548 



EXPERIMENTS AND INQUIRIES 



pound rotations seem to demonstrate to the 

 eye the existence of secondary vibrations^ 

 and to account for the acute harmonic 

 sounds wliich generallj' attend the fundu- 

 mentai sound. There is one fact respecting 

 these secondary notes, which seems entirely 

 to have escaped observation. If a chord be 

 inflected at one half, one third, or any other 

 aliquot part of its length, and tiien suddenly 

 left at liberty, the harmonic note, which 

 would be produced by dividing the chord at 

 that point, is entirely lost, and is not to be 

 distinguished during any part of the conti- 

 nuance of the sound. This demonstrates, 

 that the secondary notes do not depend upon 

 any interference of the vibrations of the air 

 with each other, nor upon any sympathetic 

 agitation of auditory fibres, nor upon any 

 effect of reflected sound upon the chord, but 

 merely upon its initial flgure and motion. If it 

 were supposed that the chord, when inflected 

 into riglit lines, resolved itself necessarily 

 into a number of secondary vibrations, ac- 

 cording to some curves which, when pro- 

 perly combined, would approximate to the 

 figure given, the supposition would indeed 

 in some respects correspond with the pheno- 

 menon related; as the cocfiicients of all the 

 curves supposed to end at the angle of in- 

 flection would vanish. But, whether we 

 trace the constituent curves of such a figure 

 through the various stages of their vibrations, 

 or whether we follow the more compendious 

 method of Euler to the same purpose, tlie 

 figures resulting from this series of vibrations 

 are in fact so simple, that it seems incon- 

 ceivable how the ear should deduce the com- 

 plicated idea of a numbei of heterogeneous 

 vibrations, from a motion of the particles of 

 air, which must be extremely regular, and 

 almost uniform ; a uniformity which, when 



proper precautions are taken, is not contra- 

 dicted by examining the motion of the chord 

 with the assistance of a powerful magnifier. 

 Tills difiiculty occurred very strongly to 

 Elder: and De la Grange even suspects that 

 there is some fallacy in the experiment, and 

 that a musical ear judges from previous as- 

 sociation. But, besides that these sounds are 

 discoverable to a ear destitute of such asso- 

 ciations, and, when the sound is produced 

 by two strings in imperfect unison, may be 

 verified by counting the number of their 

 beats, the experiment already related is an 

 undeniable proof that no fallacy of this kind 

 exists. It must be confessed, that nothing 

 fully satisfactory has yet occurred to account 

 for the phenomena; but it is highly proba- 

 ble that the slight increase of tension pro- 

 duced b3' flexure, which is omitted in the 

 calculations, the elasticity or inflexibility of 

 the chord, and the unavoidable inequality df 

 thickness of its different parts,may, b}- disturb- 

 ing the isochronism of the suboVdinate vi- 

 brations, cause all that variety of soumls 

 which is so inexplicable without them. For^ 

 when the slightest diftierence is introduced in 

 the periods, there is no difficulty in conceivJ^ 

 ing how the sounds mi>y be distinguished ; 

 and indeed, in soa>e casesi a nice ear ^^ill 

 discover a slight imperfection in the tune of 

 harmonic notes: it is- also often observed, in 

 \tuningan instrument, that some of the single 

 strings produce beating sounds, which uii- 

 doubtedly arise from their want of perfect 

 uniformity; the same circun»stance is the 

 cause of the motion of the apsides, which "is 

 often observable in the rotations already de- 

 scribed. It may be perceived that any par- 

 ticular harmonic is loudest, when the chord 

 is inflected at about one third of the corre^ 

 sponding aliquot part from one of the extre- 



