HETEROGENEOUS EQUILIBRIUM 293 



mental thermodynamic equations developed by Gibbs not only 

 lead to the qualitative generalization known as the Phase Rule, 

 but also afford a direct and detailed treatment of problems of 

 heterogeneous equilibrium. Such an analj^tical treatment is 

 illustrated for systems of two and three components. In 

 simpler systems it has the advantage of stressing the funda- 

 mental relationships that determine the course of equilibrium, 

 in contrast to the graphical method in which these fundamentals 

 may be overlooked in a geometrical maze. With increasing 

 number of components the geometrical methods become in- 

 creasingly involved, and the analytical method outlined above 

 offers the most hopeful procedure for developing the theory of 

 phase equilibrium in multi-component systems. 



