+00 
plaitpoint, will terminate in the critical point P, of the transverse 
plait, which has detached itself from the side, and a stable critical 
end-point occurs with the properties described by Sits in the system 
ether-anthraquinone. The three-phase line 5-+ L, + G then merges 
continuously into the three-phase line 5 + L, + L,. If, however, 
the transformation takes places after the state g, the three-phase line 
that has started from ZP, will pass into 5 —+ L, + L,, and terminate 
in the stable plaitpoint ?,. Then the three-phase lines S + L, 4 G 
and S + Lb, + G are continuously connected, and the latter ends 
again in a critical end-point on the closed transverse plait, which 
has detached itself. 
Finally we should still take into account the possibility that the 
line for tluid can possess the shape of line p in fig. 1, and also for 
this case we get four types of quadruple points, which, however, 
differ only slightly from the preceding types. 
All the possibilities, however, agree in this that either two critical 
points oeeur on the three-phase lines 5+ L, + L, and lL, + L, + G, 
and the continuous connection takes place between S-+L,+G and 
S +L, + G, or one of the three-phase lines S + L + G is in 
connection with 5 + L, + L,, and the other three-phase line S + L+G 
possesses one or two critical points. 
7. Im the preceding paragraphs we have pretty completely 
discussed the types which can possess quadruple points, in which the 
components occur as solid phases. The occurrence of mixed crystals 
and compounds does not give rise to essential modifications. All the 
same different types should be distinguished for these cases; this 
follows, namely, already from the fact that with the discussed 
quadruple points the solid substances always possess either the 
greatest or the smallest concentration, and so the possibility was 
excluded that the concentration of the solid substance lies between 
that of the coexisting liquid and vapour phases. To form an opinion 
of these cases the most rational way would be to have recourse to 
the y-surface ; this alone can give a complete insight into the pecu- 
liarities that oecur for a definite case. Generally, however, we can 
avoid this course; but then the danger is great to assume possibi- 
lities, which would appear to be physically impossible if the y-surface 
was consulted. To escape this danger, and to avoid on the other 
hand the more laborious way via the y-surface, | will here draw 
attention to a rule which gives a relation between the relative 
situation of the three-phase lines and the concentrations of the coexisting 
phases. 
