206 PROCEEDINGS OF THE AMERICAN ACADEMY 



a: = 1.0, probably at a; = 1.13. Hence, in constructing Line III. 

 the minimum is put hypotlietically at x = 1.13, instead of at a: =:z 1.5 

 which is the point actually determined. Inasmuch as the precipitate 

 at first jiroduced redissolves in excess of alum up to x ^ 1.13, the 

 drop in the line at this point indicates probably that this re-solution 

 also is accompanied by heat absorption. This will be evident upon 

 considering that the heat disturbance, ^, is a positive resultant, made 

 up of both positive and negative elements. The principal positive 

 element is the formation heat of potassic sulphate, and since this in all 

 probability remains approximately constant for equal portions of KOH 

 entering into combination, it follows that the negative element in- 

 creases at the point x =■ 1.13 in consequence of precipitation. In 

 other words, precipitation is accompanied by iieat evolution, and re- 

 solution of the precipitate by heat absorption.* 



Beyond x =. 1.13 there is evidently a tendency to rise slightly 

 up to X = 5, or thereabouts. The break at a; = 4.8 is within the 

 limit of error, since the larger value recorded in Table I. gives the 

 alternative point, x = 4.8, just above the line as seen in the plate. 

 Indeed, the increase between x ■= 1.13 and x = 5 depends upon differ- 

 ences which lie so close to the limit of experimental error that one 

 must hesitate to consider it more than probable. It would be inter- 

 esting to establish it beyond doubt, in view of the analytical results 

 shown in Plate II., Line VIL There can be no doubt, however, 

 that the line drops beyond x = 5.12, as would be expected. 



It is to be noted that the maximum in Line I. occurs at a? = 6 

 or 6.5 ; while in Line III. it occurs at a; = 5, which is the point at 

 which the aluniinic oxide is completely precipitated. This leads to 

 the question. What causes the continued heat evolution after the pre- 

 cipitation is total ? the discussion of which must be deferred until the 

 analytical results have been described. The three experiments re- 

 corded in Table III. serve, however, to fix one point bearing thereon. 

 4.8 mol. KOH were added to one of alum in the usual conditions. 

 Then to this mixture were ad<led in the calorimeter the remaining 

 1.2 mol. KOH, in the proportionate quantity of water, and the heat 

 evolution measured. The results are fairly satisfactory, considering 

 that the necessary conditions of the experiments were not the best for 

 calori metric measurement. They serve to show, at least, that the con- 

 tinued evolution of heat between x = 4.8 and a: = 6, in Series I., 

 may be accounted for by the action of the 1.2 mol. KOH on the 



* See similar case of lead, Tiiomsen, i. 377. 



