34. HISTORY OF ACOUSTICS. 



mass. For instance, it is not easy at first to conceive the waters of a 

 great river flowing constantly down towards the sea, while waves are 

 rolling up the very same part of the stream ; and while the great ele- 

 vation, which makes the tide, is travelling from the sea perhaps with 

 a velocity of fifty miles an hour. The motion of such a wave, or eleva- 

 tion, is distinct from any stream, and is of the nature of undulations in 

 general. The parts of the fluid stir for a short time and for a small 

 distance, so as to accumulate themselves on a neighboring part, and 

 then retire to their former place ; and this movement affects the parts 

 in the order of their places. Perhaps if the reader looks at a field of 

 standing corn when gusts of wind are sweeping over it in visible waves, 

 he will have his conception of this matter aided ; for he will see that 

 here, where each ear of grain is anchored by its stalk, there can be no 

 permanent local motion of the substance, but only a successive stooping 

 and rising of the separate straws, producing hollows and waves, closei 

 and laxer strips of the crowded ears. 



Newton had, moreover, to consider the mechanical consequences 

 which such condensations and rarefactions of the elastic medium, air, 

 would produce in the parts of the fluid itself. Employing known laws 

 of the elasticity of air, he showed, in a very remarkable proposition, 6 

 the law according to which the particles of air might vibrate. We 

 may observe, that in this solution, as in that of the vibrating string 

 already mentioned, a rule was exhibited according to which the parti- 

 cles might oscillate, but not the law to which they must conform. It 

 was proved that, by taking the motion of each particle to be perfectly 

 similar to that of a pendulum, the forces, developed by contraction and 

 expansion, were precisely such as the motion required ; but it was not 

 shown that no other type of oscillation would give rise to the same 

 accordance of force and motion. Newton's reasoning also gave a 

 determination of the speed of propagation of the pulses : it appeared 

 that sound ought to travel with the velocity which a body would 

 acquire by falling freely through half the height of a homogeneous 

 atmosphere; "the height of a homogeneous atmosphere" being the 

 lieight which the air must have, in order to produce, at the earth's 

 surface, the actual atmospheric pressure, supposing no diminution of 

 density to take place in ascending. This height is about 29,000 feet ; 

 and hence it followed that the velocity was 968 feet. This velocity is 

 really considerably less than that of sound ; but at the time of which 



6 Princ. B. ii. Prop. 48. 



