‘of Central Forces. 389 
of the hyperbolic logarithms of AB and BD mul+ 
tiplied into pyf 2 Peand, tke Cp = 25s 
then is p a point in the trajectory, as will be 
i ae = 23 ™ 
evident from the equation zr ,/ a 
Tog. tee 
P— Yr? — yf" 
Becaufe the ratio of 4B to BD is - infinitely 
great when AD is evanefcent, the number of 
“revolutions before the body arrives at tthe centre, 
amuft be infinite. 
acate 
Cor.'4: ‘If'n==4,.then, p= 
Bp aloud xrP yy 
iach and ¥? 
game 
— is the equation for 
determining the apfides; where m may be greater 
than, equal to, or lefs than unity. The ratios 
of m to unity, and of Ptor being given, it 
will be eafy to determine when all the roots 
of this laft equation are real, and when two 
of them are impoffible. If the body be pro- 
jefed from an apfe, or P==7+, then all the 
the 
