122 Experiments and Inquiries refpeEling Sound and Light. 



But, although feveral late mathematicians have given admirable folutions of all pofTible 

 cafes of the problem, yet it has ftill been fuppofed, that the diftin£tions were too minute 

 to be aftually obferved ; efpecially, as it might have been added, fince the inflexibility of a 

 wire Would difpofe it, according to the do£lrine of elaftic rods, to affume the form of the 

 harmonic curve. The theorem of Euler andDe la Grange, in the cafe where the chord is 

 fuppofed to be at firft at reft, is in effect this : continue the figure each way, alternately on 

 different fides of the axis, and in contrary pofitions ; theij, from any point of the curve, 

 take an abfcifs each way, in the fame proportion to the length of the chord as any given 

 portion of time bears to the time of one femivibration, and the half fum of the ordinates 

 will be the diftance of that point of the chord from the axis, at the expiration of the time 

 given. If the initial figure of the chord be compofed of two right lines, as generally hap.- 

 pens in mufical inftruments and experiments, its fuccefiive forms will be fuch as are re- 

 prcfented in Plate VI. Figs. 47, 48 : and this refult is fully confirmed by experiment. 

 Take one of the loweft firings of a fquare^piano forte, round which a fine filvered wire is 

 wound in a fpiral form ; contradl the light of a window, fo that, when the eye is placed in 

 a proper pofition, the image of the light may appear fmall, 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 burning coal whirled round, and will prefent 

 to the eye a line of light, which, by the affiftance of a mifcrofcope, may be very accurately 

 obferved. According to the different ways by which the wire is put in motion, the form of 

 this path is no lefs diverfified and amufing, than the multifarious forms of the quiefcent 

 lines of vibrating plates, difcovered by Profeffor Chladni, and is indeed in one refpe£l even 

 more interefting, as it appears to be more within the reach of mathematical calculation to 

 determine it ; although hitherto, excepting fome flight obfervations of Buffe and Chladni, 

 principally on the motion of rods, nothing has been attempted on the fubjecl. For the 

 prefent purpofe, the motion of the chord maybe fimplified, by tying a long fine thread to any 

 part of it, and fixing this thread in a direction perpendicular to that of the chord, without 

 drawing it fo tight as to increafe thetenfion : by thefe means, the vibrations are confined nearly 

 to one plane, which fcarcely ever happens when the chord vibrates at liberty. If the chord 

 be now infle£led in the middle, it will be found, by comparifon with an objecSl which 

 marked Its quiefcent pofition, to make equal excurfions on each fide of the axis ; and the 

 figure which it apparently occupies will be terminated by two lines, the more luminous 

 as they are nearer the ends, Plate V. Fig. 49. But, if the chord be inflefted near one of 

 its extremities,. Fig. 50,, it will proceed but a very fmall diftance on tlie oppofite fide 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 fide nearly to the point from whence it was let go, 

 but will be there faintly viCble, on account of its Qiort delay. In the middle of the chord, 

 the excurfions on each fide the axis are always equal \ and, beyond the middle, the fame 

 circumftances take place as in the half where it was inflected, but on the oppofite fide of 

 the axis ; and this appearance continues unaltered in its proportions, as long as the chord. 



vibrates, 



