ON THE LA.W OF THE CONSTANCY, &0. 



45 



reduced to the first degree and, as wiJl be seen, assume a fofm identical 

 with (a) obtained in the former case. 



lu both cases therefore the homogeueous équation reduces to one of 

 the first degree and the coefficient of each mass is a function of the 



o 



original and final températures of that mass, and of the spécial properties 

 of that substance onlj. The value of thèse coefficients lias to be deter- 

 nrined by experiment; simple observations show that their value rises 

 as the change in température (t — T) of the mass increases and approaches, 

 zéro as t and T corne nearer together. If in a mixing-experiment 

 ail the masses but one reduce to zéro, the final température becomes 

 the original température t of the remaining mass, and the équation shows 

 that the coefficient for that mass must become zéro at the same time. 

 We may indicate the above properties of the f mictions by writing the 

 équation thus: 



In a similar way it may be shown that for more than two substances 

 the équation would be : 



2 m f(t—T) = Q (O 



Eeturning for a moment to équations (1) to (4) the reader will easily 

 see that in their simplified form they completely describe ihe resuit of 

 experiment. In fact we have now : 



«i A (h~T) + m, f t {t-T) = 0 (1) 



m 3 f 3 (L-T) + m, A {t-T) = 0 (2) 



«h A ih—T) + »i A (h-T) = 0 (3) 



™* /, + *i À (.h-T) = 0 (4) 



from which it folio ws that 



(3) - 0) + (2) = (4) 



an équation expressing the mutual dependence of the 4 experiments. 



If we now want to introduce the conception of quantity of heat, 

 we must define t\ (/, — T) as the quantity of heat which the unit of 

 mass of the substance 1 gives off in cooling from /, to T and the équa- 

 tion (C) then expresses the law, that in mixing bodies of différent tem- 

 pératures the total quantity of heat remains constant. 



