in the cavity of the mouth to which it is applied. A curious instrument of the spring class is the Zanze, from Western Africa, shown in the late Loan Exhibition at South Kensington.

It consists of a carved wooden box, having at the top a number of iron tongues, which the performer sets in vibration by means of his thumbs. This approaches nearly to the musical-box, in which a "comb" of steel vibrators, weighted in the lower octaves with lead, are plucked by pins inserted in a revolving barrel. The " gongs" of American and other clocks are rods coiled into a flat spiral, attached to a heavy mass of metal at the fixed end, and firmly screwed to the wood of the case. An instrument termed the "Bell Piano," with single springs struck by hammers actuated from a keyboard, is also made. In tuning-forks, the necessity for firmly fixing the base of the rod or spring is obviated by attaching it to a second rod or spring, which vibrates in opposition, and keeps the whole mass in equilibrium.

Rods or Bars free at both ends may vibrate in several ways. In the simplest case the rod has two nodes, and three vibrating segments; the central segment is the longest, the distance of each node from the end being about one-fourth of the distance between them. In the second form the rod has three nodes, and four vibrating parts, the central segment dividing into two. The fundamental note of rods thus arranged is higher than that of a rod fixed at one end in the ratio of 4 to 25. The upper partials are not much required, the first mode of vibration being that commonly utilized.

These vibrations of rods rise to their highest musical character in instruments commonly called Harmonicons, which

may be made of wood, glass, steel, or even of compact crystalline stone. Many oriental specimens are made of the first material, usually of the siliceous outer layer of the bamboo, and are remarkable for the presence of resonators reinforcing the note, which will be adverted to farther on. The tone is astonishingly large and pure. Such an instrument of pine wood, bearing the name of Xylophone, has recently been produced at many London concerts. Another, made of compact slate in bars, the Rock Harmonicon, was exhibited a few

years back. Mozart writes for a similar instrument, probably made of steel, in his opera of the Flauto Magico, where it is intended to imitate the sounds of the classical Sistrum.

Fig 10.-Mariin ba.

By far the most important case of rods or bars free at both ends is that of the ordinary tuning-fork, named above.

The Tuning-fork, as an acoustical instrument of paramount interest, requires to be described in detail. It may be looked upon as an elastic bar, free at both ends, and supported in the

iniddle where the stem is inserted, or as two mutually antagonistic bars, vibrating in opposite phases, so that the general centre of inertia is undisturbed. It is usually made of steel, but is equally efficient if formed of hard brass, or of the compound of tin and copper, called bell- or gun-metal.1 In this case, the bar, instead of remaining straight, is bent until the two vibrating branches stand parallel to one another. Its pitch becomes somewhat flatter after this change, and the nodal points approximate to one another. The stem or handle is usually inserted into the convexity of the bend, and, in the best constructed forks, is spread into a solid block of metal continuous with the fork; indeed the writer has found the sound emitted by a fork in which the curved part is extended into a triangular prolongation fuller and more pure than in the ordinary construction. The support in this case stands at right angles to the plane of the fork's vibration, being inserted into a hole drilled at the centre of the triangular

area.

It will be seen that part of the motion given to the ordinary tuning-fork is, by its shape, transmitted in the direction of the stem or handle, which has an up-and-down oscillation at right angles to that of the prongs themselves. This component can be farther transmitted to a resonant body, and the tone materially augmented by consonance.

The sound of a tuning-fork, when struck alone, contains, besides the fundamental note, numerous upper partial tones; but the interval between them and the lower sound is infinitely greater than in the case of strings. In those examined by Helmholtz, the number of vibrations of the first harmonic varied from 5.8 to 6.6 times that of the fundamental; the rates of the whole series being as the squares of the odd numbers 3, 5, 7, 9, &c. The result of this is that the upper partials are singularly evanescent, and soon leave the fundamental practically pure and uncomplicated. This important acoustical property is materially increased by mounting the fork on a resonance chamber, which reinforces the ground tone at the expense of the others, as will be explained in a later chapter.

Besides simplicity and purity of tone, the tuning-fork

In consequence of the difference of rate in the transmission of sound through different media, the size of brass tuning-forks is much less than that of steel ones. "The velocity of sound in steel is at a maximum, amounting to 5,237 metres per second. For brass the velocity would be less in about the ratio 15: 1. So that a tuning-fork made of brass would be about a fifth lower in pitch than if the material were steel."-Lord Rayleigh, Theory of Sound, P. 220.

possesses another property which is extremely valuable for theoretical investigations; that namely of being only slightly

Fig. 11.-A tuning-fork mounted on a sounding-box.

affected by differences of temperature. Like all other metallic bodies, it expands according to a definite law, the coefficient of which expansion for each metal with given increments of heat is easily obtained; the modulus of elasticity of the material is diminished to a minute amount by the same