214 PROCEEDINGS OF THE AMERICAN ACADEMY 



The proof of equilibrium is indubitable, the initial precipitate gain- 

 ing or losing ALO, or SO3 as may be necessary to bring about the 

 characteristic distribution of constituents for the given conditions. It 

 is also apparent that KgSO^ pbiys no part, and may be considered as 

 practically outside the system, since its presence in quantity varying 

 from less than one molecule to more than ten molecules has not dis- 

 turbed the leading phenomenon. 



Another fact may be noted here. The corresponding points in the 

 Lines v., VI., VII., and VIII., that lie to the right of x = 5, ap- 

 proximate closely, probably within the limits of experimental error. 

 To the left of x = 5, the divergence is greatest, but the difference in 

 evei-y instance lies on the side of approach to the Lines V. and VIL 

 from the initial points, never going beyond. Tlie probable explana- 

 tion of this lies in the fact that, in all the experiments yielding the 

 Lines V. and VII., also the points of the other lines to the right of 

 a; = 5, the system in its initial state is homogeneous. While in the 

 remaining experiments, with the single exception of Exp. P, it is 

 non-homogeneous (liquid and solid). It is not strange, then, that tliis 

 non-homogeneity exercises a retarding influence upon the equilibrium. 

 It is rather a matter of surpi'ise that it should not prove more of an 

 obstacle than it does. 



Effect of Temperature, Time, and Dilution on the Equilibrium. 



Temperature often exerts an influence in reactions such as we have 

 been describing, and to test its effect in this instance is the object of the 

 three following experiments, E', E", and E". In the first place two 

 successive experiments were made as nearly alike as possible, in order 

 to measure the probable variation in the final results of a single experi- 

 ment. I give the details in full. The solutions were prepared in the 

 usual manner, 4 mol. KOH being added to 1 mol. alum. The tem- 

 perature of the room in both experiments was about 23° C, but the 

 contents of flasks before bringing up to standard volume and before 

 taking out portions of 50 c.c. were cooled, as in previous experiments, 

 to 20°. The results were as follows : — 



Mean = .0174 .28216 .0161 .2810: 



