ASTRONOMY.

327

the nodes having gone backward, that is, contrary to the order ofthe signs, from X to M, and from V to L, each 19} degree*.

(238.) At this rate, the nodes shift through all the signs anddegrees of the ecliptic in 18 years and 225 days; in which timethere would always be a regular period of eclipses, if any com-plete number of lunations were finished vvitnout-a friction. Hutthis never happens: for if both the Sun and Moon should startfrom aline of cony unction with either o the nodes in any point ofthe ecliptic, tin bun would perform VS annual revolutions and222 degrees over and above, and the Moon 230 lunations and 85degrees of the 231st, by the time the node, came round to thesame point of the ecliptic again ; so that the Sun woulu then be138 degrees from the node, and the Moon 85 degrees from'theSun. But in 223 mean lunations, after the Sun , Mocu, and nodes,have been once :u a line ol conjunction, they return so nearly tothe same state ar.nin, a-that the same node, which was in conjunctionwith the Sun an ! Moon at the beginning of the tir.t of tne-e lunations,will be within 28' 12" of a degree of a line of conjunction withthe Sun and Moon again, when the last of these lunations ; s com-pleted. And therefore in that time there will lie a regular periodof eclipses, or return of the same eclipse, for many ages In thisperiod, (which was first discovered by the Chaldeans,) there are18 Julian years, 11 days, 7 hours, 42 minutes, 30seconds, whenthe last day of February in leap-years is four time-included ; butwhen it is five times included, the period consists of only 18 years10 days, 7 hours, 42 minutes, 30-^ seconds. Consequently, it tothe mean time of any eclipse, either of the Sun or Moon , youadd 18 Julian years,'11 days, 7 hours, 42 minutes, 30,% seconds,when the last day in February in leap-years comes in tour times,or a day less when it comeson five times, you will have the meantime of the return of the same eclipse. But the falling back ofthe line of conjunctions or oppositions of the Sun and Moon 28'12” with respect to the line of the nodes in every period, will wearit out in process of time ; and after that, it will not return again inless than 12492 years. Those eclipses of the Sun , which happenedabout the ascending node, and begin to come in at the north poleof the Earth , will go a little southerly at each return, till they goquite oflf the Earth at the south pole ; and those which happenabout the descending nodes, and begin to come in at the southpole of the Earth , w ill go a little northerly at each return, till atlast they quite leave the Earth at the north pole.

Sect. VI. Of the Calculation of Eclipses.

(239.) When, from the rules laid down in the preceding section,we have ascertained with certainty that there will be a solar or lunareclipse at any particular New or Full Moon , and we would know

all its circumstances; it is essentially necessary for us first to be'acquainted with the approximate time of (he ecliptic conjunctionor opposition. To obtain this point we would recommend as themost safe and easy method, to calculate the lime of the sizygy fromMr. Ferguson’s Solar and Li&ar Tables published in every editionof his Astronomy , as by numerous trials they have been found togive the time exact to within 25 minutes, and commonly do notdeviate from the truth more than a quarter of an hour; with theconstant sign -j-. A person expert at figures may' easily performit in ten minwes at the farthest. Then, from correct Astrono-mical Tables proceed to calculate for the approximate time ofthe sizygy the Sun ’s true place, hourly motion, and semidiameter;the Moon ’s true longitude in her orbit and in the ecliptic, her or-bitica! and ecliptical latitude; her horizontal parallax and semi-diameter, and her horary motion in longitude and latitude. When,from the true lunar longitude and latitude combine'! with thehorary motions, we know the exact time of the ecliptic oppositionor conjunction, we must proceed to find out the inclination of thelunar orbit to the ecliptic : this is indispensably necessary, in cal-culating eclipses of the Moon ; and even those of the Sun whenwe would know their circumstances for the various regions of theEarth . We must also know the relative horary motion of theMoon towards or from the Sun , or, which is tiie same thing, thedifference of their horary motions. In the calculation of eclipsesof the Moon , it may be sufficient to add 8" to the difference ol thehorary motions in longitude to obtain the relative motion of theMoon from the Sun in her orbit. The time ofa lunar eclipse beingknown at any particular place, it is easy to know if it be visible atthat place, by knowing if the Moon be risen. Or the place willbe known where the Moon is vertical; and therefore it will, for themost part, be visible to all places, within 90° from it. If thespectator iive in the place (or in the same longitude) which theTables are calculated for; he will see the eclipse at the time deter-mined by the calculation. If not, he will see it an hour soonerfor every 15° difference of longitude, that he lives west from it.And so much later, if he lives eastward; that is, in the way ofreckoning time. But in regard to absolute time, it is seen fromall places at the same instant.

(240.) For an illustration of the method of calculating solarand lu-nar eclipses we insert the following calculations of the Sun ’s andMoon ’s longitude, semidiameter, <kc &c. for the approximatetime of the opposition, in order to determine all the differentphenomena of the great total and almost central eclipse of theMoon to take place on the night of September 2, 1830, (A’. S.)carefully calculated from the Solar and Lunar Tables prefixedto M. I)e La Lande’s Third Edition of his Astronomy'.

Calculation of the Sun 's true Place for Sept. 2, 1830, at 10 Hours and a half equal Time at Greenwich, nr at 10/(. 39m. 20s. Clock-tinte at Paris , from the Solar Tables in M. De La Lande’s Third Edition of his Astronomy.

0’s mean long.

O’s Apogee.

Arg. 1.

1)

Arg. 2.

n

Arg. 3.

?

Arg. 4.1 st of<?

Arg. 5.2(1 of<?

Arg. 6.

Si

s. o

s. 0 ' "

9 9 38 14,2

8 1 29 0,9

24 38,5

1 36,1

0,8

3 10 0 7

0 0 0 41,6

194

296

14

1

19

614

1

890

420

1

681

314

44

42

520

36

5 11 33 30,5

3 10 0 48,6

505

634

311 | <195

86

556

A. D. 1830.,

Sept. 2.

10 hours.

39 minutes..20 seconds...

0’s mean long.

Equation of 0’s orbit

0’s mean place corrected by 0’s ellip. equation.Secular equation.t.

Equation of..

First Equation of $ .

Second equation of $ .Equation of .

O’s true place.

5 9

53

2,1

+

4,8

—

,2

—

2,6

+

8,5

+

,2

+

1,5

—

5,8

5 9

53

8,5

2 1 32 41,9

O’s mean anomaly.

The Sun ’s mean Anomaly gives 2’ 25”,43 for his horary mo-tion, and 15' 53",54 for Ins apparent semidiameter. The fir.-tequation of true to mean time (Arg 0’s mean Anom.) is —6' 41",9; the second equation (Arg. 0’s true plaee)-(- 6' 10",8 ;the third equation (sum of all the small solar equations, thenutation excepted, turned into time) -f- 0",8 ; and the fourth(Arg. present obliquity of the eel ptic, 23° 27' 21",2)—0",3.'File sum, or true equation of time, is—31”,6. The equation ofthe mean to apparent time, is consequently -|- 31".6. Dailydifference j; 19", 1.

4

Th