166 Mr. J. Walker on Cauchy's Theory of 



Haughton's* suggestion that the coefficient of compressi- 

 bility is very great, but not infinite, does not help matters ; 

 so that it would appear that the only way to escape the diffi- 

 culty is by one of Lord Rayleigh'sf suggestions : — ■ 



(1) That "although the transition between the two media 

 is so sudden that the principal waves of transverse vibrations 

 are affected nearly in the same way as if it were instantaneous, 

 yet we may readily imagine that the case is different for the 

 surface-waves, whose existence is almost confined to the layer 

 of variable density." 



(2) That " the densities concerned in the propagation of the 

 so-called longitudinal waves are unknown, and may possibly not 

 be the same as those on which transverse vibrations depend." 



Eisenlohr % gives another (it appears entirely empirical) 

 value for M : it involves, as Cauchy's, a negative value for 

 the coefficient compressibility of the aether, and leads to 

 formulae closely agreeing with experiment; as, however, they 

 contain a third disposable constant, this close agreement is 

 hardly to be wondered at. 



V. 



Cauchy's formulae for metallic reflection were originally 

 published on April 15, 1839 §, and thus were obtained from his 

 second set of equations of condition, in which the pressural 

 waves "were neglected. The formulae were republished on 

 January 17, 1848 1|, and apparently no attempt was made to 

 obtain equations in which the influence of the pressural waves 

 was included. 



Cauchy considers the peculiarities of metallic reflection to 

 be due to a complex value of the refractive index. 



Writing 



we get 



4-7T 2 



2e^-l 



sin 2 - 



. N 4tt 2 



IP 



e 2uV- 



"S sa y; 





whence 







: COt 6 COS 



(2 tan" 



jsinn 





U 2 sin2w=0 2 sin2e, 



cot 2u 



— 6 = 



(12) 



Substituting 

















A, 



=r, a-- 



2tt 



COS 2, b 





2tt . . 

 — sin i, 





* Phil. Mag. [4] vi. p. 81. t Ibid. xlii. pp. 96, 97. 



% Fogg. Ann. civ. p. 356. § C. i?. viii. p. 553. 



|| Ibid. xxvi. p. 86. 



