397 
that the line for solid-fluid retains its shape a to higher temperatures, 
and that then on rise of temperature a longitudinal plait arises on 
the righthand of a, which plait extends and overtakes the line for 
solid-fluid. It is clear that then contact takes place in the unstable 
plaitpoint Z, at low temperature, and that with rising temperature 
the intersections with the longitudinal plait may take place in reversed 
order as has been described above. In this case in opposition to 
fig. 2 the three-phase line L, +4 L, + G is stable at temperatures 
below the quadruple point, and at temperatures above it metastable, 
and the stable part of S + L, + L, possesses a positive value for 
dp ? ' ; 
oF This, however, does not affect the connection between the three- 
phase lines S-+ L, + G and S + L, + G, and the two other three- 
phase lines retain their critical points just as in fig. 2. 
Finally we may assume that the line for solid-fluid forces its way 
inside the longitudinal plait in the way represented in fig. 1 by the 
line p, and this line can again be displaced in two directions with 
respect to the longitudinal plait, so that either the stable or the 
metastable plaitpoint is situated at the lower temperature. 
So we get in all four different quadruple points, when the solid 
substance is the first component, and as many when the second 
component appears as solid substance, so that we have to conclude 
to eight different types of quadruple points, at least if we disregard 
the appearance of ordinary pressure and temperature maxima, which 
occur, if the situation of the three-phase points satisfies the conditions: 
Ys Ny Mae ly Ham Cn ek 
==). 
AAS vy Ut, v as Vg, 
I will not enter into the further treatment of these cases, because 
for all these possibilities the result already obtained in $ 3 always 
remains intact that the two three-phase lines S + L,+G and 
S + 1, + G are in continuous connection, and that on the two other 
three-phase lines two eritical points occur. Nevertheless it seemed 
desirable to me to give a survey of these possible cases, because 
the appearance of these quadruple points will not be rare; they will 
occur in almost any system where unmixing continues to exist below 
the melting-points of the components. 
5. The second case. 
In the second case we have supposed that the longitudinal plait 
continues to exist to above the lower critical temperature of the 
transverse plait. So one of the components has then become critical, 
