26 Mr. E. H. M. Bosanquet on the Theory of Sound. 



wliich sound actually passes over from the inside of a tube 

 into the surrounding air. The work was based on the modern 

 potential analysis ; and some of the chief difficulties in it were 

 overcome by giving to the various expressions the meaning 

 they would have had in the theory of electricity, and employ- 

 ing the results that belong specially to that theory. 



Lord Rayleigh treated important portions of the same sub- 

 ject in a paper in the Philosophical Transactions, 1871 (Mr. 

 Strutt "On Resonance"). The analysis s much simplified, 

 but it is essentially the same in principle as Helmholtz's. The 

 reference to electrical analogies is used freely. ^"'^ 



A paper by Grinwis (Pogg. Ann. 1877, No. 2, p. 276) goes 

 over that portion of the ground which refers to resonators ; it 

 does not appear to me to differ essentially in principle from 

 the papers already mentioned. 



When sound diverges from the end of a cylinder, the mo- 

 tion is such as it would be if the cylinder were made a little 

 longer and the process of divergence were disregarded. The 

 principal numerical result, the obtaining of which is the object 

 of theory, concerns the magnitude of the length supposed to 

 be added to the cylinder as the equivalent of the divergence. 

 The whole space considered is always supposed to have its 

 dimensions small compared with the wave-length. 



The electrical method is defective in the view it affords of 

 the actions which take place, in a manner which I will endea- 

 vour shortly to explain. 



In Bernoulli's theory of organ-pipes, the hypothesis is 

 made that the change from the constraint of the pipe to a 

 condition in which no remains of constraint are to be perceived 

 takes place suddenly at the point where the wave- sj^stem leaves 

 the pipe. This theory is useful as a first approximation, but 

 entirely fails to give any idea as to the connexion between the 

 motion in the pipe and that in the surrounding air. It is, 

 however, evident that the divergence which takes place may 

 be conceived of as sending back to the pipe a series of reflected 

 impulses, instead of the single reflected impulse which returned 

 from the open end of the pipe according to the Bernoulli 

 theory, and that these elementary impulses, coming from dif- 

 ferent distances, may be together equivalent to a single 

 reflected impulse from a point at a little distance from the end 

 of the pipe. The position of the source of this equivalent 

 disturbance may be called the '^centre of phase" of the 

 reflected wave-system ; and in its relation to the series of ele- 

 mentary systems, as well as in the formulae by which it may 

 be found, it has a strikino- analoo-y to the centre of Cfravitv of 

 a svstem of material points. 



