Sound Waves hy the Cochlea. 351 



required to produce a definite movement in either direction 

 will be inversely proportional to the length of fibre extended, 

 i. e., Young's modulus, or 



stretching force per unit area -^ j , 2J 



extension per unit length for circular tibre s — ' 



If, on the other hand, the organ of Corti (including the rods of 

 Corti and the tectorial membrane) acts as a rigid structure, 

 the problem is similar to that of the bending of a bar, and 

 the force required to produce the same amount of movement 

 will be inversely proportional to the cube of the length 

 of the structure, i. e. } Young's modulus = 4FL 3 /<W 3 /. The 

 mathematical treatment of this problem is not possible because 

 we do not know the nature of the unions -nor the physical 

 properties of the structures concerned, but it is possible that 

 the variation in ease of deformation may be much greater 

 than is to be expected from the relative widths of the various 

 portions of the basilar membrane. The problem is further 

 complicated by the fact that the pectinate portion of the 

 basilar membrane must also be stretched, even if the organ 

 of Corti acts as a rigid bar. 



Thus we see that rapid variations in pressure will not be 

 able to set a long column of liquid in motion, but the 

 fenestra rotunda being at atmospheric pressure there will be 

 greater differences of pressure across the lower end of the 

 basilar membrane, with the result that the proximal end of 

 the basilar membrane will be deformed, thus stimulating the 

 hair cells at the proximal end of the cochlea. 



Slower variations in pressure will cause movement along 

 the scake without producing sufficient difference in pressure 

 to deform the proximal end of the basilar membrane. Some- 

 where along the basilar membrane the lower difference in 

 pressure will be sufficient to deform the basilar membrane, 

 with the result that the hair cells in that region will be 

 stimulated. 



Accordingly, it is evident that the impedance due to the 

 mass and friction of the perilymph will tend to produce 

 greater differences of pressure at the narrower end of the 

 basilar membrane with rapid changes, whilst slower changes 

 will cause lesser differences, so that the basilar membrane 

 will be moved at a wider part. 



Irregularities in the area of the scale will cause the 

 impedance to vary, so that certain ranges of frequencies will 

 be more accurately analysed than others. 



It must be pointed out that other factors, such as the mass 



