A DYNAMICAL THEORY OP THE ELECTROMAGNETIC FIELD. 583 



Hence D = - (80), 



P- 



or the Specific Inductive Capacity is equal to the square of the index of refrac- 

 tion divided by the coefficient of magnetic induction. 



Propagation of Electromagnetic Disturbances in a Crystallized Medium. 



(102) Let us now calculate the conditions of propagation of a plane wave 

 in a medium for which the values of k and /u, are different in different direc- 

 tions. As we do not propose to give a complete investigation of the question 

 in the present imperfect state of the theory as extended to disturbances of 

 short period, we shall assume that the axes of magnetic induction coincide in 

 direction with those of electric elasticity. 



(103) Let the values of the magnetic coefficient for the three axes be 

 X, fi, v, then the equations of magnetic force (B) become 



. dH dG 



\OL=-, -j- 



dy dz 



dF dH 

 ~fa~^ 



dG dF 



(81). 



dx dy 



The equations of electric currents (C) remain as before. 

 The equations of electric elasticity (E) will be 



................................. (82), 



R = 4irc t h\ 



where 4nu 5 , 4^6', and 4?rc J are the values of k for the axes of x, y, z. 



Combining these equations with (A) and (D), we get equations of the form 



1 /. <W? d'F^ d*F\ 1 d 

 ~' V ~~~ 



^ 



* ' 



__^ 

 dz ) ~ a\ dt* + dxdt)"' ( ^ 



(104) If /, m, n are the direction-cosines of the wave, and V its velocity, 



and if 



Ix + my + nz Vt = w .............................. (84), 



