412 The Inverfe Method 
~ ther, and confequently the motion of the apfides 
will be found, whatever be the form of the 
orbit. Henee it is evident, that if s and c be 
given, the eccentricity of the orbit and the 
motion of the apfides may be calculated. 
PROPOSITION Iv. 
ie centripetal force being reciprocally as 
the nth. power of the diftance from a 
plane parallel to the horizon, and the direétion 
and velocity of a body at any point being given; 
it is required to determine the nature of the 
curve it will defcribe. 
_ Let a= diftance of the point at which the . 
body is projected from the horizontal plane, 
6 = velocity parallel to, and c= velocity per- 
pendicular to the plane, x == any abfciffa, y= 
the correfponding ordinate, and 2 the curve 
defcribed; then X:2::46: zm == velocity of 
the body inthe curve. The force indirection of 
the ordinate 1s = the fquare of the velocity divided 
by 4 chord of curvature perpendicular to the hori- 
zon, or pafling through the centre of force, But 4 
chord of curvature when x is conftant, which is the 
cafe 
