of Central Forces. 375 
rv 
ag 4/7 ad Saray ere 
i. —_—y 
1—™m 
core tl 
If 2 == 1, then by gee in the fame 
equation, the value of p found above, we have 
Sp oe Fanless ae as 
IVT 42x lg. rx y—P 
> s* 
all the curves may be conftructed. 
~~ Tt muft be obferved, that the pofitive or nega- 
tive: fign takes place, according as the body 
afcends from, or ay ig towards the centre. 
x T? W9 ma—1 
in general, and 
z= 4 Hence 
mecale.p* == a 
yt + psi 
at an apfe it is nT that py; hence, in that 
cafe, there arifes by reduction, the following 
equation ;_ viz. Pr? eee Sy yes da 95 
from whence, and the proper equation for 2, 
the number and pofition of the apfides may be 
determined. * 
It may be obferved that the quantity under 
the radical in the value of * being put = a, 
gives the equation for determining the apfides- 
If m be fuppofed greater than unity, and y 
infinite, then will p == Y/_«~ x P==a perpen- 
dicular upon the afymptote to the curve. de- 
{cribed 
* See the note placed at the end of this Tract. 
