According to this construction, this Eclipse began at 20 minutes after 9 in the morning, at LONDON, at the points N. and O. 47 minutes and 30 seconds after 10, at the points m. and m. for the time of the greatest obscuration, and 18 minutes after 12, at R. and S. for the time when the Eclipse ends.

In this construction, it is supposed that the angles under which the Moon's disk is seen during the whole time of the Eclipse, continues invariably the same, and that the Moon's motion is uniform, and rectilinear during that time. But these suppositions do not exactly agree with the truth and therefore supposing the elements given by the Tables to be accurate, yet the times and phases of the Eclipse deduced from its construction, will not answer to exactly what passes in the Heavens, but may be at least two or three minutes wrong, though the work may be done with the greatest care and attention.

The paths also, of all places of considerable latitudes are nearer the centre of the Earth's disk as seen from the Sun, than those constructions make them; because the disk is projected as if the Earth were a perfect sphere, although it is known to be a spheroid. The Moon's shadow will consequently go farther northward in all places of northern latitude, and farther southward in all places of southern latitude, than can be shown by any projection.

WHEN the Moon is within 12 degrees of either of her nodes, at the time when she is full, she will be eclipsed, otherwise not, as before stated,

Required the true time of full Moon, at LONDON, in May, 1762, New Style, and also whether there were an Eclipse of the Moon at that time or not.

It will be found by the Precepts, that at the true time of full Moon in May, 1762, the Sun's mean distance from the ascending node was only 4 degrees, 49 minutes and 36 seconds, and the Moon being then opposite to the Sun, must have been just as near her descending node, and was therefore eclipsed. The elements for the construction of Lunar Eclipses are eight in number, as follows:

1st, The true time of full Moon.

2d. The Moon's horizontal parallax.

3d. The Sun's semi-diameter.

4th. The Moon's semi-diameter.

5th. The semi-diameter of the Earth's shadow at the Moon.

6th. The Moon's latitude.

7th. The angle of the Moon's visible path with the ecliptic.

8th. The Moon's true horary motion from the Sun. To find the true time of full Moon, proceed as directed in the Precepts, and the true time of full Moon in May, 1762, will be found on the 8th day, at 50 minutes, and 50 seconds past 3 o'clock in the morning.

To find the Moon's horizontal parallax, enter Table 15th with the Moon's mean anomaly, (at the time of the above full Moon,) namely, 9s. 2d. 42m. 42 seconds, and with it take out her horizontal parallax, which, by making the requisite proportions will be found to be 57 minutes and 23 seconds.

To find the semi-diameters of the Sun and Moon, enter Table 15th, with their respective anomalies, the Sun's being 10s. 7d. 27m. 45 seconds, and the Moon's 9s. 2d. 42m. 42 seconds, (in this case,) and with these take out their respective semi-diameters, the Sun's 15 minutes and 56 seconds, and the Moon's 15 minutes and 38 seconds.

To find the semi-diameter of the Earth's shadow at the Moon, add the Sun's horizontal parallax, (which is always 9 seconds,) to the Moon's which in the pres

ent case is 57 minutes and 23 seconds, the Sun will be 57 minutes and 32 seconds; from which subtract the Sun's semi-diameter, 15 minutes and 56 seconds, and there will remain 41 minutes and 36 seconds for the semi-diameter of that part of the Earth's shadow, which the Moon then passes through.

Find the Sun's true

To find the Moon's latitude. distance from the Moon's ascending node, (as already taught,) in the first Example for finding the Sun's true place, at the true time of full Moon, and this distance increased by 6 signs, will be the Moon's true distance from the same node, and consequently the Argument for finding her true latitude.

The Sun's mean distance from the ascending node was at the true time of full Moon, Os. 4d. 49m. 35 seconds; but it appears by the Example that the true time thereof, was 6 hours, 33 minutes and 38 seconds sooner, than the mean time, and therefore we must subtract the Sun's motion from the node during this interval, from the above mean distance Os. 4.1. 49m.and 35 seconds, in order, to have his mean distance from the node, at the time of true full Moon. Then, to this apply the eqnation of his mean distance from the node, found in Table 13th, by his mean anomaly, 10s. 7d. 27m. 45 seconds, and lastly, add six signs, and the Moon's true distance from the ascending node, will be found as follows: