164 REPORT—1885. 
Chapter ITI.—Cavucay. 
§ 1. Cauchy’s optical researches were being published about this 
same period, and a very full and interesting account of them, and of the 
work of other French authors, is given by M. de St. Venant in a paper to 
which I am greatly indebted for much valuable information.' 
Canchy’s work on elastic solids began in 1822, and in 1829 he pre- 
sented to the Academy his first memoir on isotropic media. His more 
generally known memoir followed in 1830,” containing his work on 
double refraction and the propagation of light in a crystal. An account 
of this is given in Professor Stokes’s report in 1862, His first work on 
dispersion, which he explained (following a suggestion of Coriolis) by the 
addition of terms involving differential coefficients above the second, was 
published in 1830.3 The great memoir, ‘Sur la dispersion de la 
lumiére,’ in which he developed this principle, appeared between 1830 and 
1836 ;4 and in this same memoir he first considered the problem of reflexion 
and refraction, which led him to the idea of elliptic polarisation and 
a more general expression for the possible displacements of a molecule 5 
in a plane wave. 
§ 2. Further considerations on the subject of reflexion and refraction 
led him to conclude that, in order to obtain Fresnel’s expressions for the 
intensities of the reflected and refracted rays in terms of that of the 
incident, it was necessary that not only the displacements, but their 
differential coefficients with respect to the normal to the surface of 
separation, should be continuous across that surface. This continuity 
had to be rendered compatible with the rest of his theory, in which the 
ether is considered as differing both in density and elasticity in different 
media. It is, however, quite inconsistent with the true surface con- 
ditions established by Green, Neumann, and MacCullagh on their various 
hypotheses—the conditions, namely, that the displacements and the stresses. 
over the surface should be the same in the two media; and Cauchy, in con- 
sequence, was led to conclude that the method of Lagrange, by which the 
above conditions were first established, is inapplicable to questions of this 
kind.? But, as St. Venant points out, these surface conditions do not in 
the least depend on Lagrange’s method of virtual velocities, but on the 
fundamental elementary principles of mechanics, and can never be recon- 
ciled with Canchy’s theory of continuity so long as it is supposed that 
the rigidity of the ether varies from one body to another. 
§ 3. In 18398 Cauchy re-established his equations of motion for an 
isotropic medium, basing them on analytical considerations of symmetry- 
For a perfectly isotropic body he arrived at the equations— 
du dé 
bee pes 2, 
Pag = (A B)_ + By*u : t - (13) 
pt) du dw dw 
&c., where SH TGR R, 
1 De St. Venant, ‘Sur les diverses maniéres de présenter la théorie des ondes 
lumineuses,’ Ann. de Chimie (S. iv.), t. xxv. p. 335. 
2 Cauchy, Ewercices de Mathématiques, t. v. pp. 19-72. 
3 Cauchy, Bulletin de M. de Ferussac, t. xv. p. 9. 
4 Nouveaux Exercices de Mathematiques. 5 C, R. t. vii. p. 867. 
6° C. R.t. viii. p. 374; t. x. p. 266. 
1 GC. R. t. xxvii. p. 100; t. xvi. p. 154; t. xxviii. pp. 27, 60. 
2 C. R. t. viii. p. 985; Evercices d@ Analyse, t. i. p. 101. 
