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upon the whole, and is largest of all, when it arrives at that position.

V. When the moon is in quadrature, the nodes of its orbit are always stationary; but commonly retrograde when the moon is in the syzygies. From one quadrature to another, they are most retrograde when the line of the nodes concurs with the line of the quadratures; and least, when it concurs with the line of the syzygies.

When the nodes are in quadrature, while the moon is passing from quadrature to quadrature again, she is constantly solicited towards the ecliptic by the ablatitious force of the sun, and therefore she will arrive at it before she has performed half a revolution, and consequently will meet her node, which has retrograded in the mean time so as to meet her before she has gone 180° from her other node. As she moves from west to east, her nodes move from east to west, and perform their revolution in the time before mentioned. But they are quiescent, when the line of the nodes is in the syzygies, because the ablatitious force of the sun then acts in the plane of the lunar orbit.

When the line of the nodes is in the octants, from the quadrature to the first octant, while the moon is passing by her node, the ablatitious force of the sun is directed to a point on the opposite side of the line of the node from the moon, when it increases the obliquity of the lunar orbit, and causes the node to move forward during her passage through two octants in the revolution or 90°, but they move retrograde for 270°, so that upon the whole the nodes move more backward than forward in any revolution, and therefore move round in something less than nineteen years.

What has been said of the irregularities of the moon's motions is also true of the satellites of Jupiter and Saturn; but because of their great distances from the sun, these irregularities are generally insensible, excepting in those that are nearest to the planet, on account of their nearness to it.

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The same method of reasoning shows, that the precession of the equinoxes is variable from 43′′ num to 57", being at a mean rate 50", depending on the position of the moon's nodes; being greatest when they are in Aries, least when in Libra, and at a mean, when in Cancer and Capricorn.

ECLIPSES OF THE SUN AND MOON.

AN eclipse of the sun is occasioned by the interposition of the moon between the sun and the earth, at the change of the moon; but an eclipse of the moon is occasioned by her passing through the earth's shadow, when she is full, or in opposition; so that there can be no eclipse of the sun, but at the change of the moon, and no eclipse of the moon, but when she is full. We shall first consider the

ECLIPSES OF THE MOON.

If the earth were as large as the sun, its shadow would be of equal breadth at all distances. But being much less, its shadow must terminate in a cone, whose vertex cannot reach to any of the primary planets, and therefore none of the celestial bodies can pass through it, or be eclipsed by the earth, but the moon. The semi-angle of the conical shadow of the earth, is equal to the sun's apparent semi-diameter lessened by his horizontal parallax, which is but 8".65. For TES,* the measure of the semi-diameter of the sun seen from

*See Plate Y.

the earth, is equal to EAC, the semi-angle of the cone, +ESC, the horizontal parallax of the sun; S, being the sun, and C the earth. Hence, from the known semi-diameters of the sun and earth, and the distance between them, the length of the shadow may be easily determined, which is found to be about 864,000 miles. And from the known distance of the moon, the diameter of the earth's shadow, where the moon passes through it, is also easily found, by plane trigonometry. The difference too, between the moon's horizontal parallax, and the semi-angle of the cone of the shadow, is equal to the semi-diameter of the shadow at the distance of the moon. For EBC-EAB-BED. Or it is equal to the difference between the apparent semi-diameter of the sun, and the sum of the horizontal parallaxes of the sun and moon. Hence the diameter of the section of the earth's shadow, where the moon passes through it, is nearly three times the breadth of the moon. For 62'-16′-46′ and 2x46-92′, the diameter of the section, almost three times 31', the moon's diameter.

But notwithstanding the breadth of the earth's shadow at the distance of the moon, she does not always pass through it at every opposition. Her orbit is inclined to the ecliptic in an angle of 5° 18', at a mean rate, and therefore these planes will be distant from each other about a degree, at the distance of 12 degrees from her node, where the semi-diameters of the moon and the earth's shadow added together, being about one degree, would just touch each other, so that she will not enter into any part of the shadow when full, at more than 12° from her node. This therefore is called the ecliptic limit for eclipses of the moon. If the moon be nearer to her node than 12°, she will pass

through a part of the earth's shadow, her northern or southern limb entering into it, according as she has south or north latitude; and if she be in her node, at the time of opposition, she is then in the ecliptic, where the center of the earth's shadow always is, and therefore will pass through its diameter, entering it with her eastern limb, and making the duration the longest possible, viz. 3h 57' 6", if she be then at her greatest distance from the earth, where she moves slowest; or only 3h 37′ 26′′, if she be then at her nearest distance, where she moves quickest. In this case, she is centrally eclipsed. Hence if the latitude of the moon, at her opposition, be less than the sum, but greater than the difference of her own semi-diameter and the semi-diameter of the earth's shadow, she will be partially eclipsed.

The moon even in total eclipses receives light enough to become visible; occasioned by the refraction of the sun's rays through the earth's atmosphere; by which means, many rays are refracted into the shadow, especially those of a red colour, which have the greatest momentum, and make their way through it, while others are turned off in other directions. Now these rays cross each other in a point between the earth and moon, and thence diverging into the shadow, greatly diluted, enlighten it, at the distance of the moon; from whence she not only becomes visible, but also appears of a reddish brown and dusky colour. She never enters into the dark shadow of the earth, for then she would be absolutely invisible.

Although the shadow of the earth is diametrically opposite to the sun, yet the moon has been seen totally eclipsed before the sun was set; which was occasioned by the refraction of the atmosphere, raising

both the sun and moon above their true positions, near 34 minutes.

ECLIPSES OF THE SUN.

ECLIPSES of the sun are occasioned by the interposition of the moon between him and the earth, and therefore he can never be eclipsed but at the change of the moon, when both luminaries are in the same part of the heavens. Hence the preternatural darkness at the crucifixion of our Saviour could not be effected by an eclipse of the sun, because he suffered at the Jewish passover, which was to be celebrated by their law at the full moon, or on the 14th day of their month. Unless the sun be near to the node of the moon at the change, there can be no eclipse of the sun, for otherwise she will pass by him either to the north or the south of him in the heavens. If she be then in her node her center will pass over the center of the sun, and if her diameter be then large enough, she will cover his whole disk and cause a central and total eclipse of the sun; but if she be at any distance from her node less than 17° she will only obscure a part of the sun, according as her latitude is smaller or greater.

As the moon is less than the sun, her shadow will terminate in a cone, the semi-angle of which is equal to the apparent semi-diameter of the sun viewed from the moon, when lessened by the sun's horizontal parallax seen from the moon. But as the earth and moon are nearly at the same distance from the sun, we may say, that the semi-angle of the cone of the moon's shadow is nearly equal to the apparent semi-diameter of the sun without any sensible error. As the moon is much less than the earth, her shadow must be much

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