126 L. Page — Energy of a Moving Electron. 



its motion. The mechanical force which must be applied to 

 counteract this resistance is easily found to be 



K = - fade 



_ ede vJ f3 

 6irr" 2 c 



dr' 

 ede lCtV (32) 



6ht' 2 c V1-/3 2 



since dt'—di Vl — fi* 



The total work done by this force during the shrinking on 

 of all the shells is seen to be 



3 12** VT^ 2 V^F (33) 



As this is the work done by the force applied to the shells in 

 the direction of motion in maintaining their velocity unim- 

 paired, it may properly be called the kinetic energy of the 

 electron. It is equal in value to the magnetic energy of the 

 electron's field, i. e. 



\fjS % dr (34) 



The sum of the potential and kinetic energies as determined 

 above is, of course, equal to the corresponding total energy as 

 measured by adding to the electrostatic energy of an electron 

 at rest the work done in imparting to it, by means of an infini- 

 tesimal mechanical force, a velocity v. It is to be noted, how- 

 ever, that the division of the total energy into kinetic and 

 potential is different in the two cases, as is seen by comparing 

 (31) with (18), and (33) with (12). Denoting the transverse 

 mass by m t (33) gives for the kinetic energy the familiar ex- 

 pression 



T s =jm t v* (35) 



instead of the expression (12) peculiar to Einstein's mechanics. 

 It is of interest to investigate the validity of the general- 

 ized force equation for a contracting shell. If this equation 

 holds 



