﻿Electron Tlieory of Metallic Conduction. 183 



This is the same result as obtained by Wilson, reduced, how- 

 ever by the factor 2/3 which brings it into line with the 

 result obtained by Lorentz, and which must be applicable 

 to the present problem in the limiting ease of very long 

 waves. 



Conclusion. 



It would thus appear that a rigorous treatment of the 

 problem of conduction based on the above-mentioned ideas 

 leads to a formula which is entirely consistent with the results 

 of the analysis on more general lines given by Lorentz. 

 The two methods of reasoning appear at first sight to be 

 independent. Lorentz bases his calculations on the existence 

 of an average steady state of motion, in which the law of 

 distribution of the velocities among the electrons, which 

 differs from Maxwell's well known law owing to the action 

 of the electric field, is definitely calculable by similar 

 statistical considerations of the effect of the collisions. On 

 the other hand, Thomson and Wilson merely assume that the 

 whole effect imparted by the field to the electron in it? 

 motion along a free path is destroyed by the collision at the 

 end of the path, so that the electron starts off each path with 

 the velocity which it would have according to Maxwell's 

 formula, which is presumed to hold in the absence of the ex- 

 ternal field. The two forms of the theory are thus mutually 

 consistent, and the fact that they lead to the same formula 

 for the conductivity is very strong evidence in favour of the 

 formula. 



But the two views are prob ibly much the same in the end, 

 although that of Lorentz is probably the more general. In 

 fact it is impossible to imagine the existence of an average 

 steady state, as Lorentz imagines, unless some such action as 

 that implied in Thomson's assumption is in play. Lorentz * 

 himself clearly appreciates the force of this remark and has 

 made various suggestions in explanation of it, so that it does 

 not appear necessary for me to go into further details. I 

 hope, however, to be able to return to it in a further com- 

 munication. 



The University, Sheffield. 

 Oct. 1914. 



* See Vortrage iiber die Kinctische Theoric der Materie u. der Etek 

 trizitat (Leipzig-, 1914), p. 187. 



