1206 
Pe by Lr re 
Brot Hr etten 
The &, the entropy and the volume of #, we call Z, H, and V,; 
those of F, we call Z, H, and V,; ete. 
Then we may write the conditions for equilibrium: 
OZ, OZ, : 
By tS ata Aen Tine 
5 7, MZ, EN 
3 de Sadi Ps 
viz. m equations (2) of which we only have written two. Further 
we have: 
LE 
Ox, ae Ox, 7 Che Ov, ae 5 | (3) 
A AE 
De AD pe 
The corresponding equations for the variables z, z,...u, u,... ete. 
have still to be added to (3). 
We find in (2) n, in (3) n (n—1), consequently in total n’ 
equations. Besides the n (n—1) variables 2, y,...v, y,... ete. we 
have, still the 2+ 2 variables 7 P K Kz K,... consequently in 
total n? + 2 variables. The equilibrium Z has, therefore, two degrees 
of freedom and consequently it is bivariant. 
We have assumed in (2) and (3) the general case that all phases 
have a variable composition and that each phase contains all 
components. When this is not the case, then we are able to make 
at once the necessary alterations in (2) and (3). When e.g. #, has 
a constant composition z,— a, y, = B, etc, then the first equation 
(2) passes into: 
nes. Eu a oa Ee a AND 
in which the index 7 relates then to a phase F; of variable 
composition. Then Z, is only still a function of P and 7’; in (3) 
then a Be EEn disappear. 
When we give to P JT x y... the differentials APAT Aa Ay..: 
then we have: 
WA WA 
AZ= VaP—HaT + 5 Aw +s Ay +...+ GZ 4 $aZ + te: 
Z 07 OZ 
A ree Bede Neha errs d—+id@—4... 
Ow Ow Ow Ow 
