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 terrae, does clear vanish; for in this Hypothesis there