116 L. Page — Energy of a Moving Electron. 



Art. IX. — The Energy of a Moving Electron; by Leigh 



Page. 



In a previous paper* it has been shown that the equations 

 of the electromagnetic field can be derived in their entirety 

 from two fundamental assumptions, to wit : 



(a) An etber exists which transmits, strains in accordance 

 with the postulate of the relativity of all systems moving with 

 constant velocities ; 



(b) The elementary charge is a center of discrete, uniformly 

 diverging, tubes of strain. 



The object of the present paper is to discuss and compare 

 the expressions for the energy of a Lorentz electron moving 

 with constant velocity as obtained by three distinct methods. 

 The first of these methods consists in finding the electric and 

 magnetic energies of the electron's field. The second consists 

 in subjecting an electron which is at rest relative to the 

 observer to an infinitesimal mechanical force for an infinite 

 time. In this way a finite velocity is imparted to the electron 

 without any finite radiation of energy. Hence the sum of the 

 initial electrostatic energy of the electron, the work clone by 

 the mechanical force in accelerating the electron, and the work 

 done by the ether pressure, — or whatever other force is pos- 

 tulated in order to prevent the disruption of the electron, — 

 in producing the progressive contraction of the electron as its 

 velocity relative to the observer increases, gives the energy of 

 the moving electron. The third method is analogous to that 

 used in finding the electrostatic energy of a charged conductor. 

 Starting with an uncharged moving electron, an infinite num- 

 ber of shells of infinite radius are shrunk down to the surface 

 of the electron. Each shell carries an infinitesimal charge and 

 maintains throughout the process of contraction the same veloc- 

 ity as the electron. The sum of the w r ork clone in contracting 

 the shells and that done in maintaining their constant velocity 

 against the retardation of the field gives the energy of the 

 charged electron. 



The value of the total energy is, as it must be, independent 

 of the method used. The division into kinetic and potential 

 energies is, however, not the same for the different methods. 

 In the first method the kinetic energy is taken as the magnetic 

 energy of the moving electron's field. The second method 

 gives for the kinetic energy the work done by the accelerating- 

 force. This is the expression peculiar to the dynamics of 

 relativity, and does not agree with that obtained by the first 

 *This Jour., xxxviii, p. 169, 1914. 



