164 Prof. Barton and Miss Browning on the Resonance 



Of course there is a similar group of formulae corre- 

 sponding to (1*7) ; but it seems hardly necessary to write 

 them out, as the formula? (7*4) correspond most closely tx> 

 the problems of physical importance. 



The formula? (7*4) given above agree with Macdonald's 

 on writing 



* = 57' 



but it should be observed that his J is the reciprocal of 

 ours. 



Attention may be directed to the fact that in the formula? 

 (7'4), the vanishing of Z and 7 does not involve the vanishing 

 of the other components of force, in contrast to what wa& 

 proved in § 2 for the case of spherical polar coordinates. 



XI. The Resonance Theory of Audition subjected to Expe- 

 riments. By E. H. Babtok, F.R.S., and H. M. Browning. 

 M.Sc* 



[PJates II. & III.] 



1 THEORIES of audition have been recently under consi- 

 derable discussionf : indeed this controversial subject 

 appears to be of perennial interest. Helmholtz long ago 

 advanced his hypothesis of sympathetic resonance, and 

 supposed at first that the role of resonator was played by each 

 of the arches of Corti. This latter detail was afterwards 

 modified, the basilar membrane being then considered to act 

 somewhat like a set of resonators or harp strings. It was 

 shown that this was possible owing to its fibrous nature with 

 high lateral tension and relative slackness longitudinally. 

 There are of course difficulties in the hypothesis in matters 

 of detail. But this is only to be expected in the case of so 

 small a mechanism working at such high frequencies and 

 with such minute displacements. Indeed, there are difficulties 

 in any hypothesis, and that of sympathetic resonance seems 

 to deserve careful examination from a new standpoint. Some 

 anatomists have felt considerable difficulty in accepting it, 

 others accept it unreservedly. Some ot its critics have 

 obviously not quite grasped the meaning of the hypothesis, 



* Comrnuuicated by the Authors. 



t * Analytical Mechanism of the Internal Ear * : Sir T. YVrightson and 

 Dr. A. Keith. London, 1918. "The Internal Ear,'' Nature, Aug. 8, 

 1918. Letters in 'Nature.' Oct. 17 & 31, Nov. 7 & 21, Dec. 5 & 19, 

 1918, Jan. 9, 1919. " On Sir T. "YVrightson's Theory of Hearing-," by 

 W. B. Morton, Phvs. Soc. Proc. xxxi. Part III. April 1919. 



