carriages, might go round his world in a few hours. The diameters of
Lutetia and Atalanta are only 8 and 4 miles respectively; but the whole of
the 55 telescopic planets are so small, that their united mass is probably not
more than the fifth or sixth part of that of the moon.
The densities of bodies are proportional to their masses, divided by their
volumes. Hence, if the sun and planets be assumed to be spheres, their
volumes will be as the cubes of their diameters. Now, the apparent
diameters of the sun and earth, at their mean distance, are 1923ʺ·6 and
17ʺ·1552, and the mass of the earth is the 354,936th part of that of the sun
taken as the unit. It follows, therefore, that the earth is four times as dense
as the sun. But the sun is so large that his attractive force would cause
bodies to fall through about 334·65 feet in a second. Consequently, if he

were habitable by human beings, they would be unable to move, since their
weight would be thirty times as great as it is here. A man of moderate size
would weigh about two tons at the surface of the sun; whereas at the surface
of some of the new planets he would be so light that it would be impossible
to stand steady, since he would only weigh a few pounds. The mean density
of the earth has been determined by the following method. Since a
comparison of the action of two planets upon a third gives the ratio of the
masses of these two planets, it is clear that, if we can compare the effect of
the whole earth with the effect of any part of it, a comparison may be
instituted between the mass of the whole earth and the mass of that part of
it. Now a leaden ball was weighed against the earth by comparing the
effects of each upon a pendulum; the nearness of the smaller mass making it
produce a sensible effect as compared with that of the larger: for by the
laws of attraction the whole earth must be considered as collected in its
centre. By this method it has been found that the mean density of the earth
is 5·660 times greater than that of water at the temperature of 62° of
Fahrenheit’s thermometer. The late Mr. Baily, whose accuracy as an
experimental philosopher is acknowledged, was unremittingly occupied
nearly four years in accomplishing this very important object. In order to
ascertain the mean density of the earth still more perfectly, Mr. Airy made a
series of experiments to compare the simultaneous oscillations of two
pendulums, one at the bottom of the Harton coal-pit, 1260 feet deep, in
Northumberland, and the other on the surface of the earth immediately
above it. The oscillations of the pendulums were compared with an
astronomical clock at each station, and the time was instantaneously
transmitted from one to the other by a telegraphic wire. The oscillations
were observed for more than 100 hours continuously, when it was found
that the lower pendulum made 21⁄2 oscillations more in 24 hours than the
upper one. The experiment was repeated for the same length of time with
the same result; but on this occasion the upper pendulum was taken to the
bottom of the mine and the lower brought to the surface. From the
difference between the oscillations at the two stations it appears that
gravitation at the bottom of the mine exceeds that at the surface by the
1
⁄19190 part, and that the mean density of the earth is 6·565, which is greater
than that obtained by Mr. Baily by ·89. While employed on the
trigonometrical survey of Scotland, Colonel James determined the mean
density of the earth to be 5·316, from a deviation of the plumb-line

amounting to 2ʺ, caused by the attraction of Arthur’s Seat and the heights
east of Edinburgh: it agrees more nearly with the density found by Mr.
Baily than with that deduced from Mr. Airy’s experiments. All the planets
and satellites appear to be of less density than the earth. The motions of
Jupiter’s satellites show that his density increases towards his centre. Were
his mass homogeneous, his equatorial and polar axes would be in the ratio
of 41 to 36, whereas they are observed to be only as 41 to 38. The singular
irregularities in the form of Saturn, and the great compression of Mars,
prove the internal structure of these two planets to be very far from
uniform.
Before entering on the theory of rotation, it may not be foreign to the
subject to give some idea of the methods of computing the places of the
planets, and of forming astronomical tables. Astronomy is now divided into
the three distinct departments of theory, observation, and computation.
Since the problem of the three bodies can only be solved by approximation,
the analytical astronomer determines the position of a planet in space by a
series of corrections. Its place in its circular orbit is first found, then the
addition or subtraction of the equation of the centre (N. 48) to or from its
mean place gives its position in the ellipse. This again is corrected by the
application of the principal periodic inequalities. But, as these are
determined for some particular position of the three bodies, they require to
be corrected to suit other relative positions. This process is continued till the
corrections become less than the errors of observation, when it is obviously
unnecessary to carry the approximation further. The true latitude and
distance of the planet from the sun are obtained by methods similar to those
employed for the longitude.
As the earth revolves equably about its axis in 24 hours, at the rate of 15°
in an hour, time becomes a measure of angular motion, and the principal
element in astronomy, where the object is to determine the exact state of the
heavens and the successive changes it undergoes in all ages, past, present,
and to come. Now, the longitude, latitude, and distance of a planet from the
sun are given in terms of the time, by general analytical formulæ. These
formulæ will consequently give the exact place of the body in the heavens,
for any time assumed at pleasure, provided they can be reduced to numbers.
But before the calculator begins his task the observer must furnish the
necessary data, which are, obviously, the forms of the orbits, and their
positions with regard to the plane of the ecliptic (N. 57). It is therefore

necessary to determine by observation, for each planet, the length of the
major axis of its orbit, the excentricity, the inclination of the orbit to the
plane of the ecliptic, the longitudes of its perihelion and ascending node at a
given time, the periodic time of the planet, and its longitude at any instant
arbitrarily assumed, as an origin from whence all its subsequent and
antecedent longitudes are estimated. Each of these quantities is determined
from that position of the planet on which it has most influence. For
example, the sum of the greatest and least distances of the planet from the
sun is equal to the major axis of the orbit, and their difference is equal to
twice the excentricity. The longitude of the planet, when at its least distance
from the sun, is the same with the longitude of the perihelion; the greatest
latitude of the planet is equal to the inclination of the orbit: the longitude of
the planet, when in the plane of the ecliptic in passing towards the north, is
the longitude of the ascending node, and the periodic time is the interval
between two consecutive passages of the planet through the same node, a
small correction being made for the precession of the node during the
revolution of the planet (N. 137). Notwithstanding the excellence of
instruments and the accuracy of modern observers, unavoidable errors of
observation can only be compensated by finding the value of each element
from the mean of a thousand, or even many thousands of observations. For
as it is probable that the errors are not all in one direction, but that some are
in excess and others in defect, they will compensate each other when
combined.
However, the values of the elements determined separately can only be
regarded as approximate, because they are so connected that the estimation
of any one independently will induce errors in the others. The excentricity
depends upon the longitude of the perihelion, the mean motion depends
upon the major axis, the longitude of the node upon the inclination of the
orbit, and vice versâ. Consequently, the place of a planet computed with the
approximate data will differ from its observed place. Then the difficulty is
to ascertain what elements are most in fault, since the difference in question
is the error of all; that is obviated by finding the errors of some thousands of
observations, and combining them, so as to correct the elements
simultaneously, and to make the sum of the squares of the errors a
minimum with regard to each element (N. 138). The method of
accomplishing this depends upon the Theory of Probabilities; a subject
fertile in most important results in the various departments of science and of

civil life, and quite indispensable in the determination of astronomical data.
A series of observations continued for some years will give approximate
values of the secular and periodic inequalities, which must be corrected
from time to time, till theory and observation agree. And these again will
give values of the masses of the bodies forming the solar system, which are
important data in computing their motions. The periodic inequalities
derived from a great number of observations are employed for the
determination of the values of the masses till such time as the secular
inequalities shall be perfectly known, which will then give them with all the
necessary precision. When all these quantities are determined in numbers,
the longitude, latitude, and distance of the planet from the sun are computed
for stated intervals, and formed into tables, arranged according to the time
estimated from a given epoch, so that the place of the body may be
determined from them by inspection alone, at any instant for perhaps a
thousand years before and after that epoch. By this tedious process, tables
have been computed for all the great planets, and several of the small,
besides the moon and the satellites of Jupiter. In the present state of
astronomy the masses and elements of the orbits are pretty well known, so
that the tables only require to be corrected from time to time as observations
become more accurate. Those containing the motions of Jupiter, Saturn, and
Uranus have already been twice constructed within the last thirty years, and
the tables of Jupiter and Saturn agree almost perfectly with modern
observation. The following prediction will be found in the sixth edition of
this book, published in the year 1842: “Those of Uranus, however, are
already defective, probably because the discovery of that planet in 1781 is
too recent to admit of much precision in the determination of its motions, or
that possibly it may be subject to disturbances from some unseen planet
revolving about the sun beyond the present boundaries of our system. If,
after a lapse of years, the tables formed from a combination of numerous
observations should be still inadequate to represent the motions of Uranus,
the discrepancies may reveal the existence, nay, even the mass and orbit, of
a body placed for ever beyond the sphere of vision.”[5]
That prediction has been fulfilled since the seventh edition of this book
was published. Not only the existence of Neptune, revolving at the distance
of three thousand millions of miles from the sun, has been discovered from
his disturbing action on Uranus, but his mass, the form and position of his
orbit in space, and his periodic time had been determined before the planet

had been seen, and the planet itself was discovered in the very point of the
heavens which had been assigned to it. It had been noticed for years that the
perturbation of Uranus had increased in an unaccountable manner (N. 139).
After the disturbing action of all the known planets had been determined, it
was found that, between the years 1833 and 1837, the observed and
computed distance of Uranus from the sun differed by 240,000 miles, which
is about the mean distance of the moon from the earth, while, in 1841, the
error in the geocentric longitude of the planet amounted to 96ʺ. These
discrepancies were therefore attributed to the attraction of some unseen and
unknown planet, consequently they gave rise to a case altogether
unprecedented in the history of astronomy. Heretofore it was required to
determine the disturbing action of one known planet upon another. Whereas
the inverse problem had now to be solved, in which it was required to find
the place of an unknown body in the heavens, at a given time, together with
its mass, and the form and position of its orbit, from the disturbance it
produced on the motions of another. The difficulty was extreme, because all
the elements of the orbit of Uranus were erroneous from the action of
Neptune, and those of Neptune’s orbit were unknown. In this dilemma it
was necessary to form some hypothesis with regard to the unknown planet;
it was therefore assumed, according to Bode’s empirical law on the mean
distances of the planets, that it was revolving at twice the distance of
Uranus from the sun. In fact, the periodic time of Uranus is about 84 years,
and, as the discrepancies in his motions increased slowly and regularly, it
was evident that it would require a planet with a much longer periodic time
to produce them—moreover, it was clear that the new planet must be
exterior to Uranus, otherwise it would have disturbed the motions of Saturn.
Another circumstance tended to lessen the difficulty; the latitude of
Uranus was not much affected, therefore it was concluded that the
inclination of the orbit of the unknown body must be very small, and, as
that of the orbit of Uranus is only 46ʹ 28ʺ·4, both planets were assumed to
be moving in the plane of the ecliptic, and thus the elements of the orbit of
the unknown planet were reduced from six to four. Having thus assumed
that the unknown body was revolving in a circle in the plane of the ecliptic,
the analytical expression of its action on the motion of Uranus, when in
numerous points of its orbit, was compared with the observed longitude of
Uranus, through a regular series of years, by means of which the faulty
elements of the orbit of Uranus were eliminated, or got rid of, and there

only remained a relation between the mass of the new planet and three of
the elements of its orbit; and it then was necessary to assume such a value
for two of them as would suit the rest. That was accomplished so
dexterously, that the perturbations of Uranus were perfectly conformable to
the motions of Neptune, moving in the orbit thus found, and the place of the
new planet exactly agreed with observation. Subsequently its orbit and
motions have been determined more accurately.
The honour of this admirable effort of genius is shared by Mr. Adams and
M. Le Verrier, who, independently of each other, arrived at these wonderful
results. Mr. Adams had determined the mass and apparent diameter of
Neptune, with all the circumstances of its motion, eight months before M.
Le Verrier had terminated his results, and had also pointed out the exact
spot where the planet would be found; but the English observers neglected
to look for it till M. Le Verrier made known his researches, and
communicated its position to Dr. Galle, at Berlin, who found it the very first
night he looked for it, and then it was evident that it would have been seen
in the place Mr. Adams had assigned to it eight months before had it been
looked for. So closely did the results of these two great mathematicians
agree.
Neptune has a diameter of 39,793 miles, consequently he is nearly 200
times larger than the earth, and may be seen with a telescope of moderate
power. His motion is retrograde at present, and six times slower than that of
the earth. At so great a distance from the sun it can only have the 1⁄1300th
part of the light and heat the earth receives; but having a satellite, the
deficiency of light may in some measure be supplied.
The prediction may now be transferred from Uranus to Neptune, whose
perturbations may reveal the existence of a planet still further removed,
which may for ever remain beyond the reach of telescopic vision—yet its
mass, the form and position of its orbit, and all the circumstances of its
motion may become known, and the limits of the solar system may still be
extended hundreds of millions of miles.
The mean distance of Neptune from the sun has subsequently proved to
be only 2893 millions of miles, and the period of his revolution 166 years,
so that Baron Bode’s law, of the interval between the orbits of any two
planets being twice as great as the inferior interval and half of the superior,
fails in the case of Neptune, though it was useful on the first approximation

to his motions; and since Bode’s time it has led to the discovery of fifty-five
telescopic planets revolving between the orbits of Mars and Jupiter, some
by chance, others by a systematic search on the faith that these minute
planets are fragments of a larger body that has exploded, because their
distances from the sun are nearly the same; the lines of the nodes of some of
their orbits terminate in the same points of the heavens, and the inclinations
of their orbits are such as might have taken place from their mutual
disturbances at the time of the explosion, and while yet they were near
enough for their forms to affect their motions. The orbits of the more
recently discovered asteroids show that this hypothesis is untenable.
The tables of Mars, Venus, and even those of the sun, have been greatly
improved, and still engage the attention of our Astronomer Royal, Mr. Airy,
and other eminent astronomers. We are chiefly indebted to the German
astronomers for tables of the four older telescopic planets, Vesta, Juno,
Ceres, and Pallas; the others have only been discovered since the year 1845.
The determination of the path of a planet when disturbed by all the
others, a problem which has employed the talents of the greatest
astronomers, from Newton to the present day, is only successfully
accomplished with regard to the older planets, which revolve in nearly
circular orbits, but little inclined to the plane of the ecliptic. When the
excentricity and inclination of the orbits are great, their analysis fails,
because the series expressing the co-ordinates of the bodies become
extremely complicated, and do not converge when applied to comets and
the telescopic planets. This difficulty has been overcome by Sir John
Lubbock, and other mathematicians, who have the honour of having
completed the theory of planetary motion, which becomes every day of
more importance, from the new planets that have been discovered, and also
with regard to comets, many of which return to the sun at regular intervals,
and from whose perturbations the masses of the planets will be more
accurately determined, and the retarding influence of the ethereal medium
better known.

SECTION IX.

Rotation of the Sun and Planets—Saturn’s Rings—Periods of the Rotation
of the Moon and other Satellites equal to the Periods of their Revolutions
—Form of Lunar Spheroid—Libration, Aspect, and Constitution of the
Moon—Rotation of Jupiter’s Satellites.

The oblate form of several of the planets indicates rotatory motion. This has
been confirmed in most cases by tracing spots on their surface, by which
their poles and times of rotation have been determined. The rotation of
Mercury is unknown, on account of his proximity to the sun; that of the new
planets has not yet been ascertained. The sun revolves in twenty-five days
and ten hours about an axis which is directed towards a point half-way
between the pole-star and α of Lyra, the plane of rotation being inclined by
7° 30ʹ, or a little more than seven degrees, to the plane of the ecliptic: it
may therefore be concluded that the sun’s mass is a spheroid, flattened at
the poles. From the rotation of the sun, there was every reason to believe
that he has a progressive motion in space, a circumstance which is
confirmed by observation. But, in consequence of the reaction of the
planets, he describes a small irregular orbit about the centre of gravity of
the system, never deviating from his position by more than twice his own
diameter, or a little more than seven times the distance of the moon from the
earth. The sun and all his attendants rotate from west to east, on axes that
remain nearly parallel to themselves (N. 140) in every point of their orbit,
and with angular velocities that are sensibly uniform (N. 141). Although the
uniformity in the direction of their rotation is a circumstance hitherto
unaccounted for in the economy of nature, yet, from the design and
adaptation of every other part to the perfection of the whole, a coincidence
so remarkable cannot be accidental. And, as the revolutions of the planets
and satellites are also from west to east, it is evident that both must have
arisen from the primitive cause which determined the planetary motions.[6]

Indeed, La Place has computed the probability to be as four millions to one
that all the motions of the planets, both of rotation and revolution, were at
once imparted by an original common cause, but of which we know neither
the nature nor the epoch.
The larger planets rotate in shorter periods than the smaller planets and
the earth. Their compression is consequently greater, and the action of the
sun and of their satellites occasions a nutation in their axes and a precession
of their equinoxes (N. 147) similar to that which obtains in the terrestrial
spheroid, from the attraction of the sun and moon on the prominent matter
at the equator. Jupiter revolves in less than ten hours round an axis at right
angles to certain dark belts or bands, which always cross his equator. (See
Plate 1.) This rapid rotation occasions a very great compression in his form.
His equatorial axis exceeds his polar axis by 6000 miles, whereas the
difference in the axes of the earth is only about twenty-six and a half. It is
an evident consequence of Kepler’s law of the squares of the periodic times
of the planets being as the cubes of the major axes of their orbits, that the
heavenly bodies move slower the farther they are from the sun. In
comparing the periods of the revolutions of Jupiter and Saturn with the
times of their rotation, it appears that a year of Jupiter contains nearly ten
thousand of his days, and that of Saturn about thirty thousand Saturnian
days.
The appearance of Saturn is unparalleled in the system of the world. He
is a spheroid nearly 1000 times larger than the earth, surrounded by a ring
even brighter than himself, which always remains suspended in the plane of
his equator: and, viewed with a very good telescope, it is found to consist of
two concentric rings, divided by a dark band. The exterior ring, as seen
through Mr. Lassell’s great equatorial at Malta, has a dark-striped band
through the centre, and is altogether less bright than the interior ring, one
half of which is extremely brilliant; while the interior half is shaded in rings
like the seats in an amphitheatre. Mr. Lassell made the remarkable
discovery of a dark transparent ring, whose edge coincides with the inner
edge of the interior ring, and which occupies about half the space between it
and Saturn. He compares it to a band of dark-coloured crape drawn across a
portion of the disc of the planet, and the part projected upon the blue sky is
also transparent. At the time these observations were made at Malta,
Captain Jacob discovered the transparent ring at Madras. It is conjectured to
be fluid; even the luminous rings cannot be very dense, since the density of

Saturn himself is known to be less than the eighth part of that of the earth. A
transit of the ring across a star might reveal something concerning this
wonderful object. The ball of Saturn is striped by belts of different colours.
At the time of these observations the part above the ring was bright white;
at his equator there was a ruddy belt divided in two, above which were belts
of a bluish green alternately dark and light, while at the pole there was a
circular space of a pale colour. (See Plate 2.) The mean distance of the
interior part of the double ring from the surface of the planet is about
22,240 miles, it is no less than 33,360 miles broad, but, by the estimation of
Sir John Herschel, its thickness does not much exceed 100 miles, so that it
appears like a plane. By the laws of mechanics, it is impossible that this
body can retain its position by the adhesion of its particles alone. It must
necessarily revolve with a velocity that will generate a centrifugal force
sufficient to balance the attraction of Saturn. Observation confirms the truth
of these principles, showing that the rings rotate from west to east about the
planet in ten hours and a half, which is nearly the time a satellite would take
to revolve about Saturn at the same distance. Their plane is inclined to the
ecliptic, at an angle of 28° 10ʹ 44ʺ·5; in consequence of this obliquity of
position, they always appear elliptical to us, but with an excentricity so
variable as even to be occasionally like a straight line drawn across the
planet. In the beginning of October, 1832, the plane of the rings passed
through the centre of the earth; in that position they are only visible with
very superior instruments, and appear like a fine line across the disc of
Saturn. About the middle of December, in the same year, the rings became
invisible, with ordinary instruments, on account of their plane passing
through the sun. In the end of April, 1833, the rings vanished a second time,
and reappeared in June of that year. Similar phenomena will occur as often
as Saturn has the same longitude with either node of his rings. Each side of
these rings has alternately fifteen years of sunshine and fifteen years of
darkness.
It is a singular result of theory, that the rings could not maintain their
stability of rotation if they were everywhere of uniform thickness; for the
smallest disturbance would destroy the equilibrium, which would become
more and more deranged, till, at last, they would be precipitated on the
surface of the planet. The rings of Saturn must therefore be irregular solids,
of unequal breadth in different parts of the circumference, so that their
centres of gravity do not coincide with the centres of their figures. Professor

Struve has also discovered that the centre of the rings is not concentric with
the centre of Saturn. The interval between the outer edge of the globe of the
planet and the outer edge of the rings on one side is 11ʺ·272, and, on the
other side, the interval is 11ʺ·390, consequently there is an excentricity of
the globe in the rings of 0ʺ·215. If the rings obeyed different forces, they
would not remain in the same plane, but the powerful attraction of Saturn
always maintains them and his satellites in the plane of his equator. The
rings, by their mutual action, and that of the sun and satellites, must
oscillate about the centre of Saturn, and produce phenomena of light and
shadow whose periods extend to many years. According to M. Bessel the
mass of Saturn’s ring is equal to the 1⁄118 part of that of the planet.
The periods of rotation of the moon and the other satellites are equal to
the times of their revolutions, consequently these bodies always turn the
same face to their primaries. However, as the mean motion of the moon is
subject to a secular inequality, which will ultimately amount to many
circumferences (N. 108), if the rotation of the moon were perfectly uniform
and not affected by the same inequalities, it would cease exactly to
counterbalance the motion of revolution; and the moon, in the course of
ages, would successively and gradually discover every point of her surface
to the earth. But theory proves that this never can happen; for the rotation of
the moon, though it does not partake of the periodic inequalities of her
revolution, is affected by the same secular variations, so that her motions of
rotation and revolution round the earth will always balance each other, and
remain equal. This circumstance arises from the form of the lunar spheroid,
which has three principal axes of different lengths at right angles to each
other.
The moon is flattened at her poles from her centrifugal force, therefore
her polar axis is the least. The other two are in the plane of her equator, but
that directed towards the earth is the greatest (N. 142). The attraction of the
earth, as if it had drawn out that part of the moon’s equator, constantly
brings the greatest axis, and consequently the same hemisphere, towards us,
which makes her rotation participate in the secular variations of her mean
motion of revolution. Even if the angular velocities of rotation and
revolution had not been nicely balanced in the beginning of the moon’s
motion, the attraction of the earth would have recalled the greatest axis to
the direction of the line joining the centres of the moon and earth; so that it
would have vibrated on each side of that line in the same manner as a

pendulum oscillates on each side of the vertical from the influence of
gravitation. No such libration is perceptible; and, as the smallest
disturbance would make it evident, it is clear that, if the moon has ever been
touched by a comet, the mass of the latter must have been extremely small.
If it had been only the hundred thousandth part of that of the earth, it would
have rendered the libration sensible. According to analysis, a similar
libration exists in the motions of Jupiter’s satellites, which still remains
insensible to observation, and yet the comet of 1770 passed twice through
the midst of them.
The moon, it is true, is liable to librations depending upon the position of
the spectator. At her rising, part of the western edge of her disc is visible,
which is invisible at her setting, and the contrary takes place with regard to
her eastern edge. There are also librations arising from the relative positions
of the earth and moon in their respective orbits; but, as they are only optical
appearances, one hemisphere will be eternally concealed from the earth. For
the same reason the earth, which must be so splendid an object to one lunar
hemisphere, will be for ever veiled from the other. On account of these
circumstances, the remoter hemisphere of the moon has its day a fortnight
long, and a night of the same duration, not even enlightened by a moon,
while the favoured side is illuminated by the reflection of the earth during
its long night. A planet exhibiting a surface thirteen times larger than that of
the moon, with all the varieties of clouds, land, and water, coming
successively into view, must be a splendid object to a lunar traveller in a
journey to his antipodes. The great height of the lunar mountains probably
has a considerable influence on the phenomena of her motion, the more so
as her compression is small, and her mass considerable. In the curve
passing through the poles, and that diameter of the moon which always
points to the earth, nature has furnished a permanent meridian, to which the
different spots on her surface have been referred, and their positions are
determined with as much accuracy as those of many of the most remarkable
places on the surface of our globe. According to the observations of
Professor Secchi at Rome, the mountains of the moon are mostly volcanic
and of three kinds. The first and oldest have their borders obliterated, so
that they look like deep wells; the second, which are of an intermediate
class, have elevated, and, for the most part, regular unbroken edges, with
the ground around them raised to a prodigious extent in proportion to the
size of the volcano, with generally an insulated rock in the centre of the

crater. The third, and most recent class, are very small, and seem to be the
last effort of the expiring volcanic force, which is probably now extinct.
The distance and minuteness of Jupiter’s satellites render it extremely
difficult to ascertain their rotation. It was, however, accomplished by Sir
William Herschel from their relative brightness. He observed that they
alternately exceed each other in brilliancy, and, by comparing the maxima
and minima of their illumination with their positions relatively to the sun
and to their primary, he found that, like the moon, the time of their rotation
is equal to the period of their revolution about Jupiter. Miraldi was led to
the same conclusion with regard to the fourth satellite, from the motion of a
spot on its surface.

SECTION X.

Rotation of the Earth invariable—Decrease in the Earth’s mean
Temperature—Earth originally in a state of Fusion—Length of Day
constant—Decrease of Temperature ascribed by Sir John Herschel to the
variation in the Excentricity of the Terrestrial Orbit—Difference in the
Temperature of the two Hemispheres erroneously ascribed to the Excess
in the Length of Spring and Summer in the Southern Hemisphere;
attributed by Sir Charles Lyell to the Operation of existing Causes—
Three principal Axes of Rotation—Position of the Axis of Rotation on the
Surface of the Earth invariable—Ocean not sufficient to restore the
Equilibrium of the Earth if deranged—Its Density and mean Depth—
Internal Structure of the Earth.

The rotation of the earth, which determines the length of the day, may be
regarded as one of the most important elements in the system of the world.
It serves as a measure of time, and forms the standard of comparison for the
revolutions of the celestial bodies, which, by their proportional increase or
decrease, would soon disclose any changes it might sustain. Theory and
observation concur in proving that, among the innumerable vicissitudes
which prevail throughout creation, the period of the earth’s diurnal rotation
is immutable. The water of rivers, falling from a higher to a lower level,
carries with it the velocity due to its revolution with the earth at a greater
distance from the centre; it will therefore accelerate, although to an almost
infinitesimal extent, the earth’s daily rotation. The sum of all these
increments of velocity, arising from the descent of all the rivers on the
earth’s surface, would in time become perceptible, did not nature, by the
process of evaporation, raise the waters back to their sources, and thus, by
again removing matter to a greater distance from the centre, destroy the
velocity generated by its previous approach; so that the descent of rivers
does not affect the earth’s rotation. Enormous masses projected by

volcanoes from the equator to the poles, and the contrary, would indeed
affect it, but there is no evidence of such convulsions. The disturbing action
of the moon and planets, which has so powerful an effect on the revolution
of the earth, in no way influences its rotation. The constant friction of the
trade winds on the mountains and continents between the tropics does not
impede its velocity, which theory even proves to be the same as if the sea,
together with the earth, formed one solid mass. But, although these
circumstances be insufficient, a variation in the mean temperature would
certainly occasion a corresponding change in the velocity of rotation. In the
science of dynamics it is a principle in a system of bodies or of particles
revolving about a fixed centre, that the momentum or sum of the products
of the mass of each into its angular velocity and distance from the centre is
a constant quantity, if the system be not deranged by a foreign cause. Now,
since the number of particles in the system is the same whatever its
temperature may be, when their distances from the centre are diminished,
their angular velocity must be increased, in order that the preceding
quantity may still remain constant. It follows, then, that, as the primitive
momentum of rotation with which the earth was projected into space must
necessarily remain the same, the smallest decrease in heat, by contracting
the terrestrial spheroid, would accelerate its rotation, and consequently
diminish the length of the day. Notwithstanding the constant accession of
heat from the sun’s rays, geologists have been induced to believe, from the
fossil remains, that the mean temperature of the globe is decreasing.
The high temperature of mines, hot springs, and above all the internal
fires which have produced, and do still occasion, such devastation on our
planet, indicate an augmentation of heat towards its centre. The increase of
density corresponding to the depth and the form of the spheroid, being what
theory assigns to a fluid mass in rotation, concurs to induce the idea that the
temperature of the earth was originally so high as to reduce all the
substances of which it is composed to a state of fusion or of vapour, and
that in the course of ages it has cooled down to its present state; that it is
still becoming colder; and that it will continue to do so till the whole mass
arrives at the temperature of the medium in which it is placed, or rather at a
state of equilibrium between this temperature, the cooling power of its own
radiation, and the heating effect of the sun’s rays.
Previous to the formation of ice at the poles, the ancient lands of northern
latitudes might, no doubt, have been capable of producing those tropical

plants preserved in the coal-measures, if indeed such plants could flourish
without the intense light of a tropical sun. But, even if the decreasing
temperature of the earth be sufficient to produce the observed effects, it
must be extremely slow in its operation; for, in consequence of the rotation
of the earth being a measure of the periods of the celestial motions, it has
been proved that, if the length of the day had decreased by the three-
thousandth part of a second since the observations of Hipparchus two
thousand years ago, it would have diminished the secular equation of the
moon by 44ʺ·4. It is, therefore, beyond a doubt that the mean temperature of
the earth cannot have sensibly varied during that time. If, then, the
appearances exhibited by the strata are really owing to a decrease of
internal temperature, it either shows the immense periods requisite to
produce geological changes, to which two thousand years are as nothing, or
that the mean temperature of the earth had arrived at a state of equilibrium
before these observations.
However strong the indications of the primitive fluidity of the earth, as
there is no direct proof of it, the hypothesis can only be regarded as very
probable. But one of the most profound philosophers and elegant writers of
modern times has found in the secular variation of the excentricity of the
terrestrial orbit an evident cause of decreasing temperature. That
accomplished author, in pointing out the mutual dependencies of
phenomena, says, “It is evident that the mean temperature of the whole
surface of the globe, in so far as it is maintained by the action of the sun at a
higher degree than it would have were the sun extinguished, must depend
on the mean quantity of the sun’s rays which it receives, or—which comes
to the same thing—on the total quantity received in a given invariable time;
and, the length of the year being unchangeable in all the fluctuations of the
planetary system, it follows that the total amount of solar radiation will
determine, cæteris paribus, the general climate of the earth. Now, it is not
difficult to show that this amount is inversely proportional to the minor axis
of the ellipse described by the earth about the sun (N. 143), regarded as
slowly variable; and that, therefore, the major axis remaining, as we know it
to be, constant, and the orbit being actually in a state of approach to a circle,
and consequently the minor axis being on the increase, the mean annual
amount of solar radiation received by the whole earth must be actually on
the decrease. We have, therefore, an evident real cause to account for the
phenomenon.” The limits of the variation in the excentricity of the earth’s

orbit are unknown. But, if its ellipticity has ever been as great as that of the
orbit of Mercury or Pallas, the mean temperature of the earth must have
been sensibly higher than it is at present. Whether it was great enough to
render our northern climates fit for the production of tropical plants, and for
the residence of the elephant and other animals now inhabitants of the torrid
zone, it is impossible to say.
Of the decrease in temperature of the northern hemisphere there is
abundant evidence in the fossil plants discovered in very high latitudes,
which could only have existed in a tropical climate, and which must have
grown near the spot where they are found, from the delicacy of their
structure and the perfect state of their preservation. This change of
temperature has been erroneously ascribed to an excess in the duration of
spring and summer in the northern hemisphere, in consequence of the
excentricity of the solar ellipse. The length of the seasons varies with the
position of the perihelion (N. 64) of the earth’s orbit for two reasons. On
account of the excentricity, small as it is, any line passing through the centre
of the sun divides the terrestrial ellipse into two unequal parts, and by the
laws of elliptical motion the earth moves through these two portions with
unequal velocities. The perihelion always lies in the smaller portion, and
there the earth’s motion is the most rapid. In the present position of the
perihelion, spring and summer north of the equator exceed by about eight
days the duration of the same seasons south of it. And 10,492 years ago the
southern hemisphere enjoyed the advantage we now possess from the
secular variation of the perihelion. Yet Sir John Herschel has shown that by
this alternation neither hemisphere acquires any excess of light or heat
above the other; for, although the earth is nearer to the sun while moving
through that part of its orbit in which the perihelion lies than in the other
part, and consequently receives a greater quantity of light and heat, yet as it
moves faster it is exposed to the heat for a shorter time. In the other part of
the orbit, on the contrary, the earth, being farther from the sun, receives
fewer of his rays; but because its motion is slower, it is exposed to them for
a longer time; and, as in both cases the quantity of heat and the angular
velocity vary exactly in the same proportion, a perfect compensation takes
place (N. 144). So that the excentricity of the earth’s orbit has little or no
effect on the temperature corresponding to the difference of the seasons.
Sir Charles Lyell, in his excellent works on Geology, refers the increased
cold of the northern hemisphere to the operation of existing causes with

more probability than most theories that have been advanced in solution of
this difficult subject. The loftiest mountains would be represented by a grain
of sand on a globe six feet in diameter, and the depth of the ocean by a
scratch on its surface. Consequently the gradual elevation of a continent or
chain of mountains above the surface of the ocean, or their depression
below it, is no very great event compared with the magnitude of the earth,
and the energy of its subterranean fires, if the same periods of time be
admitted in the progress of geological as in astronomical phenomena, which
the successive and various races of extinct beings show to have been
immense. Climate is always more intense in the interior of continents than
in islands or sea-coasts. An increase of land within the tropics would
therefore augment the general heat, and an increase in the temperate and
frigid zones would render the cold more severe. Now it appears that most of
the European, North Asiatic, and North American continents and islands
were raised from the deep after the coal-measures were formed in which the
fossil tropical plants are found; and a variety of geological facts indicate the
existence of an ancient and extensive archipelago throughout the greater
part of the northern hemisphere. Sir Charles Lyell is therefore of opinion
that the climate of these islands must have been sufficiently mild, in
consequence of the surrounding ocean, to clothe them with tropical plants,
and render them a fit abode for the huge animals whose fossil remains are
so often found; that the arborescent ferns and the palms of these regions,
carried by streams to the bottom of the ocean, were imbedded in the strata
which were by degrees heaved up by the subterranean fires during a long
succession of ages, till the greater part of the northern hemisphere became
dry land as it now is, and that the consequence has been a continual
decrease of temperature.
It is evident, from the marine shells found on the tops of the highest
mountains and in almost every part of the globe, that immense continents
have been elevated above the ocean which must have engulfed others. Such
a catastrophe would be occasioned by a variation in the position of the axis
of rotation on the surface of the earth; for the seas tending to a new equator
would leave some portions of the globe and overwhelm others. Now, it is
found by the laws of mechanics that in every body, be its form or density
what it may, there are at least three axes at right angles to each other, round
any one of which, if the solid begins to rotate, it will continue to revolve for
ever, provided it be not disturbed by a foreign cause, but that the rotation

about any other axis will only be for an instant, and consequently the poles
or extremities of the instantaneous axis of rotation would perpetually
change their position on the surface of the body. In an ellipsoid of
revolution the polar diameter and every diameter in the plane of the equator
are the only permanent axes of rotation (N. 145). Hence, if the ellipsoid
were to begin to revolve about any diameter between the pole and the
equator, the motion would be so unstable that the axis of rotation and the
position of the poles would change every instant. Therefore, as the earth
does not differ much from this figure, if it did not turn round one of its
principal axes, the position of the poles would change daily; the equator,
which is 90° distant, would undergo corresponding variations; and the
geographical latitudes of all places, being estimated from the equator,
assumed to be fixed, would be perpetually changing. A displacement in the
position of the poles of only two hundred miles would be sufficient to
produce these effects, and would immediately be detected. But, as the
latitudes are found to be invariable, it may be concluded that the terrestrial
spheroid must have revolved about the same axis for ages. The earth and
planets differ so little from ellipsoids of revolution, that in all probability
any libration from one axis to another, produced by the primitive impulse
which put them in motion, must have ceased soon after their creation from
the friction of the fluids at their surface.
Theory also proves that neither nutation, precession, nor any of the
disturbing forces that affect the system, have the smallest influence on the
axis of rotation, which maintains a permanent position on the surface, if the
earth be not disturbed in its rotation by a foreign cause, as the collision of a
comet, which might have happened in the immensity of time. But, had that
been the case, its effects would still have been perceptible in the variations
of the geographical latitudes. If we suppose that such an event had taken
place, and that the disturbance had been very great, equilibrium could then
only have been restored with regard to a new axis of rotation by the rushing
of the seas to the new equator, which they must have continued to do till the
surface was everywhere perpendicular to the direction of gravity. But it is
probable that such an accumulation of the waters would not be sufficient to
restore equilibrium if the derangement had been great, for the mean density
of the sea is only about a fifth part of the mean density of the earth, and the
mean depth of the Pacific Ocean is supposed not to be more than four or
five miles, whereas the equatorial diameter of the earth exceeds the polar

diameter by about 261⁄2 miles. Consequently the influence of the sea on the
direction of gravity is very small. And, as it thus appears that a great change
in the position of the axis is incompatible with the law of equilibrium, the
geological phenomena in question must be ascribed to an internal cause.
Indeed it is now demonstrated that the strata containing marine diluvia,
which are in lofty situations, must have been formed at the bottom of the
ocean, and afterwards upheaved by the action of subterraneous fires.
Besides, it is clear, from the mensuration of the arcs of the meridian and the
length of the seconds’ pendulum, as well as from the lunar theory, that the
internal strata and also the external outline of the globe are elliptical, their
centres being coincident and their axes identical with that of the surface—a
state of things which, according to the distinguished author lately quoted, is
incompatible with a subsequent accommodation of the surface to a new and
different state of rotation from that which determined the original
distribution of the component matter. Thus, amidst the mighty revolutions
which have swept innumerable races of organized beings from the earth,
which have elevated plains and buried mountains in the ocean, the rotation
of the earth and the position of the axes on its surface have undergone but
slight variations.
The strata of the terrestrial spheroid are not only concentric and elliptical,
but the lunar inequalities show that they increase in density from the surface
of the earth to its centre. This would certainly have happened if the earth
had originally been fluid, for the denser parts must have subsided towards
the centre as it approached a state of equilibrium. But the enormous
pressure of the superincumbent mass is a sufficient cause for the
phenomenon. Professor Leslie observes that air compressed into the fiftieth
part of its volume has its elasticity fifty times augmented. If it continues to
contract at that rate, it would, from its own incumbent weight, acquire the
density of water at the depth of thirty-four miles. But water itself would
have its density doubled at the depth of ninety-three miles, and would even
attain the density of quicksilver at a depth of 362 miles. Descending
therefore towards the centre through nearly 4000 miles, the condensation of
ordinary substances would surpass the utmost powers of conception. Dr.
Young says that steel would be compressed into one-fourth and stone into
one-eighth of its bulk at the earth’s centre. However, we are yet ignorant of
the laws of compression of solid bodies beyond a certain limit; from the

experiments of Mr. Perkins they appear to be capable of a greater degree of
compression than has generally been imagined.
But a density so extreme is not borne out by astronomical observation. It
might seem to follow therefore that our planet must have a widely
cavernous structure, and that we tread on a crust or shell whose thickness
bears a very small proportion to the diameter of its sphere. Possibly, too,
this great condensation at the central regions may be counterbalanced by the
increased elasticity due to a very elevated temperature.

SECTION XI.

Precession and Nutation—Their Effects on the Apparent Places of the Fixed
Stars.

It has been shown that the axis of rotation is invariable on the surface of the
earth; and observation as well as theory prove that, were it not for the action
of the sun and moon on the matter at the equator, it would remain exactly
parallel to itself in every point of its orbit.
The attraction of an external body not only draws a spheroid towards it,
but, as the force varies inversely as the square of the distance, it gives it a
motion about its centre of gravity, unless when the attracting body is
situated in the prolongation of one of the axes of the spheroid. The plane of
the equator is inclined to the plane of the ecliptic at an angle of 23° 27ʹ
28ʺ·29; and the inclination of the lunar orbit to the same is 5° 8ʹ 47ʺ·9.
Consequently, from the oblate figure of the earth, the sun and moon, acting
obliquely and unequally on the different parts of the terrestrial spheroid,
urge the plane of the equator from its direction, and force it to move from
east to west, so that the equinoctial points have a slow retrograde motion on
the plane of the ecliptic of 50ʺ·41 annually. The direct tendency of this
action is to make the planes of the equator and ecliptic coincide, but it is
balanced by the tendency of the earth to return to stable rotation about the
polar diameter, which is one of its principal axes of rotation. Therefore the
inclination of the two planes remains constant, as a top spinning preserves
the same inclination to the plane of the horizon. Were the earth spherical,
this effect would not be produced, and the equinoxes would always
correspond with the same points of the ecliptic, at least as far as this kind of
motion is concerned. But another and totally different cause which operates
on this motion has already been mentioned. The action of the planets on one
another and on the sun occasions a very slow variation in the position of the

plane of the ecliptic, which affects its inclination to the plane of the equator,
and gives the equinoctial points a slow but direct motion on the ecliptic of
0ʺ·31 annually, which is entirely independent of the figure of the earth, and
would be the same if it were a sphere. Thus the sun and moon by moving
the plane of the equator cause the equinoctial points to retrograde on the
ecliptic: and the planets by moving the plane of the ecliptic give them a
direct motion, though much less than the former. Consequently the
difference of the two is the mean precession, which is proved both by
theory and observation to be about 50ʺ·1 annually (N. 146).
As the longitudes of all the fixed stars are increased by this quantity, the
effects of precession are soon detected. It was accordingly discovered by
Hipparchus in the year 128 before Christ, from a comparison of his own
observations with those of Timocharis 155 years before. In the time of
Hipparchus the entrance of the sun into the constellation Aries was the
beginning of spring; but since that time the equinoctial points have receded
30°, so that the constellations called the signs of the zodiac are now at a
considerable distance from those divisions of the ecliptic which bear their
names. Moving at the rate of 50ʺ·1 annually, the equinoctial points will
accomplish a revolution in 25,868 years. But, as the precession varies in
different centuries, the extent of this period will be slightly modified. Since
the motion of the sun is direct, and that of the equinoctial points retrograde,
he takes a shorter time to return to the equator than to arrive at the same
stars; so that the tropical year of 365d 5h 48m 49s·7 must be increased by the
time he takes to move through an arc of 50ʺ·1, in order to have the length of
the sidereal year. The time required is 20m 19s·6, so that the sidereal year
contains 365d 6h 9m 9s·6 mean solar days.
The mean annual precession is subject to a secular variation; for,
although the change in the plane of the ecliptic in which the orbit of the sun
lies be independent of the form of the earth, yet, by bringing the sun, moon,
and earth into different relative positions from age to age, it alters the direct
action of the two first on the prominent matter at the equator: on this
account the motion of the equinox is greater by 0ʺ·455 now than it was in
the time of Hipparchus. Consequently the actual length of the tropical year
is about 4s·21 shorter than it was at that time. The utmost change that it can
experience from this cause amounts to 43 seconds.
Such is the secular motion of the equinoxes. But it is sometimes
increased and sometimes diminished by periodic variations, whose periods

depend upon the relative positions of the sun and moon with regard to the
earth, and which are occasioned by the direct action of these bodies on the
equator. Dr. Bradley discovered that by this action the moon causes the pole
of the equator to describe a small ellipse in the heavens, the axes of which
are 18ʺ·5 and 13ʺ·674, the longer being directed towards the pole of the
ecliptic. The period of this inequality is about 19 years, the time employed
by the nodes of the lunar orbit to accomplish a revolution. The sun causes a
small variation in the description of this ellipse; it runs through its period in
half a year. Since the whole earth obeys these motions, they affect the
position of its axis of rotation with regard to the starry heavens, though not
with regard to the surface of the earth; for in consequence of precession
alone the pole of the equator moves in a circle round the pole of the ecliptic
in 25,868 years, and by nutation alone it describes a small ellipse in the
heavens every 19 years, on each side of which it deviates every half-year
from the action of the sun. The real curve traced in the starry heavens by the
imaginary prolongation of the earth’s axis is compounded of these three
motions (N. 147). This nutation in the earth’s axis affects both the
precession and obliquity with small periodic variations. But in consequence
of the secular variation in the position of the terrestrial orbit, which is
chiefly owing to the disturbing energy of Jupiter on the earth, the obliquity
of the ecliptic is annually diminished, according to M. Bessel, by 0ʺ·457.
This variation in the course of ages may amount to 10 or 11 degrees; but the
obliquity of the ecliptic to the equator can never vary more than 2° 42ʹ or
3°, since the equator will follow in some measure the motion of the ecliptic.
It is evident that the places of all the celestial bodies are affected by
precession and nutation. Their longitudes estimated from the equinox are
augmented by precession; but, as it affects all the bodies equally, it makes
no change in their relative positions. Both the celestial latitudes and
longitudes are altered to a small degree by nutation; hence all observations
must be corrected for these inequalities. In consequence of this real motion
in the earth’s axis, the pole-star, forming part of the constellation of the
Little Bear, which was formerly 12° from the celestial pole, is now within
1° 24ʹ of it, and will continue to approach it till it is within 1⁄2°, after which
it will retreat from the pole for ages; and 12,934 years hence the star α Lyræ
will come within 5° of the celestial pole, and become the polar star of the
northern hemisphere.

SECTION XII.

Mean and Apparent Sidereal Time—Mean and Apparent Solar Time—
Equation of Time—English and French Subdivisions of Time—Leap Year
—Christian Era—Equinoctial Time—Remarkable Eras depending upon
the Position of the Solar Perigee—Inequality of the Lengths of the
Seasons in the two Hemispheres—Application of Astronomy to
Chronology—English and French Standards of Weights and Measures.

Astronomy has been of immediate and essential use in affording invariable
standards for measuring duration, distance, magnitude, and velocity. The
mean sidereal day measured by the time elapsed between two consecutive
transits of any star at the same meridian (N. 148), and the mean sidereal
year which is the time included between two consecutive returns of the sun
to the same star, are immutable units with which all great periods of time
are compared; the oscillations of the isochronous pendulum measure its
smaller portions. By these invariable standards alone we can judge of the
slow changes that other elements of the system may have undergone.
Apparent sidereal time, which is measured by the transit of the equinoctial
point at the meridian of any place, is a variable quantity, from the effects of
precession and nutation. Clocks showing apparent sidereal time are
employed for observation, and are so regulated that they indicate 0h 0m 0s at
the instant the equinoctial point passes the meridian of the observatory. And
as time is a measure of angular motion, the clock gives the distances of the
heavenly bodies from the equinox by observing the instant at which each
passes the meridian, and converting the interval into arcs at the rate of 15°
to an hour.
The returns of the sun to the meridian and to the same equinox or solstice
have been universally adopted as the measure of our civil days and years.
The solar or astronomical day is the time that elapses between two

consecutive noons or midnights. It is consequently longer than the sidereal
day, on account of the proper motion of the sun during a revolution of the
celestial sphere. But, as the sun moves with greater rapidity at the winter
than at the summer solstice, the astronomical day is more nearly equal to
the sidereal day in summer than in winter. The obliquity of the ecliptic also
affects its duration; for near the equinoxes the arc of the equator is less than
the corresponding arc of the ecliptic, and in the solstices it is greater
(N. 149). The astronomical day is therefore diminished in the first case, and
increased in the second. If the sun moved uniformly in the equator at the
rate of 59ʹ 8ʺ·33 every day, the solar days would be all equal. The time
therefore which is reckoned by the arrival of an imaginary sun at the
meridian, or of one which is supposed to move uniformly in the equator, is
denominated mean solar time, and is given by clocks and watches in
common life. When it is reckoned by the arrival of the real sun at the
meridian, it is true or apparent time, and is given by dials. The difference
between the time shown by a clock and a dial is the equation of time given
in the Nautical Almanac, sometimes amounting to as much as sixteen
minutes. The apparent and mean time coincide four times in the year; when
the sun’s daily motion in right ascension is equal to 59ʹ 8ʺ·33 in a mean
solar day, which happens about the 16th of April, the 16th of June, the 1st
of September, and the 25th of December.
The astronomical day begins at noon, but in common reckoning the day
begins at midnight. In England it is divided into twenty-four hours, which
are counted by twelve and twelve; but in France astronomers, adopting the
decimal division, divide the day into ten hours, the hour into one hundred
minutes, and the minute into a hundred seconds, because of the facility in
computation, and in conformity with their decimal system of weights and
measures. This subdivision is not now used in common life, nor has it been
adopted in any other country; and although some scientific writers in France
still employ that division of time, the custom is beginning to wear out. At
one period during the French Revolution, the clock in the gardens of the
Tuileries was regulated to show decimal time. The mean length of the day,
though accurately determined, is not sufficient for the purposes either of
astronomy or civil life. The tropical or civil year of 365d 5h 48m 49s·7, which
is the time elapsed between the consecutive returns of the sun to the mean
equinoxes or solstices, including all the changes of the seasons, is a natural
cycle peculiarly suited for a measure of duration. It is estimated from the

winter solstice, the middle of the long annual night under the north pole.
But although the length of the civil year is pointed out by nature as a
measure of long periods, the incommensurability that exists between the
length of the day and the revolution of the sun renders it difficult to adjust
the estimation of both in whole numbers. If the revolution of the sun were
accomplished in 365 days, all the years would be of precisely the same
number of days, and would begin and end with the sun at the same point of
the ecliptic. But as the sun’s revolution includes the fraction of a day, a civil
year and a revolution of the sun have not the same duration. Since the
fraction is nearly the fourth of a day, in four years it is nearly equal to a
revolution of the sun, so that the addition of a supernumerary day every
fourth year nearly compensates the difference. But in process of time
further correction will be necessary, because the fraction is less than the
fourth of a day. In fact, if a bissextile be suppressed at the end of three out
of four centuries, the year so determined will only exceed the true year by
an extremely small fraction of a day; and if in addition to this a bissextile be
suppressed every 4000 years, the length of the year will be nearly equal to
that given by observation. Were the fraction neglected, the beginning of the
year would precede that of the tropical year, so that it would retrograde
through the different seasons in a period of about 1507 years. The Egyptian
year began with the heliacal rising of Sirius (N. 150), and contained only
365 days, by which they lost one year in every 1461 years, their Sothaic
period, or that cycle in which the heliacal rising of Sirius passes through the
whole year and takes place again on the same day. The division of the year
into months is very old and almost universal. But the period of seven days,
by far the most permanent division of time, and the most ancient monument
of astronomical knowledge, was used by the Brahmins in India with the
same denominations employed by us, and was alike found in the calendars
of the Jews, Egyptians, Arabs, and Assyrians. It has survived the fall of
empires, and has existed among all successive generations, a proof of their
common origin.
The day of the new moon immediately following the winter solstice in
the 707th year of Rome was made the 1st of January of the first year of
Julius Cæsar. The 25th of December of his forty-fifth year is considered as
the date of Christ’s nativity; and the forty-sixth year of the Julian Calendar
is assumed to be the first of our era. The preceding year is called the first
year before Christ by chronologists, but by astronomers it is called the year

0. The astronomical year begins on the 31st of December at noon; and the
date of an observation expresses the days and hours which have actually
elapsed since that time.
Since solar and sidereal time are estimated from the passage of the sun
and the equinoctial point across the meridian of each place, the hours are
different at different places: while it is one o’clock at one place, it is two at
another, three at another, &c.; for it is obvious that it is noon at one part of
the globe at the same moment that it is midnight at another diametrically
opposite to it: consequently an event which happens at one and the same
instant of absolute time is recorded at different places as having happened at
different times. Therefore, when observations made at different places are
to be compared, they must be reduced by computation to what they would
have been had they been made under the same meridian. To obviate this it
was proposed by Sir John Herschel to employ mean equinoctial time, which
is the same for all the world, and independent alike of local circumstances
and inequalities in the sun’s motion. It is the time elapsed from the instant
the mean sun enters the mean vernal equinox, and is reckoned in mean solar
days and parts of a day.
Some remarkable astronomical eras are determined by the position of the
major axis of the solar ellipse, which depends upon the direct motion of the
perigee (N. 102) and the precession of the equinoxes conjointly, the annual
motion of the one being 11ʺ·8, and that of the other 50ʺ·1. Hence the axis,
moving at the rate of 61ʺ·9 annually, accomplishes a tropical revolution in
209·84 years. It coincided with the line of the equinoxes 4000 or 4089 years
before the Christian era, much about the time chronologists assign for the
creation of man. In 6483 the major axis will again coincide with the line of
the equinoxes; but then the solar perigee will coincide with the equinox of
autumn, whereas at the creation of man it coincided with the vernal
equinox. In the year 1246 the major axis was perpendicular to the line of the
equinoxes; then the solar perigee coincided with the solstice of summer, and
the apogee with the solstice of winter. According to La Place, who
computed these periods from different data, the last coincidence happened
in the year 1250 of our era, which induced him to propose that year as a
universal epoch, the vernal equinox of the year 1250 to be the first day of
the first year. These eras can only be regarded as approximate, since ancient
observations are too inaccurate, and modern observations too recent, to
afford data for their precise determination.

The variation in the position of the solar ellipse occasions corresponding
changes in the length of the seasons. In its present position spring is shorter
than summer, and autumn longer than winter; and while the solar perigee
continues as it now is, between the solstice of winter and the equinox of
spring, the period including spring and summer will be longer than that
including autumn and winter. In this century the difference is between seven
and eight days. The intervals will be equal towards the year 6483, when the
perigee will coincide with the equinox of spring; but, when it passes that
point, the spring and summer taken together will be shorter than the period
including the autumn and winter (N. 151). These changes will be
accomplished in a tropical revolution of the major axis of the earth’s orbit,
which includes an interval of 20,984 years. Were the orbit circular, the
seasons would be equal; their difference arises from the excentricity of the
orbit, small as it is; but the changes are so trifling as to be imperceptible in
the short span of human life.
No circumstance in the whole science of astronomy excites a deeper
interest than its application to chronology. “Whole nations,” says La Place,
“have been swept from the earth, with their languages, arts, and sciences,
leaving but confused masses of ruins to mark the place where mighty cities
stood; their history, with the exception of a few doubtful traditions, has
perished; but the perfection of their astronomical observations marks their
high antiquity, fixes the periods of their existence, and proves that, even at
that early time, they must have made considerable progress in science.” The
ancient state of the heavens may now be computed with great accuracy;
and, by comparing the results of calculation with ancient observations, the
exact period at which they were made may be verified if true, or, if false,
their error may be detected. If the date be accurate and the observation
good, it will verify the accuracy of modern tables, and will show to how
many centuries they may be extended without the fear of error. A few
examples will show the importance of the subject.
At the solstices the sun is at his greatest distance from the equator;
consequently his declination at these times is equal to the obliquity of the
ecliptic (N. 152), which was formerly determined from the meridian length
of the shadow of the stile of a dial on the day of a solstice. The lengths of
the meridian shadow at the summer and winter solstices are recorded to
have been observed at the city of Layang, in China, 1100 years before the
Christian era. From these the distances of the sun from the zenith (N. 153)

of the city of Layang are known. Half the sum of these zenith distances
determines the latitude, and half their difference gives the obliquity of the
ecliptic at the period of the observation; and, as the law of the variation of
the obliquity is known, both the time and place of the observations have
been verified by computations from modern tables. Thus the Chinese had
made some advances in the science of astronomy at that early period. Their
whole chronology is founded on the observations of eclipses, which prove
the existence of that empire for more than 4700 years. The epoch of the
lunar tables of the Indians, supposed by Bailly to be 3000 years before the
Christian era, was proved by La Place, from the acceleration of the moon,
not to be more ancient than the time of Ptolemy, who lived in the second
century after it. The great inequality of Jupiter and Saturn, whose cycle
embraces 918 years, is peculiarly fitted for marking the civilization of a
people. The Indians had determined the mean motions of these two planets
in that part of their periods when the apparent mean motion of Saturn was at
the slowest, and that of Jupiter the most rapid. The periods in which that
happened were 3102 years before the Christian era, and the year 1491 after
it. The returns of comets to their perihelia may possibly mark the present
state of astronomy to future ages.
The places of the fixed stars are affected by the precession of the
equinoxes; and, as the law of that variation is known, their positions at any
time may be computed. Now Eudoxus, a contemporary of Plato, mentions a
star situate in the pole of the equator, and it appears from computation that χ
Draconis was not very far from that place about 3000 years ago; but, as it is
only about 2150 years since Eudoxus lived, he must have described an
anterior state of the heavens, supposed to be the same that was mentioned
by Chiron about the time of the siege of Troy. Thus every circumstance
concurs in showing that astronomy was cultivated in the highest ages of
antiquity.
It is possible that a knowledge of astronomy may lead to the
interpretation of hieroglyphical characters. Astronomical signs are often
found on the ancient Egyptian monuments, probably employed by the
priests to record dates. The author had occasion to witness an instance of
this most interesting application of astronomy, in ascertaining the date of a
papyrus, sent from Egypt by Mr. Salt, in the hieroglyphical researches of
the late Dr. Thomas Young, whose profound and varied acquirements do
honour to his country, and to the age in which he lived. The manuscript was

found in a mummy case; it proved to be a horoscope of the age of Ptolemy,
and its date was determined from the configuration of the heavens at the
time of its construction.
The form of the earth furnishes a standard of weights and measures for
the ordinary purposes of life, as well as for the determination of the masses
and distances of the heavenly bodies. The length of the pendulum vibrating
seconds of mean solar time, in the latitude of London, forms the standard of
the British measure of extension. Its approximate length oscillating in vacuo
at the temperature of 62° of Fahrenheit, and reduced to the level of the sea
(N. 154), was determined by Captain Kater to be 39·1393 inches. The
weight of a cubic inch of water at the temperature of 62° of Fahrenheit,
barometer 30 inches, was also determined in parts of the imperial troy
pound, whence a standard both of weight and capacity was deduced. The
French have adopted the mètre, equal to 3·2808992 English feet, for their
unit of linear measure, which is the ten-millionth part of the arc of the
meridian which extends from the equator to the pole, as deduced from the
measures of the separate arc extending from Formentera, the most southern
of the Balearic Islands, to Dunkirk. Should the national standards of the two
countries ever be lost, both may be recovered, since they are derived from
natural and invariable ones. The length of the measure deduced from that of
the pendulum would be found again with more facility than the mètre. But,
as no measure is mathematically exact, an error in the original standard may
at length become sensible in measuring a great extent, whereas the error
that must necessarily arise in measuring the quadrant of the meridian
(N. 155) is rendered totally insensible by subdivision in taking its ten-
millionth part. The French have adopted the decimal division, not only in
time, but also in their degrees, weights, and measures, on account of the
very great facility it affords in computation. It has not been adopted by any
other country, though nothing is more desirable than that all nations should
concur in using the same standards, not only on account of convenience, but
as affording a more definite idea of quantity. It is singular that the decimal
division of the day, of space, weights, and measures, was employed in
China 4000 years ago; and that at the time Ibn Junis made his observations
at Cairo, about the year 1000 of the Christian era, the Arabs were in the
habit of employing the vibrations of the pendulum in their astronomical
observations as a measure of time.

SECTION XIII.

Tides—Forces that produce them—Origin and Course of Tidal Wave—Its
Speed—Three kinds of Oscillations in the Ocean—The Semidiurnal
Tides—Equinoctial Tides—Effects of the Declination of the Sun and
Moon—Theory insufficient without Observation—Direction of the Tidal
Wave—Height of Tides—Mass of Moon obtained from her Action on the
Tides—Interference of Undulations—Impossibility of a Universal
Inundation—Currents.

One of the most immediate and remarkable effects of a gravitating force
external to the earth is the alternate rise and fall of the surface of the sea
twice in the course of a lunar day, or 24h 50m 28s of mean solar time. As it
depends upon the action of the sun and moon, it is classed among
astronomical problems, of which it is by far the most difficult and its
explanation the least satisfactory. The form of the surface of the ocean in
equilibrio, when revolving with the earth round its axis, is an ellipsoid
flattened at the poles; but the action of the sun and moon, especially of the
moon, disturbs the equilibrium of the ocean. If the moon attracted the centre
of gravity of the earth and all its particles with equal and parallel forces, the
whole system of the earth and the waters that cover it would yield to these
forces with a common motion, and the equilibrium of the seas would
remain undisturbed. The difference of the forces and the inequality of their
directions alone disturb the equilibrium.
The particles of water under the moon are more attracted than the centre
of gravity of the earth, in the inverse ratio of the square of the distance.
Hence they have a tendency to leave the earth, but are retained by their
gravitation, which is diminished by this tendency. On the contrary, the
moon attracts the centre of the earth more powerfully than she attracts the
particles of water in the hemisphere opposite to her; so that the earth has a

tendency to leave the waters, but is retained by gravitation, which is again
diminished by this tendency. Thus the waters immediately under the moon
are drawn from the earth, at the same time that the earth is drawn from
those which are diametrically opposite to her, in both instances producing
an elevation of the ocean of nearly the same height above the surface of
equilibrium; for the diminution of the gravitation of the particles in each
position is almost the same, on account of the distance of the moon being
great in comparison of the radius of the earth. Were the earth entirely
covered by the sea, the waters thus attracted by the moon would assume the
form of an oblong spheroid whose greater axis would point towards the
moon; since the columns of water under the moon, and in the direction
diametrically opposite to her, are rendered lighter in consequence of the
diminution of their gravitation; and, in order to preserve the equilibrium, the
axes 90° distant would be shortened. The elevation, on account of the
smaller space to which it is confined, is twice as great as the depression,
because the contents of the spheroid always remain the same. If the waters
were capable of assuming the form of equilibrium instantaneously, that is,
the form of the spheroid, its summit would always point to the moon
notwithstanding the earth’s rotation. But, on account of their resistance, the
rapid motion produced in them by rotation prevents them from assuming at
every instant the form which the equilibrium of the forces acting upon them
requires. Hence, on account of the inertia of the waters, if the tides be
considered relatively to the whole earth and open seas, there is a meridian
about 30° eastward of the moon, where it is always high water both in the
hemisphere where the moon is and in that which is opposite. On the west
side of this circle the tide is flowing, on the east it is ebbing, and on every
part of the meridian at 90° distant it is low water. This great wave, which
follows all the motions of the moon as far as the rotation of the earth will
permit, is modified by the action of the sun, the effects of whose attraction
are in every respect like those produced by the moon, though greatly less in
degree. Consequently a similar wave, but much smaller, raised by the sun,
tends to follow his motions, which at times combines with the lunar wave,
and at others opposes it, according to the relative positions of the two
luminaries; but as the lunar wave is only modified a little by the solar, the
tides must necessarily happen twice in a day, since the rotation of the earth
brings the same point twice under the meridian of the moon in that time,
once under the superior and once under the inferior meridian.

The periodic motions of the waters of the ocean, on the hypothesis of an
ellipsoid of revolution, entirely covered by the sea, are, however, very far
from according with observation. This arises from the great irregularities in
the surface of the earth, which is but partially covered by the sea, from the
variety in the depths of the ocean, the manner in which it is spread out on
the earth, the position and inclination of the shores, the currents, and the
resistance which the waters meet with: causes impossible to estimate
generally, but which modify the oscillations of the great mass of the ocean.
However, amidst all these irregularities, the ebb and flow of the sea
maintain a ratio to the forces producing them sufficient to indicate their
nature, and to verify the law of the attraction of the sun and moon on the
sea. La Place observes, that the investigation of such relations between
cause and effect is no less useful in natural philosophy than the direct
solution of problems, either to prove the existence of the causes or to trace
the laws of their effects. Like the theory of probabilities, it is a happy
supplement to the ignorance and weakness of the human mind.
Since the disturbing action of the sun and moon can only become
sensible in a very great extent of deep water, the Antarctic Ocean is the
origin and birthplace of our tides. A succession of tidal waves from that
source follow one another in a north-westerly direction down the Pacific
and Atlantic Oceans, modified as they proceed by the depth of the water
and the form of the coasts. For when the sun and moon are in the same
meridian, and pass over the mass of waters lying east from Van Diemen’s
Land, New Zealand, and the South Pole, the resulting force of their
combined attraction, penetrating to the abyss of the deep and boundless
circuit of the Southern Ocean, raises a vast wave or ridge of water, which
tends to follow the luminaries to the north and west, and continues to flow
in that direction long after the bodies cease to act upon it; but it is so
retarded by the rotation of the earth and by the inertia of the water, that it
does not arrive at the different parts of the coasts till after the moon’s
southing (N. 156). When this tidal wave leaves the Antarctic Ocean and
enters the Pacific, it rushes along the western coast of America to its
farthest end, but it is so much obstructed by the number of islands in the
middle of that ocean that it is hardly perceptible among them; while on the
east it enters the Indian Ocean, strikes with violence on the coasts of
Hindostan and the shores at the mouths of the Ganges, and causes the
terrific bore in the Hoogly. The part of this tidal wave that enters the

Atlantic passes impetuously along the coasts of Africa and America,
arriving later and later at each place. It is modified, however, by a tide
raised in the Atlantic, which is deep and free from islands; and this
combined tidal wave, still coming northward, pours its surge into the Gulf
of Fundy to the height of fifty feet; then being deflected by the coast of
America at right angles, it rushes eastward, bringing high water to the
western coasts of Ireland and England. It then goes round Scotland, brings
high water to Aberdeen and the opposite coasts of Norway and Denmark,
and, continuing its course to the south, arrives at the mouth of the Thames
and fills the channels of that river on the morning of the third day after
leaving the Antarctic Ocean.
Thus the tides in our ports are owing to an impulse from the waters of the
Antarctic seas raised by the action of the sun and moon. No doubt a similar
action raised that tide in the North Polar Ocean which Dr. Kane saw rolling
on the northern coast of Greenland in 82° N. latitude, but which, in the
present state of the globe, is imprisoned by bars of ice and ice-bound lands.
The tidal wave extends to the bottom of the ocean, and moves uniformly
and with great speed in very deep water, variably and slow in shallow
water; the time of propagation depends upon the depth of the sea, as well as
on the nature and form of the coasts. It varies inversely as the square of the
depth—a law which theoretically affords the means of ascertaining the
proportionate depth of the sea in different parts. It is one of the great
constants of nature, and is to fluids what the pendulum is to solids—a
connecting link between time and force.
For example: the tidal wave moves across the Southern Ocean with the
velocity of 1000 miles an hour, and in the Atlantic it is scarcely less on
account of the deep trough which runs through the centre of that ocean; but
the sea is so shallow on the British coast that it takes more time to come
from Aberdeen to London than to travel over an arc of 120°, between 60° S.
lat. and 60° N. lat.
In deep water the tidal wave is merely a rise and fall of the surface; the
water does not advance, though the wave does. Indeed, if so heavy a body
as water were to move at the rate of 1000 miles an hour, it would cause
universal destruction, since in the most violent hurricanes the velocity of
the wind is little more than 100 miles an hour. Besides, it is evident that no

ship could either sail or steam against it. When the water is shallow,
however, there is a motion of translation in the water along with the tide.
In the deep ocean the undulating motion consists of two distinct things—
an advancing form and a molecular movement. The motion of each particle
of water is in an ellipse lying wholly in the vertical plane; so that, after the
momentary displacement during the passage of the wave, they return to
their places again. The resistance of the sea-bed is insensible in deep water;
but when the tidal wave, which extends to the very bottom of the ocean,
comes into shallow water with diminished velocity, the particles of water
moving in vertical ellipses strike the bottom, and by reaction the wave rises
higher; and that being continually repeated, as the form moves on the wave
rises higher and higher, bends more and more forward, till at last it loses its
equilibrium, and then both form and water roll to the shore, and the
elliptical trajectories of the particles, which in deep water were vertical,
incline more and more, till at length they become horizontal. The distance
from the shore at which the water begins to be translated depends upon the
depth, the nature of the coast, and the form of the shore. Mr. Scott Russell
has demonstrated that in shallow water the velocity of the wave is equal to
that which a heavy body falling freely by its gravity would acquire in
descending through half the depth of the fluid.
It is proved by daily experience, as well as by strict mathematical
reasoning, that, if a number of waves or oscillations be excited in a fluid by
different forces, each pursues its course and has its effect independently of
the rest. Now, in the tides there are three kinds of oscillations, depending on
different causes, and producing their effects independently of each other,
which may therefore be estimated separately. The oscillations of the first
kind, which are very small, are independent of the rotation of the earth, and,
as they depend upon the motion of the disturbing body in its orbit, they are
of long periods. The second kind of oscillations depend upon the rotation of
the earth, therefore their period is nearly a day. The oscillations of the third
kind vary with an angle equal to twice the angular rotation of the earth, and
consequently happen twice in twenty-four hours (N. 157). The first afford
no particular interest, and are extremely small; but the difference of two
consecutive tides depends upon the second. At the time of the solstices this
difference, which ought to be very great according to Newton’s theory, is
hardly sensible on our shores. La Place has shown that the discrepancy
arises from the depth of the sea, and that if the depth were uniform there

would be no difference in the consecutive tides but that which is occasioned
by local circumstances. It follows, therefore, that, as this difference is
extremely small, the sea, considered in a large extent, must be nearly of
uniform depth, that is to say, there is a certain mean depth from which the
deviation is not great. The mean depth of the Pacific Ocean is supposed to
be about four or five miles, that of the Atlantic only three or four, which,
however, is mere conjecture. Possibly the great extent and uniformly small
depth of the Atlantic over the telegraphic platform may prevent the
difference of the oscillations in question from being perceptible on our
shores. From the formulæ which determine the difference of these
consecutive tides it is proved that the precession of the equinoxes and the
nutation of the earth’s axis are the same as if the sea formed one solid mass
with the earth.
The oscillations of the third kind are the semi-diurnal tides so remarkable
on our coasts. In these there are two phenomena particularly to be
distinguished, one occurring twice in a month, the other twice in a year.
The first phenomenon is, that the tides are much increased in the syzygies
(N. 158), or at the time of new and full moon: in both cases the sun and
moon are in the same meridian; for when the moon is new they are in
conjunction, and when she is full they are in opposition. In each of these
positions their action is combined to produce the highest or spring tides
under that meridian, and the lowest in those points that are 90° distant. It is
observed that the higher the sea rises in full tide, the lower it is in the ebb.
The neap tides take place when the moon is in quadrature. They neither rise
so high nor sink so low as the spring tides. It is evident that the spring tides
must happen twice in a month, since in that time the moon is once new and
once full. Theory proves that each partial tide increases as the cube of the
parallax or apparent diameter of the body producing it, for the greater the
apparent diameter the nearer the body and the more intense its action upon
the sea; hence the spring tides are much increased when the moon is in
perigee, for then she is nearest to the earth.
The second phenomenon in the tides is the augmentation occurring at the
time of the equinoxes, when the sun’s declination is zero (N. 159), which
happens twice in every year. The spring tides which take place at that time
are often much increased by the equinoctial gales, and, on the hypothesis of
the whole earth covered by the ocean, would be the greatest possible if the
line of the moon’s nodes coincided with that of her perigee, for then the

whole action of the luminaries would be in the plane of the equator. But
since the Antarctic Ocean is the source of the tides, it is evident that the
spring tide must be greatest when the moon is in perigee, and when both
luminaries have their highest southern declination, for then they act most
directly upon the great circuit of the south polar seas.
The sun and moon are continually making the circuit of the heavens at
different distances from the plane of the equator, on account of the obliquity
of the ecliptic and the inclination of the lunar orbit. The moon takes about
291⁄2 days to vary through all her declinations, which sometimes extend
283⁄4° on each side of the equator, while the sun requires nearly 3651⁄4 days
to accomplish his motions through 231⁄2° on each side of the same plane, so
that their combined action causes great variations in the tides. Both the
height and time of high water are perpetually changing, and, although the
problem does not admit of a general solution, it is necessary to analyse the
phenomena which ought to arise from the attraction of the sun and moon,
but the result must be corrected in each particular case for local
circumstances, so that the theory of the tides in each port becomes really a
matter of experiment, and can only be determined by means of a vast
number of observations, including many revolutions of the moon’s nodes.
The mean height of the tides will be increased by a very small quantity
for ages to come, in consequence of the decrease in the mean distance of the
moon from the earth; the contrary effect will take place after that period has
elapsed, and the moon’s mean distance begins to increase again, which it
will continue to do for many ages. Thus the mean distance of the moon and
the consequent minute increase in the height of the tides will oscillate
between fixed limits for ever.
The height to which the tides rise is much greater in narrow channels
than in the open sea, on account of the obstructions they meet with. The sea
is so pent up in the British Channel that the tides sometimes rise as much as
fifty feet at St. Malo, on the coast of France; whereas on the shores of some
of the South Sea islands, near the centre of the Pacific, they do not exceed
one or two feet. The winds have great influence on the height of the tides,
according as they conspire with or oppose them. But the actual effect of the
wind in exciting the waves of the ocean extends very little below the
surface. Even in the most violent storms the water is probably calm at the
depth of ninety or a hundred fathoms. The tidal wave of the ocean does not

reach the Mediterranean nor the Baltic, partly from their position and partly
from the narrowness of the Straits of Gibraltar and of the Categat, but it is
very perceptible in the Red Sea and in Hudson’s Bay. The ebb and flow of
the sea are perceptible in rivers to a very great distance from their estuaries.
In the Narrows of Pauxis, in the river of the Amazons, more than five
hundred miles from the sea, the tides are evident. It requires so many days
for the tide to ascend this mighty stream, that the returning tides meet a
succession of those which are coming up; so that every possible variety
occurs at some part or other of its shores, both as to magnitude and time. It
requires a very wide expanse of water to accumulate the impulse of the sun
and moon, so as to render their influence sensible; on that account the tides
in the Mediterranean and Black Sea are scarcely perceptible.
These perpetual commotions in the waters are occasioned by forces that
bear a very small proportion to terrestrial gravitation: the sun’s action in
raising the ocean is only the 1⁄38448000 of gravitation at the earth’s surface,
and the action of the moon is little more than twice as much; these forces
being in the ratio of 1 to 2.35333, when the sun and moon are at their mean
distances from the earth. From this ratio the mass of the moon is found to
be only the 1⁄75 part of that of the earth. Had the action of the sun on the
ocean been exactly equal to that of the moon, there would have been no
neap tides, and the spring tides would have been of twice the height which
the action of either the sun or moon would have produced separately—a
phenomenon depending upon the interference of the waves or undulations.
A stone plunged into a pool of still water occasions a series of waves to
advance along the surface, though the water itself is not carried forward, but
only rises into heights and sinks into hollows, each portion of the surface
being elevated and depressed in its turn. Another stone of the same size,
thrown into the water near the first, will occasion a similar set of
undulations. Then, if an equal and similar wave from each stone arrive at
the same spot at the same time, so that the elevation of the one exactly
coincides with the elevation of the other, their united effect will produce a
wave twice the size of either. But, if one wave precede the other by exactly
half an undulation, the elevation of the one will coincide with the hollow of
the other, and the hollow of the one with the elevation of the other; and the
waves will so entirely obliterate one another, that the surface of the water
will remain smooth and level. Hence, if the length of each wave be

represented by 1, they will destroy one another at intervals of 1⁄2, 3⁄2, 5⁄2, &c.,
and will combine their effects at the intervals 1, 2, 3, &c. It will be found
according to this principle, when still water is disturbed by the fall of two
equal stones, that there are certain lines on its surface of a hyperbolic form,
where the water is smooth in consequence of the waves obliterating each
other, and that the elevation of the water in the adjacent parts corresponds to
both the waves united (N. 160). Now, in the spring and neap tides arising
from the combination of the simple solilunar waves, the spring tide is the
joint result of the combination when they coincide in time and place; and
the neap tide happens when they succeed each other by half an interval, so
as to leave only the effect of their difference sensible. It is, therefore,
evident that, if the solar and lunar tides were of the same height, there
would be no difference, consequently no neap tides, and the spring tides
would be twice as high as either separately. In the port of Batsha, in
Tonquin, where the tides arrive by two channels of lengths corresponding to
half an interval, there is neither high nor low water on account of the
interference of the waves.
The initial state of the ocean has no influence on the tides; for, whatever
its primitive conditions may have been, they must soon have vanished by
the friction and mobility of the fluid. One of the most remarkable
circumstances in the theory of the tides is the assurance that, in
consequence of the density of the sea being only one-fifth of the mean
density of the earth, and the earth itself increasing in density towards the
centre, the stability of the equilibrium of the ocean never can be subverted
by any physical cause. A general inundation arising from the mere
instability of the ocean is therefore impossible. A variety of circumstances,
however, tend to produce partial variations in the equilibrium of the seas,
which is restored by means of currents. Winds and the periodical melting of
the ice at the poles occasion temporary watercourses; but by far the most
important causes are the centrifugal force induced by the velocity of the
earth’s rotation, and variations in the density of the sea.
The centrifugal force may be resolved into two forces—one
perpendicular, and another tangent to the earth’s surface (N. 161). The
tangential force, though small, is sufficient to make the fluid particles
within the polar circles tend towards the equator, and the tendency is much
increased by the immense evaporation in the equatorial regions from the
heat of the sun, which disturbs the equilibrium of the ocean. To this may

also be added the superior density of the waters near the poles, from their
low temperature. In consequence of the combination of all these
circumstances, two great currents perpetually set from each pole towards
the equator. But, as they come from latitudes where the rotatory motion of
the surface of the earth is very much less than it is between the tropics, on
account of their inertia, they do not immediately acquire the velocity with
which the solid part of the earth’s surface is revolving at the equatorial
regions; from whence it follows that, within twenty-five or thirty degrees on
each side of the line, the ocean has a general motion from east to west,
which is much increased by the action of the trade winds. Both in the
Pacific and Atlantic currents of enormous magnitude are deflected by the
continents and islands to the north and south from this mighty mass of
rushing waters, which convey the warmth of the equator to temper the
severity of the polar regions, while to maintain the equilibrium of the seas
counter currents of cold water are poured from the polar oceans to mingle
with the warm waters at the line, so that a perpetual circulation is
maintained.
Icebergs are sometimes drifted as far as the Azores from the Polar seas,
and from the south pole they have come even to the Cape of Good Hope.
But the ice which encircles the south pole extends to lower latitudes by 10°
than that which surrounds the north. In consequence of the polar current Sir
Edward Parry was obliged to give up his attempt to reach the north pole in
the year 1827, because the fields of ice were drifting to the south faster than
his party could travel over them to the north.
Kotzebue and Sir James Ross found a stratum of constant temperature in
the ocean at a depth depending upon the latitude: at the equator it is at the
depth of 7200 feet, from whence it gradually rises till it comes to the
surface in both hemispheres about the latitude of 56° 26ʹ, where the water
has the same temperature at all depths; it then descends to 4500 feet below
the surface about the 70th parallel both in the Arctic and Antarctic Seas. The
temperature of that aqueous zone is about 39°·5 of Fahrenheit.[7] It divides
the surface of the ocean into five great zones of temperature, namely, a
medial region, in which the highest mean temperature is 82° Fahr., two
temperate zones each of 39°·5 Fahr., and two polar basins at the freezing
point of salt water.

SECTION XIV.

Molecular Forces—Permanency of the ultimate Particles of Matter—
Interstices—Mossotti’s Theory—Rankin’s Theory of Molecular Vortices
—Gases reduced to Liquids by Pressure—Gravitation of Particles—
Cohesion—Crystallization—Cleavage—Isomorphism—Minuteness of
the Particles—Height of Atmosphere—Chemical Affinity—Definite
Proportions and Relative Weights of Atoms—Faraday’s Discovery with
regard to Affinity—Capillary Attraction.

The oscillations of the atmosphere, and its action upon the rays of light
coming from the heavenly bodies, connect the science of astronomy with
the equilibrium and movements of fluids and the laws of molecular
attraction. Hitherto that force has been under consideration which acts upon
masses of matter at sensible distances; but now the effects of such forces
are to be considered as act at inappreciable distances upon the ultimate
molecules of material bodies.
All substances consist of an assemblage of material particles, or
molecules, which are far too small to be visible by any means human
ingenuity has yet been able to devise, and which are much beyond the limits
of our perceptions. They neither can be created nor destroyed; bodies may
be burned, but their particles are not consumed—they are merely liberated
from one combination to enter into another, nor are their peculiar properties
ever changed; whatever combinations they may enter into, they are ever and
invariably the same.
Since every known substance may be reduced in bulk by pressure, it
follows that the particles of matter are not in actual contact, but are
separated by interstices; and it is evident that the smaller the interstitial
spaces the greater the density. These spaces appear to be filled with air in
some cases, as may be inferred from certain semi-opaque minerals and

other substances becoming transparent when plunged into water. Sometimes
they may possibly contain some unknown and highly elastic fluid, such as
Sir David Brewster has discovered in the minute cavities of various
minerals, which occasionally causes them to explode under the hands of the
lapidary; but as it is inconceivable that the particles of matter should act
upon one another without some means of communication, it is presumed
that the interstices of material substances contain a portion of the ethereal
medium with which the regions of space are filled.
The various hypotheses that have been formed as to the nature and action
of the forces which unite the particles of matter, have been successively
given up as science advanced, and now nothing decisive has been attained,
although Professor Mossotti, of Pisa, by a very able analysis, has
endeavoured to prove the identity of the cohesive force with gravitation. As
the particles of material bodies are not in actual contact, he supposes that
each is surrounded by an atmosphere of the ethereal medium, which he
conceives to be electricity; moreover he assumes that the atoms of the
medium repel one another, that the particles of matter also repel one
another, but with less intensity, and that there is a mutual attraction between
the particles of matter and the atoms of the medium, forces which are
assumed to vary inversely as the square of the distance.
Hence, when the material molecules of a body are inappreciably near to
one another, they mutually repel each other with a force which diminishes
rapidly as the infinitely small distance between the material molecules
augments, and at last vanishes. When the molecules are still farther apart,
the force becomes attractive. At that particular point where the change takes
place the forces of repulsion and attraction balance each other, so that the
molecules of a body are neither disposed to approach nor recede, but remain
in equilibrio. If we try to press them nearer, the repulsive force resists the
attempt; and if we endeavour to break the body so as to tear the particles
asunder, the attractive force predominates and keeps them together. This is
what constitutes the cohesive force, or force of aggregation, by which the
molecules of all substances are united. The limits of the distance at which
the negative action becomes positive vary according to the temperature and
nature of the molecules, and determine whether the body which they form
be solid, liquid, or aëriform.
Beyond this neutral point the attractive force increases as the distance
between the molecules augments till it attains a maximum; when the

particles are more apart, it diminishes; and, as soon as they are separated by
finite or sensible distances, it varies directly as their mass and inversely as
the square of the distance, which is precisely the law of universal
gravitation.
Thus, on the hypothesis that the mutual repulsion between the electric
atoms is a little more powerful than the mutual repulsion between the
particles of matter, the ether and the matter attract each other with unequal
intensities, which leaves an excess of attractive force constituting
gravitation. As the gravitating force is in operation wherever there is matter,
the ethereal electric medium must encompass all the bodies in the universe;
and, as it is utterly incomprehensible that the celestial bodies should exert a
reciprocal attraction through a void, the Professor concludes that the
ethereal electrical medium fills all space.
It is true that this connexion between the molecular forces and gravitation
depends upon hypothesis; but in the greater number of physical
investigations some hypothesis is requisite in the first instance to aid the
imperfection of our senses; and when the phenomena of nature accord with
the assumption, we are justified in believing it to be a general law.
Mr. Rankin’s theory of molecular vortices, or the molecular structure of
matter, is independent of electricity. According to his hypothesis, each atom
of matter consists of an inappreciably small nucleus, encompassed by an
elastic ethereal atmosphere which is retained in its position by attractive
forces directed towards the molecule, whilst the molecules attract each
other in the direction of straight lines joining their centres. The nuclei may
either be solid, or a high condensation of the atmospheres which surround
each with decreasing density. When the attraction between the molecules is
such that the elasticity of the atmospheres is insensible, the body is a perfect
solid, the rigidity of which bears a certain definite proportion to the
elasticity of the volume. When the atmospheres are less condensed and the
attraction of the molecules merely produces a cohesive force sufficient to
balance the atomic elasticity of the atmosphere, the body is a perfect liquid;
and when the attraction of the molecules is very small compared with the
elasticity of their ethereal atmospheres, the body is a perfect gas. These
atmospheres are supposed to be portions of the ethereal medium which
penetrates into the interstices of every substance, and their elasticity to be
due to the heat generated by the centrifugal force or oscillations among

their atoms, for motion is the cause of heat, the force producing the motions
varying simply as the density of the ether.
In aëriform fluids, although the particles are more remote from each
other than in liquids and solids, yet the pressure may be so great as to
reduce an aëriform fluid to a liquid, and a liquid to a solid. Dr. Faraday has
reduced some of the gases to a liquid state by very great compression; but
although atmospheric air is capable of a diminution of volume to which we
do not know a limit, it has hitherto always retained its gaseous qualities, and
resumes its primitive volume the instant the pressure is removed.
Substances are said to be more or less elastic, according to the facility with
which they regain their bulk or volume when the pressure is removed; thus
liquids resist compression on account of their elasticity, and in solids the
resistance is much greater but variable, and the effort required to break a
substance is a measure of the cohesive force exerted by its particles. In
stone, iron, steel, and all brittle and hard substances, the cohesion of the
particles is powerful but of small extent; in elastic bodies, on the contrary,
its action is weak, but more extensive. An infinite variety of conditions may
be observed in the fusion of metals and other substances passing from
hardness to toughness, viscidity, and through all the other stages to perfect
fluidity and even to vapour. Since all bodies expand by heat, the cohesive
force is weakened by increase of temperature. The cohesion of matter or the
strength of substances forms an important branch of study in engineering.
Every particle of matter, whether it forms a constituent part of a solid,
liquid, or aëriform fluid, is subject to the law of gravitation. The weight of
the atmosphere, of gases and vapour, shows that they consist of gravitating
particles. In liquids the cohesive force is not sufficiently powerful to resist
the action of gravitation. Therefore, although their component particles still
maintain their connexion, the liquid is scattered by their weight, unless
when it is confined in a vessel or has already descended to the lowest point
possible, and assumed a level surface from the mobility of its particles and
the influence of the gravitating forces, as in the ocean, or a lake. Solids
would also fall to pieces by the weight of their particles, if the force of
cohesion were not powerful enough to resist the efforts of gravitation.
The phenomena arising from the force of cohesion are innumerable. The
spherical form of rain-drops; the difficulty of detaching a plate of glass
from the surface of water; the force with which two plane surfaces adhere
when pressed together; the drops that cling to the window-glass in a shower

of rain—are all effects of cohesion entirely independent of atmospheric
pressure, and are included in the same analytical formula (N. 162) which
expresses all the circumstances accurately, although the laws according to
which the forces of cohesion and repulsion vary are unknown. It is more
than probable that the spherical form of the sun and planets is due to the
force of cohesion, as they have every appearance of having been at one
period in a state of fusion.
A very remarkable instance has occasionally been observed in plate-glass
manufactories. After the large plates of glass of which mirrors are to be
made have received their last polish, they are carefully wiped and laid on
their edges with their surfaces resting on one another. In the course of time
the cohesion has sometimes been so powerful, that they could not be
separated without breaking. Instances have occurred where two or three
have been so perfectly united, that they have been cut and their edges
polished as if they had been fused together; and so great was the force
required to make the surfaces slide that one tore off a portion of the surface
of the other.
In liquids and gases the forms of the particles have no influence, they are
so far apart; but the structure of solids varies according to the sides which
the particles present to one another during their aggregation. Nothing is
known of their form further than the dissimilarity of their different sides in
certain cases, which appears from their reciprocal attractions during
crystallisation being more or less powerful according to the sides they
present to one another. Crystallisation is an effect of molecular attraction
regulated by certain laws, according to which atoms of the same kind of
matter unite in regular forms—a fact easily proved by dissolving a piece of
alum in pure water. The mutual attraction of the particles is destroyed by the
water; but, if it be evaporated, they unite, and form in uniting eight-sided
figures called octahedrons (N. 163). These however are not all the same.
Some have their angles cut off, others their edges, and some both, while the
remainder take the regular form. It is quite clear that the same
circumstances which cause the aggregation of a few particles would, if
continued, cause the addition of more; and the process would go on as long
as any particles remain free round the primitive nucleus, which would
increase in size, but would remain unchanged in form, the figure of the
particles being such as to maintain the regularity and smoothness of the
surfaces of the solid and their mutual inclinations. A broken crystal will by

degrees resume its regular figure when put back again into the solution of
alum, which shows that the internal and external particles are similar, and
have a similar attraction for the particles held in solution. The original
conditions of aggregation which make the molecules of the same substance
unite in different forms must be very numerous, since of carbonate of lime
alone there are many hundred varieties; and certain it is, from the motion of
polarised light through rock crystal, that a very different arrangement of
particles is requisite to produce an extremely small change in external form.
A variety of substances in crystallising combine chemically with a certain
portion of water which in a dry state forms an essential part of their crystals,
and, according to the experiments of MM. Haidinger and Mitscherlich,
seems in some cases to give the peculiar determination to their constituent
molecules. These gentlemen have observed that the same substance
crystallising at different temperatures unites with different quantities of
water and assumes a corresponding variety of forms. Seleniate of zinc, for
example, unites with three different portions of water, and assumes three
different forms, according as its temperature in the act of crystallising is
hot, lukewarm, or cold. Sulphate of soda also, which crystallises at 90° of
Fahrenheit without water of crystallisation, combines with water at the
ordinary temperature, and takes a different form. Heat appears to have a
great influence on the phenomena of crystallisation, not only when the
particles of matter are free, but even when firmly united, for it dissolves
their union, and gives them another determination. Professor Mitscherlich
found that prismatic crystals of sulphate of nickel (N. 164), exposed to a
summer’s sun in a close vessel, had their internal structure so completely
altered without any exterior change, that when broken open they were
composed internally of octahedrons with square bases. The original
aggregation of the internal particles had been dissolved, and a disposition
given to arrange themselves in a crystalline form. Crystals of sulphate of
magnesia and of sulphate of zinc, gradually heated in alcohol till it boils,
lose their transparency by degrees, and when opened are found to consist of
innumerable minute crystals totally different in form from the whole
crystals; and prismatic crystals of zinc (N. 165) are changed in a few
seconds into octahedrons by the heat of the sun: other instances might be
given of the influence of even moderate degrees of temperature on
molecular attraction in the interior of substances. It must be observed that
these experiments give entirely new views with regard to the constitution of

solid bodies. We are led from the mobility of fluids to expect great changes
in the relative positions of their molecules, which must be in perpetual
motion even in the stillest water or calmest air; but we were not prepared to
find motion to such an extent in the interior of solids. That their particles
are brought nearer by cold and pressure, or removed farther from one
another by heat, might be expected; but it could not have been anticipated
that their relative positions could be so entirely changed as to alter their
mode of aggregation. It follows, from the low temperature at which these
changes are effected, that there is probably no portion of inorganic matter
that is not in a state of relative motion.
Professor Mitscherlich’s discoveries with regard to the forms of
crystallised substances, as connected with their chemical character, have
thrown additional light on the constitution of material bodies. There is a
certain set of crystalline forms which are not susceptible of variation, as the
die or cube (N. 166), which may be small or large, but is invariably a solid
bounded by six square surfaces or planes. Such also is the tetrahedron
(N. 167) or four-sided solid contained by four equal-sided triangles. Several
other solids belong to this class, which is called the Tessular system of
crystallisation. There are other crystals which, though bounded by the same
number of sides, and having the same form, are yet susceptible of variation;
for instance, the eight-sided figure with a square base, called an octahedron
(N. 168), which is sometimes flat and low, and sometimes acute and high. It
was formerly believed that identity of form in all crystals not belonging to
the Tessular system indicated identity of chemical composition. Professor
Mitscherlich, however, has shown that substances differing to a certain
degree in chemical composition have the property of assuming the same
crystalline form. For example, the neutral phosphate of soda and the
arseniate of soda crystallise in the very same form, contain the same
quantities of acid, alkali, and water of crystallisation; yet they differ so far,
that one contains arsenic and the other an equivalent quantity of
phosphorus. Substances having such properties are said to be isomorphous,
that is, equal in form. Of these there are many groups, each group having
the same form, and similarity though not identity of chemical composition.
For instance, one of the isomorphous groups is that consisting of certain
chemical substances called the protoxides of iron, copper, zinc, nickel, and
manganese, all of which are identical in form and contain the same quantity
of oxygen, but differ in the respective metals they contain, which are,

however, nearly in the same proportion in each. All these circumstances
tend to prove that substances having the same crystalline form must consist
of ultimate atoms having the same figure and arranged in the very same
order; so that the form of crystals is dependent on their atomic constitution.
All crystallised bodies have joints called cleavages, at which they split
more easily than in other directions; on this property the whole art of
cutting diamonds depends. Each substance splits in a manner and in forms
peculiar to itself. For example, all the hundreds of forms of carbonate of
lime split into six-sided figures, called rhombohedrons (N. 169), whose
alternate angles measure 105·55° and 75·05°, however far the division may
be carried; therefore the ultimate particle of carbonate of lime is presumed
to have that form. However this may be, it is certain that all the various
crystals of that mineral may be formed by building up six-sided solids of
the form described, in the same manner as children build houses with
miniature bricks. It may be imagined that a wide difference may exist
between the particles of an unformed mass and a crystal of the same
substance—between the common shapeless limestone and the pure and
limpid crystal of Iceland spar; yet chemical analysis detects none; their
ultimate atoms are identical, and crystallisation shows that the difference
arises only from the mode of aggregation. Besides, all substances either
crystallise naturally, or may be made to do so by art. Liquids crystallise in
freezing, vapours by sublimation (N. 170); and hard bodies, when fused,
crystallise in cooling. Hence it may be inferred that all substances are
composed of atoms, on whose magnitude, density, and form, their nature
and qualities depend; and, as these qualities are unchangeable, the ultimate
particles of matter must be incapable of wear—the same now as when
created.
The size of the ultimate particles of matter must be small in the extreme.
Organised beings, possessing life and all its functions, have been discovered
so small, that a million of them would occupy less space than a grain of
sand. The malleability of gold, the perfume of musk, the odour of flowers,
and many other instances might be given of the excessive minuteness of the
atoms of matter. Supposing the density of the air at the surface of the earth
to be represented by unity, Sir John Herschel has shown that, under any
hypothesis as to its atoms, it would require a fraction having at least 1370
figures in its denominator to express its tenuity in the interplanetary space;
yet the definite proportions of chemical compounds afford a proof that

divisibility of matter has a limit. The cohesive force, which has been the
subject of the preceding considerations, only unites particles of the same
kind of matter; whereas affinity, which is the cause of chemical compounds,
is the mutual attraction between particles of different kinds of matter,
generally producing a compound which has no sensible property in
common with its component parts except that of their combined gravity, as,
for example, water, which is a compound of oxygen and hydrogen gases. It
is merely a result of the electrical state of the particles, chemical affinity
and electricity being only forms of the same power. In most cases it
produces electricity, as in the oxidation of metals and combustion, and in
every case without exception heat is evolved by bodies while combining
chemically; and as heat is an expansive force, chemical action is changed
into mechanical expansion, but it is not known in this case why heat is
produced, nor the manner in which the particles act.
It is a permanent and universal law in vast numbers of unorganised
bodies that their composition is definite and invariable, the same compound
always consisting of the same elements united together in the same
proportions. Two substances may indeed be mixed; but they will not
combine to form a third substance different from both, unless their
component particles unite in definite proportions; that is to say, one part by
weight of one of the substances will unite with one part by weight of the
other, or with two parts, or three, or four, &c., so as to form a new
substance; but in any other proportions they will only be mechanically
mixed. For example, one part by weight of hydrogen gas will combine with
eight parts by weight of oxygen gas, and form water; or it will unite with
sixteen parts by weight of oxygen, and form a substance called deutoxide of
hydrogen; but, added to any other weight of oxygen, it will produce one or
both of these compounds mingled with the portion of oxygen or hydrogen
in excess. The law of definite proportion established by Dr. Dalton, on the
principle that every compound body consists of a combination of the atoms
of its constituent parts, is of universal application, and is in fact one of the
most important discoveries in physical science, furnishing information
previously unhoped for with regard to the most secret and minute
operations of nature, in disclosing the relative weights of the ultimate atoms
of matter. Thus an atom of oxygen uniting with an atom of hydrogen forms
the compound water; but, as every drop of water however small consists of
eight parts by weight of oxygen and one part by weight of hydrogen, it

follows that an atom of oxygen is eight times heavier than an atom of
hydrogen. In the same manner sulphuretted hydrogen gas consists of sixteen
parts by weight of sulphur and one of hydrogen; therefore an atom of
sulphur is sixteen times heavier than an atom of hydrogen. Also carbonic
oxide is constituted of six parts by weight of carbon and eight of oxygen;
and, as an atom of oxygen has eight times the weight of an atom of
hydrogen, it follows that an atom of carbon is six times heavier than one of
hydrogen. Since the same definite proportion holds in the composition of a
vast number of substances that have been examined, it has been concluded
that there are great differences in the weights of the ultimate particles of
matter. Although Dalton’s law is fully established, yet instances have
occurred from which it appears that the atomic theory deduced from it is not
always maintained. M. Gay Lussac discovered that gases unite together by
their bulk or volumes, in such simple and definite proportions as one to one,
one to two, one to three, &c. For example, one volume or measure of
oxygen unites with two volumes or measures of hydrogen in the formation
of water.
Dr. Faraday has proved, by experiments on bodies both in solution and
fusion, that chemical affinity is merely a result of the electrical state of the
particles of matter. Now it must be observed that the composition of bodies,
as well as their decomposition, may be accomplished by means of
electricity; and Dr. Faraday has found that this chemical composition and
decomposition, by a given current of electricity, is always accomplished
according to the laws of definite proportions; and that the quantity of
electricity requisite for the decomposition of a substance is exactly the
quantity necessary for its composition. Thus the quantity of electricity
which can decompose a grain weight of water is exactly equal to the
quantity of electricity which unites the elements of that grain of water
together, and is equivalent to the quantity of atmospheric electricity which
is active in a very powerful flash of lightning. This law is universal, and of
that high and general order which characterises all great discoveries.
Chemical force is extremely powerful. A pound of the best coal gives when
burnt sufficient heat to raise the temperature of 8086 pounds of water one
Centigrade degree, whence Professor Helmholtz of Bonn has computed that
the magnitude of the chemical force of attraction between the particles of a
pound of coal and the quantity of oxygen that corresponds to it, is capable
of lifting a weight of 100 pounds to the height of 20 miles.

Dr. Faraday has given a singular instance of cohesive force inducing
chemical combination, by the following experiment, which seems to be
nearly allied to the discovery made by M. Dœbereiner, in 1823, of the
spontaneous combustion of spongy platinum (N. 171) exposed to a stream
of hydrogen gas mixed with common air. A plate of platinum with
extremely clean surfaces, when plunged into oxygen and hydrogen gas
mixed in the proportions which are found in the constitution of water,
causes the gases to combine and water to be formed, the platinum to
become red-hot, and at last an explosion to take place; the only conditions
necessary for this curious experiment being excessive purity in the gases
and in the surface of the plate. A sufficiently pure metallic surface can only
be obtained by immersing the platinum in very strong hot sulphuric acid
and then washing it in distilled water, or by making it the positive pole of a
galvanic pile in dilute sulphuric acid. It appears that the force of cohesion,
as well as the force of affinity, exerted by particles of matter, extends to all
the particles within a very minute distance. Hence the platinum, while
drawing the particles of the two gases towards its surface by its great
cohesive attraction, brings them so near to one another that they come
within the sphere of their mutual affinity, and a chemical combination takes
place. Dr. Faraday attributes the effect in part also to a diminution in the
elasticity of the gaseous particles on their sides adjacent to the platinum,
and to their perfect mixture or association, as well as to the positive action
of the metal in condensing them against its surface by its attractive force.
The particles when chemically united run off the surface of the metal in the
form of water by their gravitation, or pass away as aqueous vapour and
make way for others.
The oscillations of the atmosphere, and the changes in its temperature,
are measured by variations in the heights of the barometer and thermometer.
But the actual length of the liquid columns depends not only upon the force
of gravitation, but upon the cohesive force or reciprocal attraction between
the molecules of the liquid and those of the tube containing it. This peculiar
action of the cohesive force is called capillary attraction or capillarity. If a
glass tube of extremely fine bore, such as a small thermometer tube, be
plunged into a cup of water or spirit of wine, the liquid will immediately
rise in the tube above the level of that in the cup; and the surface of the little
column thus suspended will be a hollow hemisphere, whose diameter is the
interior diameter of the tube. If the same tube be plunged into a cupful of

mercury, the liquid will also rise in the tube, but it will never attain the level
of that in the cup, and its surface will be a hemisphere whose diameter is
also the diameter of the tube (N. 172). The elevation or depression of the
same liquid in different tubes of the same matter is in the inverse ratio of
their internal diameters (N. 173), and altogether independent of their
thickness; whence it follows that the molecular action is insensible at
sensible distances, and that it is only the thinnest possible film of the
interior surface of the tubes that exerts a sensible action on the liquid. So
much indeed is this the case, that, when tubes of the same bore are
completely wetted with water throughout their whole extent, mercury will
rise to the same height in all of them, whatever be their thickness or density,
because the minute coating of moisture is sufficient to remove the internal
column of mercury beyond the sphere of attraction of the tube, and to
supply the place of a tube by its own capillary attraction. The forces which
produce the capillary phenomena are the reciprocal attraction of the tube
and the liquid, and of the liquid particles on one another; and, in order that
the capillary column may be in equilibrio, the weight of that part of it which
rises above or sinks below the level of the liquid in the cup must balance
these forces.
The estimation of the action of the liquid is a difficult part of this
problem. La Place, Dr. Young, and other mathematicians, have considered
the liquid within the tube to be of uniform density; but M. Poisson, in one
of those masterly productions in which he elucidates the most abstruse
subjects, has proved that the phenomena of capillary attraction depend upon
a rapid decrease in the density of the liquid column throughout an
extremely small space at its surface. Every indefinitely thin layer of a liquid
is compressed by the liquid above it, and supported by that below. Its
degree of condensation depends upon the magnitude of the compressive
force; and, as this force decreases rapidly towards the surface, where it
vanishes the density of the liquid decreases also. M. Poisson has shown
that, when this force is omitted, the capillary surface becomes plane, and
that the liquid in the tube will neither rise above nor sink below the level of
that in the cup. In estimating the forces, it is also necessary to include the
variation in the density of the capillary surface round the edges from the
attraction of the tube.
The direction of the resulting force determines the curvature of the
surface of the capillary column. In order that a liquid may be in equilibrio,

the force resulting from all the forces acting upon it must be perpendicular
to the surface. Now it appears that, as glass is more dense than water or
alcohol, the resulting force will be inclined towards the interior side of the
tube; therefore the surface of the liquid must be more elevated at the sides
of the tube than in the centre in order to be perpendicular to it, so that it will
be concave as in the thermometer. But, as glass is less dense than mercury,
the resulting force will be inclined from the interior side of the tube
(N. 174), so that the surface of the capillary column must be more
depressed at the sides of the tube than in the centre, in order to be
perpendicular to the resulting force, and is consequently convex, as may be
perceived in the mercury of the barometer when rising. The absorption of
moisture by sponges, sugar, salt, &c., are familiar examples of capillary
attraction. Indeed the pores of sugar are so minute, that there seems to be no
limit to the ascent of the liquid. Wine is drawn up in a curve on the interior
surface of a glass; tea rises above its level on the side of a cup; but, if the
glass or cup be too full, the edges attract the liquid downwards, and give it a
rounded form. A column of liquid will rise above or sink below its level
between two plane parallel surfaces when near to one another, according to
the relative densities of the plates and the liquid (N. 175); and the
phenomena will be exactly the same as in a cylindrical tube whose diameter
is double the distance of the plates from each other. If the two surfaces be
very near to one another, and touch each other at one of their upright edges,
the liquid will rise highest at the edges that are in contact, and will
gradually diminish in height as the surfaces become more separated. The
whole outline of the liquid column will have the form of a hyperbola.
Indeed, so universal is the action of capillarity, that solids and liquids
cannot touch one another without producing a change in the form of the
surface of the liquid.
The attractions and repulsions arising from capillarity present many
curious phenomena. If two plates of glass or metal, both of which are either
dry or wet, be partly immersed in a liquid parallel to one another, the liquid
will be raised or depressed close to their surfaces, but will maintain its level
through the rest of the space that separates them. At such a distance they
neither attract nor repel one another; but the instant they are brought so near
as to make the level part of the liquid disappear, and the two curved parts of
it meet, the two plates will rush towards each other and remain pressed
together (N. 176). If one of the surfaces be wet and the other dry, they will

repel one another when so near as to have a curved surface of liquid
between them; but, if forced to approach a little nearer, the repulsion will be
overcome, and they will attract each other as if they were both wet or both
dry. Two balls of pith or wood floating in water, or two balls of tin floating
in mercury, attract one another as soon as they are so near that the surface of
the liquid is curved between them. Two ships in the ocean may be brought
into collision by this principle. But two balls, one of which is wet and the
other dry, repel one another as soon as the liquid which separates them is
curved at its surface. A bit of tea-leaf is attracted by the edge of the cup if
wet, and repelled when dry, provided it be not too far from the edge and the
cup moderately full; if too full, the contrary takes place. It is probable that
the rise of the sap in vegetables is in some degree owing to capillarity.

SECTION XV.

Analysis of the Atmosphere—Its Pressure—Law of Decrease in Density—
Law of Decrease in Temperature—Measurement of Heights by the
Barometer—Extent of the Atmosphere—Barometrical Variations—
Oscillations—Trade-Winds—Cloud-Ring—Monsoons—Rotation of
Winds—Laws of Hurricanes.

The atmosphere is not homogeneous. It appears from analysis that, of 100
parts, 99·5 consist of nitrogen and oxygen gases mixed in the proportions of
79 to 21 of volume, the remainder consists of 0·05 parts of carbonic acid
and on an average 0·45 of aqueous vapour. These proportions are found to
be the same at all heights hitherto attained by man. The air is an elastic
fluid, resisting pressure in every direction, and is subject to the law of
gravitation. As the space in the top of the tube of a barometer is a vacuum,
the column of mercury suspended by the pressure of the atmosphere on the
surface of that in the cistern is a measure of its weight. Consequently every
variation in the density occasions a corresponding rise or fall in the
barometrical column. At the level of the sea in latitude 42°, and at the
temperature of melting ice, the mean height of the barometer is 29·922 or
30 inches nearly. The pressure of the atmosphere is about fifteen pounds on
every square inch; so that the surface of the whole globe sustains a weight
of 11,671,000,000 hundreds of millions of pounds. Shell-fish, which have
the power of producing a vacuum, adhere to the rocks by a pressure of
fifteen pounds upon every square inch of contact.
The atmosphere when in equilibrio is an ellipsoid flattened at the poles
from its rotation with the earth. In that state its strata are of uniform density
at equal heights above the level of the sea; but since the air is both heavy
and elastic, its density necessarily diminishes in ascending above the
surface of the earth; for each stratum of air is compressed only by the

weight above it. Therefore the upper strata are less dense because they are
less compressed than those below them. Whence it is easy to show,
supposing the temperature to be constant, that if the heights above the earth
be taken in increasing arithmetical progression, that is, if they increase by
equal quantities, as by a foot or a mile, the densities of the strata of air, or
the heights of the barometer which are proportionate to them, will decrease
in geometrical progression. For example, at the level of the sea if the mean
height of the barometer be 29·922 inches, at the height of 18,000 feet it will
be 14·961 inches, or one half as great; at the height of 36,000 feet it will be
one-fourth as great; at 54,000 feet it will be one-eighth, and so on. Sir John
Herschel has shown that the actual decrease is much more rapid, and that, in
any hypothesis that has been formed with regard to the divisibility of the
aërial atoms, a vacuum exists at the height of 80 or 90 miles above the
earth’s surface, inconceivably more perfect than any that can be produced in
the best air-pumps. Indeed the decrease in density is so rapid that three-
fourths of all the air contained in the atmosphere is within four miles of the
earth; and, as its superficial extent is 200 millions of square miles, its
relative thickness is less than that of a sheet of paper when compared with
its breadth. The air even on mountain tops is sufficiently rare to diminish
the intensity of sound, to affect respiration, and to occasion a loss of
muscular strength. The blood burst from the lips and ears of M. de
Humboldt as he ascended the Andes; and he experienced the same difficulty
in kindling and maintaining a fire at great heights which Marco Polo, the
Venetian, felt on the mountains of Central Asia. M. Gay-Lussac ascended in
a balloon to the height of 4·36 miles, and he suffered greatly from the rarity
of the air. It is true that at the height of thirty-seven miles the atmosphere is
still dense enough to reflect the rays of the sun when 18° below the horizon;
but the tails of comets show that extremely attenuated matter is capable of
reflecting light. And although, at the height of fifty miles, the bursting of
the meteor of 1783 was heard on earth like the report of a cannon, it only
proves the immensity of the explosion of a mass half a mile in diameter,
which could produce a sound capable of penetrating air three thousand
times more rare than that we breathe. But even these heights are extremely
small when compared with the radius of the earth.
The density of the air is modified by various circumstances, chiefly by
changes of temperature, because heat dilates the air and cold contracts it,
varying 1⁄480 of the whole bulk when at 32° for every degree of Fahrenheit’s

thermometer. Experience shows that the heat of the air decreases as the
height above the surface of the earth increases. It appears that the mean
temperature of space is 226° below the zero point of Fahrenheit by the
theories of Fourier and Pouillet, but Sir John Herschel has computed it to be
-239° Fahr. from observations made during the ascent in balloons. Such
would probably be the temperature of the surface of the earth also, were it
not for the non-conducting power of the air, whence it is enabled to retain
the heat of the sun’s rays, which the earth imbibes and radiates in all
directions. The decrease in heat is very irregular; each authority gives a
different estimate, because it varies with latitude and local circumstances,
but from the mean of five different statements it seems to be about one
degree for every 334 feet; the mean of observations made in balloons is 400
feet, which is probably nearer the truth. This is the cause of the severe cold
and perpetual snow on the summits of the alpine chains. In the year 1852
four ascents in a balloon took place from the meteorological observatory at
Kew, in which the greatest height attained was 22,370 feet. The
observations then made by Mr. Welsh furnished Sir John Herschel with data
for computing that the temperature of space is minus 239°, that is 239°
below the zero point of Fahrenheit, that the limiting temperature of the
atmosphere is probably 771⁄2 degrees below that point at the equator, and
1191⁄2 below it at the poles, with a range of temperature from the surface of
1611⁄2° in the former case, and 1191⁄2° in the latter. During these ascents it
was found that the temperature of the air decreases uniformly up to a certain
point, where it is arrested and remains constant, or increases through a
depth of 2000 or 3000 feet, after which it decreases again according to the
same law as before. Throughout this zone of constant temperature it either
rains, or there is a great fall in the dew point; in short, it is the region of
clouds, and the increase of temperature is owing to the latent or absorbed
heat set free by the condensation of the aqueous vapour. In the latitude of
Kew the cloud region begins at altitudes varying between 2000 and 6500
feet, according to the state of the weather.
Were it not for the effects of temperature on the density of the air, the
heights of mountains might be determined by the barometer alone; but as
the thermometer must also be consulted, the determination becomes more
complicated. Mr. Ivory’s method of computing heights from barometrical
measurements has the advantage of combining accuracy with the greatest

simplicity. Indeed the accuracy with which the heights of mountains can be
obtained by this method is very remarkable. Admiral Smyth, R.N., and Sir
John Herschel measured the height of Etna by the barometer, without any
communication and in different years; Admiral Smyth made it 10,874 feet,
and Sir John Herschel 10,873, the difference being only one foot. In
consequence of the diminished pressure of the atmosphere water boils at a
lower temperature on mountain tops than in the valleys, which induced
Fahrenheit to propose this mode of observation as a method of ascertaining
their heights. It is very simple, as Professor Forbes ascertained that the
temperature of the boiling point varies in arithmetical proportion with the
height, or 5495 feet for every degree of Fahrenheit, so that the calculation
of height becomes one of arithmetic only, without the use of any table.
The mean pressure of the atmosphere is not the same all over the globe. It
is less by 0·24 of an inch at the equator than at the tropics or in the higher
latitudes, in consequence of the ascent of heated air and vapour from the
surface of the ocean. It is less also on the shores of the Baltic Sea than it is
in France, and it was observed by Sir James C. Ross that throughout the
whole of the Antarctic Ocean, from 68° to 74° S. latitude, and from 8° to 7°
W. longitude, there is a depression of the barometer amounting to an inch
and upwards, which is equivalent to an elevation above the sea level of 800
feet. A similar depression was observed by M. Erman in the sea of Ochotzk,
and in the adjacent continent of eastern Siberia. Sir John Herschel assigns
as the cause of these singular anomalies the great system of circulation of
the trade and antetrade winds, in both hemispheres, reacting upon the
general mass of the continents as obstacles in their path, which is modified
by the configuration of the land.
There are various periodic oscillations in the atmosphere, which, rising
and falling like waves in the sea, occasion corresponding changes in the
height of the barometer, but they differ as much from the trade-winds,
monsoons, and other currents, as the tides of the sea do from the Gulf-
stream and other oceanic rivers. The sun and moon disturb the equilibrium
of the atmosphere by their attraction, and produce annual undulations which
have their maximum altitudes at the equinoxes, and their minima at the
solstices. There are also lunar tides, which ebb and flow twice in the course
of a lunation. The diurnal tides, which accomplish their rise and fall in six
hours, are greatly modified by the heat of the sun. Between the tropics the
barometer attains its maximum height about nine in the morning, then sinks

till three or four in the afternoon; it again rises and attains a second
maximum about nine in the evening, and then it begins to fall, and reaches a
second minimum at three in the morning, again to pursue the same course.
According to M. Bouvard, the amount of the oscillations at the equator is
proportional to the temperature, and in other parallels it varies as the
temperature and the square of the cosine of the latitude conjointly;
consequently it decreases from the equator to the poles, but it is somewhat
greater in the day than in the night.
Besides these small undulations, there are vast waves perpetually moving
over the continents and oceans in separate and independent systems, being
confined to local, yet very extensive districts, probably occasioned by long-
continued rains or dry weather over large tracts of country. By numerous
barometrical observations made simultaneously in both hemispheres, the
courses of several have been traced, some of which occupy twenty-four, and
others thirty-six, hours to accomplish their rise and fall. One especially of
these vast barometric waves, many hundreds of miles in breadth, has been
traced over the greater part of Europe; and not its breadth only, but also the
direction of its front and its velocity, have been clearly ascertained.
Although, like all other waves, these are but moving forms, yet winds arise
dependent on them like tide streams in the ocean. Mr. Birt has determined
the periods of other waves of still greater extent and duration, two of which
required seventeen days to rise and fall; and another which takes fourteen
days to complete its undulation, called by Mr. Birt the November wave,
passes annually over the British Islands, probably over the whole of Europe
and the seas on its northern coasts. Its crest, which appears to be 6000 miles
in extent, moves from N.W. to S.E. at the rate of about 19 miles an hour;
while the extent of its barometrical elevation from its trough to its crest is
seldom less than an inch, sometimes double that quantity. The great crest is
preceded and followed at about five days’ interval by two lower ones, and
the beginning and end are marked by deep depressions. The researches of
M. Leverrier leave no doubt that the great Crimean storm of the 14th
November, 1854, was part of this phenomenon,[8] for even a very small
difference of atmospheric pressure is sufficient to raise a considerable wind.
Since each oscillation has its perfect effect independently of the others, each
one is marked by a change in the barometer, and this is beautifully
illustrated by curves constructed from a series of observations. The general
form of the curve shows the course of the principal wave, while small

undulations in its outline mark the maxima and minima of the minor
oscillations.
The trade-winds, which are the principal currents in the atmosphere, are
only a particular case of those very general laws which regulate the motion
of the winds depending on the rarefaction of the air combined with the
rotation of the earth on its axis. They are permanent currents of wind
between the tropics, blowing to the N.E. on the N. side of the equator, and
to the S.E. on the S. side.
If currents of air come from the poles, it is clear that equilibrium must be
restored by counter-currents from the equator; moreover, winds coming
from the poles, where there is no rotation, to the equator, which revolves
from W. to E. at the rate of 1000 miles an hour, must of necessity move in a
direction resulting from their own progressive motion and that of rotation;
hence, in blowing towards the equator the bias is to the E., and in blowing
from it the bias is to the W. Thus as N. and S. winds from the poles blow
along the surface from the tropics to the equator, in consequence of this
composition of motions that from the N. becomes the N.E. trade-wind, and
that from the S. the S.E. trade-wind. Now these winds being in contrary
directions cross at the equator, balance each other through about 6 degrees
of latitude, and produce a belt of calms of that breadth encircling the globe,
known as the calms of the equator, or the Variables of seamen. The heat of
the sun rarefies the air so much, that the trade-winds, after crossing at the
equator, ascend into the higher regions of the atmosphere, where that from
the N. goes to the tropic of Capricorn, and that from the S. to the tropic of
Cancer. But while travelling in these lofty regions they become cold and
heavy, and, sinking to the surface at the tropics, each proceeds to the
opposite pole from which it set out. Now, however, they have a greater
rotatory motion than the places they successively arrive at, so the bias is to
the W., and they become the N.W. and S.W. extra-tropical winds.
If on arriving at the poles the air were to accumulate there, the circulation
of the winds would cease; but currents rise into the upper regions, and flow
back again to the tropics, where they sink down to fill the vacuum caused
by the great precipitation of vapour in these regions, and then flow to the
equator as trade-winds (N. 177). So the currents of air cross again at the
tropics and produce two belts of calms which surround the globe, named by
Lieutenant Maury the Calms of Cancer and the Calms of Capricorn, but
generally known to sailors as the Doldrums. Thus the winds go from pole to

pole and back again, alternately as under and upper currents. In their
circuits the winds cross each other five times, producing regions of calms at
the poles, the tropics, and equator. The trade-winds generally extend for
about 28° on each side of the equator, but, on account of the greater
quantity of land in the northern hemisphere, the N.E. trade-wind is narrower
than the S.E.
The sun is perpetually raising enormous quantities of vapour from the
ocean which the trade-winds carry to the equator: it is condensed when it
rises with the air into the higher strata, and forms a ring of clouds along the
southern side of the belt of equatorial calms that surrounds the earth, which,
during the day, is perpetually pouring down torrents of rain, while the sun
continually beating upon its upper surface dissolves the clouds into
invisible vapour which is carried by the winds and condensed into rain on
the extra-tropical regions. The whole system of trade-winds, equatorial and
tropical calms, with the cloud ring, follow the sun in declination;
consequently in its journeys back and forwards it annually travels over 1000
miles of latitude, and regulates the dry and rainy season in the tropical parts
of the earth.
The monsoons, which are periodic winds in the Indian Ocean, in part
depend upon this movement. For when the sun is in the northern
hemisphere the trade-winds come northward with him; and when his
intense heat expands the air over the Great Gobi and other arid Asiatic
deserts, it ascends; the N.E. trade-wind is drawn in to fill the vacuum and
ascends with it; then the S.E. trade-wind, being no longer met and balanced
by the N.E. trade, passes into the northern hemisphere, and as it proceeds
northward from the equator it is deflected to the west by the rotation of the
earth, combined with the indraught over the heated deserts, and becomes
the S.W. monsoon, which blows while the sun is north of the equator, but as
soon as he goes south, and no longer rarefies the air over the Indian deserts,
the S.E. trade-wind resumes its usual course, and is then known as the S.E.
monsoon. The influence of the heated deserts is perceptible to the distance
of 1000 miles from the shore; the monsoons prevail with great steadiness
over the Arabian Gulf, the Indian Ocean, and part of the China Sea. At the
change, torrents of rain and violent thunderstorms accompany the conflict
between the contending winds.
The Sahara desert in North Africa, and those of Utah, Texas, and New
Mexico, occasion the monsoons which prevail in the North Atlantic and on

both sides of Central America, and the monsoons which blow to the north
of Australia show the sterility of the interior, even if other proofs were
wanting. From the powerful effect of the land in drawing off the winds from
their course, it may be seen why the N.E. trade-winds are narrower than the
S.E. trades.
In the extra-tropical winds in the North Atlantic, which blow from the
40th parallel to the pole, the north-westerly are to the easterly as 2 to 1:
hence there would be an accumulation of air at the pole at the expense of
the equator, did not a current rise at the pole and return to the equator
through the high regions of the atmosphere, which confirms the theory of
the rotation of the wind.
There are many proofs of the existence of the counter-currents above the
trade-winds. On the Peak of Teneriffe the prevailing winds are from the
west. Light clouds have frequently been seen moving rapidly from west to
east at a very great height above the trade-winds, which were sweeping
along the surface of the ocean in a contrary direction. Rains, clouds, and
nearly all the other atmospheric phenomena, occur below the height of
18,000 feet, and generally much nearer to the surface of the earth. They are
owing to currents of air running upon each other in horizontal strata,
differing in their electric state, in temperature and moisture, as well as in
velocity and direction.
When north and south winds blow alternately, the wind at any place will
veer in one uniform direction through every point of the compass, provided
the one begins before the other has ceased. In the northern hemisphere a
north wind sets out with a smaller degree of rotatory motion than the places
have at which it successively arrives, consequently it passes through all the
points of the compass from N. to N.E. and E. A current from the south, on
the contrary, sets out with a greater rotatory velocity than the places have at
which it successively arrives, so by the rotation of the earth it is deflected
from S. to S.W. and W. Now, if the vane at any place should have veered
from the N. through N.E. to E., and a south wind should spring up, it would
combine its motion with the former and cause the vane to turn successively
from the E. to S.E. and S. But by the earth’s rotation this south wind will
veer to the S.W. and W., and, if a north wind should now arise, it would
combine its motion with that of the west, and cause it to veer to the N.W.
and N. Thus two alternations of north and south wind will cause the vane at
any place to go completely round the compass, from N. to E., S., W., and N.

again. At the Royal Observatory at Greenwich the wind accomplishes five
circuits in that direction in the course of a year. When circumstances
combine to produce alternate north and south winds in the southern
hemisphere, the gyration is in the contrary direction. Although the general
tendency of the wind may be rotatory, and is so in many instances, at least
for part of the year, yet it is so often counteracted by local circumstances,
that the winds are in general very irregular, every disturbance in
atmospheric equilibrium from heat or any other cause producing a
corresponding wind. The most prevalent winds in Europe are the N.E. and
S.W.; the former arises from the north polar current, and the latter from
causes already mentioned. The law of the wind’s rotation was first
described by Dr. Dalton, but has been developed by Professor Dove, of
Berlin.
Hurricanes are those storms of wind in which the portion of the
atmosphere that forms them revolves in a horizontal circuit round a vertical
or somewhat inclined axis of rotation, while the axis itself, and
consequently the whole storm, is carried forward along the surface of the
globe, so that the direction in which the storm is advancing is quite different
from the direction in which the rotatory current may be blowing at any
point. In the West Indies, where hurricanes are frequent and destructive,
they generally originate in the tropical regions near the inner boundary of
the trade-winds, and are caused by the vertical ascent of a column of
rarefied air, whose place is supplied by a rush of wind from the surrounding
regions, set into gyration by the rotation of the earth. By far the greater
number of Atlantic hurricanes have begun eastward of the lesser Antilles or
Caribbean Islands.
In every case the axis of the storm moves in an elliptical or parabolic
curve, having its vertex in or near the tropic of Cancer, which marks the
external limit of the trade-winds north of the equator. As the motion before
it reaches the tropic is in a straight line from S.E. to N.W., and after it has
passed it from S.W. to N.E., the bend of the curve is turned towards Florida
and the Carolinas. In the southern hemisphere the body of the storm moves
in exactly the opposite direction. The hurricanes which originate south of
the equator, and whose initial path is from N.E. to S.W., bend round at the
tropic of Capricorn, and then move from N.W. to S.E.
The extent and velocity of these storms are great; for instance, the
hurricane that took place on the 12th of August, 1830, was traced from

eastward of the Caribbee Islands, along the Gulf Stream, to the bank of
Newfoundland, a distance of more than 3000 miles, which it passed over in
six days. Although the hurricane of the 1st of September, 1821, was not so
extensive, its velocity was greater, as it moved at the rate of 30 miles an
hour: small storms are generally more rapid than those of greater
dimensions.
The action of these storms seems to be at first confined to the stratum of
air nearest the earth, and then they seldom appear to be more than a mile
high, though sometimes they are raised higher; or even divided by a
mountain into two separate storms, each of which continues its new path
and gyrations with increased violence. This occurred in the gale of the 25th
of December, 1821, in the Mediterranean, when the Spanish mountains and
the Maritime Alps became new centres of motion.
By the friction of the earth the axis of the storm bends a little forward.
This causes a continual intermixture of the lower and warmer strata of air
with those that are higher and colder, producing torrents of rain and violent
electric explosions.
The breadth of the whirlwind is greatly augmented when the path of the
storm changes on crossing the tropic. The vortex of a storm has covered an
extent of the surface of the globe 500 miles in diameter.
The revolving motion accounts for the sudden and violent changes
observed during hurricanes. In consequence of the rotation of the air, the
wind blows in opposite directions on each side of the axis of the storm, and
the violence of the blast increases from the circumference towards the
centre of gyration, but in the centre itself the air is in repose: hence, when
the body of the storm passes over a place, the wind begins to blow
moderately, and increases to a hurricane as the centre of the whirlwind
approaches; then, in a moment, a dead and awful calm succeeds, suddenly
followed by a renewal of the storm in all its violence, but now blowing in a
direction diametrically opposite to its former course. This happened at the
Island of St. Thomas on the 2nd of August, 1837, where the hurricane
increased in violence till half-past seven in the morning, when perfect
stillness took place for forty minutes, after which the storm recommenced
in a contrary direction.
The sudden fall of the mercury in the barometer in the regions habitually
visited by hurricanes is a certain indication of a coming tempest. In

consequence of the centrifugal force of these rotatory storms the air
becomes rarefied, and, as the atmosphere is disturbed to some distance
beyond the actual circle of gyration or limits of the storm, the barometer
often sinks some hours before its arrival, from the original cause of the
rotatory disturbance. It continues sinking under the first half of the
hurricane, is at a maximum sometimes of two inches in the centre of
gyration, and again rises during the passage of the latter half, though it does
not attain its greatest height till the storm is over. The diminution of
atmospheric pressure is greater and extends over a wider area in the
temperate zones than in the torrid, on account of the sudden expansion of
the circle of rotation when the gale crosses the tropic.
As the fall of the barometer gives warning of the approach of a hurricane,
so the laws of the storm’s motion afford the seaman knowledge to guide
him in avoiding it. In the northern temperate zone, if the gale begins from
the S.E. and veers by S. to W., the ship should steer to the S.E.; but, if the
gale begins from the N.E., and changes through N. to N.W., the vessel
should go to the N.W. In the northern part of the torrid zone, if the storm
begin from the N.E., and veer through E. to S.E., the ship should steer to the
N.E.; but, if it begin from the N.W., and veer by W. to S.W., the ship should
steer to the S.W., because she is in the south-western side of the storm.
Since the laws of storms are reversed in the southern hemisphere, the rules
for steering vessels are necessarily reversed also. A heavy swell is
peculiarly characteristic of these storms. In the open sea the swell often
extends many leagues beyond the range of the gale which produced it.
Waterspouts are occasioned by small whirlwinds, which always have
their origin at a great distance from that part of the sea from which the spout
begins to rise, where it is generally calm. The whirl is produced by two
currents of air, which, running in opposite directions, compress one another
by their impetus, so that they rise in spiral eddies to the clouds. They move
slowly along the surface of the sea, sometimes in vertical, and sometimes in
twisted spirals, putting the sea into violent agitation as they pass, and
carrying the water aloft by the force of gyration. Occasionally the eddies
begin in the clouds and dip down to the sea.

SECTION XVI.

Sound—Propagation of Sound illustrated by a Field of Standing Corn—
Nature of Waves—Propagation of Sound through the Atmosphere—
Intensity—Noises—A Musical Sound—Quality—Pitch—Extent of
Human Hearing—Velocity of Sound in Air, Water, and Solids—Causes of
the Obstruction of Sound—Law of its Intensity—Reflection of Sound—
Echoes—Thunder—Refraction of Sound—Interference of Sounds.

One of the most important uses of the atmosphere is the conveyance of
sound. Without the air, deathlike silence would prevail through nature, for
in common with all substances it has a tendency to impart vibrations to
bodies in contact with it. Therefore undulations received by the air, whether
it be from a sudden impulse, such as an explosion or the vibrations of a
musical chord, are propagated in every direction, and produce the sensation
of sound upon the auditory nerves. A bell rung under the exhausted receiver
of an air-pump is inaudible, which shows that the atmosphere is really the
medium of sound. In the small undulations of deep water in a calm, the
vibrations of the liquid particles are made in the vertical plane, that is, up
and down, or at right angles to the direction of the transmission of the
waves. But the vibrations of the particles of air which produce sound differ
from these, being performed in the same direction in which the waves of
sound travel. The propagation of sound has been illustrated by a field of
corn agitated by the wind. However irregular the motion of the corn may
seem on a superficial view, it will be found, if the velocity of the wind be
constant, that the waves are all precisely similar and equal, and that all are
separated by equal intervals and move in equal times.
A sudden blast depresses each ear equally and successively in the
direction of the wind, but, in consequence of the elasticity of the stalks and
the force of the impulse, each ear not only rises again as soon as the

pressure is removed, but bends back nearly as much in the contrary
direction, and then continues to oscillate backwards and forwards in equal
times, like a pendulum, to a less and less extent, till the resistance of the air
puts a stop to the motion. These vibrations are the same for every individual
ear of corn. Yet, as their oscillations do not all commence at the same time,
but successively, the ears will have a variety of positions at any one instant.
Some of the advancing ears will meet others in their returning vibrations,
and, as the times of oscillation are equal for all, they will be crowded
together at regular intervals. Between these there will occur equal spaces
where the ears will be few, in consequence of being bent in opposite
directions; and at other equal intervals they will be in their natural upright
positions. So that over the whole field there will be a regular series of
condensations and rarefactions among the ears of corn, separated by equal
intervals, where they will be in their natural state of density. In consequence
of these changes the field will be marked by an alternation of bright and
dark bands. Thus the successive waves which fly over the corn with the
speed of the wind are totally distinct from, and entirely independent of the
extent of the oscillations of each individual ear, though both take place in
the same direction. The length of a wave is equal to the space between two
ears precisely in the same state of motion, or which are moving similarly,
and the time of the vibration of each ear is equal to that which elapses
between the arrival of two successive waves at the same point. The only
difference between the undulations of a corn-field and those of the air
which produce sound is, that each ear of corn is set in motion by an external
cause, and is uninfluenced by the motion of the rest; whereas in air, which
is a compressible and elastic fluid, when one particle begins to oscillate, it
communicates its vibrations to the surrounding particles, which transmit
them to those adjacent, and so on continually. Hence from the successive
vibrations of the particles of air the same regular condensations and
rarefactions take place as in the field of corn, producing waves throughout
the whole mass of air, though each molecule like each individual ear of corn
never moves far from its state of rest. The small waves of a liquid, and the
undulations of the air, like waves in the corn, are evidently not real masses
moving in the direction in which they are advancing, but merely outlines,
motions, or forms passing along, and comprehending all the particles of an
undulating fluid which are at once in a vibratory state. It is thus that an
impulse given to any one point of the atmosphere is successively

propagated in all directions, in a wave diverging as from the centre of a
sphere to greater and greater distances, but with decreasing intensity, in
consequence of the increasing number of particles of inert matter which the
force has to move; like the waves formed in still water by a falling stone,
which are propagated circularly all around the centre of disturbance
(N. 160).
The intensity of sound depends upon the violence and extent of the initial
vibrations of air; but, whatever they may be, each undulation when once
formed can only be transmitted straight forwards, and never returns back
again unless when reflected by an opposing obstacle. The vibrations of the
aërial molecules are always extremely small, whereas the waves of sound
vary from a few inches to several feet. The various musical instruments, the
human voice and that of animals, the singing of birds, the hum of insects,
the roar of the cataract, the whistling of the wind, and the other nameless
peculiarities of sound, show at once an infinite variety in the modes of
aërial vibration, and the astonishing acuteness and delicacy of the ear, thus
capable of appreciating the minutest differences in the laws of molecular
oscillation.
All mere noises are occasioned by irregular impulses communicated to
the ear; and, if they be short, sudden, and repeated beyond a certain degree
of quickness, the ear loses the intervals of silence, and the sound appears
continuous. Still such sounds will be mere noise: in order to produce a
musical sound, the impulses, and consequently the undulations of the air,
must be all exactly similar in duration and intensity, and must recur after
exactly equal intervals of time. If a blow be given to the nearest of a series
of broad, flat, and equidistant palisades, set edgewise in a line direct from
the ear, each palisade will repeat or echo the sound; and these echoes,
returning to the ear at successive equal intervals of time, will produce a
musical note. The quality of a musical note depends upon the abruptness,
and its intensity upon the violence and extent of the original impulse. In the
theory of harmony the only property of sound taken into consideration is
the pitch, which varies with the rapidity of the vibrations. The grave or low
tones are produced by very slow vibrations, which increase in frequency as
the note becomes more acute. The lowest man’s voice makes 396 vibrations
in a second, whilst the highest woman’s voice makes 2112. Very deep tones
are not heard by all alike, and Dr. Wollaston, who made a variety of
experiments on the sense of hearing, found that many people, though not at

all deaf, are quite insensible to the cry of the bat or the cricket, while to
others it is painfully shrill. From his experiments he concluded that human
hearing is limited to about nine octaves, extending from the lowest note of
the organ to the highest known cry of insects; and he observes with his
usual originality that, “as there is nothing in the nature of the atmosphere to
prevent the existence of vibrations incomparably more frequent than any of
which we are conscious, we may imagine that animals like the Grylli,
whose powers appear to commence nearly where ours terminate, may have
the faculty of hearing still sharper sounds which we do not know to exist,
and that there may be other insects hearing nothing in common with us, but
endowed with a power of exciting, and a sense which perceives vibrations,
of the same nature indeed as those which constitute our ordinary sounds,
but so remote that the animals which perceive them may be said to possess
another sense, agreeing with our own solely in the medium by which it is
excited.”
M. Savart, so well known for the number and beauty of his researches in
acoustics, has proved that a high note of a given intensity, being heard by
some ears and not by others, must not be attributed to its pitch, but to its
feebleness. His experiments, and those more recently made by Professor
Wheatstone, show that, if the pulses could be rendered sufficiently
powerful, it would be difficult to fix a limit to human hearing at either end
of the scale. M. Savart had a wheel made about nine inches in diameter with
360 teeth set at equal distances round its rim, so that while in motion each
tooth successively hit on a piece of card. The tone increased in pitch with
the rapidity of the rotation, and was very pure when the number of strokes
did not exceed three or four thousand in a second, but beyond that it became
feeble and indistinct. With a wheel of a larger size a much higher tone could
be obtained, because, the teeth being wider apart, the blows were more
intense and more separated from one another. With 720 teeth on a wheel
thirty-two inches in diameter, the sound produced by 12,000 strokes in a
second was audible, which corresponds to 24,000 vibrations of a musical
chord. So that the human ear can appreciate a sound which only lasts the
24,000th part of a second. This note was distinctly heard by M. Savart and
by several people who were present, which convinced him that with another
apparatus still more acute sounds might be rendered audible.
For the deep tones M. Savart employed a bar of iron, two feet eight
inches long, about two inches broad, and half an inch in thickness, which

revolved about its centre as if its arms were the spokes of a wheel. When
such a machine rotates, it impresses a motion on the air similar to its own,
and, when a thin board or card is brought close to its extremities, the current
of air is momentarily interrupted at the instant each arm of the bar passes
before the card; it is compressed above the card and dilated below; but the
instant the spoke has passed a rush of air to restore equilibrium makes a
kind of explosion, and, when these succeed each other rapidly, a musical
note is produced of a pitch proportional to the velocity of the revolution.
When M. Savart turned this bar slowly, a succession of single beats was
heard; as the velocity became greater, the sound was only a rattle; but, as
soon as it was sufficient to give eight beats in a second, a very deep musical
note was distinctly audible corresponding to sixteen single vibrations in a
second, which is the lowest that has hitherto been produced. When the
velocity of the bar was much increased, the intensity of the sound was
hardly bearable. The spokes of a revolving wheel produce the sensation of
sound, on the very same principle that a burning stick whirled round gives
the impression of a luminous circle. The vibrations excited in the organ of
hearing by one beat have not ceased before another impulse is given. Indeed
it is indispensable that the impressions made upon the auditory nerves
should encroach upon each other in order to produce a full and continued
note. On the whole, M. Savart has come to the conclusion, that the most
acute sounds would be heard with as much ease as those of a lower pitch, if
the duration of the sensation produced by each pulse could be diminished
proportionally to the augmentation of the number of pulses in a given time:
and on the contrary, if the duration of the sensation produced by each pulse
could be increased in proportion to their number in a given time, that the
deepest tones would be as audible as any of the others.
The velocity of sound is uniform and independent of the nature, extent,
and intensity of the primitive disturbance. Consequently sounds of every
quality and pitch travel with equal speed. The smallest difference in their
velocity is incompatible either with harmony or melody, for notes of
different pitches and intensities, sounded together at a little distance, would
arrive at the ear in different times. A rapid succession of notes would in this
case produce confusion and discord. But, as the rapidity with which sound
is transmitted depends upon the elasticity of the medium through which it
has to pass, whatever tends to increase the elasticity of the air must also
accelerate the motion of sound. On that account its velocity is greater in

warm than in cold weather, supposing the pressure of the atmosphere
constant. In dry air, at the freezing temperature, sound travels at the rate of
1090 feet in a second, and for any higher temperature one foot must be
added for every degree of the thermometer above 32°: hence at 62° of
Fahrenheit its speed in a second is 1120 feet, or 765 miles an hour, which is
about three-fourths of the diurnal velocity of the earth’s equator. Since all
the phenomena of the transmission of sound are simple consequences of the
physical properties of the air, they have been predicted and computed
rigorously by the laws of mechanics. It was found, however, that the
velocity of sound, determined by observation, exceeded what it ought to
have been theoretically by 173 feet, or about one-sixth of the whole
amount. La Place suggested that this discrepancy might arise from the
increased elasticity of the air in consequence of a development of latent or
absorbed heat (N. 178) during the undulations of sound, and calculation
confirmed the accuracy of his views. The aërial molecules being suddenly
compressed give out their absorbed heat; and, as air is too bad a conductor
to carry it rapidly off, it occasions a momentary and local rise of
temperature, which, increasing the elasticity of the air without at the same
time increasing its inertia, causes the movement to be propagated more
rapidly. Analysis gives the true velocity of sound in terms of the elevation
of temperature that a mass of air is capable of communicating to itself, by
the disengagement of its own absorbed heat when suddenly compressed in a
given ratio. This change of temperature however could not be obtained
directly by any experiments which had been made at that epoch; but by
inverting the problem, and assuming the velocity of sound as given by
experiment, it was computed that the temperature of a mass of air is raised
nine-tenths of a degree when the compression is equal to 1⁄116 of its volume.
Probably all liquids are elastic, though considerable force is required to
compress them. Water suffers a condensation of nearly 0·0000496 for every
atmosphere of pressure, and is consequently capable of conveying sound
even more rapidly than air, the velocity in the former being 4708 feet in a
second. A person under water hears sounds made in air feebly, but those
produced in water very distinctly. According to the experiments of M.
Colladon, the sound of a bell was conveyed under water through the Lake
of Geneva to the distance of about nine miles. He also perceived that the
progress of sound through water is greatly impeded by the interposition of
any object, such as a projecting wall; consequently sound under water

resembles light in having a distinct shadow. It has much less in air, being
transmitted all round buildings or other obstacles, so as to be heard in every
direction, though often with a considerable diminution of intensity, as when
a carriage turns the corner of a street.
The velocity of sound in passing through solids is in proportion to their
hardness, and is much greater than in air or water. A sound which takes
some time in travelling through the air passes almost instantaneously along
a wire six hundred feet long; consequently it is heard twice—first as
communicated by the wire, and afterwards through the medium of the air.
The facility with which the vibrations of sound are transmitted along the
grain of a log of wood is well known. Indeed they pass through iron, glass,
and some kinds of wood, at the rate of 18,530 feet in a second. The velocity
of sound is obstructed by a variety of circumstances, such as falling snow,
fog, rain, or any other cause which disturbs the homogeneity of the medium
through which it has to pass. M. de Humboldt says that it is on account of
the greater homogeneity of the atmosphere during the night that sounds are
then better heard than during the day, when its density is perpetually
changing from partial variations of temperature. His attention was called to
this subject on the plain surrounding the Mission of the Apures by the
rushing noise of the great cataracts of the Orinoco, which seemed to be
three times as loud by night as by day. This he illustrated by experiment. A
tall glass half full of champagne cannot be made to ring as long as the
effervescence lasts. In order to produce a musical note, the glass together
with the liquid it contains must vibrate in unison as a system, which it
cannot do in consequence of the fixed air rising through the wine and
disturbing its homogeneity, because, the vibrations of the gas being much
slower than those of the liquid, the velocity of the sound is perpetually
interrupted. For the same reason the transmission of sound as well as light
is impeded in passing through an atmosphere of variable density. Sir John
Herschel, in his admirable Treatise on Sound, thus explains the
phenomenon:—“It is obvious,” he says, “that sound as well as light must be
obstructed, stifled, and dissipated from its original direction by the mixture
of air of different temperatures, and consequently elasticities; and thus the
same cause which produces that extreme transparency of the air at night,
which astronomers alone fully appreciate, renders it also more favourable to
sound. There is no doubt, however, that the universal and dead silence
generally prevalent at night renders our auditory nerves sensible to

impressions which would otherwise escape notice. The analogy between
sound and light is perfect in this as in so many other respects. In the general
light of day the stars disappear. In the continual hum of voices, which is
always going on by day, and which reach us from all quarters, and never
leave the ear time to attain complete tranquillity, those feeble sounds which
catch our attention at night make no impression. The ear, like the eye,
requires long and perfect repose to attain its utmost sensibility.”
Many instances may be brought in proof of the strength and clearness
with which sound passes over the surface of water or ice. Lieutenant Forster
was able to carry on a conversation across Port Bowen Harbour, when
frozen, a distance of a mile and a half.
The intensity of sound depends upon the extent of the excursions of the
fluid molecules, on the energy of the transient condensations and
dilatations, and on the greater or less number of particles which experience
these effects. We estimate that intensity by the impetus of these fluid
molecules on our organs, which is consequently as the square of the
velocity, and not by their inertia, which is as the simple velocity. Were the
latter the case, there would be no sound, because the inertia of the receding
waves of air would destroy the equal and opposite inertia of those
advancing; whence it may be concluded that the intensity of sound
diminishes inversely as the square of the distance from its origin. In a tube,
however, the force of sound does not decay as in open air, unless perhaps by
friction against the sides. M. Biot found, from a number of highly-
interesting experiments made on the pipes of the aqueducts in Paris, that a
continued conversation could be carried on in the lowest possible whisper
through a cylindrical tube about 3120 feet long, the time of transmission
through that space being 2·79 seconds. In most cases sound diverges in all
directions so as to occupy at any one time a spherical surface; but Dr.
Young has shown that there are exceptions, as, for example, when a flat
surface vibrates only in one direction. The sound is then most intense when
the ear is at right angles to the surface, whereas it is scarcely audible in a
direction precisely perpendicular to its edge. In this case it is impossible
that the whole of the surrounding air can be affected in the same manner,
since the particles behind the sounding surface must be moving towards it
whenever the particles before it are retreating. Hence in one half of the
surrounding sphere of air its motions are retrograde, while in the other half
they are direct; consequently, at the edges where these two portions meet,

the motions of the air will neither be retrograde nor direct, and therefore it
must be at rest.
It appears, from theory as well as daily experience, that sound is capable
of reflection from surfaces (N. 179) according to the same laws as light.
Indeed any one who has observed the reflection of the waves from a wall on
the side of a river, after the passage of a steam-boat, will have a perfect idea
of the reflection of sound and of light. As every substance in nature is more
or less elastic, it may be agitated according to its own law by the impulse of
a mass of undulating air; and reciprocally the surface by its reaction will
communicate its undulations back again into the air. Such reflections
produce echoes; and as a series of them may take place between two or
more obstacles, each will cause an echo of the original sound, growing
fainter and fainter till it dies away; because sound, like light, is weakened
by reflection. Should the reflecting surface be concave towards a person,
the sound will converge towards him with increased intensity, which will be
greater still if the surface be spherical and concentric with him. Undulations
of sound diverging from one focus of an elliptical shell (N. 180) converge
in the other after reflection. Consequently a sound from the one will be
heard in the other as if it were close to the ear. The rolling noise of thunder
has been attributed to reverberation between different clouds, which may
possibly be the case to a certain extent. Sir John Herschel is of opinion that
an intensely prolonged peal is probably owing to a combination of sounds,
because, the velocity of electricity being incomparably greater than that of
sound, the thunder may be regarded as originating in every point of a flash
of lightning at the same instant. The sound from the nearest point will arrive
first; and if the flash run in a direct line from a person, the noise will come
later and later from the remote points of its path in a continued roar. Should
the direction of the flash be inclined, the succession of sounds will be more
rapid and intense: and if the lightning describe a circular curve round a
person, the sound will arrive from every point at the same instant with a
stunning crash. In like manner the subterranean noises heard during
earthquakes like distant thunder may arise from the consecutive arrival at
the ear of undulations propagated at the same instant from nearer and more
remote points; or if they originate in the same point, the sound may come
by different routes through strata of different densities.
Sounds under water are heard very distinctly in the air immediately
above; but the intensity decays with great rapidity as the observer goes

farther off, and is altogether inaudible at the distance of two or three
hundred yards. So that waves of sound, like those of light, in passing from a
dense to a rare medium, are not only refracted, but suffer total reflection at
very oblique incidences (N. 189).
The laws of interference extend also to sound. It is clear that two equal
and similar musical strings will be in unison if they communicate the same
number of vibrations to the air in the same time. But if two such strings be
so nearly in unison that one performs a hundred vibrations in a second, and
the other a hundred and one in the same period—during the first few
vibrations the two resulting sounds will combine to form one of double the
intensity of either, because the aërial waves will sensibly coincide in time
and place; but one will gradually gain on the other till at the fiftieth
vibration it will be half an oscillation in advance. Then the waves of air
which produce the sound being sensibly equal, but the receding part of the
one coinciding with the advancing part of the other, they will destroy one
another, and occasion an instant of silence. The sound will be renewed
immediately after, and will gradually increase till the hundredth vibration,
when the two waves will combine to produce a sound double the intensity
of either. These intervals of silence and greatest intensity, called beats, will
recur every second; but if the notes differ much from one another, the
alternations will resemble a rattle; and if the strings be in perfect unison,
there will be no beats, since there will be no interference. Thus by
interference is meant the co-existence of two undulations in which the
lengths of the waves are the same. And as the magnitude of an undulation
may be diminished by the addition of another transmitted in the same
direction, it follows that one undulation may be absolutely destroyed by
another when waves of the same length are transmitted in the same
direction, provided that the maxima of the undulations are equal, and that
one follows the other by half the length of a wave. A tuning-fork affords a
good example of interference. When that instrument vibrates, its two
branches alternately recede from and approach one another; each
communicates its vibrations to the air, and a musical note is the
consequence. If the fork be held upright about a foot from the ear, and
turned round its axis while vibrating, at every quarter revolution the sound
will scarcely be heard, while at the intermediate points it will be strong and
clear. This phenomenon arises from the interference of the undulations of
air coming from the two branches of the fork. When the two branches

coincide, or when they are at equal distances from the ear, the waves of air
combine to reinforce each other; but at the quadrants, where the two
branches are at unequal distances from the ear, the lengths of the waves
differ by half an undulation, and consequently destroy one another.

SECTION XVII.

Vibration of Musical Strings—Harmonic Sounds—Nodes—Vibration of
Air in Wind-Instruments—Vibration of Solids—Vibrating Plates—Bells
—Harmony—Sounding Boards—Forced Vibrations—Resonance—
Speaking Machines.

When the particles of elastic bodies are suddenly disturbed by an impulse,
they return to their natural position by a series of isochronous vibrations,
whose rapidity, force, and permanency depend upon the elasticity, the form,
and the mode of aggregation which unites the particles of the body. These
oscillations are communicated to the air, and on account of its elasticity
they excite alternate condensations and dilatations in the strata of the fluid
nearest to the vibrating body; from thence they are propagated to a distance.
A string or wire stretched between two pins, when drawn aside and
suddenly let go, will vibrate till its own rigidity and the resistance of the air
reduce it to rest. These oscillations may be rotatory, in every plane, or
confined to one plane according as the motion is communicated. In the
piano-forte, where the strings are struck by a hammer at one extremity, the
vibrations probably consist of a bulge running to and fro from end to end.
Different modes of vibration may be obtained from the same sonorous
body. Suppose a vibrating string to give the lowest C of the pianoforte
which is the fundamental note of the string; if it be lightly touched exactly
in the middle, so as to retain that point at rest, each half will then vibrate
twice as fast as the whole, but in opposite directions; the ventral or bulging
segments will be alternately above and below the natural position of the
string, and the resulting note will be the octave above C. When a point at a
third of the length of the string is kept at rest, the vibrations will be three
times as fast as those of the whole string, and will give the twelfth above C.
When the point of rest is one-fourth of the whole, the oscillations will be
four times as fast as those of the fundamental note, and will give the double

octave; and so on. These acute sounds are called the harmonics of the
fundamental note. It is clear, from what has been stated, that the string thus
vibrating could not give these harmonics spontaneously unless it divided
itself at its aliquot parts into two, three, four, or more segments in opposite
states of vibration separated by points actually at rest. In proof of this,
pieces of paper placed on the string at the half, third, fourth, or other aliquot
points, according to the corresponding harmonic sound, will remain on it
during its vibration, but will instantly fly off from any of the intermediate
points. The points of rest, called the nodal points of the string, are a mere
consequence of the law of interferences; for, if a rope fastened at one end be
moved to and fro at the other extremity so as to transmit a succession of
equal waves along it, they will be successively reflected when they arrive at
the other end of the rope by the fixed point, and in returning they will
occasionally interfere with the advancing waves; and, as these opposite
undulations will at certain points destroy one another, the point of the rope
in which this happens will remain at rest. Thus a series of nodes and ventral
segments will be produced whose number will depend upon the tension and
the frequency of the alternate motions communicated to the moveable end.
So, when a string fixed at both ends is put in motion by a sudden blow at
any point of it, the primitive impulse divides itself into two pulses running
opposite ways, which are each totally reflected at the extremities, and,
running back again along the whole length, are again reflected at the other
ends. And thus they will continue to run backwards and forwards, crossing
one another at each traverse, and occasionally interfering, so as to produce
nodes; so that the motion of a string fastened at both ends consists of a
wave or pulse continually doubled back on itself by reflection at the fixed
extremities.
Harmonics generally co-exist with the fundamental sound in the same
vibrating body. If one of the lowest strings of the pianoforte be struck, an
attentive ear will not only hear the fundamental note, but will detect all the
others sounding along with it, though with less and less intensity as their
pitch becomes higher. According to the law of co-existing undulations, the
whole string and each of its aliquot parts are in different and independent
states of vibration at the same time; and as all the resulting notes are heard
simultaneously, not only the air, but the ear also, vibrates in unison with
each at the same instant (N. 181).

Harmony consists in an agreeable combination of sounds. When two
chords perform their vibrations in the same time, they are in unison; but,
when their vibrations are so related as to have a common period, after a few
oscillations they produce concord. Thus, when the vibrations of two strings
bear a very simple relation to each other, as where one of them makes two,
three, four, &c., vibrations in the time the other makes one; or, if it
accomplishes three, four, &c., vibrations while the other makes two, the
result is a concord which is the more perfect the shorter the common period.
In discords, on the contrary, the beats are distinctly audible, which produces
a disagreeable and harsh effect, because the vibrations do not bear a simple
relation to one another, as where one of two strings makes eight vibrations
while the other accomplishes fifteen. The pleasure afforded by harmony is
attributed by Dr. Young to the love of order, and to a predilection for a
regular repetition of sensations natural to the human mind, which is
gratified by the perfect regularity and rapid recurrence of the vibrations.
The love of poetry and dancing he conceives to arise in some degree from
the rhythm of the one and the regularity of the motions in the other.
A blast of air passing over the open end of a tube, as over the reeds in
Pan’s pipes; over a hole in one side, as in the flute; or through the aperture
called a reed, with a flexible tongue, as in the clarinet, puts the internal
column of air into longitudinal vibrations by the alternate condensations
and rarefactions of its particles. At the same time the column spontaneously
divides itself into nodes, between which the air also vibrates longitudinally,
but with a rapidity inversely proportional to the length of the divisions,
giving the fundamental note or one of its harmonics. The nodes are
produced on the principle of interferences by the reflection of the
longitudinal undulations of the air at the ends of the pipe, as in the musical
string, only that in one case the undulations are longitudinal, and in the
other transverse.
A pipe, either open or shut at both ends, when sounded, vibrates entire, or
divides itself spontaneously into two, three, four, &c., segments separated
by nodes. The whole column gives the fundamental note by waves or
vibrations of the same length with the pipe. The first harmonic is produced
by waves half as long as the tube, the second harmonic by waves a third as
long, and so on. The harmonic segments in an open and shut pipe are the
same in number, but differently placed. In a shut pipe the two ends are
nodes, but in an open pipe there is half a segment at each extremity, because

the air at these points is neither rarefied nor condensed, being in contact
with that which is external. If one of the ends of the open pipe be closed, its
fundamental note will be an octave lower: the air will now divide itself into
three, five, seven, &c., segments; and the wave producing its fundamental
note will be twice as long as the pipe, so that it will be doubled back
(N. 182). All these notes may be produced separately by varying the
intensity of the blast. Blowing steadily and gently, the fundamental note
will sound; when the force of the blast is increased the note will all at once
start up an octave; when the intensity of the wind is augmented the twelfth
will be heard; and, by continuing to increase the force of the blast, the other
harmonics may be obtained, but no force of wind will produce a note
intermediate between these. The harmonics of a flute may be obtained in
this manner, from the lowest C or D upwards, without altering the
fingering, merely by increasing the intensity of the blast and altering the
form of the lips. Pipes of the same dimensions, whether of lead, glass, or
wood, give the same tone as to pitch under the same circumstances, which
shows that the air alone produces the sound.
Metal springs fastened at one end, when forcibly bent, endeavour to
return to rest by a series of vibrations, which give very pleasing tones, as in
musical boxes. Various musical instruments have been constructed,
consisting of metallic springs thrown into vibration by a current of air.
Among the most perfect of these are Mr. Wheatstone’s Symphonion,
Concertina, and Æolian Organ, instruments of different effects and
capabilities, but all possessing considerable execution and expression.
The Syren is an ingenious instrument, devised by M. Cagniard de la Tour,
for ascertaining the number of pulsations in a second, corresponding to each
pitch: the notes are produced by jets of air passing through small apertures,
arranged at regular distances in a circle on the side of a box, before which a
disc revolves pierced with the same number of holes. During a revolution of
the disc the currents are alternately intercepted and allowed to pass as many
times as there are apertures in it, and a sound is produced whose pitch
depends on the velocity of rotation.
A glass or metallic rod, when struck at one end, or rubbed in the direction
of its length with a wet finger, vibrates longitudinally, like a column of air,
by the alternate condensation and expansion of its constituent particles,
producing a clear and beautiful musical note of a high pitch, on account of
the rapidity with which these substances transmit sound. Rods, surfaces,

and, in general, all undulating bodies, resolve themselves into nodes. But in
surfaces the parts which remain at rest during their vibrations are lines
which are curved or plane according to the substance, its form, and the
mode of vibration. If a little fine dry sand be strewed over the surface of a
plate of glass or metal, and if undulations be excited by drawing the bow of
a violin across its edge, it will emit a musical sound, and the sand will
immediately arrange itself in the nodal lines, where alone it will accumulate
and remain at rest, because the segments of the surface on each side will be
in different states of vibration, the one being elevated while the other is
depressed; and, as these two motions meet in the nodal lines, they neutralise
one another. These lines vary in form and position with the part where the
bow is drawn across, and the point by which the plate is held. The motion
of the sand shows in what direction the vibrations take place. If they be
perpendicular to the surface, the sand will be violently tossed up and down
till it finds the points of rest. If they be tangential, the sand will only creep
along the surface to the nodal lines. Sometimes the undulations are oblique,
or compounded of both the preceding. If a bow be drawn across one of the
angles of a square plate of glass or metal held firmly by the centre, the sand
will arrange itself in two straight lines parallel to the sides of the plate, and
crossing in the centre so as to divide it into four equal squares, whose
motions will be contrary to each other. Two of the diagonal squares will
make their excursions on one side of the plate, while the other two make
their vibrations on the other side of it. This mode of vibration produces the
lowest tone of the plate (N. 183). If the plate be still held by the centre, and
the bow applied to the middle of one of the sides, the vibrations will be
more rapid, and the tone will be a fifth higher than in the preceding case:
now the sand will arrange itself from corner to corner, and will divide the
plate into four equal triangles, each pair of which will make their excursions
on opposite sides of the plate. The nodal lines and pitch vary not only with
the point where the bow is applied, but with the point by which the plate is
held, which being at rest necessarily determines the direction of one of the
quiescent lines. The forms assumed by the sand in square plates are very
numerous, corresponding to all the various modes of vibration. The lines in
circular plates are even more remarkable for their symmetry, and upon them
the forms assumed by the sand may be classed in three systems. The first is
the diametrical system, in which the figures consist of diameters dividing
the circumference of the plate into equal parts, each of which is in a

different state of vibration from those adjacent. Two diameters, for example,
crossing at right angles, divide the circumference into four equal parts;
three diameters divide it into six equal parts; four divide it into eight, and so
on. In a metallic plate, these divisions may amount to thirty-six or forty. The
next is the concentric system, where the sand arranges itself in circles,
having the same centre with the plate; and the third is the compound
system, where the figures assumed by the sand are compounded of the other
two, producing very complicated and beautiful forms. Galileo seems to
have been the first to notice the points of rest and motion in the sounding-
board of a musical instrument; but to Chladni is due the whole discovery of
the symmetrical forms of the nodal lines in vibrating plates (N. 184).
Professor Wheatstone has shown, in a paper read before the Royal Society
in 1833, that all Chladni’s figures, and indeed all the nodal figures of
vibrating surfaces, result from very simple modes of vibration oscillating
isochronously, and superposed upon each other; the resulting figure varying
with the component modes of vibration, the number of the superpositions,
and the angles at which they are superposed. For example, if a square plate
be vibrating so as to make the sand arrange itself in straight lines parallel to
one side of the plate, and if, in addition to this, such vibrations be excited as
would have caused the sand to form in lines perpendicular to the first had
the plate been at rest, the combined vibrations will make the sand form in
lines from corner to corner (N. 185).
M. Savart’s experiments on the vibrations of flat glass rulers are highly
interesting. Let a lamina of glass 27in·56 long, 0·59 of an inch broad, and
0·06 of an inch in thickness, be held by the edges in the middle, with its flat
surface horizontal. If this surface be strewed with sand, and set in
longitudinal vibration by rubbing its under surface with a wet cloth, the
sand on the upper surface will arrange itself in lines parallel to the ends of
the lamina, always in one or other of two systems (N. 186). Although the
same one of the two systems will always be produced by the same plate of
glass, yet among different plates of the preceding dimensions, even though
cut from the same sheet side by side, one will invariably exhibit one system,
and the other the other, without any visible reason for the difference. Now,
if the positions of these quiescent lines be marked on the upper surface, and
if the plate be turned so that the lower surface becomes the upper one, the
sand being strewed, and vibrations excited as before, the nodal lines will
still be parallel to the ends of the lamina, but their positions will be

intermediate between those of the upper surface (N. 187). Thus it appears
that all the motions of one half of the thickness of the lamina, or ruler, are
exactly contrary to those of the corresponding points of the other half. If the
thickness of the lamina be increased, the other dimensions remaining the
same, the sound will not vary, but the number of nodal lines will be less.
When the breadth of the lamina exceeds the 0·6 of an inch, the nodal lines
become curved, and are different on the two surfaces. A great variety of
forms are produced by increasing the breadth and changing the form of the
surface; but in all it appears that the motions in one half of the thickness are
opposed to those in the other half.
M. Savart also found, by placing small paper rings round a cylindrical
tube or rod, so as to rest upon it at one point only, that, when the tube or rod
is continually turned on its axis in the same direction, the rings slide along
during the vibrations, till they come to a quiescent point, where they rest.
By tracing these nodal lines he discovered that they twist in a spiral or
corkscrew round rods and cylinders, making one or more turns according to
the length; but at certain points, varying in number according to the mode
of vibration of the rod, the screw stops, and recommences on the other side,
though it is turned in a contrary direction; that is, on one side it is a right-
handed screw, on the other a left (N. 188). The nodal lines in the interior
surface of the tube are perfectly similar to those in the exterior, but they
occupy intermediate positions. If a small ivory ball be put within the tube, it
will follow these nodal lines when the tube is made to revolve on its axis.
All solids which ring when struck, such as bells, drinking glasses, gongs,
&c., have their shape momentarily and forcibly changed by the blow, and
from their elasticity, or tendency to resume their natural form, a series of
undulations take place, owing to the alternate condensations and
rarefactions of the particles of solid matter. These have also their harmonic
tones, and consequently nodes. Indeed, generally, when a rigid system of
any form whatever vibrates either transversely or longitudinally, it divides
itself into a certain number of parts which perform their vibrations without
disturbing one another. These parts are at every instant in alternate states of
undulation; and, as the points or lines where they join partake of both, they
remain at rest, because the opposing motions destroy one another.
The air, notwithstanding its rarity, is capable of transmitting its
undulations when in contact with a body susceptible of admitting and
exciting them. It is thus that sympathetic undulations are excited by a body

vibrating near insulated tended strings, capable of following its undulations,
either by vibrating entire, or by separating themselves into their harmonic
divisions. If two chords equally stretched, of which one is twice or three
times longer than the other, be placed side by side, and if the shorter be
sounded, its vibrations will be communicated by the air to the other, which
will be thrown into such a state of vibration that it will be spontaneously
divided into segments equal in length to the shorter string. When a tuning-
fork receives a blow and is made to rest upon a piano-forte during its
vibration, every string which, either by its natural length or by its
spontaneous subdivisions, is capable of executing corresponding vibrations,
responds in a sympathetic note. The same effect will be produced by the
stroke of a bell near a piano or harp. Some one or other of the notes of an
organ are generally in unison with one of the panes or with the whole sash
of a window, which consequently resounds when those notes are sounded.
A peal of thunder has frequently the same effect. The sound of very large
organ-pipes is generally inaudible till the air be set in motion by the
undulations of some of the superior accords, and then the sound becomes
extremely energetic. Recurring vibrations occasionally influence each
other’s periods. For example, two adjacent organ-pipes nearly in unison
may force themselves into concord; and two clocks, whose rates differed
considerably when separate, have been known to beat together when fixed
to the same wall, and one clock has forced the pendulum of another into
motion, when merely standing on the same stone pavement. These forced
oscillations, which correspond in their periods with those of the exciting
cause, are to be traced in every department of physical science. Several
instances of them have already occurred in this work. Such are the tides,
which follow the sun and moon in all their motions and periods. The
nutation of the earth’s axis also, which corresponds with the period, and
represents the motion of the nodes of the moon, is again reflected back to
the moon, and may be traced in the nutation of the lunar orbit. And, lastly,
the acceleration of the moon’s mean motion represents the action of the
planets on the earth reflected by the sun to the moon.
In consequence of the facility with which the air communicates
undulations, all the phenomena of vibrating plates may be exhibited by sand
strewed on paper or parchment, stretched over a harmonica glass or large
bell-shaped tumbler. In order to give due tension to the paper or vellum, it
must be wetted, stretched over the glass, gummed round the edges, allowed

to dry, and varnished over, to prevent changes in its tension from the
humidity of the atmosphere. If a circular disc of glass be held concentrically
over this apparatus, with its plane parallel to the surface of the paper, and
set in vibration by drawing a bow across its edge, so as to make sand on its
surface take any of Chladni’s figures, the sand on the paper will assume the
very same form, in consequence of the vibrations of the disc being
communicated to the paper by the air. When the disc is removed slowly in a
horizontal direction, the forms on the paper will correspond with those on
the disc, till the distance is too great for the air to convey the vibrations. If
the disc while vibrating be gradually more and more inclined to the horizon,
the figures on the paper will vary by degrees; and, when the vibrating disc
is perpendicular to the horizon, the sand on the paper will form into straight
lines parallel to the surface of the disc, by creeping along it instead of
dancing up and down. If the disc be made to turn round its vertical diameter
while vibrating, the nodal lines on the paper will revolve, and exactly
follow the motion of the disc. It appears, from this experiment, that the
motions of the aërial molecules in every part of a spherical wave,
propagated from a vibrating body as a centre, are parallel to each other, and
not divergent like the radii of a circle. When a slow air is played on a flute
near this apparatus, each note calls up a particular form in the sand, which
the next note effaces, to establish its own. The motion of the sand will even
detect sounds that are inaudible. By the vibrations of sand on a drum-head
the besieged have discovered the direction in which a counter-mine was
working. M. Savart, who made these beautiful experiments, employed this
apparatus to discover nodal lines in masses of air. He found that the air of a
room, when thrown into undulations by the continued sound of an organ-
pipe, or by any other means, divides itself into masses separated by nodal
curves of double curvature, such as spirals, on each side of which the air is
in opposite states of vibration. He even traced these quiescent lines going
out at an open window, and for a considerable distance in the open air. The
sand is violently agitated where the undulations of the air are greatest, and
remains at rest in the nodal lines. M. Savart observed, that when he moved
his head away from a quiescent line towards the right the sound appeared to
come from the right, and when he moved it towards the left the sound
seemed to come from the left, because the molecules of air are in different
states of motion on each side of the quiescent line.

A musical string gives a very feeble sound when vibrating alone, on
account of the small quantity of air set in motion; but when attached to a
sounding-board, as in the harp and piano-forte, it communicates its
undulations to that surface, and from thence to every part of the instrument;
so that the whole system vibrates isochronously, and by exposing an
extensive undulating surface, which transmits its undulations to a great
mass of air, the sound is much reinforced. The intensity is greatest when the
vibrations of the string or sounding body are perpendicular to the sounding-
board, and least when they are in the same plane with it. The sounding-
board of the piano-forte is better disposed than that of any other stringed
instrument, because the hammers strike the strings so as to make them
vibrate at right angles to it. In the guitar, on the contrary, they are struck
obliquely, which renders the tone feeble, unless when the sides, which also
act as a sounding-board, are deep. It is evident that the sounding-board and
the whole instrument are agitated at once by all the superposed vibrations
excited by the simultaneous or consecutive notes that are sounded, each
having its perfect effect independently of the rest. A sounding-board not
only reciprocates the different degrees of pitch, but all the nameless
qualities of tone. This has been beautifully illustrated by Professor
Wheatstone in a series of experiments on the transmission through solid
conductors of musical performances, from the harp, piano, violin, clarinet,
&c. He found that all the varieties of pitch, quality, and intensity are
perfectly transmitted with their relative gradations, and may be
communicated, through conducting wires or rods of very considerable
length, to a properly disposed sounding-board in a distant apartment. The
sounds of an entire orchestra may be transmitted and reciprocated by
connecting one end of a metallic rod with a sounding-board near the
orchestra, so placed as to resound to all the instruments, and the other end
with the sounding-board of a harp, piano, or guitar, in a remote apartment.
Professor Wheatstone observes, “The effect of this experiment is very
pleasing; the sounds, indeed, have so little intensity as scarcely to be heard
at a distance from the reciprocating instrument; but, on placing the ear close
to it, a diminutive band is heard in which all the instruments preserve their
distinctive qualities, and the pianos and fortes, the crescendos and
diminuendos, their relative contrasts. Compared with an ordinary band
heard at a distance through the air, the effect is as a landscape seen in

miniature beauty through a concave lens, compared with the same scene
viewed by ordinary vision through a murky atmosphere.”
Every one is aware of the reinforcement of sound by the resonance of
cavities. When singing or speaking near the aperture of a wide-mouthed
vessel, the intensity of some one note in unison with the air in the cavity is
often augmented to a great degree. Any vessel will resound if a body
vibrating the natural note of the cavity be placed opposite to its orifice, and
be large enough to cover it, or at least to set a large portion of the adjacent
air in motion. For the sound will be alternately reflected by the bottom of
the cavity and the undulating body at its mouth. The first impulse of the
undulating substance will be reflected by the bottom of the cavity, and then
by the undulating body, in time to combine with the second new impulse.
This reinforced sound will also be twice reflected in time to conspire with
the third new impulse; and, as the same process will be repeated on every
new impulse, each will combine with all its echoes to reinforce the sound
prodigiously. Professor Wheatstone, to whose ingenuity we are indebted for
so much new and valuable information on the theory of sound, has given
some very striking instances of resonance. If one of the branches of a
vibrating tuning-fork be brought near the embouchure of a flute, the lateral
apertures of which are stopped so as to render it capable of producing the
same sound as the fork, the feeble and scarcely audible sound of the fork
will be augmented by the rich resonance of the column of air within the
flute, and the tone will be full and clear. The sound will be found greatly to
decrease by closing or opening another aperture; for the alteration in the
length of the column of air renders it no longer fit perfectly to reciprocate
the sound of the fork. This experiment may be made on a concert flute with
a C tuning-fork. But Professor Wheatstone observes, that in this case it is
generally necessary to finger the flute for B, because, when blown into with
the mouth, the under-lip partly covers the embouchure, which renders the
sound about a semitone flatter than it would be were the embouchure
entirely uncovered. He has also shown, by the following experiment, that
any one among several simultaneous sounds may be rendered separately
audible. If two bottles be selected, and tuned by filling them with such a
quantity of water as will render them unisonant with two tuning-forks
which differ in pitch, on bringing both of the vibrating tuning-forks to the
mouth of each bottle alternately, in each case that sound only will be heard
which is reciprocated by the unisonant bottle.

Several attempts have been made to imitate the articulation of the letters
of the alphabet. About the year 1779, MM. Kratzenstein of St. Petersburg,
and Kempelen of Vienna, constructed instruments which articulated many
letters, words, and even sentences. Mr. Willis of Cambridge has adapted
cylindrical tubes to a reed, whose length can be varied at pleasure by sliding
joints. Upon drawing out a tube while a column of air from the bellows of
an organ is passing through it, the vowels are pronounced in the order, i, e,
a, o, u. On extending the tube, they are repeated after a certain interval, in
the inverted order, u, o, a, e, i. After another interval they are again obtained
in the direct order, and so on. When the pitch of the reed is very high, it is
impossible to sound some of the vowels, which is in perfect correspondence
with the human voice, female singers being unable to pronounce u and o in
their high notes. From the singular discoveries of M. Savart on the nature of
the human voice, and the investigations of Mr. Willis on the mechanism of
the larynx, it may be presumed that ultimately the utterance or
pronunciation of modern languages will be conveyed, not only to the eye,
but also to the ear of posterity. Had the ancients possessed the means of
transmitting such definite sounds, the civilised world would still have
responded in sympathetic notes at the distance of many ages.

SECTION XVIII.

Refraction—Astronomical Refraction and its Laws—Formation of Tables
of Refraction—Terrestrial Refraction—Its Quantity—Instances of
extraordinary Refraction—Reflection—Instances of extraordinary
Reflection—Loss of Light by the Absorbing Power of the Atmosphere—
Apparent Magnitude of Sun and Moon in the Horizon.

Not only everything we hear but all we see is through the medium of the
atmosphere. Without some knowledge of its action upon light, it would be
impossible to ascertain the position of the heavenly bodies, or even to
determine the exact place of very distant objects upon the surface of the
earth; for, in consequence of the refractive power of the air, no distant
object is seen in its true position.
All the celestial bodies appear to be more elevated than they really are;
because the rays of light, instead of moving through the atmosphere in
straight lines, are continually inflected towards the earth. Light passing
obliquely out of a rare into a denser medium, as from vacuum into air, or
from air into water, is bent or refracted from its course towards a
perpendicular to that point of the denser surface where the light enters it
(N. 189). In the same medium, the sine of the angle contained between the
incident ray and the perpendicular is in a constant ratio to the sine of the
angle contained by the refracted ray and the same perpendicular; but this
ratio varies with the refracting medium. The denser the medium, the more
the ray is bent. The barometer shows that the density of the atmosphere
decreases as the height above the earth increases. Direct experiments prove
that the refractive power of the air increases with its density. It follows
therefore that, if the temperature be uniform, the refractive power of the air
is greatest at the earth’s surface, and diminishes upwards.

A ray of light from a celestial object falling obliquely on this variable
atmosphere, instead of being refracted at once from its course, is gradually
more and more bent during its passage through it so as to move in a vertical
curved line, in the same manner as if the atmosphere consisted of an infinite
number of strata of different densities. The object is seen in the direction of
a tangent to that part of the curve which meets the eye; consequently the
apparent altitude (N. 190) of the heavenly bodies is always greater than
their true altitude. Owing to this circumstance, the stars are seen above the
horizon after they are set, and the day is lengthened from a part of the sun
being visible, though he really is behind the rotundity of the earth. It would
be easy to determine the direction of a ray of light through the atmosphere
if the law of the density were known; but, as this law is perpetually varying
with the temperature, the case is very complicated. When rays pass
perpendicularly from one medium into another, they are not bent; and
experience shows, that in the same surface, though the sines of the angles of
incidence and refraction retain the same ratio, the refraction increases with
the obliquity of incidence (N. 189). Hence it appears that the refraction is
greatest at the horizon, and at the zenith there is none. But it is proved that,
at all heights above ten degrees, refraction varies nearly as the tangent of
the angular distance of the object from the zenith, and wholly depends upon
the heights of the barometer and thermometer. For the quantity of refraction
at the same distance from the zenith varies nearly as the height of the
barometer, the temperature being constant; and the effect of the variation of
temperature is to diminish the quantity of refraction by about its 480th part
for every degree in the rise of Fahrenheit’s thermometer. Not much reliance
can be placed on celestial observations, within less than ten or twelve
degrees of the horizon, on account of irregular variations in the density of
the air near the surface of the earth, which are sometimes the cause of very
singular phenomena. The humidity of the air produces no sensible effect on
its refractive power; and it has been proved that the amount of refraction is
the same whatever be the velocity of the incident light, that is whether the
light comes from a star in that part of the heavens towards which the earth
is going, or from one in that part of the sky whence it is receding.
Bodies, whether luminous or not, are only visible by the rays which
proceed from them. As the rays must pass through strata of different
densities in coming to us, it follows that, with the exception of stars in the
zenith, no object either in or beyond our atmosphere is seen in its true place.

But the deviation is so small in ordinary cases that it causes no
inconvenience, though in astronomical and trigonometrical observations
due allowance must be made for the effects of refraction. Dr. Bradley’s
tables of refraction were formed by observing the zenith distances of the
sun at his greatest declinations, and the zenith distances of the pole-star
above and below the pole. The sum of these four quantities is equal to 180°,
diminished by the sum of the four refractions, whence the sum of the four
refractions was obtained; and, from the law of the variation of refraction
determined by theory, he assigned the quantity due to each altitude
(N. 191). The mean horizontal refraction is about 35ʹ 6ʺ, and at the height of
forty-five degrees it is 58ʺ·36. The effect of refraction upon the same star
above and below the pole was noticed by Alhazen, a Saracen astronomer of
Spain, in the ninth century; but its existence was known to Ptolemy in the
second, though he was ignorant of its quantity.
The refraction of a terrestrial object is estimated differently from that of a
celestial body. It is measured by the angle contained between the tangent to
the curvilineal path of the ray where it meets the eye, and the straight line
joining the eye and the object (N. 192). Near the earth’s surface the path of
the ray may be supposed to be circular; and the angle at the centre of the
earth corresponding to this path is called the horizontal angle. The quantity
of terrestrial refraction is obtained by measuring contemporaneously the
elevation of the top of a mountain above a point in the plain at its base, and
the depression of that point below the top of the mountain. The distance
between these two stations is the chord of the horizontal angle; and it is
easy to prove that double the refraction is equal to the horizontal angle,
increased by the difference between the apparent elevation and the apparent
depression. Whence it appears that, in the mean state of the atmosphere, the
refraction is about the fourteenth part of the horizontal angle.
Some very singular appearances occur from the accidental expansion or
condensation of the strata of the atmosphere contiguous to the surface of the
earth, by which distant objects, instead of being elevated, are depressed.
Sometimes, being at once both elevated and depressed, they appear double,
one of the images being direct, and the other inverted. In consequence of
the upper edges of the sun and moon being less refracted than the lower,
they often appear to be oval when near the horizon. The looming also or
elevation of coasts, mountains, and ships, when viewed across the sea,
arises from unusual refraction. A friend of the author’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 very long course of dry and hot
weather. Single and double images of objects at sea, arising from sudden
changes of temperature which are not so soon communicated to the water
on account of its density as to the air, occur more rarely and are of shorter
duration than similar appearances on land. In 1818 Captain Scoresby,
whose observations on the phenomena of the polar seas are so valuable,
recognised his father’s ship by its inverted image in the air, although the
vessel itself was below the horizon. He afterwards found that she was
seventeen miles beyond the horizon, and thirty miles distant. Two images
are sometimes seen suspended in the air over a ship, one direct and the
other inverted, with their topmasts or their hulls meeting, according as the
inverted image is above or below the direct image (N. 193). Dr. Wollaston
has proved that these appearances are owing to the refraction of the rays
through media of different densities, by the very simple experiment of
looking along a red-hot poker at a distant object. Two images are seen, one
direct and another inverted, in consequence of the change induced by the
heat in the density of the adjacent air. He produced the same effect by a
saline or saccharine solution with water and spirit of wine floating upon it
(N. 194).
Many of the phenomena that have been ascribed to extraordinary
refraction seem to be occasioned by a partial or total reflection of the rays
of light at the surfaces of strata of different densities (N. 189). It is well
known that, when light falls obliquely upon the external surface of a
transparent medium, as on a plate of glass or a stratum of air, one portion is
reflected and the other transmitted. But, when light falls very obliquely
upon the internal surface, the whole is reflected, and not a ray is
transmitted. In all cases the angles made by the incident and reflected rays
with a perpendicular to the surface being equal, as the brightness of the
reflected image depends on the quantity of light, those arising from total
reflection must be by far the most vivid. The delusive appearance of water,
so well known to African travellers and to the Arab of the desert as the Lake
of the Gazelles, is ascribed to the reflection which takes place between
strata of air of different densities, owing to radiation of heat from the arid
sandy plains. The mirage described by Captain Mundy in his Journal of a
Tour in India probably arises from this cause. “A deep precipitous valley

below us, at the bottom of which I had seen one or two miserable villages in
the morning, bore in the evening a complete resemblance to a beautiful
lake; the vapour which played the part of water ascending nearly half way
up the sides of the vale, and on its bright surface trees and rocks being
distinctly reflected. I had not been long contemplating this phenomenon,
before a sudden storm came on and dropped a curtain of clouds over the
scene.”
An occurrence which happened on the 18th of November, 1804, was
probably produced by reflection. Dr. Buchan, while watching the rising sun
from the cliff about a mile to the east of Brighton, at the instant the solar
disc emerged from the surface of the ocean, saw the cliff on which he was
standing, a windmill, his own figure and that of a friend, depicted
immediately opposite to him on the sea. This appearance lasted about ten
minutes, till the sun had risen nearly his own diameter above the surface of
the waves. The whole then seemed to be elevated into the air, and
successively vanished. The rays of the sun fell upon the cliff at an incidence
of 73° from the perpendicular, and the sea was covered with a dense fog
many yards in height, which gradually receded before the rising sun. When
extraordinary refraction takes place laterally, the strata of variable density
are perpendicular to the horizon, and, if combined with vertical refraction,
the objects are magnified as when seen through a telescope. From this
cause, on the 26th of July, 1798, the cliffs of France, fifty miles off, were
seen as distinctly from Hastings as if they had been close at hand; and even
Dieppe was said to have been visible in the afternoon.
The stratum of air in the horizon is so much thicker and more dense than
the stratum in the vertical, that the sun’s light is diminished 1300 times in
passing through it, which enables us to look at him when setting without
being dazzled. The loss of light, and consequently of heat, by the absorbing
power of the atmosphere, increases with the obliquity of incidence. Of ten
thousand rays falling on its surface, 8123 arrive at a given point of the earth
if they fall perpendicularly; 7024 arrive if the angle of direction be fifty
degrees; 2831, if it be seven degrees; and only five rays will arrive through
a horizontal stratum. Since so great a quantity of light is lost in passing
through the atmosphere, many celestial objects are altogether invisible from
the plain, which may be seen from elevated situations. Diminished
splendour, and the false estimate we make of distance from the number of
intervening objects, lead us to suppose the sun and moon to be much larger

when in the horizon than at any other altitude, though their apparent
diameters are then somewhat less. Instead of the sudden transitions of light
and darkness, the reflective power of the air adorns nature with the rosy and
golden hues of the Aurora and twilight. Even when the sun is eighteen
degrees below the horizon, a sufficient portion of light remains to show that
at the height of thirty miles it is still dense enough to reflect light. The
atmosphere scatters the sun’s rays, and gives all the beautiful tints and
cheerfulness of day. It transmits the blue light in greatest abundance; the
higher we ascend, the sky assumes a deeper hue; but, in the expanse of
space, the sun and stars must appear like brilliant specks in profound
blackness.

SECTION XIX.

Constitution of Light according to Sir Isaac Newton—Absorption of Light
—Colours of Bodies—Constitution of Light according to Sir David
Brewster—New Colours—Fraunhofer’s Dark Lines—Dispersion of Light
—The Achromatic Telescope—Homogeneous Light—Accidental and
Complementary Colours—M. Plateau’s Experiments and Theory of
Accidental Colours.

It is impossible thus to trace the path of a sunbeam through our atmosphere
without feeling a desire to know its nature, by what power it traverses the
immensity of space, and the various modifications it undergoes at the
surfaces and in the interior of terrestrial substances.
Sir Isaac Newton proved the compound nature of white light, as emitted
from the sun, by passing a sunbeam through a glass prism (N. 195), which,
separating the rays by refraction, formed a spectrum or oblong image of the
sun, consisting of seven colours, red, orange, yellow, green, blue, indigo,
and violet—of which the red is the least refrangible, and the violet the most.
But, when he reunited these seven rays by means of a lens, the compound
beam became pure white as before. He insulated each coloured ray, and,
finding that it was no longer capable of decomposition by refraction,
concluded that white light consists of seven kinds of homogeneous light,
and that to the same colour the same refrangibility ever belongs, and to the
same refrangibility the same colour. Since the discovery of absorbent
media, however, it appears that this is not the constitution of the solar
spectrum.
We know of no substance that is either perfectly opaque or perfectly
transparent. Even gold may be beaten so thin as to be pervious to light. On
the contrary, the clearest crystal, the purest air or water, stops or absorbs its
rays when transmitted, and gradually extinguishes them as they penetrate to

greater depths. On this account objects cannot be seen at the bottom of very
deep water, and many more stars are visible to the naked eye from the tops
of mountains than from the valleys. The quantity of light that is incident on
any transparent substance is always greater than the sum of the reflected
and refracted rays. A small quantity is irregularly reflected in all directions
by the imperfections of the polish by which we are enabled to see the
surface; but a much greater portion is absorbed by the body. Bodies that
reflect all the rays appear white, those that absorb them all seem black; but
most substances, after decomposing the white light which falls upon them,
reflect some colours and absorb the rest. A violet reflects the violet rays
alone and absorbs the others. Scarlet cloth absorbs almost all the colours
except red. Yellow cloth reflects the yellow rays most abundantly, and blue
cloth those that are blue. Consequently colour is not a property of matter,
but arises from the action of matter upon light. In fact, the law of action and
reaction obtains in light as in every other department of nature, so that light
cannot be reflected, refracted, much less absorbed, by any medium without
being reacted upon by it. Thus a white riband reflects all the rays, but, when
dyed red, the particles of the silk acquire the property of reflecting the red
rays most abundantly and of absorbing the others. Upon this property of
unequal absorption the colours of transparent media depend; for they also
receive their colour from their power of stopping or absorbing some of the
colours of white light, and transmitting others. As, for example, black and
red inks, though equally homogeneous, absorb different kinds of rays; and,
when exposed to the sun, they become heated in different degrees; while
pure water seems to transmit all rays equally, and is not sensibly heated by
the passing light of the sun. The rich dark light transmitted by a smalt-blue
finger-glass is not a homogeneous colour like the blue or indigo of the
spectrum, but is a mixture of all the colours of white light which the glass
has not absorbed. The colours absorbed are such as mixed with the blue tint
would form white light. When the spectrum of seven colours is viewed
through a thin plate of this glass, they are all visible; and, when the plate is
very thick, every colour is absorbed between the extreme red and the
extreme violet, the interval being perfectly black; but, if the spectrum be
viewed through a certain thickness of the glass intermediate between the
two, it will be found that the middle of the red space, the whole of the
orange, a great part of the green, a considerable part of the blue, a little of
the indigo, and a very little of the violet, vanish, being absorbed by the blue

glass; and that the yellow rays occupy a larger space, covering part of that
formerly occupied by the orange on one side and by the green on the other:
so that the blue glass absorbs the red light, which when mixed with the
yellow constitutes orange; and also absorbs the blue light, which when
mixed with the yellow forms the part of the green space next to the yellow.
Hence, by absorption, green light is decomposed into yellow and blue, and
orange light into yellow and red: consequently the orange and green rays,
though incapable of decomposition by refraction, can be resolved by
absorption, and actually consist of two different colours possessing the
same degree of refrangibility. Difference of colour, therefore, is not a test of
difference of refrangibility, and the conclusion deduced by Newton is no
longer admissible as a general truth. By this analysis of the spectrum, not
only with blue glass but with a variety of coloured media, Sir David
Brewster, so justly celebrated for his optical discoveries, is of opinion that
the solar spectrum consists of three primary colours, red, yellow, and blue,
each of which exists throughout its whole extent, but with different degrees
of intensity in different parts; and that the superposition of these three
produces all the seven hues according as each primary colour is in excess or
defect. That since a certain portion of red, yellow, and blue rays constitute
white light, the colour of any point of the spectrum may be considered as
consisting of the predominating colour at that point mixed with white light.
Consequently, “by absorbing the excess of any colour at any point of the
spectrum above what is necessary to form white light, such white light will
appear at that point as never mortal eye looked upon before this experiment,
since it possesses the remarkable property of remaining the same after any
number of refractions, and of being capable of decomposition by absorption
alone.” This analysis of light has been called in question by Professor
Challis, of Cambridge, who does not admit of any resolution by absorbing
media different from that by the prism, though he admits that a mixture of
blue and yellow solar light produces green. Professor Stokes, on the
contrary, does not allow that a mixture of blue and yellow solar light
produces green, although that mixture produces green when the light is
from other sources, for he found the gradation from sunlight to pass from
yellow through diluted yellow, white, diluted blue to blue; so he does not
admit of Sir David Brewster’s analysis of the spectrum; however, there
appears to be still a doubt as to the real character of the phenomena
presented by certain absorbing substances.

In addition to the seven colours of the Newtonian spectrum, Sir John
Herschel has discovered a set of very dark red rays beyond the red
extremity of the spectrum which can only be seen when the eye is defended
from the glare of the other colours by a dark blue cobalt glass. He has also
found that beyond the extreme violet there are visible rays of a lavender
gray colour, which may be seen by throwing the spectrum on a sheet of
paper moistened by the carbonate of soda. The illuminating power of the
different rays of the spectrum varies with the colour. The most intense light
is in the mean yellow ray, or, according to M. Fraunhofer, at the boundary
of the orange and yellow.
When the prism is very perfect and the sunbeam small, so that the
spectrum may be received on a sheet of white paper in its utmost state of
purity, it presents the appearance of a riband shaded with all the prismatic
colours, having its breadth irregularly striped or subdivided by an indefinite
number of dark, and sometimes black lines. The greater number of these
rayless lines are so extremely narrow that it is impossible to see them in
ordinary circumstances. The best method is to receive the spectrum on the
object-glass of a telescope, so as to magnify them sufficiently to render
them visible. This experiment may also be made, but 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 its
refracting angle parallel to the line of light. The rayless lines in the red
portion of the spectrum become most visible as the sun approaches the
horizon, while those in the blue extremity are most obvious in the middle of
the day. 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 positions. Similar dark lines
are also seen in the light of the stars, in the electric light, and in the flame of
combustible substances, though differently arranged, each star and each
flame having a system of dark lines peculiar to itself. Dr. Wollaston and M.
Fraunhofer, of Munich, discovered these lines deficient of rays
independently of each other. M. Fraunhofer found that their number extends
to nearly six hundred, but they are much more numerous. There are bright
lines in the solar spectrum which also maintain a fixed position. Among the
dark lines, M. Fraunhofer selected seven of the most remarkable, and
determined their distances so accurately, that they now form standard and

invariable points of reference for measuring the refractive powers of
different media on the rays of light, which renders this department of optics
as exact as any of the physical sciences. These lines are designated by the
letters of the alphabet, beginning with B, which is in the red near the end of
the spectrum; C is farther advanced in the red; D is in the orange; E in the
green; F in the blue; G in the indigo; and H in the violet. By means of these
fixed points, M. Fraunhofer has ascertained from prismatic observation the
refrangibility of seven of the principal rays in each of ten different
substances solid and liquid. The refraction increased in all from the red to
the violet end of the spectrum. The rays that are wanting in the solar
spectrum, which occasion the dark lines, were supposed to be absorbed by
the atmosphere of the sun. But the annular eclipse which happened on the
15th of May, 1836, afforded Professor Forbes the means of proving that the
dark lines in question cannot be attributed to the absorption of the solar
atmosphere; they were neither broader nor more numerous in the spectrum
formed during that phenomenon than at any other time, though the rays
came only from the circumference of the sun’s disc, and consequently had
to traverse a greater depth of his atmosphere.
Sir David Brewster found that in certain states of the atmosphere the
obscure lines become much broader, and some of them deeply black; and he
observed also, that, at the time the sun was setting in a veil of red light, part
of the luminous spectrum was absorbed, whence he concluded that the
earth’s atmosphere had absorbed the rays of light which occupied the dark
bands. By direct experiments also the atmosphere was observed to act
powerfully upon the rayless lines.
When a lens is used along with a prism, longitudinal dark lines of
different breadths are seen to cross the bands, already described, at right
angles; these M. Ragona-Scina and M. Babinet believe to be lines of
interference which exist in light that has passed through a convex lens.
The lines are different both in kind and number in the spectra of gases
and flames. In a highly-magnified spectrum from light passed through
nitrous acid gas, Sir David Brewster counted 2000 dark bands. In the
spectrum of a lamp, and generally of all white flames, none of the defective
lines are found; so all such flames contain rays which do not exist in the
light of the sun or stars. Brilliant red lines appear in the spectrum produced
by the combustion of nitre upon charcoal; and in all artificial flames dark

and bright bands exist, sometimes corresponding in position with those in
the solar spectrum, and sometimes not.
A sunbeam received on a screen, after passing through a small round hole
in a window-shutter, appears like a round white spot; but when a prism is
interposed, the beam no longer occupies the same space. It is separated into
the prismatic colours, and spread over a line of considerable length, while
its breadth remains the same with that of the white spot. The act of
spreading or separation is called the dispersion of the coloured rays.
Dispersion always takes place in the plane of refraction, and is greater as
the angle of incidence is greater. It varies inversely as the length of a wave
of light, and directly as its velocity: hence towards the blue end of the
spectrum, where the undulations of the rays are least, the dispersion is
greatest. Substances have very different dispersive powers; that is to say,
the spectra formed by two equal prisms of different substances, under
precisely the same circumstances, are of different lengths. Thus, if a prism
of flint-glass and one of crown-glass of equal refracting angles be presented
to two rays of white light at equal angles, it will be found that the space
over which the coloured rays are dispersed by the flint-glass is much greater
than the space occupied by that produced by the crown-glass: and as the
quantity of dispersion depends upon the refracting angle of the prism, the
angles of the two prisms may be made such that, when the prisms are
placed close together with their edges turned opposite ways, they will
exactly oppose each other’s action, and will refract the coloured rays
equally, but in contrary directions, so that an exact compensation will be
effected, and the light will be refracted without colour (N. 195). The
achromatic telescope is constructed on this principle. It consists of a tube
with an object-glass or lens at one end to bring the rays to a focus, and form
an image of the distant object, and a magnifying-glass at the other end to
view the image thus formed. Now it is found that the object-glass, instead
of making the rays converge to one point, disperses them, and gives a
confused and coloured image: but by constructing it of two lenses in
contact, one of flint and the other of crown-glass of certain forms and
proportions, the dispersion is counteracted, and a perfectly well-defined and
colourless image of the object is formed (N. 196). It was thought to be
impossible to produce refraction without colour, till Mr. Hall, a gentleman
of Worcestershire, constructed a telescope on this principle in the year

1733; and twenty-five years afterwards the achromatic telescope was
brought to perfection by Mr. Dollond, a celebrated optician in London.
By means of Mr. Fraunhofer’s determination of the refraction of the
principal rays in substances, their dispersive powers may be found (N. 197).
A perfectly homogeneous colour is very rarely to be found; but the tints
of all substances are most brilliant when viewed in light of their own colour.
The red of a wafer is much more vivid in red than in white light; whereas, if
placed in homogeneous yellow light, it can no longer appear red, because
there is not a ray of red in the yellow light. Were it not that the wafer, like
all other bodies, whether coloured or not, reflects white light at its outer
surface, it would appear absolutely black when placed in yellow light.
After looking steadily for a short time at a coloured object, such as a red
wafer, on turning the eyes to a white substance, a green image of the wafer
appears, which is called the accidental colour of red. All tints have their
accidental colours: thus the accidental colour of orange is blue; that of
yellow is indigo; of green, reddish white; of blue, orange-red; of violet,
yellow; and of white, black; and vice versâ. When the direct and accidental
colours are of the same intensity, the accidental is then called the
complementary colour, because any two colours are said to be
complementary to one another which produce white when combined.
From experiments by M. Plateau of Brussels, it appears that two
complementary colours from direct impression, which would produce white
when combined, produce black, or extinguish one another, by their union,
when accidental; and also that the combination of all the tints of the solar
spectrum produces white light if they be from a direct impression on the
eye, whereas blackness results from a union of the same tints if they be
accidental; and in every case where the real colours produce white by their
combination, the accidental colours of the same tints produce black. When
the image of an object is impressed on the retina only for a few moments,
the picture left is exactly of the same colour with the object, but in an
extremely short time the picture is succeeded by the accidental image. M.
Plateau attributes this phenomenon to a reaction of the retina after being
excited by direct vision, so that the accidental impression is of an opposite
nature to the corresponding direct impression. He conceives that when the
eye is excited by being fixed for a time on a coloured object, and then
withdrawn from the excitement, it endeavours to return to its state of

repose; but in so doing, that it passes this point, and spontaneously assumes
an opposite condition, like a spring which, bent in one direction, in
returning to its state of rest bends as much the contrary way. The accidental
image thus results from a particular modification of the organ of sight, in
virtue of which it spontaneously gives us a new sensation after it has been
excited by direct vision. If the prevailing impression be a very strong white
light, its accidental image is not black, but a variety of colours in
succession. According to M. Plateau, the retina offers a resistance to the
action of light, which increases with the duration of this action; whence,
after looking intently at an object for a long time, it appears to decrease in
brilliancy. The imagination has a powerful influence on our optical
impressions, and has been known to revive the images of highly luminous
objects months, and even years, afterwards.

SECTION XX.

Interference of Light—Undulatory Theory of Light—Propagation of Light
—Newton’s Rings—Measurement of the Length of the Waves of Light,
and of the Frequency of the Vibrations of Ether for each Colour—
Newton’s Scale of Colours—Diffraction of Light—Sir John Herschel’s
Theory of the Absorption of Light—Refraction and Reflection of Light.

Newton and most of his immediate successors imagined light to be a
material substance, emitted by all self-luminous bodies in extremely minute
particles, moving in straight lines with prodigious velocity, which, by
impinging upon the optic nerves, produce the sensation of light. Many of
the observed phenomena have been explained by this theory; it is, however,
totally inadequate to account for the following circumstances.
When two equal rays of red light, proceeding from two luminous points,
fall upon a sheet of white paper in a dark room, they produce a red spot on
it which will be twice as bright as either ray would produce singly, provided
the difference in the lengths of the two beams, from the luminous points to
the red spot on the paper, be exactly the 0·0000258th part of an inch. The
same effect will take place if the difference in the lengths be twice, three
times, four times, &c., that quantity. But if the difference in the lengths of
the two rays be equal to one-half of the 0·0000258th part of an inch, or to
its 11⁄2, 21⁄2, 31⁄2, &c., part, the one light will entirely extinguish the other,
and will produce absolute darkness on the paper where the united beams
fall. If the difference in the lengths of their paths be equal to the 11⁄4, 21⁄4,
31⁄4, &c., of the 0·0000258th part of an inch, the red spot arising from the
combined beams will be of the same intensity which one alone would
produce. If violet light be employed, the difference in the lengths of the two
beams must be equal to the 0·0000157th part of an inch, in order to produce
the same phenomena; and for the other colours, the difference must be

intermediate between the 0·0000258th and the 0·0000157th part of an inch.
Similar phenomena may be seen by viewing the flame of a candle through
two very fine slits in a card extremely near to one another (N. 198); or by
admitting the sun’s light into a dark room through a pin-hole about the
fortieth of an inch in diameter, receiving the image on a sheet of white
paper, and holding a slender wire in the light. Its shadow will be found to
consist of a bright white bar or stripe in the middle, with a series of
alternate black and brightly-coloured stripes on each side. The rays which
bend round the wire in two streams are of equal lengths in the middle stripe;
it is consequently doubly bright from their combined effect; but the rays
which fall on the paper on each side of the bright stripe, being of such
unequal lengths as to destroy one another, form black lines. On each side of
these black lines the rays are again of such lengths as to combine to form
bright stripes, and so on alternately till the light is too faint to be visible.
When any homogeneous light is used, such as red, the alternations are only
black and red; but on account of the heterogeneous nature of white light, the
black lines alternate with vivid stripes or fringes of prismatic colours,
arising from the superposition of systems of alternate black lines and lines
of each homogeneous colour. That the alternation of black lines and
coloured fringes actually does arise from the mixture of the two streams of
light which flow round the wire, is proved by their vanishing the instant one
of the streams is interrupted. It may therefore be concluded, as often as
these stripes of light and darkness occur, that they are owing to the rays
combining at certain intervals to produce a joint effect, and at others to
extinguish one another. Now it is contrary to all our ideas of matter to
suppose that two particles of it should annihilate one another under any
circumstances whatever; while, on the contrary, two opposing motions may;
and it is impossible not to be struck with the perfect similarity between the
interferences of small undulations of air or of water and the preceding
phenomena. The analogy is indeed so perfect, that philosophers of the
highest authority concur in the belief that the celestial regions are filled
with an extremely rare and highly elastic medium or ether, whose particles
are capable of receiving the vibrations communicated to them by self-
luminous bodies, and of transmitting them to the optic nerves, so as to
produce the sensation of light. The acceleration in the mean motion of
Encke’s comet, as well as of the comet discovered by M. Biela, renders the
existence of such a medium certain. It is clear that, in this hypothesis, the

alternate stripes of light and darkness are entirely the effect of the
interference of the undulations; for, by actual measurement, the length of a
wave of the mean red rays of the solar spectrum is equal to the 0·0000258th
part of an inch; consequently, when the elevations of the waves combine,
they produce double the intensity of light that each would do singly; and
when half a wave combines with a whole—that is, when the hollow of one
wave is filled up by the elevation of another—darkness is the result. At
intermediate points between these extremes, the intensity of the light
corresponds to intermediate differences in the lengths of the rays.
The theory of interferences is a particular case of the general mechanical
law of the superposition of small motions; whence it appears that the
disturbance of a particle of an elastic medium, produced by two co-existent
undulations, is the sum of the disturbances which each undulation would
produce separately; consequently, the particle will move in the diagonal of a
parallelogram, whose sides are the two undulations. If, therefore, the two
undulations agree in direction, or nearly so, the resulting motion will be
very nearly equal to their sum, and in the same direction; if they nearly
oppose one another, the resulting motion will be nearly equal to their
difference; and, if the undulations be equal and opposite, the resultant will
be zero, and the particle will remain at rest.
The preceding experiments, and the inferences deduced from them,
which have led to the establishment of the doctrine of the undulations of
light, are the most splendid memorials of our illustrious countryman Dr.
Thomas Young, though Huygens was the first to originate the idea.
It is supposed that the particles of luminous bodies are in a state of
perpetual agitation, and that they possess the property of exciting regular
vibrations in the molecules of the ethereal medium, corresponding to the
vibrations of their own molecules; and that, on account of its elastic nature,
one particle of the ether when set in motion communicates its vibrations to
those adjacent, which in succession transmit them to those farther off; so
that the primitive impulse is transferred from particle to particle, and the
undulating motion darts through ether like a wave in water; so that light is
motion, and therefore subject to the laws of dynamics and mathematical
analysis. Although the progressive motion of light is known by experience
to be uniform and in a straight line, the vibrations of the particles are always
at right angles to the direction of the ray. The propagation of light is like the
spreading of waves in water; but, if one ray alone be considered, its motion

may be conceived by supposing a rope of indefinite length stretched
horizontally, one end of which is held in the hand. If it be agitated to and fro
at regular intervals, with a motion perpendicular to its length, a series of
similar and equal tremors or waves will be propagated along it; and if the
regular impulses be given in a variety of planes, as up and down, from right
to left, and also in oblique directions, the successive undulations will take
place in every possible plane. An analogous motion in the ether, when
communicated to the optic nerves, would produce the sensation of common
light. It is evident that the waves which flow from end to end of the cord in
a serpentine form are altogether different from the perpendicular vibratory
motion of each particle of the rope, which never deviates far from a state of
rest. So, in ether, each particle vibrates perpendicularly to the direction of
the ray; but these vibrations are totally different from and independent of
the undulations which are transmitted through it, in the same manner as the
vibrations of each particular ear of corn are independent of the waves that
rush from end to end of a harvest-field when agitated by the wind.
The intensity of light depends upon the amplitude or extent of the
vibrations of the particles of ether, while its colour depends upon their
frequency. The time of the vibration of a particle of ether is, by theory, as
the length of a wave directly, and inversely as its velocity. Now, as the
velocity of light is known to be 190,000 miles in a second, if the lengths of
the waves of the different coloured rays could be measured, the number of
vibrations in a second corresponding to each could be computed. That has
been accomplished as follows:—All transparent substances of a certain
thickness, with parallel surfaces, reflect and transmit white light; but, if they
be extremely thin, both the reflected and transmitted light is coloured. The
vivid hues on soap-bubbles, the iridescent colours produced by heat on
polished steel and copper, the fringes of colour between the laminæ of
Iceland spar and sulphate of lime, all consist of a succession of hues
disposed in the same order, totally independent of the colour of the
substance, and determined solely by its greater or less thickness—a
circumstance which affords the means of ascertaining the length of the
waves of each coloured ray, and the frequency of the vibrations of the
particles producing them. If a plate of glass be laid upon a lens of almost
imperceptible curvature, before an open window, when they are pressed
together a black spot will be seen in the point of contact, surrounded by
seven rings of vivid colours, all differing from one another (N. 199). In the

first ring, estimated from the black spot, the colours succeed each other in
the following order:—black, very faint blue, brilliant white, yellow, orange,
and red. They are quite different in the other rings, and in the seventh the
only colours are pale bluish green and very pale pink. That these rings are
formed between the two surfaces in apparent contact may be proved by
laying a prism on the lens instead of the plate of glass, and viewing the
rings through the inclined side of it that is next to the eye, which
arrangement prevents the light reflected from the upper surface mixing with
that from the surfaces in contact, so that the intervals between the rings
appear perfectly black—one of the strongest circumstances in favour of the
undulatory theory; for, although the phenomena of the rings can be
explained by either hypothesis, there is this material difference, that,
according to the undulatory theory, the intervals between the rings ought to
be absolutely black, which is confirmed by experiment; whereas, by the
doctrine of emanation, they ought to be half illuminated, which is not found
to be the case. M. Fresnel, whose opinion is of the first authority, thought
this test conclusive. It may therefore be concluded that the rings arise
entirely from the interference of the rays: the light reflected from each of
the surfaces in apparent contact reaches the eye by paths of different
lengths, and produces coloured and dark rings alternately, according as the
reflected waves coincide or destroy one another. The breadths of the rings
are unequal; they decrease in width, and the colours become more crowded,
as they recede from the centre. Coloured rings are also produced by
transmitting light through the same apparatus; but the colours are less vivid,
and are complementary to those reflected, consequently the central spot is
white.
The size of the rings increases with the obliquity of the incident light, the
same colour requiring a greater thickness or space between the glasses to
produce it than when the light falls perpendicularly upon them. Now, if the
apparatus be placed in homogeneous instead of white light, the rings will all
be of the same colour with that of the light employed, that is to say, if the
light be red, the rings will be red, divided by black intervals. The size of the
rings varies with the colour of the light. They are largest in red, and
decrease in magnitude with the succeeding prismatic colours, being
smallest in violet light.
Since one of the glasses is plane and the other spherical, it is evident that
from the point of contact the space between them gradually increases in

thickness all round, so that a certain thickness of air corresponds to each
colour, which in the undulatory system measures the length of the wave
producing it (N. 200). By actual measurement Sir Isaac Newton found that
the squares of the diameters of the brightest part of each ring are as the odd
numbers, 1, 3, 5, 7, &c.; and that the squares of the diameters of the darkest
parts are as the even numbers, 0, 2, 4, 6, &c. Consequently, the intervals
between the glasses at these points are in the same proportion. If, then, the
thickness of the air corresponding to any one colour could be found, its
thickness for all the others would be known. Now, as Sir Isaac Newton
knew the radius of curvature of the lens, and the actual breadth of the rings
in parts of an inch, it was easy to compute that the thickness of air at the
darkest part of the first ring is the 1⁄89000 part of an inch, whence all the
others have been deduced. As these intervals determine the length of the
waves on the undulatory hypothesis, it appears that the length of a wave of
the extreme red of the solar spectrum is equal to the 0·0000266th part of an
inch; that the length of a wave of the extreme violet is equal to the
0·0000167th part of an inch; and, as the time of a vibration of a particle of
ether producing any particular colour is directly as the length of a wave of
that colour, and inversely as the velocity of light, it follows that the
molecules of ether producing the extreme red of the solar spectrum perform
458 millions of millions of vibrations in a second; and that those producing
the extreme violet accomplish 727 millions of millions of vibrations in the
same time. The lengths of the waves of the intermediate colours, and the
number of their vibrations, being intermediate between these two, white
light, which consists of all the colours, is consequently a mixture of waves
of all lengths between the limits of the extreme red and violet. The
determination of these minute portions of time and space, both of which
have a real existence, being the actual results of measurement, do as much
honour to the genius of Newton as that of the law of gravitation.
The number of advancing waves of light in an inch is known to be from
37,600 to 59,880, and the number of lateral vibrations is from 458 to 727
billions in a second, but the extent of these lateral vibrations of the particles
of the ethereal medium is not known, though both their extent and velocity
are probably very small compared with the length of the advancing waves
and the velocity of propagation. Colour is identified with the number of
vibrations; but whether reflection, refraction, absorption, &c., have any
relations to the lateral vibrations, or whether they are dependent in part

upon some physical action of the ethereal medium unknown and
unsuspected, are points as yet undetermined. To ascertain these
circumstances, Dr. Faraday instituted a series of the most refined
experiments upon the relation of the minute particles of metals to the
vibrations of light.
Gold acts powerfully on light, and possesses a real transparency,
transmitting green rays when very thin; and being capable of extreme
division by solvents without losing its metallic character, its particles
transmit rays of various colours according to their size; those that transmit
the rose-colour in Bohemian glass are of inconceivable minuteness. The
progressive waves of the ether are so long compared with the dimensions of
the molecules to which gold can be reduced, that it seemed probable to Dr.
Faraday when the latter were placed in a sunbeam that some effective
relation might be discovered between them and the smaller vibrations of the
ethereal medium; in which case, if reflection, refraction, &c., depended
upon such relations, there was reason to expect that these functions would
change sensibly by the substitution of different sized particles of the gold
for one another. At one time Dr. Faraday hoped he had changed one colour
into another by means of gold, which would have been equivalent to a
change in the number of vibrations; but although he has not yet confirmed
that result, his researches are of the greatest interest.[9]
The phenomenon of the coloured rings takes place in vacuo as well as in
air, which proves that it is the distance between the lenses alone, and not the
air, which produces the colours. However, if water or oil be put between
them, the rings contract, but no other change ensues; and Newton found that
the thickness of different media at which a given tint is seen is in the
inverse ratio of their refractive indices, so that the thickness of laminæ
which could not otherwise be measured may be known by their colour; and,
as the position of the colours in the rings is invariable, they form a fixed
standard of comparison, well known as Newton’s scale of colours; each tint
being estimated according to the ring to which it belongs from the central
spot inclusively. Not only the periodical colours which have been described,
but the colours seen in thick plates of transparent substances, the variable
hues of feathers, of insects’ wings, mother-of-pearl, and of striated
substances, all depend upon the same principle. To these may be added the
coloured fringes surrounding the shadows of all bodies held in an extremely

small beam of light, and the coloured rings surrounding the small beam
itself when received on a screen.
When a very slender sunbeam, passing through a small pin-hole into a
dark room, is received on a white screen, or plate of ground-glass, at the
distance of a little more than six feet, the spot of light on the screen is larger
than the pin-hole: and, instead of being bounded by shadow, it is
surrounded by a series of coloured rings separated by obscure intervals. The
rings are more distinct in proportion to the smallness of the beam (N. 201).
When the light is white there are seven rings, which dilate or contract with
the distance of the screen from the hole. As the distance of the screen
diminishes, the white central spot contracts to a point and vanishes; and, on
approaching still nearer, the rings gradually close in upon it, so that the
centre assumes successively the most intense and vivid hues. When the light
is homogeneous—red, for example—the rings are alternately red and black,
and more numerous; and their breadth varies with the colour, being broadest
in red light and narrowest in violet. The tints of the coloured fringes from
white light, and their obliteration after the seventh ring, arise from the
superposition of the different sets of fringes of all the coloured rays. The
shadows of objects are also bordered by coloured fringes when held in this
slender beam of light. If the edge of a knife or hair, for example, be held in
it, the rays, instead of proceeding in straight lines past its edge, are bent
when quite close to it, and proceed from thence to the screen in curved lines
called hyperbolas; so that the shadow of the object is enlarged, and, instead
of being at once bounded by light, is surrounded or edged with coloured
fringes alternating with black bands, which are more distinct the smaller the
pin-hole (N. 202). The fringes are altogether independent of the form or
density of the object, being the same when it is round or pointed, when of
glass or platinum. When the rays which form the fringes arrive at the
screen, they are of different lengths, in consequence of the curved path they
follow after passing the edge of the object. The waves are therefore in
different phases or states of vibration, and either conspire to form coloured
fringes or destroy one another in the obscure intervals. The coloured fringes
bordering the shadows of objects were first described by Grimaldi in 1665;
but, besides these, he noticed that there are others within the shadows of
slender bodies exposed to a small sunbeam, a phenomenon which has
already been mentioned to have afforded Dr. Young the means of proving,

beyond all controversy, that coloured rings are produced by the interference
of light.
It may be concluded that material substances derive their colours from
two different causes: some from the law of interference, such as iridescent
metals, peacocks’ feathers, &c.; others from the unequal absorption of the
rays of white light, such as vermilion, ultramarine, blue, or green cloth,
flowers, and the greater number of coloured bodies. The latter phenomena
have been considered extremely difficult to reconcile with the undulatory
theory of light, and much discussion has arisen as to what becomes of the
absorbed rays. But that embarrassing question has been ably answered by
Sir John Herschel in a most profound paper on the Absorption of Light by
coloured Media, and cannot be better given than in his own words. It must,
however, be premised, that, as all transparent bodies are traversed by light,
they are presumed to be permeable to the ether. He says,—“Now, as regards
only the general fact of the obstruction and ultimate extinction of light in its
passage through gross media, if we compare the corpuscular and undulatory
theories, we shall find that the former appeals to our ignorance, the latter to
our knowledge, for its explanation of the absorptive phenomena. In
attempting to explain the extinction of light on the corpuscular doctrine, we
have to account for the light so extinguished as a material body, which we
must not suppose annihilated. It may, however, be transformed; and among
the imponderable agents, heat, electricity, &c., it may be that we are to
search for the light which has become thus comparatively stagnant. The
heating power of the solar rays gives a primâ facie plausibility to the idea of
the transformation of light into heat by absorption. But, when we come to
examine the matter more nearly, we find it encumbered on all sides with
difficulties. How is it, for instance, that the most luminous rays are not the
most calorific, but that, on the contrary, the calorific energy accompanies, in
its greatest intensity, rays which possess comparatively feeble illuminating
powers? These and other questions of a similar nature may perhaps admit of
answer in a more advanced state of our knowledge; but at present there is
none obvious. It is not without reason, therefore, that the question, ‘What
becomes of light?’ which appears to have been agitated among the
photologists of the last century, has been regarded as one of considerable
importance as well as obscurity by the corpuscular philosophers. On the
other hand, the answer to this question, afforded by the undulatory theory of
light, is simple and distinct. The question, ‘What becomes of light?’ merges

in the more general one, ‘What becomes of motion?’ And the answer, on
dynamical principles, is, that it continues for ever. No motion is, strictly
speaking, annihilated; but it may be divided, and the divided parts made to
oppose and in effect destroy one another. A body struck, however perfectly
elastic, vibrates for a time, and then appears to sink into its original repose.
But this apparent rest (even abstracting from the inquiry that part of the
motion which may be conveyed away by the ambient air) is nothing else
than a state of subdivided and mutually destroying motion, in which every
molecule continues to be agitated by an indefinite multitude of internally
reflected waves, propagated through it in every possible direction, from
every point in its surface on which they successively impinge. The
superposition of such waves will, it is easily seen, at length operate their
mutual destruction, which will be the more complete the more irregular the
figure of the body, and the greater the number of internal reflections.” Thus
Sir John Herschel, by referring the absorption of light to the subdivision and
mutual destruction of the vibrations of ether in the interior of bodies, brings
another class of phenomena under the laws of the undulatory theory.
According to Mr. Rankin’s hypothesis of Molecular Vortices[10] the
absorption of light and radiant heat consists in the transference of motion
from the molecules to their atmospheres, and conversely the emission of
light and radiant heat is the transmission of motion from the atmospheres to
the molecules. The great velocity of light and heat is a natural consequence
of this hypothesis, according to which the vibratory masses must be
extremely small compared with the forces exerted by them.
The ethereal medium pervading space is supposed to penetrate all
material substances, occupying the interstices between their molecules; but
in the interior of refracting media it exists in a state of less elasticity
compared with its density in vacuo; and, the more refractive the medium,
the less the elasticity of the ether within it. Hence the waves of light are
transmitted with less velocity in such media as glass and water than in the
external ether. As soon as a ray of light reaches the surface of a diaphanous
reflecting substance, for example a plate of glass, it communicates its
undulations to the ether next in contact with the surface, which thus
becomes a new centre of motion, and two hemispherical waves are
propagated from each point of this surface; one of which proceeds forward
into the interior of the glass, with a less velocity than the incident waves;
and the other is transmitted back into the air, with a velocity equal to that

with which it came (N. 203). Thus, when refracted, the light moves with a
different velocity without and within the glass; when reflected, the ray
comes and goes with the same velocity. The particles of ether without the
glass, which communicate their motions to the particles of the dense and
less elastic ether within it, are analogous to small elastic balls striking large
ones; for some of the motion will be communicated to the large balls, and
the small ones will be reflected. The first would cause the refracted wave,
and the last the reflected. Conversely, when the light passes from glass to
air, the action is similar to large balls striking small ones. The small balls
receive a motion which would cause the refracted ray, and the part of the
motion retained by the large ones would occasion the reflected wave; so
that, when light passes through a plate of glass or of any other medium
differing in density from the air, there is a reflection at both surfaces; but
this difference exists between the two reflections, that one is caused by a
vibration in the same direction with that of the incident ray, and the other by
a vibration in the opposite direction.
A single wave of air or ether would not produce the sensation of sound or
light. In order to excite vision, the vibrations of the molecules of ether must
be regular, periodical, and very often repeated: and, as the ear continues to
be agitated for a short time after the impulse by which alone a sound
becomes continuous, so also the fibres of the retina, according to M.
d’Arcet, continue to vibrate for about the eighth part of a second after the
exciting cause has ceased. The interval of time during which the impression
lasts is longer for the blue than for red or white light: it must not be less
than 0ʺ·34. Every one must have observed, when a strong impression is
made by a bright light, that an object remains visible for a short time after
shutting the eyes, which is supposed to be in consequence of the continued
vibrations of the fibres of the retina. Occasionally the retina becomes
insensible to feebly illuminated objects when continuously presented. If the
eye be turned aside for a moment, the object becomes again visible. It is
probably on this account that the owl makes so peculiar a motion with its
head when looking at objects in the twilight. It is quite possible that many
vibrations may be excited in the ethereal medium incapable of producing
undulations in the fibres of the human retina, which yet have a powerful
effect on those of other animals or of insects. Such may receive luminous
impressions of which we are totally unconscious, and at the same time they

may be insensible to the light and colours which affect our eyes, their
perceptions beginning where ours end.

SECTION XXI.

Polarization of Light—Defined—Polarization by Refraction—Properties of
the Tourmaline—Double Refraction—All doubly Refracted Light is
Polarized—Properties of Iceland Spar—Tourmaline absorbs one of the
two Refracted Rays—Undulations of Natural Light—Undulations of
Polarized Light—The Optic Axes of Crystals—M. Fresnel’s Discoveries
on the Rays passing along the Optic Axis—Polarization by Reflection.

In giving a sketch of the constitution of light, it is impossible to omit the
extraordinary property of its polarization, “the phenomena of which,” Sir
John Herschel says, “are so singular and various, that to one who has only
studied the common branches of physical optics it is like entering into a
new world, so splendid as to render it one of the most delightful branches of
experimental inquiry, and so fertile in the views it lays open of the
constitution of natural bodies, and the minuter mechanism of the universe,
as to place it in the very first rank of the physico-mathematical sciences,
which it maintains by the rigorous application of geometrical reasoning its
nature admits and requires.”
Light is said to be polarized, which, by being once reflected or refracted,
is rendered incapable of being again reflected or refracted at certain angles.
In general, when a ray of light is reflected from a pane of plate-glass, or any
other substance, it may be reflected a second time from another surface, and
it will also pass freely through transparent bodies. But, if a ray of light be
reflected from a pane of plate-glass at an angle of 57°, it is rendered totally
incapable of reflection at the surface of another pane of glass in certain
definite positions, but it will be completely reflected by the second pane in
other positions. It likewise loses the property of penetrating transparent
bodies in particular positions, whilst it is freely transmitted by them in

others. Light, so modified as to be incapable of reflection and transmission
in certain directions, is said to be polarized.
Light may be polarized by reflection from any polished surface, and the
same property is also imparted by refraction. It is proposed to explain these
methods of polarizing light, to give a short account of its most remarkable
properties, and to endeavour to describe a few of the splendid phenomena it
exhibits.
If a brown tourmaline, which is a mineral generally crystallized in the
form of a long prism, be cut longitudinally, that is, parallel to the axis of the
prism, into plates about the thirtieth of an inch in thickness, and the surfaces
polished, luminous objects may be seen through them, as through plates of
coloured glass. The axis of each plate is in its longitudinal section parallel
to the axis of the prism whence it was cut (N. 204). If one of these plates be
held perpendicularly between the eye and a candle, and turned slowly round
in its own plane, no change will take place in the image of the candle. But if
the plate be held in a fixed position, with its axis or longitudinal section
vertical, when a second plate of tourmaline is interposed between it and the
eye, parallel to the first, and turned slowly round in its own plane, a
remarkable change will be found to have taken place in the nature of the
light. For the image of the candle will vanish and appear alternately at every
quarter revolution of the plate, varying through all degrees of brightness
down to total or almost total evanescence, and then increasing again by the
same degrees as it had before decreased. These changes depend upon the
relative positions of the plates. When the longitudinal sections of the two
plates are parallel, the brightness of the image is at its maximum; and, when
the axes of the sections cross at right angles, the image of the candle
vanishes. Thus the light, in passing through the first plate of tourmaline, has
acquired a property totally different from the direct light of the candle. The
direct light would have penetrated the second plate equally well in all
directions, whereas the refracted ray will only pass through it in particular
positions, and is altogether incapable of penetrating it in others. The
refracted ray is polarized in its passage through the first tourmaline, and
experience shows that it never loses that property, unless when acted upon
by a new substance. Thus, one of the properties of polarized light is the
incapability of passing through a plate of tourmaline perpendicular to it, in
certain positions, and its ready transmission in other positions at right
angles to the former.

Many other substances have the property of polarizing light. If a ray of
light falls upon a transparent medium, which has the same temperature,
density, and structure throughout every part, as fluids, gases, glass, &c., and
a few regularly crystallized minerals, it is refracted into a single pencil of
light by the laws of ordinary refraction, according to which the ray, passing
through the refracting surface from the object to the eye, never quits a plane
perpendicular to that surface. Almost all other bodies, such as the greater
number of crystallized minerals, animal and vegetable substances, gums,
resins, jellies, and all solid bodies having unequal tensions, whether from
unequal temperature or pressure, possess the property of doubling the image
or appearance of an object seen through them in certain directions; because
a ray of natural light falling upon them is refracted into two pencils which
move with different velocities, and are more or less separated, according to
the nature of the body and the direction of the incident ray. Whenever a ray
of natural light is thus divided into two pencils in its passage through a
substance, both of the transmitted rays are polarized. Iceland spar, a
carbonate of lime, which by its natural cleavage may be split into the form
of a rhombohedron, possesses the property of double refraction in an
eminent degree, as may be seen by pasting a piece of paper, with a large
pin-hole in it, on the side of the spar farthest from the eye. The hole will
appear double when held to the light (N. 205). One of these pencils is
refracted according to the same law as in glass or water, never quitting the
plane perpendicular to the refracting surface, and is therefore called the
ordinary ray. But the other does quit the plane, being refracted according to
a different and much more complicated law, and on that account is called
the extraordinary ray. For the same reason one image is called the ordinary,
and the other the extraordinary image. When the spar is turned round in the
same plane, the extraordinary image of the hole revolves about the ordinary
image, which remains fixed, both being equally bright. But if the spar be
kept in one position, and viewed through a plate of tourmaline, it will be
found that, as the tourmaline revolves, the images vary in their relative
brightness—one increases in intensity till it arrives at a maximum, at the
same time that the other diminishes till it vanishes, and so on alternately at
each quarter revolution, proving both rays to be polarized. For in one
position the tourmaline transmits the ordinary ray, and reflects the
extraordinary; and, after revolving 90°, the extraordinary ray is transmitted,
and the ordinary ray is reflected. Thus another property of polarized light is,

that it cannot be divided into two equal pencils by double refraction, in
positions of the doubly refracting bodies in which a ray of common light
would be so divided.
Were tourmaline like other doubly refracting bodies, each of the
transmitted rays would be double; but that mineral, when of a certain
thickness, after separating the light into two polarized pencils, absorbs that
which undergoes ordinary refraction, and consequently shows only one
image of an object. On this account tourmaline is peculiarly fitted for
analyzing polarized light, which shows nothing remarkable till viewed
through it or something equivalent.
The pencils of light, on leaving a double refracting substance, are
parallel; and it is clear, from the preceding experiments, that they are
polarized in planes at right angles to each other (N. 206). But that will be
better understood by considering the change produced in common light by
the action of the polarizing body. It has been shown that the undulations of
ether, which produce the sensation of common light, are performed in every
possible plane, at right angles to the direction in which the ray is moving.
But the case is very different after the ray has passed through a doubly
refracting substance, like Iceland spar. The light then proceeds in two
parallel pencils, whose undulations are still indeed transverse to the
direction of the rays, but they are accomplished in planes at right angles to
one another, analogous to two parallel stretched cords, one of which
performs its undulations only in a horizontal plane, and the other in a
vertical or upright plane (N. 206). Thus the polarizing action of Iceland spar
and of all doubly refracting substances is to separate a ray of common light,
whose waves or undulations are in every plane, into two parallel rays,
whose waves or undulations lie in planes at right angles to each other. By a
simple mechanical law each vibratory motion of the first is resolved into
two vibratory motions at right angles to one another. The ray of common
light may be assimilated to a round rod, whereas the two polarized rays are
like two parallel long flat rulers, one of which is laid horizontally on its
broad surface, and the other horizontally on its edge. The alternate
transmission and obstruction of one of these flattened beams by the
tourmaline is similar to the facility with which a card may be passed
between the bars of a grating or wires of a cage, if presented edgeways, and
the impossibility of its passing in a transverse direction.

Although it generally happens that a ray of light, in passing through
Iceland spar, is separated into two polarized rays, yet there is one direction
along which it is refracted in one ray only, and that according to the
ordinary law. This direction is called the optic axis (N. 207). Many crystals
and other substances have two optic axes, inclined to each other, along
which a ray of light is transmitted in one pencil by the law of ordinary
refraction. The extraordinary ray is sometimes refracted towards the optic
axis, as in quartz, zircon, ice, &c., which are therefore said to be positive
crystals; but when it is bent from the optic axis, as in Iceland spar,
tourmaline, emerald, beryl, &c., the crystals are negative, which is the most
numerous class. The ordinary ray moves with uniform velocity within a
doubly refracting substance, but the velocity of the extraordinary ray varies
with the position of the ray relatively to the optic axis, being a maximum
when its motion within the crystal is at right angles to the optic axis, and a
minimum when parallel to it. Between these extremes its velocity varies
according to a determinate law.
It had been inferred, from the action of Iceland spar on light, that in all
doubly refracting substances one only of two rays is turned aside from the
plane of ordinary refraction, while the other follows the ordinary law; and
the great difficulty of observing the phenomena tended to confirm that
opinion. M. Fresnel, however, proved by a most profound mathematical
inquiry, à priori, that the extraordinary ray must be wanting in glass and
other uncrystallized substances, and that it must necessarily exist in
carbonate of lime, quartz, and other bodies having one optic axis, but that in
a numerous class of substances, which possess two optic axes, both rays
must undergo extraordinary refraction, and consequently that both must
deviate from their original plane; and these results have been perfectly
confirmed by subsequent experiments. This theory of refraction, which for
generalization is perhaps only inferior to the law of gravitation, has enrolled
the name of Fresnel among those which pass not away, and makes his early
loss a subject of deep regret to all who take an interest in the higher paths of
scientific research.
When a beam of common light is partly reflected at, and partly
transmitted through a transparent surface, the reflected and refracted pencils
contain equal quantities of polarized light, and their planes of polarization
are at right angles to one another: hence, a pile of panes of glass will give a
polarized beam by refraction. For, if a ray of common light pass through

them, part of it will be polarized by the first plate, the second plate will
polarize a part of what passes through it, and the rest will do the same in
succession, till the whole beam is polarized, except what is lost by
reflection at the different surfaces, or by absorption. This beam is polarized
in a plane at right angles to the plane of reflection, that is, at right angles to
the plane passing through the incident and reflected ray (N. 208).
By far the most convenient way of polarizing light is by reflection. A
plane of plate-glass laid upon a piece of black cloth, on a table at an open
window, will appear of a uniform brightness from the reflection of the sky
or clouds. But if it be viewed through a plate of tourmaline, having its axis
vertical, instead of being illuminated as before, it will be obscured by a
large cloudy spot, having its centre quite dark, which will readily be found
by elevating or depressing the eye, and will only be visible when the angle
of incidence is 57°, that is, when the line from the eye to the centre of the
black spot makes an angle of 33° with the surface of the reflector (N. 209).
When the tourmaline is turned round in its own plane, the dark cloud will
diminish, and entirely vanish when the axis of the tourmaline is horizontal,
and then every part of the surface of the glass will be equally illuminated.
As the tourmaline revolves, the cloudy spot will appear and vanish
alternately at every quarter revolution. Thus, when a ray of light is incident
on a pane of plate-glass at an angle of 57°, the reflected ray is rendered
incapable of penetrating a plate of tourmaline whose axis is in the plane of
incidence. Consequently it has acquired the same character as if it had been
polarized by transmission through a plate of tourmaline, with its axis at
right angles to the plane of reflection. It is found by experience that this
polarized ray is incapable of a second reflection at certain angles and in
certain positions of the incident plane. For if another pane of plate-glass,
having one surface blackened, be so placed as to make an angle of 33° with
the reflected ray, the image of the first pane will be reflected in its surface,
and will be alternately illuminated and obscured at every quarter revolution
of the blackened pane, according as the plane of reflection is parallel or
perpendicular to the plane of polarization. Since this happens by whatever
means the light has been polarized, it evinces another general property of
polarized light, which is, that it is incapable of reflection in a plane at right
angles to the plane of polarization.
All reflecting surfaces are capable of polarizing light, but the angle of
incidence at which it is completely polarized is different in each substance

(N. 210). It appears that the angle for plate-glass is 57°; in crown-glass it is
56° 55ʹ, and no ray will be completely polarized by water unless the angle
of incidence be 53° 11ʹ. The angles at which different substances polarize
light are determined by a very simple and elegant law, discovered by Sir
David Brewster, “That the tangent of the polarizing angle for any medium is
equal to the sine of the angle of incidence divided by the sine of the angle
of refraction of that medium.” Whence also the refractive power even of an
opaque body is known when its polarizing angle has been determined.
If a ray, polarized by refraction or by reflection from any substance not
metallic, be viewed through a piece of Iceland spar, each image will
alternately vanish and reappear at every quarter revolution of the spar,
whether it revolves from right to left or from left to right; which shows that
the properties of the polarized ray are symmetrical on each side of the plane
of polarization.
Although there be only one angle in each substance at which light is
completely polarized by one reflection, yet it may be polarized at any angle
of incidence by a sufficient number of reflections. For, if a ray falls upon
the upper surface of a pile of plates of glass at an angle greater or less than a
polarizing angle, a part only of the reflected ray will be polarized, but a part
of what is transmitted will be polarized by reflection at the surface of the
second plate, part at the third, and so on till the whole is polarized. This is
the best apparatus; but one plate of glass having its inferior surface
blackened, or even a polished table, will answer the purpose.

SECTION XXII.

Phenomena exhibited by the Passage of Polarized Light through Mica and
Sulphate of Lime—The Coloured Images produced by Polarized Light
passing through Crystals having one and two Optic Axes—Circular
Polarization—Elliptical Polarization—Discoveries of MM. Biot, Fresnel,
and Professor Airy—Coloured Images produced by the Interference of
Polarized Rays—Fluorescence.

Such is the nature of polarized light and of the laws it follows. But it is
hardly possible to convey an idea of the splendour of the phenomena it
exhibits under circumstances which an attempt will now be made to
describe.
If light polarized by reflection from a pane of glass be viewed through a
plate of tourmaline, with its longitudinal section vertical, an obscure cloud,
with its centre totally dark, will be seen on the glass. Now, let a plate of
mica, uniformly about the thirtieth of an inch in thickness, be interposed
between the tourmaline and the glass; the dark spot will instantly vanish,
and, instead of it, a succession of the most gorgeous colours will appear,
varying with every inclination of the mica, from the richest reds, to the most
vivid greens, blues, and purples (N. 211). That they may be seen in
perfection, the mica must revolve at right angles to its own plane. When the
mica is turned round in a plane perpendicular to the polarized ray, it will be
found that there are two lines in it where the colours entirely vanish. These
are the optic axes of the mica, which is a doubly refracting substance, with
two optic axes, along which light is refracted in one pencil.
No colours are visible in the mica, whatever its position may be with
regard to the polarized light, without the aid of the tourmaline, which
separates the transmitted ray into two pencils of coloured light
complementary to one another, that is, which taken together would make

white light. One of these it absorbs, and transmits the other; it is therefore
called the analyzing plate. The truth of this will appear more readily if a
film of sulphate of lime, between the twentieth and sixtieth of an inch thick,
be used instead of the mica. When the film is of uniform thickness, only one
colour will be seen when it is placed between the analyzing plate and the
reflecting glass; as, for example, red. But, when the tourmaline revolves,
the red will vanish by degrees till the film is colourless; then it will assume
a green hue, which will increase and arrive at its maximum when the
tourmaline has turned through ninety degrees; after that, the green will
vanish and the red will reappear, alternating at each quadrant. Thus the
tourmaline separates the light which has passed through the film into a red
and a green pencil; in one position it absorbs the green and lets the red pass,
and in another it absorbs the red and transmits the green. This is proved by
analyzing the ray with Iceland spar instead of tourmaline; for, since the spar
does not absorb the light, two images of the sulphate of lime will be seen,
one red and the other green; and these exchange colours every quarter
revolution of the spar, the red becoming green, and the green red; and,
where the images overlap, the colour is white, proving the red and green to
be complementary to each other. The tint depends on the thickness of the
film. Films of sulphate of lime, the 0·00124 and 0·01818 of an inch
respectively, give white light in whatever position they may be held,
provided they be perpendicular to the polarized ray; but films of
intermediate thickness will give all colours. Consequently, a wedge of
sulphate of lime, varying in thickness between the 0·00124 and the 0·01818
of an inch, will appear to be striped with all colours when polarized light is
transmitted through it. A change in the inclination of the film, whether of
mica or sulphate of lime, is evidently equivalent to a variation in thickness.
When a plate of mica, held as close to the eye as possible, at such an
inclination as to transmit the polarized ray along one of its optic axes, is
viewed through the tourmaline with its axis vertical, a most splendid
appearance is presented. The cloudy spot in the direction of the optic axis is
seen surrounded by a set of vividly coloured rings of an oval form, divided
into two unequal parts by a black curved band passing through the cloudy
spot about which the rings are formed. The other optic axis of the mica
exhibits a similar image (N. 212).
When the two optic axes of a crystal make a small angle with one
another, as in nitre, the two sets of rings touch externally; and, if the plate of

nitre be turned round in its own plane, the black transverse bands undergo a
variety of changes, till, at last, the whole richly coloured image assumes the
form of the figure 8, traversed by a black cross (N. 213). Substances with
one optic axis have but one set of coloured circular rings, with a broad
black cross passing through its centre, dividing the rings into four equal
parts. When the analyzing plate revolves, this figure recurs at every quarter
revolution; but in the intermediate positions it assumes the complementary
colours, the black cross becoming white.
It is in vain to attempt to describe the beautiful phenomena exhibited by
innumerable bodies which undergo periodic changes in form and colour
when the analyzing plate revolves, but not one of them shows a trace of
colour without the aid of tourmaline, or something equivalent, to analyze
the light, and as it were to call these beautiful phantoms into existence.
Tourmaline has the disadvantage of being itself a coloured substance; but
that inconvenience may be obviated by employing a reflecting surface as an
analyzing plate. When polarized light is reflected by a plate of glass at the
polarizing angle, it will be separated into two coloured pencils; and, when
the analyzing plate is turned round in its own plane, it will alternately
reflect each ray at every quarter revolution, so that all the phenomena that
have been described will be seen by reflection on its surface.
Coloured rings are produced by analyzing polarized light transmitted
through glass melted and suddenly or unequally cooled; also through thin
plates of glass bent with the hand, jelly indurated or compressed, &c. &c. In
short, all the phenomena of coloured rings may be produced, either
permanently or transiently, in a variety of substances, by heat and cold,
rapid cooling, compression, dilatation, and induration; and so little
apparatus is necessary for performing the experiments, that, as Sir John
Herschel says, a piece of window glass or a polished table to polarize the
light, a sheet of clear ice to produce the rings, and a broken fragment of
plate-glass placed near the eye to analyze the light, are alone requisite to
produce one of the most splendid of optical exhibitions.
Pressure produces remarkable changes in the optical properties of
crystals. Compression, perpendicular to the axis, transforms a crystal with
one optic axis into one with two. A slice of quartz and one of beryl, both cut
perpendicularly to their axis, were compressed thus by MM. Moignot and
Soleil. They found that the single system in the quartz, which is a positive
crystal, was doubled in the direction of the compression, while in the beryl,

which is a negative crystal, the duplication was perpendicular to the
compression. In the quartz the axis of the double system coincided with the
line of pressure, but in the tourmaline, which is a negative crystal, the line
which joins the centres of the rings was perpendicular to the pressure.
If a positive crystal be compressed in the direction of its axis the tint of
the rings descends, and that of a negative crystal rises. But if the crystals be
dilated in the direction of their optic axis, the tints in positive crystals rise,
and negative descend.
It has been observed, that when a ray of light, polarized by reflection
from any surface not metallic, is analyzed by a doubly refracting substance,
it exhibits properties which are symmetrical both to the right and left of the
plane of reflection, and the ray is then said to be polarized according to that
plane. This symmetry is not destroyed when the ray, before being analyzed,
traverses the optic axis of a crystal having but one optic axis, as evidently
appears from the circular forms of the coloured rings already described.
Regularly crystallized quartz, however, forms an exception. In it, even
though the rays should pass through the optic axis itself, where there is no
double refraction, the primitive symmetry of the ray is destroyed, and the
plane of primitive polarization deviates either to the right or left of the
observer, by an angle proportional to the thickness of the plate of quartz.
This angular motion, or true rotation of the plane of polarization, which is
called circular polarization, is clearly proved by the phenomena. The
coloured rings produced by all crystals having but one optic axis are
circular, and traversed by a black cross concentric with the rings; so that the
light entirely vanishes throughout the space enclosed by the interior ring,
because there is neither double refraction nor polarization along the optic
axis. But in the system of rings produced by a plate of quartz, whose
surfaces are perpendicular to the axis of the crystal, the part within the
interior ring, instead of being void of light, is occupied by a uniform tint of
red, green, or blue, according to the thickness of the plate (N. 214). Suppose
the plate of quartz to be 1⁄25 of an inch thick, which will give the red tint to
the space within the interior ring; when the analyzing plate is turned, in its
own plane through an angle of 171⁄2°, the red hue vanishes. If a plate of rock
crystal 2⁄25 of an inch thick be used, the analyzing plate must revolve
through 35° before the red tint vanishes, and so on, every additional 25th of
an inch in thickness requiring an additional rotation of 171⁄2°; whence it is

manifest that the plane of polarization revolves in the direction of a spiral
within the rock crystal. It is remarkable that, in some crystals of quartz, the
plane of polarization revolves from right to left, and in others from left to
right, although the crystals themselves differ apparently only by a very
slight, almost imperceptible, variety in form. In these phenomena the
rotation to the right is accomplished according to the same laws, and with
the same energy, as that to the left. But if two plates of quartz be interposed,
which possess different affections, the second plate undoes, either wholly or
partly, the rotatory motion which the first had produced, according as the
plates are of equal or unequal thickness. When the plates are of unequal
thickness, the deviation is in the direction of the strongest, and exactly the
same with that which a third plate would produce equal in thickness to the
difference of the two.
M. Biot has discovered the same properties in a variety of liquids. Oil of
turpentine, and an essential oil of laurel, cause the plane of polarization to
turn to the left, whereas the syrup of sugar-cane, and a solution of natural
camphor, by alcohol, turn it to the right. A compensation is effected by the
superposition or mixture of two liquids which possess these opposite
properties, provided no chemical action takes place. A remarkable
difference was also observed by M. Biot between the action of the particles
of the same substances when in a liquid or solid state. The syrup of grapes,
for example, turns the plane of polarization to the left as long as it remains
liquid; but, as soon as it acquires the solid form of sugar, it causes the plane
of polarization to revolve towards the right, a property which it retains even
when again dissolved. Instances occur also in which these circumstances
are reversed.
A ray of light passing through a liquid possessing the power of circular
polarization is not affected by mixing other fluids with the liquid—such as
water, ether, alcohol, &c.—which do not possess circular polarization
themselves, the angle of deviation remaining exactly the same as before the
mixture. Whence M. Biot infers that the action exercised by the liquids in
question does not depend upon their mass, but that it is a molecular action
exercised by the ultimate particles of matter, which depends solely upon the
individual constitution, and is entirely independent of the positions and
mutual distances of the particles with regard to each other. These important
discoveries show that circular polarization surpasses the power of chemical
analysis in giving certain and direct evidence of the similarity or difference

existing in the molecular constitution of bodies, as well as of the
permanency of that constitution, or of the fluctuations to which it may be
liable. For example, no chemical difference has been discovered between
syrup from the sugar-cane and syrup from grapes. Yet the first causes the
plane of polarization to revolve to the right, and the other to the left;
therefore some essential difference must exist in the nature of their ultimate
molecules. The same difference is to be traced between the juices of such
plants as give sugar similar to that from the cane, and those which give
sugar like that obtained from grapes.
If chlorate of soda be dissolved in water, the liquid has no circular
polarization; but if the solution be allowed to crystallize, some of the
crystals turn the light to the right and others to the left. Now, if all those of
one kind be gathered together and dissolved a second time, the liquid will
have no circular polarization; but if crystals be allowed to form, some will
turn the light to the right and others to the left, although only one kind was
dissolved.[11]
It is a fact established by M. Biot, that in circular polarization the laws of
rotation followed by the different simple rays of light are dissimilar in
different substances. Whence he infers that the deviation of the simple rays
from one another ought not to result from a special property of the luminous
principle only, but that the proper action of the molecules must also concur
in modifying the deviations of the simple rays differently in different
substances.
One of the many brilliant discoveries of M. Fresnel is the production of
circular and elliptical polarization by the internal reflection of light from
plate-glass. He has shown that, if light polarized by any of the usual
methods be twice reflected within a glass rhomb (N. 169) of a given form,
the vibrations of the ether that are perpendicular to the plane of incidence
will be retarded a quarter of a vibration, which causes the vibrating particles
to describe circles, and the succession of such vibrating particles throughout
the extent of a wave to form altogether a circular helix, or curve like a
corkscrew. However, that only happens when the plane of polarization is
inclined at an angle of 45° to the plane of incidence. When these two planes
form an angle either greater or less, the succession of vibrating particles
forms an elliptical helix, which curve may be represented by twisting a
thread in a spiral about an oval rod. These curves will turn to the right or
left, according to the position of the incident plane.

The motion of the ethereal medium in elliptical and circular polarization
may be represented by the analogy of a stretched cord; for, if the extremity
of such a cord be agitated at equal and regular intervals by a vibratory
motion entirely confined to one plane, the cord will be thrown into an
undulating curve lying wholly in that plane. If to this motion there be
superadded another similar and equal, but perpendicular to the first, the
cord will assume the form of an elliptical helix; its extremity will describe
an ellipse, and every molecule throughout its length will successively do the
same. But, if the second system of vibrations commence exactly a quarter
of an undulation later than the first, the cord will take the form of a circular
helix or corkscrew, the extremity will move uniformly in a circle, and every
molecule throughout the cord will do the same in succession. It appears,
therefore, that both circular and elliptical polarization may be produced by
the composition of the motions of two rays in which the particles of ether
vibrate in planes at right angles to one another.
Professor Airy, in a very profound and able paper published in the
Cambridge Transactions, has proved that all the different kinds of polarized
light are obtained from rock crystal. When polarized light is transmitted
through the axis of a crystal of quartz, in the emergent ray the particles of
ether move in a circular helix; and when it is transmitted obliquely so as to
form an angle with the axis of the prism, the particles of ether move in an
elliptical helix, the ellipticity increasing with the obliquity of the incident
ray; so that, when the incident ray falls perpendicularly to the axis, the
particles of ether move in a straight line. Thus quartz exhibits every variety
of elliptical polarization, even including the extreme cases where the
excentricity is zero, or equal to the greater axis of the ellipse (N. 215). In
many crystals the two rays are so little separated, that it is only from the
nature of the transmitted light that they are known to have the property of
double refraction. M. Fresnel discovered, by experiments on the properties
of light passing through the axis of quartz, that it consists of two superposed
rays, moving with different velocities; and Professor Airy has shown that in
these two rays the molecules of ether vibrate in similar ellipses at right
angles to each other, but in different directions; that their ellipticity varies
with the angle which the incident ray makes with the axis; and that, by the
composition of their motions, they produce all the phenomena of polarized
light observed in quartz.

It appears, from what has been said, that the molecules of ether always
perform their vibrations at right angles to the direction of the ray, but very
differently in the various kinds of light. In natural light the vibrations are
rectilinear, and in every plane. In ordinary polarized light they are
rectilinear, but confined to one plane; in circular polarization the vibrations
are circular; and in elliptical polarization the molecules vibrate in ellipses.
These vibrations are communicated from molecule to molecule, in straight
lines when they are rectilinear, in a circular helix when they are circular,
and in an oval or elliptical helix when elliptical.
Some fluids possess the property of circular polarization naturally, as oil
of turpentine, the essential oils of laurel and lemon, sugar of grapes, and
various liquids.
Elliptical polarization is produced by reflection from metallic surfaces.
Mr. Baden Powell discovered it also in the light reflected from China ink,
chromate of lead, plumbago, &c. Mr. Airy observed that the light reflected
from the diamond is elliptically polarized; and Mr. Jamin has shown that
this kind of polarization is generally produced by reflection from almost all
transparent bodies, whatever their refractive power may be, especially from
glass at angles very little different from the law of the tangents.
Water polarizes light circularly when between the points of maximum
density and solidification; hence it becomes crystalline.
The coloured images from polarized light arise from the interference of
the rays (N. 216). MM. Fresnel and Arago found that two rays of polarized
light interfere and produce coloured fringes if they be polarized in the same
plane, but that they do not interfere when polarized in different planes. In
all intermediate positions, fringes of intermediate brightness are produced.
The analogy of a stretched cord will show how this happens. Suppose the
cord to be moved backwards and forwards horizontally at equal intervals; it
will be thrown into an undulating curve lying all in one plane. If to this
motion there be superadded another similar and equal, commencing exactly
half an undulation later than the first, it is evident that the direct motion
every molecule will assume, in consequence of the first system of waves,
will at every instant be exactly neutralized by the retrograde motion it
would take in virtue of the second; and the cord itself will be quiescent in
consequence of the interference. But, if the second system of waves be in a
plane perpendicular to the first, the effect would only be to twist the rope,

so that no interference would take place. Rays polarized at right angles to
each other may subsequently be brought into the same plane without
acquiring the property of producing coloured fringes; but, if they belong to
a pencil the whole of which was originally polarized in the same plane, they
will interfere.
The manner in which the coloured images are formed may be conceived
by considering that, when polarized light passes through the optic axis of a
doubly refracting substance,—as mica, for example,—it is divided into two
pencils by the analyzing tourmaline; and, as one ray is absorbed, there can
be no interference. But, when polarized light passes through the mica in any
other direction, it is separated into two white rays, and these are again
divided into four pencils by the tourmaline, which absorbs two of them; and
the other two, being transmitted in the same plane with different velocities,
interfere and produce the coloured phenomena. If the analysis be made with
Iceland spar, the single ray passing through the optic axis of the mica will
be refracted into two rays, polarized in different planes, and no interference
will happen. But, when two rays are transmitted by the mica, they will be
separated into four by the spar, two of which will interfere to form one
image, and the other two, by their interference, will produce the
complementary colours of the other image when the spar has revolved
through 90°; because, in such positions of the spar as produce the coloured
images, only two rays are visible at a time, the other two being reflected.
When the analysis is accomplished by reflection, if two rays are transmitted
by the mica, they are polarized in planes at right angles to each other. And,
if the plane of reflection of either of these rays be at right angles to the
plane of polarization, only one of them will be reflected, and therefore no
interference can take place; but in all other positions of the analyzing plate
both rays will be reflected in the same plane, and consequently will produce
coloured rings by their interference.
It is evident that a great deal of the light we see must be polarized, since
most bodies which have the power of reflecting or refracting light also have
the power of polarizing it. The blue light of the sky is completely polarized
at an angle of 74° from the sun in a plane passing through his centre.
A constellation of talent almost unrivalled at any period in the history of
science has contributed to the theory of polarization, though the original
discovery of that property of light was accidental, and arose from an
occurrence which, like thousands of others, would have passed unnoticed

had it not happened to one of those rare minds capable of drawing the most
important inferences from circumstances apparently trifling. In 1808, while
M. Malus was accidentally viewing with a doubly-refracting prism a
brilliant sunset reflected from the windows of the Luxembourg Palace in
Paris, on turning the prism slowly round, he was surprised to see a very
great difference in the intensity of the two images, the most refracted
alternately changing from brightness to obscurity at each quadrant of
revolution. A phenomenon so unlooked for induced him to investigate its
cause, whence sprung one of the most elegant and refined branches of
physical optics.
Fluorescence, or the internal dispersion of light, though far from
possessing the beauty or extensive consequences of polarized light, is
scarcely less wonderful. A variety of substances, such as canary-glass, a
solution of sulphate of quinine, fluor-spar, and a great number of organic
substances, have the property of diminishing the refrangibility of light by
internal dispersion, consequently of increasing the length of the waves, and
lowering the colour in the prismatic scale; it is therefore called degraded
light, or fluorescence, because first discovered in fluor-spar.
If a piece of glass coloured by cobalt be fixed in a hole in a window-
shutter of a dark room, a slab of white porcelain placed near it will appear
blue; but if the slab be viewed through a yellow glass coloured by silver, it
will appear to be almost quite black, because the yellow glass absorbs all
the rays transmitted by the blue glass. If, however, a piece of canary-glass
be laid on the slab while it is dark, every part of the canary-glass will shine
as if it were self-luminous, and with so bright a light that anything written
on the slab that was invisible before may now be distinctly read. Such is the
singular phenomenon of internal dispersion, degraded light, or fluorescence.
The brightness is by no means due to phosphorescence, because the canary-
glass only shines when under the influence of the active or blue rays,
whereas phosphorescent bodies shine by their own light—the latter has
independent, the former dependent, emission; it is possible, however, that a
connexion may hereafter be traced between them.
It appears from the analytical investigation of this phenomenon that the
vibrations of the fluorescent substance are analogous to those of a sonorous
body, as a bell or musical cord, which give the fundamental note and its
harmonics. Now since there is a reciprocal action between the molecules of
matter and light, when the light of the sun is absorbed by a substance

capable of fluorescence, it puts the whole of its molecules into vibrations
the same as its own, analogous to the fundamental note, while at the same
time a certain number of molecules take more rapid vibrations exactly like
the harmonics. The latter form new centres of light throughout the
substance, which impart their vibrations to the ethereal medium around, and
constitute fluorescence or degraded light. For example, in the experiment
that has been described, the blue light imparted its own vibrations to all the
molecules of the canary-glass, and also more rapid vibrations to a certain
number of them. All of the blue rays were excluded by the yellow glass held
before the eye; but it was pervious to the rays emanating in more rapid
vibrations from the smaller number of molecules, which thus became really
new centres of light, different from the sun’s light, though owing to it; the
one celestial, the other terrestrial; and the latter vibrations being more rapid
than those of the blue light, their refrangibility was less, and therefore their
colour lower in the prismatic scale. Mr. Power computed from his formulæ,
that fluorescent light is produced by undulations which are a major or minor
third below the pitch of the general vibration of the medium—that is to say,
below the vibrations which the whole molecules of the body most readily
assume.
Professor Stokes, of Cambridge, who made the preceding experiment,
found that the chemical rays from a point in the solar spectrum produced, in
a solution of the sulphate of quinine, light of a sky-blue colour, which
emanates in all directions from the liquid, and that this blue fluorescent
light contains, when analysed, all the rays of the spectrum; hence he
inferred that the dispersive power or fluorescence had lowered the
refrangibility of the chemical rays, so as to make them visible: and Sir
David Brewster observes that the new spectrum, of all colours into which
they were transformed, must possess the extraordinary property of being a
luminous spectrum, either without chemical rays or full of them. The
dispersion in the quinine solution is greatest near the surface, but the blue
emanation proceeds from every part of the liquid; and Sir John Herschel,
who discovered the fluorescent property in this liquid, and gave it the name
of epipolic light, found that the remainder of the beam, when it issued from
the solution, though not apparently different from the incident white light, is
yet so much changed in passing through the liquid, that it is no longer
capable of producing fluorescence, though still capable of common

dispersion. The blue light from the solution of quinine, when examined,
consisted of rays extending over a great part of the spectrum.
By passing a sunbeam through a bluish kind of fluor-spar, Sir David
Brewster perceived that the blue colour is not superficial, as it appears to
be, but that some veins in the interior of the crystal disperse blue light,
others pink, and even white light; in short, he met with fluorescence in such
a variety of substances, that he concludes it may prevail more or less in the
greater number of solids and liquids.
Professor Draper, of New York, proved that the result is the same
whether the incident light be polarized or not, and that the dispersed or
degraded light is never polarized, but that it emanates in all directions, as if
the substance were self-luminous; he made experiments with light from all
parts of the solar spectrum, and with various substances, and always found
that the refrangibility of the incident ray was diminished by internal
dispersion, and that the colour was changed to suit the new refrangibility.
Professor Draper has also shown that the law of action and reaction prevails
in all the phenomena of the sunbeam, as in every other department of
nature; so that a beam cannot be reflected, refracted, much less absorbed,
without producing some change upon the recipient medium; and Mr. Power
proved analytically that the solar rays can exercise no action upon any
medium through which they are transmitted, without being accompanied by
a diminution of refraction. He says, “The new light emanating from the
fluorescent media is just like any other light of the same prismatic
composition. In its physical properties it retains no trace of its parentage; it
is of terrestrial origin, and its colour depends simply on its new
refrangibility, having nothing to do with that of the producing rays, nor to
the circumstance of their belonging to the visible or invisible part of the
spectrum.” These phenomena can only be explained by the undulatory
theory of light.

SECTION XXIII.

Objections to the Undulatory Theory, from a difference in the Action of
Sound and Light under the same circumstances, removed—The
Dispersion of Light according to the Undulatory Theory—Arago’s final
proof that the Undulatory Theory is the Law of Nature.

The numerous phenomena of periodical colours arising from the
interference of light, which do not admit of satisfactory explanation on any
other principle than the undulatory theory, are the strongest arguments in
favour of that hypothesis; and even cases which at one time seemed
unfavourable to that doctrine have proved upon investigation to proceed
from it alone. Such is the erroneous objection which has been made, in
consequence of a difference in the mode of action of light and sound, under
the same circumstances, in one particular instance. When a ray of light from
a luminous point, and a diverging sound, are both transmitted through a
very small hole into a dark room, the light goes straight forward and
illuminates a small spot on the opposite wall, leaving the rest in darkness;
whereas the sound on entering diverges in all directions, and is heard in
every part of the room. These phenomena, however, instead of being at
variance with the undulatory theory, are direct consequences of it, arising
from the very great difference between the magnitude of the undulations of
sound and those of light. The undulations of light are incomparably less
than the minute aperture, while those of sound are much greater. Therefore
when light, diverging from a luminous point, enters the hole, the rays round
its edges are oblique, and consequently of different lengths, while those in
the centre are direct, and nearly or altogether of the same lengths. So that
the small undulations between the centre and the edges are in different
phases, that is, in different states of undulation. Therefore the greater
number of them interfere, and by destroying one another produce darkness
all around the edges of the aperture; whereas the central rays, having the

same phases, combine, and produce a spot of bright light on a wall or
screen directly opposite the hole. The waves of air producing sound, on the
contrary, being very large compared with the hole, do not sensibly diverge
in passing through it, and are therefore all so nearly of the same length, and
consequently in the same phase or state of undulation, that none of them
interfere sufficiently to destroy one another. Hence all the particles of air in
the room are set into a state of vibration, so that the intensity of the sound is
very nearly everywhere the same. Strong as the preceding cases may be, the
following experiment, made by M. Arago, seems to be decisive in favour of
the undulatory doctrine. Suppose a plano-convex lens of very great radius
to be placed upon a plate of very highly polished metal. When a ray of
polarized light falls upon this apparatus at a very great angle of incidence,
Newton’s rings are seen at the point of contact. But as the polarizing angle
of glass differs from that of metal, when the light falls on the lens at the
polarizing angle of glass, the black spot and the system of rings vanish. For
although light in abundance continues to be reflected from the surface of
the metal, not a ray is reflected from the surface of the glass that is in
contact with it, consequently no interference can take place; which proves
beyond a doubt that Newton’s rings result from the interference of the light
reflected from both the surfaces apparently in contact (N. 199).
Notwithstanding the successful adaptation of the undulatory system to
phenomena, the dispersion of light for a long time offered a formidable
objection to that theory, which has been removed by Professor Powell of
Oxford.
A sunbeam falling on a prism, instead of being refracted to a single point
of white light, is separated into its component colours, which are dispersed
or scattered unequally over a considerable space, of which the portion
occupied by the red rays is the least, and that over which the violet rays are
dispersed is the greatest. Thus the rays of the coloured spectrum, whose
waves are of different lengths, have different degrees of refrangibility, and
consequently move with different velocities, either in the medium which
conveys the light from the sun, or in the refracting medium, or in both;
whereas rays of all colours come from the sun to the earth with the same
velocity. If, indeed, the velocities of the various rays were different in
space, the aberration of the fixed stars, which is inversely as the velocity,
would be different for different colours, and every star would appear as a
spectrum whose length would be parallel to the direction of the earth’s

motion, which is not found to agree with observation. Besides, there is no
such difference in the velocities of the long and short waves of air in the
analogous case of sound, since notes of the lowest and highest pitch are
heard in the order in which they are struck. In fact, when the sunbeam
passes from air into the prism, its velocity is diminished; and, as its
refraction, and consequently its dispersion, depend solely upon the
diminished velocity of the transmission of its waves, they ought to be the
same for waves of all lengths, unless a connexion exists between the length
of a wave and the velocity with which it is propagated. Now, this connexion
between the length of a wave of any colour, and its velocity or refrangibility
in a given medium, has been deduced by Professor Powell from M.
Cauchy’s investigations of the properties of light on a peculiar modification
of the undulatory hypothesis. Hence the refrangibility of the various
coloured rays, computed from this relation for any given medium, when
compared with their refrangibility in the same medium determined by
actual observation, will show whether the dispersion of light comes under
the laws of that theory. But, in order to accomplish this, it is clear that the
length of the waves should be found independently of refraction, and a very
beautiful discovery of M. Fraunhofer furnishes the means of doing so.
That philosopher obtained a perfectly pure and complete coloured
spectrum, with all its dark and bright lines, by the interference of light
alone, from a sunbeam passing through a series of fine parallel wires
covering the object glass of a telescope. In this spectrum, formed
independently of prismatic refraction, the positions of the coloured rays
depend only on the lengths of their waves, and M. Fraunhofer found that the
intervals between them are precisely proportional to the differences of these
lengths. He measured the lengths of the waves of the different colours at
seven fixed points, determined by seven of the principal dark and bright
lines. Professor Powell, availing himself of these measures, has made the
requisite computations, and has found that the coincidence of theory with
observation is perfect for ten substances whose refrangibility had been
previously determined by the direct measurements of M. Fraunhofer, and
for ten others whose refrangibility has more recently been ascertained by
M. Rudberg. Thus, in the case of seven rays in each of twenty different
substances, solid and fluid, the dispersion of light takes place according to
the laws of the undulatory theory: and there can hardly be a doubt that
dispersion in all other bodies will be found to follow the same law. It is,

however, an express condition of the connexion between the velocity of
light and the length of its undulations, that the intervals between the
vibrating molecules of the ethereal fluid should bear a sensible relation to
the length of an undulation. The coincidence of the computed with the
observed refractions shows that this condition is fulfilled within the
refracting media; but the aberration of the fixed stars leads to the inference
that it does not hold in the ethereal regions, where the velocities of the rays
of all colours are the same. Strong as all that precedes is in favour of the
undulatory theory, the relative velocity of light in air and water is the final
and decisive proof. By the Newtonian theory the velocity is greater in water
than in air, by the undulatory theory it is less; hence if a comparison could
be made it would decide which is the law of nature. The difficulty consisted
in comparing the velocity of light passing through a small extent of water
with the velocity of light in air, which is 10,000 times greater than the
velocity of the earth in its orbit. This delicate and difficult experiment was
made by means of an instrument invented by Professor Wheatstone for
measuring the velocity of electricity. It consists of a small mirror which
revolves in its own plane like a coin spinning on its edge. When it revolves
very rapidly the reflected image of an object changes its place perceptibly
in an inconceivably small fraction of a second. The mirrors used in the
experiment were made to revolve more than 1000 times in a second, by
which means the places of the two images—one from light passing through
air, and the other from light passing through an equal length of water—were
found to be such as to prove that the velocity of light in air and in water is
as 4 to 3, while by the Newtonian theory it is as 3 to 4. By this final and
decisive proof the undulatory theory may from henceforth be regarded as
the law of nature. This experiment was accomplished by M. Fizeau and M.
Léon-Faucault, at the suggestion of M. Arago, whose eyesight did not
permit him to undertake it himself.

SECTION XXIV.

Chemical or Photographic Rays of Solar Spectrum—Scheele, Ritter, and
Wollaston’s Discoveries—Wedgwood’s and Sir Humphry Davy’s
Photographic Pictures—The Calotype—The Daguerreotype—The
Chromatype—The Cyanotype—Collodion—Sir John Herschel’s
Discoveries in the Chemical Spectrum—M. Becquerel’s Discoveries of
Inactive Lines in ditto—Thermic Spectrum—Phosphoric Spectrum—
Electrical Properties—Parathermic Rays—Moser and Hunt’s Experiments
—General Structure and antagonist Properties of Solar Spectrum—
Defracted Spectrum.

The Solar Spectrum exercises an energetic action on matter, producing the
most wonderful and mysterious changes on the organised and unorganised
creation.
All bodies are probably affected by light, but it acts with greatest energy
on such as are of weak chemical affinity, imparting properties to them
which they did not possess before. Collodion and metallic salts, especially
those of silver, whose molecules are held together by an unstable
equilibrium, are of all bodies the most susceptible of its influence; the
effects, however, vary with the substances employed, and with the different
rays of the solar spectrum, the chemical properties of which are by no
means alike. As early as 1772 M. Scheele showed that the pure white colour
of chloride of silver was rapidly darkened by the blue rays of the solar
spectrum, while the red rays had no effect upon it: and in 1801 M. Ritter
discovered that invisible rays beyond the violet extremity have the property
of blackening argentine salts, that this property diminishes towards the less
refrangible part of the spectrum, and that the red rays have an opposite
quality, that of restoring the blackened salt of silver to its original purity;
from which he inferred that the most refrangible extremity of the spectrum

has an oxygenising power, and the other that of deoxygenating. Dr.
Wollaston found that gum guaiacum acquires a green colour in the violet
and blue rays, and resumes its original tint in the red. No attempt had been
made to trace natural objects by means of light reflected from them, till Mr.
Wedgwood, together with Sir Humphry Davy, took up the subject: they
produced profiles and tracings of objects on surfaces prepared with nitrate
and chloride of silver, but they did not succeed in rendering their pictures
permanent. This difficulty was overcome in 1814 by M. Niepcé, who
produced a permanent picture of surrounding objects by placing in the focus
of a camera-obscura a metallic plate covered with a film of asphalt
dissolved in oil of lavender.
Mr. Fox Talbot, without any knowledge of M. Niepcé’s experiments, had
been engaged in the same pursuit, and must be regarded as an independent
inventor of photography, one of the most beautiful arts of modern times: he
was the first who succeeded in using paper chemically prepared for
receiving impressions from natural objects; and he also discovered a
method of fixing permanently the impressions—that is, of rendering the
paper insensible to any further action of light. In the calotype, one of Mr.
Talbot’s applications of the art, the photographic surface is prepared by
washing smooth writing-paper, first with a solution of nitrate of silver, then
with bromide of potassium, and again with nitrate of silver, drying it at a
fire after each washing; the paper is thus rendered so sensitive to light that
even the passage of a thin cloud is perceptible on it, consequently it must be
prepared by candle-light. Portraits, buildings, insects, leaves of plants—in
short, every object is accurately delineated in a few seconds; and in the
focus of a camera-obscura the most minute objects are so exactly depicted
that the microscope reveals new beauties.
Since the effect of the chemical agency of light is to destroy the affinity
between the salt and the silver, Mr. Talbot found that, in order to render
these impressions permanent on paper, it was only necessary to wash it with
salt and water, or with a solution of iodide of potassium. For these liquids
the liquid hyposulphites have been advantageously substituted, which are
the most efficacious in dissolving and removing the unchanged salt, leaving
the reduced silver on the paper. The calotype picture is negative, that is, the
lights and shadows are the reverse of what they are in nature, and the right-
hand side in nature is the left in the picture; but if it be placed with its face
pressed against photographic paper, between a board and a plate of glass,

and exposed to the sun a short time, a positive and direct picture, as it is in
nature, is formed: engravings may be exactly copied by this simple process,
and a direct picture may be produced at once by using photographic paper
already made brown by exposure to light.
While Mr. Fox Talbot was engaged in these very elegant discoveries in
England, M. Daguerre had brought to perfection and made public that
admirable process by which he has compelled Nature permanently to
engrave her own works; and thus the talents of France and England have
been combined in bringing to perfection this useful art. Copper, plated with
silver, was successfully employed by M. Daguerre for copying nature by the
agency of light. The surface of the plate is converted into an iodide of
silver, by placing it horizontally with its face downwards in a covered box,
in the bottom of which there is a small quantity of iodine which evaporates
spontaneously. In three or four minutes the surface acquires a yellow tint,
and then, screening it carefully from light, it must be placed in the focus of
a camera obscura, where an invisible image of external objects will be
impressed on it in a few minutes. When taken out, the plate must be
exposed in another box to the action of mercurial vapour, which attaches
itself to those parts of the plate which had been exposed to light, but does
not adhere to such parts as had been in shadow; and as the quantity of
mercury over the other parts is in exact proportion to the degree of
illumination, the shading of the picture is perfect. The image is fixed, first
by removing the iodine from the plate by plunging it into hyposulphite of
soda, and then washing it in distilled water; by this process the yellow
colour is destroyed, and in order to render the mercury permanent, the plate
must be exposed a few minutes to nitric vapour, then placed in nitric acid
containing copper or silver in solution at a temperature of 611⁄4° of
Fahrenheit for a short time, and lastly polished with chalk. This final part of
the process is due to Dr. Berre, of Vienna.
Nothing can be more beautiful than the shading of these chiaroscuro
pictures when objects are at rest, but the least motion destroys the effect; the
method therefore is more applicable to buildings than landscape. Colour is
wanting; but the researches of Sir John Herschel give reason to believe that
even this will ultimately be attained.
The most perfect impressions of seaweeds, leaves of plants, feathers, &c.,
may be formed by bringing the object into close contact with a sheet of

photographic paper, between a board and plate of glass; then exposing the
whole to the sun for a short time, and afterwards fixing it by the process
described. The colours of the pictures vary with the preparation of the
paper, by which almost any tint may be produced.
In the chromatype, a peculiar photograph discovered by Mr. Hunt,
chromate of copper is used, on which a dark brown negative image is first
formed, but by the continued action of light it is changed to a positive
yellow picture on a white ground; the farther effect of light is checked by
washing the picture in pure water.
In cyanotypes, a class of photographs discovered by Sir John Herschel, in
which cyanogen in its combinations with iron forms the ground, the
pictures are Prussian blue and white. In the chrysotype of the same eminent
philosopher, the image is first received on paper prepared with the
ammonia-citrate of iron, and afterwards washed with a neutral solution of
gold. It is fixed by water acidulated with sulphuric acid, and lastly by
hydriodate of potash, from which a white and purple photograph results. It
is vain to attempt to describe the various beautiful effects which Sir John
Herschel obtained from chemical compounds, and from the juices of plants;
the juice of the red poppy gives a positive bluish purple image, that of the
ten-week stock a fine rose colour on a pale straw-coloured ground.
Pictures may be made by exposure to sunshine, on all compound
substances having a weak chemical affinity; but the image is often invisible,
as in the Daguerreotype, till brought out by washing in some chemical
preparation. Water is frequently sufficient; indeed Sir John Herschel
brought out dormant photographs by breathing on them, and some
substances are insensible to the action of light till moistened, as for
example, gum guaiacum. Argentine papers, however, are little subject to the
influence of moisture. The power of the solar rays is augmented in certain
cases by placing a plate of glass in close contact over the sensitive surface.
All these various experiments, though highly interesting, have now been
superseded. It was found that paper did not always answer for photography,
on account of imperfections in its structure; silver plates were too
expensive; and glass was found to be unimpressable. Nevertheless, M.
Niepcé de Victor obtained beautiful results upon glass coated with albumen
mixed with sensitive substances, which suggested the medium by means of
which the art has been brought to its present perfection, and that final step is

due to Mr. Scott Archer. He coated a plate of glass thinly with collodion,
that is, gun-cotton dissolved in ether and alcohol, which dries into a delicate
transparent film of extreme adhesiveness, and of such intense sensibility
that the action of light upon it is so instantaneous that it arrests a stormy sea
or a fleeting cloud before they have time to change. Now landscapes in
chiaroscuro are produced of great beauty, which by the slower methods
were mere masses of deep shade and broad light. Architecture is even more
perfectly obtained, but it fails to give a pleasing representation of the human
countenance.
Chemical action always accompanies the sun’s light, but the analysis of
the solar spectrum has partly disclosed the wonderful nature of the
emanation. In the research, properties most important and unexpected have
been discovered by Sir John Herschel, who imprints the stamp of genius on
all he touches—his eloquent papers can alone convey an adequate idea of
their value in opening a field of inquiry vast and untrodden. The following
brief and imperfect account of his experiments is all that can be attempted
here:—
A certain degree of chemical energy is distributed through every part of
the solar spectrum, and also to a considerable extent through the dark
spaces at each extremity. This distribution does not depend on the
refrangibility of the rays alone, but also on the nature of the rays
themselves, and on the physical properties of the analyzing medium on
which the rays are received, whose changes indicate and measure their
action. The length of the photographic image of the same solar spectrum
varies with the physical qualities of the surface on which it is impressed.
When the solar spectrum is received on paper prepared with bromide of
silver, the chemical spectrum, as indicated merely by the length of the
darkened part, includes within its limits the whole luminous spectrum,
extending in one direction far beyond the extreme violet and lavender rays,
and in the other down to the extremest red: with tartrate of silver the
darkening occupies not only all the space under the most refrangible rays,
but reaches much beyond the extreme red. On paper prepared with
formobenzoate of silver the chemical spectrum is cut off at the orange rays,
with phosphate of silver in the yellow, and with chloride of gold it
terminates with the green, with carbonate of mercury it ends in the blue, and
on paper prepared with the percyanide of gold, ammonia, and nitrate of
silver, the darkening lies entirely beyond the visible spectrum at its most

refrangible extremity, and is only half its length, whereas in some cases
chemical action occupies a space more than twice the length of the
luminous image.
The point of maximum energy of chemical action varies as much for
different preparations as the scale of action. In the greater number of cases
the point of deepest blackening lies about the lower edge of the indigo rays,
though in no two cases is it exactly the same, and in many substances it is
widely different. On paper prepared with the juice of the ten-week stock
(Mathiola annua) there are two maxima, one in the mean yellow and a
weaker in the violet; and on a preparation of tartrate of silver Sir John
Herschel found three, one in the least refrangible blue, one in the indigo,
and a third beyond the visible violet. The decrease in photographic energy
is seldom perfectly alike on both sides of the maximum. Thus at the most
refrangible end of the solar spectrum the greatest chemical power is exerted
in most instances where there is least light and heat, and even in the space
where both sensibly cease.
Not only the intensity but the kind of action is different in the different
points of the solar spectrum, as evidently appears from the various colours
that are frequently impressed on the same analyzing surface, each ray
having a tendency to impart its own colour. Sir John Herschel obtained a
coloured image of the solar spectrum on paper prepared according to Mr.
Talbot’s principle, from a sunbeam refracted by a glass prism and then
highly condensed by a lens. The photographic image was rapidly formed
and very intense, and, when withdrawn from the spectrum and viewed in
common daylight, it was found to be coloured with sombre but unequivocal
tints imitating the prismatic colours, which varied gradually from red
through green and blue to a purplish black. After washing the surface in
water, the tints became more decided by being kept a few days in the dark
—a phenomenon, Sir John observes, of constant occurrence, whatever be
the preparation of the paper, provided colours are produced at all. He also
obtained a coloured image on nitrate of silver, the part under the blue rays
becoming a blue brown, while that under the violet had a pinkish shade, and
sometimes green appeared at the point corresponding to the least
refrangible blue. Mr. Hunt found on a paper prepared with fluoride of silver
that a yellow line was impressed on the space occupied by the yellow rays,
a green band on the space under the green rays, an intense blue throughout
the space on which the blue and indigo rays fell, and under the violet rays a

ruddy brown appeared; these colours remained clear and distinct after being
kept two months.
Notwithstanding the great variety in the scale of action of the solar
spectrum, the darkening or deoxydizing principle that prevails in the more
refrangible part rarely surpasses or even attains the mean yellow ray which
is the point of maximum illumination; it is generally cut off abruptly at that
point which seems to form a limit between the opposing powers which
prevail at the two ends of the spectrum. The bleaching or oxydizing effect
of the red rays on blackened muriate of silver discovered by M. Ritter of
Jena, and the restoration by the same rays of discoloured gum guaiacum to
its original tint by Dr. Wollaston, have already been mentioned as giving the
first indications of that difference in the mode of action of the chemical rays
at the two ends of the visible spectrum, now placed beyond a doubt.
The action exerted by the less refrangible rays beyond and at the red
extremity of the solar spectrum, in most instances, so far from blackening
metallic salts, protects them from the action of the diffused daylight: but, if
the prepared surface has already been blackened by exposure to the sun,
they possess the remarkable property of bleaching it in some cases, and
under other circumstances of changing the black surface into a fiery red.
Sir John Herschel, to whom we owe most of our knowledge of the
properties of the chemical spectrum, prepared a sheet of paper by washing it
with muriate of ammonia, and then with two coats of nitrate of silver; on
this surface he obtained an impression of the solar spectrum exhibiting a
range of colours very nearly corresponding with its natural hues. But a very
remarkable phenomenon occurred at the end of least refrangibility; the red
rays exerted a protecting influence which preserved the paper from the
change which it would otherwise have undergone from the deoxydizing
influence of the dispersed light which always surrounds the solar spectrum,
and this maintained its whiteness. Sir John met with another instance on
paper prepared with bromide of silver, on which the whole of the space
occupied by the visible spectrum was darkened down to the very extremity
of the red rays, but an oxydizing action commenced beyond the extreme
red, which maintained the whiteness of the paper to a considerable distance
beyond the last traceable limit of the visible rays, thus evincing decidedly
the existence of some chemical power over a considerable space beyond the
least refrangible end of the spectrum. Mr. Hunt also found that on the
Daguerreotype plate a powerful protecting influence is exercised by the

extreme red rays. In these cases the red and those dark rays beyond them
exert an action of an opposite nature to that of the violet and lavender rays.
The least refrangible part of the solar spectrum possesses also, under
certain circumstances, a bleaching property, by which the metallic salts are
restored to their original whiteness after being blackened by exposure to
common daylight, or to the most refrangible rays of the solar spectrum.
Paper prepared with iodide of silver, when washed over with ferrocyanite
of potash, blackens rapidly when exposed to the solar spectrum. It begins in
the violet rays and extends over all the space occupied by the dark chemical
rays, and over the whole visible spectrum down to the extreme red rays.
This image is coloured, the red rays giving a reddish tint and the blue a
blueish. In a short time a bleaching process begins under the red rays, and
extends upwards to the green, but the space occupied by the extreme red is
maintained perfectly dark. Mr. Hunt found that a similar bleaching power is
exerted by the red rays on paper prepared with protocyanide of potassium
and gold with a wash of nitrate of silver.
The application of a moderately strong hydriodate of potash to darkened
photographic paper renders it peculiarly susceptible of being whitened by
further exposure to light. If paper prepared with bromide of silver be
washed with ferrocyanate of potash while under the influence of the solar
spectrum, it is immediately darkened throughout the part exposed to the
visible rays down to the end of the red, some slight interference being
perceptible about the region of the orange and yellow. After this a bleaching
action begins over the part occupied by the red rays, which extends to the
green. By longer exposure an oval spot begins again to darken about the
centre of the bleached space; but, if the paper receive another wash of the
hydriodate of potash, the bleaching action extends up from the green, over
the region occupied by the most refrangible rays and considerably beyond
them, thus inducing a negative action in the most refrangible part of the
spectrum.
In certain circumstances the red rays, instead of restoring darkened
photographic paper to its original whiteness, produce a deep red colour.
When Sir John Herschel received the spectrum on paper somewhat
discoloured by exposure to direct sunshine, instead of whiteness, a red
border was formed extending from the space occupied by the orange, and
nearly covering that on which the red fell. When, instead of exposing the

paper in the first instance to direct sunshine, it was blackened by the violet
rays of a prismatic spectrum, or by a sunbeam that had undergone the
absorptive action of a solution of ammonia-sulphate of copper, the red rays
of the condensed spectrum produced on it, not whiteness, but a full and
fiery red, which occupied the whole space on which any of the visible red
rays had fallen; and this red remained unchanged, however long the paper
remained exposed to the least refrangible rays.
Sunlight transmitted through red glass produces the same effect as the red
rays of the spectrum in the foregoing experiment. Sir John Herschel placed
an engraving over a paper blackened by exposure to sunshine, covering the
whole with a dark red-brown glass previously ascertained to absorb every
ray beyond the orange: in this way a photographic copy was obtained in
which the shades were black, as in the original engraving; but the lights,
instead of being white, were of the red colour of venous blood, and no other
colour could be obtained by exposure to light, however long. Sir John
ascertained that every part of the spectrum impressed by the more
refrangible rays is equally reddened, or nearly so, by the subsequent action
of the less refrangible; thus the red rays have the very remarkable property
of assimilating to their own colour the blackness already impressed on
photographic paper.
That there is a deoxydating property in the more refrangible rays, and an
oxydating action in the less refrangible part of the spectrum, is manifest
from the blackening of one and the bleaching effect of the other; but the
peculiar action of the red rays in the experiments mentioned shows that
some other principle exists different from contrariety of action. These
opposite qualities are balanced or neutralized in the region of the mean
yellow ray. But, although this is the general character of the photographic
spectrum, under certain circumstances even the red rays have a deoxydating
power, while the blue and violet exert a contrary influence; but these are
rare exceptions.
The photographic action of the two portions of the solar spectrum being
so different, Sir John Herschel tried the effect of their united action by
superposing the less refrangible part of the spectrum over the more
refrangible portion by means of two prisms; and he thus discovered that two
rays of different refrangibility, and therefore of different lengths of
undulation, acting simultaneously, produce an effect which neither, acting
separately, can do.

Some circumstances that occurred during the analysis of the chemical
spectrum seem to indicate an absorptive action in the sun’s atmosphere. The
spectral image impressed on paper prepared with nitrate of silver and
Rochelle salt commenced at, or very little below, the mean yellow ray, of a
delicate lead colour; and when the action was arrested, such was the
character of the whole photographic spectrum. But, when the light of the
solar spectrum was allowed to continue its action, there was observed to
come on suddenly a new and much more intense impression of darkness,
confined in length to the blue and violet rays; and, what is most remarkable,
confined also in breadth to the middle of the sun’s image, so far at least as
to leave a border of the lead-coloured spectrum traceable, not only round
the clear and well-defined convexity of the dark interior spectrum at the less
refrangible end, but also laterally along both its edges; and this border was
the more easily traced, and less liable to be mistaken, from its striking
contrast of colour with the interior spectrum, the former being lead gray, the
latter an extremely rich deep velvety brown. The less refrangible end of this
interior brown spectrum presented a sharply terminated and regularly
elliptical contour, the more refrangible a less decided one. “It may seem too
hazardous,” Sir John continues, “to look for the cause of this very singular
phenomenon in a real difference between the chemical agencies of those
rays which issue from the central portion of the sun’s disc, and those which,
emanating from its borders, have undergone the absorptive action of a much
greater depth of its atmosphere; and yet I confess myself somewhat at a loss
what other cause to assign for it. It must suffice, however, to have thrown
out the hint, remarking only, that I have other, and I am disposed to think
decisive, evidence of the existence of an absorptive solar atmosphere
extending beyond the luminous one.” M. Arago observed that the rays from
the centre of the sun have a greater photographic power than those from the
edges, and the photographic images of the sun, taken on glass by M.
Niepcé, were blood-red, much deeper in the centre, and on one occasion the
image was surrounded by an auriol. Several circumstances concur in
showing that there are influences also concerned in the transmission of the
photographic action which have not yet been explained, as, for example, the
influence which the time of the day exercises on the rapidity with which
photographic impressions are made, the sun being much less effective two
hours after passing the meridian than two hours before. There is also reason
to suspect that the effect in some way depends on the latitude, since a much

longer time is required to obtain an image under the bright skies of the
tropics than in England; and it is even probable that there is a difference in
the sun’s light in high and low latitudes, because an image of the solar
spectrum, obtained on a Daguerreotype plate in Virginia, by Dr. Draper,
differed from a spectral image obtained by Mr. Hunt on a similar plate in
England. The inactive spaces discovered in the photographic spectrum by
M. E. Becquerel, similar to those in the luminous spectrum, and coinciding
with them, is also a phenomenon of which no explanation has yet been
given; possibly the chemical rays may be absorbed by the atmosphere with
those of light. Although chemical action extends over the whole luminous
spectrum, and much beyond it, in gradations of more or less intensity, it is
found by careful investigation to be by no means continuous; numerous
inactive lines cross it, coinciding with those in the luminous image as far as
it extends; besides, a very great number exist in the portions that are
obscure, and which overlap the visible part. There are three extraspectral
lines beyond the red, and some strongly marked groups on the obscure part
beyond the violet; but the whole number of those inactive lines, especially
in the dark spaces, is so great that it is impossible to count them.
Notwithstanding this coincidence in the inactive lines of the two spectra,
photographic energy is independent of both light and heat, since it exerts
the most powerful influence in those rays where they are least, and also in
spaces where neither sensibly exist; but the transmission of the sun’s light
through coloured media makes that independence quite evident. Heat and
light pass abundantly through yellow glass, or a solution of chromate of
potash; but the greater part of the chemical rays are excluded, and chlorine
gas diluted with common air, though highly pervious to the luminous and
calorific principles, has the same effect. Sir John Herschel found that a
slight degree of yellow London fog had a similar effect with that of pale
yellow media: he also remarked that a weak solution of azolitmine in
potash, which admits a great quantity of green light, excludes chemical
action; and some years ago the author, while making experiments on the
transmission of chemical rays, observed that green glass, coloured by oxide
of copper about the 20th of an inch thick, excludes the photographic rays;
and, as M. Melloni has shown that substance to be impervious to the most
refrangible calorific rays, it has the property of excluding the whole of the
most refrangible part of the solar spectrum, visible and invisible. Green
mica, if not too thin, has also the same effect, whereas amethyst, deep blue,

and violet-coloured glasses, though they transmit a very little light, allow
the chemical rays to pass freely. Thus light and photographic energy may be
regarded as distinct parts of the solar beam, and both being propagated by
vibrations of the etherial medium they are merely motion. Excellent images
have been obtained of the moon in its different phases by Professor Secchi,
at Rome; candlelight is nearly deficient of the chemical rays. How far they
may influence crystallization and other molecular arrangements is
unknown, but their power is universal wherever the solar beam falls,
although their effect only becomes evident in cases of unstable molecular
equilibrium.
It is not by vision alone that a knowledge of the sun’s rays is acquired:
touch proves that they have the power of raising the temperature of
substances exposed to their action. Sir William Herschel discovered that
rays which produce the sensation of heat exist in the solar spectrum
independent of those of light; when he used a prism of flint glass, he found
that the warm rays are most abundant in the dark space a little beyond the
red extremity of the spectrum, that from thence they decrease towards the
violet, beyond which they are insensible. It may be concluded therefore,
that the calorific rays vary in refrangibility, and that those beyond the
extreme red are less refrangible than any rays of light. Since Sir William
Herschel’s time it has been discovered that the calorific spectrum exceeds
the luminous one in length in the ratio of 42 to 25, but the most singular
phenomenon is its want of continuity. Sir John Herschel blackened the
under side of a sheet of very thin white paper by the smoke of a lamp, and,
having exposed the white side to the solar spectrum, he drew a brush dipped
in spirit of wine over it, by which the paper assumed a black hue when
sufficiently saturated. The heat in the spectrum evaporated the spirit first on
those parts of the paper where it fell with greatest intensity, thereby
restoring their white colour, and he thus discovered that the heat increases
uniformly and gradually throughout the luminous spectrum, and that it
comes to a maximum and forms a spot at a considerable distance beyond
the extreme red. It then decreases, but again increasing it forms a second
maximum spot, after which it ceases altogether through a short space, but is
again renewed and forms two more insulated spots, and even a fifth may be
traced at a little distance from the latter. These circumstances are probably
owing to the absorbing action of the atmospheres of the sun and earth. “The
effect of the former,” says Sir John, “is beyond our control, unless we could

carry our experiments to such a point of delicacy as to operate separately on
rays emanating from the centre and borders of the sun’s disc; that of the
earth’s, though it cannot be eliminated any more than in the case of the
sun’s, may yet be varied to a considerable extent by experiments made at
great elevations, under a vertical sun, and compared with others where the
sun is more oblique, the situation lower, and the atmospheric pressure of a
temporarily high amount. Should it be found that this cause is in reality
concerned in the production of the spots, we should see reason to believe
that a large portion of solar heat never reaches the earth’s surface, and that
what is incident on the summits of lofty mountains differs not only in
quantity but also in quality from what the plains receive.”
A remarkable phosphorescent property was discovered by M. E.
Becquerel in the solar spectrum. Two luminous bands separated by a dark
one are excited by the solar spectrum on paper covered with a solution of
gum arabic, and strewed with powdered sulphuret of calcium or Canton’s
phosphorus. One of the luminous bands occupies the space under the least
refrangible violet rays, and the other that beyond the lavender rays, so that
the dark band lies under the extreme violet and lavender rays. When the
action of the light is continued, the whole surface beyond the least
refrangible violet shines, the luminous bands already mentioned brightest;
but all the space from the least refrangible violet to the extreme red remains
dark. If the surface, prepared either with the sulphuret of calcium or
Bologna stone, be exposed to the sun’s light for a little time, it becomes
luminous all over; but when, in this state, a solar spectrum is thrown upon
it, the whole remains luminous except the part from the least refrangible
violet to the extreme red, on which space the light is extinguished; and
when the temperature of the surface is raised by a lamp, the bright parts
become more luminous and the dark parts remain dark. Glass stained by the
protoxide of copper, which transmits only the red and orange rays, has the
same effect with the less refrangible part of the spectrum; hence there can
be no doubt that the most refrangible and obscure rays of the spectrum
excite phosphorescence, while all the less refrangible rays of light and heat
extinguish it.
Paper prepared with the sulphuret of barium, when under the solar
spectrum, shows only one space of maximum luminous intensity, and the
destroying rays are the same as in the sulphuret of calcium. Thus the

obscure rays beyond the extreme violet produce light, while the luminous
rays extinguish it.
The phosphoric spectrum has inactive lines which coincide with those in
the luminous and chemical spectra, at least as far as it extends; but in order
to be seen the spectrum must be received for a few seconds upon the
prepared surface through an aperture in a dark room, then the aperture must
be closed, and the temperature of the surface raised two or three hundred
degrees; the phosphorescent parts then shine brilliantly and the dark lines
appear black. Since the parts of similar refrangibility in different spectra are
traversed by the same dark lines, rays of the same refrangibility are
probably absorbed at the same time by the different media through which
they pass.
It appears from the experiments of MM. Becquerel and Biot, that
electrical disturbances produce these phosphorescent effects. There is thus a
mysterious connexion between the most refrangible rays and electricity
which the experiments of M. E. Becquerel confirm, showing that electricity
is developed during chemical action by the violet rays, that it is feebly
developed by the blue and indigo, but that none is excited by the less
refrangible part of the spectrum.
A series of experiments by Sir John Herschel have disclosed a new set of
obscure rays in the solar spectrum, which seem to bear the same relation to
those of heat that the photographic or chemical rays bear to the luminous.
They are situate in that part of the spectrum which is occupied by the less
refrangible visible colours, and have been named by their discoverer
Parathermic rays. It must be held in remembrance that the region of greatest
heat in the solar spectrum lies in the dark space beyond the visible red.
Now, Sir John Herschel found that in experiments with a solution of gum
guaiacum in soda, which gives the paper a green colour, the green, yellow,
orange, and red rays of the spectrum invariably discharged the colour, while
no effect was produced by the extra-spectral rays of heat, which ought to
have had the greatest effect had heat been the cause of the phenomenon.
When an aqueous solution of chlorine was poured over a slip of paper
prepared with gum guaiacum dissolved in soda, a colour varying from a
deep somewhat greenish hue to a fine celestial blue was given to it; and,
when the solar spectrum was thrown on the paper while moist, the colour
was discharged from all the space under the less refrangible luminous rays,
at the same time that the more distant thermic rays beyond the spectrum

evaporated the moisture from the space on which they fell; so that the heat
spots became apparent. But the spots disappeared as the paper dried,
leaving the surface unchanged; while the photographic impression within
the visible spectrum increased in intensity; the non-luminous thermic rays,
though evidently active as to heat, were yet incapable of effecting that
peculiar chemical change which other rays of much less heating power were
all the time producing. Sir John having ascertained that an artificial heat
from 180° to 280° of Fahrenheit changed the green tint of gum guaiacum to
its original yellow hue when moist, but that it had no effect when dry, he
therefore tried whether heat from a hot iron applied to the back of the paper
used in the last-mentioned experiment while under the influence of the solar
spectrum might not assist the action of the calorific rays; but, instead of
doing so, it greatly accelerated the discoloration over the spaces occupied
by the less refrangible rays, but had no effect on the extra-spectral region of
maximum heat. Obscure terrestrial heat, therefore, is capable of assisting
and being assisted in effecting this peculiar change by those rays of the
spectrum, whether luminous or thermic, which occupy its red, yellow, and
green regions; while, on the other hand, it receives no such assistance from
the purely thermic rays beyond the spectrum acting under similar
circumstances and in an equal state of condensation.
The conclusions drawn from these experiments are confirmed by that
which follows: a photographic picture formed on paper prepared with a
mixture of the solutions of ammonia-citrate of iron and ferro-sesquicyanite
of potash in equal parts, then thrown into water and afterwards dried, will
be blue and negative, that is to say, the lights and shadows will be the
reverse of what they are in nature. If in this state the paper be washed with a
solution of proto-nitrate of mercury, the picture will be discharged; but if it
be well washed and dried, and a hot smoothing-iron passed over it, the
picture instantly reappears, not blue, but brown; if kept some weeks in this
state in perfect darkness between the leaves of a portfolio, it fades, and
almost entirely vanishes, but a fresh application of heat restores it to its full
original intensity. This curious change is not the effect of light, at least not
of light alone. A certain temperature must be attained, and that suffices in
total darkness; yet, on exposing to a very concentrated spectrum a slip of
the paper used in the last experiment, after the uniform blue colour has been
discharged and a white ground left, this whiteness is changed to brown over