( 652 ) 
that is to say into 
5 (v—b)? 2x (1—2) 
RT a — = = ; (av—B pa)’, 
v Be uv 
or into 
ar 
B == = E (1 — x) (av — By a)? Ha (wv — | 
Now av—PBYa=a(v—}b) + ab — Bya 
=a(v— b) + a(b, + B) — B (Wa, + aa) 
= a(v—b)4+ (ab, —BY a, )=a(v—b) (baba). 
Therefore we obtain (compare also vaN Der Waars, Cont. IL, 
p. 45): 
9 2 
gdb zalen a,— ba) + av — Hy -f- cbr} eG) 
rr 
being, with the above mentioned suppositions, the sought, quite 
general expression for 7’=/(v,x), by which for each given tem- 
perature the v, v-projeetion of the spinodal curve is entirely determined. 
We may also construct a ‘spinodal surface” 7’= fw, x), and im- 
mediately deduce from the subsequent sections 7’= const. the forms 
of the spinodal curves of the transversal- and longitudinal plaits, and 
this in just the same v, x-representation as is used by vaN pur WAALS 
for the projection of the spinodal curves of the surfaces p=/(7v,x) 
for different values of 7. 
5. The equation (6) gives rise to some results, which may be 
deduced from it without further calculation. 
Ist. Is vb, that is to say, is the limit of volume 6, reached at 
any value of w, then (6) reduces to the equation of the boundary- 
curve, lying in the v,a-plane : 
29 
I = = MUD NA Aere en 5 > (Ee) 
viz. the same expression, which was formerly found for small values 
of » by means of the approximating method. 
It is obvious at present, that only for v — b the expression (6a) 
holds rigorously good. In every other case terms with »—4 must be 
added. But it also results from the found expression (6), that as 
long as terms with v1 —6 may be neglected, the formula (6%) gives 
approximately the projection of the spinodal curve on the 7’, v-plane, 
without it being necessary to take into account the corrective-term with 
i Z 3 ; 5 
— log —, indicated by van per Waars. In a former communication 
