680 
a part of it. We therefore have to construct the curve in such a 
way that 
PPS oP = PP, = pF? (hie; 14 “attd 10) 
and . 
Q.q ax Q,q = C0; — Vg ( 3 Eh) 9 EE) ) 
72, + Qq' =aQ dansers) 
Obviously it is still possible to satisfy the above conditions in a 
great many ways. On one hand the problem becomes theoretically 
indeterminate (as a necessary consequence of giving up the provisional 
simplifications). On the other hand we gain the possibility of sim- 
plifying the curve /= ®(wx) and with it the curve z= f(x) as much 
as possible. Once the form of the curve (/,.) bas been determined, 
the curve z= f(«) may be drawn with the aid of the table (J, z). 
When the frequency-figure is symmetrical with regard to the 
Ly + En 
median, so that «,, = ——— , it is natural to eonstruct the curve 
or 
[= @ (x) in such a manner, that («= xz,, /= }) becomes the 
centre. The curve z= /(#) will also have a centre, viz. in the 
point 1 En, 25:0). 
If the frequency-curve is not symmetrical but higher in the left 
half of the domain than in the right, then in the figure z= /(2) 
the point of intersection with the axis of ws (¢ =O) will lie in the 
left half of the figure. 
The reaction-function has now the form of fig. 12a or that of fig. 120. 
! 
| | 
cs en Es En Beco Hen Xn 
Me faa. *Fie.12b. 
In w=, we have f’(«) =o. Assuming the radius of curvature 
ni 218 
Be Vi Chen, 
E f" (#) 
to be finite, /"(w) must be infinite of the same order as | /'(x)|*. For 
the reaction-funetion 
a 
ZZAN 
== 7@ 
we have 
ayy A 
Wren: 
de [7 (2)] 
