Thermodynamical Theory of Ternary Mixtures. 943 



Pure thermodynamics deals,, of course, with those relation- 

 ships between experimental data, which are deducible from 

 the two fundamental laws of thermodynamics, and which 

 are independent, therefore, of any assumption as to the 

 chemical structure of the systems under consideration. The 

 purely thermodynamical theory of a phenomenon is not only 

 interesting in itself, but forms a very desirable preliminary 

 to any chemical theorising. In the case of the systems dealt 

 with in the present paper (as in many other cases) the 

 formulation of chemical theories has preceded the develop- 

 ment of the purely thermodynamical theory — an inversion of 

 the natural order of development which has been an abundant 

 source of error. 



The method of relating thermodynamically the different 

 phenomena under consideration, adopted in the present 

 work, will be similar to the method adopted in a previous 

 work* dealing with binary mixtures. The chemical poten- 

 tials of the components will be regarded as fundamental 

 magnitudes, and in each system studied the experimental 

 data will be related to the potentials. In this way the data 

 will be related to each other in a simple and symmetrical 

 manner. 



2. 1 Tie General Theory of Chemical Potential in a 

 Ternary Mixture^. 



Consider a homogeneous system containing masses M , M l5 

 and M 2 of three components C , C 1? and C 2 respectively. 

 Let <E> (M , Mj, M 2 , p, 0) represent the thermodynamical 

 potential % of the system at a pressure p and temperature 0. 

 Let 



g^ 3> (Mo, M l3 M 2 , p, 0) =¥i (M , M l5 M» jp, 0) (i=0, 1, 2) 



(1) 



The quantities F t are called the chemical potentials of the 

 components. Since <I> is a homogeneous function of M , M x , 

 and M 2 of the first degree, we may write 



$='sF,(M ,M 1 ,M 2)iJ ,tf)M t , ... (2) 



1 = 



* Phil. Mag. xxii. p. 933 (1911) ; xxiii. p. 483 (1912) ; xxv. p. 31 

 (1913). 



f Duhem, La Mecanique Chimique, vol. iii. pp. 1-15, 306, 330. 

 X Gibbs's £ function. 



