336 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Other values. C is also dependent on the absolute value of the expo- 

 nential factors a and /3. We can however eliminate this effect by 

 writing 



(6) G = K-+^, 



in which case K remains entirely unchanged, when we substitute 



— = n. In Table VII. I ijive in the first two columns the values for 



log (7 according to the general formula -;^^ — C, when a:, y, and z are 



expressed in volumes. Since 2: = 5 in all these measurements, Table 

 VII. gives the constants of the preceding tables less the corresponding 

 values of (n + 1) log 5. It would have been better to calculate the 

 integration constant using the rational exponents a and /3 ; but only 

 their ratio can be determined by a study of equilibrium in one liquid 

 layer, and the case of two liquid layers will form the subject of a 

 separate communication. In columns three and four are the corre- 

 sponding values of K^ and A'o according to equation (6). They are 

 the constants of the preceding two columns divided by the appropriate 

 values of n -\-\. 



The values given under x and y in Tables I.-VI. are amounts of the 



liquids A and Birnx given quantity of S, — in this case c.c. A glance 



at the tables will show that these figures are very far from expressing 



volume concentrations, i. e. quantity of substance in a given volume of 



the solution. As most theoretical generalizations in chemistry are 



expressed in volume concentrations, it will be necessary to see what 



effect such a change would have on general Formula I. If there is no 



contraction or expansion on mixing, the volume of the solution will be 



the sum of the component volumes, or V=x + y-^z, and the volume 



. ... , X y z . . 



concentrations will be ; — 1 , — ; , respectively. 



x^yA^z x-Vy^z x+y + z 



This simple case may be said never to occur, and the volume of the 

 solution is an at present unknown function of the component volumes 



