338 PROCEEDINGS OF THE AMERICAN ACADEMY. 



liquids, and a third miscible in all proportions with each of the others. 

 Formula I cannot apply here, because it was deduced for two non-mis- 

 cible liquids, and this condition is no longer fulfilled. There are two 

 ways of treating a problem like this. One is to change the conditions 

 of the experiment until they agree with the formula. The other is to 

 change the formula till it conforms to the conditions of the experi- 

 ment. I have done both. I will suppose, for the sake of clearness, 

 that the two partially miscible liquids are ether and water. Saturated 

 solutions of water in ether are absolutely non-miscible at the tempera- 

 ture for which they are saturated, being thus an improvement over 

 benzol and water, which are slightly miscible theoretically. If x and 

 y in equation la mean quantities of saturated water and saturated 

 ether solutions, instead of pure water and pure ethei*, the conditions 

 are satisfied for which this formula was deduced, and the equation must 

 apply. I have found that it did, and the experimental i^roof is given 

 in Tables IX. and XI, 



This being settled, we can attack the second part of the problem. 

 Let X denote cubic centimeters of saturated solution of ether in 

 water, Y cubic centimeters of saturated solution of water in ether 

 which saturate a given quantity of a consolute liquid. It is found 

 experimentally that 



(7) Z«r^=. Constant, 



or, if we set — = n, we shall have 



(8) x» r= c. 



If Sj is the solubility of ether in water, s^ the solubility of water in 

 ether, both expressed in volumes per cubic centimeter of the solvent 

 synthetically, we shall have, if no contraction or expansion takes place 

 in forming the saturated solutions of water in ether and ether in water : 



(9) X=^ + 5iJ; Y^B^s.^B; 



(10) {A-\-s^AY{B^s^B)= G; 



where A = c.c. water in X, Bo = c.c. ether in Y As we must assume 

 some contraction or expansion, let the ratio of the actual volume to 

 the sum of the component volumes be a-y in the saturated solution of 

 ether in water, and a-2 in the saturated solution of water in ether. We 

 have then: 



(11) X=a-^(A-\- s,A); Y=cT„_{B+ SoB)', 



(12) {<j, (A + s, A)y {a, (B + s, B)} = C, ; 



