respecting Sound and Light. 131 



furnished by the phaenomena of beats, and of the grave har- 

 monics observed by Romieu and Tartini ; which M. De la 

 Grange has already considered in the same point of view. In 

 the first place, to simplify the statement, let us suppose, what 

 probably never precisely happens, that the particles of air, in 

 transmitting the pulses, proceed and return with uniform mo- 

 tions ; and, in order to represent their position to the eye, let 

 the uniform progress of time be represented by the increase of 

 the absciss, and the distance of the particle from its original 

 position, by the ordinate, Fig. 33 — 38. Then, by supposing 

 any two or more vibrations in the same direction to be com- 

 bined, the joint motion will be represented by the sum or dif- 

 ference of the ordinates. When two sounds are of equal strength, 

 and nearly of the same pitch, as in Fig. 36, the joint vibration 

 is alternately very weak and very strong, producing the effect 

 denominated a beat, Plate VI. Fig. 43, B and C ; which is slower 

 and more marked, as the sounds approach nearer to each other in 

 frequency of vibrations ; and, of these beats there may happen 

 to be several orders, according to the periodical approximations 

 of the numbers expressing the proportions of the vibrations. 

 The strength of the joint sound is double that of the simple 

 sound only at the middle of the beat, but not throughout its 

 duration ; and it may be inferred, that the strength of sound in 

 a concert will not be in exact proportion to the number of 

 instruments composing it. Could any method be devised for 

 ascertaining this by experiment, it would assist in the comparison 

 of sound with light. In Plate V. Fig. 33, let P and Q be the middle 

 points of the progress or regress of a particle in two successive 

 compound vibrations; then, CP being = PD, KR = RN, GQ 

 = QH, and MS == SO, twice their distance, 2RS = 2RN -f- 



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