Your established Character in the World as a Natural Philosopher and Master of Science, being a Native of America myself (tho’ expelled by the Fortune of War from South Carolina) induces me to address a Line to you on a Subject interesting to the World at large but particularly to all maritime States. I shall esteem the acknowledgment of the Receipt of this with your candid and free Opinion thereon as an Honor conferred on Sir Your most Obedient and most humble Servant

By measuring Space by Time The Moon appears to Me to be at the Distance of 36,313.845 Statute Miles from the Earths Center—Radius of her Orbit 2 = 72627.69 Diameter of Ditto x 3.1426968 (The true Proportion of Circumference to Diameter) = 228246.809 Miles for the Circumference of Orbit 29.530851 Days to one Revolution (= 235 migh?) = 7729.09689 Miles as the Diurnal Motion of the Moon and supposing her to revolve round her own Axis 3.1426968 = 2459.383574 Miles for her Diameter. I go on the Data that the Earths Radius is = 4000 Miles and Revolution in 24 Hours of our Time.

The Use I would recommend the above to would be to ascertain the true Longitude of Places East and West of any fixt Meridian (for which Purpose I have begun (tho a most tedious Business to calculate the sines and Co-sines to 1¹, for 45º the 8th part of Earths Circumference. As the lines of 45°, become the Co-sines for the Remainder of Quadrant by squaring the former, deducting the same from of Radius and taking the Roots of Remainders for Co-sines which are the Sines for other Part. The Sines by Logarithms are I think very untrue tho’ they answer for small Distances. Such Table being compleat for real Time, If an Observation be make on any fixt day when the Sun is in the Meridian of Observer and the Moons Angle be ascertained to the Earth’s Center by referring to the Table for Angle of Moon at fix Meridian for that day The difference of Angle of Observation from Tabulat Angle will be the Difference of Time and Distance And by simple Proportion. As suppose from 0 in Scheme, you find the Angle of Moon, as at Moon observed, and by your Table it should be in your Zenith on due South The difference between the Time being known Say As 10631.10636 Minutes in Quadrant of Moons Orbit : 3600' (=6 Hours Earths Quadrant) :: Difference of Time in Angle : Min on Earths Surface Then As 3600' : 6285.3936 Miles in Quadrant :: difference of Time : Miles in Longitude.

Suppose a Person at the Equator on any day when the Moon at any fixt Meridian should be due South at Noon but by Observation should be found to have an Angle which being corrected for Earths Center as in the Scheme below as OE Moon observed = 65° from Observer’s Zenith = 7678.021293 Minutes of Time They say As 10631.10636 : 3600' :: 7678.021293 : 2600' Time As 3600 : 6285.3936 Miles in Quadrant :: 2600' : 4539.45093 Miles But Suppose the Observer to be in Latitude 25° North and find same Angle of Difference look into Table for Cosine and you’ll find 3678.4313 1.5713484 = 5680.0971 Miles for Quadrant in that latitude then say as 90° : 5780.0971 :: 65° : 4174.514572 Miles Quare if not the true Distance of Nassau in New Providence West of such fixt Meridian. Please excuse the want of Scholastic Terms as the Ideas are my own without such Help, but from Mechanic Principles.

Quadrant of Moons Orbit at 25°. taken as a Globe of that Size as a Proof for this Globe Earths Radius 4000 1.5713484 = 6285.3936 Miles Quadrant And the Proportion is easily demonstrated tho differing from all before it. Quare How can any Person know exactly in what Latitude He is in by the usual method of taken the declination at a fixt Meridian when perhaps she be from 50° to 90° West of same when the Declination is varying constantly and at a considerable Rate and 6 Hours carries a Quadrant of this Globe to Meridian fixt.