( 322 ) 
the pressure when the whole is vapour or the whole is liquid, we 
get also: 
Pi = paA(l — 2') + pee’ 
den de 
roe PA PB 
* pal — 2) + par 
If we substitute these values in our differential equation, we find: 
dv : 
(pB—p)° (p—pa)? ap 7 wales —P) ipa) ei Pera 
zs dv , 
So we find that ee always < 0, as it ought to be, for 
je 
PB—P > PTP and pi—pa > p—pa- 
For the second differential coefficient we get 
Ge pay at 
BES PNP PAY Se ti ee ee ae 
dp (ps —p) p—pA) 
X [(pa +pB —2p) (pp —p) (pi— pa) + (p—pa)? (p1—p)]- 
d? dp\3 dv dp . ty eae 
Now “= — = and as is always negative —F has 
dv? dv/ dp? dv do? 
d dv 
the same sign as — . 
dp* 
Hence it is clear, that when 2p < pa+pz, soe < !/s, the convex 
side of the curve is always turned downward (fig. 21). If on the 
other hand # > !/s, then the whole factor is negative for p = pi ; it 
is therefore clear that on the side of the greatest pressure the empiric 
isothermal for those mixtures must begin with having its convex 
side turned upwards. But there can be but one inflection point, if 
any. For: 
I (p) = (pa +pB —2p) (ps —p) (pipa) + (P—pa)? (pi—p) 
EF" (p) = — 3 [(p1—p)? + (pipe) (PA + pa — p)] 
