174 Mr. R. H. M. Bosanquet on the Relation between the 



from the source : the sum of their absolute numerical values is 

 therefore to be taken. 



Consider a disk of air of section unity and thickness dx ; let 

 this be compressed, the section remaining the same, and its 

 thickness becoming dx—dy. Then the increment of pressure is 



■j- X atmospheric pressure x thermometric and specific-heat 



cix 



corrections. The atmospheric pressure x corrections for heat 

 = ?; 2 /0j where v 2 is the coefficient of the equation of the trans- 

 mission of sound, and p the mean density of the atmosphere. 

 Hence the pressure exerted by the compressed disk over and 



above the atmospheric pressure is •—■ .v*.p. 



(LX 



As the compression proceeds through the small distance Sdy, 

 an element of work is done 



and the sum of all the work done in the compression from dy=0 

 up to dy = dy is 



r 



* 



dy « . 1 % 2 2 



If we now assume that the sound in the tube consists of a simple 

 periodic vibration 



. 2tt 



y = asm — {vt — x) } 



we have for the work stored in any disk dx } at a distance x from 

 the end of the tube, 



? % - & * ?(?)* eos2 ¥ {vt ~ x)dsc - 



And the work stored in all the disks in a quarter wave-length, 

 or, if P be average potential work in unit of length, 



"■t=*mi~-?i«-^. 



A 



„ „ I -(^l + cos2.-^ (vt-x))dx, 



A 



i rx x r . 2tt, . /i 4 i 



