392 The Inverfe Method’ 
of force being in its centre. For, if 2 R= the 
tranfverfe, and 2 C = the conjugate axis, y =the 
diftance from the centre, and p= the perpendicu~ 
lar upon the tangent, then 2= —===——=>=>—= * 
ir UpO § P VERE Tey 
_ Compare this with the above equation, and it 
willeafily appear, that2 R= Vepy rp esPr 
+ Vary .F — 2% Pr, ang }2 C= 
PLS Toe. ser V st yr —asPr. 
The fame conclufion may likewife be deduced 
from the equation for determining the apfides, 
which has two roots pofitive, and two equal 
to them and negative. 
Cor, 6. Ifm==1,thens? — ; which, 
if a be greater than 3, is lefs than unity, 
and the body in this cafe muft fall to the 
centre; and the number of revolutions it will 
make before it arrives there, may be determined 
in the following manner. In this cafe p = 
i—1 
na—t1 
n—1 —_— 
Pith. Tas 2 Wien ry On eee 
n—1 r*3 
“o* 2 
body moves from an apfe; therefore p:y:: 
yer ‘=. But when y and pare evanefcent, 
r= is infinitely greater than p, and confe- 
quently at that time the angle x Cp (Fig. 2.) 
will be a right angle. From the equation of 
the 
