( 485 ) 
it 
or to values of BE sat But if it is asked whether it is probable 
that both cases occur, this probability depends on the value which 
[* must assume in these two cases. The point in which these spaces 
n—1)? 
touch, is the point where ¢, = n° ¢, = omen For this point to be 
possible the following equation must hold: 
(Qn He, +n’? ey —=407 (14+ &,)n’?(1 + &,) 
We find from this by substitution of the values ¢, and g, : 
fol (n +1) 
(n+ DH An — I 
So in any case a value of £ <1. It becomes smaller as 7 increases, 
i? 
and the limiting value for =o amounts to En Such a small value, 
however, / will most likely never assume. And if we now take 
into consideration that for the points of the lefthand part, for the 
ji 
points of which ee the value of / will have to be still smaller, 
we arrive at the conclusion that if is large, the case that the closed 
; 1 
curve remains restricted to values of «> rs will not have much 
chance of occurring. For the point in which the two spaces touch 
81 4 
? is equal to aE for n = 2, and this value is equal to 5 tor md; 
and we may consider these values of / as probably possible. So 
that we arrive at the conclusion that for not great values of n, e.g. 
f 1 
n = 3, the closed curve, if it exists, can occur atx > ah but that for 
higher values of mn, and also if / should be >1, the other case, 
1 
Bo is possible. 
Let us now proceed to derive some results on the miscibility or 
non-miscibility in the liquid state from what has been observed on 
the intersection of EM Sn and ee 4, for the case that the locus 
dx? dv? 
of the points of intersection is a closed curve, and to compare these 
results with the observed facts. All the properties discussed of the 
closed curve are perhaps no longer necessary if we could have 
anticipated this result. They have, however, been necessary for me 
to come to this conclusion. And if we do not content ourselves with 
