number of vibrations of various forms, and that these have been carefully studied and their importance fully understood, constitutes one of the most pregnant strides which Physics has made in this century.

Of all these vibratory movements I will treat of one group, which merits special attention on account of the great facility which it offers for its study, and for the great importance which its application has exercised on the history of human culture.

2. I wish first of all to demonstrate that sound is formed by the vibrations of the particles of bodies. To understand these vibrations we are not obliged to know the intimate structure of the bodies themselves; it is enough to know that the body can be subdivided into little particles, and that these particles can move away from one another, at least within certain limits, without thereby causing the rupture or disaggregation of the body. This is the result of everyday observation, and in regard to our present study, I have no need to go farther into the matter or to formulate a more or less hypothetical opinion on the intimate structure of the bodies. themselves. We must, however, add to this conception yet another—that of the elasticity of bodies. A body is called elastic in which a particle, moved from its natural position of equilibrium, has a tendency to return to its first position as soon as the external cause which had displaced it has ceased.

When a particle is under the circumstances here con

templated, it does what the pendulum does. The instant it is free to move, it returns towards the position it originally occupied; at first with small velocity, afterwards with constantly-increasing velocity. Arrived at its position of natural equilibrium, it continues for a certain space by its momentum the movement which it has acquired, and finally stops and retraces its steps. It oscillates then about its position of natural equilibrium, precisely as the pendulum oscillates on one side and the other of its vertical position. Mathematical investigation shows that in this case the vibration is simple, like that of the pendulum. But in the study of the vibrations to which a body, or part of a body, may be subjected, it is not enough to consider the movement of one particle only. The body is formed of a vast number of particles, and as each one vibrates, it is important to know whether they influence each other in their respective movements. In this respect any case is possible, according to the special conditions under which the vibrations take place, and the cause which excites them. It often happens that each single particle vibrates on its own account, as if the others were not in existence. Those vibrations which take place irregularly in all possible directions, acquire a great importance in respect to the phenomena of heat, and for others besides, but have no direct bearing upon sound. In order that the vibration may be sonorous, it is necessary that the particles should execute their movements together and with a certain regularity. The vibrations then acquire

a general and regular character. They may be compared to the compact manœuvres of a company of soldiers, while the thermal vibrations rather resemble the altogether irregular movements of an undisciplined crowd.

3. It can be demonstrated by a certain number of examples that sound is always accompanied by vibration of the sounding body. A metal bell is taken, mouth upwards, firmly attached to a foot A (fig. 1). A very light

A

Fig. 1.

pendulum a touches the bell to indicate the movements that it may make at a given moment. If this bell be rubbed by a violin bow, a very marked sound is obtained, and immediately the pendulum is driven away, falls back against the bell, and is again driven away, and so on; the movement of the pendulum lasts for a certain time, and

grows less as the sound dies away, and shows that the bell, so long as it sounds, is in a state of vibration in all its parts.

4. Another illustration is given by a sort of steel fork D, which, if it be held by its foot, can be easily set in vibration (fig. 2). A fork of this kind is called a tuningfork. If the tuning-fork be struck upon the table, or if it be rubbed at the extremities of its branches with a violin bow, a very faint and scarcely audible musical sound is obtained. This sound is observably strengthened if the foot of the tuning-fork be placed in contact with the table, or, better still, with a hollow box. The sound can then be clearly heard, and by this means it may be shown that the sound really exists. This being so, it is easy to believe that the two branches of the tuning-fork, when it sounds, are in a state of continual vibratory movement. The movement is very rapid and the eye cannot follow it, but the outlines of the branches no longer have a sharp and well-defined form, which clearly shows the movement of the tuning-fork. This vibratory movement is made very perceptible by touching the fork itself with the finger. If the two branches be touched, the movement ceases, and with it the sound. Sound and movement are so correlated that one is strong when the other is strong, one diminishes when the other diminishes, and the one stops when the other stops.

But the vibrations of the tuning-fork can be made visible by the following graphic method:

A plate of glass L (fig. 2), coated with lamp-black by a petroleum flame, and which slides easily in the frame G, is taken, and a point P having been attached to one of

the branches of the vibrating tuning-fork, this point is placed against it, and the plate is drawn along rapidly in such a way that the point slides continuously on it.

Or, to make the experiment still more certain and more elegant, a cylinder of brass is used, on which is stretched a sheet of paper blackened by a petroleum flame. This cylinder can be turned by means of a screw handle A moved by hand or by mechanism (fig. 3). The tuningfork is now brought close to the cylinder, so that the point D slightly scores the paper, and is fixed firmly by means of a vice. If the tuning-fork remains at rest and the cylinder turns, the point traces a straight line on the paper, or, as the movement of the cylinder is spiral, it traces a curve differing very little from a straight line.

If, on the other hand, the cylinder remains at rest and the tuning-fork vibrates, its point traces a short line perpendicular to the first. If, lastly, the tuning-fork vibrates and the cylinder turns, a regular and very characteristic