456 M. E. Jochmann on the Reflection and Refraction 

 For A= oo, D = 0, we obtain 



which are Cauchy's formulae. The symbol lim. signifies that 

 with increasing thickness d llt and b Ui approach the given limiting 

 form, A constant limiting value is only present in the limiting 



case (to be hereafter discussed) e= — . 



Systems I. and II. are essentially characterized by the peculiar 

 connexion between the periodic and the exponential functions. 

 The influence of the one or the other preponderates according to 

 the value of the quantity e-\-u, which agrees with twice the value 

 of the so-called " principal azimuth " of the elliptical polariza- 

 tion. That is to say, the value of the ratio 



— natlogD / . x 



Y — - — = tan (e + u) 



depends on this quantity. The angle e may vary between the 



limits and =r« 

 ,<? 



1. The limiting case e = corresponds to transparent media. 



In consequence of the relations subsisting between the quantities 



7T 



s i) c v € > u i then u = or u=-, according to whether s 2 <:l or 



s 2 >\. The case e = 0, w = 0, D = l, furnishes the known for- 

 mulae for ordinary reflection and refraction by transparent lamellae, 

 from which the exponential functions have vanished. 



T 



The case e=0, u— ~, from which follows L = 0, corresponds 



to reflection by a thin transparent lamella, for which the limiting 

 angle has passed beyond the total reflection. Yet, as is known 

 from the observations of Newton, Stokes, and Quincke, with 

 sufficiently small values of A light can pass from the first into 

 the third medium. In fact, according to the fundamental prin- 

 ciples of Cauchy's theory of reflection, in a very thin layer on 

 the other side of the bounding surface of the totally reflecting 

 medium a motion of the aether takes place which is analo- 

 gous to that in the superficial layer of metallic media, and can 

 be regarded as a limiting case of it. By the insertion of the 

 abo/e values for e and u } formulae I. and 1L, if we put 



