PHYSICAL MEASUREMENTS OF AUDITION 167 



The theory of maximum amplitudes was first put into definite 

 form by Gray in 1899. 69 It assumes that the position of maximum 

 amplitude of the basilar membrane varies with the pitch of the stimu- 

 lating tone. Although a considerable portion of the membrane 

 vibrates when stimulated by a pure tone, the ear judges the pitch 

 by the position of maximum response of the basilar membrane. 

 Roaf has shown that some action of this sort must take place due to 

 the dynamical constants involved. 61 It is an amplification of this 

 theory that I desire to propose as the one which most satisfactorily 

 accounts for the facts. 



When a sound wave impinges upon an ear-drum, its vibrational 

 motion is communicated through the middle ear (Fig. 11) by means 

 of the chain of small ossicles (malleus, incus and stapes) to the oval 

 window. Here the vibration is communicated to the fluid con- 

 tained in the cochlea. If the pitch of the tone is low, say below 20 

 vibrations, the fluid is moved bodily back and forth around the 

 basilar membrane through the helicotrema, the motion of the mem- 

 brane at the round window and the oval window being just opposite 

 in phase, the former moving inward while the latter moves outward. 

 For very high frequencies, the mass reactions of the ossicles and the 

 fluid are so great that very little energy can be transmitted to the 

 cochlea. For example, when the elastic forces are negligible it re- 

 quires a force 10,000 times as large as produce the same amplitude 

 of vibration at 10,000 cycles as that required at 100 cycles. For 

 intermediate frequencies the mass reactions, the elastic restoring 

 forces and the frictional resistances which are brought into play 

 are such that the wave is transmitted through the basilar membrane 

 causing the nerves to be excited. 



It is thus seen that the upper and lower limits of audibility are 

 easily explained. When the forces upon the drum of the ear or 

 walls of the ear canal are large enough to excite the sensation ,of 

 feeling and the pitch of the tone is either too low or too high to cause 

 any perceptible vibration of the basilar membrane, we are beyond 

 the lower or upper limit of audibility respectively. At frequencies 

 between these limits, the vibrational energy is first communicated 

 to the fluid in the scala vestibuli and then transmitted through the 

 two membranes into the fluid of the scala cochlea. As the basilar 

 membrane transmits the sound wave it takes up a vibration ampli- 

 tude which stimulates the nerve fibres located in it. The entire mem- 

 brane vibrates for every incident tone, but for each frequency there 

 is a corresponding spot on the membrane where the amplitude of 



