of Central Forces. 395 
1 ~- ale ° . a ] 
- the velocities in circles will © ——= 
. 2 
(Princip. Prop. 4-) confequently — x= 
ye 
= velocity ina circle at the diftance y from the 
Pv 
centre. But = velocity in the trajectory 
at the diftance y; if, therefore, we make 
Bae aoe Eee aes al” ae” thease 
P ‘ y a—1 Ay 
time the body be fappofed to arrive at an 
apfe, in which cafe p? =y*? = 
x P? 1 ad 
Ag = , it would continue to move 
yo Es ae i 
m—1 
for ever in this circle. But coming to an apfe, 
it muft afcend or defcend in a fimilar and 
equal curve, hence it never can arrive at the 
diftance y from the centre, determined from the 
above equations, in any finite number of revo- 
: b Pv 
lutions. Making, therefore, as above r = 
™—1 . 
LA 2 UV 2 2 2 y os 
so & —, we have p> = P? 3? X - = 
Athy = i 
n—1 
« tora 
Cee? Mm 
