514 
Chemistry. — ‘“/n-, mono- and divariant equilibria’. X. By Prof. 
SCHREINEMAKERS. 
(Communicated in the meeting of September 27, 1916). 
15. Special cases. 
In previous communications we have treated the reaction-equations: 
a: Hi A ap Poa tnt sole ae (1) 
and ta Brrr pii pien 0 ee 
in which a, and wu, are positive and at the same time 
RT 
We showed before in which way we are able to deduce from 
(1) and (2) the reaction-equations for the phases of each of the 
n +2 equilibria (7), (,) ete. Suppose e.g. we want to find the 
reaction between the phases of the equilibrium (#5), then we have 
to eliminate /’, from (1) and (2); then we obtain a reaction between 
n +1 phases, viz. between all phases, except /,. 
This is, however, no more the case, when two of the values of 
u in (3) are equal to each other; of course those may be only two 
values, succeeding one another, e.g. w, and u. Instead of (3) we 
write then: 
VN LS i eel oe pee ae ees 
If we put uw, = pH == u then (2) passes into: 
uE oe app + bey Eper: =O. 2 
In order to find the reaction between the phases of the equili- 
brium (4) we have to eliminate /’, from (1) and (5); with this 
however not only /’, but also 41 disappears. Consequently we 
do not obtain a reaction between #-+1 phases, but a reaction 
between the ” phases: 
a Tis nee Bi Fie B Fte 
We find the same relation between these m phases for the reaction 
between the phases of the equilibrium (/7,41). In each of the other 
reaction-equations for the monovariant equilibria however ” -} 1 
phases occur. 
In the equilibrium: 
(fy) =F, +... + Fi + My + + Pipe 
consequently the phase #41, and in the equilibrium: 
(Pay a ENE aE Uh ye = ee 
consequently the phase 4, takes no part in the reaction; for this 
