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EXAMPLE XI.

Required the Sun's true place,October 23, 0. Style, at 16 hours, 57 minutes past noon, in the 4008th year before Christ I. which was the 4007th year before the year of his birth, and the year of the Julian period, 706. This is supposed by some to be the very instant of the Creation.

BY THE PRECEPTS.

From the Radical number after Christ,.
Subtract for 5000 complete years,
Remains for a new Radix,
To which add.

Complete years,
October
Days,
Hours,

Minutes,
Sun's mean place at the given time,
Subtract equation of the Sun's centre,.
Sun's true place at that time,
Which was just entering the Sign LIBRA.

Sun's Long Sun's anomy S D M S S D M S 9 7 53 10 6 28 48 0 1 7 46 40 10 13 25 0

8 0 6 30 8 15 23 0 9000 6 48 011 21 37 0 800 0 36 16 11 29 15 0 120 0 5 26 11 29 15 0

8 29 4 54 8 29 4 0 0 22 40 12 0 22 40 12 39 26

39 26 2 20

2 20 6 0 3 4 5 28 33 58 3 4

Argt. eqt’n. 0 0 0 Sun's centre

CONCEHAZT IS Eclipses of the Sun A MIOON.

To find the Sun's true distance from the Moon's as

cending node, at the time of any given new or full Moon, and consequently to know whether there be an Eclipse at that time or not.

The Sun's mean distance from the Moon's ascending node, is the Argument for finding the Moon's fourth equation in the syzygies, and therefore it is taken into all the foregoing Examples, in finding the true times thereof. Thus at the time of mean new Moon in March, 1764, Old Style, or April in the new, the Sun's mean distance from the ascending node, is 0 signs, 35 minutes, 2 seconds. [See Table First.] The descending node is opposite to the ascending one, and consequently are exactly 6 signs distant from each other. When the Sun is within 17 degrees of either of the nodes at the time of new Moon; he will be eclipsed at that time, as before stated, and at the time of full Moon, if the Sun be within 12 degrees of either node, she will be eclipsed. Thus we find from Table First, that there was an Eclipse of the Sun, at the time of new Moon, April 1st. at 30 minutes, 25 seconds after 10 in the morning at LONDON, New Style, when the old is reduced to the new, and the mean time reduced to the true.

It will be found by the Precepts, that the true time of that new Moon is 50 minutes, 46 seconds later, than the mean time, and therefore we must add the Sun's motion from the node during that interval to the above mean distance Os. 6d. 35m. 2s, which motion is found

in Table Twelfth, for 50 minutes and 46 seconds to be 2 minutes, 12 seconds, and to this apply the equation of the Sun's mean distance from the node in Table 13th, which at the mean time of new Moon, April 1st. 1764, is 9 signs, 1 degree, 26 minutes, and 20 seconds, and we shall have the Sun's true distance from the node at the true time of new Moon, as follows :

Sun from node.

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At the mean time of N.Moon in April, 1764, 0 5 35 2 Sun's motion from node for 50 minutes,

2 10 For 46 seconds,

2 Sun's mean dist from node at true N. Moon, 0 5 37 1.1. Equation from mean dist from node, add, 25 Sun's true dist. from the ascending node, 0 7 42 14 Which being far within the above named limits of 17 degrees, the Sun was at that time eclipsed. The manner of projecting this or any other Eclipse, either of the Sun or Moon, will now be shown.

SECTION SIXTEENTH.

To Project an Eclipse of the Sun.

To project an Eclipse of the Sun, we must from the

Tables find the ten following Elements :

1st. The true time of conjunction of the Sun and Moon, and

2d. The semi-diameter of the earth's disk, as seen from the Moon, at the true time of conjunction ; which is equal to the Moon's horizontal parallax.

3d. The Sun's distance from the solstitial colure, to which he is then nearest.

4th. The Sun's declination.

5th. The angle of the Moon's visible path with the ecliptic.

6th. The Moon's latitude. 7th. The Moon's true horary motion from the Sun. 8th. The Sun's semi-diameter, 9th. The Moon's semi-diameter. 10th. The semi-diameter of the penm bra.

EXAMPLE XII.

Required the true time of New Moon at LONDON, in April, 1764, New Style, and also whether there were an Eclipse of the Sun or not at that time ; and likewise the elements necessary for its protraction, if there were at that time an Eclipse.

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mean time of Sun's mean Moons meanSun's means

New Moon anomaly. anomaly. dist”. from By the Precepts. in March.

the node. DH M

S M March 1764

2 8 55 36 8 2 20 0 10 13 35 21 11 4 54 48 Add 1 lunation 29 12 44 3 0 29 6 19 0 25 49 0 1 0 40 141 Mean New Moon 31 21 39 39 9 1 26 19 11 9 24 21! 0 5 55 2 First equation 4 10 40 Arg 1st eqt'n

1 34 57 32 1 50 19 9 1 26 19 11 10 59 18 Second equation.

3 24 49 11 10 59 18 Arg 2nd eqt'

31 22 25 30 9 20 27 111 10 59 18 0 5 35 2 Third equation 4 37 Arg 3d eqt'n

Arg 4th eqt' 31 22 30 7

Sun from 18

node True New Moon 31 22 30 25

0 5 35 2 Equation of days

3 48 31 22 26 35

The true time is April 1st, 10 hours, 26 minutes, 35 seconds in the morning, tabular time. The mean distance of the Sun at that time, being only 5 degrees, 35 minutes and 2 seconds past the ascending node, the Sun was at that time eclipsed. Now proceed to find the elements, necessary for its protraction. The true time being found as above.

To find the Moon's horizontal parallax, or semi-diameter of the Earth's disk as seen from the Moon:

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