Part 21

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.

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: 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 5-1/3 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.

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: 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 5-1/3 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.

[Sidenote: 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_.

[Sidenote: 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, 19-1/3 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 19-1/3 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.

[Sidenote: 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 2-1/2 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 2-1/2 minutes of declination from the Ecliptic in the Moon’s Orbit, is equal to 150 such miles, or 2-1/2 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.

[Sidenote: 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.

[Sidenote: 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].

[Sidenote: 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.

[Sidenote: THUCYDIDES’s Eclipse.]