Theory of Metallic Conduction. 117 



Whence we may conclude that the number of the same 

 group which collide during the small interval dt is 



a-b)dVdvdt=8T$\ e r m*L 



SNdt 



r m 

 4>dVdvdt 



Thus . <£ 



or again a _ b = l_ f _ A ^ 



I'm, t ui 



The differential equation satisfied by the function / thus 

 assumes the form 



= ke-^-f. 



In this equation r m may be taken to have the value it 

 would have in the absence of any external field, and may 

 therefore simply be put equal to 



x -^' 



U 



wherein l m denotes the mean free path of the undisturbed 

 motion of the electrons, which under the usual assumptions 

 is independent of the velocity. 



It will be convenient for the general purposes of this 

 paper if we adopt the general notation of the vectorial 

 calculus, using R for the general vector of acceleration 

 whose components are (X, Y, Z) and u as the vector of 

 velocity of the electron. The above differential equation 

 satisfied by /may then be written in the form 



(RVu)/+ («V)/+K+^ = —•-*** 



wherein Vu and V denote the usual Hamiltonian vector 

 operators whose components are 



(v„) = ( 3f , §-, ^ J, 





sr av st< 



