VOL. XC.] FHILOSOPHICAL TRANSACTIONS. 621 



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 probable that the slight increase of 

 tension produced by flexure, which is omitted in the calculations, and the unavoid- 

 able 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 differ- 

 ence 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 un- 

 doubtedly arise from their want of perfect uniformity. It may be perceived that 

 any particular harmonic is loudest, when the chord is inflected at about 4- of the 

 corresponding aliquot part from one of the extremities of that part. An observa- 

 tion 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 inflec- 

 tion, 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, destroying 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 ex- 

 tremely loud; and the fundamental note, especially in the lowest harmonics, 

 scarcely audible : the chord assumes the appearance, at the aliquot points, of as 

 many lucid lines as correspond to the number of the harmonic, more nearly ap- 

 proaching to each other as the bow approaches more nearly to the point, pi. JO, 

 fig. 51. According to the various modes of applying the bow, an immense variety 

 of figures of the orbits are produced, fig. 45, more than enough to account for all 

 the difference of tone in different performers. In observations of this kind, a 

 series of harmonics is frequently heard in drawing the bow across the same part of 

 the chord: these 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 

 bowstring, intercepted between its end and the chord, of performing its vibrations 

 in times which are aliquot parts of the vibration of the chord: hence it would seem, 

 that the bow takes effect on the chord but at one instant during each fundamental 

 vibration. In these experiments, the bow was strung with the 2d string of a violin: 

 and, in the preparatory application of resin, the longitudinal sound of Chladni was 

 sometimes heard; but it was observed to differ at least a note in different parts of 

 the string. 



14. Of the Vibrations of Rods and Plates. — Some experiments were made, 

 with the assistance of a most excellent practical musician, on the various notes pro- 

 duced by a glass tube, an iron rod, and a wooden ruler; and, in a case where the 



