672 PROCEEDINGS OF THE AMERICAN ACADEMY. 



are falling from the ends of the pipettes into the mixing vessel, the ab- 

 sorption of heat from the surroundings, by the cold liquid, exactly cancels 

 the radiation of heat from the warm liquid. Even the cooling and 

 warming due to evaporation and condensation are also jiractioally iden- 

 tical, since the air through which the liquids pass is saturated with water 

 vapor. It will be seen, in the descrij)tion of the apparatus, that not only 

 do these errors cancel, but the errors themselves have been almost elimi- 

 nated, by making it possible to raise the calorimeter, just before the 

 liquids are to run out, to such a height that the tips of the pipettes are 

 within the calorimeter. 



The possibility of an unequal radiation or absorption of heat by the 

 two liquids after transference must however be considered. Such a thing 

 could happen only if the mixing was tardy, — for example, if the cold 

 solution chanced to remain for some time close to the walls of the mix- 

 ing vessel, while the warm water, for the most part, occupied a more 

 central position. The following consideration will show how remote such 

 a contingency must be. In the first place, the stoppers, which released 

 the liquids, were pulled out within J- to ^ of a second of one another. 

 The exit tubes were identical in form and length, and were so directed 

 that the two issuing streams met before striking the walls and floor of the 

 mixing vessel. Further, the very moment that all the liquid had run oat 

 (and this required only about two seconds), active stirring of the mixed 

 liquids was begun. In less than 90 si^conds more, the precise final tem- 

 perature was established, It is evident that the great <lifference of tem- 

 perature must have been equalized within a very few seconds after 

 mixing. We have seen, then, that not only is an unsymmetrical distri- 

 bution of the hot and cold liquids unlikely, but if this should occur its 

 duration must be exceedingly brief. 



Because the errors due to radiation after, before, and during mixing 

 were thus eliminated, it is evident that the accuracy of this method must 

 depend first, on the accuracy with which the relative amounts of the two 

 liquids are known, and second, on the refinement of the temperature 

 measurements. The initial weights of the two liquids can be known 

 with all the desired accuracy. By taking care to avoid evaporation and 

 by determining the amounts of liquids left in the tubes, we can be almost 

 equally sure regarding the amounts of the liquids which actually mix. 

 It appears, then, that the accuracy of the method must depend chiefly on 

 the refinement of the temperature measurements. 



Of the temperature measurements, that of the mixture is the most 

 important; because an error in it has the greatest effect on the final 



