Plane Waves of Sound. 25 



h 



y 



2-kv y. number of vibrations per second. 

 If we take the number of vibrations to be 550 per 

 second, and the velocity of sound to be about 1 100 feet per 

 second, we obtain 



32-2 X 1-41 



so that 



thus 



•000012, 

 27r X iioo X 550 



•000006, 



v= yj \- (•000006)'^' 



cot0= - '000006, 



-T-^, - I + ~(-ooooo6)l 

 sin^f^ 2^ 



From these results we draw the following conclusions : 

 that when plane waves of sound are travelling through the 

 atmosphere and partially reflected at every part of their 

 course, the amplitude of the progressive part differs by a 

 few thousand-millionths of what it would have been if we 

 supposed that the wave progressed without the slightest 

 reflection ; and if, instead of considering the reflected waves 

 which occur at every part of the course for a number of 

 wave lengths, we considered the reflected wave as being 

 caused by a sudden change of density, then the amplitude 

 of the retrograde wave would be about a millionth part of 

 the progressive wave. 



The method employed above seems unnecessarily arti- 

 ficial, but it has enabled me to obtain a result in some 

 subsequent work which, I believe, is not only new, but 

 correct, viz., that when the atmosphere is also supposed to 

 be in a state of " convective " equilibrium the amplitude of 



y + I r 



a descending wave varies inversely as the power of 



the density. 



