﻿Electron Theory of Metallic Conduction. Ill 



in this term which is o£ the same order o£ magnitude as the 

 other term of the sum actually retained. 



The summation will be best effected if, after Lorentz, we 

 interpret it in terms of the lengths of free paths and 

 velocities in them instead of the time of duration. From 

 the equations above we find that the projections of the 

 particular path there under consideration along the co- 

 ordinate axes are of lengths 



e& r 2 

 so that the length of the path is practically 



= rV+— fr 3 , 

 m 



where we use 



r 2 = p -rrf+t, 2 



and neglect squares of the small order term involving E. 

 From this it is easy to see that to the same order of 

 magnitude 



~ r\ 2mr 3 r 



so that the above expression for the work done by the 

 electric field on the electron in its free path is to the same 

 order of approximation 



e 2 Wl 2 + eE&r eEm 

 2mr 2 r \ 2mr 3 / 



_e 2 Wl 2 / ± e\,eW 

 2m r\ r 2 ) r ' 



so that we have to evaluate 



[_ 2m ?-\ r) r J 

 Wherein it is to be remembered that all velocities are to be 

 taken at their initial value at the beginning of an impact. 



Consider first the contribution to H made by a single 

 electron which would in the absence of an electric field be 

 moving freely with a velocity r, and which will therefore 

 move so that it resumes this value at the beginning of each 

 free path. This assumes with Thomson * that the whole 



* Wilson does not state that this assumption underlies his analysis, 

 but without it his analysis is meaningless. It is, I believe, his failure to 

 realise the importance of a clear definition of this point which is the 

 cause of the errors he makes in the analysis. 



Phil. Maq. S. 6. Vol. 29. No. 169. Jan. 1915. X 



