Page:Reflections on the Motive Power of Heat.djvu/97

V + ${\tfrac {1}{267}}$V are small relatively to the volumes themselves, we may regard the quantities of heat absorbed by the air in passing from the first of these volumes to the second, and from the first to the third, as sensibly proportional to the changes of volume. We are then led to the establishment of the following relation:

The quantity of heat necessary to raise one degree air under constant pressure is to the quantity of heat necessary to raise one degree the same air under constant volume, in the ratio of the numbers

${\tfrac {1}{116}}$ + ${\tfrac {1}{267}}$   to   ${\tfrac {1}{116}}$;

or, multiplying both by 116 × 267, in the ratio of the numbers 267 + 116 to 267.

This, then, is the ratio which exists between the capacity of air for heat under constant pressure and its capacity under constant volume. If the first of these two capacities is expressed by unity, the other will be expressed by the number ${\tfrac {267}{267+116}}$, or very nearly 0.700; their difference, 1 − 0.700 or 0.300, will evidently express the quantity of heat which will produce the increase of volume in the air when it is heated one degree under constant pressure.

According to the law of MM. Gay-Lussac and Dalton, this increase of volume would be the same