MECHANICS OF THE I^fNER EAR 25 



the Stirrup at B the position of the partition in its lower limit. 

 Let us now find out when any arbitrary point x^ is jerked up 

 and when it is jerked down, measuring the time from A. It 

 is obvious that the amount of fluid for which room is made 

 by the piece of the partition from x^ to x, moving from its 

 upper to its lower limit is equal to the amount of fluid dis- 

 placed by the stirrup moving inwards through the distance 

 measured by y. (For convenience we place the zero point 

 of the system of coordinates in a minimum point of the curve.) 

 It would be very easy, therefore, to find the equation of inter- 

 dependence of X and y, if the following conditions were ful- 

 filled : 



1. If the quantity of fluid displaced were proportional to 

 the horizontal movement of the stirrup. 



2i. If the partition were perfectly in- 



,, elastic: that is, not offering any resistance 



provisionally a j 



made • not as ^° ^ displacement until either of the limits 



hypotheses, but is reached, and then offering absolute re- 

 fer the sake of a sistance. 



gradual compre- 3. if the distance between the upper 



nension ^^^ lower limits were the same at any 



point of the partition. 



4. If the width of the partition at any point near the 

 windows were the same as at any point far away from them. 



Let us temporarily regard these conditions as fulfilled. If 

 they are fulfilled, x is proportional to y. That is, a unit of 

 movement of the stirrup always pushes 

 Attempt at down (or raises, as the case may be) a 



computation unit of the partition lengthwise. Or, ex- 



continued pressed in a formula: 



(I) y = Cx 



where C is a constant dependent on the physical properties 

 of the organ. 



