Micrographia - or some physiological descriptions of minute bodies made by magnifying glasses with observations and inquiries thereupon/Chapter 58
Observ. LVIII. Of a new Property in the Air, and several other transparent Mediums nam'd Inflection, whereby very many considerable Phænomena are attempted to be solv'd, and divers other uses are hinted.
SInce the Invention (and perfecting in some measure) of Telescopes, it has been observ'd by several, that the Sun and Moon neer the Horizon, are disfigur'd (losing that exactly-smooth terminating circular limb, which they are observ'd to have when situated neerer the Zenith) and are bounded with an edge every way (especially upon the right and left sides) ragged and indented like a Saw: which inequality of their limbs, I have further observ'd, not to remain always the same, but to be continually chang'd by a kind of fluctuating motion, not unlike that of the waves of the Sea, so as that part of the limb, which was but even now nick'd or indented in, is now protuberant, and will presently be sinking again; neither is this all but the whole body of the Luminaries, do in the Telescope, seem to be depress'd and slatted, the upper, and more especially the under side appearing neerer to the middle then really they are, and the right and left appearing more remote: whence the whole Area seems to be terminated by a kind of Oval. It is further observ'd, that the body, for the most part, appears red, or of some colour approaching neer unto it, as some kind of yellow; and this I have always mark'd, that the more the limb is slatted or ovalled, the more red does the body appear, though not always the contrary. It is further observable, that both fix'd Stars and Planets, the neerer they appear to the Horizon, the more red and dull they look, and the more they are observ'd to twinkle; in so much, that I have seen the Dog-starr to vibrate so strong and bright a radiation of light, as almost to dazle my eyes, and presently, almost to disappear. It is also observable, that those bright scintillations neer the Horizon, are not by much so quick and sudden in their consecutions of one another, as the nimbler twinklings of Stars neerer the Zenith. This is also notable, that the Starrs neer the Horizon, are twinkled with several colours; so as sometimes to appear red, sometimes more yellow, and sometimes blue, and this when the Starr is a pretty way elevated above the Horizon. I have further, very often seen some of the small Starrs of the fifth or sixth magnitude, at certain times to disappear for a small moment of time, and again appear more conspicuous, and with a greater luster. I have several times, with my naked eye, seen many smaller Starrs, such as may be call'd of the seventh or eighth magnitude to appear for a short space, and then vanish, which, by directing a small Telescope towards that part they appear'd and disappear'd in; I could presently find to be indeed small Starrs so situate, as I had seen them with my naked eye, and to appear twinkling like the ordinary visible Stars; nay, in examining some very notable parts of the Heaven, with a three foot Tube, me thought I now and then, in several parts of the constellation, could perceive little twinklings of Starrs, making a very short kind of apparition, and presently vanishing, but noting diligently the places where they thus seem'd to play at boe-peep, I made use of a very good twelve foot Tube, and with that it was not uneasie to see those, and several other degrees of smaller Starrs, and some smaller yet, that seem'd again to appear and disappear, and these also by giving the same Object-glass a much bigger aperture, I could plainly and constantly see appear in their former places; so that I have observ'd some twelve several magnitudes of Starrs less then those of the six magnitudes commonly recounted in the Globes.
It has been observ'd and confirm'd by the accuratest Observations of the best of our modern Astronomers, that all the Luminous bodies appear above the Horizon, when they really are below it. So that the Sun and Moon have both been seen above the Horizon, whil'st the Moon has been in an Eclipse. I shall not here instance in the great refractions, that the tops of high mountains, seen at a distance, have been found to have; all which seem to argue the Horizontal refraction, much greater then it is hitherto generally believ'd.
I have further taken notice, that not onely the Sun, Moon and Starrs, and high tops of mountains have suffer'd these kinds of refraction, but Trees, and several bright Objects on the ground: I have often taken notice of the twinkling of the reflections of the Sun from a Glass-window at a good distance, and of a Candle in the night, but that is not so conspicuous, and in observing the setting Sun, I have often taken notice of the tremulation of the Trees and Bushes, as well as of the edges of the Sun. Divers of these Phænomena have been taken notice of by several, who have given several reasons of them, but I have not yet met with any altogether satisfactory, though some of their conjectures have been partly true, but partly also false. Setting my self therfore upon the inquiry of these Phænomena, I first endeavour'd to be very diligent in taking notice of the several particulars and circumstances observable in them; and next, in making divers particular Experiments, that might cleer some doubts, and serve to determine, confirm, and illustrate the true and adæquate cause of each; and upon the whole, I find much reason to think, that the true cause of all these Phænomena is from the inflection, or multiplicate refraction of those Rays of light within the body of the Atmosphere, and that it does not proceed from a refraction caus'd by any terminating superficies of the Air above, nor from any such exactly defin'd superficies within the body of the Atmosphere.
This Conclusion is grounded upon these two Propositions:
First, that a medium, whose parts are unequally dense, and mov'd by various motions and transpositions as to one another, will produce all these visible effects upon the Rays of light, without any other coefficient cause.
Secondly, that there is in the Air or Atmosphere such a variety in the constituent parts of it, both as to their density and rarity, and as to their divers mutations and positions one to another.
By Density and Rarity, I understand a property of a transparent body, that does either more or less refract a Ray of light (coming obliquely upon its superficies out of a third medium) toward its perpendicular: As I call Glass a more dense body then Water, and Water a more rare body then Glass, because of the refractions (more or less deflecting towards the perpendicular) that are made in them, of a Ray of light out of the Air that has the same inclination upon either of their superficies.
So as to the business of Refraction, spirit of Wine is a more dense body then Water, it having been found by an accurate Instrument that measures the angles of Refractions to Minutes that for the same refracted angle of 30°.00'. in both those Mediums, the angle of incidence in Water was but 41°.35'. but the angle of the incidence in the trial with spirit of Wine was 42°.45'. But as to gravity, Water is a more dense body then spirit of Wine, for the proportion of the same Water, to the same very well rectify'd spirit of Wine was, as 21. to 19.
So as to Refraction, Water is more Dense then Ice; for I have found by a most certain Experiment, which I exhibited before divers illustrious Persons of the Royal Society, that the Refraction of Water was greater then that of Ice, though some considerable Authors have affirm'd the contrary, and though the Ice be a very hard, and the Water a very fluid body.
That the former of the two preceding Propositions is true, may be manifested by several Experiments; As first, if you take any two liquors differing from one another in density, but yet such as will readily mix: as Salt Water, or Brine, & Fresh; almost any kind of Salt dissolv'd in Water, and filtrated, so that it be cleer, spirit of Wine and Water; nay, spirit of Wine, and spirit of Wine, one more highly rectify'd then the other, and very many other liquors; if (I say) you take any two of these liquors, and mixing them in a Glass Viol, against one side of which you have fix'd or glued a small round piece of Paper, and shaking them well together (so that the parts of them may be somewhat disturb'd and move up and down) you endeavour to see that round piece of Paper through the body of the liquors, you shall plainly perceive the Figure to wave, and to be indented much after the same manner as the limb of the Sun through a Telescope seems to be, save onely that the mutations here, are much quicker. And if, in steed of this bigger Circle, you take a very small spot, and fasten and view it as the former, you will find it to appear much like the twinkling of the Starrs, though much quicker: which two Phænomena, (for I shall take notice of no more at present, though I could instance in multitudes of others) must necessarily be caus'd by an inflection of the Rays within the terminating superficies of the compounded medium, since the surfaces of the transparent body through which the Rays pass to the eye, are not at all altered or chang'd.
This inflection (if I may so call it) I imagine to be nothing else, but a multiplicate refraction, caused by the unequal density of the constituent parts of the medium, whereby the motion, action or progress of the Ray of light is hindred from proceeding in a streight line, and inflected or deflected by a curve. Now, that it is a curve line is manifest by this Experiment: I took a Box, such as A D G E, in the first Figure of the 37. Scheme, whose sides A B C D, and E F G H, were made of two smooth flat plates of Glass, then filling it half full with a very strong solution of Salt, I filled the other half with very fair fresh water, then exposing the opacous side, D H G C, to the Sun, I observ'd both the refraction and inflection of the Sun beams, I D & K H, and marking as exactly as I could, the points, P, N, O, M, by which the Ray, K H, passed through the compounded medium, I found them to be in a curve line; for the parts of the medium being continually more dense the neerer they were to the bottom, the Ray p f was continually more and more deflected downwards from the streight line.
This Inflection may be mechanically explained, either by Monsieur
Schem. XXXVII. Des Cartes principles by conceiving the Globuls of the third Element to find less and less resistance against that side of them which is downwards, or by a way, which I have further explicated in the Inquisition about Colours, to be from an obliquation of the pulse of light, whence the under[errata 1] part is continually promoted, and consequently refracted towards the perpendicular, which cuts the Orbs at right angles. What the particular Figure of the Curve line, describ'd by this way of light, is, I shall not now stand to examine, especially since there may be so many sorts of it as there may be varieties of the Positions of the intermediat degrees of density and rarity between the bottom and the top of the inflecting Medium.
I could produce many more Examples and Experiments, to illustrate and prove this first Proposition, viz. that there is such a constitution of some bodies as will cause inflection. As not to mention those I have observ'd in Horn, Tortoise-Shell, transparent Gums, and resinous Substances: The veins of Glass, nay, of melted Crystal, found, and much complained of by Glass-grinders, and others, might sufficiently demonstrate the truth of it to any diligent Observator.
But that, I presume, I have by this Example given proof sufficient (viz. ocular demonstration) to evince, that there is such a modulation, or bending of the rayes of light, as I have call'd inflection, differing both from reflection, and refraction (since they are both made in the superficies, this only in the middle); and likewise, that this is able or sufficient to produce the effects I have ascribed to it.
It remains therefore to shew, that there is such a property in the Air, and that it is sufficient to produce all the above mentioned Phænomena, and therefore may be the principal, if not the only cause of them.
First, That there is such a property, may be proved from this, that the parts of the Air are some of them more condens'd, others more rarified, either by the differing heat, or differing pressure it sustains, or by the somewhat heterogeneous vapours interspers'd through it. For as the Air is more or less rarified, so does it more or less refract a ray of light (that comes out of a denser medium) from the perpendicular. This you may find true, if you make tryal of this Experiment.
Take a small Glass-bubble, made in the form of that in the second Figure of the 37. Scheme, and by heating the Glass very hot, and thereby very much rarifying the included Air, or, which is better, by rarifying a small quantity of water, included in it, into vapours, which will expel the most part, if not all the Air, and then sealing up the small neck of it, and letting it cool, you may find, if you place it in a convenient Instrument, that there will be a manifest difference, as to the refraction.
As if in this second Figure you suppose A to represent a small sight or hole, through which the eye looks upon an object, as C, through the Glass-bubble B, and the second sight L; all which remain exactly fixt in their several places, the object C being so cized and placed, that it may just seem to touch the upper and under edge of the hole L: and so all of it be seen through the small Glass-ball of rarified Air; then by breaking off the small seal'd neck of the Bubble (without at all stirring the sights, object, or glass) and admitting the external Air, you will find your self unable to see the utmost ends of the object; but the terminating rayes A E and A D (which were before refracted to G and F by the rarified Air) will proceed almost directly to I and H; which alteration of the rayes (seeing there is no other alteration made in the Organ by which the Experiment is tryed, save only the admission, or exclusion of the condens'd Air) must necessarily be caused by the variation of the medium contain'd in the Glass B; the greatest difficulty in the making of which Experiment, is from the uneven surfaces of the bubble, which will represent an uneven image of the object.
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.
Fig. 1.I took then a small Glass-pipe A B, 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 D E, 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.
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.
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.
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 1 of an inch more then it was at first, and to take up the room of 1 1 inch: then I raised the Tube till the Cylinder was six inches high, and found the Air to take up 12 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.
|The height of the Cylinder of Mercury, that, together with the Elater of the included Air, ballanced the pressure of the Atmosphere.||The Expansion of the Air||The height of the Mercury that counter-ballanc'd the Atmosphere.||The strength of the Elater of the expanded Air.|
The other Experiment was, to find what degrees of force were requisite to compress, or condense, the Air into such or such a bulk.
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 A D, that was open at A, was about fifty inches long, the other side B C, 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 67 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.
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 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, &c.
A Table of the Elastick power of the Air, both Experimentally and Hypothetically calculated, according to its various Dimensions.
|The dimensions of the included Air.||The height of the Mercurial Cylinder counterpois'd by the Atmosphere.||The Mercurial Cylinder taken from added, or taken from the former.||The sum or difference of these two Cylinders.||What they ought to be according to the Hypothesis.|
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 35 35 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 35 70 the third 35 105 the fourth 35 140 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.
Take a sphærical Crystalline Viol, such as is describ'd in the fifth Figure A B C D, 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 B C, and you shall perceive a bright red Ring to appear, caus'd by the refraction of the Rays, A A A A, 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) A B C D, to represent the Globe of the Atmosphere, E F G H 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.
Suppose we therefore, E F G H in the sixth Figure of the 37. Scheme, to represent the Earth; A B C D, the Atmosphere; E I, and E L, 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 atmospheree 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.
This will be more plain, if in the seventh Figure of the 37. Scheme we suppose A B to represent the sensible Horizon; C D E F, the body of the Sun really below it; G H I K, 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 I G, which will be the apparent refracted perpendicular Diameter of the Sun, will be less then C G, 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 I L, be shorter then L G, and consequently the under side of the appearing Sun more flat then the upper.
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.
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.
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.
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.
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.
This I have likewise often observ'd in a hot Sunshiny Summer's day, that looking on an Object over a hot stone, or dry hot earth, I have found the Object to be undulated or shaken, much after the same manner. And if you look upon any remote Object through a Telescope (in a hot Summer's day especially) you shall find it likewise to appear tremulous. And further, if there chance to blow any wind, or that the air between you and the Object be in a motion or current, whereby the parts of it, both rarify'd and condens'd, are swiftly remov'd towards the right or left, if then you observe the Horizontal ridge of a Hill far distant, through a very good Telescope, you shall find it to wave much like the Sea, and those waves will appear to pass the same way with the wind.
From which, and many other Experiments, 'tis cleer that the lower Region of the Air, especially that part of it which lieth neerest to the Earth, has, for the most part, its constituent parcels variously agitated, either by heat or winds, by the first of which, some of them are made more rare, and so suffer a less refraction; others are interwoven, either with ascending or descending vapours; the former of which being more light, and so more rarify'd, have likewise a less refraction; the latter being more heavie, and consequently more dense, have a greater.
Now, because that heat and cold are equally diffus'd every way; and that the further it is spread, the weaker it grows; hence it will follow, that the most part of the under Region of the Air will be made up of several kinds of lentes, some whereof will have the properties of Convex, others of Concave glasses, which, that I may the more intelligibly make out, we will suppose in the eighth Figure of the 37. Scheme, that A represents an ascending vapour, which, by reason of its being somewhat Heterogeneous to the ambient Air, is thereby thrust into a kind of Globular form, not any where terminated, but gradually finished, that is, it is most rarify'd in the middle about A. somewhat more condens'd about B B, more then that about C C; yet further, about D D, almost of the same density with the ambient Air about E E; and lastly, inclosed with the more dense Air F F, so that from A, to F F, there is a continual increase of density. The reason of which will be manifest, if we consider the rising vapour to be much warmer then the ambient heavie Air; for by the coldness of the ambient Air, the shell E E will be more refrigerated then D D, and that then C C, which will be yet more then B B, and that more then A; so that from F to A, there is a continual increase of heat, and consequently of rarity; from whence it will necessarily follow, that the Rays of light will be inflected or refracted in it, in the same manner as they would be in a Concave-glase; for the Rays G K I, G K I will be inflected by G K H, G K H, which will easily follow from what I before explained concerning the inflection of the Atmosphere.
On the other side, a descending vapour, or any part of the air included by an ascending vapour, will exhibit the same effects with a Convex lens; for, if we suppose, in the former Figure, the quite contrary constitution to that last describ'd; that is, the ambient Air F F being hotter then any part of that matter within any circle, therefore the coldest part must necessarily be A, as being farthest remov'd from the heat, all the intermediate spaces will be gradually discriminated by the continuall mixture of heat and cold, so that it will be hotter at E E, then DD, in D D then C C, in C C then B B, and in B B then A. From which, a like refraction and condensation will follow, and consequently a lesser or greater refraction, so that every included part will refract more then the including, by which means the Rays, G K I, G K I, coming from a Starr, or some remote Object, are so inflected, that they will again concurr and meet, in the point M. By the interposition therefore of this desending vapour the visible body of the Star, or other Object, is very much augmented, as by the former it was diminished.
From the quick consecutions of these two, one after another, between the Object and your eye, caused by their motion upwards or downwards, proceeding from their levity or gravity, or to the right or left, proceeding from the wind, a Starr may appear, now bigger, now less, then really it would otherwise without them; and this is that property of a Starr, which is commonly call'd twinkling, or scintillation.
The reason why a Star will now appear of one colour, now of another, which for the most part happens when 'tis neer the Horizon, may very easily be deduc'd from its appearing now in the middle of the vapour, other whiles neer the edge; for if you look against the body of a Starr with a Telescope that has a pretty deep Convex Eye-glass, and so order it, that the Star may appear sometimes in one place, and sometimes in another of it; you may perceive this or that particular colour to be predominant in the apparent Figure of the Starr, according as it is more or less remote from the middle of the Lens. This I had here further explain'd, but that it does more properly belong to another place.
I shall therefore onely add some few Quæries, which the consideration of these particulars hinted, and so finish this Section.
And the first I shall propound is, Whether there may not be made an artificial transparent body of an exact Globular Figure that shall so inflect or refract all the Rays, that, coming from one point, fall upon any Hemisphere of it; that every one of them may meet on the opposite side, and cross one another exactly in a point; and that it may do the like also with all the Rays that, coming from a lateral point, fall upon any other Hemisphere; for if so, there were to be hoped a perfection of Dioptricks, and a transmigration into heaven, even whil'st we remain here upon earth in the flesh, and a descending or penetrating into the center and innermost recesses of the earth, and all earthly bodies; nay, it would open not onely a cranney, but a large window (as I may so speak) into the Shop of Nature, whereby we might be enabled to see both the tools and operators, and the very manner of the operation it self of Nature; this, could it be effected, would as farr surpass all other kind of perspectives as the vast extent of Heaven does the small point of the Earth, which distance it would immediately remove, and unite them, as 'twere, into one, at least, that there should appear no more distance between them then the length of the Tube, into the ends of which these Glasses should be inserted: Now, whether this may not be effected with parcels of Glass of several densities, I have sometimes proceeded so farr as to doubt (though in truth, as to the general, I have wholly despair'd of it) for I have often observ'd in Optical Glasses a very great variety of the parts, which are commonly called Veins; nay, some of them round enough (for they are for the most part, drawn out into firings) to constitute a kind of lens.
This I should further proceed to hope[errata 2], had any one been so inquisitive as to have found out the way of making any transparent body, either more dense or more rare, for then it might be possible to compose a Globule that should be more dense in the middle of it, then in any other part, and to compose the whole bulk, so as that there should be a continual gradual transition from one degree of density to another; such as should be found requisite for the desired inflection of the transmigrating Rays; but of this enough at present, because I may say more of it when I set down my own Trials concerning the melioration of Dioptricks, where I shall enumerate with how many several substances I have made both Microscopes, and Telescopes, and by what and how many, ways: Let such as have leisure and opportunity farther consider it.
The next Quæry shall be, whether by the same collection of a more dense body then the other, or at least, of the denser part of the other, there might not be imagin'd a reason of the apparition of some new fix'd Stars, as those in the Swan, Cassiope's Charr, Serpentarius, Piscis, Cetus, &c.
Thirdly, Whether it be possible to define the height of the Atmosphere from this inflection of the Rays, or from the Quicksilver Experiment of the rarifaction or extension of the Air.
Fourthly, Whether the disparity between the upper and under Air be not sometimes so great, as to make a reflecting superficies; I have had several Observations which seem to have proceeded from some such cause, but it would be too long to relate and examine them. An Experiment, also somewhat analogous to this, I have made with Salt-water and Fresh, which two liquors, in most Positions, seem'd the same, and not to be separated by any determinate superficies, which separating surface yet in some other Positions did plainly appear.
And if so, Whether the reason of the equal bounding or terminus of the under parts of the clouds may not proceed from this cause; whether, secondly, the Reason of the apparition of many Suns may not be found out, by considering how the Rays of the Sun may so be reflected, as to describe a pretty true Image of the body, as we find them from any regular Superficies. Whether also this may not be found to cause the apparition of some of those Parelii, of counterfeit Suns, which appear coloured, by refracting the Rays so, as to make the body of the Sun appear in quite another place then really it is. But of this more elsewhere.
5. Whether the Phænomena of the Clouds may not be made out by this diversity of density in the upper and under parts of the Air, by supposing the Air above them to be much lighter then they themselves are, and they themselves to be yet lighter then that which is subjacent to them, many of them seeming to be the same substance with the Cobwebs that fly in the Air after a Fog.
Now that such a constitution of the Air and Clouds, if such there be, may be sufficient to perform this effect, may be confirm'd by this Experiment. Make as strong a Solution of Salt as you are able, then filling a Glass of some depth half full with it, fill the other half with fresh Water, and poyse a little Glass-bubble, so as that it may sink pretty quick in fresh Water, which take and put into the aforesaid Glass, and you shall find it to sink till it comes towards the middle, where it will remain fixt, without moving either upwards or downwards. And by a second Experiment, of poising such a bubble in water, whose upper part is warmer, and consequently lighter, then the under, which is colder and heavier; the manner of which follows in this next Quæry, which is,
6. Whether the rarifaction and condensation of Water be not made after the same manner, as those effects are produc'd in the Air by heat; for I once pois'd a seal'd up Glass-bubble so exactly, that never so small an addition would make it sink, and as small a detraction make it swim, which suffering to rest in that Vessel of Water for some time, I alwayes found it about noon to be at the bottom of the Water, and at night, and in the morning, at the top: Imagining this to proceed from the Rarifaction of the Water, caus'd by the heat, I made tryal, and found most true; for I was able at any time, either to depress, or raise it, by heat and cold; for if I let the Pipe stand for some time in cold water, I could easily raise the Bubble from the bottom, whither I had a little afore detruded it, by putting the same Pipe into warm Water. And this way I have been able, for a very considerable time, to keep a Bubble so poys'd in the Water, as that it should remain in the middle, and neither sink, nor swim: For gently heating the upper part of the Pipe with a Candle, Coal, or hot Iron, till I perceived the Bubble begin to descend, then forbearing, I have observed it to descend to such or such a station, and there to remain suspended for some hours, till the heat by degrees were quite vanished, when it would again ascend to its former place. This I have also often observed naturally performed by the heat of the Air, which being able to rarifie the upper parts of the Water sooner then the lower, by reason of its immediate contact, the heat of the Air has sometimes so slowly increased, that I have observed the Bubble to be some hours in passing between the top and bottom.
7. Whether the appearance of the Pike of Tenerif, and several other high Mountains, at so much greater a distance then seems to agree with their respective heights, be not to be attributed to the Curvature of the visual Ray, that is made by its passing obliquely through so differingly Dense a Medium from the top to the eye very far distant in the Horizon: For since we have already, I hope, made it very probable, that there is such an inflection of the Rays by the differing density of the parts of the Air; and since I have found, by several Experiments made on places comparatively not very high, and have yet found the pressure sustain'd by those parts of the Air at the top and bottom, and also their differing Expansions very considerable: Insomuch that I have found the pressure of the Atmosphere lighter at the top of St. Paul's Steeple in London (which is about two hundred foot high) then at the bottom by a sixtieth or fiftieth part, and the expansion at the top greater then that at the bottom by neer about so much also; for the Mercurial Cylinder at the bottom was about 39. inches, and at the top half an inch lower; the Air also included in the Weather-glass, that at the bottom fill'd only 155. spaces, at the top fill'd 158. though the heat at the top and bottom was found exactly the same with a scal'd Thermometer: I think it very rational to suppose, that the greatest Curvature of the Rays is made nearest the Earth, and that the inflection of the Rays, above 3. or 4. miles upwards, is very inconsiderable, and therefore that by this means such calculations of the height of Mountains, as are made from the distance they are visible in the Horizon, from the supposal that that Ray is a straight Line (that from the top of the Mountain is, as 'twere, a Tangent to the Horizon whence it is seen) which really is a Curve, is very erroneous. Whence, I suppose, proceeds the reason of the exceedingly differing Opinions and Assertions of several Authors, about the height of several very high Hills.
8. Whether this Inflection of the Air will not very much alter the supposed distances of the Planets, which seem to have a very great dependence upon the Hypothetical refraction or inflection of the Air, and that refraction upon the hypothetical height and density of the Air: For since (as I hope) I have here shewn the Air to be quite otherwise then has been hitherto suppos'd, by manifesting it to be, both of a vast, at least an uncertain, height, and of an unconstant and irregular density; It must necessarily follow, that its inflection must be varied accordingly: And therefore we may hence learn, upon what sure grounds all the Astronomers hitherto have built, who have calculated the distance of the Planets from their Horizontal Parallax; for since the Refraction and Parallax are so nearly ally'd, that the one cannot be known without the other, especially by any wayes that have been yet attempted, how uncertain must the Parallax be, when the Refraction is unknown? And how easie is it for Astronomers to assign what distance they please to the Planets, and defend them, when they have such a curious subterfuge as that of Refraction, wherein a very little variation will allow them liberty enough to place the Celestial Bodies at what distance they please. If therefore we would come to any certainty in this point, we must go other wayes to work; and as I have here examined the height and refractive property of the Air by other wayes then are usual, so must we find the Parallax of the Planets by wayes not yet practiced; and to this end, I cannot imagine any better way, then the Observations of them by two persons at very far distant parts of the Earth, that lye as neer as may be under the same Meridian, or Degree of longitude, but differing as much in latitude, as there can be places conveniently found: These two persons, at certain appointed times, should (as near as could be) both at the same time, observe the way of the Moon, Mars, Venus, Jupiter, and Saturn, amongst the fixt Stars, with a good large Telescope, and making little Iconismes, or pictures, of the small fixed Stars, that appear to each of them to lye in or near the way of the Center of the Planet, and the exact measure of the apparent Diameter; from the comparing of such Observations together, we might certainly know the true distance, or Parallax, of the Planet. And having any one true Parallax of these Planets, we might very easily have the other by their apparent Diameters, which the Telescope likewise affords us very accurately. And thence their motions might be much better known, and their Theories more exactly regulated. And for this purpose I know not any one place more convenient for such an Observation to be made in, then in the Island of St. Helena, upon the Coast of Africk, which lyes about sixteen degrees to the Southwards of the Line, and is very near, according to the latest Geographical Maps, in the same Meridian with London; for though they may not perhaps lye exactly in the same, yet their Observations, being ordered according to what I shall anon shew, it will not be difficult to find the true distance of the Planet. But were they both under the same Meridian, it would be much better.
And because Observations may be much easier, and more accurately made with good Telescopes, then with any other Instruments, it will not, I suppose, seem impertinent to explain a little what wayes I judge most fit and convenient for that particular. Such therefore as shall be the Observators for this purpose, should be furnished with the best Telescopes that can be had, the longer the better and more exact will their Observations be, though they are somewhat the more difficultly manag'd. These should be fitted with a Rete, or divided Scale, plac'd at such a distance within the Eye-glass, that they may be distinctly seen, which should be the measures of minutes and seconds; by this Instrument each Observator should, at certain prefixt times, observe the Moon, or other Planet, in, or very near, the Meridian; and because it may be very difficult to find two convenient stations that will happen to be just under the same Meridian, they shall, each of them, observe the way of the Planet, both for an hour before, and an hour after, it arrive at the Meridian; and by a line, or stroke, amongst the small fixed Stars, they shall denote out the way that each of them observ'd the Center of the Planet to be mov'd in for those two hours: These Observations each of them shall repeat for many dayes together, that both it may happen, that both of them may sometimes make their Observations together, and that from divers Experiments we may be the better assured of what certainty and exactness such kind of Observations are like to prove. And because many of the Stars which may happen to come within the compass of such an Iconism, or Map, may be such as are only visible through a good Telescope, whose Positions perhaps have not been noted, nor their longitudes, or latitudes, any where remarked; therefore each Observator should indeavour to insert some fixt Star, whose longitude, and latitude, is known; or with his Telescope he shall find the Position of some notable telescopical Star, inserted in his Map, to some known fixt Star, whose place in the Zodiack is well defin’d.
Having by this means found the true distance of the Moon, and having observed well the apparent Diameter of it at that time with a good Telescope, it is easie enough, by one single Observation of the apparent Diameter of the Moon with a good Glass, to determine her distances in any other part of her Orbit, or Dragon, and consequently, some few Observations will tell us, whether she be mov’d in an Ellipsis, (which, by the way, may also be found, even now, though I think we are yet ignorant of her true distance) and next (which without such Observations, I think, we shall not be sure of) we may know exactly the bigness of that Ellipsis, or Circle, and her true velocity in each part, and thereby be much the better inabled to find out the true cause of all her Motions. And though, even now also, we may, by such Observations in one station, as here at London, observe the apparent Diameter and motion of the Moon in her Dragon, and consequently be inabled to make a better ghess at the Species or kind of Curve, in which she is mov’d, that is whether it be sphærical, or elliptical, or neither, and with what proportional velocities she is carried in that Curve; yet till her true Parallax be known, we cannot determine either.
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 Semi-diameters 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[errata 3] 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 preferr’d 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 ot 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 consequently there can be no shadows, such as appear in the ninth Figure of the 37. Scheme, where let A B C D represent the Earth, and E F G H the Atmosphere, which according to Keplers supposition, is like a Sphære of Water terminated with an exact surface E F G H, let the lines M F, L B, I D, K H, represent the Rays of the Sun; ’tis manifest, that all the Rayes between L B, and I D, will be reflected by the surface of the Earth B A D, and consequently, the conical space B O D would be dark and obscure; but, say the followers of Kepler, the Rays between M F, and L B, and between I D, and K H, falling on the Atmosphere, are refracted, both at their ingress and egress out of the Atmosphere, nearer towards the Axis of the spærical shadow C O, 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 F P H, 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 1 2, and 3 4.
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 F Y Z Q, H X V T, and O R P S, 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 Moon[errata 4] 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 E S Q, and G S R, to be the Rays that terminate the shadow from either side of the Earth; E S Q coming from the upper limb of the Sun, and G S R from the under; it will follow, that the shadow of the Earth, within those Rays, that is, the Cone G S E, 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 E P G, which will be caus'd by the earth's hindring part of the Rays of the Sun from falling on the parts G P R, and E P Q of which halved shadow, or Penumbra, that part will appear brightest which lyes nearest the terminating Rayes G P, and E P, and those darker that lye nearest to G S, and E S: 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 R Q and S; and when she is alike light through the whole Eclypse, she must pass between R Q, and P.