Page:Scientific Memoirs, Vol. 1 (1837).djvu/368

perature $t$ of the body $B$ is lower by the infinitely small quantity $dt$, than the temperature $t$ of the body $A$. We shall suppose in the first instance that a gas serves for the transmission to the body $B$, of the caloric of the body $A$. Let $v_{0}$ be the volume of the gas under the pressure $p_{0}$ at a temperature of $t_{0}$; let $p$ and $v$ be the volume and the pressure of the same weight of gas at the temperature $t$ of the body $A$. The law enunciated by Mariotte, combined with that of Gay-Lussac, establishes between these different quantities the relation

$pv={\frac {p_{0}v_{0}}{267+t_{0}}}(267+t),$

or, for simplicity,

${\begin{aligned}&{\frac {p_{0}v_{0}}{267+t_{0}}}=R:\\&pv=R(267+t).\end{aligned}}$

The body $A$ is brought into contact with the gas. Let $me=v$, $ae=p$ (fig. 3.). If the gas be allowed to expand by the infinitely small quantity $dv=eg$, the temperature will remain constant, in consequence of the presence of the source of heat $A$; the pressure will diminish, and become equal to the ordinate $bg$. We now remove the

Fig. 3.

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body $A$, and allow the gas to expand, in an inclosure impermeable to heat, by the infinitely small quantity $gh$, until the heat becomes latent, reduces the temperature of the gas by the infinitely small quantity $dt$, and thus brings it to the temperature $t-dt$ of the body $B$. In consequence of this reduction of temperature, the pressure will diminish more rapidly than in the first part of the operation, and will become $ch$. We now take the body $B$, and reduce the volume $mh$ by the infinitely small quantity $fh$, calculated in such a manner that during this compression the gas may transmit to the body $B$ all the heat it has derived from the body $A$ during the first part of the operation. Let $fd$ be the corresponding pressure; that done, we remove