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 477 ASTRO N O M Y. very obliquely on the earth, in total eclipfes of the fun. be the ecliptic, RSTU a circle lying in the fame plane In annular eclipfes, the moon’s real fhadow ends in a with the ecliptic, and VIVXYthe moon’s orbit, ail thrown point at fome didance from the earth. The moon’s into an oblique view, which gives them an elliptical diape fmall didance from the earth, and the fhortnefs of her to the eye. One half of the moon’s orbit, as VfVX, is diadow, prove her to be lefs than the fun. And, as the always below the ecliptic, and the other half XYV above it. The points V and X, where the moon’s orbit interearth’s flradow is large enough to cover the moon, if her feCts the circle RSTU, which lies even with the ecliptic, diameter were three times as large as it is (which is evithe moon’s nodes ; and a right line, as XEF, draw® dent from her long continuance in the diadow when die are goes through its centre) it is plain, that the earth is much from one to the other, through the earth’s centre, is the line of the nodes, which is carried almoft parallel to itbigger than the moon. Though all opaque bodies, on which the fun diines, felf round the fun in a year. have their diadows, yet fuch is the bulk of the fun, and- If the moon moved round the earth in the orbit the didances of the planets, that the primary planets RSTU, which is coincident with the plane of the eclipcan never eclipfe one another. A primary can eclipfe tic, her fhadow would fall upon the earth every time die only its fecondary, or be eclipfed by it; and never but is in conjundtion with the fun, and at every oppolitiou when in oppofition or conjun&ion with the fun. The die would go through the earth’s diadow. Were this primary planets are very feldom in thefe pofitions, but the cafe, the fun would be eclipfed at every change, and the fun and moon are fo every month : Whence one may the moon at every full, as already mentioned. imagine, that thefe two luminaries diould be eclipfed e- But although the moon’s fhadow W mud fall upon the very month. But there are few eclipfes in refpeft of the earth at a, when the earth is at E, and the moon in connumber of new and full moons; the reafon of which we junction with the fun at becaufe die is then very near one of her nodes ; and at her oppofition « die mud go diall now explain. If the moon’s orbit were coincident with the plane of through the earth’s diadow I, becaufe die is then near the ecliptic, in which the earth always moves and the fun the other node ; yet, in the time that die goes round the appears to move, the moon’s diadow would fall upon the earth to her next change, according to the order of the earth at every change, and eclipfe the fun to fome parts letters XYVfV, the earth advances from E to e, accordof the earth. In like manner, the moon would go through ing to the order of the letters EFGH, and the line of the middle of the earth’s diadow, and be eclipfed at eve- the nodes VEX being carried nearly parallel to itfelf, ry full ; but with this difference, that die would be totally brings the point f of the moon’s orbit in conjunction darkened for above an hour and an half; whereas the fun with the fun at that next change; and then the moon never was above four minutes totally eclipfed by the in- being at f, is too high above the ecliptic to cad her fhaterpofition of the moon. But one half of the moon’s dow on the earth : And as the earth is dill moving fororbit is elevated y-f degrees above the ecliptic, and the ward, the moon at her next oppofition will be at g, too other half as much depreded below it; fonfequently, the far below the ecliptic to go through any part of the moon’s orbit interfedls the ecliptic in two oppofite points earth’s diadow; for by that time the point g will be at a called the moon's nodes, as has been already taken notice confiderable didance from the earth as feen from the fun. of. When thefe points are in a right line with the cen- When the earth comes to F, the moon in conjunction tre of the fun at new or full moon, the fun, moon, and with the fun Z is not at ^ in a plane coincident with earth, are all in a right line; and if the moon be then the ecliptic,, but above it at Y in the highed part of her new, her diadow falls upon the earth ; if full, the earth’s orbit: and then the point £ of her diadow 0 goes far afhadow falls upon her. When the fun and moon are bove the earth (as in fig. 2. which is an edge view of more than 17 degrees from either of the nodes at the fig. 1.) The moon, at her next oppofition, is not at o time of conjunftion, the moon is then generally too high (fig. 1.) but at W, where the earth’s diadow goes far aor too low in her orbit to cart any part of her fhadow bove her (as in fig. 2.) In both thefe cafes the line of upon the earth; when the fun is more than 12 deg. from the nodes VFX (fig. x.) is about 90 degrees from the -either of the nodes at the time of full moon, the moon is fun, and both luminaries are as far as podible from the generally too high or too low in her orbit to go thro’ any limits of the eclipfes. part of the earth’s diadow: And in both thefe cafes there When the earth has gone half round the ecliptic from will be no eclipfe. But when the moon is lefs than 17 de- E to G, the line of the nodes VGX is nearly, if not exgrees from either node at the time of conjunction, her fha- actly, direfted towards the fun at Z; and then the newdow or penumbra falls more or lefs upon the earth, as die is moon / cads her diadow P on the earth G; and the more, or lefs within this limit. And when die is lefs than full moon p goes through the earth’s diadow L ; which 12 degrees from either node at the time of oppofition, die brings on eclipfes again, as when the earth was at E. goes through a greater or lefs portion of the earth’s fha- When the earth comes to H, the new moon falls not dow, as die is more or lefs within this limit. Her orbit at tn in a plane coincident with the ecliptic CD, but at contains 360 degrees; of which 17, the limit of folar e- ^in her orbit below it; and then her diadow ^ (fee clipfes on either fide of the nodes, and 12, the limit of 2.) goes far below the earth. At the next full die lunar eclipfes, are but fmall portions : And as the fun j’gis not at q (fig. 1.) but at Y in her orbit 54 degrees acommonly pafles by the nodes but twice in a year, it is bove 7, and at her greated height above the ecliptic CZ) • no wonder that we have fo many new and full moons being then as far as podible, at any oppofition, from the without eclipfes. earth’s diadow M, as in fig. 2. To illudrate this, (Plate XLVI. fig. 1.) let dBCD So, when the earth is at E and G, the moon is about Vol. I. No. 20. 3 6E hgj-