That they do vary in the same proportion is proved by the law of Boyle and Mariotte; hence the velocity of sound in air is independent of the density of the air. But that this law shall hold good, it is necessary that the dense air and the rare air should have the same temperature. The intensity of a sound depends upon the density of the air in which it is generated, but not on that of the air in which it is heard. The velocity of sound in air of the temperature 0° C. is 1,090 feet a second; it augments nearly 2 feet for every degree Centigrade added to its temperature. Hence, given the velocity of sound in air, the temperature of the air may be readily calculated. The distance of a fired cannon or of a discharge of lightning may be determined by observing the interval which elapses between the flash and the sound. From the foregoing, it is easy to see that if a row of soldiers form a circle, and discharge their pieces all at the same time, the sound will be heard as a single discharge by a person occupying the centre of the circle. But if the men form a straight row, and if the observer stand at one end of the row, the simultaneous discharge of the men’s pieces will be prolonged to a kind of roar. A discharge of lightning along a lengthy cloud may in this way produce the prolonged roll of thunder. The roll of thunder, however, must in part at least be due to echoes from the clouds. The pupil will find no difficulty in referring many common occurrences to the fact that sound requires a sensible time to pass through any considerable length of air. For example, the fall of the axe of a distant wood-cutter is not simultaneous with the sound of the stroke. A company of soldiers marching to music along a road cannot march in time, for the notes do not reach those in front and those behind simultaneously. In the condensed portion of a sonorous wave the air is above, in the rarefied portion of the wave it is below, its average temperature. This change of temperature, produced by the passage of the sound-wave itself, virtually augments the elasticity of the air, and makes the velocity of sound about one-sixth greater than it would be if there were no change of temperature. The velocity found by Newton, who did not take this change of temperature into account, was 916 feet a second. Laplace proved that by multiplying Newton’s velocity by the square root of the ratio of the specific heat of air at constant pressure to its specific heat at constant volume, the actual or observed velocity is obtained. Conversely, from a comparison of the calculated and observed velocities, the ratio of the two specific heats may be inferred. The mechanical equivalent of heat may be deduced from this ratio; it is found to be the same as that established by direct experiment.