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
form which the formulæ undergo when we allow for changes of temperature. Weber was also the first to experiment on elastic after-strain. Other important experiments were made by different scientists, which disclosed a wider range of phenomena, and demanded a more comprehensive theory. Set was investigated by Gerstner (1756–1832) and Eaton
Hodgkinson, while the latter physicist in England and Vicat
(1786–1861) in France experimented extensively on absolute strength. Vicat boldly attacked the mathematical theories of flexure because they failed to consider shear and the time-element.
As a result, a truer theory of flexure was soon propounded by Saint-Venant. Poncelet advanced the theories of
resilience and cohesion.
Gabriel Lamé[]94 (1795–1870) was born at Tours, and graduated
at the Polytechnic School. He was called to Russia with Clapeyron and others to superintend the construction of bridges and roads. On his return, in 1832, he was elected professor of physics at the Polytechnic School. Subsequently he held various engineering posts and professorships in Paris. As engineer he took an active part in the construction of the first railroads in France. Lamé devoted his fine mathematical talents mainly to mathematical physics. In four works: Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes; Sur les coordonnées curvilignes et leurs diverses applications; Sur la théorie analytique de la chaleur; Sur la théorie mathématique de l'élasticité des corps solides (1852), and in various memoirs he displays fine analytical powers; but a certain want of physical touch sometimes reduces the value of his contributions to elasticity and other physical subjects. In considering the temperature in the interior of an ellipsoid under certain conditions, he employed functions analogous to Laplace's functions, and known by the name of "Lamé's functions."
A problem in elasticity called by Lamé's name, viz.
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