is at her highest and lowest points, called her limits, is 5 deg. 18 min.; this, with all the other intermediate degrees of latitude, are engraved on this ring, beginning at the nodes, and numbered both ways from them. At each side of the nodes, and at about 18 deg. distant from them, we find this mark O, and at about 12 deg. this D, to indicate that when the full moon has got as far from the nodes as the mark), there can be no eclipse of the moon, nor any eclipse of the sun; when the new moon has passed the mark O, these points are generally termed the limits of eclipses. The nodes of the moon do not remain fixed at the same point of the ecliptic, but have a motion contrary to the order of the signs.

TX is a small circle parallel to the ecliptic; it is divided into 12 signs, and each sign into 30 deg. ; this circle is moveable in its socket, and is to be set by hand, so that the same sign may be opposite to the sun, that is marked out by the annual index. These signs always keep parallel to themselves, as they go round the sun; but the inclined plane with its nodes go backwards, so that each node recedes through all the above signs in about 19 years, RS is a circle, on which are divided the days of the moon's age; XY is an ellipsis, to represent the moon's elliptical orbit, the direct motion of the apogee, or the line of the apsides, with the situation of the elliptical orbit of the moon, and place of the apogee in the ecliptic at all times.

To rectify the Lunarium.

Set the annual index on the large ecliptic, to the first of Capricorn; then turn the plate, with the moon's signs upon it, until the beginning of Capricorn points directly at the sun; turn the handle till the annual index comes to the first of January; then find the place of the north node in an ephemeris, to which place among the moon's signs, set the north node of her inclined orbit, by turning it till it is in its proper place in the circle of signs; set the moon to the day of her age,

GENERAL PHENOMENA OF THE MOON.

Having rectified the lunarium for use, on putting it into motion it will be evident,

1. That the moon, by the mechanism of the instrument, always moves in an orbit inclined to that of the ecliptic, and consequently in an orbit analogous to that in which the moon moves in the heavens.

2. That she moves from west to east.

3. That the white or illuminated face of the moon is always turned towards the sun.

4. That the nodes have a revolution contrary to the order of the signs, that is, from Aries to Pisces; that this revolution is performed in about 19 years, as in nature.

5. That the moon's rotation upon her axis is effected and completed in about 27÷ days, whereas it is 29 days from one conjunction with the sun to the next.

6. That every part of the moon is turned to the sun, in the space of her monthly or periodic revolution.

To be more particular. On turning the handle, you will observe another motion of the earth, which has not yet been spoken of, namely, its monthly motion about the common centre of gravity between the earth and moon, which centre of gravity is represented by the pin Z. From hence we learn, that it is not the centre of the earth which describes what is called the annual orbit, but the centre of gravity between the earth and the moon, and that the earth has an irregular, vermicular, or spiral motion about this centre, so that it is every month at one time nearer to, at another further from, the sun, It is evident from the instrument, that the moon does not regard the centre of the earth, but the centre of gravity, as the centre of her proper motion; that the centre of the earth is furthest from the sun at new-moon, and nearest at the full-moon; that in the quadratures the monthly parallax of the earth is so sensible, as to require a particular equation in astronomical tables. These particulars were first applied to the orrery, by the late learned and ingenious Mr. Benjamin Martin.

To explain the phases of the Moon.

The moon assumes different phases to us, 1, on account of her globular figure: 2, on account of the motion in her orbit, between the earth and the sun, for whenever the moon is between the earth and the sun, we call it new-moon, the enlightened part being then turned from us; but when the earth is between the sun and the moon, we then call it fullmoon, the whole of the enlightened part being then turned towards us.

The phases of the moon are clearly exhibited in this instrument; for we here see, that the half which is opposite to the sun is always dark, while that next to the sun is white, to represent the illuminated part. Thus, when it is new-moon, you will see the whole white part next the sun, and the dark part turned towards the earth, shewing thereby its disappearance, or the time of its conjunction and change on turning the handle, a small portion of the white part will begin to be seen from the earth, which portion will increase towards the end of the seventh day, when you will perceive that half of the light, and half of the dark side is turned towards the earth, thus illustrating the appearance of the moon at the first quarter. From hence the light side will continually shew itself more and more in a gibbous form, till at the end of fourteen days the whole white side will be turned towards the earth,

and the dark side from it, the earth now standing in a line between the sun and moon; and thus the instrument explains the opposition, or full-moon. On turning the handle again, some of the shaded part will begin to turn towards the earth, and the white side to turn away from it, decreasing in a gibbous form till the last quarter, when the moon will appear again as a crescent, which she preserves till she has attained another conjunction.

In this lunarium the moon has always the same face or side to the earth, as is evident from the spots delineated on the surface of the ivory ball, revolving about its axis, in the course of one revolution round the earth; in consequence of which the light and dark parts of the moon appear permanent to us, and the phases are shewn as they appear in the heavens.

The tutor will be enabled, by this instrument, to explain some other circumstances to his pupil; namely, that as the earth turns round on its axis once in 24 hours, it must in that time exhibit every part of its surface to the inhabitants of the moon, and therefore its luminous and opake parts will be seen by them in constant rotation. As that half of the earth which is opposed to the sun is always dark, the earth will exhibit the same phases to the lunarians that we do to them, orly in a contrary order, that when the moon is new to us, we shall be full to them, and vice versa. But as one hemisphere only of the moon is ever turned towards us, it is only those that are in this hemisphere that can see us; our earth will appear to them always in one place, or fixed in the