elasticity") in England, J. Binet in France, and G. A. A. Plana
in Italy, were chiefly occupied in extending and correcting the earlier labours. Between 1830 and 1840 the broad outline of the modern theory of elasticity was established. This was accomplished almost exclusively by French writers,–-Louis-Marie-Henri Navier (1785–1836), Poisson, Cauchy, Mademoiselle
Sophie Germain (1776–1831), Félix Savart (1791–1841).
Siméon Denis Poisson[]94 (1781–1840) was born at Pithiviers. The boy was put out to a nurse, and he used to tell that when his father (a common soldier) came to see him one day, the nurse had gone out and left him suspended by a thin cord to a nail in the wall in order to protect him from perishing under the teeth of the carnivorous and unclean animals that roamed on the floor. Poisson used to add that his gymnastic efforts when thus suspended caused him to swing back and forth, and thus to gain an early familiarity with the pendulum, the study of which occupied him much in his maturer life. His father destined him for the medical profession, but so repugnant was this to him that he was permitted to enter the Polytechnic School at the age of seventeen. His talents excited the interest of Lagrange and Laplace. At eighteen he wrote a memoir on finite differences which was printed on the recommendation of Legendre. He soon became a lecturer at the school, and continued through life to hold various government scientific posts and professorships. He prepared some 400 publications,
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