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 478 ASTRO her nodes, at new and full ; and in her greateft north and Jouth declination (or latitude, as it is generally called) from the ecliptic at her quarters : But when the earth is at F or H, the moon is in her greateft north and Jouth declination from the ecliptic at new and full, and in the nodes about her quarters. The point X where the moon’s orbit crofles the eeliptic, is called the afcending node, becaufe the moon afcends from it above the ecliptic : And the oppofite point of interfeftion V is called the defcending node, becaufe the moon defcends from it below the ecliptic. When the moon is at T in the higheft point of her orbit, fhe is iri her greateft north latitude; and when fhe is at IV in the lowed: point of her orbit, (he is in her greateft fouth latitude. If the line of the nodes, like the earth’s axis, was carried parallel to itfelf round the fun, there would be juft half a year between the conjunctions of the fun and. nodes. But the nodes fliift backward, or contrary to the earth’s annual mdtion, 19^-deg. every year; and therefore the fame node comes round to the fun 19 days fooner eyery year than on the year before. Confequently, from the tirrte that the afcending node X (when the earth is at £■)' pafi'es by the fun as feen from the earth, it is only 173 days (not half a year) till the defcending node V paffes by him. Therefore, in whatever time of the year we have eclipfes of the luminaries about either node, we may be fure that in 173 days afterward we {hall have edipfes about the other node. And when at any time of the year the line of the nodes is in the fituation VGX, at the fame time next year it will be in the fituation rGs; the afcending node having gone backward, that is, contrary to the order of figns, from X to /, and the defcending node from ^ to r ; each 19-y deg. At this rate the nodes {hift through all the figns and degrees of the ecliptic in 18 years and 225 days ; in which time there would always be a regular period of eclipfes, if any complete number of lunations were finiflied without a fraction. But this never happens; for if both the fun and moon fhould ftart from aline of conjunction with either of the nodes in any point of the ecliptic, the fun would perform 18 annual revolutions and 222 degrees over and above, and the moon 230 lunations and 8$ degrees of the 231ft, by the time the node came round to the fame point of the ecliptic again : So that the fun would then be 138 degrees from the node, and the moon 85 degrees from the fun. But, in 223 mean lunations, after the fun, moon, and nodes, have been once in a line of conjunction, they return fo nearly to the fame ftate again, as that the fame node, which was in'conjunction with the fun and moon at the beginning of the firft of thefe lunations, will be within 28 12" of a degree of a line of conjunction with the fun and moon again, when the iaft of thefe lunations is completed. And therefore, in that time there will be a regular period of eclipfes-, or return of the fame eclipfe, for, many ages.'—In this period, (which was firft difcovered by the Chaldeans), there are 18 JuKan years 11 days 7 hours 43 minutes 20 feconds, when the laft day of.February in, leap-years is four times included:

N O M Y. But when it is five times included, the period confifts of only 18 years 10 days 7 hours 43 minutes 20 feconds. Confequently, if to the mean time of any eclipfe, either of the fun or moon, you add 18 Julian years xx days 7 hours 43 minutes 20 feconds, when the laft day of February in leap-years comes in four times, or a day lefs when it comes in five times, you will have the mean time of the return of the fame eclipfe. But the falling back'of the line, or conjunctions, or oppofitions of the fun and moon 28/ 12" with refpeCt to the line of the nodes in every period, will wear it out in procefs of time ; and after that, it will not return again in lefs than 12492 years. — Thefe eclipfes of the fun, which happen about the afcending node, and begin to come in at the north pole of the earth, will go a little foutherly at each return, till they go quite off the earth at the fouth pole ; and thofe which happen about the defcending node, and begin to come in at the fouth pole of the earth, will go a little northerly at each return, till at laft they quite leave the earth at the north pole. To exemplify this matter, we fhall firft confider the fun’s eclipfe, (March 21ft old ftyle, April ift new ftyle), A. D. 1764, according to its mean revolutions, without equating the times, or the fun’s diftance from the node j and then according to its true equated times. This eclipfe fell in open fpace at each return, quite clear of the earth, even fince the creation, till A. D129J, June 13th old ftyle, at 12 h. 52 m. 59 fee. pojl meridiem, when the moon’s fhadow firft touched the earth at the north pole; the fun being then 170 48/ 27" from the afcending node.—In each period fince that time, the fun has come 2%' i2,r nearer and nearer the fame node, and the moon’s ftiadow has therefore gone more and more foutherly.—In the year 1962, July 18th old ftyle, at 10 h. 36 m. 21 fee. p. ni. when the fame eclipfe will have returned 38 times, the fun will.be only 24/ 45,, from the afcending node, and the centre of the moon’s fhadow will fafl a little northward of the earth’s centre. —At the end of the next following period, A D. 1980, July 28th old ftyle, ati8h. 19 m. 41 fee. p m. the fun will have receded back 3' 27" from tjre afcending node,. and the moon will have a very fmall degree of fouthern' latitude, which will caufe the centre of her (hadow to pafs a very fmall matter fouth of the earth’s centre.— After which, in every following period, the fun will be 28'. 12" farther back from the afcending node than in the period laft before ; and the moon’s ftiadow will go ftill farther and farther foutHward, until September 12th old ftyle, at 23 h. 46 m. 22 fee. p. m. A. D. 2665 ; when the eclipfe will have compleated its 77th periodical" return, and will go quite off the ,/earth at the fouth pole (the fun being then 17° jj'22 back from the node) and cannot come in at the north pole, fo as to begin the. fame courfe over again, in lefs than 12492 years afterward.—And fuch will be the cafe of’every other eclipfd of the fun: For, as there is about 18 degrees on eacli fide of the. node within which there is a paifibility of eclipfes, their whole revolution goes through 36 degrees about that node, which, taken from 360 degrees, leaves remaining 324 degrees for the eclipfes to travel in ex-.-