486 Mr-. J. J. Water ston on the Theory of Sound. 



whole static force of repulsion between two particles at the di- 



H 

 stance \. This force having to support the weight of — par- 



tides (H being the height. of a uniform atmosphere), - repre- 



TT A. 



sents the force —-£/, viz; a force that in one second is capable of 



• . fi 

 communicating a velocity of — ^ feet per second. 

 A. 



To obtain the value of the initial force acting on particle B 

 when it is at b, we have the following proportion : 

 11 1 H s^H /,r\2 



The time (t) taken by a particle to traverse 21, with this force 

 diminishing as the distance from the centre of the semicircle, is 

 the same as the time required for one oscillation of a pendulum 

 whose length is /, if subject to an influence of gravity equal to 

 this force, and is the same as the time taken by the pulse to 

 travel through iL. By the law of the pendulum, t is equal to 

 TT multiplied by the square root of quotient of length of pen- 

 dulum by force of gravity, hence 



and the velocity of the pulse per second is \^ Hff. 



This supposes Mariotte's law maintained ; but the experiments 

 made at the suggestion of Laplace, proved that for rapid com- 

 pressions the elastic force increases in a higher ratio than the 

 density ; and for small increments of density, the correspondent 

 increments of elastic force are very nearly ^ those computed on 

 the hypothesis that Mariotte's law is maintained ; that is, as if 



4H 



the repulsive force of a particle supported the weight of ^ v 



O A. 



particles : hence Newton's theorem for the velocity of sound in 

 elastic fluids is strictly represented by V^Hff. 



The numerical results from this formula, taking Itegnault's 

 data, compared with observations made at low temperatures (so 

 that the influence of aqueous vapour should be avoided), show a 

 diflPerence at most of about ^\, or as if ^ should be augmented 

 j'^th part. Thus no objection to Newton's theory can well be 

 made on the ground of its not according with observation, as no 

 theory can be expected to embrace all the circumstances that may 

 affect the result ; e. f/. the repulsive force may not emanate from 

 the centre of the particles, so that the size of the particles may 



1 



