tion; (2) that which is necessary to restore the temperature of the fluid from that of the body B to that of the body A, when, after having brought back this fluid to its primitive volume, we place it again in contact with the body A. Let us call the first of these quantities a and the second b. The total caloric furnished by the body A will be expressed by a + b.
The caloric transmitted by the fluid to the body B may also be divided into two parts: one, b', due to the cooling of the gas by the body B; the other, a', which the gas abandons as a result of its reduction of volume. The sum of these two quantities is a' + b'; it should be equal to a + b, for, after a complete cycle of operations, the gas is brought back exactly to its primitive state. It has been obliged to give up all the caloric which has first been furnished to it. We have then
a + b = a' + b';
or rather,
a - a' = b' - b.
Now, according to the theorem given on page 81, the quantities a and a' are independent of the density of the gas, provided always that the ponderable quantity remains the same and that the variations of volume be proportional to the original volume.
