( 133 ) 
Physics. — "On the solid state." IV. By Mr. J. J. van Laar. Com- 
municated by Prof. H. A. Lorentz. 
13. In the paper in the Arch. Teyler already cited a few times, 
I derived in § 6 (p. 34—35) the formula for the pressure of coexistence 
of two arbitrary phases (liquid-vapour, liquid-solid), when association 
is assumed in both phases. 
I will just state the derivation of .this fundamental formula here 
once more. 
For equilibrium between two coexisting phases the molecular 
thermodynamic potentials of the components must be the same in 
the two phases. If these components are distinguished by the indices 
1 (complex molecules) and 2 (simple molecules), we have e.g. in 
our case 
. («) 
On account of the relation of equilibrium ^ = 2/1, in both phases 
naturally (f= Now 
fi. = C x — ^ -f RT % c n.( ft ) 
on, 
in which (see I, p. 767 and 768) 
Si' = ^pdv —pv — RT 2n 1 . log 
or 
Si' = 2 ni .RTlog V -^--\-^—p v, .(«) 
when we make use of van der Waals’ equation of state: 
_ 2n l . RT a 
So we find for 
dSi' 
= R Tlog - 
— = 6, follows from b = n, 6, + n 2 b„ while from 
a — n , 5 a, -f 2 w, n, a„ + n, 2 a s is found — = 2n, a, -f 2n, a„ = 
r=(2w, while a„ is evidently =7*«i (cf. also I, p. 7$9). 
da 
Further 2«, + n, = 2 (1 — 0) -f 2 0 = 2, hence finally — = 2a,. 
