871 
We could also draw in tig. 2 still the P, 7-curve of the equilibrium 
A-+L-+ G of the binary system W 4 A; it appears from fig. 1 
that this curve must be situated in fig. 2 above the curves 7m 
and m 0. 
In our previous considerations we have followed for the deduction 
of the P,7-diagram the same way as in the deduction of the P,7- 
diagrams for some special cases in binary systems [Communication 
XI}. We have used viz. the concentration-diagrams and some of 
their properties. In the case which is discussed now, we used the 
property that the vapour-pressure increases along the saturation- 
curves in the direction of the little arrows. Further we have made 
the obvious supposition that in the concentration-diagram (fig. 1) 
the enrves mb and md go starting from im towards higher tempe- 
ratures and that curve mr goes, starting from m towards lower 
temperatures. 
We may, however, follow also quite another way, in which we 
may deduce -as well the P,7- as the concentration-diagram and in 
which we more plainly feel the suppositions which are assumed in 
the deductions. 
For this we consider the different reactions which may oceur in 
the invariant equilibriam: | 
Z+4,+A+L04+G 
With this we shall assume that the liquid Z is represented in fig. 1 
by a point m within the triangle 7,4 W. From the position of the 
five phases with respect to one another follow the reactions : 
1. For the singular equilibrium (MD) = 7+ 4, + G 
CP LZ (AV) Oa 
2. For the equilibrium (7) = Zj + A + LG 
LayG+uZ, + d—y—u) A (A Bres Rene 
Herein «, y, u, 1—# and 1—«—y have positive values, which may 
be determined when the compositions of the pbases are known. 
(AV) and (4H) are the changes in volume and entropy when 
reaction (1) proceeds from left to right, so that the indicated quan- 
tities participate in the reaction. The same is true for (A V)z and 
(AH)z. At the following reactions we shall indicate in the same 
way the changes in volume and entropy. 
Now we may deduce, as has been discussed formerly, from 1 and 2 the 
reactions for the other monovariant equilibria and also the isovolu- 
metrical and isentropical reaction. We find: 
