ee 
( 331 ) 
at that point = ep, —or = 0, B= erp er and § = 0, while 
P1: =PTpt; thus we obtain, from the equations (22), (23) and (24), 
ete ig) ie 
8 Wera eli, 3 saat CA 
Tpl = PT. SENT — 2 (27) 
Nn m?,,+ RTm,, cy eh). 
and 
Mo, 2 Emms : : 
OTpl—?Tk | a Mo TT ET .1)(28 
5 eee tom weende Jee) 
If er, prm and v7, are replaced by their expressions (17), the 
elements of the plaitpoint are thereby determined to the first approxi- 
mation as functions of the temperature 7; R7m,, may then be 
replaced by Aim. 
From equations (26) and (27) follows immediately : 
Ee A 2) 
LT pl — Tk 
In order to see how this relation holds for mixtures of carbon 
dioxide and hydrogen I consider the temperature 27,10° C. at which the 
mixture w= 0,05 has its plaitpoint (pr, = 91,85 atm.) ; at that tem- 
perature er: — 0,011 and pr, = 72,4 atm. so that Sag ee 500, 
&T yl — ©The 
in good agreement with the value 454 which I have found for m,,. 
It follows from equation (26) that #7,: can be positive or negative. 
As erk <0 is not impossible, this is equally the case with 27,1. 
It is true that from a purely physical point of view the w-surface, 
only exists between the limits «=O and «= 1 (in our case x > 0), 
but from a mathematical point of view we can imagine this surface 
to extend also beyond those limits ®). If we consider a temperature 
lying above the critical temperatures of the two components of a 
mixture, then there are, exceptional cases excluded (Hartman’s 34 
type), no co-existing phases, that is to say the real y-surface does 
not show a plait, although formula 26 shows that there is a plait- 
1) If we take the value of zj. from the equation (26), insert it in (27) and (28), 
and finally introduce the K's, a's and @’s, the formulae (27) and (28) become 
Keesom’s formulae (25) and (2c) (Comm. n°. 75), while (26) corresponds to 
Keesom’s formula (24). 
2) Outside the limits x =O and x= 1 y is imaginary owing to the presence of 
terms with log x and log (1—.x). Although this is the case the co-existing phases 
beyond those limits are real, as the co-existence conditions contain the necessarily 
1 —.t3 
I OE Jog and. 1 
real expressions (OQ — an Ol 
p 1 g x a g jess: 
