﻿430 



Mr. G. H. Livens on the 



Thus the number of electrons with velocity components 

 between the limits (f, if 1 ', f) and (g + dg, v' + dv', f' + ^'j, 

 and for which the time r lies between t and r + dr, is 



=^a/: 



8N' = — 



^e 



x d?d V 'd?dr, 



where x is used for the argument of the exponential function, 

 and is equal to 



x = — q 



l*^M*-%^) ++*?¥$' 



which is practically the same as 



Thus to the same order of approximation * we find that 



N 



4*E f 



Integrating with respect to t from to go we find the 

 total number of the electrons with their velocity components 

 between (f Vf) and (f ' + dg, q' + dq', ? + d%) is 



or again using 

 we get 



<*N' = N 



a A 3 - 



i+ 



ZekM> 



pi . \i. 



cos pt + — "' sin pt I 



~pH~* i 



dfdn'dp. 



Following Lorentz we find that under these circumstances 



the current of electricity at the instant t is 



2N^,Eq 



W? 



vw 



cos/rt + '-JlLsin^ 



dgdn'd? ; 



1 + thL 



* i, e., neglecting all terms involving squares or higher powers of E. 



