Page:Reflections on the Motive Power of Heat.djvu/108

86 The difference a - a' should fulfil the same conditions, and consequently also the difference b' - b, which is equal to it. But b' is the caloric necessary to raise the gas enclosed in abcd (Fig. 2) one degree; b' is the caloric surrendered by the gas when, enclosed in abef, it is cooled one degree. These quantities may serve as a measure for specific heats. We are then led to the establishment of the following proposition:

The change in the specific heat of a gas caused by change of volume depends entirely on the ratio between the original volume and the altered volume. That is, the difference of the specific heats does not depend on the absolute magnitude of the volumes, but only on their ratio.

This proposition might also be differently expressed, thus:

When a gas increases in volume in geometrical progression, its specific heat increases in arithmetical progression.

Thus, a being the specific heat of air taken at a given density, and a + h the specific heat for a density one half less, it will be, for a density equal to one quarter, a + 2h; for a density equal to one eighth, a + 3h; and so on.

The specific heats are here taken with reference to weight. They are supposed to be taken at an