72 UNIVERSITY OF MISSOURI STUDIES 



near the windows. We then know (Fig. 25) that the ratio 

 <■ is equal to the ratio of 



X 50Z£> 



y — w 6zv — w i 



X 50Z£> ~ 10 



. X \0'W-\-X 



J IO 10 



The area described by the cross-section of the partition in 

 being jerked from one limit to the other may be called a at 



the point where the width of the partition 

 The area 1S sma ^ est » « a t any arbitrary point of the 



described by a partition. These areas, let us assume, are 



cross-section of geometrically similar. This assumption 

 the partition possesses a higher degree of probability 



than what would follow for the areas from 

 the third provisional assumption made above for the sake of 

 simplicity. It then follows that the ratio of the areas is equal 

 to the ratio of the squares of the widths of the partition at the 

 same points. 



a _y* 



a w' 



ay' 



a= —z- 

 W 



For y we substitute its value found above and have then the 

 equation : 



a(iow+xY 



a= — - 



Kfnf 



The left side of this equation is a measure of the area 

 described by the cross-section of the partition at the point 

 x, in being jerked from one limit to the other. The right 

 side of the equation contains the variable x, the distance of 

 any point of the partition from its beginning near the windows, 



