Velocity of Sounds 12Sf 



process is meant to be regulated is briefly this : — A minute 

 cylinder of air, whose length varies without either changing its 

 mass or diameter, is supposed to be acted on by an accelerating 

 force, till it move over a small space z, and then abandoned 

 to move uniformly with the velocity so acquired along a straight 

 line a?*. This latter motion is intended to represent that of 

 sound, and its velocity is assumed, without either proof or pro- 

 bability, to be always the same, and, consequently, without 

 either decrease or end, in air of the like density and pressure. 

 It is further supposed, that the cylinder always moves over a 

 space equal to its own length during the constant fluxion of 

 time dr, and that it does so whether in passing over z or x. 



Now without enlarging on the faint enough resemblance 

 between this leading idea and the propagation of sound, it may 

 be observed, before entering on further particulars, that either 

 the space z, no matter how small, must be always of the same 

 magnitude, and therefore the intensity or loudness of sound 

 always the same in air of the like condition, which is contrary 

 to universal observation ; or else, the accelerating force must 

 be everywhere inversely proportional to the space z. Without 

 some condition of this nature, the final velocity with which the 

 cylinder is projected, or the velocity of sound, cannot, as our 



* This notion seems, in the first instance, to be borrowed from that 

 usually given in elementary books on mechanics ; where it is, in effect, 

 shown that if a series of equal and perfectly elastic bodies, such as cy- 

 linders, be placed contiguous, having their axes in a straight line ; and if 

 an impulse be given to either extreme cylinder, it will communicate an 

 equal impulse to the next, and this to the next, &c., till the whole series 

 be run over. But to this is joined the assumption, that the velocity with 

 which the impulse is propagated along the series is the same as the velo- 

 city of the first cylinder would have been, if alone, or projected by itself, — 

 a coincidence for which I know no reason, nor can I believe it to be pos- 

 sible. But admitting it were true, since, as we shall presently see, the 

 velocity of the projected cylinder must be proportional to the projecting 

 force, how does this consist with the rate of propagation being likewise 

 assumed to be ever the same in the same state of the medium ? Some, 

 perhaps, could tell us that the series of cylinders propagate the impulse, 

 as if they were so many isochronous pendulums ; but where is the proof? 

 and I may again ask, how such a determinate velocity of sound can be 

 aptly represented by the precarious velocity with which the cylinder may 

 be projected ? For, at all events, the calculus is conducted with reference 

 to a projected cylinder. But supposing the investigation were to relate 

 only to " the vibrations of a line of air," it would not be less objectionable ; 

 as, for instance, what could we make of the curious absurdity, to be 

 shortly noticed, of the small cylinders of air being compressed till ?w/?- 

 nitely dense, at the tiurn of each vibration ? 



