Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/335

 very nearly, by the analogy of the lines PS, and MN.

By the ame laws by which the body P revolves about the body T, let us uppoe many fluid bodies to move round T at equal ditances from it; and to be o numerous that they may all become contiguous to each other, o as to form a fluid annulus or ring, of a round figure and concentrical to the body T; and the everal parts of this annulus, performing their motions by the ame law as the body P, will draw nearer to the body T and move wifter in the conjunction and oppoition of themelves and the body S, than in the quadratures. And the nodes of this annulus, or its interections with the plane of the orbit of the body S, or T, will ret at the yzygies; but out of the yzygies they will be carried backward, or in antecedentia; with the greatet wiftnes in the quadratures, and more lowly in other places. The inclination of this annulus alo will vary, and its axis will ocillate each revolution, and when the revolution is compleated will return to its former ituation, except only that it will be carried round a little by the præceion of the nodes.

Suppoe now the phærical body T; coniting of ome matter not fluid, to be enlarged, and to extend it elf on every ide as far as that annulus, and that a channel were cut all round it; circumference containing water; and that this phere revolves uniformly about its own axis in the ame periodical time. This water being accelerated and retarded by turns (as in the lat corollary) will be wifter at the yzyigies, and lower at the quadratures than the urface of the globe, and o will