38 Dr. Schroder van der Kolk on the Velocity of Sound. 

 We have therefore 





where $ is the quantity by which the molecules approach, ex- 

 pressed in terms of their original distance, and is therefore 



V —V, 

 = — Q== — -. Substituting this value in the above equation, we get 



V 



* V -Vi AV 



AV , vfy + lWAVy (^ /AV , /AV\« \ 



AV 

 V 



7(7 + 1) AV . AV 



=, y + -TT2- v--- 1- vr 



AV 



Neglecting the higher powers of y—, this gives 



and hence 



and by substituting this value for 1 +# in equation (1), 



or, by binomial development of the second factor, 



V' 



ffU/3 J", , 7(7±1)=? AV \ /ox 



~"*-\ + ^Tt^'^J' " () 

 Tf we neglect AV, we obtain the common formula, which is 

 therefore to be regarded as the first term of the series. 



In deducing this formula, we have supposed that the crest of 

 the advancing wave was foremost; but there is no difficulty in 

 seeing that the formula still remains applicable if the trough of 

 the wave goes first. The propagation of the wave is the propa- 

 gation of the motion of the particles of the air ; and this is oc- 



