VOL. XC.] PHILOSOPHICAL TRANSACTIONS. 6*1 1 



sound spreads equally in every direction. In windy weather it may often be ob- 

 served, that the sound of a distant bell varies almost instantaneously in its strength, 

 so as to appear at least twice as remote at one time as at another. Now if sound 

 diverged equally in all directions, the variation produced by the wind could never 

 exceed T v of the apparent distance; but, on the supposition of a motion nearly 

 rectilinear, it may easily happen that a slight change in the direction of the wind 

 may convey the sound, either directly or after reflection, in very different degrees 

 of strength, to the same spot. From the experiments on the motion of a current 

 of air, already related, it would be expected that a sound, admitted at a con- 

 siderable distance from its origin through an aperture, would proceed, with an 

 almost imperceptible increase of divergence, in the same direction ; for, the actual 

 velocity of the particles 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 objected, not without 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 between a stream of air and a sound; that, in sound, the motions of 

 different particles of air are not synchronous: but it is not demonstrable 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 very gradual increase of intensity. 



7. On the Decay of Sound. — 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. Dan. 

 Bernoulli's equations for the sounds of conical pipes lead to a similar conclusion. 

 The same inference would follow from a completion of the reasoning of Dr. 

 Helsham, Dr. Mat. Young, and Mr. Venturi. It has been very elegantly de- 

 monstrated by Maclaurin, and may also be proved in a much more simple manner, 

 that when motion is communicated through a series of elastic 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 

 subduplicate ratio of their respective magnitudes; and since, in the case of con- 

 centric spherical laminae of air, the bulk increases in the duplicate ratio of the 

 distance, the motion will in this case be directly, and the velocity inversely, as the 

 distance. But, however true this may be of the first impulse, it will appear, by 

 pursuing the calculation a little further, that every one of the elastic bodies, except 

 the last, receives an impulse in a retrograde direction, which ultimately impedes the 

 effect of the succeeding impulse, as much as a similar cause promoted that of the 

 preceding one: and thus, as sound must be conceived to consist of an infinite 

 number of impulses, the motion of the last lamina will be precisely equal to that 

 of the first; and, as far as this mode of reasoning goes, sound must decay in the 



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