33 6 Sir ISAAC N E W T O m Book IV.

The properties, however, of this path are more simple thanperhaps will be expected on a superficial consideration of it 3and the referring of the motion of the satellite to it, may be ofuse on some occasions, particularly for resolving the difficultiessome have sound to understand Sir Isaac Newton s account ofthe motions of the satellites, from gravity. This path is, insome cases, concave towards the fun throughout; in othercafes, the part of it nearest the Tun is convex towards the fun,and the rest is concave. An instance of the former we havein the moon, of the latter in the satellites of the superior planets.

The force that bends the course of the satellite into a curve,when the motion is referred to an immoveable plane, is, at theconjunction, the difference of its gravity towards the fun, andof its gravity towards the primary. When the former prevailsover the latter, the force that bends the course of the satellitetends towards the fun ; consequently, the concavity of the pathis towards the fun : and this is the case of the Moon , as willappear afterwards. When the gravity towards the primary ex-ceeds the gravity towards the fun, at the conjunction, then theforce that bends the course ot the satellite tends towards theprimary, and therefore towards the opposition of the fun ;consequently the path is there convex towards the fun : andthis is the case of the satellites of supiter. When these two.forces are equal, the path has, at the conjunction, what mathe.-maticians call a point of reElitude ; in which case, however,the path is concave towards the fun throughout.

Because the gravity of the moon towards the fun is found tobe greater, at the conjunction, than her gravity towards theearth, so that the point of equal attraction, where those two

* powers