218 Mr. R. H. M. Bosanquet on the Theory of Sound. 



open pipeSj and from 1*3 to '38 R for stopped pipes. Helm- 

 holtz assumes in this memoir that his solution for the case of 



rrr 



a flange (hemispherical divergence), which is j( = '785)R, 



agrees sufficiently well with the experimental results. 



Lord Rayleigh noticed that the effect of a flange could be 

 determined experimentally, and has recently determined it at 

 •2R. I have determined it at -25 R. If we admit 'SR as 

 the value of the correction for hemispherical divergence (in- 



TT 



termediate value between j of Helmholtz and "82 of Rayleigh), 



we have '55 R as the value deduced from the hemispherical 

 case supposed known. (I do not express a decided opinion 

 as to the logical cogency of the old investigations ; it appears 

 to me to fail, if the considerations I have urged concerning 

 the form of outward flow be admitted.) 



I now come to my own determinations of the corrections 

 for open ends. The question resolves itself entirely into one 

 of Tonometry ; and after the light recently thrown by Mr. 

 Ellis's indefatigable comparisons on the errors of the standards 

 in ordinary use, it is not astonishing if the tonometry of the 

 old experimenters can now be improved on. The only expe- 

 riments I shall cite here were made after some experience had 

 been gained ; they were all carried out by comparisons with 

 forks which T copied myself from Appun's tonometer at South 

 Kensington. I do not, however, cite them as final. The 

 error of the transfer to the forks, and of any subsequent alte- 

 ration (to which forks are known to be liable), though small, 

 can still be avoided. If at some future time I am able to em- 

 ploy a tonometer under such circumstances that I can myself 

 verify it and then use it directly, I am satisfied that the dis- 

 cordances still outstanding may be further reduced. 



The comparison of notes was made in all cases by blowing 

 short discontinuous jets of air across the open end of the pipe. 

 The pipe is not actually made to speak; but as the disturbance 

 subsides a faint sound, not clear, but of perfectly definite pitch, 

 is emitted, which is due to the vibrations of the resonator as it 

 dies away in its own pitch. 



If I come at any future time to the discussion of the 

 theory of the speech of organ-pipes, it will be seen that 

 the existence of a steady vibration generally (not always) 

 involves a departure from the natural pitch of the pipe. 

 But it is known that the pitch in which a vibrating body 

 left to itself dies away is, for all practical purposes, the same 

 as the natural pitch (note of maximum resonance). A good 

 way of satisfying one's self that the note thus obtained is in- 



