is no refracting surface of the Air, and 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 Sphaere 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 sphaerical 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.