( 351 ) 



§ 3. Transition to FjOrentz's potential-fornnilae on the one hand, 

 and to those given by myself on the other. 



It is tempting, to perform in (7) the integration with respect to 



t\ As F is ditterent from only for the moment t':=zt , 



c 

 we get immediately 



4rr^= r^fZ5, (8) 



w^here |o| means the density, contained in the element r/ >9 at the 



time t z= t . 



c 



As for the proof of formula (8), H. A. Lorentz ') refers to tiie 

 expression (8) satisfying the differential equation (1). 



WiECHERT ') and others do not start from Green's theorem, but 

 from Beltrami's, which naturally is only a transformation of Green's 

 theorem and, it strikes me, not a very transparent one. 



Instead of performing the integration in (7) with respect to time, 

 it is better, to evaluate that in respect to space. Now for this pur- 

 pose it is necessary to add a certain supposition as to the shape of 

 the electron. In the first instance we suppose the electroii to be an 

 infinitely thin spherical shell 0Ï i\\Q radius a, on which 

 tiie charge f is uniformly distributed. So we take : 



-d o instead of g dS 



and get from (7) 



+ 00 



Fig. 1. -°° 



Let be tiie centre of tiie spherical shell. Round OA we count 

 the azimuth ii and from OA the angle {h, so that i], {y mean the 

 geographical longitnde and the complement of the latitude on the 

 surface of the electron. Let R be the distance OA from the centre 

 to the point in (piestion, it follows : 



r" = W -f a- — 2 lia cos {>, rdr = Ra sin /> dd-, 



1) La theorie électromagtuHiqiie de Maxwell, Leiden, 1892, pag. 119. 



') Elektrodynaniisclie Elementargesetze. Lorentz— Jubelband, pag. 560, Haag 1900, 



