( 325 ) 
soon, however, as pa gets a value, they appear and the region of the 
isothermals with an inflection-point decreases regularly, as appears from 
the differential coefficient which is always negative, till for y= 1, so 
PA=PB 1e ='/,. At this limit the region for isothermals with an 
inflection-point has quite disappeared, and only entirely concave or 
entirely convex isothermals exist, but it is clear that for p4= pz 
also all other pressures become equal in this case. 
In order to solve the problem to its full extent, we have still to 
examine, at what pressure the inflection-point eventually appears in 
the derived isothermal. It is clear that.in order to find that 
dependence between p and 2’, we have simply to substitute in the 
equation F'(p) = 0: 
Pi = pA +2'(pB—Pa). 
In order to determine the pressure at the inflection-point belonging 
to the mixture z' we get therefore: 
(pa + pa—2p) (ps—p)2' Para) + (P1 — PA)’ [pA—P He! (pa —pa)] = 0 
ris (p — pa)? 
~~~ (pp — pa) [(pa + pa — 2 p) (pa — Pp) + (p — pa)?] 
The condition that «' must be positive, is fulfilled, for: 
(pA+pa—P) (ps—p) + PPA)? = (papa? p)° + (p—p4) (pB—P) 
So we have for the locus of the inflection-points a cubic curve 
of which we saw before that in the heterogeneous region it cuts 
all the coordinates but once. 
We get further: 
oe LEE rt DA lr BS 
pe Pap T [eat pa — 2p) (pr — Pp) + (P— PPP 
d iat 
30 = is always > 0, and has in the beginning at 2p =p, + pr 
the value 22 = which disappears for pa = pz, as it ought to do. 
And finally we get: 
22 
Proceedings Royal Acad. Amsterdam. Vol. LV. 
