THE MOON’S MOTIONS.

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A, this body is still able to move in such a way ascontinually to increase its distance until it is as far offas a from S, bow muck more is it to be expected that,having reached this distance, where the sun’s force isso greatly reduced, the body should be able yet fartherto increase its distance, and so to travel for ever awayfrom S.

And I think that another difficulty, which is verycommonly experienced, is this :—The curve A B a b isquite symmetrical, both as respects the line A a andthe line B b. Thus the part near A is exactly like thepart near a; yet these perfectly similar parts are de-scribed under quite dissimilar circumstances, — theattraction on the body being different, the velocity ofthe body being different, and all the circumstances infine at a maximum of dissimilarity. Nay, the verycircumstance that a symmetrical orbit should be de-scribed about an eccentrically-placed point, seems ata first view inexplicable.

Let S, fig. 14, Plate IV., be the attracting orb aroundwhich a body is moving in the elliptical orbit A B a b ;and let us consider the motion of the moving bodyfrom the point A, where the velocity is greatest. Atthis point the velocity is greater than that with whicha body would describe the circle ALE around S : thetendency to travel on the tangent line A Y is thereforestronger than in the case of such a body. Thus anintermediate course, A P, is pursued, the sun’s in-fluence deflecting the moving body from the tangent-line A Y ; but not being strong enough to deflect it