( 685 ) 
dT is positive, and the second surface, which is quite enclosed in 
the first represents the surface at higher temperature. If (&21)» should 
vanish for the chosen point, then that point would not change its 
place when the temperature is changed. If (ej), should be positive 
for certain points, then that point would move away from the second 
phasis when 7 is increased. As a special case the well known 
properties of the bordering curve for a simple substance are of 
course implied in this. If we have a ternary system, one of the 
components of which is water, at a temperature below 4°, then near 
the point representing water on the coexistence surface a curve is 
to be found where the peculiarity to contract when heated ceases to exist. 
We can easily form an idea of gradual change of the coexistence 
surfaces, and the other surfaces under consideration at increasing tem- 
perature, if the critical temperature of the mixtures of the three compo- 
nents always changes in the same direction, when the quantity of the 
second, or that of the third component is augmented. According to our 
a 
Due 
(EE b 
equation of state this would signify, that ee has always the same 
v 
a 
fei 
: b 
sign, — and also that 7 has always the same sign. If we put 
(Ler)y < Ler)e Z (Ler)o, then the three surfaces, coexistence surface, 
RCL 
spinodal surface, and surface for whicl em = 0, will consist of two 
: v 
separated sheets as long as 7 < (7e). If 7 has a value between 
(Ler)y and (Fe)e, the liquid sheet and the vapour sheet have met 
for mixtures, which consist chiefly of the third component, and in 
triangle OXY a curve may be drawn, which indicates the limit be- 
tween mixtures, which yet admit of coexisting phases at the given 
value of 7, and those, which continue to fill the volume homoge- 
neously, however large or small the pressure may be. This limit 
connects in this case a point of OY with a point of the hypothenuse. 
If 7 has risen above (Ter)z, tien the limit connects a point of OX 
with a point of OY, and if 7 has reached the value (Z.,)o the limit 
has contracted to the point 0. This limit is the projection of the 
points which the coexistence surface has in common with the tangent 
cylinder parallel to the v-axis; it represents the mixtures for which 
the chosen temperature is that of the critical tangent point. In order 
to find a property of these tangent points, we put the values of df’, 
dr, and dy, equal to zero in the differential equation of the coexis- 
tence surface. So we get: 
