The amount of heat required to raise the temperature of the unit mass of a gas through a definite interval depends, as Laplace first pointed out, upon whether the gas is allowed to expand or not; in other words, the specific heat of a gas varies as the heating is at constant volume or at constant pressure. If, having raised the temperature of the unit mass, and so expanded it, we then compress it until it occupies its initial volume, a further rise of temperature takes place without any external heat having been applied. This rise of temperature is, in fact, due to the liberation of the amount of heat required merely to expand the gas without increasing its temperature. The quantity of heat needed to raise the temperature of a gas through a definite interval is therefore greater when it is allowed to expand than when its volume is kept constant; in other words, the specific heat at constant pressure is greater than the specific heat at constant volume. The ratio of the two specific heats can be calculated: on the assumption that the energy imparted to the molecules simply accelerates their mean rectilinear velocity, and that no energy is absorbed in doing internal work among them, it is found that, when the gas is permitted to expand, the amount of heat required is 1.67 times greater than that needed when its volume is kept constant. This ratio has been experimentally determined for a number of gases. For oxygen under normal conditions it is 1.408, for hydrogen 1.414, for carbon dioxide 1.264, for methane 1.269—all numbers notably below the value 1.67. The direct experimental determination of this ratio by thermometric measurements is a matter of some difficulty. It was, however, demonstrated by Dulong that it can be ascertained with comparative ease from observations on the velocity of sound in the gas—the velocity being probably a direct function of this ratio. As carried out experimentally, the method consists in sending a sound-wave through the gas contained in a glass tube along the horizontal length of which is strewn a quantity of a light powder such as the spores of lycopodium or finely divided silica. The glass tube is fitted at one end with a glass rod; by rubbing this a series of longitudinal vibrations is set up and communicated to the gas whereby the light powder is thrown up into little heaps along the tube, the distance between the heaps being equal to half a wave length. By comparative measurements with air and the gas under examination, data are obtained from which the ratio of the specific heats can be deduced.