104 
We shall presently return to these results, but we may now 
already state that with suitable values of a,, and a, really vapour 
pressure lines are obtained which perfectly agree in type with the 
experimentally determined ones. It deserves notice that this result is 
; 2 
in the first place the consequence of the great value which a 
& 
ae b. 
assumes according to our suppositions (great value of , and validity 
etd) 
el: 
of Lorentz’s formula for h,,)}. If we take 5 as linear function of 7, 
b 
as is often permissible for small values of ee nothing remains of these 
My 
results. The obtained vapour-pressure lines are namely characterised 
by this that u’, is strongly positive for values of « near 1, which 
leads to the strongly convex pz-line, whereas near «=O ws is 
strongly negative, which circumstance gives rise to the region of 
unmixing. If, however, we take 4 as linearly dependent on x, change 
of sign of u’, becomes impossible’). This quantity must have the same 
sign throughout the whole breadth of the figure; then we can have 
unmixing with negative value of «’,, but then the vapour pressure 
line ends also concave downwards on the side of the slight vapour 
pressures. This is accompanied by an extension of the region of 
unmixing over the full width of the figure as in the case of mercury- 
water. When the vapour-pressure line ends concave downward, 
however, on the side of the small vapour pressures, u’; must be 
positive, and then unmixing is impossible. And this holds whatever 
values one may choose for a, and a,,. Only for very large values of 
2 
„as they follow from the formula of Lorentz for great values of 
& 
b, Ae 3 He 
— a region of unmixing can occur in a pz-line which is convex on 
1 
the other side. Whether this region of unmixing then occurs, and how 
wide it will be, will depend on the a’s, and more particularly on 
a j : 
the ratio of —2. We have seen this already in the foregoing discus- 
a, 
sion, and we shall find confirmed in what follows that only a very 
small change of this quantity is required to make a mixture with 
an exceedingly narrow region of unmixing on the side of the small 
molecule pass into a system that is miscible over its full breadth. 
This is in accordance with Mr. Karz’s remark “limited or unlimited 
miscibility, it seems, may depend on small factors, as closely allied 
1) Cont. Il, p. 152, 
