double or complete vibration; and the time of executing a complete vibration is the period of vibration. The amplitude of vibration for any point in the spring is the distance of its middle position from one of its extreme positions. These terms have been already employed (§ 107) in connection with the movements of pendulums to which indeed the movements of vibrating springs bear an extremely close resemblance. The property of isochronism, which approximately characterizes the vibrations of the pendulum, also belongs to the spring, the approximation being usually so close that the period may practically be regarded as altogether independent of the amplitude.

When the spring is long, the extent of its movements may generally be perceived by the eye. In consequence of the persistence of impressions, we see the spring in all its positions at once; and the edges of the space moved over are more conspicuous than the central parts, because the motion of the spring is slowest at its extreme positions.

As the spring is lowered in the vice, so as to shorten the vibrating portion of it, its movements become more rapid, and at the same time

VIBRATION OF A PLATE.

867

more limited, until, when it is very short, the eye is unable to detect any sign of motion. But where sight fails us, hearing comes to our aid. As the vibrating part is shortened more and more, it emits a musical note, which continually rises in pitch; and this effect continues after the movements have become much too small to be visible. It thus appears that a vibratory movement, if sufficiently rapid, may produce a sound. The following experiments afford additional illustration of this principle, and are samples of the evidence from which it is inferred that vibratory movement is essential to the production of sound.

Vibration of a Bell.-A point is fixed on a stand, in such a position as to be nearly in contact with a glass bell (Fig. 593). If a rosined fiddle-bow is then drawn over the edge of the bell, until a

musical note is emitted, a series of taps are heard, due to the striking of the bell against the point. A pith-ball, hung by a thread, is driven out by the bell, and kept in oscillation as long as the sound continues. By lightly touching the bell, we may feel that it is vibrating; and if we press strongly, the vibration and the sound will both be stopped.

Vibration of a Plate.-Sand is strewn over the surface of a horizontal plate (Fig. 594), which is then made to vibrate by drawing a

bow over its edge. As soon as the plate begins to sound, the sand dances, leaves certain parts bare, and collects in definite lines, which are called nodal lines. These are, in fact, the lines which separate portions of the plate whose movements are in opposite directions. Their position changes whenever the plate changes its note.

The vibratory condition of the plate is also manifested by another phenomenon, opposite-so to speak -to that just described. If very fine powder, such as lycopodium, be mixed with the sand, it will not move with the sand to the nodal lines, but will form little heaps in the centre of the vibrating segments; and these heaps will be in a state of violent agitation, with more or less of gyratory movement, as long as the

plate is vibrating. This phe-
nomenon, after long baffling
explanation, was shown by
Faraday to be due to indraughts

Fig. 595.

of air, and ascending currents, Vibration of String. brought about by the move

ments of the plate. In a moderately good vacuum, the lycopodium goes with the sand to the nodal lines.

Vibration of a String.-When a note is produced from a musical string or wire, its vibrations are often of sufficient amplitude to be detected by the eye. The string thus assumes the appearance of an elongated spindle (Fig. 595).

Vibration of the Air.-The sonorous body may sometimes be air, as in the case of organpipes, which we shall describe in a later chapter. It is easy to show by experiment that when a pipe speaks, the air within it is vibrating. Let one side of the tube be of glass, and let a small membrane m, stretched over a frame, be strewed with sand, and lowered into the pipe. The sand will be thrown into violent agitation, and the rattling of the grains, as they fall back on the membrane, is loud enough to be distinctly heard.

Singing Flames.-An experiment on the production of musical sound by flame, has long been known under the name of the chemical harmonica. An appera

tus for the production of hydrogen gas (Fig. 597) is furnished with a tube, which tapers off nearly to a point at its upper end, where the gas issues and is lighted. When a tube, open at both ends, is held so as to surround the flame, a musical tone is heard, which varies with the dimensions of the tube, and often attains considerable power. The sound is due to the vibration of the air and products of combustion within the tube; and on observing the reflection of the flame in a mirror rotating about a vertical axis, it will be seen that the flame is alternately rising and falling,

Fig. 597.-Chemical Harmonica.

its successive images, as drawn out into a horizontal series by the rotation of the mirror, resembling a number of equidistant tongues of flame, with depressions between them. The experiment may also be performed with ordinary coal-gas.

Trevelyan Experiment.—A fire-shovel (Fig. 598) is heated, and balanced upon the edges of two sheets of lead fixed in a vice; it is then seen to execute a series of small oscillations-each end being alternately raised and depressed—and a sound is at the same time emitted. The oscillations are so small as to be scarcely perceptible in themselves; but they can be rendered very obvious by attaching to the shovel a small silvered mirror, on which a beam of light is directed. The reflected light can be made to form an image upon a screen, and this image is seen to be in a state of oscillation as long as the sound is heard.

The movements observed in this experiment are due to the sudden expansion of the cold lead. When the hot iron comes in contact with

it, a protuberance is instantly formed by dilatation, and the iron is thrown up. It then comes in contact with another portion of the

lead, where the same phenomenon is repeated while the first point cools. By alternate contacts and repulsions at the two points, the shovel is kept in a continual state of oscillation, and the regular succession of taps produces the sound.

The experiment is more usually performed with a special instrument invented by Trevelyan, and called a rocker, which, after being heated and laid upon a block of lead, rocks rapidly from side to side, and yields a loud note.

867. Distinctive Character of Musical Sound.-It is not easy to draw a sharp line of demarcation between musical sound and mere noise. The name of noise is usually given to any sound which seems unsuited to the requirements of music.

This unfitness may arise from one or the other of two causes. Either,

1. The sound may be unpleasant from containing discordant elements which jar with one another, as when several consecutive keys on a piano are put down together. Or,

2. It may consist of a confused succession of sounds, the changes being so rapid that the ear is unable to identify any particular note. This kind of noise may be illustrated by sliding the finger along a violin-string, while the bow is applied.

All sounds may be resolved into combinations of elementary musical tones occurring simultaneously and in succession. Hence the study of musical sounds must necessarily form the basis of acoustics.

Every sound which is recognized as musical is characterized by what may be called smoothness, evenness, or regularity; and the physical cause of this regularity is to be found in the accurate