780 PROFESSOR JOHN G. M'KENDRICK 



mcnts, as shown in the diagram on Plate III., showing the pitch of the highest and 

 of the lowest tones. The highest tone is that of the piccolo stop of the organ = 4096 

 vibrations per second, while the lowest is the deepest tone of the contra-bassoon, the 

 vibration number of which is 27. 



28. Now the interesting question arises, which was discussed by Helmholtz with 

 the data then at his disposal, of how the ear appreciates this vast number of tones, and 

 how it is that we have the power of analysing compound periodic vibrations into their 

 simplest constituents. Further, it is well known that the tones we thus sift from each 

 other by analysis correspond to the simple vibrations that are shown by mathematical 

 physics to exist in the compound movement. Now we know that such an analysis can 

 be made by a suitably arranged acoustical apparatus, and it seems to follow that 

 probably in the cochlea we might find structures presumably capable of doing such 

 work. Without discussing possible theories of the cochlea, we may assume that it might 

 work in one of two ways. Either small vibratile bodies would be introduced between 

 the pressures sent into the organ and the filaments of the auditory nerve, or that 

 individual nerve fibres were directly excitable by waves of a definite wave length, and 

 that they thus had a selective action. It will be observed, however, that in either 

 supposition the individual nerve fibres would convey impulses corresponding to the 

 number of vibrations of the tone selected, as ably argued by Professor Rutherford,* and 

 it does not follow that the number of nervous impulses sent along the filaments of the 

 auditory nerve would be independent of the number of stimuli given to the specially 

 tuned vibratile bodies that are supposed, ex hypothesi, to be at their commencements.t 

 To aid, then, in discussing this question, it is of interest to ascertain whether, as a 

 matter of fact, and without considering their mode of action, there are a sufficient 

 number of bodies in the cochlea presumably capable of acting as intermediate structures. 

 I have collected data on this point both from observations and measurements made in 

 my own laboratory, and from the exhaustive account of the cochlea given by Retzius. 



1. Audible sounds =11,064 



Less those below 64 and above 4096= 110 



Leaving . . 10,954 



Say . . 11,000 



2. Distribution of audible sounds in six octaves used in music. 



— '— — = 1833 each octave ; — -"- = 153 each semitone. 

 d 12 



Musician's ear can detect difference of pitch in tuning a violin of -£ T semitone. 



153 



— — = 2 - 4 for each Jr semitone. 



64 



1. Nerve fibres in human auditory nerve, 14,000. 



Range of audibility, 11 octaves. 



14,0C0 



— y. — = 1273 fibres for each octave. 



f Rutherford, Address to British Association for Advancement of Science, 1887. 

 t Helmholtz, Sensations of Tone, trans, by A. T. Ellis, p. 221. 



