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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 tvhole 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, only 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 same part of the heavens : the lunarians and the opposite hemisphere never see our earth, nor do we ever view that part of the moon which they inhabit. The moon's apparent diurnal motion in the heavens is produced by the daily revolution of our earth.

If we consider the moon with respect to the sun, the instrument shews plainly that one half of her globe is always enlightened by the sun; that every part of the lunar ball is turned to the sun, in the space of her monthly or periodic -revolution; and that therefore the length of the day and night in the moon is always the same, and equal to 14| of our day. When the sun sets to the lunarians in that hemisphere next the earth, the terrestrial moon rises to them, and they can therefore never have any dark night; while those in the other' hemisphere can have no light by night, but what the stars afford.

Of the periodical and synodkal month.

The difference between the periodical month, in which the moon exactly describes the ecliptic, and the synodical, or time between any two new-moons, is here rendered very evident. To shew this difference, observe at any new-moon her place in the ecliptic, then turn the handle, and when the moon has got to the same point in the ecliptic, you will see that the dial shews 27^ days, and the moon has finished her periodic revolution. But the earth, at the same time, having advanced in its annual path about 27 degrees of the ecliptic, the moon will not have got round in a direct line with the sun, but will require 28 days and 4 hours more3 to bring it into conjunction with the sun again.

Of eclipses of the Sun and Moon.

There is nothing in astronomy more worthy of our contemplation, nor any thing more sublime in natural knowledge, than rightly to comprehend those sudden obscurations of the heavenly bodies that are termed eclipses, and the accuracy with which they are now foretold. "One of the chief advantages derived by the present generation, from the improvement and diffusion of philosophy, is delivery from unnecessary terror, and exemption from false alarms. The unusual appearances, whether regular or accidental, which once spread consternation over ages of ignorance, are now- the recreations of inquisitive -security. The sun is no more lamented when it is eclipsed, than when it sets; and meteors play their corruscations without prognostic or predicr tion."

I have already observed, that the sun is the only, real luminary in the solar system, and that none of the other planets emit any light but what they.have received from the sun; that the hemisphere which is turned towards the sun is illuminated by his rays, while the other side is involved in darkness, and projects a shadow, which arises from the luminous body.

When the shadow of the earth falls upon the moon, it causes an eclipse of the moon; when the shadow of the moon falls upon the earth, it causes an eclipse of the sun.

An eclipse of the moon, therefore, never happens but when the earth's opake body interposes between the sun and the moon, that is, at the full-moon; and an eclipse of the sun never happens but when the moon comes in a line between the earth and the sun, that is, at the new-moon.

From what we have already seen by the instrument, it appears, that the moon is once every month in conjunction, and once in opposition; from hence it would appear, that there ought to be two eclipses, one of the sun, the other of the moon, every month; but this is not the case, and for two reasons: first, because the orbit of the moon is inclined in an angle of about 5 degrees to the plane of the ecliptic; and secondly, because the nodes of this orbit have a progressive motion, which causes them to change their place every lunation. Hence it often happens, that at the times of opposition or conjunction, the moon has so much latitude, or, what is the same thing, is so much below or above the plane of the ecliptic, that the light of the sun will, in the first case, reacii the moon, without any obstacle, and in the other the earth; but as the nodes are not fixed, but run successively through all the signs of the ecliptic, the moon is often, both at the times of conjunction and opposition, in or very near the plane of the ecliptic; in these cases an eclipse happens

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