Psychophysical and physiological experiments have shown that a tone transmitted to the cochlea by bone conduction can be compensated by an airborne sound. From these experiments it has been deduced that the vibration pattern of the cochlear partition does not depend upon the path by which sound is transmitted to the cochlea. This hypothesis has been confirmed by direct observation of the vibration pattern in cochlea models and by measurements of cochlear microphonics. From both kinds of experiments attempts have been made to draw conclusions concerning the theory of cochlear dynamics.
In an effort to explain the fact that the vibration pattern of the cochlear partition is independent of the path by which the sound is transmitted to the cochlea, a mathematical analysis has been performed. First, by means of the hydrodynamic principle of continuity, it has been demonstrated that the vibration of the cochlear partition caused by a tone introduced into the cochlea either through the bony wall or through an artificial window can be canceled by a tone transmitted through the oval window, irrespective of the dynamic properties of the partition. Second, a general differential equation of hydrodynamic surface waves has been established, which shows that transverse waves are propagated along the cochlear partition every time there is a difference in pressure between the two sides. According to this equation, the wavelength is independent of the place at which the sound is introduced into the cochlea. Third, it has been deduced from Hamilton's principle of stationary energy that transverse waves in the cochlea must travel from the base towards the apex, irrespective of the location of the sound source. Hence, in agreement with the experiments, the mathematical analysis shows that the vibration pattern of the cochlear partition does not depend upon the way in which sound is transmitted to the inner ear. Furthermore, it shows that the introduction of sound through the bones or through an artificial window does not provide any new clues for the explanation of this pattern.
