1022 
with the aid of the n other phases the composition of two of the 
phases of n + 2 phases, which occur in an invariant point. 
We may also say for this: in a space with »—1 dimensions we 
can represent each point with the aid of 2 other points of this space. 
We shall first apply our previous considerations to a case, 
treated already formerly, viz. to a ternary system. In an invariant 
equilibrium the phases P, Q, R, S and 7’ occur; we call the curves 
starting from the invariant point P’, Q’, R’, S’ and 7”. When the 
compositions of the phases are known, we can find the equations of 
the reactions as we have proved above. We assume that this reaction 
is for the phases of the equilibrium : 
6Q= F-23284 37f 2s 2 ee ee 
and for the phases of the equilibrium Q’: 
OPS DRS SS 4Al) oe) van ee) 
It follows from (7): 
OENE Le J ra vata et ya ee 
and from (8): 
ES ENO GH GPRS (Se rra ss NSE 
We have written (7a) and (84 in such a way that P’ is situated 
at the right of Q’. [Let the reader draw these and the following 
curves in a P,7-diagram in order to facilitate the matter; (9) gives 
a symbolical representation of the P,7-diagram. | 
Stab. Q’ P TSR Q 
ee ®) 
Metast. TSR’ Q’ P 
As in accordance with (7a) R’, S’ and 7” must be situated at the 
right of P’ and in accordance with (8a) these curves must be 
situated at the left of Q’, they are situated, therefore, between the 
metastable prolongation of P’ and Q’. Reversally the metastable 
prolongations of R’, S’ and 7” must be situated between /”/ and Q’. 
Now we have yet to define the position of the curves 2’, S’ and 
T’ with respect to one another. For this we eliminate # from (7) 
and (8); we find: 
120 = ORES en i ss ee dO 
consequently : 
NE NO LORE 
