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another particularity in the system 
B—C at the temperature of the 
eutectic point, viz. that the vapour- 
points eg, 9, and g, coincide just 
as the liquid points 7,7, and 4, 
Now that this projection has 
been briefly discussed, it is very 
easy to project the indicated spacial 
lines on -the concentration triangle, 
as has been done in fig. 4. 
We see from this figure that 
Fig. 4. the two continuous vapour-liquid 
lines of the two three-phase equilibria S3 + L-+G and So + L + G, 
indicated by the letters g,9,p,/, resp. 929, Pp. 4 intersect in two 
points g, and /,, where four-phase equilibrium prevails, and where 
accordingly also the fluid line of the three-phase equilibrium Sg-+S y+ F 
runs, which is denoted by the symbols cg, /,. It is further note- 
worthy that the liquid branches of the three-phase equilibria 
Sp +L+G and Sc +L+6G are cut by the critical isotherm Ak, 
so that p, and p, are two critical end-points. 
If we start from a temperature lying a little above that of the 
first critical end-points in the systems B—A and C—4A, we know 
that on rise of temperature not only the critical end-points p, and 
p2, but also the vapour point g, and the liquid point /, of the four 
phase equilibrium Sg +4 So + L + G will approach each other till 
they coincide in the double critical end-point. As g, is a point of 
the ternary eutectic vapour-line and /, a point of the ternary eutectic 
liquid-line it follows from what precedes that these two ternary eutectic 
lines will have to pass continuously into each other in the double critical 
end-point. In the first double critical end-point P the continuous 
eutectic line possesses in conse- 
quence a temperature maaimume- 
At higher temperature the second 
double critical end-point Q occurs, 
and from this temperature the liquid 
and vapour points of the second 
continuous part of the eutectic line 
recede more and more from each 
other, so that the second double 
critical end-point is at the same 
time the temperature minimum 
of the second continuous part of 
