Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/328

 diminihed ditance; and therefore will decribe an orbit interior to that elliptical orbit, and at the lower apis approaching nearer to the centre than before. Therefore the orbit by the acceion of this new force will become more eccentrical. If now, while the body is returning from the lower to the upper apis, it houlcl decribe by the ame degrees by which it increaed before, the body would return to its firt ditance; and therefore if the force decreaes in a yet greater ratio, the body, being now les attracted than before, will acent to a till greater ditance, and o the eccentricity of the orbit will be increaed till more. Therefore if the ratio of the increae and decreae of the centripetal force be augmented each revolution, the eccentricity will be augmented alo; and on the contrary, if that ratio decreae it will be diminihed. Now therefore in the ytem of the bodies T, P, S, when the apides of the orbit PAB are in the quadratures, the ratio of that increae and decreae is leat of all, and becomes greatet when the apides are in the yzygies. If the apides are placed in the quadratures, the ratio near the apides is les, and near the izygies greater, than the duplicate ratio of the ditances, and from that greater ratio aries a direct motion of the line of the apides as was jut now aid. But if we conider the ratio of the whole increae or decreae in the progres between the apides, this is les than the duplicate ratio of the ditances. The force in the lower is to the force in the upper apis, in les than a duplicate ratio of the ditance of the upper apis from the focus of the ellipis to the ditance of the lower apis from the ame focus; and contrary wie, when the apides are placed in the yzigies the