Laplace's investigations in physics were quite extensive. We mention here his correction of Newton's formula on the velocity of sound in gases by taking into account the changes
of elasticity due to the heat of compression and cold of rarefaction;
his researches on the theory of tides; his mathematical
theory of capillarity; his explanation of astronomical refraction;
his formulæ for measuring heights by the barometer.
Laplace's writings stand out in bold contrast to those of Lagrange in their lack of elegance and symmetry. Laplace
looked upon mathematics as the tool for the solution of physical problems. The true result being once reached, he spent little time in explaining the various steps of his analysis, or in polishing his work. The last years of his life were spent mostly at Arcueil in peaceful retirement on a country-place, where he pursued his studies with his usual vigour until his death. He was a great admirer of Euler, and would often
say, "Lisez Euler, lisez Euler, c'est notre maître à tous."
Abnit-Théophile Vandermonde (1735–1796) studied music during his youth in Paris and advocated the theory that all art rested upon one general law, through which any one could become a composer with the aid of mathematics. He was the first to give a connected and logical exposition of the theory of determinants, and may, therefore, almost be regarded as the founder of that theory. He and Lagrange originated the method of combinations in solving equations.20
Adrien Marie Legendre (1752–1833) was educated at the
Collège Mazarin in Paris, where he began the study of mathematics under Abbé Marie. His mathematical genius secured
for him the position of professor of mathematics at the military school of Paris. While there he prepared an essay on the curve described by projectiles thrown into resisting media (ballistic curve), which captured a prize offered by the Royal
Academy of Berlin. In 1780 he resigned his position in order to reserve more time for the study of higher mathematics. He was then made member of several public commissions. In 1795 he was elected professor at the Normal School and later was appointed to some minor government positions. Owing to his timidity and to Laplace's unfriendliness toward
him, but few important public offices commensurate with his ability were tendered to him.
As an analyst, second only to Laplace and Lagrange, Legendre
enriched mathematics by important contributions, mainly on elliptic integrals, theory of numbers, attraction of ellipsoids, and least squares. The most important of Legendre's works is his Fonctions elliptiques, issued in two volumes in 1825 and 1826. He took up the subject where Euler, Landen,