through these points, will represent the parallel of latitude, or path of London, on the disk as seen from the Sun from its rising to its setting.

If the Sun's declination had been south, the diurnal path of London would have been on the upper side of the line VIK VI, and would have touched the line DL E in L. It is necessary to divide the hourly spaces into quarters, and if possible into minutes also.

Make CB the radius of a line of chords on the sector, and taking therefrom the chord of 5 degrees and 35 minutes, (the angle of the Moon's visible path with the ecliptic;) set it off from H to M on the left hand of C H, (the axis of the ecliptic) because the Moon's latitude in this case is north ascending. Then draw CM for the axis of the Moon's orbit, and bisect the angle MCH by the right line CZ. If the Moon's latitude had been north descending, the axis of her orbit would have been on the right hand from the axis of the ecliptic.

The axis of the Moon's orbit lies the same way when her latitude is south ascending, as when it is north ascending, and the same way when south descending, as when north descending.

Take the Moon's latitude (40 minutes and 18 seconds) from the scale C A in your compasses, and set it from i to z in the bisecting line C Z, making i x parallel to Cy and through x at right angles; to the Moon's orbit (CM) draw the straight line Nwxys for the path of the penumbra's centre over the earth's disk.

The point win the axis of the Moon's orbit, is that, where the penumbra's centre approaches nearest to the centre of the earth's disk, and consequently is the middle of the general eclipse. The point is where the conjunction of the Sun and Moon falls, according to equal time, as calculated by the tables, and the point y is the ecliptical conjunction of the Sun and Moon.

Take the Moon's true horary motion from the Sun, (27 minutes and 54 seconds,) in your compasses, from the scale C A, (every division of which is a minute of a degree,) and with that extent make marks along the

:

path of the penumbra's centre, and divide each space from mark to inark, into 60 equal parts, or horary minutes, by dots, and set the hours to every 60th minute in such manner, that the dot signifying the instant of new Moon by the tables, may fall into the point x, half way between the axis of the Moon's orbit and the axis of the ecliptic; and then the remaining dots will be the points on the earth's disk, where the penumbra's centre is at the instants denoted by them in its transit over the earth.

Apply one side of a square to the line of the penumbra's path, and move the square backwards and forwards until the other side of it cuts the same hour and minute, (as at m and m) both in the path of the penumbra's centre and the path of London; and the particular minute or instant which the square cuts at the same time in both paths, will be the instant of the visible conjunction of the Sun and Moon, or the greatest obscuration of the Sun at the place for which the construction is made, (namely, London in this example,) and this instant is at 47 minutes and 29 seconds past 10 o'clock in the morning, which is 17 minutes, 5 seconds later than the tabular time of true conjunction.

Take the Sun's semidiameter, (16 minutes and six seconds,) in your compasses, from the scale C A, and setting one foot in the path of London at m, viz. at 47 minutes and 30 seconds past 10, with the other foot describe the circle U Y, which will represent the Sun's disk as seen from London at the greatest obscuration.

Then take the Moon's semidiameter, 14 minutes and 57 seconds, in your compasses, from the same scale, and setting one foot in the path of the penumbra's centre at m in the 47 minutes after 10, with the other foot describe the circle T Y for the Moon's disk, as seen from London at the time when the eclipse is at the greatest, and the portion of the Sun's disk, which is hidden or cut off by the disk of the Moon, will show the quantity of the eclipse at that time, which quantity may be measured on a line equal to the Sun's diameter, and divide it into 12 equal parts for digits, which, in this example, is nearly 11 digits. This eclipse was annular at Paris.

Penumbra's

Earth's semi-disk.

A

1

Lastly, take the semidiameter of the penumbra, 31 minutes and 3 seconds, from the scale A C, in your compasses, and setting one foot in the line of the penumbra's path, on the left hand, from the axis of the ecliptic, direct the other foot towards the path of London, and carry that extent backwards and forwards, until both the points of the compasses fall into the same instants in both the paths, and these instants will denote the time when the eclipse begins at London. Proceed in the same manner on the right hand of the axis of the ecliptic, and where the points of the compasses fall into the same instants in both the paths, they will show at what time the eclipse ends at London.

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.

SECTION SEVENTEENTH.

THE PROJECTION OF LUNAR ECLIPSES.

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.

1

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 fol

lows:

1st. The true time of full Moon.

2d. The Moon's horizontal parallax.

3d. The Sun's semidiameter.

4th. The Moon's semidiameter.

5th. The semidiameter 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