Pierre Simon Laplace (1749-1827)
Pierre-Simon Laplace, at the age of 16, entered Caen University. During his two years at the University of Caen, Laplace discovered his mathematical talents and his love of the subject. Once he knew that mathematics was to be his subject, Laplace left Caen without taking his degree, and went to Paris. He began producing a steady stream of remarkable mathematical papers.
Laplace's first paper which was to appear in print was one on the integral calculus. In 1771 Laplace sent a paper Recherches sur le calcul intégral aux différences infiniment petites, et aux différences finies to the Mélanges de Turin. This paper contained equations which Laplace stated were important in mechanics and physical astronomy.
Not only had he made major contributions to difference equations and differential equations but he had examined applications to mathematical astronomy and to the theory of probability, two major topics which he would work on throughout his life. His work on mathematical astronomy before his election to the Academy included work on the inclination of planetary orbits, a study of how planets were perturbed by their moons, and in a paper read to the Academy on 27 November 1771 he made a study of the motions of the planets which would be the first step towards his later masterpiece on the stability of the solar system. The 1780s were the period in which Laplace produced the depth of results which have made him one of the most important and influential scientists that the world has seen.
Laplace presented his famous nebular hypothesis in 1796 in Exposition du systeme du monde, which viewed the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas. The Exposition consisted of five books: the first was on the apparent motions of the celestial bodies, the motion of the sea, and also atmospheric refraction; the second was on the actual motion of the celestial bodies; the third was on force and momentum; the fourth was on the theory of universal gravitation and included an account of the motion of the sea and the shape of the Earth; the final book gave an historical account of astronomy and included his famous nebular hypothesis.
Exposition du systeme du monde was written as a non-mathematical introduction to Laplace's most important work Traité du Mécanique Céleste whose first volume appeared three years later. Laplace had already discovered the invariability of planetary mean motions. In 1786 he had proved that the eccentricities and inclinations of planetary orbits to each other always remain small, constant, and self-correcting. These and many other of his earlier results formed the basis for his great work the Traité du Mécanique Céleste published in 5 volumes, the first two in 1799.
The first volume of the Mécanique Céleste is divided into two books, the first on general laws of equilibrium and motion of solids and also fluids, while the second book is on the law of universal gravitation and the motions of the centers of gravity of the bodies in the solar system. The main mathematical approach here is the setting up of differential equations and solving them to describe the resulting motions. The second volume deals with mechanics applied to a study of the planets. In it Laplace included a study of the shape of the Earth which included a discussion of data obtained from several different expeditions, and Laplace applied his theory of errors to the results. In the Mécanique Céleste Laplace's equation appears but although we now name this equation after Laplace, it was in fact known before the time of Laplace.
The first edition of Laplace's Théorie Analytique des Probabilités was published in 1812. Later editions of the Théorie Analytique des Probabilités also contains supplements which consider applications of probability to: errors in observations; the determination of the masses of Jupiter, Saturn and Uranus; triangulation methods in surveying; and problems of geodesy in particular the determination of the meridian of France.
The fourth volume of the Mécanique Céleste appeared in 1805. This volume contains a study of pressure and density, astronomical refraction, barometric pressure and the transmission of gravity based on this new philosophy of physics.
After the publication of the fourth volume of the Mécanique Céleste, Laplace continued to apply his ideas of physics to other problems such as capillary action, double refraction, the velocity of sound, the theory of heat, in particular the shape and rotation of the cooling Earth, and elastic fluids.