1214 
ZZ) = A, [d(w), Az, + dy), Au, + dy 
+ 4, |d(«), Az, + dy), Ay, +-..] | B 
= An | d(x)n Ae, ai A(y)n Ayn == one | 
or also: 
3 (4d*?Z) = A, [(w*), Aa,’ H- (y?), Ay? +... + 2 (ry), sera | 
ars Pe ONE GA ce + (18) 
+ An [(@7)n Aan? + (YP) Ayn? +... + 2 (ey) AanAynl ' 
When one of the phases e.g. #,, has a constant composition, then 
in (16) d?Z, disappears when there are more phases with constant 
composition, then in (16) and consequently also in (17) and (18) 
the corresponding terms disappear. 
When the equilibrium F is stable (or, which comes to the same, 
for our considerations ‘“metastable’’) then d°Z, d?Z, — — are positive; 
when however the equilibrium is unstable, then one or more of the 
forms d’Z, — — may be negative. 
Now it follows from (15) when the temperature is a maximum 
and when it is a minimum. 
When (2H) and (/d?Z) have the same sign, then A7< O and 
| consequently 7 is a maximum 
When (4H) and 2(ad?Z) have opposite sign, then 47°>>0 and 
consequently 7’ is a minimum. | 
When 2(Ad?Z) = 0, then 7 is neither maximum nor minimum. 
In some cases it is easy to define this. Let us take e.g. an 
equilibrium 
EN EN 2 
in which Z, is a liquid and #,... F„ phases of invariable composition 
e.g. solids. 
We cause the phase-reaction 
‘. ray die ay Seeger ae ae 
to proceed in such a way that 4, quantities of Z, must be formed 
and we take 2, positive. In the equilibrium Z therefore, a reaction 
occurs [melting or conversion of solid substances] at which liquid 
is formed. As, in general, heat is to be added at this reaction, 
=(4H)>0. 
ORCL Site ir a 
id 
Consequently we have: 
BQH VERE dt AS SAL 9) 
in which 2(24H)>0 and 2,>0. d°Z, is positive when the equilibrium 
Ff, are phases with invariable composition 2(Ad?Z) = 
