190 
the eutectic line. If we represent this in a diagram, i.e. if we 
draw the projection of the pq-lines and that of the eutectic lines in 
the concentration triangle, we get fig. 5, in which the arrows again 
indicate the direction in which the temperature rises. 
It is clear, that it is also possible that the two continous p q-lines 
do not intersect. In this case there are no double critical end-points, 
and so the eutectic lines proceed undisturbed up to the ternary 
eutectic point. 
Ath case. In the fourth case we might suppose that each of the 
binary systems presents critical end-points. To realize this case we 
shall have to choose three substances, the critical temperatures of 
which lie apart as far as possible, so that in each binary system the 
triple point of one component lies far above the critical temperature 
of the other. If then double critical endpoints occur, we get a com- 
bination of fig. 2 and fig. 5. 
5th Case. It is elear that the appearance of mixed crystals in the 
system 6—C' does not bring about 
any change in the foregoing con- 
siderations, when this system has 
a eutectic point; if this is not the 
case, modifications appear which 
are most considerable when the 
components B and C are miscible 
in all proportions, as in the system 
SO,+Hebr,—HegJ,. examined by 
Nieer1'). The projection of the criti- 
cal end-point lines runs then as is 
schematically represented in fig. 6. Fig. 6. 
Now it should be pointed out, however, that when the melting- 
point line of the system 4L—C has a very marked minimum, a 
closed portion can be formed in the middle of the figure, so that no critical 
endpoints occur there then. If on the other hand the said continuous 
melting-point line has a very marked maximum, the special case might 
be found that though no critical endpoints occur in the binary systems 
A—B and A—C, they do occur in the ternary system. We can 
imagine that this case arises from the ordinary case fig. 6 by the 
points p, and gq,, and also p, and g, approaching each other and 
coinciding, in consequence of which the two critical end-point lines 
merge continuously into one another. If then this continuous curve 
contracts still further, we have obtained a closed critical end-point 
curve, which lies quite inside the concentration triangle. 
1) Niaeui, The projection. 
