page 68, that the quantities of heat consumed by each are the same, that is, that there passes from the body A to the body B the same quantity of heat in both cases.
The heat abstracted from the body A and communicated to the body B, is simply the heat absorbed during the rarefaction of the gas, and afterwards liberated by its compression. We are therefore led to establish the following theorem:
When an elastic fluid passes without change of temperature from the volume U to the volume V, and when a similar ponderable quantity of the same gas passes at the same temperature from the volume U' to the volume V', if the ratio of U' to V' is found to be the same as the ratio of U to V, the quantities of heat absorbed or disengaged in the two cases will be equal.
This theorem might also be expressed as follows:
When a gas varies in volume without change of temperature, the quantities of heat absorbed or liberated by this gas are in arithmetical progression, if the increments or the decrements of volume are found to be in geometrical progression.
When a litre of air maintained at a temperature of ten degrees is compressed, and when it is reduced to one half a litre, a certain quantity of heat is set free. This quantity will be found always
