Imágenes de páginas
PDF
EPUB

of demonstrating it; and even this share of the glory Newton must divide with his good fortune. Because he had received from Kepler the laws of the planetary motions, and from Huygens those of motion in general; because an accurate measure of the earth had been recently made; and, more than all, because he had the analysis which he himself created; Delambre would conclude, with Lagrange, that, even if Newton were the greatest of mathematicians and natural philosophers, he was also the most fortunate. "For," he says, "a world to be explained, and materials ready for its explanation, are to be met with but once; to meet with them was Newton's good fortune; he knew how to profit by it; there lies his glory."

These conclusions, not unsupported by facts, but characterized by a tone of jealousy unworthy of the amiable and illustrious Lagrange, were repeated in the "Système du Monde"; as if such good fortune were not always the lot of genius. Galileo found it in the almost accidental invention of the telescope; Kepler, in the friendship of Tycho Brahe, without whose observations he might never have left a wilderness of fanciful speculations, in which the present fashionable philosophy would have rioted, to reap his glorious harvest from the fruitful fields of inductive science; and Laplace himself found it in the ready assistance and coöperation of the first observers and calculators of Europe. Nature, indeed, seems, when casting the lot of her great men, to load her dice with peculiar care; and her favorite sons are ever born at the most fortunate epochs. But the author of the "Optics," the "Fluxions," and the "Principia," was, in no respect, the genius of accident; his thrice-won immortality towered far above his good fortune; and the striking fact must not be forgotten, that precisely the same good fortune was that of his noble rival, Leibnitz, who had likewise created the very same analysis. But, far from knowing how to profit by it, as Newton had done, he even opposed the "Principia" and the law of gravitation with all his might, was joined in his opposition by the first geometers of the age, and, in the words of Biot, "it was half a century before the great truth, contained and demonstrated in the Principia,' was, I will not say, followed and developed, but before it was even comprehended by the majority of the learned."

The recent discovery of some old papers has led to singu

lar discussions regarding the reputation of Newton; and some have pretended, that, because the observations were essential to the calculations of the lunar theory, the observer Flamsteed is entitled to a large share of Newton's glory. With equal justice the organ-blower might lay claim to the merit of the music of Mozart. The mere observer is only a higher order of mechanic; his "Historia Coelestis" displays only his untiring industry, and the acuteness of his senses; he is but the hand of astronomy, and may not wear the crown of glory fitted to the head, which combines his observations into an harmonious theory.

But the private character of Newton has suffered more severely from these developements; and the snails of literature have been most industrious in defacing the reputation once so bright and unsullied. However much their writings may please a world, but too eager to prune all men down to the same level, the generous mind will turn from them with disgust to Laplace's last labor, which, purporting to be a history of mathematical astronomy, is, in reality, the noblest and truest eulogy upon him who laid its foundations.

The first division of this volume, treating of the Mathematical Theory of the Earth's Figure, begins with the fact, that Newton founded this theory; and concludes an accurate account of Newton's labors upon it with the remark, that, notwithstanding several hypotheses, one of which is contrary to later observations, this step must be regarded as a prodigious one, considering the importance and novelty of the propositions established by its author, and the extreme difficulty of the subject. We must here give another remark of Laplace, made upon the lunar theory, that these hypotheses may be allowed to inventors in such profound researches ; and we may add, that Newton's instinct in such hypotheses was almost unerring, was altogether unrivalled, and seemed to border upon the divine. In the book upon the Attraction of Spheres, and the Motions of Elastic Fluids, Newton is said to have been the first to consider the attraction of spherical bodies, and his theory of sound is pronounced to be a monument of his genius. This theory had been objected to by Lagrange, in the "Turin Miscellany," on account of the alleged unsoundness and paradoxical nature of its reasoning; and his objections have been quoted and repeated by later mathematicians, among whom we blush to write the

name of an Englishman, and so eminent a philosopher as the younger Herschel. Herschel. These geometers seem never to have examined either the original theory, or the attack upon it; and must have been ignorant of the fact, that, with a magnanimity of which few are capable, Lagrange had, in the "Memoirs of the Berlin Academy," retrac ed his objections, and admitted the principles of Newton's theory to be indisputably correct. The arguments against the theory, far from showing its inaccuracy, were, indeed, the most conclusive demonstration of its generality, and only proved, that Newton needed not to limit it to a particular case, and should not have inferred this case to be the one of Nature, because it satisfied his theory.

In his next book, upon the Oscillations of the Fluids which cover the Planets, La Place says, that Newton first gave the true theory of the ebb and flow of the sea, attaching it to his great principle of universal gravitation. Euler, the father of modern analysis, concluded the method of Newton to be entirely erroneous, and not even to have approached the truth; but Laplace points out the cause of the difference between the results of these two profound geometers, and shows that Newton's theory, instead of deserving Euler's reproaches, was most admirable for its ingenuity.

In the chapter upon the Precession of the Equinoxes, the Newtonian solution of this most intricate of problems is carefully analyzed, and proved to have but one defect, which, though a radical one, is quite excusable in a first inventor, and would probably have been corrected, if Newton's other occupations had allowed him to pay a closer attention to the discoveries of the continental mathematicians."

The honor of discovering the law of gravitation, and thus laying the corner-stone of the celestial mechanics, is, in this volume, given most unreservedly to the author of the "Principia," and without any of those qualifying remarks upon his good fortune, which had intruded themselves into the "Système du Monde."

Newton's researches into the theory of the moon, which had met with so sad a reception from Clairaut and Delambre, are unhesitatingly pronounced, by Laplace, to be one of the most profound parts of his admirable work; and a portion of them appeared to him so remarkable for ingenuity, that he devoted a chapter to the task of translating this portion into he language of modern analysis.

Such is a brief review of Laplace's notices of Newton's labors; and they show, that, in all the profound discussions of the "Mécanique Céleste," the first steps had been taken in the "Principia." But La Place is not the only French philosopher who has risen above national prejudices, and cheerfully acknowledged all the greatness of Newton. Biot, also, calling the author of the "Principia" "the creator of natural philosophy," regarded him, moreover, as having founded the principles of the Mechanics of Chemistry, by referring its combinations to atomic attractions and repulsions, and by taking the boldest, happiest, and most original views of the composition of bodies. The evil genius even of Newton gained, however, one victory over his good fortune, and deprived the world for ever of his more sublime speculations upon this vast subject. By an unlucky accident, the labor of years was burned to cinders, the mighty soul of Newton was agitated with an emotion, which his physical powers could not resist, and from which, it is doubtful if they ever recovered, and his dog Diamond achieved for himself a share in his master's immortality. Were it not for this accident, we cannot conjecture how high the monument of his genius would have aspired, and how many later discoveries he would have anticipated; but enough remains to justify_and command the homage of every man of science, whether English or French, and to vindicate his epitaph, "Congratulentur sibi mortales tale tantumque exstitisse humani generis decus."

Although the fifth volume of the "Mecanique Céleste" was published more than twenty years after the preceding ones, it is, from its historical character, the real preface to the whole work. It will be adopted as the text for the present article, and its division into subjects will be closely followed. Returning, then, to its first chapter upon "The Figure and Rotation of the Earth," we will notice more particularly, the hypotheses assumed by Newton, without demonstration, in order to evade the difficulties of the calculus. He supposed the earth to be an ellipsoid of revolution, and to be homogeneous; and gravity to increase from the equator to the poles, in proportion to the square of the sine of the latitude. The first of these hypotheses is quite a natural one, since the ellipse is the most simple of ovals; but the last, though neat in its form, could, by no means, have been obvious to the

original inquirer. Both of these have, however, been confirmed by the successive demonstrations of Clairaut, Maclaurin, D'Alembert, Legendre, and La Place; but La Place has proved, that the second hypothesis is inconsistent with known phenomena, and that the earth is not homogeneous. The researches upon this subject assume the earth to have attained its present form while in a fluid state, or at least while covered with a fluid, and are, therefore, based upon the principles of hydrostatics.

The general principle of the equilibrium of fluids was unknown to Newton, and he adopted an imperfect one, which was, however, when combined with his hypotheses, sufficient for his purpose. He supposed a canal, consisting of two branches, to be drawn from the centre of the earth, the one branch to the pole and the other to the equator; and inferred, that the pressures upon the bases of the branches must be equal, because the fluid contained in the canal must be at rest of itself, independently of the surrounding fluid. Huygens, about the same time, introduced the condition, that the surface of the fluid must be upon a level, that is, must be perpendicular to the direction of a falling body; which was united by Bouguer with that of Newton. But the combination was not sufficient for all cases; and Maclaurin, generalizing the idea of Newton, was led to the great principle, that the pressures upon the bases of all the straight canals drawn from any point of the fluid to its surface must be equal. Clairaut's more famous and more recent principle, which has been adopted by almost all mathematicians, that, if an oval canal be drawn, of any curve whatever, the fluid contained within it must be at rest, independently of the other parts of the fluid, may easily be shown to be but a slight and unimportant generalization of that of Maclaurin; but it deserves its reputation, since its author, by translating it into algebraical language, deduced from it the equations of the equilibrium of fluids; "a discovery which," says Lagrange, "has changed the face of hydrostatics, and made it a new science." These equations can, however, be deduced from the more fundamental principle, which is almost identical with Maclaurin's, that a fluid presses equally in every direction; but this principle itself has been traced by Lagrange back to its source, and it flows directly and necessarily from the definition of a fluid, that its particles move by each other with perfect facility. That a fluid will be at rest when each particle is pressed

« AnteriorContinuar »