Energy of the Lorenlz Electron, 495 



what may be called the "nucleus" of the electron (to dis- 

 tinguish it from the surrounding electronic field), and for an 

 electron of charge e and major semi-axis a, moving with 

 velocity v=j3c, is of the amount 



Sl^-W w 



While the physical character of this internal energy is 

 largely a matter of conjecture, the postulation of its presence 

 is essential for two separate reasons. In the first place, 

 if we consider the electron to be a system capable of being 

 set in motion by a mechanical force we must have simul- 

 taneously satisfied two mechanical conditions : (1) that the 

 force is measured by the rate of increase of the momentum 

 of the system, and 2) its activity by the rate of increase of 

 the total energy. But this fundamental law of mechanics 

 is not satisfied unless to the energy of the electronic field 

 the internal energy (1) is added*. In the second place, 

 the presence of the same internal energy is required to 

 make the electron fit into a relativistic scheme, viz., to make 

 its total energy at any speed equal to c 2 times its mass. 



The object of this note is to point out that there is another 

 reason for postulating the existence of this internal energy, 

 and it is one which has a more clearly defined electro- 

 magnetic character than either of the above. It comes from 

 a consideration of the Poynting flux of energy in the field 

 of a uniformly moving electron. 



At a point whose polar coordinates are >', with reference 

 to the centre of the electron, the electric and magnetic 

 forces are 



r" (l-/3 2 sin 2 6>)£ 



radially, and 



H = £sin0.E (3) 



along the circles of latitude (calling the line of motion of 

 the centre of the nucleus the polar axis). The energy 

 density is 



">=^(E 2 + H 2 ), (4) 



and the vector flux of energy through a plane fixed in 

 space is 



*-£[■«] ^ 



* Lorentz, 'Theory of Electrons/ p. 213 (1909 edition). 



