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into the circular course ALK. Now, the distance ofthe body from S is increasing throughout this process,and this amounts to saying that a tangent-line, asP T, makes an obtuse angle with the line S P drawnto the body at the moment. But this being so, it isobvious from the figure that the orb at S must exerta retarding influence. At A there was no retardation(for the moment), because the pull was square to thebody’s course; but so soon as the body’s distance be-gins to increase, the pull is partly backwards (as at P)with reference to the body’s motion ; and thus thereis retardation. Now two opposing influences are atwork when the body is in such a position as P: one,the tendency of the body to move in the directionP T, tends to enlarge the angle S P T; the other,the pull of the orb at S, tends to reduce this angle. ISo long as the velocity exceeds a certain value, theformer influence prevails. But the velocity is beingcontinually reduced ; and though the distance of thebody is increasing, and therefore the pull from Sdiminishing, yet the power of S to deflect the bodydoes not diminish so rapidly as the absolute power ofS on the body, for deflection becomes so much theeasier as the velocity of the body is reduced. Atlength, when at B, the body has reached a positionwhere the two forces counterbalance each other inthis respect, the angle S B Z between the line of thebody’s motion and the line from S having here itsmaximum value. At this point the body is travellingon a course square to the direction it had had when