( 478 ) 



J.. 



without a term with - in Hie righthaiid member wliich enables 



(It 



us to (letcrmine the acceleration. If on the other hand in forminj^^ f 



we take into account only the external forces, we may introduce the 



electromagnetic mass ni' and write : 



d\) 

 force = m' — -. 

 (It 



The mass m', however, is not known, and we can only calcidate 

 it if we know already the law according to which the electron 

 moves. But then of course we need not make use of equation 

 (V) any more. 



Abraham '), accordingly, does not make any use of equation (V) 

 for determining the motion of the electron. He does use an ecjuation 

 which in Lohentz's notation, the ijitegrals being taken throughout 

 infinite space, may be written as follows: 



But this equation is deduced from the equations (/)... (/T) and 

 so it is not equivalent to equation ( F) which must be independent 

 of them. The only use which is made of e(|uation ( I") is the 



introduction of the name force foi- the quantity (^ ( ö + ^ t^'* '\l j, of 



the name momentum for |bb|. and of the name electric mass 



for the quotient of the so defined force and the acceleration. But 

 the real problem : how will an electron \y\th gi\en shape and 

 charge move in a given held, must be solved befoi-ehand indepen- 

 dently of this nomenclature. 



Yet it is evident that the equations (/)...(/ T) will in general 

 be insufïk'ient for the determination of the motion uf an electrical 

 system. In the case that we ascribe a real mass to the electron, it 

 is obvious that we must know the force acting on it. But also on 

 the supposition that the electron has no real mass — and in what 

 follows we will contine ourselves to this case — another set of 

 equations is required for the determination of the motion. For 

 equation (77) enables us to determine S if y is always known, and 

 inversely to determine i> if we know b, l)ut it does not enable us 

 to determine both these ([uantities. The assunq)tion that the motion 

 is quasi stationary is equivalent to a i-elation l»etween i^ and b . 



1) Abraham, «Dynamik des Elektl•on^^." Ann. der Physik IV. B. 13, 1904, bl. 105. 



