﻿180 Mr. G. H. Livens on the 



We have then the equations of motion of the typical 

 electron in the form 



7n^=zeE cos(pt + e) V t =£ t =0, 



so that now 



k=^{sin(^ + e)-sine}+£ 



vt=v> &=£ 



and also the projections of the typical free path along the 

 three coordinate axes are of lengths 



k=f t + e -A 2 1 cos e — cos(jj>t + e) — pr sin e i , 



and thus to the usual order of approximation we have the 

 length of the path given by 



„ . 26?E t r . i 



p _ r 2 T 2 + _? v i cose — cosy?r + e) —]?t sin e V , 



and again 



rr = I^l- ^-^jcos e-cosQ>r + 6)-^Tsin e j ] . 



In this case the work done by the electric field during the 

 particular free path under consideration is 



r 



eE cos(p* + e)£<ft 



= 1 eE cos(/>£ ■+■ e) | — |sin(p£ -f e) — sin e 1 -f £ 1 dt 



= 2^/{ sm ^ T + e) - Sme J 



f eE f . / v ■ . 1 



-t- - — y 1 sinf pr + e) — sm e f . 

 mp I w j 



This expression is againi better interpreted in terms of the 

 length of free path and the velocity in it. On substitution 

 therefore of the value of r from above we find that to a the 

 second order in E 2 this expression is equal to 



g 2 E 2 - < '-■* ^ 2 



2P fvl \[ /pl . \ pi 



sm e 



- 7? cos (7 + e ) { co? e ~ cos (? + 6 ) ~ , si ' 



TOO L ' V** / -i 



-r 



mp 



