760 
§ 10. We shall define a varied motion of the electric charges by 
the quantities dz, and we shall also vary the quantities y,,, so far 
as can be done without violating the connections (25) and (26). The 
possible variations dw, may be expressed in dz, and four other 
infinitesimal quantities g, which we shall presently introduce. Our 
condition will be that equation (12) shall be true if, leaving the 
gravitation field unchanged, we take for dz, and g, any continuous 
functions of the coordinates which vanish at the limits of the domain 
of integration. We shall understand by dw, du. dL the variations 
at a fixed point of this space. The variations dw, are again deter- 
mined by (13) and (14), and we have, in virtue of (26) and (25), 
Òdws, 05 
Soa =; iba = — dias, HO) Te = ding = EH) LL 
Ox» 0x4 
If therefore we put 
Os Yah Fahy en Ss eee 
we must have 
OP ab 
Dei = 0) Mia = — gs, 0). —— = 9. 
02s 
It can be shown that quantities %,, satisfying these conditions 
may be expressed in terms of four quantities q„ by means of the 
formulae 
Ogu Ògw 
Ot, Oxy 
Here a’ and /’ are the numbers that remain when of 1, 2, 3,4 
we omit a and 5, the choice of the value of a’ and that of 5’ 
being such that the order a, 6, a’, 6’ can be derived from the order 
1, 2, 3, 4 by an even number of permutations each of two numbers. 
(ab). se SS ER 
§ 11. By (34), (36) and (37) we have 
at eas Ph Oe ae 
SVN de, <= (all a ee 
Ory O2n 
+ Sb) ws Fos EEK dear 2 
Here, in the transformation of the first term on the right hand 
side it is found convenient to introduce a new notation for the 
quantities Ws. We shall put 
Wat = Wal’, 
L' = A (ad) War Was = + |p| & (abedef) 2a ab Pea Pfb Wed Wef= 
4 Pp = (cd) Wed Wed = IP | L, 
while 
ip] dS' =ds.. 
