( 521 ) 
= (<)= = (a, Vg d =F dv, — 24,4210) 
wv v 
or — when ‘we suppose for normal components the relation of 
BerTHELOT, viz. d,, =Wa,d,, as approximately exact: 
0? 2 
ia(<)= = @; VAS REE EEEN (53) 
= 
As the second member will be always positive, even if a,, might 
be Va.a, *), the curve T'= f(x) will always turn its conver side 
162 ’ v v 
to the z-axis. 
: 
We will now determine EE log . With a,, =Wa,a, *) the expres- 
av 
sion for a becomes: 
a= [(l—e) Wa, 4e Ya,]’, 
so that 
a (lez) Wa, + 2 Ya, 
log — = 2 log 
v (la) v, + ev, 
Consequently we have: 
5 eats F a ak a 1 
will be better justified to subsitute a by fRT, than 5 (and afterwards = by 
1 
a F : ; 
fRT, and De by fRT), where f will vary in the same manner as v with 
2 
temperature. For it is easy to ‘show, that the expression for the vapour-tension 
DY 
E ke A) y2 &| db P : : 
for a single substance at low temperatures is log — — —— — (v is in 
Pp RT v—b 
l 
the first two terms the liquid volume), whence we can deduce, in connexion with 
an : De Te ziel Ee a 7 
the empirical relation log" =f (7 — 1); where f is circa 7, that > fl 
The error made by supposing 7 linearly variable with z, will certainly be 
much smaller than by putting v =O. In that way errors of,at least 16°/) would 
be made, since a will be nearly */, for liquids in the neighbourhood of the 
melting-point. 
The quantities 7; and v, can now also immediately be substituted by the expe- 
rimentally determined values in the liquid state. 
1) See van DER Waars, These Proceedings of Oct. 8, 1902, p. 294. 
2) Although there is no sufficient reason for this relation, [ have supposed it 
approximately exact, also because only in this case a simple expression could 
a2 
. 0 a 
be obtained for — log —. 
Cut g Vv 
36 
