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

 -I2 action of the Sun, is to the um of the aid M--L axes as 3L X, -7 to 4.DD-+SS. Bnt according to the contruéftion 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 um, nearly as 5 to 694; and conequently the. diameters will be nearly as 689 to 699, or 69 to 7o: But by the latter mle, the difference will be to the um, nearly as I to I 19; and the diameters or ditances 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, firt 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 um, as 1 to QO; and conequently the greater axis to the leer, as 4 5-Q to 4435, ' ° B U T the difference, in thee proportions of the extream ditances, tho' it may appear coniderable, is not, however, to be diitinguiflfd by the obervations on the diameters of the Moon, whilt the variations of the diameters, from