( 339 ) 
To this can be added 
1 A ! rm ry 
M= 5 WP ak Pre hi (T— Fae oe dee 
and 
x" = — Te Ba) colt Coe . (48) 
To the first approximation equation (44) represents a parabola, of 
which the apex determines the elements of the critical point of contact 
for the mixture v. For we know that in the case of the critical 
point. of contact v,=v',=v,,, so that g"=—0 and ® = vir— Var. 
Hence it follows that’): 
ns (49) 
RT. 
ym 
Par = —— Pak ia RT. ke, U . . . . . . . (50) 
1 m? Horde; x 
Var = Vak + er, Oi (@—B) = = ma, ef RT zi a) | RT m., : (51) 
In order to derive from this the equation of the border curve in 
the p,v, T-diagram, we must express 7’ in terms of p and » by means 
of equation (13). 
Then we find: 
OS (vu) — 2 O" (v— ver) + PI pl. . (52) 
where 
en END if Mor (= | mle EL a es Ti My mo, aa 
2m le RT Silva De tie. ig 
vji(a—B) 1 m or 4 m,,m,, 
5 ke eT zi =p) + | (Se SUT AE Pen 
hm, | p> gele 
and 
oe. Fea Ne one mee 
ry le ry 
Lem, km, aL 
To a first approximation (52) is a parabola on which 
be ke 
kom: 
be _o1 30 30 
— 9°! 59 oT, — — 2 
dv? Mr, FSi 
ap 
as in the case of the border curve of the pure substance. 
The apex of the border curve is the point of the maximum co-existence 
1) We obtain the same formulae if we replace in equation (26) xz» by its value 
(17), put T= Ter and x7,= «x, solve Ty and substitute it in (39) and (40). 
