of the Hall Effect and Allied Phenomena. 533 



this acceleration depending on the magnetic force may be 

 omitted as it contributes nothing to the scalar product 



(fx+^Y+rz). 



Moreover, the parts of (f x r} 1 fj) depending on the electric 

 force may also be omitted, as their retention would merely 

 introduce the properly negligible squares and products of 

 the field and condition gradients. 



We may thus in the general form for % use 



n 1 = r} cos vti — fsin vti, 

 £1 = ? cos vti + rj sin vti, 



and 



_ ^Ef y _ e ]^y r/ __ ?E. z 



m ' m ' m ' 



Inserting these values and performing the integrations 

 with respect to ^ and t and noticing that 



f 



r m dr vr m 



sin vre — — Y — 



r 

 I • „ n 7 mdT V*T m 2 



Jo 



(1 — cos vr)e 



we find that 

 / 



♦rSbH^-ilh"!:) 



«(«-k£ +••!)}]■ 



This expresses the most general form of the required law 

 for the distribution of velocities among the electrons in the 

 metal. It might equally well have been deduced by a method 

 exactly analogous to that employed by Gans in the more 

 special case, or by the alternative method suggested by the 



