L. Page — Energy of a Moving Electron. 121 



which is obviously the rate at which work is done by the electro- 

 magnetic forces in resisting the progressive contraction of the 

 electron as its velocity increases. Changing signs and integrat- 

 ing with respect to the time, we get for the total work done in 

 contracting the electron the expression 



ap;=^[i-vt^] (is) 



Adding this to (12), the expression for the work done by the 

 mechanical force in producing the change in velocity, we get, 

 as we should, for the total increase in energy the same 

 expression (8) as obtained by subtracting the initial value of 



f/<' 



+ IP) (h 



from its final value. In accordance with the usual definitions 

 we should consider (12) as representing the kinetic energy 

 acquired, and (18) the increase in potential energy due to the 

 contraction. It is to be noted, however, that the kinetic and 

 potential energies so measured do not correspond to the 

 magnetic and electric energies respectively of the electron's 

 field. 



In order to provide a mechanism for producing the contrac- 

 tion of the electron Poincare* assumed that its surface is 

 subject to a constant hydrostatic pressure 



S = — (19) 



32 ttV v ; 



This pressure is just sufficient, when the electron is moving 

 with constant velocity, to counteract the electric forces tending 

 to disrupt the electron, and when the acceleration is infinites- 

 imal, the work done in contracting the electron against the 

 electromagnetic forces due to its own field can be accounted 

 for by the work done by this hydi-ostatic pressure. Unfortunately, 

 however, Poineare's stress loses its significance when an electron 

 is accelerated by a finite mechanical force. If the force is 

 constant, the electron's field will be such that if the 

 surface of the electron is assumed to coincide with a level 

 surface f of the electromagnetic field — and it is hard to see 



*Poincare, Kendiconti del Circolo Maternatico di Palermo, xxi, p. 129, 1906. 



f By "level surface" is meant a surface everywhere perpendicular to the 

 electromagnetic forces of the field. See " Kelativity and the Ether." This 

 Journal, xxxviii, p. 184, 1914. In the paper referred to, instead of ''level 

 surface" the term " equipotential surface " is used. The latter term is, 

 however, objectionable, since the force in an accelerated system is not 

 derivable from a scalar potential and hence there can be no meaning to 

 " equipotential surface " in the sense of a surface all points of which have 

 the same potential. 



