BANCROFT. — TERNARY MIXTURES. 



351 



mation is better than treating the esters and water as absolutely non- 

 miscible. In Table XVIII. I give the solubilities which I have used 

 in calculating Pfeiffer's results, expressed in cubic centimeters of the 

 ester in ten cubic centimeters of water. 



XVIII. 



Starting, a3 Pfeiffer did, with a constant quantity of ester, his results 

 necessarily lie almost entirely along the curve representing the equilib- 

 rium when addition of water or ester produces a precipitate of ester. 

 In a few cases there are a few measurements, never more than two, on 

 the curve where water or ester produces a precipitate of water. There 

 are not enough of these measurements to enable me to determine the 

 direction of this second curve, and in the tables I have therefore given 

 no calculated values in these cases. The point where, according to 

 Pfeiffer, infinite miscibility occurs is the beginning of the curve where 

 the solution is saturated in regard to ester ; but water produces no 

 precipitate. The corresponding curve where the solution is saturated 

 in respect to water, while addition of ester produces no precipitate, did 

 not come within the scope of Pfeiffer's investigations at all. It will be 

 noticed that in the last measurements of each series the amount of 

 water required to saturate is very generally greater than the theoreti- 

 cal quantity. I attribute this variation entirely to experimental error. 

 When one is working with one hundred cubic centimeters of solution 

 or more, it becomes almost impossible to determine the first appearance 

 of clouding with great accuracy. In Tables XIX. to XXXI. I give 

 Pfeiffer's results, with the values for the water calculated according to 

 the formula at the top of each table. It is only fair to Herr Pfeiffer to 

 say that, if I had arranged the exponential factors so that z should have 

 been raised to the first power only, the differences between the ob- 

 served and the calculated values would have been less than they now 

 are. I felt, however, that, as the water was the thing I was calculat- 

 ing, I would make its exponential factor unity instead of that of the 

 alcohol. 



