of Central Forces. 393 
the curve it will cafily appear that = — x 
. Let A, anda reprefent the. angles defcrib- 
ed by Cp, and Cx, refpectively fince the body 
tae ae 
Basie | 
BE. is A ia x a, and A= ms thse | 
left an apfe; then, becaufe A:a:: 
ae 
for A and a begin ayes But d= Q9+a 
when y= o, or the body arrives at the centre; 
Cec hence 
* If a body revolve in a curve of any kind round a 
centre of force; to compare the’ angular velocity of the 
perpendicular upon the tangent with that of the diftance 
from the centre, or radius veétor. 
Let P QW (Fig. 6.) be the curve in which the body 
moves, S the centre of force, and C the centre of cur- 
vature. Let P, Q be two points in the curve inde- 
finitely near to each other, to which the tangents P Y, 
Qy are drawn; let fall the perpendiculars SY, Sy, and 
QT, which laft may be taken for the arch of a circle 
defcribed from the center S. It is evident that the angles 
YS Oe OP ie 
PSQ, P-GQ are to each other as See 
: P Pp y 
> Gp (by fimilar triangles) ime: cp: But CP= 
: , and the angle PCQ = YS), therefore the angle. 
PSQ sie 352s a BaP 
