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

370 when the pressure is varied, enables us to calculate the value of the differential coefficient $$\frac$$.

In fact, according to our formulas, the specific caloric of the air under two pressures $$p$$ and $$p'$$ differs by $$R\frac - \log \frac$$; 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 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 $$\frac$$ between these two temperatures.

From this result we learn, that between these two limits the function $$C$$ increases, though very slowly; consequently the quantity $$\frac$$ 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 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 We may remark in passing, that at the temperature of ebullition $$\frac$$ 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 $$\frac$$ are the same for all vapours at the boiling point.