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You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org/license - - -Title: On the Connexion of the Physical Sciences - -Author: Mary Somerville - -Release Date: August 21, 2016 [EBook #52869] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK CONNEXION OF THE PHYSICAL SCIENCES *** - - - - -Produced by Sonya Schermann and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - - - - - - - - - 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. -] - - - - - 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 7925-1/2 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 16^m 26^s·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 -13^d 11^h 7^m 12^s·6 and 8^d 16^h 56^m 28^s·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 2-1/2 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 27^d 7^h 43^m 11^s·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 6793^d 9^h 23^m 9^s·3, or -about 18-6/10 years; and the perigee accomplishes a revolution, called -of the moon’s apsides, in 3232^d 13^h 48^m 29^s·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 298-3/4, 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 298-83/100) 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 69-14/100 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 2^m 28^s 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 1-1/4° 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 2-1/2 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 26-1/2 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 365^d 5^h 48^m 49^s·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 20^m 19^s·6, so -that the sidereal year contains 365^d 6^h 9^m 9^s·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 4^s·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 0^h 0^m 0^s 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 365^d 5^h 48^m 49^s·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 24^h 50^m 28^s 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 29-1/2 days to vary through all her declinations, which -sometimes extend 28-3/4° on each side of the equator, while the sun -requires nearly 365-1/4 days to accomplish his motions through 23-1/2° -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 77-1/2 degrees below that point at the -equator, and 119-1/2 below it at the poles, with a range of temperature -from the surface of 161-1/2° in the former case, and 119-1/2° 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 27^{in}·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 1-1/2, 2-1/2, 3-1/2, &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 1-1/4, 2-1/4, -3-1/4, &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 17-1/2°, 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 17-1/2°; 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 61-1/4° 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 the whole region of the red and orange rays, _but not beyond_ -the luminous spectrum. - -Sir John thence concludes:—1st. That it is the heat of these rays, not -their light, which operates the change; 2ndly. That this heat possesses -a peculiar chemical quality which is not possessed by the purely -calorific rays outside of the visible spectrum, though far more intense; -and, 3rdly. That the heat radiated from obscurely hot iron abounds -especially in rays analogous to those of the region of the spectrum -above indicated. - -Another instance of these singular transformations may be noticed. The -pictures formed on cyanotype paper rendered more sensitive by the -addition of corrosive sublimate are blue on a white ground and positive, -that is, the lights and shadows are the same as in nature, but, by the -application of heat, the colour is changed from blue to brown, from -positive to negative; even by keeping in darkness the blue colour is -restored, as well as the _positive character_. Sir John attributes this, -as in the former instance, to certain rays, which, regarded as rays of -heat or light, or of some influence _sui generis_ accompanying the red -and orange rays of the spectrum, are also copiously emitted by bodies -heated short of redness. He thinks it probable that these invisible -parathermic rays are the rays which radiate from molecule to molecule in -the interior of bodies, that they determine the discharge of vegetable -colours at the boiling temperature, and also the innumerable atomic -transformations of organic bodies which take place at the temperature -below redness, that they are distinct from those of pure heat, and that -they are sufficiently identified by these characters to become -legitimate objects of scientific discussion. - -The calorific and parathermic rays appear to be intimately connected -with the discoveries of Messrs. Draper and Moser. Daguerre has shown -that the action of light on the iodide of silver renders it capable of -condensing the vapour of mercury which adheres to the parts affected by -it. Professor Moser of Königsberg has proved that the same effect is -produced by the simple contact of bodies, and even by their very near -juxtaposition, and that in total darkness as well as in light. This -discovery he announced in the following words:—“If a surface has been -touched in any particular parts by any body, it acquires the property of -precipitating all vapours, and these adhere to it or combine chemically -with it on these spots differently from what they do on the untouched -parts.” If we write on a plate of glass or any smooth surface whatever -with blotting-paper, a brush, or anything else, and then clean it, the -characters always reappear if the plate or surface be breathed upon, and -the same effect may be produced even on the surface of mercury; nor is -absolute contact necessary. If a screen cut in a pattern be held over a -polished metallic surface at a small distance, and the whole breathed -on, after the vapour has evaporated so that no trace is left on the -surface, the pattern comes out when it is breathed on again. - -Professor Moser proved that bodies exert a very decided influence upon -each other, by placing coins, cut stones, pieces of horn, and other -substances, for a short time on a warm metallic plate: when the -substance was removed, no impression appeared on the plate till it was -breathed upon or exposed to the vapour of mercury, and then these -vapours adhered only to the parts where the substance had been placed, -making distinct images, which in some cases were permanent after the -vapour was removed. Similar impressions were obtained on glass and other -substances even when the bodies were not in contact, and the results -were the same whether the experiments were performed in light or in -darkness. - -Mr. Grove found, when plates of zinc and copper were closely -approximated, but not in contact, and suddenly separated, that one was -positively and the other negatively electric; whence he inferred that -the intervening medium was either polarised, or that a radiation -analogous, if not identical, with that which produces Moser’s images -takes place from plate to plate. - -Mr. Hunt has shown that many of these phenomena depend on difference of -temperature, and that, in order to obtain good impressions, dissimilar -metals must be used. For example, gold, silver, bronze, and copper coins -were placed on a plate of copper too hot to be touched, and allowed to -remain till the plate cooled: all the coins had made an impression, the -distinctness and intensity of which were in the order of the metals -named. When the plate was exposed to the vapour of mercury the result -was the same, but, when the vapour was wiped off, the gold and silver -coins only had left permanent images on the copper. These impressions -are often minutely perfect, whether the coins are in actual contact with -the plate or one-eighth of an inch above it. The mass of the metal has a -material influence on the result; a large copper coin makes a better -impression on a copper plate than a small silver coin. When coins of -different metals are placed on the same plate they interfere with each -other. - -When, instead of being heated, the copper plate was cooled by a freezing -mixture, and bad conductors of heat laid upon it, as wood, paper, glass, -&c., the result was similar. - -Mr. Hunt, observing that a black substance leaves a stronger impression -on a metallic surface than a white, applied the property to the art of -copying prints, woodcuts, writing, and printing, on copper amalgamated -on one surface and highly polished, merely by placing the object to be -copied smoothly on the metal, and pressing it into close contact by a -plate of glass: after some hours the plate is subjected to the vapour of -mercury, and afterwards to that of iodine, when a black and accurate -impression of the object comes out on a grey ground. Effects similar to -those attributed to heat may also be produced by electricity. Mr. -Karsten, by placing a glass plate upon one of metal, and on the glass -plate a medal subjected to discharges of electricity, found a perfect -image of the medal impressed on the glass, which could be brought into -evidence by either mercury or iodine; and, when several plates of glass -were interposed between the medal and the metallic plate, each plate of -glass received an image on its upper surface after the passage of -electrical discharges. These discharges have the remarkable power of -restoring impressions that have been long obliterated from plates by -polishing—a proof that the disturbances upon which these phenomena -depend are not confined to the surface of the metals, but that a very -decided molecular change has taken place to a considerable depth. Mr. -Hunt’s experiments prove that the electro-negative metals make the most -decided images upon electro-negative plates, and _vice versâ_. M. -Matteucci has shown that a discharge of electricity does not visibly -affect a polished silver plate, but that it produces an alteration which -renders it capable of condensing vapour. - -The impression of an engraving was made by laying it face downwards on a -silver plate iodized, and placing an amalgamated copper plate upon it; -it was left in darkness fifteen hours, during which time an impression -of the engraving had been made on the amalgamated plate _through the -paper_. - -An iodized silver plate was placed in darkness with a coil of string -laid on it, and with a polished silver plate suspended one-eighth of an -inch above it: after four hours they were exposed to the vapours of -mercury, which became uniformly deposited on the iodized plate, but on -the silver one there was a sharp image of the string, so that this image -was formed in the dark, and even without contact. Coins or other objects -leave their impressions in the same manner with perfect sharpness and -accuracy, when brought out by vapour without contact, in darkness, and -on simple metals. - -Red and orange coloured media, smoked glass, and all bodies that -transmit or absorb the hot rays freely, leave strong impressions on a -plate of copper, whether they be in contact or one-eighth of an inch -above it. Heat must be concerned in this, for a solar spectrum -concentrated by a lens was thrown on a polished plate of copper, and -kept on the same spot by a heliostat for two or three hours: when -exposed to mercurial vapour, a film of the vapour covered the plate -where the diffused light which always accompanies the solar spectrum had -fallen. On the obscure space occupied by the maximum heating power of -Sir William Herschel, and also on the great heat spot in the thermic -spectrum of Sir John Herschel, the condensation of the mercury was so -thick that it stood out a distinct white spot on the plate, while over -the whole space that had been under the visible spectrum the quantity of -vapour was much less than that which covered the other parts, affording -distinct evidence of a negative effect in the luminous spectrum and of -the power of the hot rays, which is not always confined to the surface -of the metal, since in many instances the impressions penetrated to a -considerable depth below it, and consequently were permanent. - -Several of these singular effects appear to be owing to the mutual -action of molecules in contact while in a different state, whether of -electricity or temperature: others clearly point at some unknown -influence exerted between surfaces at a distance, and affecting their -molecular structure: possibly it may be the parathermic rays, which have -a peculiar chemical action even in total darkness. In the last -experiment the effect is certainly produced by the positive portion of -one of those remarkable antagonist principles which characterise the -solar spectrum. - -Thus it appears that the prism resolves the pure white sunbeam into -three superposed spectra, each varying in refrangibility and intensity -throughout its whole length; the visible part is overlapped at one end -by the chemical or photographic rays, and at the other by the thermic, -but the two latter so much exceed the visible part, that the linear -dimensions of the three—the luminous, thermic, and photographic—are in -proportion to the numbers 25, 42·10, and 55·10, so that the whole solar -spectrum is twice as long as its visible part. The two extremities exert -a decided antagonist energy. The least refrangible luminous rays -obliterate the action of the photographic rays, while the latter produce -phosphorescent light, which is extinguished by the least refrangible -luminous rays. According to Mr. Hunt’s experiment, the hot rays condense -mercurial vapour on a polished metallic plate, while the luminous rays -prevent its formation. Electricity is excited by the chemical rays, -while the parathermic are found in the less refrangible rays alone. Each -of the spectra is crossed by coloured and rayless lines peculiar to -itself, and these are traversed at right angles by innumerable dark -lines of various breadths, the whole forming an inexpressibly wonderful -and glorious creation. - -The arrangement varies a little according to the material of the prism -and the manner of producing the spectrum, as in that obtained by -Professor Draper from diffracted light. It was formed by a beam -diffracted by passing through a netting of fine wire, or by reflection -from a polished surface of steel, having fine parallel lines drawn on -it. This diffracted spectrum is divided into two equal parts in the -centre of the yellow; and as in the prismatic spectrum, one half is -antagonist to the other half, the red or negative end undoing what the -positive or violet end has done. The centre of the yellow is the hottest -part, and the heat decreases to both extremities. A line of cold is -supposed to exist on this spectrum answering to Fraunhofer’s dark line -H. - -The undulations of the ethereal medium which constitute a sunbeam must -be infinitely varied, each influence having a vibration peculiar to -itself. Those of light are certainly transverse to the direction of the -ray; while Professor Draper believes that those of heat are normal, that -is, in the direction of the ray, like those of sound. A doubt exists -whether the vibrations of polarised light are perpendicular to the plane -of polarisation or in that plane. Professor Stokes of Cambridge has come -to the conclusion, both from the diffracted spectrum and theory, that -they are perpendicular to the plane of polarisation, but M. Holtzmann is -of opinion that they are in that plane, so the subject is still open to -discussion. - - - - - 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. - - -THE sun is a globe 880,000 miles in diameter: what his body may be it is -impossible to conjecture, but it seems to be a dark mass surrounded by -an extensive atmosphere at a certain height in which there is a stratum -of luminous clouds which constitutes the photosphere of the sun. Above -it rises the true solar atmosphere, visible as an aureola or corona -during annular and total eclipses, and probably the cause of the -peculiar phenomena in the photographic image of the sun already -mentioned. Through occasional openings in the photosphere or mottled -ocean of flame, the dark nucleus appears like black spots, often of -enormous size. These spots are almost always comprised within a zone of -the sun’s surface, whose breadth measured on a solar meridian does not -extend beyond 30-1/2° on each side of his equator, though they have been -seen at a distance of 39-1/2°. The dark central part of the spots is -surrounded by a succession of obscure cloudy envelopes increasing in -brightness up to a penumbra, sometimes there are three or more shades, -but it requires a good telescope to distinguish the intermediate ones. -The spots gradually increase in size and number from year to year to a -maximum, and then as gradually decrease to a minimum, accomplishing -regular vicissitudes in periods of about eleven years, and are -singularly connected with the cycles of terrestrial magnetism. From -their extensive and rapid changes, there is every reason to believe that -the exterior and incandescent part of the sun is gaseous. - -Doubts have arisen as to the uniformity of the quantity of heat emitted -by the sun. Sir William Herschel was the first to suspect that it was -affected by the quantity and magnitude of the spots on his surface; -Professor Secchi has observed that the spots are less hot than the -luminous part; and now Professor Wolf has perceived that the amount of -heat emitted by the sun varies periodically with the spots every 11·11 -years, or nearly nine times in a century, beginning at the commencement -of the present one. He has discovered a sub-period in that of the spots, -which no doubt has an effect on the quantity of solar heat. So the -unaccountable vicissitudes in the temperature of different years may -ultimately be found to depend upon the constitution of the sun himself. - -The intensity of the sun’s light diminishes from the centre to the -circumference of the solar disc. His direct light has been estimated to -be equal to that of 5563 wax candles of moderate size placed at the -distance of one foot from an object; that of the moon is probably only -equal to the light of one candle at the distance of 12 feet: -consequently the light of the sun is more than three hundred thousand -times greater than that of the moon. According to Professor Secchi’s -experiments at Rome, the heat of the solar image is almost twice as -great at the centre as at the edge. The maximum heat, however, is not in -the centre, but in the solar equator, and the spots are less hot than -the rest of the surface. - -The oceans of light and heat probably arising from electric or chemical -processes of immense energy that continually take place at the sun’s -surface (N. 217) are transmitted in undulations by the ethereal medium -in all directions; but notwithstanding the sun’s magnitude and the -inconceivable intensity of light and heat that must exist at his -surface, as the intensity of both diminishes as the square of the -distance increases, his kindly influence can hardly be felt at the -boundaries of our system. In Uranus the sun must be seen like a small -brilliant star not above the hundred and fiftieth part as bright as he -appears to us, but that is 2000 times brighter than our moon, so that he -is really a sun to Uranus, and may impart some degree of warmth. But if -we consider that water would not remain fluid in any part of Mars, even -at his equator, and that, in the temperate zones of the same planet, -even alcohol and quicksilver would freeze, we may form some idea of the -cold that must reign in Uranus and Neptune. The climate of Venus more -nearly resembles that of the earth, though, excepting at her poles, much -too hot for animal and vegetable life such as they exist here, for she -receives seven times as much light and heat as the earth does; but in -Mercury the mean heat from the intensity of the sun’s rays must be above -that of boiling quicksilver, and water would boil even at his poles. -Thus the planets, though kindred with the earth in motion and form, are, -according to our experience, totally unfit for the habitation of such a -being as man, unless indeed their temperature should be modified by -circumstances of which we are not aware, and which may increase or -diminish the sensible heat so as to render them habitable. In our utter -ignorance it may be observed, that the earth, if visible at all from -Neptune, can only be a minute telescopic object; that from the nearest -fixed star the sun must dwindle to a mere point of light; that the whole -solar system would there be hid by a spider’s thread; and that the -starry firmament itself is only the first series of starry systems, the -numbers of which are bounded alone by the imperfection of our -space-penetrating instruments. In this overwhelming majesty of creation, -it seems rash to affirm that the earth alone is inhabited by intelligent -beings, and thus to limit the Omnipotent, who has made nothing in vain. - -Several of the planets have extensive and dense atmospheres: according -to Schroëter the atmosphere of Ceres is more than 668 miles high, and -that of Pallas has an elevation of 465 miles, but not a trace of an -atmosphere can be perceived round Vesta. The attraction of the earth has -probably deprived the moon of hers, for the refractive power of the air -at the surface of the earth is at least a thousand times as great as at -the surface of the moon: the lunar atmosphere must therefore be of a -greater degree of rarity than can be produced by our best air-pumps. -This is confirmed by Arago’s observations during a solar eclipse, when -no trace of a lunar atmosphere could be seen. Since then, however, some -indications of air have been perceived in the lunar valleys. In taking -photographic images of the moon and Jupiter at Rome, Professor Secchi -found that the light of the full moon is to that of the quarter moon as -3 to 1. Jupiter gives a photographic image as bright and vigorous as the -brightest part of the moon; but although the light of Jupiter is less -than that of the moon, he is nearly five times farther from the sun; and -as light diminishes as the square of the distance increases, the light -of Jupiter is proportionally greater than that of the moon, consequently -Jupiter’s atmosphere reflects more light than the dark volcanic soil of -the moon; thus Professor Secchi observes photography may in time reveal -the quality of the materials of which the celestial bodies are formed. - -The effect of the earth’s atmosphere on lunar heat is remarkable. -Professor Forbes proved that the direct light of the full moon is -incapable of raising a thermometer the one three thousandth part of a -Centigrade degree, at least in England; but at an elevation of 8870 feet -on the Peak of Teneriffe, Mr. Piazzi Smyth found a very sensible heat -from the moon, although she was then 19° south of the equator; so it is -no doubt absorbed by our atmosphere at lower levels. - -Some exceedingly interesting experiments might be made by means of a -telescope having a prism attached to its objective extremity, and -furnished with a micrometer, because by it the difference of the -illumination of objects might be determined with extreme accuracy—as for -example, the comparative intensity between the bright and dark parts of -the moon, the comparative intensity of the solar light reflected by the -moon, and the lumière cendré, or the light of the earth reflected on the -moon, whence a comparison might be made between the light of the sun and -that of the earth. Hence also it might be known whether the terrestrial -hemispheres successively visible from the moon are more or less -luminous, according as they contain more land or water, and at the same -time it might be possible to appreciate the more or less cloudy or clear -state of our atmosphere, so that in time we might ultimately find in the -lumière cendré of the moon data upon the mean diaphaneity of different -terrestrial hemispheres which are of different temperatures. - -It is found by experience that heat is developed in opaque and -translucent substances by their absorption of solar light, but that the -sun’s rays do not sensibly alter the temperature of perfectly -transparent bodies through which they pass. As the temperature of the -pellucid planetary space can be but little affected by the passage of -the sun’s light and heat, neither can it be sensibly raised by the heat -now radiated from the earth. - -Doubtless the radiation of all the bodies in the universe maintains the -ethereal medium at a higher temperature than it would otherwise have, -and must eventually increase it, but by a quantity so evanescent that it -is hardly possible to conceive a time when a change will become -perceptible. - -The temperature of space being so low as -239° Fahrenheit, it becomes a -matter of no small interest to ascertain whether the earth may not be -ultimately reduced by radiation to the temperature of the surrounding -medium; what the sources of heat are; and whether they be sufficient to -compensate the loss, and to maintain the earth in a state fit for the -support of animal and vegetable life in time to come. All observations -that have been made under the surface of the ground concur in proving -that there is a stratum at the depth of from 40 to 100 feet throughout -the whole earth where the temperature is invariable at all times and -seasons, and which differs but little from the mean annual temperature -of the country above. According to M. Boussingault, that stratum at the -equator is at the depth of little more than a foot in places sheltered -from the direct rays of the sun; but in our climates it is at a much -greater depth. In the course of more than half a century the temperature -of the earth at the depth of 90 feet, in the cellars of the Observatory -at Paris, has never been above or below 53° of Fahrenheit’s thermometer, -which is only 2° above the mean annual temperature at Paris. This zone, -unaffected by the sun’s rays from above, or by the internal heat from -below, serves as an origin whence the effects of the external heat are -estimated on one side, and the internal temperature of the globe on the -other. - -As early as the year 1740 M. Gensanne discovered in the lead-mines of -Giromagny, in the Vosges mountains, three leagues from Béfort, that the -heat of the ground increases with the depth below the zone of constant -temperature. A vast number of observations have been made since that -time, in the mines of Europe and America, by MM. Saussure, Daubuisson, -Humboldt, Cordier, Fox, Reich, and others, which agree, without an -exception, in proving that the temperature of the earth becomes higher -in descending towards its centre. The greatest depth that has been -attained is in the silver-mine of Guanaxato, in Mexico, where M. de -Humboldt found a temperature of 98° at the depth of 285 fathoms, the -mean annual temperature of the country being only 61°. Next to that is -the Dalcoath copper-mine, in Cornwall, where Mr. Fox’s thermometer stood -at 68° in a hole in the rock at the depth of 230 fathoms, and at 82° in -water at the depth of 240 fathoms, the mean annual temperature at the -surface being about 50°. But it is needless to multiply examples, all of -which concur in showing that there is a very great difference between -the temperature in the interior of the earth and at its surface. Mr. -Fox’s observations on the temperature of springs which rise at profound -depths in mines afford the strongest testimony. He found considerable -streams flowing into some of the Cornish mines at the temperature of 80° -or 90°, which is about 30° or 40° above that of the surface, and also -ascertained that nearly 2,000,000 gallons of water are daily pumped from -the bottom of the Poldice mine, which is 176 fathoms deep at 90° or -100°. As this is higher than the warmth of the human body, Mr. Fox -justly observes that it amounts to a proof that the increased -temperature cannot proceed from the persons of the workmen employed in -the mines. Neither can the warmth of mines be attributed to the -condensation of the currents of air which ventilate them. Mr. Fox, whose -opinion is of high authority in these matters, states that, even in the -deepest mines, the condensation of the air would not raise the -temperature more than 5° or 6°; and that, if the heat could be -attributed to this cause, the seasons would sensibly affect the -temperature of mines, which it appears they do not where the depth is -great. Besides, the Cornish mines are generally ventilated by numerous -shafts opening into the galleries from the surface or from a higher -level. The air circulates freely in these, descending in some shafts and -ascending in others. In all cases Mr. Fox found that the upward currents -are of a higher temperature than the descending currents; so much so, -that in winter the moisture is often frozen in the latter to a -considerable depth; the circulation of air, therefore, tends to cool the -mine instead of increasing the heat. Mr. Fox has also removed the -objections arising from the comparatively low temperature of the water -in the shafts of abandoned mines, by showing that observations in them, -from a variety of circumstances which he enumerates, are too discordant -to furnish any conclusion as to the actual heat of the earth. The high -temperature of mines might be attributed to the effects of the fires, -candles, and gunpowder used by the miners, did not a similar increase -obtain in deep wells, and in borings to great depths in search of water, -where no such causes of disturbance occur. In a well dug with a view to -discover salt in the canton of Berne, and long deserted, M. de Saussure -had the most complete evidence of increasing heat. The same has been -confirmed by the temperature of many wells, both in France and England, -especially by the Artesian wells, so named from a peculiar method of -raising water first resorted to in Artois, and since become very -general. An Artesian well consists of a shaft a few inches in diameter, -bored into the earth till a spring is found. To prevent the water being -carried off by the adjacent strata, a tube is let down which exactly -fills the bore from top to bottom, in which the water rises pure to the -surface. It is clear the water could not rise unless it had previously -descended from high ground through the interior of the earth to the -bottom of the well. It partakes of the temperature of the strata through -which it passes, and in every instance has been warmer in proportion to -the depth of the well; but it is evident that the law of increase cannot -be obtained in this manner. Perhaps the most satisfactory experiments on -record are those made by MM. Auguste de la Rive and F. Marcet during the -year 1833, in a boring for water about a league from Geneva, at a place -318 feet above the level of the lake. The depth of the bore was 727 -feet, and the diameter only between four and five inches. No spring was -ever found; but the shaft filled with mud, from the moisture of the -ground mixing with the earth displaced in boring, which was peculiarly -favourable for the experiments, as the temperature at each depth may be -considered to be that of the particular stratum. In this case, where -none of the ordinary causes of disturbance could exist, and where every -precaution was employed by scientific and experienced observers, the -temperature was found to increase regularly and uniformly with the depth -at the rate of about 1° of Fahrenheit for every 52 feet. Professor Reich -of Freyberg has found that the mean of a great number of observations -both in mines and wells is 1° of Fahrenheit for every 55 feet of depth; -and from M. Arago’s observations in the Grenelle Artesian well at Paris, -the increase is 1° of Fahrenheit for every 45 feet. Though there can be -no doubt as to the increase of temperature in penetrating the crust of -the earth, there is still much uncertainty as to the law of increase, -which varies with the nature of the soil and other local circumstances; -but, on an average, it has been estimated at the rate of 1° for every 50 -or 60 feet, which corresponds with the observations of MM. Marcet and De -la Rive. In consequence of the rapid increase of internal heat, thermal -springs, or such as are independent of volcanic action, rising from a -great depth, must necessarily be very rare and of a high temperature; -and it is actually found that none are so low as 68° of Fahrenheit; that -of Chaudes Aigues, in Auvergne, is about 136°. In many places warm water -from Artesian wells will probably come into use for domestic purposes, -and it is even now employed in manufactories near Stutgardt, in Alsace, -&c. - -It is hardly to be expected that at present any information with regard -to the actual internal temperature of the earth should be obtained from -that of the ocean, on account of the mobility of fluids, by which the -colder masses sink downwards, while those that are warmer rise to the -surface. Nevertheless, it may be stated that the temperature of the sea -decreases with the depth between the tropics; while, on the contrary, -all our northern navigators found that the temperature increases with -the depth in the polar seas. The change takes place about the 70th -parallel of latitude. Some ages hence, however, it may be known whether -the earth has arrived at a permanent state as to heat, by comparing -secular observations of the temperature of the ocean if made at a great -distance from the land. - -Should the earth’s temperature increase at the rate of 1° for every 50 -feet, it is clear that at the depth of 200 miles the hardest substances -must be in a state of fusion, and our globe must in that case either be -encompassed by a stratum of melted lava at that depth, or it must be a -ball of liquid fire 7600 miles in diameter, enclosed in a thin coating -of solid matter; for 200 miles are nothing when compared with the size -of the earth. No doubt the form of the earth, as determined by the -pendulum and arcs of the meridian, as well as by the motions of the -moon, indicates original fluidity and subsequent consolidation and -reduction of temperature by radiation; but whether the law of increasing -temperature is uniform at still greater depths than those already -attained by man, it is impossible to say. At all events, internal -fluidity is not inconsistent with the present state of the earth’s -surface, since earthy matter is as bad a conductor of heat as lava, -which often retains its heat at a very little depth for years after its -surface is cool. Whatever the radiation of the earth might have been in -former times, certain it is that it goes on very slowly in our days; for -M. Fourier has computed that the central heat is decreasing from -radiation by only about the 1/30000th part of a degree in a century. If -so, there can be no doubt that it will ultimately be dissipated; but as -far as regards animal and vegetable life, it is of very little -consequence whether the centre of our planet be liquid fire or ice, -since its condition in either case could have no sensible effect on the -climate at its surface. The internal fire does not even impart heat -enough to melt the snow at the poles, though nearer to the centre than -any other part of the globe. - -The immense extent of active volcanic fire is one of the causes of heat -which must not be overlooked. - -The range of the Andes from Chile to the north of Mexico, probably from -Cape Horn to Behring Straits, is one vast district of igneous action, -including the Caribbean and the West Indian Islands on one hand; and -stretching quite across the Pacific Ocean, through the Polynesian -Archipelago, the New Hebrides, the Georgian and Friendly Islands, on the -other. Another chain begins with the Aleutian Islands, extends to -Kamtschatka, and from thence passes through the Kurile, Japanese, and -Philippine Islands, to the Moluccas, whence it spreads with terrific -violence through the Indian Archipelago, even to the Bay of Bengal. -Volcanic action may again be followed from the entrance of the Persian -Gulf to Madagascar, Bourbon, the Canaries, and Azores. Thence a -continuous igneous region extends through about 1000 geographical miles -to the Caspian Sea, including the Mediterranean, and extending north and -south between the 35th and 40th parallels of latitude; and in central -Asia a volcanic region occupies 2500 square geographical miles. The -volcanic fires are developed in Iceland in tremendous force; and the -antarctic land discovered by Sir James Ross is an igneous formation of -the boldest structure, where a volcano in high activity rises 12,000 -feet above the perpetual ice of these polar deserts, and within 19-1/2° -of the south pole. Throughout this vast portion of the world the -subterraneous fire is often intensely active, producing such violent -earthquakes and eruptions that their effects, accumulated during -millions of years, may account for many of the great geological changes -of igneous origin that have already taken place in the earth, and may -occasion others not less remarkable, should time—that essential element -in the vicissitudes of the globe—be granted, and their energy last. - -Sir Charles Lyell, who has shown the power of existing causes with great -ingenuity, estimates that on an average twenty eruptions take place -annually in different parts of the world; and many must occur or have -happened, even on the most extensive and awful scale, among people -equally incapable of estimating their effects and of recording them. We -should never have known the extent of the fearful eruption which took -place in the island of Sumbawa, in 1815, but for the accident of Sir -Stamford Raffles having been governor of Java at the time. It began on -the 5th of April, and did not entirely cease till July. The ground was -shaken through an area of 1000 miles in circumference; the tremors were -felt in Java, the Moluccas, a great part of Celebes, Sumatra, and -Borneo. The detonations were heard in Sumatra, at the distance of 970 -geographical miles in a straight line; and at Ternate, 720 miles in the -opposite direction. The most dreadful whirlwinds carried men and cattle -into the air; and with the exception of 26 persons, the whole population -of the island perished to the amount of 12,000. Ashes were carried 300 -miles to Java in such quantities that the darkness during the day was -more profound than ever had been witnessed in the most obscure night. -The face of the country was changed by the streams of lava, and by the -upheaving and sinking of the soil. The town of Tomboro was submerged, -and water stood to the depth of 18 feet in places which had been dry -land. Ships grounded where they had previously anchored, and others -could hardly penetrate the mass of cinders which floated on the surface -of the sea for several miles to the depth of two feet. A catastrophe -similar to this, though of less magnitude, took place in the island of -Bali in 1808, which was not heard of in Europe till years afterwards. -The eruption of Coseguina in the Bay of Fonseca, which began on the 19th -of January, 1835, and lasted many days, was even more dreadful and -extensive in its effects than that of Sumbawa. The ashes during this -eruption were carried by the upper current of the atmosphere as far -north as Chiassa, which is upwards of 400 leagues to the windward of -that volcano. Many volcanoes supposed to be extinct have all at once -burst out with inconceivable violence. Witness Vesuvius, on historical -record; and the volcano in the island of St. Vincent in our own days, -whose crater was lined with large trees, and which had not been active -in the memory of man. Vast tracts are of volcanic origin where volcanoes -have ceased to exist for ages. Whence it may be inferred that in some -places the subterraneous fires are in the highest state of activity, in -some they are inert, and in others they appear to be extinct. Yet there -are few countries that are not subject to earthquakes of greater or less -intensity; the tremors are propagated like a sonorous undulation to such -distances that it is impossible to say in what point they originate. In -some recent instances their power must have been tremendous. In South -America, so lately as 1822, an area of 100,000 square miles, which is -equal in extent to the half of France, was raised several feet above its -present level—a most able account of which is given in the ‘Transactions -of the Geological Society,’ by an esteemed friend of the author’s, the -late Mrs. Graham, who was present during the whole time of that -formidable earthquake, which recurred at short intervals for more than -two months, and who possessed talents to appreciate, and had -opportunities of observing, its effects under the most favourable -circumstances at Valparaiso, and for miles along the coast where it was -most intense. A considerable elevation of the land has again taken place -along the coast of Chile, in consequence of the violent earthquake which -happened on the 20th of February, 1835. In 1819 a ridge of land -stretching for 50 miles across the delta of the Indus, 16 feet broad, -was raised 10 feet above the plain. The reader is referred to Sir -Charles Lyell’s excellent ‘Principles of Geology,’ already mentioned, -for most interesting details of the phenomena and extensive effects of -volcanoes and earthquakes, too numerous to find a place here. It may -however be mentioned that innumerable earthquakes are from time to time -shaking the solid crust of the globe, and carrying destruction to -distant regions, progressively though slowly accomplishing the great -work of change. A most disastrous instance took place on the 15th of -December, 1857, in the Neapolitan provinces of La Basilicata and -Principato Citeriore, where the destruction was extensive and terrible; -the number of victims, according to the official accounts, being -returned at upwards of ten thousand. These terrible engines of ruin, -fitful and uncertain as they may seem, must, like all durable phenomena, -have a law which may in time be discovered by long-continued and -accurate observations. - -The shell of volcanic fire that girds the globe at a small depth below -our feet has been attributed to different causes. By some it is supposed -to originate in an ocean of incandescent matter, still existing in the -central abyss of the earth. Some conceive it to be superficial, and due -to chemical action, in strata at no very great depth when compared with -the size of the globe. The more so as matter on a most extensive scale -is passing from old into new combinations, which, if rapidly effected, -are capable of producing the most intense heat. According to others, -electricity, which is so universally diffused in all its forms -throughout the earth, if not the immediate cause of the volcanic -phenomena, at least determines the chemical affinities that produce -them. It is clear that a subject so involved in mystery must give rise -to much speculation, in which every hypothesis is attended with -difficulties that observation alone can remove. - -But the views of Mr. Babbage and Sir John Herschel on the general cause -of volcanic action, and the changes in the equilibrium of the internal -heat of the globe, accord more with the laws of mechanics and radiant -heat than any that have been proposed. The theory of these distinguished -philosophers, formed independently of each other, is equally consistent -with observed phenomena, whether the earth be a solid crust encompassing -a nucleus of liquid lava, or that there is merely a vast reservoir or -stratum of melted matter at a moderate depth below the superficial -crust. The author is indebted to the kindness of Sir Charles Lyell for -the perusal of a most interesting letter from Sir John Herschel, in -which he states his views on the subject. - -Supposing that the globe is merely a solid crust, resting upon fluid or -semi-fluid matter, whether extending to the centre or not, the transfer -of pressure from one part of its surface to another by the degradation -of existing continents, and the formation of new ones, would be -sufficient to subvert the equilibrium of heat in the interior, and -occasion volcanic eruptions. For, since the internal heat of the earth -is transmitted outwards by radiation, an accession of new matter on any -part of the surface, like an addition of clothing, by keeping it in, -would raise the temperature of the strata below, and in the course of -ages would even reduce those at a great depth to a state of fusion. Some -of the substances might be converted into gases; and should the -accumulation of new matter take place at the bottom of the sea, as is -generally the case, this lava would be mixed with water in a state of -ignition in consequence of the enormous pressure of the ocean, and of -the newly superimposed matter which would prevent it from expanding into -steam. Now Sir Charles Lyell has shown, with his usual talent, that the -quantity of matter carried down by rivers from the surface of the -continents is comparatively trifling, and that the great transfer to the -bottom of the ocean is produced at the coast-line by the action of the -sea; hence, says Sir John Herschel, “the greatest accumulation of local -pressure is in the central area of the deep sea, while the greatest -local relief takes place along the abraded coast-lines. Here then should -occur the chief volcanic vents.” As the crust of the earth is much -weaker on the coasts than elsewhere, it is more easily ruptured, and, as -Mr. Babbage observes, immense rents might be produced there by its -contraction in cooling down after being deprived of a portion of its -original thickness. The pressure on the bottom of the ocean would force -a column of lava mixed with ignited water and gas to rise through an -opening thus formed, and, says Sir John Herschel, “when the column -attains such a height that the ignited water can become steam, the joint -specific gravity of the column is suddenly diminished, and up comes a -jet of mixed steam and lava, till so much has escaped that the matter -deposited at the bottom of the ocean takes a fresh bearing, when the -evacuation ceases and the crack becomes sealed up.” - -This theory perfectly accords with the phenomena of nature, since there -are very few active volcanoes at a distance from the sea, and the -exceptions that do occur are generally near lakes, or they are connected -with volcanoes on the maritime coasts. Many break out even in the bottom -of the ocean, probably owing to some of the supports of the superficial -crust giving way, so that the steam and lava are forced up through the -fissures. - -Finally, Mr. Babbage observes that, “in consequence of changes -continually going on, by the destruction of forests, the filling up of -seas, the wearing down of elevated lands, the heat radiated from the -earth’s surface varies considerably at different periods. In consequence -of this variation, and also in consequence of the covering up of the -bottom of the sea by the detritus of the land, the surfaces of equal -temperature within the earth are continually changing their form, and -exposing thick beds near the exterior to alterations of temperature. The -expansion and contraction of these strata may form rents and veins, -produce earthquakes, determine volcanic eruptions, elevate continents, -and, possibly, raise mountain chains.” - -The numerous vents for the internal heat formed by volcanoes, hot -springs, and the emission of steam, so frequent in volcanic regions, no -doubt maintain the tranquillity of the interior fluid mass, which seems -to be perfectly inert unless when put in motion by unequal pressure. - -But, to whatever cause the increasing heat of the earth and the -subterranean fires may ultimately be referred, it is certain that, -except in some local instances, they have no sensible effect on the -temperature of its surface. It may therefore be concluded that the heat -of the earth, above the zone of uniform temperature, is entirely owing -to the sun. - -The power of the solar rays depends much upon the manner in which they -fall, as we readily perceive from the different climates on our globe. -Although the sun is about three millions of miles nearer to the earth in -winter than in summer, his rays strike the atmosphere in the northern -hemisphere so obliquely that it absorbs a much greater quantity of heat -than when they are more direct (N. 217). Indeed it is so great that, -when the sun has an altitude of 30°, one half of his heat is absorbed by -the atmosphere, and it increases very rapidly as he sinks towards the -horizon. However, that heat is not lost: it is most beneficial to the -earth, being really the heat which supplies the greatest part of that -which is radiated into space during the absence of the sun. Professor -Dove has shown, by taking at all seasons the mean of the temperatures of -points on the earth’s surface diametrically opposite to each other, that -the average temperature of the whole earth’s surface in June, when we -are farthest from the sun, considerably exceeds that in December, when -we are nearest to him, owing to the excess of water in the southern -hemisphere, and that of land in the northern, which gives a general -insular climate to the former, and a continental climate to the latter. - -The observations of the north polar navigators, and those of Sir John -Herschel at the Cape of Good Hope, show that the direct heating -influence of the solar rays is greatest at the equator, and that it -diminishes gradually as the latitude increases. At the equator the -maximum is 48-3/4°, while in Europe it has never exceeded 29-1/2°. - -M. Pouillet has estimated with singular ingenuity, from a series of -observations made by himself, that the whole quantity of heat which the -earth receives annually from the sun is such as would be sufficient to -melt a stratum of ice covering the whole globe 46 feet deep. Part of -this heat is radiated back into space; but by far the greater part -descends into the earth during the summer, towards the zone of uniform -temperature, whence it returns to the surface in the course of the -winter, and tempers the cold of the ground and the atmosphere in its -passage to the ethereal regions, where it is lost, or rather where it -combines with the radiation from the other bodies of the universe in -maintaining the temperature of space. The sun’s power being greatest -between the tropics, the heat sinks deeper there than elsewhere, and the -depth gradually diminishes towards the poles; but the heat is also -transmitted laterally from the warmer to the colder strata north and -south of the equator, and aids in tempering the severity of the polar -regions. - -The mean heat of the earth, above the stratum of constant temperature, -is determined from that of springs; and, if the spring be on elevated -ground, the temperature is reduced by computation to what it would be at -the level of the sea, assuming that the heat of the soil varies -according to the same law as the heat of the atmosphere, which is about -1° of Fahrenheit’s thermometer for every 333·7 feet. From a comparison -of the temperature of numerous springs with that of the air, Sir David -Brewster concludes that there is a particular line passing nearly -through Berlin, at which the temperature of springs and that of the -atmosphere coincide; that in approaching the arctic circle the -temperature of springs is always higher than that of the air, while, -proceeding towards the equator, it is lower. - -Since the warmth of the superficial strata of the earth decreases from -the equator to the poles, there are many places in both hemispheres -where the ground has the same mean temperature. If lines were drawn -through all those points in the upper strata of the globe which have the -same mean annual temperature, they would be nearly parallel to the -equator between the tropics, and would become more and more irregular -and sinuous towards the poles. These are called isogeothermal lines. A -variety of local circumstances disturb their parallelism, even between -the tropics. - -The temperature of the ground at the equator is lower on the coasts and -islands than in the interior of continents; the warmest part is in the -interior of Africa; but it is obviously affected by the nature of the -soil, especially if it be volcanic. - -Much has been done to ascertain the manner in which heat is distributed -over the surface of our planet, and the variations of climate, which, in -a general view, mean every change of the atmosphere, such as of -temperature, humidity, variations of barometric pressure, purity of air, -the serenity of the heavens, the effects of winds, and electric tension. -Temperature depends upon the property which all bodies possess, more or -less, of perpetually absorbing and emitting or radiating heat. When the -interchange is equal, the temperature of a body remains the same; but, -when the radiation exceeds the absorption, it becomes colder, and _vice -versâ_. In order to determine the distribution of heat over the surface -of the earth, it is necessary to find a standard by which the -temperature in different latitudes may be compared. For that purpose it -is requisite to ascertain, by experiment, the mean temperature of the -day, of the month, and of the year, at as many places as possible -throughout the earth. The annual average temperature may be found by -adding the mean temperatures of all the months in the year, and dividing -the sum by twelve. The average of ten or fifteen years will give it -approximately; for, although the temperature in any place maybe subject -to very great variations, yet it never deviates more than a few degrees -from its mean state, which consequently offers a good standard of -comparison. As a standard, however, much greater accuracy is required. - -If climate depended solely upon the heat of the sun, all places having -the same latitude would have the same mean annual temperature. The -motion of the sun in the ecliptic, indeed, occasions perpetual -variations in the length of the day, and in the direction of the rays -with regard to the earth; yet, as the cause is periodic, the mean annual -temperature from the sun’s motion alone must be constant in each -parallel of latitude; for it is evident that the accumulation of heat in -the long days of summer, which is but little diminished by radiation -during the short nights, is balanced by the small quantity of heat -received during the short days in winter, and its radiation in the long, -frosty, and clear nights. In fact, if the globe were everywhere on a -level with the surface of the sea, and of uniform substance, so as to -absorb and radiate heat equally, the mean heat of the sun would be -regularly distributed over its surface in zones of equal annual -temperature parallel to the equator, from which it would decrease to -each pole as the square of the cosine of the latitude; and its quantity -would only depend upon the altitude of the sun and atmospheric currents. -The distribution of heat, however, in the same parallel, is very -irregular in all latitudes except between the tropics, where the -isothermal lines, or the lines passing through places of equal mean -annual temperature, are more nearly parallel to the equator. The causes -of disturbance are very numerous; but such as have the greatest -influence, according to M. de Humboldt, to whom we are indebted for the -greater part of what is known on the subject, are the elevation of the -continents, the distribution of land and water over the surface of the -globe exposing different absorbing and radiating powers; the variations -in the surface of the land, as forests, sandy deserts, verdant plains, -rocks, &c.; mountain-chains covered with masses of snow, which diminish -the temperature; the reverberation of the sun’s rays in the valleys, -which increases it; and the interchange of currents, both of air and -water, which mitigates the rigour of climates; the warm currents from -the equator softening the severity of the polar frosts, and the cold -currents from the poles tempering the intense heat of the equatorial -regions. To these may be added cultivation, though its influence extends -over but a small portion of the globe, only a fourth part of the land -being inhabited. - -Temperature decreases with the height above the level of the sea, as -well as with the latitude. The air in the higher regions of the -atmosphere is much cooler than that below, because the warm air expands -as it rises, by which its capacity for heat is increased, a great -proportion becomes latent or absorbed, and less of it sensible. A -portion of air at the surface of the earth whose temperature is 70° of -Fahrenheit, if carried to the height of two miles and a half, would -expand so much that its temperature would be reduced 50°; and in the -ethereal regions the temperature is 239° below the zero point of -Fahrenheit. - -The height at which snow lies perpetually decreases from the equator to -the poles, and is higher in summer than in winter; but it varies from -many circumstances. Snow rarely falls when the cold is intense and the -atmosphere dry. Extensive forests produce moisture by their evaporation; -and high table-lands, on the contrary, dry and warm the air, because the -air at great elevations is too rare to absorb much of the sun’s heat. In -the Cordilleras of the Andes, plains of only twenty-five square leagues -from their extent raise the temperature as much as 3° or 4° above what -is found at the same altitude on the rapid declivity of a mountain, -consequently the line of perpetual snow varies according as one or other -of these causes prevails. Aspect in general has also a great influence; -yet the line of perpetual snow is much higher on the northern than on -the southern side of the Himalaya, partly because the air is nearly -deprived of its moisture by precipitation before it arrives at the -northern side of the mountains. On the whole, it appears that the mean -height between the tropics at which the snow lies perpetually is about -15,207 feet above the level of the sea; whereas snow does not cover the -ground continually at the level of the ocean till near the north pole. -In the southern hemisphere, however, the cold is greater than in the -northern. In Sandwich Land, between the 54th and 58th degrees of -latitude, perpetual snow and ice extend to the sea-level; and in the -island of S. Georgia, in the 53rd degree of south latitude, which -corresponds with the latitude of the central counties of England, -perpetual snow descends even to the level of the ocean. It has been -shown that this excess of cold in the southern hemisphere cannot be -attributed to the winter being longer than ours by 7-3/4 days. It is -probably owing to the open sea surrounding the south pole, which permits -the icebergs to descend to a lower latitude by 10° than they do in the -northern hemisphere, on account of the numerous obstructions opposed to -them by the islands and continents about the north pole. Icebergs from -the Arctic seas seldom float farther to the south than the Azores; -whereas those that come from the south pole descend to as low a latitude -as that of the Cape of Good Hope. - -The influence of mountain-chains does not wholly depend upon the line of -perpetual congelation. They attract and condense the vapours floating in -the air, and send them down in torrents of rain. They radiate heat into -the atmosphere at a lower elevation, and increase the temperature of the -valleys by the reflection of the sun’s rays, and by the shelter they -afford against prevailing winds. But, on the contrary, one of the most -general and powerful causes of cold arising from the vicinity of -mountains is the freezing currents of wind which rush from their lofty -peaks along the rapid declivities, chilling the surrounding valleys: -such is the cutting north wind called the bise in Switzerland. - -Next to elevation, the difference in the radiating and absorbing powers -of the sea and land has the greatest influence in disturbing the regular -distribution of heat. The extent of the dry land is not above the fourth -part of that of the ocean; so that the general temperature of the -atmosphere, regarded as the result of the partial temperatures of the -whole surface of the globe, is most powerfully modified by the sea. -Besides, the ocean acts more uniformly on the atmosphere than the -diversified surface of the solid mass does, both by the equality of its -curvature and its homogeneity. In opaque substances the accumulation of -heat is confined to the stratum nearest the surface. The seas become -less heated at their surface than the land, because the solar rays, -before being extinguished, penetrate the transparent liquid to a greater -depth and in greater numbers than in the opaque masses. On the other -hand, water has a considerable radiating power, which, together with -evaporation, would reduce the surface of the ocean to a very low -temperature, if the cold particles did not sink to the bottom on account -of their superior density. The seas preserve a considerable portion of -the heat they receive in summer, and from their saltness do not freeze -so soon as fresh water. So that, in consequence of all these -circumstances, the ocean is not subject to such variations of heat as -the land, and, by imparting its temperature to the winds and by its -currents, it diminishes the rigour of climate on the coasts and in the -islands, which are never subject to such extremes of heat and cold as -are experienced in the interior of continents, though they are liable to -fogs and rain from the evaporation of the adjacent seas. On each side of -the equator to the 48th degree of latitude, the surface of the ocean is -in general warmer than the air above it. The mean of the difference of -the temperature at noon and midnight is about 1°·37, the greatest -deviation never exceeding from 0°·36 to 2°·16, which is much cooler than -the air over the land. - -On land the temperature depends upon the nature of the soil and its -products, its habitual moisture or dryness. From the eastern extremity -of the Sahara desert quite across Africa, the soil is almost entirely -barren sand; and the Sahara desert itself extends over an area of -194,000 square leagues, equal to twice the area of the Mediterranean -Sea, and raises the temperature of the air by radiation from 90° to -100°, which must have a most extensive influence. On the contrary, -vegetation cools the air by evaporation and the apparent radiation of -cold from the leaves of plants, because they absorb more caloric than -they give out. The graminiferous plains of South America cover an extent -ten times greater than France, occupying no less than about 50,000 -square leagues, which is more than the whole chain of the Andes, and all -the scattered mountain-groups of Brazil. These, together with the plains -of North America and the steppes of Europe and Asia, must have an -extensive cooling effect on the atmosphere if it be considered that in -calm and serene nights they cause the thermometer to descend 12° or 14°, -and that in the meadows and heaths in England the absorption of heat by -the grass is sufficient to cause the temperature to sink to the point of -congelation during the night for ten months in the year. Forests cool -the air also by shading the ground from the rays of the sun, and by -evaporation from the boughs. Hales found that the leaves of a single -plant of helianthus three feet high exposed nearly forty feet of -surface; and, if it be considered that the woody regions of the river -Amazons, and the higher part of the Orinoco, occupy an area of 260,000 -square leagues, some idea may be formed of the torrents of vapour which -rise from the leaves of the forests all over the globe. However, the -frigorific effects of their evaporation are counteracted in some measure -by the perfect calm which reigns in the tropical wildernesses. The -innumerable rivers, lakes, pools, and marshes interspersed through the -continents absorb caloric, and cool the air by evaporation; but, on -account of the chilled and dense particles sinking to the bottom, deep -water diminishes the cold of winter, so long as ice is not formed. - -In consequence of the difference in the radiating and absorbing powers -of the sea and land, their configuration greatly modifies the -distribution of heat over the surface of the globe. Under the equator -only one-sixth part of the circumference is land; and the superficial -extent of land in the northern and southern hemispheres is in the -proportion of three to one. The effect of this unequal division is -greater in the temperate than in the torrid zones, for the area of land -in the northern temperate zone is to that in the southern as thirteen to -one, whereas the proportion of land between the equator and each tropic -is as five to four. It is a curious fact, noticed by Mr. Gardner, that -only one twenty-seventh part of the land of the globe has land -diametrically opposite to it. This disproportionate arrangement of the -solid part of the globe has a powerful influence on the temperature of -the southern hemisphere. But, besides these greater modifications, the -peninsulas, promontories, and capes, running out into the ocean, -together with bays and internal seas, all affect temperature. To these -may be added the position of continental masses with regard to the -cardinal points. All these diversities of land and water influence -temperature by the agency of the winds. On this account the temperature -is lower on the eastern coasts both of the New and Old World than on the -western; for, considering Europe as an island, the general temperature -is mild in proportion as the aspect is open to the Atlantic Ocean, the -superficial temperature of which, as far north as the 45th and 50th -degrees of latitude, does not fall below 48° or 51° of Fahrenheit, even -in the middle of winter. On the contrary, the cold of Russia arises from -its exposure to the northern and eastern winds. But the European part of -that empire has a less rigorous climate than the Asiatic, because it -does not extend to so high a latitude. - -The interposition of the atmosphere modifies all the effects of the -sun’s heat. The earth communicates its temperature so slowly, that M. -Arago has occasionally found as much as from 14° to 18° of difference -between the heat of the soil and that of the air two or three inches -above it. - -The circumstances which have been enumerated, and many more, concur in -disturbing the regular distribution of heat over the globe, and occasion -numberless local irregularities. Nevertheless the mean annual -temperature becomes gradually lower from the equator to the poles. But -the diminution of mean heat is most rapid between the 40th and 45th -degrees of latitude both in Europe and America, which accords perfectly -with theory; whence it appears that the variation in the square of the -cosine of the latitude (N. 127), which expresses the law of the change -of temperature, is a maximum towards the 45th degree of latitude. The -mean annual temperature under the equator in America is about 81-1/2° of -Fahrenheit: in Africa it is said to be nearly 83°. The difference -probably arises from the winds of Siberia and Canada, whose chilly -influence is sensibly felt in Asia and America, even within 18° of the -equator. - -The isothermal lines are nearly parallel to the equator, till about the -22nd degree of latitude on each side of it, where they begin to lose -their parallelism, and continue to do so more and more as the latitude -augments. With regard to the northern hemisphere, the isothermal line of -59° of Fahrenheit passes between Rome and Florence in latitude 43°; and -near Raleigh in North Carolina, latitude 36°: that of 50° of equal -annual temperature runs through the Netherlands, latitude 51°; and near -Boston in the United States, latitude 42-1/2°: that of 41° passes near -Stockholm, latitude 59-1/2°; and St. George’s Bay, Newfoundland, -latitude 48°: and lastly, the line of 32°, the freezing point of water, -passes between Ulea in Lapland, latitude 66°, and Table Bay, on the -coast of Labrador, latitude 54°. - -Thus it appears that the isothermal lines, which are nearly parallel to -the equator for about 22°, afterwards deviate more and more. From -observations made during the numerous voyages in the Arctic Seas, it is -found that the isothermal lines of Europe and America entirely separate -in the high latitudes, and surround two poles of maximum cold: one, in -79° N. lat. and 120° E. long., has a mean temperature of 2° Fahrenheit; -and the other, whose temperature was determined by Sir David Brewster to -be 3-1/2° Fahrenheit, from the observations of Sir Edward Parry is near -Melville Island. The pole of the earth’s rotation, whose mean -temperature is probably not below 15° Fahrenheit, is nearly midway -between the two; and the line which joins these points of maximum cold -is almost coincident with that diameter of the polar basin which bisects -it, and passes through its two great outlets into the Pacific and -Atlantic Oceans, a most remarkable feature, and strongly indicative of -the absence of land, and of the prevalence of a materially milder -climate in the polar Ocean, probably not under 15° Fahrenheit.[12] It is -believed that two corresponding poles of maximum cold exist in the -southern hemisphere, though observations are wanting to trace the course -of the southern isothermal lines with the same accuracy as the northern. - -The isothermal lines, or such as pass through places where the mean -annual temperature of the air is the same, do not always coincide with -the isogeothermal lines, which are those passing through places where -the mean temperature of the ground is the same. Sir David Brewster, in -discussing this subject, finds that the isogeothermal lines are always -parallel to the isothermal lines; consequently the same general formula -will serve to determine both, since the difference is a constant -quantity obtained by observation, and depending upon the distance of the -place from the neutral isothermal line. These results are confirmed by -the observations of M. Kupffer of Kasan during his excursions to the -north, which show that the European and the American portions of the -isogeothermal line of 32° of Fahrenheit actually separate, and go round -the two poles of maximum cold. This traveller remarked, also, that the -temperature both of the air and of the soil decreases most rapidly -towards the 45th degree of latitude. - -It is evident that places may have the same mean annual temperature, and -yet differ materially in climate. In one, the winters may be mild and -the summers cool; whereas another may experience the extremes of heat -and cold. Lines passing through places having the same mean summer or -winter temperature are neither parallel to the isothermal, the -geothermal lines, nor to one another, and they differ still more from -the parallels of latitude. In Europe, the latitude of two places which -have the same annual heat never differs more than 8° or 9°; whereas the -difference in the latitude of those having the same mean winter -temperature is sometimes as much as 18° or 19°. At Kasan, in the -interior of Russia, in latitude 55°·48, nearly the same with that of -Edinburgh, the mean annual temperature is about 37°·6; at Edinburgh it -is 47°·84. At Kasan the mean summer temperature is 64°·84, and that of -winter 2°·12; whereas at Edinburgh the mean summer temperature is -58°·28, and that of winter 38°·66. Whence it appears that the difference -of winter temperature is much greater than that of summer. At Quebec the -summers are as warm as those in Paris, and grapes sometimes ripen in the -open air: whereas the winters are as severe as in Petersburgh; the snow -lies five feet deep for several months, wheel carriages cannot be used, -the ice is too hard for skating, travelling is performed in sledges, and -frequently on the ice of the river St. Lawrence. The cold at Melville -Island on the 15th of January, 1820, according to Sir Edward Parry, was -55° below the zero of Fahrenheit’s thermometer; and when Dr. Kane was on -the northern coast of Greenland it was 70° below that point; yet the -summer heat during the day in these high latitudes is insupportable. - -Observations tend to prove that all the climates of the earth are -stable, and that their vicissitudes are only periods or oscillations of -more or less extent, which vanish in the mean annual temperature of a -sufficient number of years. This constancy of the mean annual -temperature of the different places on the surface of the globe shows -that the same quantity of heat which is annually received by the earth -is annually radiated into space; and that would be the case even if the -quantity of heat emitted by the sun should vary with his spots, for, if -more were received, more would be radiated. Nevertheless, a variety of -causes may disturb the climate of a place; cultivation may make it -warmer; but it is at the expense of some other place, which becomes -colder in the same proportion. There may be a succession of cold summers -and mild winters, but in some other country the contrary takes place to -effect the compensation; wind, rain, snow, fog, and the other meteoric -phenomena, are the ministers employed to accomplish the changes. The -distribution of heat may vary with a variety of circumstances; but the -absolute quantity lost and gained by the whole earth in the course of a -year, if not invariably the same, is at least periodical. - - - - - 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. - - -THE gradual decrease of temperature in the air and in the earth, from -the equator to the poles, is clearly indicated by its influence on -vegetation. In the valleys of the torrid zone, where the mean annual -temperature is very high, and where there is abundance of light and -moisture, nature adorns the soil with all the luxuriance of perpetual -summer. The palm, the bombax ceiba, and a variety of magnificent trees, -tower to the height of 150 or 200 feet above the banana, the bamboo, the -arborescent fern, and numberless other tropical productions, so -interlaced by creeping and parasitical plants, as often to present an -impenetrable barrier. But the richness of vegetation gradually -diminishes with the temperature; the splendour of the tropical forest is -succeeded by the regions of the vine and olive; these again yield to the -verdant meadows of more temperate climes; then follow the birch and the -pine, which probably owe their existence in very high latitudes more to -the warmth of the soil than to that of the air. But even these enduring -plants become dwarfish shrubs, till a verdant carpet of mosses and -lichens, enamelled with flowers, exhibits the last sign of vegetable -life during the short but fervid summers at the polar regions. Such is -the effect of cold and diminished light on the vegetable kingdom, that -the number of species growing under the equator and in the northern -latitudes of 45° and 68° are in the proportion of the numbers 12, 4, and -1. Notwithstanding the remarkable difference between a tropical and -polar flora, light and moisture seem to be almost the only requisites -for vegetation, since neither heat, cold, nor even comparative darkness, -absolutely destroy the fertility of nature. In salt plains and sandy -deserts alone hopeless barrenness prevails. Plants grow on the borders -of hot springs: they form the oases wherever moisture exists among the -burning sands of Africa; they are found in caverns almost void of light, -though generally blanched and feeble. The ocean teems with vegetation. -The snow itself not only produces a red lichen, discovered by Saussure -in the frozen declivities of the Alps, found in abundance by the author -crossing the Col de Bonhomme from Savoy to Piedmont, and by the polar -navigators in the Arctic regions, but it affords shelter to the -productions of these inhospitable climes against the piercing winds that -sweep over fields of everlasting ice. Those undaunted mariners narrate -that under this cold defence plants spring up, dissolve the snow a few -inches round, and the part above, being again quickly frozen into a -transparent sheet of ice, admits the sun’s rays, which warm and cherish -the plants in this natural hothouse, till the returning summer renders -such protection unnecessary. - -The chemical action of light is, however, absolutely requisite for the -growth of plants which derive their principal nourishment from the -atmosphere. They consume the carbonic acid gas, nitrogen, aqueous -vapour, and ammonia it contains; but it is the chemical agency of light -that enables them to absorb, decompose, and consolidate these substances -into wood, leaves, flowers, and fruit. The atmosphere would soon be -deprived of these elements of vegetable life were they not perpetually -supplied by the animal creation; while, in return, plants decompose the -moisture they imbibe, and, having assimilated the carbonic acid gas, -they exhale oxygen for the maintenance of the animated creation, and -thus preserve a just equilibrium. Hence it is the combined and powerful -influences of the whole solar beams that give such brilliancy to the -tropical forests, while, with their decreasing energy in the higher -latitudes, vegetation becomes less vigorous. On that account it is vain -to expect that the fruit and flowers raised in our hothouses can ever -have the flavour, perfume, or colouring equal to that which they acquire -from the vivid light of their native skies. - -By far the greater number of the known species of plants are indigenous -in equinoctial America; Europe contains about half the number; Asia, -with its islands, somewhat less than Europe; Australia, with the islands -in the Pacific, still less; and in Africa there are fewer known -vegetable productions than in any part of the globe of equal extent, for -that rich and luxuriant region discovered by Dr. Livingstone has yet to -be explored botanically. Very few social plants, such as grasses and -heaths that cover large tracts of land, are to be found between the -tropics, except on the sea-coasts and elevated plains. Some exceptions -to this, however, are to be met with in the jungles of the Deccan, &c. -In the equatorial regions, where the heat is always great, the -distribution of plants depends upon the mean annual temperature; whereas -in temperate zones the distribution is regulated in some degree by the -summer heat. Some plants require a gentle heat of long continuance, -others flourish most where the extremes of heat and cold are greater. -The range of wheat is very great; it may be cultivated as far north as -the 60th degree of latitude; but in the torrid zone it will seldom form -an ear below an elevation of 4500 feet above the level of the sea from -exuberance of vegetation; nor will it ripen generally above the height -of 12,000 feet; in Tibet it ripens at a still greater elevation. Colonel -Sykes states that in the Deccan wheat thrives as low as 1800 feet above -the sea. The best wines are produced between the 30th and 45th degrees -of north latitude. With regard to the vegetable kingdom, elevation is -equivalent to latitude as far as temperature is concerned. In ascending -the mountains of the torrid zone, the richness of the tropical -vegetation diminishes with the height; a succession of plants similar -to, though not identical with, those found in latitudes of corresponding -mean temperature takes place; the lofty forests by degrees lose their -splendour; stunted shrubs succeed; till at last the progress of the -lichen is checked by perpetual snow. On the volcano of Teneriffe there -are five successive zones, each producing distinct families of plants. -The first is the region of vines, the next that of laurels; these are -followed by the region of pines, of Ericas or heaths, of grass; the -whole covering the declivity of the peak through an extent of 11,200 -feet of perpendicular height. - -Near the equator oaks flourish at the height of 9200 feet above the sea; -and, on the lofty range of the Himalaya, the primula, the convallaria, -and the veronica flower, but not the primrose, the lily of the valley, -or the veronica, which adorn our meadows; for, although the herbarium -collected by Moorcroft, on his route from Neetee to Daba and Gartope in -Chinese Tartary, at elevations as high or even higher than Mont Blanc, -abound in Alpine and European genera, the species are universally -different, with the single exception of the Rhodiola rosea, which is -identical with the species that blooms in Scotland. It is not in this -instance alone that similarity of climate obtains without identity of -productions; throughout the whole globe a certain analogy both of -structure and appearance is frequently discovered between plants under -corresponding circumstances which are yet specifically different. It is -even said that a difference of 25° of latitude occasions a total change, -not only of vegetable productions, but of organised beings. Certain it -is that each separate region both of land and water, from the frozen -shores of the polar circles to the burning regions of the torrid zone, -possesses a flora peculiarly its own. The whole globe has been divided -by physical geographers into various botanical districts, differing -almost entirely in their specific vegetable productions, the limits of -which are most decided when they are separated by a wide expanse of -ocean, mountain chains, sandy deserts, salt plains, or internal seas. A -considerable number of plants are common to the northern regions of -Asia, Europe, and America, where the continents almost unite; but, in -approaching the south, the floras of these three great divisions of the -globe differ more and more even in the same parallels of latitude, which -shows that temperature alone is not the cause of the almost complete -diversity of species that everywhere prevails. The floras of China, -Siberia, Tartary, of the European district including central Europe and -the coast of the Mediterranean, and the Oriental region comprising the -countries round the Black and Caspian Seas, all differ in specific -character. Only twenty-four species were found by MM. Humboldt and -Bonpland in Equinoctial America identical with those of the Old World; -and Dr. Robert Brown not only found that a peculiar vegetation exists in -Australia between the 33rd and 35th parallels of south latitude, but -that at the eastern and western extremities of these parallels not one -species is common to both, and that certain genera also are almost -entirely confined to these spots. The number of species common to -Australia and Europe are only 166 out of 4100, and probably some of -these have been conveyed thither by the colonists; but the greater part -of that continent is still unexplored. However, this proportion exceeds -what has hitherto been observed in southern Africa, and, from what has -been already stated, the proportion of European species in Equinoctial -America is still less. - -Islands partake of the vegetation of the nearest continents; but, when -very remote from land, their floras are altogether peculiar. The -Aleutian Islands, extending between Asia and America, partake of the -vegetation of the northern parts of both continents, and may have served -as a chain of communication. In Madeira and Teneriffe, the plants of -Portugal, Spain, the Azores, and of the northern coast of Africa, are -found; and the Canaries contain a great number of plants belonging to -the African coast. But each of these islands possesses a flora that -exists nowhere else; and St. Helena, standing alone in the midst of the -Atlantic Ocean, produces only two or three species of plants recognised -as belonging to any other part of the world. - -It appears from the investigations of M. de Humboldt that between the -tropics the plants, such as grasses and palms, which have only one -seed-lobe, are to the tribe which have two seed-lobes, like most of the -European species, in the proportion of one to four; in the temperate -zones they are as one to six; and in the Arctic regions, where mosses -and lichens, which form the lowest order of the vegetable creation, -abound, the proportion is as one to two. Annuals with one and two -seed-lobes, in the temperate zones, amount to one-sixth of the whole, -omitting the cryptogamia (N. 218); in the torrid zone they scarcely form -one-twentieth, and in Lapland one-thirtieth part. In approaching the -equator the ligneous exceed the number of herbaceous plants; in America -there are 120 different species of forest trees, whereas in the same -latitudes in Europe only 34 are to be found. - -Similar laws regulate the distribution of marine plants. Groups of algæ, -or marine plants, affect particular temperatures or zones of latitude -and different depths, though some few genera prevail throughout the -ocean. The polar Atlantic basin to the 40th degree of north latitude -presents a well-defined vegetation. The West India seas, including the -Gulf of Mexico, the eastern coast of South America, the Indian Ocean and -its gulfs, the shores of New Holland, and the neighbouring islands, have -each their distinct species. The Mediterranean possesses a vegetation -peculiar to itself, extending to the Black Sea; and the species of -marine plants on the coast of Syria and in the port of Alexandria differ -almost entirely from those of Suez and the Red Sea. It is observed that -shallow seas have a different set of plants from such as are deeper and -colder; and, unlike terrestrial vegetation, the algæ are more numerous -in the mean latitudes than either towards the equator or the poles. They -vary also with the depth: completely different kinds affect different -depths, their seeds being of such specific gravity as to remain and -germinate where the parent plant grew. The quantity of algæ in that -accumulation known as the sargassa or grassy sea is so great, that the -early navigators, Columbus and Lerius, compared it to extensively -inundated meadows: it impeded their ships, and alarmed their sailors. It -is in the North Atlantic, a little to the west of the meridian of Fayal, -one of the Azores, between the 25th and 36th parallels of latitude. A -smaller bank lies between the 22nd and 26th degrees of north latitude, -about 80 leagues west of the meridian of the Bahama Islands. These -masses chiefly consist of one or two species of sargassa, the most -extensive genus of the order Fucoideæ. - -Some of the seaweeds grow to enormous lengths, and all are highly -coloured, though many of them must grow in deep water. Light, however, -may not be the only principle on which the colour of vegetables depends, -since Baron Humboldt met with green plants growing in complete darkness -in one of the mines at Freyberg. - -In the dark and tranquil caves of the ocean, on the shores alternately -covered and deserted by the restless waves, on the lofty mountain and -extended plain, in the chilly regions of the north, and in the genial -warmth of the south, specific diversity is a general law of the -vegetable kingdom, which cannot be accounted for by diversity of -climate; and yet the similarity, though not identity, of species is -such, under the same isothermal lines, that if the number of species -belonging to one of the great families of plants be known in any part of -the globe, the whole number of the flowering or more perfect plants, and -also the number of species composing the other vegetable families, may -be estimated with considerable accuracy. - -Various opinions have been formed on the original or primitive -distribution of plants over the face of the globe; but, since botanical -geography has become a science, the phenomena observed have led to the -conclusion that vegetable creation must have taken place in a number of -distinctly different centres, as the islands and continents rose above -the ocean, each of which was the original seat of a certain number of -peculiar species which at first grew there and nowhere else. Heaths are -exclusively confined to the Old World; and no indigenous rose-tree has -ever been seen in the New, the whole southern hemisphere being destitute -of that beautiful and fragrant plant. But this is still more confirmed -by multitudes of particular plants, having an entirely local and -insulated existence, growing spontaneously in some particular spot, and -in no other place: for example, the cedar of Lebanon, which grows -indigenously on that mountain, and in no other part of the world. On the -other hand, as there can be no doubt that many races of plants have been -extinguished, Sir John Herschel thinks it possible that these solitary -instances may be the last surviving remnants of the same group -universally disseminated, but in course of extinction, or that perhaps -two processes may be going on at the same time:—“Some groups may be -spreading from their foci, others retreating to their last holds.” - -The same laws obtain in the distribution of the animal creation. Even -the microscopic existences, which seem to be the most widely spread, -have their specific localities; and the zoophyte (N. 219), occupying the -next lowest place in animated nature, is widely scattered through the -seas of the torrid zone, each species being confined to the district and -depth best suited to its wants. Mollusks, or the animals of shells, -decrease in size and beauty with their distance from the equator; and -not only each sea and every basin of the ocean, but each depth, is -inhabited by its peculiar tribe of fish. Indeed, MM. Peron and Le Sueur -assert that, among the many thousands of marine animals which they had -examined, there is not a single animal of the southern regions which is -not distinguishable by essential characters from the analogous species -in the northern seas. - -Reptiles are not exempt from the general law. The saurian (N. 220) -tribes of the four quarters of the globe differ in species; and, -although warm countries abound in venomous snakes, they are specifically -different in different localities, and decrease both in numbers and in -the virulence of their poison with decrease of temperature. The -dispersion of insects necessarily follows that of the vegetables which -supply their food; and in general it is observed that each kind of plant -is peopled by its peculiar inhabitants. Each species of bird has its -peculiar haunt, notwithstanding the locomotive powers of the winged -tribes. The emu is confined to Australia, the condor to the Andes and -their declivities, and the bearded vulture or lemmergeyer to the Alps. -Some birds, like the common sparrow, have a wide range; but those met -with in every country are few in number. Quadrupeds are distributed in -the same manner wherever man has not interfered. Such as are indigenous -in one country are not the same with their congeners in another; and, -with the exception of some kind of bats, no mammiferous animal is -indigenous in the Polynesian Archipelago, nor in any of the islands on -the borders of the central part of the Pacific. - -In reviewing the infinite variety of organised beings that people the -surface of the globe, nothing is more remarkable than the distinctions -which characterise the different tribes of mankind, from the ebony skin -of the torrid zone to the fair and ruddy complexion of the -Scandinavian—a difference which existed in the earliest recorded times, -since the African is represented in the sacred writings to have been as -black as he is at the present day, and the most ancient Egyptian -paintings confirm that truth; yet it appears, from a comparison of the -principal circumstances relating to the animal economy or physical -character of the various tribes of mankind, that the different races are -identical in species. Many attempts have been made to trace the various -tribes back to a common origin, by collating the numerous languages -which are or have been spoken. Some classes of these have few or no -words in common, yet exhibit a remarkable analogy in the laws of their -grammatical construction. The languages spoken by the native American -nations afford examples of these; indeed, the refinement in the -grammatical construction of the tongues of the American savages leads to -the belief that they must originally have been spoken by a much more -civilised class of mankind. Some tongues have little or no resemblance -in structure, though they correspond extensively in their vocabularies, -as the Syrian dialects. In all these cases it may be inferred that the -nations speaking the languages in question descended from the same -stock; but the probability of a common origin is much greater in the -Indo-European nations, whose languages, such as the Sanscrit, Greek, -Latin, German, &c., have an affinity both in structure and -correspondence of vocables. In many tongues not the smallest resemblance -can be traced; length of time, however, may have obliterated original -identity; but so many ages have passed before the subject became a -study, and so many languages have worn out of use, that it may be -doubted whether any satisfactory result will ever be arrived at with -regard to the original speech of mankind. - - - - - 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. - - -THAT heat producing rays exist independently of those of light is a -matter of constant experience in the abundant emission of them from -boiling water. They dart in divergent straight lines from flame and from -each point in the surfaces of hot bodies, in the same manner as -diverging rays of light proceed from every point of those that are -luminous. According to the experiments of Sir John Leslie, radiation -proceeds not only from the surface of substances, but also from the -particles at a minute depth below it. He found that the emission is most -abundant in a direction perpendicular to the radiating surface, and that -it is more rapid from a rough than from a polished surface: radiation, -however, can only take place in air and in vacuo; it is altogether -imperceptible when the hot body is enclosed in a solid or liquid. Heated -substances, when exposed to the open air, continue to radiate heat till -they become nearly of the temperature of the surrounding medium. The -radiation is very rapid at first, but diminishes according to a known -law with the temperature of the heated body. It appears, also, that the -radiating power of a surface is inversely as its reflecting power; and -bodies that are most impermeable to heat radiate least. Substances, -however, have an elective power, only reflecting heat of a certain -refrangibility. Mr. Grove gives paper, snow, and lime as instances, -which, although all white, radiate heat of different refrangibilities, -while metals, whatever their colour may be, radiate all kinds alike. - -Rays of heat, whether they proceed from the sun, from flame, or other -terrestrial sources, luminous or non-luminous, are instantaneously -transmitted through solid and liquid substances, there being no -appreciable difference in the time they take to pass through layers of -any nature or thickness whatever. They pass also with the same facility -whether the media be agitated or at rest; and in these respects the -analogy between light and heat is perfect. Radiant heat passes through -the gases with the same facility as light; but a remarkable difference -obtains in the transmission of light and heat through most solid and -liquid substances, the same body being often perfectly permeable to the -luminous, and altogether impermeable to the calorific rays. For example, -thin and perfectly transparent plates of alum and citric acid sensibly -transmit all the rays of light from an argand lamp, but stop eight or -nine tenths of the concomitant heat; whilst a large piece of brown -rock-crystal gives a free passage to the radiant heat, but intercepts -almost all the light. Alum united to green glass is also capable of -transmitting the brightest light, but it gives not the slightest -indication of heat; while rock-salt covered thickly over with soot, so -as to be perfectly opaque to light, transmits a considerable quantity of -heat. M. Melloni has established the general law in uncrystallized -substances such as glass and liquids, that the property of -instantaneously transmitting heat is in proportion to their refractive -powers. The law, however, is entirely at fault in bodies of a -crystalline texture. Carbonate of lead, for instance, which is -colourless, and possesses a very high refractive power with regard to -light, transmits less radiant heat than Iceland spar or rock-crystal, -which are very inferior to it in the order of refrangibility; whilst -rock-salt, which has the same transparency and refractive power with -alum and citric acid, transmits six or eight times as much heat. This -remarkable difference in the transmissive power of substances having the -same appearance is attributed by M. Melloni to their crystalline form, -and not to the chemical composition of their molecules, as the following -experiments prove. A block of common salt cut into plates entirely -excludes calorific radiation; yet, when dissolved in water, it increases -the transmissive power of that liquid: moreover, the transmissive power -of water is increased in nearly the same degree, whether salt or alum be -dissolved in it; yet these two substances transmit very different -quantities of heat in their solid state. Notwithstanding the influence -of crystallization on the transmissive power of bodies, no relation has -been traced between that power and the crystalline form. - -The transmission of radiant heat is analogous to that of light through -coloured media. When common white light passes through a red liquid, -almost all the more refrangible rays, and a few of the red, are -intercepted by the first layer of the fluid; fewer are intercepted by -the second, still less by the third, and so on: till at last the losses -become very small and invariable, and those rays alone are transmitted -which give the red colour to the liquid. In a similar manner, when -plates of the same thickness of any substance, such as glass, are -exposed to an argand lamp, a considerable portion of the radiant heat is -arrested by the first plate, a less portion by the second, still less by -the third, and so on, the quantity of lost heat decreasing till at last -the loss becomes a constant quantity. The transmission of radiant heat -through a solid mass follows the same law. The losses are very -considerable on first entering it, but they rapidly diminish in -proportion as the heat penetrates deeper, and become constant at a -certain depth. Indeed, the only difference between the transmission of -radiant heat through a solid mass, or through the same mass when cut -into plates of equal thickness, arises from the small quantity of heat -that is reflected at the surface of the plates. It is evident, -therefore, that the heat gradually lost is not intercepted at the -surface, but absorbed in the interior of the substance, and that heat -which has passed through one stratum of air experiences a less -absorption in each of the succeeding strata, and may therefore be -propagated to a greater distance before it is extinguished. The -experiments of M. de Laroche show that glass, however thin, totally -intercepts the obscure rays of heat when they flow from a body whose -temperature is lower than that of boiling water; that, as the -temperature increases, the calorific rays are transmitted more and more -abundantly; and, when the body becomes highly luminous, that they -penetrate the glass with perfect ease. The extreme brilliancy of the sun -is probably the reason why his heat, when brought to a focus by a lens, -is more intense than any that has been produced artificially. It is -owing to the same cause that glass screens, which entirely exclude the -heat of a common fire, are permeable by the solar heat. - -The results obtained by M. de Laroche have been confirmed by the -experiments of M. Melloni on heat radiated from sources of different -temperatures, whence it appears that the calorific rays pass less -abundantly not only through glass, but through rock-crystal, Iceland -spar, and other diaphanous bodies, both solid and liquid, according as -the temperature of their origin is diminished, and that they are -altogether intercepted when the temperature is about that of boiling -water. - -In fact, he has proved that the heat emanating from the sun or from a -bright flame consists of rays which differ from each other as much as -the coloured rays do which constitute white light. This explains the -reason of the loss of heat as it penetrates deeper and deeper into a -solid mass, or in passing through a series of plates; for, of the -different kinds of rays which dart from a vivid flame, all are -successively extinguished by the absorbing nature of the substance -through which they pass, till those homogeneous rays alone remain which -have the greatest facility in passing through that particular substance; -exactly as in a red liquid the violet, blue, green, orange, and yellow -rays are extinguished, and the red are transmitted. - -M. Melloni employed four sources of heat, two of which were luminous and -two obscure; namely, an oil-lamp without a glass, incandescent platina, -copper heated to 696°, and a copper vessel filled with water at the -temperature of 178-1/2° of Fahrenheit. Rock-salt transmitted heat in the -proportion of 92 rays out of 100 from each of these sources; but all -other substances pervious to radiant heat, whether solid or liquid, -transmitted more heat from sources of high temperature than from such as -are low. For instance, limpid and colourless fluate of lime transmitted -in the proportion of 78 rays out of 100 from the lamp, 69 from the -platina, 42 from the copper, and 33 from the hot water; while -transparent rock-crystal transmitted 38 rays in 100 from the lamp, 28 -from the platina, 6 from the copper, and 9 from the hot water. Pure ice -transmitted only in the proportion of 6 rays in the 100 from the lamp, -and entirely excluded those from the other three sources. Out of 39 -different substances, 34 were pervious to the calorific rays from hot -water, 14 excluded those from the hot copper, and 4 did not transmit -those from the platinum. - -Thus it appears that heat proceeding from these four sources is of -different kinds: this difference in the nature of the calorific rays is -also proved by another experiment, which will be more easily understood -from the analogy of light. Red light, emanating from red glass, will -pass in abundance through another piece of red glass, but it will be -absorbed by green glass; green rays will more readily pass through a -green medium than through one of any other colour. This holds with -regard to all colours; so in heat. Rays of heat of the same intensity, -which have passed through different substances, are transmitted in -different quantities by the same piece of alum, and are sometimes -stopped altogether; showing that rays which emanate from different -substances possess different qualities. It appears that a bright flame -furnishes rays of heat of all kinds, in the same manner as it gives -light of all colours; and, as coloured media transmit some coloured rays -and absorb the rest, so bodies transmit some rays of heat and exclude -the others. Rock-salt alone resembles colourless transparent media in -transmitting all kinds of heat, even that of the hand, just as they -transmit white light, consisting of rays of all colours. Radiant heat is -unequally refracted by a prism of rock-salt like light, and the rays of -heat thus dispersed are found to possess properties analogous to the -rays of the coloured spectrum. - -The property of transmitting the calorific rays diminishes to a certain -degree with the thickness of the body they have to traverse, but not so -much as might be expected. A piece of very transparent alum transmitted -three or four times less radiant heat from the flame of a lamp than a -piece of nearly opaque quartz about a hundred times as thick. However, -the influence of thickness upon the phenomena of transmission increases -with the decrease of temperature in the origin of the rays, and becomes -very great when that temperature is low. This is a circumstance -intimately connected with the law established by M. de Laroche; for M. -Melloni observed that the difference between the quantities of heat -transmitted by the same plate of glass, exposed successively to several -sources of heat, diminished with the thinness of the plate, and vanished -altogether at a certain limit; and that a film of mica transmitted the -same quantity of heat, whether it was exposed to incandescent platinum -or to a mass of iron heated to 360°. - -Coloured glasses transmit rays of light of certain degrees of -refrangibility, and absorb those of other degrees. For example, red -glass absorbs the more refrangible rays, and transmits the red, which -are the least refrangible. On the contrary, violet glass absorbs the -least refrangible, and transmits the violet, which are the most -refrangible. Now M. Melloni has found, that, although the colouring -matter of glass diminishes its power of transmitting heat, yet red, -orange, yellow, blue, violet, and white glass transmit calorific rays of -all degrees of refrangibility; whereas green glass possesses the -peculiar property of transmitting the least refrangible calorific rays, -and stopping those that are most refrangible. It has therefore the same -elective action for heat that coloured glass has for light, and its -action on heat is analogous to that of red glass on light. Alum and -sulphate of lime are exactly opposed to green glass in their action on -heat, by transmitting the most refrangible rays with the greatest -facility. - -The heat which has already passed through green or opaque black glass -will not pass through alum, whilst that which has been transmitted -through glasses of other colours traverses it readily. - -By reversing the experiment, and exposing different substances to heat -that had already passed through alum, M. Melloni found that the heat -emerging from alum is almost totally intercepted by opaque substances, -and is abundantly transmitted by all such as are transparent and -colourless, and that it suffers no appreciable loss when the thickness -of the plate is varied within certain limits. The properties of the heat -therefore which issues from alum nearly approach to those of light and -solar heat. - -Radiant heat in traversing various media is not only rendered more or -less capable of being transmitted a second time, but, according to the -experiments of Professor Powell, it becomes more or less susceptible of -being absorbed in different quantities by black or white surfaces. - -M. Melloni has proved that solar heat contains rays which are affected -by different substances in the same way as if the heat proceeded from a -terrestrial source; whence he concludes that the difference observed -between the transmission of terrestrial and solar heat arises from the -circumstance of solar heat containing all kinds of heat, whilst in other -sources some of the kinds are wanting. - -Radiant heat, from sources of any temperature whatever, is subject to -the same laws of reflection and refraction as rays of light. The index -of refraction from a prism of rock-salt, determined experimentally, is -nearly the same for light and heat. - -Liquids, the various kinds of glass, and probably all substances, -whether solid or liquid, that do not crystallize regularly, are more -pervious to the calorific rays according as they possess a greater -refractive power. For example, the chloride of sulphur, which has a high -refractive power, transmits more of the calorific rays than the oils, -which have a less refractive power: oils transmit more radiant heat than -the acids; the acids more than aqueous solutions; and the latter more -than pure water, which of all the series has the least refractive power, -and is the least pervious to heat. M. Melloni observed also that each -ray of the solar spectrum follows the same law of action with that of -terrestrial rays having their origin in sources of different -temperatures; so that the very refrangible rays may be compared to the -heat emanating from a focus of high temperature, and the least -refrangible to the heat which comes from a source of low temperature. -Thus, if the calorific rays emerging from a prism be made to pass -through a layer of water contained between two plates of glass, it will -be found that these rays suffer a loss in passing through the liquid as -much greater as their refrangibility is less. The rays of heat that are -mixed with the blue or violet light pass in great abundance, while those -in the obscure part which follows the red light are almost totally -intercepted. The first, therefore, act like the heat of a lamp, and the -last like that of boiling water. - -These circumstances explain the phenomena observed by several -philosophers with regard to the point of greatest heat in the solar -spectrum, which varies with the substance of the prism. Sir William -Herschel, who employed a prism of flint glass, found that point to be a -little beyond the red extremity of the spectrum; but, according to M. -Seebeck, it is found to be upon the yellow, upon the orange, on the red, -or at the dark limit of the red, according as the prism consists of -water, sulphuric acid, crown or flint glass. If it be recollected that, -in the spectrum from crown glass, the maximum heat is in the red part, -and that the solar rays, in traversing a mass of water, suffer losses -inversely as their refrangibility, it will be easy to understand the -reason of the phenomenon in question. The solar heat which comes to the -anterior face of the prism of water consists of rays of all degrees of -refrangibility. Now, the rays possessing the same index of refraction -with the red light suffer a greater loss in passing through the prism -than the rays possessing the refrangibility of the orange light, and the -latter lose less in their passage than the heat of the yellow. Thus the -losses, being inversely proportional to the degree of refrangibility of -each ray, cause the point of maximum heat to tend from the red towards -the violet, and therefore it rests upon the yellow part. The prism of -sulphuric acid, acting similarly, but with less energy than that of -water, throws the point of greatest heat on the orange; for the same -reason, the crown and flint glass prisms transfer that point -respectively to the red and to its limit. M. Melloni, observing that the -maximum point of heat is transferred farther and farther towards the red -end of the spectrum, according as the substance of the prism is more and -more permeable to heat, inferred that a prism of rock-salt, which -possesses a greater power of transmitting the calorific rays than any -known body, ought to throw the point of greatest heat to a considerable -distance beyond the visible part of the spectrum,—an anticipation which -experiment fully confirmed, by placing it as much beyond the dark limits -of the red rays as the red part is distant from the blueish green band -of the spectrum. - -In all these experiments M. Melloni employed a thermomultiplier,—an -instrument that measures the intensity of the transmitted heat with an -accuracy far beyond what any thermometer ever attained. It is a very -elegant application of M. Seebeck’s discovery of thermo-electricity; but -the description of this instrument is reserved for a future occasion, -because the principle on which it is constructed has not yet been -explained. - -In the beginning of the present century, not long after M. Malus had -discovered the polarization of light, he and M. Berard proved that the -heat which accompanies the sun’s light is capable of being polarized; -but their attempts totally failed with heat derived from terrestrial, -and especially from non-luminous sources. M. Berard, indeed, imagined -that he had succeeded; but, when his experiments were repeated by Mr. -Lloyd and Professor Powell, no satisfactory result could be obtained. M. -Melloni resumed the subject, and endeavoured to effect the polarization -of heat by tourmaline, as in the case of light. It was already shown -that two slices of tourmaline, cut parallel to the axis of the crystal, -transmit a great portion of the incident light when looked through with -their axes parallel, and almost entirely exclude it when they are -perpendicular to one another. Should radiant heat be capable of -polarization, the quantity transmitted by the slices of tourmaline in -their former position ought greatly to exceed that which passes through -them in the latter, yet M. Melloni found that the quantity of heat was -the same in both cases: whence he inferred that heat from a terrestrial -source is incapable of being polarized. Professor Forbes of Edinburgh, -who prosecuted this subject with great acuteness and success, came to -the same conclusion in the first instance; but it occurred to him, that, -as the pieces of tourmaline became heated by being very near the lamp, -the secondary radiation from them rendered the very small difference in -the heat that was transmitted in the two positions of the pieces of -tourmaline imperceptible. Nevertheless he succeeded in proving, by -numerous observations, that heat from various sources is polarized by -the tourmaline; but that the effect with non-luminous heat is very -minute and difficult to perceive, on account of the secondary radiation. -Though light is almost entirely excluded in one position of the pieces -of tourmaline, and transmitted in the other, a vast quantity of radiant -heat passes through them in all positions. Eighty-four per cent. of the -heat from an argand lamp passed through them in the case where light was -altogether stopped. It is only the difference in the quantity of -transmitted heat that gives evidence of its polarization. The second -slice of tourmaline, when perpendicular to the first, stops all the -light, but transmits a great proportion of heat; alum, on the contrary, -stops almost all the heat, and transmits the light; whence it may be -concluded that heat, though intimately partaking the nature of light, -and accompanying it under certain circumstances, as in reflection and -refraction, is capable of almost complete separation from it under -others. The separation has since been perfectly effected by M. Melloni, -by passing a beam of light through a combination of water and green -glass, coloured by the oxide of copper. Even when the transmitted light -was concentrated by lenses, so as to render it almost as brilliant as -the direct light of the sun, it showed no sensible heat. - -Professor Forbes next employed two bundles of laminæ of mica, placed at -the polarizing angle, and so cut that the plane of incidence of the heat -corresponded with one of the optic axes of this mineral. The heat -transmitted through this apparatus was polarized from a source whose -temperature was even as low as 200°; heat was also polarized by -reflection; but the experiments, though perfectly successful, are more -difficult to conduct. - -It appears, from the various experiments of M. Melloni and Professor -Forbes, that all the calorific rays emanating from the sun and -terrestrial sources are equally capable of being polarized by reflection -and by refraction, whether double or single, and that they are also -capable of circular polarization by all the methods employed in the -circular polarization of light. Plates of quartz cut at right angles to -the axis of the prism possess the property of turning the calorific rays -in one direction, while other plates of the same substance from a -differently modified prism cause the rays to rotate in the contrary -direction; and two plates combined, when of different affection, and of -equal thickness, counteract each other’s effects as in the case of -light. Tourmaline separates the heat into two parts, one of which it -absorbs, while it transmits the other; in short, the transmission of -radiant heat is precisely similar to that of light. - -Since heat is polarized in the same manner as light, it may be expected -that polarized heat transmitted through doubly refracting substances -should be separated into two pencils, polarized in planes at right -angles to each other; and that when received on an analyzing plate they -should interfere and produce invisible phenomena, perfectly analogous to -those described in Section XXII. with regard to light (N. 221). - -It was shown, in the same section, that 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 wholly -dark, is seen on the glass. When, however, a plate of mica uniformly -about the thirteenth of an inch in thickness is interposed between the -tourmaline and the glass, the dark spot vanishes, and a succession of -very splendid colours are seen; and, as the mica is turned round in a -plane perpendicular to the polarized ray, the light is stopped when the -plane containing the optic axis of the mica is parallel or perpendicular -to the plane of polarization. Now, instead of light, if heat from a -non-luminous source be polarized in the manner described, it ought to be -transmitted and stopped by the interposed mica under the same -circumstances under which polarized light would be transmitted or -stopped. Professor Forbes found that this is really the case, whether he -employed heat from luminous or non-luminous sources: and he had -evidence, also, of circular and elliptical polarization of heat. It -therefore follows, that if heat were visible, under similar -circumstances we should see figures perfectly similar to those given in -Note 213, and those following; and, as these figures are formed by the -interference of undulations of light, it may be inferred that heat, like -light, is propagated by undulations of the ethereal medium, which -interfere under certain conditions, and produce figures analogous to -those of light. It appears also, from Mr. Forbes’s experiments, that the -undulations of heat are longer than the undulations of light; and it has -already been mentioned that Professor Draper considers them to be -normal, like those of sound. - -That light and heat are both vibrations of the ethereal medium is not -the less true on account of the rays of heat being unseen, for the -condition of visibility or invisibility may only depend upon the -construction of our eyes, and not upon the nature of the motion which -produces these sensations in us. The sense of seeing may be confined -within certain limits. The chemical rays beyond the violet end of the -spectrum may be too rapid, or not sufficiently excursive, in their -vibrations, to be visible to the human eye; and the calorific rays -beyond the other end of the spectrum may not be sufficiently rapid, or -too extensive, in their undulations, to affect our optic nerves, though -both may be visible to certain animals or insects. We are altogether -ignorant of the perceptions which direct the carrier-pigeon to his home, -or of those in the antennæ of insects which warn them of the approach of -danger; nor can we understand the telescopic vision which directs the -vulture to his prey before he himself is visible even as a speck in the -heavens. So, likewise, beings may exist on earth, in the air, or in the -waters, which hear sounds our ears are incapable of hearing, and which -see rays of light and heat of which we are unconscious. Our perceptions -and faculties are limited to a very small portion of that immense chain -of existence which extends from the Creator to evanescence. - -The identity of action under similar circumstances is one of the -strongest arguments in favour of the common nature of the chemical, -visible, and calorific rays. They are all capable of reflection from -polished surfaces, of refraction through diaphanous substances, of -polarization by reflection and by doubly refracting crystals; their -velocity is prodigious; they may be concentrated and dispersed by convex -and concave mirrors; they pass with equal facility through rock-salt and -are capable of radiation; and they are subject to the same law of -interference with those of light: hence there can be no doubt that the -whole assemblage of rays visible and invisible which constitute a solar -beam are propagated by the undulations of the ethereal medium, and -consequently as motions they come under the same laws of analysis. - -When radiant heat falls upon a surface, part of it is reflected and part -of it is absorbed; consequently, the best reflectors possess the least -absorbing powers. The temperature of very transparent fluids is not -raised by the passage of the sun’s rays, because they do not absorb any -of them; and, as his heat is very intense, transparent solids arrest a -very small portion of it. The absorption of the sun’s rays is the cause -both of the colour and temperature of solid bodies. A black substance -absorbs all the rays of light, and reflects none; and since it absorbs, -at the same time, all the calorific rays, it becomes sooner warm, and -rises to a higher temperature, than bodies of any other colour. Blue -bodies come next to black in their power of absorption. And, since -substances of a blue tint absorb all the other colours of the spectrum, -they absorb by far the greatest part of the calorific rays, and reflect -the blue where they are least abundant. Next in order come the green, -yellow, red, and, last of all, white bodies, which reflect nearly all -the rays both of light and heat. However, there are certain limpid and -colourless media, which in some cases intercept calorific radiations and -become heated, while in other cases they transmit them and undergo no -change of temperature. - -All substances may be considered to radiate heat, whatever their -temperature may be, though with different intensities, according to -their nature, the state of their surfaces, and the temperature of the -medium into which they are brought. But every surface absorbs as well as -radiates heat; and the power of absorption is always equal to that of -radiation; for, under the same circumstances, matter which becomes soon -warm also cools rapidly. There is a constant tendency to an equal -diffusion of heat, since every body in nature is giving and receiving it -at the same instant; each will be of uniform temperature when the -quantities of heat given and received during the same time are -equal—that is, when a perfect compensation takes place between each and -all the rest. Our sensations only measure comparative degrees of heat: -when a body, such as ice, appears to be cold, it imparts fewer calorific -rays than it receives; and when a substance seems to be warm—for -example, a fire—it gives more heat than it takes. The phenomena of dew -and hoar-frost are owing to this inequality of exchange; the heat -radiated during the night by substances on the surface of the earth, -into a clear expanse of sky, is lost to us, and no return is made from -the blue vault, so that their temperature sinks below that of the air, -whence they abstract a part of that heat which holds the atmospheric -humidity in solution, and a deposition of dew takes place. If the -radiation be great, the dew is frozen and becomes hoar-frost, which is -the ice of dew. Cloudy weather is unfavourable to the formation of dew, -by preventing the free radiation of heat; and actual contact is -requisite for its deposition, since it is never suspended in the air -like fog. Plants derive a great part of their nourishment from this -source; and, as each possesses a power of radiation peculiar to itself, -they are capable of procuring a sufficient supply for their wants. The -action of the chemical rays imparts to all substances more or less the -power of condensing vapour on those parts on which they fall, and must -therefore have a considerable influence on the deposition of dew. There -may be a low degree of humidity in the air which may yet contain a great -quantity of aqueous vapour, for vapour while it exists as gas is dry. -The temperature at which the atmosphere can contain no more vapour -without precipitation is called the dew point, and is measured by the -hygrometer. In foretelling the changes of weather it is scarcely -inferior to the barometer. - -Steam is formed throughout the whole mass of a boiling liquid, whereas -evaporation takes place only at the free surface of liquids, and that -under the ordinary temperature and pressure of the atmosphere. There is -a constant evaporation from the land and water all over the earth. The -rapidity of the formation does not depend altogether on the dryness of -the air; according to Dr. Dalton’s experiments, it depends also on the -difference between the tension of the vapour which is forming, and that -which is already in the atmosphere. In calm weather vapour accumulates -in the stratum of air immediately above the evaporating surface, and -retards the formation of more; whereas a strong wind accelerates the -process by carrying off the vapour as soon as it rises, and making way -for a succeeding portion of dry air. - -Rain is formed by the mixing of two masses of air of different -temperatures; the colder part, by abstracting from the other the heat -which holds it in solution, occasions the particles to approach each -other and form drops of water, which, becoming too heavy to be sustained -by the atmosphere, sink to the earth by gravitation in the form of rain. -The contact of two strata of air of different temperatures, moving -rapidly in opposite directions, occasions an abundant precipitation of -rain. When the masses of air differ very much in temperature, and meet -suddenly, hail is formed. This happens frequently in hot plains near a -ridge of mountains, as in the south of France, from the sudden descent -of an intensely cold current of wind into a mass of air nearly saturated -with vapour. Such also is the cause of the severe hail-storms which -occasionally take place on extensive plains within the tropics. - -An accumulation of heat invariably produces light: with the exception of -the gases, all bodies which can endure the requisite degree of heat -without decomposition begin to emit light at the same temperature; but, -when the quantity of heat is so great as to render the affinity of their -component particles less than their affinity for the oxygen of the -atmosphere, a chemical combination takes place with the oxygen, light -and heat are evolved, and fire is produced. Combustion—so essential for -our comfort, and even existence—takes place very easily from the small -affinity between the component parts of atmospheric air, the oxygen -being nearly in a free state; but, as the cohesive force of the -particles of different substances is very variable, different degrees of -heat are requisite to produce their combustion. The tendency of heat to -a state of equal diffusion or equilibrium, either by radiation or -contact, makes it necessary that the chemical combination which -occasions combustion should take place instantaneously; for, if the heat -were developed progressively, it would be dissipated by degrees, and -would never accumulate sufficiently to produce a temperature high enough -for the evolution of flame. - -It is a general law that all bodies expand by heat and contract by cold. -The expansive force of heat has a constant tendency to overcome the -attraction of cohesion, and to separate the constituent particles of -solids and fluids; by this separation the attraction of aggregation is -more and more weakened, till at last it is entirely overcome, or even -changed into repulsion. By the continual addition of heat, solids may be -made to pass into liquids, and from liquids to the aëriform state, the -dilatation increasing with the temperature; and every substance expands -according to a law of its own. Gases expand more than liquids, and -liquids more than solids. The expansion of air is more than eight times -that of water, and the increase in the bulk of water is at least -forty-five times greater than that of iron. Metals dilate uniformly from -the freezing to the boiling points of the thermometer; the uniform -expansion of the gases extends between still wider limits; but, as -liquidity is a state of transition from the solid to the aëriform -condition, the equable dilatation of liquids has not so extensive a -range. This change of bulk, corresponding to the variation of heat, is -one of the most important of its effects, since it furnishes the means -of measuring relative temperature by the thermometer and pyrometer. The -rate of expansion of solids varies at their transition to liquidity, and -that of liquidity is no longer equable near their change to an aëriform -state. There are exceptions, however, to the general laws of expansion; -some liquids have a maximum density corresponding to a certain -temperature, and dilate whether that temperature be increased or -diminished. For example—water expands whether it be heated above or -cooled below 40°. The solidification of some liquids, and especially -their crystallization, is always accompanied by an increase of bulk. -Water dilates rapidly when converted into ice, and with a force -sufficient to split the hardest substances. The formation of ice is -therefore a powerful agent in the disintegration and decomposition of -rocks, operating as one of the most efficient causes of local changes in -the structure of the crust of the earth; of which we have experience in -the tremendous _éboulemens_ of mountains in Switzerland. But Professor -W. Thomson has proved experimentally that it requires a lower -temperature to freeze water under pressure than when free. - -The dilatation of substances by heat, and their contraction by cold, -occasion such irregularities in the rate of clocks and watches as would -render them unfit for astronomical or nautical purposes, were it not for -a very beautiful application of the laws of unequal expansion. The -oscillations of a pendulum are the same as if its whole mass were united -in one dense particle, in a certain point of its length, called the -centre of oscillation. If the distance of this point from the point by -which the pendulum is suspended were invariable, the rate of the clock -would be invariable also. The difficulty is to neutralize the effects of -temperature, which is perpetually increasing or diminishing its length. -Among many contrivances, Graham’s compensation pendulum is the most -simple. He employed a glass tube containing mercury. When the tube -expands from the effects of heat, the mercury expands much more; so that -its surface rises a little more than the end of the pendulum is -depressed, and the centre of oscillation remains stationary. Harrison -invented a pendulum which consists of seven bars of steel and of brass, -joined in the shape of a gridiron, in such a manner that, if by change -of temperature the bars of brass raise the weight at the end of the -pendulum, the bars of steel depress it as much. In general, only five -bars are used; three being of steel, and two a mixture of silver and -zinc. The effects of temperature are neutralized in chronometers upon -the same principle; and to such perfection are they brought, that the -loss or gain of one second in twenty-four hours for two days running -would render one unfit for use. Accuracy in surveying depends upon the -compensation rods employed in measuring bases. Thus, the laws of the -unequal expansion of matter judiciously applied have an immediate -influence upon our estimation of time; of the motions of bodies in the -heavens, and of their fall upon the earth; on our determination of the -figure of the globe, and on our system of weights and measures; on our -commerce abroad, and the mensuration of our lands at home. - -The expansion of the crystalline substances takes place under very -different circumstances from the dilatation of such as are not -crystallized. The latter become both longer and thicker by an accession -of heat, whereas M. Mitscherlich has found that the former expand -differently in different directions; and, in a particular instance, -extension in one direction is accompanied by contraction in another: for -example, Iceland spar is dilated in the direction of its axis of double -refraction (N. 205), but at right angles to that axis it is contracted, -which brings the crystal nearer to the form of the cube and diminishes -its double refractive power. When heat is applied to crystals of -sulphate of lime, the two optical axes (N. 207) gradually approach, and -at last coincide; when the heat is increased, the axes open again, but -in a direction at right angles to their former position. By experiment -M. Senarmont has concluded, that in media constituted like crystals of -the rhomboidal (N. 169) system the conducting power varies in such a -manner, that, supposing a centre of heat to exist within them, and the -medium to be indefinitely extended in all directions, the isothermal -surfaces are concentric ellipsoids of revolution round the axes of -symmetry, or at least surfaces differing but little from them. The -internal structure of crystallized matter must be very peculiar thus to -modify the expansive power of heat. - -Heat applied to the surface of a fluid is propagated downwards very -slowly, the warmer, and consequently lighter strata, always remaining at -the top. This is the reason why the water at the bottom of lakes fed -from Alpine chains is so cold; for the heat of the sun is transfused but -a little way below the surface. When the heat is applied below a liquid, -the particles continually rise as they become specifically lighter, and -diffuse the heat through the mass, their place being perpetually -supplied by those that are more dense. The power of conducting heat -varies materially in different liquids. Mercury conducts twice as fast -as an equal bulk of water, and therefore it appears to be very cold. A -hot body diffuses its heat in the air by a double process: the air in -contact with it becoming lighter ascends and scatters its heat by -transmission, while at the same time another portion is discharged in -straight lines by the radiating power of the surface. Hence a substance -cools more rapidly in air than in vacuo, because in the latter case the -process is carried on by radiation alone. It is probable that the earth -having been originally of very high temperature has become cooler by -radiation alone, the ethereal medium being too rare to carry off much -heat by contact. - -Heat is propagated with more or less rapidity through all bodies; air is -the worst conductor, and consequently mitigates the severity of cold -climates by preserving the heat imparted to the earth by the sun. On the -contrary, dense bodies, especially metals, possess the power of -conduction in the greatest degree, but the transmission requires time. -If a bar of iron twenty inches long be heated at one extremity, the heat -takes four minutes in passing to the other. The particle of the metal -that is first heated communicates the heat to the second, and the second -to the third: so that the temperature of the intermediate molecule at -any instant is increased by the excess of the temperature of the first -above its own, and diminished by the excess of its own temperature above -that of the third. That however will not be the temperature indicated by -the thermometer, because as soon as the particle is more heated than the -surrounding atmosphere it loses its heat by radiation, in proportion to -the excess of its actual temperature above that of the air. The velocity -of the discharge is directly proportional to the temperature, and -inversely as the length of the bar. As there are perpetual variations in -the temperature of all terrestrial substances, and of the atmosphere, -from the rotation of the earth, and its revolution round the sun, from -combustion, friction, fermentation, electricity, and an infinity of -other causes, the tendency to restore the equability of temperature by -the transmission of heat must maintain all the particles of matter in a -state of perpetual oscillation, which will be more or less rapid -according to the conducting powers of the substances. From the motion of -the heavenly bodies about their axes, and also round the sun, exposing -them to perpetual changes of temperature, it may be inferred that -similar causes will produce like effects in them too. The revolutions of -the double stars show that they are not at rest; and although we are -totally ignorant of the changes that may be going on in the nebulæ and -millions of other remote bodies, it is hardly possible that they should -be in absolute repose; so that, as far as our knowledge extends, motion -is a law of the universe and the immediate cause of heat, as in the -sunbeam so also in all terrestrial phenomena. - -This is by no means hypothetical, but founded upon fact and experiment. -Heat is produced by motion and is equivalent to it, for we measure heat -by motion in the thermometer. The heat evolved by percussion is -proportional to the force of the blow; by repeated blows iron becomes -red hot; and the quantity of heat produced by friction, whether the -matter be solid or fluid, is always in proportion to the force employed: -in cold weather we rub our hands to make them warm, and the harder we -rub the warmer they become. The warmth of the sea after a storm is in -proportion to the force of the wind; and in Sir Humphry Davy’s -experiment of melting ice by friction in the receiver of an air-pump -kept at the freezing point, the heat which melted the ice was exactly -proportional to the force of friction. This experiment proves the -immateriality of heat, since the capacity of ice for heat is less than -that of water. Thus mechanical action and heat are equivalent to one -another. Mr. Joule of Manchester[13] has proved that the quantity of -heat requisite to raise the temperature of a pound of water one degree -of Fahrenheit’s thermometer, is equivalent to the mechanical force -developed by the fall of a body weighing 772·69 pounds through the -perpendicular height of one foot. This quantity is the mechanical -equivalent of heat. Thus heat is motion, and it is measured by force. In -fact, for every unit of force expended in friction or percussion, a -definite quantity of heat is generated; and conversely, when work is -performed by the consumption of heat, for each unit of force gained, a -unit of heat disappears. For since heat is a dynamical force of -mechanical effect, there must be an equivalent between mechanical work -and heat as between cause and effect. (N. 222.) - -Besides the temperature indicated by the thermometer, bodies absorb -heat, and their capacity for heat is so various that very different -quantities of heat are required to raise different substances to the -same sensible temperature. It is evident, therefore, that much of the -heat is absorbed and becomes insensible to the thermometer. That portion -of heat requisite to raise a body to a given temperature is its specific -heat, but the latent or absorbed heat is an expansive force or energy, -which, acting upon the ether surrounding the ultimate particles of -bodies, changes them from solid to liquid, and from liquid to vapour or -gas. According to the law of absorption, the transfer of heat from a -warm body to one that is cold is a mere transfer of force, in which the -force of compression is exactly proportional to the force of expansion. -Ice remains at the temperature of 32° Fahrenheit till it has absorbed -140° of heat, and then it melts, but without raising the temperature of -the water above 32°. On the contrary, when a liquid is converted into a -solid, a quantity of heat leaves it without any diminution of -temperature. Thus water at 32° must part with 140° of heat before it -freezes. The slowness with which water freezes or ice thaws, is a -consequence of the time required for the ethereal atmospheres round the -particles of the water to contract or expand with a force equivalent to -140° of heat. A considerable degree of cold is felt during a thaw, -because the ice in its transition from a solid to a liquid state absorbs -sensible heat from the atmosphere and surrounding objects. The heat -absorbed and evolved by the rarefaction and condensation of air is -exactly proportional to the force evolved and absorbed in these -operations. In fact, the changes of temperature produced by these -rarefactions and condensations of air show that the heat of elastic -fluids is the mechanical force possessed by them; and since the -temperature of a gas determines its elastic force, it follows that the -elastic force or pressure must be the effect of the motion of the -constituent particles in any gas. Sir Humphry Davy, who first -demonstrated the immateriality of heat, assumed the hypothesis that the -motion we call heat is a rotation or vibration among the particles of -the fluid, which, according to Mr. Joule, agrees perfectly with the -observed phenomena, but he prefers the more simple view of Mr. Herapath, -that the elastic force or pressure is due to the impact of the particles -against any surface presented to them. Absorbed or latent heat may be -regarded as a quiescent energy ready to be restored to the form of -sensible heat when called forth: its vibrations as heat are extinguished -for the time by being transferred to the internal expansive force, and -are restored by compression. The absorbed heat of air and all elastic -fluids may be forced out by sudden compression like squeezing water out -of a sponge. The quantity of heat brought into action in this way is -well illustrated by the experiment of igniting tinder by the sudden -compression of air by a piston thrust into a cylinder closed at one end. -The development of heat on a stupendous scale is exhibited in lightning: -it is proportional to the square of the quantity of electricity -discharged, and is due to its excessive velocity and the violent -compression of the air in its transit through the atmosphere. Prodigious -quantities of heat are constantly absorbed or disengaged by the changes -to which substances are liable in passing from the solid to the liquid -and from the liquid to the gaseous form and the contrary, causing -endless vicissitudes of temperature over the globe, and endless -expansions and contractions, which are correlative terms for heat and -cold, while radiation of heat is merely a transfer of motion from the -particles on the surface of bodies to the adjacent particles of the -atmosphere. - -By the continual application of heat, that is of the expansive force, -liquids are converted into steam or vapour, which is invisible and -highly elastic. Under the mean pressure of the atmosphere, that is when -the barometer stands at 30 inches, water in a boiler absorbs heat -continually till it attains the temperature of the boiling point, which -is 212° Fahrenheit. After that it ceases to show any increase of -sensible heat; but when it has absorbed an additional 1000° of heat or -expansive energy, that energy converts it into steam, and a condensing -force equivalent to 1000° of heat reduces it again to water. Water boils -at different temperatures under different degrees of pressure. It boils -at a lower temperature on the top of a mountain than on the plain below, -because the weight of the atmosphere is less at the higher station. -There is no limit to the temperature to which water might be raised: it -might even be made red hot, could a vessel be found strong enough to -resist the pressure, for the intensity of the expansive force prevented -from having effect by the extreme pressure of the boiler would be -converted into sensible heat which might eventually render the water red -hot. Thus, since the force of steam is in proportion to the temperature -at which the water boils, or to the pressure, it is under control, and, -perhaps with the exception of electricity, it is the greatest power that -has been made subservient to the wants of man. - -It is found that the absolute quantity of heat consumed in the process -of converting water into steam is the same at whatever temperature water -may boil, but that the absolute heat of the steam is greater exactly in -proportion as its sensible heat is less. Thus, steam raised at 212° -Fahrenheit under the mean pressure of the atmosphere, and steam raised -at 180° under half the pressure, contain the same quantity of heat, with -this difference, that the one has more absorbed heat and less sensible -heat than the other. It is evident that, as the same quantity of heat is -requisite for converting a given weight of water into steam, at whatever -temperature or under whatever pressure the water may be boiled, -therefore, in the steam engine, equal weights of steam at a high -pressure and a low pressure are produced by the same quantity of fuel; -and whatever the pressure of the steam may be, the consumption of fuel -is proportional to the quantity of water converted into vapour. Steam of -whatever tension expands on being set free, but the expansion of high -pressure steam at the expense of its sensible heat is so great, that the -hand may be plunged into it without injury the instant it issues from -the orifice of a boiler. The steam becomes hotter by friction in issuing -through the orifice which maintains it in its dry form, for there is no -doubt that high-pressure steam is dry. - -The elasticity or tension of steam, like that of common air, varies -inversely as its volume—that is, when the space it occupies is doubled, -its elastic force is reduced to one half. The expansion of steam is -indefinite; the smallest quantity of water expanded into vapour will -occupy many millions of cubic feet; a wonderful illustration of the -minuteness of the ultimate particles of matter. - -The force of steam, tremendous as the lightning itself when -uncontrolled, is merely the result of chemical affinity: it is the -chemical attraction between the particles of carbon, of coal or wood, -and the oxygen of the atmosphere. Mr. Joule has ascertained that a pound -of the best coal when burnt gives sufficient heat to raise the -temperature of 8086 pounds of water one degree of the Centigrade -thermometer, whence it has been computed by M. Helmholtz that the -chemical force arising from the combustion of that pound of coal is -capable of lifting a body of one hundred pounds weight to the height of -twenty miles. That is the _work_ performed by the heat arising from the -combustion of a pound of coal. In all cases where work is produced by -heat, a quantity of heat proportional to the work done is expended; and -conversely, by the expenditure of a like quantity of work, the same -amount of heat may be produced. The equivalence of heat and work is a -law of nature. The mechanical force exerted by the steam engine for -example is exactly proportional to the consumption of heat, nor more nor -less; if we could produce a greater quantity than its equivalent we -should have perpetual motion, which is impossible. Mechanical engines -generate no force. We cannot create force; we can only avail ourselves -of the inexhaustible stores of nature, the lightning, fire, water, wind, -chemical action, &c. The quantity of mechanical power in nature is ever -the same; it is never increased, it is never diminished, throughout the -whole circuit of natural powers. The conservation of force is as -permanent and unchangeable as matter. It may be dormant for a time, but -it ever exists. We are unconscious of the enormous dynamic power that is -either active or latent throughout the globe, because we do not attend -to it. By the ebb and flow of the tide alone a power is exerted by which -25,000 cubic miles of water is moved over a quarter of the globe every -twelve hours; and Professor W. Thomson has computed, by means of -Pouillet’s data of solar radiation and Mr. Joule’s mechanical equivalent -of heat, that the mechanical value of the whole energy active and -potential of the disturbances kept up in the ethereal medium by the -vibrations of the solar light within a cubic mile of our atmosphere is -equal to 12,050 times the unit of mechanical force, that is to say, -12,050 times the force that would raise a pound of matter to the height -of one foot, whence some idea may be formed of the vast amount of force -exerted by the sun’s light within the limits of the whole terrestrial -atmosphere. (N. 223.) - -The dynamic energy of the undulations of the solar light gives the -leaves of plants the power of decomposing carbonic acid, and of -separating the particles of carbon and hydrogen from the oxygen for -which they have so strong an affinity. In this operation the undulations -of the sunbeam are extinguished as light and heat, and Professor W. -Thomson has proved that the quantity of these undulations thus -extinguished is precisely equal to the potential or quiescent energy -thus created, and that precisely that very quantity of light and heat is -restored when the plants are burned, whatever state they may be in; and -that thus, as Mr. George Stephenson[14] has truly and beautifully -observed, our coal fires and gas lamps restore to our use the light and -heat of the sun of the early geological epochs which have rested as -dormant powers under the seas and mountains for unnumbered ages. The sun -is therefore the source of the mechanical energy of all the heat and -motion of inanimate things, of all the motions of the heat and light of -fires and artificial flames, and of the heat of all living creatures. -For animal heat, and weights raised or resistance overcome, are -mechanical effects of the chemical combination of food with oxygen; and -food is either directly or indirectly vegetable, consequently dependent -upon the sun. - -Professor Helmholtz of Bonn has put in a strong point of view the -enormous store of force possessed by our system by comparing it with its -equivalent of heat. The force with which the earth moves in its orbit is -such, that if brought to rest by a sudden shock, a quantity of heat -would be generated by the blow equal to that produced by the combustion -of fourteen such earths of solid coal; and supposing the capacity of the -earth for heat as low as that of water, the globe would be heated to -11,200° Cent. It would be quite fused and for the most part reduced to -vapour. If it should fall to the sun, which it would certainly do, the -quantity of heat developed by the shock would be four hundred times as -great. - -The application of heat to the various branches of the mechanical and -chemical arts has within the present century effected a greater change -in the condition of man than had been accomplished in any equal period -of his existence. Armed by the expansion and condensation of fluids with -a power equal to that of the lightning itself, conquering time and -space, he flies over plains, and travels on paths cut by human industry -even through mountains with a velocity and smoothness more like -planetary than terrestrial motion; he crosses the deep in opposition to -wind and tide; by releasing the strain on the cable, he rides at anchor -fearless of the storm; he makes the lightning his messenger; and like a -magician he raises from the gloomy abyss of the mine the sunbeam of -former ages to dispel the midnight darkness. - -The principal phenomena of heat may be illustrated by a comparison with -those of sound. Their excitation is not only similar but identical, as -in friction and percussion; they are both communicated by contact and -radiation; and Dr. Young observes that the effect of radiant heat in -raising the temperature of a body upon which it falls, resembles the -sympathetic agitation of a string when the sound of another string which -is in unison with it is transmitted through the air. Light, heat, sound, -and the waves of fluids are all subject to the same laws; their -undulatory theories are perfectly similar: hence the interference of two -hot rays must produce cold, that is, they must extinguish one another: -darkness results from the interference of two undulations of light, -silence ensues from the interference of two undulations of sound, and -still water or no tide is the consequence of the interference of two -tides. The propagation of sound, however, requires a much denser medium -than that of light and heat; its intensity diminishes as the rarity of -the air increases: so that, at a very small height above the surface of -the earth, the noise of the tempest ceases, and the thunder is heard no -more in those boundless regions where the heavenly bodies accomplish -their periods in eternal and sublime silence. - -A consciousness of the fallacy of our senses is one of the most -important consequences of the study of nature. This study teaches us -that no object is seen by us in its true place, owing to aberration; -that the colours of substances are solely the effects of the action of -matter upon light; and that light itself as well as heat and sound are -not real beings, but mere motions communicated to our perceptions by the -nerves. The human frame may therefore be regarded as an elastic system, -the different parts of which are capable of receiving the tremors of -elastic media, and of vibrating in unison with any number of -superimposed undulations, all of which have their perfect and -independent effect. Here our knowledge ends: the mysterious influence of -matter on mind will in all probability be for ever hid from man. - - - - - 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. - - -ELECTRICITY is a dual power which gives no visible sign of its existence -when in equilibrio, but when elicited forces are developed capable of -producing the most sudden, violent, and destructive effects in some -cases, while in others their action, though generally less energetic, is -of indefinite and uninterrupted continuance. These modifications of the -electric forces, incidentally depending upon the manner in which they -are excited, present phenomena of great diversity, but yet so connected -as to justify the conclusion that they originate in a common principle. -The hypothesis of electricity being a fluid is untenable in the present -advanced state of the science; we only know that it is a force whose -action is twofold; that bodies in one electric state attract, and in -another repel each other; in the former the electricity is said to be -positive, in the latter negative; and thus regarding it as a force, its -modes of action come under the laws of mechanics and mathematical -analysis. - -Electricity may be called into activity by the friction of heterogeneous -substances, as in the common electrifying machine, by mechanical power, -heat, chemical action, and the influence of magnetism. We are totally -ignorant why it is roused from its neutral state by these means, or of -the manner of its existence in bodies; but when excited it seems to -produce a molecular polarity or chemical change in the ultimate -particles of matter. - -The science is divided into various branches, of which static or common -electricity comes first under consideration, including that of the -atmosphere. Substances in a neutral state neither attract nor repel. -There is a numerous class called electrics in which the electric -equilibrium is destroyed by friction; then the positive and negative -electricities are called into action or separated; the positive is -impelled in one direction, and the negative in another. Electricities of -the same kind repel, whereas those of different kinds attract each -other. The attractive power is exactly equal to the repulsive power at -equal distances, and when not opposed they coalesce with great rapidity -and violence, producing the electric flash, explosion, and shock; then -the equilibrium is restored. One kind of electricity cannot be evolved -without the evolution of an equal quantity of the opposite kind. Thus -when a glass rod is rubbed with a piece of silk, as much positive -electricity is elicited in the glass as there is negative in the silk. -The kind of electricity depends more upon the mechanical condition than -on the nature of the surface; for when two plates of glass, one polished -and the other rough, are rubbed against each other, the polished surface -acquires positive and the rough negative electricity. The manner in -which friction is performed also alters the kind of electricity. Equal -lengths of black and white ribbon applied longitudinally to one another, -and drawn between the finger and thumb so as to rub their surfaces -together, become electric. When separated the white ribbon is found to -have acquired positive electricity, and the black negative; but if the -whole length of the black ribbon be drawn across the breadth of the -white, the black will be positively and the white negatively electric -when separated. The friction of the rubber on the glass plate of the -electrifying machine produces abundance of static electricity. The -friction of the steam on the valve of an insulated locomotive -steam-engine produces seven times the quantity of electricity that an -electrifying machine would do with a plate three feet in diameter, -worked at the rate of 70 revolutions in a minute. Pressure is a source -of electricity which M. Becquerel has found to be common to all bodies; -but it is necessary to separate them to prevent the reunion of the -electricities. When two substances of any kind whatever are insulated -and pressed together they assume different electric states, but they -only show contrary electricities when one of them is a good conductor. -When both are good conductors they must be separated with extreme -rapidity to prevent a return to equilibrium. When the separation is very -sudden the tension of the two electricities may be great enough to -produce light. M. Becquerel attributes the light produced by the -collision of icebergs to this cause. Iceland spar is made electric by -the smallest pressure between the finger and the thumb, and retains it -for a long time. All these circumstances are modified by the temperature -of the substances, the state of their surfaces and that of the -atmosphere. Several crystalline bodies become electric when heated, -especially tourmaline, one end of which acquires positive, and the other -negative electricity, while the intermediate part is neutral. If the -tourmaline be broken through the middle, each fragment is found to -possess positive electricity at one end and negative at the other. -Electricity is evolved by substances passing from a liquid to a solid -state, and by chemical action during the production and condensation of -vapour, which is a great source of atmospheric electricity. In short, it -may be generally stated, that when any cause whatever tends to destroy -molecular attraction there is a development of electricity; if, however, -the substances be not immediately separated, there will be an -instantaneous restoration of equilibrium. - -Electricity may be transferred from one body to another in the same -manner as heat is communicated, and like it too the body loses by the -transmission. - -Although no substance is altogether impervious to electricity, nor is -there any that does not offer some resistance to its passage, yet it -moves with more facility through a certain class of substances called -conductors, such as metals, water, the human body, &c., than through -atmospheric air, glass, silk, &c., which are therefore called -non-conductors. The conducting power is affected both by temperature and -moisture. The terrestrial globe is a conductor on account of its -moisture, though dry earth is not. Though metals are the best conductors -of electricity, it affects their molecular structure, for the heat which -accompanies its passage acts as a transverse expansive force, which -increases their breadth by diminishing their length, as may be seen by -passing electricity through a platinum wire sufficiently thick to resist -fusion. Through air the force is disruptive on account of its -non-conducting quality, and it seems to act chemically on the oxygen, -producing the substance known as ozone during its passage through the -atmosphere. If a conductor be good and of sufficient size the -electricity passes imperceptibly but it is shivered to pieces in an -instant if it be a bad conductor or too small to carry off the charge. -In that case the physical change is generally a separation of the -particles, or expansion from the heat, as in trees, where it turns the -moisture into steam, but all these effects are in proportion to the -obstacles opposed to the freedom of its course. - -Bodies surrounded by non-conductors are said to be insulated, because -when charged the electricity cannot escape. When that is not the case, -the electricity is conveyed to the earth: consequently it is impossible -to accumulate electricity in a conducting substance that is not -insulated. There are a great many substances called non-electrics in -which electricity is not sensibly developed by friction unless they be -insulated, because it is carried off by their conducting power as soon -as elicited. Metals, for example, which are said to be non-electrics can -be excited, but being conductors they cannot retain this state if in -communication with the earth. It is probable that no bodies exist which -are either perfect non-electrics or perfect non-conductors. But it is -evident that electrics must be non-conductors to a certain degree, -otherwise they could not retain their electric state. - -A body charged with electricity, although perfectly insulated, so that -all escape of electricity is prevented, tends to produce an electric -state of the opposite kind in all bodies in its vicinity. Positive -electricity tends to produce negative electricity in a body near to it, -and _vice versâ_, the effect being greater as the distance diminishes. -This power which electricity possesses of causing an opposite electrical -state in its vicinity is called induction. A Leyden jar, for example, or -glass jar coated half way up both outside and in with tin foil, when -charged with positive electricity, immediately induces negative -electricity on the tin foil outside. Notwithstanding their strong mutual -attraction they are prevented from coalescing by the glass, which is a -non-conductor; but if the tin inside and out be connected by a -conducting wire they instantly unite. When a body in either electric -state is presented to a neutral one, its tendency in consequence of the -law of induction is to disturb the condition of the neutral body by -inducing electricity contrary to its own in the adjacent side, and -therefore an electrical state similar to its own in the remote part. -Hence the neutrality of the second body is destroyed by the action of -the first, and the adjacent parts of the two, having now opposite -electricities, will attract each other. The attraction between -electrified and unelectrified substances is a consequence of the altered -state of their molecules. Induction depends upon the facility with which -the equilibrium of the neutral body can be overcome, a facility which is -proportional to its conducting power. Consequently the attraction -exerted by an electrified substance upon another substance previously -neutral will be much more energetic if the latter be a conductor than if -it be a non-conductor. - -It is clear that one body cannot act upon another at a distance without -some means of communication. Dr. Faraday has proved that the intervening -non-conducting substance or dielectric has a great influence upon -induction. Thus the inductive force is greater when sulphur is -interposed between the two bodies than when shellac is the dielectric, -and greater when shellac is the dielectric than glass, &c. Professor -Matteucci has proved by the following experiment that the intervening -substance is itself polarized by induction. A number of plates of mica -in contact were placed between two plates of metal, one of which was -electrified, so that the whole was charged like a Leyden jar. On -separating the plates with insulating handles, each plate of mica was -electrified; one side of it was positive and the other negative, showing -decidedly a polarization by induction throughout the whole intervening -non-conducting substance; and thus, although the interposed substance or -dielectric is incapable of conducting the electrical force from one body -to the other, it becomes by induction capable of transmitting it. In the -atmosphere induction is transmitted by that of the intervening strata of -air. It is true that induction takes place through the most perfect -vacuum we can make, but there always remains some highly elastic air; -and even if air could be altogether excluded, the ethereal medium -cannot, and it must be capable of induction, since, however attenuated, -it must consist of material atoms, otherwise it would be a nonentity. - -The law of electrical attraction and repulsion has been determined by -suspending a needle of gum-lac horizontally by a silk fibre, the needle -carrying at one end a piece of electrified gold leaf. A globe in the -same or opposite electrical state when presented to the gold leaf will -repel or attract it, and will therefore cause the needle to vibrate more -or less rapidly according to the distance of the globe. A comparison of -the number of oscillations performed in a given time at different -distances will determine the law of the variation of the electrical -intensity, in the same manner that the force of gravitation is measured -by the oscillations of the pendulum. Coulomb invented an instrument -which balances the forces in question by the force of the torsion of a -thread, which consequently measures the intensity; and Sir William Snow -Harris has constructed an instrument with which he has measured the -intensity of the electrical force in terms of the weight requisite to -balance it. By these methods it has been found that the intensity of -electrical attraction and repulsion varies inversely as the square of -the distance. However, the law of repulsive force is liable to great -disturbances from inductive action, which Sir William Snow Harris has -found to exist not only between a charged and neutral body, but also -between bodies similarly charged; and that, in the latter case, the -inductive process may be indefinitely modified by the various -circumstances of the quantity and intensity of the electricity and the -distance between the charged bodies. - -The quantity of electricity bodies are capable of receiving does not -follow the proportion of their bulk, but depends principally upon the -form and extent of their surface. It appears from the experiments of Sir -W. S. Harris that a given quantity of electricity, divided between two -perfectly equal and similar bodies, exerts upon external bodies only one -fourth of the attractive force apparent when disposed upon one of them; -and if it be distributed among three equal and similar bodies, the force -is one ninth of that apparent when it is disposed on one of them. Hence, -if the quantity of electricity be the same, the force varies inversely -as the square of the surface on which it is disposed; and if the surface -be the same, the force varies directly as the square of the quantity of -electricity. These laws however do not hold when the form of the surface -is changed. A given quantity of electricity disposed on a given surface -has the greatest intensity when the surface has a circular form, and the -least intensity when the surface is expanded into an indefinite straight -line. The decrease of intensity seems to arise from some peculiar -arrangement of the electricity depending on the extension of the -surface. It is quite independent of the extent of the edge, the area -being the same; for Sir W. S. Harris found that the electrical intensity -of a charged sphere is the same with that of a plane circular area of -the same superficial extent, and that of a charged cylinder the same as -if it were cut open and expanded into a plane surface. - -The same able electrician has shown that the attractive force between an -electrified and a neutral uninsulated body is the same whatever be the -forms of their unopposed parts. Thus two hemispheres attract each other -with precisely the same force as if they were spheres; and as the force -is as the number of attracting points in operation directly, and as the -squares of the respective distances inversely, it follows that the -attraction between a mere ring and a circular area is no greater than -that between two similar rings, and the force between a sphere and an -opposed spherical segment of the same curvature is no greater than that -of two similar segments, each equal to the given segment. - -Electricity may be accumulated to a great extent in insulated bodies, -and so long as it is quiescent it occasions no sensible change in their -properties. When restrained by the non-conducting power of the -atmosphere, its tension or the pressure it exerts is proportional to the -coercive force of the air. If the pressure be less than the coercive -force, the electricity is retained; but the instant it exceeds that -force in any one point it escapes, and that more readily when the air is -attenuated or saturated with moisture, for the resistance of the air is -proportional to the square of its density, but the inductive action of -electricity on distant bodies is independent of atmospheric pressure. -The power of retaining electricity depends also on the shape of the -charged body. It is most easily retained by a sphere, next to that by a -spheroid, but it readily escapes from a point, and a pointed object -receives it with most facility. - -The heat produced by the electric shock is proportional to the square of -the quantity of electricity discharged, and is so intense that it fuses -metals and volatilizes substances, but its intensity is not felt to its -full extent on account of the shortness of its duration. It is only -accompanied by light when the electricity is obstructed in its passage -through substance. - -Electrical light when analysed by a prism differs very much from solar -light. Fraunhofer found that, instead of the fixed dark lines, the -spectrum of an electric spark is crossed by numerous bright lines; and -Professor Wheatstone has observed that the number and position of the -lines differ with the metal from which the spark is taken, and believes -the spark itself results from the ignition and volatilization of the -matter of the conductor. - -According to the experiments of Sir Humphry Davy, the density of the air -has an influence on the colour. He passed the electric spark through a -vacuum over mercury, which from green became successively sea-green, -blue, and purple, on admitting different quantities of air. When the -vacuum was made over a fusible alloy of tin and bismuth, the spark was -yellowish and extremely pale. Sir Humphry thence concluded that -electrical light principally depends upon some properties belonging to -the ponderable matter through which it passes, and that space is capable -of exhibiting luminous appearances, though it does not contain an -appreciable quantity of matter. He thought that the superficial -particles of bodies which form vapour, when detached by the repulsive -power of heat, might be equally separated by the electric forces, and -produce luminous appearances in vacuo by the destruction of their -opposite electric states. - -The velocity of electricity is so great that the most rapid motion which -can be produced by art appears to be actual rest when compared with it. -A wheel revolving with celerity sufficient to render its spokes -invisible, when illuminated by a flash of lightning, is seen for an -instant with all its spokes distinct, as if it were in a state of -absolute repose; because, however rapid the rotation may be, the light -has come and already ceased before the wheel has had time to turn -through a sensible space. This beautiful experiment is due to Professor -Wheatstone, as well as the following variation of it, which is not less -striking: If a circular piece of pasteboard be divided into three -sectors, one of which is painted blue, another yellow, and a third red, -it will appear to be white when revolving quickly, because of the -rapidity with which the impressions of the colours succeed each other on -the retina. But, the instant it is illuminated by an electric spark, it -seems to stand still, and each colour is as distinct as if it were at -rest. This transcendent speed of electricity has been ingeniously -measured, as follows, by Professor Wheatstone, who has ascertained that -it much surpasses the velocity of light. - -In the horizontal diameter of a small disc, fixed on the wall of a -darkened room, are disposed six small brass balls, well insulated from -each other. An insulated copper wire, half a mile long, is disjointed in -its middle, and also near its two extremities; the six ends thus -obtained are connected with the six-balls on the disc. When an electric -discharge is sent through the wire by connecting its two extremities, -one with the positive, and the other with the negative coating of a -Leyden jar, three sparks are seen on the disc, apparently at the same -instant. At the distance of about ten feet a small revolving mirror is -placed so as to reflect these three sparks during its revolution. From -the extreme velocity of the electricity, it is clear that, if the three -sparks be simultaneous, they will be reflected, and will vanish before -the mirror has sensibly changed its position, however rapid its rotation -may be, and they will be seen in a straight line. But if the three -sparks be not simultaneously transmitted to the disc—if one, for -example, be later than the other two—the mirror will have time to -revolve through an indefinitely small arc in the interval between the -reflection of the two sparks and that of the single one. However, the -only indication of this small motion of the mirror will be, that the -single spark will not be reflected in the same straight line with the -other two, but a little above or below it, for the reflection of all -three will still be apparently simultaneous, the time intervening being -much too short to be appreciated. - -Since the number of revolutions which the revolving mirror makes in a -second is known, and the angular deviation of the reflection of the -single spark from the reflection of the other two can be measured, the -time elapsed between their consecutive reflections can be ascertained. -And, as the length of that part of the wire through which the -electricity has passed is given, its velocity may be found. - -The number of pulses in a second, requisite to produce a musical note of -any pitch, are known; hence the number of revolutions accomplished by -the mirror in a given time may be determined from the musical note -produced by a tooth or peg, in its axis of rotation, striking against a -card, or from the notes of a siren attached to the axis. It was thus -that Professor Wheatstone found the mirror which he employed in his -experiments made 800 revolutions in a second; and, as the angular -velocity of the reflected image in a revolving mirror is double that of -the mirror itself, an angular deviation of one degree in the appearance -of the two sparks would indicate an interval of the 576,000th of a -second; the deviation of half a degree would, therefore, indicate more -than the millionth of a second. The use of sound as a measure of -velocity is a happy illustration of the connexion of the physical -sciences. - -The earth possesses a powerful electrical tension, and the atmosphere -when clear is almost always positively electric. Its electricity is -stronger in winter than in summer, during the day than in the night. The -intensity increases for two or three hours from the time of sunrise, -comes to a maximum between seven and eight, then decreases towards the -middle of the day, arrives at its minimum between one and two, and again -augments as the sun declines till about the time of sunset, after which -it diminishes and continues feeble during the night. The mere -condensation of vapour is a source of atmospheric electricity; but -although it is also produced by the vapour that rises from the surface -of the earth, it is not under all circumstances. M. Pouillet found that -electricity is only developed when accompanied by chemical action: for -example, when the water whence the vapour proceeds contains lime, chalk, -or any solid alkali, negative electricity is produced; and when it holds -in solution either gas, acid, or some of the salts, the vapour is -positively electric. Besides, the contact of earth with salt and fresh -water generates positive electricity, and the contact of fresh and salt -currents of water negative, so that the ocean must afford a great supply -to the atmosphere; hence thunderstorms are most frequent near the -coasts: but as electricity of one kind or another is developed whenever -the molecules of matter are deranged from their natural state of -equilibrium, there must be many partial variations in the electric state -of the air. When the invisible vapour rises charged with electricity -into the cold regions of the atmosphere, it is condensed into cloud, in -which the tension is increased because the electricity is confined to a -smaller space; and if the condensation be sufficient to produce drops of -rain, they carry the electricity to the ground, so that in general a -shower is a conductor between the clouds and the earth. When two clouds -charged with opposite kinds, but of equal tension, approach within a -certain distance, the intensity increases on the sides of the clouds -that are nearest to one another; and when the tension is great enough to -overcome the coercive pressure of the atmosphere, a discharge takes -place which causes a flash of lightning, the stroke being given either -by the cloud or the rain. The actual quantity of electricity in any part -of a cloud is extremely small. The intensity of the flash arises from -the great extent of surface over which it is spread, so that clouds may -be compared to enormous Leyden jars thinly coated with electricity, -which only acquires its intensity by its instantaneous condensation. The -rapid and irregular motions of thunder clouds are probably more owing to -strong electrical attractions and repulsions among themselves than to -currents of air, though both are no doubt concerned in these hostile -movements. The atmosphere becomes intensely electric on the approach of -rain, hail, snow, sleet, and wind; but it varies afterwards, and the -transitions are very rapid on the approach of a thunderstorm. - -Since air is a non-conductor, it does not convey the electricity from -the clouds to the earth, but it acquires from them an opposite kind, and -when the tension is very great the force of the electricity becomes -irresistible, and an interchange takes place between the clouds and the -earth; but so rapid is the motion of lightning, that it is difficult to -ascertain whether it goes from the clouds to the earth or shoots upwards -from the earth to the clouds, though there can be no doubt that it does -both. In a storm that occurred at Manchester in June 1835, the lightning -was observed to issue from various points of a road, attended by -explosions as if pistols had been fired out of the ground, and a man -seems to have been killed by one of these explosions taking place under -his foot. M. Gay Lussac ascertained that a flash of lightning sometimes -darts more than three miles in a straight line. A person may be killed -by lightning, although the explosion takes place at a distance of twenty -miles, by what is called the back stroke. Suppose that the two -extremities of a highly charged cloud hang down towards the earth, they -will repel the electricity from the earth’s surface if it be of the same -kind with their own, and will attract the other kind; and if a discharge -should suddenly take place at one end of the cloud, the equilibrium will -be instantly restored by a flash at that point of the earth which is -under the other. Though the back stroke is often sufficiently powerful -to destroy life, it is never so terrible in its effects as the direct -stroke, which is often of inconceivable intensity. Instances have -occurred when large masses of iron and stone, and even many feet of a -stone wall, have been carried to a considerable distance by a stroke of -lightning. Rocks and the tops of mountains often bear the marks of -fusion from its intense heat; and occasionally vitreous tubes descending -many feet into banks of sand mark its path. Dr. Fiedler exhibited -several of these fulgorites in London of considerable length, which had -been dug out of the sandy plains of Silesia and Eastern Prussia. One -found at Paderborn was forty feet long. Their ramifications generally -terminate in pools or springs of water below the sand, which are -supposed to determine the course of the lightning. No doubt the soil and -substrata must influence its direction, since it is found by experience -that places which have been once struck by lightning are often struck -again. An insulated conductor on the approach of a storm gives out such -quantities of sparks that it is dangerous to approach it, as was fatally -experienced by Professor Richman at Petersburg, who was struck dead by a -globe of fire from the extremity of a conductor, while making -experiments on atmospheric electricity. Copper conductors afford the -best protection, especially if they expose a broad surface, since -electricity is conveyed along the surface of bodies. There is no -instance of an electric cloud of high tension being dispelled by a -conductor, yet those invented by Sir William Snow Harris, and -universally employed in the navy, afford a complete protection in the -most imminent danger. The Shannon, a 50-gun frigate, commanded by the -brave and lamented Sir William Peel, was enveloped in a thunder-storm -when about 90 miles to the north-west of Java. It began at fifty minutes -past four in the afternoon; the ship was driven before the storm, in a -high sea, amid streams of vivid lightning, deafening thunder, hail, and -rain. At five o’clock an immense ball of fire covered the maintopgallant -mast, ran up the royal pole, and exploded in the air with a terrific -concussion, covering all the surrounding space with sparks of electric -light, which were driven rapidly to leeward by the wind. Fifteen minutes -later an immense mass of lightning struck the mainmast, attended by a -violent gust of wind; and another heavy discharge fell on it a quarter -of an hour afterwards. From that time till six o’clock the ship was -continually encompassed by sharp forked lightning, accompanied by -incessant peals of thunder. Though actually enveloped in electricity, -and struck three times, neither the hull nor the rigging sustained the -slightest injury. - -When the air is rarefied by heat, its coercive power is diminished, so -that the electricity escapes from the clouds in those lambent diffuse -flashes without thunder so frequent in warm summer evenings; and when -the atmosphere is highly charged with electricity, it not unfrequently -happens that electric light, in the form of a star, is seen on the -topmasts and yard-arms of ships. In 1831 the French officers at Algiers -were surprised to see brushes of light on the heads of their comrades, -and at the points of their fingers when they held up their hands. This -phenomenon was well known to the ancients, who reckoned it a lucky omen. - -Many substances, in decaying, emit light, which is attributed to -electricity, such as fish and rotten wood. Oyster-shells, and a variety -of minerals, become phosphorescent at certain temperatures when exposed -to electric shocks or friction: indeed, most of the causes which disturb -molecular equilibrium give rise to phosphoric phenomena. The minerals -possessing this property are generally coloured or imperfectly -transparent; and, though the colour of this light varies in different -substances, it has no fixed relation to the colour of the mineral. An -intense heat entirely destroys this property, and the phosphorescent -light developed by heat has no connexion with light produced by -friction; for Sir David Brewster observed that bodies deprived of the -faculty of emitting the one are still capable of giving out the other. -Among the bodies which generally become phosphorescent when exposed to -heat, there are some specimens which do not possess this property; -wherefore phosphorescence cannot be regarded as an essential character -of the minerals possessing it. Sulphuret of calcium, known as Canton’s -phosphorus, and the sulphuret of barium, or Bologna stone, possess the -phosphorescent property in an eminent degree. - -Multitudes of fish are endowed with the power of emitting light at -pleasure, no doubt to enable them to pursue their prey at depths where -the sunbeams cannot penetrate. Flashes of light are frequently seen to -dart along a shoal of herrings or pilchards; and the Medusa tribes are -noted for their phosphorescent brilliancy, many of which are extremely -small, and so numerous as to make the wake of a vessel look like a -stream of silver. Nevertheless, the luminous appearance which is -frequently observed in the sea during the summer months cannot always be -attributed to marine animalculæ, as the following narrative will show:— - -Captain Bonnycastle, coming up the Gulf of St. Lawrence on the 7th of -September, 1826, was roused by the mate of the vessel in great alarm -from an unusual appearance. It was a starlight night, when suddenly the -sky became overcast in the direction of the high land, and an -instantaneous and intensely vivid light, resembling the aurora, shot out -of the hitherto gloomy and dark sea on the lee bow, which was so -brilliant that it lighted everything distinctly even to the mast-head. -The light spread over the whole sea between the two shores, and the -waves, which before had been tranquil, now began to be agitated. Captain -Bonnycastle describes the scene as that of a blazing sheet of awful and -most brilliant light. A long and vivid line of light, superior in -brightness to the parts of the sea not immediately near the vessel, -showed the base of the high, frowning, and dark land abreast; the sky -became lowering and more intensely obscure. Long tortuous lines of light -showed immense numbers of very large fish darting about as if in -consternation. The sprit-sail yard and mizen-boom were lighted by the -glare, as if gaslights had been burning directly below them; and until -just before daybreak, at four o’clock, the most minute objects were -distinctly visible. Day broke very slowly, and the sun rose of a fiery -and threatening aspect. Rain followed. Captain Bonnycastle caused a -bucket of this fiery water to be drawn up; it was one mass of light when -stirred by the hand, and not in sparks as usual, but in actual -coruscations. A portion of the water preserved its luminosity for seven -nights. On the third night, the scintillations of the sea reappeared; -the sun went down very singularly, exhibiting in its descent a double -sun; and, when only a few degrees high, its spherical figure changed -into that of a long cylinder, which reached the horizon. In the night -the sea became nearly as luminous as before, but on the fifth night the -appearance entirely ceased. Captain Bonnycastle did not think it -proceeded from animalculæ, but imagined it might be some compound of -phosphorus, suddenly evolved and disposed over the surface of the sea. -It had probably been that peculiar form of electricity known as the glow -discharge, of which the author once saw a very remarkable instance. - -M. E. Becquerel assures us that almost all substances are phosphorescent -after being exposed to the sun if instantly withdrawn into darkness, and -that it depends upon the arrangement of the particles and not upon -chemical action. The salts of uranium give the same kind of -phosphorescent light as that produced by the violet rays of the solar -spectrum. A solution of the bisulphate of quinine emits a yellow -phosphorescent light, whereas the fluorescent light of that liquid is -blue. The colours of these two kinds of light are generally -complementary to one another. - -Phosphorescence is probably more or less concerned in some, at least, of -a series of very curious experiments made by M. Niepcé de Saint-Victor, -on what he calls the saturation of substances with light. It has long -been known that, if a person in an intensely dark room should expose his -arm to the sun through a hole in a window-shutter, it will shine on -being drawn into the darkness. Now, M. de Saint-Victor found that if an -engraving be exposed for a certain time to the sun, and instantly -brought into darkness, it will make a photographic impression on a -collodion or argentine surface, and that anything written or drawn with -tartaric acid, or a solution of the salts of uranium, in large -characters, is reproduced even at a small distance from a sensitive -surface. It may be presumed that the light communicates its vibrations -to the surfaces exposed to it with sufficient force to enable them to -disturb the unstable equilibrium of such sensitive substances as -collodion or the argentine salts. M. de Saint-Victor has shown that -tartaric acid, which is readily impressed by sunlight, is neither -fluorescent nor phosphorescent, whence he concludes that his experiments -are independent of both of these modes of action. Uranium appears to -have very peculiar properties: its salts are strongly luminous when -exposed to the sun; they are very fluorescent; and the crystallized -azitote of uranium becomes phosphorescent by percussion. - - - - - 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. - - -VOLTAIC or Dynamic electricity is elicited by the force of chemical -action. It is connected with some of the most brilliant periods of -British science, from the splendid discoveries to which it led Sir -Humphry Davy and Dr. Faraday. - -In 1790, while Galvani, Professor of Anatomy in Bologna, was making -experiments on electricity, he was surprised to see convulsive motions -in the limbs of a dead frog accidentally lying near the machine during -an electrical discharge. Though a similar action had been noticed long -before his time, he was so much struck with this singular phenomenon, -that he examined all the circumstances carefully, and at length found -that convulsions take place when the nerve and muscle of a frog are -connected by a metallic conductor. This excited the attention of all -Europe; and it was not long before Volta, Professor at Pavia, showed -that the mere contact of different bodies is sufficient to disturb -electrical equilibrium, and that a current of electricity flows in one -direction through a circuit of three conducting substances. From this he -was led, by acute reasoning and experiment, to the construction of the -Voltaic pile, which, in its early form, consisted of alternate discs of -zinc and copper, separated by pieces of wet cloth, the extremities being -connected by wires. This simple apparatus, perhaps the most wonderful -instrument that has been invented by the ingenuity of man, by divesting -electricity of its sudden and uncontrollable violence, and giving in a -continued stream a greater quantity at a diminished intensity, has -exhibited that force under a new and manageable form, possessing powers -the most astonishing and unexpected. The expression current has no -relation to a fluid, which is now considered to be as inconsistent with -the phenomena of dynamic as with static electricity. It was shown by -Grotthus that the transmission of Voltaic electricity through liquids -consists of a series of chemical affinities acting in definite -directions; and Mr. Grove, from an examination of its action on the -various kinds of matter, has come to the same conclusion. Indeed it is -now the generally received opinion that a current of electricity is -merely a continuous transmission of chemical affinity from particle to -particle of the substance through which it is passing, and consequently -that it is a continuous transmission of force. As the Voltaic battery -has become one of the most important engines of physical research, some -account of its present condition may not be out of place. - -The disturbance of electric equilibrium, and a development of -electricity, invariably accompany the chemical action of a fluid on -metallic substances, and the electricity is most plentiful when that -action occasions oxidation. Metals vary in the quantity of electricity -afforded by their combination with oxygen. But the greatest abundance is -developed by the oxidation of zinc by weak sulphuric acid. And, in -conformity with the law that one kind of electricity cannot be evolved -without an equal quantity of the other being brought into activity, it -is found that the acid is positively, and the zinc negatively electric. -It has not yet been ascertained why equilibrium is not restored by the -contact of these two substances, which are both conductors, and in -opposite electrical states. However, the electrical and chemical changes -are so connected, that, unless equilibrium be restored, the action of -the acid will go on languidly, or stop as soon as a certain quantity of -electricity is accumulated in it. Equilibrium, nevertheless, will be -restored, and the action of the acid will be continuous, if a plate of -copper be placed in contact with the zinc, both being immersed in the -fluid; for the copper, not being acted upon by the acid, will serve as a -conductor to convey the positive electricity from the acid to the zinc, -and will at every instant restore the equilibrium, and then the -oxidation of the zinc will go on rapidly. Thus three substances are -concerned in forming a Voltaic circuit, but it is indispensable that one -of them should be a fluid. The electricity so obtained will be very -feeble in overcoming resistances offered by imperfect conductors -interposed in the circuit, or by very long wires, but it may be -augmented by increasing the number of plates. In the common Voltaic -battery, the electricity which the fluid has acquired from the first -plate of zinc exposed to its action is taken up by the copper plate -belonging to the second pair, and transferred to the second zinc plate, -with which it is connected. The second plate of zinc, possessing equal -powers, and acting in conformity with the first, having thus acquired a -larger portion of electricity than its natural share, communicates a -larger quantity to the fluid in the second cell. This increased quantity -is again transferred to the next pair of plates; and thus every -succeeding alternation is productive of a further increase in the -quantity of the electricity developed. This action, however, would stop -unless a vent were given to the accumulated electricity, by establishing -a communication between the positive and negative poles of the battery -by means of wires attached to the extreme plate at each end. When the -wires are brought into contact, the Voltaic circuit is completed, the -electricities meet and neutralize each other, producing the shock and -other electrical phenomena; and then the electric current continues to -flow uninterruptedly in the circuit, as long as the chemical action -lasts. The stream of positive electricity flows from the zinc to the -copper. The construction and power of the Voltaic battery have been much -improved of late years, but the most valuable improvement is the -constant battery of Professor Daniell. In all batteries of the ordinary -construction, the power, however energetic at first, rapidly diminishes, -and ultimately becomes very feeble. Professor Daniell found that this -diminution of power is occasioned by the adhesion of the evolved -hydrogen to the surface of the copper, and by the precipitation of the -sulphate formed by the action of the acid on the zinc. He prevents the -latter by interposing between the copper and the zinc, in the cell -containing the liquid, a membrane which, without impeding the electric -current, prevents the transfer of the salt; and the former, by placing -between the copper and the membrane solution of sulphate of copper, -which being reduced by the hydrogen prevents the adhesion of this gas to -the metallic surface. Each element of the battery consists of a hollow -cylinder of copper, in the axis of which is placed a cylindrical rod of -zinc; between the zinc and the copper a membranous bag is placed, which -divides the cell into two portions, the inner of which is filled with -dilute acid, and the one nearer the copper is supplied with crystals of -the sulphate of that metal. The battery consists of several of these -elementary cells connected together by metallic wires, the zinc rod of -one with the copper cylinder of that next to it. The zinc rods are -amalgamated, so that local action, which, in ordinary cases, is so -destructive of the zinc, does not take place, and no chemical action is -manifested unless the circuit be completed. The rods are easily -detached, and others substituted for them when worn out. This battery, -which possesses considerable power, and is constant in its effects for a -very long time, is greatly superior to all former arrangements, either -as an instrument of research, or for exhibiting the ordinary phenomena -of Voltaic electricity. - -A battery charged with water alone, instead of acid, is constant in its -action, but the quantity of electricity it develops is comparatively -very small. Mr. Cross, of Broomfield in Somersetshire, kept a battery of -this kind in full force during twelve months. M. Becquerel had invented -an instrument for comparing the intensities of the different kinds of -electricity by means of weights; but, as it is impossible to make the -comparison with Voltaic electricity produced by the ordinary batteries, -on account of the perpetual variation to which the intensity of the -current is liable, he has constructed a battery which affords a -continued stream of electricity of uniform power, but it is also of very -feeble force. The current is produced by the chemical combination of an -acid with an alkali. - -Metallic contact is not necessary for the production of Voltaic -electricity, which is entirely due to chemical action. The intensity of -the Voltaic electricity is in proportion to the intensity of the -affinities concerned in its production, and the quantity produced is in -proportion to the quantity of matter which has been chemically active -during its evolution. Dr. Faraday considers this definite production to -be one of the strongest proofs that electricity is of chemical origin. - -Galvanic or Voltaic electricity is manifested by two continuous forces -or currents passing in opposite directions through the circuit: the zinc -is the positive end or pole of the battery, and the copper the negative. - -Voltaic electricity is distinguished by two marked characters. Its -intensity increases with the number of plates, its quantity with the -extent of their surfaces. The most intense concentration of force is -displayed by a numerous series of large plates: light and heat are -copiously evolved, and chemical decomposition is accomplished with -extraordinary energy; whereas the electricity from one pair of plates, -whatever their size may be, is so feeble that it gives no sign either of -attraction or repulsion. Common or static electricity is of greater -intensity and has a greater power of overcoming resistance than Voltaic -electricity, but it acts upon a smaller quantity of matter. However, by -diminishing the size of the plates, and increasing their number, the -intensity of a battery may be increased till it becomes equal to that of -the electrical machine. - -The action of Voltaic electricity differs in some respects materially -from that of the ordinary kind. When a quantity of common electricity is -accumulated, the restoration of equilibrium is attended by an -instantaneous violent explosion, accompanied by the development of -light, heat, and sound. The concentrated power of the electricity forces -its way through every obstacle, disrupting and destroying the cohesion -of the particles of the bodies through which it passes, and occasionally -increasing its destructive effects by the conversion of fluids into -steam from the intensity of the momentary heat, as when trees are torn -to pieces by a stroke of lightning. Even the vivid light which marks the -path of the electricity is probably owing in part to the sudden -compression of the air and the rapidity of its passage. But the instant -equilibrium is restored by this energetic action the whole is at an end. -On the contrary, when an accumulation takes place in a Voltaic battery, -equilibrium is restored the moment the circuit is completed. But so far -is the electric stream from being exhausted, that it continues to flow -silently and invisibly in an uninterrupted current supplied by a -perpetual reproduction. And, although its action on bodies is neither so -sudden nor so intense as that of common electricity, yet it acquires -such power from constant accumulation and continued action, that it -ultimately surpasses the energy of the other. The two kinds of -electricity differ in no circumstance more than in the development of -heat. Instead of a momentary evolution, the circulation of the Voltaic -electricity is accompanied by a continued development of heat, lasting -as long as the circuit is complete, without producing either light or -sound. Its intensity from a very powerful battery is greater than that -of any heat that can be obtained by artificial means, so that it fuses -substances which resist the action of the most powerful furnaces. The -temperature of every part of a Voltaic battery itself is raised during -its activity. With the greater number of metals Mr. Grove found that the -positive terminal or pole is hotter than the negative. - -According to Mr. Joule, the quantity of heat generated in a unit of time -is proportional to the strength of the current, and when a galvanic -current is employed in chemical analysis, the heat in the entire circuit -generated in a unit of time is equal to the work expended in producing -it, minus that employed in the analysis. In fact, a current of -electricity cannot pass through a homogeneous conductor without -generating heat in overcoming resistance, an effect proved by Mr. Joule -to be proportional to the square of the force of the current, and the -same in whatever direction the current may be flowing. Any other thermal -action that can take place must depend upon the heterogeneousness of the -circuit, and must be reversible with the current. For example, if a -semicircle of bismuth be joined to a semicircle of antimony, an electric -current in passing through it produces cold where it passes from the -bismuth to the antimony by absorption, and heat where it passes from the -antimony to the bismuth. - -The transit of the electricity from pole to pole is accompanied by -light, and in consequence of the continuous current sparks occur every -time the contact of the wires is either broken or renewed; but -considerable intensity is requisite to enable the electricity to force -its way through atmospheric air or gas. Both its length and colour are -affected by the density of the medium through which it passes. If the -medium be gradually rarefied the discharge increases from a spark to a -luminous glow, differing in colour in different gases, but white in air. -When very much attenuated a discharge may be made to pass across 6 or 7 -feet of space, while in air of the ordinary density it will not pass -through an inch. In rarefied gas it resembles the Aurora by its -continuous flashes. When the battery is powerful the luminous effects -are very brilliant. - -The most splendid artificial light known is produced by fixing pencils -of charcoal at the extremities of the wires, and bringing them into -contact. This light is the more remarkable as it is independent of -combustion, since the charcoal suffers no apparent change, and, -likewise, because it is equally vivid in such gases as do not contain -oxygen. It depends upon the molecular arrangement of the charcoal; for -Mr. Grove observes that “carbon in a transparent crystalline state, as -diamond, is as perfect a non-conductor as we know, while in an opaque -amorphous state, as graphite or charcoal, it is one of the best -conductors: thus in one state it transmits light and stops electricity, -in the other it transmits electricity and stops light. It is a -circumstance worthy of remark, that the arrangement of molecules which -renders a solid body capable of transmitting light is most unfavourable -to the transmission of electricity, transparent solids being very -imperfect conductors of electricity; so all gases readily transmit -light, but are amongst the worst conductors of electricity, if indeed -they can be said to conduct it at all. The fact that the molecular -structure or arrangement of a body influences, indeed I may say -determines, its conducting power, is by no means explained by the theory -of a fluid; but if electricity be only a transmission of force or -motion, the influence of the molecular state is just what would be -expected.” - -Professor Wheatstone, by fixing metallic points at the extremities of -the wires or poles, has found that the appearance of the spectrum of the -voltaic arc or vivid flame that is seen between the terminals of a -battery, depends, as in static electricity, upon the metal from whence -it is taken. The spectrum of that from mercury consists of seven -definite rays, separated from each other by dark intervals; these -visible rays are two orange lines close together, a bright green line, -two blueish-green lines near each other, a very bright purple line, and, -lastly, a blue line. It is the same when it passes through carbonic acid -gas, oxygen gas, air, or vacuum. The light from zinc, cadmium, tin, -bismuth, and lead, in a melted state, gives similar results; but the -number, position, and colour of the lines vary so much in each case, and -the appearances are so different, that the metals may easily be -distinguished from one another by this mode of investigation. The -electric spark is considered by M. Angström to be the overlapping of two -spectra, one of which belongs to the metal, and the other to the gas -through which the spark passes, and that the bright lines vary with the -gas as well as with the metal. In an oxygen spectrum the greatest number -of bright lines occur in the blue and violet, in nitrogen in the green -and yellow, and in hydrogen in the red. These effects must necessarily -be connected with the chemical and thermal properties of the gases. - -Mr. Grove considers that the colour of the voltaic arc, or flame, which -appears between the poles of a very powerful battery, depends upon the -substance of the metal from whence it proceeds and on the medium through -which it passes. The spark from zinc is blue, from silver it is green, -from iron it is red and scintillating—precisely the colours afforded by -these metals in their ordinary combustion. But the colour varies also -with the medium through which the light passes, for when the medium is -changed a change takes place in the colour, showing an affection of the -intervening matter. A portion of the metal terminals or poles is -actually transmitted with every electrical or Voltaic discharge, whence -Mr. Grove concludes that the electrical discharge arises, at least in -part, from an actual repulsion and severance of the electrified matter -itself, which flies off at the points of least resistance. He observes -that “the phenomena attending the electric spark or Voltaic arc tends to -modify considerably our previous idea of the nature of the electric -force as a producer of ignition and combustion. The Voltaic arc is -perhaps, strictly speaking, neither ignition nor combustion. It is not -simply ignition; because the matter of the terminals is not merely -brought to a state of incandescence, but is physically separated, and -partially transferred from one terminal to another, much of it being -dissipated in a vaporous state. It is not combustion; for the phenomena -will take place independently of atmospheric air, oxygen gas, or any of -the bodies usually called supporters of combustion; combustion being in -fact chemical union attended with heat and light. In the Voltaic arc we -may have no chemical union, for if the experiment be performed in an -exhausted receiver, or in nitrogen, the substance forming the terminals -is condensed and precipitated upon the interior of the vessel, in, -chemically speaking, an unaltered state. Thus, to take a very striking -example, if the Voltaic discharge be taken between zinc terminals in an -exhausted receiver, a fine black powder of zinc is deposited on the -sides of the receiver; this can be collected, and takes fire readily in -air by being touched with a match, or ignited wire, instantly burning -into white oxide of zinc. To an ordinary observer the zinc would appear -to be burned twice—first in the receiver, where the phenomenon presents -all the appearance of combustion, and, secondly, in the real combustion -in air. With iron the experiment is equally instructive. Iron is -volatilized by the Voltaic arc in nitrogen, or in an exhausted receiver; -and when a scarcely perceptible film has lined the receiver, if it be -washed with an acid, it then gives, with ferrocyanide of potassium, the -Prussian-blue precipitate. In this case we readily distil iron, a metal -by ordinary means _fusible_ only at a very high temperature.” - -Another strong evidence that the Voltaic discharge consists of the -material itself of which the terminals are composed, is the peculiar -rotation which is observed in the light when iron is employed, the -magnetic character of this metal causing its particles to rotate by the -influence of the Voltaic current. In short, Mr. Grove concludes that, -although it would be hasty to assert that the electrical disruptive -discharge can in no case take place without the terminals being -affected, yet he had met with no instance of such a result, provided the -discharge had been sufficiently prolonged, and the terminals in such a -state as could be expected to render manifest slight changes![15] - -Some years ago Mr. Grove discovered that the electrical discharge -possesses certain phases or fits of an alternate character, forming -rings of alternate oxidation and deoxidation on metallic surfaces. A -highly polished silver plate in an air-pump was connected with the pole -of a powerful inductive battery, while a fine metallic wire, or even a -common sewing needle, was fixed at the other pole, and so arranged as to -be perpendicular to the silver plate, and very near, but not touching -it. By means of this apparatus the electrical discharge could be sent -through any kind of rarefied media. In some of the experiments a series -of concentric coloured rings of oxide alternating with rings of polished -or unoxidated silver were formed on the plate under the point of the -needle or wire. When the plate was previously coated with a film of -oxide, the oxide was removed in concentric spaces by the discharge, and -increased on the alternate ones, showing an alternate positive and -negative electricity, or electricity of an opposite character in the -same discharge. - -When the silver plate was polished the centre of the rings formed on it -was yellow-green surrounded by blue-green; then a ring of polished -silver, followed by a crimson ring with a slight orange tint on the -inner side and deep purple on the outer; lastly the indication of a -polished one. When the air-pump was filled with attenuated olefiant gas -the rings were precisely the same with those seen in thin plates; hence -the effect is the same as that produced by the interference of light. In -these experiments the luminous appearance extended from three quarters -of an inch to an inch round the point of the needle or wire. - -When the silver plate was connected with the negative pole of the -battery a polished point appeared upon it opposite the needle, -surrounded by a dusky ill-defined areola of a brown colour tinged with -purple when viewed in one direction, and greenish-white when seen in -another. - -In the present year Mr. Gassiot, Vice-President of the Royal Society, -has shown that the stratified character of the electric discharge is -remarkably developed in the Torricellian vacuum. Among the various -experiments made by that gentleman two may be selected as strongly -illustrative of this new and singular property of electrical light. - -In a closed glass tube about an inch internal diameter and 38 inches -long, in which a vacuum had been made, two platinum wires were -hermetically sealed, 32 inches apart, and connected with the poles of an -inductive battery. The luminous appearance at the two poles was very -different when electricity passed through the wires. A glow surrounded -the negative pole, and in close approximation to the glow a well-defined -dark space appeared, while from the positive pole or wire the light -proceeded in a stream; but unless the charge be great or the tube short, -the stream will not extend to the black band, which is totally different -from the intervening space. When discharges of electricity were sent -through this vacuum tube a series of bands or stratifications were -formed which were concave towards the positive pole; and as in the -changes in making and breaking the circuit the electricity emanates from -the different terminals or wires, their concavities were in opposite -directions. - -When instead of platinum wires narrow tinfoil coatings were placed round -the exterior of the glass tube and connected with the wires of the -battery, brilliant stratifications filled the interior of the tube -between the foil coatings, but no dark band appeared. At present Mr. -Gassiot is inclined to believe that the dark band is due to -interference; but that the stratifications arise from pulsations or -impulses of a force acting in a highly attenuated but resisting medium, -for even with the best air-pumps it is impossible to make a perfect -void; he is still occupied with experiments on this new subject, and no -doubt will obtain very remarkable results, of which none can be more -extraordinary than his discovery of the powerful influence of the magnet -on this electric light. The stratifications are formed in rapid -succession in the tube with platinum wires and are turned different -ways, but they can be separated at any part of the tube by the pole of a -magnet round which the whole stratifications have a tendency to revolve. -In the second experiment, where the tinfoil was used, the discharge was -divided in two by the pole of a magnet, and the two parts had a tendency -to rotate round the magnet in opposite directions. - -Voltaic electricity is a powerful agent in chemical analysis. When -transmitted through conducting fluids, it separates them into their -constituent parts, which it conveys in an invisible state through a -considerable space or quantity of liquid to the poles, where they come -into evidence. Numerous instances might be given, but the decomposition -of water is perhaps the most simple and elegant. Suppose a glass tube -filled with water, and corked at both ends; if one of the wires of an -active Voltaic battery be made to pass through one cork, and the other -through the other cork, into the water, so that the extremities of the -two wires shall be opposite and about a quarter of an inch asunder, -chemical action will immediately take place, and gas will continue to -rise from the extremities of both wires till the water has vanished. If -an electric spark be then sent through the tube, the water will -reappear. By arranging the experiment so as to have the gas given out by -each wire separately, it is found that water consists of two volumes of -hydrogen and one of oxygen. The hydrogen is given out at the positive -wire of the battery, and the oxygen at the negative. The oxides are also -decomposed; the oxygen appears at the positive pole, and the metal at -the negative. The decomposition of the alkalies and earths by Sir -Humphry Davy formed a remarkable era in the history of science. Soda, -potash, lime, magnesia, and other substances heretofore considered to be -simple bodies incapable of decomposition, were resolved by electric -agency into their constituent parts, and proved to be metallic oxides, -by that illustrious philosopher. All chemical changes produced by -electricity are accomplished on the same principle; and it appears that, -in general, combustible substances, metals, and alkalies go to the -negative wire, while acids and oxygen are evolved at the positive. The -transfer of these substances to the poles is not the least wonderful -effect of the Voltaic battery. Though the poles be at a considerable -distance from one another, nay, even in separate vessels, if a -communication be only established by a quantity of wet thread, as the -decomposition proceeds the component parts pass through the thread in an -invisible state, and arrange themselves at their respective poles. -According to Dr. Faraday, electro-chemical decomposition is simply a -case of the preponderance of one set of chemical affinities more -powerful in their nature over another set which are less powerful. And -in electro-chemical action of any kind produced by a continuous current, -the amount of action in a given time is nearly, if not rigorously, -proportional to the strength of the current. The great efficacy of -Voltaic electricity in chemical decomposition arises not from its -tension, but from the quantity set in motion and the continuance of its -action. Its agency appears to be most exerted on fluids and substances -which by conveying the electricity partially and imperfectly impede its -progress. But it is now proved to be as efficacious in the composition -as in the decomposition or analysis of bodies. - -It had been observed that, when metallic solutions are subjected to -galvanic action, a deposition of metal, sometimes in the form of minute -crystals, takes place on the negative wire. By extending this principle, -and employing a very feeble Voltaic action, M. Becquerel has succeeded -in forming crystals of a great proportion of the mineral substances, -precisely similar to those produced by nature. The electric state of -metallic veins makes it possible that many natural crystals may have -taken their form from the action of electricity bringing their ultimate -particles, when in solution, within the narrow sphere of molecular -attraction. Both light and motion favour crystallization. Crystals which -form in different liquids are generally more abundant on the side of the -jar exposed to the light; and it is well known that still water, cooled -below 32°, starts into crystals of ice the instant it is agitated. A -feeble action is alone necessary, provided it be continued for a -sufficient time. Crystals formed rapidly are generally imperfect and -soft, and M. Becquerel found that even years of constant Voltaic action -were necessary for the crystallization of some of the hard substances. -If this law be general, how many ages may be required for the formation -of a diamond! - -The deposition of metal from a metallic solution by galvanic electricity -has been most successfully applied to the arts of plating and gilding, -as well as to the more delicate process of copying medals and copper -plates. Indeed, not medals only, but any object of art or nature, may be -coated with precipitated metal, provided it be first covered with the -thinnest film of plumbago, which renders a non-conductor sufficiently -conducting to receive the metal. Photo-galvanic engraving depends upon -this. Gelatine mixed with bichromate of potash, nitrate of silver, and -iodide of potassium, is spread over a plate of glass, and when dry a -positive print is laid upon it with its face downwards, which, when -exposed to the sun, leaves its impression. When soaked in water the -gelatine swells around all those parts where the light had fallen, thus -forming an intaglio, a cast of which is taken in gutta-percha, which is -then coated with copper by the electro process, whence a copper plate in -relief is obtained. - -Static electricity, on account of its high tension, passes through water -and other liquids as soon as it is formed, whatever the length of its -course may be. Voltaic electricity, on the contrary, is weakened by the -distance it has to traverse. Pure water is a very bad conductor; but ice -absolutely stops a current of Voltaic electricity altogether, whatever -be the power of the battery, although static or common electricity has -sufficient power to overcome its resistance. Dr. Faraday has discovered -that this property is not peculiar to ice; that, with a few exceptions, -bodies which do not conduct electricity when solid acquire that -property, and are immediately decomposed, when they become fluid, and, -in general, that decomposition takes place as soon as the solution -acquires the capacity of conduction, which has led him to suspect that -the power of conduction may be only a consequence of decomposition. - -Heat increases the conducting power of some substances for Voltaic -electricity, and of the gases for both kinds. Dr. Faraday has given a -new proof of the connexion between heat and electricity, by showing -that, in general, when a solid, which is not a metal, becomes fluid, it -almost entirely loses its power of conducting heat, while it acquires a -capacity for conducting electricity in a high degree. M. Becquerel -regards the production of heat and that of electricity to be -concomitant; their dependence being such, that when one is increased the -other diminishes, and _vice versâ_, so that one may altogether disappear -with the increase of the other. For instance, when electricity -circulates in a metallic wire, the greater the heat produced, the less -the quantity of electricity which passes, and the contrary, so that the -affair proceeds as if electricity were converted into heat, and heat -into electricity. Again, in a closed galvanic circuit the sum of the -heat produced in the chemical action of the acidulated water upon the -zinc and in the conducting wire is constant, so that the quantity of -heat disengaged in the reaction is greater in proportion as less -electricity passes through the wire. These, and other circumstances, -prove such an intimate connexion between the production of heat and -electricity, that in the change of condition of substances the -electrical effects might disappear or be annulled by the calorific -effects. - -The galvanic current affects all the senses: nothing can be more -disagreeable than the shock, which may even be fatal if the battery be -very powerful. A bright flash of light is perceived with the eyes shut, -when one of the wires touches the face, and the other the hand. By -touching the ear with one wire, and holding the other, strange noises -are heard; and an acid taste is perceived when the positive wire is -applied to the tip of the tongue, and the negative wire touches some -other part of it. By reversing the poles the taste becomes alkaline. It -renders the pale light of the glow-worm more intense. Dead animals are -roused by it, as if they started again into life, and it may ultimately -prove to be the cause of muscular action in the living. - -Several fish possess the faculty of producing electrical effects. The -most remarkable are the gymnotus electricus, found in South America; and -the torpedo, a genus of ray, frequent in the Mediterranean. The -electrical action of the torpedo depends upon an apparatus apparently -analogous to the Voltaic pile, which the animal has the power of -charging at will, consisting of membranous columns filled throughout -with laminæ, separated from one another by a fluid. The absolute -quantity of electricity brought into circulation by the torpedo is so -great, that it effects the decomposition of water, has power sufficient -to make magnets, gives very severe shocks and the electric spark. It is -identical in kind with that of the galvanic battery, the electricity of -the under surface of the fish being the same with the negative pole, and -that in the upper surface the same with the positive pole. Its manner of -action is, however, somewhat different; for, although the evolution of -the electricity is continued for a sensible time, it is interrupted, -being communicated by a succession of discharges. - - - - - 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. - - -THE disturbing effects of the aurora and lightning on the mariner’s -compass had been long known. In the year 1819 M. Oersted, Professor of -Natural Philosophy at Copenhagen, discovered that a current of Voltaic -electricity exerts a powerful influence on a magnetized needle. This -observation has given rise to the theory of electro-magnetism—one of the -most interesting sciences of modern times, whether it be considered as -leading us a step farther in generalization, by identifying two agencies -hitherto referred to different causes, or as developing a new force, -unparalleled in the system of the world, which, overcoming the -retardation from friction, and the obstacle of a resisting medium, -maintains a perpetual motion as long as the action of a Voltaic battery -is continued. - -When the two poles of a Voltaic battery are connected by a metallic -wire, so as to complete a circuit, the electricity flows without -ceasing. If a straight portion of that wire be placed parallel to, and -horizontally above, a magnetized needle at rest in the magnetic -meridian, but freely poised like the mariner’s compass, the action of -the electric current flowing through the wire will instantly cause the -needle to change its position. Its extremity will deviate from the north -towards the east or west, according to the direction in which the -current is flowing; and, on reversing the direction of the current, the -motion of the needle will be reversed also. The numerous experiments -that have been made on magnetism and electricity, as well as those on -the various relative motions of a magnetic needle under the influence of -galvanic electricity, arising from all possible positions of the -conducting wire, and every direction of the Voltaic current, together -with all the other phenomena of electro-magnetism, are explained by Dr. -Roget in some excellent articles on these subjects in the Library of -Useful Knowledge. - -All experiments tend to prove that the force emanating from the electric -current, which produces such effects on the magnetic needle, acts at -right angles to the current. The action of an electrical current upon -either pole of a magnet has no tendency to cause the pole to approach or -recede, but to rotate about it. If the stream of electricity be supposed -to pass through the centre of a circle whose plane is perpendicular to -the current, the direction of the force exerted by the electricity will -always be in the tangent to the circle, or at right angles to its radius -(N. 223). Consequently, the tangential force of the electricity has a -tendency to make the pole of a magnet move in a circle round the wire of -the battery. - -Rotatory motion was suggested by Dr. Wollaston. Dr. Faraday was the -first who actually succeeded in making the pole of a magnet rotate about -a vertical conducting wire. In order to limit the action of the -electricity to one pole, about two-thirds of a small magnet were -immersed in mercury, the lower end being fastened by a thread to the -bottom of the vessel containing the mercury. When the magnet was thus -floating almost vertically with its north pole above the surface, a -current of positive electricity was made to descend perpendicularly -through a wire touching the mercury, and immediately the magnet began to -rotate from left to right about the wire. The force being uniform, the -rotation was accelerated till the tangential force was balanced by the -resistance of the mercury, when it became constant. Under the same -circumstances the south pole of the magnet rotates from right to left. -It is evident, from this experiment, that the wire may also be made to -perform a rotation round the magnet, since the action of the current of -electricity on the pole of the magnet must necessarily be accompanied by -a corresponding reaction of the pole of the magnet on the electricity in -the wire. This experiment has been accomplished by a vast number of -contrivances, and even a small battery, consisting of two plates, has -performed the rotation. Dr. Faraday produced both motions at the same -time in a vessel containing mercury; the wire and the magnet revolved in -one direction about a common centre of motion, each following the other. - -The next step was to make a magnet, and also a cylinder, revolve about -their own axes, which they do with great rapidity. Mercury has been made -to rotate by means of Voltaic electricity, and Professor Ritchie -exhibited in the Royal Institution the singular spectacle of the -rotation of water by the same means, while the vessel containing it -remained stationary. The water was in a hollow double cylinder of glass, -and, on being made the conductor of electricity, was observed to revolve -in a regular vortex, changing its direction as the poles of the battery -were alternately reversed. Professor Ritchie found that all the -different conductors hitherto tried by him, such as water, charcoal, -&c., give the same electro-magnetic results when transmitting the same -quantity of electricity, and that they deflect the magnetic needle in an -equal degree when their respective axes of conduction are at the same -distance from it. But one of the most extraordinary effects of this -force is exhibited by coiling a copper wire, so as to form a helix or -corkscrew, and connecting the extremities of the wire with the poles of -a galvanic battery. If a magnetized steel bar or needle be placed within -the screw, so as to rest upon the lower part, the instant a current of -electricity is sent through the wire of the helix, the steel bar starts -up by the influence of this invisible power, and remains suspended in -the air in opposition to the force of gravitation (N. 224). The effect -of the electro-magnetic power exerted by each turn of the wire is to -urge the north pole of the magnet in one direction, and the south pole -in the other. The force thus exerted is multiplied in degree and -increased in extent by each repetition of the turns of the wire, and in -consequence of these opposing forces the bar remains suspended. This -helix has all the properties of a magnet while the electrical current is -flowing through it, and may be substituted for one in almost every -experiment. It acts as if it had a north pole at one extremity and a -south pole at the other, and is attracted and repelled by the poles of a -magnet exactly as if it were one itself. All these results depend upon -the course of the electricity; that is, on the direction of the turns of -the screw, according as it is from right to left, or from left to right, -being contrary in the two cases. - -The action of Voltaic electricity on a magnet is not only precisely the -same with the action of two magnets on one another, but its influence in -producing temporary magnetism in iron and steel is also the same with -magnetic induction. The term induction, when applied to electric -currents, expresses the power which these currents possess of inducing a -particular state upon matter in their immediate neighbourhood, otherwise -neutral or indifferent. For example, the connecting wire of a galvanic -battery holds iron filings suspended like a magnet as long as the -current continues to flow through it: the iron becomes magnetic by the -induction of the current. The most powerful temporary magnets are -obtained by bending a thick cylinder of soft iron into the form of a -horseshoe, and surrounding it with a coil of thick copper wire covered -with silk to prevent communication between its coils. When this wire -forms part of a galvanic circuit the iron becomes so highly magnetic by -the induction of the current flowing through the wire that a temporary -magnet of this kind made by Professor Henry of the Albany Academy in the -United States sustained a weight of nearly a ton. Another by Mr. Gage -has been applied with considerable success as a moving power: its spark -is a bright flash, and the snap as loud as a pistol. But the most -powerful known is that employed by Mr. Joule in his experiments, which -sustains a weight of 2080 lbs. The iron loses its magnetism the instant -the electricity ceases to flow, and acquires it again as instantaneously -when the circuit is renewed. - -The action of an electric current causes a deviation of the compass from -the plane of the magnetic meridian. In proportion as the needle recedes -from the meridian, the intensity of the force of terrestrial magnetism -increases, while at the same time the electro-magnetic force diminishes; -the number of degrees at which the needle stops, showing where the -equilibrium between these two forces takes place, will indicate the -intensity of the galvanic current. The galvanometer, constructed upon -this principle, is employed to measure the intensity of galvanic -currents collected and conveyed to it by wires. This instrument is -rendered much more sensible by neutralizing the effects of the earth’s -magnetism on the needle, which is accomplished by placing a second -magnetised needle so as to counteract the action of the earth on the -first—a precaution requisite in all delicate magnetical experiments. - -It has been ascertained by means of this instrument that the action of -an electrical current upon a magnet is inversely as the square of the -distance, and the energy with which an electro magnet acts is directly -as the power of the galvanic battery and the number of coils round the -core, and inversely as the resistance of the wire. - - - - - 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. - - -THE science of electro-magnetism, which must render the name of M. -Oersted ever memorable, relates to the reciprocal action of electrical -and magnetic currents: M. Ampère, by discovering the mutual action of -electrical currents on one another, has added a new branch to the -subject, to which he has given the name of electro-dynamics. - -When electric currents are passing through two conducting wires, so -suspended or supported as to be capable of moving both towards and from -one another, they show mutual attraction or repulsion, according as the -currents are flowing in the same or in contrary directions; the -phenomena varying with the relative inclinations and positions of the -streams of electricity. The mutual action of such currents, whether they -flow in the same or in contrary directions, whether they be parallel, -perpendicular, diverging, converging, circular, or heliacal, all produce -different kinds of motion in a conducting wire, both rectilineal and -circular, and also the rotation of a wire helix, such as that described, -now called an electro-dynamic cylinder on account of some improvements -in its construction (N. 225). And, as the hypothesis of a force varying -inversely as the square of the distance accords perfectly with all the -observed phenomena, these motions come under the same laws of dynamics -and analysis as any other branch of physics. - -Electro-dynamic cylinders act on each other precisely as if they were -magnets during the time the electricity is flowing through them. All the -experiments that can be performed with the cylinder might be -accomplished with a magnet. That end of the cylinder in which the -current of positive electricity is moving in a direction similar to the -motion of the hands of a watch, acts as the south pole of a magnet, and -the other end, in which the current is flowing in a contrary direction, -exhibits northern polarity. - -The phenomena mark a very decided difference between the action of -electricity in motion or at rest, that is, between Voltaic and static -electricity; the laws they follow are in many respects of an entirely -different nature, though the electricities themselves are identical. -Since Voltaic electricity flows perpetually, it cannot be accumulated, -and consequently has no tension, or tendency to escape from the wires -which conduct it. Nor do these wires either attract or repel light -bodies in their vicinity, whereas static or ordinary electricity can be -accumulated in insulated bodies to a great degree, and in that state of -rest the tendency to escape is proportional to the quantity accumulated -and the resistance it meets with. In ordinary electricity, the law of -action is, that dissimilar electricities attract and similar -electricities repel one another. In Voltaic electricity, on the -contrary, similar currents, or such as are moving in the same direction, -attract one another, while a mutual repulsion is exerted between -dissimilar currents, or such as flow in opposite directions. Common -electricity escapes when the pressure of the atmosphere is removed, but -the electro-dynamical effects are the same whether the conductors be in -air or in vacuo. - -The effects produced by a current of electricity depend upon the -celerity of its motion through a conducting wire. Yet we are ignorant -whether the motion be uniform or varied, but the method of transmission -has a marked influence on the results; for, when it flows without -intermission, it occasions a deviation in the magnetic needle, but it -has no effect whatever when its motion is discontinuous or interrupted, -like the current produced by the common electrical machine when a -communication is made between the positive and negative conductors. - -M. Ampère has established a theory of electro-magnetism suggested by the -analogy between electro-dynamic cylinders and magnets, founded upon the -reciprocal attraction of electro-currents, to which he reduces all the -phenomena of magnetism and electro-magnetism, by assuming that the -magnetic properties which bodies possess derive these properties from -currents of electricity, circulating about every part in one uniform -direction. Although every particle of a magnet possesses like properties -with the whole, yet the general effect is the same as if the magnetic -properties were confined to the surface. Consequently, Ampère concludes -that the internal electro-currents must compensate one another, and that -the magnetism of a body must therefore arise from a superficial current -of electricity constantly circulating in a direction perpendicular to -the axis of the magnet; so that the reciprocal action of magnets and all -the phenomena of electro-magnetism are reduced to the action and -reaction of superficial currents of electricity, acting at right angles -to their direction. - -Notwithstanding the experiments made by Ampère to elucidate the subject, -there is still an uncertainty in the theory of the induction of -magnetism by an electric current in a body near it. It does not appear -whether electric currents which did not previously exist are actually -produced by induction, or if its effect be only to give one uniform -direction to the infinite number of electric currents previously -existing in the particles of the body, and thus rendering them capable -of exhibiting magnetic phenomena, in the same manner as polarization -reduces the undulations of light to one plane, which had previously been -performed in every plane. Possibly both may be combined in producing the -effect; for the action of the electric current may not only give a -common direction to those already existing, but may also increase their -intensity. However that may be, by assuming that the attractions and -repulsions of the elementary portions of electric currents vary -inversely as the square of the distance, the actions being at right -angles to the direction of the current, it is found that the attraction -and repulsion of a current of indefinite length on the elementary -portion of a parallel current at any distance from it are in the simple -ratio of the shortest distance between them: consequently, the -reciprocal action of electric currents is reduced to the composition and -resolution of forces, so that the phenomena of electro-magnetism are -brought under the laws of mechanics by the theory of Ampère. It appears -that Dr. Faraday’s very remarkable experiment of electrifying and -magnetising a ray of polarized light may possibly afford a demonstration -of the reality of Ampère’s explanation of the ultimate nature of -magnetism. - -In this experiment a copper wire 501 feet long was arranged in four -concentric spirals, the extremities of which were connected with the -poles of a powerful galvanic battery, and a polished prism of heavy -glass, or silicated borate of lead, was placed in the axis of the spiral -as a core, through the length or axis of which a ray of polarized light -was sent. This ray, viewed through a piece of tourmaline or a Nichol’s -eye-piece, vanished and reappeared as usual at each quarter revolution -of the eye-piece; but when a current of electricity was sent through the -spiral at the time the ray had vanished, it instantly reappeared, and -remained as long as the electric current continued to flow; but the -instant the electricity ceased the light vanished, and as often as the -electric current flowed through the spiral, or was interrupted, so often -did the polarized ray appear and vanish. - -The character of the force thus impressed on the heavy glass is that of -rotation, for the stopping and renewing of the electric current had the -same effect as the revolving motion of the eye-piece in making the light -alternately appear and vanish. Accordingly, Dr. Faraday found that, when -the electricity flowed through the spiral in one direction, the rotation -of the plane of polarization was right-handed; and when it flowed in the -other direction, the rotation of the plane of polarization was -left-handed, the rotation increasing with the length of the prism and -the intensity of the electricity. The same phenomena were produced by a -very powerful magnet when a ray of polarized light was sent through the -heavy glass parallel to the line of magnetic force. - -Heavy glass or silico-borate of lead has the property more than any -other substance of making light rotate under electric and magnetic -influence; but many substances have the property more or less, as flint -and crown glass, rock salt, all the fixed and essential oils, water, and -many other liquids, but none of the gases possess it. In those -substances that have the power of circular polarization naturally, the -magnetic and electric influences increase or diminish the rotation -according to its direction. - -Polarized heat is made to revolve in the same manner, when the medium -through which it passes is subject to magnetic influence. - -Mr. Grove observes that if light and heat be merely modes of force, -which there is every reason to believe that they are, it may be fairly -stated that in these experiments magnetism affects these forces -directly; for light and heat being, in that view, motions of ordinary -matter, magnetism in affecting these movements affects the forces which -occasion them. If, however, this effect of magnetism be a molecular -change of the matter transmitting the light and heat, then it follows -that the light and heat are indirectly affected by the electricity or -magnetism. Dr. Faraday says that the magnetic forces do not act on the -ray of light directly, without the intervention of matter, but through -the mediation of the substance in which they and the ray have a -simultaneous existence; the substances and the forces giving to and -receiving from each other the power of acting on the light. Dr. Thomson -has shown, by a mathematical investigation of the subject, that Dr. -Faraday’s discovery seems to prove the truth of Ampère’s explanation of -the ultimate nature of magnetism. However, in Ampère’s theory, the -current of electricity flowing round the iron makes it a permanent -magnet, but it does not make the heavy glass or the other bodies, which -have the same property, either temporary magnets when the light is -rotating within them, or permanent magnets when the inductive action of -the current of electricity ceases. Hence the molecular condition of the -substances, when the light is rotating in them, must be specifically -distinct from that of magnetised iron: it must therefore be a new -magnetic condition, and the force which the matter in this state -possesses must be a new magnetic force. - -After describing his admirable experiment, Dr. Faraday observes that “it -has established for the first time a true, direct relation and -dependence between light and the magnetic and electric forces; and thus -a great addition is made to the facts and considerations which tend to -prove that all natural forces are tied together, and have one common -origin. It is no doubt difficult, in the present state of our knowledge, -to express our expectations in exact terms; and though I have said that -another of the powers of nature is in these experiments directly related -to the rest, I ought perhaps rather to say that another form of the -great power is distinctly and directly related to the other forms; or -that the great power manifested by particular phenomena in particular -forms is here further identified and recognised by the direct relation -of its form of light to its forms of electricity and magnetism. The -relation existing between _polarized_ light and magnetism and -electricity is even more interesting than if it had been shown to exist -with common light only. It cannot but extend to common light; and, as it -belongs to light made in a certain respect more precise in its character -and properties by polarization, it collates and connects it with these -powers in that duality of character which they possess, and yields an -opening, which before was wanting to us, for the appliances of these to -the investigation of the nature of this and other radiant agencies.” -Thus Dr. Faraday’s experiment not only shows the increasing connexion -between the sciences, but the tendency of all the forces of nature to -merge in one great and universal power. - -In the action of a magnet upon the stratifications of an electrical -discharge Mr. Gassiot has discovered a new instance of the connexion -between magnetism and light. - - - - - 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. - - -FROM the law of action and reaction being equal and contrary, it might -be expected that, as electricity powerfully affects magnets, so, -conversely, magnetism ought to produce electrical phenomena. By proving -this very important fact from the following series of interesting and -ingenious experiments, Dr. Faraday has added another branch to the -science which he has named magneto-electricity. A great quantity of -copper wire was coiled in the form of a helix round one half of a ring -of soft iron, and connected with a galvanic battery; while a similar -helix connected with a galvanometer was wound round the other half of -the ring, but not touching the first helix. As soon as contact was made -with the battery, the needle of the galvanometer was deflected. But the -action was transitory; for, when the contact was continued, the needle -returned to its usual position, and was not affected by the continual -flow of the electricity through the wire connected with the battery. As -soon, however, as the contact was broken, the needle of the galvanometer -was again deflected, but in the contrary direction. Similar effects were -produced by an apparatus consisting of two helices of copper wire coiled -round a block of wood, instead of iron, from which Dr. Faraday infers -that the electric current passing from the battery through one wire -induces a similar current through the other wire, but only at the -instant of contact, and that a momentary current is induced in a -contrary direction when the passage of the electricity is suddenly -interrupted. These brief currents or waves of electricity were found to -be capable of magnetizing needles, of passing through a small extent of -fluid, and, when charcoal points were interposed in the current of the -induced helix, a minute spark was perceived as often as the contacts -were made or broken, but neither chemical action nor any other electric -effects were obtained. A deviation of the needle of the galvanometer -took place when common magnets were employed instead of the Voltaic -current; so that the magnetic and electric forces are identical in their -effects in this experiment. Again, when a helix formed of 220 feet of -copper wire, into which a cylinder of soft iron was introduced, was -placed between the north and south poles of two bar magnets, and -connected with the galvanometer by means of wires from each extremity, -as often as the magnets were brought into contact with the iron cylinder -it became magnetic by induction, and produced a deflection in the needle -of the galvanometer. On continuing the contact the needle resumed its -natural position, and, when the contact was broken, deflection took -place in the opposite direction; when the magnetic contacts were -reversed, the deflection was reversed also. With strong magnets, so -powerful was the action, that the needle of the galvanometer whirled -round several times successively; and similar effects were produced by -the mere approximation or removal of the helix to the poles of the -magnets. Thus it was proved that magnets produce the very same effects -on the galvanometer that electricity does. Though at that time no -chemical decomposition was effected by these momentary currents which -emanate from the magnets, they agitated the limbs of a frog; and Dr. -Faraday justly observes, that “an agent which is conducted along -metallic wires in the manner described, which, whilst so passing, -possesses the peculiar magnetic actions and force of a current of -electricity, which can agitate and convulse the limbs of a frog, and -which finally can produce a spark by its discharge through charcoal, can -only be electricity.” Soon after he completely established the identity -of the two powers by producing the spark, heating metallic wires, and -accomplishing chemical decomposition. Hence it appears that electrical -currents are evolved by magnets, which produce the same phenomena with -the electrical currents from the Voltaic battery: they, however, differ -materially in this respect—that time is required for the exercise of the -magnetico-electric induction, whereas Volta-electric induction is -instantaneous. - -Thus the effect of induction or the influence of the spiral wire in -increasing the electric and magnetic power is very great indeed, and to -that we are indebted for the electric telegraph, for Voltaic electricity -alone is too feeble to overcome the resistance of a long wire. - -Electric currents, whatever their tension may be, produce the phenomena -of induction; these again induce other currents in bodies capable of -induction, and so on indefinitely; the first and second flow in the same -direction, the others alternately opposite and direct. They all give the -shock and can decompose water, but with Volta-electric currents the -elevation of temperature as well as their physiological and magnetic -effects are produced by instantaneous actions, which only depend upon -the quantity and tension of the current, and by no means on its -duration, for induced currents only exist for a moment when the circuit -of the battery is broken. The most energetic physiological effects are -produced by a small quantity of electricity moving with great velocity. -The apparatus first employed by Dr. Faraday is in effect a battery, -where the agent is the magnetic instead of the Voltaic force, or, in -other words, electricity, and is thus constructed:— - -A very powerful horseshoe magnet, formed of twelve steel plates in close -approximation, is placed in a horizontal position. An armature, -consisting of a bar of the purest soft iron, has each of its ends bent -at right angles, so that the faces of those ends may be brought directly -opposite and close to the poles of the magnet when required. Ten copper -wires—covered with silk, in order to insulate them—are wound round one -half of the bar of soft iron, as a compound helix: ten other wires, also -insulated, are wound round the other half of the bar. The extremities of -the first set of wires are in metallic connexion with a circular disc, -which dips into a cup of mercury, while the ends of the other ten wires -in the opposite direction are soldered to a projecting screw-piece, -which carries a slip of copper with two opposite points. The steel -magnet is stationary; but when the armature, together with its -appendages, is made to rotate vertically, the edge of the disc always -remains immersed in the mercury, while the points of the copper slip -alternately dip in it and rise above it. By the ordinary laws of -induction, the armature becomes a temporary magnet while its bent ends -are opposite the poles of the steel magnet, and ceases to be magnetic -when they are at right angles to them. It imparts its temporary -magnetism to the helices which concentrate it; and, while one set -conveys a current to the disc, the other set conducts the opposite -current to the copper slip. As the edge of the revolving disc is always -immersed in the mercury, one set of wires is constantly maintained in -contact with it, and the circuit is only completed when a point of the -copper slip dips in the mercury also; but the circuit is broken the -moment that point rises above it. Thus, by the rotation of the armature, -the circuit is alternately broken and renewed; and as it is only at -these moments that electric action is manifested, a brilliant spark -takes place every time the copper point leaves the surface of the -mercury. Platinum wire is ignited, shocks smart enough to be -disagreeable are given, and water is decomposed with astonishing -rapidity, by the same means; which proves, beyond a doubt, the identity -of the magnetic and electric agencies, and places Dr. Faraday, whose -experiments established the principle, in the first rank of experimental -philosophers. - -A magneto-electric machine has been recently constructed by Mr. Henley, -of enormous power. It consists of two permanent magnets, from which the -induction is obtained; each of these is formed of thirty horseshoe steel -magnets, two feet and a half long, and from four to five inches broad, -and each is surrounded by a coil of wire six miles long, coated with -silk to insulate the coils. A shock from these wires would be -instantaneous death. This apparatus will ultimately be employed to send -a stream of electricity through long submarine and subterraneous wires; -but a Volta-electric machine has hitherto been used, in which the -electricity is generated by a galvanic battery instead of magnets. - -Induction, or the effect of the spiral wires in augmenting the power of -Voltaic electricity, is admirably illustrated in the Atlantic telegraph. - -Wires that are to convey electricity under ground, or through water, -must be defended from injury and insulated to prevent the lateral escape -of the electricity. For that purpose the cable that is laid at the -bottom of the Atlantic, from near Valentia in Ireland to Trinity Bay in -Newfoundland, is formed of seven fine copper wires which convey the -electricity, bound together by a coating of gutta percha, over which -there are layers of cloth dipped in pitch, and then the whole is covered -by steel wires twisted together in strands and twined round in long -close spirals, forming a cord or cable not more than an inch and a -quarter in diameter, and 2100 miles long. The use of the gutta percha is -to insulate the wires; the other coatings are merely for protection. - -The Voltaic battery which generates the electricity consists of 40 -cells, the plates of which are alternately of zinc and platinized -silver, each about nine inches square, the exciting fluid being dilute -sulphuric acid. Although the force developed by this battery is so great -that a piece of iron three inches long and three eighths of an inch in -diameter placed in contact with the poles may be consumed in a few -minutes, it is absolutely incapable of sending a current of electricity -through wires 2500 miles long, on account of their resistance, without -the aid of Dr. Faraday’s inductive action. It is only the primary agent -for inducing a current of sufficient strength. - -To accomplish that, many thousand yards of fine copper wire coated with -silk are wound round a hollow soft iron cylinder; the whole is then -coated by gutta percha, and the end of the wire is joined to the wires -in the cable so as to form a continuous line from Valentia to -Newfoundland. A second copper wire, shorter but thicker than the -preceding, and also insulated by a coating of silk, is wound round the -cylinder above the gutta percha: when the ends of this thick wire are -brought into contact with the poles of the battery, currents of -electricity flow through it, between pole and pole, and in their passage -temporarily convert the hollow iron cylinder into a powerful -electro-magnet, which by its reaction induces a current of electricity -in the fine wire of sufficient power to cross the Atlantic. The -efficiency of the electric telegraph depends upon the power we possess -of breaking and renewing the current at pleasure, since by that means -distinct and successive signals are made from station to station. In the -Atlantic cable positive and negative electricity are transmitted -alternately; the electricity is sent to America from alternate poles, -and the current returns again through the water, which completes the -circuit. - -The passage of electricity through a cable or telegraphic wire in air is -sensibly instantaneous; that through a cable, whether extended in water -or under ground, requires time on account of lateral induction through -the gutta percha; for the electricity, in passing through the wires, -induces the opposite electricity on the surface of the water or moist -earth in contact with the cable, and in that respect it is precisely -like a Leyden jar, the gutta percha representing the glass. As the power -of induction is proportional to the tension of the electricity, and as -the tension is continually diminished by the resistance of the wires, -the induction is continually diminished and requires a longer time. -Electricity took two seconds to pass through a cable 768 miles long, -laid under ground from London to Manchester, and back again twice; while -in air it was all but instantaneous, because the inductive capacity of -air is very much less than that of water or moist earth. In the -experiment with the cable under ground it took two-thirds of a second to -overcome the resistance of the wires, and then the velocity of the -electricity was 1000 miles in a second, and it was the same whatever the -intensity of the electricity. - -It has already been mentioned that the efficiency of the electric -telegraph depends upon the breaking and renewing the current of -electricity by means of which a succession of waves of electricity are -sent through the conducting wires. Now it has been ascertained that -three electric waves may travel simultaneously through the wires of the -Atlantic telegraph with sufficient intervals between them to record the -indications they are intended to convey; that is, three signals can be -intelligibly and practically transmitted in two seconds. - -The original design, structure, and difficulty of depositing the cable -are only equalled by the talent and perseverance with which it has been -done. The 5th of August, 1858, will be memorable for the accomplishment -of the boldest enterprise that ever was undertaken by man, and which is -only the beginning of a vast submarine communication that will -ultimately encircle the globe. It has been granted to British genius -thus to annihilate time and space, in order to connect all mankind into -one great family for their moral and religious advancement; and, -whatever may be the fate of the British Islands in the course of ages, -to their energetic race the glory will remain of having been the chief -instruments in the hands of Providence for the civilization of the -world—a civilization which will extend with the development of their -numerous colonies into great independent Christian states, like those of -the Union in North America. The thunderbolt snatched from heaven by -Franklin now passes through the depths of the Atlantic as a messenger of -peace between the kindred nations.[16] - -In telegraphs on land the intensity of the battery or magnets is -increased by induction on the same principle. It is by intensity that -the electric current is enabled to pass through the wires, and that is -augmented by increasing the number of coils round the cylinder: however, -it is only advantageous when the distance between the stations is great, -for then the resistance in the additional coils bears a small proportion -to the resistance offered by very long wires, but a very great -proportion to that opposed in very short ones. The nice adjustment for -each case has been determined by the experiments of eminent -electricians, and all the arrangements have been brought to great -perfection in this wonderful triumph of science, which is due to Volta, -who called into existence the fiery stream, and to Faraday, who has -given it the energy of the lightning. - -When the length of the wire in the helices of an electro-magnet is very -great, it offers increasing resistance to the passage of the -electricity, so that the cessation of magnetism is not instantaneous -when the contact with the Voltaic battery is broken. To remedy that -defect an instrument has been invented which instantaneously deprives -the apparatus of the remaining electricity. A great length of fine wire -gives the severest shocks, while a shorter and thicker wire gives the -longest sparks and ignites the greatest quantity of platinum wire. - -Ruhmkorff’s electro-inductive apparatus has either been improved, or new -machines constructed, by Messrs. Grove, Gassiot, and Joule, of intense -energy. Indeed, so great is the energy of electro-induction, that hopes -were entertained of its superseding steam as a motive power. For the -current of electricity from an electro-magnet can be made to flow in -opposite directions, so as to produce alternate attractions and -repulsions, and consequently a continued motion, which might be applied -as a motive force to machinery. However, Mr. Joule has proved that the -power developed by one pound of coal in combustion is to that produced -by one pound of zinc consumed in Mr. Grove’s powerful electro-magnetic -apparatus as nine to one, so that, even if zinc were as cheap as coal, -and a Voltaic battery as easily kept in order as an engine-furnace, -electricity will not supersede steam as a motive power. - -A current of electricity traversing a conductor gives out a quantity of -heat determined by fixed laws, the amount of which is invariable as long -as the machine to which it is applied remains at rest; but the instant -the machine is set in motion a reaction takes place in the intensity of -the current, causing a diminution in the quantity of heat, because the -heat that disappears is converted into the mechanical force exerted by -the engine. - -Mr. Joule’s experiments prove that, whenever a current of electricity is -generated by a magneto-electric machine, the quantity of heat evolved by -that current has a constant relation to the power required to work the -machine; and on the other hand, whenever an engine is worked by a -Voltaic battery, that the power developed is at the expense of the -calorific force of the battery for a given consumption of zinc, the -mechanical effect produced having a fixed relation to the heat lost in -the Voltaic current. The obvious conclusion Mr. Joule draws from these -experiments is, that heat and mechanical power are convertible into one -another, and it becomes evident, therefore, that heat is either the vis -viva or living force of ponderable particles, or a state of attraction -and repulsion capable of generating vis viva (N. 222). - - - - - 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. - - -M. ARAGO discovered a source of magnetism in rotatory motion. If a -circular plate of copper be made to revolve immediately above or below a -magnetic needle or magnet, suspended in such a manner that it may rotate -in a plane parallel to that of the copper plate, the magnet tends to -follow the circumvolution of the plate; or, if the magnet revolves, the -plate tends to follow its motion; so powerful is the effect, that -magnets and plates of many pounds weight have been carried round. This -is quite independent of the motion of the air, since it is the same when -a pane of glass is interposed between the magnet and the copper. When -the magnet and the plate are at rest, not the smallest effect, -attractive, repulsive, or of any kind, can be perceived between them. In -describing this phenomenon, M. Arago states that it takes place not only -with metals, but with all substances, solids, liquids, and even gases, -although the intensity depends upon the kind of substance in motion. -Experiments made by Dr. Faraday explain this singular action. He found -that, if a piece of metal or a metallic wire forming a circuit of any -form be moved from right to left across the lines of force proceeding -from the pole of a bar magnet, these lines of force induce a current of -electricity flowing in one direction; and when the motion of the metal -or wire is reversed, the direction of the current is reversed also: the -rotation of the magnet about its axis has no effect on these results, -and no current is induced when the metal or wire is at rest. A plate of -copper, twelve inches in diameter and one fifth of an inch thick, was -placed between the poles of a powerful horseshoe magnet, consequently -crossing the magnetic lines of force at right angles, and connected at -certain points with a galvanometer by copper wires. When the plate was -at rest no effect was produced; but as soon as the plate was made to -revolve rapidly the galvanometer needle was deflected sometimes as much -as 90°, and by a uniform rotation the deflection was constantly -maintained at 45°. When the motion of the copper plate was reversed, the -needle was deflected in the contrary direction, and thus a permanent -current of electricity was evolved by an ordinary magnet. The intensity -of the electricity collected by the wires, and conveyed by them to the -galvanometer, varied with the position of the plate relatively to the -poles of the magnet. - -The motion of the electricity in the copper plate may be conceived by -considering that, merely by moving a single wire, like the spoke of a -wheel, before a magnetic pole, a current of electricity tends to flow -through it from one end to the other. Hence, if a wheel be constructed -of a great many such spokes, and revolved near the pole of a magnet in -the manner of the copper disc, each radius or spoke will tend to have a -current produced in it as it passes the pole. Now, as the circular plate -is nothing more than an infinite number of radii or spokes in contact, -the currents will flow in the direction of the radii if a channel be -open for their return; and, in a continuous plate, that channel is -afforded by the lateral portions on each side of the particular radius -close to the magnetic pole. This hypothesis is confirmed by observation; -for the currents of positive electricity set from the centre to the -circumference, and the negative from the circumference to the centre, -and _vice versâ_, according to the position of the magnetic poles and -the direction of rotation; so that a collecting wire at the centre of -the copper plate conveys positive electricity to the galvanometer in one -case, and negative in another; that collected by a conducting wire in -contact with the circumference of the plate is always the opposite of -the electricity conveyed from the centre. It is evident that, when the -plate and magnet are both at rest, no effect takes place, since the -electric currents which cause the deflection of the galvanometer are -only induced by motion across the magnetic lines of force. When the -plate is placed edgewise so as to be parallel to these lines of force, -no revolution of it with the most powerful magnet produces the slightest -signs of a current at the galvanometer. The same phenomena may be -produced by electro-magnets. The effects are similar when the magnet -rotates and the plate remains at rest. When the magnet revolves -uniformly about its own axis, electricity of the same kind is collected -at its poles, and the opposite electricity at its equator. - -The phenomena which take place in M. Arago’s experiments may be -explained on this principle. When both the copper plate and the magnet -are revolving, the action of the induced electric current tends -continually to diminish their relative motion, and to bring the moving -bodies into a state of relative rest; so that, if one be made to revolve -by an extraneous force, the other will tend to revolve about it in the -same direction, and with the same velocity. - -When a plate of iron, or of any substance capable of being made either a -temporary or permanent magnet, revolves between the poles of a magnet, -it is found that dissimilar poles on opposite sides of the plate -neutralize each other’s effects, so that no electricity is evolved; -while similar poles on each side of the revolving plate increase the -quantity of electricity, and a single pole end-on is sufficient. But -when copper, and substances not sensible to ordinary magnetic -impressions, revolve, similar poles on opposite sides of the plate -neutralize each other; dissimilar poles on each side exalt the action; -and a single pole at the edge of the revolving plate, or end-on, does -nothing. This forms a test for distinguishing the ordinary magnetic -force from that produced by rotation. If unlike poles, that is, a north -and south pole, produce more effect than one pole, the force will be due -to electric currents; if similar poles produce more effect than one, -then the power is not electric. These investigations show that there are -really very few bodies magnetic in the manner of iron. Dr. Faraday -therefore arranges substances in three classes, with regard to their -relation to magnets:—those affected by the magnet when at rest, like -iron, steel, and nickel, which possess ordinary magnetic properties; -those affected when in motion, in which electric currents are evolved by -the inductive force of the magnet, such as copper; and, lastly, those -which are perfectly indifferent to the magnet, whether at rest or in -motion. - -It has already been observed that three bodies are requisite to form a -galvanic circuit, one of which must be fluid. But, in 1822, Professor -Seebeck, of Berlin, discovered that electric currents may be produced by -the partial application of heat to a circuit formed of two solid -conductors. For example, when a semicircle of bismuth, joined to a -semicircle of antimony, so as to form a ring, is heated at one of the -junctions by a lamp, a current of electricity flows through the circuit -from the antimony to the bismuth; and such thermo-electric currents -produce all the electro-magnetic effects. A compass needle, placed -either within or without the circuit, and at a small distance from it, -is deflected from its natural position, in a direction corresponding to -the way in which the electricity is flowing. If such a ring be suspended -so as to move easily in any direction, it will obey the action of a -magnet brought near it, and may even be made to revolve. According to -the researches of M. Seebeck, the same substance, unequally heated, -exhibits electrical currents; and M. Nobili observed, that in all -metals, except zinc, iron, and antimony, the electricity flows from the -hot part towards that which is cold. That philosopher attributes -terrestrial magnetism to a difference in the action of heat on the -various substances of which the crust of the earth is composed; and, in -confirmation of his views, he has produced electrical currents by the -contact of two pieces of moist clay, of which one was hotter than the -other. - -M. Becquerel constructed a thermo-electric battery of one kind of metal, -by which he has determined the relation between the heat employed and -the intensity of the resulting electricity. He found that, in most -metals, the intensity of the current increases with the heat to a -certain limit, but that this law extends much farther in metals that are -difficult to fuse, and which do not rust. The experiments of Professor -Cumming show that the mutual action of a magnet and a thermo-electric -current is subject to the same laws as those of magnets and galvanic -currents; consequently all the phenomena of repulsion, attraction, and -rotation may be exhibited by a thermo-electric current. M. Botto, of -Turin, has decomposed water and some solutions by thermo-electricity; -and the Cav. Antinori of Florence succeeded in obtaining a brilliant -spark with the aid of an electro-dynamic coil. - -The principle of thermo-electricity has been employed by MM. Nobili and -Melloni for measuring extremely minute quantities of heat in their -experiments on the instantaneous transmission of radiant heat. The -thermo-multiplier, which they constructed for that purpose, consists of -a series of alternate bars, or rather fine wires of bismuth and -antimony, placed side by side, and the extremities alternately soldered -together. When heat is applied to one end of this apparatus, the other -remaining at its natural temperature, currents of electricity flow -through each pair of bars, which are conveyed by wires to a delicate -galvanometer, the needle of which points out the intensity of the -electricity conveyed, and consequently that of the heat employed. This -instrument is so delicate that the comparative warmth of different -insects has been ascertained by means of it. - -The conservation of force is strictly maintained throughout the whole -science and different forms of electricity. In static electricity the -positive and negative forces exactly balance one another; they are -always simultaneous, and related often by curved lines of force; there -is no defect or surplus, and the existence of one kind without the other -is utterly impossible—it is absolutely a dual force. The very same may -be said of electric currents, whether produced by the Voltaic battery or -in any other way—the current in one part of the circuit is absolutely -the same in amount and dual character as the other; and in the insulated -Voltaic battery, where the sustaining power is internal, not the -slightest development of the forces of either of these can occur till -the circuit is completed or induction allowed at the extremities; for if -when there is no circuit the induction be prevented, not merely no -current, but no quantity of electricity at the poles ready to produce a -current, can be evolved in the slightest degree.[17] - - - - - 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. - - -MAGNETISM may be regarded as a new science in consequence of the -profound researches and admirable discoveries of Dr. Faraday. Since the -magnetism of matter is only known by the action of a magnet or of -electricity upon it, by using an extremely energetic magnet or -electro-magnet he has proved that all known substances, whether solid, -liquid, or aëriform, are more or less magnetic, but that the magnetism -is very different in different substances. For example, if a bar of iron -be freely suspended between the poles of a very powerful magnet or -electro-magnet, it will be attracted by both poles, and will set or rest -in the direction of a straight line joining them; but if a similar bar -of bismuth be freely suspended in the same manner, it will rest in a -direction at right angles to that which the iron bar assumed. Thus the -direction in which the iron sets is axial or in the line of force, while -that which the bismuth assumes is equatorial or perpendicular to the -line of force. Substances that are magnetic after the manner of iron are -said to be paramagnetic, those that are magnetic after the manner of -bismuth are diamagnetic. As far as we know, all matter comes under one -or other of these laws. Many bodies are paramagnetic besides iron, as -the loadstone, which consists of the peroxide and protoxide of iron -mixed with small portions of silica and alumina; also some of the gems -and metals, as cobalt, nickel, &c. A substance is often paramagnetic if -it contains only the 130,000th part of its weight of iron; but by far -the greater number are diamagnetic, as all animal and vegetable matter, -acids, oils, sugar, starch, bread, &c., and all the gases except oxygen, -which is highly paramagnetic; and its force increases with its density: -but notwithstanding the predominance of diamagnetic matter at the -surface, the terrestrial globe is paramagnetic—in fact it is a powerful -magnet. - -Besides the substances which are paramagnetic naturally, that property -may be imparted by a variety of methods, as by friction with magnets or -even juxtaposition with them; and a bar of hard steel held at the angle -of the dip will become a magnet on receiving a few strokes with a hammer -on its upper end. - -Polarity is one of the most distinguishing characters of magnetism: it -is the property which a magnet possesses when freely suspended of -resting spontaneously in the magnetic meridian, or nearly north and -south, and always returning to that position when disturbed in -consequence of the mean magnetic attraction of the earth; yet the magnet -has no tendency to move to the north or south even when floating on -water, because the same pole that attracts one end repels the other. -Both poles of a magnet attract iron, which in return attracts either -pole of the magnet with an equal and contrary force. The action of a -magnet on unmagnetised iron is confined to attraction, whereas the -reciprocal agency of magnets is characterised by a repulsive as well as -by an attractive force; for a north pole repels a north pole, and a -south pole repels a south pole; but a north and south pole mutually -attract one another—which proves that paramagnetism is a dual power in -which the conservation of force is perfectly maintained, for the force -of attraction is exactly equal to the force of repulsion. One kind of -polarity cannot exist without the other: they are absolutely -simultaneous, dependent, and of equal intensity. - -Induction is the power which a magnet possesses of exciting temporary or -permanent paramagnetism in such bodies in its vicinity as are capable of -receiving it. By this property the mere approach of a magnet renders -iron and steel paramagnetic, the more powerfully the less the distance, -but the induced force is always exactly equal to the force which -produces it. When the north end of a magnet is brought near to, and in -the line with, an unmagnetised iron bar, the bar acquires all the -properties of a perfect magnet; the end next the north pole of the -magnet becomes a south pole, while the remote end becomes a north pole. -Exactly the reverse takes place when the south end is presented to the -bar, so that each pole of a magnet induces the opposite polarity in the -adjacent end of the bar, and the same polarity in the remote extremity; -consequently the nearest extremity of the bar is attracted, and the -farther repelled; but as the action is greater on the adjacent than on -the distant part, the resulting force is that of attraction. By -induction the iron bar not only acquires polarity, but the power of -inducing paramagnetism in a third body; and although all these -properties vanish from the iron as soon as the magnet is removed, a -lasting increase of intensity is generally imparted to the magnet itself -by the reaction of the temporary paramagnetism of the iron. Iron -acquires the inductive force more rapidly than steel, yet it loses it as -quickly on the removal of the magnet, whereas the steel is impressed -with a lasting polarity. - -A certain time is requisite for induction, and it may be accelerated by -anything that excites a vibratory motion in the particles of the steel; -such as the smart stroke of a hammer, or heat succeeded by sudden cold. -A steel bar may be converted into a magnet by the transmission of an -electric discharge through it; and as its efficacy is the same in -whatever direction the electricity passes, the effect arises from its -mechanical operation exciting a vibration among the particles of the -steel. It has been observed that the particles of iron easily resume -their neutral state after induction, while those of steel resist the -restoration of equilibrium, or a return to the neutral state: it is -therefore evident that any cause which removes or diminishes the -resistance of the particles will tend to destroy the paramagnetism of -the steel; consequently the same mechanical means which develop the -power will also destroy it. On that account a steel bar may lose its -paramagnetism by any mechanical concussion, such as by falling on a hard -substance, a blow with a hammer, and heating to redness, which makes the -steel soft. The circumstances which determine whether it shall gain or -lose are its position with respect to the magnetic equator, and the -higher or lower intensity of its previous magnetic state. - -A comparison of the number of vibrations accomplished by the same -magnetised needle during the same time at different distances from a -magnet gives the law of paramagnetic intensity, which follows the -inverse ratio of the square of the distance—a law that is not affected -by the intervention of any substance whatever between the magnet and the -needle, provided the substance be not itself susceptible of magnetism. -Induction and the reciprocal action of magnets are therefore subject to -the laws of mechanics; but the composition and resolution of the forces -are complicated in consequence of four forces being constantly in -activity, two in each magnet. Mr. Were Fox discovered that the law of -the paramagnetic force changes from the inverse square of the distance -to the simple inverse ratio when the distance between two magnets is as -small as from the fourth to the eighth of an inch, or even as much as -half an inch when the magnets are large; and in the case of repulsion, -that the change takes place at a still greater distance, especially when -the two magnets differ materially in intensity. - -Without assuming any hypothesis of what magnetism is, or how that force -is originated or sustained, Dr. Faraday regards a magnet as a source of -power surrounded by curved lines of force which are not only -representants of the magnetic power in quality and direction, but also -in quantity—an hypothesis which accords perfectly with experiment, and -with the action both of electricity and magnetism. The nature and form -of these lines may be seen by placing a bar magnet upon a table, -spreading a sheet of stiff paper over it so as to be perfectly level and -free from creases, and then sifting very clean iron filings through a -fine sieve equably over it. The filings will instantly assume the form -of the curved lines represented by fig. 1, plate 7, in consequence of -the action of the magnet. These lines are the true representatives of -the magnetic forces, and being related to a polar power, they have -opposite qualities in opposite directions. When a magnet is broken -across the middle, each part is at once converted into a perfect magnet; -the part that originally had a south pole acquires a north pole at the -fractured end; the part that had originally a north pole gets a south -pole; and as far as mechanical division can be carried, it is found that -each fragment is a perfect magnet. Fig. 2, plate 7, shows the lines of -force in a fractured magnet when the ends are not yet separated; fig. 3 -shows them when they are. - -Currents of electricity are produced in conducting bodies moved across -these lines of magnetic force. If a copper wire at a little distance -above the north pole of a bar magnet be moved from left to right, at any -angle across the lines of magnetic force, they will induce a current of -electricity in the wire flowing from right to left; if the wire be moved -with the same velocity in the contrary direction, the induced current -will be of equal intensity, but it will flow from left to right. Similar -results are obtained from the south pole, and the phenomena are the same -when the magnet is moved and the wire is at rest; in both cases the -intensity is greater the swifter the motion. It appears that the -quantity of electricity induced is directly as the amount of the -magnetic curves intersected, and when a wire is moving uniformly in a -field of equal magnetic force, the current of electricity generated is -proportional to the time, and also to the velocity of motion; for when a -metallic disc is made to revolve through the lines of force, the current -induced is strongest near the edge where the velocity is greatest; and -in different substances moving across the lines of force the intensity -of the induced current is directly as the conducting power of the -substance. Thus bodies moved near a magnet have an electrical current -developed in them, and conversely bodies affected by an electric current -are definitely moved by a magnet near them. - -By the preceding experiments it appears that magnetic polarity is -manifested in two ways; in the magnetised needle, by attraction and -repulsion, and in a wire moving across lines of magnetic force it is -shown by the opposite directions in which the induced current flows -according as the body is moved from the right to the left, or left to -right. Hence polarity consists in the opposite and antithetical actions -manifested at the opposite ends or opposite sides of a limited or -unlimited line of force. Antithesis is the true and most general -character of magnetism, whatever may be its mode of action. - -It was by the induction of electric currents in copper wires moving -across the lines of magnetic force that Dr. Faraday proved that the -lines of force issuing from a magnet are closed curves which return -again and pass through the interior of the magnet. He placed two bar -magnets of the same length, size, and intensity with their similar poles -together, so that they might act as one magnet. A copper wire was then -passed between their axes, which after extending through half their -length was bent up equatorially and turned back along the outside, so -that the whole wire formed a loop, the two ends being connected with a -galvanometer. When the whole wire was made to revolve, no effect was -produced, although it crossed the lines of magnetic force; but when it -was cut in two, so as to separate the external from the internal part, -electrical currents of equal intensity, but in contrary directions, were -induced in each portion of the wire as they were made separately to -cross the lines of force, for the apparatus was so constructed that that -could be done. The exterior wire crossed the lines of force which issued -from the magnets at right angles to their axes, while the equatorial -part of the interior wire traversed the returning lines of force. It is -evident that these forces neutralized each other when the whole wire -revolved: consequently the internal and external lines of force must -have been of equal intensity and opposite in direction, so as to balance -one another. By this and a very great number of other experiments Dr. -Faraday has proved that the magnetic lines of force are continuous -closed curves alike in shape, size, and power. They extend indefinitely -beyond the magnet, and undergo no change by distance. - -Thus the magnetic force pervades the interior of the mass; if -electricity does the same, a compensation must either take place, or it -also must move in lines of force, sensible only at the surface. -Electricity has a perpetual tendency to escape, and does escape, when -not prevented by the coercive power of the air, and other non-conducting -substances. Such a tendency does not exist in magnetism, which never -leaves the substance containing it under any circumstances whatever. -There must be some coercive force, analogous to friction, which arrests -the magnetic forces, so as first to oppose their separation, and then to -prevent their reunion. In soft iron the coercive force is either wanting -or extremely feeble, since iron is easily rendered paramagnetic by -induction, and as easily loses that quality; whereas in steel the -coercive force is extremely energetic, because it prevents the steel -from acquiring the paramagnetic properties rapidly, and entirely hinders -it from losing them when acquired. The feebleness of the coercive force -in iron, and its energy in steel, with regard to the paramagnetic force, -is perfectly analogous to the facility of transmission afforded to -electricity by non-electrics, and the resistance it experiences in -electrics. At every step the analogy between electricity and magnetism -becomes more striking. The agency of attraction and repulsion is common -to both; the positive and negative electricities are similar to the -northern and southern polarities, and are governed by the same -laws—namely, that between like powers there is repulsion, and between -unlike powers there is attraction. Each of these four forces is capable -of acting most energetically when alone; but as the electric equilibrium -is restored by the union of the two electric states, and magnetic -neutrality by the combination of the two polarities, they respectively -neutralise each other when joined. All these forces vary inversely as -the square of the distance, and consequently come under the same -mechanical laws. - -A like analogy extends to magnetic and electric induction. Iron and -steel are in a state of equilibrium when neutral; but this equilibrium -is immediately disturbed on the approach of the pole of a magnet, which -by induction transfers one kind of polarity to one end of an iron or -steel bar, and the opposite kind to the other—effects exactly similar to -electrical induction. There is even a correspondence between the -fracture of a magnet and that of an electric conductor; for if an oblong -conductor be electrified by induction, its two extremities will have -opposite electricities; and if in that state it be divided across the -middle, the two portions, when removed to a distance from one another, -will each retain the electricity that has been induced upon it. The -analogy, however, does not extend to transference. A body may transfer a -redundant quantity of positive electricity to another, or deprive -another of its electricity—the one gaining at the expense of the other; -but a body cannot possess only one kind of polarity. With that -exception, there is such perfect correspondence between the theories of -magnetic attractions and repulsions, and electric forces in conducting -bodies, that they not only are the same in principle, but are determined -by the same formulæ. Experiment concurs with theory in proving the -identity of these two influences. Hence, if the electrical phenomena be -due to a modification of the ethereal medium, the magnetic phenomena -must be owing to an analogous cause. - -Curved lines of magnetic force issue from every point of the earth’s -surface where there is sensible dip, and bending round enter the earth -again at the magnetic equator. They induce electric currents in -conducting-wires, moving across them exactly the same as in artificial -magnets; and when a hollow helix, or coil of copper wire, whose -extremities are connected with a galvanometer, is placed in the magnetic -dip, and suddenly moved across the lines of force, the needle of the -galvanometer will vibrate through an arc of 80° or 90°, in consequence -of the electric current induced by these lines of magnetic force in the -wire, and the action is greater when a core of soft iron is placed in -the helix, which becomes a temporary magnet by induction. Again, if a -copper plate be connected with a galvanometer by two copper wires, one -from the centre, and another from the circumference, in order to collect -and convey the electricity, it is found that, when the plate is made to -revolve in a plane passing through the line of the dip, the galvanometer -is not affected. But as soon as the plate is inclined to that plane, -electricity begins to be developed by its motion across the lines of -magnetic force; it becomes more powerful as the inclination increases, -and arrives at a maximum when the plate revolves at right angles to the -line of dip. When the revolution is in the same direction with that of -the hands of a watch, the current of electricity flows from its centre -to the circumference; and when the rotation is in a contrary direction, -the current sets the opposite way. Thus a copper plate, revolving at -right angles to the line of the dip, becomes a new electrical machine, -differing from the common plate-glass machine by the copper being the -most perfect conductor, whereas glass is the most perfect non-conductor; -besides insulation, which is essential to the glass machine, is fatal to -the copper one. The quantity of electricity evolved by the metal does -not appear to be inferior to that devolved by the glass, though very -different in intensity. Even a ship crossing the lines of force must -have electric currents running through her. Dr. Faraday observes that -such is the facility with which electricity is generated by the magnetic -lines of force, that scarcely any piece of metal can be moved without a -development of it; consequently, among the arrangements of steam-engines -and metallic machinery, curious electro-magnetic combinations probably -exist which have never yet been noticed. Thus magnetic lines of force -certainly issue from the surface of the globe. - -No doubt the earth is a magnet on a vast scale, but it differs from all -others in having four poles of maximum magnetic force of different -intensities, the two in the northern hemisphere having a secular motion -in a contrary direction from the two in the southern. They are not even -symmetrically placed; hence the magnetic intensity varies so much in the -different points on the earth’s surface, that the dynamic equator, or -line passing through all the points of least intensity, is a very -irregular curve surrounding the globe, but by no means coinciding with -the terrestrial equator. In consequence of the mean action of these four -forces, the north end of a magnetised needle, arranged so as to revolve -in a vertical plane, dips or inclines beneath the horizon in the -northern hemisphere, and the south end in the southern. The two -hemispheres are separated by a line encircling the earth, called the -magnetic equator, or line of no dip, in which the dipping or inclination -needle is horizontal. On each side of this line the inclination -increases till at last the needle becomes perpendicular to the horizon -in two points, or rather small spaces, in each hemisphere, known as the -magnetic poles, which are quite different from the poles of the earth’s -rotation. The mean action of the four poles of magnetic intensity causes -the mariner’s compass, or a magnetic needle suspended so as to revolve -in a horizontal plane, to remain at rest when pointing to the two -magnetic poles. It is then in the magnetic meridian of the place of -observation, which is thus determined by the mean action of all the four -magnetic forces. - -These mean values of the three magnetic elements, namely, the -declination, inclination or dip, and magnetic intensity, are well known -to be subject to secular, annual, and diurnal variations. The secular -only become sensible after some years, but the annual and diurnal -variations have a double progression—that is to say, two maximum and two -minimum values in their respective periods of a year and twenty-four -hours; for example, the declination needle makes two deviations to the -west and two to the east in the course of twenty-four hours, and that -with great regularity. Now General Sabine discovered that the double -progression arises from two combined or superposed variations having -different hours of maxima and minima, and that they are due to two -distinctly different causes—the one being the difference in the sun’s -position relatively to the place of observation at the different seasons -of the year, and hours of the day and night; the other being a mean -annual and diurnal variation proved by General Sabine to exist in those -great magnetic storms or casual disturbances which affect the magnetic -elements simultaneously over enormously extensive tracts of the globe. - -Moreover the General discovered that, besides these annual and diurnal -variations, the magnetic storms have a variation which accomplishes its -vicissitudes in ten or more nearly eleven years, the increase from year -to year being gradual, till its maximum becomes twice as great as its -minimum value. In consequence of this inequality in the storms or casual -disturbances, each of the magnetic elements has a variation of similar -period and similar maxima and minima. Now the number and magnitude of -the spots on the sun had been observed by M. Schwabe, of Dessau, to -increase to a maximum, and decrease again to a minimum, regularly in the -very same period of between ten and eleven years; and General Sabine -found that this variation in the solar spots, and that in the magnetic -elements, not only have the same periods of maxima and minima, but that -they correspond in all their minutest vicissitudes. Thus a very -remarkable and unexpected connexion exists between terrestrial and solar -magnetism. The dual and antagonist principle is perfectly maintained in -the earth’s magnetism, all the phenomena and their variations being in -opposite directions in the two hemispheres. (N. 226.) - -No doubt the magnetic lines of force in the earth are closed curves, as -in artificial magnets; but in their circuitous courses they may extend -to any distance in space, or rather in the ethereal medium, even to -thousands or tens of thousands of miles; for the ethereal medium is -permeable to lines of magnetic force, or rather transmits them, -otherwise the solar spots could not affect the variations of terrestrial -magnetism; besides, they pass through the Torricellian vacuum, which is -nearly a void with respect to air, but not to the ethereal medium. - -The atmosphere which surrounds the earth to the height of about fifty -miles with sensible density, consists of three and a half parts by -weight of nitrogen gas and one part of oxygen, uniformly mixed. The -nitrogen is neutral whether dense or rare, hot or cold, while the oxygen -is highly paramagnetic; but it loses a great part of its force when -rarefied by heat; consequently the magnetic force of the atmosphere must -increase from the equator to the poles of maximum cold; it must vary -summer and winter, night and day. Its effect upon terrestrial magnetism -is unknown; but it can hardly be without some influence. M. E. Becquerel -observes—“If we reflect that the earth is encompassed by a mass of air -equivalent in weight to a layer of mercury of 30 inches, we may inquire -whether such a mass of magnetic gas, continually agitated, and submitted -to the regular and irregular variations of pressure and temperature, -does not intervene in some of the phenomena dependent upon terrestrial -magnetism. If we calculate, in fact, what is the magnetic force of this -fluid mass, we find that it is equivalent to an immense plate of iron, -of a thickness little more than 1/250 of an inch, which covers the whole -surface of the globe.” Both the conducting power of the air and its -density are increased by cold; and as the sum of the magnetic forces -which issue from the earth on one side of the line of no dip is equal to -their sum on the other side, the intensity and concentration in our -winter are coincident with a diffusion and feebleness in the opposite -hemisphere, so that the line of no dip will move annually from north to -south and back again. The same holds with regard to day and night. Thus -the law of the conservation of force is rigorously maintained; and it is -equally so in the effect of the atmosphere on the magnetic lines of -force, which refracts them as they pass through it, in one direction in -summer, and in the opposite direction in winter—in one direction in the -enlightened hemisphere, in the other in that which is dark. The whole of -the magnetic lines about the earth are held by their mutual tension in -one connected, sensitive system, which feels in every part, even to the -antipodes, a change in any particular place. - -It may be mentioned as a well-known fact, that apparent anomalies have -been found in the diurnal variation of the declination in the high -magnetic latitudes of the northern hemisphere when compared with their -great regularity in other parts of the same hemisphere, and that the -magnetic storms are of much greater magnitude there than in lower -latitudes. Moreover, although Captain Maguire’s observations at Cape -Barrow, in the North Polar Ocean, show that the annual and diurnal -variations of the casual disturbances or magnetic storms, as well as -those of the decennial period, are maintained, yet it appears that at -certain hours of the day the disturbance in the declination may be -easterly at Point Barrow, and westerly at the Magnetic Observatory at -Toronto, in Upper Canada, and _vice versâ_: in fact, the magnetic storms -are simultaneous at these two stations, but in opposite directions—a -circumstance not yet accounted for, and may possibly be due to the -increased magnetism of the air in these cold regions. The heat of the -sun has no effect upon terrestrial magnetism unless possibly by its -indirect action on the oxygen of the atmosphere; but hitherto it has -been imperceptible. It is hardly possible that the aurora can be -independent of the magnetic character of the air, since it occurs in the -high latitudes, where the atmospheric magnetism is most powerful. -Captain Maguire remarked that it frequently appeared at Point Barrow -when the magnetic storms were at a maximum. - -We are totally ignorant of the cause of terrestrial magnetism, though -the powerful influence of the solar spots renders it highly probable -that it will ultimately be found to originate in the sun himself. Mr. -Barlow’s theory of electric currents revolving round the globe is borne -out by Mr. Fox’s observations in the Cornish mines, which show that -electro-magnetism is extremely active in metallic veins; that not only -the nature of the metalliferous deposits must have been determined by -their relative electrical conditions, but that the direction of the -metallic veins must have been influenced by the direction of the -magnetic meridians, and in fact almost all the metallic deposits in the -world tend from east to west, or from north-east to south-west. However, -these currents of electricity may be regarded as magnetic lines of -force, and are more likely to be the effect than the cause of -terrestrial magnetism. They are found to have a powerful inductive -effect on the Atlantic telegraph, disturbing the needles and -galvanometers at each end of the line to a considerable degree, and on -the night of the 6th of September, 1858, a magnetic storm passed over -the cable, which violently agitated the reflecting galvanometer in -connection with the telegraphic wires. - -We are equally ignorant of the cause of the secular magnetic variations, -but we have no reason to believe that the earth is alone magnetic; on -the contrary, the planets are probably magnets, and we know that the sun -and moon are magnetic; hence, as the magnetic, like the gravitating -force, is transmitted through the ethereal medium, the induction of the -sun, moon, and planets, in all their secular and periodic changes, may -cause perpetual variations in terrestrial magnetism, and it may not be -beyond the delicacy of modern observation to ascertain whether a planet, -when nearest to the earth, has any sensible magnetism. - -Diamagnetism is also a dual power, but in complete antithesis to -paramagnetism under the same circumstances. Dr. Faraday first discovered -this property in heavy glass, or silico-borate of lead, a piece of which -was repelled by the pole of a powerful electro-magnet, and an elongated -prism of the same heavy glass, when freely suspended between the poles, -set equatorially. He then found that so great a number of substances -followed the same law, that it established the very remarkable fact of a -hitherto unknown force having acted upon the substances submitted to its -influence, a discovery which he subsequently confirmed by many -experiments, all of which proved the antithesis between the two modes of -magnetic action. He also discovered that magnetic bodies differ -exceedingly in their magnetic power: of paramagnetic bodies iron is the -most powerful; then follow nickel, cobalt, and a long gradation down to -osmium and a vacuum. The body that seems to have the lowest diamagnetic -power is arsenic, and the series ascends to heavy glass, antimony, -phosphorus, and bismuth; so iron and bismuth are the most powerful in -their respective classes, and both have a small conducting power for -electricity. It may be presumed that many remarkable instances of -diamagnetism are to be met with in nature; among others, Dr. Faraday has -suggested the idea that Saturn’s ring, from its position, may be -diamagnetic with regard to the planet. - -With very powerful magnets or electro-magnets, which are absolutely -necessary for all these experiments, it is found that no _simple_ -substance is neutral, but that such may be compounded by mixing in due -proportion a diamagnetic and paramagnetic liquid, as water and -protosulphate of iron. - -Professor Tyndall proved diamagnetic polarity by placing two bismuth -bars within two vertical coils or spirals of insulated copper wire, -through which electric currents were transmitted from a galvanic -battery, and caused to act upon a steel magnet freely suspended without -the spirals. Now, when the excited magnetism is merely by induction, the -electric current, being momentary, only causes a shock or momentary -deviation in the magnet, which returns to its original position when the -current ceases. When, on the contrary, the magnetism is permanent, the -suspended magnet does not return to its original position when the -current ceases. In Professor Tyndall’s experiment the deviation was -permanent, and it was equally so when a bismuth bar was freely suspended -and the cores within the spirals were steel magnets. Had the effect been -from currents induced in the mass of the bar of bismuth, division of the -bar would have stopped them, but the result was the same with powdered -bismuth as with the solid mass. Moreover, since the strength of induced -currents depends upon the conducting power of the substance, and as the -conducting power of copper is forty times as great as that of bismuth, -had the polarity been induced and not real, the effect ought to have -been forty times greater when copper instead of bismuth cores were put -in the spirals, whereas it was scarcely sensible. Besides these proofs, -Dr. Tyndall made experiments with eleven different diamagnetic -substances, of which water was one, with similar results. He then -determined the polarity of twelve paramagnetic bodies by the same -method, whence it appeared that the same action which produced a north -pole in the paramagnetic bodies produced a south pole in those that were -diamagnetic, and _vice versâ_, whence he concludes that diamagnetic -polarity is one of the most firmly established truths of science. It -follows from this that, when a man is standing, his head is a north pole -and his feet a south, and the top of an iron railing on which he may be -leaning is a south pole and the lower end a north. Diamagnetic bodies -thus possess a polarity, the same in kind but opposite in direction to -that possessed by paramagnetic ones.[18] They are both dual powers, and -the two diamagnetic forces like the two paramagnetic being coexistent, -simultaneous, and mutually dependent, there can be no doubt that the -diamagnetic forces also are represented, or rather consist of curved and -closed lines of force passing through the interior of the substance. Dr. -Tyndall has proved that the attraction of iron, and the repulsion of -bismuth, are as the square of the electro-magnetic current producing -them, and that diamagnetic substances are capable of induction. - -The molecular structure of substances freely suspended between the poles -of a magnet has a decided effect upon the position they assume. - -It has already been mentioned that the optic axis is a symmetrical line -in a doubly refracting crystal in which there is no double refraction, -and that in some crystals there are two such symmetrical lines. Now, -Professor Plücker of Bonn discovered, when such crystals are submitted -to powerful magnetic influence, that the single optic axis in the one, -and the resultant or mean line between the double optic axes in the -other, set diametrically or at right angles to the line of magnetic -force; and so powerful did the Professor find the action of magnetism on -crystalline form, that the mineral cyanite, when suspended, arranges -itself so definitely with regard to terrestrial magnetism, that it might -be used as a compass needle. - -Dr. Faraday afterwards observed that amorphous substances, cut in the -form of a sphere, have no tendency to set or be attracted or repelled in -one direction in preference to any other; but if the sphere be formed of -a crystallized substance, it is a general fact that, whether it be -paramagnetic or diamagnetic, it is more powerfully attracted or repelled -in one direction than in any other—a property named by Dr. Faraday -magnecrystallic action. For example, a sphere of calcareous spar, which -is a diamagnetic crystal, is most strongly repelled in the direction of -its principal optic axis, and least strongly in the direction of its -least axis. In a sphere of carbonate of iron, which has exactly the same -crystalline form and is highly paramagnetic, the line which in carbonate -of lime sets equatorially, in this case sets axially, and more strongly -in that direction than in any other. The law according to which the -attraction of the carbonate of iron increases from the least to its -greatest or principal optic axis, is precisely the same as that -according to which the repulsion of the calcareous spar increases from -the least to the principal optic axis. These relations are not altered -by the immersion of the spheres in liquids of either magnetism. Dr. -Faraday observed that a line at right angles to the planes of principal -cleavage in crystals takes the axial position, and on that account he -called it the magnecrystallic axis. Its position was proved by MM. -Tyndall and Knoblauch to depend upon the general fact, that the mass is -most strongly repelled in the direction of the planes of principal -cleavage, and that the elective position of crystals depends more upon -the direction of these planes with respect to the electric force, than -upon the optic axis. The planes of principal cleavage set themselves -equatorially in diamagnetic, and axially in paramagnetic substances: it -was thence inferred that the phenomena offered by crystals in the -magnetic field is a particular case of the general law, that the -superior action of magnets upon matter in a particular direction is due -to the particles of the body being closer together in that direction -than in any other: in short, the line of maximum density; the force -exerted being attractive or repulsive according as the particles are -paramagnetic or diamagnetic. - -It appears, however, that the set of crystals with regard to the line of -magnetic force does not depend solely upon their density in particular -directions. Professor Matteucci, of Pisa, has proved that the -diamagnetic force is inversely as the conducting power of substances for -electricity, that the conducting power is a maximum in the planes of -principal cleavage, and that a needle of crystallized bismuth, in which -the planes of cleavage are parallel to its length, places itself -equatorially with more force when these planes are vertical, or at right -angles to the force, than when they are horizontal or parallel to it. -Experiments had hitherto been made only with diamagnetic or slightly -paramagnetic bodies, which induced M. le Roux to try the effect of -magnetism on pulverized iron compressed by the hydraulic press, which -reduced the grains of iron to lamellæ equivalent to planes of cleavage. -Cubes of this substance, suspended by a thread over a horseshoe magnet, -oscillated for a longer time when the lamellæ were perpendicular than -when they were horizontal; that is, the force was stronger when the -lamellæ were equatorial than when they were axial, exactly the same -result as in Professor Matteucci’s experiment with the needle of -bismuth. Thus the vertical position of the cleavages, which increases -the diamagnetism of the bismuth, increases also the paramagnetism of the -iron. M. le Roux observes that these results are independent of the -influence of the currents of electricity induced in the oscillating -body, for the fundamental character of the phenomena of Arago’s -discovery of rotation by induction is, that the oscillations diminish -rapidly in extent without any sensible diminution in their duration, -while in his experiments the time of the oscillations varied. He -concludes that the arrangement of the molecules must be intimately -connected with paramagnetism or diamagnetism itself, since the effect of -that arrangement is equally sensible in bismuth and iron, although the -diamagnetism of the former is 25,000 times weaker than the paramagnetism -of the latter. - -The diamagnetism of conducting substances and metals, such as gold, -silver, and copper, is augmented by division. Compression has also a -great effect on magnetic action. For example, a bar of soft iron sets -with its longest dimensions from pole to pole of a magnet, but a bar of -compressed carbonate of iron-dust, whose shortest dimensions coincide -with the line of pressure, sets equatorially. A bar of bismuth whose -plane of principal cleavage is parallel to its length sets equatorially, -but a bar of compressed bismuth dust, whose shortest dimensions coincide -with the line of pressure, or a bar of bismuth whose principal planes of -cleavage are transverse to its length, sets with its length axially. The -antithesis is perfect whether the bars are under the influence of a -magnet or electro-magnet. For since the diamagnetic force is inversely -as the conducting power of a body for electricity, and that the latter -is a maximum in the direction of the planes of principal cleavage, -therefore when these planes are parallel to the axis of the bismuth bar -it sets equatorially; but as the conducting power is augmented when the -bismuth dust is compressed in the direction of the force, the -diamagnetic power is diminished, and the bar sets axially. Again, since -the paramagnetic force augments with the conducting power, the action of -the magnet on the iron is antithetic to that on the bismuth. - -The action of an electro-magnet on copper is strongly contrasted with -that which it exerts on iron or bismuth. For when a copper bar suspended -by a thread revolves before its pole, it is brought to a dead halt as -soon as the electric current acts upon it, and maintains its position -with considerable tenacity, for it does not return when pushed out of -it, but keeps its new place with stiffness; however, as soon as the -electric current ceases, there is a strong revulsion, the bar revolving -the contrary way. Even when swinging with considerable force it may be -caught and retained in any position at pleasure, but there is no -revulsion when it is arrested either in the axial or equatorial -position; at any angle between these two, but especially midway, the -electricity will make it move towards the axis, but it is arrested -before it comes to it. The action depends much on the form and -dimensions of the bar and the magnetic pole, which ought to be flat. The -phenomena are due to the high electro-conducting power of the copper, -and are met with in some of the other pure metals, though in a far -inferior degree. - -Great magnetic power is requisite for all these experiments. Dr. Faraday -employed a magnet that could sustain a weight of 450 lbs. at each pole, -and the poles were either pointed or flat surfaces at pleasure, as the -kind of experiment required. - -Heat strongly affects the magnetic properties of bodies. Dr. Faraday -found that, when the temperature of nickel is increased, its magnetic -force diminishes; when that of iron is increased its magnetic force -remains the same, while that of cobalt increases; which seems to -indicate that there is a temperature at which the magnetic force is a -maximum, above and below which it diminishes. Nickel loses its magnetism -at the temperature of boiling oil, iron at a red heat, and cobalt near -the temperature at which copper melts. Calcareous spar retains its -magnetic character at a very high temperature; but the same substance -when it contains iron, and also oxide of iron, loses it entirely at a -dull red heat. A crystal of the ferrocarbonate of lime was absolutely -reversed by change of temperature, for at a low heat the optic axis -pointed axially, and at a high temperature equatorially. With the -exception of these substances, magnecrystals, whether paramagnetic or -diamagnetic, are generally all affected alike by heat. The difference -between the forces in any two different directions, as for instance the -greatest and least principal axes, diminishes as the temperature is -raised, increases as the temperature is lowered, and is constant for a -given temperature. No _unmixed_ or _pure_ substance has as yet passed by -heat from the paramagnetic to the diamagnetic state. No _simple_ -magnecrystal has shown any inversion of this kind, nor have any of the -chief axes of power changed their characters or relations to one -another. - -It appears that, as the molecules of crystals and compressed bodies -affect magnetism, so magnetism acts upon the molecules of matter, for -torsion diminishes the magnetic force, and the elasticity of iron and -steel is altered by magnetism. M. Matteucci has found that the -mechanical compression of glass alters the rotatory power of a polarized -ray of light transmitted through it, and that a change takes place in -the temper of glass under the influence of powerful magnetism. - -Even from the limited view of the powers of nature which precedes, it is -evident that the progress of science based upon experiment tends to show -that the various forces of light, heat, motion, chemical affinity, -electricity, and magnetism will ultimately be traced to one common -origin; that they are so directly related, and mutually dependent, that -they are convertible, motion producing heat, and heat motion; chemical -affinity producing electricity, and electricity chemical action, &c., -each mediately or immediately producing the other. These forces are -transmitted through substances; they act upon matter, causing changes in -the molecular structure of bodies either momentary or permanent, and -reciprocally the changes indicate the action of these forces. Matter and -force are only known to us as manifestations of Almighty power: we are -assured that we can neither create nor destroy them—that their amount is -the same now as in the beginning. In chemical attraction the powers with -which a molecule of matter is endowed, and which give rise to various -qualities, never change; even when passing through a thousand -combinations, the molecule and its power are ever the same. - -Machinery does not create force; it only enables us to turn the forces -of nature to the best advantage; it is by the force of wind or falling -water that our corn is ground, and the steam engine owes its power to -the force of heat and chemical action. As force cannot be created, -neither can it be annihilated. It may be dispersed in various -directions, and subdivided so as to become evanescent to our -perceptions; it may be balanced so as to be in abeyance, or become -potential as in static electricity; but the instant the impediment is -removed the force is manifested by motion; it may also be turned into -heat by friction, but it is never lost. Every motion we make, every -breath, every word we utter, is a force that produces pulsations which -are communicated to continually increasing particles of air, and -conveyed through countless channels so as to become indeed imperceptible -to our senses, yet they are demonstrated to exist as witnesses of the -words we have spoken or the actions we have performed, by analysis, that -all-powerful instrument of human reason.[19] - -A body acquires heat in the exact proportion that the adjacent -substances become cold, and when heat is absorbed by a body it becomes -an expansive force at the expense of those around that contract, but it -is not lost. In chemical action at a distance the principle of the -conservation of force is maintained, for a chemical action may be -produced miles away from an electro-magnet, perfectly equivalent to the -dominant chemical action in the battery. The two electricities are -developed in equal proportions, which may be combined so as to produce -many changes in their respective relations, yet the sum of the force of -one kind can never be made in the smallest degree either to exceed or to -come short of the sum of the other. Experimental research proves that -the conservation of force is an unalterable law of nature—“a principle -in physics as large and sure as that of the indestructibility of matter -or the invariability of gravity. No hypothesis should be admitted, nor -any assertion of a fact credited, that denies this principle. No view -should be inconsistent or incompatible with it. Many of our hypotheses -in the present state of science may not comprehend it, and may be unable -to suggest its consequences, but none should oppose or contradict it.” - -Having thus expressed his conviction of the truth of this great -principle, Dr. Faraday considers the case of gravity, and concludes that -“the definition of gravity as an attractive force between the particles -of matter varying inversely as the square of the distance, while it -stands as a full definition of the power, is inconsistent with the -principle of the conservation of force.” For while in this definition -the principle is maintained of the constancy of the force _at the same -distance_, it implies a creation of force to an enormous amount when the -distance is diminished, and an equal amount annihilated when the -distance is increased,—“an effect,” he says, “which is equal in its -infinity and its consequences with creation, and only within the power -of Him who creates.” He continues, “It will not be imagined for a moment -that I am opposed to what may be called the _law of gravitating action_, -that is, the law by which all the known effects of gravity are governed; -what I am considering is the _definition_ of the _force_ of gravitation. -That the result of _one_ exercise of a power may be inversely as the -square of the distance, I believe and admit; and I know that it is so in -the case of gravity, and has been verified to an extent that could -hardly have been within the conception of Newton himself when he gave -utterance to the law; but that the _totality_ of a force can be employed -according to that law I do not believe either in relation to -gravitation, or electricity, or magnetism, or any other supposed form of -power. That there should be a power of gravitation existing by itself, -having no relation to the other natural powers, and no respect to the -law of the conservation of force, is as little likely as that there -should be a principle of levity as well as gravity. Gravity may be only -the residual part of the other forces of nature, as Mossotti has tried -to show; but that it should fall out from the law of all other forces, -and should be outside the reach either of farther experiment or -philosophical conclusions, is not probable. So we must strive to learn -more of this outstanding power, and endeavour to avoid any definition of -it which is incompatible with the principles of force generally, for all -the phenomena of nature lead us to believe that the great and governing -law is one. Thus gravitation can only be considered as part of a more -general force whose law has yet to be discovered.” - -The definition of the gravitating force immediately suggests the -question of how it is transmitted; the full force of that question was -felt by Newton himself when, in his third letter to Bentley, he wrote, -“That gravity should be innate, inherent, and essential to matter, so -that one body may act upon another at a distance, through a _vacuum_, -without the mediation of anything else by and through which their action -and force may be conveyed from one to another, is to me so great an -absurdity that I believe no man who has in philosophic matters a -competent faculty of thinking can ever fall into it. Gravity must be -caused by an agent, acting constantly according to certain laws; but -whether this agent be material or immaterial I have left to the -consideration of my readers.” - -Since Newton’s time the continual decrease in the periodic times of the -comets belonging to our system, and the undulatory theory of light and -heat, have proved the existence of an extremely rare elastic medium -filling space even to the most distant regions of which we are -cognizant. But, rare as it may be, it has inertia enough to resist the -motion of comets, and therefore must be material, whether considered to -be ether or, according to Mr. Grove, the highly attenuated atmospheres -of the celestial bodies. Professor William Thomson of Glasgow has -computed that in the space traversed by the earth in its annual -revolution, a cube whose side is 1000 miles would contain not less than -a pound weight of the ethereal medium, and that the earth, in moving -through it, would not displace the ·250th part of that pound of matter. -Yet that is enormously more dense than the continuation of the earth’s -atmosphere would be in interplanetary space, if rarefied according to -Bayle’s law. But whatever be the density or nature of the ether, there -is every reason to believe that it is the medium which transmits the -gravitating force from one celestial object to another, or possibly it -may possess a higher attribute with regard to gravity than its mere -transmission. - -Dr. Faraday, who discovered the magnetism of the atmosphere, is led to -believe that the ethereal medium too is magnetic by the following -experiment. Three solutions of the protosulphate of iron, _l_, _m_, _n_, -the first of which contained 4 grains of the salt dissolved in a cubic -inch of water, the second 8 grains, and the third 16 grains—these were -respectively enclosed in three glass globules, all of which were -attracted by the pole of a magnet. A quantity of the mean solution _m_ -was then put into a vessel, and the globule containing the strongest -solution _n_ was immersed in it, which was attracted as before, but the -globule _l_, containing the weakest solution, was repelled when plunged -into the same liquid. Here there was a diamagnetic phenomenon, although -the glass globules and the liquid in which they were immersed contained -iron. The effect was evidently differential, for when the liquid was -less attracted than the globule, the globule approached the pole, and -when the liquid was more attracted than the globule, the latter appeared -to recede from the pole. In fact, the effect is the same as that of -gravity on a body immersed in water; if it be more forcibly attracted -than the water, it sinks; if less forcibly attracted, it rises, the -effect being the same as if it were repelled by the earth. Hence the -question, are all magnetic phenomena the result of a differential action -of this kind, and is the ethereal medium less strongly attracted than -soft iron, and more strongly attracted than bismuth, thus permitting the -approach of the iron, but causing the bismuth to recede from the pole of -a magnet? If such a medium exist, that is, if the ethereal medium be -magnetic, then diamagnetism is the same with paramagnetism, and the -polarity of the magnetic force in iron and bismuth is one and the same. - -The ethereal medium may be presumed to transmit the gravitating force; -it transmits the magnetism of the solar spots, its undulations -constitute light, heat, and all the influences bound up in the solar -beam; and the most perfect vacuum we can make is capable of transmitting -mechanical energy in enormous quantities, some of which differ but -little from that of air or oxygen at an ordinary barometric pressure; -and why not thus admit, says Mr. Thomson, the magnetic property, of -which we know so little that we have no right to pronounce a negative? - -Mr. Waterstone is also of opinion that it would be taking too narrow a -view if we limited the function of the luminiferous ether to the -conveying of physical pulses only. The atmosphere also conveys physical -pulses, but that is the least important of its functions in the economy -of nature. There is nothing that should hinder us attributing to the -media concerned in the radiation of light and heat the higher functions -of electrical polarity and gravitation. The special dynamic arrangements -by which this is effected may ever elude our research; but as there is -no limit to the vis viva (N. 222) which such media may conserve in their -minutest parts, so there is no physical impossibility in that vis viva -being suddenly transferred to the molecules of ordinary matter in the -proportion and sequence required to carry out the order and system of -nature. - -The fundamental principle of action in such media must be in accordance -with _elastic impact_, for upon that the dynamic theory of heat and -conservation of force rests as a foundation. The statical and dynamical -characteristics of gravitation and transfusion of force conform to it, -so that all the forces that hold the molecules of bodies together must -also be in subjection to it.[20] - - - - - 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. - - -IN considering the constitution of the earth, and the fluids which -surround it, various subjects have presented themselves to our notice, -of which some, for aught we know, are confined to the planet we inhabit; -some are common to it and to the other bodies of our system. But an -all-pervading ether must fill the whole visible creation, since it -conveys, in the form of light, tremors which may have been excited in -the deepest recesses of the universe thousands of years before we were -called into being. The existence of such a medium, though at first -hypothetical, is proved by the undulatory theory of light, and rendered -certain by the motion of comets, and by its action upon the vapours of -which they are chiefly composed. It has often been imagined that the -tails of comets have infused new substances into our atmosphere. -Possibly the earth may attract some of that nebulous matter, since the -vapours raised by the sun’s heat, when the comets are in perihelio, and -which form their tails, are scattered through space in their passage to -their aphelion; but it has hitherto produced no effect, nor have the -seasons ever been influenced by these bodies. The light of the comet of -the year 1811, which was so brilliant, did not impart any heat even when -condensed on the bulb of a thermometer of a structure so delicate that -it would have made the hundredth part of a degree evident. In all -probability, the tails of comets may have passed over the earth without -its inhabitants being conscious of their presence; and there is reason -to believe that the tail of the great comet of 1843 did so. M. Valz -observed that the light of a brilliant comet was eclipsed as it passed -over a star of the 7th magnitude, whence M. Babinet computed that the -light of the comet must have been sixty times less than that of the -star, and that matter so attenuated could not penetrate the earth’s -atmosphere, but the constitution of these bodies is still a matter of -conjecture. - -The passage of comets has never sensibly disturbed the stability of the -solar system; their nucleus, being in general only a mass of vapour, is -so rare, and their transit so rapid, even when they had a solid part, -that the time has not been long enough to admit of a sufficient -accumulation of impetus to produce a perceptible action. Indeed, M. -Dusejour has shown that, under the most favourable circumstances, a -comet cannot remain longer than two hours and a half at a less distance -from the earth than 10,500 leagues. The comet of 1770 passed within -about six times the distance of the moon from the earth, without even -affecting our tides. According to La Place, the action of the earth on -the comet of 1770 augmented the period of its revolution by more than -two days; and, if comets had any perceptible disturbing energy, the -reaction of the comet ought to have increased the length of our year. -Had the mass of that comet been equal to the mass of the earth, its -disturbing action would have increased the length of the sidereal year -by 2^h 53^m; but, as Delambre’s computations from the Greenwich -observations of the sun show that the length of the year has not been -increased by the fraction of a second, its mass could not have been -equal to the 1/5000th part of that of the earth. This accounts for the -same comet having twice swept through the system of Jupiter’s satellites -without deranging the motion of these moons. M. Dusejour has computed -that a comet, equal in mass to the earth, passing at the distance of -12,150 leagues from our planet, would increase the length of the year to -367^d 16^h 5^m, and the obliquity of the ecliptic as much as 2°. So -the principal action of comets would be to alter the calendar, even if -they were dense enough to affect the earth. - -Comets traverse all parts of the heavens; their paths have every -possible inclination to the plane of the ecliptic, and, unlike the -planets, the motion of more than half of those that have appeared has -been retrograde, that is, from east to west. They are only visible when -near their perihelia; then their velocity is such, that its square is -twice as great as that of a body moving in a circle at the same -distance: they consequently remain but a very short time within the -planetary orbits. And, as all the conic sections of the same focal -distance sensibly coincide, through a small arc, on each side of the -extremity of their axis, it is difficult to ascertain in which of these -curves the comets move, from observations made, as they necessarily must -be, near their perihelia (N. 227). Probably they all move in extremely -excentric ellipses; although, in most cases, the parabolic curve -coincides most nearly with their observed motions. Some few seem to -describe hyperbolas; such, being once visible to us, would vanish for -ever, to wander through boundless space, to the remote systems of the -universe. If a planet be supposed to revolve in a circular orbit, whose -radius is equal to the perihelion distance of a comet moving in a -parabola, the areas described by these two bodies in the same time will -be as unity to the square root of two, which forms such a connexion -between the motion of comets and planets, that, by Kepler’s law, the -ratio of the areas described during the same time by the comet and the -earth may be found; so that the place of a comet may be computed at any -time in its parabolic orbit, estimated from the instant of its passage -at the perihelion. It is a problem of very great difficulty to determine -all the other elements of parabolic motion—namely, the comet’s -perihelion distance, or shortest distance from the sun, estimated in -parts of the mean distance of the earth from the sun; the longitude of -the perihelion; the inclination of the orbit on the plane of the -ecliptic; and the longitude of the ascending node. Three observed -longitudes and latitudes of a comet are sufficient for computing the -approximate values of these quantities; but an accurate estimation of -them can only be obtained by successive corrections, from a number of -observations, distant from one another. When the motion of a comet is -retrograde, the place of the ascending node is exactly opposite to what -it is when the motion is direct. Hence the place of the ascending node, -together with the direction of the comet’s motion, show whether the -inclination of the orbit is on the north or south side of the plane of -the ecliptic. If the motion be direct, the inclination is on the north -side; if retrograde, it is on the south side. - -The identity of the elements is the only proof of the return of a comet -to our system. Should the elements of a new comet be the same, or nearly -the same, with those of any one previously known, the probability of the -identity of the two bodies is very great, since the similarity extends -to no less than four elements, every one of which is capable of an -infinity of variations. But, even if the orbit be determined with all -the accuracy the case admits of, it may be difficult, or even -impossible, to recognize a comet on its return, because its orbit would -be very much changed if it passed near any of the large planets of this -or of any other system, in consequence of their disturbing energy, which -would be very great on bodies of so rare a nature. - -By far the most curious and interesting instance of the disturbing -action of the great bodies of our system is found in the comet of 1770. -The elements of its orbit, determined by Messier, did not agree with -those of any comet that had hitherto been computed, yet Lexel -ascertained that it described an ellipse about the sun, whose major axis -was only equal to three times the length of the diameter of the -terrestrial orbit, and consequently that it must return to the sun at -intervals of five years and a half. This result was confirmed by -numerous observations, as the comet was visible through an arc of 170°; -yet this comet had never been observed before the year 1770, nor has it -ever again been seen till 1843, though very brilliant. The disturbing -action of the larger planets affords a solution of this anomaly, as -Lexel ascertained that in 1767 the comet must have passed Jupiter at a -distance less than the fifty-eighth part of its distance from the sun, -and that in 1779 it would be 500 times nearer Jupiter than the sun; -consequently the action of the sun on the comet would not be the -fiftieth part of what it would experience from Jupiter, so that Jupiter -became the primum mobile. Assuming the orbit to be such as Lexel had -determined in 1770, La Place found that the action of Jupiter, previous -to the year 1770, had so completely changed the form of it, that the -comet which had been invisible to us before 1770 was then brought into -view, and that the action of the same planet, producing a contrary -effect, has subsequently to that year removed it from our sight, since -it was computed to be revolving in an orbit whose perihelion was beyond -the orbit of Ceres. However, the action of Jupiter during the summer of -1840 must have been so great, from his proximity to that singular body, -that he seems to have brought it back to its former path as he had done -in 1767, for the elements of the orbit of a comet which was discovered -in November 1843, by M. Faye, agree so nearly with those of the orbit of -Lexel’s comet that the two bodies were supposed to be identical; by the -subsequent computation of M. le Verrier, it appears, however, that they -are not the same, that they were both brought to our system by Jupiter’s -attraction, and that they have been in it more than a century, and have -frequently come near the earth without having been seen. From the -smallness of the excentricity of Lexel’s comet, the orbit resembles -those of the planets, but this comet is liable to greater perturbations -than any other body in the system, because it comes very near the orbit -of Mars when in perihelion, and very near that of Jupiter when in -aphelion; besides, it passes within a comparatively small distance of -the orbits of the minor planets; and as it will continue to cross the -orbit of Jupiter at each revolution till the two bodies meet, its -periodic time, now about seven years, will again be changed, but in the -mean time it ought to have returned to its perihelion in the year 1851. -This comet might have been seen from the earth in 1776, had its light -not been eclipsed by that of the sun. There is still so much doubt with -regard to Lexel’s comet that during the present year, 1858, M. le -Verrier has constructed a table of all the orbits in which the comet may -have moved after leaving Jupiter in 1770, which will enable astronomers -to recognise the comet even should the elements of its orbit be much -altered. He thinks it possible that its path may have become hyperbolic, -but that it is more likely an augmentation of its periodic time may have -taken place. It is quite possible that comets frequenting our system may -be turned away, or others brought to the sun, by the attraction of -planets revolving beyond the orbit of Neptune, or by bodies still -farther removed from the solar influence. - -Other comets, liable to less disturbance, return to the sun at stated -intervals. Halley computed the elements of the orbit of a comet that -appeared in the year 1682, which agreed so nearly with those of the -comets of 1607 and 1531, that he concluded it to be the same body -returning to the sun at intervals of about seventy-five years. He -consequently predicted its reappearance in the year 1758, or in the -beginning of 1759. Science was not sufficiently advanced in the time of -Halley to enable him to determine the perturbations this comet might -experience; but Clairaut computed that, in consequence of the attraction -of Jupiter and Saturn, its periodic time would be so much shorter than -during its revolution between 1607 and 1682, that it would pass its -perihelion on the 18th of April, 1759. The comet did arrive at that -point of its orbit on the 12th of March, which was thirty-seven days -before the time assigned. Clairaut subsequently reduced the error to -twenty-three days; and La Place has since shown that it would only have -been thirteen days if the mass of Saturn had been as well known as it is -now. It appears, from this, that the path of the comet was not quite -known at that period; and, although many observations were then made, -they were far from attaining the accuracy of those of the present day. -Besides, since the year 1759, the orbit of the comet has been altered by -the attraction of Jupiter in one direction, and that of Saturn, Uranus, -and Neptune in the other; yet, notwithstanding these sources of -uncertainty, and our ignorance of all the possible causes of derangement -from unknown bodies on the confines of our system, or in the regions -beyond it, the comet appeared exactly at the time, and not far from the -place assigned to it by astronomers; and its actual arrival at its -perihelion a little before noon on the 16th of November, 1835, only -differed from the computed time by a very few days, which was probably -owing to the attraction of Neptune. - -The fulfilment of this astronomical prediction is truly wonderful, if it -be considered that the comet is seen only for a few weeks during its -passage through our system, and that it wanders from the sun for -seventy-five years to twice the distance of Uranus. This enormous orbit -is four times longer than it is broad; its length is about 3420 millions -of miles, or about thirty-six times the mean distance of the earth from -the sun. At its perihelion the comet comes within nearly fifty-seven -millions of miles of the sun, and at its aphelion it is sixty times more -distant. On account of this extensive range it must experience 3600 -times more light and heat when nearest to the sun than in the most -remote point of its orbit. In the one position the sun will seem to be -four times larger than he appears to us, and at the other he will not be -apparently larger than a star (N. 228.) - -On the first appearance of Halley’s comet, early in August 1835, it -seemed to be merely a globular mass of dim vapour, without a tail. A -concentration of light, a little on one side of the centre, increased as -the comet approached the sun and earth, and latterly looked so like the -disc of a small planet, that it might have been mistaken for a solid -nucleus. M. Struve, however, saw a central occultation of a star of the -ninth magnitude by the comet, at Dorpat, on the 29th of September. The -star remained constantly visible, without any considerable diminution of -light; and, instead of being eclipsed, the nucleus of the comet -disappeared at the moment of conjunction from the brilliancy of the -star. The tail increased as the comet approached its perihelion, and -shortly before it was lost in the sun’s rays it was between thirty and -forty degrees in length. - -According to the observations of M. Valz, the nebulosity increased in -magnitude as it approached the sun; but no other comet on record has -exhibited such sudden and unaccountable changes of aspect. It was -invisible for two months when near its perihelion passage, and when it -reappeared on the 24th of January, 1836, its aspect was completely -changed; it had no tail, and to the naked eye was like a hazy star; but -with a powerful telescope it presented a small, round, planetary-looking -nucleus 2ʺ in diameter, surrounded by an extensive coma, and in the -centre it had a small, bright, solid part. The nucleus, clear and well -defined, like the disc of a planet, was observed on one occasion to -become obscure and enlarged in the course of a few hours. But by far the -most remarkable circumstance was the sudden appearance of certain -luminous brushes or sectors, diverging from the centre of the nucleus -through the nebulosity. M. Struve describes the nucleus of the comet, in -the beginning of October, as elliptical, and like a burning coal, out of -which there issued, in a direction nearly opposite to the tail, a -divergent flame, varying in intensity, form, and direction, appearing -occasionally even double, and suggesting the idea of luminous gas -bursting from the nucleus. On one occasion M. Arago saw three of these -divergent flames on the side opposite the tail, rising through the -nebulosity, which they greatly exceeded in brilliancy: after the comet -had passed its perihelion, it acquired another of these luminous fans, -which was observed by Sir John Herschel at the Cape of Good Hope. -Hevelius describes an appearance precisely similar, which he had -witnessed in this comet at its approach to the sun in the year 1682, and -something of the kind seems to have been noticed in the comet of 1744. -Possibly the second tail of the comet of 1724, which was directed -towards the sun, may have been of this nature. - -The influence of the ethereal medium on the motions of Halley’s comet -will be known after another revolution, and future astronomers will -learn, by the accuracy of its returns, whether it has met with any -unknown cause of disturbance in its distant journey. Undiscovered -planets, beyond the visible boundary of our system, may change its path -and the period of its revolution, and thus may indirectly reveal to us -their existence, and even their physical nature and orbit. The secrets -of the yet more distant heavens may be disclosed to future generations -by comets which penetrate still farther into space, such as that of -1763, which, if any faith may be placed in the computation, goes nearly -forty-three times farther from the sun than Halley’s does, and shows -that the sun’s attraction is powerful enough, at the enormous distance -of 15,500 millions of miles, to recall the comet to its perihelion. The -periods of some comets are said to be of many thousand years, and even -the average time of the revolution of comets generally is about a -thousand years; which proves that the sun’s gravitating force extends -very far. La Place estimates that the solar attraction is felt -throughout a sphere whose radius is a hundred millions of times greater -than the distance of the earth from the sun. - -Authentic records of Halley’s comet do not extend beyond the year 1456, -yet it may be traced, with some degree of probability, even to a period -preceding the Christian era. But as the evidence only rests upon -coincidences of its periodic time, which may vary as much as eighteen -months from the disturbing action of the planets, its identity with -comets of such remote times must be regarded as extremely doubtful. - -This is the first comet whose periodicity has been established. It is -also the first whose elements have been determined from observations -made in Europe; for, although the comets which appeared in the years -240, 539, 565, and 837, are the most ancient of those whose orbits have -been traced, their elements were computed from Chinese observations. - -Besides Halley’s and Lexel’s comets, ten or twelve others are now known -to form part of the solar system; that is to say, they return to the sun -at stated periods. Six of them have periods of less than eight years. -That generally called Encke’s comet, or the comet of the short period, -was first seen by MM. Messier and Mechain in 1786, again by Miss -Herschel in 1805, and its returns, in the years 1805 and 1819, were -observed by other astronomers, under the impression that all four were -different bodies. However, Professor Encke not only proved their -identity, but determined the circumstances of the comet’s motion. Its -reappearance in the years 1825, 1828, and 1832, accorded with the orbit -assigned by M. Encke, who thus established the length of its period to -be 1204 days, nearly. This comet is very small, of feeble light, and -invisible to the naked eye, except under very favourable circumstances, -and in particular positions. It has no tail, it revolves in an ellipse -of great excentricity inclined at an angle of 13° 22ʹ to the plane of -the ecliptic, and is subject to considerable perturbations from the -attraction of the planets, which occasion variations in its periodic -time. Among the many perturbations to which the planets are liable, -their mean motions, and therefore the major axes of their orbits, -experience no change; while, on the contrary, the mean motion of the -moon is accelerated from age to age—a circumstance at first attributed -to the resistance of an ethereal medium pervading space, but -subsequently proved to arise from the secular diminution of the -excentricity of the terrestrial orbit. Although the resistance of such a -medium has not hitherto been perceived in the motions of such dense -bodies as the planets and satellites, its effects on the revolutions of -the comets leave no doubt of its existence. From the numerous -observations that have been made on each return of the comet of the -short period, the elements have been computed with great accuracy on the -hypothesis of its moving in vacuo. Its perturbations occasioned by the -disturbing action of the planets have been determined; and, after -everything that could influence its motion had been duly considered, M. -Encke found that an acceleration of about two days in each revolution -has taken place in its mean motion, precisely similar to that which -would be occasioned by the resistance of an ethereal medium. And, as it -cannot be attributed to a cause like that which produces the -acceleration of the moon, it must be concluded that the celestial bodies -do not perform their revolutions in an absolute void, and that, although -the medium be too rare to have a sensible effect on the masses of the -planets and satellites, it nevertheless has a considerable influence on -so rare a body as a comet. Contradictory as it may seem that the motion -of a body should be accelerated by the resistance of an ethereal medium, -the truth becomes evident if it be considered that both planets and -comets are retained in their orbits by two forces which exactly balance -one another; namely, the centrifugal force producing the velocity in the -tangent, and the attraction of the gravitating force directed to the -centre of the sun. If one of these forces be diminished by any cause, -the other will be proportionally increased. Now, the necessary effect of -a resisting medium is to diminish the tangential velocity, so that the -balance is destroyed, gravity preponderates, the body descends towards -the sun till equilibrium is again restored between the two forces; and, -as it then describes a smaller orbit, it moves with increased velocity. -Thus, the resistance of an ethereal medium actually accelerates the -motion of a body; but, as the resisting force is confined to the plane -of the orbit, it has no influence whatever on the inclination of the -orbit, or on the place of the nodes. In computing its effect, M. Encke -assumed the increase to be inversely as the square of the distance, and -that its resistance acts as a tangential force proportional to the -squares of the comet’s actual velocity in each point of its orbit. -Another comet belonging to our system, which returns to its perihelion -after a period of 6-3/4 years, has been accelerated in its motion by a -whole day during one revolution, which puts the existence of ether -beyond a doubt, and confirms the undulatory theory of light. Since this -comet, which revolves nearly between the orbits of the earth and -Jupiter, is only accelerated one day at each revolution, while Encke’s, -revolving nearly between the orbits of Mercury and Pallas, is -accelerated two, the ethereal medium must increase in density towards -the sun. The comet in question was discovered by M. Biela at Josephstadt -on the 27th of February, 1826, and ten days afterwards it was seen by M. -Gambart at Marseilles, who computed its parabolic elements, and found -that they agreed with those of the comets which had appeared in the -years 1789 and 1795, whence he concluded them to be the same body moving -in an ellipse, and accomplishing its revolution in 2460 days. The -perturbations of this comet were computed by M. Damoiseau, who predicted -that it would cross the plane of the ecliptic on the 29th of October, -1832, a little before midnight, at a point nearly 18,484 miles within -the earth’s orbit; and as M. Olbers of Bremen, in 1805, had determined -the radius of the comet’s head to be about 21,136 miles, it was evident -that its nebulosity would envelop a portion of the earth’s orbit,—a -circumstance which caused some alarm in France, from the notion that, if -any disturbing cause had delayed the arrival of the comet for one month, -the earth must have passed through its head. M. Arago dispelled these -fears by his excellent treatise on comets, in the Annuaire of 1832, -where he proves that, as the earth would never be nearer the comet than -18,000,000 British leagues, there could be no danger of collision. The -earth is in more danger from these two small comets than from any other. -Encke’s crosses the terrestrial orbit sixty times in a century, and may -ultimately come into collision, but both are so extremely rare, that -little injury is to be apprehended. - -The earth would fall to the sun in 64-1/2 days, if it were struck by a -comet with sufficient impetus to destroy its centrifugal force. What the -earth’s primitive velocity may have been it is impossible to say. -Therefore a comet may have given it a shock without changing the axis of -rotation, but only destroying part of its tangential velocity, so as to -diminish the size of the orbit—a thing by no means impossible, though -highly improbable. At all events, there is no proof of this having -occurred; and it is manifest that the axis of the earth’s rotation has -not been changed, because, as the ether offers no sensible resistance to -so dense a body as the earth, the libration would to this day be evident -in the variation it must have occasioned in the terrestrial latitudes. -Supposing the nucleus of a comet to have a diameter only equal to the -fourth part of that of the earth, and that its perihelion is nearer to -the sun than we are ourselves, its orbit being otherwise unknown, M. -Arago has computed that the probability of the earth receiving a shock -from it is only one in 281 millions, and that the chance of our coming -in contact with its nebulosity is about ten or twelve times greater. -Only comets with retrograde motions can come into direct collision with -the earth, and if the momentum were great the event might be fatal; but -in general the substance of comets is so rare, that it is likely they -would not do much harm if they were to impinge; and even then the -mischief would probably be local, and the equilibrium soon restored, -provided the nucleus were gaseous, or very small. It is, however, more -probable that the earth would only be deflected a little from its course -by the approach of a comet, without being touched by it. The comets that -have come nearest to the earth were that of the year 837, which remained -four days within less than 1,240,000 leagues from our orbit: that of -1770, which approached within about six times the distance of the moon. -The celebrated comet of 1680 also came very near to us; and the comet -whose period is 6-3/4 years was ten times nearer the earth in 1805 than -in 1832, when it caused so much alarm. - -Encke’s and Biela’s comets are at present far removed from the influence -of Jupiter, but they will not always remain so, because, the aphelia and -nodes of the orbits of these two comets being the points which approach -nearest to the orbit of Jupiter at each meeting of the planet and -comets, the major axis of Encke’s comet will be increased and that of -Biela’s diminished, till in the course of time, when the proximity has -increased sufficiently, the orbits will be completely changed, as that -of Lexel’s was in 1770. Every twenty-third year, or after seven -revolutions of Encke’s comet, its greatest proximity to Jupiter takes -place, and at that time his attraction increases the period of its -revolution by nine days—a circumstance which took place in the end of -the years 1820 and 1843. But from the position of the bodies there is a -diminution of three days in the six following revolutions, which reduces -the increase to six days in seven revolutions. Thus, before the year -1819, the periodic time of Encke’s comet was 1204 days, and it was 1219 -days in accomplishing the revolution that ended in 1845. By this -progressive increase the orbit of the comet will reach that of Jupiter -in seven or eight centuries, and then by the very near approach of the -two bodies it will be completely changed. - -At present the Earth and Mercury have the most powerful influence on the -motions of Encke’s and Biela’s comets; and have had for so long a time -that, according to the computation of Mr. Airy, the present orbit of the -latter was formed by the attraction of the Earth, and that of Encke’s by -the action of Mercury. With regard to the latter comet, that event must -have taken place in February 1776. In 1786 Encke’s comet had both a tail -and a nucleus, now it has neither; a singular instance of the -possibility of their disappearance. It was in perihelio in 1855. - -In 1846 Biela’s comet was divided into two distinct bodies, by what -strange accident is altogether a mystery. The nuclei of the two comets -were separated by about 150,000 miles, and they travelled together with -their tails parallel, and an arch of light over their heads. Till that -time Biela’s comet never had been seen with a tail. The new head was -dull at first, but increased in size and brightness till it surpassed -its companion in both; besides, it had a bright flashing diamond-like -point in its centre—gradually it resumed its dull appearance, and its -period was computed to be eight days longer than that of the original -head. They had separated to a greater distance from one another in 1853, -but were still travelling together, one having become smaller than the -other. - -A comet discovered by M. Brorsen of Kiel, on the 26th of February, 1846, -came, on the 20th of April following, nearly as close to Jupiter as his -fourth satellite, when Jupiter’s attraction must have been ten times -greater than that of the sun; so there is every reason to believe that -the comet’s orbit will be as much altered as that of Lexel’s; and -another discovered by Padre de Vico at Rome, on the 22nd of August, -will, in all probability, be as much disturbed by the same cause. One of -the comets found by that astronomer has a period which varies, according -to different computations, from 55 to 99 years; it certainly has an -elliptical orbit. That discovered at Naples by Mr. Peters revolves about -the sun in 16 years; but Olbers’s comet of 1815 must go nearly the same -distance into space with Halley’s, since its period is 74 years. Two -discovered by M. Brorsen have periods, one of 500 and the other of 28 -years; but of the latter there is some uncertainty. - -The comet which appeared in 1596 and 1845 has a period of 249 years; and -should M. Argelander’s computation be accurate, the orbit which has -hitherto been assigned to the great comet of 1811 must be erroneous, -since he has ascertained its period to be 3066 years. - -The great comet of 1264, which had a tail that extended over 100° of the -celestial vault, was observed and recorded by the Chinese, and was -ascertained to be the same that had appeared in 1556, and of whose -motions observations were taken at Vienna in the reign of the Emperor -Charles V., but it was then less brilliant. In consequence of the -discovery of the original observations of the comet of 1556, by -Fabricius at Vienna, and by Heller at Nuremburg, Mr. Hind was induced to -compute its orbit for that year; but after much labour, aided by all the -improved methods of calculation, he found Heller’s observations so -confused, and even erroneous, that he could not determine the curve -described by the comet at that time with any precision, and therefore -could only predict that the epoch of its return would be some time -between 1848 and 1861. Before comets reach the sun they are rarely -conspicuous; but if after passing their perihelion they come near the -earth, then they have tails, and become brilliant in consequence of the -sun’s action upon the matter of which they are formed. Now if the comet -in question should pass its perihelion between the months of March and -October, it possibly may be as remarkable as ever; but should it come -nearest to the sun in winter, such is the position of its orbit with -regard to the earth, that it may pass unnoticed—which is very unlikely, -as search is being made for it at almost all the observatories in Europe -and in the United States. Nearly the whole of its orbit lies below the -plane of the ecliptic, and far from the paths of the larger planets, but -it extends into space more than twice the distance of Neptune, or nearly -six thousand millions of miles from the sun. - -Comets in or near their perihelion move with prodigious velocity. That -of 1680 appears to have gone half round the sun in ten hours and a half, -moving at the rate of 880,000 miles an hour. If its enormous centrifugal -force had ceased when passing its perihelion, it would have fallen to -the sun in about three minutes, as it was then less than 147,000 miles -from his surface. So near the sun, it would be exposed to a heat 27,500 -times greater than that received by the earth; and as the sun’s heat is -supposed to be in proportion to the intensity of his light, it is -probable that a degree of heat so intense would be sufficient to convert -into vapour every terrestrial substance with which we are acquainted. At -the perihelion distance the sun’s diameter would be seen from the comet -under an angle of 73°, so that the sun, viewed from the comet, would -nearly cover the whole extent of the heavens from the horizon to the -zenith. As this comet is presumed to have a period of 575 years, the -major axis of its orbit must be so great, that at the aphelion the sun’s -diameter would only subtend an angle of about fourteen seconds, which is -not so great by half as the diameter of Mars appears to us when in -opposition. The sun would consequently impart no heat, so that the comet -would then be exposed to the temperature of the ethereal regions, which -is 239° below the zero point of Fahrenheit. A body of such tenuity as -the comet, moving with such velocity, must have met with great -resistance from the dense atmosphere of the sun, while passing so near -his surface at its perihelion. The centrifugal force must consequently -have been diminished, and the sun’s attraction proportionally augmented, -so that it must have come nearer to the sun in 1680 than in its -preceding revolution, and would subsequently describe a smaller orbit. -As this diminution of its orbit will be repeated at each revolution, the -comet will infallibly end by falling on the surface of the sun, unless -its course be changed by the disturbing influence of some large body in -the unknown expanse of creation. Our ignorance of the actual density of -the sun’s atmosphere, of the density of the comet, and of the period of -its revolution, renders it impossible to form any idea of the number of -centuries which must elapse before this event takes place. - -The same cause may affect the motions of the planets, and ultimately be -the means of destroying the solar system. But, as Sir John Herschel -observes, they could hardly all revolve in the same direction round the -sun for so many ages without impressing a corresponding motion on the -ethereal medium, which may preserve them from the accumulated effects of -its resistance. Should this material medium revolve about the sun like a -vortex, it will accelerate the revolutions of such comets as have direct -motions, and retard those that have retrograde motions. - -The comet which appeared unexpectedly in the beginning of the year 1843 -was one of the most splendid that ever visited the solar system. It was -in the constellation of Antinous in the end of January, at a distance of -115 millions of miles from the earth, and it passed through its -perihelion on the 27th of February, when it was lost in the sun’s rays; -but it began to be visible about the 3rd of March, at which time it was -near the star Iota Cetæ, and its tail extended towards the Hare. Before -the passage at the perihelion it had no tail; but at that epoch the tail -suddenly darted out, and extended to a distance of 1826 millions of -miles in about an hour and a half—a most inexplicable speed of -development, which indicates some powerful repulsive force at the moment -of the greatest proximity to the sun, at which time the tails are -formed. The brightness of the comet and the length of its tail continued -to increase till the latter stretched far beyond the constellation of -the Hare towards a point above Sirius. Stars were distinctly seen -through it, and when near perihelion the comet was so bright that it was -seen in clear sunshine, in the United States, like a white cloud. The -motion was retrograde, and on leaving the solar system it retreated so -rapidly at once from the sun and earth that it was soon lost sight of -for want of light. On the 1st of April it was between the sun and the -earth, and only 40 millions of miles from the latter; and as its tail -was at least 60 millions of miles long, and 20 millions of miles broad, -we probably passed through it without being aware of it. There is some -discrepancy in the different computations of the elements of the orbit, -but in the greater number of cases the perihelion distance was found to -be less than the semidiameter of the sun, so that the comet must have -grazed his surface, if it did not actually impinge obliquely on him. - -The perihelion distance of this comet differs little from that of the -great comet of 1668, which came so near the sun. The motion of both was -retrograde, and a certain resemblance in the two orbits makes it -probable that they are the same body performing a revolution in 175 -years. - -Though already so well acquainted with the motions of comets, we know -nothing of their physical constitution. A vast number, especially of -telescopic comets, are only like clouds or masses of vapour, often -without tails. The head commonly consists of a concentrated mass of -light, like a planet, surrounded by a very transparent atmosphere, and -the whole, viewed with a telescope, is so diaphanous, that the smallest -star may be seen even through the densest part of the nucleus; in -general their solid parts, when they have any, are so minute, that they -have no sensible diameter, like that of the comet of 1811, which -appeared to Sir William Herschel like a luminous point in the middle of -the nebulous matter. The nuclei, which seem to be formed of the denser -strata of that nebulous matter in successive coatings, are sometimes of -great magnitude. Those comets which came to the sun in the years 1799 -and 1807 had nuclei whose diameters measured 180 and 275 leagues -respectively, and the second comet of 1811 had a nucleus 1350 leagues in -diameter. - -It must, however, be stated that, as comets are generally at prodigious -distances from the earth, the solid parts of the nuclei appear like mere -points of light, so minute that it is impossible to measure them with -any kind of accuracy, so that the best astronomers often differ in the -estimation of their size by one-half of the whole diameter. The transit -of a comet across the sun would afford the best information with regard -to the nature of the nuclei. It was computed that such an event was to -take place in the year 1827; unfortunately the sun was hid by clouds -from the British astronomers, but it was examined at Viviers and at -Marseilles at the time the comet must have been projected on its disc, -but no spot or cloud was to be seen, so that it must have had no solid -part whatever. The nuclei of many comets which seemed solid and -brilliant to the naked eye have been resolved into mere vapour by -telescopes of high powers; in Halley’s comet there was no solid part at -all. - -The nebulosity immediately round the nucleus is so diaphanous, that it -gives little light; but at a small distance the nebulous matter becomes -suddenly brilliant, so as to look like a bright ring round the body. -Sometimes there are two or three of these luminous concentric rings -separated by dark intervals, but they are generally incomplete on the -part next the tail. - -These annular appearances are an optical effect, arising from a -succession of envelopes of the nebulous matter with intervals between -them, of which the first is sometimes in contact with the nucleus and -sometimes not. The thickness of these bright diaphanous coatings in the -comets of 1799 and 1807 was about 7000 and 10,000 leagues respectively; -and in the first comet of 1811 the luminous ring was 8000 leagues thick, -and the distance between its interior surface and the centre of the head -was 10,000 leagues. The latter comet was by much the most brilliant that -has been seen in modern times; it was first discovered in this country -by Mr. James Vietch of Inchbonny, and was observed in all its changes by -Sir William Herschel and M. Olbers. To the naked eye, the head had the -appearance of an ill-defined round mass of light, which was resolved -into several distinct parts when viewed with a telescope. A very -brilliant interior circular mass of nebulous matter was surrounded by a -black space having a parabolic form, very distinct from the dark blue of -the sky. This dark space was of a very appreciable breadth. Exterior to -the black interval there was a luminous parabolic contour of -considerable thickness, which was prolonged on each side in two -diverging branches, which formed the bifid tail of the comet. Sir -William Herschel found that the brilliant interior circular mass lost -the distinctness of its outline as he increased the magnifying power of -the telescope, and presented the appearance of a more and more diffuse -mass of greenish or blueish green light, whose intensity decreased -gradually, not from the centre, but from an eccentric brilliant speck, -supposed to be the truly solid part of the comet. The luminous envelope -was of a decided yellow, which contrasted strongly with the greenish -tint of the interior nebulous mass. Stars were nearly veiled by the -luminous envelope, whilst, on the contrary, Sir William Herschel saw -three extremely small stars shining clearly in the black space, which -was singularly transparent. As the envelopes were formed in succession -as the comet approached the sun, Sir William Herschel conceived them to -be vapours raised by his heat at the surface of the nucleus, and -suspended round it like a vault or dome by the elastic force of an -extensive and highly transparent atmosphere. In coming to the sun, the -coatings began to form when the comet was as distant as the orbit of -Jupiter, and in its return they very soon entirely vanished; but a new -one was formed after it had retreated as far as the orbit of Mars, which -lasted for a few days. Indeed, comets in general are subject to sudden -and violent convulsions in their interior, even when far from the sun, -which produce changes that are visible at enormous distances, and baffle -all attempts at explanation—probably arising from electricity, or even -causes with which we are unacquainted. The envelopes surrounding the -nucleus of the comet on the side next to the sun diverge on the opposite -side, where they are prolonged into the form of a hollow cone, which is -the tail. Two repulsive forces seem to be concerned in producing this -effect; one from the comet and another from the sun, the latter being -the most powerful. The envelopes are nearer the centre of the comet on -the side next to the sun, where these forces are opposed to one another; -but on the other side the forces conspire to form the tail, conveying -the nebulous particles to enormous distances. - -The lateral edges of the tail reflect more light than the central part, -because the line of vision passes through a greater depth of nebulous -matter, which produces the effect of two streams somewhat like the -aurora. Stars shine with undiminished lustre through the central part of -the tail, because their rays traverse it perpendicularly to its -thickness; but, though distinctly seen through its edges, their light is -weakened by its oblique transmission. The tail of the great comet of -1811 was of wonderful tenuity; stars which would have been entirely -concealed by the slightest fog were seen through 64,000 leagues of -nebulous matter without the smallest refraction. Possibly some part of -the changes in the appearance of the tails arises from rotation. Several -comets have been observed to rotate about an axis passing through the -centre of the tail. That of 1825 performed its rotation in 20-1/2 hours, -and the rapid changes in the luminous sectors which issued from the -nucleus of Halley’s comet in all probability were owing to rotatory -motion. - -The two streams of light which form the edges of the tail in most cases -unite at a greater or less distance from the nucleus, and are generally -situate in the plane of the orbit. The tails follow comets in their -descent towards the sun, but precede them in their return, with a small -degree of curvature; their apparent extent and form vary according to -the positions of the orbits with regard to the ecliptic. In some cases -the tail has been at right angles to the line joining the sun and comet. -The curvature is in part owing to the resistance of the ether, and -partly to the velocity of the comet being greater than that of the -particles at the extremity of its tail, which lag behind. The tails are -generally of enormous lengths; the comet of 1811 had one no less than a -hundred millions of miles in length, and those which appeared in the -years 1618, 1680, and 1769, had tails which extended respectively over -104, 90, and 97 degrees of space. Consequently, when the heads of these -comets were set, a portion of the extremity of their tails was still in -the zenith. Sometimes the tail is divided into several branches, like -the comet of 1744, which had six, separated by dark intervals, each of -them about 4° broad, and from 30° to 44° long. They were probably formed -by three hollow cones of the nebulous matter proceeding from the -different envelopes, and enclosing one another, with intervals between; -the lateral edges of these cones would give the appearance of six -streams of light. The tails do not attain their full magnitude till the -comet has left the sun. When comets first appear, they resemble round -films of vapour, with little or no tail. As they approach the sun, they -increase in brilliancy, and their tail in length, till they are lost in -his rays; and it is not till they emerge from the sun’s more vivid light -that they assume their full splendour. They then gradually decrease, -their tails diminish, and they disappear, nearly or altogether, before -they are beyond the sphere of telescopic vision. Many comets have no -tails, as, for example, Encke’s comet. Those which appeared in the years -1585, 1763, and 1682, were also without tails, though the latter is -recorded to have been as bright as Jupiter. The matter of the tail must -be extremely buoyant to precede a body moving with such velocity: -indeed, the rapidity of its ascent cannot be accounted for. It has been -attributed to that power in the sun which produces those vibrations of -ether which constitute light; but as this theory will not account for -the comet of 1824, which is said to have had two tails, one directed -towards the sun, and a very short one diametrically opposite to it, our -ignorance on this subject must be confessed. In this case the repelling -power of the comet seems to have been greater than that of the sun. -Whatever that unknown power may be, there are instances in which its -effects are enormous; for, immediately after the great comet of 1680 had -passed its perihelion, its tail was 100,000,000 miles in length, and was -projected from the comet’s head in the short space of two days. A body -of such extreme tenuity as a comet is most likely incapable of an -attraction powerful enough to recall matter sent to such an enormous -distance; it is therefore, in all probability, scattered in space or -absorbed by the zodiacal light or nebula that surrounds the sun, which -may account for the rapid decrease observed in the tails of comets every -time they return to their perihelia. Should the great comet of 1843 -prove to be the same with that of 1668, its tail must have diminished -considerably. - -It is remarkable that, although the tails of comets increase in length -as they approach their perihelia, there is reason to believe that the -real diameter of the head contracts on coming near the sun, and expands -rapidly on leaving him. Hevelius first observed this phenomenon, which -Encke’s comet has exhibited in a very extraordinary degree. On the 28th -of October, 1828, this comet was about three times as far from the sun -as it was on the 24th of December; yet at the first date its apparent -diameter was twenty-five times greater than at the second, the decrease -being progressive. M. Valz attributes the circumstance to a real -condensation of volume from the pressure of the ethereal medium, which -increases most rapidly in density towards the surface of the sun, and -forms an extensive atmosphere around him. It did not occur to M. Valz, -however, that the ethereal fluid would penetrate the nebulous matter -instead of compressing it. Sir John Herschel, on the contrary, -conjectures that it may be owing to the alternate conversion of -evaporable materials in the upper regions of the transparent atmosphere -of comets into the states of visible cloud and invisible gas by the -effects of heat and cold; or that some of the external nebulous -envelopes may come into view when the comet arrives at a darker part of -the sky, which were overpowered by the superior light of the sun while -in his vicinity. The first of these hypotheses he considers to be -perfectly confirmed by his observations on Halley’s comet, made at the -Cape of Good Hope, after its return from the sun. He thinks that, in all -probability, the whole comet, except the densest part of its head, -vanished, and was reduced to a transparent and invisible state during -its passage at its perihelion: for when it first came into view, after -leaving the sun, it had no tail, and its aspect was completely changed. -A parabolic envelope soon began to appear, and increased so much and so -rapidly that its augmentation was visible to the eye. This increase -continued till it became so large and so faint, that at last it vanished -entirely, leaving only the nucleus and a tail, which it had again -acquired, but which also vanished; so that at last the nucleus alone -remained. Not only the tails, but the nebulous part of comets, -diminishes every time they return to their perihelia; after frequent -returns they ought to lose it altogether, and present the appearance of -a fixed nucleus: this ought to happen sooner to comets of short periods. -M. de la Place supposes that the comet of 1682 must be approaching -rapidly to that state. Should the substances be altogether, or even to a -great degree, evaporated, the comet would disappear for ever. Possibly -comets may have vanished from our view sooner than they would otherwise -have done from this cause. - -The comet discovered at Florence by Signore Donati, on the 2nd of June, -1858, was one of the most beautiful that has been seen from our planet -for many years, whether for the brightness of the _nucleus_, or the -length and graceful form of the _coma_; when first discovered it was -near the star λ in the constellation of the Lion, being then at a -distance of 288,000,000 miles from the earth; during the month of August -its nucleus assumed an almost planetary aspect from the concentration of -its light; on the 27th of September the head appeared almost as bright -as Mercury, but smaller; when near its perihelion passage, on September -30th, its diameter, as ascertained by Signore Donati, was 3ʺ; during the -early part of October it continued to increase in brilliancy, the tail -becoming more elongated, and describing a beautiful arc in the heavens, -occupying a space of nearly 40°, or a length of 40,000,000 miles in the -solar system. On the evening of the 5th of October it was seen from most -parts of Britain, within 20ʹ of Arcturus, the brightest star in the -northern heavens, across which the densest part nearly of the tail -passed, and through which notwithstanding the star shone with -undiminished brilliancy. On the 30th of October, when in perihelio, the -comet was only 55,000,000 miles from the sun; on the 10th it approached -nearest to the earth, from which it was then distant 51,000,000 miles; -and on the 15th of the same month near to Venus, being at that time less -than one-tenth the distance of the earth from the Sun; if the comet had -reached its perihelion a few days earlier, Venus might have passed -through its nucleus, the consequences of which to the planet it would be -very difficult to imagine. The motion of Donati’s comet is what -astronomer’s call _retrograde_, or from east to west. It ceased to be -visible in our northern latitudes in the last week in October, having -passed into the southern heavens, where it will traverse the -constellations of Sagittarius, Telescopium, and Indus, approaching the -large star of Toucan; after which it will disappear until it has nearly -completed its revolution round the sun. The observed orbit of this -remarkable comet coincides more nearly with an ellipse than a parabola; -the longer diameter of the ellipse being 184 times that of the earth’s -orbit, or the immense distance of 35,100,000,000 miles—a space which, -however great, is less than the thousandth of the distance of the -nearest fixed star. According to the calculations of M. Loewy, and -adopting an elliptic orbit, Donati’s comet will not return to the same -places in the heavens for 2495 years, being 500 less than the period of -revolution of the great comet of 1811. - -Signore Donati observed that between the 25th and 30th September two -concentric, luminous, semicircular envelopes, with a dark space between -them, were formed in the head. From the extremities of these the cone of -the tail extended, and a non-luminous or dark space stretched for 20° -from the nucleus into the tail. On the 1st October the two envelopes -were combined into one. This comet, like Halley’s, has shown some -singular irregularities, supposed to arise from the action of the sun -when near its perihelion. At different periods of its apparition a -violent agitation was observed in its nucleus, with luminous jets, -spiral offshoots, &c., as in the great comets of 1680, 1744, 1811. A ray -of light was thrown out from one side of the nucleus towards the sun, -while a gas-like jet proceeded from the other side, which appeared to -form the origin of a second tail within the great tail, and which was -traced for half a degree by Mr. Hind on the 19th September. He observed -decided spiral convolutions in the tail, which show that this comet has -a rotatory motion about an axis passing through the tail. - -If comets shine by borrowed light, they ought, in certain positions, to -exhibit phases like the moon; but no such appearance has been detected, -except in one instance, when they are said to have been observed by -Hevelius and La Hire, in the year 1682. In general, the light of comets -is dull—that of the comet of 1811 was only equal to the tenth part of -the light of the full moon—yet some have been brilliant enough to be -visible in full daylight, especially the comet of 1744, which was seen -without a telescope at one o’clock in the afternoon, while the sun was -shining. Hence it may be inferred that, although some comets may be -altogether diaphanous, others seem to possess a solid mass resembling a -planet. But whether they shine by their own or by reflected light has -never been satisfactorily made out till now. Even if the light of a -comet were polarized, it would not afford a decisive test, since a body -is capable of reflecting light, though it shines by its own. M. Arago, -however, has, with great ingenuity, discovered a method of ascertaining -this point, independent both of phases and polarization. - -Since the rays of light diverge from a luminous point, they will be -scattered over a greater space as the distance increases, so that the -intensity of the light on a screen two feet from the object is four -times less than at the distance of one foot; three feet from the object -it is nine times less; and so on, decreasing in intensity as the square -of the distance increases. As a self-luminous surface consists of an -infinite number of luminous points, it is clear that, the greater the -extent of surface, the more intense will be the light; whence it may be -concluded that the illuminating power of such a surface is proportional -to its extent, and decreases inversely as the square of the distance. -Notwithstanding this, a self-luminous surface, plane or curved, viewed -through a hole in a plate of metal, is of the same brilliancy at all -possible distances as long as it subtends a sensible angle, because, as -the distance increases, a greater portion comes into view; and, as the -augmentation of surface is as the square of the diameter of the part -seen through the whole, it increases as the square of the distance. -Hence, though the number of rays from any one point of the surface which -pass through the hole decreases inversely as the square of the distance, -yet, as the extent of surface which comes into view increases also in -that ratio, the brightness of the object is the same to the eye as long -as it has a sensible diameter. For example—Uranus is about nineteen -times farther from the sun than we are, so that the sun, seen from that -planet, must appear like a star with a diameter of a hundred seconds, -and must have the same brilliancy to the inhabitants that he would have -to us if viewed through a small circular hole having a diameter of a -hundred seconds. For it is obvious that light comes from every point of -the sun’s surface to Uranus, whereas a very small portion of his disc is -visible through the hole; so that extent of surface exactly compensates -distance. Since, then, the visibility of a self-luminous object does not -depend upon the angle it subtends as long as it is of sensible -magnitude, if a comet shines by its own light, it should retain its -brilliancy as long as its diameter is of a sensible magnitude; and, even -after it has lost an apparent diameter, it ought to be visible, like the -fixed stars, and should only vanish in consequence of extreme -remoteness. That, however, is far from being the case—comets gradually -become dim as their distance increases, and vanish merely from loss of -light, while they still retain a sensible diameter, which is proved by -observations made the evening before they disappear. It may therefore be -concluded that comets shine by reflecting the sun’s light. The most -brilliant comets have hitherto ceased to be visible when about five -times as far from the sun as we are. Most of the comets that have been -visible from the earth have their perihelia within the orbit of Mars, -because they are invisible when as distant as the orbit of Saturn: on -that account there is not one on record whose perihelion is situate -beyond the orbit of Jupiter. Indeed, the comet of 1756, after its last -appearance, remained five whole years within the ellipse described by -Saturn without being once seen. More than a hundred and forty comets -have appeared within the earth’s orbit during the last century that have -not again been seen. If a thousand years be allowed as the average -period of each, it may be computed, by the theory of probabilities, that -the whole number which range within the earth’s orbit must be 1400; but, -Uranus being about nineteen times more distant, there may be no less -than 11,200,000 comets that come within the orbit of Uranus. M. Arago -makes a different estimate; he considers that, as thirty comets are -known to have their perihelion distance within the orbit of Mercury, if -it be assumed that comets are uniformly distributed in space, the number -having their perihelion within the orbit of Uranus must be to thirty as -the cube of the radius of the orbit of Uranus to the cube of the radius -of the orbit of Mercury, which makes the number of comets amount to -3,529,470. But that number may be doubled, if it be considered that, in -consequence of daylight, fogs, and great southern declination, one comet -out of two must be hid from us. According to M. Arago, more than seven -millions of comets come within the orbit of Uranus. - -The different degrees of velocity with which the planets and comets were -originally propelled in space is the sole cause of the diversity in the -form of their orbits, which depends only upon the mutual relation -between the projectile force and the sun’s attraction. - -When the two forces are exactly equal to one another, circular motion is -produced; when the ratio of the projectile to the central force is -exactly that of 1 to the square root of 2, the motion is parabolic; any -ratio between these two will cause a body to move in an ellipse, and any -ratio greater than that of 1 to the square root of 2 will produce -hyperbolic motion (N. 229). - -The celestial bodies might move in any one of these four curves by the -law of gravitation: but, as one particular velocity is necessary to -produce either circular or parabolic motion, such motions can hardly be -supposed to exist in the solar system, where the bodies are liable to -such mutual disturbances as would infallibly change the ratio of the -forces, and cause them to move in ellipses in the first case, and -hyperbolas in the other. On the contrary, since every ratio between -equality and that of 1 to the square root of 2 will produce elliptical -motion, it is found in the solar system in all its varieties, from that -which is nearly circular to such as borders on the parabolic from -excessive ellipticity. On this depends the stability of the system; the -mutual disturbances only cause the orbits to become more or less -excentric without changing their nature. - -For the same reason the bodies of the solar system might have moved in -an infinite variety of hyperbolas, since any ratio of the forces, -greater than that which causes parabolic motion, will make a body move -in one of these curves. Hyperbolic motion is however very rare; only two -comets appear to move in orbits of that nature, those of 1771 and 1824; -probably all such comets have already come to their perihelia, and -consequently will never return. - -The ratio of the forces which fixed the nature of the celestial orbits -is thus easily explained; but the circumstances which determined these -ratios, which caused some bodies to move nearly in circles and others to -wander towards the limits of the solar attraction, and which made all -the heavenly bodies to rotate and revolve in the same direction, must -have had their origin in the primeval state of things; but as it pleases -the Supreme Intelligence to employ gravitation alone in the maintenance -of this fair system, it may be presumed to have presided at its -creation. - - - - - 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. - - -GREAT as the number of comets appears to be, it is absolutely nothing in -comparison of the multitude of the fixed stars. About 2000 only are -visible to the naked eye; but when the heavens are viewed through a -telescope, their number seems to be limited only by the imperfection of -the instrument. The number registered amounts to 200,000; their places -are determined with great precision, and they are formed into a -catalogue, not only for the purpose of ascertaining geographical -positions by the occultations of the brightest among them, but also to -serve as points of reference for marking the places of comets and other -celestial phenomena. Sirius, α Centauri, and Arcturus are the brightest -stars in the heavens; the others are classed according to their apparent -lustre, from the first to the seventeenth magnitudes. Capella, α Lyræ, -Procyon, and twenty or twenty-one more, are of the first magnitude; α -Persei, γ Orionis, α Cygni, and in all fifty or sixty, are of the -second; and of the third there are about 200, such as η Bootis and η -Draconis, the numbers increasing as the magnitude diminishes. Those of -the eighth magnitude are scarcely visible to the naked eye, and it -requires a very good telescope to see stars of the seventeenth. This -sequence is perfectly arbitrary; but Sir John Herschel has ascertained -by actual measurement the comparative lustre of a great many—for -example, he found that the light of a star of the sixth magnitude is 100 -times less than that of one of the first magnitude, and that Sirius -would make between three and four hundred of such little stars. Were the -photometric scale completed, it would be of the greatest importance with -regard to the variable stars. - -The three or four brightest classes of stars are scattered pretty -equably over the sky, with the exception of a zone or belt following the -course of the great circle passing through ε Orionis and α Crucis, where -they are very numerous, especially in the southern hemisphere. The stars -of all magnitudes visible to the naked eye increase in numbers towards -the borders of the Milky Way, which derives its lustre and name from the -diffused light of myriads of stars; so numerous are they in some parts -of it that more than 50,000 passed through the field of Sir William -Herschel’s telescope in the course of an hour, in a zone only two -degrees broad; in many places they are numerous beyond estimation, and -most of them are extremely small on account of their enormous distances. - -The Milky Way, which forms so conspicuous a part of the firmament, is a -vast and somewhat flattened stratum or congeries of stars, encircling -the heavens in a broad band, split through one part of its circumference -into two streams of stars, bearing a strong resemblance to fig. 5, plate -5. It is contorted and broken in some places, and occasionally -lengthened into branches stretching far into space. Its thickness is -small compared with its length and breadth; yet in some places it is -unfathomable even with the best telescopes; in others there is reason to -believe that it is possible to see through it, and even beyond it, in -its own plane. There is a gradual but rapid increase in the crowding of -the stars on each side of the flat stratum towards the centre. - -The solar system is deeply though excentrically plunged into this mass -of stars, near that point where the circular stratum splits into two -streams. Sir John Herschel’s description of the stars of the southern -hemisphere shows that the Milky Way is a most magnificent object there. -“The general aspect of the southern circumpolar regions (including in -that expression 60° or 70° of south polar distance) is in a high degree -rich and magnificent, owing to the superior brilliancy and large -development of the Milky Way, which, from the constellation of Orion to -that of Antinous, is a blaze of light, strangely interrupted, however, -with vacant and entirely starless patches, especially in Scorpio, near α -Centauri and the Cross, while to the north it fades away pale and dim, -and is in comparison hardly traceable. I think it is impossible to view -this splendid zone, with the astonishingly rich and evenly distributed -fringe of stars of the 3rd and 4th magnitude, which forms a broad skirt -to its southern border like a vast curtain, without an impression -amounting almost to conviction, that the Milky Way is not a mere -stratum, but annular, or at least that our system is placed within one -of the poorer or almost vacant parts of its general mass, and that -eccentrically, so as to be much nearer to the region about the Cross -than to that diametrically opposite to it.” - -Those dark vacuities called “Coal Sacks” by the ancient navigators, -which are so numerous between α Centauri and α Antaris, are among the -most extraordinary phenomena in the southern hemisphere; they are of -intense blackness, though by no means void of extremely small telescopic -stars; the darkness arises from the contrast these nearly vacant spaces -form with the excessive brilliancy of the surrounding part of the Milky -Way, and the sudden sharp transition from light to darkness. The largest -and most conspicuous of them is a pear-shaped vacuity close to the -Southern Cross. That portion of the Milky Way that is split -longitudinally through its centre lies between α Centauri and the -constellation of Cygnus: the two bands are joined here and there by -narrow bridges of condensed stars, stretching across the darker space -between them. In Scorpio and Sagittarius Sir John Herschel describes the -Milky Way as composed of definite clouds of light running into clusters -of extremely minute stars like sand, not strewed evenly as with a sieve, -but as if thrown down by handfuls, and by both hands at once, leaving -dark intervals. In this astonishing profusion the stars are of all -sizes, from the 14th to the 20th magnitude, and even down to nebulosity. -After an interval the same profusion is renewed, the stars being -inconceivably minute and numerous beyond description—they are in -millions and millions. Thus there is great irregularity in their -diffusion as well as magnitude—in some places intensely crowded, in -others the deep blackness of the sky, over which they are thinly -scattered, irresistibly led to believe that in these regions the power -of our telescopes fairly penetrates through the starry stratum, and -beyond it. Sometimes we look through a sheet of stars nearly of the same -size, of no great thickness compared with their distance from us, and -not unfrequently there is a double stratum, one of large stars spread -over another of very small ones. - -The most southerly of the two streams of stars which form the Milky Way -in this part of the firmament maintains an unbroken course of extreme -brilliancy, containing some of the finest clusters of stars in the -heavens. One round γ Sagittarii is an intense aggregate of stars, in -some parts of which they are so crowded as to exceed enumeration; at a -very moderate estimate Sir John Herschel thinks this group cannot -contain fewer than a hundred thousand stars. Other two groups between -the constellations of the Shield and Ophiuchus stand out like -promontories of intense brilliancy in the dark space that separates the -starry streams of the Milky Way. - -The distance of the fixed stars is too great to admit of their -exhibiting a sensible disc, but they must be spherical if gravitation -pervades all space, as there is every reason to believe it does. With a -powerful telescope the stars are like points of light: their -occultations by the moon are therefore instantaneous. Their twinkling -arises from sudden changes in the refractive power of the air, which -would not be sensible if they had discs like planets. Thus nothing can -be known of their distance from us or from one another by their apparent -diameters. Although from the appearance of the stars no inference can be -drawn as to their distance, yet among the multitudes in the heavens a -few are found near enough to exhibit distinct parallactic motions -arising from the revolution of the earth in its orbit, from whence their -distance from the sun has been computed: α Centauri, the brightest star -in the southern hemisphere, is a very remarkable instance. Professor -Henderson at the Cape of Good Hope determined its parallax to be 1ʺ by a -series of observations on its position at opposite periods of the year, -that is, from opposite points in the earth’s orbit. The result was -afterwards confirmed by Mr. Maclear, who found the amount to be 0ʺ·913. -The difference between the two is wonderfully small, considering the -many unavoidable sources of error in the determination of such minute -quantities (N. 230). - -Since no star in the northern hemisphere has so great an amount of -parallax, an arc of 1ʺ is assumed as the parallactic unit. Now radius is -to the sine of 1ʺ as 206,265 is to 1; hence, α Centauri is 206,265 times -more distant from the sun than the sun is from the earth. Light flying -at the rate of 192,000 miles in a second must take 3 years and 83 days -to come to us from that star. - -One or two tenths of a second becomes a very great error when the -maximum amount of parallax is only 1ʺ, and on that account, with the -exception of α Centauri, it has been found impracticable to determine -the annual changes in the apparent motions of single stars affected by -precession, nutation, aberration, and the variations of temperature of -the instruments used in observing. However, as two stars in -juxtaposition are equally affected by all of these; the difference in -their motions is independent of them. Of two stars apparently in close -approximation, one may be far behind the other in space. They may seem -near to one another when viewed from the earth in one part of its orbit, -but may separate widely when seen from the earth in another position, -just as two terrestrial objects appear to be one when viewed in the same -straight line, but separate as the observer changes his position. In -this case the stars would not have real, but only apparent motion. One -of them would seem to oscillate annually to and fro in a straight line -on each side of the other, a motion that could not be mistaken for that -of a binary system where one star describes an ellipse about the other; -or if the edge of the orbit be turned towards the earth, where the -oscillations require years for their accomplishment. The only -circumstances that can affect the stars unequally, and which must be -eliminated, are the proper motion of the stars in space, and specific -aberration, a very minute quantity arising from peculiarities in the -star’s light. This method of finding the distances of the fixed stars -was proposed by Galileo and attempted by Dr. Long without success. Sir -William Herschel afterwards applied it to some of the binary groups; and -although he did not find the thing he sought for, it led to the -discovery of the orbital motions of the double stars. - -M. Struve was the first to apply this method, and that in a very -difficult case. He perceived that a very small star is close to α Lyræ, -and by a series of most accurate differential measurements from 1835 to -1838 he found that α Lyræ has a parallax of 0ʺ·261, which was afterwards -corroborated by the observations of M. Peters; hence α Lyræ is 789,600 -times more distant from the sun than the earth is. - -It was natural to suppose that in general the large stars are nearer to -the earth than the small ones; but there is now reason to believe that -some stars, though by no means brilliant, are nearer to us than others -which shine with greater splendour. This is inferred from the -comparative velocity of their proper motions; all the stars have a -general motion of translation, which tends ultimately to mix those of -the different constellations; but none that we know of moves so rapidly -as 61 Cygni, and on that account it was reckoned to be nearer to us than -any other, for an object seems to move more quickly the nearer it is. -Now M. Bessel saw that two minute and probably very remote stars are -very near 61 Cygni, their directions from that star being at right -angles to one another; so that, during the revolution of the earth, one -of these distances was a maximum and the other a minimum alternately -every three months. This alternation, although it indicated a parallax -or difference of parallaxes of only 0ʺ·348, was maintained with such -perfect regularity every three months, that it leaves not a doubt of its -accuracy, which was afterwards confirmed by the observations of M. -Peters at Polkova. It follows from that small parallax that 61 Cygni -must be 592,700 times farther from the earth than the sun is—a distance -that light would not pass over in less than nine years and three months. - -Mr. Henderson found the parallax of Sirius, the brightest of all the -stars, to be only 0ʺ·230; it is consequently more distant than 61 Cygni, -though the latter is but of the 6th magnitude. - -M. Argelander has calculated that the apparent magnitude of the stars -depends upon their distance. Supposing them all to be of the same size, -the smallest visible in Sir William Herschel’s 20 feet reflecting -telescope, namely those of the 17th magnitude, would be 228 times -farther off than those of the first magnitude; and M. Peters of Polkova -from the annual parallax of thirty-five, seven of which are now very -accurately determined, has ascertained the distance of the nearest of -them to be such, that light flying at the rate of 95 millions of miles -in a second would take 15 years and a half to come from them to the -earth, and that a star of the 17th magnitude might be extinguished for -3541 years before we should be aware of it. (N. 231.) - -The great gulfs that separate the stars from the sun, and probably from -one another, no doubt maintain the stability of the stellar system, in -the same manner that in the solar system the distances of the planets -from the sun and the satellites from their primaries are so arranged as -to preserve their mutual disturbances within due limits. The stars -supposed to be nearest the sun are probably in a great zone which -crosses the Milky Way between η Argûs and α Crucis. It comprises the -bright stars of the constellations Orion, Canis Major, the Southern -Cross, Centaur, Lupus, and Scorpio. The axis of the zone is inclined at -an angle of 20° to the medial line, or circle, passing through the -centre of the Milky Way. - -A very great number of stars undergo periodical changes of lustre, -varying in some cases from complete extinction to their original -brilliancy, strongly suggesting the idea that they are temporarily -obscured, and sometimes completely hid, by opaque bodies revolving round -them in regular periodic times, as the planets do about the sun. - -The star Mira, or ω Ceti, which was first noticed to be periodical by -Fabricius, in 1596, appears about twelve times in eleven years, or in -periods of 331^d 8^h 4^m 16^s; it remains at its greatest brightness -about a fortnight, being then on some occasions equal to a large star of -the second magnitude; then it decreases during about three months, till -it becomes completely invisible to the naked eye, in which state it -remains about five months; after that it continues increasing during the -remainder of its period. Such is the general course of its changes; but -it does not always return to the same degree of brightness, nor increase -and diminish by the same gradations, neither are the successive -intervals of its maxima equal. From the observations and investigations -of M. Argelander, the mean period given is subject to fluctuation, -embracing 88 such periods, and having the effect of gradually -lengthening and shortening alternately those intervals to the extent of -25 days one way and the other. The irregularities in the degree of -brightness attained at the maximum are probably also periodical. For -four years previous to 1676 it did not appear at all; and on October 5, -1839, it exceeded α Ceti, and equalled β Aurigæ, in lustre. These -irregularities may be occasioned by periodical perturbations among -opaque bodies revolving about the star. Algol, or β Persei, is another -very remarkable instance of a variable star. It has the size of a star -of the second magnitude for two days and thirteen and a half hours, and -then suddenly begins to diminish in splendour, till, in about three -hours and a half, it is reduced to the size of a star of the fourth -magnitude; it then begins again to increase, and in three hours and a -half more regains its brightness, going through all these vicissitudes -in 2^d 20^h 48^m 54^s·7. Sir John Herschel and Mr. Goodricke, by -whom the variable nature of this star was discovered in 1782, considered -this to be a case strongly indicative of the revolution of an opaque -body, which, coming between us and Algol, cuts off a large portion of -the light. This star has been constantly observed, and the more recent -observations, compared with the ancient ones, indicated a diminution in -the periodic time. It is even proved that this decrease is not uniformly -progressive, but is actually proceeding with accelerated rapidity, -which, however, will probably not continue, but will by degrees relax, -and then be changed into increase, according to the laws of periodicity, -which, as well as their causes, remain to be discovered. The first -minimum of this star, in 1844, happened on January 3rd, at 4^h 14^m -Greenwich time. γ Hydræ also vanishes and reappears every 494 days. β -Lyræ was discovered to be variable, in 1784, by Mr. Goodricke, and its -period was ascertained by Argelander to be 12^d 21^h 53^m 10^s, in -which time a double maximum and minimum takes place, the two maxima -being nearly equal, but the two minima unequal; besides these -semi-periods, there is a slow aberration of period, which appears to be -periodical itself: from its discovery to 1840 the time was continually -lengthening, but more and more slowly, till, in 1840, it ceased to -increase, and has since been slowly on the decrease. - -The stars δ Cephei and η Aquilæ, or Antinoi, were discovered to be -variable in 1784; their respective periods, being 5^d 8^h 47^m 39^s -and 7^d 4^h 13^m 53^s, have since been accurately determined. -Besides these, the variations of between 30 and 40 have been -approximately ascertained, and a great many more among the smaller stars -have been discovered to be variable by Mr. Hind, who has remarked that -many of those stars which continue visible at their minimum appear hazy -and indistinct, as though some cloudy or nebulous medium intervened. -Some of the variable stars are red, and others present successive -changes through blue, yellow, and red. When the brightness is increasing -the star has a blueish tinge, when it is past its maximum lustre it -assumes a yellow tint, and while on its decrease it becomes ruddy with -flashes of bright red light. These changes are very marked in a small -star near the star 77, at the extremity of the south wing of Virgo. - -Sir John Herschel, after having described the glory of the starry -heavens, asks, “For what purpose are we to suppose such magnificent -bodies scattered through the abyss of space? Surely not to illuminate -_our_ nights, which an additional moon of the thousandth part the size -of our own would do much better, nor to sparkle as a pageant void of -meaning and reality, and bewilder us with vain conjectures. Useful, it -is true, they are to man as points of exact and permanent reference; but -he must have studied astronomy to little purpose who can suppose man to -be the only object of his Creator’s care, or who does not see in the -vast and wonderful apparatus around us provision for other races of -animated beings. The planets, we have seen, derive their light from the -sun, but that cannot be the case with the stars. These doubtless then -are themselves suns, and may perhaps, each in its sphere, be the -presiding centre round which other planets or bodies, of which we can -form no conception from any analogy offered by our own system, may be -circulating.” - -Another circumstance shows how probable it is that dark bodies are -revolving among the stars. The proper motion of Sirius is very -irregular—sometimes it is rapid, and at other times slow; the cause is -ascribed by MM. Bessel and Peters to a dark companion which revolves -with Sirius about their common centre of gravity, and by its attraction -disturbs the equable motion of the star. - -Sometimes stars have all at once appeared, shone with a bright light, -and vanished. Several instances of these temporary stars are on record. -A remarkable one occurred in the year 125, which is said to have induced -Hipparchus to form the first catalogue of stars. Another star appeared -suddenly near α Aquilæ in the year 389, which vanished after remaining -for three weeks as bright as Venus. On the 10th of October, 1604, a -brilliant star burst forth in the constellation of Serpentarius, which -continued visible for a year; and on the 11th of November, 1572, a star -all at once shone forth in Cassiopeia, which rapidly increased in -brightness till it surpassed that of Jupiter so much as to be visible at -midday. It began to decrease in December of the same year, and, in -March, 1574, it had entirely disappeared, having exhibited a variety of -tints. It is suspected, however, that this star is periodically variable -and identical with stars which appeared in the years 945 and 1264. A -more recent case occurred in the year 1670, when a new star was -discovered in the head of the Swan, which, after becoming invisible, -reappeared, and, having undergone many variations in light, vanished -after two years, and has never since been seen. On the 28th of April, -1848, Mr. Hind discovered a star of the 5th magnitude in the -constellation Ophiuchus, which was very conspicuous to the naked eye, -and where he was certain no star even so bright as the 9th magnitude had -ever existed, nor was there any record of such a star. From the time of -its discovery it continued to diminish till it became extinct. Its -colour was ruddy, and was thought to undergo remarkable changes, -probably an effect of its low position, as its polar distance was 102° -39ʹ 14ʺ. - -Sir John Herschel discovered very singular variations in the star η of -the constellation Argo. It is surrounded by a wonderful nebula, and -between the years 1677 and 1826 it varied twice from the 4th to the 2nd -magnitude; but in the beginning of 1838 it suddenly increased in lustre, -so as to be nearly as bright as α Centauri. Thence it diminished, but -not below the first magnitude till April 1843, when it had again -increased, so as to surpass Canopus, and nearly equal Sirius in -splendour. With regard to this singular phenomenon, Sir John Herschel -observes, that “Temporary stars heretofore recorded have all become -totally extinct. Variable stars, as far as they have been carefully -attended to, have exhibited periodical and regular alternations (in some -degree at least) of splendour and comparative obscurity; but here we -have a star fitfully variable to an astonishing extent, and whose -fluctuations are spread over centuries, apparently in no settled period, -and in no regular progression. What origin can we ascribe to these -sudden flashes and relapses? What conclusions are we to draw as to the -comfort or habitability of a system depending for its supply of light -and heat on so variable a source? Its future career will be a subject of -high physical interest. To this account I will only add, that in the -beginning of 1838 the brightness of this star was so great as materially -to interfere with the observations of that part of the nebula -surrounding it.” Sir John has also discovered that α Orionis is -variable, a circumstance the more remarkable as it is one of the -conspicuous stars of our hemisphere, and yet its changes had never been -remarked. The inferences Sir John draws from the phenomena of variable -stars are too interesting not to be given in his own words. “A periodic -change existing to so great an extent in so large and brilliant a star -as α Orionis cannot fail to awaken attention to the subject, and to -revive the consideration of those speculations respecting the -possibility of a change in the lustre of our sun itself, which were -first put forth by my father. If there be really a community of nature -between the sun and the fixed stars, every proof that we obtain of the -extensive prevalence of such periodical changes in those remote bodies -adds to the probability of finding something of the kind nearer home. If -our sun were ever intrinsically much brighter than at present, the mean -temperature of the surface of our globe would of course be -proportionally greater. I speak now not of periodical, but secular -changes. But the argument is complicated with the consideration of the -possible imperfect transparency of space, which may be due to material -non-luminous particles, diffused irregularly in patches analogous to -nebulæ, but of great extent—to cosmical clouds, in short, of whose -existence we have, I think, some indication in the singular and -apparently capricious phenomena of temporary stars, and perhaps in the -recent extraordinary increase, and hardly less sudden diminution, of η -Argûs.” Mr. Hind has come to the same conclusion with Goodricke and Sir -John Herschel, that the changes in the variable stars are owing to -opaque bodies revolving round them; indeed there are strong reasons to -believe that there are solar systems analogous to our own in the remote -regions of space. Our sun requires nine times the period of Algol to -perform a revolution on its axis, while, on the other hand, the periodic -time of an opaque revolving body, sufficiently large to produce a -similar temporary obscuration of the sun seen from a fixed star, would -be less than fourteen hours. - -It is possible that the decrease of light in some of the variable stars -may arise from large spots on their surface, like those occasionally -seen in the radiant fluid masses on the surface of the sun. One of these -spots which was measured by Sir John Herschel on the 20th of March, -1836, with its penumbra, occupied an area of 3780 millions of square -miles; and the black central part of a spot that appeared on the 25th of -May following would have allowed the globe of the earth to drop through -it, leaving a thousand miles clear of contact all around this tremendous -abyss. - -All the variable stars on record of which the places are distinctly -indicated have occurred without exception in, or close upon, the borders -of the Milky Way, and that only within the following semicircle, the -preceding having offered no example of the kind. - -Many stars have actually disappeared from the heavens. 42 Virginis seems -to be of the number, having been missed by Sir John Herschel on the 9th -of May, 1828, and not again found, though he frequently had occasion to -observe that part of the sky. Mr. Cooper, of the Markree Observatory, -has given a list of fifty stars that are missing since the publication -of his list of stars in 1847. Comparing the present state of the heavens -with more ancient catalogues, a much greater number have disappeared. - -Thousands of stars that seem to be only brilliant points of light, when -carefully examined are found to be in reality systems of two or more -suns, many of which are known to revolve about one another. These binary -and multiple systems are very remote, requiring powerful telescopes to -show the stars separately. They are divided into eight classes, -according to the proximity of the two stars. The first class comprises -only such as are less than 1ʺ of space apart; those of the second class -are more apart than 1ʺ and less than 2ʺ, &c. &c. Sometimes the two stars -are of equal magnitude, but more frequently a conspicuous star is -accompanied by a smaller companion. In some cases the conspicuous star -itself is double, as in ζ Cancri, ξ Scorpio, 11 Monocerotis, and 12 -Lyncis, which are triple stars. Each of the two stars of ε Lyræ is a -beautiful and close double star; so that which in a common telescope -appears merely to be a double star, is found to be quadruple with a very -excellent instrument. The multiple system of θ Orionis is one of the -most remarkable objects in our hemisphere. To the naked eye and with an -ordinary telescope it seems to be a single star, but it really consists -of four brilliant stars forming a trapezium, and accompanied by two -excessively minute and very close companions, to perceive _both_ of -which is the severest test of a telescope. - -The first catalogue of double stars in which their places and relative -positions are given was accomplished by the talent and industry of Sir -William Herschel, who made so many great discoveries, and with whom the -idea of their combination in binary and multiple systems originated; and -that important fact he established by the discovery of a revolving -motion in 50 or 60, and by the determination of the revolution of one -star about the other of Castor or α Geminorum, the largest and finest -double star in the northern hemisphere. He even assigned the approximate -periodic times of this and of several other binary systems. More than -100 stars are now known to be stellar systems. The positions of many -hundreds were measured by Sir John Herschel and Sir James South; and the -catalogue of the double stars in the northern hemisphere, which have -been micrometrically measured, has been increased to more than 6000 by -MM. Bessel, Struve, and British astronomers. - -Extensive catalogues of double stars in the southern hemisphere have -been published by the astronomers in our colonial establishments. To -these Sir John Herschel added 1081 during his residence at the Cape of -Good Hope: the angles of position and distances of the stars from one -another he measured, and found that many of them have very rapid orbital -motions. The elliptical elements of the orbits and periodic times of -fifteen have been determined by the most eminent astronomers with -wonderful accuracy, considering the enormous distances and the extreme -delicacy and difficulty of the subject. M. Savary has the merit of -having first determined the elements of the orbit of a double star from -observation. The difficulty of doing so is great, because the nearest -fixed star is 211,000 times farther from the sun than the earth is, and -the orbit itself is only visible with the best telescopes; consequently -a very small error in observation occasions an enormous error in the -determination of quantities at that distance. - -In observing the relative position of the stars of a binary system, the -distance between them, and also the angle of position, that is, the -angle which the meridian, or a parallel to the equator, makes with the -line joining the two stars, are measured. The different values of the -angle of position show whether the revolving star moves from east to -west, or the contrary; whether the motion be uniform or variable, and at -what points it is greatest or least. The measures of the distances show -whether the two stars approach or recede from one another. From these -the form and nature of the orbit are determined. Were observations -perfectly accurate, four values of the angle of position, and of the -corresponding distances at given epochs, would be sufficient to assign -the form and position of the curve described by the revolving star; -this, however, scarcely ever happens. The accuracy of each result -depends upon taking the mean of a great number of the best observations, -and eliminating error by mutual comparison. The distances between the -stars are so minute that they cannot be measured with the same accuracy -as the angles of position; therefore, in order to determine the orbit of -a star independently of the distance, it is necessary to assume, as the -most probable hypothesis, that the stars are subject to the law of -gravitation, and consequently that one of the two stars revolves in an -ellipse about the other, supposed to be at rest, though not necessarily -in the focus. A curve is thus constructed graphically by means of the -angles of position and the corresponding times of observation. The -angular velocities of the stars are obtained by drawing tangents to this -curve at stated intervals, whence the apparent distances, or radii -vectores of the revolving star, become known for each angle of position, -because, by the laws of elliptical motion, they are equal to the square -roots of the apparent angular velocities. Now that the angles of -position estimated from a given line, and the corresponding distances of -the two stars, are known, another curve may be drawn, which will -represent on paper the actual orbit of the star projected on the visible -surface of the heavens; so that the elliptical elements of the true -orbit, and its position in space, may be determined by a combined system -of measurements and computation. But, as this orbit has been obtained on -the hypothesis that gravitation prevails in these distant regions, which -could not be known _à priori_, it must be compared with as many -observations as can be obtained, to ascertain how far the computed -ellipse agrees with the curve actually described by the star. - -γ Virginis consists of two stars of nearly the same magnitude; they were -so far apart in the beginning and middle of last century, that they were -mentioned by Bradley, and marked in Mayer’s catalogue, as two distinct -stars. Since that time they have been continually approaching each -other, till in January, 1836, one star was seen to eclipse the other, by -Admiral Smyth at his Observatory at Bedford, and by Sir John Herschel at -the Cape of Good Hope. A series of observations since the beginning of -the present century has enabled Sir John to determine the form and -position of the elliptical orbit of the revolving star with -extraordinary truth by the preceding method. According to his -calculation, it came to its perihelion on the 18th of August of the year -1834. Its previous velocity was so great that the revolving star -described an angle of 68° in one year. By the laws of elliptical motion -its angular velocity must diminish till it arrives at its aphelion. The -accuracy with which the motions of the binary systems are measured, and -the skill employed in the deduction of the elliptical elements, are now -so great, that the periodic time of γ Virginis, determined by Sir John -Herschel and Admiral Smyth from their respective observatories, combined -with those of Sir William Herschel, only differ by two years, Sir John -having obtained a period of 182 years, Admiral Smyth that of 180. By the -aid of more numerous observations Mr. Fletcher has found that the true -period is 184·53 years, and that the revolving star passed its -perihelion in 1837. It is by such successive steps that astronomy is -brought to perfection (N. 232). - -Some of the double stars have very long periods, such as ς Coronæ, where -the revolving star takes 737 years nearly to accomplish a circuit. -Others again have very short periods, as η Coronæ, ζ Cancri, and ξ Ursæ -Majoris, whose periodic times are 42·500, 58·91, and 58·26 years -respectively: therefore each of these has performed more than one entire -revolution since their motions were observed. ζ Herculis, whose periodic -time is only about 30-1/4 years, has accomplished two complete circuits, -the lesser star having been eclipsed by the greater each time. The first -of these two truly wonderful events, of one sun eclipsing another sun, -was seen by Sir William Herschel in 1782. - -The orbits and periodic times of so many of these binary systems having -been determined proves beyond a doubt that sun revolves about sun in the -starry firmament by the same law of gravitation that makes the earth and -planets revolve about the sun (N. 232). - -Since the parallax of 61 Cygni and that of α Centauri have been -determined, Sir John Herschel has made the following approximation to -the dimensions of their orbits and masses. The distance between the two -stars of 61 Cygni, that is the radius vector of the revolving star, has -hardly varied from 15ʺ·5 ever since the earliest observations; while in -that time the star has moved through 50°; it is evident therefore that -the orbit must be nearly circular. It is at right angles to the visual -ray, and the periodic time is 514 years. The parallax or radius of the -earth’s orbit as seen from the star is 0ʺ·348, while the radius of the -star’s orbit as seen from the earth is 15ʺ·5; hence the radius of the -star’s orbit is to that of the earth’s orbit as 15ʺ·5 to 0ʺ·348, or -nearly as 45 to 1. So the orbit described by the two stars of 61 Cygni -about one another greatly exceeds that which Neptune describes about the -sun. Since the mean distance of the stars and their periodic time are -given, the sum of the masses of the two stars is computed to be 0·3529, -that of the sun being 1. Thus our sun is not vastly greater nor vastly -less than the stars composing 61 Cygni, which is a small inconspicuous -star to the naked eye, not exceeding the 6th magnitude. - -Of all the double stars α Centauri is the most beautiful: it is the -brightest star in the southern hemisphere, equal, if not superior, to -Arcturus in lustre. The distance between the two stars has been -decreasing at the rate of half a second annually since the year 1822, -while the angular motion has undergone very little change, which shows -that the plane of the orbit passes through the earth like the orbits of -44 Boötes, and π Serpentarii; that is to say, the edge of the orbit in -these three stellar systems is presented to the earth, so that the -revolving star seems to move in a straight line, and to oscillate on -each side of its primary. Were this libration owing to parallax, it -would be annual from the revolution of the earth about the sun; but as -years elapse before it amounts to a sensible quantity, it can only arise -from a real orbital motion seen obliquely. In this case five -observations are sufficient for the determination of the orbit, provided -they be exact; but the quantities to be measured are so minute, that it -is only by a very long series of observations that accuracy can be -attained. In 1834 Captain Jacob determined the periodic time of the -revolving star of α Centauri to be 77 years, and the distance between -the two to be 17ʺ·5; and since the decrease is half a second annually, -the distance or radius vector of the revolving star was 12ʺ·5 in the -year 1822; and as Mr. Henderson had determined the parallax or radius of -the earth’s orbit as seen from the star to be ·913, it follows that the -real semi-axis of the revolving star’s orbit is 13-1/2 times greater -than the semi-axis of the earth’s orbit as a minimum. The real -dimensions of the ellipse therefore cannot be so small as the orbit of -Saturn, and may possibly exceed that of Uranus. It is very probable that -an occultation of one of the suns by the other will take place in 1867, -or a very close appulse of the two stars. - -Singular anomalies have appeared in the motions of 70 Ophiuchi, which -was discovered to be a binary system by Sir William Herschel in 1779, -and which has since nearly accomplished a revolution. Various orbits -have been computed: those which best represent the angles of position -fail with regard to the distances of the stars from one another, and -_vice versâ_. But it is a very remarkable fact that the errors are -periodical, being for considerable periods of time alternately in excess -and defect. Captain W. S. Jacob, who determined the periodic time of the -revolving star to be 93 years, attributes this anomaly to the disturbing -action of an opaque body revolving round the lesser star. Assuming that -to be the case, and computing, he found that the errors were -considerably diminished both in the angle of position and distance. It -is a subject of the highest interest, and well worthy of the attention -of such astronomers as have the means of making the necessary -observations. Among the triple systems, as ζ Cancri, two of the stars -revolve about one another in 58·9 years; but the motion of the third and -most distant is so slow, that it has only accomplished a tenth part of -its revolution about the other two since the system was discovered. - -It appears from the calculations of Mr. Dunlop that ς Eridani -accomplishes a revolution in little more than 30 years. The motion of -Mercury is more rapid than that of any of the planets, being at the rate -of 107,000 miles an hour. The perihelion velocity of the comet of 1680 -was 880,000 miles an hour; but, if the two stars of ς Eridani, or of ξ -Ursæ Majoris, be as remote from one another as the nearest fixed star is -from the sun, the velocity of the revolving star must exceed the power -of imagination to conceive. The elliptical motion of the double stars -shows that gravitation is not confined to the planetary motions, but -that systems of suns in the far distant regions of the universe are also -obedient to its laws. The stellar systems present a kind of sidereal -chronometer, by which the chronology of the heavens will be marked out -to future ages by epochs of their own, liable to no fluctuations from -such disturbances as take place in our system. Some stars are apparently -double, though altogether unconnected, one being far behind the other in -space, as α Lyræ, which apparently consists of two stars, one of the -first, the other of the eleventh magnitude. Aldebaran, α Aquilæ, and -Pollux are remarkable instances of these optically double stars. It has -been shown how favourable that circumstance is for ascertaining the -parallax of the nearest of the two. (N. 232.) - -The double stars are of various hues: sometimes both stars are of the -same colour, as in α Centauri and 61 Cygni, where the larger stars are -of a bright orange and the smaller ones a deeper tint of the same, but -they most frequently exhibit the contrasted colours. The large star is -generally yellow, orange, or red; and the small star blue, purple, or -green. Sometimes a white star is combined with a blue or a purple, and -more rarely a red and white are united. In many cases these appearances -are due to the influence of contrast on our judgment of colours. For -example, in observing a double star, where the large one is a full ruby -red, or almost blood colour, and the small one a fine green, the latter -loses its colour when the former is hid by the cross wires of the -telescope. That is the case with γ Andromedæ, which is a triple star, -the small one, which appears green, being closely double. ι Cancri is an -instance of a large yellow star and a small one which appears blue by -contrast. Still there are a vast number where the colours are decidedly -different, and suggest the curious idea of two suns, a red and a green, -or a yellow and a blue, so that a planet circulating round one of them -may have the variety of a red day and a green day, a yellow day and a -blue day. Sir John Herschel observes, in one of his papers in the -Philosophical Transactions, as a very remarkable fact, that, although -red stars are common enough, no example of a solitary blue, green, or -purple star has yet been produced. - -Sirius is the only star on record whose colour has changed. In the time -of Ptolemy it was red; now it is one of the whitest stars in the -heavens. - -M. Struve has found that, out of 596 bright double stars, 375 pairs have -the same intensity of light and colour; 101 pairs have different -intensity, but the same colour; and 120 pairs have the colours of the -two stars decidedly different. - -Certain rays, which exist in the sun’s light, are wanting in the spectra -of every coloured star, and probably never existed in the light of these -stars, as there is no reason to believe that they are absorbed by the -stars’ atmosphere, though they may be by the earth’s. There are no -defective rays in the white light of Sirius, Procyon, and others; but -Sir David Brewster found in the spectrum of the orange-coloured light of -ζ Herculis a defective band in the red space, and two or more in the -blue; consequently, the orange colour of the star is owing to a want of -blue rays; for flames in which certain rays are wanting take the colour -of the predominating rays. If the black rays in the solar spectrum were -owing to the absorption of the sun’s atmosphere, the light from the -margin of his disc, having to pass through a greater thickness of it, -would exhibit deeper lines than that which comes from his centre; but, -as no difference is perceptible, it may be inferred that the analogous -bands in the light of the coloured stars are not due to the absorption -of their atmospheres, but that they arise from the different kinds of -combustion by which these bodies are lighted up. - -All the ordinary methods fail for finding the parallax when the -distances of the stars are very great. An angle even of one or two -seconds, viewed in the focus of our largest telescopes, does not equal -the thickness of a spider’s thread, which makes it impossible to measure -such minute quantities with any degree of accuracy. In some cases, -however, the binary systems of stars furnish a method of estimating an -angle of even the tenth of a second, which is thirty times more accurate -than by any other means. From them the actual distances of some of the -more remote stars will ultimately be known. - -Suppose that one star revolves round another in an orbit which is so -obliquely seen from the earth as to look like an ellipse in a horizontal -position, then it is clear that one-half of the orbit will be nearer to -us than the other half. Now, in consequence of the time which light -takes to travel, we always see the satellite star in a place which it -has already left. Hence, when that star sets out from the point of its -orbit which is nearest to us, its light will take more and more time to -come to us in proportion as the star moves round to the most distant -point in its orbit. On that account the star will appear to us to take -more time in moving through that half of its orbit than it really does. -Exactly the contrary takes place on the other half; for the light will -take less and less time to arrive at the earth in proportion as the star -approaches nearer to us; and therefore it will seem to move through this -half of its orbit in less time than it really does. This circumstance -furnishes the means of finding the absolute breadth of the orbit in -miles, and from that the true distance of the star from the earth. For, -since the greatest and least distances of the satellite star from the -earth differ by the breadth of its orbit, the time which the star takes -to move from the nearest to the remotest point of its orbit is greater -than it ought to be by the whole time its light takes to cross the -orbit, and the period of moving through the other half is exactly as -much less. Hence the difference between the observed times of these two -semi-revolutions of the star is equal to twice the time that its light -employs to cross its orbit; and, as we know the velocity of light, the -diameter of the orbit may be found in miles, and from that its whole -dimensions; for the position of the orbit with regard to us is known by -observation, as well as the place, inclination, and apparent magnitude -of its major axis, or, which is the same thing, the angle under which it -is seen from the earth. Since, then, three things are known in this -great triangle, namely, the base or major axis of the orbit in miles, -the angle opposite to it at the earth, and the angle it makes with the -visual ray, the distance of the satellite star from the earth may be -found by the most simple of calculations. The merit of having first -proposed this very ingenious method of finding the distance of the stars -is due to M. Savary; but, unfortunately, it is not of general -application, as it depends upon the position of the orbit, and a long -time must elapse before observation can furnish data, since the shortest -period of any revolving star that we know of is 30 years. Still the -distances of a vast number of stars may ultimately be made out in this -way; and, as one important discovery almost always leads to another, -their masses may thus be weighed against that of the earth or sun. - -The only data employed for finding the mass of the earth, as compared -with that of the sun, are, the angular motion of our globe round the sun -in a second of time, and the distance of the earth from the sun in miles -(N. 233). Now, by observations of the binary systems, we know the -angular velocity of the small star round the great one; and, when we -know the distance between the two stars in miles, it will be easy to -compute how many miles the small star would fall through by the -attraction of the great one in a second of time. A comparison of this -space with the space through which the earth would descend towards the -sun in a second will give the ratio of the mass of the great star to -that of the sun or earth. According to M. Bessel, the weight of the two -stars of 61 Cygni is equal to half the weight of the sun. Little as we -know of the absolute magnitude of the fixed stars, the quantity of light -emitted by many of them shows that they must be much larger than the -sun. Dr. Wollaston determined the approximate ratio which the light of a -wax candle bears to that of the sun, moon, and stars, by comparing their -respective images reflected from small glass globes filled with mercury, -whence a comparison was established between the quantities of light -emitted by the celestial bodies themselves. By this method he found that -the light of α Lyræ is five and a half times greater than that of the -sun. Sir John Herschel reflected the moon’s light _totally_ by a prism, -which, concentrated by a lens, was compared directly with that of α -Centauri. After making allowance for the quantity of the moon’s light -lost in passing through the lens and prism, he found that the mean -quantity of light sent to the earth by a full moon exceeds that sent by -α Centauri in the proportion of 27,408 to 1. Now, Dr. Wollaston found -the proportion of the sun’s light to that of the full moon to be that of -801,072 to 1. Hence, the light sent to us by the sun is to that sent by -α Centauri as about twenty-two thousand millions to one. But, as the -parallax of α Centauri is 1ʺ, it really is two and a half times brighter -than the sun. The light of Sirius is four times that of α Centauri, but -its parallax is only 0ʺ·230: hence it has an intrinsic splendour 63·02 -times that of our luminary. It is therefore estimated to be a hundred -times as large; so that, were Sirius in the earth’s place, its surface -would extend 150 times as far as the orbit of the moon. The light of -Sirius, according to the observations of Sir John Herschel, is 324 times -greater than that of a star of the sixth magnitude; if we suppose the -two to be really of the same size, their distances from us must be in -the ratio of 57·3 to 1, because light diminishes as the square of the -distance of the luminous body increases. - -So many of the stars have proper motions altogether independent of the -annual rotation of the earth in its orbit, that it may be doubted -whether there be such a thing as a fixed star. Groombridge is the most -rapid known: it has a proper motion of 7ʺ of arc annually; α Centauri -moves at the rate of 3ʺ·58 annually, and 61 Cygni describes a line in -space of 5ʺ·12 in the same time. These motions are probably in curves, -but at the distance of the earth they will appear to be rectilineal for -ages to come. The motion of little more than five seconds of space, -which 61 Cygni describes annually, seems to us to be extremely small; -but at the distance of that star an angle of one second corresponds to -twenty-four millions of millions of miles; consequently the annual -motion of 61 Cygni is 120 millions of millions of miles, and yet, as M. -Arago observes, we call it a fixed star. From the same cause it is -evident that the crowding of the stars in the Milky Way may be apparent -only, and that the stars may be at vast distances from one another, and -no doubt are. - -Were the solar system and the whole of the stars visible to us carried -forward in space by a motion common to all, like ships drifting in a -current, it would be impossible for us, moving with the rest, to -ascertain its direction. Sir William Herschel perceived that a great -part of the motions of the stars is only apparent, arising from a real -motion of the sun in a contrary direction. Among many discrepancies he -found that the stars in the northern hemisphere have a general tendency -to move towards a point diametrically opposite to λ Herculis, which he -attributed to a motion of the solar system in a contrary direction. For -it was evident to him, that the stars, from the effects of perspective -alone, would seem to diverge in the direction to which the solar system -was going, and would converge towards the space it had left, and that -there would be a regularity in these apparent motions which would -hereafter be detected. Since Sir William Herschel’s time the proper -motions of the stars have been determined with much greater accuracy, -and many have been added to the list by comparing the ancient and modern -tables of their places; his views have been established by four of the -greatest astronomers of the age, MM. Lundahles, Argelander, Otto Struve, -and Peters, who have clearly proved the motion of the sun from that of -the stars in the northern hemisphere, and Mr. Galloway has come to the -same conclusion from the motions of the stars in the southern hemisphere -(N. 234). The result is, that the sun, accompanied by all his attendant -planets, is moving at the rate of 422,424 miles—or over a space nearly -equal to his own diameter—in the course of a day, and that the motion is -directed towards a point in a line joining the two stars μ and π -Herculis at a quarter of the apparent distance of these two stars, -reckoning from π Herculis. This investigation was founded upon no law -assumed or observed, such as the circulation of all the stars of our -firmament about a common centre, though philosophers have speculated as -to the probability of such a motion in the sun and stars in the plane of -the Milky Way. Should the sun and his stellar companions be moving in a -nearly circular orbit, the centre of motion would be in the plane -passing through the sun perpendicular to the direction of his motion. -The constellations through which that great circle would pass are -Pisces, Australis, Pegasus, Andromeda, Perseus, &c. M. Argelander is of -opinion that the sun’s orbit is nearly in the plane of the Milky Way, -and, therefore, that its centre must probably be in Perseus, while M. -Mädler places it in the Pleiades, which seems to be inadmissible; but -the data are too uncertain at present to admit of any absolute -conclusion as to the sun’s orbit and the general motion of the stellar -firmament: for though the stars in every region of the sky tend towards -a point in Hercules, it is not yet known whether their motions are -uniform or variable, whether the sun’s motion be gradually changing, and -whether the stars form different independent systems, each having its -own centre of attraction, or if all obey one powerful controlling force -which pervades the whole universe. Accurate observations of the places -of a select number of stars of all dimensions in the Milky Way continued -for a series of years would no doubt decide this point. - -The proper motion of a star combined with the progressive velocity of -light alters the apparent periodic time of the revolving star of a -binary system. If the orbit of a double star be at right angles to the -visual ray, and both the sun and the star at rest, the periodic time of -the revolving star, say of 10,000 days, would always be the same. But if -the centre of gravity of the star were to recede in a direct line from -the sun with the velocity of one tenth of the radius of the earth’s -orbit in a day, then at the end of 10,000 days it would be more remote -from us by 1000 of such radii—a space light would take 57 days to -traverse: hence, although the periodic time of the star would really be -the same, the completion of its period would only be known to us 57 days -after it had taken place, so that the periodic time would appear to us -to be 10,057 days instead of 10,000. Were the star to approach to the -sun by the same quantity instead of receding, the apparent periodic time -would be diminished by 57 days. - -As the sun is only a unit in the stellar system, so the Milky Way, and -all the stars that adorn the firmament of both hemispheres, constitute a -group which is but a unit among the infinite numbers of starry clusters -and nebulæ that are profusely scattered throughout the universe. - -By the aid of a good telescope there may be seen on the clear vault of -heaven, between the stars of our own stellar system, and far in the -depths of space, an immense multitude of objects like comets or clouds -of white vapour of all forms and sizes. Some are mixed with stars, -others are entirely formed of them. Many appear as if they were stellar, -but required a telescope of higher power to resolve them, and vast -numbers appear to be matter rarefied in the highest possible degree, -giving no indication of a stellar nature; and these are in every state -of condensation, from a vague film hardly to be discerned to such as -have actually arrived at a solid nucleus of stars. The cloudy appearance -is merely the blending of the rays of innumerable stars which are -themselves invisible from their extreme distance, like parts of the -Milky Way. Sir William Herschel was at first of that opinion, and the -nebulæ that have been resolved by Lord Rosse’s telescope have led -astronomers to believe that such is the case. Yet the tails of comets, -the zodiacal light, and the extensive luminous atmospheres which -encompass many of the stars, show that, in all probability, a -self-luminous phosphorescent material substance in a highly diluted or -gaseous form exists in vast abundance. - -The number of the nebulæ, like that of the stars, is only limited by the -imperfection of our instruments, for each improvement in the telescope -only enables us to penetrate a little farther into the infinity of -space—to see a few more of these shadowy existences in the far distance, -and to resolve a few more of those that are comparatively near. Sir -William Herschel examined the nature and determined the position of 2500 -nebulæ in the northern hemisphere whose places were computed from his -observations, reduced to a common epoch, and arranged into a catalogue, -in order of right ascension, by his sister, Miss Caroline Herschel, who -added lustre to the name she bore by her eminence in astronomical -knowledge and discovery. Sir John Herschel revised his father’s -observations, and added 800 nebulæ to the catalogue before he went to -the Cape of Good Hope, in order to complete the survey of the heavens. -On his return he published a catalogue of 2049 nebulæ of the southern -hemisphere, of which 500 were previously unknown, with their position in -the heavens. In a work unparalleled for elegance of style, depth of -knowledge, and originality of views, he has given engravings from his -drawings of the most remarkable objects, so that whatever changes may -take place in their form, place, or condensation, will be known by -astronomers of future ages. - -Though infinite in variety, the nebulæ are of two distinct classes; one -consists of patches of great dimensions, capriciously irregular, -assuming all the fantastic forms of clouds, now bright, now obscure; -sometimes like vapour flying before the wind; sometimes stretching long -arms into space. Many present an ill-defined surface, in which it is -difficult to say where the centre of the greatest brightness is. Large -portions are resolvable into stars; many have a granulated appearance, -as if they were resolvable; and others probably are not so merely from -the smallness and closeness of the stars, and possibly from their -remoteness, indicating the complex and irregular form the Milky Way -would present if seen from a distance. A wonderful nebula of this kind -is visible to the naked eye in the constellation of Orion; it is of vast -extent, sending branches even into the southern hemisphere; and, -although Lord Rosse’s telescope has resolved much that had hitherto -resisted others, there are parts that still maintain their nebulous -appearance from extreme remoteness, presenting a kind of mottled aspect, -like flocks or wisps of wool, or mackerel sky. There can be no doubt of -its being an unfathomable congeries of stars, which there is reason to -believe has changed its form in some parts within the last fifty years. -Vast multitudes of nebulæ of this kind are so faint as to be with -difficulty discerned at all till they have been for some time in the -field of the telescope, or are just about to quit it. Occasionally they -are so vague, that the eye is conscious of something being present, -without being able to define what it is; but the unchangeableness of its -position convinces the mind that it is a real object—“an image was -before mine eyes, but I could not discern the form thereof.” - -No drawing can give an idea of the boundaries of such nebulæ as that of -Orion; even with Lord Rosse’s telescope the edges either fade into a -luminous mist, which becomes more rare till it is imperceptible, or end -in a tissue of faintish flocculi, or in filaments which become finer and -more scattered till they cease to be visible, showing that the real -boundaries have not been seen. - -The other class of nebulæ, vastly inferior in size, of definite forms -and great variety of character, are scattered through the remote -heavens, or congregated in a great nebulous district far from the Milky -Way. Many cling to stars like wisps of clouds, others are exactly like -comets with comæ and tails; but the most definite forms are annular and -lenticular nebulæ, nebulous stars, planetary and elliptical nebulæ, and -starry clusters. However, there are two in the northern hemisphere -differing from all of these, which are described by Sir John Herschel as -amazing objects. One in Vulpecula is like an hourglass or dumb bell of -bright matter, surrounded by a thin hazy atmosphere so as to give the -whole an oval form, or the appearance of an oblate spheroid; with a -higher optical power its form is much the same, but the brighter part is -resolved into stars, and the hazy part, though still nebulous, assumes -that mottled appearance which shows that the whole is a stellar system -of the most peculiar structure: it is a phenomenon that bears no -resemblance to any known object. (Fig. 3, plate 8, and fig. 3, plate 9). -The other is indeed most wonderful, and its history shows the gradual -increase in the space-penetrating power of telescopes. To Messier it -appeared merely to be a double nebula with stars; with Sir William -Herschel’s telescope it presented the appearance of a bright round -nebula encompassed at a little distance by a halo or glory, and -accompanied by a companion; while in Sir John Herschel’s 20 feet -reflector it appeared to “consist of a bright round nucleus, surrounded -at a distance by a nebulous ring split through half its circumference, -and having the split portions separated at an angle of 45 degrees each -to the plane of the other.” (Fig. 1, plate 10.) This nebula appeared to -Sir John to “bear a strong similitude to the Milky Way, suggesting the -idea of a brother system bearing a real physical resemblance and strong -analogy of structure to our own.” - -This object, which disclosed to Lord Rosse the astonishing phenomenon of -spiral nebulæ seen in his telescope, presents the appearance of the fig. -1 in plate 10, in which the partial division of the limb of the ring -into two branches is at once recognised in the bright convolutions of -the spiral. The outlying nebula is connected by a narrow curved band of -light with the ring; the whole is either resolved into stars, or -evidently might be with a still higher optical power. With regard to the -marvellous nebula in question Lord Rosse observes, that “with each -increase of optical power the structure has become more complicated, and -more unlike anything that could result from any form of a dynamical law -of which we find a counterpart in our system. The connection of the -companion with this great nebula, of which there is not the least doubt, -adds to the difficulty of forming any hypothesis. It is impossible that -such a system could exist without internal movement, to which may be -added a resisting medium; but it cannot be regarded as a case of mere -static equilibrium.” This is by no means the only instance of a spiral -nebula; Lord Rosse has discovered several others: some are easily -seen—others require the highest powers of his telescope. From the -numerous offsets that branch from the Milky Way and run far into space, -it may possibly partake also of the spiral form. - -There are seven annular nebulæ in the northern hemisphere, since Lord -Rosse has discovered that five of the planetary nebulæ belong to this -class. One of the finest examples of an annular nebula is to be seen -midway between β and γ Lyræ (fig. 2, plate 9). According to Sir John -Herschel, it is elliptical in the ratio of 4 to 5, and is sharply -defined—the internal opening occupying about half the diameter. This -opening is not entirely dark, but filled with a faint hazy light like -fine gauze stretched over a hoop. Its diameter, if it is as far from us -as 61 Cygni, must be 1300 times greater than the diameter of the earth’s -orbit—dimensions that are most astounding. Lord Rosse’s telescope -resolves this object into stars of extreme minuteness, with filaments of -stars adhering to its edges and a pretty bright star in its interior. -These rings are like hollow shells whose borders seem brighter because -the nebulous substance, whatever it may be, is more condensed to -appearance than the central part. The other annular nebula in the -northern hemisphere described by Sir John Herschel is a small faint -object, and more easily resolvable into stars. One of the annular nebulæ -seen by Lord Rosse is surrounded by a faint external flat ring; another -has ansæ, as if an annular nebulous ring encompassed it and was -foreshortened. Two annular nebulæ have perforations as if the black sky -was seen through openings in the interior haze, for in no instance is -the central opening quite dark. - -Some nebulæ are like very elliptical annular systems seen obliquely. If -they be elliptical flat rings, the dark centre may be a real opening; -but should the systems be a series of very long elliptical concentric -shells surrounding a hollow, the dark axis may be merely a line of -comparative darkness. - -The connection of the elliptical nebulæ with double stars is mentioned -as very remarkable. In one elliptical nebula whose longer axis is 50ʺ -there are two individuals of a double star each of the 10th magnitude -symmetrically placed rather nearer the vertex of the ellipse than the -foci; in another the stars are unequal, but placed exactly at the -extremities of the major axis, as in plate 8: besides these there are -several other instances. - -Double nebulæ are not unfrequent in both hemispheres, exhibiting all the -varieties of distance, position, and relative brightness, with their -counterparts the double stars. The rarity of single nebulæ as large, -faint, and as little condensed in the centre as these, makes it -extremely improbable that two such bodies should be accidentally so near -as to touch, and often in part to overlap each other, as these do. It is -much more likely that they constitute systems; and, if so, it will form -an interesting object of future inquiry to discover whether they possess -orbital motion. - -Nebulous stars are beautiful objects, quite different from all the -preceding. They are round or oval, increasing in density towards the -centre. Sometimes the central matter is so vividly and sharply condensed -and defined that the nebula might be taken for a bright star surrounded -by a thin atmosphere. One is a star of the 8th magnitude exactly in the -centre of a round bright atmosphere 25ʺ in diameter; the star is quite -stellar, and not a nucleus: it has not the smallest appearance of being -resolvable. Another nebulous star is ι Orionis, which has a broad -atmosphere in which is a dark cavity not symmetrical with the star, and -a small double star with a similar opening on the edge of the -atmosphere. Lord Rosse observes that these openings appear to be of the -same nature with that within the bright stars in the trapezium of Orion, -the stars being at its edge; and he is convinced that the stars are not -only connected with the nebula, but that they are equidistant with it; -hence, if their parallax can be found, the distance of this nebula would -be determined. The zodiacal light or lenticular shaped luminous haze -surrounding the sun which may be seen extending beyond the orbits of -Mercury and Venus soon after sunset in the months of April and May, or -before dawn in November and December, seems to place our luminary in the -class of nebulous stars. The extensive and delicate atmosphere of these -nebulous stars assumes all degrees of ellipticity, from the circular to -the spindle-shaped ray, or almost the right line. - -Planetary nebulæ have exactly the appearance of planets with round or -oval discs, sometimes sharply terminated, at other times hazy and -ill-defined. Their surface, which is blue or blueish white, is equable -or slightly mottled, and their light occasionally rivals that of the -planets in vividness. They are generally attended by minute stars, which -give the idea of accompanying satellites. These nebulæ are of enormous -dimensions. One near γ Aquarii has a sensible diameter of about twenty -seconds, and another presents a diameter of twelve. Sir John Herschel -has computed that, if these objects be as far from us as the stars, -their real magnitude, on the lowest estimation, must be such as would -fill the orbit of Uranus. He concludes that, if they be solid bodies of -a solar nature, their intrinsic splendour must be far inferior to that -of the sun, because a circular portion of the sun’s disc subtending an -angle of twenty seconds would give a light equal to that of a hundred -full moons; while, on the contrary, the objects in question are hardly, -if at all, visible to the naked eye. From the uniformity of the discs of -these planetary nebulæ, and their apparent want of condensation, he -presumes that they may be hollow shells emitting light from their -surface only. The southern hemisphere is very rich in them, where -twenty-eight or twenty-nine have been discovered, some in the midst of a -cluster of stars, with which they form a beautiful contrast. Three are -of a decided blue colour, one Prussian blue, or verditer green, the -other two of a bright sky blue, of great beauty and delicacy. One seems -to belong to the class of double nebulæ or double stellar nebulæ of the -utmost remoteness. Since Lord Rosse’s telescope has shown that five of -the planetary nebulæ are annular, some of those in the southern -hemisphere may ultimately be found to belong to the same class. - -Probably nine tenths at least of the nebulous contents of the heavens -consist of spherical or elliptical forms presenting every variety of -elongation and central condensation. Of these a great number have been -resolved into stars, and a great many present that mottled appearance -which renders it certain that an increase of optical power would -decompose them. Those which resist do so on account of the smallness and -closeness of the stars of which they consist. - -Elliptical nebulæ are very common; by much the finest may be seen near -the star υ in the girdle of Andromeda. It is visible to the naked eye, -and has frequently been taken for a comet. With a low optical power it -has the spindle-shaped form of fig. 6, plate 5, the brightness being at -first gradually and then rapidly condensed towards the centre, so that -it has been compared to a star shining through horn, but had never -appeared resolvable even with high optical powers till Mr. Bond examined -it at the observatory of Cambridge in the United States. He found that -its brightness extends over 2-1/2 degrees in length, and more than a -degree in breadth, including two small adjacent nebulæ, so that it is -oval. It is strongly and rapidly condensed into a nucleus on its -northern side; and although it was not all resolved, it was seen to be -strewed over with star dust, or extremely minute visible stars, which -leaves not a doubt of its being a starry system. The most remarkable -part of Mr. Bond’s discovery are two very narrow dark lines which extend -along one side of the oval parallel to its major axis. These black -streaks, difficult to distinguish, indicate a stratified structure, and -are not the only instance of that arrangement in nebulæ. Fig. 1, in -plate 9, is from Mr. Bond’s drawing of this nebula. - -Multitudes of nebulæ appear to the unassisted eye, or are seen with -ordinary telescopes, like round comets without tails; but when viewed -with powerful instruments they convey the idea of a globular space, -insulated in the heavens and full of stars, constituting a family or -society apart from the rest, subject only to its own internal laws. To -attempt to count the stars in one of these globular clusters, Sir John -Herschel says, would be a vain task; they are not to be reckoned by -hundreds. On a rough computation, it appears that many clusters of this -description must contain ten or twenty thousand stars compacted and -wedged together in a round space, whose apparent area is not more than a -tenth part of that covered by the moon; so that its centre, where the -stars are seen projected on each other, is one blaze of light. If each -of these stars be a sun, and if they be separated by intervals equal to -that which separates our sun from the nearest fixed star, the distance -which renders the whole cluster barely visible to the naked eye must be -so great, that the existence of such a splendid assemblage can only be -known to us by light which must have left it at least a thousand years -ago. These magnificent globular or spheroidal aggregates of stars are so -arranged that the interior strata are more crowded and become more -nearly spherical as they approach the centre. A most splendid object of -this nature may be seen in the constellation Hercules (N. 235). - -Of 131 of these magnificent objects in the southern hemisphere, two of -them are pre-eminently splendid. The globular cluster of α Centauri is -beyond comparison the finest of its kind: it is perfectly spherical, and -occupies a quarter of a square degree; the stars in it are literally -innumerable, crowding and densely aggregated towards the centre; and, as -its light is not more to the naked eye than that of a star of the 4th or -5th magnitude, their minuteness is extreme. It has a dark hole in its -centre, with a bridge of stars across,—a circumstance peculiar to this -cluster. - -Lacaille’s globular cluster, or 47 Toucani, is completely insulated in a -very dark part of the sky not far from the lesser of the Magellanic -clouds. The stars, which are of the 14th magnitude, immensely numerous, -compressed and white, form three distinct stages round a centre, where -they suddenly change in hue, and form a blaze of rose-coloured light. -One cluster consists of large ruddy stars and small white ones; another -of greater beauty consists of shells or coats of stars of the 11th and -15th magnitude. There are thirty globular clusters of extreme beauty -collected within a circular space of not more than eighteen degrees -radius, which lies in the part of the sky occupied by the constellations -Corona Australis, the body and head of Sagittarius, the tail of Scorpio, -part of Telescopium and Ara. The Milky Way passes diametrically across -the circular area in question, which gives prodigious brilliancy to this -part of the sky. For besides these globular clusters, which all lie in -the starry part, and not in the dark spaces, there are the only two -annular nebulæ known to exist in the southern hemisphere. No part of the -heavens is fuller of objects beautiful and remarkable in themselves, and -rendered still more so by their mode of association, and by the peculiar -features assumed by the Milky Way, which are without a parallel for -richness and magnificence in any other part of the sky. Some of the -globular clusters are so remote that the stars are scarcely -discernible—mere star dust. There is a double globular cluster in the -southern hemisphere of very small dimensions, separated by a minute -interval,—a combination which suggests the idea of a globular cluster -revolving about a very oblate spheroidal one in the plane of the -equator, and in an orbit which is circular, and seen obliquely like the -central nebula itself, with a diameter somewhat more than four times the -latter,—a stupendous system doubtless, but of which the reality can -hardly be supposed improbable. - -There appears to be some connexion between ellipticity of form and -difficulty of resolution, for spherical clusters are in general easily -resolved into their component stars, while there is scarcely an instance -of an elliptical cluster yielding except to a very high optical power. -Vast masses of the nebulæ have never been resolved. Lord Rosse’s great -telescope has resolved parts of the nebula of Orion, and various others -which had not yielded to instruments of less power; it enables the -astronomer to penetrate farther into space, and shows objects with -greater clearness, than any other. But, excellent as this instrument is, -thousands of nebulæ are not to be resolved even by it. Those who imagine -that any work of man can resolve all the nebulous matter in the heavens -must have a very limited idea of the extent and sublimity of creation. - -Innumerable nebulæ in both hemispheres take the form of clusters of -stars, but are totally different from the globular clusters, inasmuch as -they are of irregular form and follow no uniform law of condensation. -The Pleiades is an instance in our own stellar system; for although only -7 or 8 stars are visible to the naked eye, telescopes show that more -than 200 belong to the group. In the constellation Cancer there is a -luminous spot called the Præsepe or Beehive, which a very low power -resolves into stars; and the constellation Coma Berenices is another -stellar group. Many are of exquisite beauty, as that round α Crucis, -which, though consisting of only a hundred and ten stars, is like a -piece of fancy jewellery, from the colours of the stars, which are -greenish white, green, blueish green, and red. Many of these clusters -contain thousands of stars, and are frequently in the poorer parts of -the sky, as if in the course of ages the stars had been attracted -towards a centre. - -The existence of every degree of ellipticity in the nebulæ—from long -lenticular rays to the exact circular form—and of every shade of central -condensation, from the slightest increase of density to apparently a -solid nucleus—may be accounted for by supposing the general -constitutions of those nebulæ to be that of oblate spheroidal masses of -every degree of flatness from the sphere to the disc, and of every -variety in their density and ellipticity towards the centre. It would be -erroneous, however, to imagine that the forms of these systems are -maintained by forces identical with those already described, which -determine the form of a fluid mass in rotation; because, if the nebulæ -be only clusters of separate stars, as in the greater number of cases -there is every reason to believe them to be, no pressure can be -propagated through them. Consequently, since no general rotation of such -a system as one mass can be supposed, it may be conceived to be a -quiescent form, comprising within its limits an indefinite number of -stars, each of which may be moving in an orbit about the common centre -of the whole, in virtue of a law of internal gravitation resulting from -the compound gravitation of all its parts. Sir John Herschel has proved -that the existence of such a system is not inconsistent with the law of -gravitation under certain conditions. - -The distribution of the nebulæ over the heavens is even more irregular -than that of the stars. In some places they are so crowded together as -scarcely to allow one to pass through the field of the telescope before -another appears, while in other parts hours elapse without a single -nebula occurring. They are in general only to be seen with the best -telescopes, and are most abundant in a zone whose general direction is -not far from the hour circles 0^h and 12^h, and which crosses the -Milky Way nearly at right angles. Where that nebulous zone passes over -the constellations Virgo, Coma Berenices, and the Great Bear, they are -to be found in multitudes. - -The nebulous system is nearly divided into two parts by the Milky Way. -One-third of the whole visible nebulous contents of the heavens forms a -broad irregular mass, interspersed with vacant intervals, which fills -about an eighth of the surface of the northern hemisphere. It occupies -the constellations Leo, Leo Minor, the body, tail, and hind legs of Ursa -Major, the nose of Camelopard, the point of the tail of Draco, Canis -Venatica, Coma Berenices, the preceding leg of Boötes, and the head, -wings, and shoulder of Virgo, which is the richest part. There is a -lesser nebulous region in this hemisphere, but entirely separated from -the preceding, which occupies the chest and wing of Pegasus, the -constellations Pisces and Andromeda. If we could imagine the ring or -zone of the Milky Way to encircle or coincide with the horizon, the -great nebulous mass would form a canopy over head, descending down to a -considerable distance on all sides, chiefly towards the north pole; and -the richest part, which is in Virgo, would then be directly over head in -the north pole of the Milky Way, that is in 12^h 47^m right ascension, -and 64° north polar distance. - -With the exception of the Magellanic clouds, there is a much greater -uniformity in the distribution of the nebulæ in the southern hemisphere -than in the northern. They are separated by spaces of vacuity of greater -or less dimensions. One of these barren regions extends for nearly -fifteen degrees all around the south pole, and close on its border; the -lesser of the Magellanic clouds occurs completely insulated; while the -greater Magellanic cloud is in connexion with something approaching to a -zone of connected nebulous patches which extends along the back of -Doradus, through a portion of Horologium and Eridanus, part of Fornix, -and over the paws of Cetus to the equator, where it unites with the -nebulous regions of Pisces. - -The Magellanic clouds form two of the most striking features in the -southern hemisphere; both of these nebulæ are visible to the unassisted -eye, being nearly of the same intensity as the brighter portions of the -Milky Way; but the smaller is entirely effaced by moonlight, and the -larger nearly so. They are altogether unconnected with the Milky Way and -with one another. The Nubecula Major is far superior to the Nubecula -Minor in every respect, though they are similar in internal structure. -The former consists of large tracts and ill-defined patches of -irresolvable nebulæ, and nebulosity in every stage of resolution, up to -perfectly resolved stars like the Milky Way; and also of regular and -irregular nebulæ, properly so called; of globular clusters in every -stage of resolvability; and of clustering groups sufficiently insulated -and condensed to come under the designation of clusters of stars. Of -these the nebula known as Lacaille’s 30 Doradus is too remarkable to be -passed over. It is very large, situate within the Nubecula Major, and -consists of an assemblage of nearly circular loops uniting in a centre, -in or near which there is a circular black hole. In short, for the -number and variety of the objects, there is nothing like this cloud. -Within an area of only forty-two square degrees, Sir John Herschel has -determined the places, and registered 278 nebulæ and clusters of stars, -with fifty or sixty in outlying members immediately adjacent. Even the -most crowded parts of the stratum of Virgo, in the wing of that -constellation, or in Coma Berenices, offer nothing approaching to it. It -is evident, from the intermixture of stars and unresolved nebulosity, -which probably might be resolved with a higher optical power, that the -nubeculæ are to be regarded as systems _sui generis_, to which there is -nothing analogous in our hemisphere. - -Next to the Magellanic clouds the great nebula round η Argûs is one of -the most wonderful objects of the southern sky. It is situate in that -part of the Milky Way which lies between the Centaur and the body of -Argus, in the midst of one of those rich and brilliant masses, a -succession of which is so curiously contrasted with the profoundly dark -adjacent spaces, and surrounded by one of the most beautiful parts of -the southern heavens. Sir John Herschel says: “It would be impossible, -by verbal description, to give any just idea of the capricious forms and -irregular gradations of light affected by the different branches and -appendages of this nebula. Nor is it easy for language to convey a full -impression of the beauty and sublimity of the spectacle it offers when -viewed in a sweep, ushered in as it is by so glorious and innumerable a -procession of stars, to which it forms a sort of climax, justifying -expressions which, though I find them written in my journal in the -excitement of the moment, would be thought extravagant if transferred to -these pages. In fact, it is impossible for any one, with the least spark -of astronomical enthusiasm about him, to pass soberly in review with a -powerful telescope, and on a fine night, that portion of the southern -sky which is comprised between the 6th and 13th degrees of right -ascension, and from 146° to 149° of north polar distance; such are the -variety and interest of the objects he will encounter, and such the -dazzling richness of the starry ground on which they are represented to -his gaze.” In that portion of the sky there are many fine double -stars—rich starry clusters; the elegant cluster of variously coloured -stars round κ Crucis; a large planetary nebula with a satellite star; -another of a bright blue colour, exquisitely beautiful and unique; and, -lastly, η Argûs itself, the most extraordinary instance of a variable -star in astronomical history. - -It frequently occurred, during Sir John Herschel’s survey of the -southern heavens, that some parts of the sky were noted for deeper -blackness than others, and no stars could be seen; it frequently -happened that far from the Milky Way, or any large nebula or cluster of -stars, there were some indications of very remote branches of the Milky -Way, or of an independent sidereal system or systems, bearing a -resemblance to such branches. These were indicated by an exceedingly -delicate and uniform dotting or stippling of the sky by points of light -too small to admit of any one of them being steadily and fixedly viewed, -and too numerous to be counted even if possible to view them. The truth -of this existence was felt at the moment of observation; but the -conviction, though often renewed, was not permanent. The places where -these appearances occurred are given, in order that those who wish to -verify them may have it in their power. - -Such is a brief account of a very few of the discoveries contained in -Sir John Herschel’s great work on the Nebulæ and other Phenomena of the -Southern Hemisphere,—a work which will rise in estimation with the lapse -of years. No doubt the form and internal structure of many of these -nebulæ will be changed by telescopes of higher power; but as the places -of the leading phenomena have been determined, the date of that great -work may be regarded as the epoch of nebular time whence the relative -changes that take place in the most distant regions of the universe will -be estimated for ages to come; and in the inimitable writings of the -highly gifted father and son the reader will find these subjects treated -of in a style worthy of it and of them. Of late years the excellence of -the instruments, and still more of the astronomers, in the foreign -observatories, have aided the progress of sidereal astronomy immensely. -Nor has it been cultivated with less success in our home and colonial -establishments: certainly one of the most remarkable features of the -times is the number of private observatories, built and furnished with -the best instruments by private gentlemen, whose zeal has been rewarded -by eminent success in all departments of the science. (N. 236.) - -So numerous are the objects which meet our view in the heavens, that we -cannot imagine a point of space where some light would not strike the -eye;—innumerable stars, thousands of double and multiple systems, -clusters in one blaze with their tens of thousands of stars, and the -nebulæ amazing us by the strangeness of their forms and the -incomprehensibility of their nature, till at last, from the limit of our -senses, even these thin and airy phantoms vanish in the distance. If -such remote bodies shone by reflected light, we should be unconscious of -their existence. Each star must then be a sun, and may be presumed to -have its system of planets, satellites, and comets, like our own; and, -for aught we know, myriads of bodies may be wandering in space unseen by -us, of whose nature we can form no idea, and still less of the part they -perform in the economy of the universe. Even in our own system, or at -its farthest limits, minute bodies may be revolving like the telescopic -planets, which are so small that their masses have hitherto been -inappreciable, and there may be many still smaller. Nor is this an -unwarranted presumption; many such do come within the sphere of the -earth’s attraction, are ignited by the velocity with which they pass -through the atmosphere, but leave no residuum. These, which are known as -falling stars and meteors, are periodical; but that is by no means the -case with aërolites, which are also ignited by the sudden condensation -of the air on entering our atmosphere, and are precipitated in solid -masses with such violence on the earth’s surface that they are often -deeply buried in the ground. - -The fall of meteoric stones is much more frequent than is generally -believed. Hardly a year passes without some instances occurring; and, if -it be considered that only a small part of the earth is inhabited, it -may be presumed that numbers fall in the ocean, or on the uninhabited -part of the land, unseen by man. They are sometimes of great magnitude; -the volume of several has exceeded that of the planet Ceres, which is -about 70 miles in diameter. One which passed within 25 miles of us was -estimated to weigh about 600,000 tons, and to move with a velocity of -about 20 miles in a second; a fragment of it alone reached the earth. -The obliquity of the descent of meteorites, the peculiar substances they -are composed of, and the explosion accompanying their fall, show that -they are foreign to our system; but whence derived is still a mystery. - -Shooting stars and meteors burst from the clear azure sky, and, darting -along the heavens, are extinguished without leaving any residuum except -a vapour-like smoke, and generally without noise. Their parallax shows -them to be very high in the atmosphere, sometimes even beyond its -supposed limit, and the direction of their motion is for the most part -diametrically opposite to the motion of the earth in its orbit. The -astonishing multitudes of shooting stars and fire-balls that have -appeared at stated periods over different parts of the globe, warrant -the conclusion that there is either a nebula or that there are myriads -of bodies revolving in groups round the sun which only become visible -when inflamed by entering our atmosphere. - -One of these nebulæ or groups seems to meet the earth in its annual -revolution on the 12th and 13th of November. - -On the morning of the 12th of November, 1799, thousands of shooting -stars, mixed with large meteors, illuminated the heavens for many hours -over the whole continent of America, from Brazil to Labrador: it -extended to Greenland, and even Germany. Meteoric showers were seen off -the coast of Spain, and in the Ohio country, on the morning of the 13th -of November, 1831; and during many hours on the morning of the 13th -November, 1832, prodigious multitudes of shooting stars and meteors fell -at Mocha on the Red Sea, in the Atlantic, in Switzerland, and at many -places in England. But by much the most splendid meteoric shower on -record began at nine o’clock in the evening of the 12th of November, -1833, and lasted till sunrise next morning. It extended from Niagara and -the northern lakes of America to the south of Jamaica, and from 61° of -longitude in the Atlantic to 100° of longitude in central Mexico. -Shooting stars and meteors, of the apparent size of Jupiter, Venus, and -even the full moon, darted in myriads towards the horizon, as if every -star in the heavens had started from their spheres. They are described -as having been frequent as flakes of snow in a snow-storm, and to have -been seen with equal brilliancy over the greater part of the continent -of North America. - -Those who witnessed this grand spectacle were surprised to see that -every one of the luminous bodies, without exception, moved in lines -which converged in one point in the heavens: none of them started from -that point; but their paths, when traced backwards, met in it like rays -in a focus, and the manner of their fall showed that they descended from -it in nearly parallel straight lines towards the earth. - -By far the most extraordinary part of the whole phenomenon is, that this -radiant point was observed to remain stationary near the star γ Leonis -for more than two hours and a half, which proved the source of the -meteoric shower to be altogether independent of the earth’s rotation, -and its parallax showed it to be far above the atmosphere. - -As a body could not be actually at rest in that position, the group or -nebula must either have been moving round the earth or the sun. Had it -been moving about the earth, the course of the meteors would have been -tangential to its surface; whereas they fell almost perpendicularly, so -that the earth in its annual revolution must have met with the group. -The bodies or the parts of the nebula that were nearest must have been -attracted towards the earth by its gravity, and, as they were estimated -to move at the rate of fourteen miles in a second, they must have taken -fire on entering our atmosphere, and been consumed in their passage -through it. - -As all the circumstances of the phenomena were similar on the same day -and during the same hours in 1832, and as extraordinary flights of -shooting stars were seen at many places both in Europe and America on -the 13th of November, 1834, 1835, and 1836, tending also from a fixed -point in the constellation Leo, it has been conjectured, with much -apparent probability, that this nebula or group of bodies performs its -revolution round the sun in a period of about 182 days, in an elliptical -orbit, whose major axis is 119 millions of miles; and that its aphelion -distance, where it comes in contact with the earth’s atmosphere, is -about 95 millions of miles, or nearly the same with the mean distance of -the earth from the sun. This body must have met with disturbances after -1799, which prevented it from encountering the earth for 32 years, and -it may again deviate from its path from the same cause. - -It is now well ascertained that great showers of shooting stars occur -also on the 12th of August, whose point of divergence is β -Camelopardali, so that the earth’s atmosphere comes into contact with a -zone of these small bodies twice in the year. By a systematic series of -observations, MM. Benzenberg and Brand have clearly made out that the -heights at which the falling stars appear and vanish vary from 16 miles -to 140, and their velocities from 18 to 36 miles in a second, velocities -so great as certainly to indicate a planetary revolution round the sun. -As shooting stars are seen almost every night when the sky is clear, Sir -John Lubbock has thought it probable that some of these bodies may have -come so near, that the attraction of the earth has overcome that of the -sun, and caused them to revolve as satellites round it. Should that be -the case, they might shine by the reflected light of the sun, and -suddenly cease to be visible on entering the earth’s shadow. The -splitting of the falling stars like a rocket, and the trains of light, -may be accounted for by supposing the stars to graze the surface of the -shadow before being eclipsed; and the disappearance would be more or -less rapid according to the breadth of the penumbra traversed. The -calculations of M. Petit, Director of the Observatory of Toulouse, not -only render probable the existence of small satellites, but tend to -establish the identity of a body revolving round the earth in three -hours and twenty minutes, at a distance of 5000 miles above its surface. -It is evident that in this case the same satellite would be seen very -often, and a very few would be sufficient to account for their nightly -appearance. It is possible, however, that some shooting stars may belong -to one class, and some to the other, since one group may be revolving -about the sun, and another round the earth. In the case of a satellite -shooting star, geometry furnishes the means of ascertaining its exact -distance from the spectator, or from the centre of the earth, if the -time and place of its disappearance be known with regard to the -neighbouring stars. Since the falling stars are consumed in the -atmosphere, their masses must be small, but it is possible that -occasionally one may be large enough to arrive at the surface of the -earth as an aërolite. - - - - - 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. - - -THE known quantity of matter bears a very small proportion to the -immensity of space. Large as the bodies are, the distances which -separate them are immeasurably greater; but, as design is manifest in -every part of creation, it is probable that, if the various systems in -the universe had been nearer to one another, their mutual disturbances -would have been inconsistent with the harmony and stability of the -whole. It is clear that space is not pervaded by atmospheric air of such -density as that we breathe, since its resistance would long ere this -have arrested the motion of the planets: it certainly is not a void, but -replete with a medium possibly in itself electric or magnetic, but at -all events capable of transmitting light, heat, magnetism, gravity, and -probably influences of which we can form no idea. - -Whatever the laws may be that obtain in the more distant regions of -creation, we are assured that one alone regulates the motions, not only -of our own system, but also of the binary systems of the fixed stars; -and, as general laws form the ultimate object of philosophical research, -we cannot conclude these remarks without considering the nature of -gravitation—that extraordinary power whose effects we have been -endeavouring to trace through some of their mazes. It was at one time -imagined that the acceleration in the moon’s mean motion was occasioned -by the successive transmission of the gravitating force. It has been -proved that, in order to produce this effect, its velocity must be about -fifty millions of times greater than that of light, which flies at the -rate of 192,000 miles in a second. Its action, even at the distance of -the sun, may therefore be regarded as instantaneous; yet, remote as the -fixed stars are, the solar gravitation must have some influence on the -nearest of them, as, for example, α Centauri, which is only 20,602 times -the radius of the earth’s orbit from the sun, while La Place has -computed that the solar gravitation extends a hundred millions of times -farther than the semidiameter of the terrestrial orbit. Possibly the -star dust in the Milky Way may be beyond, or on the verge of, that -enormous limit; yet it is very unlikely that either the sun, or any of -the stars which form the great cluster to which we belong, should be -unconnected bodies. - -The curves in which the celestial bodies move by the force of -gravitation are only lines of the second order. The attraction of -spheroids, according to any other law of force than that of gravitation, -would be much more complicated; and, as it is easy to prove that matter -might have been moved according to an infinite variety of laws, it may -be concluded that gravitation must have been selected by Divine Wisdom -out of an infinity of others, as being the most simple, and that which -gives the greatest stability to the celestial motions. - -It is a singular result of the simplicity of the laws of nature, which -admit only of the observation and comparison of ratios, that the -gravitation and theory of the motions of the celestial bodies are -independent of their absolute magnitudes and distances. Consequently, if -all the bodies of the solar system, their mutual distances, and their -velocities, were to diminish proportionally, they would describe curves -in all respects similar to those in which they now move; and the system -might be successively reduced to the smallest sensible dimensions, and -still exhibit the same appearances. - -The action of the gravitating force is not impeded by the intervention -even of the densest substances. If the attraction of the sun for the -centre of the earth, and of the hemisphere diametrically opposite to -him, were diminished by a difficulty in penetrating the interposed -matter, the tides would be more obviously affected. Its attraction is -the same also, whatever the substances of the celestial bodies may be; -for, if the action of the sun upon the earth differed by a millionth -part from his action upon the moon, the difference would occasion a -periodical variation in the moon’s parallax, whose maximum would be the -1/15 of a second, and also a variation in her longitude amounting to -several seconds—a supposition proved to be impossible by the agreement -of theory with observation. Thus all matter is pervious to gravitation, -and is equally attracted by it. - -Gravitation is a feeble force, vastly inferior to electric action, -chemical affinity, and cohesion; yet, as far as human knowledge extends, -the intensity of gravitation has never varied within the limits of the -solar system; nor does even analogy lead us to expect that it should: on -the contrary, there is every reason to be assured that the great laws of -the universe are immutable, like their Author. Nor can we suppose the -structure of the globe alone to be exempt from the universal fiat of -general laws, though ages may pass before the changes it has undergone, -or that are now in progress, can be referred to existing causes with the -same certainty with which the motions of the planets, and all their -periodic and secular variations, are referable to the law of -gravitation. The traces of extreme antiquity perpetually occurring to -the geologist give that information, as to the origin of things, in vain -looked for in the other parts of the universe. They date the beginning -of time with regard to our system, since there is ground to believe that -the formation of the earth was contemporaneous with that of the rest of -the planets; but they show that creation is the work of Him with whom “a -thousand years are as one day, and one day as a thousand years.” - -In the work now brought to a conclusion, it has been necessary to select -from the whole circle of the sciences a few of the most obvious of those -proximate links which connect them together, and to pass over -innumerable cases both of evident and occult alliance. Any one branch -traced through its ramifications would alone have occupied a volume; it -is hoped, nevertheless, that the view here given will suffice to show -the extent to which a consideration of the reciprocal influence of even -a few of these subjects may ultimately lead. It thus appears that the -theory of dynamics, founded upon terrestrial phenomena, is indispensable -for acquiring a knowledge of the revolutions of the celestial bodies and -their reciprocal influences. The motions of the satellites are affected -by the forms of their primaries, and the figures of the planets -themselves depend upon their rotations. The symmetry of their internal -structure proves the stability of these rotatory motions, and the -immutability of the length of the day, which furnishes an invariable -standard of time; and the actual size of the terrestrial spheroid -affords the means of ascertaining the dimensions of the solar system, -and provides an invariable foundation for a system of weights and -measures. The mutual attraction of the celestial bodies disturbs the -fluids at their surfaces, whence the theory of the tides and of the -oscillations of the atmosphere. The density and elasticity of the air, -varying with every alternation of temperature, lead to the consideration -of barometrical changes, the measurement of heights, and capillary -attraction; and the doctrine of sound, including the theory of music, is -to be referred to the small undulations of the aërial medium. A -knowledge of the action of matter upon light is requisite for tracing -the curved path of its rays through the atmosphere, by which the true -places of distant objects are determined, whether in the heavens or on -the earth. By this we learn the nature and properties of the sunbeam, -the mode of its propagation through the ethereal medium, or in the -interior of material bodies, and the origin of colour. By the eclipses -of Jupiter’s satellites the velocity of light is ascertained; and that -velocity, in the aberration of the fixed stars, furnishes a direct proof -of the real motion of the earth (N. 237). The effects of the invisible -rays of the spectrum are immediately connected with chemical action; and -heat, forming a part of the solar ray, so essential to animated and -inanimated existence, is too important an agent in the economy of -creation not to hold a principal place in the connexion of physical -sciences; whence follows its distribution in the interior and over the -surface of the globe, its power on the geological convulsions of our -planet, its influence on the atmosphere and on climate, and its effects -on vegetable and animal life, evinced in the localities of organized -beings on the earth, in the waters, and in the air. The correlation -between molecular and chemical action, light, heat, electricity, and -magnetism, is continually becoming more perfect, and there is every -reason to believe that these different modes of force, as well as -gravity itself, will ultimately be found to merge in one great and -universal power. Many more instances might be given in illustration of -the immediate connexion of the physical sciences, most of which are -united still more closely by the common bond of analysis, which is daily -extending its empire, and will ultimately embrace almost every subject -in nature in its formulæ. - -These formulæ, emblematic of Omniscience, condense into a few symbols -the immutable laws of the universe. This mighty instrument of human -power itself originates in the primitive constitution of the human mind, -and rests upon a few fundamental axioms, which have eternally existed in -Him who implanted them in the breast of man when He created him after -His own image. - - - - - NOTES. - - -NOTE 1, page 2. _Diameter._ A straight line passing through the centre, -and terminated both ways by the sides or surface of a figure, such as of -a circle or sphere. In fig. 1, q Q, N S, are diameters. - - -NOTE 2, p. 2. _Mathematical and mechanical sciences._ Mathematics teach -the laws of number and quantity; mechanics treat of the equilibrium and -motion of bodies. - - -NOTE 3, p. 2. _Analysis_ is a series of reasoning conducted by signs or -symbols of the quantities whose relations form the subject of inquiry. - - -NOTE 4, p. 3. _Oscillations_ are movements to and fro, like the swinging -of the pendulum of a clock, or waves in water. The tides are -oscillations of the sea. - - -NOTE 5, p. 3. _Gravitation._ _Gravity_ is the reciprocal attraction of -matter on matter; _gravitation_ is the difference between gravity and -the centrifugal force induced by the velocity of rotation or revolution. -Sensible gravity, or weight, is a particular instance of gravitation. It -is the force which causes substances to fall to the surface of the -earth, and which retains the celestial bodies in their orbits. Its -intensity increases as the squares of the distance decrease. - - -NOTE 6, p. 4. _Particles of matter_ are the indefinitely small or -ultimate atoms into which matter is believed to be divisible. Their form -is unknown; but, though too small to be visible, they must have -magnitude. - - -NOTE 7, p. 4. _A hollow sphere._ A hollow ball, like a bomb-shell. A -sphere is a ball or solid body, such, that all lines drawn from its -centre to its surface are equal. They are called radii, and every line -passing through the centre and terminated both ways by the surface is a -diameter, which is consequently equal to twice the radius. In fig. 3, Q -q or N S is a diameter, and C Q, C N are radii. A great circle of the -sphere has the same centre with the sphere as the circles Q E q d and Q -N q S. The circle A B is a lesser circle of the sphere. - - -NOTE 8, p. 4. _Concentric hollow spheres._ Shells, or hollow spheres, -having the same centre, like the coats of an onion. - -[Illustration: _Fig. 1._] - - -NOTE 9, p. 4. _Spheroid._ A solid body, which sometimes has the shape of -an orange, as in fig. 1; it is then called an oblate spheroid, because -it is flattened at the poles N and S. Such is the form of the earth and -planets. When, on the contrary, it is drawn out at the poles like an -egg, as in fig. 2, it is called a prolate spheroid. It is evident that -in both these solids the radii C q, C a, C N, &c., are generally -unequal; whereas in the sphere they are all equal. - -[Illustration: _Fig. 2._] - - -NOTE 10, p. 4. _Centre of gravity._ A point in every body, which if -supported, the body will remain at rest in whatever position it may be -placed. About that point all the parts exactly balance one another. The -celestial bodies attract each other as if each were condensed into a -single particle situate in the centre of gravity, or the particle -situate in the centre of gravity of each may be regarded as possessing -the resultant power of the innumerable oblique forces which constitute -the whole attraction of the body. - - -NOTE 11, pp. 4, 6. _Poles and equator._ Let fig. 1 or 3 represent the -earth, C its centre, N C S the axis of rotation, or the imaginary line -about which it performs its daily revolution. Then N and S are the north -and south poles, and the great circle q E Q, which divides the earth -into two equal parts, is the equator. The earth is flattened at the -poles, fig. 1, the equatorial diameter, q Q, exceeding the polar -diameter, N S, by about 26-1/2 miles. Lesser circles, A B G, which are -parallel to the equator, are circles or parallels of latitude, which is -estimated in degrees, minutes, and seconds, north and south of the -equator, every place in the same parallel having the same latitude. -Greenwich is in the parallel of 51° 28ʹ 40ʺ. Thus terrestrial latitude -is the angular distance between the direction of a plumb-line at any -place and the plane of the equator. Lines such as N Q S, N G E S, fig. -3, are called meridians; all the places in any one of these lines have -noon at the same instant. The meridian of Greenwich has been chosen by -the British as the origin of terrestrial longitude, which is estimated -in degrees, minutes, and seconds, east and west of that line. If N G E S -be the meridian of Greenwich, the position of any place, B, is -determined, when its latitude, Q C B, and its longitude, E C Q, are -known. - -[Illustration: _Fig. 3._] - - -NOTE 12, p. 4. _Mean quantities_ are such as are intermediate between -others that are greater and less. The mean of any number of unequal -quantities is equal to their sum divided by their number. For instance, -the mean between two unequal quantities is equal to half their sum. - - -NOTE 13, p. 4. _A certain mean latitude._ The attraction of a sphere on -an external body is the same as if its mass were collected into one -heavy particle in its centre of gravity, and the intensity of its -attraction diminishes as the square of its distance from the external -body increases. But the attraction of a spheroid, fig. 1, on an external -body at m in the plane of its equator, E Q, is greater, and its -attraction on the same body when at mʹ in the axis N S less, than if it -were a sphere. Therefore, in both cases, the force deviates from the -exact law of gravity. This deviation arises from the protuberant matter -at the equator; and, as it diminishes towards the poles, so does the -attractive force of the spheroid. But there is one mean latitude, where -the attraction of a spheroid is the same as if it were a sphere. It is a -part of the spheroid intermediate between the equator and the pole. In -that latitude the square of the sine is equal to 1/3 of the equatorial -radius. - - -NOTE 14, p. 4. _Mean distance._ The mean distance of a planet from the -centre of the sun, or of a satellite from the centre of its planet, is -equal to half the sum of its greatest and least distances, and, -consequently, is equal to half the major axis of its orbit. For example, -let P Q A D, fig. 6, be the orbit or path of the moon or of a planet; -then P A is the major axis, C the centre, and C S is equal to C F. Now, -since the earth or the sun is supposed to be in the point S according as -P D A Q is regarded as the orbit of the moon or that of a planet, S A, S -P are the greatest and least distances. But half the sum of S A and S P -is equal to half of A P, the major axis of the orbit. When the body is -at Q or D, it is at its mean distance from S, for S Q, S D, are each -equal to C P, half the major axis by the nature of the curve. - - -NOTE 15, p. 4. _Mean radius of the earth._ The distance from the centre -to the surface of the earth, regarded as a sphere. It is intermediate -between the distances of the centre of the earth from the pole and from -the equator. - - -NOTE 16, p. 5. _Ratio._ The relation which one quantity bears to -another. - - -NOTE 17, p. 5. _Square of moon’s distance._ In order to avoid large -numbers, the mean radius of the earth is taken for unity: then the mean -distance of the moon is expressed by 60; and the square of that number -is 3600, or 60 times 60. - -[Illustration: _Fig. 4_] - - -NOTE 18, p. 5. _Centrifugal force._ The force with which a revolving -body tends to fly from the centre of motion: a sling tends to fly from -the hand in consequence of the centrifugal force. A tangent is a -straight line touching a curved line in one point without cutting it, as -m T, fig. 4. The direction of the centrifugal force is in the tangent to -the curved line or path in which the body revolves, and its intensity -increases with the angular swing of the body, and with its distance from -the centre of motion. As the orbit of the moon does not differ much from -a circle, let it be represented by m d g h, fig. 4, the earth being in -C. The centrifugal force arising from the velocity of the moon in her -orbit balances the attraction of the earth. By their joint action, the -moon moves through the arc m n during the time that she would fly off in -the tangent m T by the action of the centrifugal force alone, or fall -through m p by the earth’s attraction alone. T n, the deflection from -the tangent, is parallel and equal to m p, the versed sine of the arc m -n, supposed to be moved over by the moon in a second, and therefore so -very small that it may be regarded as a straight line. T n, or m p, is -the space the moon would fall through in the first second of her descent -to the earth, were she not retained in her orbit by her centrifugal -force. - - -NOTE 19, p. 5. _Action and reaction._ When motion is communicated by -collision or pressure, the action of the body which strikes is returned -with equal force by the body which receives the blow. The pressure of a -hand on a table is resisted with an equal and contrary force. This -necessarily follows from the impenetrability of matter, a property by -which no two particles of matter can occupy the same identical portion -of space at the same time. When motion is communicated without apparent -contact, as in gravitation, attraction, and repulsion, the quantity of -motion gained by the one body is exactly equal to that lost by the -other, but in a contrary direction; a circumstance known by experience -only. - - -NOTE 20, p. 5. _Projected._ A body is projected when it is thrown: a -ball fired from a gun is projected; it is therefore called a projectile. -But the word has also another meaning. A line, surface, or solid body, -is said to be projected upon a plane, when parallel straight lines are -drawn from every point of it to the plane. The figure so traced upon a -plane is a projection. The projection of a terrestrial object is -therefore its daylight shadow, since the sun’s rays are sensibly -parallel. - - -NOTE 21, p. 5. _Space._ The boundless region which contains all -creation. - -[Illustration: _Fig. 5._] - -[Illustration: _Fig. 6._] - - -NOTE 22, pp. 5, 11. _Conic sections._ Lines formed by any plane cutting -a cone. A cone is a solid figure, like a sugar-loaf, fig. 5, of which A -is the apex, A D the axis, and the plane B E C F the base. The axis may -or may not be perpendicular to the base, and the base may be a circle, -or any other curved line. When the axis is perpendicular to the base, -the solid is a right cone. If a right cone with a circular base be cut -at right angles to the base by a plane passing through the apex, the -section will be a triangle. If the cone be cut through both sides by a -plane parallel to the base, the section will be a circle. If the cone be -cut slanting quite through both sides, the section will be an ellipse, -fig. 6. If the cone be cut parallel to one of the sloping sides as A B, -the section will be a parabola, fig. 7. And if the plane cut only one -side of the cone, and be not parallel to the other, the section will be -a hyperbola, fig. 8. Thus there are five conic sections. - -[Illustration: _Fig. 7._] - -[Illustration: _Fig. 8._] - - -NOTE 23, p. 5. _Inverse square of distance._ The attraction of one body -for another at the distance of two miles is four times less than at the -distance of one mile; at three miles, it is nine times less than at one; -at four miles, it is sixteen times less, and so on. That is, the -gravitating force decreases in intensity as the squares of the distance -increase. - - -NOTE 24, p. 5. _Ellipse._ One of the conic sections, fig. 6. An ellipse -may be drawn by fixing the ends of a string to two points, S and F, in a -sheet of paper, and then carrying the point of a pencil round in the -loop of the string kept stretched, the length of the string being -greater than the distance between the two points. The points S and F are -called the foci, C the centre, S C or C F the excentricity, A P the -major axis, Q D the minor axis, and P S the focal distance. It is -evident that, the less the excentricity C S, the nearer does the ellipse -approach to a circle; and from the construction it is clear that the -length of the string S m F is equal to the major axis P A. If T t be a -tangent to the ellipse at m, then the angle T m S is equal to the angle -t m F; and, as this is true for every point in the ellipse, it follows -that, in an elliptical reflecting surface, rays of light or sound coming -from one focus S will be reflected by the surface to the other focus F, -since the angle of incidence is equal to the angle of reflection by the -theories of light and sound. - - -NOTE 25, p. 5. _Periodic time._ The time in which a planet or comet -performs a revolution round the sun, or a satellite about its planet. - - -NOTE 26, p. 5. Kepler discovered three laws in the planetary motions by -which the principle of gravitation is established:—1st law, That the -radii vectores of the planets and comets describe areas proportional to -the time.—Let fig. 9 be the orbit of a planet; then, supposing the -spaces or areas P S p, p S a, a S b, &c., equal to one another, the -radius vector S P, which is the line joining the centres of the sun and -planet, passes over these equal spaces in equal times; that is, if the -line S P passes to S p in one day, it will come to S a in two days, to S -b in three days, and so on. 2nd law, That the orbits or paths of the -planets and comets are conic sections, having the sun in one of their -foci. The orbits of the planets and satellites are curves like fig. 6 or -9, called ellipses, having the sun in the focus S. Several comets are -known to move in ellipses; but the greater part seem to move in -parabolas, fig. 7, having the sun in S, though it is probable that they -really move in very long flat ellipses; others appear to move in -hyperbolas, like fig. 8. The third law is, that the squares of the -periodic times of the planets are proportional to the cubes of their -mean distances from the sun. The square of a number is that number -multiplied by itself, and the cube of a number is that number twice -multiplied by itself. For example, the squares of the numbers 2, 3, 4, -&c., are 4, 9, 16, &c., but their cubes are 8, 27, 64, &c. Then the -squares of the numbers representing the periodic times of two planets -are to one another as the cubes of the numbers representing their mean -distances from the sun. So that, three of these quantities being known, -the other may be found by the rule of three. The mean distances are -measured in miles or terrestrial radii, and the periodic times are -estimated in years, days, and parts of a day. Kepler’s laws extend to -the satellites. - -[Illustration: _Fig. 9._] - - -NOTE 27, p. 5. _Mass._ The quantity of matter in a given bulk. It is -proportional to the density and volume or bulk conjointly. - - -NOTE 28, p. 5. _Gravitation proportional to mass._ But for the -resistance of the air, all bodies would fall to the ground in equal -times. In fact, a hundred equal particles of matter at equal distances -from the surface of the earth would fall to the ground in parallel -straight lines with equal rapidity, and no change whatever would take -place in the circumstances of their descent, if 99 of them were united -in one solid mass; for the solid mass and the single particle would -touch the ground at the same instant, were it not for the resistance of -the air. - - -NOTE 29, p. 5. _Primary_ signifies, in astronomy, the planet about which -a satellite revolves. The earth is primary to the moon. - - -NOTE 30, p. 6. _Rotation._ Motion round an axis, real or imaginary. - - -NOTE 31, p. 7. _Compression of a spheroid._ The flattening at the poles. -It is equal to the difference between the greatest and least diameters, -divided by the greatest, these quantities being expressed in some -standard measure, as miles. - - -NOTE 32, p. 7. SATELLITES. Small bodies revolving about some of the -planets. The moon is a satellite to the earth. - - -NOTE 33, p. 7. _Nutation._ A nodding motion in the earth’s axis while in -rotation, similar to that observed in the spinning of a top. It is -produced by the attraction of the sun and moon on the protuberant matter -at the terrestrial equator. - - -NOTE 34, p. 7. _Axis of rotation._ The line, real or imaginary, about -which a body revolves. The axis of the earth’s rotation is that -diameter, or imaginary line, passing through the centre and both poles. -Fig. 1 being the earth, N S is the axis of rotation. - - -NOTE 35, p. 7. _Nutation of lunar orbit._ The action of the bulging -matter at the earth’s equator on the moon occasions a variation in the -inclination of the lunar orbit to the plane of the ecliptic. Suppose the -plane N p n, fig. 13, to be the orbit of the moon, and N m n the plane -of the ecliptic, the earth’s action on the moon causes the angle p N m -to become less or greater than its mean state. The nutation in the lunar -orbit is the reaction of the nutation in the earth’s axis. - - -NOTE 36, p. 7. _Translated._ Carried forward in space. - - -NOTE 37, p. 7. _Force proportional to velocity._ Since a force is -measured by its effect, the motions of the bodies of the solar system -among themselves would be the same whether the system be at rest or not. -The real motion of a person walking the deck of a ship at sea is -compounded of his own motion and that of the ship, yet each takes place -independently of the other. We walk about as if the earth were at rest, -though it has the double motion of rotation on its axis and revolution -round the sun. - - -NOTE 38, p. 8. _Tangent._ A straight line which touches a curved line in -one point without cutting it. In fig. 4, m T is tangent to the curve in -the point m. In a circle the tangent is at right angles to the radius, C -m. - - -NOTE 39, p. 8. _Motion in an elliptical orbit._ A planet m, fig. 6, -moves round the sun at S in an ellipse P D A Q, in consequence of two -forces, one urging it in the direction of the tangent m T, and another -pulling it towards the sun in the direction m S. Its velocity, which is -greatest at P, decreases throughout the arc to P D A to A, where it is -least, and increases continually as it moves along the arc A Q P till it -comes to P again. The whole force producing the elliptical motion varies -inversely as the square of the distance. See note 23. - - -NOTE 40, p. 8. _Radii vectores._ Imaginary lines adjoining the centre of -the sun and the centre of a planet or comet, or the centres of a planet -and its satellite. In the circle, the radii are all equal; but in an -ellipse, fig. 6, the radius vector S A is greater, and S P less than all -the others. The radii vectores S Q, S D, are equal to C A or C P, half -the major axis P A, and consequently equal to the mean distance. A -planet is at its mean distance from the sun when in the points Q and D. - - -NOTE 41, p. 8. _Equal areas in equal times._ See Kepler’s 1st law, in -note 26, p. 5. - - -NOTE 42, p. 8. _Major axis._ The line P A, fig. 6 or 10. - - -NOTE 43, p. 8. _If the planet described a circle, &c._ The motion of a -planet about the sun, in a circle A B P, fig. 10, whose radius C A is -equal to the planet’s mean distance from him, would be equable, that is, -its velocity, or speed, would always be the same. Whereas, if it moved -in the ellipse A Q P, its speed would be continually varying, by note -39; but its motion is such, that the time elapsing between its departure -from P and its return to that point again would be the same whether it -moved in the circle or in the ellipse; for these curves coincide in the -points P and A. - - -NOTE 44, p. 8. _True motion._ The motion of a body in its real orbit P D -A Q, fig. 10. - -[Illustration: _Fig. 10._] - - -NOTE 45, p. 9. _Mean motion._ Equable motion in a circle P E A B, fig. -10, at the mean distance C P or C m, in the time that the body would -accomplish a revolution in its elliptical orbit P D A Q. - - -NOTE 46, p. 9. _The equinox._ Fig. 11 represents the celestial sphere, -and C its centre, where the earth is supposed to be. q ♈ Q ♎ is the -equinoctial or great circle, traced in the starry heavens by an -imaginary extension of the plane of the terrestrial equator, and E ♈ e ♎ -is the ecliptic, or apparent path of the sun round the earth. ♈ ♎, the -intersection of these two planes, is the line of the equinoxes; ♈ is the -vernal equinox, and ♎ the autumnal. When the sun is in these points, the -days and nights are equal. They are distant from one another by a -semicircle, or two right angles. The points E and e are the solstices, -where the sun is at his greatest distance from the equinoctial. The -equinoctial is everywhere ninety degrees distant from its poles N and S, -which are two points diametrically opposite to one another, where the -axis of the earth’s rotation, if prolonged, would meet the heavens. The -northern celestial pole N is within 1° 24ʹ of the pole star. As the -latitude of any place on the surface of the earth is equal to the height -of the pole above the horizon, it is easily determined by observation. -The ecliptic E ♈ e ♎ is also everywhere ninety degrees distant from its -poles P and p. The angle P C N, between the poles P and N of the -equinoctial and ecliptic, is equal to the angle e C Q, called the -obliquity of the ecliptic. - -[Illustration: _Fig. 11._] - - -NOTE 47, p. 9. _Longitude._ The vernal equinox, ♈, fig. 11, is the zero -point in the heavens whence celestial longitudes, or the angular motions -of the celestial bodies, are estimated from west to east, the direction -in which they all revolve. The vernal equinox is generally called the -first point of Aries, though these two points have not coincided since -the early ages of astronomy, about 2233 years ago, on account of a -motion in the equinoctial points, to be explained hereafter. If S ♈, -fig. 10, be the line of the equinoxes, and ♈ the vernal equinox, the -true longitude of a planet p is the angle ♈ S p, and its mean longitude -is the angle ♈ C m, the sun being in S. Celestial longitude is the -angular distance of a heavenly body from the vernal equinox; whereas -terrestrial longitude is the angular distance of a place on the surface -of the earth from a meridian arbitrarily chosen, as that of Greenwich. - - -NOTE 48, pp. 9, 58. _Equation of the centre._ The difference between ♈ C -m and ♈ S p, fig. 10; that is, the difference between the true and mean -longitudes of a planet or satellite. The true and mean places only -coincide in the points P and A; in every other point of the orbit, the -true place is either before or behind the mean place. In moving from A -through the arc A Q P, the true place p is behind the mean place m; and -through the arc P D A the true place is before the mean place. At its -maximum, the equation of the centre measures C S, the excentricity of -the orbit, since it is the difference between the motion of a body in an -ellipse and in a circle whose diameter A P is the major axis of the -ellipse. - - -NOTE 49, p. 9. _Apsides._ The points P and A, fig. 10, at the -extremities of the major axis of an orbit. P is commonly called the -perihelion, a Greek term signifying _round the sun_; and the point A is -called the aphelion, a Greek term signifying _at a distance from the -sun_. - - -NOTE 50, p. 9. _Ninety degrees._ A circle is divided into 360 equal -parts, or degrees; each degree into 60 equal parts, called minutes; and -each minute into 60 equal parts, called seconds. It is usual to write -these quantities thus, 15° 16ʹ 10ʺ, which means fifteen degrees, sixteen -minutes, and ten seconds. It is clear that an arc m n, fig. 4, measures -the angle m C n; hence we may say, an arc of so many degrees, or an -angle of so many degrees; for, if there be ten degrees in the angle m C -n, there will be ten degrees in the arc m n. It is evident that there -are 90° in a right angle, m C d, or quadrant, since it is the fourth -part of 360°. - - -NOTE 51, p. 9. _Quadratures._ A celestial body is said to be in -quadrature when it is 90 degrees distant from the sun. For example, in -fig. 14, if d be the sun, S the earth, and p the moon, then the moon is -said to be in quadrature when she is in either of the points Q or D, -because the angles Q S d and D S d, which measure her apparent distance -from the sun, are right angles. - - -NOTE 52, p. 9. _Excentricity._ Deviation from circular form. In fig. 6, -C S is the excentricity of the orbit P Q A D. The less C S, the more -nearly does the orbit or ellipse approach the circular form; and, when C -S is zero, the ellipse becomes a circle. - - -NOTE 53, p. 9. _Inclination of an orbit._ Let S, fig. 12, be the centre -of the sun, P N A n the orbit of a planet moving from west to east in -the direction N p. Let E N m e n be the shadow or projection of the -orbit on the plane of the ecliptic, then N S n is the intersection of -these two planes, for the orbit rises above the plane of the ecliptic -towards N p, and sinks below it at N P. The angle p N m, which these two -planes make with one another, is the inclination of the orbit P N p A to -the plane of the ecliptic. - - -NOTE 54, p. 9. _Latitude of a planet._ The angle p S m, fig. 12, or the -height of the planet p above the ecliptic E N m. In this case the -latitude is north. Thus, celestial latitude is the angular distance of a -celestial body from the plane of the ecliptic, whereas terrestrial -latitude is the angular distance of a place on the surface of the earth -from the equator. - -[Illustration: _Fig. 12._] - - -NOTE 55, p. 9. _Nodes._ The two points N and n, fig. 12, in which the -orbit N A n P of a planet or comet intersects the plane of the ecliptic -e N E n. The part N A n of the orbit lies above the plane of the -ecliptic, and the part n P N below it. The ascending node N is the point -through which the body passes in rising above the plane of the ecliptic, -and the descending node n is the point in which the body sinks below it. -The nodes of a satellite’s orbit are the points in which it intersects -the plane of the orbit of the planet. - - -NOTE 56, p. 10. _Distance from the sun._ S p in fig. 12. If ♈ be the -vernal equinox, then ♈ S p is the longitude of the planet p, m S p is -its latitude, and S p its distance from the sun. When these three -quantities are known, the place of the planet p is determined in space. - - -NOTE 57, pp. 10, 59. _Elements of an orbit._ Of these there are seven. -Let P N A n, fig. 12, be the elliptical orbit of a planet, C its centre, -S the sun in one of the foci, ♈ the point of Aries, and E N e n the -plane of the ecliptic. The elements are—the major axis A P; the -excentricity C S; the periodic time, that is, the time of a complete -revolution of the body in its orbit; and the fourth is the longitude of -the body at any given instant—for example, that at which it passes -through the perihelion P, the point of its orbit nearest to the sun. -That instant is assumed as the origin of time, whence all preceding and -succeeding periods are estimated. These four quantities are sufficient -to determine the form of the orbit, and the motion of the body in it. -Three other elements are requisite for determining the position of the -orbit in space. These are, the angle ♈ S P, the longitude of the -perihelion; the angle A N e, which is the inclination of the orbit to -the plane of the ecliptic; and, lastly, the angle ♈ S N, the longitude -of N the ascending node. - - -NOTE 58, p. 10. _Whose planes, &c._ The planes of the orbits, as P N A -n, fig. 12, in which the planets move, are inclined or make small angles -e N A with the plane of the ecliptic E N e n, and cut it in straight -lines, N S n passing through S, the centre of the sun. - - -NOTE 59, p. 11. _Momentum._ Force measured by the weight of a body and -its speed, or simple velocity, conjointly. The primitive momentum of the -planets is, therefore, the quantity of motion which was impressed upon -them when they were first thrown into space. - - -NOTE 60, p. 11. _Unstable equilibrium._ A body is said to be in -equilibrium when it is so balanced as to remain at rest. But there are -two kinds of equilibrium, _stable_ and _unstable_. If a body balanced in -stable equilibrium be slightly disturbed, it will endeavour to return to -rest by a number of movements to and fro, which will continually -decrease till they cease altogether, and then the body will be restored -to its original state of repose. But, if the equilibrium be unstable, -these movements to and fro, or oscillations, will become greater and -greater till the equilibrium is destroyed. - - -NOTE 61, p. 14. _Retrograde._ Going backwards, as from east to west, -contrary to the motion of the planets. - - -NOTE 62, p. 14. _Parallel directions._ Such as never meet, though -prolonged ever so far. - -[Illustration: _Fig. 13._] - -[Illustration: _Fig. 14._] - - -NOTE 63, pp. 14, 16. _The whole force, &c._ Let S, fig. 13, be the sun, -N m n the plane of the ecliptic, p the disturbed planet moving in its -orbit n p N, and d the disturbing planet. Now, d attracts the sun and -the planet p with different intensities in the directions d S, d p: the -difference only of these forces disturbs the motion of p; it is -therefore called the disturbing force. But this whole disturbing force -may be regarded as equivalent to three forces, acting in the directions -p S, p T, and p m. The force acting in the radius vector p S, joining -the centres of the sun and planet, is called the _radial force_. It -sometimes draws the disturbed planet p from the sun, and sometimes -brings it nearer to him. The force which acts in the direction of the -tangent p T is called the _tangential force_. It disturbs the motion of -p in longitude, that is, it accelerates its motion in some parts of its -orbit and retards it in others, so that the radius vector S p does not -move over equal areas in equal times. (See note 26.) For example, in the -position of the bodies in fig. 14, it is evident that, in consequence of -the attraction of d, the planet p will have its motion accelerated from -Q to C, retarded from C to D, again accelerated from D to O, and lastly -retarded from O to Q. The disturbing body is here supposed to be at -rest, and the orbit circular; but, as both bodies are perpetually moving -with different velocities in ellipses, the perturbations or changes in -the motions of p are very numerous. Lastly, that part of the disturbing -force which acts in the direction of a line p m, fig. 13, at right -angles to the plane of the orbit N p n, may be called the perpendicular -force. It sometimes causes the body to approach nearer, and sometimes to -recede farther from, the plane of the ecliptic N m n, than it would -otherwise do. The action of the disturbing forces is admirably explained -in a work on gravitation, by Mr. Airy, the Astronomer Royal. - - -NOTE 64, pp. 16, 74. _Perihelion._ Fig. 10, P, the point of an orbit -nearest the sun. - - -NOTE 65, p. 16. _Aphelion._ Fig. 10, A, the point of an orbit farthest -from the sun. - - -NOTE 66, pp. 16, 17. In fig. 15 the central force is greater than the -exact law of gravity; therefore the curvature P p a is greater than P p -A the real ellipse; hence the planet p comes to the point a, called the -aphelion, sooner than if it moved in the orbit P p A, which makes the -line P S A advance to a. In fig. 16, on the contrary, the curvature P p -a is less than in the true ellipse, so that the planet p must move -through more than the arc P p A, or 180°, before it comes to the -aphelion a, which causes the greater axis P S A to recede to a. - -[Illustration: _Fig. 15._] - -[Illustration: _Fig. 16._] - - -NOTE 67, pp. 16, 17. _Motion of apsides._ Let P S A, fig. 17, be the -position of the elliptical orbit of a planet, at any time; then, by the -action of the disturbing forces, it successively takes the position Pʹ S -Aʹ, Pʺ S Aʺ, &c., till by this direct motion it has accomplished a -revolution, and then it begins again; so that the motion is perpetual. - -[Illustration: _Fig. 17._] - - -NOTE 68, p. 17. _Sidereal revolution._ The consecutive return of an -object to the same star. - - -NOTE 69, p. 17. _Tropical revolution._ The consecutive return of an -object to the same tropic or equinox. - - -NOTE 70, p. 17. _The orbit only bulges, &c._ In fig. 18 the effect of -the variation in the excentricity is shown where P p A is the elliptical -orbit at any given instant; after a time it will take the form P pʹ A, -in consequence of the decrease in the excentricity C S; then the forms P -pʺ A, P pʹʹʹ A, &c., consecutively from the same cause; and, as the -major axis P A always retains the same length, the orbit approaches more -and more nearly to the circular form. But, after this has gone on for -some thousands of years, the orbit contracts again, and becomes more and -more elliptical. - -[Illustration: _Fig. 18._] - - -NOTE 71, pp. 18, 19. _The ecliptic_ is the apparent path of the sun in -the heavens. See note 46. - - -NOTE 72, p. 18. _This force tends to pull, &c._ The force in question, -acting in the direction p m, fig. 13, pulls the planet p towards the -plane N m n, or pushes it farther above it, giving the planet a tendency -to move in an orbit above or below its undisturbed orbit N p n, which -alters the angle p N m, and makes the node N and the line of nodes N n -change their positions. - -[Illustration: _Fig. 19._] - - -NOTE 73, p. 18. _Motion of the nodes._ Let S, fig. 19, be the sun; S N n -the plane of the ecliptic; P the disturbing body; and p a planet moving -in its orbit p n, of which p n is so small a part that it is represented -as a straight line. The plane S n p of this orbit cuts the plane of the -ecliptic in the straight line S n. Suppose the disturbing force begins -to act on p, so as to draw the planet into the arc p pʹ; then, instead -of moving in the orbit p n, it will tend to move in the orbit p pʹ nʹ, -whose plane cuts the ecliptic in the straight line S nʹ. If the -disturbing force acts again upon the body when at pʹ, so as to draw it -into the arc pʹ pʺ, the planet will now tend to move in the orbit pʹ pʺ -nʺ, whose plane cuts the ecliptic in the straight line S nʺ. The action -of the disturbing force on the planet when at pʺ will bring the node to -nʹʹʹ, and so on. In this manner the node goes backwards through the -successive points n, nʹ, nʺ, nʹʹʹ, &c., and the line of nodes S n has a -perpetual retrograde motion about S, the centre of the sun. The -disturbing force has been represented as acting at intervals for the -sake of illustration: in nature it is continuous, so that the motion of -the node is continuous also; though it is sometimes rapid and sometimes -slow, now retrograde and now direct; but, on the whole, the motion is -slowly retrograde. - - -NOTE 74, p. 18. _When the disturbing planet_ is anywhere in the line S -N, fig. 19, or in its prolongation, it is in the same plane with the -disturbed planet; and, however much it may affect its motions in that -plane, it can have no tendency to draw it out of it. But when the -disturbing planet is in P, at right angles to the line S N, and not in -the plane of the orbit, it has a powerful effect on the motion of the -nodes: between these two positions there is great variety of action. - - -NOTE 75, p. 19. _The changes in the inclination_ are extremely minute -when compared with the motion of the node, as evidently appears from -fig. 19, where the angles n p nʹ, nʹ pʹ nʺ, &c., are much smaller than -the corresponding angles n S nʹ, S nʺ, &c. - - -NOTE 76, p. 20. _Sines and cosines._ Figure 4 is a circle; n p is the -sine, and C p is the cosine of an arc m n. Suppose the radius C m to -begin to revolve at m, in the direction m n a; then at the point m the -sine is zero, and the cosine is equal to the radius C m. As the line C m -revolves and takes the successive positions C n, C a, C b, &c., the -sines n p, a q, b r, &c., of the arcs m n, m a, m h, &c., increase, -while the corresponding cosines C p, C q, C r, &c., decrease; and when -the revolving radius takes the position C d, at right angles to the -diameter g m, the sine becomes equal to the radius C d, and the cosine -is zero. After passing the point d, the contrary happens; for the sines -e K, l V, &c., diminish, and the cosines C K, C V, &c., go on -increasing, till at g the sine is zero, and the cosine is equal to the -radius C g. The same alternation takes place through the remaining parts -g h, h m, of the circle, so that a sine or cosine never can exceed the -radius. As the rotation of the earth is invariable, each point of its -surface passes through a complete circle, or 360 degrees, in twenty-four -hours, at a rate of 15 degrees in an hour. Time, therefore, becomes a -measure of angular motion, and _vice versâ_, the arcs of a circle a -measure of time, since these two quantities vary simultaneously and -equably; and, as the sines and cosines of the arcs are expressed in -terms of the time, they vary with it. Therefore, however long the time -may be, and how often soever the radius may revolve round the circle, -the sines and cosines never can exceed the radius; and, as the radius is -assumed to be equal to unity, their values oscillate between unity and -zero. - - -NOTE 77, p. 20. The small excentricities and inclinations of the -planetary orbits, and the revolutions of all the bodies in the same -direction, were proved by Euler, La Grange, and La Place, to be -conditions necessary for the stability of the solar system. -Subsequently, however, the periodicity of the terms of the series -expressing the perturbations was supposed to be sufficient _alone_, but -M. Poisson has shown that to be a mistake; that these three conditions -are requisite for the necessary convergence of the series, and that -therefore the stability of the system depends on them _conjointly_ with -the periodicity of the sines and cosines of each term. The author is -aware that this note can only be intelligible to the analyst, but she is -desirous of correcting an error, and the more so as the conditions of -stability afford one of the most striking instances of design in the -original construction of our system, and of the foresight and supreme -wisdom of the Divine Architect. - - -NOTE 78, p. 22. _Resisting medium._ A fluid which resists the motions of -bodies, such as atmospheric air, or the highly elastic fluid called -ether, with which space is filled. - - -NOTE 79, p. 23. _Obliquity of the ecliptic._ The angle e ♈ q, fig. 11, -between the plane of the terrestrial equator q ♈ Q, and the plane of the -ecliptic E ♈ e. The obliquity is variable. - - -NOTE 80, p. 23. _Invariable plane._ In the earth the equator is the -invariable plane which nearly maintains a parallel position with regard -to itself while revolving about the sun, as in fig. 20, where E Q -represents it. The two hemispheres balance one another on each side of -this plane, and would still do so if all the particles of which they -consist were moveable among themselves, provided the earth were not -disturbed by the action of the sun and moon, which alters the -parallelism of the equator by the small variation called nutation, to be -explained hereafter. - -[Illustration: _Fig. 20._] - -[Illustration: _Fig. 21._] - - -NOTE 81, p. 24. _If each particle, &c._ Let P, Pʹ, Pʺ, &c., fig. 21, be -planets moving in their orbits about the centre of gravity of the -system. Let P S M, Pʹ S Mʹ, &c., be portions of these orbits moved over -by the radii vectores S P, S Pʹ, &c., in a given time, and let p S m, pʹ -S mʹ, &c., be their shadows or projections on the invariable plane. -Then, if the numbers which represent the masses of the planets P, Pʹ, -&c., be respectively multiplied by the numbers representing the areas or -spaces p S m, pʹ S mʹ, &c., the sum of the whole will be greater for the -invariable plane than it would be for any plane that could pass through -S, the centre of gravity of the system. - - -NOTE 82, p. 24. _The centre of gravity_ of the solar system lies within -the body of the sun, because his mass is much greater than the masses of -all the planets and satellites added together. - - -NOTE 83, pp. 25, 36. _Conjunction._ A planet is said to be in -conjunction when it has the same longitude with the sun, and in -opposition when its longitude differs from that of the sun by 180 -degrees. Thus two bodies are said to be in conjunction when they are -seen exactly in the same part of the heavens, and in opposition when -diametrically opposite to one another. Mercury and Venus, which are -nearer to the sun than the earth, are called inferior planets; while all -the others, being farther from the sun than the earth, are said to be -superior planets. Suppose the earth to be at E, fig. 24; then a superior -planet will be in conjunction with the sun at C, and in opposition to -him when at O. Again, suppose the earth to be in O, then an inferior -planet will be in conjunction when at E, and in opposition when at F. - - -NOTE 84, p. 26. _The periodic inequalities_ are computed for a given -time; and consequently for a given form and position of the orbits of -the disturbed and disturbing bodies. Although the elements of the orbits -vary so slowly that no sensible effect is produced on inequalities of a -short period, yet, in the course of time, the secular variations of the -elements change the forms and relative positions of the orbits so much, -that Jupiter and Saturn, which would have come to the same relative -positions with regard to the sun and to one another after 850 years, do -not arrive at the same relative positions till after 918 years. - - -NOTE 85, p. 26. _Configuration._ The relative position of the planets -with regard to one another, to the sun, and to the plane of the -ecliptic. - - -NOTE 86, p. 27. In the same manner that the excentricity of an -elliptical orbit may be increased or diminished by the action of the -disturbing forces, so a circular orbit may acquire less or more -ellipticity from the same cause. It is thus that the forms of the orbits -of the first and second satellites of Jupiter oscillate between circles -and ellipses differing very little from circles. - -[Illustration: _Fig. 22._] - - -NOTE 87, p. 28. _The plane of Jupiter’s equator_ is the imaginary plane -passing through his centre at right angles to his axis of rotation, and -corresponds to the plane q E Q e, in fig. 1. The satellites move very -nearly in the plane of Jupiter’s equator; for, if J be Jupiter, fig. 22, -P p his axis of rotation, e Q his equatorial diameter, which is 6000 -miles longer than P p, and if J O and J E be the planes of his orbit and -equator seen edgewise, then the orbits of his four satellites seen -edgewise will have the positions J1, J2, J3, J4. These are extremely -near to one another, for the angle E J O is only 3° 5ʹ 30ʺ. - - -NOTE 88, p. 28. In consequence of the satellites moving so nearly in the -plane of Jupiter’s equator, when seen from the earth, they appear to be -always very nearly in a straight line, however much they may change -their positions with regard to one another and to their primary. For -example, on the evenings of the 3rd, 4th, 5th, and 6th of January, 1835, -the satellites had the configurations given in fig. 23, where O is -Jupiter, and 1, 2, 3, 4, are the first, second, third, and fourth -satellites. The satellite is supposed to be moving in a direction from -the figure towards the point. On the sixth evening the second satellite -was seen on the disc of the planet. - -[Illustration: _Fig. 23._] - - -NOTE 89, p. 28. _Angular motion or velocity_ is the swiftness with which -a body revolves—a sling, for example; or the speed with which the -surface of the earth performs its daily rotation about its axis. - - -NOTE 90, p. 29. _Displacement of Jupiter’s orbit._ The action of the -planets occasions secular variations in the position of Jupiter’s orbit -J O, fig. 22, without affecting the plane of his equator J E. Again, the -sun and satellites themselves, by attracting the protuberant matter at -Jupiter’s equator, change the position of the plane J E without -affecting J O. Both of these cause perturbations in the motions of the -satellites. - - -NOTE 91, p. 29. _Precession_, with regard to Jupiter, is a retrograde -motion of the point where the lines J O, J E, intersect fig. 22. - - -NOTE 92, p. 30. _Synodic motion of a satellite._ Its motion during the -interval between two of its consecutive eclipses. - -[Illustration: _Fig. 24._] - - -NOTE 93, p. 30. _Opposition._ A body is said to be in opposition when -its longitude differs from that of the sun by 180°. If S, fig. 24, be -the sun, and E the earth, then Jupiter is in opposition when at O, and -in conjunction when at C. In these positions the three bodies are in the -same straight line. - - -NOTE 94, p. 30. _Eclipses of the satellites._ Let S, fig. 25, be the -sun, J Jupiter, and a B b his shadow. Let the earth be moving in its -orbit, in the direction E A R T H, and the third satellite in the -direction a b m n. When the earth is at E, the satellite, in moving -through the arc a b, will vanish at a, and reappear at b, on the same -side of Jupiter. If the earth be in R, Jupiter will be in opposition; -and then the satellite, in moving through the arc a b, will vanish close -to the disc of the planet, and will reappear on the other side of it. -But, if the satellite be moving through the arc m n, it will appear to -pass over the disc, and eclipse the planet. - -[Illustration: _Fig. 25._] - - -NOTE 95, pp. 30, 43. _Meridian._ A terrestrial meridian is a line -passing round the earth and through both poles. In every part of it noon -happens at the same instant. In figures 1 and 3, the lines N Q S and N G -S are meridians, C being the centre of the earth, and N S its axis of -rotation. The meridian passing through the Observatory at Greenwich is -assumed by the British as a fixed origin from whence terrestrial -longitudes are measured. And as each point on the surface of the earth -passes through 360°, or a complete circle, in twenty-four hours, at the -rate of 15° in an hour, time becomes a representative of angular motion. -Hence, if the eclipse of a satellite happens at any place at eight -o’clock in the evening, and the Nautical Almanac shows that the same -phenomenon will take place at Greenwich at nine, the place of -observation will be in the 15° of west longitude. - - -NOTE 96, p. 31. _Conjunction._ Let S be the sun, fig. 24, E the earth, -and J O Jʹ Cʹ the orbit of Jupiter. Then the eclipses which happen when -Jupiter is in O are seen 16^m 26^s sooner than those which take place -when the planet is in C. Jupiter is in conjunction when at C, and in -opposition when in O. - -[Illustration: _Fig. 26._] - - -NOTE 97, p. 31. _In the diagonal, &c._ Were the line A S, fig. 26, -100,000 times longer than A B, Jupiter’s true place would be in the -direction A Sʹ, the diagonal of the figure A B Sʹ S, which is, of -course, out of proportion. - - -NOTE 98, p. 31. _Aberration of light._ The celestial bodies are so -distant that the rays of light coming from them may be reckoned -parallel. Therefore, let S A, Sʹ B, fig. 26, be two rays of light coming -from the sun, or a planet, to the earth moving in its orbit in the -direction A B. If a telescope be held in the direction A S, the ray S A, -instead of going down the tube, will impinge on its side, and be lost in -consequence of the telescope being carried with the earth in the -direction A B. But, if the tube be held in the position A E, so that A B -is to A S as the velocity of the earth to the velocity of light, the ray -will pass through Sʹ E A. The star appears to be in the direction A Sʹ, -when it really is in the direction A S; hence the angle S A Sʹ is the -angle of aberration. - - -NOTE 99, p. 32. _Density proportional to elasticity._ The more a fluid, -such as atmospheric air, is reduced in dimensions by pressure, the more -it resists the pressure. - - -NOTE 100, p. 32. _Oscillations of pendulum retarded._ If a clock be -carried from the pole to the equator, its rate will be gradually -diminished, that is, it will go slower and slower: because the -centrifugal force, which increases from the pole to the equator, -diminishes the force of gravity. - - -NOTE 101, p. 34. _Disturbing action._ The disturbing force acts here in -the very same manner as in note 63; only that the disturbing body d, -fig. 14, is the sun, S the earth, and p the moon. - - -NOTE 102, pp. 35, 36, 86. _Perigee._ A Greek word, signifying round the -earth. The perigee of the lunar orbit is the point P, fig. 6, where the -moon is nearest to the earth. It corresponds to the perihelion of a -planet. Sometimes the word is used to denote the point where the sun is -nearest to the earth. - - -NOTE 103, p. 35. _Evection._ The evection is produced by the action of -the radial force in the direction S p, fig. 14, which sometimes -increases and sometimes diminishes the earth’s attraction to the moon. -It produces a corresponding temporary change in the excentricity, which -varies with the position of the major axis of the lunar orbit in respect -of the line S d, joining the centres of the earth and sun. - - -NOTE 104, p. 35. _Variation._ The lunar perturbation called the -variation is the alternate acceleration and retardation of the moon in -longitude, from the action of the tangential force. She is accelerated -in going from quadratures in Q and D, fig. 14, to the points C and O, -called syzygies, and is retarded in going from the syzygies C and O to Q -and D again. - - -NOTE 105, p. 36. _Square of time._ If the times increase at the rate of -1, 2, 3, 4, &c., years or hundreds of years, the squares of the times -will be 1, 4, 9, 16, &c., years or hundreds of years. - - -NOTE 106, p. 37. In all investigations hitherto made with regard to the -acceleration, it was tacitly assumed that the areas described by the -radius vector of the moon were not permanently altered; that is to say, -that the tangential disturbing force produced no permanent effect. But -Mr. Adams has discovered that, in consequence of the constant decrease -in the excentricity of the earth’s orbit, there is a gradual change in -the central disturbing force which affects the aërial velocity, and -consequently it alters the amount of the acceleration by a very small -quantity, as well as the variation and other periodical inequalities of -the moon. On the latter, however, it has no permanent effect, because it -affects them in opposite directions in very moderate intervals of time, -whereas a very small error in the amount of the acceleration goes on -increasing as long as the excentricity of the earth’s orbit diminishes, -so that it would ultimately vitiate calculations of the moon’s place for -distant periods of time. This shows how complicated the moon’s motions -are, and what rigorous accuracy is required in their determination. - -To give an idea of the labour requisite _merely_ to _perfect_ or -_correct_ the lunar tables, the moon’s place was determined by -observation at the Greenwich Observatory in 6000 different points of her -orbit, each of which was compared with the same points calculated from -Baron Plana’s formulæ, and to do that _sixteen computers_ were -constantly employed for _eight years_. Since the longitude is determined -by the motions of the moon, the lunar tables are of the greatest -importance. - - -NOTE 107, p. 37. _Mean anomaly._ The mean anomaly of a planet is its -angular distance from the perihelion, supposing it to move in a circle. -The true anomaly is its angular distance from the perihelion in its -elliptical orbit. For example, in fig. 10, the mean anomaly is P C m, -and the true anomaly is P S p. - - -NOTE 108, pp. 38, 68. _Many circumferences._ There are 360 degrees or -1,296,000 seconds in a circumference; and, as the acceleration of the -moon only increases at the rate of eleven seconds in a century, it must -be a prodigious number of ages before it accumulates to many -circumferences. - - -NOTE 109, p. 39. _Phases of the moon._ The periodical changes in the -enlightened part of her disc, from a crescent to a circle, depending -upon her position with regard to the sun and earth. - - -NOTE 110, p. 39. _Lunar eclipse._ Let S, fig. 27, be the sun, E the -earth, and m the moon. The space a A b is a section of the shadow, which -has the form of a cone or sugar-loaf, and the spaces A a c, A b d, are -the penumbra. The axis of the cone passes through A, and through E and -S, the centres of the sun and earth, and n m nʹ is the path of the moon -through the shadow. - -[Illustration: _Fig. 27._] - - -NOTE 111, p. 39. _Apparent diameter._ The diameter of a celestial body -as seen from the earth. - - -NOTE 112, p. 40. _Penumbra._ The shadow or imperfect darkness which -precedes and follows an eclipse. - - -NOTE 113, p. 40. _Synodic revolution of the moon._ The time between two -consecutive new or full moons. - - -NOTE 114, p. 40. _Horizontal refraction._ The light, in coming from a -celestial object, is bent into a curve as soon as it enters our -atmosphere; and that bending is greatest when the object is in the -horizon. - -[Illustration: _Fig. 28._] - - -NOTE 115, p. 40. _Solar eclipse._ Let S, fig. 28, be the sun, m the -moon, and E the earth. Then a E b is the moon’s shadow, which sometimes -eclipses a small portion of the earth’s surface at e, and sometimes -falls short of it. To a person at e, in the centre of the shadow, the -eclipse may be total or annular; to a person not in the centre of the -shadow a part of the sun will be eclipsed; and to one at the edge of the -shadow there will be no eclipse at all. The spaces P b E, Pʹ a E, are -the penumbra. - - -NOTE 116, p. 43. _From the extremities, &c._ If the length of the line a -b, fig. 29, be measured, in feet or fathoms, the angles S b a, S a b, -can be measured, and then the angle a S b is known, whence the length of -the line S C may be computed. a S b is the parallax of the object S; and -it is clear that, the greater the distance of S, the less the base a b -will appear, because the angle a Sʹ b is less than a S b. - -[Illustration: _Fig. 29._] - - -NOTE 117, p. 44. _Every particle will describe a circle, &c._ If N S, -fig. 3, be the axis about which the body revolves, then particles at B, -Q, &c., will whirl in the circles B G A a, Q E q d, whose centres are in -the axis N S, and their planes parallel to one another. They are, in -fact, parallels of latitude, Q E q d being the equator. - - -NOTE 118, p. 44. _The force of gravity, &c._ Gravity at the equator acts -in the direction Q C, fig. 30. Whereas the direction of the centrifugal -force is exactly contrary, being in the direction C Q; hence the -difference of the two is the force called gravitation, which makes -bodies fall to the surface of the earth. At any point, m, not at the -equator, the direction of gravity is m b, perpendicular to the surface, -but the centrifugal force acts perpendicularly to N S, the axis of -rotation. Now the effect of the centrifugal force is the same as if it -were two forces, one of which acting in the direction b m, diminishes -the force of gravity, and another which, acting in the direction m t, -tangent to the surface at m, urges the particles towards Q, and tends to -swell out the earth at the equator. - -[Illustration: _Fig. 30._] - - -NOTE 119, p. 45. _Homogeneous mass._ A quantity of matter, everywhere of -the same density. - - -NOTE 120, p. 45. _Ellipsoid of revolution._ A solid formed by the -revolution of an ellipse about its axis. If the ellipse revolve about -its minor axis Q D, fig. 6, the ellipsoid will be _oblate_, or flattened -at the poles like an orange. If the revolution be about the greater axis -A P, the ellipsoid will be prolate, like an egg. - - -NOTE 121, p. 45. _Concentric elliptical strata._ Strata, or layers, -having an elliptical form and the same centre. - - -NOTE 122, p. 46. _On the whole, &c._ The line N Q S q, fig. 1, -represents the ellipse in question, its major axis being Q q, its minor -axis N S. - - -NOTE 123, p. 46. _Increase in the length of the radii, &c._ The radii -gradually increase from the polar radius C N, fig. 30, which is least, -to the equatorial radius C Q, which is greatest. There is also an -increase in the lengths of the arcs corresponding to the same number of -degrees from the equator to the poles; for, the angle N C r being equal -to q C d, the elliptical arc N r is less than q d. - - -NOTE 124, p. 46. _Cosine of latitude._ The angles m C a, m C b, fig. 4, -being the latitudes of the points a, b, &c., the cosines are C q, C r, -&c. - - -NOTE 125, p. 47. _An arc of the meridian._ Let N Q S q, fig. 30, be the -meridian, and m n the arc to be measured. Then, if Zʹ m, Z n, be -verticals, or lines perpendicular to the surface of the earth, at the -extremities of the arc m n they will meet in p. Q a n, Q b m, are the -latitudes of the points m and n, and their difference is the angle m p -n. Since the latitudes are equal to the height of the pole of the -equinoctial above the horizon of the places m and n, the angle m p n may -be found by observation. When the distance m n is measured in feet or -fathoms, and divided by the number of degrees and parts of a degree -contained in the angle m p n, the length of an arc of one degree is -obtained. - - -NOTE 126, p. 47. _A series of triangles._ Let M Mʹ, fig. 31, be the -meridian of any place. A line A B is measured with rods, on level -ground, of any number of fathoms, C being some point seen from both ends -of it. As two of the angles of the triangle A B C can be measured, the -lengths of the sides A C, B C, can be computed; and if the angle m A B, -which the base A B makes with the meridian, be measured, the length of -the sides B m, A m, may be obtained by computation, so that A m, a small -part of the meridian, is determined. Again, if D be a point visible from -the extremities of the known line B C, two of the angles of the triangle -B C D may be measured, and the length of the sides C D, B D, computed. -Then, if the angle B m mʹ be measured, all the angles and the side B m -of the triangle B m mʹ are known, whence the length of the line m mʹ may -be computed, so that the portion A mʹ of the meridian is determined, and -in the same manner it may be prolonged indefinitely. - -[Illustration: _Fig. 31._] - - -NOTE 127, pp. 47, 49. _The square of the sine of the latitude._ Q b m, -fig. 30, being the latitude of m, e m is the sine and b e the cosine. -Then the number expressing the length of e m, multiplied by itself, is -the square of the sine of the latitude; and the number expressing the -length of b e, multiplied by itself, is the square of the cosine of the -latitude. - - -NOTE 128, p. 48. The polar diameter of the earth determined by the -survey of Great Britain is 7900 miles; the equatorial is 7926, which -gives a compression of 1/299·33. - - -NOTE 129, p. 50. _A pendulum_ is that part of a clock which swings to -and fro. - -[Illustration: _Fig. 32._] - - -NOTE 130, p. 52. _Parallax._ The angle a S b, fig. 29, under which we -view an object a b: it therefore diminishes as the distance increases. -The parallax of a celestial object is the angle which the radius of the -earth would be seen under, if viewed from that object. Let E, fig. 32, -be the centre of the earth, E H its radius, and m H O the horizon of an -observer at H. Then H m E is the parallax of a body m, the moon for -example. As m rises higher and higher in the heavens to the points mʹ, -mʺ, &c., the parallax H mʹ E, H mʺ E, &c., decreases. At Z, the zenith, -or point immediately above the head of the observer, it is zero; and at -m, where the body is in the horizon, the angle H m E is the greatest -possible, and is called the horizontal parallax. It is clear that with -regard to celestial bodies the whole effect of parallax is in the -vertical, or in the direction m mʹ Z; and as a person at H sees mʹ in -the direction H mʹ A, when it really is in the direction E mʹ B, it -makes celestial objects appear to be lower than they really are. The -distance of the moon from the earth has been determined from her -horizontal parallax. The angle E m H can be measured. E H m is a right -angle, and E H, the radius of the earth, is known in miles; whence the -distance of the moon E m is easily found. Annual parallax is the angle -under which the diameter of the earth’s orbit would be seen if viewed -from a star. - - -NOTE 131, p. 52. _The radii_ n B, n G, &c., fig. 3, are equal in any one -parallel of latitude, A a B G; therefore a change in the parallax -observed in that parallel can only arise from a change in the moon’s -distance from the earth; and when the moon is at her mean distance, -which is a constant quantity equal to half the major axis of her orbit, -a change in the parallax observed in different latitudes, G and E, must -arise from the difference in the lengths of the radii n G and C E. - - -NOTE 132, p. 52. _When Venus is in her nodes._ She must be in the line N -S n where her orbit P N A n cuts the plane of the ecliptic E N e n, fig. -12. - - -NOTE 133, p. 53. _The line described, &c._ Let E, fig. 33, be the earth, -S the centre of the sun, and V the planet Venus. The real transit of the -planet, seen from E the centre of the earth, would be in the direction A -B. A person at W would see it pass over the sun in the line v a, and a -person at O would see it move across him in the direction vʹ aʹ. - -[Illustration: _Fig. 33._] - - -NOTE 134, p. 54. _Kepler’s law._ Suppose it were required to find the -distance of Jupiter from the sun. The periodic times of Jupiter and -Venus are given by observation, and the mean distance of Venus from the -centre of the sun is known in miles or terrestrial radii; therefore, by -the rule of three, the square root of the periodic time of Venus is to -the square root of the periodic time of Jupiter as the cube root of the -mean distance of Venus from the sun to the cube root of the mean -distance of Jupiter from the sun, which is thus obtained in miles or -terrestrial radii. The root of a number is that number which, once -multiplied by itself, gives its square; twice multiplied by itself, -gives its cube, &c. For example, twice 2 are 4, and twice 4 are 8; 2 is -therefore the square root of 4, and the cube root of 8. In the same -manner 3 times 3 are 9, and 3 times 9 are 27; 3 is therefore the square -root of 9, and the cube root of 27. - - -NOTE 135, p. 55. _Inversely, &c._ The quantities of matter in any two -primary planets are greater in proportion as the cubes of the numbers -representing the mean distances of their satellites are greater, and -also in proportion as the squares of their periodic times are less. - - -NOTE 136, p. 55. As hardly anything appears more impossible than that -man should have been able to weigh the sun as it were in scales and the -earth in a balance, the method of doing so may have some interest. The -attraction of the sun is to the attraction of the earth as the quantity -of matter in the sun to the quantity of matter in the earth; and, as the -force of this reciprocal attraction is measured by its effects, the -space the earth would fall through in a second by the sun’s attraction -is to the space which the sun would fall through by the earth’s -attraction as the mass of the sun to the mass of the earth. Hence, as -many times as the fall of the earth to the sun in a second exceeds the -fall of the sun to the earth in the same time, so many times does the -mass of the sun exceed the mass of the earth. Thus the weight of the sun -will be known if the length of these two spaces can be found in miles or -parts of a mile. Nothing can be easier. A heavy body falls through -16·0697 feet in a second at the surface of the earth by the earth’s -attraction; and, as the force of gravity is inversely as the square of -the distance, it is clear that 16·0697 feet are to the space a body -would fall through at the distance of the sun by the earth’s attraction, -as the square of the distance of the sun from the earth to the square of -the distance of the centre of the earth from its surface; that is, as -the square of 95,000,000 miles to the square of 4000 miles. And thus, by -a simple question in the rule of three, the space which the sun would -fall through in a second by the attraction of the earth may be found in -parts of a mile. The space the earth would fall through in a second, by -the attraction of the sun, must now be found in miles also. Suppose m n, -fig. 4, to be the arc which the earth describes round the sun in C, in a -second of time, by the joint action of the sun and the centrifugal -force. By the centrifugal force alone the earth would move from m to T -in a second, and by the sun’s attraction alone it would fall through T n -in the same time. Hence the length of T n, in miles, is the space the -earth would fall through in a second by the sun’s attraction. Now, as -the earth’s orbit is very nearly a circle, if 360 degrees be divided by -the number of seconds in a sidereal year of 365-1/4 days, it will give m -n, the arc which the earth moves through in a second, and then the -tables will give the length of the line C T in numbers corresponding to -that angle; but, as the radius C n is assumed to be unity in the tables, -if 1 be subtracted from the number representing C T, the length of T n -will be obtained; and, when multiplied by 95,000,000, to reduce it to -miles, the space which the earth falls through, by the sun’s attraction, -will be obtained in miles. By this simple process it is found that, if -the sun were placed in one scale of a balance, it would require 354,936 -earths to form a counterpoise. - - -NOTE 137, p. 59. The sum of the greatest and least distances S P, S A, -fig. 12, is equal to P A, the major axis; and their difference is equal -to twice the excentricity C S. The longitude ♈ S P of the planet, when -in the point P, at its least distance from the sun, is the longitude of -the perihelion. The greatest height of the planet above the plane of the -ecliptic E N e n, is equal to the inclination of the orbit P N A n to -that plane. The longitude of the planet, when in the plane of the -ecliptic, can only be the longitude of one of the points N or n; and, -when one of these points is known, the other is given, being 180° -distant from it. Lastly, the time included between two consecutive -passages of the planet through the same node N or n, is its periodic -time, allowance being made for the recess of the node in the interval. - - -NOTE 138, p. 60. Suppose that it were required to find the position of a -point in space, as of a planet, and that one observation places it in n, -fig. 34, another observation places it in nʹ, another in nʺ, and so on; -all the points n, nʹ, nʺ, nʹʹʹ, &c., being very near to one another. The -true place of the planet P will not differ much from any of these -positions. It is evident, from this view of the subject, that P n, P nʹ, -P nʺ, &c., are the errors of observation. The true position of the -planet P is found by this property, that the squares of the numbers -representing the lines P n, P nʹ, &c., when added together, is the least -possible. Each line P n, P nʹ, &c., being the whole error in the place -of the planet, is made up of the errors of all the elements; and, when -compared with the errors obtained from theory, it affords the means of -finding each. The principle of least squares is of very general -application; its demonstration cannot find a place here; but the reader -is referred to Biot’s Astronomy, vol. ii. p. 203. - -[Illustration: _Fig. 34._] - - -NOTE 139, p. 61. The true longitude of Uranus was in advance of the -tables previous to 1795, and continued to advance till 1822, after which -it diminished rapidly till 1830-1, when the observed and calculated -longitudes agreed, but then the planet fell behind the calculated place -so rapidly that it was clear the tables could no longer represent its -motion. - - -NOTE 140, p. 65. _An axis that, &c._ Fig. 20 represents the earth -revolving in its orbit about the sun in S, the axis of rotation P p -being everywhere parallel to itself. - - -NOTE 141, p. 65. _Angular velocities that are sensibly uniform._ The -earth and planets revolve about their axis with an equable motion, which -is never either faster or slower. For example, the length of the day is -never more nor less than twenty-four hours. - - -NOTE 142, p. 68. If fig. 1 be the moon, her polar diameter N S is the -shortest; and of those in the plane of the equator, Q E q, that which -points to the earth is greater than all the others. - - -NOTE 143, p. 73. _Inversely proportional, &c._ That is, the total amount -of solar radiation becomes less as the minor axis C Cʹ, fig. 20, of the -earth’s orbit becomes greater. - - -NOTE 144, p. 75. Fig. 35 represents the position of the apparent orbit -of the sun as it is at present, the earth being in E. The sun is nearer -to the earth in moving through ♎ P ♈ than in moving through ♈ A ♎, but -its motion through ♎ P ♈ is more rapid than its motion through ♈ A ♎; -and, as the swiftness of the motion and the quantity of heat received -vary in the same proportion, a compensation takes place. - -[Illustration: _Fig. 35._] - - -NOTE 145, p. 76. _In an ellipsoid of revolution_, fig. 1, the polar -diameter N S, and every diameter in the equator q E Q e, are permanent -axes of rotation, but the rotation would be unstable about any other. -Were the earth to begin to rotate about C a, the angular distance from a -to the equator at q would no longer be ninety degrees, which would be -immediately detected by the change it would occasion in the latitudes. - - -NOTE 146, pp. 50, 80. Let q ♈ Q, and E ♎ e, fig. 11, be the planes of -the equator and ecliptic. The angle e ♈ Q, which separates them, called -the obliquity of the ecliptic, varies in consequence of the action of -the sun and moon upon the protuberant matter at the earth’s equator. -That action brings the point Q towards e, and tends to make the plane q -♈ Q coincide with the ecliptic E ♈ e, which causes the equinoctial -points ♈ and ♎ to move slowly backwards on the plane e ♈ E, at the rate -of 50ʺ·41 annually. This part of the motion, which depends upon the form -of the earth, is called luni-solar precession. Another part, totally -independent of the form of the earth, arises from the mutual action of -the earth, planets, and sun, which, altering the position of the plane -of the ecliptic e ♈ E, causes the equinoctial points ♈ and ♎ to advance -at the rate of Oʺ·31 annually; but, as this motion is much less than the -former, the equinoctial points recede on the plane of the ecliptic at -the rate of 50ʺ·1 annually. This motion is called the precession of the -equinoxes. - - -NOTE 147, p. 81. Let q ♈ Q, e ♈ E, fig. 36, be the planes of the -equinoctial or celestial equator and ecliptic, and p, P, their poles. -Then suppose p, the pole of the equator, to revolve with a tremulous or -wavy motion in the little ellipse p c d b in about 19 years, both -motions being very small, while the point a is carried round in the -circle a A B in 25,868 years. The tremulous motion may represent the -half-yearly variation, the motion in the ellipse gives an idea of the -nutation discovered by Bradley, and the motion in the circle a A B -arises from the precession of the equinoxes. The greater axis p d of the -small ellipse is 18ʺ·5, its minor axis b c is 13ʺ·74. These motions are -so small that they have very little effect on the parallelism of the -axis of the earth’s rotation during its revolution round the sun, as -represented in fig. 20. As the stars are fixed, this real motion in the -pole of the earth must cause an apparent change in their places. - -[Illustration: _Fig. 36._] - -[Illustration: figure: equidistant wires in an eye-piece] - - -NOTE 148, p. 83. By means of a transit instrument, which is a telescope -mounted so as to revolve only in the plane of the meridian, the instant -of the transit or passage of a celestial body across the meridian can be -determined. The transits of the principal stars are used to ascertain -the time, or, which is the same thing, the amount of the error of -clocks. A system of equidistant wires, as represented in the figure, is -placed in the focus of the eye-piece, so that the middle wire is -perpendicular and at right angles to the axis of the telescope. It -consequently represents a portion of the celestial meridian; and when a -star is seen to cross that wire it then crosses the celestial meridian -of the place of observation. A clock beating seconds being close at -hand, the duty of an observer is to note the exact second and part of a -second at which a star crosses each wire successively in consequence of -the rotation of the earth. Then the mean of all these observations will -give the time at which the star crosses the celestial meridian of the -place of observation to the tenth of a second, provided the observations -are accurate. Now it happens that the simultaneous impression on the eye -and ear is estimated differently by different observers, so that one -person will note the transit of a star, for example, as happening the -fraction of a second sooner or later than another person; and as that is -the case in every observation he makes, it is called his _personal -equation_, that is to say, it is a correction that must be applied to -all the observations of the individual, and a curious instance of -individuality it is. For instance, M. Otto Struve notes every -observation Oʺ·11 too soon, M. Peters Oʺ·13 too late; M. Struve noted -every observation one second later than M. Bessel, and M. Argelander -estimated the transit of a star 1ʺ·2 later than M. Bessel. All these -gentlemen were or are first-rate observers; and when the personal -equation is known it is easy to correct the observations. However, to -avoid that inconvenience Mr. Bond has introduced a method in the -Observatory at Cambridge in the United States in which touch is combined -with sight instead of hearing, which is now used also at Greenwich. The -observer at the moment of the observation presses his fingers on a -machine which by means of a galvanic battery conveys the impression to -where time is measured and marked, so that the observation is at once -recorded and the personal equation avoided. - - -NOTE 149, p. 84. _Let_ N be the pole, fig. 11, e E the ecliptic, and Q q -the equator. Then, N n m S being a meridian, and at right angles to the -equator, the arc ♈ m is less than the arc ♈ n. - - -NOTE 150, p. 85. _Heliacal rising of Sirius._ When the star appears in -the morning, in the horizon, a little before the rising of the sun. - - -NOTE 151, p. 87. Let P ♈ A ♎, fig. 35, be the apparent orbit or path of -the sun, the earth being in E. Its major axis, A P, is at present -situate as in the figure, where the solar perigee P is between the -solstice of winter and the equinox of spring. So that the time of the -sun’s passage through the arc ♈ A ♎ is greater than the time he takes to -go through the arc ♎ P ♈. The major axis A P coincided with ♎ ♈, the -line of the equinoxes, 4000 years before the Christian era; at that time -P was in the point ♈. In 6468 of the Christian era the perigee P will -coincide with ♎. In 1234 A.D. the major axis was perpendicular to ♈ ♎, -and then P was in the winter solstice. - - -NOTE 152, p. 88. _At the solstices, &c._ Since the declination of a -celestial object is its angular distance from the equinoctial, the -declination of the sun at the solstice is equal to the arc Q e, fig. 11, -which measures the obliquity of the ecliptic, or angular distance of the -plane ♈ e ♎ from the plane ♈ Q ♎. - - -NOTE 153, p. 88. _Zenith distance_ is the angular distance of a -celestial object from the point immediately over the head of an -observer. - - -NOTE 154, p. 89. _Reduced to the level of the sea._ The force of -gravitation decreases as the square of the height above the surface of -the earth increases, so that a pendulum vibrates slower on high ground; -and, in order to have a standard independent of local circumstances, it -is necessary to reduce it to the length that would exactly make 86,400 -vibrations in a mean solar day at the level of the sea. - - -NOTE 155, p. 90. _A quadrant of the meridian_ is a fourth part of a -meridian, or an arc of a meridian containing 90°, as N Q, fig. 11. - - -NOTE 156, p. 93. _Moon’s southing._ The time when the moon is on the -meridian of any place, which happens about forty-eight minutes later -every day. - - -NOTE 157, p. 96. _The angular velocity of the earth’s rotation_ is at -the rate of 180° in twelve hours, which is the time included between the -passages of the moon at the upper and under meridian. - - -NOTE 158, p. 96. If S be the earth, fig. 14, d the sun, and C Q O D the -orbit of the moon, then C and O are the syzygies. When the moon is new, -she is at C, and when full she is at O; and, as both sun and moon are -then on the same meridian, it occasions the spring-tides, it being high -water at places under C and O, while it is low water at those under Q -and D. The neap-tides happen when the moon is in quadrature at Q or D, -for then she is distant from the sun by the angle d S Q, or d S D, each -of which is 90°. - - -NOTE 159, p. 97. _Declination._ If the earth be in C, fig. 11, and if q -♈ Q be the equinoctial, and N m S a meridian, then m C n is the -declination of a body at n. Therefore the cosine of that angle is the -cosine of the declination. - - -NOTE 160, pp. 99, 131. Fig 37 shows the propagation of waves from two -points C and Cʹ, where stones are supposed to have fallen. Those points -in which the waves cross each other are the places where they counteract -each other’s effects, so that the water is smooth there, while it is -agitated in the intermediate spaces. - - -NOTE 161, p. 100. _The centrifugal force may, &c._ The centrifugal force -acts in a direction at right angles to N S, the axis of rotation, fig. -30. Its effects are equivalent to two forces, one of which is in the -direction b m perpendicular to the surface Q m n of the earth, and -diminishes the force of gravity at m. The other acts in the direction of -the tangent m T, which makes the fluid particles tend towards the -equator. - -[Illustration: _Fig. 37._] - - -NOTE 162, p. 106. _Analytical formula or expression._ A combination of -symbols or signs expressing or representing a series of calculation, and -including every particular case that can arise from a general law. - - -NOTE 163, p. 106. _Fig. 38 is a perfect octahedron._ Sometimes its -angles, A, X, a, a, &c., are truncated, or cut off. Sometimes a slice is -cut off its edges A a, X a, a a, &c. Occasionally both these -modifications take place. - -[Illustration: _Fig. 38._] - - -NOTE 164, p. 107. Prismatic crystals of sulphate of nickel are somewhat -like fig. 62, only that they are thin, like a hair. - - -NOTE 165, p. 108. _Zinc_, a metal either found as an ore or mixed with -other metals. It is used in making brass. - - -NOTE 166, p. 108. _A cube_ is a solid contained by six plane square -surfaces, as fig. 39. - -[Illustration: _Fig. 39._] - - -NOTE 167, p. 108. _A tetrahedron_ is a solid contained by four -triangular surfaces, as fig. 40: of this solid there are many varieties. - -[Illustration: _Fig. 40._] - - -NOTE 168, p. 108. There are many varieties of the octahedron. In that -mentioned in the text, the base a a a a, fig. 38, is a square, but the -base may be a rhomb; this solid may also be elongated in the direction -of its axis A X, or it may be depressed. - - -NOTE 169, pp. 109, 192, 273. _A rhombohedron_ is a solid contained by -six plane surfaces, as in fig. 63, the opposite planes being equal and -similar rhombs parallel to one another; but all the planes are not -necessarily equal or similar, nor are its angles right angles. In -carbonate of lime the angle C A B is 105°·55, and the angle B or C is -75°·05. - - -NOTE 170, p. 109. _Sublimation._ Bodies raised into vapour which is -again condensed into a solid state. - - -NOTE 171, p. 112. _Platinum._ The heaviest of metals; its colour is -between that of silver and lead. - - -NOTE 172, p. 113. The surface of a column of water, or spirit of wine, -in a capillary tube, is hollow; and that of a column of quicksilver is -convex, or rounded, as in fig. 41. - - -NOTE 173, p. 113. _Inverse ratio, &c._ The elevation of the liquid is -greater in proportion as the internal diameter of the tube is less. - - -NOTE 174, p. 114. In fig. 41 the line c d shows the direction of the -resulting force in the two cases. - -[Illustration: _Fig. 41._] - - -NOTE 175, p. 115. When two plates of glass are brought near to one -another in water, the liquid rises between them; and, if the plates -touch each other at one of their upright edges, the outline of the water -will become an hyperbola. - - -NOTE 176, p. 115. Let A Aʹ, fig. 42, be two plates, both of which are -wet, and B Bʹ two that are dry. When partly immersed in a liquid, its -surface will be curved close to them, but will be of its usual level for -the rest of the distance. At such a distance they will neither attract -nor repel one another. But, as soon as they are brought near enough to -have the whole of the liquid surface between them curved, as in a aʹ, b -bʹ, they will rush together. If one be wet and another dry, as C Cʹ, -they will repel one another at a certain distance; but, as soon as they -are brought very near, they will rush together, as in the former cases. - -[Illustration: _Fig. 42._] - - -NOTE 177, p. 123. In a paper on the atmospheric changes that produce -rain and wind, by Thomas Hopkins, Esq., in the Geographical Journal, it -is shown that, when vapour is condensed and falls in rain, a partial -vacuum is formed, and that heavier air presses in as a current of wind. -Thus the vacuum arising from the great precipitation at the tropics -causes the polar winds to descend from the upper regions of the -atmosphere and blow along the surface to the equator as trade winds to -supply the place of the hot currents that are continually raising them -into the higher regions. This circumstance removes the only difficulty -in Lieutenant Maury’s theory of the winds. - - -NOTE 178, p. 134. _Latent or absorbed heat._ There is a certain quantity -of heat in all bodies, which cannot be detected by the thermometer, but -which may become sensible by compression. - - -NOTE 179, p. 137. _Reflected waves._ A series of waves of light, sound, -or water, diverge in all directions from their origin I, fig. 43, as -from a centre. When they meet with an obstacle S S, they strike against -it, and are reflected or turned back by it in the same form as if they -had proceeded from the centre C, at an equal distance on the other side -of the surface S S. - -[Illustration: _Fig. 43._] - - -NOTE 180, p. 138. _Elliptical shell._ If fig. 6 be a section of an -elliptical shell, then all sounds coming from the focus S to different -points on the surface, as m, are reflected back to F, because the angle -T m S is equal to t m F. In a spherical hollow shell, a sound diverging -from the centre is reflected back to the centre again. - - -NOTE 181, p. 142. Fig. 44 represents musical strings in vibration; the -straight lines are the strings when at rest. The first figure of the -four would give the fundamental note, as, for example, the low C. The -second and third figures would give the first and second harmonics; that -is, the octave and the 12th above C, n n n being the points at rest; the -fourth figure shows the real motion when compounded of all three. - -[Illustration: _Fig. 44._] - - -NOTE 182, p. 143. Fig. 45 represents sections of an open and of a shut -pipe, and of a pipe open at one end. When sounded, the air spontaneously -divides itself into segments. It remains at rest in the divisions or -nodes n nʹ, &c., but vibrates between them in the direction of the -arrow-heads. The undulations of the whole column of air give the -fundamental note, while the vibrations of the divisions give the -harmonics. - -[Illustration: _Fig. 45._] - - -NOTE 183, p. 144. Fig. 1, plate 1, shows the vibrating surface when the -sand divides it into squares, and fig. 2 represents the same when the -nodal lines divide it into triangles. The portions marked a a are in -different states of vibration from those marked b b. - - -NOTE 184, p. 145. Plates 1 and 2 contain a few of Chladni’s figures. The -white lines are the forms assumed by the sand, from different modes of -vibration, corresponding to musical notes of different degrees of pitch. -Plate 3 contains six of Chladni’s circular figures. - - -NOTE 185, p. 145. Mr. Wheatstone’s principle is, that when vibrations -producing the forms of figs. 1 and 2, plate 3, are united in the same -surface, they make the sand assume the form of fig. 3. In the same -manner, the vibrations which would separately cause the sand to take the -forms of figs. 4 and 5, would make it assume the form in fig. 6 when -united. The figure 9 results from the modes of vibration of 7 and 8 -combined. The parts marked a a are in different states of vibration from -those marked b b. Figs. 1, 2, and 3, plate 4, represent forms which the -sand takes in consequence of simple modes of vibration; 4 and 5 are -those arising from two combined modes of vibration; and the last six -figures arise from four superimposed simple modes of vibration. These -complicated figures are determined by computation independent of -experiment. - - -NOTE 186, p. 146. The long cross-lines of fig. 46 show the two systems -of nodal lines given by M. Savart’s laminæ. - -[Illustration: _Fig. 46._] - - -NOTE 187, p. 146. The short lines on fig. 46 show the positions of the -nodal lines on the other sides of the same laminæ. - - -NOTE 188, p. 146. Fig. 47 gives the nodal lines on a cylinder, with the -paper rings that mark the quiescent points. - -[Illustration: _Fig. 47._] - -[Illustration: _Fig. 48._] - - -NOTE 189, pp. 138, 153, 156. _Reflection and Refraction._ Let P C p, -fig. 48, be perpendicular to a surface of glass or water A B. When a ray -of light, passing through the air, falls on this surface in any -direction I C, part of it is reflected in the direction C S, and the -other part is bent at C, and passes through the glass or water in the -direction C R. I C is called the incident ray, and I C P the angle of -incidence; C S is the reflected ray, and P C S the angle of reflection; -C R is the refracted ray, and p C R the angle of refraction. The plane -passing through S C and I C is the plane of reflection, and the plane -passing through I C and C R is the plane of refraction. In ordinary -cases, C I, C S, C R, are all in the same plane. We see the surface by -means of the reflected light, which would otherwise be invisible. -Whatever the reflecting surface may be, and however obliquely the light -may fall upon it, the angle of reflection is always equal to the angle -of incidence. Thus I C, Iʹ C, being rays incident on the surface at C, -they will be reflected into C S, C Sʹ, so that the angle S C P will be -equal to the angle I C P, and Sʹ C P equal to Iʹ C P. That is by no -means the case with the refracted rays. The incident rays I C, Iʹ C, are -bent at C towards the perpendicular, in the direction C R, C Rʹ; and the -law of refraction is such, that the sine of the angle of incidence has a -constant ratio to the sine of the angle of refraction; that is to say, -the number expressing the length of I m, the sine of I C P, divided by -the number expressing the length of R n, the sine of R C p, is the same -for all the rays of light that can fall upon the surface of any one -substance, and is called its index of refraction. Though the index of -refraction be the same for any one substance, it is not the same for all -substances. For water it is 1·336; for crown-glass it is 1·535; for -flint-glass, 1·6; for diamond, 2·487; and for chromate of lead it is 3, -which substance has a higher refractive power than any other known. -Light falling perpendicularly on a surface passes through it without -being refracted. If the light be now supposed to pass from a dense into -a rare medium, as from glass or water into air, then R C, Rʹ C, become -the incident rays; and in this case the refracted rays, C I, C Iʹ, are -bent from the perpendicular instead of towards it. When the incidence is -very oblique, as r C, the light never passes into the air at all, but it -is _totally_ reflected in the direction C rʹ, so that the angle p C r is -equal to p C rʹ; that frequently happens at the second surface of glass. -When a ray I C falls from air upon a piece of glass A B, it is in -general refracted at each surface. At C it is bent towards the -perpendicular, and at R from it, and the ray emerges parallel to I C; -but, when the ray is very oblique to the second surface, it is totally -reflected. An object seen by total reflection is nearly as vivid as when -seen by direct vision, because no part of the light is refracted. When -light falls upon a plate of crown-glass, at an angle of 4° 32ʹ counted -from the surface, the glass reflects 4 times more light than it -transmits. At an angle of 7° 1ʹ the reflected light is double of the -transmitted; at an angle of 11° 8ʹ the light reflected is equal to that -transmitted; at 17° 17ʹ the reflected is equal to 1/2 the transmitted -light; at 26° 38ʹ it is equal to 1/4, the variation, according to Arago, -being as the square of the cosine. - - -NOTE 189, p. 154. _Atmospheric refraction._ Let a b, a b, &c., fig. 49, -be strata, or extremely thin layers, of the atmosphere, which increase -in density towards m n, the surface of the earth. A ray coming from a -star meeting the surface of the atmosphere at S would be refracted at -the surface of each layer, and would consequently move in the curved -line S v v v A; and as an object is seen in the direction of the ray -that meets the eye, the star, which really is in the direction A S, -would seem to a person at A to be in s. So that refraction, which always -acts in a vertical direction, raises objects above their true place. For -that reason, a body at Sʹ, below the horizon H A O, would be raised, and -would be seen in sʹ. The sun is frequently visible by refraction after -he is set, or before he is risen. There is no refraction in the zenith -at Z. It increases all the way to the horizon, where it is greatest, the -variation being proportional to the tangent of the angles Z A S, Z A Sʹ, -the distances of the bodies S Sʹ from the zenith. The more obliquely the -rays fall, the greater the refraction. - -[Illustration: _Fig. 49._] - -[Illustration: _Fig. 50._] - - -NOTE 190, p. 154. _Bradley’s method of ascertaining the amount of -refraction._ Let Z, fig. 50, be the zenith or point immediately above an -observer at A; let H O be his horizon, and P the pole of the equinoctial -A Q. Hence P A Q is a right angle. A star as near to the pole as s would -appear to revolve about it, in consequence of the rotation of the earth. -At noon, for example, it would be at s above the pole, and at midnight -it would be in sʹ below it. The sum of the true zenith distances, Z A s, -Z A sʹ, is equal to twice the angle Z A P. Again, S and Sʹ being the sun -at his greatest distances from the equinoctial A Q when in the -solstices, the sum of his true zenith distances, Z A S, Z A Sʹ, is equal -to twice the angle Z A Q. Consequently, the four true zenith distances, -when added together, are equal to twice the right angle Q A P; that is, -they are equal to 180°. But the observed or apparent zenith distances -are less than the true on account of refraction; therefore the sum of -the four apparent zenith distances is less than 180° by the whole amount -of the four refractions. - - -NOTE 191, p. 155. _Terrestrial refraction._ Let C, fig. 51, be the -centre of the earth, A an observer at its surface, A H his horizon, and -B some distant point, as the top of a hill. Let the arc B A be the path -of a ray coming from B to A; E B, E A, tangents to its extremities; and -A G, B F, perpendicular to C B. However high the hill B may be, it is -nothing when compared with C A, the radius of the earth; consequently, A -B differs so little from A D that the angles A E B and A C B are -supplementary to one another; that is, the two taken together are equal -to 180°. A C B is called the horizontal angle. Now B A H is the real -height of B, and E A H its apparent height; hence refraction raises the -object B, by the angle E A B, above its real place. Again, the real -depression of A, when viewed from B, is F B A, whereas its apparent -depression is F B E, so E B A is due to refraction. The angle F B A is -equal to the sum of the angles B A H and A C B; that is, the true -elevation is equal to the true depression and the horizontal angle. But -the true elevation is equal to the apparent elevation diminished by the -refraction; and the true depression is equal to the apparent depression -increased by refraction. Hence twice the refraction is equal to the -horizontal angle augmented by the difference between the apparent -elevation and the apparent depression. - -[Illustration: _Fig. 51._] - - -NOTE 192, p. 155. Fig. 52 represents the phenomenon in question. S P is -the real ship, with its inverted and direct images seen in the air. Were -there no refraction, the rays would come from the ship S P to the eye E -in the direction of the straight lines; but, on account of the variable -density of the inferior strata of the atmosphere, the rays are bent in -the curved lines P c E, P d E, S m E, S n E. Since an object is seen in -the direction of the tangent to that point of the ray which meets the -eye, the point P of the real ship is seen at p and pʹ, and the point S -seems to be in s and sʹ; and, as all the other points are transferred in -the same manner, direct and inverted images of the ship are formed in -the air above it. - -[Illustration: _Fig. 52._] - - -NOTE 193, p. 156. Fig. 53 represents the section of a poker, with the -refraction produced by the hot air surrounding it. - -[Illustration: _Fig. 53._] - - -NOTE 194, p. 156. _The solar spectrum._ A ray from the sun at S, fig. -54, admitted into a dark room, through a small round hole H in a -window-shutter, proceeds in a straight line to a screen D, on which it -forms a bright circular spot of white light, of nearly the same diameter -with the hole H. But when the refracting angle B A C of a glass prism is -interposed, so that the sunbeam falls on A C the first surface of the -prism, and emerges from the second surface A B at equal angles, it -causes the rays to deviate from the straight path S D, and bends them to -the screen M N, where they form a coloured image V R of the sun, of the -same breadth with the diameter of the hole H, but much longer. The space -V R consists of seven colours—violet, indigo, blue, green, yellow, -orange, and red. The violet and red, being the most and least -refrangible rays, are at the extremities, and the green occupy the -middle part at G. The angle D g G is called the mean _deviation_, and -the spreading of the coloured rays over the angle V g R the -_dispersion_. The deviation and dispersion vary with the refracting -angle B A C of the prism, and with the substance of which it is made. - -[Illustration: _Fig. 54._] - - -NOTE 195, pp. 159, 164. Under the same circumstances, and where the -refracting angles of the two prisms are equal, the angles D g G and V g -R, fig. 54, are greater for flint-glass than for crown-glass. But, as -they vary with the angle of the prism, it is only necessary to augment -the refracting angle of the crown-glass prism by a certain quantity, to -produce nearly the same deviation and dispersion with the flint-glass -prism. Hence, when the two prisms are placed with their refracting -angles in opposite directions, as in fig. 54, they nearly neutralize -each other’s effects, and refract a beam of light without resolving it -into its elementary coloured rays. Sir David Brewster has come to the -conclusion that there may be refraction without colour by means of two -prisms, or two lenses, when properly adjusted, even though they be made -of the same kind of glass. - - -NOTE 196, p. 165. The object glass of the achromatic telescope consists -of a convex lens A B, fig. 55, of crown-glass placed on the outside, -towards the object, and of a concave-convex lens C D of flint-glass, -placed towards the eye. The focal length of a lens is the distance of -its centre from the point in which the rays converge, as F, fig. 60. If, -then, the lenses A B and C D be so constructed that their focal lengths -are in the same proportion as their dispersive powers, they will refract -rays of light without colour. - -[Illustration: _Fig. 55._] - - -NOTE 197, p. 165. If the mean refracting angle of the prism D g G, fig. -54, were the same for all substances, then the difference D g V - D g R -would be the dispersion. But the angle of the prism being the same, all -these angles are different in each substance, so that in order to obtain -the dispersion of any substance the angle D g V - D g R must be divided -by the angle D g G or its excess above unity, to which the mean -refraction is always proportional. According to Mr. Fraunhofer the -refraction of the extreme violet and red rays in crown-glass is 1·5466 -and 1·5258; so D g V - D g R = 1·5466 - 1·5258 = ·0208, and half the sum -of the excess of each above unity is = ·5362; consequently - - (D g V - D g R)/D g G = ·0208/·5362 = 0·03879; for diamond - - (D g V - D g R)/D g G = (2·467 - 2·411)/1·439 = 0·0389; - -so that the dispersive power of diamond is a little less than that of -crown-glass; hence the splendid refracted colours which distinguish -diamond from every other precious stone are not owing to its high -dispersive power, but to its great mean refraction.—SIR DAVID BREWSTER. - - -NOTE 198, p. 168. When a sunbeam, after having passed through a coloured -glass V Vʹ, fig. 56, enters a dark room by two small slits O Oʹ in a -card, or piece of tin, they produce alternate bright and black bands on -a screen S Sʹ at a little distance. When either one or other of the -slits O or Oʹ is stopped, the dark bands vanish, and the screen is -illuminated by a uniform light, proving that the dark bands are produced -by the interference of the two sets of rays. Again, let H m, fig. 57, be -a beam of white light passing through a hole at H, made with a fine -needle in a piece of lead or a card, and received on a screen S Sʹ. When -a hair, or a small slip of card h hʹ, about the 30th of an inch in -breadth, is held in the beam, the rays bend round on each side of it, -and, arriving at the screen in different states of vibration, interfere -and form a series of coloured fringes on each side of a central white -band m. When a piece of card is interposed at C, so as to intercept the -light which passes on one side of the hair, the coloured fringes vanish. -When homogeneous light is used, the fringes are broadest in red, and -become narrower for each colour of the spectrum progressively to the -violet, which gives the narrowest and most crowded fringes. These very -elegant experiments are due to Dr. Thomas Young. - -[Illustration: _Fig. 56._] - -[Illustration: _Fig. 57._] - -[Illustration: _Fig. 58._] - - -NOTE 199, pp. 171, 200. Fig. 58 shows Newton’s rings, of which there are -seven, formed by screwing two lenses of glass together. Provided the -incident light be white, they always succeed each other in the following -order:— - -1st ring, or 1st order of colours: Black, very faint blue, brilliant -white, yellow, orange, red. - -2nd ring: Dark purple, or rather violet, blue, a very imperfect yellow -green, vivid yellow, crimson red. - -3rd ring: Purple, blue, rich grass green, fine yellow, pink, crimson. - -4th ring: Dull blueish green, pale yellowish pink, red. - -5th ring: Pale blueish green, white, pink. - -6th ring: Pale blue green, pale pink. - -7th ring: Very pale blueish green, very pale pink. - -After the seventh order the colours become too faint to be -distinguished. The rings decrease in breadth, and the colours become -more crowded together, as they recede from the centre. When the light is -homogeneous, the rings are broadest in the red, and decrease in breadth -with every successive colour of the spectrum to the violet. - - -NOTE 200, p. 172. The absolute thickness of the film of air between the -glasses is found as follows:—Let A F B C, fig. 59, be the section of a -lens lying on a plane surface or plate of glass P Pʹ, seen edgewise, and -let E C be the diameter of the sphere of which the lens is a segment. If -A B be the diameter of any one of Newton’s rings, and B D parallel to C -E, then B D or C F is the thickness of the air producing it. E C is a -known quantity; and when A B, the diameter, is measured with compasses, -B D or F C can be computed. Newton found that the length of B D, -corresponding to the darkest part of the first ring, is the 98,000th -part of an inch when the rays fall perpendicularly on the lens, and from -this he deduced the thickness corresponding to each colour in the system -of rings. By passing each colour of the solar spectrum in succession -over the lenses, Newton also determined the thickness of the film of air -corresponding to each colour, from the breadth of the rings, which are -always of the same colour with the homogeneous light. - -[Illustration: _Fig. 59._] - - -NOTE 201, p. 174. The focal length or distance of a lens is the distance -from its centre to the point F, fig. 60, in which the refracted rays -meet. Let L Lʹ be a lens of very short focal distance fixed in the -window-shutter of a dark room. A sunbeam S L Lʹ passing through the lens -will be brought to a focus in F, whence it will diverge in lines F C, F -D, and will form a circular image of light on the opposite wall. Suppose -a sheet of lead, having a small pin-hole pierced through it, to be -placed in this beam; when the pin-hole is viewed from behind with a lens -at E, it is surrounded with a series of coloured rings, which vary in -appearance with the relative positions of the pin-hole and eye with -regard to the point F. When the hole is the 30th of an inch in diameter -and at the distance of 6-1/2 feet from F, when viewed at the distance of -24 inches, there are seven rings of the following colours:— - -1st order: White, pale yellow, yellow, orange, dull red. - -2nd order: Violet, blue, whitish, greenish yellow, fine yellow, orange -red. - -3rd order: Purple, indigo blue, greenish blue, brilliant green, yellow -green, red. - -4th order: Blueish green, blueish white, red. - -5th order: Dull green, faint blueish white, faint red. - -6th order: Very faint green, very faint red. - -7th order: A trace of green and red. - -[Illustration: _Fig. 60._] - -[Illustration: _Fig. 61._] - -[Illustration: _Fig. 62._] - - -NOTE 202, p. 175. Let L Lʹ, fig. 61, be the section of a lens placed in -a window-shutter, through which a very small beam of light S L Lʹ passes -into a dark room, and comes to a focus in F. If the edge of a knife K N -be held in the beam, the rays bend away from it in hyperbolic curves K -r, K rʹ, &c., instead of coming directly to the screen in the straight -line K E, which is the boundary of the shadow. As these bending rays -arrive at the screen in different states of undulation, they interfere, -and form a series of coloured fringes, r rʹ, &c., along the edge of the -shadow K E S N of the knife. The fringes vary in breadth with the -relative distances of the knife-edge and screen from F. - - -NOTE 203, p. 177. Fig. 43 represents the phenomena in question, where S -S is the surface, and I the centre of incident waves. The reflected -waves are the dark lines returning towards I, which are the same as if -they had originated in C on the other side of the surface. - - -NOTE 204, p. 180. Fig. 62 represents a prismatic crystal of tourmaline, -whose axis is A X. The slices that are used for polarising light are cut -parallel to A X. - - -NOTE 205, p. 181. _Double refraction._ If a pencil of light R r, fig. -63, falls upon a rhombohedron of Iceland spar A B X C, it is separated -into two equal pencils of light at r, which are refracted in the -directions r O, r E: when these arrive at O and E they are again -refracted, and pass into the air in the directions O o, E o, parallel to -one another and to the incident ray R r. The ray r O is refracted -according to the ordinary law, which is, that the sines of the angles of -incidence and refraction bear a constant ratio to one another (see Note -184), and the rays R r, r O, O o, are all in the same plane. The pencil -r E, on the contrary, is bent aside out of that plane, and its -refraction does not follow the constant ratio of the sines; r E is -therefore called the extraordinary ray, and r O the ordinary ray. In -consequence of this bisection of the light, a spot of ink at O is seen -double at O and E, when viewed from r I; and when the crystal is turned -round, the image E revolves about O, which remains stationary. - -[Illustration: _Fig. 63._] - - -NOTE 206, p. 182. Both of the parallel rays O o and E o, fig. 63, are -polarised on leaving the doubly refracting crystal, and in both the -particles of light make their vibrations at right angles to the lines O -o, E o. In the one, however, these vibrations lie, for example, in the -plane of the horizon, while the vibrations of the other lie in the -vertical plane perpendicular to the horizon. - - -NOTE 207, p. 183. If light be made to fall in various directions on the -natural faces of a crystal of Iceland spar, or on faces cut and polished -artificially, one direction A X, fig. 63, will be found, along which the -light passes without being separated into two pencils. A X is the optic -axis. In some substances there are two optic axes forming an angle with -each other. The optic axis is not a fixed line, it only has a fixed -direction; for if a crystal of Iceland spar be divided into smaller -crystals, each will have its optic axis; but if all these pieces be put -together again, their optic axes will be parallel to A X. Every line, -therefore, within the crystal parallel to A X is an optic axis; but as -these lines have all the same direction, the crystal is still said to -have but one optic axis. - - -NOTE 208, p. 184. If I C, fig. 48, be the incident and C S the reflected -rays, then the particles of polarised light make their vibrations at -right angles to the plane of the paper. - - -NOTE 209, p. 184. Let A A, fig. 48, be the surface of the reflector, I C -the incident and C S the reflected rays; then, when the angle S C B is -57°, and consequently the angle P C S equal to 33°, the black spot will -be seen at C by an eye at S. - - -NOTE 210, p. 185. Let A B, fig. 48, be a reflecting surface, I C the -incident and C S the reflected rays; then, if the surface be -plate-glass, the angle S C B must be 57°, in order that C S may be -polarised. If the surface be crown-glass or water, the angle S C B must -be 56° 55ʹ for the first, and 53° 11ʹ for the second, in order to give a -polarised ray. - - -NOTE 211, p. 186. A polarising apparatus is represented in fig. 64, -where R r is a ray of light falling on a piece of glass r at an angle of -57°: the reflected ray r s is then polarised, and may be viewed through -a piece of tourmaline in s, or it may be received on another plate of -glass, B, whose surface is at right angles to the surface of r. The ray -r s is again reflected in s, and comes to the eye in the direction s E. -The plate of mica, M I, or of any substance that is to be examined, is -placed between the points r and s. - -[Illustration: _Fig. 64._] - - -NOTE 212, p. 187. In order to see these figures, the polarised ray r s, -fig. 64, must pass through the optic axis of the crystal, which must be -held as near as possible to s on one side, and the eye placed as near as -possible to s on the other. Fig. 65 shows the image formed by a crystal -of Iceland spar which has one optic axis. The colours in the rings are -exactly the same with those of Newton’s rings given in Note 199, and the -cross is black. If the spar be turned round its axis, the rings suffer -no change; but if the tourmaline through which it is viewed, or the -plate of glass, B, be turned round, this figure will be seen at the -angles 0°, 90°, 180°, and 270° of its revolution. But in the -intermediate points, that is, at the angles 45°, 135°, 225°, and 315°, -another system will appear, such as represented in fig. 66, where all -the colours of the rings are complementary to those of fig. 65, and the -cross is white. The two systems of rings, if superposed, would produce -white light. - -[Illustration: _Fig. 65._] - -[Illustration: _Fig. 66._] - - -NOTE 213, p. 188. Saltpetre, or nitre, crystallises in six-sided prisms -having two optic axes inclined to one another at an angle of 5°. A slice -of this substance about the 6th or 8th of an inch thick, cut -perpendicularly to the axis of the prism, and placed very near to s, -fig. 64, so that the polarised ray r s may pass through it, exhibits the -system of rings represented in fig. 67, where the points C and C mark -the position of the optic axes. When the plate B, fig. 64, is turned -round, the image changes successively to those given in figs. 68, 69, -and 70. The colours of the rings are the same with those of thin plates, -but they vary with the thickness of the nitre. Their breadth enlarges or -diminishes also with the colour, when homogeneous light is used. - -[Illustration: _Fig. 67._] - -[Illustration: _Fig. 68._] - -[Illustration: _Fig. 69._] - -[Illustration: _Fig. 70._] - -[Illustration: _Fig. 71._] - - -NOTE 214, p. 189. Fig. 71 represents the appearance produced by placing -a slice of rock crystal in the polarised ray r s, fig. 64. The uniform -colour in the interior of the image depends upon the thickness of the -slice; but whatever that colour may be, it will alternately attain a -maximum brightness and vanish with the revolution of the glass B. It may -be observed, that the two kinds of quartz, or rock crystal, mentioned in -the text, are combined in the amethyst, which consists of alternate -layers of right-handed and left-handed quartz, whose planes are parallel -to the axis of the crystal. - - -NOTE 215, p. 193. Suppose the major axis A P of an ellipse, fig. 18, to -be invariable, but the excentricity C S continually to diminish, the -ellipse would bulge more and more; and when C S vanished, it would -become a circle whose diameter is A P. Again, if the excentricity were -continually to increase, the ellipse would be more and more flattened -till C S was equal to C P, when it would become a straight line A P. The -circle and straight line are therefore the limits of the ellipse. - - -NOTE 216, p. 194. The coloured rings are produced by the interference of -two polarised rays in different states of undulation, on the principle -explained for common light. - - -NOTE 217, p. 225. According to Mr. Joule, that heat is produced by -motion, and that it is equivalent to it, Mr. Thompson of Glasgow -investigates from whence the sun derives his heat, since he shows that -neither combustion nor his primitive heat could have supplied the waste -during 6000 years. He concludes that the solar heat is maintained by -myriads of minute bodies that are revolving at the edge of his dense -nebulosity or atmosphere, some of which are often seen by us as falling -stars. These, vaporized by his heat, and drawn by his attraction, meet -with intense resistance on entering the solar atmosphere as a shower of -meteoric rain; through it they descend in spiral lines to the sun’s -surface, producing enormous heat by friction during their fall, and -serving for fuel on their arrival. - - -NOTE 218, p. 252. The class Cryptogamia contains the ferns, mosses, -funguses, and sea-weeds; in all of which the parts of the flowers are in -general too minute to be evident. - - -NOTE 219, p. 254. Zoophytes are the animals which form madrepores, -corals, sponges, &c. - - -NOTE 220, p. 254. The Saurian tribe are creatures of the crocodile and -lizard kind. - - -NOTE 221, p. 266. If heat from a non-luminous source be polarised by -reflection or refraction at r, fig. 64, the polarised ray r s will be -stopped or transmitted by a plate of mica M I, under the same -circumstances that it would stop or transmit light; and if heat were -visible, images analogous to those of figs. 65, 67, &c., would be seen -at the point s. - - -NOTE 222, pp. 275, 329, 357. The foot-pound, or unit of mechanical force -established by Mr. Joule, is the force that would raise one pound weight -of matter to the height of one foot; or it is the impetus or force -generated by a body of one pound weight falling by its gravitation -through the height of one foot. - -Impetus, vis viva, or living force, is equal to the mass of a body -multiplied by the square of the velocity with which it is moving, and is -the true measure of work or labour. For if a weight be raised 10 feet, -it will require four times the labour to raise an equal weight 40 feet. -If both these weights be allowed to descend freely by their gravitation, -at the end of their fall their velocities will be as 1 to 2; that is, as -the square roots of their heights; but the _effect produced_ will be as -their masses multiplied by 1 and 4; but these are the squares of their -velocities: hence the impetus or vis viva is as the mass into the square -of the velocity. - -Thus impetus is the true measure of the labour employed to raise the -weights, and of the _effect_ of their descent, and is entirely -independent of time. Now heat is proportional to impetus, and impetus is -the true measure of labour. In percussion the heat evolved is in -proportion to the force of the impetus, and is thus measured by labour. - -Travail is a word used in mechanics, to express that _work done_ is -equal to the labouring force employed. The work done may be resistance -overcome or any other effect produced, while the labouring force may be -a horse, a steam-engine, wind, falling water, &c. - - -NOTE 223, p. 313. When a stream of positive electricity descends from P -to n, fig. 72, in a vertical wire at right angles to the plane of the -horizontal circle A B, the negative electricity ascends from n to P, and -the force exerted by the current makes the north pole of a magnet -revolve about the wire in the direction of the arrow-heads in the -circumference, and it makes the south pole revolve in the opposite -direction. When the current of positive electricity flows upwards from n -to P, these effects are reversed. - -[Illustration: _Fig. 72._] - -[Illustration: _Fig. 73._] - - -NOTE 224, p. 314. Fig. 73 represents a helix or coil of copper wire, -terminated by two cups containing a little quicksilver. When the -positive wire of a Voltaic battery is immersed in the cup p, and the -negative wire in the cup n, the circuit is completed. The quicksilver -ensures the connection between the battery and the helix, by conveying -the electricity from the one to the other. While the electricity flows -through the helix, the magnet S N remains suspended within it, but falls -down the moment it ceases. The magnet always turns its south pole S -towards P, the positive wire of the battery, and its north pole towards -the negative wire. - - -NOTE 225, p. 316. A copper wire coiled in the form represented in fig. -73 was the first and most simple form of the electro-dynamic cylinder. -When its extremities P and n are connected with the positive and -negative poles of a Voltaic battery, it becomes a perfect magnet during -the time that a current of electricity is flowing through it, P and n -being its north and south poles. - - -NOTE 226, p. 344. It is to Halley we are indebted for the first -declination chart and the theory of 4 poles of maximum magnetic -intensity, since confirmed by observation, as well as the earliest -authentic values of the magnetic elements in London and St. Helena, -where he went on purpose to make observations on terrestrial magnetism. -Since that time M. Gauss has formed charts of the magnetic lines, and -published a theory which very nearly represents the magnetic state of -the globe. The mass of observations daily making by our cruizers and our -Government surveys in every part of the earth is enormous. - - -NOTE 227, p. 360. In fig. 74 the hyperbola H P Y, the parabola p P R, -and the ellipse A E P L, have the focal distance S P, and coincide -through a small space on each side of the perihelion P; and, as a comet -is only visible when near P, it is difficult to ascertain which of the -three curves it moves in. - -[Illustration: _Fig. 74._] - - -NOTE 228, p. 363. In fig. 75, E A represents the orbit of Halley’s -comet, E T the orbit of the earth, and S the sun. The proportions are -very nearly exact. - -[Illustration: _Fig. 75._] - - -NOTE 229, p. 382. Fig. 74 represents the curves in question. It is -evident that, for the same focal distance S P, there can be but one -circle and one parabola p P R, but that there may be an infinity of -ellipses between the circle and the parabola, and an infinity of -hyperbolas H P Y exterior to the parabola p P R. - - -NOTE 230, p. 387. Let A B, fig. 26, be the diameter of the earth’s -orbit, and suppose a star to be seen in the direction A Sʹ from the -earth when at A. Six months afterwards, the earth, having moved through -half of its orbit, would arrive at B, and then the star would appear in -the direction B Sʹ, if the diameter A B, as seen from Sʹ, had any -sensible magnitude. But A B, which is 190,000,000 of miles, does not -appear to be greater than the thickness of a spider’s thread, as seen -from 61 Cygni, supposed to be the nearest of the fixed stars. - - -NOTE 231, p. 389. Stars whose parallax and proper motions are known. - - Name of Star. Proper Motion. Parallax. Observers and Computers. - - α Centauri 3ʺ·764 0ʺ·92 Maclear. - „ .. 1ʺ Henderson. - 61 Cygni 5ʺ·123 0ʺ·374 Bessel. - α Lyræ 0ʺ·364 0ʺ·207 Peters. - Sirius 1ʺ·234 0ʺ·230 Henderson. - Arcturus 2ʺ·269 0ʺ·127 Peters. - Pole Star 0ʺ·035 0ʺ·106 Peters. - Capella .. 0ʺ·046 Peters. - La Chevre 0ʺ·461 0ʺ·046 Peters. - ι Great Bear 0ʺ·746 0ʺ·133 Peters. - -The space run through in one second by these stars is therefore— - - α Centauri 5 leagues Henderson and Maclear. - 61 Cygni 10 leagues Bessel. - α Lyræ 2 leagues Struve and Peters. - Sirius 6 leagues Henderson and Maclear. - Arcturus 22 leagues Peters. - Pole Star ½ league Lindenau and Struve. - La Chevre 12 leagues Peters. - ι Great Bear 7 leagues Peters. - -There are three great discrepancies in the parallax of the star -Argelander or 1830 Groombridge. M. Otto Struve makes it 0ʺ·034, which -gives it a velocity of 251 leagues per second, while M. Faye finds the -parallax to be between 0ʺ·03 and 0ʺ·01, which makes its velocity from 30 -to 85 leagues per second. - -These are all minimum velocities, because we can only determine on the -celestial vault a projection perhaps much foreshortened of the real -motions of the stars. - - -NOTE 232, pp. 398, 401. The following are the binary systems whose -orbits have been accurately determined:— - - Name of Star. Period in Perihelion By whom Computed. - Years. Passage. - - ζ Herculis 30·216 1831·41 Madler. - - η Coronæ 42·500 1807·21 Madler. - - ζ Cancri 58·910 1853·37 Madler. - - ξ Ursæ Majoris 58·262 1817·25 Savary. - - ω Leonis 82·533 1849·76 Villarceaux. - - ρ Ophiuchi 73·862 1806·83 Encke. - - 3062 in Dorpat 94·765 1837·41 Madler. - Catalogue - - ξ Bootis 117·140 1779·88 Sir J. Herschel. - - δ Cygni 178·700 1862·87 Hind. - - γ Virginis 182·120 1836·43 Sir J. Herschel. - - Castor 252·660 1855·83 Sir J. Herschel. - - ς Coronæ 736·880 1826·48 Hind. - - γ Virginis 632·270 1699 Hind. - - α Centauri 77·000 1851·50 Jacob. - - - Orbit of γ Virginis. - - Perihelion passage 1836·40 - - Inclination 27° 36ʹ - - Position of ascending Node 19 7 - - Angle between line of Nodes and 295° 13 - Apsides - - Excentricity 0·8794 - - Period in years 184·53 - - - Orbit of ζ Herculis. - - Perihelion passage 1830·56 - Inclination 140° 39ʹ - Position of ascending Node 217° 14ʹ - Angle between line of Nodes and Apsides 266·53 - Eccentricity 0·4381 - Period in years 37·21 - - _Computed by J. Fletcher, Esq._, 1853. - - -NOTE 233, p. 403. The mass is found in the manner explained in the text; -but the method of computing the distance of the star may be made more -clear by what follows. Though the orbit of the satellite star is really -and apparently elliptical, let it be represented by C D O, fig. 14, for -the sake of illustration, the earth being in d. It is clear that, when -the star moves through C D O, its light will take longer in coming to -the earth from O than from C, by the whole time it employs in passing -through O C, the breadth of its orbit. When that time is known by -observation, reduced to seconds, and multiplied by 190,000, which is the -number of miles light darts through in a second, the product will be the -breadth of the orbit in miles. From this the dimensions of the ellipse -will be obtained by the aid of observation; the length and position of -any diameter as S p may be found; and as all the angles of the triangle -d S p can be determined by observation, the distance of the star from -the earth may be computed. - - -NOTE 234, p. 405. The mean results of MM. Argelander, Otto Struve, and -Luhndahl for stars in the northern hemisphere and the epoch 1790, places -the point to which the sun is tending in 259° 5ʹ of right ascension and -55° 23ʹ of north polar distance. Mr. Gallaway computed from stars in the -southern hemisphere, at the same epoch, the point to have been in 260° -1ʹ right ascension and 55° 37ʹ north polar distance, results nearly -identical, though from very different data. - - -NOTE 235, p. 414. One of the globular clusters mentioned in the text is -represented in fig. 1, plate 8. The stars are gradually condensed -towards the centre, where they run together in a blaze. The more -condensed part is projected on a ground of irregularly scattered stars, -which fills the whole field of the telescope. There are few stars near -this cluster. - - -NOTE 236, p. 420. Plate 8 shows five nebulæ as seen in Sir John -Herschel’s 20-feet telescope. - -1. An enormous ring seen obliquely with a dark centre and a small star -at each extremity. - -2. The ring in the constellation Lyra. - -3. The dumb-bell nebula in Vulpicula. - -4. The spiral nebula or brother system in the 20-feet telescope. - -5. A spindle-shaped nebula. - -Plate 9 represents some of the same objects as seen by Lord Rosse. - -1. Nebula in the girdle of Andromeda. - -2. The circular nebula of Lyra. - -3. The dumb-bell nebula in Vulpicula. - -The spiral nebulæ of 51 Messier, as seen by Lord Rosse, 1 in plate 10, -represents fig. 4 of plate 8; and fig. 2 in the same plate is part of -the great nebula in Orion, for the whole has never been seen, on account -of extreme remoteness. - - -NOTE 237, pp. 32, 427. The motion of the earth is visibly proved by M. -Foucault’s experiments. If a pendulum be left to oscillate quite freely, -the forces producing the oscillations being in the vertical plane, there -is no cause that can produce an absolute change in its position with -regard to space; but the motion of the earth changes the position of a -spectator with respect to the vertical plane, and he refers his own -motion to it, which seems gradually to turn away from its position, -precisely as a person in a boat refers his own motion to that of the -land, and thus the motion of the earth is truly and visibly proved. - - - - - INDEX. - - Aberdeen, high water at, 94. - - Absorption, influence of, on temperature, 239; - difference of sea and land in power of, 242; - gradually decreasing, in transmission of radiant heat, 259; - of radiant heat, varying with substances, 268; - a transfer of force, 275, 276. - - Acceleration of the moon’s mean motion, 37, 38. - - Adams, Mr., perturbation in Uranus’s motion computed by, 22; - discovery of Neptune, 62. - - Aërolites, theory of, 420, 423. - - Africa, tidal wave passing, 94; - mean annual equatorial temperature in, 245; - indigenous productions of, 249, 250. - - Air, comparative velocity of light in water and, 202. - _See_ Atmosphere. - - Airy, Professor, periodic inequality in the solar system worked out by, - 26; - phenomenon observed by, during an eclipse, 41; - mass of Jupiter ascertained by, 55; - experiments ascertaining its density, 57; - astronomical tables improved by, 63; - discoveries in polarization of light, 192, 193. - - Aldebaran, an optically double star, 401. - - Aleutian Islands, the, vegetation of, 252. - - Alexandria, arc of the meridian measured between Syene and, 49. - - Algæ, districts of distinct species of, 252; - banks of, in the Atlantic, 253. - - Algol, fluctuations in lustre of, 390, 391. - - Alhazen, effects of refraction observed by, 155. - - Alkalies, resolved into metallic oxides, 307. - - Alpha Antaris, “Coal Sacks” between α Centauri and, 386. - - Alpha Aquilæ, an optically double star, 401. - - —— Centauri, the parallax of, 54; - its rank, 384; - the Milky Way near, 386; - parallax, as determined by Henderson and Maclear, 387; - distance from the sun, 388; - orbit and mass of, 399, 400; - colour, 401; - amount of light emitted by, 404; - rate of its proper motion, 404, 405; - globular nebulous cluster, 414. - - —— Crucis, zone of stars passing through, 385; - zone between η Argûs and, 390; - nebulous cluster round, 415. - - —— Lyræ, the polar star of the northern hemisphere, 82; - parallax of, 388; - distance from the sun, 389; - an optically double star, 400; - amount of light emitted by, 404. - - —— Orionis, a variable star, 393, 394. - - Alum, experiments on the crystallization of, 106, 107; - heat transmitted through, 261, 262. - - Amazons, the river of, distance from its mouth where tides are - perceptible, 98; - area occupied by forests on, 243. - - America, course of the tidal wave along its coasts, 93, 94; - mean annual equatorial temperature in, 245; - separation of isothermal lines in high latitudes, _ib._; - number of known species of plants indigenous in, 249; - number of species of trees, 252; - shooting stars over the continent of, 421. - - ——, South, area of country raised by an earthquake in, 234. - - Ampère, M., his discovery in electricity, 316; - theory of magnetism, 317, 318; - experiment testing his theory, 319, 320. - - Analysis, boundless dominion of, 427, 428. - - Andes, the, proportion of, to the earth’s mass, 6; - increasing rarity of the air experienced in ascending, 118. - - Andromeda, nebula in, 413; - nebulous region of, 417. - - Angström, the electric spark defined by, 303. - - Animals, specific diversity of, laws regulating their distribution, - 254, 255. - - Annual equation, the, of the moon, 35, 36. - - —— variations in mean values of the magnetic elements, 343. - - Annular nebulæ, 409; - in the northern hemisphere, 410, 411. - - Antarctic Ocean, tidal wave rising in 93; - period of its passage to the Thames, 94; - depth of the stratum of constant temperature in, 101; - depression of the barometer observed in, 120. - - Antilles Islands, hurricanes beginning at, 126. - - Antinori, Cav., experiments of, in electricity, 333. - - Antinous, comet observed in the constellation of, 372; - the Milky Way between Orion and, 386. - - Antithesis, the general character of magnetism, 339. - - Aphelion of a planet’s path defined, 16. - - Apogee, solar, its coincidence with the solstices, 86, 87. - - April, 1833, disappearance of Saturn’s rings, 67; - apparent and mean time coinciding in, 84. - - Apsides of an axis defined, 9; - direct, variable motion of, 14; - cause of their advance, or recession, 16. - - Apures, the mission of the, Humboldt’s observations on sound at, 135. - - Aqueous vapour, proportion of, in the atmosphere, 117. - - Ara, nebula in, 414. - - Arabian Gulf, the, monsoons blowing over, 124. - - Arabs, the, their observations on planetary irregularities, 26; - lunar eclipses observed by, 38; - their division of time, 85; - the pendulum used as a measure of time by, 90. - - Arago, François, experiment by, in proof of the undulatory theory of - light, 200; - decisive experiment suggested by, 202; - observations in photography, 213; - observations on the moon’s atmosphere, 226; - increase of temperature below the earth’s surface calculated by, 230; - slow communication of temperature from the earth, observed, 244; - source of magnetism discovered, 330; - theory of his magnetic experiments, 332; - divergent flames of a comet described by, 364; - his treatise on comets, 368; - nature of comet’s light determined by, 380, 381; - numbers of comets computed, 381, 382; - remark of, on _fixed_ stars, 405. - - Arc, the Voltaic, 303-305. - - Arcet, M. d’, vibration of fibres of the retina according to, 178. - - Archer, Scott, stimulus given to photography by, 207. - - Arcs of the meridian, mode of measuring, 47. - - Arctic Sea, depth of the zone of constant temperature, 101. - - —— regions, vegetation found in, 249. - - Arcturus, comet bearing comparison with, 379; - rank of, 384. - - Areas, described by the radii vectores of planets, a test of disturbing - forces, 10; - unequable description of, 15. - - Argelander, M., period of a comet calculated by, 370; - his mode of estimating distance of fixed stars, 389; - periods of fluctuation in stars computed by, 390, 391; - sun’s motion proved, 405. - - Argentine preparations in photography, chemical energy varying with, - 207, 208; - changes effected by washing with alkalies, 210, 211. - - Argo, variable star in, 393. - - Aries, season of the sun’s entrance into, in Hipparchus’ age, 80. - - Arseniate of soda, its crystals, 109. - - Artesian wells, mode of sinking, origin of the name, 230. - - Asia, indigenous productions of, 249. - - Assyrians, the, division of time by, 85. - - Astronomers, fruits of their labours, 3; - question still to be resolved by, 24; - terrestrial orbit differently measured by, 36. - - Astronomical distances, method of measuring, 43; - tables, method of forming, 58-64. - - Astronomy, its rank in the physical sciences, an important office of, - 1; - studies necessary to the study of, 2; - the key to divers problems in physical science, 3; - the two greatest discoveries in, 23; - the three departments of, 58; - standards for measurement afforded by, 83; - application of, to chronology, 87-89; - furnishing standards of weights and measures, 89, 90; - atmospheric effects connecting the laws of molecular attraction with, - 102; - progress lately made by, 419, 420. - - Atalanta, diameter of, 56. - - Atlantic Ocean, direction of tidal waves in, 93; - conditions modifying tides, 94; - depth of, 96; - currents, 100; - origin of hurricanes, 126; - superficial temperature of, 244; - distinct vegetation of the polar basin, 252; - beds of algæ in, 253; - meteors falling in, 421. - - —— telegraph, 325, 326; - terrestrial magnetism disturbing, 346. - - Atmosphere of nebulous stars, 411, 412. - - —— of planets, 226, 227. - - —— of the sun, its constitution, 42; - indications of an absorptive surrounding the luminous, 213; - the true, 224. - - —— terrestrial, solar rays bent by, in lunar eclipses, 40; - influence of, in solar eclipses, 41; - its analysis, pressure on the surface of the globe, 117; - form of, gradual decrease in density of its strata, 117, 118; - influence of temperature on its density, 119; - mean pressure of, variable, 120; - the medium conveying sound, 129; - sympathetic vibrations transmitted by, 147, 148; - its action on light, falsifying vision, 153; - phenomena produced by accidental - changes in its strata, 155-156; - effects of increased density in the stratum in the horizon, 157, 158; - lunar heat absorbed by, 227; - cause of the cooler air in higher regions of, 240, 241; - sun’s heat modified by, 244; - action of electricity in, 284; - transmission of electricity by induction, 286; - periodical variations of electricity in, 291; - accidental developments of electricity, 291, 292; - cause of variations in its magnetism, 344, 345; - nebulous bodies made visible by, 421-423. - - Atmospheric air, extreme elasticity of, 105. - - —— pressure, effect of, on electricity, 288. - - Atomic constitution determining crystalline forms, 109. - - Atoms, qualities of, determining the nature of substances, 110; - differences in weight of, 111. - - Attraction, modes of, in spheres, in the celestial bodies, 4; - determining the forms of planets, 6; - determining the motions of planets, 7; - solar, compelling the elliptical revolutions of planets, 8; - mutual, of planets, complicating their motions, 10; - interference of, disturbing the motions of heavenly bodies, 11; - disturbances from the operation of reciprocal, 13; - disturbances from inequality of, 14; - of satellites to primaries, little disturbed, 26; - disturbing force of, in spheroids, 27; - its effects on Jupiter’s satellites, 28; - sun’s, of the moon, 34; - principle modifying the earth’s, 37; - local, affecting the plumb-line, 48; - comparative force of the sun’s, 57; - of an external body affecting a spheroid, 79; - producing tides, 91, 92; - of particles of matter, 103; - capillary, 113; - producing annual atmospheric undulations, 121; - the lunar atmosphere affected by, 226; - expansive force of heat overcoming, 271; - of electricities, 283; - destruction of, producing electricity, 284; - laws of electrical, 286-288; - modes of, in static and in voltaic electricity, 317; - action of planetary, on comet’s orbits, 361-363; - range of solar, 365. - - Aurora, the, affecting the compass, 312. - - Australia, evidence of deserts in the interior of, 124; - species of plants common to Europe and, 251. - - Auvergne, temperature of hot springs in, 231. - - Axes, change in form of masses revolving round, 6. - - ——, major, length of, in orbits, invariable, 20; - of the orbits of Jupiter’s satellites, cause of the direct motion - observed in, 28; - position of, in the solar system, 65; - a nutation in planetary, 66; - of the moon, 68, 69; - mechanical law affecting, 76. - - ——, optic, of crystals, 183. - - Axis, greater, of the earth’s orbit, period of its revolution, 38; - period of the earth’s revolution, 58; - excess of Jupiter’s equatorial over his polar, 66; - of rotation, proof of its being invariable, 76, 77. - - ——, major, of a planet’s orbit, distance from the sun measured by, 8; - designation of its extremities, 9; - length of, determining the form of the orbit, 10; - periods of its revolutions, 17; - length of, not permanently changed, 20; - Jupiter’s periodically diminished, Saturn’s increased, 26; - of the solar ellipse, period of its revolution, 86. - - ——, magnecrystallic, 349. - - Azores, the, icebergs reaching, 100. - - - Babbage, Charles, his theory of volcanic action, 235-237; - quotation from, on the nature of force, 353. - - Babinet, M., his theory of dark lines observed in the solar spectrum, - 163; - comet’s light computed by, 359. - - Babylon, eclipse observed at, 36. - - Bacon, Francis, anticipation of discovery by, 32. - - Baily, Mr., compression of the terrestrial spheroid calculated by, 50; - density of the earth determined, 57; - fictitious antiquity ascribed to Indian astronomical observations, - 88. - - Bali, volcanic eruption in, 233. - - Balloon, rarity of the air felt in a, 118; - observations made from, 119. - - Baltic, the, a tideless sea, 98; - decreased atmospheric pressure on the shores of, 120. - - Barlow, Mr., observations supporting his theory of electric currents, - 346. - - Barometer, the, principles of cohesion and attraction applied to the - construction of, 113; - density of the atmosphere measured by, 117; - mean heights of, varying with atmospheric densities, 118; - mountain heights measured by, 119, 120; - atmospheric phenomena affecting, 120; - used to trace the course of atmospheric waves, 121; - cause of sudden fall in, before hurricanes, 127; - refraction varying with, 154. - - Barrow, Cape, observations on magnetic storms at, 345, 346. - - Battery, voltaic, construction of, 298, 299; - Professor Daniell’s improvements, 299, 300; - action of, charged with water, 300; - constant flow of electricity obtained by means of, 312. - - ——, magnetic, constructed by Dr. Faraday, 324, 325; - Mr. Henley’s magneto-electric, 325; - Atlantic telegraph, 326; - structure of, for land telegraphs, 328; - relation of heat to power of, 329; - thermo-electric, 333. - - Batsha, port of, tides neutralised in, 99. - - Bayle, comparative density of the atmosphere in interplanetary space - according to his law, 356. - - Bear, Little, the, the polar star in, 82. - - Becquerel, M. E., unexplained photographic phenomenon observed by, 213; - phosphorescent property in the solar spectrum discovered, 216; - cause of phosphorescence, 217; - electricity excited by pressure, 283; - light attributed to electricity by, 284; - cause of phosphorescence investigated, 296; - instrument comparing intensities of electricities invented, 300; - crystals formed by agency of electricity, 308; - thermo-electric battery constructed by, 333; - effect of atmospheric on terrestrial magnetism estimated, 345. - - Beehive, the, a nebulous star, 415. - - Berard, M., experiments of, in polarizing heat, 264. - - Berlin, line of coincidence in temperature passing through, 238. - - Berne, increasing temperature of a deserted mine in, 230. - - Berre, Dr., photographic pictures perfected by, 205. - - Bessel, M., his calculations from measurements of arcs of the meridian, - 48; - calculation of the sun’s mean apparent diameter, 56; - his computation of the mass of Saturn’s ring, 68; - diminished obliquity of the ecliptic observed by, 81; - parallax calculated, 389; - his theory of Sirius’s irregular motions, 392; - catalogue of double stars, 396; - mass of 61 Cygni found by, 404. - - Beta Lyræ, a variable star, 391; - nebula between γ Lyræ and, 410. - - Benzenberg, M., velocities of falling stars computed by, 423. - - Biela, M., date of the discovery of his comet, 367; - possibility of collision with the earth, 368; - present and prospective planetary influence on, 369; - becoming two distinct bodies, 369, 370. - - Binary systems of stars, 395-406. - _See_ Double stars. - - Biot, M., his ascent in a balloon, 118; - experiments of, on the transmission of sounds through pipes, 137; - liquids possessing the power of circular polarization discovered by, - 190; - his theory of circular polarization, 191; - cause of phosphorescence in the solar spectrum investigated by, 217. - - Birds, distribution of distinct species of, 255. - - Birt, Mr., atmospheric waves measured by, 121, 122. - - Bise, in Switzerland, cause of, 242. - - Bismuth, its magnetic and electric properties, 347. - - Black Sea, the, scarcely affected by tides, 98. - - Bode, Baron, law of, assumed in computing Neptune’s position, 61; - failing in the case of Neptune, 63. - - Bond, Mr., satellite of Saturn discovered by, 32; - elliptical nebula resolved, 413. - - Bonnycastle, Captain, phosphorescent phenomenon observed by, 295, 296. - - Bonpland, M., identical productions of the Old and New World found by, - 251. - - Boötes, nebulous system in, 417. - - Bore, the, of the Hoogly, its origin, 94. - - Botanical districts, distinct, of the globe, 251, 252. - - Botto, M., thermo-electricity used in decomposition by, 333. - - Bouguer, degrees of the meridian measured by, 48. - - Boussingault, M., depth of the underground stratum of constant heat - calculated by, 228. - - Bouvard, M., atmospheric undulations estimated by, 121. - - Bradley, Dr., motion of the pole of the equator discovered by, 84; - his tables of refraction, 155. - - Brahmins, measurement of time by, 85. - - Brand, M., observation of, on meteors, 423. - - Brewster, Sir David, his analysis of the solar spectrum, 161; - experiments on rayless lines, 163; - experiments on spectra of flames, 164; - law discovered by, determining angles of polarization for light, 183; - experiments on fluorescence of light, 197; - line of coincidence in temperature of springs and of the atmosphere - determined by, 238; - temperature of a pole of maximum cold determined, 245; - isogeothermal lines determined by, 246; - observations on the light of fixed stars, 402. - - Brighton, phenomenon caused by reflection observed from, 157. - - Brinkley, Bishop, mass of the moon determined by, 56. - - British Channel, height of tides in, 98. - - —— Isles, atmospheric wave passing over, 121. - - Brorsen, M., periods of comets discovered by, 370. - - Brown, Dr. Robert, peculiar vegetation found by, in Australia, 251. - - Buchan, Dr., phenomenon caused by reflection observed by, 157. - - - Cæsar, Julius, era computed from his reign, 85. - - Cagniard de la Tour, M., instrument designed by, measuring musical - notes, 143. - - Calms produced by the trade-winds, 122, 123. - - Calorific rays. - _See_ Rays of heat. - - Calotype, the invention of, 204. - - Camelopard, nebulous system in, 417. - - Canaries, the, vegetation of, 252. - - Canary-glass, fluorescence of light in, 196. - - Cancer, the calms of, 123; - the tropic of, marking the limit of the trade-winds, 126; - nebulous cluster in, 415. - - Canis Major, position of, 390. - - —— Venatica, nebulous system in, 417. - - Capillarity, theory of, 113; - forces producing, 114; - familiar examples of, 115; - curious phenomena, 115, 116. - - Capricorn, the calms of, 123; - the tropic of, hurricanes changing their direction at, 126. - - Carbon, its powers contrasted as a crystal and as an opaque amorphous - substance, 302, 303. - - Carbonate of lime. - _See_ Lime. - - Carbonic oxide, its constituent parts, 111. - - —— acid, proportion of, in the atmosphere, 117. - - Cardinal points, the, position of continental masses with regard to, - influencing temperature, 244. - - Caribbean Islands, hurricanes beginning at, 126. - - Castor, discovered by Sir William Herschel, 396. - - Cassiopeia, star appearing and vanishing in, 392, 393. - - Categat, the, consequence of its narrowness, 98. - - Cauchy, M., data furnished by, for investigation of the theory of - light, 201. - - Cayenne, variation in length of the pendulum between Paris and, 51. - - Celestial bodies: - law of their mutual attraction, 4; - of the solar system: - law determining their attraction to the sun, 5; - problem to fix the positions of, on occurrence of disturbance in - their motions through counteracting attractions, 11; - theory of their mutual connection and dependence, 24; - mode of finding the absolute distances of, 43; - distances of, computed from their parallax, 52, 54; - apparent position of, affected by refraction, 153, 154; - apparent infinity of, 420. - - Centaur, position of, 390; - brilliant double star in, 399. - - Central Asia, the mountains of, their ascent by Marco Polo, 118. - - Centre of gravity. - _See_ Gravity. - - Centrifugal force, moon’s motions modified by, 5; - influence of, on planet-forms, 6; - retarding oscillations of the pendulum, 32; - action of, in determining the figure of the earth, 44, 45; - measurement of its intensity, 49; - resolved into two forces, its action on the sea, 100. - - Ceres, astronomical tables of, 63; - height of her atmosphere, 226; - comet of 1770 revolving beyond the orbit of, 361. - - Cetus, nebulous patches crossing, 417. - - Chaldeans, the, mean longitude found from observations of, 36; - result of comparison of their observations with modern, 38. - - Challis, Professor, Brewster’s analysis of light questioned by, 161. - - Charcoal, light produced by electricity from, 302-303. - - Charles V., the Emperor, observations on comets, made in his reign, - 370. - - Chaudes Aigues, temperature of, 231. - - Chemical action of rays of the solar spectrum, 203, 207; - varying maximum of energy, 208; - action varying with refrangibility, 209-212; - action in luminous spectrum not continuous, 213; - energy an independent property of rays, 214; - properties of the parathermic rays, 219; - action of light maintaining vegetation, 249; - affinities the source of the power of steam, 278; - of electricity on oxygen, 284; - eliciting voltaic electricity, 297, 300; - voltaic electricity, an agent in, analysis, 307, 308. - - —— combinations, theory of, 110; - invariable proportions of, 111; - cohesive force inducing, 112; - producing combustion, 270. - - —— force, the power of, 112. - - —— rays, causing the deposition of dew, 269. - - Chile, elevation of land by an earthquake in, 234. - - China, distinct flora of, 251. - - —— Sea, the, monsoons blowing over, 124. - - —— ink, polarized light reflected from, 193. - - Chinese, the, observations of, on the mean motions of Jupiter and - Saturn, 25; - proof of their early study of astronomy, 88; - decimal divisions used by, 90; - elements of comets computed from their observation, 365; - comet of 1264 recorded by, 370. - - —— Tartary, herbarium collected in, 250, 251. - - Chladni, discovery of, in musical science, 145. - - Christian era, traces of astronomical records before, 365. - - Chromatype, the invention of, 206. - - Chronology, dependent on astronomy, 87-89. - - Chrysotype, the, coloured photographs obtained from, 206. - - Circuit, galvanic, modes of obtaining, 332. - - Circular arcs, principle with regard to their sines and cosines, a - pledge for the stability of the solar system, 20. - - —— motion, ratio of forces procuring, 382. - - —— orbits of planets distinguished from elliptical, 8; - of satellites, 27. - - —— polarization of light, 189-192; - of heat, 266. - - Circumference of the earth, 49. - - Civil time, measure of its periods, 83; - not precisely adjusted to solar revolutions, 85. - - Clairaut, periodic time of Halley’s comet computed by, 362, 363. - - Cleavages of crystals, 109; - position of, affecting the intensity of magnetic action, 350. - - Climates, planetary, 225, 226; - cause of the different terrestrial, 237; - phenomena affecting, 239, 240; - causes of variety of, 243, 244; - milder, of the Polar Ocean, 245, 246; - like mean annual temperatures not ensuring like, 246; - compensations of irregularities, 247. - - Clocks, showing apparent sidereal time, 83; - regulated to show decimal time, 84; - irregular action of, corrected by the laws of unequal expansion, 272. - - Clouds, circling the belt of equatorial calms, 123; - region of, 124; - electricity evolved from, 291-292. - - Cloyne, Bishop of, his calculation of the moon’s mass, 56. - - Coal-measures, tropical plants in, 72, 73; - age of their formation, 75. - - Coal, chemical force evolved from, by combustion, 278; - source of its combustible qualities, 279, 280. - - “Coal Sacks” in the Milky Way, 386. - - Cohesion, influence of, on matter, 105; - phenomena arising from its force, 106; - attraction of, overcome by the expansive power of heat, 271. - - Cohesive force, properties of material molecules constituting, 103; - effectual only to unite particles of like nature, 110; - inducing chemical combination, 112; - capillary attraction, an action of, 113. - - Coins, impressions taken from, by contact, 220; - by electricity, 221. - - Cold, contraction caused by, 271, 272; - mitigated by slow propagation of heat in air, 273; - generated by voltaic electricity, 302; - increasing the conducting power of the air, 345. - - Colladon, M., experiments of, testing the velocity of sound, 135. - - Collision between the earth and comets, possibilities, possible effects - of, 367, 369. - - Collodion, sensitiveness of, to light, 203; - properties of, as an agent in photography, 207. - - Colours, seven primary, 159; - theory of the decomposition of white light into, 160; - degree of refrangibility not invariable, 161; - three primary, _ib._; - new, discovered by Sir John Herschel, 162; - rays refracted without, 164; - rarely homogeneous, 165; - experiments on accidental and complementary, 165, 166; - determined by undulations of ether, experiments, 170-175; - of material substances, whence derived, 175; - produced by analyzing polarized light, 186-188; - varying with refrangibility of rays, 198; - obtained in photography, 206; - images of the solar spectrum imitating the prismatic, 208-209; - of seaweeds, 253; - not invariably dependent on light, _ib._; - affected by absorption and reflection, 268; - of the electric spark, affected by the atmosphere, 289; - of the voltaic spectrum, 303; - of the electric spark, 304; - produced by oxidation on silver, 305; - of the fixed stars, 401, 402; - of planetary nebulæ, 412; - of nebulous clusters, 415. - - Columbus, beds of algæ found by, 253. - - Column, capillary, forces producing changes in its form, 114, 115. - - Coma Berenices, a nebulous cluster, 415; - nebulous zone passing, 416, 417. - - Combustion, cause of, 270; - defined, 304. - - Comets, attraction by the sun of, 5; - disturbances in the motion of, a key to the nature of the ethereal - medium, 22; - retrograde motion in, 33; - passing through Jupiter’s satellites, 69; - return of, to their perihelia, furnishing historical data, 88; - existence of the luminous ether demonstrated by, 168, 169; - terrestrial atmosphere unaffected by, 358; - amount of their light computed, 358, 359; - passages of, through the solar system, 359; - velocity, paths of, 359, 360; - proof of the return of, 360; - disturbing action of planets on their orbits, 361; - of 1770, an example, 361, 362; - computed return of Halley’s, 362, 363; - aspects, records of Halley’s, 363-365; - discoveries made by the revolutions of, 365; - of the solar system, Encke’s, 365, 366; - Biela’s, possibility of collision with, 367, 370; - periods of various, 370; - cause of their brilliancy, 371; - velocity, sun’s influence on, 371, 372; - of 1843, 372, 373; - their constitution, 373, 374; - of 1811, its luminous envelopes, 374, 375; - sudden convulsions in, 375; - tails, 375-377; - causes assigned for contraction of diameter in, 377, 378; - Donati’s, 378, 379; - nature of their light, 379-381; - computations of their numbers, 381, 382; - orbits of, 383; - nebula resembling, 413. - - Compass, mariner’s, phenomena disturbing, 312; - intensity of a galvanic current measured by, 315. - - Compression of the terrestrial spheroid, calculations of, 48-51; - cause of the great, in Jupiter, 66; - measures of, from pressure of superincumbent mass, 78; - effect of, on magnetic action, 351. - - Concord, a, in music, 142. - - Conductors of electricity, 284, 285; - lightning, 293; - molecular structure determining the power of, 303. - - Conic sections, conditions compelling bodies in space to move in, 5; - principle determining their nature, 11. - - Constellations, nearest the sun, 390; - where the orbit of the solar system lies, 406; - occupied by the nebulous system, 417. - - Contraction caused by cold, 271, 272. - - Cook, Captain, object of his first voyage, 53. - - Cooper, Mr., list of missing stars drawn up by, 395. - - Copper, electricity communicated to plates of, 220; - lightning-conductors of, 293; - action of an electro-magnet on, 351, 352. - - Cordier, temperature of mines observed by, 228. - - Cordilleras, effect on temperature of their table-lands, 241. - - Corn, a, field used to illustrate the propagation of sound, 129, 130. - - Cornwall, hot-springs in mines of, 229. - - Corona Australis, nebula in, 414. - - Corpuscular theory of light, 167; - phenomena disproving, 171, 175, 176. - - Coseguina, volcanic irruption of, 233. - - Coulomb, instrument measuring electrical intensity, invented by, 287. - - Creation, vastness and magnificence of, 2. - - Crimea, cause of the great storm in the, 122. - - Cross, Mr., voltaic battery with constant action invented by, 300. - - Cross, the Southern, vacant patches of the Milky Way near, 386. - - Crystallization defined, 106; - forms of, their variety affected by temperature, 107, 108; - permanent and variable forms, 108, 109; - cleavages in, 109; - common to all substances, _ib._; - by the agency of electricity, 308, 309. - - Crystals, conditions determining their forms, 107-109; - optic axes of, 183; - used in polarizing light, 186, 188; - changes in, effected by compression, 189; - transmission of rays of heat by, 258; - expansion of, by heat, 272, 273; - formed by electricity, 308; - action of magnetism in, 349, 350; - circumstances determining the set of, 350, 351; - effect of temperature on magnetized, 352. - - Cumming, Professor, experiments of, in thermo-electricity, 333. - - Currents, two great, setting from each pole towards the equator, 100; - proving the rotation of winds, 124, 125. - - ——, electric, flow of, regulated by Volta, 297-299; - characteristics of Voltaic, 301; - conductors, non-conductors of, 309; - continuous flow of Voltaic, 312; - action of, on magnets, 313-315; - reciprocal and mutual action of magnetic and electric, 316, 317; - Ampère’s theory of, unsolved difficulties, 317, 318; - effect of, on polarized rays, 319; - electric, evolved by magnets, 322, 323; - their power of producing induction, 324; - direction of, produced by rotation, 330-332; - evolved by application of heat, 332, 333; - produced by intersecting magnetic curves, 339; - induced by crossing terrestrial lines of magnetic force, 342. - - Curves, described by bodies projected in space, 5. - - ——, magnetic, 338; - electricity produced by intersecting, 339; - nature of, proved by Dr. Faraday, 339, 340; - terrestrial, 341, 342; - extent of the range of terrestrial, 344; - complete connected system of the terrestrial, 345; - inductive effect on the Atlantic telegraph, 346; - diamagnetic, 348. - - Cyanite, changes effected in, by magnetism, 349. - - Cyanotypes, coloured photographs obtained by, 206. - - Cygni 61, distance from the sun of, 389; - orbit and mass of, 398, 399; - colours, 401; - mass, 404; - proper motion, 405. - - Cygnus, portion of the Milky Way lying between α Centauri and, 386. - - Cylinders, rotating by electricity, 313; - electro-dynamic, 316. - - - Dalcoath copper-mine, its temperature, 228. - - Daguerre, M., his inventions in photography, 205; - action of light on the iodide of silver explained by, 219. - - Daguerreotype, the, invention of, 205. - - Dalton, Dr., law of definite proportion established by, 111; - law of the wind’s rotation observed by, 125. - - Damoiseau, M., perturbations of a comet computed by, 367. - - Daniell, Professor, Voltaic battery improved by, 299. - - Daubuisson, M., observations of, in mines, 228. - - Davy, Sir Humphry, his first attempts to produce photographic pictures, - 203-204; - experiment of, proving identity of heat and motion, 275; - experiments on the electric spectrum, 289; - alkalies, earths decomposed by, 307. - - Days, law determining the length of, 71; - period of the mean sidereal and solar, 83; - varying with the seasons, 84; - decimal division of, 84; - seven, the most permanent division of time, 85. - - Deccan, the, wheat ripening in, 250. - - December, 1832, disappearance of Saturn’s rings in, 67; - coincidence of mean and apparent time in, 84; - date of Christ’s nativity, 85; - the astronomical year beginning in, 86. - - Decimal division of time, 84. - - Declinations of the moon, 97. - - Decomposition, effected by electricity, 307-308; - by magnetism, 323; - by thermo-electricity, 333. - - Delambre, his computations of the length of the year, 359. - - Delta Cephei, a variable star, 391. - - Denmark, course of the tidal wave to, 94. - - Density, variable, impeding sound, 135, 136: - of media, modifying refraction, 153. - - Densities of heavenly bodies, formula finding, 56; - experiments, 57, 58; - comparative of the terrestrial globe, 77, 78. - - Deserts, causing monsoons, 124; - influence of, on temperature, 243. - - Dew, cause of its deposition, 269. - - Diamagnetic substances, 335, 336. - - Diamagnetism defined, 335; - substances it is resident in, 336; - discovery, characteristics of, 347; - neutral substances obtained by proportionate combination of, with - paramagnetism, _ib._; - polarity of, 348; - connected with arrangement of molecules, 350-351; - affected by division and compression, 351; - possibly identical with paramagnetism, 356, 357. - - Diameter of the earth, 21; - Jupiter’s polar, 27; - excess of his equatorial, 39; - apparent, of the sun and moon, nearly equal, 40; - of the earth, 49; - of bodies composing the solar system, 56; - of Neptune, 63; - comets lacking a sensible, 373; - contraction of, in comets, 377; - causes assigned for, 377, 378. - - —— of an annular nebula, 410; - sensible, of a planetary nebula, 412. - - Diamond, the, polarized light reflected from, 193. - - Dielectrics in electricity, 286. - - Dieppe, seen from Hastings, 157. - - Differential telescope, the, experiments to be made by, 227. - - Discord, a, in music, 142. - - Diurnal tides of the atmosphere, their duration, 121. - - —— variations in mean values of the magnetic elements, 343. - - Dœbereiner, M., spontaneous combustion discovered by, 112. - - Doldrums, region of the, 123. - - Dollond, Mr., achromatic telescope perfected by, 165. - - Donati, Signore, discovery of his comet, 378; - changes in, its irregularities, 379. - - Doradus, nebulous patches on, 417. - - Dorpat, occultation of a star observed from, 364. - - Double nebulæ, 411. - - Double stars, catalogues of, 395, 396; - formulæ obtaining the relative position and motions, 396, 397; - eclipse in γ Virginis, 397; - orbit of, determined, 398; - eclipse in ζ Herculis, _ib._; - orbits and periodic times of, 398, 399; - anomalies in motions, 400; - optically double, 400, 401; - colours of, 401; - rays composing the light of, 401, 402; - passage of light from, furnishing data to ascertaining their actual - distance, 402, 403; - data for finding their masses, 403, 404; - calculations founded on the quantity of light emitted from, 404; - real and apparent motions of, 404-406; - apparent periodic time, 406, 407; - connection of elliptical nebulæ with, 411. - - Dove, Professor, law of the wind’s rotation developed by, 125; - average temperature of the earth’s surface estimated by, 237. - - Draco, nebulous system in, 417. - - Draper, Professor, experiments of, on fluorescence of light, 198; - experiments in photography, 213; - properties of parathermic rays discovered by, 219; - spectrum produced from diffracted light, 223; - theory of heat propagated by undulations, 267. - - Dunlop, Mr., revolution of a double star calculated by, 400. - - Dusejour, M., distances of comets computed by, 359. - - Dynamic electricity, 297. - _See_ Voltaic. - - —— theory of heat, fundamental principle of, 357. - - Dynamic equator of the earth, 343. - - Dynamical theory of heat, 274, 275; - illustrated by liquefaction and condensation, 278; - by generation of steam, 276, 277; - power of nature, 279-281. - - Dynamics, principle in, a law, with regard to the earth’s rotation, 72; - electro, discovery of action of currents in, 316; - the theory of, universal application of, 426, 427. - - - Earth, the, influence of its form on attraction, 4; - square of the moon’s distance from, 5; - form of, 6, 7; - moon’s influence on its rotations, 7; - diameter of, 21; - mean distance from the sun, _ib. note_; - permanence of revolution in its times and seasons, 23; - perturbation in the mean motion of Venus and, 26; - proof of the motion of, in its orbit, of its rotation, 32; - variations in its attraction of the moon, 37; - compression of its spheroid, 38; - internal structure of, 39; - its mean distance from the sun, 43; - theoretical investigation of its figure, 44-46; - dimensions of, determined, 48, 49; - figure of, found by calculating its variations in gravitation, 49-51; - density compared with the sun, 56; - experiments finding its mean density, 57, 58; - rate of revolution round its axis, 58; - its diurnal rotation immutable, 71, 72; - changes in temperature and their causes, 73, 74; - nature of the revolutions producing geological changes, 76, 77; - conjectures touching its internal structure, 78; - effects produced by solar and lunar attraction affecting its equator, - 79-81; - its form furnishing standards of weight and measure, 89; - rotation of, acting on tides, 92; - attraction of, affecting the lunar atmosphere, 226; - conjectured constitution of its interior, 231, 232; - principles regulating the diffusion of solar heat, 237-247; - distribution of known species of plants over, 249-252; - electric tension of, 291; - lines of magnetic force issuing from, 341; - magnetic properties of, 342, 343; - effect of its collision with a comet, 368; - nearest approach of comets to, 369; - passage of light from α Centauri to, 388; - theories of meteors falling on, 421-423. - - Earthquakes in South America, 234. - - Earths, decomposed by voltaic electricity, 307. - - Eastern coasts, cause of their colder climates, 244. - - Ebb, _see_ Tides. - - Éboulemens of mountains in Switzerland, cause of, 271. - - Echoes, theory of their origin, 137, 138. - - Eclipses, lunar, accelerated revolutions proved by observations of, 36; - observations of, confirming results of analysis, 38; - principle regulating their return, 39; - refraction of rays by the terrestrial atmosphere, 40. - - ——, solar, 40; - effects of light in, 41. - - ——, planetary, 42; - the solar atmosphere visible in, 224; - of double stars, 397, 398. - - Ecliptic, the, forming the equinoxes, 9; - latitude reckoned from the plane of, _ib._; - deviations of planetary orbits from, 10; - forces affecting their position towards, 15; - their compensated and uncompensated variations to the plane of, 18, - 19; - secular variation in the plane of, 23; - orbits of satellites, nearly perpendicular to, 33; - lunar motions towards, 35; - inclination of the sun’s plane of rotation to, 65; - inclination of the plane of Saturn’s rings, 67; - inclination of the plane of the terrestrial equator, 79; - tendency of its plane to coincide with the equatorial, _ib._; - retrograde motion of the equinoctial points on, 80; - obliquity of, affecting the duration of time, 84. - - Edinburgh, comparatively equal mean annual temperature of, 246. - - Egypt, hieroglyphic manuscript from, interpreted by astronomy, 89. - - Egyptians, the civil year of, 85. - - Elastic impact, the foundation of dynamical theories, 357. - - Elasticity, property of, resisting compression, 105. - - Electric telegraphs, experiment suggesting the principle of, 323; - construction of, 325-328. - - Electricity assumed as the medium attracting particles of matter, 103, - 104; - identical with chemical affinity, 110; - in composition and decomposition, subject to laws of definite - proportion, 112; - influencing winds, 125; - its comparative velocity, 138; - producing phosphorescence, 217; - communicated to metal plates by juxtaposition, 220; - impressions traced on glass by, 221; - rays exciting, 223; - a dual power, 282; - modes of exciting by disturbing equilibrium, 282-284; - transmission of, 284, 285; - transmission by induction, 285, 286; - laws of attraction and repulsion determining intensity of, 286-288; - heat and light produced by, 288; - velocity of, 289; - experiment determining its velocity, 290; - development of, in the atmosphere, 291, 292; - phosphorescence excited by, 294; - Voltaic, _see_ Voltaic; - conduction of static, contrasted with Voltaic, 309; - laws of action in, distinguishing it from Voltaic, 317; - relation between 322, 323; - telegraphs working by, 323-328; - produced by rotation, 330, 331; - thermo, 332, 333; - exact balance of its dual force, 334; - points of analogy between magnetism and, 340, 341; - causing convulsions in comets, 375. - - Electro-dynamics, _see_ Dynamics. - - —— magnetism, _see_ Magnetism. - - Elements, the three terrestrial magnetic, 343; - variations in, _ib._; - storms affecting, 344. - - Elevation, effect of, on temperature, 240-242; - on vegetation, 250. - - Ellipses, described by planets, 5; - paths of planets describing, 10; - preventing compensation of disturbance, 15; - cause and measures of variation in, 17; - described by comets, 363, 366. - - Ellipsoid, an, of revolution, mass assuming the form of, 45; - its equatorial and its polar radius, 48; - permanent axes of rotation, 76. - - Elliptic motion, ratio of forces procuring, 382. - - Elliptical polarization of light, 192, 193; - of heat, 267. - - —— nebulæ, 409; - their connection with double stars, 411; - frequency, 413; - difficult of resolution, 415. - - Encke, Professor, sun’s parallax found by, 53; - his comet, 169; - aspects, period of his comet, 365, 366; - cause of acceleration in its revolution, 366, 367; - crossing the terrestrial orbit, 368; - prospective and present planetary influence on, 369; - disappearance of its tail and nucleus, 369; - referred to, 377; - contraction of diameter, _ib._ - - England, arcs of the meridian measured in, 48; - course of the tidal wave towards its west coast, 94; - peculiarities of photography in, 213; - meteors falling in, 421. - - Engravings copied by photography, 204; - impressions taken by contact with iodized silver, 221; - impressions taken from, by galvanism, 309. - - Epipolic light, 197. - - Epsilon Orionis, zone of stars passing through, 385. - - Equation of the centre, defined, 9; - lunar, 35. - - Equator, the, forces compelling the wider circle of, 6; - inclination of the terrestrial to the plane of the ecliptic, 23; - of the solar system, 24; - measure of the centrifugal force at, 49; - calculation from lunar action on the terrestrial, 55; - effects produced by external attraction influencing the direction of - its plane, 79, 80; - inequality in its polar motion, 81; - cause of the calms at, 122; - depth of the underground stratum of constant temperature at, 228; - maximum of solar heating influence, 238; - superficial extent of land, 244; - mean annual temperature, 245. - - Equator of the sun, maximum of solar heat attained in, 225. - - ——, dynamic, surrounding the terrestrial globe, 343. - - ——, magnetic, of the earth, 343. - - Equinoctial circle, the, defined, 9. - - —— points, effects of solar and lunar attraction on, 79; - period of their revolution, 80; - measuring time, 83. - - Equinoxes, the, defined, 9; - venial, a point whence planetary motions are estimated, _ib._; - of the planets, cause of a precession in, 66; - causes preventing their invariable correspondence with points of the - ecliptic, 79; - precession affecting the seasons, 80; - secular motion of, periodic variations, 80, 81; - eras depending on the precession of, 86, 87; - tides augmented in, 97. - - Eras, astronomical, determined by the position of the major axis of the - solar ellipse, 86, 87. - - Eratosthenes, the earth’s circumference measured by, 49. - - Eridanus, nebulous patches crossing, 417. - - Erman, M., depression of the barometer observed by, 120. - - Eruptions, volcanic, recorded, 234. - - Eta Aquilæ, a variable star, 391. - - —— Argûs, zone stretching from, 390; - nebula round, 418, 419. - - —— Coronæ, periodic time of, 398. - - Etna, measurements of, 120. - - Ethereal medium, undulations of, propagating heat, 267; - permeable to lines of magnetic force, 344; - its density, 356; - transmitting gravity, _ib._; - magnetic, 356, 357; - offices discharged by, 357; - pervading the visible creation, 358; - influence of, on comet motion, 365; - astral revolutions accelerated by, 366; - probable increase in density of, 367. - - Europe, atmospheric wave passing over, 121; - causes of variation of climate in, 244; - separation of isothermal lines in high latitudes of, 245; - differences of latitude enjoying the same mean temperature, 246; - indigenous productions of, 249; - number of indigenous productions common to Australia and, 251; - number of species of forest trees, 252. - - Eudoxus, Plato’s contemporary, astronomical observation of, 88. - - Evaporation, conditions affecting, 269, 270. - - Everest, Colonel, arc of the meridian measured by, 48. - - Excentricity of planetary orbits measured, 17. - - Expansion, universal law of, 271; - accuracy in measurement ensured by laws of unequal, 272; - of crystals, 272, 273; - theory of, 275, 277; - of steam, 278; - by electricity, 285. - - Extra-tropical winds, 124. - - - Fabricius, the comet of 1556 observed by, 370; - variable star, 390. - - Fahrenheit, mode of ascertaining heights proposed by, 120. - - Falling stars, 420; - theories of, 422, 423. - - Faraday, Dr., gases reduced to liquids by, 105; - experiments testing chemical affinity, 111; - instance of cohesive force inducing chemical combination, 112; - experiments on vibrations producing colour, 173; - influence of dialectrics, 286; - chemical origin of electricity defended by, 300; - electro-chemical decomposition defined by, 308; - remarks of, on conduction of voltaic electricity, 309; - experiments on magnetic rotation, 313; - experiment magnetizing polarized light, 318, 319; - importance of his experiment, 320; - experiment establishing the identity of magnetism and electricity, - 322, 323; - his magnetic battery, 324, 325; - aid given by, in construction of telegraphs, 326, 328; - electricity produced by rotatory motion explained, 330; - his classification of substances according to magnetic qualities, - 332; - quotation from, on conservation of force in electricity, 334; - magnetism raised to a new science by, 335; - the magnet as represented by, 338; - experiment determining the forms of magnetic lines of force, 339, - 340; - accidental electro-magnetic combinations pointed out by, 342; - his discovery of diamagnetism, 347; - experiments on magnetic action in crystals, 349; - observations on influence of heat in magnetism, 352; - definition of gravity questioned by, 354, 355; - magnetism of the ethereal medium tested, 356. - - Fauna, distinct, of separate regions, 254, 255. - - Faye, M., his conception of the sun’s constitution, 41; - his theory of phenomena observed in eclipses, 42; - comet of 1843 discovered by, 361. - - Fiedler, Dr., fulgorites exhibited by, 293. - - Fire, chemical combination producing, 270. - - —— balls, theory of, 421. - - Fires, central, subterranean, 231-237. - - Fish, phosphorescent, 294, 295; - electric, 310. - - Fixed stars. - _See_ Stars. - - Fizeau, M., decisive experiment in proof of the undulatory theory of - light accomplished by, 202. - - Flame, chemical combination evolving, 270, 271. - - Flames, lambent, caused by electricity, 294. - - —— divergent from the nucleus of a comet, 364. - - Fletcher, Mr., periodic time of γ Virginis determined by, 398. - - Flora of the Himalaya, 250; - distinct, in separate regions, 251; - condition establishing distinct, in islands, 252. - - Florence, comet discovered from, 378. - - Fluor-spar, its property of diminishing refrangibility of light, 196. - - Fluorescence of light, definition of, 195; - vibrations of the substance producing, 196; - experiments, 197, 198. - - Focus of a meteoric shower, 422. - - Fog, yellow, excluding the chemical action of rays, 214. - - Forbes, Professor, temperature of the boiling point ascertained by, - 120; - observations of, on rayless lines, 163; - lunar heat tested by, 227; - experiments of, in polarization of heat, 264, 267. - - Force, relation of, to heat, 275; - transforming solids to liquids and to vapour, 275, 277; - a power of nature, 279; - light and heat modes of, 219, 220; - heat a living, 329; - lines of magnetic, 338, 340; - conservation of, maintained in periodic variation of atmospheric - magnetism, 345; - increatable, indestructible, 353; - examples of conservation of, 354; - fundamental principle of conservation, 357; - influence and action of the gravitating, 424, 426. - - Forces, the unknown cause of motion, 5 _et passim_; - counteraction of solar and tangential, in planetary motion, 8; - adjustment of, ensuring the permanence of the solar system, 11, 12; - three partial, causing perturbation in planetary motion, 14, 15; - excess of equatorial diameter the origin of, 27, 28; - three, disturbing lunar motions, 34, 35; - determining planet forms, 44, 45; - producing tides, 91, 92; - combining to form the centrifugal, 100; - acting on molecules of matter, 102, 105; - producing capillary phenomena, 114; - latent, in nature, 279, 280; - one universal power, the root of all, 321; - exact balance of, in electricity, 334; - kindred and convertible, 353; - developing comets’ tails, 375; - determining the forms of orbits, 382, 383; - maintaining the stability of the solar system, 426; - mutual relations of, 427. - - Forests, change produced in the atmosphere by, 241, 243; - number of species of trees found in American and European, 252. - - Formentera, quadrant of the meridian passing through, furnishing a unit - of linear measure, 89. - - Fornix, nebulous patches crossing, 417. - - Forster, Lieutenant, conversation carried on by, across Port Bowen - Harbour, 136. - - Fossil plants, an evidence of change in temperature, 74. - - Fourier, mean temperature of space according to, 119; - rate of decrease in the earth’s central heat computed by, 232. - - Fox, Mr., temperatures in mines tested by, 228, 229; - law of paramagnetic force ascertained by, 338; - observations in mines, proving agency of electro-magnetism, 346. - - France, arcs of the meridian measured in, 48; - unit of linear measure in, 89; - mode of arithmetical computation, 90; - atmospheric pressure in, 120; - cliffs of, seen from Hastings, 157. - - Fraunhofer, M., discovery of rayless lines in the solar spectrum, 162; - comparative refrangibility of rays ascertained by, 163; - data furnished by, to determine the dispersive power of rays, 165; - his discovery determining the length of waves independently of - refraction, 201; - spectrum of an electric spark observed by, 289. - - Freezing, temperature required for, under pressure, 271; - theory of, 276. - - Fresnel, M., his testimony in favour of the undulatory theory of light, - 171; - theory of refraction, 183; - discoveries in polarization of light, 191, 193. - - Freyberg, green plants found in mines at, 253. - - Friction evolving heat, 274, 275; - electricity, 282, 283. - - Fringes of coloured light bordering shadows, 174, 175; - produced by interference of polarized rays, 194. - - Fulgorites, found in Silesia, 293. - - Fundy, the Gulf of, cross tides pouring into, 94. - - - Gage, Mr., experiments of, on magnetism, 315. - - Gales. - _See_ Winds. - - Galileo, laws affecting music discovered by, 145; - his method of finding distances of fixed stars, 388. - - Galle, Dr., Neptune’s place communicated to, by Le Verrier, 62. - - Galloway, Mr., sun’s motion proved by, 405. - - Galvani, Professor, peculiar effects of electricity suggested to, 297. - - Galvanism, phenomenon suggesting the theory of, 297; - batteries, 298, 300; - heat and light evolved by currents of, 300, 304; - decomposition and composition, 307, 308; - applied to plating and gilding, 309; - effect of heat on, 310; - effect of, on the senses, _ib._; - fish exhibiting analogous phenomena, 310, 311; - phenomena exhibited by currents of, on magnets, 312, 314: - intensity of a current measured, 315; - conditions obtaining a circuit in, 332. - - Galvanometer, the principle of its construction, 315; - experiment by means of, identifying magnetism and electricity, 322, - 323. - - Gambart, M., parabolic elements of a comet computed by, 367. - - Gamma Andromeda, colours of, 401. - - —— Aquarii, planetary nebula near, 412. - - —— Hydræ, a variable star, 391. - - —— Leonis, focus of a meteoric shower in, 422. - - —— Sagittarii, cluster of the Milky Way round, 387. - - —— Virginis, eclipse in, 397; - orbit of the revolving star determined, 398. - - Ganges, the, tidal wave at the mouths of, 94. - - Gardner, Mr., extent of diametrically opposite lands estimated by, 244. - - Gases, conditions retaining matter in the form of, 104, 105; - combinations of, 111; - transmission of radiant heat through, 258; - expansion of, 271; - voltaic spectrum modified by, 303; - effect of heat on the conducting powers of, 309. - - Gassiot, Mr., experiments of, on the electric discharge, 306; - connexion between magnetism and light discovered by, 321; - electric apparatus improved, 328. - - Geneva, the Lake of, experiment on the velocity of sound in, 135. - - Gensanne, M., increasing temperature of mines tested by, 228. - - Geographers, lunar motions important to, 42. - - Geological changes, probable cause of, 77. - - Geology, the lessons of, 326. - - Georgia Island, S., excess of cold in, over corresponding latitudes, - 241. - - Germany, shooting stars seen from, 421. - - Gibraltar, the Straits of, turning aside the tidal wave, 98. - - Giromagny, temperature of the lead-mines of, 228. - - Glass, effect of cohesion on plates of, 106; - musical notes elicited from rods and plates of, 144-147; - transmission of waves of light in, 177; - polarizing light, 184, 185; - elliptical polarization produced by, 193, 194; - used in photography, 207; - impressions on, from bodies in contact with, 220; - impressions on, traced by electricity, 221; - transmission of radiant heat by, 259; - by coloured, 261, 262; - its temper altered by magnetism, 352, 353. - - Globular clusters of nebulæ, 413-415. - - Glow-discharge observed by Captain Bonnycastle, 295, 296. - - Gold, action of, on light, 173. - - Good Hope, the Cape of, icebergs drifted to, 101. - - Goodricke, Mr., variable stars discovered by, 391; - opaque bodies represented as revolving round fixed stars by, 394. - - Graham, Mrs., account of an earthquake by, 234. - - Graham’s compensation pendulum, 272. - - Gravitating force of the sun, 365, 424, 425. - - Gravitation, offices of, in the material creation, 1, 2; - process of reasoning in ascertaining the law of, 3; - law determining its intensity in the solar system, 5; - complex action of, by attraction in mass and in particles, 6; - increase of, towards the poles of the earth, 45; - calculations founded on its increase, 49-51; - in a mine, its excess over surface, 57; - action of, modifying tides, 92, 93; - law, universally acting on matter, 105; - the air subject to, 117; - influence of, in motions of the heavenly bodies, 382, 383; - double stars revolving by, 398; - stellar systems subject to, 400; - influence of, on nebulæ, 416; - a general law of the visible creation, 424; - mode of its action, 425, 426. - - Gravity, centre of, in spheres, effect of impulses passing through, 7; - of the solar system, invariable plane passing through, 23; - straight line described by, 24; - action of, in determining the figure of the earth, 44, 45; - definition irreconcilable with the conservation of force, 354, 355; - question of its transmission, 355, 356. - - Great Bear, the nebulous zone passing, 416. - - —— Gobi, the, effect of the expansion of air over, 124. - - Greeks, astronomical observations of, confirming results of analysis, - 38. - - Greenland, ocean on the northern coast of, 94. - - Greenwich, lunar distances computed for, 43; - quadrant of the meridian passing through, furnishing a unit of linear - measure, 89; - periodic circuits of winds, 125. - - Grimaldi, coloured fringes bordering shadows described by, 175. - - Groombridge, velocity of his proper motion, 404. - - Grotthus, the transmission of voltaic electricity investigated by, 298. - - Grove, Mr., copper and zinc plates electrified by, 220; - substances radiating heat of different refrangibilities enumerated - by, 257; - the transmission of voltaic electricity investigated by, 298; - electric heat tested by, 301, 302; - remarks of, on carbon, 302, 303; - on the voltaic arc, 304, 305; - remarks of, on light and heat, 319; - electric apparatus improved by, 328; - his definition of the ethereal medium, 355. - - Grylli, supposed delicate sense of hearing in, 132. - - Guanaxato, temperature of the silver-mine of, 228. - - Gulfs separating stars, 390. - - Gum-guaiacum, chemically affected by rays of the solar spectrum, 203; - condition of its sensibility to light, 206; - effect of red rays on, 209; - used in experiments on parathermic rays, 217, 218. - - Gum-lac, electrical intensity measured by means of, 286, 287. - - Gymnotus electricus, the, 310. - - - Haidinger, M., experiments of, proving water an essential part of - crystals, 107. - - Hail, formation of, 270. - - Hales, his calculation of the amount of surface exposed by the leaves - of a helianthus, 243. - - Hall, Mr., achromatic telescope constructed by, 165. - - Halley, elements of a comet’s orbit computed by, 362; - return of his comet, 363; - changes in its aspect, 363, 364; - records of, 365; - no solid nucleus in, 374; - cause of its luminous sectors, 376; - Sir John Herschel’s observations on, 378. - - Hare, the, comet observed near, 372, 373. - - Harmonics of the fundamental note in music, 140, 141. - - Harmony, property of sound regulating, 131; - definition of, vibrations producing, 142. - - Harris, Sir William Snow, experiments of, in electricity, 287, 288; - lightning-conductors invented by, 293. - - Harrison, pendulum invented by, 272. - - Hastings, coast of France distinctly seen from, 157. - - Heat affecting the form of crystals, 107; - evolved in chemical combinations, 110; - irregular decrease of, in the atmosphere, 119; - maxima of, in the solar spectrum, 215; - peculiar chemical quality of, in parathermic rays, 218; - impressions traced by, 220-222; - periodical variations in the sun’s, 225; - different proportions of solar, reaching the planets, 225, 226; - effect of the terrestrial atmosphere on lunar, 227; - mode of its development in opaque bodies, _ib._; - sources of terrestrial, 228-238; - irregular distribution of, 239-247; - laws affecting its radiation, 257; - its transmission, 258-262; - polarization of, 264-267; - undulatory theory, 267; - absorption and reflection of radiant, 268; - phenomena caused by radiation of, 269; - accumulation of, producing light, 270; - expansive force of, 271, 272; - modes of propagation, 273, 274; - produced by motion and equivalent to it, 274-277; - laws regulating the force of artificial, 279, 280; - power evolved by application of, 280; - identical in nature with sound, 281; - electrical, 288; - sheet-lightning caused by, 294; - phosphorescence, 294; - developed by voltaic electricity, 301, 302; - effect of, on electrical conductors, 309; - connexion between the production of electricity and, 310; - its direct relation to magnetism and electricity, 319, 320; - mechanical power and convertible forces, 329; - terrestrial magnetism attributed to the action of, 333; - measured by electric currents, 334; - affecting atmospheric magnetism, 344; - fundamental principle of the dynamic theory, 357. - - Helena, St., distinct flora of, 252. - - Helix, circular and elliptical, described in polarization of light, - 192, 193; - electrical experiments by means of, 314; - induction of, increasing electric power, 322, 323. - - Heller, his observations on the comet of 1556, 370, 371. - - Helmholtz, Professor, power of chemical force estimated by, 112; - his calculation of the chemical force developed by combustion, 278; - of the amount of latent force in our system, 280. - - Hemisphere, cause of excess of cold in the southern, 241; - superficial extent of land in northern and southern, 244. - - Henley, Mr., magneto-electric machine constructed by, 325. - - Henderson, Professor, parallax of α Centauri calculated by, 387; - of Sirius, 389. - - Henry, Professor, experiments of, on magnetism, 315. - - Herapath, Mr., his view of elastic force preferred to Sir Humphry - Davy’s, 276. - - Hercules, eclipse of a double star in, 398; - globular nebulous cluster, 414. - - Herschel, Sir William, observations of Saturn’s and Uranus’s satellites - by, 32, 33; - theory of, regarding the solar constitution, 41; - cause of effects of light in eclipses according to, 42; - rotation of Jupiter’s satellites determined by, 70; - mutual independence of light and heat, 214, 215; - influence of the sun’s spots on heat, 225; - point of maximum heat in the solar spectrum, 263; - comet of 1811 observed by, 374; - its luminous envelopes examined, 375; - the Milky Way examined by, 385; - his discovery of the orbital motions of double stars, 388; - catalogue of double stars by, 395, 396; - periodic time of γ Virginis determined by, 398; - eclipse of a double star observed, _ib._; - binary system discovered, 400; - remarks on the motions of the stars, 405; - nebulæ resolvable into stars, 507. - - Herschel, Sir John, approximate periods of satellites ascertained by, - 33; - thickness of Saturn’s ring computed, 67; - observations of, on seasons, 74; - difficulty of varying time, in observations at distances, obviated - by, 86; - tenuity of atmospheric air demonstrated, 110; - rapid decrease of density in the atmosphere, 118; - mean temperature of space computed by, 119; - height of Etna measured, 120; - his explanation of anomalies in atmospheric phenomena, _ib._; - quotation from, on the transmission of sound, 136; - observations of, on thunder, 138; - remarks on the absorption of light by coloured media, 175, 176; - on polarization of light, 179; - experimentalising apparatus, 188; - discovery of epipolic light, 197; - discoveries in photography, 205, 206; - analysis of the solar spectrum, discovery of its chemical properties, - 207-219; - his theory of volcanic action, 235-237; - observations showing the maximum of heating influence of the solar - rays, 238; - theory of the original distribution of plants, 254; - divergent flame of a comet observed by, 364; - remarks on the possible destruction of the solar system, 372; - causes assigned by, for contraction of diameter in comets, 378; - comparative lustre of stars measured by, 384, 385; - the Milky Way described, 385, 386; - number of stars in a group of the Milky Way computed, 387; - variable star discovered, 391; - remarks of, on the nature of the fixed stars, 392; - variable stars discovered by, 393; - remarks on variable stars, 394; - star missed by, 395; - double stars discovered, 396; - eclipse of a double star observed, 397; - orbits determined, 398, 399; - observations on colours of double stars, 401; - light of α Centauri compared with the moon’s by, 404; - light of the fixed stars calculated, _ib._; - observations on nebulæ corrected, 407; - catalogues of nebulæ, 408; - nebulæ discovered by, 409; - annular nebula described, 410; - magnitude of planetary nebulæ computed, 412; - globular nebulous cluster described, 413; - law of gravitation ascribed to nebulæ, 416; - nebula round η Argus described, 418; - his work on Nebulæ, 419. - - Herschel, Miss, Encke’s comet seen by, 365; - catalogue of nebulæ, 407. - - Hevelius, divergent flames of a comet described by, 364; - contraction in diameter of comets observed, 377; - phases in comets observed, 380. - - Hieroglyphics interpreted by astronomy, 89. - - Himalaya, the, inappreciable effect of, on the globe’s surface, 6; - singular effect of refraction on, 156; - cause of greater elevation of the snow-line on the northern side of, - 241; - flora of, 250. - - Hind, Mr., comet’s orbit computed by, 370, 371; - observations of, on Donati’s comet, 379; - variable stars discovered by, 391; - vanishing star discovered, 393; - his belief in planetary systems, 394. - - Hindostan, the tidal wave striking on its coasts, 94. - - Hipparchus, precession discovered by, change of seasons since his age, - 80; - phenomenon suggesting his catalogue of the stars, 392. - - History corroborated and corrected by astronomy, 87, 89. - - Hoar-frost, cause of, 269. - - Holtzmann, M., opinion of, with regard to the vibrations of polarized - light, 223. - - Hoogly, the, bore of, 94. - - Horizon, effects produced by the denser stratum of air in, 157, 158. - - Horologium, nebulous patches in, 417. - - Horton coal-mine, experiments with the pendulum in, 57. - - Hours, cause of their mal-correspondence over the globe, 86. - - Hudson’s Bay, tide in, 98. - - Humboldt, his sufferings from rarity of the atmosphere, 118; - his explanation of the apparent greater acuteness of hearing observed - at night, 135; - observations of, in mines, 228; - causes of disturbance in the equal diffusion of heat enumerated by, - 240; - identical productions of the Old and New World found by, 251; - his distribution of palms and grasses, 252; - green plants found growing in mines by, 253. - - Hunt, Mr., coloured image of the solar spectrum obtained by, 209; - image obtained in England, 213; - his experiments in tracing images by juxtaposition of bodies, 220, - 221; - experiments on the condensing power of rays, 223. - - Hurricanes, origin and cause of, 125, 126; - curve described by the axis of, _ib._; - their extent and velocity, 126,127; - phenomena resulting from their revolving motion, 127; - laws of, making avoidance possible, 128. - - Huygens, theory originated by, 169. - - Hydrogen, proportion of, in water and gases, 111; - spectrum from, 303; - separated from water by electricity, 307. - - Hygrometer, dew-point measured by, 269. - - Hyperbolic motion, ratio of forces procuring, 382. - - - Iapetus, seen by Mr. Lassell, 33. - - Ibn Junis, progress of science in his time, 90. - - Ice, formation of, 271; - force acting in its formation, 276; - stopping the current of voltaic electricity, 309. - - Icebergs, drifting of, 100, 101; - farthest range of northern and southern, 241; - effect of electricity in collisions, 284. - - Iceland spar, its property of double refraction, 181; - polarized ray analyzed by, 187; - transmission of radiant heat by, 258; - electricity elicited from, 284. - - Illumination, comparative, of objects, experiments determining, 227. - - Images, coloured, of the solar spectrum, 208-211; - traced by contact and juxtaposition of bodies, 219, 220; - by electricity, 221; - by media absorbing hot rays, 222. - - India, arcs of the meridian measured in, 48; - discovery of Saturn’s ring, 66; - ancient monument of astronomical knowledge, 85; - observations confirming the antiquity of astronomical science in, 88. - - Indian Ocean, the tidal wave in, 94; - monsoons blowing over, 124. - - Induction, law of, in electricity, 285, 286; - magnetic, 314, 315; - phenomena of, produced by electric currents, 324; - illustrated by the Atlantic telegraph, 325, 326; - velocity of electricity modified by power of, 327; - possibility of electro, furnishing a motive power, 328; - of electricity by rotation of magnets, 330-332; - as possessed by magnets, 336; - paramagnetism evolved by, 337; - means of accelerating, _ib._; - subject to the laws of mechanics, 338; - analogy between electric and magnetic, 341; - of heavenly bodies, affecting terrestrial magnetism, 346, 347; - diamagnetic substances capable of, 348. - - Indus, comet passing through the constellation of, 379. - - Inequality, the, of Jupiter and Saturn marking historical epochs, 88. - - Insects, law of their dispersion, 255. - - Instruments, musical, 143, 149, 150; - imitating articulation of letters, 151, 152. - - Insulation in electricity, 285. - - Interference, laws of, neutralizing undulations, 138, 139; - the theory of, referred to a general law, 169. - - Iota Cetæ, comet observed near, 372. - - —— Orionis, a nebulous star, 411. - - Ireland, progress of the tidal wave towards, 94. - - Iron, distilled, 305; - rotation of its particles, _ib._; - magnetized by electricity, 314, 315; - magnetic properties of, 332; - rendered paramagnetic, 336, 337; - magnetic and electric properties of, 347; - elasticity of, affected by magnetism, 352. - - Islands, character of their floras, 252. - - Isogeothermal lines of temperature defined, 238, 239; - parallel with the isothermal lines, 246. - - Isomorphous crystals, 109. - - Isothermal lines of temperature defined, 240; - latitudes of, deviation from the line of the equator, 245; - formula determining, 246; - similarity of vegetation in the same, 253. - - Italy, local attraction, occasioning inaccuracy in measurement, 48. - - Ivory, M., his method of computing heights, 120; - his theoretical investigation of planet forms, 44; - deduction from measurement of arcs of the meridian, 48. - - - Jacob, Mr., discovery of Saturn’s ring by, 66; - periodic time of α Centauri determined by, 399; - periodic time of 70 Ophiuchi, 400. - - James, Colonel, measurements of, in the General Survey of Great - Britain, 47; - density of the earth determined by, 58. - - Jamin, M., remarks of, on substances producing elliptical polarization, - 193. - - January, epoch of its beginning the year, 85. - - Jews, denominations of time in their calendars, 85. - - Josephstadt, discovery of a comet from, 367. - - Joule, Mr., heat considered a mechanical force by, 275; - his view of elastic force, 276; - amount of latent force in a pound of coal, computed by, 278; - furnishing data to Professor Thomson, 279; - quantity of heat generated in a unit of time by electricity computed - by, 302; - powerful magnet obtained by electricity, 315; - electric machines constructed by, 328; - experiments proving heat and mechanical power convertible, 329. - - Jovial system, mass of the whole, 55. - - Julian Calendar, year of, the first of our era, 86. - - June, 1833, reappearance of Saturn’s rings, 67; - coincidence of times in, 84. - - Juno, the diameter of, 56; - astronomical tables of, 63. - - Jupiter, rotation of, distinguished from the other planets, 7; - periodical inequality in his motions, 15; - discovery of telescopic planets between Mars and, 20, 21; - diameter of, 21; - his position with respect to the equator of the solar system, 24; - inequalities in the motion of, apparently anomalous, 25, 26; - his mass proved not homogeneous, 29; - eclipses, 30, 31; - compression of his spheroid computed, 39; - eclipsed by Mars, 42; - mass of, compared with the sun, 55; - his diameter, 56; - increase of density in, 58; - astronomical tables of, 60; - rapid rotation, 66; - period of a year in, _ib._; - effect of his disturbing energy, 81; - photographic images of, 226; - light reflected by his atmosphere, 227; - action of, on the comet of 1770, 361, 362; - on Halley’s comet, 362, 363; - comet revolving between the orbits of the earth and, 367; - future influence of, on comets, 369; - comet nearly approaching his fourth satellite, 370; - comets having their perihelia in his orbit, 381. - - ——, orbit of, revolutions of its major axis, source of variation in - excentricity, 17; - slow revolution of its nodes, decrease in its inclination to the - ecliptic, 19. - - —— with his satellites, an epitome of the solar system, 27; - effect of his excessive equatorial diameter on their orbits, 28; - satellites, libration in, 69; - rotation of, 70. - - - Kane, Dr., Polar Sea discovered by, 94; - cold of Northern Greenland marked by, 247. - - Kappa Crucis, cluster of coloured stars round, 419. - - —— Draconis, seen in the pole of the equator, 88, 89. - - Karsten, Mr., impressions made on glass by electricity, 221. - - Kasan, summer and winter mean temperature of, compared with Edinburgh, - 246, 247. - - Kater, Captain, approximate length of the pendulum, determined by, 89. - - Kempelen, M., speaking-machine invented by, 151. - - Kepler, paths, revolutions of planets discovered by, 5; - his law regarding the mean distances of planets from the sun, 19; - law of, applied to calculating distances, 53, 54; - rapidity of planetary revolutions determined by his law, 66; - his law finding areas described by heavenly bodies, referred to, 360. - - Kew, balloon ascent from, 119. - - Knoblauch, position of the magnecrystallic axis proved by, 349. - - Knowledge, limited nature of human, 2. - - Kotzebue, stratum in the ocean discovered by, 101. - - Kratzenstein, M., instrument invented by, articulating words, 151. - - Kupffer, M., observations of, on temperature, 246. - - - La Basilicata, earthquake in, 234. - - Lacaille, his globular nebulous cluster, 414; - nebula, 418. - - La Grange, his investigations into the stability of the solar system, - 20, 21; - greatest discovery of, 23. - - La Hire, phases in comets observed by, 380. - - La Place, stability of the solar system proved by, 20; - principle in astronomical calculations established, 23; - angle of inclination fixed, 24; - his theory accounting for acceleration in the moon’s mean motion, 36, - 37; - result of observations compared with his theory of Jupiter’s - satellites, 55; - theory of planetary motion, 65, 66; - universal epoch proposed by, 87; - scientific observations complementing historical records, 87; - date fixed by, for the lunar tables of the Indians, 88; - justifies Newton’s theory of tides, 96; - density of a liquid column estimated by, 114; - action of the earth on a comet, 359; - change in a comet’s orbit, 361; - cause of error in Clairaut’s calculation pointed out by, 363; - opinion of, as to the comet of 1682, 378. - - “Lake of the Gazelles” ascribed to an effect of reflection, 157. - - Lalande, epochs of conjunctions computed by, 42. - - Lambda Herculis, general motion of the stars determined by, 405. - - Land, dry, comparative extent of, on the globe, 242, 244; - extent of, in diametrical opposition, 244. - - Landscapes in chiaroscuro, produced by photography, 207. - - Languages, resemblances and analogies between, 255, 256. - - Lapland, arcs of the meridian measured in, 48; - transit of Venus observed in, 53. - - Laroche, M., his experiments on transmission of radiant heat, 259, 261. - - Lassell, Mr., satellite of Saturn discovered by, 32; - observations of, on Uranus’ satellites, 33; - his discovery of Neptune’s satellite, _ib._; - observations on Saturn’s rings, 66. - - Latent heat, energetic action of, on matter, 275-277. - - Latitude, the, of a planet defined, mode of obtaining, 9, 10; - cause of periodical inequalities in, 15; - perturbations from action of the perpendicular force, 18; - moon’s motion in, disturbed, 35; - effects of disturbance, 38; - data of, used in computing a planet’s place in the heavens, 58-60; - conditions ensuring the invariability of geographical, 76, 77; - change effected by nutation in, 81; - climate not invariable in the same, 239; - degrees of, where diminution of mean heat is most rapid, 244, 245; - the same mean temperature in different, 246, 247; - of wine-growing, 250; - magnetic storms varying with, 345. - - Layang, observations made at, 1100 years before the Christian era, 88. - - Le Sueur, specific diversity of marine animals observed by, 254. - - Le Verrier, M., principle of La Grange applied by, 21; - zone of instability found, _ib._; - discovery of Neptune, 62; - his observations on atmospheric waves, 122; - comets identified by, 362; - his table of comets’ orbits, _ib._ - - Lenticular nebulæ, 409; - haze surrounding the sun, 412. - - Leo, nebulous system in, 417. - - Léon-Faucault, M., velocity of light in air and water ascertained by, - 202. - - Lerius, banks of algæ found by, 253. - - Leslie, Professor, compression of air calculated by, 78; - experiments on radiation of heat, 257. - - Lexel, observations of, on the comet of 1770, 361, 362. - - Libra, the five great planets in conjunction near, 42. - - Librations of the moon, of Jupiter’s satellites, 69; - of α Centauri, 399. - - Lichen, red, growing on snow, 249. - - Light, rate of its velocity, 31; - truth deduced from the uniformity of its velocity, 32; - from the aberration of, _ib._; - period required to reach the earth from α Centauri, 54; - action of the atmosphere on, 153; - conditions regulating the transmission and reflection of, 156; - loss of, transmitted by the horizontal stratum, 157; - effects of transmission through the atmosphere, 158; - Newton’s analysis of, 159; - Brewster’s, 161; - phenomena disproving Newton’s theory, 167, 168; - undulatory theory, 168-170; - conditions affecting its intensity and colour, 170; - experiments testing the mutual relations of colour and, 171-175; - law of its absorption identical with a law of motion, 175-177; - repeated vibrations producing the sensation of, 178; - polarized, defined, 179; - modes of polarization, substances polarizing, 179-185; - accidental polarization of, 195; - degraded, or fluorescence, 196; - objections to the undulatory theory analyzed and disproved, 199-202; - comparative velocity of, in air and water, 202; - pictures produced by reflected, 203-207; - rays of, independent of heat, 214, 215; - comparative amounts of solar and lunar, 225; - different measures of illumination from, 227; - influence of, on vegetation, 249; - colour developed without the influence of, 253; - separated from heat by Melloni, 265; - produced by accumulation of heat, 270; - law regulating the force of artificial, 279, 280; - electrical, 288, 289; - produced by voltaic electricity, 302; - stratifications of the electric, 306; - influence of magnetism and electricity on, 319, 320; - of comets, 379-381; - of the fixed stars, 401-404. - - Lightning, development of heat exhibited by, 276, 277; - experiment showing the velocity of, 289; - theory of, 292; - the back stroke, _ib._; - force of the direct stroke, 293; - sheet, 294; - effect of, on the compass, 312. - - Lime, carbonate of, variety of form in its crystals, 107; - invariable form ultimately assumed by, 109. - - Lines of magnetic force, 338, 339; - experiment ascertaining the form of, 339, 340; - terrestrial, 341, 342; - extensive courses of, 344; - a connected system, 345; - diamagnetic, 348. - - Lion, the, conjunction of planets in, 42. - - Liquids, balance of forces constituting, 104, 105; - action of capillary attraction on, 113-116. - - —— possessing the property of circular polarization of light, 190, - 191-193. - - Liquids, conditions affecting the transmission of radiant heat by, 263; - evaporation from, 269; - expansion of, by heat, 271; - propagation of heat in, 273; - action of heat as a mechanical force on, 275-277. - - London, retarding of the tidal wave between Aberdeen and, 94. - - ——, pendulum vibrating in its latitude, a standard of measurement, 89; - fulgorites exhibited in, 293. - - Long, Dr., his attempt to measure distances of fixed stars, 388. - - Longitude, mode of reckoning mean and true, 9; - of the perihelion and of the epoch defined, 10; - cause of periodical perturbations in, 14; - calculation from the moon’s influence on the sun’s, 55; - data of, used in computing a planet’s place in the heavens, 58-60; - change effected by precession and nutation in, 81. - - Lloyd, experiments of, in polarization of heat, 264. - - Lubbock, Sir John, theory of planetary motion completed by, 64; - his theory of shooting stars, 423. - - Lumière cendré, definition of, 227. - - Lunar distance, defined, 43. - - —— theory, mean distances obtained from, 43. - - —— tides of the terrestrial atmosphere, 121. - - Lundahles, M., motions of heavenly bodies investigated by, 405. - - Lupus, position of, 390. - - Lussac, Gay, M., uniting of gases by volumes discovered by, 111; - ascent of, in a balloon, 118; - course of a lightning flash ascertained by, 292. - - Lutetia, diameter of, 56. - - Lyell, Sir Charles, his theory of changes of temperature in the - northern hemisphere, 75; - annual number of volcanic eruptions computed by, 233; - volcanic phenomena related by, 234. - - Lyncis 12, a triple star, 395. - - Lyra, a variable star in, 391; - a double star, 395; - nebula, 410. - - - Machinery, relations of, to force, 353. - - Mackintosh, Sir James, quotation from, illustrating the essential - advantages of study, 1. - - Maclear, Mr., parallax calculated by, 387. - - Madeira, vegetation of, 252. - - Madras, Saturn’s ring discovered from, 66. - - Magellanic clouds, the, 417, 418. - - Magnecrystallic action, 349; - temperature affecting, 352. - - Magnetic bodies, difference in power of, 347. - - —— elements, the three terrestrial, 343. - - —— equator of the earth, 343. - - —— meridian, the, mean action of forces determining, 343. - - —— poles of the earth, 343. - - —— storms, 344; - varying with latitude, 345, 346. - - Magnetism, source of, 318; - producing electrical phenomena, 322, 323; - rotatory motion a source of, 330; - classification of substances, with regard to their susceptibility of, - 332; - residing in substances after two manners, 335; - experiment illustrating the forces of, 338; - antithesis, its general character, 339; - form of its lines of force, 339, 340; - analogous properties of electricity and of, 340, 341; - terrestrial, 342-347; - connexion between solar and terrestrial, 344; - action of, in crystals, 349-351; - influence of temperature in, 352; - affecting elasticity of matter, 352, 353; - a property of the ethereal medium (?), 356, 357. - - ——, electro, discovery, importance of the science, 312; - rotation effected by, 313, 314; - electric intensity measured, 315; - action of currents in, defined, 316; - Ampère’s theory of, 317, 318; - causing rotation of polarized rays, 319; - action of, on light, 320; - accidental combinations, 342; - influencing metalliferous deposits, 346. - - Magneto-electricity, principle suggesting, 322; - machine constructed on the principle of, 325; - relation of heat to, 329. - - Magnets, influence of, on electric light, 307; - fish possessing the power of making, 311; - effect of an electric stream on, 312-314; - obtained by electricity, 315; - power of electro, measured, 315; - cylinders acting as, 316, 317; - producing electrical effects, 322, 323; - evolving electricity by rotation, 330; - classification of substances in relation to, 332; - polarity a property of, 336; - effect on themselves of imparting paramagnetism, 337; - experiment showing the lines of force of, 338; - properties of, indestructible by subdivision, 338, 339; - the earth reckoned among, 342; - planets reckoned among, 346; - action of an electro, on copper, 351. - - Maguire, Captain, his observations on magnetic storms, 345, 346. - - Malo, St., rising of the tide at, 98. - - Malus, M., discovery of polarization of light by, 195; - attempts of, to polarize heat, 264. - - Malta, observations on Saturn’s rings made at, 66. - - Manchester, thunderstorm near, in 1835, 292. - - Mankind, distinct tribes of, 255; - limited perceptions of, 267. - - Marcet, M., rate of increase in temperature below the earth’s surface - calculated by, 230. - - Marco Polo, atmospheric effects observed by, in ascending mountains, - 118. - - Marine plants, laws regulating their distribution, 252, 253; - animals, specific localities of, 254. - - Mariner’s compass. - _See_ Compass. - - Mars, used in illustrating the possible effects of the radial - distributing force, 19; - telescopic planets between Jupiter and, 20, 21; - diameter of, 21; - mean distance from the sun, _ib. note_; - eclipse of Jupiter by, 42; - parallax found by observing his oppositions, parallax of, 53; - internal structure, 58; - astronomical tables of, 63; - climate of, 225; - approach of the comet of 1770 to, 362; - comets having their perihelia in his orbit, 381. - - Marseilles, transit of a comet across the sun observed from, 374. - - Masses, of the sun, of planets and their satellites, computations - finding, 55, 56. - - Mathematics, use of, in the study of astronomy, 2. - - Matter, theory of its constitution, 102; - hypotheses as to forces uniting its particles, 103, 104; - counterbalancing action of elasticity and cohesion, 105; - crystallization common to all forms of, 109; - indestructibility of its particles, 110; - composition of unorganised bodies, subject to permanent law, 110, - 111; - agent composing or decomposing, 112; - mode of ascertaining the magnetism of, 335; - increatable, indestructible, 353; - proportion of, to spare, 424. - - Matteucci, M., effect of electricity on polished silver observed by, - 221; - experiment showing polarization by electricity, 286; - doubts of, on the polarity of diamagnetism, 348 _note_; - experiments on magnetic action in crystals, 350; - observation on the action of compression, 352. - - Maury, Lieutenant, calms named by, 123. - - Measurement of astronomical distances, formula assisting, 43. - - Mechain, M., Encke’s comet seen by, 365. - - Mechanical equivalent of heat, 275. - - —— engines, incapable of generating force, 279. - - Mediterranean, the, conditions of, shutting out the tidal wave, 98; - hurricane in, divided into two storms, 126; - vegetation of, 252. - - Medium, ethereal, transmitting magnetism, 344; - density of, 356; - probable relations of, to gravity, _ib._; - experiment testing its magnetic properties, 356, 357; - functions of, 357; - pervading the visible creation, 358; - unsolved question touching, 365; - a cause of accelerated revolutions of comets, 366, 367; - direction of its increase in density, 367. - - Medium occupying space, 424. - - Medusa tribes, the, phosphorescent brilliancy of, 295. - - Melloni, M., experiments of, in photography, 214; - his application of the principle of thermo-electricity, 333; - experiments of, in transmission of heat, 258-263; - fixing the maximum of heat in the solar spectrum, 264; - in polarization of heat, 264-266; - light separated from heat by, 265. - - Melville Island, height of the thermometer in, in January, 247. - - Mercury, inclination of his orbit to the plane of the ecliptic, 21; - eclipse of, 42; - cause of his rotation unknown, 65; - ellipticity of his orbit compared with the terrestrial, 74; - climate of, 226; - comet revolving between the orbits of Pallas and, 367; - attraction of, determining a comet’s orbit, 369; - comets revolving in his orbit, 381; - velocity of, 400. - - ——, propagation of heat in, 273; - rotating by electricity, 314. - - Meridian, constant, of high water, 92. - - ——, mode of determining the magnetic, 343. - - Meridians, size and form of the earth determined from, 46; - measurement of arcs, 47; - anomalies from local attraction, 48; - result of the computations, 48, 49; - permanent, of the moon, 69, 70. - - ——, magnetic, influencing the direction of metallic veins, 346. - - Messier, comet of 1770 observed by, 361; - Encke’s comet seen by, 365; - nebula described by, 409. - - Metallic salts, action of the rays of the solar spectrum on, 203. - - —— springs used in construction of musical instruments, 143; - rods giving musical notes, 144. - - Metallic surfaces, polarized light reflected from, 193; - plates, impressions on, from bodies in contact with, 220. - - Metals, expansion of, by heat, 271; - propagation of heat in, 274; - transmission of electricity by, 284; - electricity developed by oxidation of, 298; - determining the appearance of a spectrum of voltaic flame, 303; - distilled in the voltaic arc, 304, 305; - electro-plating of, 309; - properties of, modifying electric susceptibility, 333; - magnetism an agent in the formation of, 346. - - Meteor, the bursting of a, 118. - - Meteors, 420; - theory of, 421-423. - - Meteoric stones, proofs of their foreign origin, 420, 421; - shower of, 421, 422. - - Mètre, adopted by the French as their unit of linear measure, 89. - - Mica, polarization by induction effected with, 286. - - Milky Way, the, described, 385; - Sir John Herschel’s description, 385, 386; - “Coal Sacks,” 386; - stars composing, 286, 287; - zone of stars crossing, 390; - position of variable stars with regard to, 395; - crowding in, apparent only, 405; - orbit in the plane of, 406; - relation of, to the stellar universe, 407; - nebula resembling, 409; - its quarter of the heavens, 414, 415; - dividing the nebulous system, 416, 417; - great nebula in, 418; - remote branches of, 419. - - Minerals, possessing the phosphorescent property, 294. - - Mines, cause of increased temperature in, 229; - green plants growing in, 253. - - Mira, periods of its fluctuations in lustre, 390. - - Mirage, supposed cause of, 157. - - Miraldi, rotation of Jupiter’s satellite determined by, 70. - - Mitscherlich, M., his experiments on crystals, 107; - discoveries, 108; - experiments of, in expansions of crystals, 272. - - Mocha, meteors falling at, 421. - - Moignot, M., crystals compressed by, 189. - - Moisture, an indispensable requisite for vegetation, 248; - transmission of electricity effected by, 284, 288. - - Molecular polarity, produced by electricity, 282; - attraction, electricity developed by destruction of, 284. - - —— structure affecting transmission of electricity, 303. - - —— vortices, hypothesis of, accounting for the absorption of light, - 177. - - Molecules, material, attraction and repulsion of, 103; - effect of elasticity and cohesion on, 104-106; - uniting to form crystals, 107-109; - extreme minuteness of ultimate, 110; - of ether, modes of their vibration in natural and polarized light, - 193; - in fluorescent light, 196, 197; - images traced by the mutual action of, 219-222; - arrangement of, connected with magnetism, 350-352. - - Mollusks, distinct species of, 254. - - Monocerotis 11, a triple star, 395. - - Monsoons, theory of the, 123, 124. - - Months, antiquity of, as a measure of time, 85. - - Moon, the, force restraining, 4, 5; - mean distance of, from the earth, 4; - results effected by her nearness to the earth, 7; - annual rate of decrease in her orbit’s excentricity, 17; - average distance of, from the earth’s centre, period of her circuit - of the heavens, 34; - her periodic perturbations, 35-38; - causes assigned for acceleration of her mean motion, 36, 37; - eclipses of, 39, 40; - longitudes determined by observations of, 42, 43; - her mean horizontal parallax, 52; - sources whence her mass may be determined, 55, 56; - her diameter, 56; - rotation of, 68; - librations, 69; - mountains, 70; - precession resulting from her attraction, 79-81; - influence of, producing tides, 91, 92, 96-98; - period of her declinations, 97; - atmospheric equilibrium disturbed by her attraction, 121; - cause of her apparent increased magnitude in the horizon, 158; - photographic image of, 214; - comparative amount of light emitted by, 225; - cause of the rarity of her atmosphere, 226; - increased intensity of light at full, _ib._; - effect of the terrestrial atmosphere on heat radiated from, 227; - cause of acceleration in the mean motion of, 366; - light reaching the earth from, 404. - - Moorcroft, herbarium collected by, 250, 251. - - Moser, Professor, mutual influence of bodies in contact tested by, 219, - 220. - - Mossotti, Professor, his analysis to prove the identity of the cohesive - force with gravitation, 103, 104; - his definition of gravity, 355. - - Motion, a law of the universe, 274; - perpetual, impossible, 279. - - Mountains, anomalies in measurement caused by, 48; - rarity of atmosphere on, 118; - cause of perpetual snow, 119; - modes of determining heights of, 120; - becoming new centres of motion in hurricanes, 126; - influence of chains on temperature, 241, 242; - cause of éboulemens in, 271; - tops of, fused by lightning, 293. - - ——, lunar, effect of solar rays passing between, in eclipses, 41; - influence of, on the moon’s motions, 96; - three classes of, 70. - - Mu Herculis, direction of solar motion with regard to, 406. - - Multiple systems of stars, 395. - - Mundy, Captain, mirage described by, 157. - - Music, comparison instituted of sympathetic notes in, 2; - regulated undulations of sound producing, 142; - instruments of, 143; - experiments by means of vibrating plates, 144-146; - sympathetic vibrations, 147, 148; - experiments showing, 148, 149. - - Musical instruments constructed by Professor Wheatstone, 143. - - - Naples, comet discovered from, 370. - - Nautical Almanac, computations for calculating longitudes, 43; - time calculated by, 84. - - Navigation, importance of lunar motions in, 42; - laws of storms to be observed in, 127, 128. - - Neap-tides, 96, 99. - - Nebulæ, number and general aspect of, 407; - catalogues, 407, 408; - classes, 408; - irregular, 408, 409; - of definite form, 409; - spiral, 409, 410; - annular, 410, 411; - elliptical, double, 411; - distance of a nebulous star discoverable, 411, 412; - aspect and colour of planetary, 412; - elliptical common, 413; - globular clusters, 413-415; - resolution of, 415; - star clusters, 415, 416; - probable law of motion, 416; - distribution of, 416, 417; - the Magellanic clouds, 417, 418; - round η Argûs, 418, 419; - remote systems, 419; - invisible solar, 421; - meteors falling from, 422. - - Nebulous appearances of a comet, 364; - extent of, matter surrounding a comet, 373; - its variable brilliancy, 374; - appearances round the sun, 412. - - —— stars, 411, 412. - - Needle, magnetized, effect of Voltaic electricity on a, 312, 313; - suspended by means of electricity, 314; - condition of its deviation by an electric current, 317. - - Negative electricity defined, 282; - mode of exciting, 283. - - —— impressions in photography, 204. - - Neptune, periodical variations in his orbit, 22; - revolution of his satellite from east to west, 33; - remoteness of, 54; - anticipation of discovery, 61; - orbit and motions of, determined, 62; - his diameter, mean distance from the sun, 63; - temperature of, 225; - action of, on Halley’s comet, 363. - - Neutral phosphate of soda, its crystals, 109. - - New Mexico, monsoons occasioned by its deserts, 124. - - Newton, Sir Isaac, steps of his argument for the universal influence of - gravitation, 3; - his discoveries of modes of attraction, 4; - motions of bodies projected in space, ascertained by, 5; - form of a fluid mass in rotation ascertained, 45; - problem occupying astronomers since, 64; - discrepancy between his theory of tides and observations, 96; - compound nature of white light proved by, 159; - his analysis of the solar spectrum disputed, 161; - his theory of light disproved, 167; - measurements of coloured rays, 172, 173; - scale of colours, 174; - decisive experiment disproving the theory of light, 202; - remarks on the transmission of gravity, 355. - - Niagara, the falls of, not independent of the influence of astronomy, - 1. - - Nickel, sulphate of, change in its crystals, when exposed to the sun, - 107. - - Niepcé, M., photographic pictures rendered permanent by, 204; - discovery in photography suggested, 207; - colours of images of the sun taken, 213; - experiments by, on saturation of substances with light, 296. - - Nimes, discovery of a telescopic planet at, 21. - - Nitrogen, proportion of, in the atmosphere, 117; - spectrum from, 303; - iron volatilized by the Voltaic arc in, 304; - unaffected by magnetism, 344. - - Nobili, M., direction of electric currents ascertained by, 333. - - Nodes, ascending and descending, of a planet defined, 9; - movement of their lines in secular disturbances, 14; - advance and recession of, 18; - supposed recession of, on the equator of the solar system, 24; - of the moon, period of their sidereal revolution, 37; - secular inequality affecting, 38; - influence of, on eclipses, 39; - cause of their rapid motion, 55; - points of rest on a vibrating string, 141; - in the vibrations of an undulating column of air, 142; - in vibrations of solids, 147. - - Non-conductors of electricity, 284, 285. - - Non-electrics, 285. - - North Atlantic, the, winds in, 124. - - —— Polar Ocean, tide in the, 94. - - Norway, course of the tidal wave to, 94. - - Notes in music, 142, 143. - - Nubecula, Major and Minor, 417, 418. - - Nucleus, of Halley’s comet, changes in its aspect, 364; - disappearance of, in Encke’s, 369; - division, in Biela’s, 369, 370; - diaphanous, 373; - solidity of, tested, 374; - of a spiral nebula, 409. - - Nuremburg, observations on a comet from, 370. - - Nutations produced by the moon’s nearness to the earth, 7; - in Jupiter’s equator, 29; - in the planetary axes, 66; - effect of, on the pole of the equator, longitudes and latitudes - altered by, 81. - - Nysa, nearness of its orbit to the earth, 21. - - - Oaks, range of, near the equator, 250. - - Occultation, central, by Halley’s comet, 364; - geographical position ascertained by, 384; - prospective, by a sun of α Centauri, 400. - - Occultations of stars, 42, 43. - - Ocean, the, density and mean depth of, 51; - mean density, compared with the earth’s, 77; - its form in equilibrio, when revolving round an axis, 92; - solar and lunar attraction disturbing its equilibrium, _ib._; - inequalities in periodic motions, 93; - motions of the tidal wave in 95; - stability of its equilibrium, 100; - circulation of currents in, _ib._; - stratum of constant temperature in, 101; - zones of, _ib._; - decrease and increase of temperature with depth, 231; - absorption and radiation of heat by, 242; - electricity evolved from, 291. - - Oceans of light and heat, processes producing, 225. - - Ochotzk, the sea of, depression of the barometer observed in, 120. - - October, 1832, position of Saturn’s rings in, 67. - - Olbers, M., computations for a comet by, 367; - period of his comet, 370; - comet of 1811 observed by, 374. - - Opaque bodies, mode in which heat is developed in, 227. - - Ophiuchi 70, anomalies in the motions of, 400. - - Ophiuchus, clusters of the Milky Way between the Shield and, 387; - new star disappearing from, 393. - - Optic axis, the, of crystals, 183; - phenomena exhibited by transmission of a polarized ray along, 187, - 188; - affected by compression, 189. - - Orbit, the, of the earth, attraction intensified by its diminished - excentricity, 37; - excentricity of, affecting temperature, 74, 75; - crossed by comets, 368. - - —— of the moon, force ruling, 4; - its excentricity, 34; - changes in, 35; - its inclination to the plane of the ecliptic, 79. - - —— of a nebula, 415. - - —— of the solar system, 405, 406. - - Orbits of comets, subject to variation, 361; - examples, 361-363; - prospective changes in, 369, 370; - of Donati’s, 379; - forces determining their forms, 382, 383. - - —— of double stars, 396-400. - - —— of planets, force regulating a planet’s velocity in, 8; - measurement of their excentricity, 9; - seven elements of, determining their position in space, 10; - unequal movements in, 15; - variation from elliptical to circular, 17; - secular variations of, in inclination to the plane of the ecliptic, - 18, 19; - stable and unstable in form, 21, 22; - influence of the ethereal medium on, 22; - principle facilitating observations on secular inequalities, 23, 24; - revolutions of Saturn compared with Jupiter, 25; - periodic inequality increased by secular variations in their - elements, 26; - comets revolving in, 381, 382; - cause of diversity in form of, 382. - - Orbits of satellites, forms of Jupiter’s, 27; - their inclinations, 28; - inclinations of Saturn’s, 32; - positions of Uranus’s, 33; - forms of data in computing a planet’s place in the heavens, 59. - - Orinoco, the cataracts of the, heard by day and by night, 135; - area occupied by forests on, 243. - - Orion, the Milky Way between Antinous and, 385, 386; - position of, 390; - variable star in, 393, 394; - multiple system in, 395; - nebula in, 408. - - Oersted, Professor, discovery of, suggesting the theory of - electro-magnetism, 312; - science founding the reputation of, 316. - - Oscillations, wide-spreading, produced by gravitation, 2; - mechanical principle affecting small, 11; - of the sines and cosines of circular arcs, 20; - invariable plane whence they may be estimated, 24; - of the pendulum retarded, 32; - of the pendulum, experiments founded on, 50, 51; - experiments testing the earth’s density, 57; - a measure of time, 83; - produced by tides, 95, 96; - instruments measuring atmospheric, 113; - barometer affected by periodic atmospheric, 120, 122; - of ears of corn, 129, 130; - producing musical notes, 140-142; - instances of forced sympathetic, 148; - causing vicissitudes in climates, 247; - of the pendulum, disturbed by effects of temperature, 272; - measuring variation of electrical intensity, 287. - - Otto, M., motions of the heavenly bodies observed by, 405. - - Oxidation of metals, electricity developed by, 298; - by the Voltaic discharge on polished silver, 305. - - Oxides decomposed by electricity, 307; - alkalies resolved into metallic, 307. - - Oxygen, in crystals, 109; - proportion of, in water and carbonic oxide, 111; - in the atmosphere, 117; - chemical combination with, evolving light and heat, 270; - action of electricity on, 284; - electricity afforded by combination of metals with, 298; - spectrum from, 303; - separated from water by electricity, 307; - paramagnetic, 344. - - Ozone, produced by electricity, 284. - - - Pacific Ocean, mean depth of, 77; - course of tidal waves down, 93; - mean depth of, 96; - currents, 100. - - Paderborn, fulgorites from, 293. - - Pallas, inclination of its orbit to the ecliptic, 10; - diameter of, 21; - astronomical tables, 63; - ellipticity of its orbit compared with the terrestrial, 74; - height of its atmosphere, 226; - comet revolving between the orbits of Mercury and, 367. - - Pan’s pipes, vibrations in the air passing over, 142. - - Parabolic motion, ratio of forces procuring, 382. - - Parallax of the sun, circumstance favourable to its correction, 21. - - —— of an object defined, 43. - - ——, definition, mode of ascertaining, 52; - distances computed from, 52-54; - calculation from the moon’s horizontal, 55. - - —— of fixed stars, 387-390. - - —— of meteors, 421, 422. - - Paramagnetic substances, 335, 336. - - Paramagnetism defined, 335; - substances it is resident in, 336; - modes of imparting, _ib._; - a dual power, _ib._; - imparted by induction, 337; - law of its intensity, 338; - a property of oxygen, 344; - in antithesis to diamagnetism, 347; - neutral substances obtained by combinations of diamagnetism and, - _ib._; - Dr. Tyndall’s experiments on polarity of, 348; - dependent on arrangement of molecules, 350, 351; - affected by compression, 351; - truth establishing its identity with diamagnetism, 356, 357. - - Parathermic rays, analyzed by Sir John Herschel, 217-219. - - Paris, variation in length of the pendulum at, 51; - mean annual temperature, 228; - temperature of an Artesian well in, 230. - - Paths of comets, 359, 360; - secrets disclosed by their excentricities, 365. - - Parry, Sir Edward, turned back by the Polar current, 101; - mean temperature calculated from observations of, 245; - thermometer at Melville Island marked by, 247. - - Pauxis, the Straits of, ebb and flow of the sea in, 98. - - Peel, Sir William, thunderstorm experienced by, 293, 294. - - Pegasus, nebulous region of, 417. - - Pendulum, the, principle equalizing its oscillations, 50; - the earth’s figure calculated by, 50, 51; - experiments ascertaining the earth’s density, 57; - isochronous, a measure of time, 83; - a standard of the measure of extension, 89; - the, a connecting link between time and force, 94; - inventions to neutralise the effects of temperature, 272. - - Penumbra, in lunar eclipse, breadth of space occupied by, 40. - - Perigee, of the lunar orbit, period of its revolution, 37, 38; - cause of its rapid motion, 55. - - ——, solar, periods of its coincidence with the equinoxes, 86. - - Perihelion of a planet’s path defined, 16. - - —— of the earth’s orbit, its position regulating the length of seasons, - 74. - - Periodic inequalities of planets, 13, 14; - law from which they are deduced, 24, 25; - of Jupiter’s satellites, 28, 29; - lunar, 35. - - Perkins, Mr., experiments of, testing the laws of compression, 78. - - Peron, M., specific diversity of marine animals asserted by, 254. - - Perpendicular force, the source of periodic inequalities, 15; - effects produced by, 18. - - Perpetual motion, invariable proportion between heat and force - precluding, 279. - - Perseus, variable star in, 390, 391. - - Peters, Mr., comet discovered by, 370; - parallax of α Lyræ, 388, 389; - distances of fixed stars calculated, 389; - his theory of Sirius’ irregular motions, 392; - sun’s motion proved by, 405. - - Petit, M., observations of, on meteoric satellites, 423. - - Peru, arcs of the meridian measured in, 48. - - Phases of the moon, regulating returns of eclipses, 39. - - Phenomena, of effects of light in eclipses, 41, 42; - applied to computing longitudes, 43; - caused by tidal oscillation, 96; - from force of cohesion, 106, 107; - of capillary attraction, 115; - produced by refraction and reflection, 155-157; - by polarization of light, 186-190; - exhibited in fluorescence of light, 196, 197; - resulting from interaction of rays and molecules, analogous to - effects of photography, 219-222; - phosphorescent, 295, 296; - of galvanism, 310; - of magnetism, 335, 345-348; - magnecrystallic, 349, 350; - exhibited by comets, 363, 364, 369, 370, 372-376; - by the Milky Way, 385-387; - by variable stars, 390-393; - by double stars, 397-401; - by nebulæ, 409-415, 417-419; - by meteoric showers, 421, 422. - - Phosphorescence, rays of the solar spectrum exciting, 216; - cause of, in the solar spectrum, 217; - excited by electricity, 294; - fish possessing the property of, 295; - the glow discharge, 295, 296; - experiments investigating the nature of, 296. - - Photo-galvanic engraving, 309. - - Photography, first suggestions, 203; - discoveries and improvements in, 204-207; - conditions affecting the chemical properties of rays producing, 207, - 208; - images of the solar spectrum obtained by, 208-210; - coloured copy of an engraving, 211; - phenomena in, suggesting an absorptive action in the solar - atmosphere, 212, 213; - chemical energy producing, distinct from light and heat, 214; - experiments by means of, testing the properties of rays, 218, 219; - experiments on action of light, heat, electricity, producing results - analogous to effects of, 219-223. - - Photosphere, the, of the sun described, 224. - - Physical Sciences, the most extensive example of their connection, mode - of its operation, 1. - - Pi Herculis, direction of solar motion with regard to, 406. - - Pisces, nebulous region of, 417. - - Planetary motion, representation of, 14. - - —— nebulæ, 409; - appearance of, 412. - - Planets, paths round the sun described by, 5; - law determining their revolutions, _ib._; - forces adjusting their forms, 6; - their motions in elliptical orbits, mean distance from the sun, 8; - mode of obtaining the place of, in their orbits, 9; - computations giving the place of, in space, 10; - disturbances from reciprocal attraction affecting, compensations, - 13-19; - telescopic, 20, 21; - perturbations in the mean motions of, 25, 26; - influence of, on lunar motions, 36; - eclipses and conjunctions of, 42; - formula finding their masses, 55; - their diameters, 56; - mass of the telescopic, compared with the moon, _ib._; - comparative density, 58; - method of computing their places, 58-64; - discovery of, 61-63; - exploded theory touching telescopic, 63; - periods of their rotations, 66; - variation and position of the plane of the ecliptic produced by, 79; - its effect on the equinoctial points, 80; - climates of, 225, 226; - probably magnets, 346; - constant velocity of their mean motions, 366. - - Plants, distribution of known species over the globe, 249, 250. - - Plates, vibrating, experiments by means of, 144-146. - - Plateau, M., experiments of, on colour, 165, 166. - - Platina, incandescent, used as a source of heat, 260. - - Platinum, experiment producing spontaneous combustion of, 112, 113. - - Playfair, Professor, quoted in reference to La Grange’s discovery, 23. - - Pleiades, the, nebulous stars, 415. - - Plücker, Professor, discoveries of, in the action of magnetism in - crystals, 349. - - Plumb-line, deviations of, from local attraction, 48; - earth’s density calculated from a deviation of, 58. - - Poinsot, M., La Place’s discovery extended by, 23; - comparison by, 24. - - Point, ready escape of electricity from a, 288. - - Poisson, M., decisions of, on the phenomena of capillary attraction, - 114. - - Polar basin, probable temperature of, 245, 246. - - —— star, change of position in the, 81, 82. - - —— vegetation, contrasted with tropical, 248. - - Polarity, produced by electricity, 282; - of magnets defined, 336; - induced in iron, 337; - its antithetical manifestations of, 339; - invariably dual, 341; - of diamagnetic substances, 347, 348. - - Polarization of light, definition of, 179; - refracted by various substances, 180-183; - by reflection, 184; - angles of, 185; - phenomena exhibited by transmission through analyzing media, 186-188; - circular, 189-191; - theory of circular and elliptical, 192, 193; - substances producing, 193, 194; - theory of coloured images formed by, 194; - accidental, 195; - discovery of, _ib._; - degraded light incapable of, 198; - communicating electricity, 220; - plane of motion of vibrations in, 223. - - Polarization of heat, first attempts, 264; - successful experiments, 265-267. - - —— of electricity by induction, 286. - - ——, experiment showing the action of magnetism on, 319; - affected by mechanical compression, 352. - - Poldice mine, the, temperature of the water pumped from, 229. - - Poles, the, cause of the flattening of a spheroidal mass at, 6; - diameter of Jupiter at, 27; - experiment determining the increase of gravitation towards, 49, 50; - the, drifting of ice from, 100, 101; - of maximum cold, centres of the isothermal lines, 245, 246; - nature of magnetic force distinguished by, 332; - four terrestrial, of maximum magnetic force, two magnetic, 343. - - Pollux, an optically double star, 401. - - Port Bowen Harbour, transmission of sound across, when frozen, 136. - - Positive electricity, defined, 282; - mode of exciting, 283. - - —— impressions in photography, 204. - - Pouillet, M., his estimate of the mean temperature of space, 119; - quantity of solar heat received by the earth computed by, 238; - data furnished by, to Professor Thomson, 279; - development of electricity investigated by, 291. - - Powell, Baden, substances producing elliptical polarization enumerated - by, 193; - dispersion of light accounted for by the undulatory theory, 200, 201; - experiments in transmission of radiant heat, 262; - attempts to polarise heat, 264. - - Power, Mr., undulations producing fluorescent light computed by, 197; - law of solar rays acting on media, 198. - - Præsepe, the, in Cancer, 415. - - Precession, a, in the equinoxes of planets, its cause, 66; - mean, of the equinoctial points, defined and calculated, 80; - influence of, on the pole of the equator, on longitudes, 81. - - Pressure, electricity elicited by, 283, 284; - law of electrical, 288. - - Principato Citeriore, earthquake in, 234. - - Prisms, solar spectrum formed by, 159; - neutralizing effects of colour, 164; - of brown tourmaline, light polarized by, 180; - resolution of the pure white sunbeam by, 222; - substance of, determining the point of maximum heat in the solar - spectrum, 263, 264; - electrical light analysed by, 288. - - Problem determining the motions of translation of the celestial bodies, - 11; - of the three bodies, 58; - the hardest astronomical, 92. - - Procyon, light of, 402. - - Proportion, definite, the law of, in mixing substances, 111, 112. - - Protoxides of metals, their crystals, 109. - - Prussia, Eastern, fulgorites from, 293. - - Ptolemy, decrease in the inclination of Jupiter’s orbit since the age - of, 19; - discovery of the Evection by, 35; - Indian lunar tables calculated in his time, 88; - horoscope ascribed to the age of, 89; - effects of refraction observed by, 155; - colour of Sirius in his time, 401. - - - Quadratures, the equation of the centre in, 9; - lunar orbit augmented in, 35; - tides affected by the moon in, 96. - - Quadrupeds, distribution of distinct species of, 255. - - Quartz, crystallised, light polarized circularly by, 189, 190; - varieties of polarization exhibited by, 193. - - Quebec, extremes of temperature found in, 247. - - Quinine, sulphate of, producing fluorescence of light, 197. - - - Radial force producing periodical changes in relative positions of the - heavenly bodies, 15; - effects produced by, 16, 17; - principle neutralising its ultimate result, 19, 20. - - Radiation of heat, laws regulating, 257; - universal from substances, 268; - natural phenomena resulting from, 269; - slow decrease of the earth’s central heat from, 232; - influence of, on temperature, 239; - power of, in water compared with dry land, 242; - of heat, a transfer of motion, 277. - - Radii vectores, signification of, 8; - areas described by, 10; - force disturbing in the direction of, 14, 15. - - Ragona-Scina, M., his theory of rayless lines in the spectrum, 163. - - Rain, force shaping drops, 106; - cause of periodic tropical, 123; - region of, 124; - theory of its formation, 270; - an electric conductor, 292. - - Rankine, Mr., his theory of the structure of matter, 104; - his theory of the absorption of light, 177. - - Rays, common nature and common properties of, 268. - - —— of heat, existing independently of luminous, 257; - laws of transmission of, 258; - analogy between transmission of luminous rays and, 259; - temperature of their source affecting transmission, 260; - varying in nature with their origin, 261; - transmitted through coloured glass, 262; - traversing various media, _ib._; - subject to refraction and reflection, 263; - polarized, 265-267; - absorption and reflection of, 268; - rotation of polarized, caused by magnetism, 319. - - —— of light, bent by passing from rare into dense media, 153; - partial and total reflection of, 156; - loss of, by obliquity of incidence, 158; - theory of their transmission and absorption, 159-161; - comparative refrangibility of, 163; - experiments on dispersion of, 164; - principle determining their colour, 170, 171; - transmission of, in glass or water, 177, 178; - conditions of polarized, 179; - double refraction, 181-183; - polarized by reflection, 184, 185; - coloured images produced by interference of, 194, 195; - internal dispersion of, 195-198; - heat, light, chemical action, independent properties of, 214, 215; - undulations constituting, 223; - conditions modifying the power of solar, to produce heat, 237; - transmitted independently of calorific rays, 258; - magnetizing of polarized, 318, 319. - - Rays, solar, effect produced by their refraction in lunar eclipse, 40; - passing between lunar mountains in solar eclipse, 41. - - —— of the solar spectrum, their chemical properties, 203; - varying chemical energy, 207, 208; - varying nature of their action, 208; - peculiar chemical action of the red, 209-211; - deoxydating and oxydating action of, 211, 212; - experiments detailed, 212-215; - new, obscure, detected by Sir John Herschel, 217. - - Red Sea, the, tide in, 98. - - Reflection of waves of sound, 137, 138; - of rays at surfaces of strata differing in density, phenomena - occasioned by, 156, 157; - affecting colour, 160; - motion of a ray of light in, 177; - light polarized by, 184, 185; - elliptical polarization produced by, 193; - heat polarized by, 266; - of radiant heat from surfaces, 268. - - Refraction of the sun’s rays in lunar eclipses, 40; - of waves of sound, 138; - of light by the atmosphere, 153, 154; - mode of estimating, in case of celestial bodies, 155; - formulæ obtaining in case of terrestrial objects, _ib._; - phenomena occasioned by, 155, 156; - colours decomposed by, 159, 160; - produced without colour, 164, 165; - power of, in media affecting the elasticity of the luminous ether, - 177; - of a polarized ray, 180; - double, 181, 182; - Fresnel’s theory of, 183; - diminished capability of producing fluorescence, 196; - capability of, in rays, affecting their chemical action, 209-212; - effect of, on the lunar atmosphere, 226; - influence of, on transmission of heat, 258; - of rays of heat, 261-264; - heat polarized by, 266. - - Refrangibility, substances diminishing, of light, 196; - affecting the chemical action of rays, 209-212; - affecting radiation of heat, 257; - affecting transmission of radiant heat, 261-263. - - Reich, Professor, temperature of mines observed by, 228; - mean increase calculated by, 230. - - Reptiles, distribution of distinct species of, 254. - - Repulsion of electricities, 283; - experiments determining the laws of electrical, 286, 287; - modes of, in static and in Voltaic electricity, 317; - developing comets’ tails, 375-377. - - Resistance, a cause of accelerated motion, 367. - - Retina, the, action of, in receiving impressions, 166; - comparative sensibility of its fibres to light, 178. - - Retrograde motion of comets, 359, 368, 373, 379. - - Rhodiola rosea, identical species of, found in Tartary and in Scotland, - 251. - - Rhombohedrons of carbonate of lime, 109. - - Richman, Professor, killed by lightning, 293. - - Richter, variation in length of the pendulum observed by, 51. - - Rings of Saturn, 66-68; - Saturn’s, diamagnetic, 347; - luminous, surrounding comets, 374, 375; - surrounding Donati’s, 379. - - Ritchie, Professor, electrical experiments of, 314. - - Ritter, M., chemical properties of the solar spectrum observed by, 203; - oxydizing effect of red rays, 209. - - Rive, M. Auguste de la, rate of increase of temperature in wells - observed by, 230. - - Rivers, curvature of the land proved by, 46; - influence of, on the earth’s rotation, 71; - rising of tides in, 98; - effect of, in cooling the atmosphere, 243. - - Roget, Dr., phenomena of electro-magnetism explained by, 313. - - Rome, observations on lunar mountains made at, 70; - era fixed at, 85; - comet discovered from, 370. - - Ross, Sir James, stratum in the ocean discovered by, 101; - depressure of the barometer observed by, 120; - volcanic region discovered, 232. - - Rosse, Lord, nebulæ resolved by his telescope, 407, 408; - spiral nebula, 409, 410; - annular nebulæ discovered by, 410; - nebulous star, 411; - planetary nebulæ, 412; - nebulæ resolved by, 415. - - Rotation affecting winds, 122-127; - of winds, 124, 125; - of hurricanes, 125, 126; - produced by the Voltaic current acting on iron, 305; - of stratifications of electrical light, 307; - caused by electricity, 313, 314; - of light caused by an electric current, 319; - of magnets producing electricity, 330-332; - changes produced in comets by, 376. - - Rotations of the solar system, 7; - of the sun, 65; - of the planets, 66; - of satellites, 68; - of Jupiter’s satellites, 70; - of the earth, a measure of time, 71; - influence of temperature on, 72; - axis of, invariable, 76, 77. - - Rotatory motion, form indicating, 65; - of Donati’s comet, 379. - - Roux, M. le, observations on magnetic action in crystals, 350. - - Rudberg, M., refrangibility of substances ascertained by, 201, 202. - - Ruhmkorff, M., improvements on his electro-inductive apparatus, 328. - - Russell, Scott, Mr., velocity of the tidal wave estimated by, 95. - - Russia, arc of the meridian measured in, 48; - climates of, 244. - - - Sabine, General, variations in the magnetic elements investigated by, - 343, 344. - - Sagittarius, comet traversing the constellation of, 379; - the Milky Way in, 386; - nebula, 414. - - Sahara, the, causing monsoons, 124. - - —— desert, extent, influence of, on the atmosphere, 243. - - Salt, Mr., papyrus sent from Egypt by, 89. - - Sand, tubes in, formed by lightning, 293. - - Sandy deserts influencing temperature, 243. - - Sandwich Land, excess of cold in, over corresponding latitudes, 241. - - Sargassa, or grassy sea, found in the Atlantic, 253. - - Satellites, intensified action of attraction upon, 7; - intimate union of, with their primaries, 26; - exceptions to a general law of the solar system, 65, _note_; - rotations equal to the times of their revolutions, 68; - comet passing through, 69. - - ——, Jupiter’s, proportion of their mass to that of their primary, 27; - disturbing force of attraction affecting their orbits, 28; - periodic and secular inequalities, 28, 29; - eclipses, 30; - rotation, 70; - passage of a comet through, 359; - comet nearly approaching, 370. - - —— of Saturn, 32; - of Uranus and Neptune, 33. - - ——, mode of computing their masses, 55; - comparative density of, 58. - - —— of Neptune, 63. - - —— of the earth, shooting stars, 423. - - Saturn, unequally occurring compensations of disturbance in its - motions, 15; - disturbing influence of, on Jupiter, excentricity of its orbit - compared with Jupiter’s, 17; - retarding the revolution of Jupiter’s nodes, 19; - invariable plane passing between Jupiter and, 24; - observations on the mean motions of Jupiter and, 25, 26; - eclipse of, 42; - internal structure, 58; - astronomical tables of, 60; - period of his year, 66; - the rings of, described, 66-68; - his ring probably diamagnetic, 347; - action of, on Halley’s comet, 362, 363; - comets having their perihelia in his orbit, 381. - - Saurian reptiles, distinct tribes of, 254. - - Saussure, M., temperature of mines observed by, 228, 229; - lichen discovered by, 249. - - Savart, M., his researches and experiments in acoustics, 132, 133; - experiments on vibrations of glass rulers, 145-147; - experiments showing sympathetic undulations, 148, 149; - discoveries on the nature of voice, 152. - - Savary, M., orbital elements of a double star determined by, 396; - his mode of ascertaining the actual distances of fixed stars, 402, - 403. - - Scheele, M., chemical changes effected by the solar spectrum observed - by, 203. - - Schroëter, height of planetary atmospheres calculated by, 226. - - Schwabe, M., periodic variation in the solar spots observed by, 344. - - Science, its value regarded as the pursuit of truth, 1; - errors of the senses corrected by, 32; - evidence of its antiquity, 87. - - Sciences, mutual relations of forces proving the connexion between, - 319-321; - analysis proving the whole circle of, kin, 427, 428. - - Scoresby, Captain, phenomenon occasioned by refraction observed by, - 156. - - Scorpio, vacant patch of the Milky Way in, 386; - position of, 390; - a double star in, 395; - nebula in, 414. - - Scotland, progress of the tidal wave round, 94. - - Sea, the, inappreciable influence of, on the direction of gravity, 77; - mean height of snow-line above the level of, 241; - comparative extent of, 242. - - Seasons, conditions determining the duration of, 74; - cause of their unequal periods, 87; - theory of the tropical dry and rainy, 123. - - Seaweeds, photographic impressions of, 205, 206; - luxuriance, deep colours of, 253. - - Secchi, Professor, mountains of the moon observed by, 70; - photographic image of the moon obtained, 214; - temperatures of the sun’s surface estimated, 225; - experiments of, in photographing the moon and Jupiter, 226, 227. - - Secular inequalities of planets, 13, 14; - means of discovering, 24, 25; - effect of, on the mean motion of the moon, 36, 37. - - —— variations in mean values of the magnetic elements, 343. - - Seebeck, point of maximum heat in solar spectrum fixed by, 263; - discovery of, 264; - relations of heat to electricity discovered by, 332, 333. - - Seed-lobes, proportion in the distribution of plants having one or two, - 252. - - Seleniate of zinc, crystals of, 107. - - Senarmont, M., experiments of, in expansion of crystals, 273. - - Senses, necessarily inaccurate testimony of the, 281. - - September, times coinciding in, 84. - - Serpentarius, star in, vanishing, 392. - - Shell-fish, their mode of clinging to rocks, 117. - - Shield, the, clusters of the Milky Way between Ophiuchus and, 387. - - Shooting stars, phenomena of, described, 421, 422; - theories of, 423. - - Siberia, Eastern, depression of the barometer observed in, 120. - - Sidereal times, mean, periods of, 83; - measurement of apparent, _ib._ - - Sigma Eridani, period of revolution in, 400. - - Silesia, fulgorites from, 293. - - Silver iodized, its sensitiveness to impressions, 221. - - Sirius, the Egyptian year estimated from, 85; - comet’s tail extending from the Hare to, 373; - rank of, 384; - comparative magnitude, 385; - parallax, 389; - cause of his irregular motion, 392; - change in colour, 401; - light, 402; - extent of surface, 404. - - Smyth, Admiral, his measurement of Etna compared with Sir John - Herschel’s, 120; - eclipse of a double star observed by, 397; - its periodic time determined, 398. - - ——, Piazzi, heat of the moon felt by, 227. - - Snow, cause of perpetual, on summits of alpine chains, 119; - causes modifying the height of the line of perpetual, 241; - protecting vegetation, 249; - radiation of heat by, 257. - - Soda, sulphate of, change of form in its crystals, 107; - crystals of the neutral phosphate and the arseniate of, 109. - - Soil, the, dependence of temperature on the nature of its products, - 243. - - Solar gravitation, 424, 425. - - —— magnetism, its connexion with terrestrial, 344. - - —— spectrum, cause of the point of maximum heat varying in, 263, 264. - - —— system, the, gravitation of the bodies composing, 5; - conditions securing the stability of, 11, 12; - proof of its stability, 20; - equilibrium of, underanged by the ethereal medium, 22; - invariable plane, forming the equator of, 23, 24; - question of its revolution round a common centre, 24; - properties of its medium, 32; - masses of bodies composing, 55, 56; - their diameters, 56; - uniform direction of rotation in, 65; - comparative apparent importance of, in creation, 226; - probably magnetic throughout, 346; - comets forming part of, 365; - possible ultimate destruction of, 372; - computations of comets revolving within, 381, 382; - paths described by heavenly bodies in, 382, 383; - position of, relative to the Milky Way, 385; - direction of its motion, 405. - - Soleil, M., crystals compressed by, 189. - - Solids, conditions reducing molecular particles to, 104, 105; - distinctive forms taken by matter in, 106; - velocity of sound passing through, 135; - change of shape in, accompanying ringing sound, 147; - expansion of, by heat, 271. - - Solstices, the, solar motion at, affecting the duration of time, 84; - the year estimated from the winter, 85; - periodical coincidence of the solar perigee and apogee with, 86, 87. - - Sothaic period, the, of the Egyptians, 85. - - Sound, medium conveying, 129; - its propagation by undulations illustrated, 129, 130; - conditions modifying the intensity of, musical notes, 131; - experiments testing the compass of audible, 132, 133; - media modifying the velocity of, 133-137; - laws of its reflection from surfaces, 137, 138; - undulations of, subject to the laws of interference, 138, 139; - laws of the foundation of musical science, 140-143; - reinforced by resonance of cavities, 150, 151; - repeated vibrations required to produce, 178; - different modes of action in undulations producing light and, 199, - 200; - identical nature of heat and, 280, 281; - measuring velocity, 290, 291. - - Sounding boards, intensifying musical vibrations, 149; - action of, in musical instruments, 150. - - South, Sir James, positions of stellar systems measured by, 396. - - South pole, the, excess of cold at, 241. - - —— Sea islands, height of tides at, 98. - - Southern Ocean, rise of the tidal wave in, 93; - velocity of the wave, 94. - - Spain, meteoric showers off the coast of, 421. - - Specific heat defined, 275. - - Spectra of gases and flames, their characteristic peculiarities, 163, - 164; - three superposed, of the pure white sunbeam, 222. - - Spectrum, the solar, decomposed into seven colours, 159; - colours of, modified by thickness of the medium absorbing, 160; - decomposed into three colours, 161; - rayless lines in, 162; - observations and experiments on rayless lines, 163, 164; - experiment of fluorescent light, 197; - obtained independently of prismatic refraction, 201; - energetic action of, on matter, 203; - photographic coloured images of, 208-210; - analysis, properties of, experiments, 211-219; - complex nature of, 222; - produced from diffracted light, 223. - - —— of an electric spark, 289. - - —— of the Voltaic arc, 303. - - Spheres, mode of attraction in hollow and solid, 4; - planets partaking the nature of, 7; - impulses regulating rotations, _ib._; - conditions procuring the figure of, 44; - formula finding the density, 56; - force giving the form of, 106; - power of retaining electricity, 288. - - Spherical form, the result of cohesion, 106. - - Spheroids, influencing attraction differently from spheres, 4; - force disturbing attraction in, 27; - compression of the terrestrial and of Jupiter’s, computed, 38, 39; - of elliptical strata, quantities invariable in, 46; - of the sun, 65; - effect produced by the attraction of an external body on, 79; - power of retaining electricity, 288. - - Spiral nebula, 409, 410. - - Spots on the sun’s surface, periods of their vicissitudes, 224; - amount of heat varying with, 225. - - Spring tides, 96-99. - - Springs, hot, rising in mines, 229; - mean heat of the earth determined from, 238. - - Standards of weights and measures, whence derived, 89, 90. - - Stars, fixed, the, the solar system probably not independent of, 24; - velocity of light deduced from aberration of, 31; - vast distances of, 54; - precession affecting their longitudes, 80; - computations of their positions furnishing historical data, 88, 89; - made visible by refraction, 154; - peculiar law of light demonstrated by the aberration of, 202; - magnitude of the solar system seen from, 226; - numbers, classification of, 384; - positions, 385; - the Milky Way, 385-387; - parallaxes and distances of, 387-389; - variable, 390-395; - missing, 395; - systems of multiple, classified, _ib._; - binary, 395-406 (_see_ Double stars); - nebulous, 406-419 (_see_ Nebulæ); - seemingly innumerable, 420; - meteors, 420-423. - - Static electricity, 282: - _see_ Electricity. - - Steam, formation of, 269; - force converting liquids into, 277; - measure of its elasticity, 278; - question of its being superseded by electricity, 328. - - Steel, paramagnetism induced in, 336; - conditions of magnetic power remaining permanently in, 337, 338; - its elasticity affected by magnetism, 352. - - Stephenson, George, quotation from, 279-280. - - Stokes, Professor, remarks of, on gradation of colours, 161; - experiments on fluorescence of light, 197; - his decision with regard to vibrations of polarised light, 223. - - Storms, magnetic, 344; - varying with latitude, 345, 346. - - Strata of the earth, position and comparative density of, 77. - - Stratifications, experiments showing, in electric light, 306, 307. - - Struve, M., measurement by, 48; - his observations on Saturn’s rings, 68; - occultation by a comet observed by, 364; - comet’s nucleus described, _ib._; - distance of a fixed star measured by, 388, 389; - catalogue of double stars, 396; - remarks on colour and light of double stars, 401; - sun’s motion proved by, 405. - - Stutgardt, natural hot springs used in manufactories near, 231. - - Submarine telegraph, 325-327. - - Sulphate of magnesia, its crystals boiled in alcohol, 108. - - —— of nickel, effect of exposure to the sun, on its crystals, 107. - - —— of soda, its crystals, 107. - - —— of zinc, experiment on its crystals, 108. - - Sulphuretted hydrogen gas, its constituent parts, 111. - - Sumbawa, volcanic eruption of, 233. - - Summer, mean temperature of, varying in the same latitude, 246, 247; - atmospheric electricity in, 291. - - Sun, the, law regulating his attraction of heavenly bodies, 5; - effect of his attraction on planetary orbits, mean distance of - planets from, 8; - importance of his magnitude in the solar system, 12; - disturbances in the relative positions of planets and, 14; - force modifying his intensity of attraction, 16; - resistance offered by, to the power of disturbing forces, 20; - periods of conjunctions of Jupiter, Saturn, and, 25; - influence of, on lunar motions, 34, 35; - action of the planets reflected by, 37; - eclipses of, 40, 41; - supposed constitution of, 41; - his atmosphere, 42; - mode of finding his parallax, 52, 53; - mean distance from the earth, 53; - mass of, 55; - diameter, 56; - comparative density, attractive force, 56, 57; - astronomical tables of, 63; - deductions from his rotation about an axis, period of, 65; - attraction of, producing a precession of the equinoxes, 79, 81; - returns of, a measure of time, 83-85; - divisions of time, dependent on revolutions of the major axis of his - orbit, 86, 87; - action on tides, 92, 97; - disturbing the equilibrium of the atmosphere, 121; - dry and rainy seasons regulated by, 123; - cause of decreased light and heat in horizontal rays, 157, 158; - distance of, falsely estimated, 158; - light polarized by, 195; - indications of an absorptive atmosphere surrounding, 212, 213; - his diameter, 224; - appearance of, through his atmospheres, _ib._; - variations in heat and light emitted from, 225, 226; - amount of heat annually received by the earth from, 238; - effect of his brilliancy on the heat emitted by, 259; - his position affecting variations in the magnetic elements, 343, 344; - connexion between periodic variation in his spots and in the magnetic - elements, 344; - vast sweep of his gravitating force, 365; - increased attraction of, for comets, 372; - gulfs separating stars from, 390; - possibility of change in his lustre, 394; - spot on, measured by Sir John Herschel, 394, 395; - proportion of his light to the moon’s, 404; - rate and orbit of motion with his system, 405, 406; - a nebulous star, 412; - meteoric nebula revolving round, 422; - gravitating force of, 424, 425. - - Sunbeams, resolved into their component colours, 159-162; - law prevailing in the phenomena of, 198; - light a distinct property of, 214; - resolved into three spectra, 222; - undulations constituting, 223; - their influence on vegetation, 249. - - Swan, the, vanishing star in, 393. - - Switzerland, meteors falling in, 421. - - Syene, arc of the meridian measured between Alexandria and, 49. - - Sykes, Colonel, extensive range of cultivation of wheat observed by, - 250. - - Sympathetic vibrations in musical instruments, 147-149. - - Syren, the, an instrument ascertaining the number of musical pulsations - in a second, 143. - - Syzygies, tides increased in the, 96. - - - Table-lands, high, influence of, on the atmosphere, 241. - - Tahiti, transit of Venus observed at, 53. - - Tail of comets, sudden development of, 372; - forces producing, 375; - unequal illumination of, 375, 376; - change in position of, 376; - divided, _ib._; - constitution of, 377. - - Talbot, Fox, his inventions in photography, 204. - - Tangent, a, to planetary orbits, planets impelled in the direction of, - 8; - force, disturbing, in the direction of, 14, 15; - deflection from, a measurement of centrifugal force, 49. - - Tangential force, occasioning secular inequalities, 14; - effects produced by, 15; - producing the variation of the moon, 35; - force acting on the sea, 100. - - —— velocity, effects produced by modifications of, 16; - undiminished by the ethereal medium, 22. - - Telegraph, the electric, discovery leading to the invention of, 323, - 324; - the Atlantic, 325; - principles of its construction, 326, 327; - date of its completion, 327. - - Telegraphs, land, principle of their construction, 328. - - Telescope, the achromatic, principle of its construction, 164. - - ——, the differential, differences in illumination determined by, 227. - - ——, Lord Rosse’s, nebulæ resolved by, 407, 415. - - Telescopium, comet traversing the constellation of, 379; - nebula in, 414. - - Temperature, a decrease in, affecting the earth’s rotation, 72; - excentricity of the terrestrial orbit, a cause of decreasing, 73; - law equalising, 74; - geological changes affecting, 75. - - ——, varying in the terrestrial atmosphere, zone of constant, 119; - affecting atmospheric undulations, 121; - modifying the velocity of sound, 134; - chemical action of light affected by, 218-222; - of the ethereal medium, 227, 228; - underground stratum of constant, 228; - rate of increase in, below the earth’s crust, 228, 231; - of the ocean, 231; - mode of finding annual average, 239; - causes of disturbance in regular variation of, 240-245; - variations in the same latitude, 246, 247; - influence of, on vegetation, 248; - affecting transmission of heat, 259, 260; - of solid bodies, caused by absorption of rays, 268; - affecting the length of the pendulum, 272; - causes of perpetual variations in, 274; - transmission of electricity affected by, 284; - affecting magnetism, 352. - - Teneriffe, the Peak of, prevailing winds on, 124; - lunar heat on, 227; - zones of vegetation, 250; - character of its flora, 252. - - Terrestrial globe, the, a magnet, 336. - - —— magnetism, 341-343; - the three elements and their variations, 343, 344; - storms, period of their variation, 344; - its connexion with solar magnetism, _ib._; - effect of atmospheric magnetism on, 345; - probable cause of, 346; - effect of planetary magnetism on, 346, 347. - - —— meridian, a, defined, 46. - - Tessular system of crystallization, 108. - - Texas, monsoons occasioned by its deserts, 124. - - Thames, the, period occupied by the tidal wave in reaching, 94. - - Thaw, cause of the sensible chilliness of, 276. - - Theory of probabilities, use of, in determining astronomical data, 60. - - Thermo-electric currents, discovery of, 332; - phenomena exhibited by, 333; - principle of, applied to measuring heat, 333, 334. - - Thermography, examples of, 219-221. - - Thermometer, the, principles applied to the construction of, 113; - consulted in determining mountain heights, 119, 120; - refraction varying with, 154; - heat measured by motion in, 274. - - Thermomultiplier, use of, in experiments, 264; - principle of its construction, 333, 334. - - Theta Orionis, the multiple system of, 395. - - Thomas, St., the island of, hurricane with pauses at, 127. - - Thomson, W., Professor, experiments of, in freezing water, 271; - dynamical theory of heat maintained by, 275 _note_; - his calculation of the force exerted in vibrations of light, 279; - investigation into the relations of light and magnetism, 320; - density of the ethereal medium computed by, 356; - magnetic property of the ethereal medium pleaded for, 357. - - Thunder, theory of prolonged peals of, 138. - - Tibet, wheat ripening in, 250. - - Tidal wave, theory of, 92; - its birthplace, 93; - course of, 93, 94; - velocity, 94; - effect of depth on its motion, 95. - - Tides, calculation from the moon’s action on, 55; - theory of forces producing, 91, 92; - circumstances occasioning irregularities, 93; - rising, progress of, 93, 94; - three kinds of oscillations in, 95, 96; - variations in, from lunar and solar influence, 96-98; - effect of interference of waves on, 99; - the sea’s equilibrium underanged by, 100. - - ——, lunar and diurnal, of the terrestrial atmosphere, 121; - examples of sympathetic undulation, 148. - - Time, a measure of motion, 58; - a measure of angular motion, 83; - difference between mean and apparent solar, 84; - mean equinoctial, mode of computing its object, 86; - estimation of, corrected by means of laws of unequal expansion, 272. - - Timocharis, comparison of his observations with Hipparchus, 80. - - Tomboro, submerged in a volcanic eruption, 233. - - Toronto, observations on magnetic storms at, 346. - - Torpedo, the, electrical action of, 310, 311. - - Torricellian vacuum, experiment on the electric discharge in the, 306; - lines of magnetic force passing through, 344. - - Toucan, comet approaching the constellation of, 379; - a nebula in, 414. - - Toucani, 47; - globular nebulous cluster, 414. - - Tourmaline, brown, light polarized by prisms of, 180; - property qualifying it to analyze polarized light, 182; - coloured images produced by, 186, 187; - changed by compression, 189; - heat polarized by, 265; - electricity communicated to, 284. - - Trade winds, friction of, not affecting the earth’s velocity, 72; - action on the general motion of the sea, 100; - system of, accounting for atmospheric anomalies, 120; - theory of their origin, phenomena connected with, 122, 123; - becoming monsoons, 124. - - Transits of Venus, 52, 53. - - ——, two consecutive, of any star, a measure of time, 83. - - Transmission of radiant heat, 258, 262; - of electricity, 284, 285; - of voltaic electricity, 298; - molecular structure affecting, 303; - method of, determining the influence of electric currents, 317; - of gravity, an unsolved question, 355; - probable agent, 356; - medium of, in space, 424. - - Transparent bodies, temperature of, unaffected by the sun’s rays, 227. - - Trees, number of species of forest, found in America and Europe, 252. - - Tribes, apparently distinct, of the human race, 255. - - Triple stars, 395; - periods of revolution in, 400. - - Tropical year, change in its length, 80; - period of, 83; - difficulty of adjusting its estimation, 85. - - —— revolution of the major axis of the solar ellipse, its period, 86. - - —— vegetation, the luxuriance of, 248. - - Tuileries, clock in the, showing decimal time, 84. - - Twilight, caused by refraction, 154; - effect of reflection, 158. - - Tyndall, Professor, his experiments proving diamagnetic polarity, 348; - on magnetic action in crystals, 349. - - - Undulations, theory of, 99; - of the atmosphere, 121, 122; - of the waves of sound, 129, 130; - intervals produced by interference, 139; - giving musical notes, 142, 143; - sympathetic, 147, 149; - of the luminous ether, 169, 170; - in refraction and reflection, 177; - producing fluorescence, 197; - different, in light and sound, 199, 200; - constituting a sunbeam, 223; - heat propagated by, 267; - of light, evolution of latent force in extinguished, 279, 280; - of natural forces identical, 281. - - Undulatory theory of light, 168-170; - law of motion affecting, 176, 177; - phenomena proving, 198; - objection, from the different action of light and sound, refuted, - 199; - proving the existence of the ethereal medium, 358; - acceleration in comet’s motion proving, 367. - - —— theory, experiments determining in favour of, 200, 201; - final and decisive experiment, 202; - of heat, 267. - - Unison, note in, 142. - - United States, astronomical observations made in, 371, 373. - - Uranium, phosphorescent property of, 296; - peculiar luminous properties of, 296. - - Uranus, effect of reciprocal attraction between Neptune and, 22; - periods of the revolutions of his satellites, 33; - distance from the sun, 54; - astronomical tables of, 60; - discovery suggested by his perturbations, 61; - observations on, leading to Neptune’s discovery, 62; - sun’s influence in, 225; - action of, on Halley’s comet, 363; - appearance of the sun to, 380, 381; - comets in his orbit, 381, 382. - - Ursa Major, periodic time of a double star in, 398; - nebulous region of, 417. - - Utah, deserts of, causing monsoons, 124. - - - Vacuum produced by shell-fish, 117; - existing in the air, 118. - - Valz, M., telescopic planet discovered by, 21; - comet observed by, 358; - observations on a comet’s approach to the sun, 364; - cause assigned by, for contraction in diameter of comets, 377, 378. - - Vapour, formation and dispersion of, 269, 270; - force developing, 277. - - Variable stars, periodic fluctuation of lustre in, 390, 391; - new, appearing and vanishing, 392, 394; - missing, 395. - - Variables, region of the, 122. - - Vegetation, effect of, in lowering temperature, 243; - the two requisites for, 248; - strength and vitality of, 249; - chemical action of light influencing, _ib._; - laws of its distribution, 249-252; - distribution of marine, 252, 253; - theories of specific diversity of original distribution of, 253, 254. - - Venus, zone of instability between the sun and, 21; - perturbation in the mean motion of the earth and, 26; - eclipsing Mercury, 42; - transits of, parallaxes calculated from, 52, 53; - astronomical tables of, 63; - climate, 226. - - Vernal equinox, planetary motions estimated from, 9. - - Vesta, astronomical tables of, 63; - no atmosphere surrounding, 226. - - Vesuvius, revived volcanic action of, 234. - - Vibrating plates used in experiments on musical sound, 144, 147. - - Vibrations of the air producing sound, 129; - in music, 131; - number made by the human voice in a second, 132. - - —— of the ether in natural and polarized light, 193; - in fluorescence of light, 196; - plane of, in polarized light, 223. - - Vico, Padre de, comet discovered by, 370. - - Vienna, observations on comets from, 370. - - Vietch, James, comet with luminous rings discovered by, 374, 375. - - Vincent, St., revival of an extinct volcano in, 234. - - Virginia, daguerreotyped spectral image obtained in, 213. - - Virgo, planetary conjunction between Libra and, 42; - variable star in, 392; - star vanished from, 395; - nebulous zone passing, 416, 417. - - Viviers, transit of a comet across the sun observed from, 374. - - Volcanic regions of the globe, 232; - annual number of eruptions, 233; - celebrated eruptions, _ib._; - earthquakes caused by, 234; - supposed causes of action, 235; - Sir John Herschel’s theory, 235-237. - - Volta, Professor, electricity rendered manageable by, 297; - the world’s debt to, 328. - - Voltaic electricity, first suggestions of, 297; - theory of the transmission of, 298; - construction of the battery, 298, 299; - theory of its production, 300; - characteristic properties, 300, 301; - action of, generating heat and light, 301-303; - arc, experiments, 303-305; - the, discharge oxidizing silver, 305, 306; - stratified light, 306, 307; - chemical decomposition effected by agency of, 307, 308; - crystallization, 308; - an agent in the fine arts, 309; - conductors of, _ib._; - relations of heat and, 310; - fish producing effects of, 310, 311; - science suggested by its influence on a magnetized needle, 312; - rotation effected by, 313, 314; - inducing magnetism, 314, 315; - distinction between static electricity and, 317; - unvarying dual force of, 334. - - Voltaic pile, the, invention of, 297; - perfected, 298-300. - - Vortices, molecular, theory of, 104. - - Vosges mountains, temperature of mines in the, 228. - - Vulpecula, nebula in, 409. - - - Wardhus, transit of Venus observed at, 53. - - Watches, irregular action of, corrected by the laws of unequal - expansion, 272. - - Water, constituent parts of, 111; - boiling point of, an estimate of mountain heights, 120; - as a medium for sound, 135; - light polarized circularly by, 194; - experiment deciding the velocity of light in, 202; - law of expansion of, 271; - process of congelation, 276; - boiling points of, 277; - decomposed by electric agency, 307; - as an electric conductor, 309; - rotating by electricity, 314. - - Waterspouts, origin and cause of, 128. - - Waterstone, Mr., magnetic property of the ethereal medium maintained - by, 357. - - Waves neutralized by interference, 99. - - ——, atmospheric, over local districts, periods, dimensions of, 121, - 122. - - —— of sound, 131; - furnishing an illustration of reflections of sound and light, 137; - interference of, producing calm, 139. - - Wedgwood, Dr., attempts of, to trace objects by means of light, 203, - 204. - - Week, the, of seven days, the most ancient and universal division of - time, 85. - - Wells, increase of temperature in, 230, 231. - - Welsh, Mr., observations made by, in a balloon ascent, 119. - - West Indies, the, cause of hurricanes in, 126. - - Wheels invented to test intensity of sound, 132, 133. - - Wheat, range of its cultivation, 250. - - Wheatstone, Professor, experiments in acoustics of, 132; - musical instruments invented by, 143; - paper on musical vibrations read by, 145; - experiments on sounding boards of, 150; - experiments on sound reinforced by resonance, 151; - instrument measuring velocities of electricity and light invented by, - 202; - spectrum of an electric spark observed, 289; - speed of electricity measured, 289, 290; - experiments on the spectrum of Voltaic flame, 303. - - Willis, Mr., articulating machine invented by, 151; - investigations of, into the mechanism of the larynx, 152. - - Winds, trade, 122, 123; - monsoons, 124; - extra-tropical, in the North Atlantic, _ib._; - currents above the trade winds, 124, 125; - phenomena of rotatory motion, 125; - hurricanes, 125, 128; - agency of, influencing temperature, 244, 245. - - Wines, range of cultivation of the best, 250. - - Winter, atmospheric electricity in, 291. - - ——, mean temperature of, varying in the same latitude, 246, 247. - - Wolf, Professor, periods of variation in solar heat computed by, 225. - - Wollaston, Dr., experiments of, on sensitiveness to sound, quotation - from, 132; - experiment of, to show the effect of variable media on refraction, - 156; - discovery of rayless lines in the solar spectrum, 162; - observations of, on the chemical properties of the solar spectrum, - 203, 209; - magnetic rotation suggested by, 313; - light emitted by the heavenly bodies calculated, 404. - - - Xi Ursæ Majoris, periodic time of, 398; - velocity of the revolving star, 400. - - - Year, a, in Jupiter and Saturn, 66; - tropical change in its length, 80; - length of the sidereal, _ib._; - period of the mean, 83; - estimation of the Egyptian, 85; - first of our era, 86; - length of the, affected by a comet’s passage, 359. - - Young, Dr., his calculation of the possible compression of solids, 78; - date of a horoscope determined by, 89; - density of a liquid column estimated by, 114; - exception adduced by, to a general law in acoustics, 137; - his theory of the pleasures of harmony, 142; - undulatory theory established by, 169; - data used by, to test his theory of light, 175; - illustration of, proving sound and heat kindred forces, 280, 281. - - - Zeta Cancri, a triple star, 395; - periodic time of, 398; - revolution, 400; - colours, 401. - - Zeta Herculis, periodic time, eclipse of, 398; - light, 402. - - Zinc, seleniate of, effect of temperature on its crystals, 107; - sulphate of, its crystals boiled in alcohol, 108. - - ——, electricity communicated to plates of, 220. - - Zodiac, the, signs of, change in their positions, 80. - - Zone of constant temperature in the atmosphere, 119; - laws of storms in the temperate and torrid, 127, 128; - of spots on the sun’s surface, its breadth, 224; - of constant temperature below the earth’s crust, 228; - comparative unequal distribution of land in temperate and torrid, - 244; - of fixed stars, 385; - of stars nearest the sun, 390; - nebulous, 416; - of nebulous patches, 417; - of meteoric nebulæ, 423. - - Zones of instability of planetary orbits, 21. - - —— of temperature in the ocean, 101. - - —— of vegetation on the Peak of Teneriffe, 250. - - Zoophytes, specific distribution of, 254. - - - THE END. - - - LONDON: PRINTED BY W. CLOWES AND SONS, STAMFORD STREET, - AND CHARING CROSS. - -[Illustration: PLATE 1.] - -[Illustration: PLATE 2.] - -[Illustration: PLATE 3.] - -[Illustration: PLATE 4.] - -[Illustration: PLATE 5.] - -[Illustration: PLATE 6.] - -[Illustration: PLATE 7.] - -These correspond to No. 1, 6, and 7 of Faraday’s plate in his 29th -Series of Experimental Researches in Electricity. - -[Illustration: PLATE 8.] - -[Illustration: PLATE 9.] - -[Illustration: PLATE 10. - - Fig. 1. - Spiral nebulæ of 51 Messier, as seen by Lord Rosse. - - Fig. 2. - Great nebula of Orion. - ] - - - - - Footnotes - -Footnote 1: - - The mean distance of the earth from the sun is 95,000,000 miles, but - to avoid the inconvenience of large numbers, it is assumed to be the - unit of distance; hence the mean distance of Mars is 1·52369, or 1·5 - nearly, that of the earth being = 1. - -Footnote 2: - - The obliquity given in the text is for the year 1858. - -Footnote 3: - - Sir John Herschel remarks that there are just as many thousands of - feet in a degree of the meridian in our latitude as there are days in - the year, viz. 365,000. - - The Greenwich Observatory is in N. lat. 51° 28ʹ40ʺ. - -Footnote 4: - - Or more correctly 3422ʺ·325 and 238,793 miles, as deduced from Mr. - Adams’ more accurate calculations. - -Footnote 5: - - Neptune was discovered in the year 1846. - -Footnote 6: - - The satellites of the two great planets on the farthest verge of the - solar system form a singular exception to this law. - -Footnote 7: - - See the chapter on the Tides and Currents in the ‘Physical Geography,’ - by the author, 4th edition. - -Footnote 8: - - Sir John Herschel on Meteorology. - -Footnote 9: - - Bakerian Lecture, by Michael Faraday, Esq. Phil. Trans. 1857. - -Footnote 10: - - See page 104. - -Footnote 11: - - M. Marbach of Breslau. - -Footnote 12: - - ‘Meteorology,’ by Sir J. Herschel. - -Footnote 13: - - This theory of heat and motion originated with Mr. Joule, of - Manchester, who has maintained it with the greatest talent, both by - experiment and analysis; and it has had an able advocate in Professor - W. Thomson, of Glasgow. - -Footnote 14: - - To this remarkable man the world is indebted for the locomotive - railway system, which is rapidly advancing the civilization of - mankind. Britain may well be proud of its working classes, which can - produce such men; and Mr. George Stephenson is not the only one; there - are many others; but no man has ever had greater influence by his - labours and discoveries on human affairs. - -Footnote 15: - - ‘Correlation of the Physical Forces, by W. R. Grove, Esq.,’ one of the - most remarkable and talented works that has appeared, to which the - author with pleasure acknowledges her obligations. - -Footnote 16: - - “Eripuit fulmen Cœlo, sceptrumque tyrannis,” is the inscription on a - medal struck in honour of Franklin. - -Footnote 17: - - Faraday. - -Footnote 18: - - Professor Matteucci still expresses doubts on this subject, but has - not yet finished his experiments. - -Footnote 19: - - Babbage. - -Footnote 20: - - Phil. Mag. for May 1858. - - - - - Transcriber's Notes - - -Some corrections were made to the original text. In particular, -punctuation was corrected without further note. Inconsistent spelling -and hyphenation was retained unless noted otherwise. There were two -Notes 189 in the original; this was retained as printed. Spelling of -Index entries was changed to reflect the body text where inconsistencies -were found. Index page numbers were corrected where errors were found. -Further corrections are noted below: - - p. 50 0·005·1449 -> 0·0051449 - p. 61 24,000 -> 240,000 - p. 62 M. Leverrier -> M. Le Verrier - p. 84 in mean solar day -> in a mean solar day - p. 96 syzigies -> syzygies - p. 115 arrising -> arising - p. 120 Herchel -> Herschel - p. 123 generally know -> generally known - p. 159 Fraunhoffer’s -> Fraunhofer’s - p. 168 contaary -> contrary - p. 214 oxyde -> oxide - p. 216 aperature -> aperture - p. 296 M Niepce -> M. Niepcé - p. 306 torrecelian -> Torricellian - p. 307 potass -> potash - p. 350 de Roux -> le Roux - p. 423 Β -> β - p. 447 areal -> aërial - p. 456 perigree -> perigee - p. 471 108° -> 180° - p. 478 Meissier -> Messier - - - - - -End of the Project Gutenberg EBook of On the Connexion of the Physical -Sciences, by Mary Somerville - -*** END OF THIS PROJECT GUTENBERG EBOOK CONNEXION OF THE PHYSICAL SCIENCES *** - -***** This file should be named 52869-0.txt or 52869-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/5/2/8/6/52869/ - -Produced by Sonya Schermann and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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