But the Cartesian theory, like the later speculations of Kant and Laplace, proposes to give a hypothetical explanation of the circumstances and motions which in the normal course of things led to the state of things required by the law of attraction.
In preparation for these he spent the winter of 1877-1878 in reading up original treatises like those of Laplace and Lagrange on mathematics and mechanics, and in attending courses on practical physics under P. G.
The application of this to telegraphic purposes was suggested by Laplace and taken up by Ampere, and afterwards by Triboaillet and by Schilling, whose work forms the foundation of much of modern telegraphy.
In his Naturgeschichte des Himmels, in which he anticipated the nebular theory afterwards more fully developed by Laplace, Kant sought to explain the genesis of the cosmos as a product of physical forces and laws.
Laplace supposed the existence of a primeval nebula which extended so far out as to fill all the space at present occupied by the planets.
Considering that our sun is but a star, or but one of the millions of stars, it is of interest to see whether any other systems present indication of a nebulous origin analogous to that which Laplace proposed for the solar system.
- Laplace, Systeme du monde; Sir William Herschel, Phil.
Laplace, P. L.
Their quantitative experiments were, however, too rough to permit of accurate generalization; and although Lavoisier and Laplace stated the principle that the same amount of heat must be supplied to decompose a compound as would be produced on its formation, the statement was not based on exact experiment, and only received experimental confirmation much later.
Lavoisier and Laplace, ante, § 1).
As the result of an examination conducted in September 1785 by Laplace, Bonaparte was included among those who entered the army without going through an intermediate stage.
After serving for a short time in the artillery, he was appointed in 1797 professor of mathematics at Beauvais, and in 1800 he became professor of physics at the College de France, through the influence of Laplace, from whom he had sought and obtained the favour of reading the proof sheets of the Mecanique celeste.
Laplace (1801); Traite analytique des courbes et des surfaces du second degre (1802); Recherches sur l'integration des equations differentielles partielles et sur les vibrations des surfaces (1803); Traite de physique (1816); Recueil d'observations geodesiques, astronomiques et physiques executees en Espagne et Ecosse, with Arago (1821); Memoire sur la vraie constitution de l'atmosphere terrestre (1841); Traite elementaire d'astronomie physique (1805); Recherches sur plusieurs points de l'astronomie egyptienne (1823); Recherches sur l'ancienne astronomic chinoise (1840); Etudes sur l'astronomie indienne et sur l'astronomie chinoise (1862); Essai sur l'histoire generale des sciences pendant la Revolution (1803); Discours sur Montaigne (1812); Lettres sur l'approvisionnement de Paris et sur le commerce des grains (1835); Mélanges scientifiques et litteraires (1858).
Laplace is due the theoretical proof that this function is independent of temperature and pressure, and apparent experimental confirmation was provided by Biot and Arago's, and by Dulong's observations on gases and vapours.
Similarly, by putting one or more of the deleted rows or columns equal to rows or columns which are not deleted, we obtain, with Laplace, a number of identities between products of determinants of complementary orders.
They remained untold, for he died two days later on the 10th of April, and was buried in the Pantheon, the funeral oration being pronounced by Laplace and Lacepede.
This is especially the case between Lagrange and Euler on the one side, and between Lagrange and Laplace on the other.
Laplace owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way.
But Laplace unquestionably surpassed his rival in practical sagacity and the intuition of physical truth.
Lagrange saw in the problems of nature so many occasions for analytical triumphs; Laplace regarded analytical triumphs as the means of solving the problems of nature.
It deserves to be recorded as one of the numerous coincidences of discovery that Laplace, on being made acquainted by Lagrange with his new method, produced analogous expressions, to which his independent researches had led him.
PIERRE SIMON LAPLACE, MARQUIS DE (1749-1827), French mathematician and astronomer, was born at Beaumont-en-Auge in Normandy, on the 28th of March 1749.
The letters remained unnoticed, but Laplace was not crushed by the rebuff.
Laplace had not yet completed his twenty-fourth year when he entered upon the course of discovery which earned him the title of "the Newton of France."
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.
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.
It was followed 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, 1 "Recherches sur le calcul integral," Mélanges de la Soc. Roy.
The famous "nebular hypothesis" of Laplace made its appearance in the Systeme du monde.
It is curious that Laplace, while bestowing more attention than they deserved on the crude conjectures of Buffon, seems to have been unaware that he had been, to some extent, anticipated by Kant, who had put forward in 1755, in his Allgemeine Naturgeschichte, a true though defective nebular cosmogony.
The career of Laplace was one of scarcely interrupted prosperity.
During the later years of his life, Laplace lived much at Arcueil, where he had a country-place adjoining that of his friend C. L.
Biot relates that, when he himself was beginning his career, Laplace introduced him at the Institute for the purpose of explaining his supposed discovery of equations of mixed differences, and afterwards showed him, under a strict pledge of secrecy, the papers, then yellow with age, in which he had long before obtained the same results.
With Lagrange, on the other hand, he always remained on the best of terms. Laplace left a son, Charles Emile Pierre Joseph Laplace (1789-1874), who succeeded to his title, and rose to the rank of general in the artillery.
It might be said that Laplace was a great mathematician by the original structure of his mind, and became a great discoverer through the sentiment which animated it.
Laplace was, moreover, the first to offer a complete analysis of capillary action based upon a definite hypothesis - that of forces "sensible only at insensible distances"; and he made strenuous but unsuccessful efforts to explain the phenomena of light on an identical principle.
Laplace treated the subject from the point of view of the gradual aggregation and cooling of a mass of matter, and demonstrated that the form which such a mass would ultimately assume must be an ellipsoid of revolution whose equator was determined by the primitive plane of maximum areas.
Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids.
Finally, in a celebrated memoir, Theorie des attractions des spheroides et de la figure des planetes, published in 1785 among the Paris Memoirs for the year 1782, although written after the treatise of 1784, Laplace treated exhaustively the general problem of the attraction of any spheroid upon a particle situated outside or upon its surface.
By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the direct process of differentiating a single function, Laplace laid the foundations of the mathematical sciences of heat, electricity and magnetism.
Laplace nowhere displayed the massiveness of his genius more conspicuously than in the theory of probabilities.
The theory of probabilities, which Laplace described as common sense expressed in mathematical language, engaged his attention from its importance in physics and astronomy; and he applied his theory, not only to the ordinary problems of chances, but also to the inquiry into the causes of phenomena, vital statistics and future events.
The device known as the method of least squares, for reducing numerous equations of condition to the number of unknown quantities to be determined, had been adopted as a practically convenient rule by Gauss and Legendre; but Laplace first treated it as a problem in probabilities, and proved by an intricate and difficult course of reasoning that it was also the most advantageous, the mean of the probabilities of error in the determination of the elements being thereby reduced to a minimum.
Laplace published in 1779 the method of generating functions, the foundation of his theory of probabilities, and the first part of his Theorie analytique is devoted to the exposition of its principles, which in their simplest form consist in treating the successive values of any function as the coefficients in the expansion of another function with reference to a different variable.
The first formal proof of Lagrange's theorem for the development in a series of an implicit function was furnished by Laplace, who gave to it an extended generality.
In 1842, the works of Laplace being nearly out of print, his widow was about to sell a farm to procure funds for a new impression, when the government of Louis Philippe took the matter in hand.
A grant of 40,000 francs having been obtained from the chamber, a national edition was issued in seven 4to vols., bearing the title Ouvres de Laplace (1843-1847).
An edition entitled Les Ouvres completes de Laplace (1878), &c., which is to include all his memoirs as well as his separate works, is in course of publication under the auspices of the Academy of Sciences.
Meanwhile the astronomical theories of development of the solar system from a gaseous condition to its present form, put forward by Kant and by Laplace, had impressed men's minds with the conception of a general movement of spontaneous progress or development in all nature.
Thus he carried on the narrative of orderly development from the point at which it was left by Kant and Laplace - explaining by reference to the ascertained laws of physics and chemistry the configuration of the earth, its mountains and seas, its igneous and its stratified rocks, just as the astronomers had explained by those same laws the evolution of the sun and planets from diffused gaseous matter of high temperature.