EXAMPLE X.

Pequired the true time of new Moon in July, Old Style, 2180 at WASHINGTON.

FOUR CENTURIES ADDED TO 1780 MAKE 2180.

Mean new
Moon in
March.

Sun's mean

Moon's

mean

Sun's dist. fr. Moon's

anomaly. anomaly. ascen.node

D. H. M. S. S. D. M. S. S. D. M. S. S. D. M. S.

By the PRECEPTS.

March, 1780.

23 23 1 44

9 4 18 13 1 21 7 47 10 18 21 1

Add 400 years.

17 8 43 29

0 13 24 0 10 1 28 0 6 17 49 0

New Moon, July, 2180

First equation.

24 12

Time once equated.

Second equation.

Third equation.

Fourth equation.

F. Clock.

True time at London. Difference of long.

True time at Washing'n

7 21 57 22 0 15 111 2 10 2 49 8 8 1 43 1 3 39 Arg. 1st eqt.

7 20 53 43 0 15 111 2 9 38 37 8 8 10 43 9 24 8 2 9 38 37 Arg. 2d eqt. Arg. 4th eqt.

8 6 17 51 10 5 22 34

3 56 Arg. 3d eqt.

8 6 21 47

18

8 6 22 55

4 30

8 6 18 25
58

8 1 10 25

The true time of new Moon, Old Style, will then be on the 8th day of July, 1 hour 10 minutes and 25 seconds afternoon; or the 22d day, at the same hour, minute and second, New Style.

EXAMPLE I.

For finding the Sun's true place.

Required the Sun's true place, March 20th, 1764, Old Style, at 22 hours, 30 minutes, 25 seconds past noon. In common reckoning, March 21st, at 10 hours 30 minutes and 25 seconds in the morning.

EXAMPLE II.

Required the Sun's true place, October 23, Old Style, at 16 hours, 57 minutes past noon in the 4008th year before Christ; 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.

CONCERNING ECLIPSES OF THE SUN AND MOON.

To find the Sun's true distance from the Moon's ascending 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 in 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 Example 11th.] The descending node is opposite to the ascending one, and consequently they 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 1st, 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 0 signs, 6 degrees, 35 minutes, 2 seconds, which motion is found, in Table 12th, 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.

S. D. M. S.

At the mean time of new Moon in April, 1764, 0 5 35 2
Sun's motion from node for 50 minutes,
For 46 seconds,

2 10

2

Suns mean dist. from node at true new Moon, 0 5 37 14 Equation from mean dist. from node, add, 250

Sun's true dist from the ascending node, 07 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 SIXTEENΝΤΗ.

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 semidiameter 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 semidiameter.

9th. The Moon's semidiameter.

10th. The semidiameter of the penumbra.