515 
wis 
reason we call /, and #4, indifferent phases. The equilibrium: 
Sj FH +}. nk. a Epa + Ee + PACA oa Fre 
shows something particular. Generally between ” phases of a 
system of ” components no phase-reaction can occur, viz. a reaction 
at which not the compositions, but the quantities of the phases 
change. [Indeed, however, a reaction may occur at which as well 
the composition as the quantities of the phases change). In the 
equilibrium M however a reaction may occur, viz. : 
(ai wait Wap -1 La Hp Wael pe +...=0.(6) 
The phases of this equilibrium J/ have, therefore, something 
particular, we call them therefore ‘singular phases’ and the 
equilibria M, (f,) = M+ Fa and (Hip) = M+ F, singular 
equilibria. 
When in (3) three values of u are equal to one another, then (3) 
passes into: 
{ty = neee > Ul En Up — U — Upt-2 — {ty +3 > ed oe > = (7) 
Then we find for the reaction between the phases of each of the 
equilibria (45), (47,41) and (£742) a relation between the »—1 phases: 
F, Da ey En Pi ide as 
Then in the equilibrium (/,) the phases #41, and Hz, in (/7,41) 
the phases /, and #42 and in tbe equilibrium (4,49) the phases 
Ff, and 4, do not participate in the reaction. The phases of the 
p + I I 
equilibrium : 
M=F,+....+ Fit Post... + Pips Raak) 
have, therefore, again something particular viz. that between them 
a phase-reaction is possible. Consequently we call them again sin- 
gular phases and the equilibria: 
ME) MH Bt Erge Em) = ME Fin 
and (re) = M + F, + Ka singular equilibria. 
Of course we may imagine still more of those particular cases; 
we shall refer to this later. 
16. The occurrence of two indifferent phases. 
When in an invariant point of a system of 7 components two 
indifferent phases occur, then the singular equilibrium consists of 7 
phases. 
When in a binary system two indifferent phases occur, then 
the singular equilibrium 7 contains, therefore, also two phases. 
These singular phases must be, therefore, convertible one into the 
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