548 
figs. 2, 4 and 5 (XVI). When (dT’)p is negative and (dP)r consequently 
positive, then the region is situated at tbe left and above the 
branch; this is the case with respect to branch ab in figs. 3 and 
5 (XVI), and with respect to branch cd in the figs. 1 and 3 (XVI). 
Consequently we find: A region is situated always at the right 
and below or at the left and above the ascending branch of its 
limit-curve. 
: dP d 
On the descending branch of a limit-curve ( ) is negative. It 
de 
follows from (18) that then (dP)r and (dT)p have the same sign. 
When both are positive, then the region is situated, therefore, at 
the right and above the branch. When both are negative, then it is 
situated at the left and below the branch. In fig. 5 (XVI) the region 
is situated at the right and above branch 6c; in fig. 3 (XVI) the 
region is situated at the right and above the part bf, and at the 
left and below the part fc of branch 5 c. 
Consequently we find: 
a region is situated at the right and below, or at the left and 
above the ascending branch of its limit-curve; it is situated at the 
right and above, or at the left and below the descending branch of 
its limit-curve. 
In Communication XI on: Equilibria in ternary systems, we 
have already deduced this same property for a special case viz. for 
the ternary region # + LG, in which ¥ represents a binary 
compound, with respect to its binary limit curve #+L-+G. 
Now it appears that this is true in general for each arbitrary 
region with respect to all its limit-curves. 
We may express the results obtained above also in another 
way. The equilibrium H= F,+...+ F,0f2—1 components in 
n phases is monovariant or invariant (P or 7’). When we add a 
little of a new substance X, then a new equilibrium #'— FF", +...+ F'n 
may arise. Herein the invariable phases have the same composition 
as in HH; the variable phases (which of course not all need to 
contain the new substance X) differ still only very little from 
those in #. 
We now may put the question: 
how must the temperature change under constant P or: how 
must the pressure change at constant 7’ in order that in both cases 
the equilibrium £ passes into EH’. 
It is clear that both questions are only another form of the 
questions, treated above: how must the temperature be changed 
