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which are first situated separated from one another; when in a 
ternary system three points, which first form a triangle, take their 
place on a straight line, when in a quaternary system four points, 
which first form a tetrahedron, fall in a plane; in general when 
between the phases of the equilibrium a reaction: 
asF, Hal, H.+ An 4-2 Fy+e = RER (6) 
can occur. 
(We might imagine the phases of (/’,/,) also in such a way that 
they satisfy (3) in the invariant point not always, but casually. In 
both cases the phases have then already something particular in 
the invariant point. The corresponding P,7-diagram forms then a 
transition-type, to which we shall refer later]. 
When between the phases of the complex X reaction (3) can 
occur, then at constant 7 the pressure —, and under constant P the 
temperature is for this complex a maximum or minimum. 
When the temperature is a maximum (minimum) under constant 
P, then the complex X no more exists above (below) this tem- 
perature; below (above) this temperature then however at each 7’ 
two equilibria A’ and X’’ may occur, in which the variable 
phases have different compositions. When the pressure is a maximum 
(minimum) at constant 7, then the complex no more exists 
under higher (lower) pressures; under lower (higher) pressures how- 
ever two different equilibria A’ and X’’ occur again. 
Hence it is apparent that the bivariant field (/'/’,) is limited by 
a curve (J/) which is defined, because in the equilibrium: 
Gb == (EF) = Tike + Ji alee otis: fae 
reaction (3) occurs. , 
Each point of this region (/’,/’,) represents, therefore, two different 
equilibria (PF) and (F,F,)" which pass into one another at the 
limit of this field. Curve (JV) is, therefore, the turning-line of this 
field. Consequently the field consists of two leaves, which cover one 
another and which we shall call leaf (/’,/,)' and leaf (7, F,)". 
In fig. 2 dg is the turning-line of the field 7,LG; each equilibrium 
Z,LG has on this turning-line at constant 7’ a point of maximum- 
pressure and under constant P a point of minimum-temperature. 
The same applies in fig. + to the equilibrium Z,LG. 
In our previous considerations ‘Equilibria in ternary systems 
XVII’ we have fully examined different ternary turning-lines 
under the name of M-curves. They may have different forms, we 
find one of those in fig. 5 which represents a general form of the 
turning-lines dg (fig. 3) and eh (fig. 4). 
