172 Reflection and Refraction of Light. 



azimuth with respect to the plane of incidence given by 



sin 1 n 



tan /3 = tan 2i . 



M 



VII. 



In the same year (1850) Cauchy extended his method to 

 the problem of crystalline reflection : the complete solution 

 was given in a memoir presented to the French Academy on 

 September 16, 1850*. 



This memoir was never published, though it was announced! 

 to appear in the 23rd volume of the Memoir es cle VAcademie ; 

 and we have only slight indications of Cauchy 's manner of 

 dealing with the problem. 



In accordance with the results of his theory of double 

 refraction, Cauchy does not suppose the vibrations to be 

 necessarily strictly transversal and longitudinal J. In order 

 to eliminate the amplitudes of the latter vibrations, he assumes 

 as an approximation the strict transversality of the former, 

 and thus obtains § four equations between the quasi-transversal 

 amplitudes, which contain three coefficients, whose values are 

 known when coordinate axes are taken depending on the re- 

 fracting surface and the plane of incidence. 



A second memoir || is devoted to the determination of the 

 value of these coefficients, when fixed directions in the crystal 

 are taken as the axes. The value of this determination is 

 lessened by the fact, that at the very commencement an 

 approximation is made depending on the peculiar relation 

 between the coefficients of elasticity, which we have considered 

 above. 



This is all that has been published, except some notes indi- 

 cating a few of the results of his analysis ; it is, however, 

 probable^ that Cauchy first obtained a solution on the assump- 

 tion of the strict transversality of the luminous vibrations, 

 and then proceeded to apply corrections to the values thus 

 obtained, and it is possible** that he adopted in the solution 

 MacCullagh's idea of uniradial directions. 



There is no need to enter further into this part of Cauchy's 

 work, as Briotff has employed both these methods in his excel- 

 lent adaptation of Cauchy's theory to the problem of Crystalline 

 Reflection. 



* a JR. xxxi. p. 422. f Tom. cit. p. 509. 



% Tom. cit. pp. 258, 299. § Tom. cit. p. 257. 



|| Tom. cit. p. 297. If Tom. cit. p. 160. 



** Tom. cit. p. 532. ft Liouv. Jmirn. [2] xii. p. 185. 



