fundamental tone, determines the timbre or quality of the sound. When a bell is sounded the attentive ear can distinguish the harmonics produced by the vibrating segments as well as the fundamental note produced by the whole.

Chladni's Figures.-The oscillations of sonorous bodies are too rapid to be either seen or counted; but by a simple experiment we can make them manifest to the eye. Sprinkle some fine dry sand on a plate of thin metal or glass, holding the plate with a pair of pincers, or better, with a holder provided with a screw b to fix it firmly to the edge of a table, and another screw c to grasp the plates firmly. (Fig. 7.) Then draw a violin bow over one of its

edges; the particles of sand will be seen to dance up and down, and finally arrange themselves in curious figures. Now this motion is due to the vibrations of the plate. The lines where the sand collects and rests are the nodal lines, or lines of rest, whilst the vibrating segments of the plate have the sand completely removed from them by the vibratory motion. If we strike a tuning-fork, and then touch the surface of some mercury, the undulations or waves are distinctly visible.

Fig. 7.

I

By experiments made by Chladni, the following laws were detected:

1. Any particular sound always produces the same figure, the plate being held in the same position. If the sound be changed, the figure disappears at once and a new one is formed.

2. The gravest sound is accompanied by the sim

plest figure, and the more acute the sound, the more complex the figure-that is, the more nodal lines and points will be produced on the plate. The nodal lines and points are the fixed lines and points at which the sonorous body remains still, while the vibratory parts are in motion. In the last-mentioned experiment, if the plate of metal or glass be square, on agitation, so as to obtain the lowest note, there will be produced an arrangement of the sand particles into four smaller squares, giving two lines of sand crossing each other at the centre and parallel to the sides of the plate (Fig. 8, a). The next lowest note gives an arrangement as in Fig. 8, b.

a

Fig. 8.

X

Round plates may also be divided into zones, the nodal lines forming circles; or into vibratory sectors, the nodal lines coinciding with the diameters. Most complex and beautiful figures are in this manner produced by the higher notes.

The experiments of Savart show that the molecular motions of one body may be communicated to another if there exist any intervening medium, and the more perfect the medium the more perfect the communication.

Moisten a thin membrane, stretch it over the top of a tumbler, and secure it with a piece of twine; place

it in a horizontal position, and, when dry, strew fine sand over the surface; hold a glass plate, covered with fine dry sand, horizontally over the membrane, and set it in vibration by drawing a violin bow over one of its edges, so as to produce the acoustic figures; these figures will be immediately imitated and produced in the sand on the membrane. If the plate be inclined to the plane of the membrane, the figures will change, although the vibrations will remain the

same.

α

Fig. 9.

Organ Pipes.-In organ pipes a column of air is the vibrating body. Such pipes are either stopped or open. An open organ pipe yields a note an octave

higher than that of a closed pipe of the same length: this necessarily follows from the different modes of vibration. When a stopped organ pipe sounds its deepest note, the column of air is undivided, but when the deepest note of an open pipe is sounded, the column is divided by a node at its centre: the open pipe forms, as it were, two stopped pipes with a common base at the centre. In Fig. 9 we have a representation of the wave formation in the two classes of pipes; a, open pipe; b, stopped pipe; c represents a useful pipe for experiment: one side is of glass, and the piston or stopper is moveable. Any sound can be obtained, and position of the stopper be noticed. The order of the tones of an open pipe is that of the even numbers, 2, 4, 6, 8, &c. A closed pipe divides itself into vibratory segments, whose rates of vibration are in the proportion of the numbers 1, 3, 5, 7, &c. The length of a stopped pipe is one-fourth that of the sonorous wave which it produces, while the length of an open pipe is one-half of its sonorous

wave.

In the harmonium and accordion the vibrations are produced by metallic tongues called reeds; these are also sometimes associated with organ pipes.

Vibrations of Rods, Discs, Bells, and Tuning Forks.-A rod fixed at both ends vibrates transversely as a string in some circumstances, with this difference, that the series of tones emitted by the string is as 1: 2: 3: 4, &c.: while in the case of the rod it is as the squares of the odd numbers, 3, 5, 7, &c. A rod free at one end can vibrate as a whole, or in segments. Vibrations of fundamental tone are to vibration of first harmonic or overtone as 4: 25, and so on, proportional to the squares of the odd numbers. A musical box is a good example of this class of

instrument. The rods or reeds are fixed at one end. A rod fixed at both ends will also give vibrations; the middle section curves, and the ends fan-like forms. The glass harmonica is an example of this class of rods. There are, of course, two nodes at the points of rest, and beginning with these the series of tones are again as the square of the odd numbers.

The transition from the latter class of rods to the tuning fork is easily made with the help of Fig. 10.

U

Fig. 10.

The vibrations possible to a tuning fork are

Ist. One node on each prong.

2nd.

and two at the bottom. 3rd. Two nodes on each prong, and one at the bottom.

The overtones rise with great rapidity compared with those of a string: as the squares of the odd numbers.

The vibrations of a disc are beautifully exemplified by Chladni's figures :—