( 714 ) 
a 1e, 
ae B D 1 
represented by ¢, and e,‚ positive in the equations — = 
= — and 
c (n—1)? 
a, n*( l He.) 
oe ney? 
the curve a’,, = /a,a, lies outside this region, and the occurrence 
of the discussed phenomena will, therefore, have to be considered 
as comparatively rare. If we descend in the region OPQ, so that 
either «, or €, or both become negative, then (but the consequence 
of a negative value of ¢, and «, has not yet been discussed) three- 
phase-pressure is to be expectel already at 7’= 0. If we go upwards 
along the curve a’,,=fa,a,, and if we get above the paraboia 
with ¢, and «,, there is perfect miscibility. (For the values of ¢, and 
é, required for perfect miscibility consult Contribution XI p. 448). 
As the upward movement along the curve a*,, = (a,a, is attended 
and n—1 >Ve«,-+nVe,. By far the greater part of 
A Pleo e e Fy . 
with decrease of zor it follows from this that if in analogous cases 
Ph, 
> Pka _ N ° af en erris pl 
the ratio ~~ decreases, we pass trom non-miscibility to perfect 
Pk, 
miscibility. 
The conclusions in the derivation of which we have supposed to 
treat only normal cases, viz. such for which no chemical action takes 
place between the two components, or for which each of the com- 
ponents behaves normally, are quite corroberated by the observations. 
I know only of one exception, namely that the case of fig. 40 occurs 
also in the observations of KueNeN for mixtures of ethane and aethy1- 
aleohol, ete. In this case we have to put nm either below or just 
above 2. How it is that the abnormal behaviour of alcohol has here 
an influence as if 2 were increased, cannot be accounted for as yet. 
But in the cases of Bicuner for mixtures of carbonic acid and organic 
liquids, tor which also fig. 40 gives the course schematically, 7 will, 
no doubt, have the value found by calculation. (Böcunrer, Thesis for 
the doctorate 1905). 
In conclusion a few remarks. 
1. In fig. 30 of Contribution VI I have already given the course 
of the plaitpoint line for the case of fig. 39, and also of the three- 
phase-pressure of 7. 
2. The upper and the lower sheet of the surface of saturation 
are subjected to some modification in the case of fig. 39 only between 
the two temperatures between which there is three-phase-pressure. 
The modification for the upper sheet consists in what follows. Between 
the limiting values of w of the dotted closed curve of fig. 39 the _ 
