522 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XIII. 



putting the integration constant equal to zero for the same reason 

 as before. Accordingly the fields are 



, , 



V6 V V 



, , , . . 



Vjj, V > V/A 



The two fields are accordingly propagated together. 

 Comparing the energies of unit volume we find 



07T O7T O7T 



or the energy is equally divided between the two fields. 



The radiant vector VFH is of course in the direction of 

 propagation. 



250. Propagation in a Conductor. In 247 in deducing 

 the equations of propagation we have supposed the conductivity to 

 be zero. If we do not make this assumption in substituting the 

 value of the curl-components on the left of equation (i) we obtain 



and in like manner all the components of both fields satisfy the 

 equation 



The general solution of this equation has been given by 

 Boussinesq, but it is too complicated to be given here. A 

 particularly interesting special case will be treated below. In the 

 mean time we shall content ourselves with the consideration of 

 disturbances which are harmonic functions of the time. For this 

 purpose we shall assume 



(3) <t> = **U(a,y,*), 



when our equation becomes 



(4) ^ 2 ( 



The equation 

 (5) 



