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XXI. Correction to a Paper " On an Experimental Determina- 

 tion of the Relation between the Energy and Apparent Intensity 

 of Sounds of different Pitch." By R. H. M. Bosanquet, 

 Fellow of St. John's College, Oxford*. 



IN the paper above referred to it was sought to establish 

 directly, by experiment, the following relation : — " The ap- 

 parent intensity of a musical note is proportional to the mecha- 

 nical energy expended in the production of the tone, and in- 

 versely as the wave-length or periodic time." At the end of 

 the paper certain deductions were made from this law, with 

 reference to the relations connecting amplitude, pitch, and pe- 

 riodic time with apparent intensity. The writer has to acknow- 

 ledge with regret that the reasoning of this latter portion is 

 erroneous. The error does not seem to be very obvious, as no 

 one has yet pointed it out, to the writer's knowledge. It was 

 intended to wait until some measures could be completed by an 

 improved method, and to make a more complete communication. 

 But as the performance of this has been unavoidably delayed, 

 and the writer finds the erroneous result quoted as correct by 

 Dr. Mayer, in his interesting paper, Phil. Mag. Feb. 1873, it is 

 desirable that the mistake should be corrected at once. 



The error committed was precisely of the nature against which 

 a warning was given on the last page of the paper. It was 

 assumed that the energy of the vibration of the plate of air con- 

 sidered was identical with the total energy transferred through 

 the plate. The assumption was simply a non sequitur. The 

 following is believed to be correct. 



To find the total energy of the sound which crosses a given 

 plane section in one second, in terms of the amplitude and wave- 

 length. 



Let the sound consist of a succession of plane waves generated 

 at one end of a straight cylindrical tube having the given section. 

 The waves then traverse the cylinder without sensible diminution 

 of intensity, if we neglect the influence of the walls. Let the 

 delivery of the sound commence at the beginning of a second 

 and continue throughout the second, and suppose that the con- 

 dition of the air in the tube at the expiratiou of the second is 

 photographed. Then the sum of the potential and kinetic 

 energy of the disturbed air in the tube, through a length equal 

 to the velocity of sound per second, is the energy supplied from 

 the source in one second. 



First for the potential energy. This consists partly of com- 

 pressions and partly of dilatations, both of which are supplied 



* Communicated by the Author. 



