of Central Forces. 41s 
bn cat ila 
Vx V2 Vr yo 
© Cor. 2. If2=-3,then the laft equation in the 
; ik yy 
propofition becomesx=— es 
ni | 0h m—1 XY + r** 
The fluent therefore being taken and correéted, 
by fuppofing x and y to begin together, we 
b ee 2 2] Hix 
have x == — x #—1 x7 + 7'ld 3 there- 
: om «+ Vv. r' ~ | sk «=~ on * +. : 
m1 
: won epee ee eg 
fore, by reduction, y* == m—1: yx. 7 x? ot >re 
Para) ¢ a 
=F rx —im x roa “an equation to a co= 
nic fection ; which will bean hyperbola, parabola 
to ellipfis, according as m is greater, equal to, ar 
lefs than~ unity;- that is, according as the 
velocity with which the body is projected in a 
direction perpendicular to the horizon, is greater; - 
equal to, or lefs than that acquired. by falling 
from an infinite height. | 
2 - noanty 
, If in x os = 1, Of Im Xs pet 
2r 
then the equation becomes | 
1—71 
x——x*; therefore the curve is a circle, whofe ra- 
i - - , 
But V? #1 — ee Kaa ake 
l—m 2m 
dius = 
therefore 
