(813) 



As to the coefficient /, it is to be considered as a function of iv, 

 whose value is i for ^p = 0, and which, for sinall values of ^r, differs 

 from unity no more than by an amount of the second order. 



The variable t' may be called the "local time"; indeed, for /;=: 1, 

 1=^1 it becomes identical with what I have formerly understood by 

 this name. 



If, finally, we put 



Fi'^ = ^' <^' 



/■■ u,. = u',, . k Uy =1 n\, , k U; = ii'~ , .... (8) 



these latter quautitics Ueiu^- considered as (he compuueuts uf a new 

 vector u', the equations take tlie toUowing form: 



dio' b' = 1 ;- fV . div' I)' = 0, 



1 /Ob' \ 



"''^-V^'-^^''} .... (9) 



1 d(>' \ 



rot b = — -, ) 



c dt' 



f, = I' b', -}-['.- (U', f)', - U', ()',/) + l^ . -^ (U', b', + U', b',), 



c ' c 



K K C fC C I 



l^ PI I'' IC 1 



f. = — I''. + ^^ «r b', - U', h'.,) - — . - U'.,. b'.. 1 



A; fi' c k c 



The meaning of the symbols dir' and rot' in (9) is siinilai- to that 

 of div and rot in (2); only, the differeutations witli respect to ,/',//, c 

 are to be replaced hy the correspoudiug ones with i-espect to ./■',//', ^'. 



§ 5. Tlie equations (9) lead to the conclusion that the vectors 

 b' and I)' may l)e represented by means of a sealar potemial (f' and 

 a vector potential ^i'. These potentials satisfy the equations ^) 



1 d'V 



A a' ^ - = p' u' (12) 



and in terms of them b' and I)' are gi\eii by 



1) M. E., §§ 4 and 10. 



