Experiments and Inquiries refpeBlng Sound and Light. laj 



vibrates at all : fully confirming the non-exiftence of the harmonic curve, and the accuracy 

 of the conftrudion of Euler and De la Grange. At the fame time, as M. Betnouilli has 

 juftly obferved, fmce every figure may be infinitely approximated, by confidering its 

 ordinates as compofed of the ordinates of an infinite number of trochoids of different mag- 

 nitudes, it may be demonftrated, that all thefe conftituent curves would revert to their 

 initial (late, in the fame time that a fimilar chord bent into a trochoidal curve would per- 

 form a fingle vibration ; and this is in fome refpc£ls a convenient and compendious method 

 of confidering the problem. But, when a chord vibrates freely, it never remains long in 

 motion, without a very evident departure from the plane of the vibration ; and, whether 

 from the original obliquity of the impulfe, or from an interference with the refle£led 

 vibrations of the air, or from the incquability of its own weight or flexibility, or from the 

 immediate refiftance of the particles of air in contafl with it, it is thrown into a very 

 evident rotatory motion, more or lefs fimple and uniform according to circumftanceS. 

 Some fpecimens of the figures of the orbits of chords are exhibited in Plate V. Fig. 44. 

 At the middle of the chord, its orbit has always two equal halves, but feldom at any other 

 point. The curves of Fig. 46, are defcribed by combining together various circular 

 motions, fuppofed to be performed in aliquot parts of the primitive orbit : and fome of 

 them approach nearly to the figures adlually obferved. When the chord is of unequal 

 thicknefs, or when it is loofely tended and forcibly Inflefted, the apfides and double points 

 of the orbits have a very evident rotatory motion. The compound rotations feem tc» 

 demonftrate to the eye the exiftence of fecondary vibrations, and to account for the acute 

 harmonic founds which generally attend the fundamental found. There is one fa£i: re- 

 fpefting thefe fecondary notes, which feems intirely to have efcSped obfervatioh. If a 

 chord be infle£led at one-half, one-third, or any other aliquot part of its length, and then 

 fuddenly left at liberty, the harmonic, note which would be produced by dividing the chord 

 at that point is intirely loft, and is not to be diftinguiflied during any part of the con- 

 tinuance of the found. This demonftrates, that the fecondary notes do not depend upon 

 any interference of the vibrations of the air with each other, nor upon any fympathetic 

 agitation of auditory fibres, nor upon any efFeft of reflefted found upon the chord, but 

 merely upon its initial figure and motion. If it were fuppofed that the chord, when in- 

 flefted into right lines, refolved itfelf neceflarily into a number of fecondary vibrations, 

 according to fome curves which, when properly combined, would approximate to the 

 figure given, the fuppofition would indeed in fome refpects correfpond with the phenome- 

 non related ; as the coefficients of all the curves fuppofed to end at the angle of inflexion 

 would vanifli. But, whether we trace the conftituent curves of fuch a figure through the 

 various flages of their vibrations, or whether we follow the more compendious method of 

 Euler to the fame purpofe, the figures refulting from this feries of vibrations are in fact fo 

 (imple, that it feems inconceivable how the ear fliould deduce the complicated idea of a 

 number of heterogeneous vibrations, from a motion of the particles of air which muft be 



R 2 extremely 



