116 BUTLER ART. D 



Since similar equations can be obtained for the other com- 

 ponents, the pressure will thus in general be a maximum or a 

 minimum at constant temperature, and the temperature a 

 maximum or minimum at constant pressure when the foregoing 

 condition is fulfilled. 



For example, the three components water, alcohol, salt may 

 give rise to a system of the three phases, solid, salt-solution, 

 vapor. When the composition of the solution is such that it 

 can be formed by combining quantities of the salt and the 

 vapor, i.e., when the proportions of alcohol and water in the 

 vapor are the same as in the solution, the pressure is a maxi- 

 mum or a minimum at constant temperature. Again, in the 

 three component system; potassium sulphate, aluminium 

 sulphate, water; with the three phases, viz., solid potassium 

 alum, solution, vapor, the vapor pressure is a maximum or a 

 minimum when the solution can be formed out of the solid salt 

 and the vapor, i.e., when it contains the two salts in the same 

 proportions as in the solid phase. 



VI. Values of the Potentials in Very Dilute Solutions 



16. A Priori Considerations * We may draw some con- 

 clusions as to the values of the potentials in a homogeneous 

 mass, when the quantity of one of the components is very 

 small, from the form of (56). Applying this equation to a 

 homogeneous mass having two independently variable com- 

 ponents, we obtain, when t, p and nii are constant 



m(^) +n,J^) =0. (110) [210] 



When TUi = 0, this equation requires that either 



( 



P) = 0, (111) [211] 



mi 



or 



' d\x 



( 



, . =00. (112) [212] 



dm^/ 1, p, m, 



*Gibbs, I, 135-138. 



