104 The Inverse Method of Central Forces. 
siXn— 1-1-6; whence, by substitution and reduc- 
2 
fiver m—1 1—q 
2rxX {c—- X 1—Cy te 
: —1' q—1 
aon, $* = CS ee ee eee 
at = 
ge 4", ee cee (2 cr Pr x c=") 
Hence the velocity is determined with which a 
body must be projected, so as never to arrive at an 
apse, nor ascend beyond, or descend to a circle, 
described at the distance c*" x y from the centre 
of force. 
If n= 2,9 =—1,and P=r, thens?= 
z 
=< 
2+c—363 
atc—3ct 
— 
yoac X 1 Gt tex ape Xie 
Wherefore, if the velocity were known with which 
a body (as the moon) would move in a circle round 
another (as the earth) at the distance 7 of the lower 
apse, with the compound force 1 — ¢; then the 
velocity is determined with which it must be pro- 
jected from that apse, to move in the manner de- 
scribed in this Scholium 3 or in such a manner as, 
never to arrive at another in any finite number of 
revolutions. 
Hence it will easily appear, that a very small ya- 
riation in the value of s, will occasion a very large 
one in the excentricity of the orbit, and in the mo- 
tion of the apsides: it is therefore evident that the 
two last will increase or decrease at the same time. 
