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wards and forwards, alternately withdrawing her poles from our sight.

As she revolves round the earth in an elliptic orbit, she moves slower in her apogee, and faster in her i perigee than at her mean distance, and therefore she will pass over the lower half of her orbit in less time than half her revolution, and consequently before she has revolved half round her axis, the motion on which is equable and exactly commensurate to her periodical time. The consequence of this is, that she will alternately exhibit to us a small segment of her eastern and western limbs, which causes her to appear to librate from east to west on her axis.

Although the moon revolves round the earth as her center of attraction, and is sometimes between the sun and earth, yet her path is always concave towards the sun. For she only approaches nearer to the sun than the earth is, by 240,000 miles, when at her change; but the versed sine of half the arc of the earth's motion for a month is at least 400,000 miles.

The moon when new is more attracted by the sun than by the earth; because the point in which any body situate between the sun and earth would be equally attracted by them, is at least 70,000 miles nearer to the earth than the moon is at her change, and consequently she must be more attracted by the sun than by the earth at that time. It may then seem strange, that she has not long ago deserted the earth, and revolved round the sun. But we must remember, that the distance between the earth and moon is so small, that if the sun could carry off the moon, the earth must also follow, which is prevented by the projectile force of the earth. One body would move round another in the cabin of a ship under sail in the

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!! same manner, as if it were at rest. For an impulse on a system of bodies affects them all equally, and they would circulate round one another, by any other : forces, in the same manner as if no such impulse had existed.

TIME OF THE MOON'S RISING, AND HORIZONTAL MOON.

As the moon performs her revolution in about 271⁄2 days, she will advance to the eastward about 13° daily, and the sun advancing the same way only at the rate of one degree daily, she will gain on him about 12° every day; which to the inhabitants about our equator will retard the time of her rising about 48′ daily. But in different latitudes, this retardation will be dif ferent, so that in high latitudes she will rise for some evenings together with much less difference of time. To illustrate this, we may consider her path as nearly in the ecliptic, as it differs from it but about 5° 18'. Now in high north latitudes, the ecliptic is very much inclined to the horizon about the beginning of Aries; and therefore a short space of time will be sufficient, to bring 30 or 40' of the ecliptic above the horizon, in this part of it, by the rotation of the earth on her axis. At the poles, one half of the ecliptic never sets, but is constantly above the horizon, and therefore while the moon is in this half, it can never set, nor does it rise while in the other half, for a fortnight together. Now the moon is twelve times in the year about the beginning of Aries, and must at these times 'rise for a few days, with very little difference of time. But her rising nearly at the same hour for a few days together is never so particularly noticed, as when she is

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full about the beginning of Aries, and this sign rises in the evening, the sun being in the opposite sign Libra, which is in the autumn. The full moons at this season of the year rising for a few evenings together nearly at the same time, have occasioned them to be particularly remarked, and to obtain the name of the harvest moons. In the winter, this part of the ecliptic rises at noon, and if the moon be in it, she must then be about her first quarter, when the time of her rising is not observed. In the spring, it rises with the sun, when the moon, if in it, must be new, and therefore invisible. In summer, it rises about midnight, and the moon being in it must be in her third quarter, when few are awake to observe the time of her rising. But in the autumn, it rises in the evening, when the moon, in it, must be full; and therefore it is more particularly ob'served.

The moon and sun, when seen in or near the horizon, appear larger, than at any other altitude, although they subtend nearly the same angle. This is owing to an optical illusion, and the method we have of judging of distances by sight. We judge the concave heavens to be a part of a greater sphere, whereof the horizontal base is nearly four times as long as the height above our heads: hence we naturally refer the sun and moon to a greater distance when seen in the horizon, than when near the zenith, and therefore we judge them to be larger to cause them to appear under the same angle at the eye. The indistinctness with which they are viewed in the horizon, on account of the greater refraction of the rays of light through a denser part of the atmosphere, may also contribute to this optical deception. For observing that an object gradually appears more obscure, as its distance from the

eye increases, we naturally judge it to be more distant, the more obscurely it appears: and if more distant, consequently larger. And we are also compelled to judge the horizon to be more distant than the zenith, by the number of intermediate objects along the horizon, whereas we have none between the eye and the zenith. This will contribute to the same effect.

LUNAR INEQUALITIES.

ASTRONOMERS have found that the moon goes through her orbit from any given star to the same again, at a mean rate, in 27d 7h 43' 4"; from her apogee to her apogee, in 27a 13h 18′ 43′′; and from the sun to the sun again, in 29d 12h 44' 3". Now since the moon is 5h 35′ 39′′ longer in going from her apogee to her apogee again than from a fixed star to the same, this shows that her apogee moves from west to east, as she moves in her orbit. And because she requires less time by 2h 38′ 27" to revolve from her node to her node again, than from a star to the same again; this shows that her nodes revolve from east to west. So that her apogee makes a complete revolution in eight common years, 311a and 8h; its annual motion being 40° 39′ 52", and daily motion 6' 44" 1". And her node makes a complete revolution in eighteen common years, 254d 7h 33', its annual motion being 19° 15', and daily motion 3' 10" 38"".

A mean lunation is 2d 5h 1' longer than a periodical revolution; because the earth has advanced so far in her orbit during a revolution of the moon, that it requires this time for the moon to advance to the same position again, with respect to the sun and earth, that she had at the beginning of her revolution.

If the moon in her motion round the earth were only affected by her gravitation towards it, she would follow the same laws which regulate the motions of the primary planets, describing areas proportional to the times of description. But as her distance from the sun is nearly the same with that of the earth, she must also feel the force of his attraction, sometimes conspiring with the attractive force of the earth, and sometimes acting against it, and thereby producing great irregu larities in her motions, according to her positions with respect to the sun and the earth.

When the moon is in quadrature, the attraction of the sun increases her gravitation or tendency to the earth. The sun's attraction affects both the earth and the moon, and did it attract them in parallel lines, so that if their projectile force were destroyed, and they were to descend to the sun in parallel lines, such an attraction could not bring them nearer together in their descent; but the sun attracts them in lines which meet in the sun; and therefore the effect of this attraction of the sun must be to bring them nearer together, or to increase the tendency of the moon to the earth in her quadratures.

When the moon is in the syzygies, her tendency to the earth is diminished by the attraction of the sun. The sun attracts both the earth and the moon, but with different forces, as one is nearer to him than the other; and as the attraction of two bodies is mutual, whatever diminishes the attraction of the earth towards the moon, diminishes the tendency of the moon to the earth, and therefore in the conjunction and opposition of the sun and moon, their tendencies will, by the action of the sun, be diminished. But the

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