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tory of the discovery, let us employ the elements ac-tually adopted by Newton at this stage of his labours.
Newton adopted for the moon’s distance in termsof the earth’s radius a value very closely correspond-ing to that now in use. We may, for our presentpurpose, regard this estimate as placing the moonat a distance equal to sixty terrestrial radii. Thusthe attraction of the earth is reduced at the moon’sdistance in the proportion of the square of sixty, or3,600, to unity. Now, let us suppose the moon’sorbit circular, and let to m', fig. 13, Plate IN., be thearc traversed by the moon in a second around theearth at B (to to' is of course much larger in proportionthan the arc really traversed by the moon in a second),then when at to the moon’s course was such, that ifthe earth had not attracted her, she would have beencarried along the tangent line m t; and if t be theplace she would have reached in a second, then m tis equal to m to', and E t will pass almost exactlythrough the point to'. Thus t to', which representsthe amount of fall towards the earth in one second,may be regarded as lying on the line t E.* Nowto' E is equal to to E, and therefore t to' represents thedifference between the two sides to E and t E of the
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* In the account ordinarily given, t m' is taken as lying parallelto to E. This is also approximately true. As a matter of fact thepoint to' lies a little outside t E (that is on the side away from m)and a little within the parallel to to E, through t. But the anglet Em is exceedingly minute; this angle as drawn represent-ing the moon’s motion for about half a day instead of a singlesecond of time.