THERMODYNAMICAL SYSTEM OF GIBBS 



149 



the values of f for the unit mass of the different phases (i.e., 

 nil -\- nh = I) against the composition. Thus the point Z (Fig. 

 5) represents a phase for which 



XZ 



Mi 



Wi + nii XY 



and the value of f for this phase is represented by ZE. The 

 curve AB represents the values of f for all homogeneous phases 



Fia. 5 



when the composition is varied from that of the phase for which 

 Wi = 1 (represented by point X) to that for which nh =1 

 (point Y). CD is the tangent to the f curve at the point E. 

 It can be shown that intercepts made by this tangent on the 

 axes at X and Y are equal to the values of Mi and M^ for the 

 phase represented by E, i.e., XC = Mi and YD = Mi* The 



* If the potentials of ;Si and St in the phase E are ixi and m2, the tangent 

 CD is characterized by the equation df = ixidm,]. + y^idmi, or since when 



