Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/338

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ceaſe to attract the water upwards, and begin to attract the water downwards in the octants after the ſyzygies. And thence the greateſt height of the water may happen about the octants after the ſyzygies; and the leaſt height about the octants after the quadratures; excepting only ſo far as the motion of aſcent or deſcent impreſſed by theſe forces may by the vis inſita of the water continue a little longer, or be ſtopt a little ſooner by impediments in its channel.

Cor. 21. For the ſame reaſon that redundant matter in the æquatorial regions of a globe cauſes the nodes to go backwards, and therefore by the increaſe of that matter that retrogradation is increaſed, by the diminution is diminiſhed, and by the removal quite ceaſes; it follows, that if more than that redundant matter be taken away, that is, if the globe be either more depreſſed, or of a more rare conſiſtence near the æquator than near the poles, there will ariſe a motion of the nodes in conſequentia.

Cor. 22. And thence from the motion of the nodes is known the conſtitution of the globe. That is if the globe retains unalterably the ſame poles; and the motion (of the nodes) be in antecedentia, there is a redundancy of the matter near the equator; but if in conſequentia, a deficiency. Suppoſe an uniform and exactly ſphærical globe to be firſt at reſt in a free ſpace; then by ſome impulſe made obliquely upon its ſuperficies to be driven from its place, and to receive a motion, partly circular and partly right forward. Becauſe this globe is perfectly indifferent to all the axes that paſs through its centre, nor has a greater propenſity to one axis or to one ſituation of the axis than to any others