Thermodynamical) Theory of Ternary Mixtures. 961 



special case is, o£ course, a mere- coincidence. The fact that 

 in the experiment P is not found to be much greater than 

 12 simply demonstrates the incorrectness of the initial as- 

 sumption that the effect of the ether dissolved in the water 

 phase is negligible*. 



8. The Freezing oj Ternary Mixtures. 



Suppose that we have a solution of two substances C\ and 

 C 2 in a liquid C , and that C in the solid state is in equili- 

 brium with the solution at a temperature T, and with C in 

 the pure liquid state at a temperature T . 



The equation 



i)(s,,s 2 ,^T)=^ (p,T), .... (67) 



where ijr is the chemical potential of C in the solid state, 

 determines T as a function of s 1? s 2 , and v. 

 The equation 



*o(p,T )-^(p,T ), .... (68) 



where <£ is the chemical potential of C in the liquid state, 

 determines T as a function of p. 



If C is the only volatile component, the theory of the 

 relation between the vapour pressure and the freezing-point 

 is a particular case of a more general theory which I have 

 developed in a previous work "f. The same is true of the 

 theory of the relation between the freezing-point and the 

 osmotic pressure, if the latter is measured by means of a 

 membrane permeable to C only. 



In the above work I have given formulae by means of 

 which the difference (at any temperature) between the 

 chemical potentials of C in the pure liquid state and in the 

 solution, can be calculated from the freezing-point. The 

 exact expression for this difference is rather complicated. 

 If we suppose that l Q , the heat of dilution, and 7, the dif- 

 ference between the specific heats of C in the liquid and 

 solid states, are independent of the temperature, the expres- 

 sion reduces to the simpler form 



(■ 1 1 \ n rp 

 f —if) FjT-'o 



-7*(^-logT-°) • • (69) 



where 6 is any temperature, and L is the latent heat of 

 fusion of solid C . 



* A further investigation, treating the water phase as a ternary 

 mixture, shows that this assumption is valid only if the coefficient S 0l is 

 negligible in comparison with S n . 



t Phil. Mag. vol. xxv. p. 38, Jan. 1913. 



