RESPECTING SOUND AND LIGHT. 



5S9 



cfease of divergence, in the same direction ; 

 for, the actual velocity of the pa i tides of air, 

 in the strongest sound, is incomparably less 

 than that of the slowest of the currents in 

 the experiments related, where the beginning 

 of the conical divergence took place at the 

 greatest distance. Dr. Matthew Young has ob- 

 jected, not withoutsome reason, to M. Hube, 

 that the existence of a condensation will 

 cause a divergence in sound : but a much 

 greater degree of condensation must have 

 existed in the currents described than in any 

 sound. There is indeed one difference be- 

 tween a stream of air and a sound ; that, in 

 sound, the motions of different particles of 

 4Ur are not synchronous : but it is not demon- 

 strable that this circumstance would affect 

 the divergency of the motion, except at the 

 instant of its commencement, and perhaps 

 not even then in a material degree ; for, in 

 general, the motion is communicated with a 

 veiy gradual increase of intensity, so that there 

 isnosudden condensation nor rarefaction. The 

 subject, however, deserves a more particular 

 investigation ; and, in order to obtain a more 

 solid foundation for the argument, it is pro- 

 posed, as soon as circumstances permit, to in- 

 stitute a course of experiments for ascertain- 

 ing, as accurately as possible, the different 

 strength of a sound once projected in a given 

 direction, at different distances from the axis 

 of its motion. 



VII. 0/ the Lkcay of Soimd. 



Various opinions have been entertained 

 respecting the decay of sound. M. De la 

 Grange has published a calculation, by 

 which its force is shown to decay nearly in 

 the simple ratio of the distances; and M. 

 Daniel Bernoulli's equations for the sounds 



of conical pipes lead to a similar conclusion. 

 The same inference follows from a comple- 

 tion of the reasoning of Dr. Helsham, Dr. 

 Matthew Young, and Professor Venturi. It 

 has been very elegantly demonstrated by 

 Maclaufin, and may also be proved in a 

 much more simple manner, that, when mo- 

 tion is communicated through a series of elas- 

 tic bodies increasing in magnitude, if the 

 number of bodies be supposed infinitely 

 great, and their difference infinitely small, 

 the motion of the last will be to that of the 

 first in the subdupiicate ratio of their respec- 

 tive magnitudes ; and since, in the case of 

 concentric spherical laminae of air, the bulk 

 increases in the duplicate ratio of the dis- 

 tance, the motion will in this case be directly, 

 and the velocity inversely, as the distance. It 

 may, however, be questioned, whether or no 

 the strength of sound is to be considered as 

 simpl)' proportional to the velocity of the 

 particles concerned in transmitting it. 



VIII. Of the harmonic Sounds of Pipes. 



In order to ascertain the velocity with 

 whidh organ pipes of different lengths require 

 to be supplied with air, according to the va- 

 rious appropriate sounds which they produce, 

 a set of experiments was made, with the 

 same mouth piece, on pipes of the same 

 bore, and of different lengths, both stopped 

 and open. The general result was, that a 

 similar blast produced as nearly the same 

 sound as the length of the pipes would per- 

 mit ; or at least that the exceptions, though 

 very numerous, lay equally on each side of 

 this conclusion. The particular results are 

 expressed in Table XI, and in Plate 3. Tig. 

 3 1 . They explain how a note may be made 

 much louder on a wind instrument by a swell. 



