1213 
22 (AH ‘ 
Ao = = Bie Ar. nae EL 
—A 
Hence it appears that to each definite value of 4 7’ two values 
of Ar, (and consequently also of Arv,... Ay, Ay,...) belong, which 
differ from one another in sign only. When the form under the 
root in (20) is positive, then Aw, Az,... Ay, Ay, ... have, therefore, 
each two real values; when this form is negative, then Az, . 
are imaginary. ; 
Consequently we distinguish two cases. 
When ZH) and A have the same sign, then we must take 
AT negative in order to obtain real values for Aw,...; the tem- 
perature Tr is, therefore, a maximum. At Tr there exists therefore 
one single equilibrium Zr; at 7r+AT' (we take A70) no equi- 
librium Z exists; at 7r—A 7, however, two different equilibria exist, 
which we shall call #' and Z". 
When %(A#) and A have the same sign, then we have to take 
A T positive, in order to obtain real values for Aw, ... Consequently 
Tr is a minimum. Then at Pr A7 two different equilibria 
E' and £" exist, at Zr—A 7 no equilibrium £ exists. 
We may also express the previous in the following way. 
When under constant P the temperature is a maximum on the 
turning-line Hp, then two leaves of the region go, starting from 
this turning-line, towards lower 7 and not a single leaf towards 
higher 7. 
When under constant ‘P the temperature is a minimum on the 
turning-line Hp, then two leaves of the region go towards higher 
7 starting from this turning-line, and no single leaf towards lower 7’. 
With our considerations on the region # in the previous com- 
munication XVI, we have already applied these results. The figs. 2 
(XVI) and 4 (XVI) in which ef represents a turning-line, are in 
accordance with this. In fig. 7 (XVI) g/ and dm are the limit-lines, 
MSm a turning-line. In order to show that also this diagram is in 
accordance with those results, we consider the horizontal line qrst; 
in order to show more distinctly the situation of those leaves, it is 
partly dotted and curved in r and s. In r 7 is a maximum, this 
corresponds to the fact that two, leaves go, starting from curve mS 
towards lower and no leaf towards higher 7. In s 7 isa minimum, 
two leaves go towards higher- and no leaf towards lower temperatures. 
We have seen that at the temperature 7’, only one single equi- 
librium Hr= F,+ F, +... exists and that a phase-reaction may 
occur between the phases of this equilibrium. At Pr + AMAT <0 
