( 460 ) 
Now we may proceed to investigate what geometrical configuration 
the ¢-surface will show for a ternary system, specially at the critical 
circumstances of the gas- and liquid state. Let us assume an « and 
an y-axis, in order to be able to indicate by means of the values 
of « and y the composition of the mixture, which consists of 1—z—y 
molecules of the first substance, z molecules of the second substance 
and y molecules of the third substance. The ¢-surface can only extend 
over points lying within the right-angled triangle of which the sides 
containing the right angle are lying on the « and y axes and havea 
length equal to unity. For x negative, for y negative or for 1—z—y 
negative, the first part of ¢, viz. the pure function of z and y, 1s 
imaginary. Let us now think the conditions of fig. 2 satisfied for the 
«component so that the temperature lies between the critical tempera- 
tures of the first and the second component, and the ¢-curve as having 
the shape of fig. 3 above oe for a certain pressure below the plait- 
point pressure. Let us assume the same of the y component. 
The temperature is chosen in such a way, that (see fig. 6) 
(Ter)o< T, but (Ter)a> T and also (Te) > T. If the two com- 
ponents « and y were identical, we could construe in the OX Y-plane 
within the triangle OAB, the following rectiliniar projections, 
parallel to the hypothenuse. Ist The projection of the double points. 
2nd The projections of the points of contact B and £', which lie 
on the double tangent. 3'¢ The projections of the points of 
inflection FE and £' and 4. The projections of the cusps 
D and D'. In this case, however, the system is only seemingly 
ternary, but in reality it is a binary mixture with rz + y molecules 
of a second component. A pair of coexisting phases are then indicated 
by two points of the projection mentioned sub 2, chosen in such a 
way that the line which connects them, passes through the origin O. 
But if the third component is made to differ from the second com- 
ponent, so that the ¢-curve over OB, though it has in its main 
features the form of fig. 3, yet in details deviates from it, then we 
get four curvilinear projections instead of the four rectiliniar projections. 
Then we get again 1st the locus of the projection of the double 
points. The existence of such a locus may be derived from the 
following considerations. We wish to represent the value of ¢ for 
homogeneous phases, and we have had to assume for the isothermal for 
homogeneous phases according to the principle of continuity that 
below a certain temperature, the pressure will have a maximum 
value and a minimum value and that it will therefore be possible 
to draw a straight line in accordance with the criterium of Max WELL. 
_— is des 
