( 340 ) 
pressure *). Let Prom, Vim, Tm, be its coordinates, then we find by 
putting yg” =0 and ®" = van — Vek 
Pon =P — fe OS) NN 
nin = tae + | mele —B gy (my ba — ST zi COR 
TDi Gt J. 
Hence to the first an PaP and N= Tar, but 
vow — ta = — 5 ae le EEEN 
for real mixtures, that is to say «>0O, the latter expression is neces- 
sarily negative, so that the critical point of contact is always situated 
on the descending (right) branch of the border curve. We cannot 
call it the vapour branch, because here the apex of the border curve 
is not the plaitpoint as in the p,v,.-diagram. The critical point 
of contact is situated thus, because the critical isothermal touches the 
border curve at that point, and because on that isothermal and hence 
also at the critical point of contact 7, >> Tx (at least for real mixtures), 
0 
therefore <0 for the border curve. This corresponds to a diagram- 
v 
matical representation of a p, v, T-diagram for a mixture given by 
KvuENEN *) and also with the experimental diagram for the mixture: 
0.95 carbon dioxide, 0.05 hydrogen which I have given in my thesis 
for the doctorate. In spite of the small value of zr, terms of higher 
order appear to have such a great influence in the case of this mixture 
that the apex of the border curve lies far outside the area investigated, 
and the border curve at the critical point of contact is no longer 
concave towards the v-axis but convex. 
The plaitpoint elements for the mixture of composition z are found 
by substituting 77, for ZY and « for x7,, in equation (26), by 
solving 7: and substituting that value in (27) and (28). Then 
we find 
3 
Tj ee ee 
; RT py 
tpt =e È zin dn en at d 
RTym,, 
km? km? 
Pal Pl pee «| =p 2 Co. rk KO 
Rm, 
1) Comp. Hartman, Journ. Phys. Chem., 5, 437, 1901. Communications Leiden 
Suppl. N° 3 p. 14. 
*) Zeitschr. f. physik. Chem., XXIV, 672, 1897. 
