MECHANICS OF THE INNER EAR Z'J 



Remembering that (III) is valid for jerking down, (V) 

 for jerking up, we notice that the arc of cos 2irMf runs through 

 the first and second quadrant while the partition is being 

 jerked down, through the third and fourth quadrant while 

 the partition is being jerked up. Therefore, since we found 

 that the time of jerking down of a definite point x^ and the 

 time of jerking up of the same point are subject to the con- 

 dition that cos 2ifnt yields the same absolute value, but differ- 

 ing in sign, the time of jerking up must be found in a quad- 

 rant opposite to the quadrant wherein the time of jerking down 

 occurred, never in an adjoining quadrant; that is, if the 

 former time is to be found in the arc 2Trnt, the latter must 



be found in the arc 2.Trn(t -j- — ), since the addition of 



2 ft 



J^ to t means the addition of two quadrants. The differ- 



ence of time, therefore, is always ~ . In other words, the 



2« 

 time interval from a jerk down to a jerk up and from a jerk 



up to a jerk down of any definite point is with this particular 

 curve always the same, being exactly one half of the whole 

 period. We have thus found by computation the exact move- 

 ment of the partition in case the movement of the stirrup 

 is of the form of a sinusoid. 



We have seen then that, provided a certain set of condi- 

 tions (our four provisional assumptions) is fulfilled, and pro- 

 vided the movement of the stirrup is of the 

 Summary of form of a simple sine (or cosine, as this 



the foregoing means the same) curve, computation of 



discussion the movement of the partition is possible. 



But computation is neither particularly 

 clear — at least those who are not professional mathemati- 

 cians will think so — nor is it universally applicable, but only 

 in a few cases of stirrup movement, the above, the case of 

 straight lines connecting the maxima and minima, and a very 

 small number of others. 



