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2. The two indifferent phases have opposite sign or in other 
words: the singular equilibrium (J/) is not transformable. Curve (M) 
is bidirectionable; both the other singular curves coincide in opposite 
direction (fig. 2 (X), 3(X) and 4{X)]. 
The four types of P,7-diagram [figs. 2, 4, 6 and 8] are in 
accordance with those rules. In figs. 5 and 7 the singular equili- 
brium (M)= C+ D+ E is viz. transformable: in accordance with 
rule 1 in figs. 6 and 8 the (J/)-curve is monodirectionable. In figs. 
1 and 3 the singular equilibrinm (M) is not transformable; in 
accordance with rule 2 the (M)-curve is bidirectionable in figs. 2 
and 4. 
We may also deduce the types of P,7-diagram from the types, 
which are valid for ternary systems without indifferent phases; we 
find them in the figs. 2 (II), 4 (II) and 6 (ID. [We have to bear in 
mind that the figs. (Il) and 6 (II) must be changed mutually. | 
We may consider viz. fig. 1 as a particular case of fig. 1 (II) or 
3 (II). When viz. in fig. 1 (II) we let point 5 coincide with a point 
of the line 2.3, then this concentration-diagram passes into the type 
of fig. 1; this is also the case when point 4 coincides with a point 
of the line 12, or point 3 with a point of the line 15 ete. When 
point 5 coincides with a point of the line 23, then 1 and 4 are 
the indifferent phases and (J) and (4) the singular equilibria. In the 
P.-T-diagvam of fig. 2 (Il) the singular curves (1) and (4) must then 
coimeide; it is apparent from the figure that this coincidence must 
take place in opposite direction. The P,7-diagram of fig. 2 (II) passes 
then into the type of fig. 2. 
When in fig. 3 (II) point 4 coincides with a point of the line 12, 
then this concentration-diagram passes also into that of fig. 1. The 
indifferent phases are then represented by 3 and 5, the singular 
equilibria by (3) and (5). In the P,7-diagram of fig. 4 (II) the curves 
(3) and (5) coincide then in opposite direction ; then the ?,7-diagram 
becomes the same as that of fig. J. 
In the same way we are also able to deduce the other types of 
the P,7-diagram. We may viz. consider fig. 3 as a particular case 
of fig. 3 (If) or 5 (1). Fig. 5 is to be considered as a special case 
of fig. 3; fig. 7 as a particular case of fig. 5. 
When in a ternary system no indifferent phases occur, then, as 
we have seen in communication Il. the eurves succeed one another 
in “diagonal succession”. With the aid of this rule we are also able 
to find the succession of the curves, when two indifferent phases occur. 
