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‹Better GutenbergAstronomy Explained Upon Sir Isaac Newton’s PrinciplesChap. XVIII — Of Eclipses: Their Number and Periods. A large Catalo… · 13 of 16Contents›

Astronomy Explained Upon Sir Isaac Newton’s Principles

by James Ferguson

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Chap. XVIII Of Eclipses: Their Number and Periods. A large Catalogue of Ancient and Modern Eclipses.

A shadow, what.

312. Every Planet and Satellite is illuminated by the Sun; and casts a shadow towards that point of the Heavens which is opposite to the Sun. This shadow is nothing but a privation of light in the space hid from the Sun by the opake body that intercepts his rays.

Eclipses of the Sun and Moon, what.

313. When the Sun’s light is so intercepted by the Moon, that to any place of the Earth the Sun appears partly or wholly covered, he is said to undergo an Eclipse; though properly speaking, ’tis only an Eclipse of that part of the Earth where the Moon’s shadow or [64]Penumbra falls. When the Earth comes between the Sun and Moon, the Moon falls into the Earth’s shadow; and having no light of her own, she suffers a real Eclipse from the interception of the Sun’s rays. When the Sun is eclipsed to us, the Moon’s Inhabitants on the side next the Earth (if any such there be) see her shadow like a dark spot travelling over the Earth, about twice as fast as its equatoreal parts move, and the same way as they move. When the Moon is in an Eclipse, the Sun appears eclipsed to her, total to all those parts on which the Earth’s shadow falls, and of as long continuance as they are in the shadow.

Plate X.

J. Ferguson delin.

J. Mynde Sculp.

A proof that the Earth and Moon are globular bodies.

314. That the Earth is spherical (for the hills take off no more from the roundness of the Earth, than grains of dust do from the roundness of a common Globe) is evident from the figure of its shadow on the Moon; which is always bounded by a circular line, although the Earth is incessantly turning its different sides to the Moon, and very seldom shews the same side to her in different Eclipses, because they seldom happen at the same hours. Were the Earth shaped like a round flat plate, its shadow would only be circular when either of its sides directly faced the Moon; and more or less elliptical as the Earth happened to be turned more or less obliquely towards the Moon when she is eclipsed. The Moon’s different Phases prove her to be round § 254; for, as she keeps still the same side towards the earth, if that side were flat, as it appears to be, she would never be visible from the third Quarter to the first; and from the first Quarter to the third, she would appear as round as when we say she is Full: because at the end of her first Quarter the Sun’s light would come as suddenly on all her side next the Earth, as it does on a flat wall, and go off as abruptly at the end of her third Quarter.

And that the Sun is much bigger than the Earth, and the Moon much less.

315. If the Earth and Sun were equally big, the Earth’s shadow would be infinitely extended, and all of the same breadth; and the Planet Mars, in either of its nodes and opposite to the Sun, would be eclipsed in the Earth’s shadow. Were the Earth bigger than the Sun, it’s shadow would increase in breadth the farther it was extended, and would eclipse the great Planets Jupiter and Saturn, with all their Moons, when they were opposite to the Sun. But as Mars in opposition never falls into the Earth’s shadow, although he is not then above 42 millions of miles from the Earth, ’tis plain that the Earth is much less than the Sun; for otherwise it’s shadow could not end in a point at so small a distance. If the Sun and Moon were equally big, the Moon’s shadow would go on to the Earth with an equal breadth, and cover a portion of the Earth’s surface more than 2000 miles broad, even if it fell directly against the Earth’s center, as seen from the Moon: and much more if it fell obliquely on the Earth: but the Moon’s shadow is seldom 150 miles broad at the Earth, unless when it falls very obliquely on the Earth, in total Eclipses of the Sun. In annular Eclipses, the Moon’s real shadow ends in a point at some distance from the Earth. The Moon’s small distance from the Earth, and the shortness of her shadow, prove her to be less than the Sun. And, as the Earth’s shadow is large enough to cover the Moon, if her diameter was three times as large as it is (which is evident from her long continuance in the shadow when she goes through it’s center) ’tis plain, that the Earth is much bigger than the Moon.

The primary Planets never eclipse one another.

PLATE X.

316. Though all opake bodies on which the Sun shines have their shadows, yet such is the bulk of the Sun, and the distances of the Planets, that the primary Planets can never eclipse one another. A Primary can eclipse only it’s secondary, or be eclipsed by it; and never but when in opposition or conjunction with the Sun. The primary Planets are very seldom in these positions, but the Sun and Moon are so every month: whence one may imagine that these two Luminaries should be eclipsed every month. But there are few Eclipses in respect of the number of New and Full Moons; the reason of which we shall now explain.

Why there are so few Eclipses.

The Moon’s Nodes.

Limits of Eclipses.

317. If the Moon’s Orbit were coincident with the Plane of the Ecliptic, in which the Earth always moves and the Sun appears to move, the Moon’s shadow would fall upon the Earth at every Change, and eclipse the Sun to some parts of the Earth. In like manner the Moon would go through the middle of the Earth’s shadow, and be eclipsed at every Full; but with this difference, that she would be totally darkened for above an hour and half; whereas the Sun never was above four minutes totally eclipsed by the interposition of the Moon. But one half of the Moon’s Orbit, is elevated 51⁄3 degrees above the Ecliptic, and the other half as much depressed below it: consequently, the Moon’s Orbit intersects the Ecliptic in two opposite points called the Moon’s Nodes, as has been already taken notice of § 288. When these points are in a right line with the center of the Sun at New or Full Moon, the Sun, Moon, and Earth are all in a right line; and if the Moon be then New, her shadow falls upon the Earth; if Full the Earth’s shadow falls upon her. When the Sun and Moon are more than 17 degrees from either of the Nodes at the time of Conjunction, the Moon is then too high or too low in her Orbit to cast any part of her shadow upon the Earth. And when the Sun is more than 12 degrees from either of the Nodes at the time of Full Moon, the Moon is too high or too low in her Orbit to go through any part of the Earth’s shadow: and in both these cases there will be no Eclipse. But when the Moon is less than 17 degrees from either Node at the time of Conjunction, her shadow or Penumbra falls more or less upon the Earth, as she is more or less within this limit. And when she is less than 12 degrees from either Node at the time of opposition, she goes through a greater or less portion of the Earth’s shadow, as she is more or less within this limit. Her Orbit contains 360 degrees; of which 17, the limit of solar Eclipses on either side of the Nodes, and 12 the limit of lunar Eclipses, are but small portions: and as the Sun commonly passes by the Nodes but twice in a year, it is no wonder that we have so many New and Full Moons without Eclipses.

Fig. I.

PLATE X.

Line of the Nodes.

To illustrate this, let ABCD be the Ecliptic, RSTU a Circle lying in the same Plane with the Ecliptic, and VWXY the Moon’s Orbit, all thrown into an oblique view, which gives them an elliptical shape to the eye. One half of the Moon’s Orbit, as VWX, is always below the Ecliptic, and the other half XYV above it. The points V and X, where the Moon’s Orbit intersects the Circle RSTU, which lies even with the Ecliptic, are the Moon’s Nodes; and a right line as XEV drawn from one to the other, through the Earth’s center, is the Line of the Nodes, which is carried almost parallel to itself round the Sun in a year.

If the Moon moved round the Earth in the Orbit RSTU, which is coincident with the Plane of the Ecliptic, her shadow would fall upon the Earth every time she is in conjunction with the Sun; and at every opposition she would go through the Earth’s shadow. Were this the case, the Sun would be eclipsed at every Change, and the Moon at every Full, as already mentioned.

But although the Moon’s shadow N must fall upon the Earth at a, when the Earth is at E, and the Moon in conjunction with the Sun at i, because she is then very near one of her Nodes; and at her opposition n she must go through the Earth’s shadow I, because she is then near the other Node; yet, in the time that she goes round the Earth to her next Change, according to the order of the letters XYVW, the Earth advances from E to e, according to the order of the letters EFGH, and the line of the Nodes VEX being carried nearly parallel to itself, brings the point f of the Moon’s Orbit in conjunction with the Sun at that next Change; and then the Moon being at f is too high above the Ecliptic to cast her shadow on the Earth: and as the Earth is still moving forward, the Moon at her next opposition will be at g, too far below the Ecliptic to go through any part of the Earth’s shadow; for by that time the point g will be at a considerable distance from the Earth as seen from the Sun.

Fig. I and II.

When the Earth comes to F, the Moon in conjunction with the Sun Z is not at k, in a Plane coincident with the Ecliptic, but above it at Y in the highest part of her Orbit: and then the point b of her shadow O goes far above the Earth (as in Fig. II, which is an edge view of Fig. I.) The Moon at her next opposition is not at o (Fig I) but at W where the Earth’s shadow goes far above her, (as in Fig. II.) In both these cases the line of the Nodes VFX (Fig. I.) is about 90 degrees from the Sun, and both Luminaries as far as possible from the limits of Eclipses.

PLATE X.

When the Earth has gone half round the Ecliptic from E to G, the line of the Nodes VGX is nearly, if not exactly, directed towards the Sun at Z; and then the New Moon l casts her shadow P on the Earth G; and the Full Moon p goes through the Earth’s shadow L; which brings on Eclipses again, as when the Earth was at E.

When the Earth comes to H the New Moon falls not at m in a plane coincident with the Ecliptic CD, but at W in her Orbit below it: and then her shadow Q (see Fig. II) goes far below the Earth. At the next Full she is not at q (Fig. I) but at Y in her orbit 51⁄3 degrees above q, and at her greatest height above the Ecliptic CD; being then as far as possible, at any opposition, from the Earth’s shadow M (as in Fig. II.)

So, when the Earth is at E and G, the Moon is about her Nodes at New and Full; and in her greatest North and South 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 greatest North and South Declination from the Ecliptic at New and Full, and in the Nodes about her Quarters.

The Moon’s ascending and descending Node.

Her North and South Latitude.

318. The point X where the Moon’s Orbit crosses the Ecliptic is called the Ascending Node, because the Moon ascends from it above the Ecliptic: and the opposite point of intersection V is called the Descending Node, because the Moon descends from it below the Ecliptic. When the Moon is at Y in the highest point of her Orbit, she is in her greatest North Latitude; and when she is at W in the lowest point of her Orbit, she is in her greatest South Latitude.

The Nodes have a retrograde motion.

Fig. I.

Which brings on the Eclipses sooner every year than they would
be if the Nodes had not such a motion.

319. If the line of the Nodes, like the Earth’s Axis, was carried parallel to itself round the Sun, there would be just half a year between the conjunctions of the Sun and Nodes. But the Nodes shift backward, or contrary to the Earth’s annual motion, 191⁄3 degrees every year; and therefore the same Node comes round to the Sun 19 days sooner every year than on the year before. Consequently, from the time that the ascending Node X (when the Earth is at E) passes by the Sun as seen from the Earth, it is only 173 days (not half a year) till the descending Node V passes by him. Therefore, in whatever time of the year we have Eclipses of the Luminaries about either Node, we may be sure that in 173 days afterward we shall have Eclipses about the other Node. And when at any time of the year the line of the Nodes is in the situation VGX, at the same time next year it will be in the situation rGs; the ascending Node having gone backward, that is, contrary to the order of Signs from X to s, and the descending Node from V to r; each 191⁄3 degrees. At this rate the Nodes shift through all the Signs and degrees of the Ecliptic in 18 years and 225 days; in which time there would always be a regular period of Eclipses, if any compleat number of Lunations were finished without a fraction. But this never happens, for if the Sun and Moon should start from a conjunction with either of the Nodes in any point of the Ecliptic, whilst the same Node is going round to that point again the Earth performs 18 annual revolutions about the Sun and 222 Degrees (or 7 Signs 12 Degrees) over; and the Moon 230 Lunations or Courses from Change to Change and 85 Degrees (or 2 Signs 25 Degrees) over; so that the Sun will be 138 Degrees from the same Node when it comes round, and the Moon 85 Degrees from the Sun. Hence, the period of Eclipses and revolution of the Nodes are completed in different times.

A period of Eclipses.

The defects of it.

320. In 18 years 10 days 7 hours 43 minutes after the Sun Moon and Nodes have been in a line of conjunction, they come very near to a conjunction again: only, if the conjunction from which you reckon falls in a leap-year, the return of the conjunction will be one day later. Therefore, if to the [65]mean time of any Eclipse of the Sun or Moon in leap-year, you add 18 years 11 days 7 hours 43 minutes; or in a common year a day less, you will have the mean time of that Eclipse returned again for some ages; though not always visible, because the 7 hours 43 minutes may shift a solar Eclipse into the night, and a lunar Eclipse into the day. In this period there are just 223 Lunations, and the Sun is again within half a degree of the same Node, but short of it. Therefore, although this period will serve tolerably well for some ages to examine Eclipses by, it cannot hold long; because half a degree from the Node sets the Moon 21⁄2 minutes of a degree from the Ecliptic. And as the Moon’s mean distance from the Earth is equal to 60 Semidiameters of the Earth, every minute of a degree at that distance is equal to 60 geographical miles, or one degree on the Earth; consequently 21⁄2 minutes of declination from the Ecliptic in the Moon’s Orbit, is equal to 150 such miles, or 21⁄2 degrees on the Earth. Consequently, if the Moon be passing by her ascending Node at the end of this period, her shadow will go 150 miles more southward on the Earth than it did at the beginning thereof. If the Moon be passing by her descending Node, her shadow will go 150 miles more northward: and in either case, in 500 years the shadow will have too great a Latitude to touch the Earth. So that any Eclipse of the Sun, which begins (for example) to touch the Earth at the south Pole (and that must be when the Moon is 17 degrees past her descending Node) will advance gradually northward in every return for about a thousand years, and then go off at the north Pole; and cannot take such another course again in less than 11,683 years.

This falling back of the Sun and Moon in every period, with respect to the Nodes, will occasion those Eclipses which happen about the ascending Node to go more southerly in each return; and those which happen about the descending Node to go more northerly: for the farther the Moon is short of the ascending Node, within the limits of Eclipses, the farther she is south of the Ecliptic; and on the contrary, the more she is short of the descending Node, the farther she is northward of the Ecliptic.

From Mr. G. Smith’s dissertation on Eclipses, printed at London, by E. Cave, in the year 1748.

321. “To illustrate this a little farther, we shall examine some of the most remarkable circumstances of the returns of the Eclipse which happened July 14, 1748, about noon: This Eclipse, after traversing the voids of space from the Creation, at last began to enter the Terra Australis Incognita, about 88 years after the Conquest, which was the last of King Stephen’s reign; every [66]Chaldean period it has crept more northerly, but was still invisible in Britain before the year 1622; when on the 30th of April it began to touch the south parts of England about 2 in the afternoon; its central appearance rising in the American South Seas, and traversing Peru and the Amazon’s country, through the Atlantic ocean into Africa, and setting in the Æthiopian continent, not far from the beginning of the Red Sea.

“Its next visible period was after three Chaldean revolutions in 1676, on the first of June, rising central in the Atlantic ocean, passing us about 9 in the morning, with four [67]Digits eclipsed on the under limb; and setting in the gulf of Cochinchina in the East-Indies.

“It being now near the Solstice, this Eclipse was visible the very next return in 1694, in the evening; and in two periods more, which was in 1730, on the 4th of July, was seen above half eclipsed just after Sun-rise, and observed both at Wirtemberg in Germany, and Pekin in China, soon after which it went off.

“Eighteen years more afforded us the Eclipse which fell on the 14th of July 1748.

“The next visible return will happen on July 25, 1766, in the evening, about four Digits eclipsed; and after two periods more, on August 16th, 1802, early in the morning, about five Digits, the center coming from the north frozen continent, by the capes of Norway, through Tartary, China, and Japan, to the Ladrone islands, where it goes off.

“Again, in 1820, August 26, betwixt one and two, there will be another great Eclipse at London, about 10 Digits; but happening so near the Equinox, the center will leave every part of Britain to the West, and enter Germany at Embden, passing by Venice, Naples, Grand Cairo, and set in the gulf of Bassora near that city.

“It will be no more visible till 1874, when five Digits will be obscured, the center being now about to leave the Earth on September 28. In 1892 the Sun will go down eclipsed at London, and again in 1928 the passage of the center will be in the expansum, though there will be two Digits eclipsed at London, October the 31st of that year; and about the year 2090 the whole Penumbra will be wore off; whence no more returns of this Eclipse can happen till after a revolution of 10 thousand years.

“From these remarks on the intire revolution of this Eclipse, we may gather, that a thousand years, more or less (for there are some irregularities that may protract or lengthen this period 100 years) complete the whole terrestrial Phenomena of any single Eclipse: and since 20 periods of 54 years each, and about 33 days, comprehend the intire extent of their revolution, ’tis evident that the times of the returns will pass through a circuit of one year and ten months, every Chaldean period being ten or eleven days later, and of the equable appearances about 32 or 33 days. Thus, though this Eclipse happens about the middle of July, no other subsequent Eclipse of this period will return to the middle of the same month again; but wear constantly each period 10 or 11 days forward, and at last appear in Winter, but then it begins to cease from affecting us.

“Another conclusion from this revolution may be drawn, that there will seldom be any more than two great Eclipses of the Sun in the interval of this period, and these follow sometimes next return, and often at greater distances. That of 1715 returned again in 1733 very great; but this present Eclipse will not be great till the arrival of 1820, which is a revolution of four Chaldean periods: so that the irregularities of their circuits must undergo new computations to assign them exactly.

“Nor do all Eclipses come in at the south Pole: that depends altogether on the position of the lunar Nodes, which will bring in as many from the expansum one way as the other; and such Eclipses will wear more southerly by degrees, contrary to what happens in the present case.

“The Eclipse, for example, of 1736, in September, had its center in the expansum, and set about the middle of its obscurity in Britain; it will wear in at the north Pole, and in the year 2600, or thereabouts, go off into the expansum on the south side of the Earth.

“The Eclipses therefore which happened about the Creation are little more than half way yet of their etherial circuit; and will be 4000 years before they enter the Earth any more. This grand revolution seems to have been entirely unknown to the antients.

Why our present Tables agree not with antient observations.

“322. It is particularly to be noted, that Eclipses which have happened many centuries ago, will not be found by our present Tables to agree exactly with antient observations, by reason of the great Anomalies in the lunar motions; which appears an incontestable demonstration of the non-eternity of the Universe. For it seems confirmed by undeniable proofs, that the Moon now finishes her period in less time than formerly, and will continue by the centripetal law to approach nearer and nearer the Earth, and to go sooner and sooner round it: nor will the centrifugal power be sufficient to compensate the different gravitations of such an assemblage of bodies as constitute the solar system, which would come to ruin of itself, without some new regulation and adjustment of their original motions[68].

Thales’s Eclipse.

“323. We are credibly informed from the testimony of the antients, that there was a total Eclipse of the Sun predicted by Thales to happen in the fourth year of the 48th [69]Olympiad, either at Sardis or Miletus in Asia, where Thales then resided. That year corresponds to the 585th year before Christ; when accordingly there happened a very signal Eclipse of the Sun, on the 28th of May, answering to the present 10th of that month[70], central through North America, the south parts of France, Italy, &c. as far as Athens, or the Isles in the Ægean Sea; which is the farthest that even the Caroline Tables carry it; and consequently make it invisible to any part of Asia, in the total character; though I have good reasons to believe that it extended to Babylon, and went down central over that city. We are not however to imagine, that it was set before it past Sardis and the Asiatic towns, where the predictor lived; because an invisible Eclipse could have been of no service to demonstrate his ability in Astronomical Sciences to his countrymen, as it could give no proof of its reality.

Thucydides’s Eclipse.

“324. For a farther illustration, Thucydides relates, that a solar Eclipse happened on a Summer’s day in the afternoon, in the first year of the Peloponnesian war, so great that the Stars appeared. Rhodius was victor in the Olympic games the fourth year of the said war, being also the fourth of the 87th Olympiad, on the 428th year before Christ. So that the Eclipse must have happened in the 431st year before Christ; and by computation it appears, that on the 3d of August there was a signal Eclipse which would have past over Athens, central about 6 in the evening, but which our present Tables bring no farther than the antient Syrtes on the African coast, above 400 miles from Athens; which suffering in that case but 9 Digits, could by no means exhibit the remarkable darkness recited by this historian; the center therefore seems to have past Athens about 6 in the evening, and probably might go down about Jerusalem, or near it, contrary to the construction of the present Tables. I have only obviated these things by way of caution to the present Astronomers, in re-computing antient Eclipses; and refer them to examine the Eclipse of Nicias, so fatal to the Athenian fleet[71]; that which overthrew the Macedonian Army[72] &c.” So far Mr. Smith.

The number of Eclipses.

325. In any year, the number of Eclipses of both Luminaries cannot be less than two, nor more than seven; the most usual number is four, and it is very rare to have more than six. For the Sun passes by both the Nodes but once a year, unless he passes by one of them in the beginning of the year; and if he does, he will pass by the same Node again a little before the year be finished; because, as these points move 19 degrees backward every year, the Sun will come to either of them 173 days after the other § 319. And when either Node is within 17 degrees of the Sun at the time of New Moon, the Sun will be eclipsed. At the subsequent opposition the Moon will be eclipsed in the other Node; and come round to the next conjunction again ere the former Node be 17 degrees past the Sun, and will therefore eclipse him again. When three Eclipses fall about either Node, the like number generally falls about the opposite; as the Sun comes to it in 173 days afterward: and six Lunations contain but four days more. Thus, there may be two Eclipses of the Sun and one of the Moon about each of her Nodes. But when the Moon changes in either of the Nodes, she cannot be near enough the other Node at the next Full to be eclipsed; and in six lunar months afterward she will change near the other Node: in these cases there can be but two Eclipses in a year, and they are both of the Sun.

Two periods of Eclipses.

326. A longer, and consequently more exact period than the above-mentioned § 320, for comparing and examining Eclipses which happen at long intervals of time, is 57 Julian years 324 days 21 hours 41 minutes and 35 seconds; in which time there are just 716 mean Lunations, and the Sun is again within 5 minutes of the same Node as before. But a still better period is 557 years 21 days 18 hours 30 minutes 12 seconds; in which time there are 6890 mean Lunations; and the Sun and Node meet again so nearly as to be but 11 seconds distant.

An account of the following catalogue of Eclipses.

327. We shall subjoin a catalogue of Eclipses recorded in history, from 721 years before Christ to A. D. 1485; of computed Eclipses from 1485 to 1700; and of all the Eclipses visible in Europe from 1700 to 1800. From the beginning of the catalogue to A.D. 1485 the Eclipses are taken from Struyk’s Introduction to universal Geography, as that indefatigable author has, with much labour, collected them from Ptolemy, Thucydides, Plutarch, Calvisius, Xenophon, Diodorus Siculus, Justin, Polybius, Titus Livius, Cicero, Lucanus, Theophanes, Dion Cassius, and many others. From 1485 to 1700 the Eclipses are taken from Ricciolus’s Almagest: and from 1700 to 1800 from L’art de verifier les Dates[73]. Those from Struyk have all the places mentioned where they were observed: Those from the French authors, viz. the religious Benedictines of the Congregation of St. Maur, are fitted to the Meridian of Paris: And concerning those from Ricciolus, that author gives the following account.

Because it is of great use for fixing the Cycles or Revolutions of Eclipses, to have at hand, without the trouble of calculation, a list of successive Eclipses for many years, computed by authors of Ephemerides, although from Tables not perfect in all respects, I shall for the benefit of Astronomers give a summary collection of such. The authors I extract from are, an anonymous one who published Ephemerides from 1484 to 1506 inclusive; Jacobus Pflaumen and Jo. Stæflerinus, to the Meridian of Ulm, from 1507 to 1534: Lucas Gauricus, to the Latitude of 45 degrees, from 1534 to 1551: Peter Appian, to the Meridian of Leysing, from 1538 to 1578: Jo. Stæflerus to the Meridian of Tubing, from 1543 to 1554: Petrus Pitatus, to the Meridian of Venice from 1544 to 1556: Georgius-Joachimus Rheticus, for the year 1551: Nicholaus Simus, to the Meridian of Bologna, from 1552 to 1568: Michael Mæstlin, to the Meridian of Tubing, from 1557 to 1590: Jo. Stadius, to the Meridian of Antwerp, from 1554 to 1574: Jo. Antoninus Maginus, to the Meridian of Venice, from 1581 to 1630: David Origan, to the Meridian of Franckfort on the Oder, from 1595 to 1664: Andrew Argol, to the Meridian of Rome, from 1630 to 1700: Franciscus Montebrunus, to the Meridian of Bologna, from 1461 to 1660: Among which, Stadius, Mæstlin, and Maginus, used the Prutenic Tables; Origan the Prutenic and Tychonic; Montebrunus the Lansbergian, as likewise those of Duret. Almost all the rest the Alphonsine.

But, that the places may readily be known for which these Eclipses were computed, and from what Tables, consult the following list, in which the years inclusive are also set down.

From 1485to1506The place and author unknown.
15071553Ulm in Suabia, from the Alphonsine.
15541576Antwerp, from the Prutenic.
15771585Tubing, from the Prutenic.
15861594Venice, from the Prutenic.
15951600Franckfort on Oder, from the Prutenic.
16011640Franckfort on Oder, from the Tychonic.
16411660Bologna, from the Lansbergian.
16611700Rome, from the Tychonic.

So far Ricciolus.

N. B. The Eclipses marked with an Asterisk are not in Ricciolus’s catalogue; but are supplied from L’art de verifier les Dates.

From the beginning of the catalogue to A. D. 1700, the time is reckoned from the noon of the day mentioned to the noon of the following day; but from 1700 to 1800 the time is set down according to our common way of reckoning. Those marked Pekin and Canton are Eclipses from the Chinese chronology according to Struyk; and throughout the Table this mark sun signifies Sun, and this moon Moon.

Struyk’s Catalogue of ECLIPSES.

Bef. Chr.Eclipses of the Sun and Moon seen atM. & D.MiddleDigits eclipsed
H.M.
721BabylonmoonMar. 191034Total
720BabylonmoonMar. 8115615
720BabylonmoonSept. 1101854
621BabylonmoonApr. 211822236
523BabylonmoonJuly 161247724
502BabylonmoonNov. 191221152
491BabylonmoonApr. 251212144
431AthenssunAug. 3635110
425AthensmoonOct. 9645Total
424AthenssunMar. 20201790
413AthensmoonAug. 271015Total
406AthensmoonApr. 15850Total
404AthenssunSept. 22112840
403PekinsunAug. 285531040
394GnidesunAug. 132217110
383AthensmoonDec. 2219621
382AthensmoonJune 18854615
382AthensmoonDec. 121021Total
364ThebessunJuly 122351610
357SyracusesunFeb. 2822--333
357ZantmoonAug. 29729421
340ZantsunSept. 1418--90
331ArbelamoonSept. 20109Total
310Sicily IslandsunAug. 142051022
219MysiamoonMar. 19145Total
218PergamosmoonSept. 1risingTotal
217SardiniasunFeb. 1115796
203FrusinisunMay 6252540
202CumissunOct. 18222410
201AthensmoonSept. 22714858
200AthensmoonMar. 19139Total
200AthensmoonSept. 111448Total
198RomesunAug. 6--------
190RomesunMar. 1318--110
188RomesunJuly 1620381048
174AthensmoonApr. 30143371
168MacedoniamoonJune 2182Total
141RhodesmoonJan. 27108326
104RomesunJuly 182201152
63RomemoonOct. 27622Total
60GibraltersunMar. 16settingCentral
54CantonsunMay 9341Total
51RomesunMar. 721290
48RomemoonJan. 18100Total
45RomemoonNov. 614--Total
36RomesunMay 19352647
31RomesunAug. 20settingGr. Ecl.
29CantonsunJan. 542110
28PekinsunJune 182348Total
26CantonsunOct. 234161115
24PekinsunApril 741120
16PekinsunNov. 151328
2CantonsunFeb. 12081142
Aft. Chr.Eclipses of the Sun and Moon seen atM. & D.MiddleDigits eclipsed
H.M.
1PekinsunJune 101101143
5RomesunMar. 28413445
14PanoniamoonSept. 261715Total
27CantonsunJuly 22856Total
30CantonsunNov. 1319201030
40PekinsunApr. 30550734
45RomesunJuly 31221517
46PekinsunJuly 212225210
46RomemoonDec. 31952Total
49PekinsunMay 20716108
53CantonsunMar. 82042116
55PekinsunJuly 122150640
56CantonsunDec. 25028920
59RomesunApr. 30381038
60CantonsunOct. 133311030
65CantonsunDec. 1521501023
69RomemoonOct. 1810431049
70CantonsunSept. 222113826
71RomemoonMar. 483260
95EphesussunMay 21----10
125AlexandriamoonApril 5916144
133AlexandriamoonMay 61144Total
134AlexandriamoonOct. 201151019
136AlexandriamoonMar. 51556517
237BolognasunApr. 12----Total
238RomesunApril 12020845
290CarthagesunMay 153201120
304RomemoonAug. 31936Total
316ConstantinoplesunDec. 301953218
334ToledosunJuly 17at noonCentral
348ConstantinoplesunOct. 8192480
360IspahansunAug. 27180Central
364AlexandriamoonNov. 251524Total
401RomemoonJune 11----Total
401RomemoonDec. 61215Total
402RomemoonJune 1843102
402RomesunNov. 1020331030
447CompostellosunDec. 230461--
451CompostellomoonApril 116341952
451CompostellomoonSept. 2663002
458ChavessunMay 2723161853
462CompostellomoonMar. 11321111
464ChavessunJuly 191911015
484ConstantinoplesunJan. 13195300
486ConstantinoplesunMay 19110515
497ConstantinoplesunApr. 18651757
512ConstantinoplesunJune 28238150
538EnglandsunFeb. 1419--823
540LondonsunJune 1920158--
577ToursmoonDec. 101728646
581ParismoonApril 41333642
582ParismoonSept. 171241Total
590ParismoonOct. 18630925
592ConstantinoplesunMar. 18226100
603ParissunAug. 12331120
622ConstantinoplemoonFebr. 11128Total
644ParissunNov. 5030953
680ParismoonJune 171230Total
683ParismoonApril 161130Total
693ConstantinoplesunOct. 423541154
716ConstantinoplemoonJan. 137--Total
718ConstantinoplesunJune 3115Total
733EnglandsunAug. 1320--111
734EnglandmoonJan. 2314--Total
752EnglandmoonJuly 3013--Total
753EnglandsunJune 822--1035
753EnglandmoonJan. 2313--Total
760EnglandsunAug. 154--815
760LondonmoonAug. 305501040
764EnglandsunJune 4at noon715
770LondonmoonFeb. 14712Total
774RomemoonNov. 2214371158
784LondonmoonNov. 1142Total
787ConstantinoplesunSept. 142043947
796ConstantinoplemoonMar. 271622Total
800RomemoonJan. 15901017
807AngoulesmesunFeb. 102124942
807ParismoonFeb. 251343Total
807ParismoonAug. 211020Total
809ParissunJuly 15213388
809ParismoonDec. 258--Total
810ParismoonJune 208--Total
810ParissunNov. 30012Total
810ParismoonDec. 148--Total
812ConstantinoplesunMay 142139--
813CappadociasunMay 31751035
817ParismoonFeb. 5542Total
818ParissunJuly 618--655
820ParismoonNov. 23626Total
824ParismoonMar. 18755Total
828ParismoonJune 3015--Total
828ParismoonDec. 241345Total
831ParismoonApril 30619118
831ParissunMay 1523--424
831ParismoonOct. 241118Total
832FuldamoonApr. 1890Total
840ParissunMay 42322920
841ParissunOct. 171858524
842ParismoonMar. 291438Total
843ParismoonMar. 1971Total
861ParismoonMar. 29157Total
878ParismoonOct. 1416--Total
878ParissunOct. 291--1114
883ArractamoonJuly 2374411--
889ConstantinoplesunApril 31752923
891ConstantinoplesunAug. 723481030
901ArractamoonAug. 2157Total
904LondonmoonMay 311147Total
904LondonmoonNov. 2590Total
912LondonmoonJan. 61512Total
926ParismoonMar. 311517Total
934ParissunApr. 164301136
939ParissunJuly 181945107
955ParismoonSept. 41118Total
961R pl prhemessunMay 162013918
970ConstantinoplesunMay 718381122
976LondonmoonJuly 13157Total
985MessinasunJuly 20352410
989ConstantinoplesunMay 28654840
990FuldamoonApr. 12102295
990FuldamoonOct. 61541110
990ConstantinoplesunOct. 21045105
995AugsburghmoonJuly 141127Total
1009FerraramoonOct. 61138Total
1010MessinasunMar. 18541912
1016NimeguenmoonNov. 161639Total
1017NimeguensunOct. 22286--
1020ColognemoonSept. 41138Total
1023LondonsunJan. 23232911--
1030RomemoonFeb. 201143Total
1031ParismoonFeb. 91151Total
1033ParismoonDec. 81111917
1034MilanmoonJune 498Total
1037ParissunApr. 1720451045
1039AuxerresunAug. 212340115
1042RomemoonJan. 81639Total
1044AuxerremoonNov. 71612101
1044ClunysunNov. 21221211--
1056NuremburgmoonApril 2129Total
1063RomemoonNov. 81216Total
1074AugsburghmoonOct. 71013Total
1080ConstantinoplemoonNov. 291112936
1082LondonmoonMay 141032102
1086ConstantinoplesunFeb. 1647Total
1089NaplesmoonJune 2566Total
1093AugsburghsunSept. 2222351012
1096GembloursmoonFeb. 10164Total
1096AugsburghmoonAug. 6821Total
1098AugsburghsunDec. 251251012
1099NaplesmoonNov. 30458Total
1103RomemoonSept. 171018Total
1106ErfurdmoonJuly 1711281154
1107NaplesmoonJan. 101316Total
1109ErfurdsunMay 311301020
1110LondonmoonMay 51051Total
1113JerusalemsunMar. 18190912
1114LondonmoonAug. 17155Total
1117TriermoonJune 151326Total
1117TriermoonDec. 101251Total
1118NaplesmoonNov. 291546411
1121TriermoonSept. 271647Total
1122PraguemoonMar. 241120349
1124ErfurdmoonFeb. 1643839
1124LondonsunAug. 102329958
1132ErfurdmoonMarch 3814Total
1133PraguemoonFeb. 201641323
1135LondonmoonDec. 222011Total
1142RomemoonFeb. 111417830
1143RomemoonFeb. 1636Total
1147AuranchessunOct. 252238720
1149BarymoonMar. 251354529
1151EimbeckmoonAug. 28124429
1153AugsburghsunJan. 2604211--
1154ParismoonJune 26161Total
1154ParismoonDec. 21830442
1155AuranchesmoonJune 10845053
1160RomemoonAug. 18753649
1161RomemoonAug. 7815Total
1162ErfurdmoonFeb. 1640556
1162ErfurdmoonJuly 271230411
1163Mont Cassin.sunJuly 374020
1164MilanmoonJune 6100Total
1168LondonmoonSept. 18140Total
1172ColognemoonJan. 111331Total
1176AuranchesmoonApril 257286
1176AuranchesmoonOct. 191120853
1178ColognemoonMarch 5setting752
1178AuranchesmoonAug. 291352531
1178ColognesunSept. 12----1051
1179ColognemoonAug. 181428Total
1180AuranchessunJan. 284141034
1181AuranchessunJuly 13315348
1181AuranchesmoonDec. 22858440
1185RhemessunMay 115390
1186ColognemoonApril 56--Total
1186FranckfortsunApril 2071940
1187ParismoonMar. 251617842
1187EnglandsunSept. 3215486
1189EnglandmoonFeb. 210--9--
1191EnglandsunJune 230201132
1192FrancemoonNov. 2014--6--
1193FrancemoonNov. 10527Total
1194LondonsunApril 22215649
1200LondonmoonJan. 2172435
1201LondonmoonJune 17154Total
1204EnglandmoonApril 151239Total
1204SaltzburgmoonOct. 10632Total
1207RhemessunFeb. 2710501020
1208RhemesmoonFeb. 2510Total
1211ViennamoonNov. 211357Total
1215ColognemoonMar. 161535Total
1216AcresunFeb. 1821151136
1216AcremoonMarch 593874
1218DamiettamoonJuly 99461131
1222RomemoonOct. 221428Total
1223ColmarmoonApril 16813110
1228NaplessunDec. 27955919
1230NaplessunMay 1317--Total
1230LondonmoonNov. 211321934
1232RhemessunOct. 15429425
1245RhemessunJuly 2417476--
1248LondonmoonJune 7849Total
1255LondonmoonJuly 20947Total
1255ConstantinoplesunDec. 30252Annul.
1258AugsburghmoonMay 181117Total
1261ViennasunMar. 31224098
1262ViennamoonMarch 7550Total
1262ViennamoonAug. 301439Total
1263ViennamoonFeb. 24652629
1263AugsburghsunAug. 53241117
1263ViennamoonAug. 2073597
1265ViennamoonDec. 231625Total
1267ConstantinoplesunMay 2423111140
1270ViennasunMar. 2218471040
1272ViennamoonAug. 10727853
1274ViennamoonJan. 231039925
1275LaubenmoonDec. 4620429
1276ViennamoonNov. 2215--Total
1277ViennamoonMay 18----Total
1279FranckfortsunApr. 12655106
1280LondonmoonMar. 171212Total
1284ReggiomoonDec. 231611913
1290WittemburgsunSept. 419371030
1291LondonmoonFeb. 14102Total
1302ConstantinoplemoonJan. 141025Total
1307FerrarasunApril 22218054
1309LondonmoonFeb. 241744Total
1309LuccamoonAug. 211032Total
1310WittemburgsunJan. 31221010
1310TorcellomoonFeb. 14481020
1310TorcellomoonAug. 101533716
1312WittemburgsunJuly 41949323
1312PlaisancemoonDec. 14719Total
1313TorcellomoonDec. 3858934
1316ModenamoonOct. 11455Total
1321WittemburgsunJune 251811117
1323FlorencemoonMay 201524Total
1324FlorencemoonMay 963Total
1324WittemburgsunApr. 2363588
1327ConstantinoplemoonAug. 311826Total
1328ConstantinoplemoonFeb. 25134711--
1330FlorencemoonJune 301510734
1330ConstantinoplesunJuly 16451043
1330PraguemoonDec. 251549Total
1331PraguesunNov. 292026741
1331PraguemoonDec. 1418--11--
1333WittemburgsunMay 143--1018
1334CesenamoonApr. 191033Total
1341ConstantinoplemoonNov. 231223Total
1341ConstantinoplesunDec. 82215630
1342ConstantinoplemoonMay 201427Total
1344AlexandriasunOct. 61840855
1349WittemburgmoonJune 301220Total
1354WittemburgsunSept. 162045843
1356FlorencemoonFeb. 161143Total
1361ConstantinoplesunMay 42215854
1367In ChinamoonJan. 16827Total
1389EugibinmoonNov. 3175Total
1396AugsburgsunJan. 11016622
1396AugsburgmoonJune 211110Total
1399ForlisunOct. 290439--
1406ConstantinoplemoonJune 113--1031
1406ConstantinoplesunJune 151811138
1408ForlisunOct. 182147932
1409ConstantinoplesunApr. 15311048
1410ViennamoonMar. 201313Total
1415WittemburgsunJune 6643Total
1419FranckfortsunMar. 25225145
1421ForlimoonFeb. 1782Total
1422ForlimoonFeb. 6826117
1424WittemburgsunJune 263571120
1431ForlisunFeb. 1224139
1433WittemburgsunJune 175--Total
1438WittemburgsunSept. 18205987
1442RomemoonDec. 17356Total
1448TubingsunAug. 282223853
1450ConstantinoplemoonJuly 24719Total
1457ViennamoonSept. 31117Total
1460AustriamoonJuly 3731523
1460AustriasunJuly 1717321119
1460ViennamoonDec. 271330Total
1461ViennamoonJune 221150Total
1461RomemoonDec. 17----Total
1462ViterbomoonJune 1115--738
1462ViterbosunNov. 2101026
1464PaduamoonApr. 211243Total
1465RomesunSept. 20515846
1465RomemoonOct. 4512Total
1469RomemoonJan. 2779Total
1485NorimburgsunMar. 1635311--

The following ECLIPSES are all taken from Ricciolus, except those marked

with an Asterisk, which are from L’Art de verifier les Dates.

Aft. Chr.M. & D.MiddleDigits eclipsed
H.M.
1486moonFeb. 18541Total
1486sunMar. 5174390
1487moonFeb. 71549Total
1487sunJuly 202670
1488moonJan. 286--*
1488sunJuly 8173040
1489moonDec. 71741Total
1490sunMay 19Noon*
1490moonJune 2106Total
1490moonNov. 261825Total
1491sunMay 821990
1491moonNov. 1518--*
1492sunApr. 267--*
1492sunOct. 2023--*
1493moonApril 1140Total
1493sunOct. 1024080
1494sunMar. 741240
1494moonMar. 211438Total
1494moonSept. 141945Total
1495moonMar. 1016--*
1495sunAug. 1917--*
1496moonJan. 2914--*
1497moonJan. 18638Total
1497sunJuly 293230
1499moonJune 2217--*
1499sunAug. 2318--*
1499moonNov. 1710--*
1500sunMar. 27In the Night
1500moonApr. 11At Noon
1500moonOct. 5142100
1501moonMay 21749Total
1502sunSept. 301945100
1502moonOct. 15122020
1503moonMar. 129--*
1503sunSept. 1922--*
1504moonFeb. 291336Total
1504sunMar. 163--*
1505moonAug. 14818Total
1506moonFeb. 715--*
1506sunJuly 2031120
1506moonAug. 310--*
1507sunJan. 1219--*
1508sunJan. 24--*
1508sunMay 296--*
1508moonJune 121740Total
1509moonJune 2111170
1509sunNov. 1122--*
1510moonOct. 1619--*
1511moonOct. 61150Total
1512moonSept. 25356Total
1513sunMar. 703060
1513sunAug. 301--*
1515moonJan. 291518Total
1516moonJan. 1960Total
1516moonJuly 131137Total
1516sunDec. 2334730
1517sunJune 1816--*
1517moonNov. 2719--*
1518moonMay 241119911
1518sunJune 71756110
1519sunMay 281--*
1519sunOct. 2343360
1519moonNov. 6624Total
1520moonMay 27--*
1520sunOct. 115223
1520moonOct. 2519--*
1520moonMar. 2117--*
1521sunApril 619--*
1521sunSept. 303--*
1522moonSept. 51217Total
1523moonMar. 1826Total
1523moonAug. 251524Total
1524sunFeb. 41--*
1524moonAug. 1616--*
1525sunJan. 234--*
1525moonJuly 41010Total
1525moonDec. 291046Total
1526moonDec. 181030Total
1527sunJan. 23--*
1527moonDec. 710--*
1528sunMay 1720--*
1529moonOct. 1620231155
1530sunMar. 281823824
1530moonOct. 61211Total
1531moonApril 17--*
1532sunAug. 30049335
1533moonAug. 41150Total
1533sunAug. 1917--*
1534sunJan. 14142545
1534moonJan. 291425Total
1535sunJune 30Noon*
1535moonJuly 148--*
1535sunDec. 242--*
1536sunJune 182280
1536moonNov. 276211015
1537moonMay 2483Total
1537sunJune 77--*
1537moonNov. 161456Total
1538moonMay 13142430
1538moonNov. 6531337
1539sunApr. 1843390
1540sunApril 61715Total
1541moonMar. 111634Total
1541sunAug. 2105630
1542moonMar. 1846138
1542sunAug. 1017--*
1543moonJuly 1516--*
1544moonJan. 91813Total
1544sunJan. 2321161117
1544moonJuly 4831Total
1544moonDec. 281827Total
1545sunJune 82048345
1545moonDec. 1718--*
1546sunMay 305--*
1546sunNov. 2223--*
1547moonMay 4102780
1547moonOct. 284561134
1547sunNov. 1229930
1548sunApril 83--*
1548moonApr. 221124Total
1549moonApr. 11151920
1549moonOct. 66--*
1550sunMar. 1620--*
1551moonFeb. 20821Total
1551sunAug. 3120152
1553sunJan. 122254122
1553sunJuly 107--*
1553moonJuly 24160031
1554sunJune 296--*
1554moonDec. 81371012
1555moonJune 4150Total
1555sunNov. 1319--*
1556sunNov. 1180941
1556moonNov. 161244655
1557sunOct. 2020--*
1558moonApril 2110950
1558sunApr. 181--*
1559moonApr. 16450Total
1560moonMar. 111540413
1560sunAug. 2110622
1560moonSept. 47--*
1561sunFeb. 1319--*
1562sunFeb. 35--*
1562moonJuly 151550Total
1563sunJan. 2219--*
1563sunJune 20450838
1563moonJuly 5841134
1565sunMar. 71253------
1565moonMay 1416--*
1565moonNov. 712461146
1566moonOct. 28538Total
1567sunApril 8234934
1567moonOct. 171343240
1568sunMar. 285--*
1569moonMar. 21518Total
1570moonFeb. 20546Total
1570moonAug. 15917Total
1571sunJan. 254--*
1572sunJan. 1419--*
1572moonJune 2590526
1573sunJune 2818--*
1573sunNov. 244--*
1573moonDec. 8651Total
1574sunNov. 13350521
1575sunMay 198--*
1575sunNov. 25--*
1576moonOct. 7945------
1577moonApril 2833Total
1577moonSept. 26134Total
1578moonSept. 15134220
1579sunFeb. 15541836
1579sunAug. 20190*
1580moonJan. 31107Total
1581moonJan. 19922Total
1581moonJuly 151751Total
1582moonJan. 81029053
1582sunJune 1917575
1583moonNov. 282151Total
1584sunMay 91820336
1584moonNov. 171415Total
1585sunApr. 29753117
1585moonMay 1352654
1586moonSept. 278--*
1586sunOct. 12Noon*
1587moonSept. 16928102
1588sunFeb. 2612313
1588moonMar. 121414Total
1588moonSept. 41730Total
1589sunAug. 1018--*
1589sunAug. 2581354
1590sunFeb. 45--*
1590moonJuly 16174354
1590sunJuly 3019571027
1591moonJan. 9621940
1591moonJuly 658Total
1591sunJuly 204210
1591moonDec. 291611Total
1592moonJune 241013858
1592moonDec. 18724554
1593sunMay 30230238
1594sunMay 1914581023
1594moonOct. 281915940
1595sunApril 9Ter. de Fuego
1595moonApr. 24412Total
1595sunMay 722--*
1595sunOct. 324518
1595moonOct. 182047Total
1596sunMar. 28In Chili
1596moonApr. 1285264
1596sunSept. 21In China
1596moonOct. 62115333
1597sunMar. 17St. Pet. Isle
1597sunSept. 11Picora949
1598moonFeb. 2018121055
1598sunMar. 622121157
1598moonAug. 16815Total
1598sunAug. 31Magel.834
1599moonFeb. 101721Total
1599sunJuly 22431418
1599moonAug. 6------Total
1600sunJan. 15Java1148
1600moonJan. 30640258
1600sunJuly 10210539
1601sunJan. 4Ethiop.940
1601moonJune 15618452
1601sunJune 29China429
1601moonDec. 9761053
1601sunDec. 24246952
1602sunMay 21Greenl.241
1602moonJune 4718Total
1602sunJune 19N. Gra.543
1602sunNov. 13Magel.3--
1602moonNov. 28102Total
1603sunMay 10China1121
1603moonMay 241141759
1603sunNov. 3Rom. I.1117
1603moonNov. 18731326
1604sunApr. 29Arabia932
1604sunOct. 22Peru649
1605moonApril 39191149
1605sunApr. 18Madag.531
1605moonSept. 27427926
1605sunOct. 12232924
1606sunMar. 8Mexico60
1606moonMar. 241117Total
1606sunSept. 2Magel.640
1606moonSept. 16156Total
1607sunFeb. 252148113
1607moonMar. 13636122
1607sunSept. 5154047
1608sunFeb. 15at the Antipo.
1608moonJuly 27030153
1608sunAug. 9439040
1609moonJan. 1915211032
1609sunFeb. 4Fuego522
1609moonJuly 16128Total
1609sunJuly 30Canada410
1609sunDec. 2619--550
1610moonJan. 9131Total
1610sunJune 20Java1046
1610moonJuly 516581113
1610sunDec. 15Cyprus450
1610moonDec. 291647423
1611sunJune 10Califor.1130
1612moonMay 141038722
1612sunMay 292338714
1612moonNov. 8322949
1612sunNov. 22Magel.90
1613sunApr. 20Magellanica
1613moonMay 4035Total
1613sunMay 19East Tartary
1613sunOct. 13South Amer.
1613moonOct. 28419Total
1614sunApril 8N. Gui.844
1614moonApr. 231736525
1614sunOct. 305752
1614moonOct. 17438456
1615sunMar. 29Goa1038
1615sunSept. 22Salom Isle
1616moonMar. 3158Total
1616sunMar. 17Mexico647
1616moonAug. 261533Total
1616sunSept. 10Magel.1033
1617sunFeb. 5Magellanica
1617moonFeb. 20149Total
1617sunMar 622--*
1617sunAug. 1Biarmia
1617moonAug. 16822Total
1618sunJan. 26Magellanica
1618moonFeb. 9329257
1618sunJuly 21Mexico------
1619sunJan. 15California
1619moonJune 261240310
1619sunJuly 11Africa1139
1619moonDec. 2015531047
1620sunMay 31Arctic Circle
1620moonJune 141347Total
1620sunJune 29Magel.720
1620moonDec. 9639Total
1620sunDec. 23Magellanica
1621sunMay 2014541044
1621moonJune 31942953
1621sunNov. 13Magellanica
1621moonNov. 281543338
1622sunMay 10C. Verd1152
1622sunNov. 2Malacca In.
1623moonApr. 147191054
1623sunApr. 29------------
1623moonOct. 8022835
1623sunOct. 23Califor.1046
1624sunMay 18N. Zem.60
1624moonApr. 379Total
1624sunApr. 17Antar. Circle
1624sunSept. 12Magellanica
1624moonSept. 26855Total
1625sunMar. 8Florida
1625moonMar. 231411211
1625sunSept. 1St. Peter’s Isl.
1625moonSept. 16114156
1626sunFeb. 25Madag.827
1626moonAug. 7748025
1626sunAug. 21In | Mexico
1627moonJan. 3011381021
1627sunFeb. 15Magellanica
1627moonJuly 2794Total
1627sunAug. 11Tenduc100
1628sunJan. 6Tenduc540
1628moonJan. 201011Total
1628sunJuly 1C Good Hope
1628moonJuly 161126Total
1628sunDec. 25In England
1629moonJan. 9136427
1629sunJune 21Ganges1125
1629sunDec. 14Peru1014
1630moonMay 25175660
1630sunJune 1074798
1630moonNov. 191124927
1630sunDec. 3N. Gui.1010
1631sunApr. 30Antar. Circle
1631moonMay 15815Total
1631sunOct. 24C Good Hope
1631moonNov. 8120Total
1632sunApr. 19C Good Hope
1632moonMay 4124635
1632sunOct. 13Mexico837
1632moonOct. 271223531
1633sunApril 8514430
1633sunOct. 3Maldiv.Total
1634moonMar. 149351118
1634sunMar. 28Japan1019
1634moonSept. 750Total
1634sunSept. 22C.G.H.954
1635sunFeb. 17Antar. Circle
1635moonMar. 3926Total
1635sunMar. 18Mexico016
1635sunAug. 12Iceland50
1635moonAug. 27164Total
1636sunFeb. 6In Peru
1636moonFeb. 201134323
1636sunAug. 1Tartary1120
1636moonAug. 16434125
1637sunJan. 26Camboya
1637sunJuly 21Jucutan
1637moonDec. 310441045
1638sunJan. 14Persia945
1638moonJune 252017Total
1638sunJuly 11Magellan95
1638sunDec. 5Magellan210
1638moonDec. 201516Total
1639sunJan. 4Tartary030
1639sunJune 15591040
1639moonJune 15241119
1639sunNov. 24Magel.110
1639moonDec. 91157346
1640sunMay 20N. Spa.1030
1640sunNov. 13Peru1036
1641moonApr. 2512949
1641sunMay 9Peru1016
1641moonOct. 18819631
1641sunNov. 21846------
1642sunMar. 30Estotl.40
1642moonApr. 141431Total
1642sunSept. 25Magellan
1642moonOct. 71645Total
1643sunMar. 191353------
1643moonApril 3211039
1643sunSept. 12170------
1643moonSept. 2773860
1644sunMar. 8620------
1644sunAug. 311810------
1645moonFeb. 10745852
1645sunFeb. 26Rom. I.1046
1645moonAug. 724Total
1645sunAug. 21035440
1646sunJan. 16Str. of Anian.
1646moonJan. 301811Total
1646sunJuly 12657------
1646moonJuly 2762Total
1647sunJan. 51210------
1647moonJan. 20943447
1647sunJuly 209------
1647sunDec. 251338------
1648moonJune 5055428
1648sunJune 201328------
1648moonNov. 291917740
1648sunDec. 132148------
1649moonMay 251520Total
1649sunJune 9Arct. C.40
1649sunNov. 4210519
1649moonNov. 181956Total
1650sunApr. 30554------
1650moonMay 15837757
1650sunOct. 241717------
1650moonNov. 7202953
1651sunApr. 19Tuber.------
1651sunOct. 14215------
1652moonMar. 241652850
1652sunApril 72240959
1652moonSept. 17727949
1652sunOct. 252------
1653sunFeb. 27----------
1653moonMar. 13179Total
1653sunAug. 22----------
1653moonSept. 62345Total
1654sunFeb. 16910------
1654moonMar. 21925314
1654sunAug. 112224228
1654moonAug. 271149153
1655sunFeb. 6237420
1655sunAug. 11419------
1655moonAug. 1616--*
1656moonJan. 1194100
1656moonJuly 6317Total
1656sunJuly 211148------
1656moonDec. 302330Total
1657sunJune 111120------
1657moonJune 25935Total
1657sunDec. 4200------
1657moonDec. 2074739
1658sunMay 31160------
1658moonJune 142258------
1658moonNov. 91356010
1658sunNov. 241136------
1659moonMay 683485
1659sunMay 20174------
1659moonOct. 291616552
1659sunNov. 14425951
1660moonApr. 242158Total
1660sunOct. 32234------
1660moonOct. 18032Total
1660sunNov. 21348------
1661sunMar. 292232------
1661moonApr. 14428------
1661sunSept. 231361119
1661moonOct. 7145174
1662sunMar. 19158------
1662sunApr. 1218------
1663sunFeb. 211611314
1663sunMar. 9547------
1663moonAug. 18845Total
1663sunSept. 188------
1664sunJan. 272040------
1664moonFeb. 11316------
1664sunJuly 221448------
1664sunAug. 202210------
1665moonJan. 301847434
1665sunJuly 12748------
1665moonJuly 261331010
1666sunJan. 42133------
1666sunJuly 11901110
1667moonJune 5Noon------
1667sunJuly 21232------
1667sunNov. 151130------
1668sunMay 10Setting------
1668moonMay 251626932
1668sunNov. 4253950
1668moonNov. 18354645
1669sunApr. 291818------
1669sunOct. 241013------
1670sunApr. 1970------
1670sunSept. 10190------
1670moonSept. 28154397
1670sunOct. 13125------
1671sunApril 82329------
1671sunSept. 22125------
1671moonSept. 18744Total
1672sunFeb. 28338------
1672moonMar. 13317------
1672sunAug. 22643------
1672moonSept. 61854------
1673sunFeb. 16729------
1673sunAug. 112144------
1674moonJan. 2118221121
1674sunFeb. 594------
1674moonJuly 17940Total
1675moonJan. 11829Total
1675sunJan. 251036------
1675moonJuly 61631Total
1676sunJune 102126434
1676moonJune 25626------
1676sunDec. 42052------
1677sunNov. 24125------
1677moonMay 161625815
1678moonMay 6530------
1678moonOct. 29917Total
1679sunApr. 10210------
1679moonApr. 251153547
1680sunMar. 292322------
1680sunSept. 22757------
1681moonMar. 4Noon------
1681sunMar. 101343------
1681moonAug. 2815221035
1681sunSept. 111543------
1682moonFeb. 211228Total
1682moonAug. 171856Total
1683sunJan. 271351030
1683moonFeb. 9339------
1683moonAug. 62036------
1684sunJan. 16634------
1684moonJune 261518135
1684sunJuly 12326Total
1684moonDec. 211118945
1685sunJan. 4160------
1685moonJune 1660------
1685moonDec. 101126Total
1686sunMay 21179------
1686moonJune 6Noon------
1686moonNov. 291222Total
1687sunMay 111--*
1687moonMay 2614--*
1687moonApr. 1574649
1688sunApr. 291627------
1688moonOct. 9Noon------
1688sunOct. 251940------
1689moonApril 4742Total
1689moonSept. 281546Total
1690sunMar. 10----------
1690moonMar. 241114543
1690sunSept. 3----------
1690moonSept. 18242------
1691sunFeb. 271730------
1691sunAug. 23551------
1692moonFeb. 2320------
1692sunFeb. 161731------
1692moonJuly 27169Total
1693moonJan. 211725Total
1693moonJuly 17Noon------
1694moonJan. 11Noon------
1694sunJune 22422622
1694moonJuly 61351047
1695sunMay 1163------
1695moonMay 28Noon------
1695moonNov. 2080655
1695sunDec. 5177------
1696moonMay 161245Total
1696sunMay 301256------
1696moonNov. 81730Total
1696sunNov. 231732------
1697sunApr. 201432------
1697moonMay 51827------
1697moonOct. 29844854
1698sunApr. 10913------
1698sunOct. 31529------
1699moonMar. 1581497
1699sunMar. 30220------
1699moonSept. 82322------
1699sunSept. 232238958
1700moonMar. 42011------
1700moonAug. 29142------

The Eclipses from Struyk were observed: those from Ricciolus calculated: the following from L’Art de verifier les Dates, are only those which are visible in Europe for the present century: those which are total are marked with a T; and M signifies Morning, A Afternoon.

Visible ECLIPSES from 1700 to 1800.

Aft. Chr.Months and Days.Time of the Day or Night.
1701moonFeb. 2211 A.
1703moonJan. 37 M.
1703moonJune 291 M.T.
1703moonDec. 237 M.T.
1704moonDec. 117 M.
1706moonApr. 282 M.
1706sunMay 1210 M.
1706moonOct. 217 A.
1707moonApr. 172 M.T.
1708moonApril 56 M.
1708sunDec. 148 M.
1708moonSept. 299 A.
1709sunMar. 112 A.
1710moonFeb. 1311 A.
1710sunFeb. 281 A.
1711sunJuly 158 A.
1711moonJuly 296 A.T.
1712moonJan. 238 A.
1713moonJune 86 A.
1713moonDec. 24 M.
1715sunMay 39 M.T.
1715moonNov. 115 M.
1717moonMar. 273 M.
1717moonMay 206 A.
1718moonSept. 98 A.T.
1719moonAug. 299 A.
1721moonJan. 133 A.
1722moonJune 293 M.
1722sunDec. 83 A.
1722moonDec. 224 A.
1724sunMay 227 A.T.
1724moonNov. 14 M.
1725moonOct. 217 A.
1726sunSept. 256 A.
1726moonOct. 115 M.
1727sunSept. 157 M.
1729moonFeb. 139 A.T.
1729moonAug. 91 M.
1730moonFeb. 44 M.
1731moonJune 202 M.
1732moonDec. 110 A.T.
1733sunMay 137 A.
1733moonMay 287 A.
1735moonOct. 21 M.
1736moonMar. 2612 A.T.
1736moonSept. 203 M.T.
1736sunOct. 46 A.
1737sunMar. 14 A.
1737moonSept. 94 M.
1738sunAug. 1511 M.
1739moonJan. 2411 A.
1739sunAug. 45 A.
1739sunDec. 309 M.
1740moonJan. 1311 A.T.
1741moonJan. 112 A.
1743moonNov. 23 M.T.
1744moonAug. 269 A.
1746moonAug. 3012 A.
1747moonFeb. 145 M.T.
1748sunJuly 2511 M.
1748moonAug. 812 A.
1749moonDec. 238 A.
1750sunJan. 89 M.
1750moonJune 199 A.T.
1750moonDec. 137 M.
1751moonJune 92 M.
1751moonDec. 210 A.
1752sunMay 138 A.
1753moonApr. 177 A.
1753sunOct. 2610 M.
1755moonMar. 281 M.
1757moonFeb. 46 M.
1757moonJuly 3012 A.
1758moonJan. 247 M.T.
1758sunDec. 307 M.
1759sunJune 247 A.
1759sunDec. 192 A.
1760moonMay 299 A.
1760sunJune 137 M.
1760moonNov. 229 A.
1761moonMay 1811 A.T.
1762moonMay 84 M.
1762sunOct. 178 M.
1762moonNov. 18 A.
1763sunApr. 138 M.
1764sunApr. 110 M.
1764moonApr. 161 M.
1765sunMar. 212 A.
1765sunAug. 165 A.
1766moonFeb. 247 A.
1766sunAug. 57 A.
1768moonJan. 45 M.
1768moonJune 304 M.T.
1768moonDec. 234 A.T.
1769sunJune 48 M.
1769moonDec. 137 M.
1770sunNov. 1710 M.
1771moonApr. 282 M.
1771moonOct. 235 A.
1772moonOct. 116 A.T.
1772sunOct. 2610 M.
1773sunMar. 235 M.
1773moonSept. 307 A.
1774sunMar. 1210 M.
1776moonJuly 311 M.T.
1776sunAug. 145 M.
1777sunJan. 95 A.
1778sunJune 244 A.
1778moonDec. 46 M.
1779moonMay 305 M.T.
1779sunJune 148 M.
1779moonNov. 238 A.
1780sunOct. 276 A.
1780moonNov. 124 M.
1781sunApr. 236 A.
1781sunOct. 178 M.
1782moonApr. 127 A.
1783moonMar. 189 A.T.
1783moonSept. 1011 A.T.
1784moonMar. 73 M.
1785sunFeb. 91 A.
1787moonJan. 312 A.T.
1787sunJan. 1910 M.
1787sunJune 155 A.
1787moonDec. 243 A.
1788sunJune 49 M.
1789moonNov. 212 A.
1790moonApr. 2812 A.T.
1790moonOct. 231 M.T.
1791sunApril 31 A.
1791moonOct. 123 M.
1792sunSept. 1611 M.
1793moonFeb. 2510 A.
1793sunSept. 53 A.
1794sunJan. 314 A.
1794moonFeb. 1411 A.T.
1794sunAug. 255 A.
1795moonFeb. 41 M.
1795sunJuly 169 M.
1795moonJuly 318 A.
1797sunJune 258 A.
1797moonDec. 46 M.
1798moonMay 277 A.T.
1800moonOct. 211 A.

328. A List of Eclipses, and historical Events, which happened about the same Times, from Ricciolus.

Historical Eclipses.

Before Christ.
754July 5But according to an old Calendar this Eclipse of the Sun was on the 21st of April, on which day the Foundations of Rome were laid if we may believe Taruntius Firmanus.
721March 19A total Eclipse of the Moon. The Assyrian Empire at an end; the Babylonian established.
585May 28An Eclipse of the Sun foretold by Thales, by which a peace was brought about between the Medes and Lydians.
523July 16An Eclipse of the Moon, which was followed by the death of Cambyses.
502Nov. 19An Eclipse of the Moon, which was followed by the slaughter of the Sabines, and death of Valerius Publicola.
463April 30An Eclipse of the Sun. The Persian war, and the falling off of the Persians from the Egyptians.
431April 25An Eclipse of the Moon, which was followed by a great famine at Rome; and the beginning of the Peloponnesian war.
431August 3A total Eclipse of the Sun. A Comet and Plague at Athens[74].
413Aug. 27A total Eclipse of the Moon. Nicias with his ship destroyed at Syracuse.
394Aug. 14An Eclipse of the Sun. The Persians beat by Conon in a sea engagement.
168June 21A total Eclipse of the Moon. The next day Perseus King of Macedonia was conquered by Paulus Emilius.
After Christ.
59April 30An Eclipse of the Sun. This is reckoned among the prodigies, on account of the murther of Agrippinus by Nero.
237April 12A total Eclipse of the Sun. A sign that the reign of the Gordiani would not continue long. A sixth persecution of the Christians.
306July 27An Eclipse of the Sun. The Stars were seen, and the Emperor Constantius died.
840May 4A dreadful Eclipse of the Sun. And Lewis the Pious died within six months after it.
1009----An Eclipse of the Sun. And Jerusalem taken by the Saracens.
1133Aug. 2A terrible Eclipse of the Sun. The Stars were seen. A schism in the church, occasioned by there being three Popes at once.

Plate XI.

J. Ferguson delin.

J. Mynde Sculp.

The superstitious notions of the antients with regard to
Eclipses.

PLATE XI.

329. I have not cited one half of Ricciolus’s list of potentous Eclipses; and for the same reason that he declines giving any more of them than what that list contains: namely, that ’tis most disagreeable to dwell any longer on such nonsense, and as much as possible to avoid tiring the reader: the superstition of the antients may be seen by the few here copied. My author farther says, that there were treatises written to shew against what regions the malevolent effects of any particular Eclipse was aimed: and the writers affirmed, that the effects of an Eclipse of the Sun continued as many years as the Eclipse lasted hours; and that of the Moon as many months.

Very fortunate once for Christopher Columbus.

330. Yet such idle notions were once of no small advantage to Christopher Columbus; who, in the year 1493, was driven on the island of Jamaica, where he was in the greatest distress for want of provisions, and was moreover refused any assistance from the inhabitants; on which he threatened them with a plague, and that in token of it there should be an Eclipse: which accordingly fell on the day he had foretold, and so terrified the Barbarians, that they strove who should be first in bringing him all sorts of provisions; throwing them at his feet, and imploring his forgiveness. Ricciolus’s Almagest, Vol. I. 1. v. c. ii.

Why there are more visible Eclipses of the Moon than of the Sun.

331. Eclipses of the Sun are more frequent than of the Moon, because the Sun’s ecliptic limits are greater than the Moon’s § 317: yet we have more visible Eclipses of the Moon than of the Sun, because Eclipses of the Moon are seen from all parts of that Hemisphere of the Earth which is next her, and equally great to each of these parts; but the Sun’s Eclipses are visible only to that small portion of the Hemisphere next him whereon the Moon’s shadow falls; as shall be explained by and by at large.

Fig. I.

Total and annular Eclipses of the Sun.

PLATE XI.

332. The Moon’s Orbit being elliptical, and the Earth in one of its focuses, she is once at her least distance from the Earth, and once at her greatest in every Lunation. When the Moon changes at her least distance from the Earth, and so near the Node that her dark shadow falls on the Earth, she appears big enough to cover the whole [75]Disc of the Sun from that part on which her shadow falls; and the Sun appears totally eclipsed there, as at A, for some minutes: But when the Moon changes at her greatest distance from the Earth, and so near the Node that her dark shadow is directed towards the Earth, her diameter subtends a less angle than the Sun’s; and therefore she cannot hide his whole Disc from any part of the Earth, nor does her shadow reach it at that time; and to the place over which the point of her shadow hangs, the Eclipse is annular as at B; the Sun’s edge appearing like a luminous ring all around the body of the Moon. When the Change happens within 17 degrees of the Node, and the Moon at her mean distance from the Earth, the point of her shadow just touches the Earth, and she eclipseth the Sun totally to that small spot whereon her shadow falls; but the darkness is not of a moment’s continuance.

The longest duration of total Eclipses of the Sun.

333. The Moon’s apparent diameter when largest exceeds the Sun’s when least only 1 minute 38 seconds of a degree: And in the greatest Eclipse of the Sun that can happen at any time and place, the total darkness continues no longer than whilst the Moon is going 1 minute 38 seconds from the Sun in her Orbit; which is about 3 minutes and 13 seconds of an hour.

To how much of the Earth the Sun may be totally or partially eclipsed at once.

334. The Moon’s dark shadow covers only a spot on the Earth’s surface, about 180 English miles broad, when the Moon’s diameter appears largest and the Sun’s least; and the total darkness can extend no farther than the dark shadow covers. Yet the Moon’s partial Shadow or Penumbra may then cover a circular space 4900 miles in diameter, within all which the Sun is more or less eclipsed as the places are less or more distant from the Center of the Penumbra. When the Moon changes exactly in the Node, the Penumbra is circular on the Earth at the middle of the general Eclipse; because at that time it falls perpendicularly on the Earth’s surface: But at every other moment it falls obliquely, and will therefore be elliptical; and the more so, as the time is longer before or after the middle of the general Eclipse; and then, much greater portions of the Earth’s surface are involved in the Penumbra.

Duration of general and particular Eclipses.

The Moon’s dark shadow.

And Penumbra.

335. When the Penumbra first touches the Earth the general Eclipse begins: when it leaves the Earth the general Eclipse ends: from the beginning to the end the Sun appears eclipsed in some part of the Earth or other. When the Penumbra touches any place the Eclipse begins at that place, and ends when the Penumbra leaves it. When the Moon changes in the Node, the Penumbra goes over the center of the Earth’s Disc as seen from the Moon; and consequently, by describing the longest line possible on the Earth, continues the longest upon it; namely, at a mean rate, 5 hours 50 minutes: more, if the Moon be at her greatest distance from the Earth, because she then moves slowest; less, if she be at her least distance, because of her quicker motion.

Fig. II.

336. To make the last five articles and several other Phenomena plainer, let S be the Sun, E the Earth, M the Moon, and AMP the Moon’s Orbit. Draw the right line Wc 12 from the western edge of the Sun at W, touching the western edge of the Moon at c and the Earth at 12: draw also the right line Vd 12 from the eastern edge of the Sun at V, touching the eastern edge of the Moon at d and the Earth at 12: the dark space ce 12 d included between those lines is the Moon’s shadow, ending in a point at 12 where it touches the Earth; because in this case the Moon is supposed to change at M in the middle between A the Apogee, or farthest point of her Orbit from the Earth, and P the Perigee, or nearest point to it. For, had the point P been at M, the Moon had been nearer the Earth; and her dark shadow at e would have covered a space upon it about 180 miles broad, and the Sun would have been totally darkened as at A (Fig I) with some continuance: but had the point A (Fig. II) been at M, the Moon would have been farther from the Earth, and her shadow would have ended in a point about e, and therefore the Sun would have appeared as at B (Fig. I) like a luminous ring all around the Moon. Draw the right lines WXdh and VXcg, touching the contrary sides of the Sun and Moon, and ending on the Earth at a and b: draw also the right line SXM 12, from the center of the Sun’s Disc, through the Moon’s center, to the Earth at 12; and suppose the two former lines WXdh and VXcg to revolve on the line SXM 12 as an Axis, and their points a and b will describe the limits of the Penumbra TT on the Earth’s surface, including the large space a0b12a; within which the Sun appears more or less eclipsed as the places are more or less distant from the verge of the Penumbra a0b.

Digits, what.

Draw the right line y 12 across the Sun’s Disc, and parallel to the plane of the Moon’s Orbit; divide this line into twelve equal parts, as in the Figure, for the twelve [76]Digits of the Sun’s diameter: and at equal distances from the center of the Penumbra TT to its edge on the Earth, or from 12 to 0, draw twelve concentric Circles, as marked with the numeral Figures 1 2 3 4 &c. and remember that the Moon’s motion in her Orbit AMP is from west to east, as from s to t. Then,

The different phases of a solar Eclipse.

PLATE XI.

Fig. III.

To an observer on the Earth at b, the eastern limb of the Moon at d seems to touch the western limb of the Sun at W, when the Moon is at M; and the Sun’s Eclipse begins at b; appearing as at A in Fig. III at the left hand; but at the same moment of absolute time to an observer at a in Fig. II the western edge of the Moon at c leaves the eastern edge of the Sun at V, and the Eclipse ends, as at the right hand C of Fig. III. At the very same instant, to all those who live on the Circle marked 1 on the Earth E in Fig. II, the Moon M cuts off or darkens a twelfth part of the Sun S, and eclipses him one Digit, as at 1 in Fig. III: to those who live on the Circle marked 2 in Fig. II the Moon cuts off two twelfth parts of the Sun, as at 2 in Fig. III: to those on the Circle 3, three parts; and so on to the center at 12 in Fig. II, where the Sun is centrally eclipsed as at B in the middle of Fig. III: under which Figure there is a scale of hours and minutes, to shew at a mean state how long it is from the beginning to the end of a central Eclipse of the Sun on the parallel of London; and how many Digits are eclipsed at any particular time from the beginning at A to the middle at B, or the end at C. Thus in 16 minutes from the beginning, the Sun is two Digits eclipsed; in an hour and five minutes, 8 Digits; and in an hour and thirty-seven minutes, 12 Digits.

Fig. II.

The Velocity of the Moon’s shadow on the Earth.

Fig. IV.

337. By Fig. II it is plain, that the Sun is totally or centrally eclipsed but to a small part of the Earth at any time; because the dark conical shadow e of the Moon M falls but on a small part of the Earth: and that the partial Eclipse is confined at that time to the space included by the Circle a 0 b, of which only one half can be projected in the Figure, the other half being supposed to be hid by the convexity of the Earth E: and likewise, that no part of the Sun is eclipsed to the large space YY of the Earth, because the Moon is not between the Sun and that part of the Earth: and therefore to all that part the Eclipse is invisible. The Earth turns eastward on its Axis, as from g to h, which is the same way that the Moon’s shadow moves; but the Moon’s motion is much swifter in her Orbit from s to t: and therefore, altho’ Eclipses of the Sun are of longer duration on account of the Earth’s motion on its Axis, than they would be if that motion was stopt, yet in 3 minutes and 13 seconds of time, the Moon’s swifter motion carries her dark shadow quite over any place that its center touches at the time of greatest obscuration. The motion of the shadow on the Earth’s Disc is equal to the Moon’s motion from the Sun, which is about 301⁄2 minutes of a degree every hour at a mean rate; but so much of the Moon’s Orbit is equal to 301⁄2 degrees of a great Circle on the Earth, § 320; and therefore the Moon’s shadow goes 301⁄2 degrees or 1830 geographical miles on the Earth in an hour, or 301⁄2 miles in a minute, which is almost four times as swift as the motion of a cannon-ball.

PLATE XI.

Fig. IV.

Phenomena of the Earth as seen from the Sun or New Moon
at different times of the year.

338. As seen from the Sun or Moon, the Earth’s Axis appears differently inclined every day of the year, on account of keeping its parallelism throughout its annual course. Let E, D, O, N, be the Earth at the two Equinoxes and the two Solstices; N S its Axis, N the North Pole, S the South Pole, Æ Q the Equator, T the Tropic of Cancer, t the Tropick of Capricorn, and ABC the Circumference of the Earth’s enlightened Disc as seen from the Sun or New Moon at these times. The Earth’s Axis has the position NES at the vernal Equinox, lying towards the right hand, as seen from the Sun or New Moon; its Poles N and S being then in the Circumference of the Disc; and the Equator and all its parallels seem to be straight lines, because their planes pass through the observer’s eye looking down upon the Earth from the Sun or Moon directly over E, where the Ecliptic FG intersects the Equator Æ. At the Summer Solstice, the Earth’s Axis has the position NDS; and that part of the Ecliptic FG in which the Moon is then New, touches the Tropic of Cancer T at D. The North Pole N at that time inclining 231⁄2 degrees towards the Sun, falls so many degrees within the Earth’s enlightened Disc, because the Sun is then vertical to D, 231⁄2 degrees north of the Equator ÆQ; and the Equator with all its parallels seem elliptic curves bending downward, or towards the South Pole as seen from the Sun: which Pole, together with 231⁄2 degrees all round it, is hid behind the Disc in the dark Hemisphere of the Earth. At the autumnal Equinox the Earth’s Axis has the position NOS, lying to the left hand as seen from the Sun or New Moon, which are then vertical to O, where the Ecliptic cuts the Equator ÆQ. Both Poles now lie in the circumference of the Disc, the North Pole just going to disappear behind it, and the South Pole just entering into it; and the Equator with all its parallels seem to be straight lines, because their planes pass through the observer’s eye, as seen from the Sun, and very nearly so as seen from the Moon. At the Winter Solstice the Earth’s Axis has the position NNS; when its South Pole S inclining 231⁄2 degrees toward the Sun falls 231⁄2 degrees within the enlightened Disc, as seen from the Sun or New Moon which are then vertical to the Tropic of Capricorn t, 231⁄2 degrees south of the Equator ÆQ; and the Equator with all its parallels seem elliptic curves bending upward; the North Pole being as far hid behind the Disc in the dark Hemisphere, as the South Pole is come into the light. The nearer that any time of the year is to the Equinoxes or Solstices, the more it partakes of the Phenomena relating to them.

PLATE XI.

Various positions of the Earth’s Axis, as seen from the Sun
at different times of the year.

339. Thus it appears, that from the vernal equinox to the autumnal, the North Pole is enlightened; and the Equator and all its parallels appear Semi-ellipses as seen from the Sun, more or less curved as the time is nearer to or farther from the Summer Solstice; and bending downwards or towards the South Pole; the reverse of which happens from the autumnal Equinox to the vernal. A little consideration will be sufficient to convince the reader, that the Earth’s Axis inclines towards the Sun at the Summer Solstice; from the Sun at the Winter Solstice; and sidewise to the Sun at the Equinoxes; but towards the right hand, as seen from the Sun at the vernal Equinox; and towards the left hand at the autumnal. From the Winter to the Summer Solstice, the Earth’s Axis inclines more or less to the right hand, as seen from the Sun; and the contrary from the Summer to the Winter Solstice.

How these positions affect solar Eclipses.

340. The different positions of the Earth’s Axis, as seen from the Sun at different times of the year, affect solar Eclipses greatly with regard to particular places; yea so far as would make central Eclipses which fall at one time of the year invisible if they fell at another, even though the Moon should always change in the Nodes and at the same hour of the day: of which indefinitely various affections, we shall only give Examples for the times of the Equinoxes and Solstices.

Fig. IV.

In the same Diagram, let FG be part of the Ecliptic, and IK ik ik ik part of the Moon’s Orbit; both seen edgewise, and therefore projected into right lines; and let the intersections N, O, D, E be one and the same Node at the above times, when the Earth has the forementioned different positions; and let the spaces included by the Circles P, p, p, p be the Penumbra at these times, as its center is passing over the center of the Earth’s Disc. At the Winter Solstice, when the Earth’s Axis has the position NNS, the center of the Penumbra P touches the Tropic of Capricorn t in N at the middle of the general Eclipse; but no part of the Penumbra touches the Tropic of Cancer T. At the Summer Solstice, when the Earth’s Axis has the position NDS (iDk being then part of the Moon’s Orbit whose Node is at D) the Penumbra p has its center on the Tropic of Cancer T at the middle of the general Eclipse, and then no part of it touches the Tropic of Capricorn t. At the autumnal Equinox the Earth’s Axis has the position NOS (iOk being then part of the Moon’s Orbit) and the Penumbra equally includes part of both Tropics T and t at the middle of the general Eclipse: at the vernal Equinox it does the same, because the Earth’s Axis has the position NES: But, in the former of these two last cases, the Penumbra enters the Earth at A, north of the Tropic of Cancer T, and leaves it at m, south of the Tropic of Capricorn t; having gone over the Earth obliquely southward, as its center described the line AOm: whereas in the latter case the Penumbra touches the Earth at n, south of the Equator ÆQ, and describing the line nEq (similar to the former line AOm in open space) goes obliquely northward over the Earth, and leaves it at q, north of the Equator.

In all these circumstances, the Moon has been supposed to change at noon in her descending Node: had she changed in her ascending Node, the Phenomena would have been as various the contrary way, with respect to the Penumbra’s going northward or southward over the Earth. But because the Moon changes at all hours, as often in one Node as the other, and at all distances from them both at different times as it happens, the variety of the Phases of Eclipses are almost innumerable, even at the same places, considering also how variously the same places are situated on the enlightened Disc of the Earth, with respect to the Penumbra’s motion, at the different hours that Eclipses happen.

How much of the Penumbra falls on the Earth at different distances from the Nodes.

341. When the Moon changes 17 degrees short of her descending Node, the Penumbra P 18 just touches the northern part of the Earth’s Disc, near the North Pole N; and, as seen from that place the Moon appears to touch the Sun, but hides no part of him from sight. Had the Change been as far short of the ascending Node, the Penumbra would have touched the southern part of the Disc near the South Pole S. When the Moon changes 12 degrees short of the descending Node, more than a third part of the Penumbra P 12 falls on the northern parts of the Earth at the middle of the general Eclipse: had she changed as far past the same Node, as much of the other side of the Penumbra about P would have fallen on the southern part of the Earth; all the rest in the expansum, or open space. When the Moon changes 6 degrees from the Node, almost the whole Penumbra P6 falls on the Earth at the middle of the general Eclipse. And lastly, when the Moon changes in the Node, the Penumbra PN takes the longest course possible on the Earth’s Disc; its center falling on the middle thereof, at the middle of the general Eclipse. The farther the Moon changes from either Node within 17 degrees of it, the shorter is the Penumbra’s continuance on the Earth, because it goes over a less portion of the Disc, as is evident by the Figure.

The Earth’s diurnal motion lengthens the duration of solar Eclipses, which fall without the polar Circles.

342. The nearer that the Penumbra’s center is to the Equator at the middle of the general Eclipse, the longer is the duration of the Eclipse at all those places where it is central; because, the nearer that any place is to the Equator, the greater is the Circle it describes by the Earth’s motion on its Axis: and so, the place moving quicker keeps longer in the Penumbra whose motion is the same way with that of the place, tho’ faster as has been already mentioned § 337. Thus, (see the Earth at D and the Penumbra at 12) whilst the point b in the polar Circle abcd is carried from b to c by the Earth’s diurnal motion, the point d on the Tropick of Cancer T is carried a much greater length from d to D: and therefore, if the Penumbra’s center goes one time over c and another time over D, the Penumbra will be longer in passing over the moving place d than it was in passing over the moving place b. Consequently, central Eclipses about the Poles are of the shortest duration; and about the Equator of the longest.

And shortens the duration of some which fall within these Circles.

343. In the middle of Summer the whole frigid Zone included by the polar Circle abcd is enlightened; and if it then happens that the Penumbra’s center goes over the north Pole, the Sun will be eclipsed much the same number of Digits at a as at c; but whilst the Penumbra moves eastward over c it moves westward over a, because with respect to the Penumbra, the motions of a and c are contrary: for c moves the same way with the Penumbra towards d, but a moves the contrary way towards b; and therefore the Eclipse will be of longer duration at c than at a. At a the Eclipse begins on the Sun’s eastern limb, but at c on his western: at all places lying without the polar Circles, the Sun’s Eclipses begin on his western limb, or near it, and end on or near his eastern. At those places where the Penumbra touches the Earth, the Eclipse begins with the rising Sun, on the top of his western or uppermost edge; and at those places where the Penumbra leaves the Earth, the Eclipse ends with the setting Sun, on the top of his eastern edge which is then the uppermost, just at its disappearing in the Horizon.

The Moon has no Atmosphere.

344. If the Moon were surrounded by an Atmosphere of any considerable Density, it would seem to touch the Sun a little before the Moon made her appulse to his edge, and we should see a little faintness on that edge before it were eclipsed by the Moon: But as no such faintness has been observed, at least so far as I ever heard, it seems plain, that the Moon has no such Atmosphere as that of the Earth. The faint ring of light surrounding the Sun in total Eclipses, called by Cassini la Chevelure du Soleil, seems to be the Atmosphere of the Sun; because it has been observed to move equally with the Sun, not with the Moon.

PLATE XI.

345. Having been so prolix concerning Eclipses of the Sun, we shall drop that subject at present, and proceed to the doctrine of lunar Eclipses; which, being more simple, may be explained in less time.

Eclipses of the Moon.

Fig. II.

That the Moon can never be eclipsed but at the time of her being Full, and the reason why she is not eclipsed at every Full, have been shewn already § 316, 317. Let S be the Sun, E the Earth, RR the Earth’s shadow, and B the Moon in opposition to the Sun: in this situation the Earth intercepts the Sun’s light in its way to the Moon; and when the Moon touches the Earth’s shadow at v she begins to be eclipsed on her eastern limb x, and continues eclipsed until her western limb y leaves the shadow at w: at B she is in the middle of the shadow, and consequently in the middle of the Eclipse.

Why the Moon is visible in a total Eclipse.

346. The Moon when totally eclipsed, is not invisible if she be above the Horizon and the Sky be clear; but appears generally of a dusky colour like tarnished copper, which some have thought to be the Moon’s native light. But the true cause of her being visible is the scattered beams of the Sun, bent into the Earth’s shadow by going through the Atmosphere; which, being more dense near the Earth than at considerable heights above it, refracts or bends the Sun’s rays more inward § 179, the nearer they are passing by the Earth’s surface, than those rays which go through higher parts of the Atmosphere, where it is less dense according to its height, until it be so thin or rare as to lose its refractive power. Let the Circle fghi, concentric to the Earth, include the Atmosphere whose refractive power vanishes at the heights f and i; so that the rays Wfw and Viv go on straight without suffering the least refraction: But all those rays which enter the Atmosphere between f and k, and between i and l, on opposite sides of the Earth, are gradually more bent inward as they go through a greater portion of the Atmosphere, until the rays Wk and Vl, touching the Earth at m and n, are bent so as to meet at q, a little short of the Moon; and therefore the dark shadow of the Earth is contained in the space moqpn where none of the Sun’s rays can enter: all the rest RR, being mixed by the scattered rays which are refracted as above, is in some measure enlightened by them; and some of those rays falling on the Moon give her the colour of tarnished copper, or of iron almost red hot. So that if the Earth had no Atmosphere, the Moon would be as invisible in total Eclipses as she is when New. If the Moon were so near the Earth as to go into its dark shadow, suppose about po, she would be invisible during her stay in it; but visible before and after in the fainter shadow RR.

PLATE XI.

Why the Sun and Moon are sometimes visible when the Moon is
totally eclipsed.

347. When the Moon goes through the center of the Earth’s shadow she is directly opposite to the Sun: yet the Moon has been often seen totally eclipsed in the Horizon when the Sun was also visible in the opposite part of it: for, the horizontal refraction being almost 34 minutes of a degree § 181, and the diameter of the Sun and Moon being each at a mean state but 32 minutes, the refraction causes both Luminaries to appear above the Horizon when they are really below it § 179.

Fig. V.

Duration of central Eclipses of the Moon.

348. When the Moon is Full at 12 degrees from either of her Nodes, she just touches the Earth’s shadow but enters not into it. Let GH be the Ecliptic, ef the Moon’s Orbit where she is 12 degrees from the Node at her Full; cd her Orbit where she is 6 degrees from the Node, ab her Orbit where she is Full in the Node, AB the Earth’s shadow, and M the Moon. When the Moon describes the line ef she just touches the shadow but does not enter into it; when she describes the line cd she is totally though not centrally immersed in the shadow; and when she describes the line ab she passes by the Node at M in the center of the shadow, and takes the longest line possible, which is a diameter, through it: and such an Eclipse being both total and central is of the longest duration, namely, 3 hours 57 minutes 6 seconds from the beginning to the end, if the Moon be at her greatest distance from the Earth: and 3 hours 37 minutes 26 seconds, if she be at her least distance. The reason of this difference is, that when the Moon is farthest from the Earth she moves slowest; and when nearest to it, quickest.

Digits.

349. The Moon’s diameter, as well as the Sun’s, is supposed to be divided into twelve equal parts called Digits; and so many of these parts as are darkened by the Earth’s shadow, so many Digits is the Moon eclipsed. All that the Moon is eclipsed above 12 Digits, shew how far the shadow of the Earth is over the body of the Moon, on that edge to which she is nearest at the middle of the Eclipse.

Why the beginning and end of a lunar Eclipse is so difficult to be determined by observation.

350. It is difficult to observe exactly either the beginning or ending of a lunar Eclipse, even with a good Telescope; because the Earth’s shadow is so faint, and ill defined about the edges, that when the Moon is either just touching or leaving it, the obscuration of her limb is scarce sensible; and therefore the nicest observers can hardly be certain to four or five seconds of time. But both the beginning and ending of solar Eclipses are visibly instantaneous; for the moment that the edge of the Moon’s Disc touches the Sun’s, his roundness seems a little broke on that part; and the moment she leaves it he appears perfectly round again.

The use of Eclipses in Astronomy, Geography, and Chronology.

351. In Astronomy, Eclipses of the Moon are of great use for ascertaining the periods of her motions; especially such Eclipses as are observed to be alike in all circumstances, and have long intervals of time between them. In Geography, the Longitudes of places are found by Eclipses, as already shewn in the eleventh chapter: but for this purpose Eclipses of the Moon are more useful than those of the Sun, because they are more frequently visible, and the same lunar Eclipse is of equal largeness and duration at all places where it is seen. In Chronology, both solar and lunar Eclipses serve to determine exactly the time of any past event: for there are so many particulars observable in every Eclipse, with respect to its quantity, the places where it is visible (if of the Sun) and the time of the day or night; that ’tis impossible there can be two Eclipses in the course of many ages which are alike in all circumstances.

The darkness at our Saviour’s crucifixion supernatural.

352. From the above explanation of the doctrine of Eclipses it is evident, that the darkness at our Saviour’s crucifixion was supernatural. For he suffered on the next day after eating his last Passover-Supper, on which day it was impossible that the Moon’s shadow could fall on the Earth, for the Jews kept the Passover at the time of Full Moon: nor does the darkness in total Eclipses of the Sun last four minutes in any place § 333, whereas the darkness at the crucifixion lasted three hours, Matt. xxviii. 15. and overspread at least all the land of Judea.

CHAP. XIX.

The Calculation of New and Full Moons and Eclipses. The geometrical Construction of Solar and Lunar Eclipses. The examination of antient Eclipses.

353. To construct an Eclipse of the Sun, we must collect these ten Elements or Requisites from the following Astronomical Tables.

Requisites for a solar Eclipse.

I. The true time of conjunction of the Sun and Moon: to know at what conjunctions the Sun must be eclipsed; and to the times of those conjunctions,

II. The Moon’s horizontal parallax, or angle which the semi-diameter of the Earth subtends as seen from the Moon.

III. The Sun’s true place, and distance from the solstitial colure to which he is then nearest, either in coming to it or going from it.

IV. The Sun’s declination.

V. The angle of the Moon’s visible path with the Ecliptic.

VI. The Moon’s Latitude or Declination from the Ecliptic.

VII. The Moon’s true hourly motion from the Sun.

VIII. The Angle of the Sun’s semi-diameter as seen from the Earth.

IX. The Angle of the Moon’s semi-diameter as seen from the Earth.

X. The semi-diameter of the Penumbra.

And for an Eclipse of the Moon, the following Elements.

Requisites for a lunar Eclipse.

I. The true time of opposition of the Sun and Moon; and for that time,

II. The Moon’s horizontal parallax.

III. The Sun’s semi-diameter.

IV. The semi-diameter of the Earth’s shadow.

V. The Moon’s semi-diameter.

VI. The Moon’s Latitude.

VII. The Moon’s true hourly motion from the Sun.

VIII. The Angle of the Moon’s visible path with the Ecliptic.

These Elements are easily found from the following Tables and Precepts, by the common Rules of Arithmetic.

Note, 60 minutes make a Degree, 30 degrees a Sign, and 12 Signs a Circle. A Sign is marked thus s, a Degree thus °, and a Minute thus ʹ.

When you exceed 12 Signs, always reject them and set down the remainder. When the number of Signs to be subtracted is greater than the number you subtract from, add 12 Signs to that which you subtract from; and then you will have a remainder to set down.

How the Signs are reckoned.

354. As we fix arbitrarily upon the beginning of the Sign Aries to reckon from, when we speak of the places of the Sun, Moon, and Nodes; we call Aries 0 Signs, Taurus 1 Sign, Gemini 2 Signs, Cancer 3 Signs, &c. So, when the Sun is in the 10th degree of Aries, we say his Place or Longitude is 0 Signs 10 Degrees, because he is only 10 Degrees from the beginning of Aries: if he is in the 5th, 10th, &c. Degree of Taurus, we say his Place or Longitude is 1 Sign, 5, 10, &c. Degrees: and so on, till he comes quite round again. But in reckoning the Anomalies of the Sun and Moon, and their distance from the Nodes, we only consider the number of Signs and Degrees the Luminaries are gone past their Apogee or Nodes; not how far they have to go to these points, were the distance ever so little. The Sun, Moon, and Apogee move according to the order of Signs, but the Nodes contrary. We shall now give the Precepts and Examples for the above Requisites in their due order.

To calculate the time of New and Full Moon.

First Element or Requisite.

355. Precept I. For any proposed year in the 18th Century, take out the mean time of the New Moon in March from Table I., and the mean time of Full Moon from Table III., for the Old Stile; or from Tables II and IV for New Stile; with the mean Anomalies of the Sun and Moon for these times, and set them by themselves. Then, from Table VI, take out as many Lunations as the proposed Month is after March, with the days, hours, and minutes belonging to them; and also the mean Anomalies of the Sun and Moon for these Lunations.

II. Add the days, hours, and minutes of these Lunations to the time of New or Full Moon in March, and the Anomalies for the Lunations to the Anomalies for March: the sums give the hours and minutes of the mean New or Full Moon required, and the mean Anomalies of the Sun and Moon for that time.

III. Then, with the number of days enter Table VII, under the given Month, and right against this number, in the left hand column you have the day of New or Full Moon; which set before the hours and minutes above-mentioned.

IV. But, (as it will sometimes happen) if the number of days fall short of all those under the given Month, add one Lunation with its Anomalies from Table VI to the foresaid sums; so you will have a new sum of days wherewith to enter the 7th Table under the given Month, where you are sure to find that sum the second time, if the first falls short.

V. With the Signs and Degrees of the Sun’s Anomaly enter Table VIII, The Moon’s annual Equation, and take out the minutes of time of that Equation by the Anomaly; remembring, that if the Signs are at the head of the Table, the degrees are at the left hand, in which case the Equation found in the Angle of meeting must be subtracted from the mean time of New or Full Moon, as the title Subtract, at the head of the Table directs: but if the Signs are at the foot of the Table their degrees are in the right-hand column, and the Equation where the Signs and Degrees meet in the Table is to be added to the mean time, as the title Add, at the foot of the Table directs; which Equation, so applied, gives the mean time of New or Full Moon corrected.

VI. With the Signs and Degrees of the Sun’s Anomaly enter Table IX, Equation of the Moon’s mean Anomaly, and take out the Equation thereof; adding it to the mean Anomaly or subtracting it therefrom, as the titles at the head or foot of the Table direct; and it gives the mean Anomaly corrected. Then, with the Sun’s Anomaly enter Table XII, Equation of the Sun’s mean Place, and take out that Equation, applying it to the Moon’s corrected Anomaly as the titles direct; and it will give the Moon’s Anomaly equated[77]. N. B. In all these Equations, care must be taken to make proper allowance for the odd minutes of Anomaly; the Tables having the Equations only for compleat Degrees.

VII. With the Moon’s equated Anomaly enter Table X, The Moon’s elliptic Equation, and take out that Equation in the same manner as the preceding: adding it to the former corrected time if the Signs be at the head of the Table, or subtracting it if they be at the foot, as the Table directs; and this gives the mean time equated.

VIII. Lastly, enter Table XI, The Sun’s Equation at New and Full Moon, with the Sun’s Anomaly, and take out the Sun’s Equation in the same manner as the others; adding it to, or subtracting it from the former equated time, as the titles direct: and by this last Equation you have the true time of New or Full Moon, agreeing with well regulated Clocks and Watches. But to make it agree with true Sun-Dials, the Equation of time must be applied as taught § 225.

Example I. To find the time of New Moon in April 1764, N. S.

DaysHoursMin.Sun’s Anom.Moon’s Ano.
s°ʹs°ʹ
Tab. II. Mean time of New Moon in March28578223101332
Add, for Lunation, from Tab. VI.291244029602549
Mean New Moon and Anomaly312141012911921
To which Time add the Moon’s Ann. Equ. Tab. VIII.+022Equ. Moon’s Anom.-20
And it gives the Mean time corrected31223Anom. cor.1191
From which subtract the Moon’s elliptic Equ. Tab. X.-310Sun’s Equat.+156
Moon’s Ano.111057
And it gives the Mean time equated311853h.m.
To which add the Sun’s Equation, Tab. XI.+332Moon’s ann. Equ.022add
Her ellipt. Equ.310sub.
And it gives the true time of Conjunction312225Sun’s Equation332add

Which true time answers to the first of April, at 25 minutes past 10 in the forenoon: for, as the Astronomical Day begins at Noon, then 22 hours 25 min. after the Noon of March 31, is April 1, at 10 hours 25 min. in the Forenoon.

Example II. To find the time of Full Moon in May 1761, N. S.

DaysHoursMin.Sun’s Anom.Moon’s Ano.
s°ʹs°ʹ
Mean time of Full Moon in March2012982029113
Add, for two Lunations591281281312138
The several sums are791337101815102251
The days, in Tab. VII, answer to May 18181337Equ. Moon’s Anom.-13
Moon’s annual Equation add+14Anom. cor.102238
Mean time corrected181351Sun’s Equat.+115
Moon’s elliptic Equation subtract-538Moon’s Ano.102353
Mean time equated18813h.m.
Sun’s Equation add+219Moon’s ann. Equ.014add
Her ellipt. Equ.538sub.
True time of Opposition, May181032Sun’s Equation219add

Namely, the 18th day, at 32 minutes past 10 at night.

The Leap-years are allowed for in the Tables, so as to give no Trouble in these Calculations.

To compute the time of New and Full Moon in a given year and month, of any particular Century, between the Christian Æra[78] and 18th Century.

Precept I. Find the like year of the 18th Century in Table I., for New Moon, or Table III., for Full Moon; and take out the New or Full Moon in March for that year, with the Anomalies of the Sun and Moon.

II. From Table V, take as many compleat Centuries, as when subtracted from the above year of the 18th Century, will answer to the given year; and take out the Conjunctions and Anomalies of these Centuries.

III. Subtract the Conjunctions and Anomalies of these Centuries from those of the New or Full Moon in March above taken out, and the remainders will shew the mean time of New or Full Moon in March the given year, with the Anomalies of the Sun and Moon at that time. Then, work in all respects for the true time of the proposed New or Full Moon, as taught by the Precepts already given § 355.

Example I. To find the time of New Moon in July 1581, O. S.

From 1781 subtract 200 years, and there remains 1581.

DaysHoursMin.Sun’s Anom.Moon’s Ano.
s°ʹs°ʹ
Table I. Mean time of New Moon in March 178113752823370053
Tab. V. Conj. and Anom. for 200 years subtract8162206425044
Remain the Conj. and Anom. for March 15814153081655709
Tab. VI. Add, for five Lunations, to bring it to July147154042532495
The sums are1527101122711914
The Days in Tab. VII. answer to July 30th30710Equ. Moon’s Anom.+13
Sum of the three Equations subtract-79Anom. cor.11927
Sun’s Equat.-116
True time of Conjunction, July3001Moon’s Ano.11811
Which is the 30th day, at one minute past noon, as shewn by well regulated Clocks or WatchesMoon’s ann. Eq.0h14msub.
Her ellipt. Equ.335sub.
Sun’s Equation320sub.
Sum79sub.

EXAMPLE II.

To find the time of Full Moon in April A. D. 30, O. S.

From 1730 subtract 1700, and there remains 30.

DaysHoursMin.Sun’s Anom.Moon’s Ano.
s°ʹs°ʹ
Tab. III. Mean time of Full Moon in March 173022658924031323
Tab. V. Conj. and Anom. for 1700 years subtract141737112846102936
Rem. the Opposition and Anom. in March A. D. 3071321935441347
Tab. V. Add, for one Lunation, to bring it into April291244029602549
The sums are372510305936
The Days in Tab. VII. answer to April 6625Equ. Moon’s Anom.-17
To which add the sum of the three Equations61Anom. cor.5919
Sun’s Equat.+135
True time of Opposition April A. D. 30686Moon’s Ano.51054
Which is the 6th day, at 6 minutes past 8 in the Evening. And thus, the time of New or Full Moon may be found for any given year and month after the Christian Æra.Moon’s ann. Eq.0h18madd
Her ellipt. Equ.246add
Sun’s Equat.257add
Sum61add

Remark.

N. B. Sometimes it happens that the days annexed to the Centuries in Table V are more in number than the days on which the New or Full Moon happens in March the year of the 18th Century, with which the computation begins; as in the third following Example, viz. for the Full Moon in March the year before Christ 721: in which case, a Lunation and it’s Anomalies must be added, from Table VI, to the days and Anomalies of the New or Full Moon in March; and then, subtraction can be made: and having gained a remainder, work in all respects as taught in § 355.

To find the time of New or Full Moon in any given year and month before the Christian Æra.

356. Precept I. Find a year of the 18th Century, which added to the given number of years before Christ, diminished by one, shall make a number of whole Centuries.

II. Find this number of Centuries in Table V, and subtract the Time and Anomalies answering to it from the Time and Anomalies answering to the mean New or Full Moon in March the year of the 18th Century thus found; and they will give the mean time of New or Full Moon in March the given year before Christ, with the Anomalies answering thereto. Whence the true time of that New or Full Moon may be had by the Precepts already delivered § 355.

III. The Tables are calculated for the Meridian of London: therefore, in computing for any place westward of London, four minutes of time must be subtracted from the time shewn by the Tables, for every degree the place is westward; and added for every degree it is eastward. See § 210.

Example I. To find the time of New Moon at London and Athens in March, the year before Christ 424.

The years 423 added to 1777 make 2200, or 22 Centuries.

DaysHoursMin.Sun’s Anom.Moon’s Ano.
s°ʹs°ʹ
Tab. I. Mean New Moon in March A. D. 177727753972752551
From which subtract 2200 years in Tab. V.6214711162642037
Mean Conj. and Anom. in March before Chr. 4242010692111514
Which with, the total of the three Equations added920Equ. Moon’s Anom.-19
Anom. cor.1455
Gives the true time of Conjunction201926Sun’s Equat.+148
Which was the 21st day of March, at 26 minutes past 7 in the morning at London: and if 1 hour 35 minutes be added for Athens, which is 23° 52ʹ east of the meridian of London, we have the time at Athens; namely, 1 minute past 9 in the morning.Moon’s Ano.1643
Moon’s ann. Eq.0h20madd
Her ellipt. Equ.543add
Sun’s Equation317add
Total920add

Example II. To find the time of Full Moon in October, the year before Christ 4030 .

The years 1771 added to 4029 make 5800, or 58 Centuries.

DaysHoursMin.Sun’s Anom.Moon’s Ano.
s°ʹs°ʹ
Tab. III. From the mean Full Moon in March 177119711829672230
Tab. V. Subtr. the numbers for 5800 years50001075610235601736
8005443112743777
Which collected make15123910213972443
Rem. the mean Full Moon &c. March before Chr. 40303183210727112747
To which add eight Lunations to carry it to October2365527225062632
And the several sums will be240024601762419
Which, for Full Moon day, Tab. VII, is October 2626024h.m.
Moon’s ellipt. Equation subtr. there being none besides328Moon’s Ann. Eq.00add
Moon’s ellipt. Eq.328sub.
Rem. the true time of Full Moon, October252056Sun’s Equation00add
Which is the 26th day, at 8 hours 26 minutes in the forenoon[79].Total328sub.

Age of the world uncertain.

By the method prescribed § 248 it will be found, that the Autumnal Equinox in the year before Christ 4030, fell on the 26th of October; as this Example shews the Full Moon to have been on the same day: and by working as hereafter taught, it will appear that the Dominical Letter was then G, which shews the 26th of that October to have been on a Friday; namely our sixth day of the week, but the Ante-Mosaic fifth day. And as, according to Genesis, chap. i. ver. 14. the Sun and Moon were created on the fourth day of the week, those who are of opinion that the world was made at the time of the Autumnal Equinox, and that the Moon at her first appearance was in full lustre, opposite to the Sun, or nearly so, may perhaps look upon this as a Criterion for ascertaining the year of the creation; since it shews the Moon to have been Full the next day after she was made: and this is only 9 years sooner than Rheinholt makes it, and 11 years later than according to Lange. Whereas, they who maintain that the world was created in the 4007th year before Christ, with the Sun on the Autumnal Equinoctial Point, October 26, and the Moon then Full; will find, if they compute by the best Tables extant, that the Moon was New, instead of being Full, on that day.

If it could be proved from the writings of Moses that the Sun was created on the point of the Autumnal Equinox, and the Moon in opposition; as well as it can be proved that these Luminaries were made (or according to some, did not shine out till) on the fourth day of the creation-week, there would be Data enough for ascertaining the age of the world: for supposing the Moon to have been Full on an Equinoctial Day, which was the fourth day of the week, it would require many thousands of years to bring these three characters together again. For, the soonest in which the Moon returns to be New or Full on the same days of the Months as before, is 19 years wanting an hour and half, but then the days of the week return not to the same days of the months in less than 28 years, in which time the Moon has gone through one Course of Lunations, and 9 years over; therefore a co-incidence of the Full Moon and day of the Week and Month cannot happen in that time, and if we multiply 19 by 28, which is the nearest co-incidence of these three characters, namely 532 years; the Moon’s falling back an hour and half every 19 years will amount to 42 hours in so many years; and the Equinox will have anticipated five days. From all which we may venture to say, that 200000 years would not be sufficient to bring all these circumstances together again.

Example III. To find the time of Full Moon at Babylon in March, the year before Christ 721 .

The years 720 added to 1780 make 2500, or 25 Centuries.

DaysHoursMin.Sun’s Anom.Moon’s Ano.
s°ʹs°ʹ
Tab. I. To the mean F. Moon and Anom. in Mar. 17809441819487810
Add one Lunation and it’s Anomalies from Tab. VI[80]291244029602549
The several sums are381725918548359
Fr. which subt. the Days & Anom. of 2500 years, Tab. V1922201126196643
Rem. the mean time and Anom. of F.M. in Mar. b.C. 721181959222512716
To which add the sum of the three Equations+1136Equ. Moon’s Anom.-18
And it gives the true time of Full Moon, Mar. b.C. 72118641Anom. cor.12648
Sun’s Equat.+147
Which was the 19th day, at 41 minutes past 6 in the evening, at London; to which time, if[81] 2 hours 51 minutes be added, we shall have the time at Babylon, namely, 9 hours 51 minutes.Moon’s Anom.12835
Moon’s ann. Eq.0h20madd
Her ellipt. Equ.81add
Sun’s Equation315add
Sum1136add

357. To know whether the Sun will be eclipsed or no, at the time of any given New Moon; collect the Sun’s distance from the Node at that time, and if it be less than 17 degrees he will be eclipsed, otherwise not.

Example. For the time of New Moon in April 1764.

Sun from Node
s°ʹ
Table II, mean New Moon in March 1764, New Stile,11457
Table VI, add for 1 Lunation to carry it to April1040
Sun’s distance from the Node at New Moon in April0537

Which, being within the above limit, the Sun must be eclipsed: and therefore, we proceed to find the rest of the Elements for computing this Eclipse.

To find the Moons Horizontal Parallax, or the Angle of the Earth’s semi-diameter as seen from the Moon.

Second Element.

358. Precept. Having found the Moon’s mean Anomaly for the above time, by the first and second Precepts of § 355, enter the XVth Table with the signs and degrees of that Anomaly, and thereby take out the Moon’s Horizontal Parallax: only note, that this is given but to every 6th degree of Anomaly in the Table, because it is very easy to make proper allowance by sight. So the Moon’s Horizontal Parallax April the 1st 1764, at 10 hours 25 minutes in the Forenoon, answering to her mean Anomaly at that time (namely 11s 9° 21ʹ) is 55ʹ 7ʺ; which, diminished by 10ʺ, the Sun’s constant Horizontal Parallax, gives for the semi-diameter of the Earth’s Disc 54ʹ 57ʺ.

To find the Sun’s true Place, and his distance from the nearest Solstice.

Third Element.

359. Precept I. We are to consider, that the beginning of Aries and of Libra, which are the Equinoctial Points, are equidistant from the beginning of Cancer and of Capricorn, which are the Solstitial Points. Hence, when we know in what Sign and Degree the Sun is, we can easily find his distance from the nearest Solstice. Now, to find the Sun’s Place, or Longitude from Aries, April the 1st, 1764, at 10 hours 21 minutes in the Forenoon; being the equated time of New Moon.

Precept II. This being to the time of New Moon, take out the Sun’s mean Place and Anomaly from Table II. for that time, and the Equation of his mean Place from Table XII by his Anomaly; adding the Equation to his mean Place or subtracting it from the same, as the Table directs, will give his true Place.

Example.

Sun’s Long. from Aries.Sun’s mean Anomaly.
s°ʹs°ʹ
Table I. To the Sun’s mean Place and Anomaly at the mean time of New Moon in March 1764, N. S.111778223
Add the same from Tab. VI. for one Lunation, to carry it to April02960296
Mean Place and Anomaly at the time of New Moon in April010139129
To which place add the Sun’s Equation from Tab. XII.156Equal1°56ʹ
And it gives the Sun’s true place0129Additive.

Which is Aries 12° 9ʹ; and this, when taken from three Signs, or the beginning of Cancer, leaves 2 signs 17 deg. 51 min., or 77° 51ʹ for the Sun’s distance from the then nearest Solstice.

360. But because the Sun’s true Place is often wanted when the Moon is neither New nor Full, we shall next shew how it may be found for any given moment of time: though this be digressing from our present purpose.

In Table XVI find the nearest lesser year to that in which the Sun’s Place is sought; and take out the Sun’s mean Longitude and Anomaly answering thereto; to which add his mean motion and Anomaly for the compleat residue of the years, with the month, day, hour, and minute, all taken from the same Table, and you have the Sun’s mean Longitude and Anomaly for the given time. Then, from Table XII take out the Sun’s Equation by means of his Anomaly (making proportions for the odd minutes of Anomaly) which Equation being added to or subtracted from the Sun’s mean Longitude from Aries, as the titles in the Table direct, gives his true Place, or Longitude from the beginning of Aries, reckoned according to the order of the Signs § 354.

EXAMPLE.

To find the Sun’s true Place April 30th, A. D. 1757, at 18 minutes 40 seconds past 10 in the morning.

Sun’s Long.Sun’s Anom.
s°ʹʺs°ʹ
The year next less than 1757 in the Table is 1753, at the beginning of which, the Sun’s mean Longitude from the beginning of Aries, and his mean Anomaly, is91016526138
To which add his mean Mot. and Anom. for four years to make 175700149112958
And likewise his mean Mot. and Anom. forApril228423022842
days2902835202835
hours2205413054
min.180441
sec.4920
Sun’s mean Longitude and Anomaly for the given time is18311292948
To which add the Equation of the Sun’s mean Place14014Sun’s Eq.
And it gives his true Place, viz. ♉ Taurus 10° 11ʹ 26ʺ11011261°40ʹ14ʺ

N. B. In leap-years after February, the Sun’s mean Motion and Anomaly must be taken out for the day next after the given one.

361. To calculate the Sun’s true Place for any time in a given year before the first year of Christ: subtract the mean Motions and Anomalies for the compleat hundreds next above the given year; to the remainder add those for the residue of years, months, &c. and then work in all respects as above taught.

EXAMPLE.

To find the Suns true Place May the 28th at 4 hours 3 min. 42 sec. in the afternoon, the year before Christ 585, which was a Leap year[82].

Sun’s Long.Sun’s Anom.
s°ʹʺs°ʹ
From the Sun’s mean Longitude and Anomaly at the beginning of the year Christ 197531062954
Subtract his mean Motion and Anomaly for 600 years0432011242
And the remainder, or radix, is9321107552
To which add what 585 wants of 600, viz. 15 years1129222711297
And also those ofMay328164032817
days28Bissextile02835202835
hours40951010
min.307
sec.422021
Sun’s Anom.
Sun’s mean Long. May 28th, at 4 hour 3 min. 24 sec. afternoon1294519
Equation of the Sun’s mean Place subtract222ʹ 22ʺ
Sun’s Equat.
Rem. his true Place for the same time, viz. ♉ Taurus 29° 43ʹ 17ʺ1294317subtract.

N. B. As the Longitudes or Places of all the visible Stars in the Heavens are well known, we have an easy method of finding the Sun’s true Place in the Ecliptic: for the Sun is directly opposite to that Point of the Ecliptic which comes to the Meridian at mid-night.

To find the Sun’s Declination.

Fourth Element.

362. Precept. Enter Table XVII with the Signs and Degrees of the Sun’s Place; and making proportions, take out his Declination answering thereto. If the Signs are at the head of the Table, the Degrees are at the left hand; but if the Signs are at the foot of the Table, the Degrees are at the right hand. So, the Sun’s Declination answering to his true Place (found by § 359 to be 0s 12° 9ʹ) is 4 degrees 48 minutes 54 seconds, making allowance for the 9ʹ that his Place exceeds 12°.

To find the Angle of the Moon’s visible Path with the Ecliptic.

Fifth Element.

Precept. This we may state at 5 degrees 38 minutes, as near enough for the purpose; since it is never above 8 minutes of a degree more or less.

To find the Moon’s Latitude.

Sixth Element.

363. Precept. Having found the Sun’s distance from the Ascending Node by § 357, at the mean time of New Moon, and his Anomaly for that time by § 359, find the Equation of the Node in Table XIII, by the Sun’s Anomaly, and the Equation of the Sun’s mean Place in Table XII by his Anomaly: these two Equations applied (as the titles direct) to the Sun’s mean distance from the Ascending Node, give his true distance from it, and also the Moon’s true distance at the time of Change: but when the Moon is Full, this distance must be increased by the addition of 6 Signs, which will then be the Moon’s true distance from the same Node.

The Moon’s true distance from the Ascending Node is called the Argument of the Moon’s Latitude; with the Signs of which, at the head of Table XIV, and Degrees at the left hand, or with the Signs at the foot of the Table and Degrees at the right hand, take out the Moon’s Latitude: which is North Ascending, North Descending, South Ascending, or South Descending, according to the letters NA, ND, SA or SD, annexed to the Signs of the said Argument.

Plate XII.

The Geometrical Construction of Solar and Lunar Eclipses.

J. Ferguson delin.

J. Mynde Sculp.

Example.

s°ʹ
Sun’s mean Dist. from the [83]Node at New Moon in April 17640537
To which add the Equation of the Node+10
And it gives the Sun’s corrected Distance from the Node0547
To which cor. Dist. add the Eq. of the Sun’s mean Place+156
And it gives the Sun’s true Distance from the Node0743

Which, being at the time of New Moon, is the Argument of Latitude; and in Table XIV, (making proportions for the 43ʹ) shews the Moon’s Latitude to be 40ʹ 9ʺ North Ascending[84].

To find the Moon’s true hourly Motion from the Sun.

Seventh Element.

364. Precept. With the Moon’s Anomaly enter Table XV, and thereby take out her true hourly Motion: then with the Sun’s Anomaly take out his true hourly Motion from the same Table: which done, subtract the Sun’s hourly Motion from the Moon’s, and the remainder will be the Moon’s true hourly Motion from the Sun; which, for the above time § 359, is 27ʹ 50ʺ.

To find the Semi-diameters of the Sun and Moon as seen from the Earth at the above-mentioned time.

Eighth and Ninth Elements.

365. Precept. Enter the XVth Table with the Sun’s Anomaly, and thereby take out his Semi-diameter; and in the same manner take out the Moon’s Semi-diameter by her Anomaly. The former of which for the above time will be found to be 16ʹ 6ʺ; the latter 14ʹ 58ʺ.

To find the Semi-diameter of the Penumbra.

Tenth Element.

366. Precept. Add the Sun’s semi-diameter to the Moon’s, and their Sum will be the Semi-diameter of the Penumbra; namely, at the above time 31ʹ 4ʺ.

Pl. XII.

366. Having found the proper Elements or Requisites for the Sun’s Eclipse April 1, 1764, and intending to project this Eclipse Geometrically, we shall now collect them under the eye, that they may be the more readily found as they are wanted in order for the Projection.

The proper Elements collected.

DHM
367. I. The true time of Conj. or New Moon April11025
°ʹʺ
II. The Earth’s Semi-Disc, which is equal to the Moon’s Horizontal Parallax 55ʹ 7ʺ diminished by the Sun’s Horizontal Parallax which is always 10ʺ05457
III. The Sun’s distance from the nearest Solstice, viz. ♋77510
IV. The Sun’s Declination, North44854
V. The Angle of the Moon’s vis. path with the Eclipt.5380
VI. The Moon’s true Latitude, North Ascending409
VII. The Moon’s true Horary Motion from the Sun2750
VIII. The Sun’s Semi-diameter166
IX. The Moon’s Semi-diameter1458
X. The Semi-diameter of the Penumbra314

368. Having collected these Elements or Requisites, the following part of the work may be very much facilitated by means of a good Sector, with the use of which the reader should be so well acquainted, as to know how to open it to any given Radius, as far as it will go; and to take off the Chord or Sine of any Arc of that Radius. This is done by first taking the extent of the given Radius in your Compasses, and then opening the Sector so as the distance cross-wise between the ends of the lines of Sines or Chords at S or C, from Leg to Leg of the Sector, may be equal to that extent; then, without altering the Sector, take the Sine or Chord of the given Arc with your Compasses extended cross-wise from Leg to Leg of the Sector in these lines. But if the operator has not a Sector, he must construct these lines to such different lengths as he wants them in the projection. And lest this Treatise should fall into the hands of any person who would wish to project the Figure of a solar or lunar Eclipse, and has not a Sector to do it by, we shall shew how he may make a line of Sines or Chords to any Radius.

Fig. II.

How to make a line of Chords.

Pl. XII.

369. Draw the right line BCA at pleasure; and upon C as a Center, with the distance CA or CB as a Radius, describe the Semi-circle BDA; and from the Center C draw AC perpendicular to BCA. Then divide the Quadrants AD and BD each into 90 equal parts or degrees, and join the right line AD for the Chord of the Quadrant AD. This done, setting one foot of the Compasses in A, extend the other to the different divisions of the Quadrant AD; and so transfer them to the right line AD as in the Figure, and you have a line of Chords AD to the Radius CA. N. B. 60 Degrees on the Line of Chords is always equal to the Radius of the Circle it is made from; as is evident by the Figure, where the Arch E, whose Center is A, drawn from 60 on the Quadrant AD, cuts the Chord line in 60 degrees, and terminates in the Center C.

And of Sines.

Then, from the divisions or degrees of the Quadrant BD, draw lines parallel to CD, which will fall perpendicularly on the Radius BC, dividing it into a line of Sines; and it will be near enough for the present purpose, to have them to every fifth Degree, as in the Figure. And thus the young Tyro may supply himself with Chords and Sines, if he has not a Sector. But as the Sector greatly shortens the work, we shall describe the projection as done by it, so far as Signs and Chords are required.

Fig. II.

Earth’s Semi-Disc.

370. Make a Scale of any convenient length (six inches at least) as AC, and divide it into as many equal parts as the semi-diameter of the Earth’s Disc contains minutes, which in this construction of the Eclipse for London in April 1764, is 54 minutes and 57 seconds; but as it wants only 3ʺ of 55ʹ the Scale may be divided into 55 equal parts, as in the Figure. Then, with the whole length of the Scale as a Radius, setting one foot of your Compasses in C as a center, describe the Semi-circle AMB for the northern Hemisphere or Semi-disc of the Earth, as seen from the Sun at that time. Had the Place for which the Construction is made been in South Latitude, this Semi-circle would have been the Southern Hemisphere of the Earth’s Disc.

Axis of the Ecliptic.

371. Upon the center C raise the straight line CH for the Axis of the Ecliptic, perpendicular to ACB.

North Pole of the Earth.

372. Make a line of Chords to the Radius AC, and taking from thence the Chord of 231⁄2 Degrees, set it off from H to g and to h, on the periphery of the Semi-disc; and draw the straight line gNh, in which the North Pole of the Disc is always found.

373. While the Sun is in Aries, Taurus, Gemini, Cancer, Leo, and Virgo, the North Pole of the Disc is illuminated; but while the Sun is in Libra, Scorpio, Sagittary, Capricorn, and Aquarius, the North Pole is hid in the obscure part behind the Disc.

374. And, whilst the Sun is in Capricorn, Aquarius, Pisces, Aries, Taurus, and Gemini, the Earth’s Axis CP lies to the right hand of the Axis of the Ecliptic CH as seen from the Sun, and to the left hand while the Sun is in the other six Signs.

Earth’s Axis.

Universal Meridian.

375. Make a line of Sines equal in length to Ng or Nh, and take off with your Compasses from it the Sine of the Sun’s distance from the nearest Solstice, which in the present case is 77° 51ʹ § 367, and set that distance to the right hand, from N to P, on the line gNh, because the Sun being in Aries § 359, the Earth’s Axis lies to the right hand of the Axis of the Ecliptic § 374: then draw the straight line CXIIP, for the Earth’s Axis and the Universal Meridian; of both which P is the North Pole.

Path of a given Place on the Disc as seen from the Sun.

376. To draw the parallel of Latitude of any given Place (suppose London) which parallel is the visible Path of the Place On the Disc, as seen from the Sun, from the time that the Sun rises till it sets; subtract the Latitude of the Place (London) 511⁄2 degrees from 90 degrees, and there remains 381⁄2; which take from the Line of Chords in your Compasses, and set it from h (where the Universal Meridian CP cuts the periphery of the Semi-disc) to VI and VI; and draw the occult Line VILVI. Then, on the left hand of the Earth’s Axis, set off the Chord of the Sun’s Declination 4° 48ʹ 5ʺ § 367, from VI to D and to F; set off the same on the right hand from VI to E and to G; and draw the occult Lines DsE and FXIIG parallel to VI L VI.

Situation of the Place on the Disk from Sun-rise to Sun-set.

377. Bisect s XII in K, and through the point K draw the black Line VIKV1 parallel to the occult or dotted Line VILVI. Then, making AC the Radius or length of a Line of Lines, set off the Sine of 381⁄2 degrees, the Co-Latitude of London, from K to VI and VI; and with that extent as a Radius, describe the Semi-Circle VI 7 8 9 &c. and divide it into 12 equal parts, beginning at VI. From these divisions, draw the occult Lines 7m, 8l, 9k, &c. all to the Line VIKVI, and parallel to CXIIP. Then, with KXII as a Radius, describe the Circle abcdef, round the Center K, and divide the Quadrant aXII into six equal parts, as ab, bc, cd, de, &c. Then, through these points of division b, c, d, e, and f, draw the occult Lines VIIbV, VIIIcIIII, IXdIII, &c. intersecting the former Lines 7m, 8l, 9k, 10i, &c. in the points VII, VIII, IX, X, XI, &c. which points mark the situation of London on the Earth’s Disc as seen from the Sun at these hours respectively, from six in the morning till six at night: and if the elliptic Curve VI, VII, VIII, &c. be drawn through these points, it will represent the parallel of London, or the path it seems to describe as viewed from the Sun, from Sun-rise to Sun-set. N.B. When the Sun’s Declination is North, the said Curve is the diurnal Path of London; and the opposite part VIsVI is it’s nocturnal Path behind the Disc, or in the obscure part thereof, § 338, 339. But if the Sun’s Declination had been South, the Curve VIsVI would have been the diurnal path of London; in which case the Lines 7m, 8l, &c. must have been continued thro’ the right Line VIKVI, and their lengths beyond that line determined by dividing the Quadrant s a of the little Circle abcd into six equal parts, and drawing the parallels VIIb, VIIIc &c. through that division, in the same manner as done on the side K XII; and the Curve VII, VIII, IX, &c. would have been the nocturnal Path. It is requisite to divide the hours of the diurnal Path into quarters, as in the Diagram; and if possible into minutes also.

Axis of the Moon’s Orbit.

378. From the Line of Chords § 372 take the Angle of the Moon’s visible Path with the Ecliptic, viz. 5° 38ʹ § 367: and note, that when the Moon’s Latitude is North Ascending, as in the present case, the Chord of this Angle must be set off to the left hand of the Axis of the Ecliptic CH, as from H to M, and the right line CM drawn for the Axis of the Moon’s Orbit: but when the Moon’s Latitude is North Descending, this Angle and Axis must be set to the right hand, or from H toward h. When the Moon’s Latitude South Ascending, the Axis of her Orbit lies the same way as when her Latitude is North Ascending; and when South Descending, the same way as when North Descending.

Path of the Penumbra’s center over the Earth.

379. Take the Moon’s Latitude, 40ʹ 9ʺ § 367, from the Scale CA, and set it from C to T on the Axis of the Ecliptic; and through T, at right Angles to the Axis of the Moon’s Orbit CM, draw the straight Line RTS; which is the Moon’s Path, or Line that the center of her shadow and Penumbra describes in going over the Earth’s Disc. The Point T in the Axis of the Ecliptic is the Place where the true Conjunction of the Sun and Moon falls, according to the Tables; and the Point W, in the Axis of the Moon’s Orbit, is that where the center of the Penumbra approaches nearest to the center of the Earth’s Disc, and consequently the middle of the general Eclipse.

It’s Place on the Earth’s Disc shewn for every minute of it’s Transit.

380. Take the Moon’s true Horary Motion from the Sun 27ʹ 50ʺ § 367, from the Scale CA with your Compasses (every division of the Scale being a minute of a Degree) and with that extent make marks in the Line of the Moon’s Path RTS: then divide each of these equal spaces by dots into 60 equal parts or horary minutes, and set the hours to every 60th minute, in such a manner that the dot; signifying the precise minute of New Moon by the Tables, may fall in the Point T where the Axis of the Ecliptic cuts the Line of the Moon’s Path; which, in this Eclipse, is the 25th minute past ten in the Forenoon: and then the other marks will shew the places on the Earth’s Disc where the center of the Penumbra is, at the hours and minutes denoted by them, during its transit over the Earth.

Middle of the Eclipse.

It’s Phases.

381. Apply one side of a Square to the Line of the Moon’s Path, and move the Square backward or forward until the other side cuts the same hour and minute both in the Path of the Place (London, in this Construction) and Path of the Moon; and that minute, cut at the same time in both Paths, will be the precise minute of visible Conjunction of the Sun and Moon at London, and therefore the time of greatest obscuration, or middle of the Eclipse at London; which time, in this Projection, falls at t, 34 minutes past 10 in the Moon’s Path; and at u, 34 minutes past 10 in the Path of London. Then, upon the Point u as a center, describe the Circle zYy whose Radius uy is equal to the Sun’s semi-diameter 16ʹ 6ʺ § 367, taken from the Scale CA: And upon the Point t as a center, describe the Circle Hy whose Radius is equal to the Moon’s semi-diameter 14ʹ 58ʺ § 367, taken from the same Scale. The Circle zYy represents the Disc of the Sun as seen from the Earth, and the Circle Hy the Disc of the Moon. The portion of the Sun’s Disc cut off by the Moon’s shews the Quantity of the Eclipse at the time of greatest obscuration: and if a right Line as yz be drawn across the Sun’s Disc through t and u, the minute of greatest obscuration in both Paths, and divided into 12 equal parts, it will shew what number of Digits are then eclipsed. If these two Circles do not touch one another, the Eclipse will not be visible at the given Place.

It’s beginning and ending.

382. Lastly, take the Semi-diameter of the Penumbra 31ʹ 4ʺ § 367, from the Scale CA with your Compasses; and setting one foot in the Moon’s Path, to the left hand of the Axis of the Ecliptic, direct the other toward the Path of London; and carry this extent backwards or forwards until both Points of the Compasses fall into the same instants of time in both Paths: which will denote the time of the beginning of the Eclipse: then, do the same on the right hand of the Axis of the Ecliptic, and where both Points mark the same instants in both Paths, they will shew at what time the Eclipse ends. These trials give the Points R in the Moon’s Path and r in the Path of London, namely 9 minutes past 9 in the Morning for the beginning of the Eclipse at London, April 1, 1764: t and u for the middle or greatest obscuration, at 35 minutes past 10; when the Eclipse will be barely annular on the Sun’s lower-most edge, and only two thirds of a Digit left free on his upper-most edge: and for the end of the Eclipse, S in the Moon’s Path and x in the Path of London, at 4 minutes past 12 at Noon.

In this Construction it is supposed that the Equator, Tropics, Parallel of London, and Meridians through every 15th degree of Longitude are projected in visible Lines on the Earth’s Disc, as seen from the Sun at almost an infinite distance; that the Angle under which the Moon’s diameter is seen, during the time of the Eclipse, continues invariably the same; that the Moon’s motion is uniform, and her Path rectilineal, for that time. But all these suppositions do not exactly agree with the truth; and therefore, supposing the Elements § 367, given by the Tables to be perfectly accurate, yet the time and phases of the Eclipse deduced from it’s Construction will not answer exactly to what passeth in the Heavens; but may be two or three minutes wrong though done with the utmost care. Moreover, the Paths of all Places of considerable Latitude go nearer the center of the Disc as seen from the Moon than these Constructions make them; because the Earth’s Disc is projected as if the Earth were a perfect sphere, although it is known to be a spheroid. Consequently, the Moon’s shadow will go farther North in places of northern Latitude, and farther South in places of southern Latitude than these projections answer to. Hence we may venture to predict that this Eclipse will be more annular at London (that is, the annulus will be somewhat broader on the southern Limb of the Sun) than the Diagram shews it.

383. Having shewn how to compute the times and project the phases of a Solar Eclipse, we now proceed to those of the Lunar. And it has been already mentioned § 317, that when the Full Moon is within 12 degrees of either of her Nodes, she must be eclipsed. We shall now enquire whether or no the Moon will be eclipsed May 18, 1761, N. S. at 32 minutes past 10 at Night. See page 193.

Table IV.

Table VI.

s°ʹ
Sun from Node at Full Moon in March 176192527
Add his distance for two Lunations, to bring it into May2120
And his distance at Full Moon in that month is112647

Subtract this from a Circle, or 12 Signs, and there will remain 3° 13ʹ; which is all that the Sun wants of coming round to the Ascending Node; and the Moon being then opposite to the Sun, must be just as near the Descending Node: consequently, far within the limit of an Eclipse.

384. Knowing then that the Moon will be eclipsed in May 1761, we must find her true distance from the Node at that time, by applying the proper Equations as taught § 363, and then find her true Latitude as taught in that article.

Table IV.

Table XIII.

Table XII.

s°ʹ
Sun’s mean distance from the Node at F. Moon in May 1761112647
Add the Equation of the Node, for the Sun’s Anomaly 10s 18° 15ʹ[85]+6
Sun’s mean distance from the Node corrected112653
Add the Equation of the Sun’s mean Place+115
Sun’s true distance from the Ascending Node11288
To which add 6 Signs, See § 3636
The sum is the Moon’s true distance from the same Node5288

Pl. XII.

Or the Argument of her Latitude; which in Table XIV, gives the Moon’s true Latitude, viz. 9ʹ 56ʺ North Descending.

385. Having by the foregoing precepts § 355 found the true time of Opposition of the Sun and Moon in a lunar Eclipse, with the Moon’s Anomaly enter Table XV and take out her horizontal Parallax, also her true horary Motion and Semi-diameter: and likewise those of the Sun by his Anomaly, as already taught § 364 & seq. Then add the Sun’s horizontal Parallax, which is always 10 Seconds, to the Moon’s horizontal Parallax, and from their sum subtract the Sun’s Semi-diameter; the remainder will be the Semi-diameter of that part of the Earth’s shadow which the Moon goes through.

386. From the Sum of the Semi-diameters of the Moon and Earth’s Shadow, subtract the Moon’s Latitude; the remainder is the parts deficient. Then, as the Semi-diameter of the Moon is to 6 Digits, so are the parts deficient to the Digits eclipsed.

387. If the parts deficient be more than the Moon’s Diameter, the Eclipse will be total with continuance; if less, it will not be total; if equal, it will be total, but without continuance.

388. Now collect the Elements for projecting this Eclipse.

ʹʺ
Moon’s horizontal Parallax5532
Sun’s horizontal Parallax (always)10
The Sum of both Parallaxes5542
From which subtract the Sun’s Semi-diameter1554
Remains the Semi-diameter of the Earth’s Shadow3948
Semidiameter of the Moon152
Sum of the two last5450
Moon’s Latitude subtract956
Remains the parts deficient450
Moon’s horary motion3046
Sun’s horary motion subtract224
Remains the Moon’s horary motion from the Sun2822

To project a lunar Eclipse.

Fig. III.

389. This done, make a Scale of any convenient length as W, whereof each division is a minute of a degree; and take from it in your Compasses 54 Minutes 50 Seconds, the Sum of Semi-diameters of the Moon and Earth’s shadow; and with that extent as a Radius, describe that Circle OVLG round C as a Center.

From the same Scale take 39 Minutes 48 Seconds, the Semi-diameter of the Earth’s shadow, and therewith as a Radius, describe the Circle UUUU for the Earth’s shadow, round C as a Center. Subtract the Moon’s Semi-diameter from the Semi-diameter of the Shadow, and with the difference 24 Minutes 46 seconds as a Radius, taken from the Scale W, describe the Circle YZ round the Center C.

Draw the right line AB through the Center C for the Ecliptic, and cross it at right Angles with the line EG for the Axis of the Ecliptic.

Because the Moon’s Latitude in this Eclipse is North Descending, § 384, set off the Angle of her visible Path with the Ecliptic 5 Degrees 38 Minutes (Page 202.) from E to V; and draw VCv for the Axis of the Moon’s Orbit. Had the Moon’s Latitude been North Ascending, this Angle must have been set off from E to f. N. B. When the Moon’s Latitude is South Ascending, the Axis of her Orbit lies the same way as when she has North Ascending Latitude; and when her Latitude is North Descending, the Axis of her Orbit lies the same way as when her Latitude is South Descending.

Take the Moon’s true Latitude 9ʹ 56ʺ in your Compasses from the Scale W, and set it off from C to F on the Axis of the Ecliptic because the Moon is north of the Ecliptic; (had she been to the South of it, her Latitude must have been set off the contrary way, as from C towards v:) and through F, at right Angles to the Axis of the Moon’s Orbit VCv, draw the right line LMHNO for the Moon’s Orbit, or her Path through the Earth’s shadow. N. B. When the Moon’s Latitude is North Ascending, or North Descending, she is above the Ecliptic: but when her Latitude is South Ascending, or South Descending, she is below it.

Take the Moon’s true horary motion from the Sun, viz. 28 Minutes 22 Seconds, from the Scale W in your Compasses; and with that extent make marks in the line of the Moon’s Path LMHNO: then divide each of these equal spaces into 60 equal parts or minutes of time: and set the hours to them as in the Figure, in such a manner that the precise time of Full Moon, as shewn by the Tables, may fall in the Axis of the Ecliptic at F, where the line of the Moon Path cuts it.

Lastly, Take the Moon’s Semi-diameter 15 Minutes 2 Seconds from the Scale W in your Compasses, and therewith as a Radius describe the Circles P, Q, R, S, and T on the Centers L, M, H, N, and O; the Circles P and T just touching the Earth’s Shadow UU, but no part of them within it; the Circles Q and S all within it, but touching at its edges; and the Circle R in the middle of the Moon’s Path through the shadow. So the Circle P shall be the Moon touching the shadow at the moment the Eclipse begins; the Circle Q the Moon just immersed into the shadow at the moment she is totally eclipsed; the Circle R the Moon at the greatest obscuration, in the middle of the Eclipse; the Circle S the Moon just beginning to be enlightened on her western limb at the end of total darkness; and the Circle T the Moon quite clear of the Earth’s shadow at the moment the Eclipse ends. The moments of time marked at the points L, M, H, N and O answer to these Phenomena: and according to this small projection are as follow. The beginning of the Eclipse at 8 Hours 36 Minutes P. M. The total immersion at 9 Hours 42 Minutes. The middle of the Eclipse at 10 Hours 26 Minutes. The end of total darkness at 11 Hours 12 Minutes. And the end of the Eclipse at 12 Hours 18 Minutes; but the Figure is too small to admit of precision.

The examination of antient Eclipses.

390. By computing the times of New and Full Moons, together with the distance of the Sun and Moon from the Nodes; and knowing that when the Sun is within 17 Degrees of either Node at New Moon he must be eclipsed; and when the Moon is within 12 Degrees of either Node at Full she cannot escape an Eclipse; and that there can be no Eclipses without these limits; ’tis easy to examine whether the accounts of antient Eclipses recorded in history be true. I shall take the liberty to examine two of those mentioned in the foregoing catalogue, namely, that of the Moon at Babylon on the 19th of March in the 721st year before Christ; and that of the Sun at Athens, on the 20th of March, in the 424th year before Christ.

The time of Full Moon for the former of these Eclipses is already calculated, Page 198, and the time of New Moon for the latter, Page 196, both to the Old Style; so that we have nothing now to do but find the Sun’s distance from the Nodes the same way as we did the Anomalies; and if the Full Moon in March 721 years before Christ was within 12 degrees of either Node, she was then eclipsed; and if the Sun, at the time of New Moon in March 424 years before Christ was within 17 degrees of either Node, he must have been eclipsed at that time.

EXAMPLE I.

To find the distance of the Sun and Moon from the Nodes, at the time of Full Moon in March, the year before Christ 721, O. S.

The years 720 added to 1780 make 2500, or 25 Centuries.

Sun from Node
s°ʹ
To the mean time of Full Moon in March 1780, Table III.1031
Add the distance for 1 Lunation [See N. B. Page 195, and Example III, Page 198]1040
Sum11341
From which subtract the Sun’s distance from the Node for 2500 years, Table V5411
Remains the Sun’s distance from the Node, March 19, 721 years before Christ52930
To which add 6 Signs for the Moon’s distance, because she was then in opposition to the Sun600
The Sum is the Moon’s dist. from the Ascend. Node112930

That is, she was within half a degree of coming round to it again; and therefore, being so near, she must have been totally, and almost centrally eclipsed.

EXAMPLE II

To find the Suns distance from the Node at the Time of New Moon in March, the year before Christ 424, O. S.

The years 423 added to 1777 make 2200, or 22 Centuries.

Sun from Node
s°ʹ
At the mean time of New Moon in March 1777, Tab. I.82333
From which subtract the Sun’s distance from the Node for 2200 years, Table V360
Remains the Sun’s distance from the Ascending Node, March 21, 424 years before Christ51733
Which, taken from 6 Signs, the distance of the Nodes from each other600
Leaves the Sun’s distance at that time from the Descending Node, Descending viz.01227

Which being less than 17 degrees, shews that the Sun was then eclipsed. And as from these short Calculations we find those two antient Eclipses taken at a venture, to be truly recorded; it is natural to imagine that so are all the rest in the catalogue.

Here follow Astronomical Tables, for calculating the Times of New and Full Moons and Eclipses.

Table I. The mean time of New Moon in March, the mean Anomaly of the Sun and Moon, the Sun’s mean Distance from the Ascending Node; with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, at the times of all the New Moons in March for 100 years, Old Style.

Years of Christ.Mean time of New Moon in March.The Sun’s mean Anomaly.The Moon’s mean Anomaly.The Sun’s distance from the Node.The Sun’s Longitude from Aries.The Node’s Longitude from Aries.
D.H.M.s°ʹs°ʹs°ʹs°ʹs°ʹ
17012713459823028572315016342248
1702162234827391175381170520443
170367238165591741892011243731517
1704244559430823189183013022457
170513134482354736926602172611
1706222328134851254104911213411725
17072120592174183111125209570275
17081045482110228191120551129140819
170929226994823560293801737111759
1710181116828320134417400654102914
171172058172710233311543112611101028
17122517369589291022426014349208
171315225825488858322903509121
1714411148145261646310321123781235
171523846933752422419150113072215
17161117358212644114271800477329
17171223811582135955201120461444
17181923569031119366143082752424
171998458194711292462261127435537
17202761798911518049016641517
17211615682725914498852052332631
1722523558164172438816551124403745
1723242127953701592538013421726
17241361682419510310341022212841
1725215481345319511011431121391956
1726211237915722528112026010301937
17271021268211315161128291129200051
1728281858993501053171301743111030
1729183478285110204111515070102145
173071236818790291231811261710259
17312610896298663210144091239
173214185782545615543103035782354
1733434581449425433186112314857
17342311893254120426490113771448
173512107822392118545200546261
17363073901111164561335019176542
173719162890111263362138083451656
173891178193310621629421127514289
17392722499755911588824016144750
17401673882711721468162705303193
174151626816276134824301124473016
17422413599449571110312013102958
1743132248824531659101115022712112
1744273681321126481019181121441225
17452159914312251128001070127
174610135882059111213063112944112320
1747291130992110175011445017471132
1748172019828378273812249074101415
1749758817537726205311262192528
17502624096156133393501444959
175115112982532422513173804181623
1752320178144732393254111231872737
1753221750931028165424011417717
17541223982226018451227005961832
175511127811411027525203011201652945
17561990904103306291308395927
17578174981920813187101511275642041
175827152197427185581558016194021
17591701082658528438241053631136
1760585881613483192411245322249
17612463194353148101047013162229
17621315198235212356101851023311344
17633088137034410265311215002457
17642021419129119210536010130437
17651063082046919901338112930111552
17662942998824461222101753102532
17671812518282474352024071010647
176862139817395142328271126279181
1769251912962420031700145082741
177015418251722948325120478856
17714124981433193643161123247208
1772221022925601513511490114762948
1773111910822111025152010146113
17741359811279449528411202152217
177520132829508102676408445157
177681020819562014714501128141312
177727753972752551823230162432252
177816164282643454091360541346
177961308155921528993911245821519
178023233942112151018220132112459
17811375282337005310262402381614
178221640812531010411142711215401727
1783211413911591618013100101711277
178492328203272660211311293411822
178528203598547143129560175710182
1786185238289511312759071492916
1787714118172532119216211263191029
178825114495472265632445014548209
178914203382531645424704118125
17904521814191116334105011232871238
1791232549241102210519330115162218
1792111143821579158527560176332
1793020318111271145653911202451445
179419184829356172371422084842427
17959252818514271172225112864541
179627025971342489180162931521
17971691482629212369910054622636
17985182815440222491713112532750
1799241535946112811025560132611730
180013024823231074911359024302844

Table II. The mean New Moons, &c. in March to the New Style .

Years of Christ.Mean time of New Moon in March.The Sun’s mean Anomaly.The Moon’s mean Anomaly.The Sun’s distance from the Node.The Sun’s Longitude from Aries.The Node’s Longitude from Aries.
D.H.M.s°ʹs°ʹs°ʹs°ʹs°ʹ
17534567421122743441112357850
17542323982226018451227005961832
1755121127811411027525202911201652945
17563090903103296291208395927
17571917498191981317771511275642041
1758923788356235715181117134154
1759280982658528438241053631136
17601685881614483192411245322249
176157478529218199109111410241
17622415198235212356101851023311344
176314088137034410265311215002457
17642857822310133211457111170610
17652163082046919901338112930111552
17661015188101728580214111184710275
17672912518282374352023071010647
1768172139817395142328261126279181
176976288655324112162911154482915
177026418251822948325110478856
177115124981433193643161123247208
1772321388349111924411191112417122
1773221910822111025152010146113
177412359811279449528411202152217
177511248804371437667119385330
1776191020819562014714501128141312
1777819988215027225311171832425
177827164282643454091360541346
1779171308155921528993911245821519
1780510198515025169174211141512632
17812475282337005310262402381614
1782131640812531010411142711215401727
1783312982882029111230111111112840
1784202328203272660211311293411822
1785107508947655402916111851101935
1786295238289511312759071492916
17871814118172532119216211263191029
178862308641217224511154882143
178925203382531645424704118125
179015521814191116334105011232871238
1791414108334926214185311124462351
1792221143821579158527360176332
17931120318111271145653911202451445
1794162080295213461342119224715
179520252818514271172225112864541
1796811418863659802811172331654
17972791482629212369910054622636
179816182815440222491713112532750
1799625185011212925161114201193
180025024823231074911359024302844

Table III. The mean time of Full Moon in March, the mean Anomaly of the Sun and Moon, the Sun’s mean Distance from the Ascending Node; with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, at the time of all the Full Moons in March for 100 years, Old Style.

Years of Christ.Mean time of Full Moon in March.The Sun’s mean Anomaly.The Moon’s mean Anomaly.The Sun’s distance from the Node.The Sun’s Longitude from Aries.The Node’s Longitude from Aries.
D.H.M.s°ʹs°ʹs°ʹs°ʹs°ʹ
170112192382356615117755013042335
17022412813642459715571120474448
1703211459128403582440091031430
1704910338195721024924311282722543
1705288698271160101126016502525
17061716548281111254810192906711638s
17077143817441053710273211252402751
17082423169543911140615013470733
1709148482515721201418034111846
171031654813596050022211122211100
171122142792056272130104410942
1712102314820353161629600192055
1713292047910212215231748018239035
17141953682925114032553074081148
171581424819411112843561126577231
17162611579559017551238015207243
17171520458263118265352041043761356
171855348155876425284411235452510
171924379420612187726012175452
17201211558233642277152901344165
1721120448125231557233211205132718
172220181791142732921509143659
1723103582030017219101811283121812
1724280389852112257101900165512755
1725179268281810245102730612199
1726618158172481234115611253002023
17272515489546718100134901353005
172814036825252759021520310111118
1729392581418474702955112227102232
17302265892403132328380105010213
173111154682156123122164100791326
1732291319910180284832523018308238
1733182278292211837432607478421
173486568185091826411291127471534
17352742997128242520120152762515
17361513178262973515281504446629
17374226815445133966181124151742
17382319399464191571510122442724
173913427823222294723401414837
17401131681238185281711205731950
1741201048910014289949092022930
174291937820161024179175211283721044
1743281710983892953102635017012026
1744171588275489421143806171139
174561047817106193111124111253401252
174625819953252570212401357112234
17471417882448445602927031411347
17483157814421444173011223110150
1749212330922612020216120105492442
175011818821420092241500119559
17513055191051154542580183481537
175218143982920915334111075172650
1753723187183572521419411278784
17542621196597058727470153261745
1755165498261451046654904495290
1756414388153032035613521124651014
1757231211935322612725350122941954
17581220598238155980380146419
175925478122511154888411121331222
17602032090461021259172409262222
1761912982029113925271128432316
1762289419825865011411017611257
17631718308274061638111213062302411
1764631981656426261120161125400524
176525052951942302858014311155
17661494082434211521710320102620
1767718298135002141115411223710734
176821161921211271722347011091714
1769110508212810793149001782828
17700939810448165739521119548942
17711971182967223041836075771921
17727160818226218426391127147035
17732613329644575565210153761016
177415222182603174361324045452131
177557108151612731621271124115244
177623442933813880100123441225
1777121331822541112568813015182330
177812220812109224581616112183452
177920195290328282292459093121432
17809441819487810103111284812547
17812821498961347111144017111527
178219112827284233411194706270641
178361951816443323112750112544112754
17842417249542901635014711735
1785142128242001848114360324101848
1786311181336102837122391122411002
178722833915710413312201149942
17881017228211481423925002182057
17892914559936719394187018448038
179018234382852529274261008171151
179188328188491554131127176234
1792266596203145261256015406245
1793151453825461244062059045851359
17944234281520429629211241542513
17952321149314111058745012394454
1796126382239919538154801563168
17971145281155729428235011211322723
17982012249077518102330936273
17999211381933515610103611285311818
18002718469746420431119190171602757

Table IV. The mean Full Moons, &c. in March to the New Style .

Years of Christ.Mean time of Full Moon in March.The Sun’s mean Anomaly.The Moon’s mean Anomaly.The Sun’s distance from the Node.The Sun’s Longitude from Aries.The Node’s Longitude from Aries.
D.H.M.s°ʹs°ʹs°ʹs°ʹs°ʹ
17531823187183572521419411278784
1754881777536510427711162661918
1755275498261451046654904495290
17561514388153032035613521124651014
175742327843620236215511132342127
17582320598238155980380146419
1759135478122511154888411121331222
1760114368141925378164411102022335
17612012982029113925271128432316
17629205789197112103311118011429
17632818308274061638111213062302411
17641731981656426261120161125400524
1765612886133615112819111457111638
17662594082434211521710320102620
17671818298135002141115411223710733
1768331783611129123711115491846
1769220508212810753149001782828
177011939815458165439521119348942
17713071182967223041836075771921
177218160818226218426391127147035
1773804887384127544211163161149
177426222182603174361324045452131
1775167108151612731621271124115244
177641558843207206293011132841358
1777231331822541112568813015132339
1778122220812109224581616112183452
177927881268234824191110252165
178020441819487810103111284812547
178191330894517591011411185170
1782281128272842334111947062701641
1783171951816443323112750112544112754
178464408559113120553111511197
1785252128242001848114360324101848
17861411181336102837122391122411002
17873194982529825204211115891115
17882117228211481423925002182057
1789112118103062351317281119388210
179029234382852529274261008171151
1791198328188491554131127176234
17927172187242194512161116346417
1793261453825461244062059045851359
179415234281520429629211241542513
179558308418101417775013324626
1796236382239919538154801563168
179712145281155729428235011211322723
1798123408111693091531110302836
179920211381933515610103611285311818
1800106288503245510183911181002931

Tab. V. The first mean Conjunction of the Sun and Moon after a compleat Century, beginning with March, for 5000 years 10 days 7 hours 56 minutes (in which time there are just 61843 mean Lunations) with the mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, and the mean Long. of the Sun and Node from the beginning of the sign Aries, at the times of all those mean Conjunctions.

Centuries of Julian Years.First Conjunction after a Century.The Sun’s mean Anomaly.The Moon’s mean Anomaly.The Sun’s distance from the Node.The Sun’s Longitude from Aries.The Node’s Longitude from Aries.
D.H.M.s°ʹs°ʹs°ʹs°ʹs°ʹ
10048110321815224192705241425
20081622064250449855010482851
300130330103116612822015611316
40017843013241012861749020852741
5002116540164661650117160251010126
60026150207321232644101222632
70002032112422102145715310677924
800544311274377704580119112349
900912540143222942425016124813
10001321504250751913530211482239
110018516074682313232002616174
12002213260117583562247111852129
13002621370142812357111215162010555
14001174111843913303120121521847
15006115112245285272029017177312
16001092611252521414095602219111737
17001417371128461029364292302722422
1800191480287145891851122481627
19002395805294020281817261052
200027189085001542627451122851517
210021336111358515101632018249288
220062147111626420373600232621234
2300115581119471559725270282862659
2400151491123892121014541330111124
250019222011262966435411183232549
2600246311129502224923491133581014
27002814410311111726213161183702439
280031081172662659623024315733
290071819111047312211021300293392158
300012230111481127433105814352623
3100161041111730813581025193762048
320020185211205142827019521143911513
330025331124111134959201194131939
3400291114112732929119284712443844
35004641111475184411734104101653
3600814521145824667115425119
37001223311891019281026281104391545
380017714111120745031555115452010
39002115251114314201285221204761435
40002523361117421534024491254910290
41000193102256825741336104531251
420053141026175102993316477616
430091125102937125511123011148112539
4400131936112581011136157116514104
45001834611618626351021241215382931
46002211571193931115310511265511356
4700262071112591127198016215752819
48001153410171471652111941753101111
490052345102035421448301125522535
5000107561023560173682757117577100

Table VI. The mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, for 13 mean Lunations.

Lunations.Mean Lunations.The Sun’s mean Anomaly.The Moon’s mean Anomaly.The Sun’s motion from the Node.The Sun’s mean Motion.The Node’s retrograde Motion.
D.H.M.s°ʹs°ʹs°ʹs°ʹs°ʹ
1291244029602549104002960134
2591281281312138212012813038
38814122271921727321227190441
411825632626313164241326260615
5147154425324955321425320749
6177424524385454641524380923
720617862344604374426234501057
8236552722506263285227225101231
926518368215772221962821580144
1029572192138181010642921401538
1132420510209913591172210201001712
123548491119161094808311191701846
133832133018221153718430182302020

The first, second, third, and fourth Tables may be continued, by means of the sixth, to any length of time: for, by adding 12 Lunations to the mean time of the New or Full Moon which happens next after the 11th day of March, and then, casting out 365 days in common years, and 366 days in leap-years, we have the mean time of New or Full Moon in March the following year. But when the mean New or Full Moon happens on or before the 11th of March, there must be 13 Lunations added to carry it to March again. The Anomalies, Sun’s distance from the Node, and Longitude of the Sun, are found the same way, by adding them for 12 or 13 Lunations. But the retrograde Motion of the Node for these Lunations must be subtracted from it’s longitude from Aries in March, to have it’s Longitude or Place in the March following.

Table VII. The number of Days, reckoned from the beginning of March, answering to the Days of all the mean New and Full Moons.

Days.March.April.May.June.July.August.September.October.November.December.January.February.
11326293123154185215246276307338
22336394124155186216247277308339
33346495125156187217248278309340
44356596126157188218249279310341
55366697127158189219250280311342
66376798128159190220251281312343
77386899129160191221252282313344
883969100130161192222253283314345
994070101131162193223254284315346
10104171102132163194224255285316347
11114272103133164195225256286317348
12124373104134165196226257287318349
13134474105135166197227258288319350
14144575106136167198228259289320351
15154676107137168199229260290321352
16164777108138169200230261291322353
17174878109139170201231262292323354
18184979110140171202232263293324355
19195080111141172203233264294325356
20205181112142173204234265295326357
21215282113143174205235266296327358
22225383114144175206236267297328359
23235484115145176207237268298329360
24245585116146177208238269299330361
25255686117147178209239270300331362
26265787118148179210240271301332363
27275888119149180211241272302333364
28285989120150181212242273303334365
29296090121151182213243274304335366
30306191122152183214244275305336—
3131—92—153184—245—306337—

Table VIII. The Moon’s annual Equation.

Sun’s Ano.SubtractSun’s Ano.
012345
S.S.S.S.S.S.
D.M.M.M.M.M.M.D.
00111822191130
10111922191129
21111922181028
31111922181027
41121922181026
5212192218925
6212192118924
7313202117923
8313202117822
9313202117821
10414202117820
11414202116719
12414202116718
13514202116617
14515202116616
15515212115615
16615212115514
17615212115513
18616212115512
19716212014411
20716212014410
2171621201439
2281721201338
2381721201337
2491721201326
2591721201325
2691821201224
27101821191213
28101821191212
29101822191101
30111822191100
Sun’s Ano.11109876Sun’s Ano.
S.S.S.S.S.S.
Add

Table IX. Equation of the Moon’s mean Anomaly.

Sun’s Anom.AddSun’s Anom.
012345
S.S.S.S.S.S.
°ʹʹʹʹʹʹ°
00101720171030
10101720171029
2111172017928
3111182017927
4111182017926
5212182017925
6212182016824
7212182016823
8312182016822
9312192016721
10313192016720
11413192015719
12413192015618
13413191915617
14514191915616
15514191914515
16514191914514
17614191914513
18615191914412
19615201913411
20715201913410
2171520191339
2271620191338
2381620191237
2481620181226
2581620181225
2691620181114
2791720181113
2891720181112
29101720181001
30101720171000
Sun’s Anom.11109876Sun’s Anom.
S.S.S.S.S.S.
Subtract

Table X. The Moon’s elliptic Equation.

Moon’s Ano.AddMoon’s Ano.
012345
SignsSignsSignsSignsSignsSigns
°H.M.H.M.H.M.H.M.H.M.H.M.°
000449889273241430
1010457812917274629
2020558169072235828
303051382085971735027
404052182485871234226
50505298288577633425
6105378318557032624
711054583485365431823
812055383785164831022
9130618408496423221
101406984384763625320
1115061684584463024519
122062384784162423718
1321063084983861822917
1422063785183561122116
152306448538326421215
162406518558295572314
1725065885782655015413
18307485982354314512
193107109082053613611
203197169181652912710
21328722928125221199
2233772892885151118
23346733938458137
243557389380510546
2544743947564540455
26413748947524460364
27422753947474380273
28431758937424300182
294408393737422091
304498892732414000
Moon’s Ano.11109876Moon’s Ano.
SignsSignsSignsSignsSignsSigns
Subtract

Table XI. The Sun’s Equation at the time of New and Full Moon.

Sun’s Anom.SubtractSun’s Anom.
012345
SignsSignsSignsSignsSignsSigns
°H.M.H.M.H.M.H.M.H.M.H.M.°
000144323323514830
104147333323314529
207150353323214228
3011153373323013827
40141573933225813526
50182031033125613125
60222331233125412824
70252631433125212423
80292831633025012122
903221131743024811721
1003621431833024511420
1104021731932924311119
120432203203292401718
130472223213282371417
140502253223272351016
1505422832332623205615
1605723032432522905214
171023232532422604913
181423532632322304512
191723832732222104111
2011124032832121803810
211142433283202150349
221172453293192120308
231212473293182100267
24124249330317270236
25128251330315240195
26131254331313210154
271342573313111580113
2813825933139155072
291413133237152041
301443233235148000
Sun’s Anom.11109876Sun’s Anom.
SignsSignsSignsSignsSignsSigns
Add

Table XII. Equation of the Sun’s mean Place.

Sun’s Anom.SubtractSun’s Anom.
012345
SignsSignsSignsSignsSignsSigns
°°ʹ°ʹ°ʹ°ʹ°ʹ°ʹ°
00005714015614205930
10205914115614105729
2041014215614005628
3061114315613905427
4081214415613805226
50101414515613605025
60121614515613504824
70141714615513404623
80161914715513304422
901811014815513204221
1002011214815413004120
1102211414915412903919
1202411515015412803718
1302611715115312603517
1402811815115312503316
1503012015215212303115
1603112115215212202914
1703312215315112102713
1803512415315111902512
1903712515415011802311
2003912715414911602110
210411281551491140199
220431291551481130178
230451301551471110147
240461321561461100126
25048133156146180105
2605013415614516084
2705213515614515063
2805413615614413042
2905513815614311021
30057140156142059000
Sun’s Anom.11109876Sun’s Anom.
SignsSignsSignsSignsSignsSigns
Add

Table XIII. Equation of the Moon’s Nodes.

Sun’s Ano.SubtractSun’s Ano.
012345
S.S.S.S.S.S.
°ʹʹʹʹʹʹ°
0058108530
1058108529
2058108528
3058108427
4158108426
5158108425
6169108424
716998423
816998422
916997321
1026997320
1126997319
1226997318
1326997317
1427997316
1527997315
1627997214
1737997213
1837996212
1937996211
2037996210
213799629
224799618
234899617
244899616
254899615
2648109514
2748109513
2848108502
2958108501
3058108500
Sun’s Ano.11109876Sun’s Ano.
S.S.S.S.S.S.
Add

The above titles, Add and Subtract, are right when the Equation is applied to the Sun’s mean distance from the Node; but when it is applied to the mean place of the Node, the titles must be changed.

Tab. XIV. The Moon’s latitude in Eclipses.

Argument of Latit.
Moon fr. the Node.Sig. 0 N. A.
Sig. 6 S. D.
°°ʹʺ°
000030
1051529
20103028
30154427
40205926
50261325
60312624
70363923
80415122
9047221
100521320
110572319
12123118
13173817
141124416
151174915
161225214
171275313
181325412
N. D. Sig. 5Moon fr. the Node.
S. A. Sig. 11
Argument of Latit.

This Table extends no farther than the limits of Eclipses. N. A. signifies North Ascending Lat. S. A. South Ascending; N. D. North Descending; and S. D. South Descending.

Table XV. The Moons Horizontal Parallax; the Semidiameters and true Horary motions of the Sun and Moon.

Anomaly of the Sun and Moon.Moon’s Horizontal Parallax.Sun’s Semidiameter.Moon’s Semidiamet.Moon’s horary Mot.Sun’s horary Mot.Anomaly of the Sun and Moon.
s°ʹʺʹʺʹʺʹʺʹʺs°
005459155014543010223120
6545915501455301222324
1255015501456301522318
1855415511457301822312
2455111551145830262236
105520155214593034223110
655301553151304422424
1255401354154305522418
185551155515831922412
245601556151231232256
205611155815173140225100
6562415591522315822624
1256411611526321722718
1857121621530323922712
245730164153633112286
3057491661541332322890
658101681546334722924
1258311691552341122918
18585216111558343422912
245911161316334582306
4059301614169352223080
6595216151614354523124
126091617161936023118
18602616191624362023212
2460401620162836402326
5060541621163137023270
661416211634371023324
12611116221637371923318
18611616221638372823312
2461201623163937362336
60612416231639374023360

The gradual increase or decrease of the above numbers being so small, it is sufficient to have them to every sixth degree; the proportions for the intermediate degrees being easily made by sight.

Table XVI. The Sun’s mean Motion and Anomaly.

Years of Christ beginningSun’s mean Longitude from Aries.Sun’s mean Anomaly.
s°ʹʺs°ʹ
O.S.197531062954
1301917423061658
1401918275061559
1501919131061459
1601919583061359
1701920435061259
N.S.175391016526138
18019939396010
Old Style to the beginning of A. D. 1753; then New StyleYears of Christ compleatSun’s mean Motion.Sun’s mean Anomaly.
s°ʹʺs°ʹ
111294540112945
211293120112929
31129170112914
400149112958
511294729112942
61129339112927
711291849112911
800338112955
911294918112940
1011293458112924
111129203811299
1200526112953
131129517112937
1411293647112922
151129222711297
1600715112950
1711295255112935
1811293835112920
191129241611294
200094112948
4000188112936
60002712112924
80003616112912
10000452011290
20001304011281
3000216011271
4000312011261
50003464011252
6000432011242
70005172011232
8000624011223
9000648011213
100007332011203
200001564011107
300002240011010
4000101320102013
5000174640101016
600011520010019
MonthsSun’s mean Motion.Sun’s mean Anomaly.
s°ʹʺs°ʹ
Jan.0000000
Feb.1033181033
Mar.1289111289
Apr.228423022842
May.328164032817
June428495842850
July52824852824
Aug.628572662857
Sep.729304472930
Oct.8294548294
Nov.929381292937
Dec.10291222102911
Days.Sun’s mean Motion and Anomaly.
s°ʹʺ
100598
2015817
3025725
4035633
5045542
6055450
7055358
807537
9085215
10095123
110105032
120114940
130124848
140134757
15014475
160154613
170164522
180174430
190184338
200194247
210204155
22021413
230224012
240233920
250243828
260253737
270263645
280273553
29028352
300293410
31103318

In Leap-years, after February, add one Day and one Day’s motion.

Sun’s mean Motion and Anomaly.

Hours.Mot. & Ano.
°ʹʺ
ʹʹʺʺʹ
ʺʺʺʹʺʺ
10228
20456
30724
40951
501219
601447
701715
801943
902211
1002438
110276
1202934
130322
1403430
1503658
1603926
1704153
1804421
1904649
2004917
2105145
2205413
2305640
240598
251136
26144
271632
28190
2911128
3011355
3111623
3211851
3312119
3412347
3512615
3612842
3713110
3813338
391366
4013834
411412
4214330
4314557
4414825
4515053
4615321
4715549
4815817
492044
502312
512540
52288
5321036
542134
5521532
5621759
5722027
5822255
5922523
6022751

In Leap-years, after February, add one Day and one Day’s motion.

Table XVII. The Sun’s Declination in every Degree of the Ecliptic.

Signs♈♎♉♏♊♐
061728
Nor.Sou.Nor.Sou.Nor.Sou.
°°ʹʺ°ʹʺ°ʹʺ°
000011293320111630
10235411503520234929
2047481211262036028
3111421232520474827
41353412523120591326
51592513124421101525
62231413325421205324
724711352322131723
8310451412521405822
93342614312421502421
10358414502821592520
114213815917228219
12445815275122161418
135834154692224017
14531551641122312116
155551116215722381615
166182116392622444514
176412516563722504913
18742317133122562612
1972715173072313611
2075001746152362010
2181236182242310389
228355181832314298
23857261833242317527
24919391848252320496
259414319352323195
26103371917262325224
271025211931252326573
2810465619453232852
29118201958202328461
30112933201116232900
Signs♓♍♒♌♑♋
1510493
Sou.Nor.Sou.Nor.Sou.Nor.

If the Sun’s place be taken from the Tables on pag. 114 and 115, his declination may be had thereby, near enough for common use, from this Table, by entering it with the signs at the head and degrees at the left hand; or with the signs at the foot and degrees at the right hand. Thus, March the 5th, the Sun’s place is ♓ 14° 53ʹ (call it 15°, being so near) to which answers 5° 55ʹ 11ʺ of the south declination.

Table XVIII. Lunations from 1 to 100000.

Lunat.Days.H.M.S.
1Contain 2912443
2591286
38814129
411825613
5147154016
617742419
720617822
823655225
9265183628
1029572031
2059014413
3088522134
4011815226
501476124237
6017712039
70206732340
802362104412
90265718443
100295312515
200590625030
300885941545
400118125410
500147657615
6001771883130
7002067195645
8002362411220
90026577124715
100029530141230
2000590614250
300088591183730
40001181228500
500014765223230
600017718313150
700020671432730
800023624417400
900026577575230
10000295305225
200005906112010
300008859171815
4000011812231620
5000014765291425
6000017718351230
7000020671411035
800002362447840
900002657753645
1000002953059450

By comparing this Table with the Table on page 113, it is easy to find how many Lunations are contained in any given number of Sidereal, Julian, and Solar years, from 1 to 8000.

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