The Exposition du système du monde (Paris, 1796) has been styled by Arago “the Mécanique céleste disembarrassed of its analytical 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 charm of a popular dissertation. The style is lucid and masterly, and the summary of astronomical history with which it terminates has been reckoned one of the masterpieces of the language. To this linguistic excellence the writer owed the place accorded to him in 1816 in the Academy, of which institution he became president in the following year. The famous “nebular hypothesis” of Laplace made its appearance in the Système du monde. Although relegated to a note (vii.), and propounded “Avec la défiance que doit inspirer tout ce qui n’est point un résultat de l’observation ou du calcul,” it is plain, from the complacency with which he recurred to it[4] at a later date, that he regarded the 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 evidence of its truth. 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. Admitted to the Academy of Sciences as an associate in 1773, he became a member in 1785, having, about a year previously, succeeded E. Bezout as examiner to the royal artillery. During an access of revolutionary suspicion, he was removed from the commission of weights and measures; but the slight was quickly effaced by new honours. He was one of the first members, and became president of the Bureau of Longitudes, took a prominent place at the Institute (founded in 1796), professed analysis at the École Normale, and aided in the organization of the decimal system. The publication of the Mécanique céleste gained him world-wide celebrity, and his name appeared on the lists of the principal scientific associations of Europe, including the Royal Society. But scientific distinctions by no means satisfied his ambition. He aspired to the rôle of a politician, and has left a memorable example of genius degraded to servility for the sake of a riband and a title. The ardour of his republican principles gave place, after the 18th Brumaire, to devotion towards the first consul, a sentiment promptly rewarded with the post of minister of the interior. His incapacity for affairs was, however, so flagrant that it became necessary to supersede him at the end of six weeks, when Lucien Bonaparte became his successor. “He brought into the administration,” said Napoleon, “the spirit of the infinitesimals.” His failure was consoled by elevation to the senate, of which body he became chancellor in September 1803. He was at the same time named grand officer of the Legion of Honour, and obtained in 1813 the same rank in the new order of Reunion. The title of count he had acquired on the creation of the empire. Nevertheless he cheerfully gave his voice in 1814 for the dethronement of his 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 Système du monde was inscribed to the Council of Five Hundred; to the third volume of the Mécanique céleste (1802) was prefixed the declaration that, of all the truths contained in the work, that most 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 editions of the Théorie des probabilités subsequent to the restoration, of the original dedication to the emperor formed a fitting commentary.
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. Berthollet. With his co-operation the Société 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 uniform courtesy distinguished visitors from all parts of the world. Here, too, he died, attended by his physician, Dr Majendie, and his mathematical coadjutor, Alexis Bouvard, on the 5th of March 1827. His last words were: “Ce que nous connaissons est peu de chose, ce que nous ignorons est immense.”
Expressions occur in Laplace’s private letters inconsistent with the atheistical opinions he is commonly believed to have held. His character, notwithstanding the egotism by which it was disfigured, had an amiable and engaging side. Young men of science found in him an active benefactor. His relations with these “adopted children of his thought” possessed a singular charm of affectionate simplicity; their intellectual progress and material interests were objects of equal solicitude to him, and he demanded in return only 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 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. This instance of abnegation is the more worthy of record that it formed a marked exception to Laplace’s usual course. Between him and A. M. Legendre there was a feeling of “more than coldness,” owing to his appropriation, with scant acknowledgment, of the fruits of the other’s labours; and Dr Thomas Young counted himself, rightly or wrongly, amongst the number of those similarly aggrieved by him. 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. The regulated enthusiasm with which he regarded the system of nature was with him from first to last. It can be traced in his earliest essay, and it dictated the ravings of his final illness. By it his extraordinary analytical powers became strictly subordinated to physical investigations. To this lofty quality of intellect he added a rare sagacity in perceiving analogies, and in detecting the new truths that lay concealed in his formulae, and a tenacity of mental grip, by which problems, once seized, were held fast, year after year, until they yielded up their solutions. In every branch of physical astronomy, accordingly, deep traces of his work are visible. “He would have completed the science of the skies,” Baron Fourier remarked, “had the science been capable of completion.”
It may be added that he first examined the conditions of stability of the system formed by Saturn’s rings, pointed out the necessity for their rotation, and fixed for it a period (10h 33m) virtually identical with that established by the observations of Herschel; that he detected the existence in the solar system of an invariable plane such that the sum of the products of the planetary masses by the projections upon it of the areas described by their radii vectores in a given time is a maximum; and made notable advances in the theory of astronomical refraction (Méc. cél. tom. iv. p. 258), besides constructing satisfactory formulae for the barometrical determination of heights (Méc. cél. tom. iv. p. 324). His removal of the considerable discrepancy between the actual and Newtonian velocities of sound,[5] by taking into account the increase of elasticity due to the heat of compression, would alone have sufficed to illustrate a lesser name. Molecular physics also attracted his notice, and he announced in 1824 his purpose of treating the subject in a separate work. With A. Lavoisier he made an important series of experiments on specific heat (1782-1784), in the course of which the “ice calorimeter” was invented; and they contributed jointly to the Memoirs of the Academy (1781) a paper on the development of 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 light on an identical principle. It was a favourite idea of his that chemical 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 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 les plus intéressans du système du monde”—are embodied in the Mécanique céleste, and furnish one of the most remarkable proofs of his analytical genius. C. Maclaurin, Legendre and d’Alembert had furnished partial solutions of the problem, confining their attention to the possible figures which would satisfy the conditions of equilibrium. 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.
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 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 Théorie du mouvement et de la figure elliptique des planètes (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, Théorie des attractions des sphéroides et de la figure des planètes, 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.
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 function. 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. The expressions designated by Dr 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. Gauss in particular employed it in the calculation of the magnetic potential of the earth, and it received new light from Clerk Maxwell’s interpretation of harmonics with reference to poles on the sphere.
Laplace nowhere displayed the massiveness of his genius more conspicuously than in the theory of probabilities. The science which B. Pascal and P. de 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 Théorie analytique (1812) is to the best mathematicians a work requiring most arduous study. 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.