717 
In order to examine whether the two indifferent phases /’, and 
F, in fig. 1 have the same sign or not, we take e.g. the reaction: 
PL +P, 2F, or #,—F,+ F,—0. 
Hence it appears that /’, and /’, have opposite signs so that the 
singular equilibrium (J/) = H+ F, is not transformable. Moreover 
the latter appears also at once from fig. 1; it appears viz. from the 
position of the points /,,/’,,/°,, and #, with respect to one another, 
that a complex of the phases #, and #, can never be converted 
into the invariant equilibrium /, + /, + FP, + F4. 
In accordance with rule 2 curve (J/) must be therefore bidirect- 
ionable and the two other singular curves |(3) and (4)| have to coincide 
in opposite direction. We see that this is in accordance with fig, 1. 
In the same way it appears that the indifferent phases /’, and 
I’, from fig. 2 have the same sign and that the singular equilibrium 
(M)—F,+ F, is transformable. In accordance with rule 1 curve 
CM) must then be monodirectionable and the three singular curves 
have to coincide in the same direction. This is in accordance with 
tig. 2. 
Now we shall contemplate more in detail some P,7-diagrams. 
We take a binary system: water +a salt S, of which we may 
assume that S is not volatile; consequently the gasphase G consists 
of water-vapour only. When no hydrates of the salt S occur, then 
we find in the eryonydratie point the invariant equilibrium : 
lee + GH LHS, 
in which Z is the solution saturated with ice + S. As the water- 
vapour G and the ice / | fig. 4] have the same composition, G and 
Ice are the singular phases, ZL and S the indifferent ones. Con- 
sequently we have the singular equilibria: 
(M) = lee + G (eurve (J/) in fig. 4]. 
(L)= leed GHS [eurve (L) in fig. 4). 
(S)=lee + GH  {[eurve (S) or gt fig. 4 and gt fig. 3| 
and further the equilibria: 
(Ice) =G + LS [eurve (J) or ga fig. 4 and qa fig. 3| 
(GQ) =lee+L-+S_ [eurve (G) fig. 4]. 
In fig. 3 a concentration-temperaturediagram of this binary system 
is drawn; Wand S represent the two components, g is the eryohy- 
dratic solution Z. The curves gt and ga go towards higher tempe- 
ratures starting from q; qt is the ice-curve, it represents the solutions 
of the equilibrium (S) = ce + G + L; ga represents the solutions, 
saturated with the salt S, viz. the solutions of the equilibrium 
