PG15491.B01073
Now, that there is such a difference of the upper and under parts of the Air is clear enough evinc’d from the late improvement of the _Torricellian_ Experiment, which has been tryed at the tops and feet of Mountains; and may be further illustrated, and inquired into, by a means, which some whiles since I thought of, and us’d, for the finding by what degrees the Air passes from such a degree of Density to such a degree of Rarity. And another, for the finding what pressure was requisite to make it pass from such a degree of Rarefaction to a determinate Density: Which Experiments, because they may be useful to illustrate the present Inquiry, I shall briefly describe.

PG15491.B01074
[16] I took then a small Glass-pipe AB, about the bigness of a Swans quill, and about four foot long, which was very equally drawn, so that, as far as I could perceive, no one part was bigger then another: This Tube (being open at both ends) I fitted into another small Tube DE, that had a small bore just big enough to contain the small Pipe, and this was seal’d up at one, and open at the other, end; about which open end I fastned a small wooden box C with cement, so that filling the bigger Tube, and part of the box, with Quicksilver, I could thrust the smaller Tube into it, till it were all covered with the Quicksilver: Having thus done, I fastned my bigger Tube against the side of a wall, that it might stand the steadier, and plunging the small Tube cleer under the _Mercury_ in the box, I stopt the upper end of it very fast with cement, then lifting up the small Tube, I drew it up by a small pully, and a string that I had fastned to the top of the Room, and found the height of the _Mercurial Cylinder_ to be about twenty nine inches.

PG15491.B01075
Then letting down the Tube again, I opened the top, and then thrust down the small Tube, till I perceived the Quicksilver to rise within it to a mark that I had plac’d just an inch from the top; and immediately clapping on a small piece of cement that I had kept warm, I with a hot Iron seal’d up the top very fast, then letting it cool (that both the cement might grow hard, and more especially, that the Air might come to its temper, natural for the Day I try’d the Experiment in) I observ’d diligently, and found the included Air to be exactly an Inch.

PG15491.B01076
Here you are to take notice, that after the Air is seal’d up, the top of the Tube is not to be elevated above the superficies of the Quicksilver in the box, till the surface of that within the Tube be equal to it, for the Quicksilver (as I have elsewhere prov’d) being more heterogeneous to the Glass then the Air, will not naturally rise up so high within the small Pipe, as the superficies of the _Mercury_ in the box, and therefore you are to observe, how much below the outward superficies of the _Mercury_ in the box, that of the same in the Tube does stand, when the top being open, free ingress is admitted to the outward Air.

PG15491.B01077
Having thus done, I permitted the _Cylinder_, or small Pipe, to rise out of the box, till I found the surface of the Quicksilver in the Pipe to be two inches above that in the box, and found the Air to have expanded it self but one sixteenth part of an inch; then drawing up the small pipe, till I found the height of the Quicksilver within to be four inches above that without, I observed the Air to be expanded only ⅐ of an inch more then it was at first, and to take up the room of 1⅐ inch: then I raised the Tube till the Cylinder was six inches high, and found the Air to take up 1²⁄₉ inches of room in the Pipe; then to 8, 10, 12. &c. the expansion of the Air that I found to each of which Cylinders are set down in the following Table; where the first row signifies the height of the _Mercurial Cylinder_; the next, the expansion of the Air; the third, the pressure of the _Atmosphere_, or the highest _Cylinder_ of _Mercury_, which was then neer thirty inches: The last signifies the force of the Air so expanded, which is found by substracting the first row of numbers out of the third; for having found, that the outward Air would then keep up the Quicksilver to thirty inches, look whatever of that height is wanting must be attributed to the Elater of the Air depressing. And therefore having the Expansion in the second row, and the height of the subjacent _Cylinder_ of _Mercury_ in the first, and the greatest height of the _Cylinder_ of _Mercury_, which of it self counterballances the whole pressure of the _Atmosphere_; by substracting the numbers of the first row out of the numbers of the third, you will have the measure of the _Cylinders_ so deprest, and consequently the force of the Air, in the several Expansions, registred.

PG15491.B01078
The height of the The Expansion The height of The strength Cylinder of Mercury, of the Air. the Mercury of the Elater that, together with that counter- of the expanded the Elater of the ballanc’d the Air. included Air, Atmosphere. ballanced the pressure of the Atmosphere. ---------- ---------- ---------- ---------- 00 01 30 30 02 01¹⁄₁₆ 30 28 04 01⅐ 30 26 06 01²⁄₉ 30 24 08 01⅓ 30 22 10 01½ 30 20 12 01⅔ 30 18 14 01⅚ 30 16 16 02²⁄₂₇ 30 14 18 02⁴⁄₉ 30 12 20 03 30 10 22 03⁷⁄₉ 30 8 24 05⁷⁄₁₈ 30 6 25 06⅔ 30 5 26 08½ 30 4 26¼ 09½ 30 3¾ 26½ 10¾ 30 3½ 26¾ 13 30 3¼ 27 15½ 30 3

PG15491.B01079
I had several other Tables of my Observations, and Calculations, which I then made; but it being above a twelve month since I made them; and by that means having forgot many circumstances and particulars, I was resolved to make them over once again, which I did _August_ the second 1661. with the very same Tube which I used the year before, when I first made the Experiment (for it being a very good one, I had carefully preserv’d it:) And after having tryed it over and over again; and being not well satisfied of some particulars, I, at last, having put all things in very good order, and being as attentive, and observant, as possibly I could, of every circumstance requisite to be taken notice of, did register my several Observations in this following Table. In the making of which, I did not exactly follow the method that I had used at first; but, having lately heard of Mr. _Townly_’s _Hypothesis_, I shap’d my course in such sort, as would be most convenient for the examination of that _Hypothesis_; the event of which you have in the latter part of the last Table.

PG15491.B01080
The other Experiment was, to find what degrees of force were requisite to compress, or condense, the Air into such or such a bulk.

PG15491.B01081
The manner of proceeding therein was this: I took a Tube about five foot long, one of whose ends was sealed up, and bended in the form of a _Syphon_, much like that represented in the fourth Figure of the 37. _Scheme_, one side whereof AD, that was open at A, was about fifty inches long, the other side BC, shut at B, was not much above seven inches long, then placing it exactly perpendicular, I pour’d in a little Quicksilver, and found that the Air BC was 6⅞ inches, or very near to seven; then pouring in Quicksilver at the longer Tube, I continued filling of it till the Air in the shorter part of it was contracted into half the former dimensions, and found the height exactly nine and twenty inches; and by making several other tryals, in several other degrees of condensation of the Air, I found them exactly answer the former _Hypothesis_.

PG15491.B01082
But having (by reason it was a good while since I first made) forgotten many particulars, and being much unsatisfied in others, I made the Experiment over again, and, from the several tryals, collected the former part of the following Table: Where in the row next the left hand 24. signifies the dimensions of the Air, sustaining only the pressure of the _Atmosphere_, which at that time was equal to a _Cylinder_ of _Mercury_ of nine and twenty inches: The next Figure above it (20) was the dimensions of the Air induring the first compression, made by a _Cylinder_ of _Mercury_ 5³⁄₁₆ high, to which the pressure of the _Atmosphere_ nine and twenty inches being added, the elastick strength of the Air so comprest will be found 34³⁄₁₆, &c.

PG15491.B01083
_A Table of the Elastick power of the Air, both Experimentally and Hypothetically calculated, according to its various Dimensions._

PG15491.B01084
The dimensions The height The Mercurial The sum or What they of the included of the Cylinder difference ought to Air. Mercurial added, or of these be according Cylinder taken from two to the counter- the former. Cylinders. Hypothesis. pois’d by the Atmosphere. ---------- ---------- ---------- ---------- ---------- 12 29 + 29 = 58 58 13 29 + 24¹¹⁄₁₆ = 53¹¹⁄₁₆ 53⁷⁄₁₃ 14 29 + 20³⁄₁₆ = 49³⁄₁₆ 49⁵⁄₇ 16 29 + 14 = 43 43½ 18 29 + 9⅛ = 38⅛ 38⅔ 20 29 + 5³⁄₁₆ = 34³⁄₁₆ 34⅘ 24 29 0 = 29 29 48 29 − 14⅝ = 14⅜ 14½ 96 29 − 22⅛ = 6⅞ 7²⁄₈ 192 29 − 25⅝ = 3⅜ 3⅝ 384 29 − 27²⁄₈ = 1⁶⁄₈ 1⁷⁄₁₆ 576 29 − 27⅞ = 1⅛ 1⁵⁄₂₄ 768 29 − 28⅛ = 0⅞ 0[7¼]⁄₈ 960 29 − 28⅜ = 0⅝ 0[5⅘]⁄₈ 1152 29 − 28⁷⁄₁₆ = 0⁹⁄₁₆ 0¹⁰⁄₁₆

PG15491.B01085
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.

PG15491.B01086
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.

PG15491.B01087
This granted, the reason of all the above recited _Phænomena_, concerning the appearance of the Celestial Bodies, will very easily be deduced. As,

PG15491.B01088
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:

PG15491.B01089
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.

PG15491.B01090
But thirdly, That it proceeds from the refraction, or inflection, of the rays by the _Atmosphere_, this following Experiment will, I suppose, sufficiently manifest.

PG15491.B01091
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.

PG15491.B01092
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.

PG15491.B01093
Suppose we therefore, EFGH in the sixth _Figure_ of the 37. _Scheme_, to represent the Earth; ABCD, the _Atmosphere_; EI, and EL, two Rays coming from the Sun, the one from the upper, the other from the neather Limb, these Rays, being by the _Atmosphere_ inflected, appear to the eye at E, as if they had come from the points, N and O; and because the Ray L has a greater inclination upon the inequality of the _Atmosphere_ then I, therefore must it suffer a greater inflection, and consequently be further elevated above its true place, then the Ray I, which has a less inclination, will be elevated above its true place; whence it will follow, that the lower side appearing neerer the upper then really it is, and the two _lateral_ sides, _viz._ the right and left side, suffering no sensible alteration from the inflection, at least what it does suffer, does rather increase the visible Diameter then diminish it, as I shall shew by and by, the Figure of the luminous body must necessarily appear somewhat _Elliptical_.

PG15491.B01094
This will be more plain, if in the seventh _Figure_ of the 37. _Scheme_ we suppose AB to represent the sensible Horizon; CDEF, the body of the Sun really below it; GHIK, the same appearing above it, elevated by the inflection of the _Atmosphere_: For if, according to the best observation, we make the visible Diameter of the Sun to be about three or four and thirty minutes, and the Horizontal refraction according to _Ticho_ be thereabout, or somewhat more, the lower limb of the Sun E, will be elevated to I; but because, by his account, the point C will be elevated but 29. minutes, as having not so great an inclination upon the inequality of the Air, therefore IG, which will be the apparent refracted perpendicular Diameter of the Sun, will be less then CG, which is but 29. minutes, and consequently six or seven minutes shorter then the unrefracted apparent Diameter. The parts, D and F, will be likewise elevated to H and K, whose refraction, by reason of its inclination, will be bigger then that of the point C, though less then that of E; therefore will the semidiameter IL, be shorter then LG, and consequently the under side of the appearing Sun more flat then the upper.

PG15491.B01095
Now, because the Rays from the right and left sides of the Sun, &c. have been observ’d by _Ricciolo_ and _Grimaldus_, to appear more distant one from another then really they are, though (by very many Observations that I have made for that purpose, with a very good _Telescope_, fitted with a divided Ruler) I could never perceive any great alteration, yet there being really some, it will not be amiss, to shew that this also proceeds from the refraction or inflection of the _Atmosphere_; and this will be manifest, if we consider the _Atmosphere_ as a transparent Globe, or at least a transparent shell, encompassing an opacous Globe, which, being more dense then the _medium_ encompassing it, refracts or inflects all the entring parallel Rays into a point or focus, so that wheresoever the Observator is plac’d within the _Atmosphere_, between the focus and the luminous body, the _lateral_ Rays must necessarily be more converg’d towards his eye by the refraction or inflection, then they would have been without it; and therefore the Horizontal Diameter of the luminous body must necessarily be augmented.

PG15491.B01096
This might be more plainly manifest to the eye by the sixth _Figure_; but because it would be somwhat tedious, and the thing being obvious enough to be imagin’d by any one that attentively considers it, I shall rather omit it, and proceed to shew, that the mass of Air neer the surface of the Earth, consists, or is made up, of parcels, which do very much differ from one another in point of density and rarity; and consequently the Rays of light that pass through them will be variously inflected, here one way, and there another, according as they pass so or so through those differing parts; and those parts being always in motion, either upwards or downwards, or to the right or left, or in some way compounded of these, they do by this their motion inflect the Rays, now this way, and presently that way.

PG15491.B01097
This irregular, unequal and unconstant inflection of the Rays of light, is the reason why the limb of the _Sun_, _Moon_, _Jupiter_, _Saturn_, _Mars_, and _Venus_, appear to wave or dance; and why the body of the Starrs appear to tremulate or twinkle, their bodies, by this means, being sometimes magnify’d, and sometimes diminished; sometimes elevated, otherwhiles depress’d; now thrown to the right hand, and then to the left.

PG15491.B01098
And that there is such a property or unequal distribution of parts, is manifest from the various degrees of heat and cold that are found in the Air; from whence will follow a differing density and rarity, both as to quantity and refraction; and likewise from the vapours that are interpos’d, (which, by the way, I imagine, as to refraction or inflection, to do the same thing, as if they were rarify’d Air; and that those vapours that ascend, are both lighter, and less dense, then the ambient Air which boys them up; and that those which descend, are heavier and more dense) The first of these may be found true, if you take a good thick piece of Glass, and heating it pretty hot in the fire, lay it upon such another piece of Glass, or hang it in the open Air by a piece of Wire, then looking upon some far distant Object (such as a Steeple or Tree) so as the Rays from that Object pass directly over the Glass before they enter your eye, you shall find such a tremulation and wavering of the remote Object, as will very much offend your eye: The like tremulous motion you may observe to be caus’d by the ascending steams of Water, and the like. Now, from the first of these it is manifest, that from the rarifaction of the parts of the Air, by heat, there is caus’d a differing refraction, and from the ascension of the more rarify’d parts of the Air, which are thrust up by the colder, and therefore more condens’d and heavie, is caus’d an undulation or wavering of the Object; for I think, that there are very few will grant, that Glass, by as gentle a heat as may be endur’d by ones hand, should send forth any of its parts in steams or vapours, which does not seem to be much wasted by that violent fire of the green Glass-house; but, if yet it be doubted, let Experiment be further made with that body that is accounted, by Chymists and others, the most ponderous and fix’d in the world; for by heating of a piece of Gold, and proceeding in the same manner, you may find the same effects.

PG15491.B01099
This trembling and shaking of the Rays, is more sensibly caus’d by an actual flame, or quick fire, or anything else heated glowing hot; as by a Candle, live Coal, red-hot Iron, or a piece of Silver, and the like: the same also appears very conspicuous, if you look at an Object betwixt which and your eye, the rising smoak of some Chimney is interpos’d; which brings into my mind what I had once the opportunity to observe, which was, the Sun rising to my eye just over a Chimney that sent forth a copious steam of smoak; and taking a short _Telescope_, which I had then by me, I observ’d the body of the Sun, though it was but just peep’d above the Horizon, to have its underside, not onely flatted, and press’d inward, as it usually is when neer the Earth; but to appear more protuberant downwards then if it had suffered no refraction at all; and besides all this, the whole body of the Sun appear’d to tremble or dance, and the edges or limb to be very ragged or indented, undulating or waving, much in the manner of a flag in the Wind.
