_For the time of New Moon in_ April 1764.
Sun from Node
s ° ʹ
Table II, mean New Moon in _March 1764, New Stile_, 11 4 57
Table VI, add for 1 Lunation to carry it to _April_ 1 0 40
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Sun’s distance from the Node at New Moon in _April_ 0 5 37
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Which, being within the above limit, the Sun must be eclipsed: and
therefore, we proceed to find the rest of the Elements for computing
this Eclipse.
_To find the Moons Horizontal Parallax, or the Angle of the Earth’s
semi-diameter as seen from the Moon._
[Sidenote: Second Element.]
358. PRECEPT. Having found the Moon’s mean Anomaly for the above time,
by the first and second Precepts of § 355, enter the XVth Table with the
signs and degrees of that Anomaly, and thereby take out the Moon’s
Horizontal Parallax: only note, that this is given but to every 6th
degree of Anomaly in the Table, because it is very easy to make proper
allowance by sight. So the Moon’s Horizontal Parallax _April_ the 1st
1764, at 10 hours 25 minutes in the Forenoon, answering to her mean
Anomaly at that time (namely 11^s 9° 21ʹ) is 55ʹ 7ʺ; which, diminished
by 10ʺ, the Sun’s constant Horizontal Parallax, gives for the
semi-diameter of the Earth’s Disc 54ʹ 57ʺ.
_To find the Sun’s true Place, and his distance from the nearest
Solstice._
[Sidenote: Third Element.]
359. PRECEPT I. We are to consider, that the beginning of Aries and of
Libra, which are the Equinoctial Points, are equidistant from the
beginning of Cancer and of Capricorn, which are the Solstitial Points.
Hence, when we know in what Sign and Degree the Sun is, we can easily
find his distance from the nearest Solstice. Now, to find the Sun’s
Place, or Longitude from Aries, _April_ the 1st, 1764, at 10 hours 21
minutes in the Forenoon; being the equated time of New Moon.
PRECEPT II. This being to the time of New Moon, take out the Sun’s mean
Place and Anomaly from Table II. for that time, and the Equation of his
mean Place from Table XII by his Anomaly; adding the Equation to his
mean Place or subtracting it from the same, as the Table directs, will
give his true Place.