384 
in the system ether-water In fig. 43 the case has been drawn that 
the three-phase line would just terminate at the minimum critical 
temperature; in the 17th contribution, however, it is pointed out 
that this end-point of the three-phase line, which we will designate 
by the name of “critical endpoint” in our further considerations, 
may occur both on the branch AQ, and on the branch Q, Pea. 
Hence we shall have to distinguish three cases as regards the 
relative situation of the critical end-point and the minimum critical 
temperature, viz. : 
1. If the critical end-point lies on the branch AQ,, the critical 
line in its P,7-projection will have the shape as has been drawn 
in fig. 51 of the paper that has already been cited several times. 
Then the minimum critical temperature is found in the metastable 
region, and cannot be experimentally realized except by the appear- 
ance of phenomena of retardation. 
2. If the three-phase line terminates exactly in the point Q, 
(fig. 43), the minimum critical temperature would occur just on the 
boundary of metastable and stable phases, and so it could be demon- 
strated by experiment. The P,7-projection for this case has been 
represented in fig. 50. 
3. If lastly the three-phase line terminates on the branch Q, Pa, 
the critical end-point lies on the righthand of the minimum critical 
temperature. Accordingly the latter, if really present, will lie in the 
stable region, and might be found experimentally. If, however, it is 
not present, it might be imagined to lie outside the figure, and the 
plaitpoint curve on the side of the ether would have to exhibit the 
tendency to this minimum. At last as transition case we might still 
suppose that the minimum critical temperature would just coincide 
with the critical point of ether, and that therefore it could just be 
still demonstrated. As far as the P,7-projection is concerned, the 
presence or absence of the minimum critical temperature would have 
to manifest itself in a strong negative rise with vertical tangent, 
resp. in a very strong positive rise on the ether side. 
From the above-cited experiments by KuerNeN it may be already 
inferred that the system ether-water is a case as mentioned under 
3. The eritical temperature of the upper layer lies, namely, at 
higher temperature than the critical temperature of pure ether. So 
the critical end-point lies on the ascending branch in the 7’,a-pro- 
jection. 
In the cited treatise case 3 has therefore been fully examined, 
and Prof. van DER WAAIs arrives at the conclusion that it is possible 
that the three-phase line before terminating on the critical line, first 
