﻿Electron Theory of Metallic Conduction. 179 



and q is a constant which is connected with the mean square 

 of the velocities, viz. u m , by the relation 



— u m 



The contribution of this group of electrons to H is thus 



Integration of this expression over all positive and negative 

 values of the variables (f, 77, f) furnishes the complete value 

 for H. The integral due to the second part of the expres- 

 sion obviously vanishes, and so we are left with 



H= EW^ 



vsirnro-s)^* 



To evaluate this we may, as usual, put £ 2 equal to \r^ and 

 dgdrjd^ equal to Airr'dr, and then we find that 





V 3tt mtt. 



37r mw,„ 

 And since H = o-E 2 we see that 



V ^7T ?»M TO 



which is precisely Lorentz's result. 



Analysis for rapidly varying fields. 



The ideas of the preceding analysis are directly applicable 

 in the more general case of a rapidly alternating field such 

 as we find associated with radiation. We may, for such a 

 case, take the electric force E to be simple harmonic with a 

 period p : say 



E = E cos( pt + e). 



N2 



