492 Mr. J.J. Waterston on the Theory of Sound. 



of the theory; but it is difficult to limit these to one branch, all 

 the physical properties of elastic fluids being so interwoven with 

 each other ; and it is an admirable instance of the simplicity of 

 nature, that the cluster of elegant quantitative relations which 

 the physics of gases present, should flow from the constitution 

 assigned, which indeed is the simplest that it is possible to 

 imagine. . - ■ ■ 



The velocity of sound is liot affected by the height of the ba- 

 rometer, but it is sensibly influenced by a change of temperature. 

 This latter is to be looked for ; since the velocity of the particles 

 of air increases with the . temperature, the velocity with which 

 they convey pvxlses must increase in the same proportion : but 

 it is not so obvious that the height of the barometer or weight 

 of the atmosphere should have no effect either to accelerate or 

 retard. 



Let m be an elastic ball traversing the ver- 

 tical P M backwards and forwards from the 

 sphere, M, to the plane, P, the surfaces of 

 7n, M, and P being perfectly elastic. The 

 condition of permanence in the mean di- 

 stance of M from P requires that the im- j| 

 pacts of m upon M should have the effect of j 1 

 changing the velocity of M downwards into j 

 the same velocity upwards. Gravity affects p ' 

 M in the interval of time that elapses while 

 m descends from M to P and ascends from P to M ; during half 

 this time gravity is employed in destroying the upward motion 

 of M, and during the second half in producing the velocity 

 downwards with which it encounters m on its return, — m and M 

 thus meeting each other, and separating after impact with the 

 same velocity, but with directions reversed. 



The relation between the distance MP(=X,), the velocity of 



m{ = v), the weight of M( = ^"'■)> ^^^ ^^ '"j ^^ ^^U simple, and 



enables us to compute the absolute value of v. 



The time taken bv m to traverse MP is - part of a second ; 



and in this time gravity communicates to M the velocity - ff. 



From the law of elastic collision, two bodies impinging and 

 reflected back in the direction they came with unaltered veloci- 

 ties, must have their velocities inversely proportioned to their 

 masses, so that 



vm X Xn , 

 M : ?« : : u : Tf^ = 77 1/= -^ as above. 

 M H V 



