and the contrast is very marked. We may shorten or lengthen our cylinder within certain limits and still obtain the phenomenon of resonance, but the greatest reinforcement of tone attainable with the fork selected will be produced by an air-column about twelve inches long.

If we close one end of the paper cylinder, by placing it, for instance, on a table, and repeat our experiment at the open end, only a very weak resonance is produced; but we obtain a powerful resonance by operating with a fork of pitch making

half as many vibrations per second as that before employed. In this case, then, a column of air contained in a cylinder of which one end was closed resounded powerfully to a note an Octave below that which elicited its most vigorous resonance when the air-column was contained in a cylinder open at both ends.

By operating in this fashion, with forks of dif ferent pitch, on air-columns of different lengths, we arrive at the following laws, which are universally true :

1. For every single musical note there exists a corresponding air-column of definite length which, when enclosed in a pipe, open at both ends, resounds the most powerfully to that note.

T.

2. The maximum resonance of air in a pipe, with one end closed is produced by a note one Octave below that to which a pipe of the same length, open at both ends, resounds the most powerfully.

40. In order to ascertain the precise relation between the pitch of a note and the length of the corresponding air-column, we will examine the way in which resonance is produced in a column of air contained in a pipe closed at one end.

Let A, Fig. 23, be the open, and B the closed, ends of the pipe, and let us for a moment replace the contained air by an elastic spiral spring fastened at B, and of length equal to AB.

Fig. 23.

B

A

Suppose the end of the spring suddenly pushed a little way from A towards B. The coils of the spring nearest A will be squeezed together, and this condensed state of the spring will be transmitted to B, where further movement to the left is stopped by the fixed end of the spring. Hence the coils crowded together near B will begin expanding towards the right, i.e. the condensed state of the spring will be turned back, or 'reflected,' at B and will then travel to A. In virtue of the elasticity

of the spring its free end will now be caused to protrude beyond the mouth of the pipe as far as it

was at first pushed into it. thus drawn somewhat more

The coils near A being apart than was the case

when they were in their undisturbed condition, will exert a pull on those near them, which will in their turn be drawn further apart, and thus a rarefied state of the spring will be produced at A and transmitted to B. On reaching the fixed end there, the increased tension will act on the coils near B, i.e. the rarefied state of the spring will be reflected at B, just as its condensation was in the case previously considered. When this rarefaction returns to A, the free end of the spring will momentarily resume the position within the mouth of the pipe to which it was originally pushed. The elasticity of the spring thus causes it to lengthen and shorten as a whole in consequence of the single push originally given it, and this motion would for a time continue, its successive periods being four times the space of time occupied by a pulse of condensation or rarefaction in traversing the length of the pipe. The free end of the spring may, however, be pushed and pulled alternately so as to reinforce each pulse as it arrives at the mouth of the pipe, and in this manner the maximum of motion will be communicated to the spring. In this case, one outward and one

inward impulse must be communicated to the free end of the spring during the time which elapses while a pulse traverses four times the length of the pipe. Reverting to the actual conditions of our problem, we have the resonance of the air-column in place of the alternate lengthening and shortening of the spring. The to-and-fro impulses at A are impressed by a vibrating fork. The Sound-pulse traverses four times the length of the pipe while the fork is performing one complete vibration. We know, however [§ 15 p. 32], that during this latter period the Sound-pulse produced by the fork's action traverses precisely one wave-length corresponding to the pitch of the note produced by the fork. Hence, for maximum resonance in the case of a pipe closed at one end, the wave-length corresponding to the note sounded must be four times as great as the length of the air-column, or the length of the column one quarter of the wave-length.

41. These principles give us the explanation of a valuable appliance for intensifying the sound of a tuning-fork. Such a fork, when held in the hand after being struck, communicates but little of its vibrations to the surrounding air; when, however, its handle is screwed into one side of a wooden box of suitable dimensions, in the way shown in Fig. 24, the tone becomes much louder. The vibrations of

the fork pass from its handle to the wood of the box,

Fig.24

and thence to the air-column within, which is of appropriate length for maximum resonance to the fork's note. This convenient adjunct to a tuningfork goes by the name of a 'resonance-box.'

42. When a number of musical sounds are simultaneously sustained it is generally difficult, and often impossible, for the unaided ear to decide whether an individual note is, or is not, present in the mass of sound heard. If, however, we had an instrument which intensified the note of which we were in

search, without similarly reinforcing others which there was any risk of our mistaking for it, our power