of Central Forcess 401 
ave we qe eee oe. 
n—1 x 1 ie 
Vo Pr wi et alee a Let # = force 
u—l1 XK y"—* 
of gravity; and fuppofe the force at V, or at 
the diftance r from the centre of force: force 
of gravity (g) ::7:1,; then 7g == force at V, 
meafured by the velocity in the time (1) ; 
2 
hence; 2 = ey or V* ==/7gr, therefore by fub- 
* ys Jes rong 
flitution Y= ,/ v? —2 psi a cr 
7—1 x See 
whe +a2lgr aS Zed When Hat, if 
Sk. K gre 
the above value of s? be fubftituted we have 
Vv =)" + 2 ler x tg mano age x hg. 
es 
Becaufe P does not enter into the values of 
U, it is evident that the velocity of the body 
will be the fame, whether it move in a curve 
line, or dire€tly to or from the centre; the dif- 
tance of y being the fame in both cafes. 
By the help of the 4th. theorem, it will be 
eafy to determine how far a body muft fall 
towards the centre, to acquire the velocity it 
has in the curve. For the value of ¥ there 
Ddd given 
