of Central Forces. 38 7 
duced’ we have z = r P. ar og 
r” —m P? 
JE: — m P* GS sige 5% eam 
1 1—-n 1—m 
fe) == 
t+log. ; 7 
fae FP’ fie m P* ‘ 
log. fae - Berg a) 
If P=r, or the body be proje€ted from an 
apfe, thenz—=r — x log. 
A i 6 Ve —y’ 
and when y==o, the value of the fra@ion 
>? 
OY is infinite, as may be found either 
by taking the fluxions of the numerator and 
denominator, or by expanding 3+ —— ys ang 
dividing y by the denominator; hence the body 
will make an infinite number of revolutions 
before it arrives at the centre. . 
The orbit may be conftructed in the following 
manner. Let the rectangular hyperbole V 4 
(Fig. 3.) be defcribed, whofe centre is C and 
vertex V; join C A, and draw the the tangent 
AT tothe point 4, and A B perpendicular to 
the axis VB. Let CV=r, CB=x, and CT ==y. 
It is well known that the fluxion of the feétor 
Bbb2 CV A 
