1367 
in positive directions. To the right hand sides of the equations (34) 
we may apply transformation (35) with these values of aa, d2 
being infinitely small of the fourth order and it being allowed to 
confine ourselves to quantities of this order. 
On the left hand sides of (34), however, we must take into 
consideration, the surface being of the third order, that the values 
of ars, change from point to point. Let X,, . . . . X, be the changes 
WOR a z, undergo when we pass from to any other 
point of the surface. Then we must write for the value of the 
coefficient at this last point 
da 
Nba + & (c) de En: 
dee 
We thus have 
Oba 
ug da = > (b) aha] us ds + & (b) | us = (c) 5 x, do. 
It will be shown presently that the last term vanishes. This being 
proved, it is clear that the relations (34) follow from (83); indeed, 
multiplying equations (33) by aria, .. « « %4u respectively and adding 
them we find 
fe. dou. 
0 
LE cae ELO 
Òz, 5 
$ 30. The proof for 
zo fm = (c) 
rests on the relations 
> 
OX5a O%ea 
Owe Owe’ See 
_ which follow from 
de, U2'a 
pian Ox, oe Oae 
The integral which occurs in (36) differs from 
ie toes akerin! 
by the infinitely small factor under the sign of integration 
OX ha 
Ox, 
Now we have calculated in § 26 integrals like (88) by taking 
together each time two opposite sides, one of which >=, passes through 
P while the second =, is obtained from the first by a shift in the 
= (c) 
> Hi 
