Next, for the true distance of the Sun, the best way will be, by accurate Observations, made in both these forementioned stations, of some convenient Eclipse of the Sun, many of which may so happen, as to be seen by both; for the Penumbra of the Moon may, if she be sixty Semidiameters distant from the Earth, and the Sun above seven thousand, extend to about seventy degrees on the Earth, and consequently be seen by Observators as far distant as London, and St. Helena, which are not full sixty nine degrees distant. And this would much more accurately, then any way that has been yet used, determine the Parallax, and distance, of the Sun; for as for the Horizontal Parallax I have already shewn it sufficiently uncertain; nor is the way of finding it by the Eclipse of the Moon any other then hypothetical; and that by the difference of the true and apparent quadrature of the Moon is not less uncertain, witness their Deductions from it, who have made use of it; for Vendeline puts that difference to be but 4′.30″. whence he deduces a vast distance of the Sun, as I have before shewn. Ricciolo makes it full 30′.00. but Reinoldus, and Kircher, no less then three degrees. And no wonder, for if we examine the Theory, we shall find it so complicated with uncertainties.

First, From the irregular surface of the Moon, and from several Parallaxes, that unless the Dichotomy happen in the Nonagesimus of the Ecliptick, and that in the Meridian, &c. all which happen so very seldom, that it is almost impossible to make them otherwise then uncertainly. Besides, we are not yet certain, but that there may be somewhat about the Moon analogus to the Air about the Earth, which may cause a refraction of the light of the Sun, and consequently make a great difference in the apparent dichotomy of the Moon. Their way indeed is very rational and ingenious; and such as is much to be preferred before the way by the Horizontal Parallax, could all the uncertainties be remov’d, and were the true distance of the Moon known.

But because we find by the Experiments of Vendiline, Reinoldus, &c. that Observations of this kind are very uncertain also: It were to be wisht, that such kind of Observations, made at two very distant stations, were promoted. And it is so much the more desirable, because, from what I have now shewn of the nature of the Air, it is evident, that the refraction may be very much greater then all the Astronomers hitherto have imagined it: And consequently, that the distance of the Moon, and other Planets, may be much lesse then what they have hitherto made it.

For first, this Inflection, I have here propounded, will allow the shadow of the Earth to be much shorter then it can be made by the other Hypothesis of refraction, and consequently, the Moon will not suffer an Eclipse, unless it comes very much nearer the Earth then the Astronomers hitherto have supposed it.

Secondly, There will not in this Hypothesis be any other shadow of the Earth, such as Kepler supposes, and calls the Penumbra, which is the shadow of the refracting Atmosphere; for the bending of the Rays being altogether caus’d by Inflection, as I have already shewn, all that part which is ascribed by Kepler, and others after him, to the Penumbra, or dark part, which is without the umbra terræ, does clear vanish; for in this Hypothesis there is no refracting surface of the Air, and [Schem. 37.]
Fig. 9. consequently there can be no shadows, such as appear in the ninth Figure of the 37. Scheme, where let ABCD represent the Earth, and EFGH the Atmosphere, which according to Keplers supposition, is like a Sphære of Water terminated with an exact surface EFGH, let the lines MF, LB, ID, KH, represent the Rays of the Sun; ’tis manifest, that all the Rayes between LB, and ID, will be reflected by the surface of the Earth BAD, and consequently, the conical space BOD would be dark and obscure; but, say the followers of Kepler, the Rays between MF, and LB, and between ID, and KH, falling on the Atmosphere, are refracted, both at their ingress and egress out of the Atmosphere, nearer towards the Axis of the sphærical shadow CO, and consequently, inlighten a great part of that former dark Cone, and shorten, and contract, its top to N. And because of this Reflection of these Rays, say they, there is superinduc’d another shell of a dark Cone FPH, whose Apex P is yet further distant from the Earth: By this Penumbra, say they, the Moon is Eclipsed, for it alwayes passes between the lines 12, and 34.

To which I say, That if the Air be such, as I have newly shewn it to be, and consequently cause such an inflection of the Rays that fall into it, those dark Penumbra’s FYZQ, HXVT, and ORPS, will all vanish. For if we suppose the Air indefinitely extended, and to be no where bounded with a determinate refracting surface, as I have shewn it uncapable of having, from the nature of it; it will follow, that the Moon will no where be totally obscured, but when it is below the Apex N, of the dark blunt Cone of the Earth’s shadow: Now, from the supposition, that the Sun is distant about seven thousand Diameters, the point N, according to calculation, being not above twenty five terrestrial Semidiameters from the Center of the Earth: It follows, that whensoever the Moon eclipsed is totally darkned, without affording any kind of light, it must be within twenty five Semidiameters of the Earth, and consequently much lower then any Astronomers have hitherto put it.

This will seem much more consonant to the rest of the secundary Planets; for the highest of Jupiter’s Moons is between twenty and thirty Jovial Semidiameters distant from the Center of Jupiter; and the Moons of Saturn much about the same number of Saturnial Semidiameters from the Center of that Planet.

But these are but conjectures also, and must be determin’d by such kind of Observations as I have newly mention’d.

Nor will it be difficult, by this Hypothesis, to salve all the appearances of Eclipses of the Moon, for in this Hypothesis also, there will be on each side of the shadow of the Earth, a Penumbra, not caus’d by the Refraction of the Air, as in the Hypothesis of Kepler; but by the faint inlightning of it by the Sun: For if, in the sixth Figure, we suppose ESQ, and GSR, to be the Rays that terminate the shadow from either side of the Earth; ESQ coming from the upper limb of the Sun, and GSR from the under; it will follow, that the shadow of the Earth, within those Rays, that is, the Cone GSE, will be totally dark. But the Sun being not a point, but a large area of light, there will be a secondary dark Cone of shadow EPG, which will be caus’d by the earth’s hindring part of the Rays of the Sun from falling on the parts GPR, and EPQ, of which halved shadow, or Penumbra, that part will appear brightest which lyes nearest the terminating Rayes GP, and EP, and those darker that lye nearest to GS, and ES: when therefore the Moon appears quite dark in the middle of the Eclipse, she must be below S, that is, between S and F; when she appears lighter near the middle of the Eclipse, she must pass some where between RQ and S; and when she is alike light through the whole Eclipse, she must pass between RQ, and P.