OF ARTS AND SCIENCES. 205 



part in more than twenty thousand. The KOH solution is titrated 

 aG;ainst oxahc acid, and its titration confirmed gravimetrically. The 

 quantity used in an experiment varied from 10.67 c.c. to over 200 c.c. 

 This was measured in a burette to .05 c.c, which would make the maxi- 

 mum variation considerably less than one per cent of the quantity 

 measured, even when the latter was at its minimum. Whereas, if we 

 put the limit of temperature reading at .005°, and consider that the 

 change in temperature depends upon three separate readings, the 

 maximum of error should be .01°, or .005° putting the limit of 

 reading at .0025°. This would be a very large per-cent variation in 

 many of the experiments when the quantity measured falls consid- 

 erably below 1°. Inspection of the tabulated data will show that in 

 many cases the observed variation of T^ is much smaller than the 

 calculated maximum ; e. g. the first six experiments of Table I., where 

 it is only .001°. In most of the experiments a variation of .005° in 

 T^ makes a variation of .24 Cal. in H. 



Series I. 



The numerical data of these experiments are recorded in Table I. 

 The alum used was the commercial article, well crystallized and free 

 of iron. Of it 20.067 grm. were used in each experiment, and the 

 solution prepared as already described. The proportion of water was 

 about 2,600 molecules to one of alum ; in Thomsen's experiments, 

 2,400. In column h is recoixled the rate of heat disturbance per mole- 

 cule of KOH. The results H and h are seen graphically expressed 

 in Plate I., where x is the number of molecules of KOH added, and 

 y m Line I. represents H^ in Line III., h X 10* 



Inspection of Line I. shows that the heat evolution increases with 

 the quantity of KOH, reaching a maximum at ar =z 6 or 6.5, and from 

 this point dmiinishes until a: = 10, when the re-solution of the pre- 

 cipitate in the excess of KOH is complete. This means that the 

 solution of the precipitate in excess of KOH is accompanied by 

 heat absorption, or is endothermic. It will be shown farther on that 

 the addition of KOH beyond x = 8.5 causes no further heat disturb- 

 ance, and that 8.13 mol. KOH completely redissolve the precipitate; 

 hence, in constructing the line, the value of y at a; = 8.13 is made the 

 same as at a; = 10. 



Line III. reveals still more. It shows a constant rate of heat 

 evolution per molecule of K(^H from a; = .5 to a: = 1. At this point 

 it drops abruptly. Now in the analytical part it will be shown (see 

 Plate II. Line V.) that precipitation begins between a: = 1 and 



