dol 
was shown before for the case 5 with regard to the three-phase 
lines S, + 5,+1 and 5, +S, +G Y). 
If, however, we compare the three-phase lines S$, + L, + L, and 
S, + L, + L, of case 3 with the corresponding lines S,+L+G and 
S, JLG of case 5, it is clear that in the latter case the two 
lines terminate in the melting-points of the two components, at least 
if we have a case of the ordinary spacial figure. In case 3 on the 
other hand, the binodal line of the two liquids can be an entirely 
closed curve with two plaitpoints. Each of the three-phase lines 
8, +L, + L, and 5, + L, + L, will then possess two critical end- 
points in the /P,7-projection. Yet this difference between the cases 
3 and 5 is not so great as one would be led to expect at first sight. 
The occurrence of critical end-points is not confined to the case 3; 
also in case 5 it is possible that the three-phase lines 8, + L + G 
and S, + L + G do not reach the melting-point, but come into con- 
tact with a critical line. This case, which is pretty well the prevailing 
one in case 8, has been shown by Smits for case 5 in the system 
ether-anthraquinone. 
2. The quadruple point S+ L, + L, + G. 
So we have seen that the quadruple points 3 and 5 give rise to 
analogous phenomena; the only remaining case 6, however, deviates 
from what we discussed in many respects. Where in the quadruple 
points 8 and 5 continuity is always only possible between two 
phases we have three phases L,, Lb, and G, in the quadruple point 
6, which all three may pass continuously into each other. So the 
phenomena become more complicated here, and it is already a priori 
clear that the connection between the three-phase Jines may take 
place in different ways. What cases we have to distinguish for this 
quadruple point can be easily derived from Prof. vaN Der WaAats’ 
investigations on unmixing. It is known that the critical line can 
present very different shapes when a longitudinal plait exists on the 
w-surface. . 
In the first place we may imagine that at low temperature solely 
a transverse plait occurs on the w-surface, that on rise of tempera- 
ture a longitudinal plait is formed (insiae the transverse plait), that 
on further rise of temperature it makes its way outside the transverse 
plait, and that it afterwards again retreats inside the plait, and dis- 
appears at a temperature which lies lower than the lowest critical 
temperature of the transverse plait. This case, to which we shall 
") Cf. also § 3. 
