1337 
of two different solid phases in the unary system (monotropy and 
enantiotropy), the S-values for the different solid mixtures of the 
pseudo-binary system must present {vo minima at constant T and P. 
Whether these two minima lie on the same continuous §,x-line, or 
on two different branches, which have nothing to do with each 
other, is a question which, as I already demonstrated before, is of 
minor importance for the theory of allotropy. 5) The principal thing 
is that these two minima must exist, and must lie on the same 
horizontal bi-tangent at the transition point. 
All this was already fully explained and applied before, to indicate 
the situation of the T,x-lines of the unary system in the T,x-figure 
of the pseudo-binary system. 
We may also express this as follows: we considered the (T,X)p 
sections of the pseudo binary P,T,X spacial representation, which 
of course also contains the P,T.X spacial representation of the 
unary system. 
Now it is of importance with a view to investigations which are 
in progress, also to examine the P,Xj;-sections of the spacial repre- 
sentation under discussion, about which a few general remarks will 
first be made. 
2. PT,N-spacial representation. 
/ 1 
The P,T,X spacial representation of the pseudo-binary system 
consists, as is known, of a number of systems of two surfaces 
belonging together. At the place where two homonymous surfaces 
intersect, three-phase coexistences arise, and at the place where 
three homonymous surfaces meet a four-phase coexistence occurs. 
The P,T,X-spacial figure of the unary system consists of a number 
of surfaces of internal equilibrium, and where one of these surfaces 
meets a homonymous surface of the pseudo-binary system, a two- 
phase coexistence of the unary system occurs. Thus the surface 
for the internal liquid equilibria e.g. intersects the liquid surface 
for the coexistence liquid-vapour in the pseudo-binary system. Hence 
every point of this line of intersection represents a liquid coexisting 
with vapour in the wrary system. The intersection of the plane 
for the internal vapour equilibria with the vapour surface for the 
coexistence liquid-vapour in the pseudo-binary system equally yields 
a line of intersection, every point of which indicates a vapour 
coexisting with liquid in the wrary system. These vapour and 
1) These Proc. XVII p. 672. 
Zeitschr. f. physik. Chemie 89, 257 (1915). 
