that they be taken and maintained at a certain invariable temperature. But these theories furnish no means of comparing the quantities of heat liberated or absorbed by elastic fluids which change in volume at different temperatures. Thus we are ignorant what relation exists between the heat relinquished by a litre of air reduced one half, the temperature being kept at zero, and the heat relinquished by the same litre of air reduced one half, the temperature being kept at 100°. The knowledge of this relation is closely connected with that of the specific heat of gases at various temperatures, and to some other data that Physics as yet does not supply.
The second of our theorems offers us a means of determining according to what law the specific heat of gases varies with their density.
Let us suppose that the operations described on p. 70, instead of being performed with two bodies, A, B, of temperatures differing indefinitely small, were carried on with two bodies whose temperatures differ by a finite quantity—one degree, for example. In a complete circle of operations the body A furnishes to the elastic fluid a certain quantity of heat, which may be divided into two portions: (1) That which is necessary to maintain the temperature of the fluid constant during dilata-
