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(192
ward, the Angle CPO, or 12'31",92 in right Ascension measured about the Pole P by the Arc DO, in reference to the fixed Stars.  Which Arc expressed in Parts of a great Circle comes to 11'11",17; and, by a Medium, may well require 22 Minutes Time, or else, considerably more, for its Description.  Now an Error of 22 Minutes in Time would cause an Error of 5 Degrees 30' in Longitude.  And, As the Radius, Is to the Sine of the Latitude of the Place of Observation; So would be the Sine of 5 degrees 30', To the Sine of the [[underlined]] Error [[/underlined]] in Longitude [[underlined]] reduced [[/underlined]] into Minutes or Marine Miles of 60 in a Degree of a great Circle; supposing the Earth to be Spherical.  And so, upon the whole, the Error, in the concluded Longitude of the Place of Observation, might well amount to or exceed three hundred Geographical Miles of sixty in a Degree, For the [[underlined]] Difference [[/underlined]] of about three Minutes fifty-six Seconds between one Revolution of the fixed Stars and one Solar Day, which is [[underlined]] neglected [[/underlined]], here, would make the Error still greater.  And likewise in the Triangle CPo, the Angle CPo would be found of 12' 33" 1/4.  But the Angle CP [[underlined]] O [[/underlined]] would be of 8' 31",19 4/9; and the Angle CP [[underlined]] o [[/underlined]] of 8' 32",11 1/2.
13. As to the [[underlined]] least Errors [[/underlined]] in the Longitude, [[underlined]] which [[/underlined]] may be caused by a double horizontal Refraction of Light in the Moon's Atmosphere, they would never amount to less than does result from the Time required for the Moon to advance in her proper Motion Eastward, by 2'24".  Now, by the ord'nary Tables, she does advance in her Orbit at most 30 Minutes in one Hour, and at least

Transcription Notes:
minor edits; mainly spacing, but also "Sine" not "Line" several times. -megshu