﻿784 



Mr. B. B. Baker on the Path of an 



opposite direction, passing away again to infinity on the 

 same side of the wheel from which it came originally, the 

 previous motion being exactly reversed. From equations 

 (8) and (14) it follows that, in the return path, the electron 

 receives back from the magnetic structure the kinetic energy 

 it had previously lent to it^ and the magnetic wheel will 

 return finally to rest. 



The value of Aw given by equation (18) is obtained on the 

 assumption that the electron give3 up to the magnetic struc- 

 ture all its kinetic energy ; that this is so in general can 

 be seen from the following considerations. When ijr has 

 reached its maximum value, ^ = 0, and therefore from 

 equation (10) 



M , + W - . 



0. 



(19) 



From the expansions for F(r, 0) in powers of r given from 



equations (1) and (2) it is apparent that ^— and ^ cannot 



be simultaneously zero except when r is infinite ; we have, 

 in fact : 



= + 



when r<&, 



*?_ 



Sr ~ 

 when r>a. 



1 3 r 2 



- cos + - -5 (5 cos 3 — 3 cos 6) — . 

 a 2 a 6 7 



"I 3 



-sin 0-i ^(15 cos 2 0-3) sin + 

 a Z a 



a 2 3 a 4 



- 3 cos 0+^-^(5 cos 3 — 3 cos 0) — 



1 a 



3 a 4 



=r^r = — « -5 sin 0-\- -x— A (15 cos 2 — 3) sin 

 7)0 2 r 2 8 r 4 v y 



(20) 



BF 



and therefore, when r^co , ^ =0 only when cos = 0, i. e., 



only when sin = 0, i. e., 



, n 7T n 3tt -, BF 

 when 0= - or 0= -^ and _^- 



when = or = 7r. 



In general, therefore, equation (19) will only be satisfied 

 when r = and = simultaneously, i. £., when all the 

 kinetic energy of the electron has been given up to the 

 wheel. 



