A NEW THEOEY OF HEAEING. 341 



and we have to consider whether the results of such 

 passing as set forth in the previous problem will be brought 

 about at all these points or only at some of them ; and if 

 only at some, at how many, and at which. 



It has already been shown that the effect of the 

 mechanism of the middle ear is to "level down" the 

 amplitudes of the displacements brought about by notes 

 of very different intensities, very intense (i.e. loud) sounds 

 being prevented by this mechanism from producing a 

 very much larger displacement of the fenestra ovalis than 

 is produced by a much less intense sound. Pure tones 

 of the same pitch but of enormously different intensity. 

 are by this mechanism caused to give rise to displace- 

 ments of the ovalis which though greater for intense 

 sounds than for weak ones, are far more nearly equal than 

 are the displacements of the tympanic membrane. We 

 will first suppose that sounds are under consideration 

 ranging between the very faintest audible tone on one 

 hand, and a tone of such intensity as will cause double 

 the amplitude of displacement of the basilar produced by 

 that faintest audible tone of the same pitch. It must not 

 be supposed that this means that the second (upper) limit 

 of intensity represents an intensity of sound twice as 

 great as the lower limit. To suppose this would be to 

 ignore what has been said about the mechanism of the 

 middle ear. A two-fold increase of amplitude of displace- 

 ment of the basilar will correspond to an increase of 

 intensity of the exciting sound greater than two-fold. 



The effect upon the amplitude of displacement of the 

 basilar arising from the narrowing of the canals towards 

 the apex of the spiral and the cooperating and intensifying 

 effect of the widening out of the basilar itself towards the 

 apex have already been referred to. The net result of 



