158 The Aether as an Elastic Solid. 



The work of Green proved a stimulus not only to 

 MacCullagh but to Cauchy, who now (1839) published yet 

 a third theory of reflexion.* This appears to have owed its 

 origin to a remark of Green's, f that the longitudinal wave 

 might be avoided in either of two ways namely, by supposing 

 its velocity to be indefinitely great or indefinitely small. Green 

 curtly dismissed the latter alternative and adopted the former, 

 on the ground that the equilibrium of the medium would be 

 unstable if its compressibility were negative (as it must be if 

 the velocity of longitudinal waves is to vanish). Cauchy, without 

 attempting to meet Green's objection, took up the study of a 

 medium whose elastic constants are connected by the equation 



k + n = 0, 



so that the longitudinal vibrations have zero velocity; and showed 

 that if the aethereal vibrations are supposed to be executed at 

 right angles to the plane of polarization, and if the rigidity 

 of the aether is assumed to be the same in all media, a ray 

 which is reflected will obey the sine-law and tangent-law of 

 Fresnel. The boundary-conditions which he adopted in order to 

 obtain this result were the continuity of the displacement e and 

 -of its derivate 3e/9#, where the axis of x is taken at right 

 angles to the interface.* These are not the true boundary-con- 

 ditions for general elastic solids ; but in the particular case now 

 under discussion, where the rigidity is the same in the two 

 media, they yield the same equations as the conditions correctly 

 given by Green. 



The aether of Cauchy's third theory of reflexion is well 

 worthy of some further study. It is generally known as the y 

 .contractile or labile^ aether, the names being due to William 



* Comptes Rendus, ix, p. 676 (25 NOT., 1839), and p. 726 (2 Dec., 1839). 



t Green's Math. Papers, p. 246. 



J Comptes Eendus, x, p. 347 (March 2, 1840) : xxvii, p. 621 (1848) ; sxviii, p. 25 

 (1849). Mem. de 1'Acad., xxii (1848), pp. 17, 29. 



Labile or neutral is a term used of such equilibrium as that of a rigid body oil 

 -a perfectly smooth horizontal plane. 



