( 814 ) 



1 da' , , IC , , 

 b' = — <ira(l <f -\ iinuJ a , (lo) 



e Ot' ' e 



l)' — rol' a' (14) 



fV^ o"' d' 



The .s\iiil>()l L' is iiii .ihhrcx i.-ilioii foi' ., , + ^^7 + ^^ri' 'i''"l.'/'"'"^V^ 



d(p' d(f d(f' 



(1(»1M»(('S a \('('|(l|- A\ llOSC COIlllXIIKMlIS aiT ^7, ^r— r, 7-7. TIlC ('X 1 tTC^Ssioll 



Ö.V 01/ ()z 



ijnul' k\' ,■ luis a similar iiicaiiiiiii'. 



hl order lo obtain llie soliilioii of (11) ami (12) in a siiii|»le torn», 

 Ave niav take .r', //',:' as the coordinates oj" a point /*' in a spaee 

 .S", and aserilte to this point, tor each value of /', the values of 

 Q',ii.(f\a', heloJiging to the eoi'i-espondinji' [»oint /* (.r, //, c) of the 

 eleetroniagnetie system. For a(letinit(> \ alne /' of the fonrth independent 

 variable, the poteidials </' and a' in the point /' of the system or in 

 the eorrespondin^U' point /'' of the spaee S', are ,uiven Ity ^) 



'^ 4.tJ r' 



4nr.J 



dS'. 



(15) 



■ . (10) 



Here dS' is an element of the spaee ,S", /•' its distance l'r(»m P' 

 and the bra(d<ets serve to denote the (piantily {>' and the vector 



o' u', snch as they are in the element dS', t'oi' the \alne /' 



of 



(he fonrlh independent variable. 



Instead of (J5) and (J(i) we may also Avi-ite, takin,u iido acconnt 

 (4) and (7), 



a =- — I '/'S 



4.Tt'J r 



. (17) 



(18) 



the integrations now extending o\er the electromagnetic system itself. 

 It slionhl be kei)t in nund that in these formnlae r' does not denote 

 the distance between the element dS and the point (,/',ƒ/,:) for which 

 the calcidation is to be p(,'i'forme<l. If the clement lies at the point 



It is also to i»(' I'cmcndx'icd that, if \\ e wish to dctcM-mine r/ ' and 



1) M. E., §i< 5 ami 10. 



