REPRESENTATION BY ZETA FUNCTION 



299 



If we now call s' the f-point of the system, then we can state 

 that the f -point of system (1) is represented by the centre of 

 gravity of masses nii and m2 at the f-points a' and h'. From 

 this it appears that each point of the line a'b' represents the 

 f-point of a system (1) ; the closer this point lies to a' the greater 

 the value of Wi:w2, the closer to h' the smaller the value of 

 mi : rrii. For this reason we shall call a'b' the f-line of the two- 

 phase system or phase complex A -}- B. 



4. According to a theorem of Gibbs, at constant t and p 

 a given quantity of substance arranges itself in such a way that 

 the total ^ is a minimum. Or, of all systems (phases) at con- 

 stant t and p with the same total composition (in regard to the 

 independent components), that is the most stable one which 



/K 



Fig. 3 



has the smallest f . In order to apply this in the graphical repre- 

 sentation, we take a point e (Fig. 3). This point e may repre- 

 sent a single phase, e.g., a liquid, a vapor, a mixed crystal, or 

 possibly a compound. The point e may represent also various 

 phase-complexes or systems, e.g., of the phases a and h, or z and u 

 (see Fig. 4). We shall represent all these possible or conceivable 

 phases and systems, which have the same composition e, by 

 El, E2, Ez etc., and their ^-points by e', e" , e'" etc. It is clear 

 that all these ^-points are situated on a vertical line (ordinate) 

 through the point e. Since each of the phases or phase- 

 complexes denoted by Ei, E2, Ez etc. contains in toto one mol of 

 the components W and X and has the same composition with 

 respect to these components, it foUows that each of these phases 



