370 M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 



when the pressure is varied, enables us to calculate the value of the dif- 



ferential coefficient — — 

 at 



In fact, according to our formulas, the specific caloric of the air un- 

 der two pressures p and p' differs by R - - — log ^^ ; rendering this 



quantity equal to the difference of the specific calorics, as it has been 

 deduced from tlie results of MM. De Laroche and Berard ; taking the 

 mean of two experiments, we find 



dC 



-j-^ = 0-002565. 



In these experiments the air entered into the calorimeter at the tem- 

 perature of 96°-90, and quitted it at that of 22°'83 ; 0*002565 is therefore 



the mean value of the differential coefficient — between these two 



dt 



temperatures. 



Fi'om this result we learn, that between these two limits the function 



C increases, though very slowly; consequently the quantity ^ dimi- 

 nishes ; whence it follows that the effect produced by the heat diminishes 

 at high temperatures, though very slowly. 



The theory of vapoui's will furnish us with new values of the func- 

 tion C at other temperatures. Let us return to the formula 



(l - E\ ^P 

 1 _ \ pj dt 



C ~ k ' 



which we have demonstrated in paragraph IV. If we neglect the den- 

 sity of the vapour before that of the fluid, this formula will be reduced 

 to 



dp 



1 = ^ 



C k ' 



We may remark in passing, that at the temperature of ebullition -^ 



is nearly the same for all vapours; C itself vaiies little with the tempe- 

 rature, so that k is nearly constant. This explains the observations of 

 certain philosophers, who have remarked that at the boiling point, equal 

 volumes of all vapours contain the same quantity of latent caloric ; but 

 we see at the same time that we are only approximating to this law, since 



it supposes that C and -E are the same for all vapours at the boiling 

 point. 



