If we put 
*— 
n, iN 
then 
a a 
a ae et sg ea 5 
A (5 ‚)f n, + 2, ( ; of 
This gives to (3) the form: 
VEN (C,—S) EO ng iy ee ee (0) 
where & represents a constant. 
The first equation of (2) becomes by introduction of ¢: 
§ = 2p" Van, Fa) kVEE—C) (Golan > .- (7) 
Elimination of g between (6) and (7) furnishes 
d 8 
+ VEE—C,) (C,—8) — 
On account of this ¢ can be determined as function of 7, which 
makes a,, @,, and a, to be known; then p can be found out of 
(3); finally @,, 6,, and 8, out of (2). 
es Vun, (n, + n,) hdt. 
§. Let us suppose relation (6): 
VS (S—C,) (C,—$) cos p =k 
to represent a curve on polar coordinates; we take § as radius vector, 
p as polar angle. 
As a,, a,, and @, are positive, &, 5— C, and (,; —§ are positive, 
S remains between (C, and C,. So we have to regard only curves 
situated between the circles ¢= C, and S= C,. 
The curves remain on the right or on the left of O according to 
k being positive or negative. In fig. 1 the curves have been drawn 
for definite values of C, and C,, for some values of 4. 
The distances of the points of intersection of a curve with the 
axis of the angles is found as the positive roots of the equation: 
CEM 
For a given value of C, and C, there is a maximal value of 4”, 
for which this equation has two equal roots and below which it 
has 3 real ones. For this {value the curve has contracted to an 
isolated point. This concerns a special case of motion. 
Another special case we have for 4° =0. Degeneration takes 
place to the point $= 0, the circles § = C. and ¢= GC, and the 
right line cos p = 0. 
Further more there are special cases for special values of C, and 
