of Central Forces. 399 
the diftance of that place from the centre of 
force. if it afcend, the velocity muft be greater 
than that acquired by defcending from an in- 
finite height, but lefs than that of a body in 
a circle at that diftance. Within thefe limits 
the conftruction is general. 
PROPOSITION If, 
THE fame things being given as in the 
laft propofition; to determine the velocity and 
time correfponding to any given diftance of 
the body from the centre of force. 
_ Let the velocities of bodies in a circle at 
the diftance r in the curve, at V and n, be = 
V,v and v refpectively (Fig. 1.); then § = 
te If therefore the feveral values of p, de- 
pending upon the different values af m, be 
fubftituted, we fhall have 
po 
Vv n—1. 
ea" Wigs av ey (nk em xy 4 rt ie yh—t 
—————— eee 2 
i, yr m >.< yr -t 
ome ees 
N—1 2 
m being greater than 1. 
its 
