1208 
ed ete HARE ®, [d (), sh a ] ste Yi, Ld (y), = oe] ar 7 
APS eT eS RAR 
—V,AP + HAT He, [d(e), +--.]+4,[d(y), +--+... Ae 
gee REE Spee SAE | 
and still »—2 other equations. It follows from (3) 
Ale), + Ad (©), + =de), + Hd (2), +. = AK a 
d(y), +4@(y), +... =d(y), + Ed (Ys +... =AK, 
ete. In accordance with our notation is e.g. 
d (a), = (Px), AP + (Te), AT + (2), Az, + (wy), Ay, Ho 
ov OH 0°Z d°Z 
4 *AP— = AT + — Az —— A 
ts ca Se age ng ae ed 
d(y), = (Py), AP + (Ty), AT + (ay), Oe, + (y’), Oy, + ++: 
OV. 0H eZ PZ 
' LAP — - wt AT + —~ aN Ly 
2 Oy, Oy, he: Òz,Òr, Ok Oy? nt 
When a phase eg. /, has a sense composition, then for this 
(4) is true; instead of the first equation (7) we find then: 
-~_VAPLHAT baldo |e le@iss- JAE 
Consequently in the first equation (7) are missing then the terms 
tf nO, ete. 
Equilibria of n components in n phases under constant pressure. 
When we keep the pressure constant, then we have to omit in 
(7) and (8) all the terms with AP; the sign d indicates then that we 
have to differentiate according to all variables, except P. 
Now we have in (7) and (8) n° equations and n’+-1 differentials 
AT, Ax,..., so that their relations are defined. Consequently to 
each definite differential of one of the variables e.g. Ar, belongs a 
detinite differential of each of the other variables, therefore, e.g. also 
of AT. On change of x, (or one of the other variables) the equi- 
librium £ follows, therefore, in the P,7-diagram a straight line, 
parallel to the 7’axis. 
Now we shall put the question: when wilt the temperature 
be maximum or minimum? 
For this it is necessary that A7' is of the second order; then it 
follows from (7) and (8) that it must be possible to satisfy: 
w,d(«), +y¥,d(y),+..-= AK 
. 
and 
