32 Mr. R. H. M. Bosiinquet on the Theory of Sound, 

 The total energy per second across the surface is 



pi 



^SV^ 



or 



2 -B~ S '''^' 

 that of each of the component streams mto which it is above 

 decomposed being half this amount^ = ^, where 



•^^^ 2 0* 



Consider the divergent stream which starts from Sq, and has 



the energy per second ^ as it passes through each surface S. 



As the divergence proceeds elements are reflected ; and the 

 element reflected in expansion from S to S + f/S is 



K.ZS 



These reflected elements would probably diverge in turn but 

 for the symmetry ; all we can say here is that the actual mo- 

 tion is represented by treating them as forming a convergent 

 stream. 



Summing the reflected elements, then, from any value of S 

 up to an infinite value, we have for the total reflected energy 



(numerically) ^, the same value as that of the divergent stream 



at the point. 



Hence the motion of spherical divergence in air is com- 

 pletely represented by decomposing the motion into a diver- 

 gent and a convergent stream of energy, the latter of which is 

 made up of the reflected elements of the former. And the 

 mechanism by which the maintenance of the flow is continued 

 when once started, as proved above, is the suction exerted at 

 the source S^ by the reflected convergent stream of energy, 

 which is accompanied with rarefaction. 



This really amounts to making a supposition that the con- 

 straint terminates at Sq, a supposition which cannot be actually 

 realized, involving a Bernoulli reflexion of the rarefaction into 

 pressure at Sq. Supposing a pipe to be terminated by two such 

 spherical divergences, the air flowing inward at the one end and 

 outward at the other, the convergent rarefaction would travel 

 along the tube to the other end, whence issuing as a divergent 



