244 — Review of the Principia of Newton- 
ject of the analysis of forces, is employed principally on sacl 
as are situated in the centre of the figure, and of consequence 
i ich had 
been before treated of by Hooke, Huygens, and others, but 
going far beyond them. In this part are demonstrated, for 
the first time, the laws of Kepler, and the formulas for the een- 
tripetal force as dependant on the velocity of a body, and the 
chord of curvature of the osculatory cirele. "Fhe author ap- 
plies them to the principal and most elegant propositions of 
motion in the circumference of a circle, and investigates @ 
theorem for the law of force transferred from one point to 
of the apsides and the variable eccentricity of the lunar or 
bit, but it is that which causes anet or comet, moviDg 
in an ellipsis, when it has arrived at its perihelion, or nearest 
distance from the sun, to recede from it in an equic 
curve, through a deficiency of centripetal force to retain 3 
ultimately terminate in an apsis or a rectilinear direction, 
coinciding with the radius yeetor.* 
once verse:-of this: problem, viz. that the law of the force being in the 
ce; the body will move in an equiangular 
inverse triptic he distar 
‘Spiral, el not obtain, but in particular cas S, as may be inferred from the 
pete aor Ist proposition, and fs admirably illustrated by Dr. Keil, io nUOr 
mag, Lae the philosophical transactions, curve would more generally 
Bs erbolic spiral, the most remarkable pr f which is, *hat © 
= curve will always produce e Saf ceatehietal and centrifuge 
therefore the paracentric velocity is muiform. 
o~ 
tion in 
forces, 
