Oil. L1V.] THEOKIES OF THE COCHLEA 749 



Difference-tones are produced when two tones of different pitch, 

 m and n, are sounded together. A tone having the pitch m minus n 

 is then heard in addition to the tones m and n : also a summation 

 tone of pitch m plus n may be heard, but with greater difficulty. 

 When m and n are nearly equal, a beating tone, instead of a difference- 

 tone, results, having a pitch scfmewhere intermediate between m and n. 

 If the difference between m and n is exceedingly small, this beating- 

 tone alone is heard. The frequency of the beats corresponds to the 

 difference in vibration-rates, m and n. Under certain conditions the 

 difference and summation-tones (which are collectively called combina- 

 tion-tones) exist in the air; their presence being demonstrable by 

 their re-inforcement before appropriate resonators. More generally, 

 however, they appear to be produced within the ear, i.e., they have 

 merely a subjective origin. 



The smallest perceptible difference in pitch between two successive 

 tones is about 0'2 vibrations in the middle region of the piano for 

 trained subjects. Practice effects extraordinary improvement, even 

 among the most unmusical. 



There can be little doubt that the cochlea is the organ specially 

 concerned in hearing. It first appears among vertebrata in certain 

 fishes as a very rudimentary structure. If the cochlea is removed 

 from dogs, they become deaf. The utricle and saccule are probably 

 only stimulated by gross disturbances in the surrounding media (see 

 the functions of the semicircular canals in Chapter XLIX.). 



There are two classes of theories of hearing, in both of which the 

 basilar membrane of the cochlea plays the essential part. 



The one class comprises the many "sound-picture" theories 

 which have been advanced in very various forms by Eutherford, 

 Waller, Hurst, Ewald, and Meyer. The entire basilar membrane is 

 supposed to vibrate either as a telephone plate, or as an elastic mem- 

 brane, different tones or combinations of tones giving rise to different 

 patterns of vibrations which are communicated to the hair-cells and 

 thence carried by the auditory nerve-fibres to the brain, where (in 

 Eutherford's theory) the analysis of these patterns is held to take 

 place. 



The other is the resonance-theory of Helmholtz, in which the 

 pitch of a tone, or the analysis of a complex sound into its constituent 

 tones, is determined not in the brain but in the cochlea. It depends 

 on the principle of sympathetic vibration. As is well known, if a 

 tone is sung in front of a piano (best with the loud pedal held down), 

 the string of the piano which is attuned to that tone will immediately 

 respond; another tone will elicit response from another string. So 

 in the cochlea the appropriate fibre of the basilar membrane is thrown 

 into vibration when the tone to which it is attuned reaches it. The 

 fibre thus stimulated affects the hair-cells above it, whence the 



