892 
Physics. — “The equations of the theory of electrons in a gravita- 
tion field of Einstein deduced from a variation principle. 
The principal function of the motion of the electrons.” By 
J. Trestinc. (Communicated by Prof. H. A. Lorentz). 
(Communicated in the meeting of November 25, 1916) 
Hinpert') derived the fundamental equation of the electro-magnetic 
field in the empty space from a variation principle, in which the 
principal funetion is considered as dependent on a four-dimensional 
vector potential and its differential quotients with respect to the 
four coordinates. :, 
In this paper it will be shown that this method may be extended 
to a space in which electrons are moving. For this purpose a new 
term must be added to the principal function as it was used by 
Hivpert, by which term the influence of those electrons is repre- 
sented. Only then the connexion between vector potential and the 
intensities of the field can be indicated, as the equations give us the 
influence of the potential on the charges, while it is just in this 
influence that the intensities of the field are expressed. 
In another way Prof. Lorentz?) had already deduced the funda- 
mental equations from a variation principle. In my opinion however 
the generalization of HiLBert’s method solves the problem in the 
finest possible form. Nearly the whole following way of calculation 
is taken from the mentioned paper of LoRENTz. 
The components of the vector potential are indicated by qs, a 
four-dimensional element of volume de, de, dx, dt by dS. We shall 
also write de, for dt. Let the density of the electric charge be g. 
da; 
Then the charge of a volume JV is edV =e. We put on =i 
( from 1 to 4). 
These quantities wi are-no vector-components. They become so 
WE 
4 
however when they are divided by } 
dxj;dVYq ede; daj — 
Poro nig wien dean 
* Bde dtdVyq dVide hr: AC ; 
represent the volume resp. the density of e when at rest. 
da; , 
= 
s 
Qo 
1) Davip Hisspert. Die Grurdlagen der Physik (Erste Mitteilung) Nachrichten 
von der Königlichen Gesellschaft der Wissenschaften zu Göttingen 1915, S. 395. 
2) H. A. Lorentz. Hamitron’s principle in Ernstern’s theory of gravitation. 
These Proc. XIX p. 751. 
