Laplace, Pierre Simon, marquis de

Born Mar. 23, 1749, in Beaumont-en-Auge, Normandy; died Mar. 5, 1827, in Paris. French astronomer, mathematician, and physicist. Member of the Paris Academy of Sciences (1785; adjunct, from 1773) and member of the Académie Française (1816).

Laplace studied at a Benedictine school, which he left, however, as a confirmed atheist. In 1766 he went to Paris, where after five years J. D’Alembert helped him obtain a professorship at the École Militaire. Laplace was active in the reorganization of the system of higher learning in France and in the founding of the Ecole Normale and École Polytechnique. Appointed chairman of the Commission of Weights and Measures in 1790, he directed the introduction of the new metric system of measures. In 1795 he joined the staff of the Bureau of Longitudes.

Laplace’s scientific heritage lies in celestial mechanics, mathematics, and mathematical physics. His studies on differential equations, particularly on the integration of partial differential equations by the “cascade” method, are fundamental. Spherical harmonics, introduced by Laplace, have a variety of applications. In algebra, Laplace derived an important theorem of representing determinants by the sum of the products of the complementary minors. In order to develop further the mathematical theory of probability that he originated, Laplace introduced generating functions and widely used the transformation that bears his name (Laplace transform). The theory of probability became the basis of the study of different statistical laws, particularly in the natural sciences. Laplace’s efforts along these lines were preceded by those of B. Pascal, P. Fermat, and Jakob Bernoulli, among others. Laplace reduced their results to a system and perfected methods of proofs, making them less cumbersome. He also proved the theorem that bears his name and developed the theory of errors and the method of least squares, which made it possible to find the most probable values of measured quantities and to ascertain the degree of reliability of these computations. His classical work Théorie analytique des probabilités was reprinted three times during his lifetime (1812, 1814, 1820). The work Essai philosophique sur les probabilités (1814), in which he explained the primary propositions and significance of the theory of probability to the general reader, was the Introduction in the last two printings.

From 1779 to 1784, Laplace worked with A. Lavoisier in physics. Together they investigated the latent heat of fusion of bodies and conducted studies using an ice calorimeter that they had designed. They were the first to use an optic tube to measure the linear expansion of bodies; they also studied the combustion of hydrogen in oxygen. Laplace actively opposed the fallacious phlogiston theory. Subsequently returning to physics and mathematics, he published a number of works on the theory of capillarity and established the law that bears his name. In 1809 he turned to problems in acoustics and derived a formula for the velocity of propagation of sound in air. Laplace also derived the barometric formula for calculating the change in air density with height above the surface of the earth, taking into account the effects of the air humidity and the variation in free-fall acceleration. He also conducted studies in geodesy.

Laplace developed the methods of celestial mechanics and nearly completely explained the motions of the bodies of the solar system on the basis of Newton’s law of universal gravitation, something his predecessors had not been able to accomplish. He succeeded in showing that the law of universal gravitation completely accounts for the motion of these planets if their mutual perturbations are represented in the form of series. He also proved that these perturbations are periodic. In 1780, Laplace proposed a new method for calculating the orbits of celestial bodies. His studies demonstrated the stability of the solar system over a long period of time. Laplace later concluded that the rings of Saturn could not be a uniform solid body, since in this case they would be unstable, and predicted that Saturn would prove to be highly compressed at the poles. In 1789 he examined the theory of the motion of Jupiter’s satellites under the effects of mutual perturbations and attraction by the sun. He found complete agreement between theory and observation and established a number of laws of these motions.

One of Laplace’s greatest achievements was the discovery of the cause of the acceleration of the moon’s motion. In 1787 he showed that the mean motion of the moon depends on the eccentricity of the earth’s orbit and that the latter varies as a result of the attraction between planets. He proved that this perturbation was not secular but a long-period one and that the moon would in the future move with negative acceleration. Laplace determined the magnitude of the earth’s compression at the poles from inequalities in the moon’s motions. He also developed the dynamic theory of tides. Celestial mechanics is greatly indebted to Laplace’s studies, which were summed up by him in the classical work Traité de mécanique céleste (vols. 1–5, 1798–1825).

Of great philosophical importance was Laplace’s cosmogonic hypothesis, which he expounded in the Appendix to his book Exposition du système du monde (vols. 1–2, 1796).

In his philosophical views Laplace agreed with the French materialists; his reply to Napoleon that he did not need a hypothesis about the existence of god in his theory of the origin of the solar system is well known. The limitations of his mechanistic materialism are apparent in his attempt to explain the entire world, including physiological, psychological, and social phenomena, from the standpoint of mechanistic determinism. He considered his conception of determinism as the methodological principle for the construction of any science. Laplace viewed celestial mechanics as a model of the definitive form of scientific knowledge. Laplacian determinism has become synonymous with the mechanistic methodology of classical physics.

Laplace’s materialistic world view, clearly expressed in his scientific works, contrasted with his political instability. With each political upheaval, Laplace switched to the victorious side. At first he was a republican; then, after Napoleon came to power, he was minister of the interior. Subsequently, he was made a member and vice-president of the Senate. Under Napoleon he received the title of count of the empire. In 1814 he supported the deposition of Napoleon and, after the restoration of the Bourbons, received a peerage and the title of marquis.