Page:Scientific Memoirs, Vol. 1 (1837).djvu/375

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

With regard to the generality of vapours, the ratio ${\frac {\delta }{\rho }}$ of the density of the vapour to that of the liquid from which it is formed may be neglected before it arrives at unity, so long as the temperature is not very high; we shall have therefore, sensibly,

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

This equation expresses that the latent caloric contained in equal volumes of the vapour of different liquids at the same temperature, and under the corresponding pressure, is proportional to the coefficient ${\frac {d\,p}{d\,t}}$ of the pressure with regard to the temperature.

Whence it results, that the latent caloric contained in the vapours of liquids which commence boiling only at high temperatures, as mercury for example, is very feeble, since for these vapours the quantity ${\frac {d\,p}{d\,t}}$ is very small.

We shall not insist upon the consequences which result from the equation

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

We shall simply remark that if, as everything leads us to believe, $C$ and ${\frac {d\,p}{d\,t}}$ do not become infinite for any value of the temperature, $k$ will become null when we have $\delta =\rho$, that is, that when the pressure is strong enough, and the temperature sufficiently elevated to render the density of the vapour equal to that of the liquid, the latent caloric is reduced to zero.

§ V.

Variation is produced in the volume of all the substances of nature by changes in the temperature and pressure to which they are subjected; liquids and solids are amenable to this law, and serve equally to develop the motive power of heat; it has been proposed to substitute them for the vapour of water, in order to render this motive force available; they have even occasionally been advantageously employed, particularly when it was necessary to develop a very considerable momentaneous effort, exerted within narrow limits.

In bodies of these kinds, as in the gases, it may be remarked, that of the four quantities, the volume $v$, the pressure $p$, the temperature $T$, and the absolute quantity of heat $Q$, two being determined, the others are