204 
so that 7 must be >a, if L? or, what comes to the same thing, 
ds* shall be positive. 
Formula (17) is the same as in Newron’s theory. 
7. We will now consider the case of y being continually zero, 
i.e. that the particle always moves on the same radius. From (13) 
we easily conclude (we shall afterwards show this in general i.e. 
if be not identical zero) that the particle never reaches sphere r = a. 
If we call 
r ew 
foo a ee i 
( 5 dt 
er 
7 
for abbreviation velocity and acceleration, then (13) gives us for the 
velocity the formula 
pa(1—S\(1-44a8) Weta 
sy 7 r ; 
and (16) for the acceleration 
di | Te 26° 
27? le a 
If we substitute (18) in (19) we obtain 
3 a a Te 
Jd = — (: nae eA 14 bl 2 APEN 
2r? r id ed 
From (19) follows, that the algebraic value of the acceleration 
only depends on the position and the velocity of the particle and 
does not change if we reverse the direction of the velocity. The 
constant A is never negative (as L > 0). If A lies between O and 
1 (A4=1 included), then every value of 7 is possible according to 
(15). We then have a particle moving towards infinity or coming 
from it. For this motion the acceleration will, according to (20), 
once become zero, if 2A—1>0, ie. A> 3, viz. for 
2Aa 
oP | 
for greater values of 7 the acceleration is directed towards the centre 
(attraction), for smaller values of 7 from the centre (repulsion). The 
acceleration is then zero in these positions viz. 7 = a, r = 2Aa/(A—1), 
7=o. In the first interval there will be repulsion, in the second 
attraction; within either interval there is an extreme. If A> 1 
then, according to (18), 7 cannot be greater than A¢/(A—1). Then 
. 
’ 
