Electrodynamics for Moving Ponderable Media. 53 



■orl'E'—f, 



where 



E'=E-[>, H], H' = H+[>,E], (14) 



and Ave have put J = 0, B = H, since we are dealing only 

 with a crystalline medium. 



Further, we can from equations (14) above replace 

 E and H by their values in terms of E' and H', viz., 



H = € 2 {H'+[>, W]-w{w,B.')} 

 and 



E=e 2 {E'-|>, H. t ]-w(w, E')}. 



If we now consider a plane wave of light travelling in the 

 direction of motion of the medium, i. e. along the axis of &',, 

 and assume 



E' = E e { < Yt '~ x '\ W = H e is ^~ x '>, 



so that V is the velocity of the wave relative to the medium, 

 the circuital relations above reduce to 



H ,= 6*yE^+eVyH oi+ JJ 7 (I> y -E,) 



- H % = e 2 VE (1 ,-e=«.VH 0y + 4 -g, (D,-E = ). 

 -E 0z=6 -'VH Oy -^u-VE o .. 



while 



E 0y =6^VH 0l + ^VE Oy j 



E„,= H 0X =0. 



If we eliminate H 0y , H 02 , we have 



(l-e'wV)' _ ,u, n ; "i 



h 



(15) 



In order to proceed further, we must investigate the 

 relation connecting D-E with E' for the case of matter in 

 motion, and this is to be done by transforming the corre- 

 sponding relation for matter at rest. 



