The resonance of caves and of rocky inclosures is well known. Bunsen notices the thunder-like sound produced when one of the steam jets of Iceland breaks out near the mouth of a cavern. Most travellers in Switzerland have noticed the deafening sound produced by the fall of the Reuss at the Devil’s Bridge. The sound heard when a hollow shell is placed close to the ear is a case of resonance. Children think they hear in it the sound of the sea. The noise is really due to the reinforcement of the feeble sounds with which even the stillest air is pervaded, and also in part to the noise produced by the pressure of the shell against the ear itself. By using tubes of different lengths, the variation of the resonance with the length of the tube may be studied. The channel of the ear itself is also a resonant cavity. When a poker is held by two strings, and when the fingers of the hands holding the poker are thrust into the ears on striking the poker against a piece of wood, a sound is heard as deep and sonorous as that of a cathedral bell. When open, the channel of the ear resounds to notes whose periods of vibration are about 3,000 per second. This has been shown by Helmholtz, and Madame Seiler has found that dogs which howl to music are particularly sensitive to the same notes. We may expect from Mr. Francis Galton interesting results in connection with this subject. SUMMARY OF CHAPTER V When a stretched wire is suitably rubbed, in the direction of its length, it is thrown into longitudinal vibrations: the wire can either vibrate as a whole or divide itself into vibrating segments separated from each other by nodes. The tones of such a wire follow the order of the numbers 1, 2, 3, 4, etc. The _transverse_ vibrations of a rod fixed at both ends do not follow the same order as the transverse vibrations of a stretched wire; for here the forces brought into play, as explained in Lecture IV., are different. But the longitudinal vibrations of a stretched wire do follow the same order as the longitudinal vibrations of a rod fixed at both ends, for here the forces brought into play are the same, being in both cases the elasticity of the material. A rod fixed at one end vibrates longitudinally as a whole, or it divides into two, three, four, etc., vibrating parts, separated from each other by nodes. The order of the tones of such a rod is that of the odd numbers 1, 3, 5, 7, etc. A rod free at both ends can also vibrate longitudinally. Its lowest note corresponds to a division of the rod into two vibrating parts by a node at its centre. The overtones of such a rod correspond to its division into three, four, five, etc., vibrating parts, separated from each other by two, three, four, etc., nodes. The order of the tones of such a rod is that of the numbers 1, 2, 3, 4, 5, etc.