﻿24: Mr. G. A.Schott on the 



The following table gives approximate values of /3 calculated 



for -=10- 16 and - =10-« 

 a a 



n ... 



10 



20 



50 



100 



1000 



n 



? =10-16 



a 



•023 



■131 



•398 



•566 



•894 



a 

 -=10-46 



•00074 



•023 



•187 



•398 



•833 



It is noteworthy how little difference even the order 

 of - makes in the value of y3 when n is at all large. 



§ 5. We shall now consider in what way we must modify 

 the common view as to the constitution of the electron and of 

 the gether, so as to allow of the expansion of the electron, 

 w T hich we have found necessary to account for the definiteness 

 in the structure of the atom on the electron theory. 



When the electron is invariable the energy equation may 

 be written in the form. 



■■*-?+* 



w 



where vT is the rate of working of the mechanical force acting 

 on the electron, E is a function of its velocity, m;iss. and 

 acceleration, and R is the rate at which the electron loses 

 energy by radiation. E includes the electromagnetic energy 

 of the electron ; its characteristic is that c?E is a perfect 

 differential while Rdt is not. 



When the electron varies in radius (4) is no longer true, 

 but must be completed by the addition of a term to the right- 



hand member of the form — ^/(yS). This additional term 



represents the rate at which work is done by the internal 

 electromotive forces of the electron on account of the expansion. 

 The form of /(£), like that of f{/3) in § 2, depends on the 

 assumptions made as to the structure of the electron. 



We must assume the existence of internal stresses in the 

 electron which resist its expansion. 



In calculating the internal electromotive force we find that 

 the principal term is derived from a potential <I>, the " con- 

 vection potential " of Searle and Lorentz ; the value of <!> 

 is the same as it would be if the electron were moving 



