(wand w + de). If this point of intersection is situated at a finite distance 
from the point prs, vrz, it lies outside the limits we are con- 
sidering; but if it lies infinitely ‘near this point, then it practically 
co-incides with it; then m,,—=0O and all the isothermals in the 
neighbourhood will intersect each other approximately at the point 
prk vrm This case is shown in fig. 13, where I have also supposed 
a<0 and 7< 7. The isothermals intersect in pairs, and the curve 
formed by all the points of intersection of two consecutive isother- 
mals, also passes through the critical point (pry, v77) ; this is repre- 
sented in fig. 13. The connecting line of the points of contact enve- 
lops the isothermals; its equation is found by eliminating « from 
. . bn 
equation (18) and from —-==0, where we also put m,, == 0 ; hence 
Ow 
we find to the first approximation : 
Tee; aoe Bote 
P—PTk = — 7 —— Cere)’ 
4E’ bos 
This parabola is turned upwards (as in fig. 13) if m,, is negative. 
4. The w-surface. 
In order to find from equation (18) the phases co-existing at the 
temperature 7’, I shall make use of the properties of the y-surface 
of van DER Waars. The equation of that surface is: 
WES _f pdv + RT| « log « + A—2#) log (l—e) J, 
where f is the gas constant for a gramme molecule, hence the 
same quantity for all substances. Neglecting the linear functions of , 
we may write: 
1 t 1 
yy = - m, (v-v7p) — 5M (wor) - 3 m, (v-v7T;)* — 1 m, (v-v 7)? +... 
1 1 
+RT [wx loge + ae + a Fla RE et ian CaN ties RAPTOR a ao yo ANA 
5. The co-existing phases. 
The co-existing phases are now determined by the co-existence 
conditions : 
dw 0 Ow Ow 
a =(5) | (Ge) (a) AR A Se HA 
if u represents the thermodynamic potential : 
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