Mr. R. H. M. Bosanquet on the Theory/ of Sound. 133 



other such pair is -555, '53. Hence we infer that a flange 

 which imposes hemispherical divergence affects the numerical 

 result by altering the form of motion near the source, and 

 that the difference between the results of various forms at 

 great distances is insignificant if the form near the source is 

 constrained to be the same. 



Secondly, according to the law of reflexion as from an image 

 of the source, 



C"^ d^ -f^^S 



- 'ft '^ . ; n 



8" 



4SJ 



We can determine an approximately conical form of expansion 

 in this case which agrees fairly with the observed conditions, 

 as far as the position of the centre of phase and angle of diver- 

 gent cone are concerned ; but the part of the observed pheno- 

 menon which consists of the flow of the surrounding air 

 towards the diverging cone is not truly represented ; and we 

 have seen that the hypothesis, of which the law is an expres- 

 sion, is not admissible. Assume 



S = 7r(a + Jcry, 



which represents a plane circle of radius a-\-kr ; this may be 

 represented as tracing out a cone of semivertical angle k. If 

 we then calculate r by the above formula, we find 



__ a 



Ascribing the known values to r, we find 



r. tan~^ k, 



•8a 10° 8' 



•55 a 14° 35' nearly, 



which correspond to cones of about 20° and 29° vertical angle 

 respectively. This corresponds fairly with experiment, and 

 shows that we are approximating to the form of function which 

 is capable of representing the observed facts. 



Let us now turn to the state of things experimentally found 

 in the case of outward flow. We shall, as above, put 



but from S we shall suppose the reflected rarefaction to diverge 

 in the manner represented by drawing spheres from the dis- 

 turbed points as centres, and we consider the surface S thus 

 covered after divergence through r. The wave-front on circle 



