( 486 ) 
more or less vague indications, but want to give clearly defined 
statements, the knowledge of most of the properties discussed is 
necessary. 
I already treated one of the meanings of the closed curve, p. 331 
2 2 
ae d d 
Contribution X. In this case contact of e= 0 and —" =0 occurs 
TL v 
for the first time at low temperature 7; at rising temperature there 
is intersection of these two curves. But with further rise of 7’ the 
two points of intersection draw nearer together, and at 7’= 7’, there 
2 
dy 
is again contact. For the case mentioned —- — 0 had again to lie 
at 
dp 
in the region where = = 0 is negative above 7'= 7,. But a second 
v 
ease is possible. 
With constantly rising temperature the intersection of the two 
curves may always proceed in the same sense, and then there can 
bl 
d 
also be contact at 7'= 7. Then the curve nl = 0 must disappear 
at 
a? 
in the region where er is positive. In Contribution HI I gave the 
av 
See dp 
equation which is to decide whether =e is to disappear in the 
Ai 
one region or in the other, viz. : 
cx (1 — #4) > Ay? 
a a +49 
d? ; : d? 
If the sign > holds, = = 0 disappears in the region where — : 
Ax Vv 
is positive, and the other way about. And now, to answer the 
question whether the first mentioned case takes place or the second, 
we must examine this equation, bearing in mind that «, and e, is 
positive, and that the points (¢,,¢,) lie below the parabola OPQ. 
The values of x, and Yg are dependent on mn, and quite determined 
by this quantity; and according to the list of calculated values 
occurring in the beginning of Contribution III, z, can only vary 
between */, and */,, and y, between */, and 0. So the second member 
of the inequality to be investigated is entirely determined by the 
ratio of the size of the molecules, but the first member depends 
moreover on ¢, and &,. 
Let us write this first member, omitting the index to z,: 
