390 
fully I have, however, managed to give a survey of the phenomena 
which in general present themselves in quadruple points. It seems 
to me that the construction of the figures referring to a definite 
case will not present any difficulties, if this survey is consulted. 
In the first place I will assume in the following considerations 
that continuity only takes place between liquid and gas phases. So 
I preclude an eventually present continuity between solid and fluid. 
If it should appear that van Laar’s theory, which leads to this con- 
tinuity, is valid, this transition will also have to be reckoned with 
for a complete treatment. On the appearance of a quadruple point 
S,+58,+5,-+5, the four solid phases could then pass continuously 
into each other. Until, however, the existence of the continuity in 
question shall have been experimentally realized, it seems better to 
me not to take it into account to prevent our entering into an ela- 
borate consideration of a great many cases which may appear later 
on to be physically impossible. 
In the second place I exclude a continuity between solid phases. 
Their occurrence has indeed been ascertained, but until certainty 
has been obtained as to how the crystallographic orientation in the 
equation of state of the solid substance is to be taken into account, 
it seems impossible to me to obtain certainty about the connection 
of the three-phase lines in consequence of this continuity. 
If we now consider that in a binary system unmixing in the 
gaseous state has never been found as yet, and never more than 
two simultaneous liquid layers, it appears that in all six different 
quadruple points can occur: 
108 SAS AS 4.8 LE LL tb oe 
DS HS, LS, 14, 455, 4 82S 6G 6 SL 
In the quadruple points 1, 2, and 4 no continuities can appear 
between the three-phase lines, in which liquid and gas phases par- 
ticipate. Of the three cases 8, 5, and 6, which accordingly remain 
for our consideration, the case 5 has already been fully examined 
in the cited paper. 
Case 8 only differs slightly from 5. In the quadruple point 3 the 
the three-phase lines 8, +8, + L,, $8, +5, + L,, S, + L, + L, and 
S, + L, + L, occur, of which only the two first are in continuous 
connection with each other. It is easy to see by the aid of the V,2- 
projection, that this connection again takes place by means of an 
unstable branch with two cusps in the P,7-projection, just as this 
