Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/26

Rh Planets all atronomers conent. Therefore the centripetal forces of all the Planets are reciprocally as the quares of the ditances from the centres of their orbits. If any hould object, that the apides of the Planets, and epecially of the Moon, are not perfectly at ret; but are carried with a low kind of motion in conequentia; one may give this anwer, that though we hould grant this very low motion to arie from hence, that the proportion of the centripetal force is a little different from the duplicate, yet that we are able to compute mathematically the quantity of that aberration, and find it perfectly inenible. For the ratio of the Lunar centripetal force it elf, which mut be the mot irregular of them all, will be indeed a little greater than the duplicate, but will be near ixty times nearer to that than it is to the triplicate. But we may give a truer anwer, by aying that this progreion of the apides aries not from an aberration from the duplicate proportion, but from a quite different caue, as is mot admirably hewn in this philoophy. It is certain then that the centripetal forces with which the primary Planets tend to the Sun, and the econdary to their primary, are accurately as the quares of the ditances reciprocally.

From what has been hitherto aid, it is plain that the Planets are retained in their orbits by ome force perpetually acting upon them; it is plain that that force is always directed towards the centres of their orbits; it is plain that its efficacy is augmented with the nearnes to the centre, and diminihed with the ame; and that it is augmented in the ame proportion with which the quare of the ditance is diminihed, and diminihed in the ame Rh