586 



The equations (8) and (9) are substantially tiie same as the 

 formulae (36) and (46) from Lorentz' paper I.e. above, only simpli- 

 fied according to the conditions of the problem before us. 



dU 

 Now firstly — =— will be eliminated from eq. (9) by the aid of (8): 

 dy 



I I 



- S CdyQÜv = j'cly\Q'{7vy +iJ.'S^\. . . . (10) 







Secondly by integrating (8): 



liV = Sl + i dyQ^ (11) 







This equation allows the elimination of S from (10): 



j dy]Q' {uvY + f.' S' j _ 1 fj dy Q m^ j 

 H^ of 



I 



— I %9' 



(12) 







In order to simplify the equations we may introduce niidimen- 

 sioned variables by means of the formulae: 



V 



.c = I a-', y — ly' ; 7i — Vu', v — Vv' ; C == - 5' . . (13) 



If now in the following equations the accents are omitted again, 

 we obtain : 



1 1 1 



I dy (uv)' — I I dy iivj I dy C' j 



^=' ? +1-° ) . . (14) 



— I dy uv — I dy uv\ 







and by the same substitutions, from (11): 



S r - \ 



= — I dij uv -{ . 



iF' J • R 



(15) 







The equations take a very simple form if the following abbre- 

 viations are used : 



I 



