40 



UNIVERSITY OF MISSOURI STUDIES 



is merely an approximate representation of the actual move- 

 ment of the partition. These horizontal parallels are auxiliary- 

 lines, serving the purpose of a measuring scale. The second 

 thing we have to do is to draw a second, independent, S3'stem 

 of auxiliary lines enclosing a corresponding number of spaces. 

 These lines are the thirty-one vertical parallels in figure 13. 

 The horizontal lines here indicate for the times A, B, C, and 

 so forth, the positions of the different points of the parti- 

 tion at the upper or lower limit of movement. The vertical 



A 



£ 

 C 

 D 



£ 

 F 



a 



3 2 



Fig. 13. Successive positions of the partition. The combination 2 and 3. 

 First characteristic phase. Compare figure 11 



auxiliaries serve the purpose of cutting off the partition a 

 number of equal sections corresponding to the number of parts 

 into which we divided the total amplitude of the given curve 

 representing the movement of the stirrup. To the right of 

 these sections which move are to be imagined the parts of the 

 partition nearer the apex which do not move at all in this spe- 

 cial case and which do not, for this reason, concern us here. 

 At the time A, all the moving parts of the partition are at 

 their upper limits, since the stirrup has at this time its extreme 

 outward position. From A to B, the stirrup moves through 



