L. Page — Energy of a Moving Electron. 117 



method. In the third method the kinetic energy is measured 

 by the work done in maintaining unimpaired the velocity of 

 the contracting shells. Its value is equal to that of the mag- 

 netic energy of the moving electron's field as given by the first 

 method. Of the three methods the second would appear to be 

 the least trustworthy on account of the necessity of dealing 

 with an accelerated system. 



If the elementary charge or electron is a uniformly charged 

 spherical shell of radius a to an observer relative to 

 whom it is at rest, it will appear as an oblate spheroid to an 

 observer relative to whom it has a constant velocity v, the 

 dimensions at right angles to the direction of motion being the 

 same as when at rest, and the dimensions in the direction of motion 



v 



being shortened in the ratio V 1 — ft 2 : 1 where c = — = 



velocity of light. If a mechanical force be applied to such an 

 electron, the electron's own field will exert a force opposite and 

 proportional to the acceleration produced. By means of this 

 retarding force Lorentz* explains the inertia mass of a moving 

 electron. For a quasi-stationary state of motion he finds the 

 transverse mass to be given by 



(1) 



and the longitudinal mass by 



m t = - «■ = Vb. s (2) 



1 67rac a (l-/3 2 )^ {l-PY 



If the acceleration is finite and in the direction of relative 

 velocity, it must be remembered that the acceleration of the 

 front of the electron is less than that of the rear, since the 

 electron contracts progressively as its velocity relative to the 

 observer increases. The author has shown, in the paper 

 already referred to, that Lorentz's expressions for the mass 

 hold good for any acceleration which is constant relative to 

 the electron's own system, provided we take as the acceleration 

 of the electron, not the acceleration of its geometric center, but 

 that of the plane perpendicular to the direction of motion, 

 which divides the electron into two parts having equal charges. 

 The point where the axis of the electron cuts this plane may 

 appropriately be called the center of acceleration. The restric- 

 tion of constant acceleration relative to the electron's own 

 system is not serious, since a constant acceleration for a time 

 comparable to that taken by light to travel a distance equal to 



* Theory of Electrons, p. 212. 



