﻿190 Mr. R. Moon on the Theory of Sound. 



velocity of sound has been calculated to be 916*322 feet per 

 second*, the true velocity being about one-fifth greater. 



The discrepancy thus evinced between the results of theory 

 and of experiment was long supposed to have been removed by 

 the celebrated correction of (3) on account of temperature pro- 

 posed by Laplace, by means of which the theoretical and the as- 

 certained values of the velocity of sound were conceived to have 

 been brought within a very small fraction of each other. 



A most competent judge f has pronounced, however, that the 

 experimental processes of Clement and Desormes, and of Gay- 

 Lussac and Welter, upon which this supposed coincidence has 

 been founded, are worthy of no confidence whatever; "de sorte 

 que F explication de Laplace n'est encore aujourd'hui qu'une 

 hypothese, tres-ingenieuse sans doute, mais qui a besoin d'etre 

 confirmee par P experience." 



A further and decisive objection may be taken also to La- 

 place's correction in the form in which it is actually presented to 

 us on the following ground. 



The correction depends upon the assumption that " for very 

 small condensations the rise of temperature will be proportional 

 to the increase of density" (Encyc. Met. No. 72). 



Now if t denote the excess of temperature at the time t 

 above the mean temperature, it is clear that in any case of mo- 

 tion the value of t at a given time and place must be known, i. e. 

 we must have 



t= funct. (y, t) ; 



and if s denote the condensation and v the velocity at the time t 

 at the point whose ordinate is y, we shall have in like manner 



s= funct. (y, /), 



v= funct. (y, t). 

 Hence, eliminating y and / between the last three equations, we 

 have 



t= funct. (s.v); 



and since it is evident that t will not become infinite when either 

 s or v vanishes, we are warranted in concluding that, when the 

 motions are small, 



t = A . s + B . v, 



where A and B are constants ; and we are not warranted in assu- 

 ming that t=A\sJ, 

 as in effect has been done by Laplace and Poisson. 



* Encyc. Met. art. Sound, No. 66. 



f M. Regnault, see Mem. de VAcad. vol. xxiv. p. 40 (1862). 

 % The comparative success which had attended the bold hypothesis of 

 the uniformity of the law of pressure in the cases of motion and of equili- 



