Page:Scientific Memoirs, Vol. 1 (1837).djvu/382

when the pressure is varied, enables us to calculate the value of the differential coefficient ${\frac {d\,C}{d\,t}}$.

In fact, according to our formulas, the specific caloric of the air under two pressures $p$ and $p'$ differs by $R{\frac {d\,C}{d\,t}}-\log {\frac {p}{p'}}$; rendering this 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

${\frac {d\,C}{d\,t}}=0.002565.$

In these experiments the air entered into the calorimeter at the temperature of $96^{\circ }.90$, and quitted it at that of $22^{\circ }.83$; $0.002565$ is therefore the mean value of the differential coefficient ${\frac {d\,C}{d\,t}}$ between these two temperatures.

From this result we learn, that between these two limits the function $C$ increases, though very slowly; consequently the quantity ${\frac {1}{C}}$ diminishes; 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 function $C$ at other temperatures. Let us return to the formula

${\frac {1}{C}}={\frac {\left(1-{\frac {\delta }{\rho }}\right){\frac {d\,p}{d\,t}}}{k}},$

which we have demonstrated in paragraph IV. If we neglect the density of the vapour before that of the fluid, this formula will be reduced to

${\frac {1}{C}}={\frac {\frac {d\,p}{d\,t}}{k}}.$

We may remark in passing, that at the temperature of ebullition ${\frac {d\,p}{d\,t}}$ is nearly the same for all vapours; $C$ itself varies little with the temperature, 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 ${\frac {d\,p}{d\,t}}$ are the same for all vapours at the boiling point.