Page:Scientific Memoirs, Vol. 1 (1837).djvu/373

We shall add that the equation

$Q=R(B-C\log p)$

gives the law of the specific calorics at a constant pressure and volume.

The expression of the first is

$R\left({\frac {d\,B}{d\,t}}-{\frac {d\,C}{d\,t}}\log p\right);\qquad \qquad$

of the second,

$R\left({\frac {d\,B}{d\,t}}-{\frac {d\,C}{d\,t}}\log p-C{\frac {1}{p}}{\frac {d\,p}{d\,t}}\right),$

equal to

$R\left({\frac {d\,B}{d\,t}}-{\frac {d\,C}{d\,t}}\log p-{\frac {C}{267+t}}\right).$

The first may be obtained by differentiating $Q$ with relation to $t$, supposing $p$ constant; the second, by supposing $v$ constant. If we take equal volumes of different gases at the same temperature and under the same pressure, the quantity $R$ will be the same for all; and accordingly we see that the excess of specific caloric at a constant pressure, over the specific caloric of a constant volume, is the same for all, and equal to ${\frac {R}{267+t}}C$.

§ IV.

The same method of reasoning applied to vapours enables us to establish a new relation between their latent caloric, their volume, and their pressure.

We have shown in the second paragraph how a liquid passing into the state of vapour may serve to transmit the caloric from a body maintained at a temperature $T$, to a body maintained at a lower temperature $t$, and how this transmission develops the motive force.

Let us suppose that the temperature of the body $B$ is lower by the infinitely small quantity $d\,t$ than the temperature of the body $A$. We have seen that if $c\,b$ (fig. 4.) represents the pressure of the vapour

Fig. 4.

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