CHAPTER VIII. 



WAVES IN AIR*. 



165. We investigate in this chapter the general laws of the 

 propagation of small disturbances produced in a mass of air (or 

 other gas) originally at rest at a uniform temperature, avoiding 

 such details as are more properly treated in books specially devoted 

 to the theory of Sound. 



Plane waves. 



We take first the case where the motion is in one dimension x 

 only. Let f be the displacement at time t of the particles which 

 in the undisturbed state occupy the position x. The stratum of 

 air originally bounded by the planes x and x -f dx is at the time t 



bounded by the planes x + j; , and x+ % + fl + -?-\ dx, so that the 

 equation of continuity is 



P ( 1 + ~dx) ==po W 



where p Q is the density in the undisturbed state. The equation 

 of motion of the stratum is 



and if we suppose the condensations and rarefactions to succeed 

 one another so rapidly that there is no sensible gain or loss of heat 

 in any stratum by conduction or radiation, the relation between p 

 and p is 



P = V p y (3). 



* This chapter was -written independently of the corresponding portion of Lord 

 R-ayleigh s Theory of Sound, the second volume of which did not come into the 

 author s hands until after the MS. of this treatise had been despatched to England 

 (October 1878). 



