OF ARTS AND SCIENCES. 211 



The calculation of the composition of the precipitate is similar to 

 that ill tlie preceding series, except that account must be taken of the 

 SO3 added. 



In three experiments, viz. H^ T, and S'" (in H and T the total 

 amount of precipitate was at its maximum), the \v.f) in the filtrate 

 was determined. The full calculated amount being found, it was 

 deemed unnecessary to determine it at other points, since it evidently 

 formed no part of the precipitate. 



Discussion. — The results of the first two series are graphically 

 expressed in Lines V., VI., VII., and VIII., Plate II. In Line 

 v., X = number of molecules of KOH added, and y = per cent of 

 total AlgOg found in the precipitate. While in Line VII., x = the 

 same, but y = parts of ALO3 in 100 parts of anhydrous precipitate. 

 Continuing Line V. beyond x = 1.5 and x = 8 toward the axis of x 

 indicates x ^= 1.13 and x = 8.13 as the probable points respectively 

 of initial and final precipitation. The line reaches its maximum at 

 X = 4.8, making the precipitation of the Aip,. complete at this point. 



Line VII. shows that the first precipitate is the least basic, contain- 

 ing only 64% of AljOg; that from a: = 1.5 to a; = 4 there is appar- 

 ently a slight increase of basicity, but that from x = 4 to x = 4.8 

 the increase is more rapid; that between x = 4.8 and a; = 6 the 

 rapidity of change is still greater ; that at a; = 6 it drops back again, 

 leaving a precipitate free of SO3 at x = 7. It will be noticed that 

 X =■ 4.8 and x = Q are salient points in these lines, as they are in 

 Lines I. and III., expressing the thermal phenomena. 



The points in Line VI., a; = 5, 6, and 7, are obtained from Exp. 

 N', 0, and T, by making x the number of molecules of KOH left 

 unneutralized by the H^SO^ added. It will be seen that they approxi- 

 mate closely to the corresponding points in Line V., the difference 

 being probably within the limits of experimental error. This evi- 

 dently means that, when the same am.ount of free KOH is present, the 

 same precipitate is obtained, whether it come from adding KOH to 

 alum, or from neutralizing the excess of KOH in the alkaline solu- 

 tion of Al.^Oa obtained by adding 10 KOH to alum. This result was 

 unexpected, and suggested at once the possibility of a chemical equilib- 

 rium existing between the constituents of the soluble and of the insol- 

 uble portions of the system. To test this idea, Exp. P was made, using 

 4 mol. II.JSO4. Assuming that 4 mol. KOH out of the ten added are 

 uncombined with H2SO4, the 4 mol. H._.S04 now added would neutral- 

 ize them, leaving an excess of 2 mol. H.3SO4, and making a system, 

 neglecting the K.SOi, constituted of 1 mol. Al^Os and 2 H2SO4, the 



