From which Experiments, I think, we may safely conclude, that the Elater of the Air is reciprocal to its extension, or at least very neer. So that to apply it to our present purpose (which was indeed the chief cause of inventing these wayes of tryal) we will suppose a Cylinder indefinitely extended upwards, [I say a Cylinder, not a piece of a Cone, because, as I may elsewhere shew in the Explication of Gravity, that triplicate proportion of the shels of a Sphere, to their respective diameters, I suppose to be removed in this case by the decrease of the power of Gravity] and the pressure of the Air at the bottom of this Cylinder to be strong enough to keep up a Cylinder of Mercury of thirty inches: Now because by the most accurate tryals of the most illustrious and incomparable Mr. Boyle, published in his deservedly famous Pneumatick Book, the weight of Quicksilver, to that of the Air here below, is found neer about as fourteen thousand to one: If we suppose the parts of the Cylinder of the Atmosphere to be every where of an equal density, we shall (as he there deduces) find it extended to the height of thirty five thousand feet, or seven miles: But because by these Experiments we have somewhat confirm’d the hypothesis of the reciprocal proportion of the Elaters to the Extensions we shall find, that by supposing this Cylinder of the Atmosphere divided into a thousand parts, each of which being equivalent to thirty five feet, or seven geometrical paces, that is, each of these divisions containing as much Air as is suppos’d in a Cylinder neer the earth of equal diameter, and thirty five foot high, we shall find the lowermost to press against the surface of the Earth with the whole weight of the above mentioned thousand parts; the pressure of the bottom of the second against the top of the first to be 1000 − 1 = 999. of the third against the second to be 1000 − 2 = 998. of the fourth against the third to be 1000 − 3 = 997. of the uppermost against the 999. or that next below it, to be 1000 − 999 = 1. so that the extension of the lowermost next the Earth, will be to the extension of the next below the uppermost, as 1. to 999. for as the pressure sustained by the 999. is to the pressure sustain’d by the first, so is the extension of the first to the extension of the 999. so that, from this hypothetical calculation, we shall find the Air to be indefinitely extended: For if we suppose the whole thickness of the Air to be divided, as I just now instanced, into a thousand parts, and each of those under differing Dimensions, or Altitudes, to contain an equall quantity of Air, we shall find, that the first Cylinder, whose Base is supposed to lean on the Earth, will be found to be extended 35³⁵⁄₉₉₉ foot; the second equal Division, or Cylinder, whose basis is supposed to lean on the top of the first, shall have its top extended higher by 35⁷⁰⁄₉₉₈ the third 35¹⁰⁵⁄₉₉₇ the fourth 35¹⁴⁰⁄₉₉₆ and so onward, each equal quantity of Air having its dimensions measured by 35. and some additional number exprest alwayes in the manner of a fraction, whose numerator is alway the number of the place multipli’d by 35. and whose denominator is alwayes the pressure of the Atmosphere sustain’d by that part, so that by this means we may easily calculate the height of 999. divisions of those 1000. divisions, I suppos’d; whereas the uppermost may extend it self more then as high again, nay, perhaps indefinitely, or beyond the Moon; for the Elaters and Expansions being in reciprocal proportions, since we cannot yet find the plus ultra, beyond which the Air will not expand it self, we cannot determine the height of the Air: for since, as we have shewn, the proportion will be alway as the pressure sustain’d by any part is to 35. so 1000. to the expansion of that part; the multiplication or product therefore of the pressure, and expansion, that is, of the two extream proportionals, being alwayes equal to the product of the means, or 35000. it follows, since that Rectangle or Product may be made up of the multiplication of infinite diversities of numbers, that the height of the Air is also indefinite; for since (as far as I have yet been able to try) the Air seems capable of an indefinite Expansion, the pressure may be decreased in infinitum, and consequently its expansion upwards indefinite also.

There being therefore such a difference of density, and no Experiment yet known to prove a Saltus, or skipping from one degree of rarity to another much differing from it, that is, that an upper part of the Air should so much differ from that immediately subjacent to it, as to make a distinct superficies, such as we observe between the Air and Water, &c. But it being more likely, that there is a continual increase of rarity in the parts of the Air, the further they are removed from the surface of the Earth: It will hence necessarily follow, that (as in the Experiment of the salt and fresh Water) the ray of Light passing obliquely through the Air also, which is of very different density, will be continually, and infinitely inflected, or bended, from a streight, or direct motion.

This granted, the reason of all the above recited Phænomena, concerning the appearance of the Celestial Bodies, will very easily be deduced. As,

First, The redness of the Sun, Moon, and Stars, will be found to be caused by the inflection of the rays within the Atmosphere. That it is not really in or near the luminous bodies, will, I suppose, be very easily granted, seeing that this redness is observable in several places differing in Longitude, to be at the same time different, the setting and rising Sun of all parts being for the most part red:

And secondly, That it is not meerly the colour of the Air interpos’d, will, I suppose, without much more difficulty be yielded, seeing that we may observe a very great interstitium of Air betwixt the Object, and the Eye, makes it appear of a dead blew, far enough differing from a red, or yellow.

But thirdly, That it proceeds from the refraction, or inflection, of the rays by the Atmosphere, this following Experiment will, I suppose, sufficiently manifest.

[Schem. 37.]
Fig. 5.

Take a sphærical Crystalline Viol, such as is describ’d in the fifth Figure ABCD, and, having fill’d it with pure clear Water, expose it to the Sun beams; then taking a piece of very fine Venice Paper, apply it against that side of the Globe that is opposite to the Sun, as against the side BC, and you shall perceive a bright red Ring to appear, caus’d by the refraction of the Rays, AAAA, which is made by the Globe; in which Experiment, if the Glass and Water be very cleer, so that there be no Sands nor bubbles in the Glass, nor dirt in the Water, you shall not perceive any appearance of any other colour. To apply which Experiment, we may imagine the Atmosphere to be a great transparent Globe, which being of a substance more dense then the other, or (which comes to the same) that has its parts more dense towards the middle, the Sun beams that are tangents, or next within the tangents of this Globe, will be refracted or inflected from their direct passage towards the center of the Globe, whence, according to the laws of refractions made in a triangular Prism, and the generation of colour set down in the description of Muscovi-glass there must necessarily appear a red colour in the transitus or passage of those tangent Rays. To make this more plain, we will suppose (in the sixth Figure) ABCD, to represent the Globe of the Atmosphere, EFGH to represent the opacous Globe of the Earth, lying in the midst of it, neer to which, the parts of the Air, sustaining a very great pressure, are thereby very much condens’d, from whence those Rays that are by inflection made tangents to the Globe of the Earth, and those without them, that pass through the more condens’d part of the Atmosphere, as suppose between A and E, are by reason of the inequality of the medium, inflected towards the center, whereby there must necessarily be generated a red colour, as is more plainly shewn in the former cited place; hence whatsoever opacous bodies (as vapours, or the like) shall chance to be elevated into those parts, will reflect a red towards the eye; and therefore those evenings and mornings appear reddest, that have the most store of vapours and halituous substances exhaled to a convenient distance from the Earth; for thereby the inflection is made the greater, and thereby the colour also the more intense; and several of those exhalations being opacous, reflect several of those Rays, which, through an Homogeneous transparent medium would pass unseen; and therefore we see, that when there chances to be any clouds situated in those Regions they reflect a strong and vivid red. Now, though one great cause of the redness may be this inflection, yet I cannot wholly exclude the colour of the vapours themselves, which may have something of redness in them, they being partly nitrous; and partly fuliginous; both which steams tinge the Rays that pass through them, as is made evident by looking at bodies through the fumes of Aqua fortis or spirit of Nitre [as the newly mentioned Illustrious Person has demonstrated] and also through the smoak of a Fire or Chimney.

Having therefore made it probable at least, that the morning and evening redness may partly proceed from this inflection or refraction of the Rays, we shall next shew how the Oval Figure will be likewise easily deduced.

[Schem. 37.]
Fig. 6.