1389 
regions of the equilibria, which are represented by a point of a 
P,T-diagram, can never coincide completely or partly. 
It appears from the previous that this is really possible, when 
we take also metastable conditions into consideration. When we 
take e.g. a point on the metastable part of curve (1) in fig. 2 (ID, 
then this point represents the metastable equilibrium (1) = 2845 
and the stable equilibria 124, 125 and 135. In fig. 1 (1D) quadrangle 
2345 coincides partly with each of the triangles 124, 125, and 135. 
Now we shall prove the second of the rules mentioned above. 
We call the pressure and the temperature of the invariant point 
P, and 7, those of a point Q in the P, T-diagram P, and 7’. 
We consider of the phases occurring in the invariant point, a complex: 
X=a,F, + 4,F, +... + Gate Pate 
and we imagine this to be represented by a point X of the concen- 
tration-diagram. When we change pressure and temperature from 
P 
or bivariant equilibrium |S 
and 7, to P, and 7’, then the complex .Y passes into a mono- 
When we change now the composition 
0 
- 
of the complex AN, then we may distinguish two cases, viz. the 
equilibrium |S. remains or a new equilibrium S,, is formed. In 
the first case, however, the ratios of the quantities of the phases, 
of which SN, is composed change. 
Now we change the composition of the complex \ in such a 
way that the point \ traces the whole concentration-region of the 
invariant point; then in the point @Q occur one or more equilibria 
S)S,... and no others can exist. The sum of the concentrationregions 
of these equilibria must, therefore, be equal to the concentration- 
region of the invariant point. 
In our considerations we have assumed that the phases in the 
invariant point and in the point @ have still the same composition, 
this is no more the case when gases, solutions or mixed crystals 
occur. When this is the case, then those phases have no more the 
same composition in the invariant point and in the point Q, so that 
also the points, representing those pliases in the concentration-dia- 
gram, are displaced a little. Also a same phase can be indicated 
by different points, when it belongs to different equilibria. All those 
differences are however smaller, in proportion as the point Q is taken 
more closely to the invariant point. When we take into consider- 
ation those differences, then we have to formulate the rule a little 
differently. This is, however, not necessary for the application and 
we have to keep the same composition as in the invariant point 
for all phases in the point Q. 
