Cleon. That I may give you a good Idea of fuch Things, it is neceffary you fhould conceive it by a little eafy Inftrument of two circular Pieces of Pafteboard which I have here prepared, and contrived to fhew the Nature of the Thing. One of these Pieces AFMP is to reprefent the Plane of the Moon's Orbit.

Euphrof. Very good! and what is the other defign'd

for?

Cleon. The other Piece UFLP, reprefents the Plane in which the Sun, or the Earth's Shadow appears to move in at the Distance of the Moon. For in the Firmament, the Sun feems to go in the fame Tract very nearly with the Moon; and if the conical Shadow of the Earth were cut through, at the Distance of the Moon, that Section would appear a dark circular Space, and to move in the fame Tract with the Sun.

Euphrof. Well; and how then?

+

Cleon. Then the Edge of the circular Piece AFMP will represent the Orbit of the Moon, and that of the other Piece the Orbit of the Sun, or (in other Words) the Ecliptic, at the Distance of the Moon."

Euphrof. So far I apprehend you pretty well; pray, proceed.

Clean. In the laft Place, you must know, that the Plane of the Moon's Orbit does not lie exactly level with the Plane of the Ecliptic, but one Half below it, and the other above it, juft as you fee me put these two Pieces of Pafteboard together.

Euphrof. I fee your Meaning plain; the Half FAP lies below the Ecliptic, and the other Half FMP above it.

Cleon. Well, then the Distance between these Planes is called the Latitude of the Moon; that below the Ecliptic is the South Latitude, the other above it the North Latitude; because the Moon in defcribing the lower Part FAP is Southward of the Sun; but in the o.her Half FMP fhe is Northward of it,

Euphrof. I understand you fo far very well; pray

go on.

Cleon. Alfo the Points F and P, where the Planes cross each other, are called the Nodes; and F the Afcending Node, because there the Moon rifes above the Ecliptic,

3

Ecliptic, and is thus marked ; the other, P, is the Defcending Node, marked thus 8 And now having fufficiently explained the Inftrument, it will be very eafy to understand the Things you enquire farther of Eclipfes.

Euphrof. If fo, I fhall be very glad; and pray let me know when, or in what Part of the Moon's Orbit there may, and when there may not be an Eclipfe?

Cleon. I fhall fatisfy your Enquiry firft of Solar Eclipfes; and therefore from what I have already faid, you will eafily conceive, that a Spectator at the Earth, abc, will view the apparent Faces of the Sun and Moon very nearly equal at the Distance of the Moon; and confequently the Moon journeying round every Month in her Örbit AFMP, and the equal Solar Disk moving round the Ecliptic UFLP, which two Orbits interfect each other at F and P; it must happen that in the Courfe of a Year the Sun will be seen in the Nodes F and P, at two different, and almoft oppofite Seasons of the Year; and will be for fome Time fo near them on each Side, that when the Moon paffes that Part of her Orbit, she must neceffarily hide or cover either the Whole or Part of the Sun's Difk or Face, and fo produce an Eclipfe of the Sun, total or partial: For fince the Inclination or Distance between the two Orbits grows lefs and lefs from AU, where it is greateft, towards the Nodes where it is nothing; fo there must be a certain vifible Latitude or Distance as at C, B, which is juft equal to the Sum of half the Diameters of the Moon B, and Sun C; (because the greatest Latitude, AU or IM, far exceeds that Sum.) Again, fince the vifible Latitude BC is equal to the half Diameters of the Sun and Moon, the Moon in paffing along will just touch the lower or Southern Limb of the Sun, but cover no Part of his Surface: Confequently any new Moon before the Point B, as at d, will have fuch a Latitude from the Sun at e, as will exceed the Sum of their half Diameters, and fo will be seen to pafs at fome Distance below the Sun, and not touch it.-But if the new Moon appears nearer to the Node F, as at D, where her Latitude from the Sun at E is less than the faid Sum of the half Diameters of the Sun and Moon, then the Moon will be feen to pass over a Part of the

Sun's

Sun's Difk, and fo caufe a partial Eclipfe of the Sun where it is visible.

Once more; if the new Moon happens in the very Node itself, as at P, the Sun being there alfo, the Moon then having no Latitude muft neceffarily pafs over the whole Difk of the Sun, and fo produce a central and total Eclipfe of the Sun.

Laftly; New Moons on the other Side of the Node F, to the fame Distance GH, will produce Eclipfes, more or lefs, on the upper or northern Part of the Sun; but at H the Sum of the half Diameters and visible Latitude being again equal, the Luminaries will there but juft touch each other; and in all Parts farther from the Node, as at K, there will be no Eclipfe poffible; for the Moon will then pafs above the Difk of the Sun.

Euphrof. It is ali very evident; and therefore I prefume the Points B and H in the Moon's Orbit are what you call the ecliptic Boundaries, or Limits of Solar Eclipfes.

Cleon. Yes, they are fo; and now with Respect to Lunar Eclipfes, we must turn our Eye to the oppofite Parts of the Orbits on each Side the Node P, where we fhall view the Full-Moon in her Orbit, and the Section of the Earth's Shadow at the Distance of the Moon's Orbit in the Points O, P, Q, S.

Now, in the firit Place, let us confider that if the Full-Moon happens at N or R, where the Earth's Shadow paffing by, juft touches it, then in any Point between N and R, the faid Shadow will more or lefs involve the Moon, and fo caufe a Lunar Eclipfe in a greater or lefler Degree; and therefore those two Points, N and R, in the Lunar Orbit, where the Sum of the half Diameters of the Moon and Earth's Shadow is equal to the true Latitude of the Moon, are the Boundaries or Limits of Lunar Eclipfes, on each Side the Node P.

Again, in the fecond Place; the nearer the Moon is to the Node P, the greater will be the Eclipfe, and therefore greatest of all, and central, in the Node itself, where the Shadow of the Earth is near three Times greater than the Moon, as I formerly told you.

Euphrof. The Manner of explaining the Boundaries of a Lunar Eclipfe I fee is the fame nearly as that of the

Solar

Solar ones, and as easily understood. But unless I could tell which were greateft, the Sum of the half Diameters of the Sun and Moon, or of the Shadow and Moon, I can't tell which would be greatest, the Limits of a Solar or Lunar Eclipfe.

Cleon. Though the latter Sum be in itself greater than the former, yet the former, with Refpect to the visible Latitude of the Moon, is greater than the latter, in Regard of her true Latitude; and therefore the Limits of a Solar Eclipfe exceed thofe of a Lunar one.

Euphrof. I fhould be glad to know in what Time the Sun moves over the ecliptic Limit CG.

Cleon. Thefe Limits are fomewhat variable; but when CG is leaft, the Sun takes up about 28 Days in paffing over it, and 32 Days when greatest.

Euphrof. And pray what is the Time between one new Moon and another?

Cleon. Twenty-nine Days and an half.

Euphrof. Why then, when the Limit CG is greateft, there must neceffarily be an Eclipfe of the Sun during his Stay within that Limit; but when it is leaft, I perceive it is poffible there may be no Eclipfe of the Sun that Node.

Cleon. 'Tis indeed poffible there may not; but the Chance there will not is fo very great, that it was never known to happen, I believe. On the other Hand, when the Limit is leaft there is one Eclipfe very certain, and there may be two when greateft; and this fometimes happens, as in the Year 1736, 1743, &c. But these twin Eclipfes are very fmall, and almoft always to us invisible.

Euphrof. Of all this I conceive the Reafon pretty well; and now for the other Node: Pray how long is the Shadow of the Earth within the Lunar Limit OQ?

Cleon. This Limit is alfo variable; and when greateft, the Shadow paffeth it in 24 Days; and when least, in 19 Days.

Euphrof. Then fince from Full Moon to Full Moon there is 29 Days and an half, if the Full Moon fhould happen in the Beginning of the Limit, as at N, before the Moon could again return to the fame Node, the Shadow would be past the other Limit Q; and fo there

would

would be no Eclipfe of the Moon, in fuch a Cafe, at that Node, even when the Limit is the greatest of all.

Cleon. Very well obferved, Euphrofyne; nor can there ever be two Lunar Eclipfes together at the fame Node, when the Limit is greateft; fo that upon the whole you fee there can be but one Eclipfe of the Moon within the Lunar Limits, and fometimes none at all.

Euphrof. Then I fee 'tis poffible, that in fome Years there may be no Lunar Eclipfe at all.

Clean. Yes, it is; and thus it happened in the Years 1734, 1738, 1745, 1752, and in the prefent Year 1756, and will again happen in 1763; for in thefe Years there was no Eclipfe of the Moon; and but two of the Sun, and both invifible to us, except that of Auguft the 3d, 1738.

Euphrof. We find by Experience that the Solar and Lunar Eclipfes happen both at the fame Times of the Year, which is alfo evident from the Inftrument.

Cleon. It is fo; for the new Moon, which obfcures the Sun in the Solar Limit, is itself eclipfed by the Shadow of the Earth at the Lunar Limit, when it is next at Full.

Euphrof. I understand you very well; and I farther obferve, that as the Nodes F and P are in oppofite Points of the Orbit, fo after half a Year, the Nodes will change their Nature, and that which is now the Solar Node will then become the Lunar; and the Lunar Node that now is, will then become the Solar Node, and will be the Season of Eclipfes again.

Cleon. It will not be quite half a Year between, because the Sun, for Inftance, may be eclipfed at the End of one Limit, as at G, (as in the Year 1732, December 6) and at the Beginning of the other at O, (as May 2, 1733) in which Time there intervened not above 147 Days, which is fhort of half a Year by 35 Days. Yea, the Sun may leave one Limit, and arrive to the next in about four Months and an half, as in the Year 1740 the Sun was eclipfed Jan. 17, and again in June 12; and another Reason for this is, that the Nodes F and P are not fixed, but move in a retrograde Manner, fo as that the diftant Node is carried towards the Sun, and they meet near ten Days fooner than if the Node were fixed.