A HISTORY OF SCIENCE

BY HENRY SMITH WILLIAMS, M.D., LL.D.


ASSISTED BY EDWARD H. WILLIAMS, M.D.


IN FIVE VOLUMES

VOLUME III.

CONTENTS

DETAILED CONTENTS

BOOK III. MODERN DEVELOPMENT OF THE PHYSICAL SCIENCES

I. THE SUCCESSORS OF NEWTON IN ASTRONOMY

II. THE PROGRESS OF MODERN ASTRONOMY

III. THE NEW SCIENCE OF PALEONTOLOGY

IV. THE ORIGIN AND DEVELOPMENT OF MODERN GEOLOGY

V. THE NEW SCIENCE OF METEOROLOGY

VI. MODERN THEORIES OF HEAT AND LIGHT

VII. THE MODERN DEVELOPMENT OF ELECTRICITY AND MAGNETISM

VIII. THE CONSERVATION OF ENERGY

IX. THE ETHER AND PONDERABLE MATTER

APPENDIX

CONTENTS

BOOK III
CHAPTER I. THE SUCCESSORS OF NEWTON IN ASTRONOMY
The work of Johannes Hevelius—Halley and Hevelius—Halley's observation
of the transit of Mercury, and his method of determining the parallax of
the planets—Halley's observation of meteors—His inability to
explain these bodies—The important work of James Bradley—Lacaille's
measurement of the arc of the meridian—The determination of the
question as to the exact shape of the earth—D'Alembert and his
influence upon science—Delambre's History of Astronomy—The
astronomical work of Euler.
CHAPTER II. THE PROGRESS OF MODERN ASTRONOMY
The work of William Herschel—His discovery of Uranus—His discovery
that the stars are suns—His conception of the universe—His deduction
that gravitation has caused the grouping of the heavenly bodies—The
nebula, hypothesis,—Immanuel Kant's conception of the formation of the
world—Defects in Kant's conception—Laplace's final solution of the
problem—His explanation in detail—Change in the mental attitude of the
world since Bruno—Asteroids and satellites—Discoveries of Olbersl—The
mathematical calculations of Adams and Leverrier—The discovery of the
inner ring of Saturn—Clerk Maxwell's paper on the stability of Saturn's
rings—Helmholtz's conception of the action of tidal friction—Professor
G. H. Darwin's estimate of the consequences of tidal action—Comets
and meteors—Bredichin's cometary theory—The final solution of the
structure of comets—Newcomb's estimate of the amount of cometary dust
swept up daily by the earth—The fixed stars—John Herschel's studies
of double stars—Fraunhofer's perfection of the refracting
telescope—Bessel's measurement of the parallax of a star,—Henderson's
measurements—Kirchhoff and Bunsen's perfection of the
spectroscope—Wonderful revelations of the spectroscope—Lord Kelvin's
estimate of the time that will be required for the earth to become
completely cooled—Alvan Clark's discovery of the companion star of
Sirius—The advent of the photographic film in astronomy—Dr. Huggins's
studies of nebulae—Sir Norman Lockyer's "cosmogonic guess,"—Croll's
pre-nebular theory.
CHAPTER III. THE NEW SCIENCE OF PALEONTOLOGY
William Smith and fossil shells—His discovery that fossil rocks are
arranged in regular systems—Smith's inquiries taken up by Cuvier—His
Ossements Fossiles containing the first description of hairy
elephant—His contention that fossils represent extinct species
only—Dr. Buckland's studies of English fossil-beds—Charles Lyell
combats catastrophism,—Elaboration of his ideas with reference to
the rotation of species—The establishment of the doctrine of
uniformitarianism,—Darwin's Origin of Species—Fossil man—Dr.
Falconer's visit to the fossil-beds in the valley of the
Somme—Investigations of Prestwich and Sir John Evans—Discovery of the
Neanderthal skull,—Cuvier's rejection of human fossils—The finding
of prehistoric carving on ivory—The fossil-beds of America—Professor
Marsh's paper on the fossil horses in America—The Warren mastodon,—The
Java fossil, Pithecanthropus Erectus.
CHAPTER IV. THE ORIGIN AND DEVELOPMENT OF MODERN GEOLOGY
James Hutton and the study of the rocks—His theory of the earth—His
belief in volcanic cataclysms in raising and forming the continents—His
famous paper before the Royal Society of Edinburgh, 1781—-His
conclusions that all strata of the earth have their origin at the bottom
of the sea—-His deduction that heated and expanded matter caused the
elevation of land above the sea-level—Indifference at first shown this
remarkable paper—Neptunists versus Plutonists—Scrope's classical work
on volcanoes—Final acceptance of Hutton's explanation of the origin
of granites—Lyell and uniformitarianism—Observations on the gradual
elevation of the coast-lines of Sweden and Patagonia—Observations on
the enormous amount of land erosion constantly taking place,—Agassiz
and the glacial theory—Perraudin the chamois-hunter, and his
explanation of perched bowlders—De Charpentier's acceptance of
Perraudin's explanation—Agassiz's paper on his Alpine studies—His
conclusion that the Alps were once covered with an ice-sheet—Final
acceptance of the glacial theory—The geological ages—The work of
Murchison and Sedgwick—Formation of the American continents—Past,
present, and future.
CHAPTER V. THE NEW SCIENCE OF METEOROLOGY
Biot's investigations of meteors—The observations of Brandes and
Benzenberg on the velocity of falling stars—Professor Olmstead's
observations on the meteoric shower of 1833—Confirmation of Chladni's
hypothesis of 1794—The aurora borealis—Franklin's suggestion that
it is of electrical origin—Its close association with terrestrial
magnetism—Evaporation, cloud-formation, and dew—Dalton's demonstration
that water exists in the air as an independent gas—Hutton's theory of
rain—Luke Howard's paper on clouds—Observations on dew, by Professor
Wilson and Mr. Six—Dr. Wells's essay on dew—His observations
on several appearances connected with dew—Isotherms and ocean
currents—Humboldt and the-science of comparative climatology—His
studies of ocean currents—Maury's theory that gravity is the cause
of ocean currents—Dr. Croll on Climate and Time—Cyclones and
anti-cyclones,—Dove's studies in climatology—Professor Ferrel's
mathematical law of the deflection of winds—Tyndall's estimate of
the amount of heat given off by the liberation of a pound of
vapor—Meteorological observations and weather predictions.
CHAPTER VI. MODERN THEORIES OF HEAT AND LIGHT
Josiah Wedgwood and the clay pyrometer—Count Rumford and the vibratory
theory of heat—His experiments with boring cannon to determine the
nature of heat—Causing water to boil by the friction of the borer—His
final determination that heat is a form of motion—Thomas Young and the
wave theory of light—His paper on the theory of light and colors—His
exposition of the colors of thin plates—Of the colors of thick
plates, and of striated surfaces,—Arago and Fresnel champion the wave
theory—opposition to the theory by Biot—The French Academy's tacit
acceptance of the correctness of the theory by its admission of Fresnel
as a member.
CHAPTER VII. THE MODERN DEVELOPMENT OF ELECTRICITY AND MAGNETISM
Galvani and the beginning of modern electricity—The construction of
the voltaic pile—Nicholson's and Carlisle's discovery that the galvanic
current decomposes water—Decomposition of various substances by Sir
Humphry Davy—His construction of an arc-light—The deflection of the
magnetic needle by electricity demonstrated by Oersted—Effect of
this important discovery—Ampere creates the science of
electro-dynamics—Joseph Henry's studies of electromagnets—Michael
Faraday begins his studies of electromagnetic induction—His famous
paper before the Royal Society, in 1831, in which he demonstrates
electro-magnetic induction—His explanation of Arago's
rotating disk—The search for a satisfactory method of storing
electricity—Roentgen rays, or X-rays.
CHAPTER VIII. THE CONSERVATION OF ENERGY
Faraday narrowly misses the discovery of the doctrine of
conservation—Carnot's belief that a definite quantity of work can be
transformed into a definite quantity of heat—The work of James Prescott
Joule—Investigations begun by Dr. Mayer—Mayer's paper of 1842—His
statement of the law of the conservation of energy—Mayer and
Helmholtz—Joule's paper of 1843—Joule or Mayer—Lord Kelvin and the
dissipation of energy-The final unification.
CHAPTER IX. THE ETHER AND PONDERABLE MATTER
James Clerk-Maxwell's conception of ether—Thomas Young and
"Luminiferous ether,"—Young's and Fresnel's conception of transverse
luminiferous undulations—Faraday's experiments pointing to the
existence of ether—Professor Lodge's suggestion of two ethers—Lord
Kelvin's calculation of the probable density of ether—The vortex theory
of atoms—Helmholtz's calculations in vortex motions—Professor
Tait's apparatus for creating vortex rings in the air—-The ultimate
constitution of matter as conceived by Boscovich—Davy's speculations
as to the changes that occur in the substance of matter at different
temperatures—Clausius's and Maxwell's investigations of the
kinetic theory of gases—Lord Kelvin's estimate of the size of the
molecule—Studies of the potential energy of molecules—Action of gases
at low temperatures.
APPENDIX

A HISTORY OF SCIENCE

BOOK III. MODERN DEVELOPMENT OF THE PHYSICAL SCIENCES

With the present book we enter the field of the distinctively modern. There is no precise date at which we take up each of the successive stories, but the main sweep of development has to do in each case with the nineteenth century. We shall see at once that this is a time both of rapid progress and of great differentiation. We have heard almost nothing hitherto of such sciences as paleontology, geology, and meteorology, each of which now demands full attention. Meantime, astronomy and what the workers of the elder day called natural philosophy become wonderfully diversified and present numerous phases that would have been startling enough to the star-gazers and philosophers of the earlier epoch.

Thus, for example, in the field of astronomy, Herschel is able, thanks to his perfected telescope, to discover a new planet and then to reach out into the depths of space and gain such knowledge of stars and nebulae as hitherto no one had more than dreamed of. Then, in rapid sequence, a whole coterie of hitherto unsuspected minor planets is discovered, stellar distances are measured, some members of the starry galaxy are timed in their flight, the direction of movement of the solar system itself is investigated, the spectroscope reveals the chemical composition even of suns that are unthinkably distant, and a tangible theory is grasped of the universal cycle which includes the birth and death of worlds.

Similarly the new studies of the earth's surface reveal secrets of planetary formation hitherto quite inscrutable. It becomes known that the strata of the earth's surface have been forming throughout untold ages, and that successive populations differing utterly from one another have peopled the earth in different geological epochs. The entire point of view of thoughtful men becomes changed in contemplating the history of the world in which we live—albeit the newest thought harks back to some extent to those days when the inspired thinkers of early Greece dreamed out the wonderful theories with which our earlier chapters have made our readers familiar.

In the region of natural philosophy progress is no less pronounced and no less striking. It suffices here, however, by way of anticipation, simply to name the greatest generalization of the century in physical science—the doctrine of the conservation of energy.

I. THE SUCCESSORS OF NEWTON IN ASTRONOMY

HEVELIUS AND HALLEY

STRANGELY enough, the decade immediately following Newton was one of comparative barrenness in scientific progress, the early years of the eighteenth century not being as productive of great astronomers as the later years of the seventeenth, or, for that matter, as the later years of the eighteenth century itself. Several of the prominent astronomers of the later seventeenth century lived on into the opening years of the following century, however, and the younger generation soon developed a coterie of astronomers, among whom Euler, Lagrange, Laplace, and Herschel, as we shall see, were to accomplish great things in this field before the century closed.

One of the great seventeenth-century astronomers, who died just before the close of the century, was Johannes Hevelius (1611-1687), of Dantzig, who advanced astronomy by his accurate description of the face and the spots of the moon. But he is remembered also for having retarded progress by his influence in refusing to use telescopic sights in his observations, preferring until his death the plain sights long before discarded by most other astronomers. The advantages of these telescope sights have been discussed under the article treating of Robert Hooke, but no such advantages were ever recognized by Hevelius. So great was Hevelius's reputation as an astronomer that his refusal to recognize the advantage of the telescope sights caused many astronomers to hesitate before accepting them as superior to the plain; and even the famous Halley, of whom we shall speak further in a moment, was sufficiently in doubt over the matter to pay the aged astronomer a visit to test his skill in using the old-style sights. Side by side, Hevelius and Halley made their observations, Hevelius with his old instrument and Halley with the new. The results showed slightly in the younger man's favor, but not enough to make it an entirely convincing demonstration. The explanation of this, however, did not lie in the lack of superiority of the telescopic instrument, but rather in the marvellous skill of the aged Hevelius, whose dexterity almost compensated for the defect of his instrument. What he might have accomplished could he have been induced to adopt the telescope can only be surmised.

Halley himself was by no means a tyro in matters astronomical at that time. As the only son of a wealthy soap-boiler living near London, he had been given a liberal education, and even before leaving college made such novel scientific observations as that of the change in the variation of the compass. At nineteen years of age he discovered a new method of determining the elements of the planetary orbits which was a distinct improvement over the old. The year following he sailed for the Island of St, Helena to make observations of the heavens in the southern hemisphere.

It was while in St. Helena that Halley made his famous observation of the transit of Mercury over the sun's disk, this observation being connected, indirectly at least, with his discovery of a method of determining the parallax of the planets. By parallax is meant the apparent change in the position of an object, due really to a change in the position of the observer. Thus, if we imagine two astronomers making observations of the sun from opposite sides of the earth at the same time, it is obvious that to these observers the sun will appear to be at two different points in the sky. Half the angle measuring this difference would be known as the sun's parallax. This would depend, then, upon the distance of the earth from the sun and the length of the earth's radius. Since the actual length of this radius has been determined, the parallax of any heavenly body enables the astronomer to determine its exact distance.

The parallaxes can be determined equally well, however, if two observers are separated by exactly known distances, several hundreds or thousands of miles apart. In the case of a transit of Venus across the sun's disk, for example, an observer at New York notes the image of the planet moving across the sun's disk, and notes also the exact time of this observation. In the same manner an observer at London makes similar observations. Knowing the distance between New York and London, and the different time of the passage, it is thus possible to calculate the difference of the parallaxes of the sun and a planet crossing its disk. The idea of thus determining the parallax of the planets originated, or at least was developed, by Halley, and from this phenomenon he thought it possible to conclude the dimensions of all the planetary orbits. As we shall see further on, his views were found to be correct by later astronomers.

In 1721 Halley succeeded Flamsteed as astronomer royal at the Greenwich Observatory. Although sixty-four years of age at that time his activity in astronomy continued unabated for another score of years. At Greenwich he undertook some tedious observations of the moon, and during those observations was first to detect the acceleration of mean motion. He was unable to explain this, however, and it remained for Laplace in the closing years of the century to do so, as we shall see later.

Halley's book, the Synopsis Astronomiae Cometicae, is one of the most valuable additions to astronomical literature since the time of Kepler. He was first to attempt the calculation of the orbit of a comet, having revived the ancient opinion that comets belong to the solar system, moving in eccentric orbits round the sun, and his calculation of the orbit of the comet of 1682 led him to predict correctly the return of that comet in 1758. Halley's Study of Meteors.

Like other astronomers of his time he was greatly puzzled over the well-known phenomena of shooting-stars, or meteors, making many observations himself, and examining carefully the observations of other astronomers. In 1714 he gave his views as to the origin and composition of these mysterious visitors in the earth's atmosphere. As this subject will be again referred to in a later chapter, Halley's views, representing the most advanced views of his age, are of interest.

"The theory of the air seemeth at present," he says, "to be perfectly well understood, and the differing densities thereof at all altitudes; for supposing the same air to occupy spaces reciprocally proportional to the quantity of the superior or incumbent air, I have elsewhere proved that at forty miles high the air is rarer than at the surface of the earth at three thousand times; and that the utmost height of the atmosphere, which reflects light in the Crepusculum, is not fully forty-five miles, notwithstanding which 'tis still manifest that some sort of vapors, and those in no small quantity, arise nearly to that height. An instance of this may be given in the great light the society had an account of (vide Transact. Sep., 1676) from Dr. Wallis, which was seen in very distant counties almost over all the south part of England. Of which though the doctor could not get so particular a relation as was requisite to determine the height thereof, yet from the distant places it was seen in, it could not but be very many miles high.

"So likewise that meteor which was seen in 1708, on the 31st of July, between nine and ten o'clock at night, was evidently between forty and fifty miles perpendicularly high, and as near as I can gather, over Shereness and the buoy on the Nore. For it was seen at London moving horizontally from east by north to east by south at least fifty degrees high, and at Redgrove, in Suffolk, on the Yarmouth road, about twenty miles from the east coast of England, and at least forty miles to the eastward of London, it appeared a little to the westward of the south, suppose south by west, and was seen about thirty degrees high, sliding obliquely downward. I was shown in both places the situation thereof, which was as described, but could wish some person skilled in astronomical matters bad seen it, that we might pronounce concerning its height with more certainty. Yet, as it is, we may securely conclude that it was not many more miles westerly than Redgrove, which, as I said before, is about forty miles more easterly than London. Suppose it, therefore, where perpendicular, to have been thirty-five miles east from London, and by the altitude it appeared at in London—viz., fifty degrees, its tangent will be forty-two miles, for the height of the meteor above the surface of the earth; which also is rather of the least, because the altitude of the place shown me is rather more than less than fifty degrees; and the like may be concluded from the altitude it appeared in at Redgrove, near seventy miles distant. Though at this very great distance, it appeared to move with an incredible velocity, darting, in a very few seconds of time, for about twelve degrees of a great circle from north to south, being very bright at its first appearance; and it died away at the east of its course, leaving for some time a pale whiteness in the place, with some remains of it in the track where it had gone; but no hissing sound as it passed, or bounce of an explosion were heard.

"It may deserve the honorable society's thoughts, how so great a quantity of vapor should be raised to the top of the atmosphere, and there collected, so as upon its ascension or otherwise illumination, to give a light to a circle of above one hundred miles diameter, not much inferior to the light of the moon; so as one might see to take a pin from the ground in the otherwise dark night. 'Tis hard to conceive what sort of exhalations should rise from the earth, either by the action of the sun or subterranean heat, so as to surmount the extreme cold and rareness of the air in those upper regions: but the fact is indisputable, and therefore requires a solution."

From this much of the paper it appears that there was a general belief that this burning mass was heated vapor thrown off from the earth in some mysterious manner, yet this is unsatisfactory to Halley, for after citing various other meteors that have appeared within his knowledge, he goes on to say:

"What sort of substance it must be, that could be so impelled and ignited at the same time; there being no Vulcano or other Spiraculum of subterraneous fire in the northeast parts of the world, that we ever yet heard of, from whence it might be projected.

"I have much considered this appearance, and think it one of the hardest things to account for that I have yet met with in the phenomena of meteors, and I am induced to think that it must be some collection of matter formed in the aether, as it were, by some fortuitous concourse of atoms, and that the earth met with it as it passed along in its orb, then but newly formed, and before it had conceived any great impetus of descent towards the sun. For the direction of it was exactly opposite to that of the earth, which made an angle with the meridian at that time of sixty-seven gr., that is, its course was from west southwest to east northeast, wherefore the meteor seemed to move the contrary way. And besides falling into the power of the earth's gravity, and losing its motion from the opposition of the medium, it seems that it descended towards the earth, and was extinguished in the Tyrrhene Sea, to the west southwest of Leghorn. The great blow being heard upon its first immersion into the water, and the rattling like the driving of a cart over stones being what succeeded upon its quenching; something like this is always heard upon quenching a very hot iron in water. These facts being past dispute, I would be glad to have the opinion of the learned thereon, and what objection can be reasonably made against the above hypothesis, which I humbly submit to their censure."(1)

These few paragraphs, coming as they do from a leading eighteenth-century astronomer, convey more clearly than any comment the actual state of the meteorological learning at that time. That this ball of fire, rushing "at a greater velocity than the swiftest cannon-ball," was simply a mass of heated rock passing through our atmosphere, did not occur to him, or at least was not credited. Nor is this surprising when we reflect that at that time universal gravitation had been but recently discovered; heat had not as yet been recognized as simply a form of motion; and thunder and lightning were unexplained mysteries, not to be explained for another three-quarters of a century. In the chapter on meteorology we shall see how the solution of this mystery that puzzled Halley and his associates all their lives was finally attained.

BRADLEY AND THE ABERRATION OF LIGHT

Halley was succeeded as astronomer royal by a man whose useful additions to the science were not to be recognized or appreciated fully until brought to light by the Prussian astronomer Bessel early in the nineteenth century. This was Dr. James Bradley, an ecclesiastic, who ranks as one of the most eminent astronomers of the eighteenth century. His most remarkable discovery was the explanation of a peculiar motion of the pole-star, first observed, but not explained, by Picard a century before. For many years a satisfactory explanation was sought unsuccessfully by Bradley and his fellow-astronomers, but at last he was able to demonstrate that the stary Draconis, on which he was making his observations, described, or appeared to describe, a small ellipse. If this observation was correct, it afforded a means of computing the aberration of any star at all times. The explanation of the physical cause of this aberration, as Bradley thought, and afterwards demonstrated, was the result of the combination of the motion of light with the annual motion of the earth. Bradley first formulated this theory in 1728, but it was not until 1748—twenty years of continuous struggle and observation by him—that he was prepared to communicate the results of his efforts to the Royal Society. This remarkable paper is thought by the Frenchman, Delambre, to entitle its author to a place in science beside such astronomers as Hipparcbus and Kepler.

Bradley's studies led him to discover also the libratory motion of the earth's axis. "As this appearance of Draconis indicated a diminution of the inclination of the earth's axis to the plane of the ecliptic," he says; "and as several astronomers have supposed THAT inclination to diminish regularly; if this phenomenon depended upon such a cause, and amounted to 18" in nine years, the obliquity of the ecliptic would, at that rate, alter a whole minute in thirty years; which is much faster than any observations, before made, would allow. I had reason, therefore, to think that some part of this motion at the least, if not the whole, was owing to the moon's action upon the equatorial parts of the earth; which, I conceived, might cause a libratory motion of the earth's axis. But as I was unable to judge, from only nine years observations, whether the axis would entirely recover the same position that it had in the year 1727, I found it necessary to continue my observations through a whole period of the moon's nodes; at the end of which I had the satisfaction to see, that the stars, returned into the same position again; as if there had been no alteration at all in the inclination of the earth's axis; which fully convinced me that I had guessed rightly as to the cause of the phenomena. This circumstance proves likewise, that if there be a gradual diminution of the obliquity of the ecliptic, it does not arise only from an alteration in the position of the earth's axis, but rather from some change in the plane of the ecliptic itself; because the stars, at the end of the period of the moon's nodes, appeared in the same places, with respect to the equator, as they ought to have done, if the earth's axis had retained the same inclination to an invariable plane."(2)

FRENCH ASTRONOMERS

Meanwhile, astronomers across the channel were by no means idle. In France several successful observers were making many additions to the already long list of observations of the first astronomer of the Royal Observatory of Paris, Dominic Cassini (1625-1712), whose reputation among his contemporaries was much greater than among succeeding generations of astronomers. Perhaps the most deserving of these successors was Nicolas Louis de Lacaille (1713-1762), a theologian who had been educated at the expense of the Duke of Bourbon, and who, soon after completing his clerical studies, came under the patronage of Cassini, whose attention had been called to the young man's interest in the sciences. One of Lacaille's first under-takings was the remeasuring of the French are of the meridian, which had been incorrectly measured by his patron in 1684. This was begun in 1739, and occupied him for two years before successfully completed. As a reward, however, he was admitted to the academy and appointed mathematical professor in Mazarin College.

In 1751 he went to the Cape of Good Hope for the purpose of determining the sun's parallax by observations of the parallaxes of Mars and Venus, and incidentally to make observations on the other southern hemisphere stars. The results of this undertaking were most successful, and were given in his Coelum australe stelligerum, etc., published in 1763. In this he shows that in the course of a single year he had observed some ten thousand stars, and computed the places of one thousand nine hundred and forty-two of them, measured a degree of the meridian, and made many observations of the moon—productive industry seldom equalled in a single year in any field. These observations were of great service to the astronomers, as they afforded the opportunity of comparing the stars of the southern hemisphere with those of the northern, which were being observed simultaneously by Lelande at Berlin.

Lacaille's observations followed closely upon the determination of an absorbing question which occupied the attention of the astronomers in the early part of the century. This question was as to the shape of the earth—whether it was actually flattened at the poles. To settle this question once for all the Academy of Sciences decided to make the actual measurement of the length of two degrees, one as near the pole as possible, the other at the equator. Accordingly, three astronomers, Godin, Bouguer, and La Condamine, made the journey to a spot on the equator in Peru, while four astronomers, Camus, Clairaut, Maupertuis, and Lemonnier, made a voyage to a place selected in Lapland. The result of these expeditions was the determination that the globe is oblately spheroidal.

A great contemporary and fellow-countryman of Lacaille was Jean Le Rond d'Alembert (1717-1783), who, although not primarily an astronomer, did so much with his mathematical calculations to aid that science that his name is closely connected with its progress during the eighteenth century. D'Alembert, who became one of the best-known men of science of his day, and whose services were eagerly sought by the rulers of Europe, began life as a foundling, having been exposed in one of the markets of Paris. The sickly infant was adopted and cared for in the family of a poor glazier, and treated as a member of the family. In later years, however, after the foundling had become famous throughout Europe, his mother, Madame Tencin, sent for him, and acknowledged her relationship. It is more than likely that the great philosopher believed her story, but if so he did not allow her the satisfaction of knowing his belief, declaring always that Madame Tencin could "not be nearer than a step-mother to him, since his mother was the wife of the glazier."

D'Alembert did much for the cause of science by his example as well as by his discoveries. By living a plain but honest life, declining magnificent offers of positions from royal patrons, at the same time refusing to grovel before nobility, he set a worthy example to other philosophers whose cringing and pusillanimous attitude towards persons of wealth or position had hitherto earned them the contempt of the upper classes.

His direct additions to astronomy are several, among others the determination of the mutation of the axis of the earth. He also determined the ratio of the attractive forces of the sun and moon, which he found to be about as seven to three. From this he reached the conclusion that the earth must be seventy times greater than the moon. The first two volumes of his Researches on the Systems of the World, published in 1754, are largely devoted to mathematical and astronomical problems, many of them of little importance now, but of great interest to astronomers at that time.

Another great contemporary of D'Alembert, whose name is closely associated and frequently confounded with his, was Jean Baptiste Joseph Delambre (1749-1822). More fortunate in birth as also in his educational advantages, Delambre as a youth began his studies under the celebrated poet Delille. Later he was obliged to struggle against poverty, supporting himself for a time by making translations from Latin, Greek, Italian, and English, and acting as tutor in private families. The turning-point of his fortune came when the attention of Lalande was called to the young man by his remarkable memory, and Lalande soon showed his admiration by giving Delambre certain difficult astronomical problems to solve. By performing these tasks successfully his future as an astronomer became assured. At that time the planet Uranus had just been discovered by Herschel, and the Academy of Sciences offered as the subject for one of its prizes the determination of the planet's orbit. Delambre made this determination and won the prize—a feat that brought him at once into prominence.

By his writings he probably did as much towards perfecting modern astronomy as any one man. His History of Astronomy is not merely a narrative of progress of astronomy but a complete abstract of all the celebrated works written on the subject. Thus he became famous as an historian as well as an astronomer.

LEONARD EULER

Still another contemporary of D'Alembert and Delambre, and somewhat older than either of them, was Leonard Euler (1707-1783), of Basel, whose fame as a philosopher equals that of either of the great Frenchmen. He is of particular interest here in his capacity of astronomer, but astronomy was only one of the many fields of science in which he shone. Surely something out of the ordinary was to be expected of the man who could "repeat the AEneid of Virgil from the beginning to the end without hesitation, and indicate the first and last line of every page of the edition which he used." Something was expected, and he fulfilled these expectations.

In early life he devoted himself to the study of theology and the Oriental languages, at the request of his father, but his love of mathematics proved too strong, and, with his father's consent, he finally gave up his classical studies and turned to his favorite study, geometry. In 1727 he was invited by Catharine I. to reside in St. Petersburg, and on accepting this invitation he was made an associate of the Academy of Sciences. A little later he was made professor of physics, and in 1733 professor of mathematics. In 1735 he solved a problem in three days which some of the eminent mathematicians would not undertake under several months. In 1741 Frederick the Great invited him to Berlin, where he soon became a member of the Academy of Sciences and professor of mathematics; but in 1766 he returned to St. Petersburg. Towards the close of his life he became virtually blind, being obliged to dictate his thoughts, sometimes to persons entirely ignorant of the subject in hand. Nevertheless, his remarkable memory, still further heightened by his blindness, enabled him to carry out the elaborate computations frequently involved.

Euler's first memoir, transmitted to the Academy of Sciences of Paris in 1747, was on the planetary perturbations. This memoir carried off the prize that had been offered for the analytical theory of the motions of Jupiter and Saturn. Other memoirs followed, one in 1749 and another in 1750, with further expansions of the same subject. As some slight errors were found in these, such as a mistake in some of the formulae expressing the secular and periodic inequalities, the academy proposed the same subject for the prize of 1752. Euler again competed, and won this prize also. The contents of this memoir laid the foundation for the subsequent demonstration of the permanent stability of the planetary system by Laplace and Lagrange.

It was Euler also who demonstrated that within certain fixed limits the eccentricities and places of the aphelia of Saturn and Jupiter are subject to constant variation, and he calculated that after a lapse of about thirty thousand years the elements of the orbits of these two planets recover their original values.

II. THE PROGRESS OF MODERN ASTRONOMY

A NEW epoch in astronomy begins with the work of William Herschel, the Hanoverian, whom England made hers by adoption. He was a man with a positive genius for sidereal discovery. At first a mere amateur in astronomy, he snatched time from his duties as music-teacher to grind him a telescopic mirror, and began gazing at the stars. Not content with his first telescope, he made another and another, and he had such genius for the work that he soon possessed a better instrument than was ever made before. His patience in grinding the curved reflective surface was monumental. Sometimes for sixteen hours together he must walk steadily about the mirror, polishing it, without once removing his hands. Meantime his sister, always his chief lieutenant, cheered him with her presence, and from time to time put food into his mouth. The telescope completed, the astronomer turned night into day, and from sunset to sunrise, year in and year out, swept the heavens unceasingly, unless prevented by clouds or the brightness of the moon. His sister sat always at his side, recording his observations. They were in the open air, perched high at the mouth of the reflector, and sometimes it was so cold that the ink froze in the bottle in Caroline Herschel's hand; but the two enthusiasts hardly noticed a thing so common-place as terrestrial weather. They were living in distant worlds.

The results? What could they be? Such enthusiasm would move mountains. But, after all, the moving of mountains seems a liliputian task compared with what Herschel really did with those wonderful telescopes. He moved worlds, stars, a universe—even, if you please, a galaxy of universes; at least he proved that they move, which seems scarcely less wonderful; and he expanded the cosmos, as man conceives it, to thousands of times the dimensions it had before. As a mere beginning, he doubled the diameter of the solar system by observing the great outlying planet which we now call Uranus, but which he christened Georgium Sidus, in honor of his sovereign, and which his French contemporaries, not relishing that name, preferred to call Herschel.

This discovery was but a trifle compared with what Herschel did later on, but it gave him world-wide reputation none the less. Comets and moons aside, this was the first addition to the solar system that had been made within historic times, and it created a veritable furor of popular interest and enthusiasm. Incidentally King George was flattered at having a world named after him, and he smiled on the astronomer, and came with his court to have a look at his namesake. The inspection was highly satisfactory; and presently the royal favor enabled the astronomer to escape the thraldom of teaching music and to devote his entire time to the more congenial task of star-gazing.

Thus relieved from the burden of mundane embarrassments, he turned with fresh enthusiasm to the skies, and his discoveries followed one another in bewildering profusion. He found various hitherto unseen moons of our sister planets; he made special studies of Saturn, and proved that this planet, with its rings, revolves on its axis; he scanned the spots on the sun, and suggested that they influence the weather of our earth; in short, he extended the entire field of solar astronomy. But very soon this field became too small for him, and his most important researches carried him out into the regions of space compared with which the span of our solar system is a mere point. With his perfected telescopes he entered abysmal vistas which no human eve ever penetrated before, which no human mind had hitherto more than vaguely imagined. He tells us that his forty-foot reflector will bring him light from a distance of "at least eleven and three-fourths millions of millions of millions of miles"—light which left its source two million years ago. The smallest stars visible to the unaided eye are those of the sixth magnitude; this telescope, he thinks, has power to reveal stars of the 1342d magnitude.

But what did Herschel learn regarding these awful depths of space and the stars that people them? That was what the world wished to know. Copernicus, Galileo, Kepler, had given us a solar system, but the stars had been a mystery. What says the great reflector—are the stars points of light, as the ancients taught, and as more than one philosopher of the eighteenth century has still contended, or are they suns, as others hold? Herschel answers, they are suns, each and every one of all the millions—suns, many of them, larger than the one that is the centre of our tiny system. Not only so, but they are moving suns. Instead of being fixed in space, as has been thought, they are whirling in gigantic orbits about some common centre. Is our sun that centre? Far from it. Our sun is only a star like all the rest, circling on with its attendant satellites—our giant sun a star, no different from myriad other stars, not even so large as some; a mere insignificant spark of matter in an infinite shower of sparks.

Nor is this all. Looking beyond the few thousand stars that are visible to the naked eye, Herschel sees series after series of more distant stars, marshalled in galaxies of millions; but at last he reaches a distance beyond which the galaxies no longer increase. And yet—so he thinks—he has not reached the limits of his vision. What then? He has come to the bounds of the sidereal system—seen to the confines of the universe. He believes that he can outline this system, this universe, and prove that it has the shape of an irregular globe, oblately flattened to almost disklike proportions, and divided at one edge—a bifurcation that is revealed even to the naked eye in the forking of the Milky Way.

This, then, is our universe as Herschel conceives it—a vast galaxy of suns, held to one centre, revolving, poised in space. But even here those marvellous telescopes do not pause. Far, far out beyond the confines of our universe, so far that the awful span of our own system might serve as a unit of measure, are revealed other systems, other universes, like our own, each composed, as he thinks, of myriads of suns, clustered like our galaxy into an isolated system—mere islands of matter in an infinite ocean of space. So distant from our universe are these now universes of Herschel's discovery that their light reaches us only as a dim, nebulous glow, in most cases invisible to the unaided eye. About a hundred of these nebulae were known when Herschel began his studies. Before the close of the century he had discovered about two thousand more of them, and many of these had been resolved by his largest telescopes into clusters of stars. He believed that the farthest of these nebulae that he could see was at least three hundred thousand times as distant from us as the nearest fixed star. Yet that nearest star—so more recent studies prove—is so remote that its light, travelling one hundred and eighty thousand miles a second, requires three and one-half years to reach our planet.

As if to give the finishing touches to this novel scheme of cosmology, Herschel, though in the main very little given to unsustained theorizing, allows himself the privilege of one belief that he cannot call upon his telescope to substantiate. He thinks that all the myriad suns of his numberless systems are instinct with life in the human sense. Giordano Bruno and a long line of his followers had held that some of our sister planets may be inhabited, but Herschel extends the thought to include the moon, the sun, the stars—all the heavenly bodies. He believes that he can demonstrate the habitability of our own sun, and, reasoning from analogy, he is firmly convinced that all the suns of all the systems are "well supplied with inhabitants." In this, as in some other inferences, Herschel is misled by the faulty physics of his time. Future generations, working with perfected instruments, may not sustain him all along the line of his observations, even, let alone his inferences. But how one's egotism shrivels and shrinks as one grasps the import of his sweeping thoughts!

Continuing his observations of the innumerable nebulae, Herschel is led presently to another curious speculative inference. He notes that some star groups are much more thickly clustered than others, and he is led to infer that such varied clustering tells of varying ages of the different nebulae. He thinks that at first all space may have been evenly sprinkled with the stars and that the grouping has resulted from the action of gravitation.

"That the Milky Way is a most extensive stratum of stars of various sizes admits no longer of lasting doubt," he declares, "and that our sun is actually one of the heavenly bodies belonging to it is as evident. I have now viewed and gauged this shining zone in almost every direction and find it composed of stars whose number... constantly increases and decreases in proportion to its apparent brightness to the naked eye.

"Let us suppose numberless stars of various sizes, scattered over an indefinite portion of space in such a manner as to be almost equally distributed throughout the whole. The laws of attraction which no doubt extend to the remotest regions of the fixed stars will operate in such a manner as most probably to produce the following effects:

"In the first case, since we have supposed the stars to be of various sizes, it will happen that a star, being considerably larger than its neighboring ones, will attract them more than they will be attracted by others that are immediately around them; by which means they will be, in time, as it were, condensed about a centre, or, in other words, form themselves into a cluster of stars of almost a globular figure, more or less regular according to the size and distance of the surrounding stars....

"The next case, which will also happen almost as frequently as the former, is where a few stars, though not superior in size to the rest, may chance to be rather nearer one another than the surrounding ones,... and this construction admits of the utmost variety of shapes....

"From the composition and repeated conjunction of both the foregoing formations, a third may be derived when many large stars, or combined small ones, are spread in long, extended, regular, or crooked rows, streaks, or branches; for they will also draw the surrounding stars, so as to produce figures of condensed stars curiously similar to the former which gave rise to these condensations.

"We may likewise admit still more extensive combinations; when, at the same time that a cluster of stars is forming at the one part of space, there may be another collection in a different but perhaps not far-distant quarter, which may occasion a mutual approach towards their own centre of gravity.

"In the last place, as a natural conclusion of the former cases, there will be formed great cavities or vacancies by the retreating of the stars towards the various centres which attract them."(1)

Looking forward, it appears that the time must come when all the suns of a system will be drawn together and destroyed by impact at a common centre. Already, it seems to Herschel, the thickest clusters have "outlived their usefulness" and are verging towards their doom.

But again, other nebulae present an appearance suggestive of an opposite condition. They are not resolvable into stars, but present an almost uniform appearance throughout, and are hence believed to be composed of a shining fluid, which in some instances is seen to be condensed at the centre into a glowing mass. In such a nebula Herschel thinks he sees a sun in process of formation.

THE NEBULAR HYPOTHESIS OF KANT

Taken together, these two conceptions outline a majestic cycle of world formation and world destruction—a broad scheme of cosmogony, such as had been vaguely adumbrated two centuries before by Kepler and in more recent times by Wright and Swedenborg. This so-called "nebular hypothesis" assumes that in the beginning all space was uniformly filled with cosmic matter in a state of nebular or "fire-mist" diffusion, "formless and void." It pictures the condensation—coagulation, if you will—of portions of this mass to form segregated masses, and the ultimate development out of these masses of the sidereal bodies that we see.

Perhaps the first elaborate exposition of this idea was that given by the great German philosopher Immanuel Kant (born at Konigsberg in 1724, died in 1804), known to every one as the author of the Critique of Pure Reason. Let us learn from his own words how the imaginative philosopher conceived the world to have come into existence.

"I assume," says Kant, "that all the material of which the globes belonging to our solar system—all the planets and comets—consist, at the beginning of all things was decomposed into its primary elements, and filled the whole space of the universe in which the bodies formed out of it now revolve. This state of nature, when viewed in and by itself without any reference to a system, seems to be the very simplest that can follow upon nothing. At that time nothing has yet been formed. The construction of heavenly bodies at a distance from one another, their distances regulated by their attraction, their form arising out of the equilibrium of their collected matter, exhibit a later state.... In a region of space filled in this manner, a universal repose could last only a moment. The elements have essential forces with which to put each other in motion, and thus are themselves a source of life. Matter immediately begins to strive to fashion itself. The scattered elements of a denser kind, by means of their attraction, gather from a sphere around them all the matter of less specific gravity; again, these elements themselves, together with the material which they have united with them, collect in those points where the particles of a still denser kind are found; these in like manner join still denser particles, and so on. If we follow in imagination this process by which nature fashions itself into form through the whole extent of chaos, we easily perceive that all the results of the process would consist in the formation of divers masses which, when their formation was complete, would by the equality of their attraction be at rest and be forever unmoved.

"But nature has other forces in store which are specially exerted when matter is decomposed into fine particles. They are those forces by which these particles repel one another, and which, by their conflict with attractions, bring forth that movement which is, as it were, the lasting life of nature. This force of repulsion is manifested in the elasticity of vapors, the effluences of strong-smelling bodies, and the diffusion of all spirituous matters. This force is an uncontestable phenomenon of matter. It is by it that the elements, which may be falling to the point attracting them, are turned sideways promiscuously from their movement in a straight line; and their perpendicular fall thereby issues in circular movements, which encompass the centre towards which they were falling. In order to make the formation of the world more distinctly conceivable, we will limit our view by withdrawing it from the infinite universe of nature and directing it to a particular system, as the one which belongs to our sun. Having considered the generation of this system, we shall be able to advance to a similar consideration of the origin of the great world-systems, and thus to embrace the infinitude of the whole creation in one conception.

"From what has been said, it will appear that if a point is situated in a very large space where the attraction of the elements there situated acts more strongly than elsewhere, then the matter of the elementary particles scattered throughout the whole region will fall to that point. The first effect of this general fall is the formation of a body at this centre of attraction, which, so to speak, grows from an infinitely small nucleus by rapid strides; and in the proportion in which this mass increases, it also draws with greater force the surrounding particles to unite with it. When the mass of this central body has grown so great that the velocity with which it draws the particles to itself with great distances is bent sideways by the feeble degree of repulsion with which they impede one another, and when it issues in lateral movements which are capable by means of the centrifugal force of encompassing the central body in an orbit, then there are produced whirls or vortices of particles, each of which by itself describes a curved line by the composition of the attracting force and the force of revolution that had been bent sideways. These kinds of orbits all intersect one another, for which their great dispersion in this space gives place. Yet these movements are in many ways in conflict with one another, and they naturally tend to bring one another to a uniformity—that is, into a state in which one movement is as little obstructive to the other as possible. This happens in two ways: first by the particles limiting one another's movement till they all advance in one direction; and, secondly, in this way, that the particles limit their vertical movements in virtue of which they are approaching the centre of attraction, till they all move horizontally—i. e., in parallel circles round the sun as their centre, no longer intercept one another, and by the centrifugal force becoming equal with the falling force they keep themselves constantly in free circular orbits at the distance at which they move. The result, finally, is that only those particles continue to move in this region of space which have acquired by their fall a velocity, and through the resistance of the other particles a direction, by which they can continue to maintain a FREE CIRCULAR MOVEMENT....

"The view of the formation of the planets in this system has the advantage over every other possible theory in holding that the origin of the movements, and the position of the orbits in arising at that same point of time—nay, more, in showing that even the deviations from the greatest possible exactness in their determinations, as well as the accordances themselves, become clear at a glance. The planets are formed out of particles which, at the distance at which they move, have exact movements in circular orbits; and therefore the masses composed out of them will continue the same movements and at the same rate and in the same direction."(2)

It must be admitted that this explanation leaves a good deal to be desired. It is the explanation of a metaphysician rather than that of an experimental scientist. Such phrases as "matter immediately begins to strive to fashion itself," for example, have no place in the reasoning of inductive science. Nevertheless, the hypothesis of Kant is a remarkable conception; it attempts to explain along rational lines something which hitherto had for the most part been considered altogether inexplicable.

But there are various questions that at once suggest themselves which the Kantian theory leaves unanswered. How happens it, for example, that the cosmic mass which gave birth to our solar system was divided into several planetary bodies instead of remaining a single mass? Were the planets struck from the sun by the chance impact of comets, as Buffon has suggested? or thrown out by explosive volcanic action, in accordance with the theory of Dr. Darwin? or do they owe their origin to some unknown law? In any event, how chanced it that all were projected in nearly the same plane as we now find them?

LAPLACE AND THE NEBULAR HYPOTHESIS

It remained for a mathematical astronomer to solve these puzzles. The man of all others competent to take the subject in hand was the French astronomer Laplace. For a quarter of a century he had devoted his transcendent mathematical abilities to the solution of problems of motion of the heavenly bodies. Working in friendly rivalry with his countryman Lagrange, his only peer among the mathematicians of the age, he had taken up and solved one by one the problems that Newton left obscure. Largely through the efforts of these two men the last lingering doubts as to the solidarity of the Newtonian hypothesis of universal gravitation had been removed. The share of Lagrange was hardly less than that of his co-worker; but Laplace will longer be remembered, because he ultimately brought his completed labors into a system, and, incorporating with them the labors of his contemporaries, produced in the Mecanique Celeste the undisputed mathematical monument of the century, a fitting complement to the Principia of Newton, which it supplements and in a sense completes.

In the closing years of the eighteenth century Laplace took up the nebular hypothesis of cosmogony, to which we have just referred, and gave it definite proportions; in fact, made it so thoroughly his own that posterity will always link it with his name. Discarding the crude notions of cometary impact and volcanic eruption, Laplace filled up the gaps in the hypothesis with the aid of well-known laws of gravitation and motion. He assumed that the primitive mass of cosmic matter which was destined to form our solar system was revolving on its axis even at a time when it was still nebular in character, and filled all space to a distance far beyond the present limits of the system. As this vaporous mass contracted through loss of heat, it revolved more and more swiftly, and from time to time, through balance of forces at its periphery, rings of its substance were whirled off and left revolving there, subsequently to become condensed into planets, and in their turn whirl off minor rings that became moons. The main body of the original mass remains in the present as the still contracting and rotating body which we call the sun.

Let us allow Laplace to explain all this in detail:

"In order to explain the prime movements of the planetary system," he says, "there are the five following phenomena: The movement of the planets in the same direction and very nearly in the same plane; the movement of the satellites in the same direction as that of the planets; the rotation of these different bodies and the sun in the same direction as their revolution, and in nearly the same plane; the slight eccentricity of the orbits of the planets and of the satellites; and, finally, the great eccentricity of the orbits of the comets, as if their inclinations had been left to chance.

"Buffon is the only man I know who, since the discovery of the true system of the world, has endeavored to show the origin of the planets and their satellites. He supposes that a comet, in falling into the sun, drove from it a mass of matter which was reassembled at a distance in the form of various globes more or less large, and more or less removed from the sun, and that these globes, becoming opaque and solid, are now the planets and their satellites.

"This hypothesis satisfies the first of the five preceding phenomena; for it is clear that all the bodies thus formed would move very nearly in the plane which passed through the centre of the sun, and in the direction of the torrent of matter which was produced; but the four other phenomena appear to be inexplicable to me by this means. Indeed, the absolute movement of the molecules of a planet ought then to be in the direction of the movement of its centre of gravity; but it does not at all follow that the motion of the rotation of the planets should be in the same direction. Thus the earth should rotate from east to west, but nevertheless the absolute movement of its molecules should be from east to west; and this ought also to apply to the movement of the revolution of the satellites, in which the direction, according to the hypothesis which he offers, is not necessarily the same as that of the progressive movement of the planets.

"A phenomenon not only very difficult to explain under this hypothesis, but one which is even contrary to it, is the slight eccentricity of the planetary orbits. We know, by the theory of central forces, that if a body moves in a closed orbit around the sun and touches it, it also always comes back to that point at every revolution; whence it follows that if the planets were originally detached from the sun, they would touch it at each return towards it, and their orbits, far from being circular, would be very eccentric. It is true that a mass of matter driven from the sun cannot be exactly compared to a globe which touches its surface, for the impulse which the particles of this mass receive from one another and the reciprocal attractions which they exert among themselves, could, in changing the direction of their movements, remove their perihelions from the sun; but their orbits would be always most eccentric, or at least they would not have slight eccentricities except by the most extraordinary chance. Thus we cannot see, according to the hypothesis of Buffon, why the orbits of more than a hundred comets already observed are so elliptical. This hypothesis is therefore very far from satisfying the preceding phenomena. Let us see if it is possible to trace them back to their true cause.

"Whatever may be its ultimate nature, seeing that it has caused or modified the movements of the planets, it is necessary that this cause should embrace every body, and, in view of the enormous distances which separate them, it could only have been a fluid of immense extent. In order to have given them an almost circular movement in the same direction around the sun, it is necessary that this fluid should have enveloped the sun as in an atmosphere. The consideration of the planetary movements leads us then to think that, on account of excessive heat, the atmosphere of the sun originally extended beyond the orbits of all the planets, and that it was successively contracted to its present limits.

"In the primitive condition in which we suppose the sun to have been, it resembled a nebula such as the telescope shows is composed of a nucleus more or less brilliant, surrounded by a nebulosity which, on condensing itself towards the centre, forms a star. If it is conceived by analogy that all the stars were formed in this manner, it is possible to imagine their previous condition of nebulosity, itself preceded by other states in which the nebulous matter was still more diffused, the nucleus being less and less luminous. By going back as far as possible, we thus arrive at a nebulosity so diffused that its existence could hardly be suspected.

"For a long time the peculiar disposition of certain stars, visible to the unaided eye, has struck philosophical observers. Mitchell has already remarked how little probable it is that the stars in the Pleiades, for example, could have been contracted into the small space which encloses them by the fortuity of chance alone, and he has concluded that this group of stars, and similar groups which the skies present to us, are the necessary result of the condensation of a nebula, with several nuclei, and it is evident that a nebula, by continually contracting, towards these various nuclei, at length would form a group of stars similar to the Pleiades. The condensation of a nebula with two nuclei would form a system of stars close together, turning one upon the other, such as those double stars of which we already know the respective movements.

"But how did the solar atmosphere determine the movements of the rotation and revolution of the planets and satellites? If these bodies had penetrated very deeply into this atmosphere, its resistance would have caused them to fall into the sun. We can therefore conjecture that the planets were formed at their successive limits by the condensation of a zone of vapors which the sun, on cooling, left behind, in the plane of his equator.

"Let us recall the results which we have given in a preceding chapter. The atmosphere of the sun could not have extended indefinitely. Its limit was the point where the centrifugal force due to its movement of rotation balanced its weight. But in proportion as the cooling contracted the atmosphere, and those molecules which were near to them condensed upon the surface of the body, the movement of the rotation increased; for, on account of the Law of Areas, the sum of the areas described by the vector of each molecule of the sun and its atmosphere and projected in the plane of the equator being always the same, the rotation should increase when these molecules approach the centre of the sun. The centrifugal force due to this movement becoming thus larger, the point where the weight is equal to it is nearer the sun. Supposing, then, as it is natural to admit, that the atmosphere extended at some period to its very limits, it should, on cooling, leave molecules behind at this limit and at limits successively occasioned by the increased rotation of the sun. The abandoned molecules would continue to revolve around this body, since their centrifugal force was balanced by their weight. But this equilibrium not arising in regard to the atmospheric molecules parallel to the solar equator, the latter, on account of their weight, approached the atmosphere as they condensed, and did not cease to belong to it until by this motion they came upon the equator.

"Let us consider now the zones of vapor successively left behind. These zones ought, according to appearance, by the condensation and mutual attraction of their molecules, to form various concentric rings of vapor revolving around the sun. The mutual gravitational friction of each ring would accelerate some and retard others, until they had all acquired the same angular velocity. Thus the actual velocity of the molecules most removed from the sun would be the greatest. The following cause would also operate to bring about this difference of speed. The molecules farthest from the sun, and which by the effects of cooling and condensation approached one another to form the outer part of the ring, would have always described areas proportional to the time since the central force by which they were controlled has been constantly directed towards this body. But this constancy of areas necessitates an increase of velocity proportional to the distance. It is thus seen that the same cause would diminish the velocity of the molecules which form the inner part of the ring.