The Aether as an Elastic Solid. 147 



reject the first theory of crystal-optics in favour of the second. 

 After 1836 he consistently adhered to the view that the vibra- 

 tions of the aether are performed at right angles to the plane of 

 polarization. In that year he made another attempt to frame a 

 satisfactory theory of reflexion,* based on the assumption just 

 mentioned, and on the following boundary-conditions: At 

 the interface between two media curl e is to be continuous, and 

 (taking the axis of x normal to the interface) de x /dx is also to 

 be continuous. 



Again we find no very satisfactory reasons assigned for the 

 choice of the boundary- conditions ; and_as the continuity of e 

 itself across the interface is not included amongst the conditions 

 cHosen, they are obviously open to criticism ; but they lead to 

 Fresnel's sine- and tangent-equations, which correctly express 

 the actual behaviour of light. f Cauchy remarks that in order to 

 justify them it is necessary to abandon the assumption of his 

 earlier theory, that the density of the aether is the same in all 

 material bodies. 



It may be remarked that neither in this nor in Cauchy's 

 earlier theory of reflexion is any trouble caused by the appear- 

 ance of longitudinal waves when a transverse wave is reflected, 

 for the simple reason that he assumes the boundary-conditions to 

 be only four in number ; and these can all be satisfied without 

 the necessity for introducing any but transverse vibrations. 



These features bring out the weakness of Cauchy's method of 

 attacking the problem. His object was to derive the properties 

 of light from a theory of the vibrations of elastic solids. At the 

 outset he had already in his possession the differential equations 

 of motion of the solid, which were to be his starting-point, and 

 the equations of Fresnel, which were to be his goal. It only 



* Comptes Rendus, ii. (1836), p. 341 : " Meraoire sur la dispersion delalumiere " 

 (Nouveaux exercices de Math., 1836), p. 203. 



t These boundary -conditions of Cauchy's are, as a matter of fact, satisfied by 

 the electric force in the electro-magnetic theory of light. The continuity of 

 <;url e is equivalent to the continuity of the magnetic vector across the interface, 

 and the continuity of (tex/dx leads to the same equation as the continuity of 

 the component of electric force in the direction of the intersection of the 

 interface with the plane of incidence. 



L 2 



