Description of the Kaleidophotilii 



347 



No. %, On causing the entire rod to vibrate, so that its 

 lowest sound be produced ♦, as it is seldom that the motions of 

 a cylindrical rod can be confined to a plane, the vibrations will 

 almost always be combined with a circular motion, When the 

 pressure on the fixed end is exerted on two opposite points, 

 and the rod put in motion in the direction of the pressure, thq 

 following progression in the changes of form will be distinctly 

 observed ; the track will commence as a line, and almost imme-^ 

 diately open into an ellipse, the lesser axis of which will gradvii^ 

 ally extend as the larger axis diminishes, until it becomes B^ 

 circle ; what was before the lesser will then become the larger 

 axis, and thus the motions will alternate until, from their 



* The most simple mode of vibration of a rod vibrating transversely, 

 when one of its extremities is fixed and the other is free, is that in which 

 the entire rod makes its vibrations alternately on each side of the axi^, 

 which is nowhere intersected by the curve, but only touched at the fixed 

 end. This gives the gravest sound which can be produced fi-om the rod. 

 In the other modes of vibration, the axis is intersected by the curve 1, 2, 

 3, or more times. The best means to command the production of these 

 sounds is to touch a node of vibration hghtly with the finger, and to put 

 ,a vibrating part in motion by a violin-bow. In thje second sound, the 

 n^^ber of vibrations is to that of the first, as 5 ^ : 2 a, or as 25 : 4 ; the 

 difference of the sounds is, thei'efore, two octaves and an augmented fifth. 

 Separating the first sound fi*om the series, the number of the vibrations 

 of all the others will be to one another as the squares of the numbers 3, 

 5, 7, 9, &c. ; the third, in which there are three nodes, will therefore 

 exce«d the second by an octave and an augmented fourth; in the fourth, 

 the acuteness will be augmented by nearly an octave ; in the fifth, by 

 nearly a major sixth, &c. To reduce to the same pitch all the propor- 

 tions of the sounds which such a rod is capable of producing, I shall 

 regard the sound corresponding with the most simple motion as the C 

 one octave lower than the lowest of the pianp-forte ; the proportions of 

 the sounds will then be — 



The possible series of sounds, regarding the fundamental as unity, will 

 therefore bo— l, 6i, 17i|, 343'gV 561, &c. ; or expressed in integral num- 

 bers--36, 225,va25, 1225, 2025> kc.-^CiTLADm, Traitc dAcoustique, 

 p. 91. v . ^ \ 



2 A2 



