94 The Hon. J. W. Strutt on the Reflection of 



sudden as we have hitherto considered it, occupies a distance not 

 immeasurably less than the wave-length, — certainly a very rea- 

 sonable supposition. But there are two objections to his view 

 which are, to my mind, fatal. In the first place, FresneVs tangent- 

 formula does not express the result of a sudden transition ; and 

 what is more, Green's formula (17), which does express it, de- 

 viates from the truth on the other side. The difficulty is not to 

 explain why Fresnel's formula is not accurately correct, but why 

 the divergences from it are not greater than we actually find 

 them. According to (17), the light reflected at the polarizing 

 angle from the diamond or any other substances of high refrac- 

 tive index would be a very considerable fraction of the whole, 

 very much greater than what is observed. Another objection to 

 the view that the light reflected at the polarizing angle is due to 

 the want of abruptness in the transition, seems to be contained 

 in the consideration that, if this were really its origin, it ought 

 to show a colour corresponding to the blue of the first order in 

 Newton's scale, being to all intents and purposes reflected from 

 a thin plate. Observation, so far as I am aware, gives no sup- 

 port to such an idea. 



Cauchy' s formulae, which differ from (15), (16), (17) merely 

 by the substitution of — esin# for M, agree very well with ex- 

 periment ; but I cannot regard them as having a sound dyna- 

 mical foundation. The introduction of evanescent waves of the 

 kind used by Cauchy involves, as Lorenz remarks, a theory of 

 imperfectly elastic media. But the case is even worse than this ; 

 for it may, I believe, be shown that no reasonable theory could 

 lead to the peculiar form of evanescence assumed by Cauchy. 

 Let us examine this point. 



If, in the investigation of Cauchy's formulae as given by Beer, 

 we introduce the functions (f> and ^ used by Green, we find that 

 <£> is still expressed by an exponential function of the same form 

 as before, viz € K*'*+h+ct) a The only difference is that, whereas 

 in Green's theory « /2 + 6 2 =c 2 -=-^ 2 , the relation between a', b, c, 

 according to Cauchy, is 



a>* + b*=-k*, ...... (20) 



where k is the so-called coefficient of extinction. The working 

 out is nearly the same as before. Instead of (8) we have 



Again, since, according to Cauchy's principle, m ] — m!n ] — n i 

 (9') becomes, in virtue of (20), 



***-*,**„ "• • (22) 



