apparent orbit; because the moon appears to the inhabitants of the earth to move in that circle, through the twelve signs of the zodiac, in a periodical month. This position is illustrated by the following figure; let EFGHI, plate 9, fig. 3, be the orbit of the earth; $ the sun; abcd the orbit of the moon, when the earth is at E: let ABCD be a great circle in the sphere of the heaven, in the same plane with the moon's orbit.

The moon, by going round her orbit according to the order of letters, appears to an inhabitant of the earth to go round in the great circle ABCD, according to the order of those letters: for, when the moon is at a, seen from the earth at E, she appears at A; when the moon is got to b, she appears at B; when to c, she will appear at C; when arrived at d, she will appear at D. It is true, when the moon is at b, the visual line drawn from E, through the moon, terminates in L; as it does in M, when the moon is at d; but the lines LM, and DB, being pas rallel, and not farther distant from each other than the distance of the earth's orbit, are, as to sense, coincident; their distance measured in the sphere of the heaven being insensible: for the same reason, though the earth moves from E to F, in the time that the moon goes round her orbit, so that, at the end of a periodical month, the moon will be at a, and is seen from the earth at F, in the line FN; the moon will, notwithstanding, appear at A, the lines FN and EA being parallel, and, as to sense, coincident: in like manner, in whatever part of her orbit the earth is, as at H or I, the moon, by going round in her orbit;

will appear to an inhabitant of the earth to go round in the great circle ABCD.

The plane of the moon's orbit extended to the heaven's, cuts the ecliptic in two opposite points.

The two points where the moon's apparent orbit thus cuts the ecliptic, are called the moon's nodes.

The point where the moon appears to cross the ecliptic, as she goes into north latitude, is called the moon's ascending node, of which this is the character; the point where the moon goes into south latitude is her descending node, and is marked thus ; the moon's ascending node is often called the dragon's head; her descending node the dragon's tail.

The line of the moon's node is a line drawn from one node to the other.

The extremities of the line of the nodes are not always directed towards the same points of the ecliptic, but continually shift their places from east to west; or, contrary to the order of the signs, performing an entire revolution about the earth, in the space of something less than nineteen years.

The moon appears in the ecliptic only when she is in one of her nodes; in all other parts of her orbit she is either in north or south latitude, sometimes nearer to, sometimes further removed from the ecliptic, according as she happens to be more or less distant from the nodes.

When the place, in which the moon appears to an inhabitant of the earth, is the same with the sun's place, she is said to be in conjunction. When the

moon's place is opposite to the sun's place, she is said to be in opposition. When she is a quarter of a circle distant from the sun, she is said to be in quadrature. Both the conjunction and the opposition of the moon are termed syzigies.

The common lunar month, or the time that passes between any new-moon and the next that follows, is called a synodical month, or a or a lunation. This month contains 29 days, 12 hours, 44 minutes, 3 seconds.

A periodical month is the time the moon takes up to describe her orbit: or, in other words, the time in which the moon performs one entire revolution about the earth, from any point in the zodiac to the same again; and contains 27 days, 7 hours, 43 minutes.

If the earth had no revolution round the sun, or the sun had no apparent motion in the ecliptic, the periodical and synodical month would be the same; but as this is not the case, the moon takes up a longer time to pass from one conjunction to the next, than to describe its whole orbit; or the time between one new-moon and the next, is longer than the moon's periodical time.

The moon revolves round the earth from west. to. east, and the sun apparently revolves round the earth the same way. Now at the new-moon, or when the sun and moon are in conjunction, they both set out. from the same place, to move the same way round, the earth; but the moon moves, much faster than the sun, and, consequently, will overtake it; and when the moon does overtake it, it will be a new-moon

again. If the sun had no apparent motion in the ecliptic, the moon, would come up to it, or be in conjunction again, after it had gone once round in its orbit; but as the sun moves forward in the ecliptic, whilst the moon is going round, the moon must move a little more than once round, before it comes even with the sun, or before it comes to conjunction. Hence it is that the time between one conjunction and the next in succession, is something more than the time the moon takes up to go once round its orbit; or a synodical month is longer than a periodical one.

In plate 8, fig. 3, let S be the sun; CF a part of the earth's orbit; MD a diameter of the moon's orbit when the earth is at A; and md another diameter parallel to the former, when the earth is at B. Whilst the earth is at A, if the moon be at D, she will be in conjunction; and if the earth was to continue at A, when the moon had gone once round its orbit, from D through M, so as to return to D again, it would be again in conjunction. Therefore, upon the supposition that the earth has no motion in its orbit, the periodical and synodical months would be equal to one another. But as the earth does not continue at A, it will move forward in its orbit, during the revolution of the moon from A to B ; and as the moon's orbit moves with it, the diameter MD will then be in the position md; therefore, when the moon has described its orbit, it will be at d in this diameter md; but if the moon is at d, and the sun at S, the moon will not be in conjunction;

consequently, the periodical month is completed before the synodical, The moon, in order to come' to conjunction, when the earth is at B, must be at e, in the diameter ef; or, besides going once round its orbit, it must also describe the arc de. The synodical month is therefore longer than the periodical, by the time the moon takes up to describe the are de.

This may also be explained in another manner, by considering the apparent motion of the sun; a view of the subject, that may render it more easy to some young minds than the foregoing. Thus, let us suppose the earth at rest at E, plate 8, fig. 4; M the moon in conjunction with the sun at S, while the moon describes her orbit ABC about the earth at E; let the sun advance, by his apparent annual motion, from S to D. It is plain that the moon will not come in conjunction with the sun again, till, besides describing her orbit, she hath described, over and above, the arc MF corresponding to the arc SD,

OF THE PHASES OF THE MOON,

As the moon goes round the earth in a much smaller orbit than that in which the earth revolves round the sun, sometimes more, sometimes less, and sometimes no part of her enlightened-half will be towards us; hence she is incessantly varying her appearance; sometimes she looks full upon us, and her visage is all lustre ; sometimes she shews only