The Propagation of Sound. 223 



So that to determine A and B we have the equations 



2 dK .tdq .'i- dp 

 - 'T^ + A- -/ + A— -7- - 0. 

 q dx q- dx pq dx 



= 0. 



A/- 



v-'/e-/»--'-t^/y^ 



9 



where A and B must now be regarded as constants. This 

 result holds, whatever be the law of variation of pressure 

 and density, provided that their variation is slow. 



If /<=«p'>', which is the case for convective equilibrium of 

 the atmosphere, we see that the amplitude of vibration 



varies inversely as the th power of the density. 



4 



If /o<:p, we see in the same way that the amplitude of 

 vibration varies inversely as the square root of the density. 



In the case of a constant temperature, where the varia- 

 tion of density is caused by a constant gravitational force 

 g, the terms which we have neglected in equation (iv.), viz., 



\dx:^ Q dx dx) 



p dx dx 

 are actually zero. 



