144 The Aether as an Elastic Solid. 



the theory based on this supposition is known as Caucliy's 

 Second Theory : it was published in 1836.* 



In both theories, Cauchy imposes the condition that the 

 section of two of the sheets of the wave-surface made by any 

 one of the coordinate planes is to be formed of a circle and an 

 ellipse, as in Fresnel's theory ; this yields the three conditions 



3c = f(b + c +/) ; 3ca = g(c + a + g) ; Sab = h(a + b + Ji). 



Thus in the first theory we have these together with the 



equations 



= 0, H=Q, 1=0, 



which express the condition that the undisturbed state of the 

 aether is unstressed ; and the aethereal vibrations are executed 

 parallel to the plane of polarization. In the second theory we 

 have the three first equations, together with 

 f-Q-h-I-g-H; 



and the plane of polarization is interpreted to be the plane at 

 right angles to the direction of vibration of the aether. 



Either of Cauchy's theories accounts tolerably well for the 

 phenomena of crystal-optics; but the wave-surface (or rather 

 the two sheets of it which correspond to nearly transverse 

 waves) is not exactly Fresnel's. In both theories the existence 

 of a third wave, formed of nearly longitudinal vibrations, is a 

 formidable difficulty. Cauchy himself anticipated that the 

 existence of these vibrations would ultimately be demonstrated 

 by experiment, and in one placef conjectured that they might 

 be of a calorific nature. A further objection to Cauchy's 

 theories is that the relations between the constants do not 

 appear to admit of any simple physical interpretation, being 

 evidently assumed for the sole purpose of forcing the formulae 

 into some degree of conformity with the results of experiment. 

 And further difficulties will appear when we proceed subse- 

 quently to compare the properties which are assigned to the 

 aether in crystal- op tics with those which must be postulated in 

 order to account for reflexion and refraction. 



* Comptes Rendus, ii (1836), p. 341 : Mem. de 1'Acad. xviii (1839), p. 153. 

 f Mem. de 1'Acad. xviii, p. 161. 



