449 
order in (1). The second part of G;; contributes nothing, and in the 
first part we need only substitute the first term of (2). We so get 
0 al 0 ij 
2x > all — ; = 
Be Gala RB 
Sell 0°Bu BG Orpen Bing En 
| da 0x qi Ow)? Oa) Ow j Ow 0x; 
If we indicate an index, that does not take the value 4, by placing 
it in parentheses, we can write for this 
gp tee ne ORE 
aD \ Oer °C OaOa; Ox 0a; 
ade je Bij OB rae) 
aie een Set 
Ow Ow; Oe? Ow AOP Ow 0a; 
in which the last term is at least of the second order. 
The terms of the first order become 
= (Pris ÒBu Bn 4 4 Sal 08u 
Oe,” 0.vj/0a; Ox 02; . 
(4) 
in the case i=|= 4,) S= 
“nk 
in the casei I= 4,7 — 4: zero, 
3 
in the casei—j—=4:—x > OP se NG i 
a) Ox)? 
1, to be the only of all 7, 
which contains a term o of order 0. Then the term of order O in 
= 
T being also e, we obtain 
0°78; ; 07 Bil 0785) 0231) 
eee ee 
Se dada; 0a Ow; i 7 dje. (2 | j = 4) 
We now suppose the quantity 7 
The equations are satisfied by 
Bij = 0 (7 nn) ’ By, a Pas — Py; = Bas = Ps ae WN ade (5) 
8 being a solution of 
This solution, however, is by no means unique. We may e.g. 
add to it 
dy 
Ox; Ow; 
where p is a function of 7,, 7, 2,; we will, however, not do so. 
[i j — 
3. Substituting the solution (5) into the expression (4) and omitting 
the terms of order 2, we obtain 
29 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
