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care, and with instrumental appliances superior toany which had been hitherto employed. The newestimate of the earth’s dimensions differed consider-ably from the estimate employed by Newton before.Instead of a degree of arc at the equator being but 60miles in length, it now appeared that there are rathermore than 69 miles in each degree. The effect of thischange will be at once apparent. The earth’s attrac-tive energy at the moon’s distance remains unaffected,simply because the proportion of the moon’s distanceto the earth’s diameter had alone been in question.Newton, therefore, still estimated the earth’s attrac-tion at the moon’s distance as less than her attractionat her own surface, in the proportion of 1 to 3,600.But now all the real dimensions, as well of the earthas of the moon’s orbit, were enlarged linearly in theproportion of 69| to 60. Therefore the fall of themoon per second towards the earth, increased in theproportion of 3,600 to 1, was enlarged from ratherless than 14 feet to rather more than 16 feet,—agree-ing, therefore, quite as closely as could be expectedwith the observed fall of 16 T m feet per second ina body acted upon by gravity and starting fromrest.
It is said that as Newton found his figures tendingto the desired end, he was so agitated that he wascompelled to ask a friend to complete the calculations.The story is probably apocryphal, because the calcu-lations actually required were of extreme simplicity.Yet if any circumstance could have rendered Newton