( 631 ) 
«, = * R > N ' h ' S * = -5). 
Further we have according to § 4 as an integral of the system : 
Introducing £, it becomes 
5? cos <p — a" (1-5) = A'; 
where AT is a constant and 
V d 3 R 0 h 
In the same way as this was done for the case ^ = 0 we may 
write down the differential relation between S and t and find x and y 
in the way indicated there as functions of the time; they get quite 
the same form as for p =r= 0 1 ). 
In general 5 keeps changing periodically between two limits l, 
and C 9 "j hi and £, being the positive roots of 
s e (1 — £) — + (>" (1—5)}* — 0. . 
Yet there is a considerable difference between the cases p = 0 and 
p of order A. 
§11. We notice this difference most distinctly when we represent 
the relation established between l, and <p in polar coordinates. 
If we put 
then we find : 
Q” = ~ 9"* 
** 9 Ifl 
We take <p as polar angle, V 1 — £ as radius vector and we inves¬ 
tigate the site and shape of the curves for positive values of pand 
for all possible values of K. 
For K = p"' there is degeneration into the circle £ = 0 and a straight 
line normal to the origin of the angles at a distance p f " from pole O x . 
We have two cases now: p"' <[ 1 and p" ]> 1 
o'" < 1. Let us now investigate the shape of the curves for different 
values of K. For K^> p'" they lie to the left of the straight line just 
mentioned, for increasing value of K they contract more and more 
until for the maximal value of K, belonging to a certain value of 
V Vide Chapter V of my dissertation. 
