j\Ir. R. H. M. Bosauqnct on tlie T/ieory of Sound. 39 

 and 



.2 . 

 ' 



Another interpretation may be obtained by supposing the 

 tube to have a section equal to the surface of the hemisphere. 

 Under these circumstances we find / = ^'o, a result numerically 

 the same as that of our direct investigation. It is, however, 

 clear that the electrical resistance does not, in this case at 

 least, really represent any thing strictly analogous to r (which 

 we may call the "distance of centre of phase ") in the direct 

 investigation ; for the latter subsists in the case of the sphe- 

 rical divergence itself, but it is impossible to assign any 

 similar meaning to the electrical result while the spherical 

 form is maintained. In the case of unsymmetrical divergence 

 the law is different ; for the reflected energy diverges so that 

 only a portion of it reaches the initial surface. 



. According to the motion above investigated, on the con- 

 trary, the whole of the reflected energy returns in the reflected 

 stream ; a tube terminated by such a divergence would con- 

 sequently, in a frictionless fluid, be a perfect resonator, from 

 which no energy would be lost in steady vibration, so far as 

 this divergence is concerned. As, however, symmetrical sphe- 

 rical divergence cannot be actually set up with any approach 

 to accuracy, it is impossible to check the theary in this man- 

 ner. The trumpet-shaped mouths of w^ind-instruments, how- 

 ever, probably cause some approximation to this type of motion. 

 To allude only to the question whether sound varies inversely 

 as the square of the distance, we notice that, under the con- 

 ditions of spherical divergelice with great wave-length, the 



total energy per second a ■^; consequently the energy per 



second through unit surface GC ^, or oc-x. But at sfreat 



distances from the source, or when the distance is great com- 

 pared vv^ith the wave-length, the motion is that of an ordinary 

 transmitted wave-system whose total energy per second through 

 surface S is constant ; so that at such distances the energy per 

 second on unit surface does vary inversely as the square of 

 the distance. 



In the next note I shall attempt to deal with unsymmetrical 

 divergence, such as that from the ends of organ-pipes, and 

 shall discuss the experimental treatment of this part of the 

 subject. 



