SECTION I._On the Connexion of the Physical Sciences

Transcriber’s Note

When italics were used in the original book, the corresponding text has

been surrounded by _underscores_ except in the case of single letter

variables used in the Notes section, where the italics were not

represented. Mixed fractions have been displayed with a hyphen between

whole number and fraction for clarity. Superscripted characters are

preceded by ^ and when more than one character is superscripted, they

are surrounded by {}. 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.

Some corrections have been made to the printed text. These are listed in

a second transcriber’s note at the end of the text.

[Illustration:

MARY SOMERVILLE

J. COOPER S^c.

]

THE CONNEXION

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

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

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

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

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

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

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

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

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

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

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

SECTION XI.

Precession and Nutation—Their Effects on the Apparent Places of the

Fixed Stars

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

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

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

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.