Cay) 
to the right angle. If p, <p <p, then they cut the hypothenuse 
and the other side corresponding with the third component. If 
p=p, then the two branches cut one another in the angle of the 
second component. We might find the equation of these curves if 
0% 07s 07g 
and 
02,7 Ow, Oy, Oy,” 
were known. And though this is not completely possible in all cases, 
we could express zr, and y, in wv, and y,, and if 
yet in some cases we may find the equation approximately. A 
digression in order to discuss these quantities cannot be left out here; 
else we shall always be confronted with the same unanswered 
questions in all subsequent problems. 
The value of § is given p. 449, vol. IV, in the following form: 
$= MRT \(1—a—y) log 1 —a—y) + a log a + y log y} + pv =) pdv. 
We omit the linear function of rv and y, as it has no influence 
on the phenomena of equilibrium. So the value of & consists of a 
pure function of « and y, and of another part which fulfils the well 
known condition : 
(dr = vdp. 
This second part is known if the equation of state is known. In 
fig. 1, p. 450 1 have represented graphically this second part such 
as we may conclude its course to be if we only assume the principle 
of continuity. In what follows we will extend the principle of con- 
tinuity so far, that we assume the equation of state to vary fluently 
if « and y vary fluently. We now imagine the second part of § to 
be construed for all mixtures, i. e. for all values of x and y, and 
for all values of p. If we now put p == constant, then we have an 
auxiliary quantity, which varies with « and y, and the knowledge 
of whose properties is the condition for the solving of all questions 
relating to the equilibrium, either of a binary, or of a ternary mixture, 
or of any system of still more components. As we have already stated 
the knowledge of this quantity depends on the knowledge of the 
equation of state. From this appears, how absurd the opinion is, that 
knowledge of the equation of state would not be required for the 
knowledge of these systems. Yet we find this opinion often expressed. 
For the knowledge of the equilibrium of a simple substance it would 
be required, but for much more complicated systems it would be 
totally superfluous! I have introduced this auxiliary quantity already 
before (see i. a. Cont. II, p. 147); I shall represent by u the quotient, 
obtained by dividing it by MRT. Now we have: 
