547 
positive in part abf of curve abed fig. 3 (XVI) and negative 
in the part fed. Then it follows from (12) and (15) that the region 
must be situated as is drawn in fig. 3 (XVI) viz. that a part a fe 
of this region must be situated outside the limit-line and that this 
region must have a turning line ef. 
It appears from the following that this point f must be a point 
of the turning-line. In this point 2(2e)— 0. As in this point also 
the equations (10) are valid, a phase reaction 2,#, +... ar #,=0 
may oecur between the » phases of the equilibrium H= F, +...+ F,, 
in which an infinitely small quantity of the component X occurs 
now also. ; 
Consequently when ina definite point f of curve abcd ZY (Ar) = 0, 
then f is a common point of turning- and limit-line; later we 
shall see that f is a point of contact. When (42) changes in 
sign in f, then f is a terminating point of the turning-line as in 
fig. 3 (XVI); when however (Ax) does not change its sign in f, 
then f is not a terminating point, but the curve proceeds further. 
From (12), (15) and (17) follows the relation: 
: dP 
(dP)r : (aT) p -— (55) ze oen nem ks) 
d1 Ti 0 
5 yaar dP 
The index =O in the second part of (18) indicates that TP 
C 
is true for the limit-curve, in which the component X is missing. 
In order to comprehend the meaning of (18), we imagine the 
P,T-eurve of the limit-equilibrium, to be drawn in which the com- 
ponent X does not occur, therefore. For this we take the curves 
ab and ed in the figures 1, 2 and 4 (XVI) and curve abed in 
the figures 3 and 5 (XVI). [We have to place again the latter figure 
in the right position |. 
We shall call the branches on which the pressure increases with 
increase of 7 the “ascending” branches, e.g. the branches « b and 
ed in the figures 1, 2, 3, 4 and 5 (XVI). A branch like eg. be in 
figs. 3 and 5 (XVI), on which the pressure decreases at increase 
of 7, is called a “descending” branch. 
: ENS she ; 
On an ascending branch (=) iE positive, then it follows from (18) 
that (/P?)7 and (dT)p have opposite signs. When (/7’)p is positive 
and consequently (d/’)y negative, then the region is situated at the 
right and below the branch; this is the case with respect to branch 
ab in the figs. 1, 2 and 4 (XVI) and with respect to branch ed in the 
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