( 687 ) 
minimum value for a certain mixture, i.e. according to our equation 
of state, if a value of 2 and y is to be found between 0 and 1, 
for which 
a 
We 
b 
aes: 
and 
a 
d- 
b 
== 0 
dy 
then the connection between liquid- and vapour sheet is established 
in the middle of the triangle OXY. 
If 7 has reached its minimum value, the sheets of the coexistence 
surface have not yet coincided but the two sheets of the surface, 
Meee : : 
for which = 0, have. For the point at which this takes place, the 
VU 
following conditions must be satisfied : 
dp 0°p dp 
= == Oy and = 0. 
Ov? ” Qxdu En dydv 
op dp 
We deduce from the circumstance that — a, L and a vanish at the same 
time, that this coincidence of the two sheets occurs at the ordinary 
dp 0? 
critical circumstances. The two other equations ee — Oand 
zov dydv 
Ter Ter 
must be equivalent with nk == OR ae 
oz dy 
lows immediately from our equation of state. 
Only at a somewhat higher temperature the sheets of the coexis- 
tence surface coincide in one point, — and at the same time in the 
same point the two sheets of the spinodal surface ; but we will not 
deduce the equations for the moment. At a still higher temperature 
a closed curve is to be found within the triangle OXY, the points 
inside which represent mixtures, which do not admit of coexisting phases 
at this value of 7. This closed curve extends if 7 increases, which exten- 
sion may take place in different ways, as we have mentioned before. 
Before leaving off the discussion of the general properties of these 
surfaces, we will still make a remark of general character. 
Let us imagine a point on the liquid sheet of the surface repre- 
senting the limit between stable and unstable phases. The equation 
of that surface may be written as follows: 
925 95 95 \2 
= (5), eon (a), 
id 
= 0. This equivalence fol- 
