﻿Electron in the Neighbourhood of an Atom. 785 



There may, however, be certain exceptional values of r, 0, 

 ?•, 6 which will satisfy equation (19), even though the electron 

 continues in motion ; that even in these circumstances the 

 electron will pass through the magnetic structure on its 

 return path may be demonstrated thus. 



Denote by <x r and a e the accelerations of the electron in 

 the directions of r increasing and increasing respectively ; 

 then equations (11) and (12) may be written 



«r= ^=T~> ( 21 ) 



m or 



m l too 



Suppose, for definiteness, that the electron is projected from 

 a part of the plane of xy for which both x and y are positive ; 

 then ^r will be always positive and from equations (20), 

 (21), and (22) we obtain the results: 



TT 



when r > a and < 6 < 9 ; a r > and u e > 0; 



rrr 



when r > a and ^ < 6 < it ; «.,, < and a e > ; 

 when r > a and it < 6 < ; <x r < and a d < ; 



37T 



when r > a and -^ < 6 < 2tt ; «,. > and ot e < ; 



when 



7T 



< a and < 6 < ; a,. > and « < 



IT 



when r < a and -r < < ?r ; «r < arid a e < ; 



when y < a and it < 9 < ~ i} ; « r < and a fl > ; 



when r < a and -^ < < 2tt ; a, > and ««, > 0. 



The radial acceleration is therefore directed away from the 

 centre of the magnetic wheel when x is positive, and towards 

 the centre when x is negative, and thus always tends to 

 retard the motion of the electron on its outward journey. 

 Moreover, when x is positive and r>a the curvature of the 

 path is towards the axis of y ; when x is positive and r<a 

 the curvature is towards the axis of x ; when x is negative 

 and r<a the curvature is towards the axis of y\ and when 

 Phil. Mag. B. 6. Vol. 44. No. 262. Oct. 1922. 3 E 



