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curves (Z,) and (Z). The turning-line of this region has a form, 
as curve wzyzu in fig. 5; we imagine the curves za and 7b entirely 
within this turning-line and the point of contact d from fig. 3 between 
x and y in fig. 5. 
In fig. 3 we now have an example of that which we have called 
above the deformation of a region; we see that it is connected here 
with the occurrence of point d, in fig. 1 the point of intersection 
of curve La with the line G'Z,. 
In the invariant a and also as long as the liquid of the 
equilibrium (4,) = 7,+ 74, + LG is represented by a point of 
curve Ld, the reac non in this equilibrium (Z,) is: 
; Z+L2Z4,4+G 
When, however, the liquid is represented by the point d, then 
the reaction is: 
L2Z,+G 
and when the liquid is represented by a point of da: 
L24,4+Z2,4+4. 
When the equilibrium (7,) therefore follows, the curve La, then 
the phase-reaction gets another form in the point d. As it appears 
from fig. 3 in the P,7-diagram the deformation of the region begins 
in the point d. 
Previously we have deduced: each region, which covers a curve 
(fF), contains the phase #,. In fig. 3 the region Z,LG covers, 
however, the curve (Z,) [viz. the part da) and yet this region does 
not contain the phase Z,. When we bear in mind the first condi- 
tion, viz. that we are allowed to consider regions only, which are 
situated not too far from the invariant point, then this region 7, LG 
does not cover the curve (Z,). 
We may imagine the point d indeed in the vicinity of 7, but not 
coinciding with it. For, in this case in fig. 1 the point Z would 
coincide with point d; three of the five phases of the invariant 
equilibrium, viz. G, L and Z, should then be situated on a straight 
line, so that the invariant equilibrium should show a particularity 
which we have exeluded up to now. For, in the three types of 
concentration-diagrams which are represented in the figs. 1 (11), 3 (ID 
and 5 (IL), no three points are situated on a straight line. When 
this is the case, then we have a transition-type, to which we shall 
refer later. 
We shall also show that also the second condition, mentioned 
above, has a meaning in some cases. 
For this we consider the bivariant region Z,LG. In the P,7- 
