( 639 ) 
indicated in a recent communication of BAkHvis RoozrBoom and 
Bicuner !), the first of which is amply considered above. 
Fig. 7 gives the p,7-representation of it; fig. 8 the 7, r-diagram 
of some sections at constant pressure (the dotted boundary-curves are 
relative to pressures between that of J/" and C,, and to that below M'). 
The series of p,v-diagrams, and also the space-representation (also 
projected already by Bicnner) are omitted here. We find that case 
with mixtures of ethane and ethyl-, propyl-, isopropyl- and normal 
butylalcohol, all examined by Kurnen *). Also triethylamine + water, 
and some other mixtures *) with a lower critical point (this lies at 
18°,3 C in the last mentioned case) belong to that type. Indeed, it 
is obvious from fig.8 and from the p‚r-diagrams, that JL’ is at 
present a lower critical point, contrary to M in fig. 1, which was an 
upper critical point. For, whereas in M (fig. 1) the threephase-pressure 
ends, this pressure commences in M'. Farther however, in JZ", the 
gaseous phase coincides again with the first liquid phase (rich in ethane) 
(because the threephasepressure-curve J/M" anew meets the critical 
curve CC), after which the further course is the same as with the 
preceding type. The 7’,x-representation with variable threephase- 
pressure, that is to say between J/’ and J/" (fig. 9a), is in agreement 
with it. 
It appears that, as little as with the preceding type, there exists 
here a properly-said upper critical point. For in both cases 1 and 3 
coincide, when the threephase-pressure comes to an end, and not 1 and 2 
(see fig. 3a and 9a). The vapour-phase becomes identical with the 
upper liquid layer and vanishes, but then there remain still two 
phases, the lower liquid layer 2 and the fluid phase 1,3. These 
however always pass into each other with further increase of the 
temperature, as is plainly indicated by the space-representations 
(see e.g. fig. 4), at the vapourpressure-curve of the second component 
at we, =,= 1 (also compare the dotted boundary-curves in fig. 2 
and 8). So, if we begin with a mixture of a definite composition, 
then with increase of temperature we come finally beyond the bourdary- 
curve 1,3 at the moment, that the liquid layer 2 has entirely vanished. 
So we have demonstrated more exactly at the same time what I have 
said in my preceding communication, namely that the existence of 
a lower critical point involves necessarily that of a higher upper one. 
It is however not, as we have seen, a critical point proper. 
1) Id. 28 Jan. 1905, p. 531—537. 
2) Z. f. Ph. Ch. 28, p. 358—363 (1899). 
8) Among others €-collidine, and the bases of the pyridine- and chinoline-series 
with H,0. 
