1904.] An Experiment Illustrating Harmonic Undertones. 119 



their frequencies being 64 : 63. We can thus obtain from the paper 

 the series of harmonic undertones 



c',/,.c, A, F, D + ,C,B / [, l A,b,etc. 



It is easy to obtain about the first ten of these when a small slip of 

 paper is used and is held close to the ear. There is some difficulty in 

 making the lower notes audible on a large scale without depriving the 

 experiment of the simplicity which is probably its chief merit ; it is 

 perhaps best to use a large sheet of paper suspended in a vertical 

 plane with one edge pasted to a vertical edge of an empty wooden 

 box which may reinforce the sound. The tuning-fork can be held in 

 the hand or clamped so as to touch the paper near its edge ; the 

 undertone usually given will vary with the position of the point of 

 contact. The effect might be prolonged for any time by using an 

 electrically maintained fork. 



Some further information as to the behaviour of a light object 

 under the influence of a series of periodic blows was obtained by means 

 of a large steel tuning-fork with prongs about a foot long, which was 

 clamped in such a position that one of its ends, vibrating horizontally, 

 struck the upper end of a small vertical card (usually an ordinary 

 visiting card), the lower end of which was fixed, so that the card 

 behaved somewhat as a clamped-free rod of considerable width in 

 comparison with its length. The average pressure and the position 

 of the point of contact could be varied at will. The fundamental 

 pitch of the fork was itself so low that harmonic undertones, produced 

 by the card in the way described above, were practically inaudible ; 

 the nature of the vibration was, however, examined by looking through 

 a lens at the upper edge of the card against a dark background. The 

 edge appeared to be drawn out into a continuously shaded band, in 

 which occurred at intervals somewhat abrupt white lines, indicating 

 positions at which the card was nearly or quite stationary. When 

 contact was being broken several of these lines were usually visible, 

 and it was possible to get them to remain steady, though sometimes 

 they flickered rapidly. The line at the end of the band nearest the 

 fork was usually very faint, often practically invisible, which points 

 to the suddenness with which the card is driven away from the fork 

 when they come into contact. 



The presence of these white lines shows that the card executes 

 vibrations corresponding to more than one of its free modes, and that 

 the resultant vibration differs considerably from the simple harmonic 

 form. (This agrees with the audible presence of harmonics in the 

 experiment first described, where a sheet of paper is struck by an 

 ordinary tuning-fork.) 



As the vibrations of the large fork diminish in amplitude the white 

 lines become fewer, until generally only two or one remain in the 



