30 UNIVERSITY OF MISSOURI STUDIES 



fact that it is jerked later is represented by a position farther 

 to the right. Now, since the velocity of the stirrup increases 

 as shown by figure 8, the following marks have to be placed 

 higher than proportionate to their advance to the right. That 

 is, points marked off by equal steps on the partition are now 

 jerked successively in briefer time intervals than before. 

 Later approaching the time B in figure 8, the stirrup moves 

 again more slowly, and the marks in figure 10 advance there- 

 fore more rapidly towards the right, as seen in f and g. If 

 we now draw a complete curve through the marks a, b, c, d, 

 ^> f' S> we convince ourselves readily that the new curve is 

 the same curve as the one in figure 8 from A to B. Of course, 

 if we have not chosen the same vertical and horizontal scales 

 in both figures, the new curve must appear more or less steep 

 than the old one. But the selection of a scale for a graphic 

 representation is entirely a matter of convenience. Choosing 

 identical scales, we simply have to transplant the first half 

 of the curve in figure 8 from A to B into the new figure. 



But now the stirrup begins to move in the opposite di- 

 rection, causing the partition to be jerked upwards gradually. 

 The point of the partition nearest the windows is jerked up 

 first, the others later in regular order. Now, it can be easily 

 seen where we have to place the further marks in our new fig- 

 ure, namely k, i, j, k, I, m, n. We find them, or rather immed- 

 iately the complete curve of which they are points, by simply 

 turning the second half (B to C) of the curve in figure 8 up- 

 side down, without, however, making any change between 

 right and left. In this way we go on, simply transplanting the 

 parts of the stirrup curve, leaving the rising ones in the same 

 position, but turning the falling parts upside down. 



If we now desire to find out for any point of the parti- 

 tion, for example, for x , the exact time when it is jerked 

 down and when it is jerked up, all we have to do is to pass 

 on from this point (Fig. 10) to the right (along the dotted 



