40 



J. P. KUENEN. 



count of the subject, wliicb is not discussed by Mach and appears to me 

 of sufficient interest to justify a separate treatment. In the folio wing 

 lines I will try to deal with the question more fully than could be done 

 in the textbook referred to. 



Historically the conception "quantity of beat", as used by Black and 

 his followers, dépends upon the law revealed by experiments in whicK 

 nneqnally tempered bodies are "mixed" (in its well known calorimetric 

 sensé) — in the sequel I shall refer to tins law as the law ofmixing. When 

 it was found that two quantifies of a substance at différent températures, 

 when mixed, assumed a final température such that the change of tem- 

 pérature in each one of the quantifies was prqportional to the other 

 quantity, this was "explained' 1 or as we would now say "described" by 

 assuming the existence of an agent "beat", the quantity of which was 

 proportional to the quantity of the substance in which it was contained, 

 and to the change of température which it produced in this substance on 

 entering or on leaving it. In this way the law of mixing was readily 

 explained, as due to the transference of a certain quantity of beat from 

 the one portion to the other. 



When two différent substances were mixed the phenomena were 

 différent, but it appearecl possible to retain the notion of quantity of 

 beat, if the further assumption was made that, in addition to being pro- 

 portional to the quantity of the substance and the change of température 

 which it produces, the quantity of beat also depended on the nature of 

 the substance, in such a manner that a constant ratio existed between 

 the quantifies of beat required for given changes of température in equal 

 quantifies (say masses) of two given différent substances. 



Beferring this ratio to a standard-substance, water, and calling it spé- 

 cifie beat, the resuit of the experiments could be written in the following 

 manner : 



m t (iî, 



T) c x + m 2 (i 2 — T) c 2 = 0 



and in gênerai for more substances 



2 m c (t — T) = 0 



(4 



where m represents the mass, c the spécifie beat, t the original and 7' the 

 common final température. Each one of the terms m c (l— T) is now 



