MECHANICS OF THE INNER EAR 99 



for x. This is impossible because the equations to be solved 

 would be of the eighth degree. We have to use, therefore, 

 the only method left, however great our sacrifice of time, and 

 to calculate directly a sufficiently large number of values from 

 which we then select the largest and smallest. In this way the 

 values of the table have been obtained. By adding 19& to each 

 of the values of the first column we get the third column, 

 which offers the advantage of containing only positive ordi- 

 nates. This procedure is equivalent to selecting a different 

 horizontal coordinate, which is always dependent on our 

 choice. The ordinate value zero, thus obtained, is the one which 

 belongs to point A in figure 30. The successive positions of 

 the partition corresponding, under the sixth provisional as- 

 sumption, to all the maxima, minima, and inflection points of 

 the curve are shown in figure 31. 



Let us at once examine the movements of the three sec- 

 tions, the fiftieth, the fifty-first, and the fifty-second.* At A, we 

 find these sections occupying a medium up- 

 What tones do ward position. From A to B they move down. 

 we hear? The From B to C they begin to move up. 

 tone 8 From C to D they continue to move up. 



From D to E they begin to move down 

 and continue to move down until G. From G to H they move 

 up, completing thus the second down and up movement. 

 From II to J they move down, and from J to L up, complet- 

 ing the third down and up movement. From L to N they move 

 down, and from N to Q up, completing the fourth down and 

 up movement. From Q to R they move down, and from R to T 

 up, completing the fifth down and up movement. From T to 

 V they move down, and from V to X up, completing the sixth 



* For a perfect understanding of the details, the reader will have to 

 draw figure 31 (and the similar figures following) for himself on a larger 

 scale, and to inscribe the exact values as derived from each corresponding 

 table. 



