Part 1

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.

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.