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deducible from them; if then we take two of them, $p$ and $v$ for example, as independent variables, the two others $T$ and $Q$ may be considered as functions of the former two.

In what manner the quantities $T$, $p$, and $v$, vary with respect to each other may be ascertained by direct experiments upon the elasticity and dilatability of bodies; it is thus that Mariotte's law relative to the elasticity of the gases, and Gay Lussac's relative to their dilatability, lead to the equation

$pv=R(267+t);$

all that remains is to determine $Q$ in functions of $p$ and $v$.

A relation exists between the functions $T$ and $Q$, which may be deduced from principles analogous to those which we have just established. Let us increase the temperature of the body by the infinitely small quantity $d\,T$, and at the same time prevent the increase of the volume; the pressure will then be augmented; if we represent the volume $v$ by the absciss $a\,b$ (fig. 5), and the primitive pressure by the ordinate $b\,d$, this

Fig. 5.

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augmentation of pressure may be represented by the quantity $d\,f$, which will be of the same order as the increase of temperature $d\,T$ to which it is owing, that is infinitely small.

Now we will take a source of heat $A$, maintained at the temperature $T+d\,T$, and allow the volume $v$ to increase by the quantity $b\,c$; the presence of the source $A$, maintained at the temperature $T+d\,T$, prevents the reduction of the temperature. During this contact, the quantity $Q$ of heat that the body possesses will increase by the quantity $d\,Q$, which will be derived from the source $A$. We will afterwards remove the source $A$, and the given body will become cool by the quantity $d\,T$, at the same time retaining the volume $a\,c$. The pressure will then diminish by the infinitely small quantity $g\,e$.

The temperature of the body being thus reduced to $T$, which is that of the source of heat $B$, we will take $B$, and reduce the volume of the