664 



may be represented hj n — 1 variables; in order to represent it 

 graphically, we want, therefore, a space with n — 1 dimensions. 



We now take an equilibrium E =^ F^ -\- . . . ~\- Fn' under the 

 pressure P^; we call this the equilibrium F{P=:I\). Besides the' 

 7i{7i—l) variables .l\y^ . . . .r^y, . . , etc. we then have also the n -j- 1 

 variables T K /C • • •, consequently in total n^ -\- 1 \ariables. They 

 are connected to one another by the n^ equations (2) [XVII j and 

 (3) [XVII]. We imagine now all variables to be eliminated, except 

 those, which relate to a phase Fi [consequently except xiyi. . .]. 

 Then we keep n — 2 equations between the n — 1 variables Xiyi... 

 Consequently the phase Fi follows in the concentration-diagram on 

 change of T an {n — 1) dimensional curve; we call this "curve 

 Fi(P= Po)"- Of course the position of this curve depends on the 

 assumed pressure P^ and it changes with this pressure. 



Consequently the pressure is P^ in each point of this curve 

 Fi{P = P^)- T changes however from point to point ; it is maximum 

 or minimum when a phase-reaction can occur, consequently when 

 the equilibrium Ë [)asses into an equilibrium £/?. 



As the equilibriuui F {P = P^) contains u phases, it is represented, 

 therefore, by ?i curves Fi {P =:: P^) in a space with 7i — 1 dimensions. 



Now we take an equilibrium E at constant temperature J*,; we 

 call this E{T= T^). A phase Fi of this e([uilibrium now follows 

 on change of P a curve Fi{T ■= 1\). Of course the position of this 

 curve depends on the assumed temperature 'd\, and changes with 

 this. Consequently the temperature is 1\ in each point of this curve; 

 the pressure changes, however from point to point and is maximum 

 or minimum when the equilibrium E passes into an equilibrium ^/£. 



Finel}'^ we still take an equilibrium of n components in n phases, 

 between which a phase-reaction may occur, consequently the equili- 

 brium Er. Each phase Fi of this equilibrium follows a curve /^,(/?; 

 in the concentration-diagram. The P and T change along this curve 

 from point to point. 



Consequently we have the following. Each of the equilibria 

 E{P=Pj, E{T-=:1\) and Er is represented in the concentration- 

 diagram by n curves Fi; these are situated in a space with n — 1 

 dimensions. When one or more phases have a constant composition, 

 then the corresponding curves disappear of course. As we may 

 change P^ and T^, an intinife number of curves Fi{F=P) and 

 Fi{T= J\) exist, therefoi-e; one single curve Fi {R) exists however. 



We now take a point A' on curve FiiR); through this point goes 

 a curve F{{P=: Px) and Fi(T ^ Tx), which touch one another in 

 the point A'. Curve Fi{P=^ Px) has viz. a maximum- or minimum 



