respecting Sound and Light. 1 33 



to a representation of the actual circumstances ; but, as the laws 

 by which the motion of the particles of air is regulated, differ 

 according to the different origin and nature of the sound, it is 

 impossible to adapt a demonstration to them all : if, however, 

 the particles be supposed to follow the law of the harmonic 

 curve, derived from uniform circular motion, the compound 

 vibration will be the harmonic instead of the arithmetical mean; 

 and the secondary sound of the interrupted vibrations will be 

 more accurately formed, and more strongly marked, Plate VI. 

 Figs. 4,1, 42 : the demonstration is deducible from the pro- 

 perties of the circle. It is remarkable, that the law by which the 

 motion of the particles is governed, is capable of some singular 

 alterations by a combination of vibrations. By adding to a given 

 sound other similar sounds, related to it in frequency as the 

 series of odd numbers, and in strength inversely in the same 

 ratios, the right lines indicating an uniform motion may be con- 

 verted very nearly into figures of sines, and the figures of sines 

 into right lines, as in Plate V. Figs. 39, 40. 



XII. Of the Frequency of Vibrations constituting a given 



Note. 



The number of vibrations performed by a given sound in a 

 second, has been variously ascertained ; first, by Sauveur, by a 

 very ingenious inference from the beats of two sounds; and 

 since, by the same observer and 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 Mersennus, 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, 



