The Aether as an Elastic Solid. 145 



To the latter problem Cauchy soon addressed himself, his 

 investigations being in fact published* in the same year (1830) 

 as the first of his theories of crystal-optics. 



At the outset of any work on refraction, it is necessary to 

 assign a cause for the existence of refractive indices, i.e. for the 

 variation in the velocity of light from one body to another. 

 Huygens, as we have seen, suggested that transparent bodies 

 consist of hard particles which interact with the aethereal matter, 

 modifying its elasticity- Cauchy in his earlier papersf followed 

 this lead more or less closely, assuming that the density p of the 

 aether is the same in all media, but that its rigidity n varies 

 from one medium to another. 



Let the axis of x be taken at right angles to the surface of 

 separation of the media, and the axis of z parallel to the inter- 

 section of this interface with the incident wave-front; and 

 suppose, first, that the incident vibration is executed at right 

 angles to the plane of incidence, so that it may be represented 

 .by 



e~ = /( - x cos i -y sin i + rL t \ 



where i denotes the angle of incidence ; the reflected wave may 

 be represented by 



e z = FX cos i - y sin i + t 

 V \/ 



and the refracted wave by 



e z = fi I x cos r y sin r + KLt\ 



where r denotes the angle of refraction, and n' the rigidity of 

 the second medium. 



To obtain the conditions satisfied at the reflecting surface, 

 Cauchy assumed (without assigning reasons) that the x- and 

 ^/-components of the stress across the #y-plane are equal in 



* Bull, des Sciences Math. xiv. (1830), p. 6. 



t As will appear, his views on this subject subsequently changed. 



L 



