RESPECTrXG SOUND AND LIGHT. 



547 



tliis path is no less diversified and amusing, 

 than the multifarious forms of the quiescent 

 lines of vibrating plates, discovered by Pro- 

 fessor Chladni ; and it is indeed in one re- 

 spect even more interesting, at it appears to 

 be more within the reach of mathematical 

 calculation to determine it ; although liither- 

 to, excepting some slight observations of 

 Busse and Chladni, principally on the mo- 

 tion of rods, nothing has been attempted on 

 the subject. For the present purpose, the 

 motion of the chord may be simplified, by 

 tying a long fine thread to any part of it, 

 and fixing tliis thread in a direction perpen- 

 dicular to that of the chord, without drawing 

 it so tight as to increase the tension : by 

 these means, the vibrations are confined 

 nearly to one plane, which scarcely ever 

 happens when the chord vibrates at liberty. 

 If the chord be now inflected in the middle, 

 it will be found, by comparison with an ob- 

 ject which marked its quiestfent position, to 

 make equal excursions on each side of the 

 axis ; and the figure which it apparently oc- 

 cupies will be terminated by two lines, the 

 more luminous as they are nearer the ends. 

 (Plate 3. Fig. 52.) But, if the chord be in- 

 flected near one of its extremities, (Fig. 53,) 

 it will proceed but a very small distance on 

 the opposite side of the axis, and will there 

 form a very bright line, indicating its longer 

 continuance in that place; yet it will return 

 on the former side nearly to the point from 

 whence it was let go, but will be there very 

 faintly visible, on account of its short delay. 

 In the middle of the chord, the excursions on 

 each side of the axis are always equal ; and, 

 beyond the middle, the same circumstances 

 take place as in the half where it was in* 

 fleeted, but on the opposite side of the axis ; 

 and this apjwarance continues unaltered in 



its proportions, as long as the chord vibrates 

 at all : fully confirming the nonexistence of 

 the harmonic curve, and the accuracy of 

 the construction of Eulcr and De la Grange. 

 At the same tiine, as Mr. Bernoulli has justly 

 observed, since every figure may be infinitely 

 approximated, by considering its ordinates as 

 composed of the ordinates of an infinite 

 number of harmonic curves of different mag- 

 nitudes, it may be demonstrated, that all 

 these constituent curves would revert to their 

 initial state, in the same time that a similar 

 chord bent into a harmonic curve would per- 

 form a single vibration ; and this is in some 

 respects a convenient and compendious me- 

 thod of considering the problem. But, 

 when a chord vibrates freely, it never re- 

 mains long in motion, without a very evir 

 dent departure from the plane of the vibra- 

 tion ; and, whether from the original obli- 

 quity of the impulse, or from an interference 

 with the reflected vibrations of the air, or 

 from the inequabiiity of its own weight of 

 flexibility, or from the immediate resistance 

 of the particles of air in contact with it, it 

 is thrown into a very evident rotatory mo- 

 tion, more or less simple and uniform ac- 

 cording to circumstances. Some specimens 

 of the figures of the orbits of chords are ex- 

 hibited in Plate 5. Fig. 47. At the middle 

 of the chord, its orbit has always two equal 

 halves, but seldom at any other point. The 

 curves of Fig. 49, are described by combin- 

 ing together va^'ious circular motions, sup- 

 posed to be performed in aliquot parts of the 

 primitive orbit : and some of them approach 

 nearly to the figures actually observed. When 

 the chord is of unequal thickness, or when it 

 is loosely tended and forcibly inflected, the 

 apsides and double points of the orbits haver 

 a very evident rotator}' motion. The coui- 



