438 Mr. G. H. Livens on the Electron 



so that 



I 



4j 

 .1 — 



then the differential equation for /is 



df dv OS d« ay af ot 

 f-fo 



— / • 



T 

 m 



Throughout the present paper we may assume that the 

 thermal conditions are uniform throughout the metal, so 

 that the function / will not depend on the coordinates 

 (w,y,z). We may also restrict our analysis to the simple 

 case when Y = Z = 0, so that the differential equation for/ 

 is of the form 



x 5? + a^ = -^- 



The general solution of this equation appropriate to the 

 present type of problem is easily obtained and can be 

 written in the form 



H v %E>i)A 



The suffix 1 indicating that the integrand, interpreted 

 explicitly as a function of the time t, is to be taken for the 

 time t x . Using the value of f given above, this becomes 



r 



We may now, as in all these problems, neglect squares of 

 the accelerations produced by the external fields ; this means 

 that we can ignore the variable part of f, and thus we may 

 write 



r 



