Lord Rayleigh's Acoustical Observations. 461 



stalk, the necessary curvature of the paths would give rise to 

 an unbalanced centrifugal force tending to set the sounding- 

 board in vibration. The force thus arising is indeed of the 

 second order, and might probably be neglected, were it not 

 that the apparatus is especially suited to bring it into pro- 

 minence. 



In order to test the soundness of this view as to the origin 

 of the octave, the following experiment was contrived. A 

 256 tuning-fork was screwed on to a resonance-box intended 

 for a 512 tuning-fork, and therefore approximately in tune 

 with the octave of the first fork. When a powerful vibration 

 was excited by means of a bow, the octave sound was predomi- 

 nant, and but little could be heard of the proper tone of the 

 fork. In order to place the two sounds on a more equal foot- 

 ing, a resonator, consisting of a bottle tuned by pouring water 

 into it to a frequency of 256, was brought near the ends of the 

 vibrating prongs. By adjusting the distance it was easy to 

 arrange matters so that at the beginning of the vibration 

 neither sound had a conspicuous advantage. But, as the am- 

 plitude of vibration diminished, the graver tone continually 

 gained on its rival, and was left at last in complete possession 

 of the field. The purity of the remaining sound could be 

 tested at anytime by the perfection of the silence obtained by 

 removing the air-resonator. This arrangement may be recom- 

 mended to any one who wishes to practise his ears in hearing 

 octaves. 



From the above experiment (in which, if desired, the ear 

 may be replaced by Konig's manometric flames), it appears 

 that the octave sound is to be attributed to a motion of the 

 second order, which is rendered important by the peculiar iso- 

 lation of the motion of the first order. The harmonic sounds 

 heard when suitably tuned resonators are presented to the free 

 ends of the prongs, though also dependent on orders of the 

 motion higher than the first, have a somewhat different origin. 



Influence of a Flange on the Correction for the Open End of 



a Pipe. 



In theoretical investigations* as to the amount of the cor- 

 rection to the length of an open pipe due to the inertia of the 

 external air, it has been usual, for the sake of facilitating the 

 calculations, to suppose that the open end is provided with an 

 infinite flange. Even with this simplification no exact solution 

 of the problem has been obtained. It has been proved, how- 

 ever, that, provided the wave-length be sufficient in relation 



' * Helmholtz, Crelle, 1860. Also a memoir by myself " On Eesonance," 

 Phil. Trans. 1871. 



