252 Prof. J. J. Thomson, On the rotation of the plane [April 20, 



differentiating (13) with regard to y, (14) with regard to z and 

 subtracting we get, since 



dx dy dz 



kiridy dy <££)■ ( <L <L> §!<!£_ 



K \dx* + dy' + dz 2 j~ ^ \ P dcc + q dy + T dz] dt 



d , 7 , f d d d) d 2 f 



or as it is more convenient to write it 



_i_ J^+^ + ^ULA + a d 4- r *l#+ » ^-» ^ + ?f 



fiK [da? dy' + rf? j \ P dx ±q dy + dz) dr 3 dt 2 (ft "*" df ' 



with similar equations for g and A. 



We may easily prove that a, b, c satisfy equations of an exactly 

 similar type. 



We shall apply these equations to a very simple case, let us 

 suppose that the light is propagated along the axis of z and that 

 the medium is rotating round this axis with an angular velocity co. 



In this case /and g are functions of z only so that our equations 

 become, writing v 2 for l/fJiK, 



dz* 3 dt df 



„d 2 g df oVg 



v ~d?~ W "tt + M i ' 



Suppose a circularly polarized ray goes along the axis of z, 

 for which f= a sin (nt — Iz), 



g — — acos (nt- Iz). 



Substituting we get 



v 2 l 2 +w s n-n 2 =0. 



If the ray had been circularly polarized in the opposite sense we 

 should have 



v 2 l 2 — (o 3 n — n 2 = 0. 



If co s be small compared with n, then in the first case 



vl = n{:\ -*- 8 



n 



2 



And if in the second l t be written for I 



•V-"(i+0) 



