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[[Left margin]] From Gents. Mag. for 1737. Vol. 7 p. 490. [[/left margin]]

[[Underline]] A Demonstration that the Center of the Orb described annually by the common Center of Gravity of the Earth and of the Moon, and improperly called the Great Orb, is vastly nearer to the Earth, and that Orb much smaller, than is commonly supposed.
   This Demonstration is drawn from the Smallness of the Fall of the Moon and the Earth towards the Sun in two Minutes Time. [[/underline]]
   1. SUPPOSING the periodic or annual Revolution of the Earth, in reference to the fixed Stars, to be performed in her Orbit, in 365 Days, 6 Hours and 9 Minutes; Then in two Minutes Time the Earth would describe in a circular Orbit an Arc of 4",920'040'; of which Number the Logarithim is 0.6926749.
   2. Now, As 60" quad. Is to 4", 920'040' quad. So is 2.6264222 the Logarithmic Versed Sine of 60", or of 1 Minute in the Tables; To the Logarithmic Versed Sine that would belong to 4", 920'040' in the Tables, which Logarithmic Versed Sine is found to be 0.4554695. And therefore this is the Logarithim of the mean Fall in 2 Minutes Time, of G ye common Center of Gravity of Earth & of ye Moon 

[[Left margin]] Fig. 50. [[/left margin]]

toward ye Sun, or toward ye Center O of the Great Orb; taking the Radius GO, or the mean Distance betwixt the Center of the great Orb and the common Center of Gravity of the Moon and of the Earth. But when the Triangle LST is equicrural, the three Falls toward the Sun in two Minutes, or in an insensible Time, of the Moon, of the Earth; and of the Center G, are nearly equal; and the one being found, they are all three known.
  3. And whereas by Sir [[Underline]] Isaac Newton's [[/underline]] Theory of the Moon, as amended by what I demonstrate we