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



These relations give 



V (^m + rc) sm z z V e z sin' 1 ^ e sin i 



€ smr 

 Hence 



M= _ = esini — € f sinr = E sin i. 



2 e 2 1 1 



e z e sin i e sm r 

 if E = e--*. 



No attempt has been made, so far as 1 am aware, to indi- 

 cate the reasons which led to Cauchy's adoption of the above 

 remarkable relations between the coefficients of compressibility 

 and rigidity of the aether in a medium. 



In order to find a relation between the coefficients, Canchy 

 considered the condition which must be fulfilled if the 

 incident light is completely polarized by reflection. 



This condition is that M = 0, giving since 



/Vfy/ + u " l ~" u n u " ' 

 where u in u" are both positive, that 



ii P P' 



11,,= u", or — = —7— — ,. 



" m + n m' + n 



In his first memoir on the subject, Cauchyj, forgetting to 

 take into account the fact of the media being on different sides 

 of the plane of yz, wrote 



where u u is positive. 

 Hence he obtained 



M= Mo*- 1 = ?/ 7/ + ^' 



where u u , u n are both positive, giving as the condition for 

 complete polarization 



u n = u n = co , or m + n = = m' + n'. 



* C. R. xxviii. p. 64. Originally Cauchy took e = 0. 

 t Ibid. ix. p. 94. Ex. $ An. et de Phys. i. p. 167. 



