Electromagnetic Theory of Light, 83 



From (2), (4), and (5) we get 



A ( d f d 9\ d / dF da \ dc St /Q-X 



In the case of K constant, equation (8) expresses that the 

 electric displacement §(fdx + gdy) round a small circuit in 

 the plane of xy corresponds to the electromotive force round 

 the circuit, represented by dc' dt. 



Again, from (1), (2), (3), (6), (7), 



. (df 47rC ,\ d e d b e /n . 



From equations (8) and (9) the problem of reflection can be 

 investigated. In order to limit ourselves to plane waves of 

 simple type, we shall suppose that K, fj,, and C are indepen- 

 dent of z, and that the electric and magnetic functions are inde- 

 pendent of z and (as dependent upon the time) proportional to 

 e int . The two principal cases will be considered separately, 

 (1) when the electric displacements are perpendicular to the 

 plane of incidence, (2) when they are executed in that plane. 

 Case 1. This is defined by the conditions 



/=0, #=0, and (accordingly) c=0. 

 Thus 



ina=-tor±± inb = 4*±^ . . (10) 

 . /. 47rC\, d b da /11N 



Eliminating a and b from (10) and (11), we get 



d (1 d\ h , d /I d\h , — A, . 4ttC\ h A /10 . 



Case 2. Here the special conditions are 



7i=0, a=0, 6=0. 

 We have 



4 KJk-bI)=«. < 13 > 



whence by elimination of/ and g, 



d_ f 1 i-( c \\ 



dx\ Kn 2 (l-47T7i- 1 CK- 1 ) da\fi) ) 



+ dy{ Kn a (l-47m-»OK-0 dy(fy } + ^) = °- (15) 



G2 



