Mr. R. H. M. Bosauquet on the Theory of Sound. 127 



I failed to get any distinct difference in the vertical angle 

 with and without the flange, though it is clear some such dif- 

 ference must exist ; I also failed to ascertain any dependence 

 of the vertical angle on the pressnre or velocity of issue. Pos- 

 sibly with an ap})aratus adapted for accurate measures differ- 

 ences of this kind may be shown to exist. 



Secondly, as to air sucked into the orifice of the pipe. I 

 have made but few experiments in this case ; but there can be 

 little doubt that the currents all tend towards the orifice, and 

 that at a moderate distance the supposition of spherical con- 

 vergence is approximately applicable to the case without a 

 flange, and that of hemispherical convergence to the case with 

 a flange. 



It would appear that the character of the motion is quite 

 difl^erent in the two cases. In the case of the issuing air we 

 may regard the motion approximately as being at first the 

 mere impact of a series of disks travelling forward ; the amount 

 of divergence I am unable to give any theoretical account of. 

 But when this divergence is once established, it appears as if 

 the motion decomposed itself into two opposite streams of 

 energy — the divergent stream (pressures) travelling forward 

 through its cone, as in symmetrical sectorial divergence, 

 while the stream of rarefactions, having the constraint of the 

 symmetry removed, diverges through the sides of the cone 

 from every surface and gives rise to the observed currents in 

 the air outside the cone. In the case of suction or inward 

 flow, on the other hand, it would appear that the conditions 

 of symmetrical divergence of energy subsist in substance. 



We shall return later to the interpretation of these results, 

 and shall now proceed to the calculation of the ^^ centre of 

 phase " for cases of divergence supposed symmetrical. We 

 shall base these calculations on the construction of a wave- 

 front, in a manner somewhat analogous to the construction of 

 Huyghens in optics ; i. e. spheres with radius r are described 

 from all points of the source-surface So, and the external en- 

 velope of these spheres is treated as the wave-front. This 

 involves several hypotheses which are certainly not accurately 

 fulfilled ; at the same time it affords a sufficiently close ap- 

 proximation for many purposes to the state of things supposed 

 in the theory of Helmholtz. 



If in this case we suppose the disturbance uniformly distri- 

 buted over each wave-front, we have general conditions resem- 

 bling in their symmetry those of symmetrical spherical diver- 

 gence. Under these circumstances we may assume that all 

 the energy-elements are reflected back into the source Sq ; and. 

 we easily obtain values for the centre of phase fairly agreeing 



