Velocity of Sound, 127 



observed that dx is invariably of the same magnitude, whatever 

 be the position of the small cylinder of air, and that dz alone 

 varies in different places of the tube, and at different times. 

 It follows, therefore, that x is independent on the time t, and z 

 is a function of x and t. It is to be observed too, that the air 

 is supposed to undergo very small condensations and rarefac- 

 tions in proportion to its original bulk in the state of equili- 

 brium ; that is, dz must be considered as very small when 

 compared to dx*. Let §' denote the density of the air in equU 



from the sonorous body, and, consequently, the velocities of the atoms 

 slower and slower at those similar points of their vibrations in which the 

 densities of the cylinders become equal to the mean density of the me- 

 dium ? But ample reason may be given for the fundamental fact just 

 stated, though Mr. Ivory has entirely overlooked both it and the reason. 

 For admitting that the motion of the cylinder were, as he assumes, uni- 

 form in a tube, yet in the free air, sound is sent off as from a radiant 

 point, in every open direction not opposed to the wind. Nay, sound 

 reaches many a place by a curvilinear rout, even without being reflected. 

 It is therefore plain, that the area of each wave or spherical shell of air, to 

 which the tremor is communicated in succession, will increase as fast, at 

 least, as the square of its radius, or of its distance from the radiant point. 

 In other words, the number of atoms or the mass to be successively set 

 in motion will, supposing the medium uniform, increase as fast, at least 

 as the square of its distance from the sonorous body. This is a very dif- 

 ferent thing from saying off hand, that ** the cylinder in motion has always 

 the same mass." Hence, as might easily be shown from known princi- 

 ples, the motion of sound computed on projectile principles, instead of 

 being uniform, ought to decrease as fast, at least, as the reciprocal of the 

 distance from its source decreases. 



Sir Isaac Newton's view of the subject is incomparably more consistent 

 than the one before us. He supposed all the vibrations in the same uni- 

 form medium to be isochronous, or performed in equal times, however 

 different their lengths, and, consequently, however different the velocities 

 of the atoms at like points of their vibrations. Indeed, it is easy to see 

 that there is no way in which the velocity of sound could be uniform, but 

 by the vibrations, however different in length, being isochronous. New- 

 ton, and his earlier followers, were well aware of this circumstance ; but 

 vibrations of different lengths are quite at variance with, and cannot enter 

 as an element into, the refined mode of viewing sound under the emblem of 

 a projected cylinder, going on for ever, as the theory implies, without 

 either decrease of velocity or of loudness. There is, however, no reason 

 to think that every conceivable or possible law of elasticity in air would 

 give isochronous vibrations ; nor am I aware that such has been proved, 

 from legitimate theoretical principles, to hold of even one particular 

 law, far less of that which belongs to the atmosphere. — H. M. 



* It would be difficult to reconcile almost any of these remarks either 

 with each other, or with the very opposite principles acted on in the rest 

 of this research. As, for instance, by strictly following up the leading 

 principles of the investigation, it appears that dz, instead of being incom- 

 parably smaller than dx^ must occasionally equal it \ and that the con- 



