BANCROFT. — TERNARY MIXTURES. 335 



solutions," without noticing any disturbing effect due to " variations 

 from the gas laws." The series benzol-water-alcohol is represented by 

 a single curve ; but it must not be thought that in this it forms a real 

 exception to the other mixtures. Theoretically, there are two curves 

 for this series ; but the two happen to have the same direction, and 

 therefore appear as one. The point where the precipitate ceases to be 

 less dense tlian the original solution lies between the mixtures benzol 

 2.00 c.c, water 1.45 c.c, and benzol 3.57 c.c, water 1.00 c.c. 



The formula x°- yP= Constant is not satisfactory, because it contains 

 no term expressing the variation of the consolute liquid in case one of 

 the non-miscible liquids is kept constant, and also because a change in 

 the units in which x and y are expressed or a change in the amount 

 of the consolute liquid taken affects the constant of the formula. This 

 can be remedied by the following reasoning. According to Gibbs and 

 to experiment, the absolute mass of a phase has no effect on the equi- 

 librium. Therefore increasing the quantities of x and y ?n-fold in- 

 volves inC'reasing the quantity of the consolute liquid m-fold if the 

 solutions are to remain at the saturation point. This would increase 

 the value of the constant m='+^ times. If then x and y denote the 

 values in cubic centimeters of the non-miscible liquids A and B, z the 

 corresponding value for the consolute liquid S^ we have as equation of 

 equilibrium for saturated solutions the expression : 



If, as was done, z is kept constant, this simplifies to formula (4), which 

 I will renumber la . 



la. - a^"/ = (^1- 



\i y is constant, x and z varying, we have : 



lb. -^ = c 



And if X is constant, y and z varying, we have : 



In equation I the value of C is a function of the nature of the units 

 in which x, y, and z are expressed ; but independent of the size. Thus 

 grams and kilograms give the same result, cubic centimeters and litres ; 

 but the weight constant is different from the volume constant, and the 

 constants for reacting weights or reacting volumes would have still 



