249, 250] ELECTROMAGNETIC WAVES. 523 



has been made the subject of a treatise by Pockels. We shall 

 here consider only the case in which U depends on a single 

 rectangular coordinate #, the circumstances being the same all 

 over each plane perpendicular to the X-axis. In a conducting 

 dielectric the value of k 2 is complex. In metals we know nothing 

 regarding the value of the electric inductivity e, for whereas 

 electrostatic phenomena may be explained by supposing it to be 

 infinite, in variable states this is far from being the case. In 

 fact in all experiments that have been performed with electric 

 waves thus far the value of co has not been great enough to make 

 the influence of the term containing e appreciable in comparison 

 with that containing X. (See 206.) We shall therefore neglect 

 the first term, so that our equation of propagation is 



(6) tatajfctff-A*' 



ot 



This is the equation for the conduction of heat, as given by 

 Fourier. We shall consider it in some detail below ( 254), but 

 shall now return to the consideration of the equation 



in which k 2 is the pure imaginary 



(8) te 



The solution of equation (7) is 



(9) U^C^ 



Since we have *Ji = (1 + i)/V2 the value of k is 



(10) k=A V27rXyLto) . (1 + i). 



Accordingly the real and imaginary parts of 



i (<at A >/27rA/xw. 



furnish us with particular solutions of (6). We thus obtain 



s in ( m t - A V2^^T. a?), 



cos ^t + A 27rXyLto) . x) t 



