﻿Mr. R. Moon on the Theory of Sound. 



191 



But the objections to the principle upon which equations (2) 

 and (3) have been obtained are not confined to the failure of the 

 latter equation to give a calculated velocity of sound reconcilable 

 with the experimental velocity. 



The principle in question, viz. that the equation p = a 2 p holds 

 in all cases irrespective of the state of rest or motion of the fluid, 

 is a pure assumption, having no basis of fact or argument to rest 

 upon. This will appear most clearly as follows. 



In any case of motion under the circumstances we are consi- 

 dering, the pressure at a given point at a given time must be 

 known : the same may be said of the velocity ; the same of the 

 density ; so that we must have 



v— funct - (y>*)> 



v= funct. (y } t), 



p = funct. (?/, t). 



Eliminating y and / between these three equations, and solving 

 the result with respect to p, we shall get 



p = funct. (v, p) (4) 



It is evident that this last equation affords no more proof of 

 the truth under all circumstances of the equation 



p = a'p 

 than the fact that the series 



(5) 



A + A^ + A 2 # 2 + &c. in inf. 



becomes A when x = affords that the same series has the value 

 A whatever be the value of x. 



If the substitution for the general equation (4) of its parti- 

 cular case (5) enabled us to escape from difficulties which other- 

 wise are insurmountable, the continuing to adopt such substitu- 

 tion could be readily understood. The truth is, however, that 

 the exact contrary is the fact. 



All efforts hitherto have failed to elicit a solution of the pro- 

 blem of adequate generality from (2), which is what (1), the 

 true indisputable equation of motion, becomes when (5) is taken 

 to represent the law of pressure, the most general solution hi- 

 therto so obtained (that of Poisson) involving only one arbitrary 





briura naturally tempted Laplace to hazard the corresponding and equally 

 unwarranted assumption with regard to the temperature. At a time like 

 the present, when the principles of the mechanical theory of heat are gene- 

 rally diffused and recognized, a suggestion that the law of temperature in 

 a fluid is irrespective of the fluid's state of rest or motion could hardly be 

 entertained. 



