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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

“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].

“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.

“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.

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.

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.

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 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.