fae || 
543 
0Z,' 0Z,' 
AR Ee es BS = | 
2, Oy, 
VAR 2 
Ze — RT zE Ya .-.-- == 
Oz, ~~ Oy, 
ete. The first series of the equations (3) (XVII) passes into: 
0Z,' 0Z,' 
Slog ae ted logian wat, KG SEE (84) 
Ox, Ox, 
The following series of the equations (3) (XVII) become: 
dZ,' 0Z,' OZ, (5) 
SS SS = +0000 == = vo 
dy, Oy, un 
etc. It follows from (4): 
x, 0Z,' 0Z,' 
RT log == 
UE OER 4 
(6) 
OO, 
RT log —= 
1 Oz, Ox, 
or 
=n By SMG, oo eos =o s (U) 
in which u,‚u,... are defined by (6). 
For values infinitely small of z,2,... the ratios between 
LE, L,--- En are consequently defined by (7). 
Now we give the increments: d7’.x,2,... dy,... dy, etc, to 
the variables 727, 2,...4,y,-.-. etc, in which we put z,=— 0 
== : 
Now it follows from (3): 
0Z,' 
H dT + RT a, + y,¢d— + oib & oe = — dK 
oy, 
(8) 
nr 0Z,' pd 
B Elendes dk | 
Ya 
ete. in which the sign d indicates that we have to differentiate 
according to all variables. 
Now we add the m equations (8) after having multiplied the 
first by 4,, the second by 2, ete. Then we obtain, when we 
use the relations which follow from (5): 
; 0Z,' 
2(AH) dT + RT Z (A 2) 4 zona) ) +...=— ZS (3) dK (9) 
Ji 
Now we define 2,À,... in such a way that they satisfy the 
n—1 equations (10) 
36* 
