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half her enlightened face, soon she appears as a radiant crescent, in a little time all her brightness vanishes, and she becomes a beamless orb.

The full moon, or opposition, is that state in which her whole disc is enlightened, and we see it all bright, and of a circular figure. The new-moon is when she is in conjunction with the sun; in this state, the whole surface turned towards us is dark, and is therefore invisible to us.

The first quarter of the moon she appears in the form of a semicircle, but with the circumference turned towards the west. At the last quarter, she appears again under the form of a semicircle, but with the circumference turned towards the east.

These phases may be illustrated in a very pleasing manner to the pupil, by exposing an ivory ball to the sun, in a variety of positions, by which it may present a greater or smaller part of its illuminated surface to the observer. If it be held nearly in opposition, so that the eye of the observer may be almost immediately between it and the sun, the greatest part of the enlightened side will be seen; but if it be moved in a circular orbit, towards the sun, the visible enlightened part will gradually decrease, and at last disappear, when the ball is held directly towards the sun. Or, to apply the experiment more immediately to our purpose; if the ball, at any time when the sun and moon are both visible, be held directly between the eye of the observer and the moon, that part of the ball on which the sun shines, will appear exactly of the same figure as the moon itself.

The phases of the moon, like those of Venus, may also be illustrated by a diagram; thus, in plate 9, fig. 1, let S be the sun, T the earth, ABCDEFGH the orbit of the moon. The first observation to be deduced from this figure is, that the half of the earth and moon, which is towards the sun, is wholly enlightened by it; and the other half, which is turned from it, is totally dark. When the moon is in conjunction with the sun at A, her enlightened hemisphere is turned towards the sun, and the dark one towards the earth; in which case we cannot see her, and it is said to be new-moon. When the moon has moved from A to B, a small portion, ab, of her enlightened hemisphere will be turned towards the earth;, which portion will appear of the form represented at B, fig. 2, (a figure which exhibits the phases as they appear to us).

As the moon proceeds in her orbit, according to the order of the letters, more and more of her enlightened part is turned towards the earth. When she arrives at C, in which position she is said to be in quadrature, one-half of that part towards the earth is enlightened, appearing as at C among the phases; this appearance is called a half-moon. When she comes to D, the greatest part of that half which is towards us is enlightened; the moon is then said to be gibbous, and of that figure which is seen at D,

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in fig. 2.

When the moon comes to E, she is in opposition to the sun, and consequently turns all her illuminated surface towards the earth, and shines with a full face, for which reason she is called a full-moon. As she passes through the other half of her orbit, from E, by FG, and H, to A again, she puts on the same phases as before, but in a contrary order or position.

As the moon, by reflected light from the sun, illuminates the earth; so the earth, does more than repay her kindness, in enlightening the surface of the moon, by the sun's reflex light, which she diffuses more abundantly upon the moon, than the moon does upon us: for the surface of the earth is considerably greater than that of the moon; and consequently, if both bodies reflect light in proportion to their size, the earth will reflect much more light upon the moon than it receives from it.

In a new-moon, the illuminated side of the earth is fully turned towards the moon, and the Lunarians will have a full earth, as we, in a similar position, have a full-moon. And from thence arises that dim light which is observed in the old and newmoons; whereby, besides the bright and shining horns, we can perceive the rest of her body behind them, though but dark and obscure. Now, when the moon comes to be in opposition to the sun, the earth, seen from the moon, will appear in conjunction with him, and its dark side will be turned towards the moon, in which position the earth will be invisible to the Lunarians; after this, the earth will appear to them as a crescent. In a word, the earth

exhibits the same appearance to the inhabitants of the moon, as the moon does to us.

The moon turns about its own axis in the same time that it moves round the earth; it is on this account that she always presents nearly the same face to us: for, by this motion round her axis, she turns just so much of her surface constantly towards us, as by her motion about the earth would be turned from us. This motion about her axis is equable and tiniform, but that about the earth is unequal and irregular, as being performed in an ellipses; consequently, the same precise part of the moon's surface can never be shewn constantly to the earth; which is confirmed by a telescope, by which we often observe a little segment on the eastern and western limb, appear and disappear by turns as if her body librated to and fro; this phenomenon is called the moon's libration. The lunar motions are subject to several other irregularities, which are fully discussed in the larger works on astronomy.

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OF THE SATELLITES OF JUPITER, SATURN, AND
THE GEORGIUM SIDUS. :

The existence of all the satellites, except the moon, must have remained unknown, without the assistance of the telescope... By the assistance of this instrument, Jupiter is found to be attended by four, Saturn by seven, and the Georgium Sidus by six.

The satellites are distinguished according to their

places; into first, second, &c.; the first being that which is nearest the planet. They revolve round their respective primaries in elliptic orbits, the primary planets being in the focus.

The planes of the orbits of the secondary planets produced, intersect the heliocentric orbits of their primaries in two opposite points; which are called their nodes.

Again, the planes of the orbits of the satellites produced, intersect the ecliptic in two opposite points, these are called the geocentric nodes of the satellites...

The orbits of Jupiter's satellites are nearly, but not exactly, in the same plane. This plane produced makes an angle of about 3o with Jupiter's orbit. The second deviates a little from the rest.

The orbits of Saturn's satellites, except the 5th, which deviates from the rest several degrees, are nearly in the same plane. They are nearly parallel to the plane of the equator. The orbit of the 5th satellite makes an angle with the orbits of its primary of 13° 8'.

The system of Jupiter and his satellites is very large in itself; yet, on account of its immense distance from us, it appears to occupy but a small space in the sphere of the starry heavens; and, consequently, every satellite of Jupiter appears to us always near its primary, and to have an oscillatory motion, like that of a pendulum; going alternately from its greatest digression on one side the planet, to its

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