diminiſhed diſtance; and therefore will deſcribe an orbit interior to that elliptical orbit, and at the lower apſis approaching nearer to the centre than before. Therefore the orbit by the acceſſion of this new force will become more eccentrical. If now, while the body is returning from the lower to the upper apſis, it ſhoulcl deſcribe by the ſame degrees by which it increaſed before, the body would return to its firſt diſtance; and therefore if the force decreaſes in a yet greater ratio, the body, being now leſs attracted than before, will aſcent to a ſtill greater diſtance, and ſo the eccentricity of the orbit will be increaſed ſtill more. Therefore if the ratio of the increaſe and decreaſe of the centripetal force be augmented each revolution, the eccentricity will be augmented alſo; and on the contrary, if that ratio decreaſe it will be diminiſhed. Now therefore in the ſyſtem of the bodies T, P, S, when the apſides of the orbit PAB are in the quadratures, the ratio of that increaſe and decreaſe is leaſt of all, and becomes greateſt when the apſides are in the ſyzygies. If the apſides are placed in the quadratures, the ratio near the apſides is leſs, and near the ſizygies greater, than the duplicate ratio of the diſtances, and from that greater ratio ariſes a direct motion of the line of the apſideſs as was juſt now ſaid. But if we conſider the ratio of the whole increaſe or decreaſe in the progreſs between the apſides, this is leſs than the duplicate ratio of the diſtances. The force in the lower is to the force in the upper apſis, in leſs than a duplicate ratio of the diſtance of the upper apſis from the focus of the ellipſis to the diſtance of the lower apſis from the ſame focus; and contrary wiſe, when the apſides are placed in the ſyzigies the
