and Electromagnetic Theory. 319 



l"u + m"v + n"w or U". The comparison of arguments 

 gives 



pl p"l" pm p"m" J ™\»(, vn").') 



and then ^-^/'(l- ^) i 



follows by combining the other ratios. The correspondence 

 of p and p r/ is the same whether deduced from agreement at 

 a moving point or surface. If the ratio p : p" is eliminated, 



(l-n 2 )l{Y-ivny={l-n /f2 )l{D,-.wn"y, -. 



or (l-n a )/(V-U) 2 =(l-n W3 )/(a-U ,, ) 2 .J ^ 



An azimuthal angle <£ (1= \l — ri 2 cos (f>) is the same for 

 both waves, this fact and (10) together constituting the law 

 of refraction. Since <f) is the same for both waves it may be 

 ignored in forming the differentials of (10), and we take 

 account of the dependence of V\ m" on n" by writing 



dl" -n"dn" dm" 



H 



ence 



or 



1-n' 



^tf^^tudl", 

 (l-n //2 )dn=^ 7 (w-n"W)dri 



and the differential of (10) yields 



Either form of (10) may be used, and the denominators 

 here may be replaced by (V — wn) B and (H— wn"y. The 

 numerators contain a differential and a velocity of transit, 

 and d<b may be appended to each side. [If Q, is defined as a 

 function of l'm"n!' without reference to U", the transit- 

 form is 



With FresneFs modification, which is used throughout, 



