394 The Inverfe Method 
2 
hence we have a= ——~ x Qa 
2X n—3 hie 
ee Q being a Re and C = the circum- 
ference of a circle whofe radius =r. ‘The num- 
! ’ i 
ber of revolutions therefore = 
2X 1—3 
If x be lefs than 3, s muft be greater than 
unity; therefore the body projected at right 
angles to a line drawn from the centre of force, 
and with a greater velocity than would make it 
defcribe a circle, it muft begin to afcend; and 
it muft ever continue rifing, as its velocity is 
equal to that acquired by ain from an infinite 
height. Becaufe p:y: :y°>, therefore 
when y is infinite, p is alte and hence 
the angle pC Pr a at ine time is a right angle. 
As above, A= by a, anda= 9-4, there- 
2 1 
fore a= x Q=—==— x C._ Hence 
oes 2.3-—2 
the number of revolutions the body defcribes 
in afcending to an infinite height = $5402: 
2X 37% 
SCHOLIUM. 
{ Vv . - e . 
Becaufe hoe velocity in a circle at the dif- 
tance r from the centre, and if the force OC 
i 
