528 
We have therefore, independently of the number of phases, provided 
L<n, a “bivariant system with constant total composition”. 
2. We shall now investigate for a bivariant system consisting of 
n components in / phases (/l<%) a relation between the pressure- 
and temperature-coefficients for the transition of the components from 
one phase.to another, and the heat effects and volume changes which 
accompany this transition. 
The composition of the different phases may be represented as 
before. The <-function of the system is represented by Z, the entropy 
by H, and the volume by JV. For the separate phases these quan- 
tities are represented by Z,, H,, V,, ete. 
We have then: 
EAN eZ) 
Ve Vira aL; 
These quantities are given as functions of p and T and also of 
KU +5 hs, Y,----, eter in which p) and 7% are the only ande- 
pendent variables. With regard to notation, the following may be 
remarked. Partial differentiation with respect to one independent 
variable, the other independent variable alone being kept constant, 
(Le, in a state of equilibrium), is indicated by a stroke above the 
differential coefficient; partial differentiation with respect to one 
variable, all other variables being considered constant, (in this case 
heterogeneous equilibrium is not necessarily present) is indicated by 
the absence of the stroke. 
We can establish the desired relations by the method described 
in a previous communication for an analogous case. We differentiate 
the equations (2) partially, first with respect to p, and then with 
respect to 7. After multiplication by suitably chosen factors the 
equations are added together. The following, however, is a shorter 
and, in my opinion, a more elegant method. 
We begin with the simple, purely analytical equation : 
eZ eZ 
Top AT’ 
This may be written: 
WV oH OF On 
= =), 6 oc (3 
we awe ae |S) 
But 
OV ov OV /ox, OV /0x, . OV (dy, OV (oy, 4 
pears ce en Gee Ge) () 
