of Central Forces. 403 
It the body be fuppofed to move in a circle, 
and therefore s==1, then r—y = - 
orc 
= 2 
meal sie. ver falo= 
oie 
n-+-1| 71 at 
If n==2, then r—y= $r. 
If it be required to find how high a body 
will afcend, if projected upwards with the ve- 
locity it has in the curve; or how far it mutt 
fall externally, to acquire that velocity, pyt the 
value of v, in the third theorem, = 0, then y*— 
yn Q yi ; 
= ————, and y= r X 
1—m pea Ie I aie 2 
1 
eS RE ee 
2 nu—1 
9— 5? .n—I1 
6 | 
If. a= 2, :then:y = ;77(X Sl lara the great- 
er axis of the ellipfe. 
g 
If s==1, theny=r7r X jy 27 
—» 
Laftly, when m is greater than unity, it may 
be determined by the firft theorem, what pro- 
' portion the velocity in the curve bears to 
that velocity, towards which it continually 
_ approaches as the body recedes indefinitely from 
the centre. For, if y be fuppofed infinite, 
Ddd2 then 
