Page:Scientific Memoirs, Vol. 1 (1837).djvu/385

would conduce to the determination of several other important elements of the theory of heat, with regard to which we know nothing, or have arrived by our experiments at very insufficient approximations only. In this number may be included the heat disengaged by the compression of solid or liquid bodies; the theory that we have enunciated enables us to determine it numerically for all the values of the temperature for which the function $C$ is known in a manner sufficiently exact, that is to say, from $t=0$ to $t=224^{\circ }$.

We have seen that the heat disengaged by the augmentation of pressure $d\,p$ is equal to the dilatation by the heat of the body subjected to experiment, multiplied by $C$. With regard to the air taken at zero, the quantity of heat disengaged may be directly deduced from the experiments upon sound in the following manner.

M. Dulong has shown that a compression of ${\frac {1}{267}}$ raises the temperature of a volume of air taken at zero by $0^{\circ }\centerdot 421$. Now the $0.267$ unity of heat necessary to elevate a kilogramme of air taken at zero under a constant pressure by 1°, are equal to the heat necessary to maintain the temperature of the gas dilated by ${\frac {1}{267}}$ of its volume at zero, above the heat necessary to elevate the dilated volume, maintained constant, by 1°; the last is equal to ${\frac {1}{0.421}}$ of the first; their sum is therefore equal to the first multiplied by $1+{\frac {0}{0.421}}$; the former therefore, that is the heat necessary to maintain the temperature of 1 kil. of air, dilated by ${\frac {1}{267}}$ of its volume, at zero, is equal to $(0.267):\left(1+{\frac {1}{0.421}}\right)$, or to $0.07911$.

We arrive at the same results by the application of the formula

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

whence

$d\,Q=RC{\frac {d\,v}{v}},$

putting $C={\frac {1}{410}}$, and observing that a diminution of volume of ${\frac {1}{267}}$ corresponds to an increase of pressure equal to ${\frac {1}{267}}$ of an atmosphere.

Knowing the quantity of heat disengaged from gases by compression, to ascertain that which a similar pressure would disengage from any substance whatever, from iron for example, we write the proportion: $0.07911$ of heat disengaged by a volume of air equal to $0.77$ of a cubic metre, subjected to an increase of pressure equal to ${\frac {1}{267}}$ of an at-