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



These equations express Cauchy's principle of the continuity 

 of the motion of the aether, according to which the incident 

 wave passes into the reflected and refracted waves " sans 

 transition brusque." 



Judging from the historical sequence of Cauchy's papers, 

 there can be little doubt that he enunciated this principle as 

 the physical interpretation of the result arrived at by reason- 

 ing analogous to the above ; it is, however, impossible to 

 agree with v. Ettingshausen that " Cauchy hat diese Gleich- 

 ungen (6) anfanglich aus Griinden gerechtfertigt, die sich 

 auf das Yerfahren der Variationen der Constanten zuriick- 

 fuhren lassen ;" * as the principle is already involved in the 

 assumption (5)f. 



All that the above analysis really leads to, and all that 

 Cauchy t claimed to have established by it, is the necessity for 

 including the pressural waves in the problem of reflection and 

 refraction. 



Since the true dynamical equations of condition, given by 

 the equality of displacements and pressures, are that for # = 0, 



r=i, v=j, f=?, 



(m — n)S + 2n-j- == ( m' — n')B' + 2n'— > > (7) 



(f+gMf+l). <MmM)J 



it is clear, as has been often pointed out, that Cauchy's 

 assumption involves that of the identity of the statical pro- 

 perties of the aether in the two media. Lundquist§, however, 

 considers that " Cauchy has established his principle of con- 

 tinuity by the aid of analysis, the exactitude of which it is 

 not easy to contest ;" and hence that this result, combined 

 with the dynamically exact conditions (7), proves " the legiti- 

 macy of Green's assumption of the equality of the compres- 

 sibility and the rigidity of the aether in the two media.'"' 

 Cauchy himself did not see that this was involved in his 



* Sitzb. der Wien. Akad. xviii. p. 371. 



t I do not think Cauchy contemplated a continuous rapid transition 

 of one medium into the other (cf. C. R. x. p. 347) ; neither does 

 v. Ettingshausen in his paper. Supposing the assumption justified on 

 these grounds, yet, as von der Miihl has pointed out, the former assump- 

 tion respecting the coefficients of the additional terms in the modified 

 equations precludes the assumption of a finite change in the statical pro- 

 perties of the media {Matt. Ann. v. p. 477). 



% C. H. x. p. 347. ' § Pogg. Ann. clii. p. 185. 



