.90 Experiments and Inquiries rtfpeBing Sound and Light. 



cxafl proportion to the number of inftruments compofing h. Could any method be 

 devifed for afcertairiing this by experiment, it would affift in the comparifon of found 

 with light. In Plate V. Fig. 33, let P and Q^be the middle points of the progrefs or 

 regrefs of a particle in two fuccefiive compound vibrations ; then, CP being ~ PD, 

 KR = RN, GQj= QH, and MS = SO, twice their diftance, 2 RS = 2 RN + 2 NM + 

 2MS = KN + NM + NM + MO = KM + NO, is equal to the fum of the diftances of 

 the correfponding parts of the fimple vibrations. For inftance, if the two founds be as 

 80 : 81, the joint vibration will be as 80.5 ; the arithmetical mean between the periods of 

 the fingie vibrations. The greater the difference in the pitch of two founds, the more 

 rapid the beats, t,ill at laft, like the diftln£l: puffs of air in the experiments already related, 

 they communicate the idea of a continued found ; and this is the fundamental harmonic 

 defcribed by Tartini. For inftance, in Plate V. Fig. 34 — 37, the vibrations of founds 

 related as i : 2, 4 : 5, 9 : 10, and 5 : 8, are rcprefented; wiiere the beats, if the founds 

 be not taken too grave, conftitute a diftin£t found, which correfponds with the time 

 elapfing between two fucceffive coincidences, or near approaches to coincidence : for, that 

 fuch a tempered interval ftill produces a harmonic, appears from Plate V. Fig. 38. But, 

 bcfides this primary harmonic, a fecondary note is fometimes heard, where the intermediate 

 compound vibrations occur at a certain interval, though interruptedly; for inftance, in the 

 coalefcence of two founds related to each other as 7 : 8, 5 : 7, or 4 : 5, there is a re- 

 currence of a fimilar ftate of the joint motion, nearly at the interval of -j',-, -j^^, or | of the 

 whole period : hence, in the concord of a major third, the fourth below the key note is 

 heard as diftin£tly as the double oftave, as is feen in fome degree in Plate V. Fig. 35 ; 

 AB being nearly two-thirds of CD. The fame found is fometimes produced by taking the 

 minor ftxth below the key note ; probably becaufe this fixth, like every other note, is 

 almoft always attended by an octave, as a harmonic. If the angles of all the figures 

 refulting "from the motion thus affumed be rounded off, they will approach more nearly 

 to a reprefentation of the adhial circumftances ; but, as the laws by which the motion pf 

 the particles of air is regulated, differ according to the different origin and nature of the 

 found, it i« impoffible to adapt a demonftration to them all : if, however, the particles be 

 fuppofed to follow the law of the harmonic curve, derived from uniform circular motion, 

 the compound vibration will be the harmonic jnftead of the arithmetical mean ; and 

 the fecondary found of the interrupted vibrations will be more accurately formed, and 

 more ftrongly marked Plate VI. Figs. 41, 42: the demonftration is deducible from the 

 properties of the circle. It is remarkable, that the law by which the motion of the particles 

 is governed, is capable of fome fingular alterations by a combination of vibrations. By 

 adding to a given found other fimilar founds, related to it in frequency as the feries of odd 

 numbers and in ftrength inverfely in the fame ratios, the right lines indicating an uniform 

 motion may be converted very nearly into figures of fines, and the figures of fines into 

 light lifles^ as in Plate V^ Figs. 39, 4a 



VII. Cf 



