Chapter 36

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 strings) to constitute a kind of _lens_.

This I should further proceed to hope, 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 Semidiameters 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 uncertain, witness their Deductions from it, who have made use of it; for _Vendeline_ puts that difference to be but 4′.30″. whence he deduces a vast distance of the Sun, as I have before shewn. _Ricciolo_ makes it full 30′.00. but _Reinoldus_, and _Kircher_, no less then three degrees. And no wonder, for if we examine the _Theory_, we shall find it so complicated with uncertainties.

First, From the irregular surface of the Moon, and from several Parallaxes, that unless the _Dichotomy_ happen in the _Nonagesimus_ of the _Ecliptick_, and that in the Meridian, &c. all which happen so very seldom, that it is almost impossible to make them otherwise then uncertainly. Besides, we are not yet certain, but that there may be somewhat about the Moon _analogus_ to the Air about the Earth, which may cause a refraction of the light of the Sun, and consequently make a great difference in the apparent _dichotomy_ of the Moon. Their way indeed is very rational and ingenious; and such as is much to be preferred before the way by the Horizontal Parallax, could all the uncertainties be remov’d, and were the true distance of the Moon known.

But because we find by the Experiments of _Vendiline_, _Reinoldus_, &c. that Observations of this kind are very uncertain also: It were to be wisht, that such kind of Observations, made at two very distant stations, were promoted. And it is so much the more desirable, because, from what I have now shewn of the nature of the Air, it is evident, that the refraction may be very much greater then all the Astronomers hitherto have imagined it: And consequently, that the distance of the Moon, and other Planets, may be much lesse then what they have hitherto made it.

For first, this Inflection, I have here propounded, will allow the shadow of the Earth to be much shorter then it can be made by the other _Hypothesis_ of refraction, and consequently, the Moon will not suffer an Eclipse, unless it comes very much nearer the Earth then the Astronomers hitherto have supposed it.

Secondly, There will not in this _Hypothesis_ be any other shadow of the Earth, such as _Kepler_ supposes, and calls the _Penumbra_, which is the shadow of the refracting _Atmosphere_; for the bending of the Rays being altogether caus’d by _Inflection_, as I have already shewn, all that part which is ascribed by _Kepler_, and others after him, to the _Penumbra_, or dark part, which is without the _umbra 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 ABCD represent the Earth, and EFGH the _Atmosphere_, which according to _Keplers_ supposition, is like a Sphære of Water terminated with an exact surface EFGH, let the lines MF, LB, ID, KH, represent the Rays of the Sun; ’tis manifest, that all the Rayes between LB, and ID, will be reflected by the surface of the Earth BAD, and consequently, the conical space BOD would be dark and obscure; but, say the followers of _Kepler_, the Rays between MF, and LB, and between ID, and KH, falling on the _Atmosphere_, are refracted, both at their ingress and egress out of the _Atmosphere_, nearer towards the Axis of the sphærical shadow CO, and consequently, inlighten a great part of that former dark Cone, and shorten, and contract, its top to N. And because of this Reflection of these Rays, say they, there is superinduc’d another shell of a dark Cone FPH, whose Apex P is yet further distant from the Earth: By this _Penumbra_, say they, the Moon is Eclipsed, for it alwayes passes between the lines 12, and 34.

To which I say, That if the Air be such, as I have newly shewn it to be, and consequently cause such an inflection of the Rays that fall into it, those dark _Penumbra’s_ FYZQ, HXVT, and ORPS, will all vanish. For if we suppose the Air indefinitely extended, and to be no where bounded with a determinate refracting surface, as I have shewn it uncapable of having, from the nature of it; it will follow, that the Moon will no where be totally obscured, but when it is below the Apex N, of the dark blunt Cone of the Earth’s shadow: Now, from the supposition, that the Sun is distant about seven thousand Diameters, the point N, according to calculation, being not above twenty five terrestrial Semidiameters from the Center of the Earth: It follows, that whensoever the Moon eclipsed is totally darkned, without affording any kind of light, it must be within twenty five Semidiameters of the Earth, and consequently much lower then any Astronomers have hitherto put it.

This will seem much more consonant to the rest of the secundary Planets; for the highest of _Jupiter’s_ Moons is between twenty and thirty _Jovial Semidiameters_ distant from the Center of _Jupiter_; and the Moons of _Saturn_ much about the same number of _Saturnial Semidiameters_ from the Center of that Planet.

But these are but conjectures also, and must be determin’d by such kind of Observations as I have newly mention’d.

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 ESQ, and GSR, to be the Rays that terminate the shadow from either side of the Earth; ESQ coming from the upper limb of the Sun, and GSR from the under; it will follow, that the shadow of the Earth, within those Rays, that is, the Cone GSE, 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 EPG, which will be caus’d by the earth’s hindring part of the Rays of the Sun from falling on the parts GPR, and EPQ, of which halved shadow, or _Penumbra_, that part will appear brightest which lyes nearest the terminating Rayes GP, and EP, and those darker that lye nearest to GS, and ES: 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 RQ and S; and when she is alike light through the whole Eclipse, she must pass between RQ, and P.

* * * * *

Observ. LIX. _Of multitudes of small _Stars_ discoverable by the _Telescope_._