﻿194 Mr. R. Moon on the Theory of Bound. 



suppose, where it denotes an arbitrary function. Therefore 



and substituting these values in the equation of motion (7), we get 



2 d*y 



dx*' 



d u d u 

 and putting v = and D = p in the coefficients of , ' , -j-f-, as 



we may do when the motions are small, we get, observing that 

 dx~ p 



If we consider the case of a disturbance confined to a portion 

 of the tube defined by planes perpendicular to the axis, and in 

 which the law of continuity is preserved (that is, which offers no 

 sudden changes of velocity or density), it is clear that the values 

 of p at the boundaries of the disturbance will follow Mariotte's 

 law ; so that we shall have 



-(±S)-*- D =±*-(±Sr 



Substituting this value, (10) becomes 



df* -VD uldxdt dx l 



where a and D are known and a is an unknown constant ; or we 

 get, finally, for the approximate equation of motion, 



°-$*-£s-*% • • • • cm 



where e is a constant the value of which must be determined by 

 experiment. 



and 



