nance is at first extremely feeble, and gradually increases in intensity under the continued action of the originally-excited fork. Some seconds must elapse before the maximum resonance is attained. The conditions of our experiment show that the resonance of the second fork was due to the transmission by the air of the vibrations of the first, the successive air-impulses falling in such a manner on the fork as to produce a cumulative effect. If we bear in mind the disproportionate mass of the body set in motion compared to that of the air acting upon it,-steel being more than six thousand times as heavy as atmospheric air for equal bulks-we cannot fail to regard this as a very surprising fact.

Let us examine the mechanical causes to which it is due. Suppose a heavy weight to be suspended from a fixed support by a flexible string, so as to form a pendulum of the simplest kind. In order to cause it to perform oscillations of considerable extent by the application of a number of small impulses, we proceed as follows. As soon as, by the first impulse, the weight has been set vibrating through a small distance, we take care that every succeeding impulse is impressed in the direction in which the weight is moving at the time. Each impulse thus applied will cause the pendulum to oscillate through a larger angle [19] than before, and, the effects of many

impulses being in this way added together, an extensive swing of the pendulum is the result.

When the distance through which the weight travels to and fro, though in itself considerable, is small compared to the length of the supporting string, the time of oscillation is the same for any extent of swing within this limit, and depends only on the length of the string. My readers will find this important principle illustrated in any manual of Elementary Mechanics, and I must ask them to take it for granted here. For the sake of simplicity, let us suppose that we are dealing with a pendulum of such a length as to perform one complete oscillation in each second, and therefore to make a single forward or backward swing in each half second. It will be clear, from what has been said above, that the maximum effect will be produced on the motion of the pendulum by applying a forward and a backward impulse respectively during each alternate half-second, or which is the same thing, by administering a pair of to-and-fro impulses during each complete oscillation of the pendulum. We have a simple instance of such a proceeding in the way in which two boys set a heavily-laden swing in extensive motion. They stand facing each other, and each boy, when the swing is moving away from him, helps it along with a vigorous push.

38. The above considerations enable us to explain how a sounding fork can set another fork in unison with itself into vibration by the action of the intervening air. When a continuous musical note is being transmitted, we know that, at any one point we choose to fix upon, the air is undergoing a series of rapid changes, becoming alternately denser and less dense than it would be but for the passage of the sound. The increase of density is accompanied by an increase of pressure; its diminution by a diminution of pressure [§ 20].

Fig. 21.

dac

B

Let A, Fig. 21, be the sounding fork, B that whose vibrations are to be excited by resonance, and let us consider the effect of the alternations of pressure of the air at a on the prong ba. Let the first pulse which arrives at a be one of condensation, and let its increased pressure cause the prong ba to swing as far as bc1. The elastic recoil of the fork would alone cause the prong to spring back to an equally inclined position on the other side of ba. Since,

1

The extents of vibration shown in this figure are of necessity enormously exaggerated.

however, the period of vibration is by supposition the same for the two forks, a pulse of rarefaction, entailing diminished pressure, will arrive at a just as the prong is passing through its erect position ba. The prong will therefore swing a little further to the left than it would otherwise have done, say to bd, making the angle abd slightly larger than the angle abc. The prong then starts to the right and is, while passing through the position ba, again helped on by the arrival there of a new pulse of condensation. Thus the alternate condensations and rarefactions of the Sound-waves play towards the fork exactly the parts sustained by the two boys in our illustration of the swing. Accordingly, these airimpulses are applied under precisely the conditions which we saw to be most favourable to the rapid development of vibratory motion. Their large number makes up for the feebleness of each separate impulse. Accordingly resonance is produced more slowly between unison-forks of low than of high pitch. I find, for example, that, with two forks making 256 vibrations per second, about one second is requisite to bring out an audible resonance; while with another pair, making 1,920 vibrations per second, I can with difficulty damp the first fork sufficiently soon after striking it to prevent the other from making itself heard.

39. A column of air is easily set in resonant vibration by a note of suitable pitch. The roughest experiment suffices to establish this fact. We have only to roll up a piece of paper, so as to make a cylinder twelve inches long and an inch or two in diameter, with both ends open, strike a common C tuning-fork, and hold it close to

one of the apertures. As soon as the fork reaches the position (1) Fig. 221, its tone will unmistakably swell out. In order to estimate the increase of intensity produced, it is a good plan to move the fork rapidly to and fro, a few times, between the positions (1) and (2).

In the first case we have the full effect of resonance, in the second only the unassisted tone of the fork,

1 This figure was drawn for a cylinder only six inches in length, but suffices for the purpose of illustration for which it is here used.