1368 
direction of one of the coordinates e.g. of z, over the distance de, 
We had then to keep in mind that for the two sides the values of 
wp, Which have opposite signs, are a little different ; and it was 
precisely this difference that was of importance. In the calculation 
of the integral 
02a 
fu zo ee NEA ee ee 
Ow 
le 
however it may be neglected. Hence, when we express the compo- 
nents ws in terms of the quantities wos, we may give to these latter 
the values which they have at the point P. 
Let us consider two sides situated at the ends of the edges dv,, and 
whose magnitude we may therefore express in w-units by da; der da; 
if j, #, l are the numbers which are left of 1, 2, 3, 4 when the number 
e is omitted. For the part contributed to (38) by the side =, we 
found in $ 26 
Whe da; daz, da, . 
We now find for the part of (39) due to the two sides 
Whe & (c) = fs do —{x. zo| 
we 
1 
2 
where the first integral relates to 2, and the second to &,. It is 
clear that but one value of c, viz. e has to be considered. As every- 
where in >,:xX,—==0 and everywhere in >,:x,— dz, it is further 
evident that the above expression becomes 
Oba 
dW. 
Ove 
Web 
This is one part contributed to the expression (36). A second part, 
the origin of which will be immediately understood, is found by 
interchanging 6 and e. With a view to (37) and because of 
Web = — Whe 
we have for each term of (36) another by which it is cancelled. 
This is what had to be proved. 
§ 31. Now that we have shown that equation (32) holds for each 
element (dz,,...dz,) we may conclude by the considerations of $ 21 
that this is equally true for any arbitrarily chosen magnitude and 
shape of the extension 2. In particular the equation may be applied 
to an element (da’,...d2',) and by considerations exactly similar to 
