( 649 ) 
dw 0 fa 
the former simple expression eau) may be safely used, at 
& wv 
least in the case of normal substances; but at higher temperatures 
0 a 
equally the new expression with the term =a log — will be insufficient. 
U v 
4 0% 070 
And we want a more accurate expression for Ae and = the 
U Hij 
more, when we — specially with respect to the course of the plait- 
point-curve also wish to know anything about the course of the 
spinodal curves from the lowest temperatures to the highest critical 
temperature. 
I therefore tried to solve that problem; I was the more encou- 
raged to do so, as soon it appeared to me, that the entirely accurate 
expressions are not so complicated as was expected. On the contrary, 
the often occurring fact presented itself here, that the exact expres- 
sion is relatively more simply than the approximated one. 
2. If we write the equation (2) in the form 
ys = + RT log (v—b) — p (v—b) — pb, 
Vv 
then we obtain: 
dw 0 = Ra O(v—b) db 
de Ox\v/) | ( =O P Ow P de : 
\ 
N ARAL a 
Now meee 2 = 
consequently we find further: 
yp? 
dw 1 da a Ov a Ov a db db 
ae eee et eo ee 
Ox v de v°Òr v 0x v? de de 
or 
dw 1 da út ld 5 
= jn WEER eh 
Ow v dx f v? ) dx’ 6) 
Ov 
where 5, Wpears no more. 
v 
If we write now: 
a=(l—2)’? a, + 2x (1—2) a,, + 2 a,, 
and if we put «,, = Wa, a, by which the calculations and the results 
are simplified in some way, without affecting much the exactness of 
these results’), then we have: 
1) J am convinced, that the expression aj = a @ 1s exact in the case of nor- 
mal substances. At all events the inaccuracy, which results from this supposition, 
will certainly not be greater than that of the equation of state used. 
