212 PROCEEDINGS OF THE AMERICAN ACADEMY 



same which we suppose to exist when 2 mol. KOH ave added to 

 1 mol. ahim. Putting a; = 2, therefore, the results of Exp. Pgive the 

 points P in the Lines VI. and VIII., which approach at least the cor- 

 responding points in V. and VII. Regarding this as a further indi- 

 cation of an equilibrium, I varied the experiment in the following 

 manner (Exp. Q) : The usual 50 c.c. of alum solution were taken, 

 G mol. KOH added, and the whole made up to 250 c.c. Another 

 portion of 50 c.c. alum solution was then taken, and made up to nearly 

 250 c.c. The two solutions thus prepared were then mixed, made up 

 to 500 c.c, thoroughly shaken, filtered, and portions of 50 c.c. taken 

 from the filtrate for analysis, as usual. The total system here is evi- 

 dently the same in the proportion of its constituents (water included) 

 as would be obtained by mixing 1 mol. alum and 3 mol. KOH in a 

 volume of 250 c.c. At the same time, we can calculate from Exp. I, 

 Table VII., what would be the composition of the precipitate, assum- 

 ing that it remained the same as produced by 6 mol. KOH in the 

 first mixture, increased only by the remaining 9.47 p;^ of the total 

 AI2O3 of the first portion; the KOH uncorabined with H2SO4 in that 

 portion taking SO3 from the second portion of alum, but causing no 

 increase of precipitate since it is equivalent to only about .14 mol. 

 KOH. The precipitate thus calculated would contain 50% of the 

 total AloOg of the system, and have a composition of 95.29% AUOg to 

 4.71 % of SO3. This gives the crossed points Q(x=^ 3). But actual 

 analysis of the filtrate gives for the precipitate the results recorded in 

 Q, Table VIII., and the points Q in the Lines VI. and VIII. This 

 shows that the initial distribution of constituents between the soluble 

 and insoluble portions of the system has changed completely, ap- 

 proaching that obtained by adding to 1 mol. alum 3 mol. KOH. 

 The change in this case consists only in an increase of SO3 in the 

 precipitate. 



Another experiment was then made (Exp. E) by mixing in similar 

 manner (1 alum -|- 6 KOH) in 250 c.c. and (1 alum 4-1.5 KOH) 

 in 250 c.c. ; making a total system equivalent to 1 alum -\- 3.8 KOH 

 in 250 c.c. Calculating as in Q, from Exp. B and /, the initial com- 

 liosition of this mixed precipitate, and on the assumption that the 

 unneutralized .1 mol. KOH of the 6 mol. KOH is added to the 1.5 

 mol. in the second portion, we obtain the crossed points R {x z= 3.8). 

 Analysis of the filtrate, on the other hand, gives the points R {x = 3.8) 

 in the Lines VI. and VIII. , which likewise shows a very considerable 

 cliange in the precipitate, and a close approach to the system obtained 

 by adding 3.8 mol. KOH to 1 mol. alum. In this case the change 



