408 WRIGHT— POLARIZED LIGHT IN THE 



In light-waves the disturbance is periodic in effect and the time occurs 



onl}'- in the form of a factor the most general expression for which is Ae^ t ; 

 in this factor T is the period of vibration and A, which may be real, imagi- 

 nary, or complex, is the amplitude vector. Under these conditions the ex- 

 pression (4) for the current may be written 



— (€ - 2T(n)-—. 

 47r at 



The only difference between this expression for the current and that for 

 dielectrics is the replacement of the dielectric constant e by the complex quan- 

 tity (e — zTcri), in which z = V — i. 



In crystals the dielectric constant and the conductivity are different in 

 different directions. Experience has shown that the components of the elec- 

 tric displacement for any direction of wave propagation are homogeneous, 

 linear functions of the field components. Thus the X, Y , Z components of 

 the conduction current are 



those of the displacement current 



47r \ 



ax , ay , az\ 



wherein omc = o-^ft and ^lik = ^/.-ft. The first Maxwell equation becomes for 

 absorbing crystals 



or if Fftfc be substituted for the complex expression (cftt — 2T<rhki) the Max- 

 well equations can be written 



I / - dX , _ dV , . dZ\ dw dv 

 C \ 6t dt dt ) dy dz 



I /- ax , . aF , . az\ du dw , , 



-{e-n-^^ .22^ + .23^ j = ^- ^ = ., ^ (5a) 



I /. ax , . aF , . az\ dv du 



- I ^31 -rr + 632-^7 +^33-^ I = -7- = f , 



C\dt Bl dt / dx dy 



iaM_aF_az i^_^_^ i^-^_^ ( h) 



c dt ~ 'dz ay ' c dt~ dx dz ' c lit ~ dy dx ' ^^ ^ 



wherein eitk = fhh. 



If for abbreviation the right hand side of equations (50) be made equal 

 respectively to ^, v, f, the differential dXjdt, BY/dt, dZjdt can be expressed 



