546 



tXPERIMENTS AND INQUIRIES 



several others, by calculation from the 

 weight and tension of a chord. It was 

 thought worth while, as a confirmation, to 

 make an experiment, suggested, but coarsely 

 conducted, by Mersenne, on a chord 200 

 inches in length, stretched so loosely as to 

 have its single vibrations visible; and, by 

 holding a quill nearly in contact with the 

 chord, they were made audible, and were 

 found, in one experiment, to recur 8.3 times 

 in a second. By lightly pressing the chord 

 at one eighth of its length from the end, 

 and at other shorter aliquot distances, the 

 fundamental note was found to be one sixth 

 of a tone higher than the respective octave 

 of a tuning fork marked C : hence the fork 

 was a comma and a half above the pitch as- 

 sumed by Sauveur, of an imaginary C, con- 

 sisting of one vibration in a second. 



XIII. Of the Vibrations of Chords. 



By a singular oversight "in the demonstra- 

 tion of Dr. Brook Taylor, adopted as it has 

 been by a number of later authors, it is as- 

 serted, that if a chord be once inflected info 

 any other form than that of the harmonic 

 curve, it will, since those parts which are 

 without this figure are impelled towards it 

 by an excess of force, and those within it by 

 a deficiency, in a very short time arrive at 

 or very near the form of this precise curve. It 

 would be easy to prove, if this reasoning 

 were allowed, that the form of the curve can 

 be no other than that of the axis, since the 

 lending force is continually impelling the 

 chord towards this line. The case is very 

 similar to that of the Newtonian proposition 

 respecting sound. It may be proved, that 

 every impulse is communicated along a 

 tended chord with a uniform velocity; and 



this velocity is the same which is inferred 

 from Dr. Taylor's theorem ; just as that of 

 sound, determined by other methods, coin- 

 cides with the Newtonian result. But, al- 

 though several late mathematicians have 

 given admirable solutions of all possible cases 

 of the problem, yet it has still been supposed, 

 that the distinctions were too minute to be 

 actually observed. The theorem of Euler and 

 De la Grange, in the case where the chord 

 is supposed to be at first at rest, is in effect 

 this: continue the figure each way, alter- 

 nately on dilferent sides of the axis, and in 

 contrary positions; then, from any point of 

 the curve, take an absciss each way, in the 

 same proportion to the length of the chord 

 as any given portion of time bears to the 

 time of one seinivibration, and the half sum 

 of the ordinates will be the distance of that 

 point of the chord from the axis, at the ex- 

 piration of the time given. If the initial 

 figure of the chord be composed of two right 

 lines, as generally happens in musical in- 

 struments and experiments, its successive 

 forms will be such as are represented in 

 (Plate 5. Fig. 50,51 :) and this result is fully 

 confirmed by experiment. Take one of the 

 lowest strings of a square piano forte, round 

 which a fine silvered wire is wound in a spi- 

 ral form ; contract the light of a window, so 

 that, when the eye is placed in a proper po- 

 sition, the image of the light may appear 

 small, bright, and well defined, on each of 

 the convolutions of the wire. Let the chord 

 be now made to vibrate, and the luminous 

 point will delineate its path, like a burninf' 

 coal whirled round, and will present to the 

 eye a line of light, w;hich, by the assistance 

 of a microscope, nmy be very accurately ob- 

 served. According to the different ways by 

 which the wire is put in motion, the form of 



