﻿Mr. R. Moon on the Theory of Sound. 199 



then in the other case, the particle-motion being to the left, x 

 being measured as before, the pressure must be represented by 



p=— 2T>aev + Da*{l+s) } 

 and vice versa. 



The occurrence of the double sign in the value of p and in 

 the (11) is thus at once accounted for. Ir still remains to 

 be determined, however, whether, when the particle-motion at a 

 given point is to the right, the coefficient of v in the expression 

 for the pressure should have a positive or negative sign affixed 

 to it. 



Suppose that, the air being of uniform density and at rest, a 

 disturbance is suddenly impressed upon a limited portion of it 

 of this kind, viz. a velocity which beginning at zero gradually 

 increases till it attains the value v v and thence diminishes by the 

 same gradations till it finally vanishes, the density throughout 

 being unaffected. According to the formula (19), we shall have 

 under these circumstances, 



p = J)a Q ±2J)aev, 



i. e. the pressure will be either increased or decreased by the 

 impressed velocity. 



The sign to be attributed to the coefficient of v in the 

 last expression, equally with the numerical value of the con- 

 stant e, is a proper subject for experiment ; nevertheless I think 

 we may conclude with perfect certainty that the lower sign is to 

 be taken (in other words, that the effect of the impressed velo- 

 city is to diminish the pressure in the portion of the air affected 

 by it), on the following grounds. 



We have before us the following alternative. For the sake of 

 perspicuity, assuming that the particle-motion thus supposed to 

 be impressed tends to the right, we must either have the pres- 

 sure gradually increasing as we move from the left of the dis- 

 turbance till we reach its middle point, and thence gradually 

 diminishing until it again assumes at the right-hand extremity 

 the value of equilibrium, or else the pressure will diminish from 

 the left-hand extremity up to the middle point, and will thence 

 increase till it ultimately regains the value of equilibrium. 



But in either case we shall have in the first half of the dis- 

 turbance (beginning from the left) the particles in each element 

 flying from each other, the tendency, by reason of the impressed 

 velocity, being to expansion ; while in the second half the parti- 

 cles in each element are moving towards each other, the ten- 

 dency in this latter case being towards compression. 



