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 to investigate the conditions for equilibrium of a spherical elastic envelope subject to a given distribution of load on the bounding spherical surfaces, and the determination of the resulting shifts is the only completely general problem on elasticity which can be said to be completely solved. He deserves much credit for his derivation and transformation of the general elastic equations, and for his application of them to double refraction. Rectangular and triangular membranes were shown by him to be connected with questions in the theory of numbers. The field of photo-elasticity was entered upon by Lamé, F. E. Neumann, Clerk Maxwell. Stokes, Wertheim, R. Clausius, Jellett, threw new light upon the subject of "rari-constancy" and "multi-constancy," which has long divided elasticians into two opposing factions. The uni-constant isotropy of Navier and Poisson had been questioned by Cauchy, and was now severely criticised by Green and Stokes.

Barré de Saint-Venant (1797–1886), ingénieur des ponts et chaussées, made it his life-work to render the theory of elasticity of practical value. The charge brought by practical engineers, like Vicat, against the theorists led Saint-Venant to place the theory in its true place as a guide to the practical man. Numerous errors committed by his predecessors were removed. He corrected the theory of flexure by the consideration of slide, the theory of elastic rods of double curvature by the introduction of the third moment, and the theory of torsion by the discovery of the distortion of the primitively plane section. His results on torsion abound in beautiful graphic illustrations. In case of a rod, upon the side surfaces of which no forces act, he showed that the problems of flexure and torsion can be solved, if the end-forces are distributed over the end-surfaces by a definite law. Clebsch, in his Lehrbuch der Elasticität, 1862, showed that this problem is