BANCROFT. — TERNARY MIXTURES. 339 



which can be rewritten : 



(13) (A + si Ay (B +s,B) = -^. 



(Ji 0-2 



If X and y denote cubic centimeters of pure water and pure ether 

 dissolved in a given quantity of the consolute liquid, we have : 



(14) x = A+s2B; y = B+SiA. 

 Solving for A and B: — 



(15) ^ = -^^l^; i? = p^^. 



i — Si $2 1 — Si s^ 



Substituting these values in (13) : — 



Since cTj, o-o, Si, S2) ^^e constants for constant temperature, we can 

 simplify equation (16) into: 



(17) (^^-s,^jy(y-s,x)= C^, 



where the relation between Ci and C^ is 



nR-\ ^1 _ C Tl" 0-2 (1 + S,Y (1 + So) 



Eliminating the effect due to the arbitrary quantity of consolute liquid 



used, we have : 



n Q\ {x - SoyY iy - sr oc) _ 



(ly; 2„+i — —^3, 



Q 



where Cg = ^^ . Reverting to the most general form, so as to make 

 the equation correspond in form to Equation I., 

 n (a: - Sa yT {V - Si ^Y ^ g^ 



Equation II. is more general than Equation I., the latter being merely 

 a special case of the former, where the terms representing the mutual 

 solubilities are so small that they can be neglected. 



In testing these equations I took, as pairs of partially miscible 

 liquids, ether and water, ethylacetate and water. The ether was 

 distilled over sodium, the ethylacetate dried with calcium chloride and 

 fractionated, the boiling point rising a full degree for a litre distilled 

 off. I think however that no essential error was introduced in this 

 way, and that, for my purposes, it was sufficiently pure. The solubili- 



