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right-angled triangle m E t. Newton adopted themeasure of the earth in vogue at the time, accordingto which a degree of arc on the equator was supposedequal in length to 60 miles, or the earth’s equatorialcircumference equal to 21,600 miles. This gave for thecircumference of the moon’s orbit 1,296,000 miles, andfor the moon’s motion in one second rather less thanhalf a mile. Thus t m and in B are known, for m Eis equal to thirty terrestrial diameters ; and thus it iseasy to determine t E.* Now Newton found, thatwith the estimate he had adopted for the earth’sdimensions, t E exceeded m E by an amount which,increased 3,600-fold, only gave about 14 feet,—insteadof 16 T V feet, the actual fall in a second at the earth’ssurface.
This discordance appeared to Newton to be toogreat to admit of being reconciled in any way withthe theory he had conceived. If the deflection of themoon’s path had given a result greater than the actualvalue of gravity, he could have explained the discre-pancy as due to the circumstance that the moon’sown mass adds to the attraction between the earthand herself. But a less value was quite inexplicable.He therefore laid aside the investigation.
Fourteen years later Newton’s attention was againattracted to the subject, by a remark in a letteraddressed to him by Dr. Hooke, to the effect that abody attracted by a force varying inversely as the
* By Euc. I. 47 the square on t E is equal to the squares on l Mand M E.