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acd or it is partly two-leafed with the turning-line ef or gh. Also 
in fig. 5 a critical curve Ex is represented by acd; the region E 
is situated here, however, completely outside the critical curve and 
it may have a turning-line also in this case. 
We take in figs. 3 and 5 two points / and m on a vertical line; 
consequently we have 7; = 7. At the temperature 7; = 7%, two 
equilibria Ex exist, therefore, the one | £'x = L'x + G’'} under the 
pressure /, the other |Z", = L"x-+ G"| under the pressure P,,. 
The critical liquids Z'x and Lx may now belong either or not 
to the same region of un-mixing under its own vapour-pressure of 
the temperature 7) = 7;,. When they belong to the same region 
of un-mixing, then the region # is situated as in fig. 3; when 
they belong to different regions of un-mixing, then the region £ is 
situated as in fig. 5; in both cases either a turning-line may 
occur or not. 
We might think that in point c of figs. 3 or 5 two critical liquids 
get the same composition, so that 4, should be a critical liquid of 
the 2°¢ order. This is, however, not the case in the point c, but in 
another point A’ of the curve; this is drawn in fig. 5 on branch 
de. Curve acd touches in this point a curve KK, (not drawn in 
the figure); the points of this curve KK, represent critical liquids 
of the 2rd order. Of all those liquids only the liquid A can be in 
equilibrium with vapour. 
More-leafed regions. 
Besides one- and two-leafed regions, of which we have considered 
above some examples, also more-leafed regions may occur. This 
may take place e.g. when in the region Z occur two turning-lines. 
We shall. consider a definite case for fixing the ideas. For this we 
take the equilibrium == A+ L4G of a ternary system with 
the three volatile components A, B, and C. This equilibrium Z has 
two limit-lines H4—o and Ec=y; these are represented in the con- 
centration-diagram (fig. 6) by the sides BC and BA of the triangle 
ABC, in the P,T-diagram (fig. 7) by the curves ae! and dhkn. 
When we imagine in fig. 7 those two curves to be prolonged towards 
‚higher 7, then both curves terminate in a point B, which represents 
the P and 7 of the melting-point under its own vapour-pressure of 
the substance B. Above we have already said: that these curves 
may have a maximum of pressure or not. 
The equilibrium E= B + L + G consists at a temperature T, of 
a series of solutions, which are saturated with solid B and a series 
of corresponding vapours. This series of solutions forms the saturation 
77 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
