7 
in a paper by Mr. Timmermans and myself *) have drawn my 
attention to. some other conclusions from the formulae derived 
Le. particularly with regard to systems the components of which 
differ much in vapour pressure. I shall deal with this in the following 
pages. 
Let us first give the formulae which we shall want. A p‚r‚-line 
. ee, 8 dp 
will ascend or descend with increase of x, according as En is 
„0 
positive or negative. Let us call the substance with the larger value 
of 6 the second component w==1), and put: 
620) Orhan aa, 
Gs; b, b, se T iy 
——=g9 =h M= M= 
b, b, 1 ky Hij 
then 
dl 2f 
( Ps) =— fee (kl—1—g) + 2(kI—1—29) . . , (1) 
de Jao m, 
Ht 2 I 
(‘ Ps) staf (1-1-7) ue (Lan ;) ai 
de Ll M, k 
The question whether the p‚z‚-line is concave or convex downward 
2 
d?l 
at the border, depends on the sign of ze in this way that —— 
at vy 
2 5 dlp. 
will have the same sign as En 
U 
for a line that ascends from the 
border, or if it descends so long as #, >'/, x, resp. l—r, >} (l—a.). 
If #,<'/,#, resp. le, <'/,(1—«,), the vapour-pressure line is convex 
d?l 
when 
dlp 
Cc . . Omg eye 
is negative, and concave when ue positive. Also the 
ak 
stability or unstability of the liquid phases depends on this quantity. 
We are, namely, on the verge of stability when: 
a?l; 
Le, (le) = 
So we are certain to be in the stable region everywhere where 
dlp. 
dx? 
then (for not too small value of a(1—w)) we shall be in the unstable 
region, i.e. unmixing will take place. Expressed in the quantities 
defined just now we find for the required value at the two borders: 
re d*lpe 
is positive; if on the other hand = has a large negative value, 
lij 
5) These Proc. Vol. XIII p. 865. 
Proceedings Royal Acad. Amsterdam. Vol. XY. 
