Page:Reflections on the Motive Power of Heat.djvu/269

from the volume of one litre to the volume of v litres under constant temperature. If v increases by the infinitely small quantity dv, r will increase by the quantity dr, which, according to the nature of motive power, will be equal to the increase dv of volume multiplied by the expansive force which the elastic fluid then possesses; let p be this expansive force. We should have the equation

$dr=pdv$

(1)

Let us suppose the constant temperature under which the dilatation takes place equal to t degrees Centigrade. If we call q the elastic force of the air occupying the volume 1 litre at the same temperature t we shall have, according to the law of Mariotte,

${\frac {v}{1}}={\frac {q}{p}},$ whence $p={\frac {q}{v}}.$

If now P is the elastic force of this same air at the constant volume 1, but at the temperature zero, we shall have, according to the rule of M. Gay-Lussac,

$q=P+P{\frac {t}{267}}={\frac {P}{267}}{(267+t)};$

whence

$q=p={\frac {P}{267}}{\frac {267+t}{v}}.$