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perturbing action, the law of gravitation would beestablished in a manner there could be no disputing.
In presenting so much of the history of this inquiryas is necessary for my present purpose, it is necessary,in the first instance, to show generally how the motionof a body in an elliptic orbit accords with the actionof a force like gravity. Absolute proof of the factrequires in the learner an amount of mathematicalknowledge, which the general reader cannot be sup-posed to possess. But the difficulties which at a firstview surround the idea of elliptic motion, or of motion jin any non-circular orbit, described under attractive ;influences, can be removed without dealing withmathematical considerations. I think the most salientdifficulties are the following:—
Suppose A B a b, fig. 14, Plate IV., to be an ellipticpath described about an attracting body S, placed |at one focus of the ellipse,—then the learner findssome difficulty in understanding how the change ofdistance from the small distance S A to the greatdistance S a, and, vice versa, can proceed in regularalternation. Because, if the attracting force, greatlyreduced at the distance S a, can nevertheless compelthe body to approach from that distance until itsdistance is reduced to S A, how much more, it wouldseem, should the much greater attraction exerted atthis reduced distance S A, continue to cause the ap-proach of the body, until finally the latter is broughtto rest at S. Or again, if when the attracting orb isexerting its greatest influence on the moving body at