32 PHYSICS 



The wave-motion in an isotropic medium was first deduced by 

 Poisson in 1828, showing the occurrence of longitudinal and trans- 

 verse waves of different velocities; the general problem of wave- 

 motion in seolotropic media, though treated by Green (1842), was 

 attacked with requisite power by Blanchet (1840-1842) and by 

 Christoffel (1877). 



Poisson also treated the case of radial vibrations of a sphere (1828), 

 a problem which, without this restriction, awaited the solutions of 

 Jaerisch (1879) and of Lamb (1882). The theory of the free vibra- 

 tions of solids, however, is a generalization due to Clebsch (1857-58, 

 Vorlesungen, 1862). 



Elasticity received a final phenomenal advance through the long- 

 continued labors of de St. Venant (1839-55), which in the course of 

 his editions of the work of Moigno, of Navier (1863), and of Clebsch 

 (1864), effectually overhauled the whole subject. He was the first to 

 assert adequately the fundamental importance of the shear. The pro- 

 found researches of de St. Venant on the torsion of prisms and on the 

 flexure of prisms appeared in their complete form in 1855 and 1856. 

 In both cases the right sections of the stressed solids are shown to 

 be curved, and the curvature is succinctly specified; in the former 

 Coulomb's inadequate torsion formula is superseded, and in the latter 

 flexural stress is reduced to a transverse force and a couple. But 

 these mere statements convey no impression of the magnitude of 

 the work. 



Among other notable creations with a special bearing on the theory 

 of elasticity there is only time to mention the invention and applica- 

 tion of curvilinear coordinates by Lam6 (1852) ; the reciprocal the- 

 orem of Betti (1872), applied by Cerruti (1882) to solids with a plane 

 boundary problems to which Lame" and Clapeyron (1828) and 

 Boussinesq (1879-85) contributed by other methods; the case of 

 the strained sphere studied by Lame" (1854) and others; Kirchhoff's 

 flexed plate (1850); Rayleigh's treatment of the oscillations of 

 systems of finite freedom (1873); the thermo-elastic equations of 

 Duhamel (1838), of F. Neumann (1841), of Kelvin (1878); Kelvin's 

 analogy of the torsion of prisms with the supposed rotation of an 

 incompressible fluid within (1878); his splendid investigations 

 (1863) of the dynamics of elastic spheroids and the geophysical 

 applications to which they were put. 



Finally, the battle royal of the molecular school following Navier, 

 Poisson, Cauchy, and championed by de St. Venant, with the disciples 

 of Green, headed by Kelvin and Kirchhoff , the struggle of the fif- 

 teen constants with the twenty-one constants, in other words, 

 seems to have temporarily subsided with a victory for the latter 

 through the researches of Voigt (1887-89). 



