530 
transition of one mol of the component (wv) from an infinitely large 
quantity of the first phase into an infinitely large quantity of the second 
phase, the variables p, 7’, and the other components remaining constant. 
This volume increase may be denoted by Vasa. The expression 
Ole Oat , . me 
Sg represents the heat absorbed in the same operation divided 
cy x, 
by 7. This heat effect may be denoted by Q,12. For the correspond- 
ing differences for the other phases and components analogous 
symbols may be used. We have now: 
Of, Qed Oz) Qs 0x. 
Vaart op tert rop to 
5 an (7) 
Yo 12 Us 
eeN: 12 op t T UN 0 
This is one of the relations which it was our object to establish. 
From (6) other /—1 similar relations may be derived, in which the 
pressure and temperature coefficients of the components of one of 
the /—1 other phases do not occur. We obtain other less symme- 
trical relations, when we eliminate for the one component the coef- 
ficients for one of the phases, for a second component its coefficients 
for another phase. If a component is absent in one of the phases, 
the corresponding coefficients vanish. 
Note J. If one of the phases consists of all the components, and 
the other phases are all pure components, then we have the case 
for which in the previous communication the “generalised BRAUN’s 
law” was established. If these conditions are introduced into equa- 
tion (6), an expression of this law results. The verification of this 
may be left to the reader. 
Note II. If there are n components in » phases, the heat effects 
and the volume increments occurring in (7) have values which are 
independent of the total composition. When the number of phases 
is less than n, that is, when the equilibrium is merely ‘‘bivariant 
with constant total composition” then the values are functions of the 
total composition. 
Note I//. In our discussion we have nowhere made use of any 
explicit relation connecting Z with the composition. The results are 
therefore valid also in the case of reacting components. 
Note IV. The line of argument adopted leads to a similar 
formula in the case of homogeneous equilibria. This will be discussed 
in a future communication. 
Katwyk a. d. Ryn, August 1919. 
