Mr. R. H. M. Boscanquet on the Theory of Sound. 217 



(It is necessary to take care and arranoe the tube in the most 

 advantageous position for hearing, which is with the two ends 

 equidistant from the head. If the tube is held upright with 

 one end near the face, no response will be heard from it at all.) 

 If the openings are then partially covered, so as to bring both 

 resonator and tube into tune with the fork, the maximum re- 

 sonance is also about the same in both cases. 



The response in the case of a minor third is faint but quite 

 audible ; it is not inconsistent with the supposition that it is 

 in amount ^^ of the maximum response. Now, if the loss of 

 energy is equal in amount to ^ the whole store in each vibra- 

 tion, according to the preceding reasoning it would take a 

 little over 3 vibrations to diminish the store to ^^ (for 3 

 vibrations would diminish it to ^). This would correspond to 

 the 7th step of Helmholtz's scale, which is as follows (/. c.)\ — 



Difference of pitch which Number of vibrations after 



reduces sympathetic vi- which intensity of tone (? energy 



bration to -^q. of vibration) reduces to -^q. 



7. Minor third. 3*17 



We may assign both our experimental and theoretical results 

 to this case without substantial discordance_, considering the 

 small degree of accuracy of the estimations. 



It only remains to give some account of the experimental 

 determination of the position of the centre of phase. In 

 Helmholtz's memoir in CorMe, Ivii., Wertheim's results are 

 stated as follows: — 



Mean for pipes open at both ends = '66311, the determina- 

 tions ranging from '56 R to '82 R. 



Mean for pipes closed at one end =-746R, the determina- 

 tions ranging from •64R to "86 R. 



I have to thank Lord Rayleigh for lists of the Wertheim 

 determinations, with the numerical results reduced to the pre- 

 sent form. These accord substantially with the above account, 

 making the means •665R for open pipes and '7 66 R for stopped 

 pipes. The discordances of separate experiments are greater 

 according to these lists than according to Helmholtz's account. 



The open pipes considered are plain cylinders, not organ- 

 pipes; and the datum to w^hich the number refers is the cor- 

 rection to the length for one open end, the same quantity that 

 I call the distance of the centre of phase of the reflected Vibra- 

 tion from the end of the pipe. 



The results of Zamminer, also quoted by Helmholtz, are 

 rather wild. They appear to show a diminution of the cor- 

 rection with the wave-length, and vary from '85 to "5 R for 



