364: M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 
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 elasti- 
city of the gases, and Gay Lussac’s relative to their dilatability, lead to 
the equation 
pv=R (27+ 24); 
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 de- 
duced from principles analogous to those which we have just established. 
Let us increase the temperature of the body by the infinitely small quan- 
tity 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 ab (fig.5), and the primitive pressure by the ordinate 4 d, this 
Fig. 5. 
augmentation of pressure may be represented by the quantity df, which 
will be of the same order as the increase of temperature dT to which it 
is owing, that is infinitely small. 
Now we will take a source of heat A, maintained at the temperature 
T+ dT, and allow the volume v to increase by the quantity 6c; the 
presence of the source A, maintained at the temperature T + dT, pre- 
vents the reduction of the temperature. During this contact, the quan- 
tity Q of heat that the body possesses will increase by the quantity 
dQ, which will be derived from the source A. We will afterwards re- 
move the source A, and the given body will become cool by the quan- 
tity d T, at the same time retaining the volume ae. The pressure will 
then diminish by the infinitely small quantity ge. 
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 
