168 BELL SYSTEM TECHNICAL JOURNAL 



the vibration is greater than anywhere else. Our postulate is that 

 only those nerves are stimulated which are at the particular parts of 

 the membrane vibrating with more than a certain critical amplitude; 

 and that we judge the pitch from the part of the membrane where 

 the nerves are stimulated. According to this conception, the varia- 

 tion with frequency of the minimum audible intensity is due prin- 

 cipally to the variation with frequency of the transmission efficiency 

 of the mechanical system between the auditory meatus and the 

 basilar membrane. Pure tones of equal loudness correspond either 

 to equal amplitudes or to equal velocities of vibration of the basilar 

 membrane or to some function of the two. Whatever is assumed, 

 the dependence of the minimum audible intensity upon frequency 

 for the ear can be explained entirely by the vibrational character- 

 istics of the ear mechanism. For the sake of clearness it will be 

 assumed that equal amplitudes of vibration of the basilar membrane 

 correspond to equal sensations. For loud pure tones, there are 

 several regions of maximum amplitude on the membrane, corre- 

 sponding to the tone and to the harmonic introduced by the non- 

 linear response of the middle ear, the latter maxima increasing very 

 rapidly as the stimulation increases. 



It is a strange thing that the phenomenon of the masking of tones 

 which, as stated in the beginning, has been considered by some to 

 be so fatal to any resonator theory, is the very thing that has fur- 

 nished experimental data which makes it possible to calculate the 

 vibration characteristics of the inner ear. Such a calculation must 

 be based upon assumptions which will be uncertain, but will seem 

 reasonable. It is not my purpose to discuss those here, but I shall 

 give only the final result of such a calculation made by Mr. Wegel 

 and Mr. Lane of our laboratories. At the bottom of Fig. 11, the two 

 curves show the amplitude of vibration of different portions of the 

 basilar membrane for the two frequencies 400 and 1,200 cycles. For 

 purposes here these curves may be considered to be simply illus- 

 trative. This membrane has a length of 31 mm. and a width of .2 mm. 

 at the base and .36 mm. at the helicotrema end. The x-axis in this 

 figure gives the distance in millimeters from the oval window and 

 the v-axis gives the amplitudes of vibration in terms of the amplitude 

 corresponding to the threshold of audibility. The loudness of the 

 stimulating tones in both cases is 80 units. It will be seen that the 

 maximum response for the high frequencies is near the base of the 

 cochlea, while that for the low frequencies is near the helicoptrema. 

 It will be noticed that the amplitude of the membrane has several 

 maxima corresponding to the subjective harmonics. 



