It is

cause. Hence all forks flatten somewhat with warmth. not very difficult, however, to apply a proper correction to this error, and they then become far the most trustworthy standards of pitch we are acquainted with.'

On the other hand their greatest disadvantage is due to the rapid falling off of vibration from internal friction and resistance of the air. Nor is it easy to find a means of exciting them which shall elicit a sustained tone. The usual excitant is a blow with a heavy body, covered with leather or flannel. French forks are made with a slight convergence between the inner sides of the prongs, and are excited by drawing a pin somewhat larger than the aperture through it from below. The writer has succeeded in keeping large forks of comparatively slow motion excited, by striking one prong gently but repeatedly with a small hammer attached to the mechanism of an electric "trembler" bell. But by far the best method is that largely and successfully employed by Helmholtz in the investigation of vowel sounds, and in his "Vibration Microscope," that namely of causing the fork itself, or one in harmonic relation with it, to become the contact breaker in a galvanic circuit, including an electro-magnet, which keeps up a series of synchronous impulses on the steel prongs of the tuning-fork itself. It has been common to place the electro-magnet on one side of the fork, but this is liable to draw down the fork into firm adhesion to its pole. Helmholtz places the two poles of a rather wide horseshoe-magnet outside the two prongs of the fork, so as simultaneously to draw them apart, but a still simpler and more effective method was illustrated in the Loan Collection by some French instruments, and is figured diagrammatically by Lord Rayleigh2 in which a single short straight magnet, with wire wound in one coil around a core of bobbin shape is interposed between the two prongs, thus tending to draw them closer together at every contact without exerting any strain upon the supporting stem of the fork.

1 Tuning-forks are among the instruments the use of which has extended from sound into other branches of physics, after a pleasant fashion of reciprocity. They have been employed as measurers of small intervals of time; their pendular vibrations are so regular, so accurate, and so easily adjusted to any one period of vibration, that they furnish an admirable means toward this end. A beautiful instruinent of this nature was contributed to the Loan Exhibition at South Kensington by the French Conservatoire des Arts et Métiers.

2 Theory of Sound, p. 56, where it is stated that such interruptors are within the capacity of a village blacksmith. The only drawback is the need of special wide forks; those usually made not leaving sufficient room for the interposed electro-magnet.

Harmonics generally distant from prime.

Follow series of odd numbers. Often discordant.

Vibration of Plates.--When the rods or bars are expanded into plates, the second dimension of which bears a large ratio

to their linear extension, we enter upon the study of the beautiful figures named after their discoverer Chladni, and subsequently investigated by Wheatstone.

Chladni's method of investigation consisted in supporting plates of glass or metal, either square, circular, or of some other regular outline, by means of a kind of clamp, and bowing

Fig. 13.-Nodal lines of vibrating circular or polygonal plates, according to Chladni and Savart.

the edge in different points with an ordinary rosined bow. The vibrations thus excited were analysed by means of sand previously strewn on the plate; it left the vibrating segments

to heap itself on the quiescent nodes. A vast variety of beautiful figures was thus obtained, each corresponding to a particular note, and to a special mode of vibration. The more complicated forms were obtained by a combination of bowing and damping; the latter being accomplished by touching the edge of the plate in various places with the tips of the fingers, and thus hindering the motion of the spots touched. The rate of vibration in a disc was found to be proportional to its thickness and inversely proportional to the square of its diameter.

These experiments were continued by Faraday among others, who modified them by adding a light powder such as the spores of lycopodium mixed with the sand. This instead, like the sand, of seeking the nodal points of rest, collected at the places of most violent vibration, a phenomenon ultimately explained by the currents of air surrounding the vibrating plate, and not occurring in vacuo.

The laws which regulate the vibrations of plates have been much discussed by mathematicians; and indeed furnish problems of considerable complexity. But as no practical application of this method of eliciting sound occurs, it will be sufficient to refer the reader to the works in question for further details.1

Bells may be considered to hold the same relation to plates in their mode of vibration that the tuning-fork does to the linear bar or rod. Indeed gongs and some varieties of oriental bells are very little modified from the original shape of the plate.

Not

The gong is usually a circular sheet of hard metal, rendered more elastic by hammering, strengthened at the edge by a deep flange of the same nature. The vibrations here are very complex and irregular, approximating somewhat to those of a tense membrane, and the note, if note it can be called, is a fortuitous combination of several discordant tones. very dissimilar from these is the cymbal; a noise-producing machine, intended, like the drum, rather to mark rhythm and accent than to emit a definite note. It differs from the gong in speaking from the treble register, and in intentionally reinforcing the high clashing harmonics. For this end the two cymbals are sharply struck together, touching in a few limited points; whereas the gong, like the string in the pianoforte, is gently but rapidly struck with a large soft beater over a

1 Thomson and Tait's Natural Philosophy; Lord Rayleigh, Theory of Sound, p. 293; Donkin; Kirchoff.

circle about one-third less in diameter than the instrument itself. No doubt this situation for the blows indicates the ring of greatest vibration discovered empirically. The same position, it will be found, produces the best quality of tone from the kettledrum.

Bells proper are usually in the form of vessels, either of hemispherical shape, as in clock-bells; or of a very complex outline, as in church and house bells. They give a note rich in upper partial tones, or harmonics, usually discordant to the foundation tone, as will be seen farther on, vibrating along the free edge, either in four, six, or more sections. The deepest note is given by the division of the edge into four segments, in which case the bell itself is momentarily disfigured by the blow of the hammer into an elliptical figure; returning by its elasticity into one with its major axis at right angles to that originally formed. Other

V

N

Fig. 14.-Nodes and segments of a vibrating bell.

segmentations of the vibrating edge or sound-bow can be produced, as in the plate, always preserving an even number of 4, 6, 8, 10, or more vibrating parts. The sound of the hemispherical bell is far more pure and uniform than that of the ordinary church bell. Hence this shape is commonly used for clock chimes, and for carillons, to which also its compact outline, graduated size, and convenient facility of stowage in a limited space render it specially fitted. A large number of these hemispheres can be arranged on a single axis, with just so much of the free edge projecting as is needed for the hammer