r i5i 



XX. An Account 0/ Cauchy's Theory of Reflection and Refrac- 

 tion of Light. By James Walker, M.A., Demonstrator at 

 the Clarendon Laboratory, Oxford*. 



rj^HE theory of reflection and refraction of light holds such 

 JL an important place among the problems of Optics which 

 await their solution that it is advantageous to have a clear 

 idea of the work which has been previously done in the subject. 



The theory advanced by Green has been so thoroughly 

 discussed by Lord Rayleigh and Sir W. Thomson that all 

 questions connected with it may be considered as completely 

 settled. But this is by no means the case with Cauchy's 

 work on the subject; and some account of it may be of in- 

 terest, even though the theory cannot be said to contribute 

 much towards a solution of the problem. 



Several " reproductions "f of Cauchy's work have indeed 

 appeared in French and German, but in most of them the 

 elegance, and therewith the clearness, of Cauchy's method 

 have been given up ; while they leave in more or less ob- 

 scurity the reasoning which led him to enunciate his "principle 

 of continuity," and make no mention of a point of considerable 

 interest, viz. the mistake which originally led to his adoption 

 of a theory involving the strange assumption of a negative 

 value for the coefficient of compressibility of the aether. 



I. 



Cauchy, at different periods, gave three distinct theories of 

 reflection : the first two, however, require only a passing- 

 notice, as they were afterwards rejected by him as in no 

 respect affording a complete solution of the problem. 



The first theory was published in the Bulletin de Ferussac 

 of 1S30. It rested on the true dynamical basis of the equality 

 of pressures^ at the interface of the media ; but was vitiated 

 by the neglect of the pressural waves, which must take part 

 in the act of reflection and refraction. The method led, on 

 the assumption of the equality of the density of the aether in 

 the two media, to the formulae given by Fresnel § . 



The second theory was based on a method of obtaining the 



* Communicated by the Physical Society : read December 11, 1886. 



t A. v. Ettingshausen, Pogg. Ann. 1. p. 409 ; Sitzb. der Wien. Akad. 

 xviii. p. 369. Beer, Pogg. Ann. xci. pp. 268, 467, 561 ; xcii. p. 402. 

 Eisenlolir, Pogg. Ann. civ. p. 346. Briot, Liouv. Journ. (2nd) xi. p. 305 ; 

 xii. p. 185. Lundquist, Pogg. Ann. clii. pp. 177, 398, 565. 



t Cauchy's reasons for rejecting the principle of the equality of pres- 

 sures at the interface are given in Comptes Rendus, xxviii. p. 60. 



§ Cauchy, Memoire sur la Dispersion, § 10. 



