999 
Chemistry. — ““/n-, mono- and divariant equilibria’. XV. By 
Prof. F. A. H. SCHREINEMAKERS. 
(Communicated in the meeting of February 24, 1917). 
The occurrence of two indifferent phases; the equilibrium M is 
variable singular. 
Now we consider the case that the singular equilibrium (M) is 
no more constant, but variable; one or more phases of J/ have, 
therefore, a variable composition. (Comm. X). 
When (M) is constant singular, then, as we have deduced in 
communication A, the following propositions hold: 
1. When the two indifferent phases have the same sign, then J/ 
is transformable. 
2. When the two indifferent phases have opposite sign, then M/ 
is not transformable. 
It is evident that the same rules are valid also when M is a 
variable singular equilibrium. 
In order to examine what P,7-diagrams can occur now, we 
take an invariant point with the phases /’,... E42, in which 
F, and F,4, are the indifferent — and consequently the other 
ones are the singular phases. Then we have the singular equilibria: 
M= EH... Ep + Popet..- Ene 
(Er ) + Epi and Sa ery tas Oi) Bay ae 
in which (J/) now contains one or more phases of variable composition. 
When (M) is constant singular, then curve (J/) is monodirection- 
able [fig. 1(X)] or bidirectionable [fig. 2 (X)|; in the first case 
the 3 singular curves coincide in the same direction, in the second 
case (Pp) and (/,+1) coincide in opposite direction. 
When (M) is however variable singular then the three singular 
curves can no more coincide. Let viz. P, and 7’, be the pressure 
and temperature of the invariant equilibrium and let us assume that 
in (M) and consequently also in (/) and (/,41) the phases #5, #, 
ete. of variable composition occur. Under P, and at 7, £ and Fy 
have then the same composition in (J/) and (/,). Now we take a 
temperature 7’. When we bring (J/) to the temperature T, and 
under the corresponding pressure, then /’, and /, get another 
composition F,' and F,'. Those compositions are of course such 
compositions that between the phases of (J/) the phases-reaction is 
still always possible. 
When we bring (/,) to the temperature 7’, and under the corres- 
