</" we get an isolated point. If 0 <[ Kq" the curves surround ,j 
point 0 x ; if K= 0 we have a curve through 0 X , for /f< 0 they «j 
lie to the left of 0 X ; for the minimal value of K we again get an 
isolated point (fig. 5). 
For increasing values of p"' the straight line separating the domains^ 
JT> p"' and K < p'" moves to the right. The domain K > q'" becomes | 
smaller and vanishes for q'" = 1. For p’"^:l we therefore have 
curves surrounding 0 X and curves to the left of O x only. When p"'| 
increases still more the remaining isolated point approaches to O x and * 
the curves farther from O x approach to circles. 
For q = 0 we had (with the exception of the special case K= 0) 
only curves to the right of O x , and curves to the left of 0 X . For p■ ■ 
of order h we have moreover curves around O x , which are even 
Q 
more frequent for great values of —: 
h 
The curves around O x point to a form qf motion, where tp takes 
all values, the nodes of the osculating curves lie then above as well 
as below the point 0 of fig. 2; the osculating parabolae have their 
openings turned to opposite sides. 
That for increasing values of p'" the curves in general begin to| 
resemble circles more and more, indicates that £ is about constant; 
it changes between narrow limits. 
This also appears in this way. From (16) we deduce: 
k - p'" (i ~c x )z=dc 
k-q”' (i - Q ;yu^. 
By subtraction we find: 
'■ ± cy\—c x 
= - __ . 
Q'" 
For greater values of p" we find becoming very small. 
In this way we approach the general case where there is no 
question about relation. jj 
$ 12. How the transition to this general case takes place is also 
clearly evident from the limitation of the domain of motion, which 
limitation we find by determining the envelope of the osculating 
curves In the same way as this was done for the case p 0, we 
find that the envelope degenerates into three parabolae, of which the 
equations are : 
