Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/476

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-I2 action of the Sun, is to the ſum of the ſaid M--L axes as 3L X, -7 to 4.DD-+SS. Bnt according to the conſtruéftion before laid down; the iiid proportion is -as 3LL I0 ZSS—L.L. ' e . B Y Sir I/bac Newforfs rule, the difference will he to the ſum, nearly as 5 to 694; and conſequently the. diameters will be nearly as 689 to 699, or 69 to 7o: But by the latter mle, the difference will be to the ſum, nearly as I to I 19; and the diameters or diſtances of the Moon, in its conjun€tion and quadrature with the Sun, will be as 59 to 60. Dr. Halley, (who in his remarks upon the Lunar theory, at the end of his catalogue of the Southern Ptars, firſt took notice- of this contraction of the Lunar orbit in the Syzygies from the phenomena of the Moonis motion) makes the difference of the diameters to the ſum, as 1 to QO; and conſequently the greater axis to the leſſer, as 4 5-Q to 4435, ' ° B U T the difference, in theſe proportions of the extream diſtances, tho' it may appear conſiderable, is not, however, to be diitinguiflfd by the obſervations on the diameters of the Moon, whilſt the variations of the diameters, from