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LAPLACE, PIERRE SIMON, MARQUIS DE (17...
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See also:LAPLACE, See also:PIERRE See also:SIMON, See also:MARQUIS DE (1749—1827) , See also:French mathematician and astronomer, was See also:born at See also:Beaumont-en-Auge in See also:Normandy, on the 28th of See also: The discordance of their results incited Laplace to a searching examination of the whole subject of planetary perturbations, and his See also:maiden effort was rewarded with a discovery which constituted, when See also:developed and completely demonstrated by his own further labours and those of his illustrious See also:rival Lagrange, the most important advance made in See also:physical See also:astronomy since the See also:time of Newton. In a paper read before the See also:Academy of Sciences, on the loth of See also:February 1773 (Mem. presentee See also:par See also:divers savans, tom. vii., 1776), Laplace announced his celebrated conclusion of the invariability of planetary mean motions, carrying the See also:proof as far as the cubes of the eccentricities and inclinations. This was the first and most important step in the See also:establishment of the stability of the See also:solar See also:system. It was followed by a See also: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 See also:analytical See also:tournament closed with the communication to the Academy by Laplace, 1 " Recherches sur le calcul integral," Melanges de la See also:Soc. See also:Roy. de See also:Turin (1766-1769). in 1787, of an entire See also: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 See also: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, independently of any except the most See also:general considerations as to See also:mass, that the mutual See also:action of the See also:planets could never largely affect the eccentricities and inclinations of their orbits; and the singular peculiarities detected by him in the See also:Jovian system were expressed in the so-called " See also:laws of Laplace." He completed the theory of these bodies in a See also:treatise published among the Paris See also:Memoirs for 1788 and 1789; and the striking superiority of the tables computed by J. B. J. See also:Delambre from the data there supplied marked the profit derived from the investigation by See also:practical astronomy. The year 1787 was rendered further memorable by Laplace's announcement on the 19th of See also:November (Memoirs, 1786), of the dependence of lunar See also:acceleration upon the See also:secular changes in the eccentricity of the See also:earth's See also:orbit. The last apparent See also:anomaly, and the last See also:threat of instability, thus disappeared from the solar system. W'ith these brilliant performances the first See also:period of Laplace's scientific career may be said to have closed. If he ceased to make striking discoveries in celestial mechanics, it was rather their subject-See also:matter than his See also:powers that failed. The general working of the great See also:machine was now laid See also:bare, and it needed a further advance of knowledge to bring a fresh set of problems within reach of investigation. The time had come when the results obtained in the development and application of the See also:law of See also:gravitation by three generations of illustrious mathematicians might be presented from a single point of view. To this task the second period of Laplace's activity was devoted. As a See also:monument of mathematical See also:genius applied to the celestial revolutions, the Mecanique See also:celeste ranks second only to the Principle of Newton. The declared aim of the author 1 was to offer a See also:complete See also:solution of the great See also: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 See also:place in astronomical tables. His success in both respects See also:fell little See also:short of his lofty ideal. The first See also:part of the See also:work (2 vols. 4to, Paris, 1799) contains methods for calculating the movements of See also: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 formulae; while a fifth See also:volume, published in three instalments, 1823-1825, comprises the results of Laplace's latest researches, together with a valuable See also:history of progress in each See also:separate See also:branch of his subject. In the delicate task of apportioning his own large See also:share of merit, he certainly does not err on the See also:side of modesty; but it would perhaps be as difficult to produce an instance of injustice, as of generosity in his estimate of others. Far more serious blame attaches to his all but See also:total suppression in the See also:body of the work—and the See also:fault pervades the whole of his writings—of the names of his predecessors and contemporaries. Theorems and formulae are appropriated wholesale without See also:acknowledgment, and a See also:production which may be described as the organized result of a See also:century of patient toil presents itself to the See also:world as the offspring of a single See also:brain. The Mecanique celeste is, even to those most conversant with analytical methods, by no means easy See also:reading. J. B. See also:Biot, who assisted in the correction of its proof sheets, re-marked that it would have extended, had the demonstrations been fully developed, to eight or ten instead of five volumes; and he saw at times the author himself obliged to devote an See also:hour's labour to recovering the dropped links in the See also:chain of reasoning covered by the recurring See also:formula. " Il est aise a voir." 2 The Exposition du systeme du monde (Paris, 1996) has been styled by See also:Arago " the Mecanique celeste disembarrassed of its analytical See also:paraphernalia." Conclusions are not merely stated in it, but the methods pursued for their attainment are indicated. It has the strength of an analytical treatise, the See also:charm of a popular dissertation. The See also:style is lucid and masterly, and the See also:summary of astronomical history with which it terminates has been reckoned one of the masterpieces of the See also:language. To this linguistic excellence the writer owed the place accorded to him " See also:Plan de 1'Ouvrage," CEuvres, tom. i. p 1. 2 See also:Journal See also:des savants (1850).in 1816 in the Academy, of which institution he became See also:president in the following year. The famous " nebular See also:hypothesis " of Laplace made its See also:appearance in the Systesne du monde. Although relegated to a See also:note (vii.), and propounded " Avec la See also:defiance que dolt inspirer tout ce qui n'est point un resultat de 1'observation ou du calcul," it is See also:plain, from the complacency with which he recurred to it at a later date, that he regarded the See also:speculation with considerable interest. That it formed the starting-point, and largely prescribed the course of thought on the subject of planetary origin is due to the simplicity of its assumptions, and the clearness of the mechanical principles involved, rather than to any cogent See also:evidence of its truth. It is curious that Laplace, while bestowing more See also:attention than they deserved on the crude conjectures of See also:Buffon, seems to have been unaware that he had been, to some extent, anticipated by See also:Kant, who had put forward in 1755, in his Allgemeine Naturgesclzichte, a true though defective nebular See also:cosmogony. The career of Laplace was one of scarcely interrupted prosperity. Admitted to the Academy of Sciences as an See also:associate in 1773, he became a member in 1785, having, about a year previously, succeeded E. Bezout as examiner to the royal See also:artillery. During an See also:access of revolutionary suspicion, he was removed from the See also:commission of weights and See also:measures; but the slight was quickly effaced by new honours. He was one of the first members, and became president of the See also:Bureau of Longitudes, took a prominent place at the See also:Institute (founded in 1796), professed analysis at the Ecole Normale, and aided in the organization of the decimal system. The publication of the Mecanique celeste gained him world-wide celebrity, and his name appeared on the lists of the See also:principal scientific associations of See also:Europe, including the Royal Society. But scientific distinctions by no means satisfied his ambition. He aspired to the role of a politician, and has See also:left a memorable example of genius degraded to servility for the See also:sake of a riband and a title. The ardour of his republican principles gave place, after the 18th See also:Brumaire, to devotion towards the first See also:consul, a sentiment promptly rewarded with the See also:post of See also:minister of the interior. His incapacity for affairs was, however, so flagrant that it became necessary to supersede him at the end of six See also:weeks, when Lucien See also:Bonaparte became his successor. " He brought into the See also:administration," said See also:Napoleon, " the spirit of the infinitesimals." His failure was consoled by See also:elevation to the See also:senate, of which body he became See also:chancellor in See also:September 1803. He was at the same time named See also:grand officer of the See also:Legion of See also:Honour, and obtained in 1813 the same See also:rank in the new See also:order of See also:Reunion. The title of See also:count he had acquired on the creation of the See also:empire. Nevertheless he cheer-fully gave his See also:voice in 1814 for the dethronement of his See also:patron, and his " suppleness " merited a seat in the chamber of peers, and, in 1817, the dignity of a marquisate. The memory of these tergiversations is perpetuated in his writings- The first edition of the Systeme du monde was inscribed to the See also:Council of Five See also:Hundred; to the third volume of the Mecanique celeste (1802) was prefixed the See also:declaration that, of all the truths contained in the work, that most See also:precious to the author was the expression of his gratitude and devotion towards the " pacificator of Europe "; upon which noteworthy protestation the suppression in the See also:editions of the Theorie des probabilites subsequent to the restoration, of the See also:original See also:dedication to the See also:emperor formed a fitting commentary. During the later years of his See also:life, Laplace lived much at See also:Arcueil, where he had a See also:country-place adjoining that of his friend C. L. Berthollet. With his co-operation the Societe d'Arcueil was formed, and he occasionally contributed to its Memoirs. In this peaceful retirement he pursued his studies with unabated ardour, and received with See also:uniform See also:courtesy distinguished visitors from all parts of the world. Here, too, he died, attended by his physician, Dr Majendie, and his mathematical coadjutor, See also:Alexis Bouvard, on the 5th of March 1827. His last words were: " Ce que nous connaissons est peu de See also:chose, ce que nous ignorons est immense."
Expressions occur in Laplace's private letters inconsistent Mec. See also:eel., torn. v. p. 346.
with the atheistical opinions he is commonly believed to have held. His See also:character, notwithstanding the egotism by which it was disfigured, had an amiable and engaging side. See also:Young men of See also:science found in him an active benefactor. His relations with these " adopted See also:children of his thought " possessed a singular charm of affectionate simplicity; their intellectual progress and material interests were See also:objects of equal solicitude to him, and he demanded in return only See also:diligence in the pursuit of knowledge. 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 See also:differences, and afterwards showed him, under a strict See also:pledge of secrecy, the papers, then yellow with age, in which he had long before obtained the same results. This instance of abnegation is the more worthy of See also:record that it formed a marked exception to Laplace's usual course. Between him and A. M. See also:Legendre there was a feeling of " more than coldness," owing to his See also:appropriation, with scant acknowledgment, of the fruits of the other's labours; and Dr See also: With Lagrange, on the other See also:hand, he always remained on the best of terms. Laplace left a son, See also: Molecular physics also attracted his See also:notice, and he announced in 1824 his purpose of treating the subject in a separate work. With A. See also:Lavoisier he made an important series of experiments on specific heat (1782–1784), in the course of which the " See also:ice calorimeter " was invented; and they contributed jointly to the Memoirs of the Academy (1781) a paper on the development of See also:electricity by evaporation. 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 See also:light on an identical principle. It was a favourite See also:idea of his that chemical See also:affinity and capillary attraction would eventually be included under the same law, and it was perhaps because of its recalcitrance to this cherished generalization that the undulatory theory of light was distasteful to him. The investigation of the figure of See also:equilibrium of a rotating fluid mass engaged the persistent attention of Laplace. His first memoir was communicated to the Academy in 1773, when he was only twenty-four, his last in 1817, when he was sixty-eight. The results of his many papers on this subject—characterized by him as " un des points See also:les plus interessans du systeme du monde "—are embodied in the Mccanique celeste, and furnish one of the most remarkable proofs of his analytical genius. C. See also:Maclaurin, Legendre and d'Alembert had furnished partial solutions of the problem, confining their T 1 Annales de chimie et de physique (1816), torn. iii. p. 238.attention to the possible figures which would satisfy the conditions of equilibrium. Laplace treated the subject from the point of view of the See also:gradual See also:aggregation and cooling of a mass of matter, and demonstrated that the See also:form which such a mass would ultimately assume must be an See also:ellipsoid of revolution whose See also:equator was determined by the See also:primitive plane of maximum areas. The related subject of the attraction of spheroids was also signally promoted by him. Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the See also:case of any See also:spheroid of revolution where the attracted point, instead of being limited to the See also:axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planeles (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 See also:surface. These researches derive additional importance from having introduced two powerful engines of analysis for the treatment of physical problems, Laplace's coefficients and the potential See also:function. By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the See also:direct See also:process of differentiating a single function, Laplace laid the See also:foundations of the mathematical sciences of heat, electricity and See also:magnetism. The expressions ]esignated by Dr See also:Whewell, Laplace's coefficients (see SPHERICAL HARMONICS) were definitely introduced in the memoir of 1785 on attractions above referred to. In the figure of the earth, the theory of attractions, and the sciences of electricity and magnetism this powerful calculus occupies a prominent place. C. F. See also:Gauss in particular employed it in the calculation of the magnetic potential of the earth, and it received new light .from Clerk See also:Maxwell's See also:interpretation of harmonics with reference to poles on the See also:sphere. Laplace nowhere displayed the massiveness of his genius more conspicuously than in the theory of probabilities. The science which B. See also:Pascal and P. de See also:Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Theorie analytique (1812) is to the best mathematicians a work requiring most arduous study. The theory of probabilities, which Laplace described as See also: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 See also:statistics and future events.
The See also:device known as the method of least squares, for reducing numerous equations of See also:condition to the number of unknown quantities to be determined, had been adopted as a practically convenient See also: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 See also:error in the determination of the elements being thereby reduced to a minimum.
Laplace published in 1779 the method of generating functions, the See also: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 latter is there-fore called the generating function of the former. A direct and an inverse calculus is thus created, the See also:object of the former being to determine the coefficients from the generating function, of the latter to discover the generating function from the coefficients. The one is a problem of See also:interpolation, the other a step towards the solution of an See also:equation' in finite differences. The method, however, is now obsolete owing to the more extended facilities afforded by the calculus of operations.
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. He also showed that every equation of an even degree must have at least one real quadratic See also:factor, reduced the solution of linear See also:differential equations to definite integrals, and furnished an elegant method by which the linear partial differential equation of the second order might be solved. He was also the first to consider the difficult problems involved in equations of mixed differences, and to prove that an equation in finite differences of the first degree and the second order might always be converted into a continued fraction.
In 1842, the See also:works of Laplace being nearly out of See also:print, his widow was about to sell a See also:farm to procure funds for a new impression, when the See also:government of See also: A See also: ; a compendium of certain portions of the same work by Mrs See also:Somerville appeared in 1831, and a See also:German version of the first 2 vols, by See also:Burckhardt at See also:Berlin in 18oi. English See also:translations of the Systeme du monde by J. See also:Pond and H. H. See also:Harte were published, the first in 1809, the second in 1830. An edition entitled Les (Euvres 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. The thirteenth 4to volume was issued in 1904. Some of Laplace's results in the theory of probabilities are simplified in S. F. See also:Lacroix's Traite elementaire du calcul des probabilites and De See also:Morgan's Essay, published in See also:Lardner's See also:Cabinet Cyclopaedia. For the history of the subject see A History of the Mathematical Theory of See also:Probability, by See also:Isaac See also:Todhunter (1865). Laplace's treatise on specific heat was published in German in 1892 as No. 4o of W. Ostwald's Klassiker der exacten Wissenschaften. Additional information and CommentsThere are no comments yet for this article.
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