1 24 Experiments and InquirUf refpeHing Sound and Light. 



extremely regular, and almoft uniform ; an uniformity which, when proper precautions 

 are taken, is not contradiiSted by examining the motion of the chord with the affiftance of 

 a powerful magnifier. This difficulty occurred very ftrongly to Euler; and De la Grange 

 even fufpefts fome fallacy in the experiment, and that a mufical ear judges from previous 

 aflbciation. But, beCdes that thefe founds are difcoverable to an ear deftitute of fuch 

 aflbciations, and, when the found is produced by two firings in imperfe£t unifon, may be 

 verified by counting the number of their beats, the experiment already related is an un- 

 deniable proof that no fallacy of this kind exifls. It muft be confefled, that nothing fully 

 fatlsfa£tory has yet occurred to account for the phsenomena ; but it is highly probable that 

 the flight increafe of tenfion produced by flexure, which is omitted in the calculations, and 

 the unavoidable inequality of thicknefs or flexibility of different parts of the fame chord, 

 may, by difturbing the ifochronifm of the fubordlnate vibrations, caufe all that variety of 

 founds which is fo inexplicable without them. For, when the flighted difference is in- 

 troduced in the periods, there is no difficulty in conceiving how the founds may be diftin- 

 guifhed; and indeed, in fome cafes, a nice ear will difcover a flight lmperfe£tion in the 

 .tune of harmonic notes : it is alfo often obferved, in tuning an inn:rument, that fbme of 

 the fingle chords produce beating founds, which undoubtedly arife from their want of per- 

 feft uniformity. It may be perceived that any particular harmonic is loudeft, when the 

 chord is inflefled at about one-third of the correfponding aliquot part from one of the ex- 

 tremities of that part. An obfervation of Dr. Wallis feems to have pafTed unnoticed by 

 later writers on harmonics. If the firing of a violin be {Iruck in the middle, or at any 

 other aliquot part, it will give either no found at all, or a very obfcure one. This is true, 

 not of infleftion, but of the motion communicated by a bow ; and may be explained from 

 the circumftance of the fuccefl"ive impulfes, refledled from the fixed points at each end, 

 deltroying each other : an explanation nearly analogous to fome obfervations of Dr. Mat- 

 thew Young on the motion of chords. When the bow is applied not exadlly at the aliquot 

 point, but very near it, the correfponding harmonic is extremely loud ; and the funda- 

 mental note, efpecially in the lowefl: harmonics, fcarcely audible : the chord afTumes the 

 appearance, at ihe aliquot points, of as many lucid lines as correfpond to the number of 

 the harmonic, more nearly approaching to each other as the bow approaches more nearly 

 to the point, Plate VI. Fig. 51. According to the various modes of applying the bow, an 

 immenfe variety of figures of the orbits are produced, Fig. 45, more than enough to ac- 

 count for all the difference of tone in different performers. In obfervations of this kind, 

 a feries of harmonics is frequently heard in drawing the bow acrofs the fame part of the 

 chord : thefe are produced by the bow; they are however not proportionate to the whole 

 length of the bow,, but depend on the capability of the portion of the bowftring, inters 

 cepted between its end and the chord, of performing its vibrations in times which arc 

 aliquot parts of the vibration of the chord : hence it would feem, that the bow takes efFe£t 

 en the chord but at one inftant during each fundamental vibration. In thefe experiments,. 



tha. 



