I iS UNIVERSITY OF MISSOURI STUDIES 



The curve in figure 38 represents the function 



f(x) = s'mox -j- SsinS.r. 



mu u- The stirrup movement eight has an ampli- 



The combination r o r 



5 and 8. The tude three times as great as that of five, 



amplitude of 8 The table below contains the abscissa and 



is three times ordinate values of the maxima, minima, 



that of 5 anc ] inflection points. 



The successive positions of the partition corresponding, 

 under the sixth provisional assumption, to the maxima, min- 

 ima, and inflection points of the curve are shown in figure 39. 

 The four hundred and thirty-eight initial sections of the 

 partition move down and up eight times during the period. 



L«t us examine those from the three hun- 

 The tone 8 dred and eighty-sixth to the four hundred 



and thirty-eighth. They move down from 

 A to C and up from C to E. Down from E to G, and up from 

 G to I. Down from I to K and up from K to M. Down from 

 M to O, and up from O to Q. Down from O to S, and up 

 from S to U. Down from U to W, and up from W to Y. 

 Down from Y to 5f, and up from 5t to S. Down from g to S, 

 and up from <S to @=A. The nerve ends located on these sec- 

 tions therefore receive eight shocks during the period. 



The sections from the four hundred and thirty-ninth to 

 the four hundred and fifty-first move down and up only seven 

 times, since they do not make a double movement between 

 E and I. In accordance with our former considerations, how- 

 ever, in similar cases, it does not seem probable that the nerve 

 ends located on these sections should convey any other tone 

 than the tone S of a slight roughness. 



The sections of the partition from the four hundred and 

 fifty-second to the six hundred and forty-seventh move down 



five times during the period. Let 

 The tone 5 us examine those from the four hundred 



and fifty-second to the four hundred and 

 eighty-ninth. They move down from A to C, and up from 



