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 
In fact, according to our formulas, the specific calorie of the air un- 
[Ray log 2; rendering this 
dt p' 
der two pressures p and p! differs by 
quantity equal to the difference of the specific calorics, as it has been 
deduced from the results of MM. De Laroche and Bérard ; taking the 
mean of two experiments, we find 
oO oe i o098 
dt = 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 ; 0002565 is therefore 
the mean value of the differential coefficient S between these two 
temperatures. 
From this result we learn, that between these two limits the function 
C increases, though very slowly; consequently the quantity m dimi- 
nishes ; whence it follows that the effect produced by the heat diminishes 
at high temperatures, though very slowly. 
The theory of vapours will furnish us with new values of the func- 
tion C at other temperatures. Let us return to the formula 
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 
We may remark in passing, that at the temperature of ebullition - 
is nearly the same for all vapours; C itself varies little with the tempe- 
rature, so that & 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 = are the same for all vapours at the boiling 
point. 
