mainly on applied mathematics. His Traité de Mécanique, 2 vols., 1811 and 1833, was long a standard work. He wrote on the mathematical theory of heat, capillary action, probability of judgment, the mathematical theory of electricity and magnetism, physical astronomy, the attraction of ellipsoids, definite integrals, series, and the theory of elasticity. He was considered one of the leading analysts of his time.
His work on elasticity is hardly excelled by that of Cauchy, and second only to that of Saint-Venant. There is hardly a problem in elasticity to which he has not contributed, while many of his inquiries were new. The equilibrium and motion of a circular plate was first successfully treated by him. Instead of the definite integrals of earlier writers, he used preferably finite summations. Poisson's contour conditions for elastic plates were objected to by Gustav Kirchhoff of Berlin, who established new conditions. But Thomson and Tait in their Treatise on Natural Philosophy have explained the discrepancy between Poisson's and Kirchhoff's boundary conditions, and established a reconciliation between them.
Important contributions to the theory of elasticity were made by Cauchy. To him we owe the origin of the theory of stress, and the transition from the consideration of the force upon a molecule exerted by its neighbours to the consideration of the stress upon a small plane at a point. He anticipated Green and Stokes in giving the equations of isotropic elasticity with two constants. The theory of elasticity was presented by Gabrio Piola of Italy according to the principles of Lagrange's Mécanique Analytique, but the superiority of this method over that of Poisson and Cauchy is far from evident. The influence of temperature on stress was first investigated experimentally by Wilhelm Weber of Göttingen, and afterwards mathematically by Duhamel, who, assuming Poisson's theory of elasticity, examined the alterations of
