326

ASTRONOMY.

•the Sun . Compute the time between these two eclipses or op- [positions, and divide this by the number of lunations that haveintervened, and the quotient will be the synodical month, ortime the Moon takes to pass from one conjunction to another, orfrom one opposition to another. Compute the Sun ’s mean mo-tion in the time of the synodical month, and add this to the en-tire circle described by the Moon . Then, as that sum is to 360°,so is the quantity of the synodical month to the periodical, ortime that the Moon takes to move from one point of her orbit tothe same point again. Thus the synodical month is found to be29 degrees, 11 hours, 43 minutes, 3 seconds; irom whence themean periodical time of the Moon comes to 27 days, 7 hours, 43minutes, 5 seconds.

(233.) When the quantity of the periodical month is found, wemay find the Moon ’s diurnal and liorarv motion; and thus may-tables of the Moon ’s mean motion be constructed: and if fromthe Moon’s mean diurnal motion that of the Sun be subtracted,the remainder will be the Moon ’s mean diurnal motion from theSun .

(234.) Having found the Moon’s distance from the Sun , herphasis for that time may be easily delineated by' the following me-thod laid down by Keil: let the circle COBP, (Plate XX. tig 11and 12,) represent the disk of the Moon , w hich is turned towardsthe Earth ; and let OP be cut by the diameter BC at right angles;and making LP the radius, take LF equal to the cosine of theelongation of the Moon from the Sun ; and then upon BC, as thereat axis, and LF the leaser axis, describe the semi-ellipse BFC.his ellipse will cut off from the disk of the Moon the portionBFC P of the illuminated face, which is visible to us from the Earth .

(235.) As the Moon in the middle of a central eclipse, is exactlyin the node ; if the Sun ’s place be found for that time, and sixsigns added to it, the sum will give the place of the node, pro-vided the eclipse be lunar ; but if solar, the place of the nodeand of the Sun are the same. From comparing two eclipses to-gether, the mean motion of the nodes will thus be found. Theapogee of the Moon may be known from her apparent dia-meter ; and by comparing her place when in apogee at dif-ferent times, the motion of the apogee itself may also be de-termined.

Sect. V. Preliminary Observations respecting Eclipses.

(236.) Before we lay down rules for calculating eclipses, it isnecessary to make a few general observations respecting theirnature and causes. All the planets and satellites being illumi-nated by the Sun , cast tlreir shadow towards tliat point of the hea-vens which is opposite to the Sun . This shadow is nothing but aprivation of light, in the spare hid from the Sun by the opaquebody that intercepts his rays. When the Sun ’s light is interceptedby the Moon , so that he appears covered in whole, or in part, toauy p’ace of the Earth , he is said to undergo an Eclipse ; though,properly speaking, it is only an eclipse of that part of the Earth where the Moon’s shadow or penumbra falls. When the Earth comes between the Sun and Moon, the Moon passe; through theEarth ’s shadow ; .*nd having no light of her own, she suffers a realand total eclipse from the interception of the Sun ’s rays. W henthe Sun is eclipsed to us, the Moon ’s inhabitants, on the side nextthe Earth, see a shadow likea dark circle travelling over the Earth ,about twice as fast as its equatorial parts move, and the same wayas they move. When the Moon is in an eclipse, the Sun appearseclipsed to her inhabitants ; totally to all those parts on which theEarth ’s shadow falls, and of as lon<! continuance as they are in theshadow. Although all opaque bodies, on which the Sun shines,have their shadows, vet such are the distances of the planets, andthe size of the Sun , that the primary planets can never eclipse oneanother. A primary can eclipse only its secondary, or be eclipsedby it; and never but when in opposition or conjunction with theSun. If the Moon ’s orbit were coincident w ith the plane of theecliptic, in which the Earth always moves, and the Sun appears tomove, the Moon’s shadow would fall upon the Earth at everychange, and eclipse, the Sun to some parts of the Earth . Inlike manner, the Moon would go through the middle of theEarth ’s shadow, and be eclipsed at every full. But one half ofthe Moon ’s orbit is elevated 54 degrees above the ecliptic, andthe other half as much depressed below it; and when the Sun andMoon are more than 17 degrees from either of the nodes at thetime of conjunction, ($,) the Moon is then generally too high or too

low in her orbit to cast any part of her shadow upon the Earth ;when the Sun is more than 12° from either of the nodes at the timeof Full Moon, (O,) the Moon is generally too high or too low in herorbit to go through any part of the Earth ’s shadow : and in boththese cases there will be no eclipse. But when the Moon is lessthan 17° from cither node at the time of conjunction, her shadowor penumbra falls more or less upon the Earth , as she is more orless within this limit. And when she is less than 12° from either nodeat the time of opposition, she goes through a greater or less por-tion of the Earth ’s shadow, as she is more or less within this limit.Her orbit contains 360°; of which, 17°, the limit of solar eclipseson either side of the nodes, and 12°, the limit of lunar eclipses, arebut small portions; and as the Sun commonly passes by thenodes but twice in a year, it is no wonder that we have so manyNew and Full Moons without eclipses.

(237) To illustrate this, let ABC,&c. (Plate XXIII. fig. 7,) bethe ecliptic, the shaded part lying in the same plane with me eclip-tic, and VYXVV the Moon ’s orbit, one half of which, as VYX, isalways below the ecliptic, and the other half XWV above it.The points V and X are the Moon ’s nodes; and a right lineXAV, drawn from one to the other, through the Earth ’s centre, isthe line of the nodes which is carried almost parallel to itself roundthe Sun in a year. If the Moon moved round the Earth in theplane of the ecliptic, her shadow would tall upon the Earth everytime she is in conjunction with the Sun , and at every oppositionshe would go through the Earth’s shadow; and thus the Sun would be eclipsed at every change, and the Moon at every full.When the Earth is at C, if the Moon be in conjunction with theSun , and in or very near one of her nodes, her shadow will fall onthe Eardi, and at her opposition V she must go through the Earth ’sshadow, because she is then near the other node ; yet, in the timethat she goes round the Earth to her next change, according to theorder of XYVW, the Earth advances from C toward I), and theline of the nodes VX being carried nearly parallel to itself, bringssome point, asT, of the Moon’s orbit in conjunction with the Sun atthat next change. The Moon being then at T is too much below theecliptic to cast her shadow on the Earth : and as the Earth is stillmoving forward, the Moon at her next opposition will be toofar above the ecliptic to go through any part of the Earth ’s shadow.When the Earth comes to E the Moon , in conjunction with theSun Z, is not in the shaded part or plane of the ecliptic, but aboveit at Y in the lowest part of her orbit ; and then her shadow Ogoes far below the Earth ; as in Fig. 9. The Moon , at her nextopposition, is at W, where the Earth ’s shadow goes far below her,as in Fig. 9. In both these cases, the line of the nodes is about90° from the Sun , and both luminaries are as far as possible fromthe limits of the eclipses. When the Earth has gone half roundthe ecliptic, from C to G, the line of the nodes VX is nearlydirected towards the Sun ; and the New Moon casts her shadowP on the Earth G ; and the Full Moon goes through the Earth ’s sha-dow L ; which brings on eclipses again, as when the F.artli was at C.When the Earth comes to A, the New Moon is at W in her orbitbelow the ecliptic; and then her shadow <4 (see Fig. 9) goes farabove the Earth . At the next full she is (Fig. 7) at Y in herorbit, 5-j degrees below the ecliptic ; being then as far as possible,at any opposition, from the Earth ’s shadow M, as in Fig. 9. Thepoint V where the Moon ’s orbit crosses the ecliptic, is called theascending node, (Q,) because the Moon ascends from it above ti eecliptic: and the opposite point of intersection X is called thedescending node (gj.) When the Moon is at W, in the highest pointof her orbit, she is in her greatest north latitude; and when she isat Y, in the lowest point of her orbit, site is in her greatest southlatitude. If the line of the nodes, like the’Earth's axis, werecarried parallel to itself round the Sun , there would be just half ayear between the conjunctions of the Sun and nodes. But (henodes shift backwards, or contrary to the Earth ’s annual motion,19 ’ deg. every year ; and therefore the same node comes roundtoihe Sun 19 days sooner every year (ban on the year "before. Con-sequently, from the time that the descending node X (when theEarth is at C > passes bv the Sun as seen from the Earth , it is only173 (lavs (not half a year) till the ascending node V passes by him.Therefore in whatever time of the year we leave eclipses of theluminaries about either node, we may he sure that in 173 days af-terward we shall have eclipses about the other node. Auri whenat any time ot the year tile line of the nodes js in the SituationVCX, at the same time next year it "will be hr the situation MCL :