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 tube. The free end of the wire may, however, be pulled and pushed, alternately, so as to reinforce each pulse as it arrives at the open end of the tube, and in this manner the maximum of motion will be communicated to the spring. In this case, one outward, and one inward, impulse of the hand must be communicated to the free end of the string, during the time which elapses while a pulse traverses four times the length of the tube. 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. For the to and fro motion of the hand at A, we must substitute that of the prong of the vibrating fork. The sound-pulse traverses four times the length of the tube while the fork is performing one complete vibration. We know, however [SS 8 and 15], that, during this latter period, the sound-pulse due to 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 closed pipe, 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 useful 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 vibration to the surrounding air; when, however, its handle is screwed into one side of an empty 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 going on at once, it is generally difficult, and often impossible, for the unaided ear to decide whether an individual note is, or is not, present in the whole mass of sound heard. If, however, we had an instrument which intensified the tone of the note of

which we were in search, without similarly reinforcing others which there was any risk of our mistaking for it, our power of recognizing the note in question would be proportionately increased. Such an instrument has been invented by Helmholtz. It consists of a hollow ball of brass with two apertures at opposite ends of a diameter, as shown in Fig. 25.

The larger aperture allows the vibrations of the external air to be communicated to that within the ball; the smaller aperture passes through a nipple of convenient form for insertion in the ear of the observer. The air contained in the ball resounds very powerfully to one single note of definite pitch, whence the instrument has been named, by its inventor, a resonator. The best way of using it is, first, to stop one ear closely, and then to insert the nipple of the instrument in the other; as often as the

resonator's own note is sounded in the external air, the instrument will sing it into the ear of the observer with extraordinary emphasis, and thus at once single out that note from among a crowd of others differing from it in pitch. A series of such resonators, tuned to particular previously selected notes, constitutes an apparatus for analyzing a composite sound into the simple tones of which it is made up.

CHAPTER IV.

ON QUALITY.

43. The laws of resonance enable us to establish a remarkable, and by most persons utterly unsuspected, fact, viz. that the notes of nearly every regular musical instrument with which we are familiar, are not, as they are ordinarily taken to be, single tones of one determinate pitch, but composite sounds containing an assemblage of such tones. These are always members of a regular series, forming fixed intervals with each other, which may be thus stated if we number the separate single tones, of which any given sound is made up, 1, 2, 3, &c., beginning with the lowest, and ascending in pitch, we have

(1) The deepest, or fundamental, tone, which is

commonly treated as determining the pitch of the whole sound.

(2) A tone one octave above (1).

(3) A tone a Fifth above (2), i. e. a Twelfth above (1).