Mr. J.J. Waters ton on the Theory of Sound. 493 



Thus we have u^ = Hy, or the velocity is that produced by gravity 

 in a body falling through iH. [Strictly, the square velocity of 

 air-molecules must be six times this, because the above calculus 

 only takes account of the action in one of the six rectangular 

 directions of space.] 



To trace the influence of the barometer or weight of the imi- 

 form atmosphere, we may suppose the weight of M doubled and 

 A. reduced one-half: this leaves H.and v unaltered; so that if 

 the density of air increases as the weight of the uniform atmo- 

 sphere, the velocity of sound is unaffected by the barometer. If 



with M constant the density represented by - diminishes, H 



must increase in the same ratio, and thence v^ =\, or the volume 

 under constant pressure as the square molecular velocity, — which 

 conforms to Dalton and Gay-Lussac's law, if v^= temperature 

 from zero of gaseous tension. 



If we view these relations in another elastic fluid, where the 

 weight of the molecule is twice that of air, M being unaltered, 

 and the number of molecules in a unit volume also the same as 

 with air, we have H inversely as m, or one-half the height of a 

 uniform atmosphere of air, and v^ reduced in the same propor- 

 tion ; also the velocity of sound reduced inversely as the square 

 root of the molecular weight or specific gravity of the gas. 



To explain the increase of temperature that arises from sud- 

 denly condensing air, we may imagine an elastic ball traversing 

 a vertical between two horizontal plates and striking alternately 

 against them. Those plates being also considered as perfectly 

 elastic, the velocity of the ball will continue uniform without its 

 motion being impaired. If we now suppose the distance between 

 the plates to be gradually diminished by one of them assuming 

 a velocity incomparably less than that of the ball, the ball will, 

 each time it strikes this advancing plane, receive an increment 

 to its velocity, and thus to its vis viva. 



Let V represent the velocity of the ball, B the distance between 



the planes, - the velocity of the plane. The number of impacts 

 upon the advancing plate in a unit of time is ^. The velocity 



after one impact has increased from y to u-f _, and the square 



velocity from v^ to u^H , the increment being — of the square 



velocity ; at the same time the decrement of space is — (the space 

 moved over by the plate in a unit of time) divided by ^ ; this 



