( 349 ) 

 Tiet V be an auxiliary function 



v=^F{r-c{t-i:)) , (2) 



r 



I' the distance of a certain point in question A from any })oint l\ 



t the moment, for which the value of (p at tlie point A is required, 



/' a variable moment of time. Our auxiliary function v then satisfies 



the differential equation : 



•1 b'o 

 Lv — ^-— (3) 



Like KiRCHHOFF we shall suppose, that the function F{,i;) is 

 represented by a narrow prong, enclosing the area 1, x'va. that F{jj) 

 vanishes foi' all abscissae different from ,;• = 0, but in the point 

 X = increases so strongly and so suddenly, that notwithstanding 



.6') tLv — 1 (4) 



Jf,, 



If we apply Green's theorem in its most common form (o the 

 functions g) and v, we liave : 



J(„A,.-.A^,).5=J'(y^-,.|),^, . . . (Ó) 



The surface integral on the right hand side is to be extended over 

 tlie border of the space >S' and over an infinite^ small surface, 

 enclosing the point A, in as much as this point is contained in 

 ,S'. This holds good, because we shall let S finally expand i]ito 

 infinity. The part of the surface integral, relating to the surface 

 enclosing A, is known to give : 



4.jt<p^^Fi-c{t-t')). 



If we use on the left side of (5) the differential equations (J) 

 and (3), substituting in (f as variable time t' and noticing, that 



. . = TT,, it follows 



lor/ dv d(f\ 'r rf or 



't^'^^ 



+ 4rry:iF(-c-(i- 0) (6) 



The second integral on the left is extended over the charge of the 

 electron, the first on the right no more than over the surface of S. 

 Multiply the last equation with cd( and infegrale with respect to 

 /' from — GO to -|- oc. Thereby (he first terui on llie left \auishes 

 on account of the nature of the function F. In fact this member 

 relates, after the integration is performed, oidy to the moments 



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