﻿658 Mr. G. H. Livens on the Electron 



where also 



and r m is the mean value of r for all the SN electrons and 

 which is identical with the mean time between two encounters 

 for an electron with velocity u . 



The velocities of these electrons at the instant t are 

 given by 



m Jt' = t-r 



where t' is used as an auxiliary time variable for the 

 integration. We write the first of these equations in the 

 form 



so that 



ft'=t 

 $= \ Edt' 



Thus if we interpret the function gN T in terms of (f, 77, f) 

 instead of (f 05 Vo, fo) 5 we & n & tnat the number ot electrons 

 at the instant £ with their velocity components between 

 (f, 77, £) and (f-fdf, »/ + ^, ?+d£) and for which the 

 value of r is as specified is 



T m V 7r 



wherein we have neglected squares of the small quantity <£, 

 as is usually done in these theories, and used 



tt » = p + ^ + {4 



To the same order of approximation we may also write 



On integration over all values of t from to c© we find the 

 total number of electrons per unit volume at the instant t 

 with their velocity components between (f, 77, f) and 

 (f + <*?, *7 + d*7, ?+^?) in the form 



