A musical sound may be produced by _taps_ which rapidly and regularly succeed each other. The taps of a card against the cogs of a rotating wheel are usually employed to illustrate this point. A musical sound may also be produced by a succession of _puffs_. The siren is an instrument by which such puffs are generated. The pitch of a musical note depends solely on the number of vibrations concerned in its production. The more rapid the vibrations, the higher the pitch. By means of the siren the rate of vibration of any sounding body may be determined. It is only necessary to render the sound of the siren and that of the body identical in pitch to maintain both sounds in unison for a certain time, and to ascertain, by means of the counter of the siren, how many puffs have issued from, the instrument in that time. This number expresses the number of vibrations executed by the sounding body. When a body capable of emitting a musical sound—a tuning-fork, for example—vibrates, it molds the surrounding air into sonorous waves, each of which consists of a condensation and a rarefaction. The length of the sonorous wave is measured from condensation to condensation, or from rarefaction to rarefaction. The wave-length is found by dividing the velocity of sound per second by the number of vibrations executed by the sounding body in a second. Thus a tuning-fork which vibrates 256 times in a second produces in air of 15° C., where the velocity is 1,120 feet a second, waves 4 feet 4 inches long. While two other forks, vibrating respectively 320 and 384 times a second, generate waves 3 feet 6 inches, and 2 feet 11 inches long. A vibration, as defined in England and Germany, comprises a motion to _and_ fro. It is a _complete_ vibration. In France, on the contrary, a vibration comprises a movement to _or_ fro. The French vibrations are with us semi-vibrations. The time required by a particle of air over which a sonorous wave passes to execute a complete vibration is that required by the wave to move through a distance equal to its own length. The higher the temperature of the air, the longer is the sonorous wave corresponding to any particular rate of vibration. Given the wave-length and the rate of vibration, we can readily deduce the temperature of the air. The human ear is limited in its range of hearing musical sounds. If the vibrations number less than 16 a second, we are conscious only of the separate shocks. If they exceed 38,000 a second, the consciousness of sound ceases altogether. The range of the best ear covers about 11 octaves, but an auditory range limited to 6 or 7 octaves is not uncommon. The sounds available in music are produced by vibrations comprised between the limits of 40 and 4,000 a second. They embrace 7 octaves. The range of the ear far transcends that of the eye, which hardly exceeds an octave.