BANCROFT. — TERNARY MIXTURES. 327 



where a and h are proportionality factors and constants. This equa- 

 tion may be rejected on a 'priori grounds, because it does not show that 

 when B is absent, the miscibility of A with S is infinite, and also 

 because it has no similarity with the other equations representing 

 chemical equilibrium. The second assumption is that the change in 

 solubility may be a function of the amounts of A and J5 already 

 present. This is the usual condition of chemical equilibrium, and is 

 known as the Mass Law. Its mathematical expression is 



a dx , B dy ^ 



+ - — - — 0, or 



X y 



(3) a d log X -\- 13 d log y = 0, 



where x and y denote the amounts of A and B in a constant quantity 

 of S, a and /3 are proportionality factors, and the logarithms are natural 

 logarithms. 



If a and /3 are constants, this equation is integrable, and gives when 

 cleared of logarithms : 



(4) x"/ = Constant. 



If we make — = w, we Ishall have : 



(5) x-y^C, 



where C is of course different in value from the constant in equa- 

 tion (4). 



Before we proceed to test equation (5) experimentally, it remains 

 to be seen in what unit x and y should be expressed. It is obvious 

 that the nature of the unit has no effect on the general form of the 

 equation, nor upon the exponential factor n. The only change will be 

 in the value of the integration constant log G, so that the measurements 

 may be expressed in any form that is convenient, as chemical units,* 

 for example, grams per litre, volumes, reacting volumes, or anything 

 else. It is not even necessary that x and y be expressed in the same 

 unit, though it would probably always be more practical. In my own 



* I have adopted the following nomenclature for molecular and atomic 

 weights, viz. reacting and combining weights. As the reacting weight is pro- 

 portional to the chemical unit experimentally, I propose that the gram molecule 

 in the unit of volume (reacting weight in grams per litre) be called the chemical 

 unit, or simply the unit. Tlie object of these arbitrary changes in our chemical 

 terms is to do away with everything involving or implying the assumption of 

 the existence of molecules and atoms. 



