L. Page — Energy of a Moving Electron. 127 



-^ d , ■, dm . . 



dv 

 since —rr = 0. 

 at 



The mass of the electron plus the mutual mass of electron and 

 shell is 



r e 2 ede ~\ 1 .... 



»i t = i + - — — 2 , (37 



Hence 



JT: 



dr' 



ede -— B 



<ft (38) 



Zitr'-c Vl— £ 2 



Which is a force in the same direction as that given by (32) 

 but twice as great. 



However, while the force K x given by (32) is the only force 

 in the direction of motion that does any ivorJc, it is not the 

 total force that must be applied to the contracting shell in 

 order to keep its velocity unimpaired. In fact (3) shows that 

 the magnetic field exerts a resultant force on the shell in such 

 a direction as to decrease the velocity. The mechanical force 

 which must be applied to counteract this resistance is 



Substituting the value of de from (21) and that of II from (23) 

 we get upon integration 



, dr' n 



ede —=- B 



dt H 



K„= 



(40) 



■irr"cVl— B 2 



Adding this force to the resisting force due to the electric 

 field as given by (32) we get 



dr' 



ede — B 



K=K+K= - 



iff (4i) 



3 7rr"cv/l — )8' 



which agrees with the expression for the applied force as 

 obtained from the generalized force equation. 



At first it may seem surprising that there can be a force on 

 the contracting shell that does no work. A consideration of 

 figure 2 explains the apparent anomaly. The shell AB con- 

 tracts to A'B' as it moves along. The charge which follows 



