Library of the World's Best Literature, Ancient and Modern — Volume 02

by Unknown

Astronomy is the science of which the human mind may justly feel proudest. It owes this pre-eminence to the elevated nature of its object; to the enormous scale of its operations; to the certainty, the utility, and the stupendousness of its results. From the very beginnings of civilization the study of the heavenly bodies and their movements has attracted the attention of governments and peoples. The greatest captains, statesmen, philosophers, and orators of Greece and Rome found it a subject of delight. Yet astronomy worthy of the name is a modern science: it dates from the sixteenth century only. Three great, three brilliant phases have marked its progress. In 1543 the bold and firm hand of Copernicus overthrew the greater part of the venerable scaffolding which had propped the illusions and the pride of many generations. The earth ceased to be the centre, the pivot, of celestial movements. Henceforward it ranged itself modestly among the other planets, its relative importance as one member of the solar system reduced almost to that of a grain of sand.

Twenty-eight years had elapsed from the day when the Canon of Thorn expired while holding in his trembling hands the first copy of the work which was to glorify the name of Poland, when Würtemberg witnessed the birth of a man who was destined to achieve a revolution in science not less fertile in consequences, and still more difficult to accomplish. This man was Kepler. Endowed with two qualities which seem incompatible,--a volcanic imagination, and a dogged pertinacity which the most tedious calculations could not tire,--Kepler conjectured that celestial movements must be connected with each other by simple laws; or, to use his own expression, by harmonic laws. These laws he undertook to discover. A thousand fruitless attempts--the errors of calculation inseparable from a colossal undertaking--did not hinder his resolute advance toward the goal his imagination descried. Twenty-two years he devoted to it, and still he was not weary. What are twenty-two years of labor to him who is about to become the lawgiver of worlds; whose name is to be ineffaceably inscribed on the frontispiece of an immortal code; who can exclaim in dithyrambic language, "The die is cast: I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader since God has waited six thousand years for an interpreter of his works"?

These celebrated laws, known in astronomy as Kepler's laws, are three in number. The first law is, that the planets describe ellipses around the sun, which is placed in their common focus; the second, that a line joining a planet and the sun sweeps over equal areas in equal times; the third, that the squares of the times of revolution of the planets about the sun are proportional to the cubes of their mean distances from that body. The first two laws were discovered by Kepler in the course of a laborious examination of the theory of the planet Mars. A full account of this inquiry is contained in his famous work, 'De Stella Martis' [Of the Planet Mars], published in 1609. The discovery of the third law was announced to the world in his treatise on Harmonics (1628).

To seek a physical cause adequate to retain the planets in their closed orbits; to make the stability of the universe depend on mechanical forces, and not on solid supports like the crystalline spheres imagined by our ancestors; to extend to the heavenly bodies in their courses the laws of earthly mechanics,--such were the problems which remained for solution after Kepler's discoveries had been announced. Traces of these great problems may be clearly perceived here and there among ancient and modern writers, from Lucretius and Plutarch down to Kepler, Bouillaud, and Borelli. It is to Newton, however, that we must award the merit of their solution. This great man, like several of his predecessors, imagined the celestial bodies to have a tendency to approach each other in virtue of some attractive force, and from the laws of Kepler he deduced the mathematical characteristics of this force. He extended it to all the material molecules of the solar system; and developed his brilliant discovery in a work which, even at the present day, is regarded as the supremest product of the human intellect.

The contributions of France to these revolutions in astronomical science consisted, in 1740, in the determination by experiment of the spheroidal figure of the earth, and in the discovery of the local variations of gravity upon the surface of our planet. These were two great results; but whenever France is not first in science she has lost her place. This rank, lost for a moment, was brilliantly regained by the labors of four geometers. When Newton, giving to his discoveries a generality which the laws of Kepler did not suggest, imagined that the different planets were not only attracted by the sun, but that they also attracted each other, he introduced into the heavens a cause of universal perturbation. Astronomers then saw at a glance that in no part of the universe would the Keplerian laws suffice for the exact representation of the phenomena of motion; that the simple regular movements with which the imaginations of the ancients were pleased to endow the heavenly bodies must experience numerous, considerable, perpetually changing perturbations. To discover a few of these perturbations, and to assign their nature and in a few rare cases their numerical value, was the object which Newton proposed to himself in writing his famous book, the 'Principia Mathematica Philosophiæ Naturalis' [Mathematical Principles of Natural Philosophy], Notwithstanding the incomparable sagacity of its author, the 'Principia' contained merely a rough outline of planetary perturbations, though not through any lack of ardor or perseverance. The efforts of the great philosopher were always superhuman, and the questions which he did not solve were simply incapable of solution in his time.

Five geometers--Clairaut, Euler, D'Alembert, Lagrange, and Laplace--shared between them the world whose existence Newton had disclosed. They explored it in all directions, penetrated into regions hitherto inaccessible, and pointed out phenomena hitherto undetected. Finally--and it is this which constitutes their imperishable glory--they brought under the domain of a single principle, a single law, everything that seemed most occult and mysterious in the celestial movements. Geometry had thus the hardihood to dispose of the future, while the centuries as they unroll scrupulously ratify the decisions of science.

If Newton gave a complete solution of celestial movements where but two bodies attract each other, he did not even attempt the infinitely more difficult problem of three. The "problem of three bodies" (this is the name by which it has become celebrated)--the problem of determining the movement of a body subjected to the attractive influence of two others--was solved for the first time by our countryman, Clairaut. Though he enumerated the various forces which must result from the mutual action of the planets and satellites of our system, even the great Newton did not venture to investigate the general nature of their effects. In the midst of the labyrinth formed by increments and diminutions of velocity, variations in the forms of orbits, changes in distances and inclinations, which these forces must evidently produce, the most learned geometer would fail to discover a trustworthy guide. Forces so numerous, so variable in direction, so different in intensity, seemed to be incapable of maintaining a condition of equilibrium except by a sort of miracle. Newton even suggested that the planetary system did not contain within itself the elements of indefinite stability. He was of opinion that a powerful hand must intervene from time to time to repair the derangements occasioned by the mutual action of the various bodies. Euler, better instructed than Newton in a knowledge of these perturbations, also refused to admit that the solar system was constituted so as to endure forever.

Never did a greater philosophical question offer itself to the inquiries of mankind. Laplace attacked it with boldness, perseverance, and success. The profound and long-continued researches of the illustrious geometer completely established the perpetual variability of the planetary ellipses. He demonstrated that the extremities of their major axes make the circuit of the heavens; that independent of oscillation, the planes of their orbits undergo displacements by which their intersections with the plane of the terrestrial orbit are each year directed toward different stars. But in the midst of this apparant chaos, there is one element which remains constant, or is merely subject to small and periodic changes; namely, the major axis of each orbit, and consequently the time of revolution of each planet. This is the element which ought to have varied most, on the principles held by Newton and Euler. Gravitation, then, suffices to preserve the stability of the solar system. It maintains the forms and inclinations of the orbits in an average position, subject to slight oscillations only; variety does not entail disorder; the universe offers an example of harmonious relations, of a state of perfection which Newton himself doubted.

This condition of harmony depends on circumstances disclosed to Laplace by analysis; circumstances which on the surface do not seem capable of exercising so great an influence. If instead of planets all revolving in the same direction, in orbits but slightly eccentric and in planes inclined at but small angles toward each other, we should substitute different conditions, the stability of the universe would be jeopardized, and a frightful chaos would pretty certainly result. The discovery of the actual conditions excluded the idea, at least so far as the solar system was concerned, that the Newtonian attraction might be a cause of disorder. But might not other forces, combined with the attraction of gravitation, produce gradually increasing perturbations such as Newton and Euler feared? Known facts seemed to justify the apprehension. A comparison of ancient with modern observations revealed a continual acceleration in the mean motions of the moon and of Jupiter, and an equally striking diminution of the mean motion of Saturn. These variations led to a very important conclusion. In accordance with their presumed cause, to say that the velocity of a body increased from century to century was equivalent to asserting that the body continually approached the centre of motion; on the other hand, when the velocity diminished, the body must be receding from the centre. Thus, by a strange ordering of nature, our planetary system seemed destined to lose Saturn, its most mysterious ornament; to see the planet with its ring and seven satellites plunge gradually into those unknown regions where the eye armed with the most powerful telescope has never penetrated. Jupiter, on the other hand, the planet compared with which the earth is so insignificant, appeared to be moving in the opposite direction, so that it would ultimately be absorbed into the incandescent matter of the sun. Finally, it seemed that the moon would one day precipitate itself upon the earth.

There was nothing doubtful or speculative in these sinister forebodings. The precise dates of the approaching catastrophes were alone uncertain. It was known, however, that they were very distant. Accordingly, neither the learned dissertations of men of science nor the animated descriptions of certain poets produced any impression upon the public mind. The members of our scientific societies, however, believed with regret the approaching destruction of the planetary system. The Academy of Sciences called the attention of geometers of all countries to these menacing perturbations. Euler and Lagrange descended into the arena. Never did their mathematical genius shine with a brighter lustre. Still the question remained undecided, when from two obscure corners of the theories of analysis, Laplace, the author of the 'Mécanique Céleste,' brought the laws of these great phenomena clearly to light. The variations in velocity of Jupiter, Saturn, and the moon, were proved to flow from evident physical causes, and to belong in the category of ordinary periodic perturbations depending solely on gravitation. These dreaded variations in orbital dimensions resolved themselves into simple oscillations included within narrow limits. In a word, by the powerful instrumentality of mathematical analysis, the physical universe was again established on a demonstrably firm foundation.