Electron necessarily Radiate Energy ? 415 



the increase in the internal energy of the electron, When 

 the electrons, having been brought to rest, begin to move 

 away from each other, the stored internal energy comes out 

 into the field, and at the same time the excess of electric 

 energy which has accumulated in the field is reconverted 

 into the magnetic form. -„ 2 -^ 



If we distinguish that part of W given by — as the 



" electronic " from the " mutual/' — — - A — '-^ , and the 

 ^2 4tt 



"external field/'' -5—, energy densities, the equations (8) 



and (11) show that the total electronic energy id and 

 momentum g fit into a mechanical scheme. In fact, since 



do „ , dw v n 



their rates of increase are identical with those v\ hich would 

 be created by a mechanical force X^ acting on the moving 

 nucleus. This shows that the system formally satisfies the 

 Lorentz equation 



F = ^E + -[vH]), 



as applied to a point-charge e in a uniform electric 

 field X *. 



There seem to be only two respects in which the solution 

 fails to represent a real case of electronic motion. (1) It 

 refers to a limiting case in which the electrons are concen- 

 trated to a point and are moving in a correspondingly 

 infinite field. (2) Extending over all space and time, it 

 does not represent the initiation of the motion, and does not 

 correspond substantially with a practical case, such as is 

 given when an electron, passing through a hole in a charged 

 plate, comes into an ultimately uniform held. Neither of 

 these points, I imagine, has any significance with regard to 

 the question at issue. (1) clearly does not affect the 

 radiation from the system ; and with regard to (2), electro- 

 magnetic solutions, like those of other differential equations, 

 in general only represent steady states under idealized 

 conditions, and without reference to the manner of their 

 initiation (cf. the solution for the uniformly moving- 

 electron). 



* 



It may be noted that the example does not reveal whether a term 

 of the order e 2 /4£ 2 , expressing- a mutual action of the charges, should be 

 included, as, if present, it would be negligible compared with the 

 infinite Xe. 



