CL) 
height, we get a third line, which lies between the two former ones, and 
which we have already mentioned in our first Communication as the 
projection of the line of the double-points. The equation of this line 
may be found from the equations of p. 8 and 9 namely from: 
1 dp' 
Sha ea 
p de 
i dp! : 
and en | 
p dy 
: Pp Bau: ‘ 
In this case we have p’,, = log — and u’, = log; integrating we 
Pi Pr 
find for the equation of this curve: 
log p' = ¢ + « log Pa + y log Ps : 
Pi Py 
If 2 and y = O, this third sheet coincides with the two others, and 
p'=p.; from this the value of C may be calculated. We may also 
write this equation in the following form: 
p =p, (l—z—y) pps? 
or logp = (lL—a—y) log p, + w log p, + ylogps- 
This equation also represents a right line, which is displaced parallel 
to itself, if p' varies. 
So we find very simple lines for the three curves, which we get 
in this case for a binary system, namely a right line, a hyperbola, 
and between them an exponential curve. 
We shall now discuss the case which differs most from that which we 
have treated, namely that, in which each of the pairs that may be 
formed from the components of the ternary system, presents a maxi- 
mum pressure. The critical temperatures of the components do not 
differ much in this case, and for each pair a composition may be 
found, for which the function u’ vanishes. Then we may expect, 
that for the ternary system a value for x, and for y, may be found 
for which the values of w’,, and u’, are equal to zero. If the function 
uw’ depended only on 7%, then we might simply express this in 
properties of 7, and we might say: for each of the pairs a mini- 
mum critical temperature occurs, so we may also expect a minimum 
value for 7, for the ternary system. As u still contains the term 
log per, the same set of values of x, and y, which yields the mini- 
mum value of 7, will not make u’, and u’, vanish. This agrees 
indeed with the considerations for a binary mixture, given in Cont. II. 
For values of v, and y, differing only slightly from those, for which 
2 
Proceedings Royal Acad, Amsterdam, Vol, V, 
