( 344 ) 
A 
Pri =F (v—vTk) («—«x7%) + RT, (v—vT,z) « + m,, (v—v7z)’, 
and according to (33) this may be written 
pp, = koo (e— Te) [(0—PTe)* — Y")- 
We see that in this form the experimental isothermal intersects 
the theoretical at three points’), viz. v=vum+gq’, v=orr— gp! 
and v= v7, (all to the first approximation) ; the two first points are 
the points at which condensation begins and ends (®’ has been 
neglected as being of higher order than g’), the third lies between 
the two first. 
When va + pf >v >> vr, that is to say at the beginning of the 
condensation, p >p, and the theoretical isothermal lies above the 
experimental ; when vz >v > vr: — gy, Le. at the end of the con- 
densation, p > p, and the experimental isothermal is the higher *); this, 
indeed, follows necessarily from the s-shape of the theoretical isother- 
mal, and the approximate straightness of the experimental. 
According to thermodynamics the two areas enclosed by the 
theoretical and the experimental isothermal must be equivalent ®), 
that is to say: 
v's 
f ep) dui): 
v’, 
+,’ 
(p—p,) d (v—vrx) = 0, 
or 
‘ 
ae 
and this actually follows from the form, found just now for p—p,. 
This has only been proved for the terms considered here; but obvi- 
ously it must also be possible to prove this for terms of higher order. 
13. The p, T diagram. 
a. The vapour pressure curve of the pure substance. We have 
found to a first approximation : 
Pe, == Pleo eye ie 
As &,, is positive, this straight line rises and terminates at the 
1) Comp. for this Hartman, Comm., n°. 56 and Suppl. n°. 3 p. 25; Journ. Phys. 
Chem., 5, 450, 1901. 
*) Here the proof is only given for mixtures with small composition. For a general 
proof comp. Kuenen, Zeitschr. f. Physik. Chem., XLI, 46, 1902. 
3) It has escaped Brümcke's notice, who mentions this theorem in 1890 (Zeitschr. 
f. physik. Chem., VI, p. 157) that it occurs already in a treatise of van DER WAALS 
of 1880 (Verh. Kon, Akad., Bd. 20, p. 23). 
