respecting Sound and Light. 139 



of this kind exists. It must be confessed, that nothing fully 

 satisfactory has yet occurred to account for the phaenomena; 

 but it is highly probable that the slight increase of tension pro- 

 duced by flexure, which is omitted in the calculations, and the 

 unavoidable inequality of thickness or flexibility of different 

 parts of the same chord, may, by disturbing the isochronism of 

 the subordinate vibrations, cause all that variety of sounds 

 which is so inexplicable without them. For, when the slightest 

 difference is introduced in the periods, there is no difficulty in 

 conceiving how the sounds may be distinguished ; and indeed, 

 in some cases, a nice ear will discover a slight imperfection in 

 the tune of harmonic notes : it is also often observed, in tuning 

 an instrument, that some of the single chords produce beating 

 sounds, which undoubtedly arise from their want of perfect 

 uniformity. It may be perceived that any particular harmonic 

 is loudest, when the chord is inflected at about one-third of the 

 corresponding aliquot part from one of the extremities of that 

 part. An observation of Dr. Wallis seems to have passed 

 unnoticed by later writers on harmonics. If the string of a violin 

 be struck in the middle, or at any other aliquot part, it will 

 give either no sound at all, or a very obscure one. This is true, 

 not of inflection, but of the motion communicated by a bow ; 

 and may be explained from the circumstance of the successive 

 impulses, reflected from the fixed points at each end, destroy- 

 ing each other: an explanation nearly analogous to some 

 observations of Dr. Matthew Young on the motion of chords. 

 When the bow is applied not exactly at the aliquot point, but 

 very near it, the corresponding harmonic is extremely loud; 

 and the fundamental note, especially in the lowest harmonics, 

 scarcely audible : the chord assumes the appearance, at the 



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