430 Prof. Clausius on the Application of the Mechanical 



number which, according to Regnault, expresses its specific heat 

 at 100°, and thus set 



c= 1-0130 (51) 



In the determination of r we shall start from the equation 



X= 606-5 + 0-305. ^ 



given by Regnault as expressing the whole quantity of heat 

 necessary to raise the unit of weight of water from 0° to the 

 temperature t, and afterwards to evaporate it at that temperature. 

 According to this definition, however. 



cdt-\-r, 



Jo 



so that 



-£■ 



-J"' 



Jo 



i 



r =606-5 +0-305. ^- 1 cdt. 

 Jo 



In order to obtain precisely Eegnault's value of r, we ought 

 to substitute for c in the above integral, the function of the tem- 

 perature which Regnault determined. For our present purpose, 

 however, I think it will suffice to give to c the constant above 

 selected, by means of which 

 it 

 cdt=l'01S.t, 



10 



and the two terms in the above equation involving t combine to 

 form the single one ^0-708 . t. 



At the same time we must alter the constant term of the equa- 

 tion a little, and determine it so that the formula will correctly 

 express that observed value of r which in all probability is most 

 accurate. As a mean of thirty-eight observations, Regnault 

 found the value of \ at 100° to be 636-67. Deducting the 

 quantity of heat necessary to raise the unit of weight of water 

 from 0° to 100°, which, according to Regnault, amounts to 100*5 

 units of heat, and contenting ourselves with one decimal, there 

 remains 



rioo=536-2*. 



Employing this value, we obtain the following formula : — 



r«*607-0-708.^ (52) 



The following comparison of a few values calculated herefrom, 

 with the corresponding ones given by Regnault in his tables f, 



* In his tables Regnault gives, instead of tliis, the number 536*5 ; tbe 

 reason is, however, that instead of the above value 63667 for X at 100°, he 

 used the round number 637 in his calculations. 



t Mitn, de I'Aoadt, des Sciences, vol. xxi. p. 748. 



