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doubt that such a moralized view is of later growth, and inconsistent with the original character of mythology; though the battle is certainly conceived under this form from an early time, and universally throughout the historical period. But on the other hand the genealogies given of the Lapithæ make them a brother race with the Centaurs. Pirithpus, king of the Lapithæ, was son of Ixion; so were the Centaurs. Various other accounts lead to the same result. Ultimately then the battle of Lapithæ with Centaurs is a contest of the physical powers of nature; and the excellent discussion of Professor S. Colvin (Journ. Hell. Stud., i. p. 164) leaves little room for doubt that the Centaurs represent the power – dangerous, yet sometimes beneficent – of mountain floods, and that the battle is the mythic expression of the terrible effects of swollen waters. No satisfactory derivation of the word Lapithes has yet been found, but some of the names of individual Lapithæ, such as Dryas, Charaxus, Caineus son of Elate, &c., refer us to the trees and ravines of the mountains.
Beside the article of Professor Colvin, and the numerous works on Greek mythology, see Welcker, Kl. Schr., vol. ii.
LAPLACE, Pierre Simon, Marquis de (1749-1827), one of the greatest mathematicians and physical astronomers who ever lived, was born at Beaumont-en-Auge in Normandy, March 28, 1749. His early years have remained in the obscurity with which poverty and some ignoble shame of poverty combined to cover them. It is known, however, that his father was a small farmer, and that he owed his education to the interest excited by his lively parts in some persons of position. His first distinctions are said, singularly enough, to have been gained in theological controversy, but at an early age he became mathematical teacher in the military school of Beaumont, the classes of which he had attended as an extern. He was not more than eighteen when, armed with letters of recommendation, he approached D'Alembert, then at the height of his fame and influence, in the hope of finding a career in Paris. The letters remained unnoticed, but Laplace was not a man to be crushed by the first rebuff of fortune. He wrote to the great geometer a letter on the principles of mechanics, which evoked an immediate and enthusiastic response. "You," said D'Alembert to him, "needed no introduction; you have recommended yourself; my support is your due." He accordingly obtained for him an appointment as professor of mathematics in the École Militaire of Paris, and continued to forward his interests with zeal and constancy.
The future of the young mathematician was now assured, and his scientific vocation finally determined. He had not yet completed his twenty-fourth year when he entered upon the course of discovery which has earned him the title of "the Newton of France." Having, in his first published paper,[1] shown his mastery of analysis, he immediately proceeded to apply the powerful instrument at his command to the great outstanding problems in the application of the law of gravitation to the celestial motions. Of these the most conspicuous was offered by the opposite inequalities of Jupiter and Saturn, which the emulous efforts of Euler and Lagrange had failed to bring within the bounds of theory. The discordance of their results incited Laplace to a searching examination of the whole subject of planetary perturbations, and his maiden effort was rewarded with a discovery which constituted, when developed and completely demonstrated by his own further labours and those of his illustrious rival Lagrange, the most important advance made in physical astronomy since the time of Newton. In a paper read before the Academy of Sciences, February 10, 1773 (Mém. présentés par divers Savans, tom. vii., 1776), Laplace announced his celebrated conclusion of the invariability of planetary mean motions, carrying the proof as far as the cubes of the eccentricities and inclinations. This was the first and most important step in the establishment of the stability of the solar system. It was followed up by a series of profound investigations, in which Lagrange and Laplace alternately surpassed and supplemented each other in assigning limits of variation to the several elements of the planetary orbits. The analytical tournament closed with the communication to the Academy by Laplace, in 1787, of an entire group of remarkable discoveries. It would be difficult, in the whole range of scientific literature, to point to a memoir of equal brilliancy with that published (divided into three parts) in the volumes of the Academy for 1784, 1785, and 1786. The long-sought cause of the "great inequality" of Jupiter and Saturn was found in the near approach to commensurability of their mean motions; it was demonstrated in two elegant theorems (see ASTRONOMY, vol. ii. p. 781), independently of any except the most general considerations as to mass, that the mutual action of the planets could never largely affect the eccentricities and inclinations of their orbits; and the singular peculiarities detected by him in the Jovian system were expressed in the so-called "laws of Laplace" (ASTRONOMY, p. 810). He completed the theory of these bodies in a treatise contained amongst the Paris Memoirs for 1788 and 1789; and the tables computed by Delambre from the data there supplied served, by their striking superiority to those hitherto available, to mark the profit derived from the investigation by practical astronomy.[2] The year 1787 was rendered further memorable by Laplace's announcement, November 19 (Memoirs, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit. The last apparent anomaly, and the last threat of instability, thus disappeared from the solar system.
With these brilliant performances the first period of Laplace's scientific career may be said to have closed. If he made no more striking discoveries in celestial mechanics, it was rather their subject matter than his powers that failed. The general working of the great machine was now laid bare, and it needed a further advance of knowledge to render a fresh set of problems accessible to investigation. The time had come when the results obtained in the development and application of the law of gravitation by three generations of illustrious mathematicians might be collected in a single work, and presented from a single point of view. It was to this task that the second period of Laplace's activity was devoted. As a monument of mathematical genius applied to the celestial revolutions the Mécanique Céleste ranks second only to the Principia of Newton.
The declared aim of the author[3] was to offer a complete solution of the great mechanical problem presented by the solar system, and to bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables. His success in both respects fell but little short of his lofty ideal. The first part of the work (2 vols. 4to, Paris, 1799) contains methods for calculating the movements of translation and rotation of the heavenly bodies, for determining their figures, and resolving tidal problems; the second, especially dedicated to the improvement of tables, exhibits in the third and fourth volumes (1802 and 1805) the application of these formulæ; while a fifth volume, published in three instalments, 1823-25, comprises the results of Laplace's latest researches, together with a valuable history of progress in each separate branch of his subject. In the delicate task of apportioning his own large share of merit, he certainly does not err on
