Physics. — ''(hl the Enevijy of the (Jravitatlon Field in Einstein's 

 Theori/" Hy Dr. Gunnar Nordstrom. (Commimieated by Prof. 



H. A. LORENTZ.) 



(Communicated in the meeting of January 26, 1918.) 



Ill a preceding paper we considered some general theorems derived 

 from Einstein's gravitation theory, and especiall}' afield with spherical 

 symmetry.') Referring to this paper, which in the following will be 

 denoted by a Roman I, the energy of the gravitation field will now 

 be calcnlated, according to Einstein's conce|)tion vi/.. characterized 

 by the tpiantity t/ ') tVom tbrmida- (10) I. in order to obtain a 

 result that holds for an electric field too, 1 shall first calculate the 

 gravitation field of an electric centre. 



§ 1. The field of (in electric centre. 



The gravitation field of an electric body can be calculated by the 

 aid of the variation princii)le in the form (1)1 or (1^)1, if only we 

 keep in mind that the electro-magnetic fiehl gives an additive con- 

 tribution to Hamii,ton's function 'ODï. 



We put 



iSï = •?3ï(«) + SÜ^^"'), (1) 



where '^ï"" refers to the electro-magnetic field, ^^l'"' to the matter 

 (in a limited sense). Eor ^)3Z!^'^ we have ''') 



where fp indicates the components of the 4 dimensional potential, 

 a\ the components of the 4 dimensional electric current. 



When the field is stationary and all electric charges at rest, 

 we have 



<f^ =r (f^ — (p^ — 0. 11^' = i\)' = ro' = 0. 



1) G. Nordstrom, "On the mass of a material system accoiding to the 

 gravitation tlieory of Einstein. These Proceedings, XX, 1917, p. 1Ü76. 



2) It will be known that a different conception of the gravitation theory has been 

 enunciated by H. A. Lorentz. 



3) J. Tresling, These l^roceedings XIX, p. 892. 

 A. D. ['"OKKER, These Proceedings XIX, p. 968 



