Thermodynamical Theory of Ternary Mixtures. 953 



If we differentiate equation (38) with respect to the 

 pressure, we obtain the equation 



ds 2 _ v 2 (p,0) — P 2 0i,s 2 ,ff, 6) , 41 . 



where v 2 is the specific volume of C 2 in the solid state. When 

 a mass 5M 2 of C 2 passes from the solid to the liquid mixture 

 in the neighbourhood of saturation the decrease of volume 

 is (v 2 — P 2 ) SM 2 . Moreover, S 22 is always positive. Hence 

 equation (41) is in agreement with the general principle of 

 the displacement of equilibrium by variations of pressure*. 



Differentiating equation (38) with respect to the tempera- 

 ture, we obtain the equation 



ds 2 fa'(p, 0)— ./Vfa, s 2 , ;?, 6) 



where fa'=bfal^6* If now Zs(«i, s 2 , p, 6) denote the heat 

 of solution of C 2 in the saturated liquid mixture (heat 

 evolved) we have f 



0(f,'-fa') = k(s 1 ,s 2 ,p,6). 

 Hence we have * 



Bs 2 h(h,S2>P, 0) /,qn 



W e^s^a^p^ey ' ' ' K0) 



It will readily be seen that this equation is in agreement 

 with the general principle of the displacement of equilibrium 

 by variations of temperature J. 



From equations (41) and (43) we obtain 



(44) 



5s 2 



B# l 2 (s u s 2 ,p,6) 



(3s 2 0{v 2 {p } 6)-Y 2 {s 1} ^p,6)}' ' 



"dp 



Hence if simultaneous increments Sp and 86 of the pressure 

 and temperature respectively, cause no change in the solu- 

 bility, we have 



&P h(*i,**p 9 0) a *x 



86-6{v 2 ( P ,6)-P 2 (s l)S2 ,p,6)}' ' * ^ 



An equation similar to this, applicable to a binary solution, 



* Duhem, La M&canique Chimique, vol. i. p. 145. 

 f Duhein, loc. cit. vol. iii. p. 127. 

 X Duhem, loc. cit. vol. i. p. 184. 



