( 816 ) 
be divided by the same homogeneous function of the first degree. 
In the special case that L, =a,#-+ b,y, M,=a,¢-+ b,y, N,=er ddy 
the tangents to the integral curves in the different points of the line 
y = mez, meet in the pole 
ea ene rem 
Kr c, + d, m c, + d, m 
Hence the locus of these poles for all the rays of the pencil y= ma 
is the polar line 
De okey ee 
he a, —c,| = 0 
oe Rea 
This is the case in the examples II—VI given by Prof. pe Vries. 
As to the examples I and VII we have respectively 
TO M =ae + 2y ni 
1 
i, =9 Wh N= — 
1 
Physics. — “Contribution to the theory of binary mixtures.” XIV. 
By Prof. J. D. van DER WAALS. 
(DOUBLE RETROGRADE CONDENSATION). 
Before proceeding to the discussion of the significance of negative 
value of «, and «,, L shall make a few remarks to elucidate what 
was mentioned in the preceding contribution — and that chiefly on 
the shape of the surface of saturation in the cases represented by 
figs. 39 and 40, and the relative position of the three-phase-pressure 
with respect to the sections of that surface for given value of z. 
In ease of complete miscibility such a section of the surface of 
saturation consists of a vapour branch and a liquid branch, which 
have a continuous course, in which the pressure gradually increases 
with ascending 7’, and which for certain value of 7, which may 
be indicated by 7, pass into each other continuously. The pressure 
must then before have had a maximum on the liquid branch, and 
then decrease. It passes into the pressure of the vapour branch at 
7’. This gradual merging of the two branches into each other con- 
tinues to exist also for non-complete miscibility. 
In the case of fig. 39 the upper sheet of the surface of saturation 
undergoes, however, first of all a modification, which, however, is 
