﻿198 Mr. It. Moon on the Theory of Sound. 



to the right with the velocity a(l—e) represented by the equations 



(l+e)v=iY{x-a(l-e)t\ + ^£^ [l-f{x-a(l-e)t}, 



as={\-\-e)v) 



while to the left will be propagated, with the velocity «(l + «), a 

 disturbance represented by 



Cl-*)«=*F{«+«(1 +e)t\ -Bj^VX -/{»+«(! +«)<}]> 



— as —(l—e)v. 



It only remains, therefore, to determine under what circumstances 

 (12), and under what circumstances (18) is to be taken as the 

 equation of motion. 



Comparing (11) with (1), we get 



J) dx — dx dx dx J 

 or, since 



dx"J)(l+s)~ l S > 



* = ±2D«£+D^ 



ax dx dx 



.-. p= + 2Daev -f Da?s + const. 



= ±2T>aev + T>a>{l+s). .... (19) 



Now it is obviously impossible that in any particular case of 

 motion p should have two values. We have therefore to deter- 

 mine in each particular case of motion which of the above values 

 is to be taken. 



Suppose that we have at a given epoch, in two different tubes, 

 exactly the same kind of disturbance, with this difference, viz. 

 that the velocity at each point of the one is in the opposite di- 

 rection to that at the corresponding point of the other. At a 

 point in each for which the values of v and s are identical except 

 as regards the sign of the former, it is clear that the pressure 

 must have the same absolute value; but it is equally clear that 

 the expression for the pressure must differ in the two cases. 



If in the one case, the particle-motion being to the right, and 

 x being measured positively in the same direction, the pressure 

 is represented by 



