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latter of which contains the vapours and liquids which can be in 
equilibrium with solid C. 
If the liquid-vapour-surface touches the solubility isotherm of 
Sg + Sc, it is clear that also the lines starting from the nodes g,, /, 
and g,/, must touch, which accordingly takes place on the critical 
isotherm. 
If we now think the temperature still a little lower, the just 
mentioned contact will change into an intersection, and so two points 
of intersection will occur, one of which indicates the vapour phase, 
and the other the liquid phase of the four phase equilibrium 
Sp + So 4 LG. 
The intersection of these lines, which are indicated in projection 
by 9:9, Pi 4,4, and g,g, p, ll, means of course that the liquid- 
vapour surface intersects the solubility surfaces, in consequence of 
which the liquid-vapour equilibria get partly into the stable region. 
These stable liquid-vapour equilibria lie within the two intersecting 
lines g, p, 2, and g,p,/,. The first intersection line, which refers to 
the liquid and vapour phases which coexist with solid B, possesses 
a critical end-point in p,, and the second intersection line, which 
indicates the liquid and vapour phases which can be in equilibrium 
with solid C, possesses a critical end-point in p,. The points g, and 
J, denote, as was already said, the vapour and liquid coexisting 
with Sp +Sc, and so it is evident that through these two points 
the line must pass which has its origin in C, and indicates 
the coexistence of a fluid phase with a conglomerate of Sg 
and Su. : 
If we lower the temperature still more, the points g, and /,, and 
also p, and p, move more and more apart, whereas on rise of tem- 
perature they draw nearer and nearer together, and coincide in the 
double critical end-point, for which the symbol is Sa + Sc + (L=G). 
At temperatures above this double critical end-point there. will exist 
only fluid phases or coexistence between fluid phases with solid B 
resp. with solid C, or with the two solid substances at the same 
time. It is, however, clear that as was already observed, liquid will 
have to appear again in the ternary system before the eutectic tem- 
perature of the system B—C is reached, and so we see that when at 
lower temperature a double critical end-point has appeared, a second 
double critical end-point will occur at higher temperature, so that then 
at rise of temperature a repetition will take place of what has happened 
at lower temperature, but in the reversed order. So after the second 
double critical end-point has appeared, the stable part of the liquid- 
vapour-surface will continually increase in extent. To this is added 
