28 UNIVERSITY OF MISSOURI STUDIES 



To prove that computation is not universally applicable 

 let the movement of the stirrup be represented by the function 



y =z c(2' — COS 2tjrmt — COS 2Trnt) 



and let m be equal to 4 and n equal to 



^b"^d"*^d°" ^ *^*^ ^^'"P'^ *^^^^ °^ ^ ^^^^^ *^''^' 



musically speaking). Even in a case like 



this, by no means far fetched, rather the 

 contrary, computation is impossible since it would involve, 

 as the mathematical reader may easily convince himself, the 

 solution of an equation of the fifth degree in order to find the 

 mutually corresponding values of y and t for the maxima and 

 minima of the curve. Without these values for the maxima 

 and minima, which are the points of discontinuity of the func- 

 tion representing the movement of the partition, we could 

 not proceed at all. It is out of the question, therefore, to ex- 

 pect that computation pure and simple, even under the four 

 assumptions provisionally made, will ever give us a satisfac- 

 tory comprehension of the function of the inner ear. We 

 must look for other means in order to obtain our end, an 

 insight into the details of movement of the partition. 



Let us, then, try to represent the movement of the par- 

 tition in the above case as well as in others graphically. I 



^ , . , , shall offer to the reader two methods of 



Graphic methods -ru ^ ^ ^ 4.1, 



of determining graphic representation. The first of these 



the exact '^ more accurate in some respects than the 



movement of second, but a little more difficult of ap- 



the partition plication. 



The vertical axis of our system of coordinates in figure 



10 may represent the succession of points of the partition, be- 

 ginning from next to the windows. The 



First graphic horizontal axis may represent the time. I 



method must warn the reader against thinking 



that the figures resulting on the paper are 



pictures of something that exists in the ear or elsewhere. The 



