(SM) 
of not perfect miscibility can occur, and is at least partially known, 
I shall, before returning to the interrupted subject, first describe this 
form, and subject it to a closer investigation. 
The case that the spinodal line splits up into two parts, is fre- 
quently met with for binary mixtures. In this case two homogeneous 
plaitpoints arise, according to Kortmnwne’s terminology. And the first 
example of such a splitting up we met long ago also for perfectly 
miscible liquids, if minimum 7% occurs. I may consider this case as 
perfectly known. Then there is also minimum plaitpoint temperature 
which does not lie much higher than the minimum value of 7%, 
and occurs for a value of # and v which differs little from that for 
which this minimum value of 7% occurs. At the moment at which 
these two plaitpoints originate, we may consider them as a pair, 
but further there is no reason whatever to consider them as conjugate. 
d 2 
Then == for the plaitpoiut line is equal to o, because == Os 
©) 
NO But eo igi equal 160 d phas neitl 
urther ar ut | aT de is equal to 0 X ow, and p has neither 
minimum nor maximum value. I shall leave undiscussed the case 
that 7 would have maximum value, in which case the plait would 
contract to. a single point, as this case is unknown for normal 
substances. As the differential equation of the spinodal line, as I 
showed in Contribution II, may be written in the form: 
d?v 
dv = dv dx” }y 
de we de }n=q (3) 
p 
dx? 
: dv\ . ; dv d'oN 
and in the double point ee is undetermined, both ed and ) 
p q 
WJ spin & da? 
will have to be equal to 0. The condition for a double point of the 
spinodal line is therefore, that in such a point both the p-lines and 
the g-lines present points of inflection. And so, if we wish to know 
the cases in which splitting up of the spinodal line can take place, 
we must know the course of the points of inflection of the p- and q-lines, 
Aen dv dv 
ascertain where the loci represented by (<2) = 0 and ()=0 
da? }y dx*]q 
intersect, and solve the question whether also the spinodal line can pass 
k 2 
through such a point of intersection. Both (33) = 0, and Ge) = @ 
dx* Jy dz* }g 
has, expressed in x, v, and 7’, such an intricate form that it seems 
60* 
