Prof. J. D. Everett on Resultant Tones. 201 



But z may be regarded as a random magnitude, hence it is 

 infinitely improbable that its different values exactly fulfil the 

 condition J z cos 0dd—O. Therefore the new A is finite ; and 

 similar reasoning shows that the new B is finite. 



If all the ordinates were changed in one uniform ratio, A 

 and B would remain zero, and no new constituent would be 

 introduced ; but any other change, unless specially planned 

 to avoid introducing A and B, is practically certain to give 

 A 2 + B 2 a finite value. 



5. I maintain that such a change is effected in the form of 

 sonorous waves during their transmission from the external 

 air to the sensory fibres by which we distinguish pitch. The 

 waves are transmitted first from the air to the drumskin, then 

 through two successive levers, the hammer and anvil, to the 

 head of the stirrup, while the foot of the stirrup sits upon the 

 membrane of the oval window, and passes on the vibrations 

 through the membrane to the liquid on the other side in 

 which the sensory fibres are immersed. The levers turn upon 

 ligamentous fulcra, and have rubbing contact with each other. 

 The wave-form cannot run the gauntlet of all these trans- 

 missions without being to some extent knocked out of shape. 

 It is much as if a very accurately drawn curve, representing 

 the original wave-form, were copied and recopied, five times 

 in succession, by five different pantagraphs not very firm in 

 their connexions. The final copy so obtained would be sure 

 to exhibit sensible departures from the original. 



6. It appears likely that the chief seat of the disturbing 

 actions in the ear is the junction of the hammer and anvil. 

 " When the drumskin with the hammer is driven outwards, 

 the anvil is not obliged to follow it. The interlocking teeth 

 of the surfaces of the joint then separate, and the surfaces 

 glide over each other with very little friction "** Such action 

 is likely to introduce derangement, increasing generally with 

 the excursions of the drumskin, but not expressible as a defi- 

 nite function of the ordinates of the wave-curve. For a 

 given pressure on the drumskin, the pressure communicated 

 to the liquid in the cochlea will vary according to the relative 

 position and relative motion of the two portions of this joint. 



7. The principal resultant tone due to these actions is likely 

 to be that which corresponds to the complete period of the 

 actions, in other words the highest common fundamental of 

 the two primaries, or what old writers called the " grave har- 

 monic" This will not be the same as the u first difference- 

 tone " unless the ratio of the two primaries is of the form 



* Ellis's * Helmholtz/ p. 133, 2nd edition. 

 Phil Mag. S. 5. Vol. 41. No. 250. March 1896. P 



