PG33504.B00506
And hence we may understand that Bodies are much more rare and porous than is commonly believed. Water is nineteen times lighter, and by consequence nineteen times rarer than Gold; and Gold is so rare as very readily and without the least opposition to transmit the magnetick Effluvia, and easily to admit Quicksilver into its Pores, and to let Water pass through it. For a concave Sphere of Gold filled with Water, and solder'd up, has, upon pressing the Sphere with great force, let the Water squeeze through it, and stand all over its outside in multitudes of small Drops, like Dew, without bursting or cracking the Body of the Gold, as I have been inform'd by an Eye witness. From all which we may conclude, that Gold has more Pores than solid parts, and by consequence that Water has above forty times more Pores than Parts. And he that shall find out an Hypothesis, by which Water may be so rare, and yet not be capable of compression by force, may doubtless by the same Hypothesis make Gold, and Water, and all other Bodies, as much rarer as he pleases; so that Light may find a ready passage through transparent Substances.

PG33504.B00507
The Magnet acts upon Iron through all dense Bodies not magnetick nor red hot, without any diminution of its Virtue; as for instance, through Gold, Silver, Lead, Glass, Water. The gravitating Power of the Sun is transmitted through the vast Bodies of the Planets without any diminution, so as to act upon all their parts to their very centers with the same Force and according to the same Laws, as if the part upon which it acts were not surrounded with the Body of the Planet, The Rays of Light, whether they be very small Bodies projected, or only Motion or Force propagated, are moved in right Lines; and whenever a Ray of Light is by any Obstacle turned out of its rectilinear way, it will never return into the same rectilinear way, unless perhaps by very great accident. And yet Light is transmitted through pellucid solid Bodies in right Lines to very great distances. How Bodies can have a sufficient quantity of Pores for producing these Effects is very difficult to conceive, but perhaps not altogether impossible. For the Colours of Bodies arise from the Magnitudes of the Particles which reflect them, as was explained above. Now if we conceive these Particles of Bodies to be so disposed amongst themselves, that the Intervals or empty Spaces between them may be equal in magnitude to them all; and that these Particles may be composed of other Particles much smaller, which have as much empty Space between them as equals all the Magnitudes of these smaller Particles: And that in like manner these smaller Particles are again composed of others much smaller, all which together are equal to all the Pores or empty Spaces between them; and so on perpetually till you come to solid Particles, such as have no Pores or empty Spaces within them: And if in any gross Body there be, for instance, three such degrees of Particles, the least of which are solid; this Body will have seven times more Pores than solid Parts. But if there be four such degrees of Particles, the least of which are solid, the Body will have fifteen times more Pores than solid Parts. If there be five degrees, the Body will have one and thirty times more Pores than solid Parts. If six degrees, the Body will have sixty and three times more Pores than solid Parts. And so on perpetually. And there are other ways of conceiving how Bodies may be exceeding porous. But what is really their inward Frame is not yet known to us.

PG33504.B00508
PROP. IX.

PG33504.B00509
_Bodies reflect and refract Light by one and the same power, variously exercised in various Circumstances._

PG33504.B00510
This appears by several Considerations. First, Because when Light goes out of Glass into Air, as obliquely as it can possibly do. If its Incidence be made still more oblique, it becomes totally reflected. For the power of the Glass after it has refracted the Light as obliquely as is possible, if the Incidence be still made more oblique, becomes too strong to let any of its Rays go through, and by consequence causes total Reflexions. Secondly, Because Light is alternately reflected and transmitted by thin Plates of Glass for many Successions, accordingly as the thickness of the Plate increases in an arithmetical Progression. For here the thickness of the Glass determines whether that Power by which Glass acts upon Light shall cause it to be reflected, or suffer it to be transmitted. And, Thirdly, because those Surfaces of transparent Bodies which have the greatest refracting power, reflect the greatest quantity of Light, as was shewn in the first Proposition.

PG33504.B00511
PROP. X.

PG33504.B00512
_If Light be swifter in Bodies than in Vacuo, in the proportion of the Sines which measure the Refraction of the Bodies, the Forces of the Bodies to reflect and refract Light, are very nearly proportional to the densities of the same Bodies; excepting that unctuous and sulphureous Bodies refract more than others of this same density._

PG33504.B00513
[Illustration: FIG. 8.]

PG33504.B00514
Let AB represent the refracting plane Surface of any Body, and IC a Ray incident very obliquely upon the Body in C, so that the Angle ACI may be infinitely little, and let CR be the refracted Ray. From a given Point B perpendicular to the refracting Surface erect BR meeting with the refracting Ray CR in R, and if CR represent the Motion of the refracted Ray, and this Motion be distinguish'd into two Motions CB and BR, whereof CB is parallel to the refracting Plane, and BR perpendicular to it: CB shall represent the Motion of the incident Ray, and BR the Motion generated by the Refraction, as Opticians have of late explain'd.

PG33504.B00515
Now if any Body or Thing, in moving through any Space of a given breadth terminated on both sides by two parallel Planes, be urged forward in all parts of that Space by Forces tending directly forwards towards the last Plane, and before its Incidence on the first Plane, had no Motion towards it, or but an infinitely little one; and if the Forces in all parts of that Space, between the Planes, be at equal distances from the Planes equal to one another, but at several distances be bigger or less in any given Proportion, the Motion generated by the Forces in the whole passage of the Body or thing through that Space shall be in a subduplicate Proportion of the Forces, as Mathematicians will easily understand. And therefore, if the Space of activity of the refracting Superficies of the Body be consider'd as such a Space, the Motion of the Ray generated by the refracting Force of the Body, during its passage through that Space, that is, the Motion BR, must be in subduplicate Proportion of that refracting Force. I say therefore, that the Square of the Line BR, and by consequence the refracting Force of the Body, is very nearly as the density of the same Body. For this will appear by the following Table, wherein the Proportion of the Sines which measure the Refractions of several Bodies, the Square of BR, supposing CB an unite, the Densities of the Bodies estimated by their Specifick Gravities, and their Refractive Power in respect of their Densities are set down in several Columns.

PG33504.B00516
---------------------+----------------+----------------+----------+----------- | | | | | | The Square | The | The | | of BR, to | density | refractive | The Proportion | which the | and | Power of | of the Sines of| refracting | specifick| the Body | Incidence and | force of the | gravity | in respect The refracting | Refraction of | Body is | of the | of its Bodies. | yellow Light. | proportionate. | Body. | density. ---------------------+----------------+----------------+----------+----------- A Pseudo-Topazius, | | | | being a natural, | | | | pellucid, brittle, | 23 to 14 | 1'699 | 4'27 | 3979 hairy Stone, of a | | | | yellow Colour. | | | | Air. | 3201 to 3200 | 0'000625 | 0'0012 | 5208 Glass of Antimony. | 17 to 9 | 2'568 | 5'28 | 4864 A Selenitis. | 61 to 41 | 1'213 | 2'252 | 5386 Glass vulgar. | 31 to 20 | 1'4025 | 2'58 | 5436 Crystal of the Rock. | 25 to 16 | 1'445 | 2'65 | 5450 Island Crystal. | 5 to 3 | 1'778 | 2'72 | 6536 Sal Gemmae. | 17 to 11 | 1'388 | 2'143 | 6477 Alume. | 35 to 24 | 1'1267 | 1'714 | 6570 Borax. | 22 to 15 | 1'1511 | 1'714 | 6716 Niter. | 32 to 21 | 1'345 | 1'9 | 7079 Dantzick Vitriol. | 303 to 200 | 1'295 | 1'715 | 7551 Oil of Vitriol. | 10 to 7 | 1'041 | 1'7 | 6124 Rain Water. | 529 to 396 | 0'7845 | 1' | 7845 Gum Arabick. | 31 to 21 | 1'179 | 1'375 | 8574 Spirit of Wine well | | | | rectified. | 100 to 73 | 0'8765 | 0'866 | 10121 Camphire. | 3 to 2 | 1'25 | 0'996 | 12551 Oil Olive. | 22 to 15 | 1'1511 | 0'913 | 12607 Linseed Oil. | 40 to 27 | 1'1948 | 0'932 | 12819 Spirit of Turpentine.| 25 to 17 | 1'1626 | 0'874 | 13222 Amber. | 14 to 9 | 1'42 | 1'04 | 13654 A Diamond. | 100 to 41 | 4'949 | 3'4 | 14556 ---------------------+----------------+----------------+----------+-----------

PG33504.B00517
The Refraction of the Air in this Table is determin'd by that of the Atmosphere observed by Astronomers. For, if Light pass through many refracting Substances or Mediums gradually denser and denser, and terminated with parallel Surfaces, the Sum of all the Refractions will be equal to the single Refraction which it would have suffer'd in passing immediately out of the first Medium into the last. And this holds true, though the Number of the refracting Substances be increased to Infinity, and the Distances from one another as much decreased, so that the Light may be refracted in every Point of its Passage, and by continual Refractions bent into a Curve-Line. And therefore the whole Refraction of Light in passing through the Atmosphere from the highest and rarest Part thereof down to the lowest and densest Part, must be equal to the Refraction which it would suffer in passing at like Obliquity out of a Vacuum immediately into Air of equal Density with that in the lowest Part of the Atmosphere.

PG33504.B00518
Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal, Vulgar Glass (that is, Sand melted together) and Glass of Antimony, which are terrestrial stony alcalizate Concretes, and Air which probably arises from such Substances by Fermentation, be Substances very differing from one another in Density, yet by this Table, they have their refractive Powers almost in the same Proportion to one another as their Densities are, excepting that the Refraction of that strange Substance, Island Crystal is a little bigger than the rest. And particularly Air, which is 3500 Times rarer than the Pseudo-Topaz, and 4400 Times rarer than Glass of Antimony, and 2000 Times rarer than the Selenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding its rarity the same refractive Power in respect of its Density which those very dense Substances have in respect of theirs, excepting so far as those differ from one another.

PG33504.B00519
Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit of Turpentine and Amber, which are fat sulphureous unctuous Bodies, and a Diamond, which probably is an unctuous Substance coagulated, have their refractive Powers in Proportion to one another as their Densities without any considerable Variation. But the refractive Powers of these unctuous Substances are two or three Times greater in respect of their Densities than the refractive Powers of the former Substances in respect of theirs.

PG33504.B00520
Water has a refractive Power in a middle degree between those two sorts of Substances, and probably is of a middle nature. For out of it grow all vegetable and animal Substances, which consist as well of sulphureous fat and inflamable Parts, as of earthy lean and alcalizate ones.

PG33504.B00521
Salts and Vitriols have refractive Powers in a middle degree between those of earthy Substances and Water, and accordingly are composed of those two sorts of Substances. For by distillation and rectification of their Spirits a great Part of them goes into Water, and a great Part remains behind in the form of a dry fix'd Earth capable of Vitrification.

PG33504.B00522
Spirit of Wine has a refractive Power in a middle degree between those of Water and oily Substances, and accordingly seems to be composed of both, united by Fermentation; the Water, by means of some saline Spirits with which 'tis impregnated, dissolving the Oil, and volatizing it by the Action. For Spirit of Wine is inflamable by means of its oily Parts, and being distilled often from Salt of Tartar, grow by every distillation more and more aqueous and phlegmatick. And Chymists observe, that Vegetables (as Lavender, Rue, Marjoram, &c.) distilled _per se_, before fermentation yield Oils without any burning Spirits, but after fermentation yield ardent Spirits without Oils: Which shews, that their Oil is by fermentation converted into Spirit. They find also, that if Oils be poured in a small quantity upon fermentating Vegetables, they distil over after fermentation in the form of Spirits.

PG33504.B00523
So then, by the foregoing Table, all Bodies seem to have their refractive Powers proportional to their Densities, (or very nearly;) excepting so far as they partake more or less of sulphureous oily Particles, and thereby have their refractive Power made greater or less. Whence it seems rational to attribute the refractive Power of all Bodies chiefly, if not wholly, to the sulphureous Parts with which they abound. For it's probable that all Bodies abound more or less with Sulphurs. And as Light congregated by a Burning-glass acts most upon sulphureous Bodies, to turn them into Fire and Flame; so, since all Action is mutual, Sulphurs ought to act most upon Light. For that the action between Light and Bodies is mutual, may appear from this Consideration; That the densest Bodies which refract and reflect Light most strongly, grow hottest in the Summer Sun, by the action of the refracted or reflected Light.

PG33504.B00524
I have hitherto explain'd the power of Bodies to reflect and refract, and shew'd, that thin transparent Plates, Fibres, and Particles, do, according to their several thicknesses and densities, reflect several sorts of Rays, and thereby appear of several Colours; and by consequence that nothing more is requisite for producing all the Colours of natural Bodies, than the several sizes and densities of their transparent Particles. But whence it is that these Plates, Fibres, and Particles, do, according to their several thicknesses and densities, reflect several sorts of Rays, I have not yet explain'd. To give some insight into this matter, and make way for understanding the next part of this Book, I shall conclude this part with a few more Propositions. Those which preceded respect the nature of Bodies, these the nature of Light: For both must be understood, before the reason of their Actions upon one another can be known. And because the last Proposition depended upon the velocity of Light, I will begin with a Proposition of that kind.

PG33504.B00525
PROP. XI.

PG33504.B00526
_Light is propagated from luminous Bodies in time, and spends about seven or eight Minutes of an Hour in passing from the Sun to the Earth._

PG33504.B00527
This was observed first by _Roemer_, and then by others, by means of the Eclipses of the Satellites of _Jupiter_. For these Eclipses, when the Earth is between the Sun and _Jupiter_, happen about seven or eight Minutes sooner than they ought to do by the Tables, and when the Earth is beyond the Sun they happen about seven or eight Minutes later than they ought to do; the reason being, that the Light of the Satellites has farther to go in the latter case than in the former by the Diameter of the Earth's Orbit. Some inequalities of time may arise from the Excentricities of the Orbs of the Satellites; but those cannot answer in all the Satellites, and at all times to the Position and Distance of the Earth from the Sun. The mean motions of _Jupiter_'s Satellites is also swifter in his descent from his Aphelium to his Perihelium, than in his ascent in the other half of his Orb. But this inequality has no respect to the position of the Earth, and in the three interior Satellites is insensible, as I find by computation from the Theory of their Gravity.

PG33504.B00528
PROP. XII.

PG33504.B00529
_Every Ray of Light in its passage through any refracting Surface is put into a certain transient Constitution or State, which in the progress of the Ray returns at equal Intervals, and disposes the Ray at every return to be easily transmitted through the next refracting Surface, and between the returns to be easily reflected by it._

PG33504.B00530
This is manifest by the 5th, 9th, 12th, and 15th Observations. For by those Observations it appears, that one and the same sort of Rays at equal Angles of Incidence on any thin transparent Plate, is alternately reflected and transmitted for many Successions accordingly as the thickness of the Plate increases in arithmetical Progression of the Numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, &c. so that if the first Reflexion (that which makes the first or innermost of the Rings of Colours there described) be made at the thickness 1, the Rays shall be transmitted at the thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the central Spot and Rings of Light, which appear by transmission, and be reflected at the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings which appear by Reflexion. And this alternate Reflexion and Transmission, as I gather by the 24th Observation, continues for above an hundred vicissitudes, and by the Observations in the next part of this Book, for many thousands, being propagated from one Surface of a Glass Plate to the other, though the thickness of the Plate be a quarter of an Inch or above: So that this alternation seems to be propagated from every refracting Surface to all distances without end or limitation.

PG33504.B00531
This alternate Reflexion and Refraction depends on both the Surfaces of every thin Plate, because it depends on their distance. By the 21st Observation, if either Surface of a thin Plate of _Muscovy_ Glass be wetted, the Colours caused by the alternate Reflexion and Refraction grow faint, and therefore it depends on them both.

PG33504.B00532
It is therefore perform'd at the second Surface; for if it were perform'd at the first, before the Rays arrive at the second, it would not depend on the second.

PG33504.B00533
It is also influenced by some action or disposition, propagated from the first to the second, because otherwise at the second it would not depend on the first. And this action or disposition, in its propagation, intermits and returns by equal Intervals, because in all its progress it inclines the Ray at one distance from the first Surface to be reflected by the second, at another to be transmitted by it, and that by equal Intervals for innumerable vicissitudes. And because the Ray is disposed to Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission at the distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through the first Surface, is at the distance 0, and it is transmitted through both together, if their distance be infinitely little or much less than 1) the disposition to be transmitted at the distances 2, 4, 6, 8, 10, &c. is to be accounted a return of the same disposition which the Ray first had at the distance 0, that is at its transmission through the first refracting Surface. All which is the thing I would prove.

PG33504.B00534
What kind of action or disposition this is; Whether it consists in a circulating or a vibrating motion of the Ray, or of the Medium, or something else, I do not here enquire. Those that are averse from assenting to any new Discoveries, but such as they can explain by an Hypothesis, may for the present suppose, that as Stones by falling upon Water put the Water into an undulating Motion, and all Bodies by percussion excite vibrations in the Air; so the Rays of Light, by impinging on any refracting or reflecting Surface, excite vibrations in the refracting or reflecting Medium or Substance, and by exciting them agitate the solid parts of the refracting or reflecting Body, and by agitating them cause the Body to grow warm or hot; that the vibrations thus excited are propagated in the refracting or reflecting Medium or Substance, much after the manner that vibrations are propagated in the Air for causing Sound, and move faster than the Rays so as to overtake them; and that when any Ray is in that part of the vibration which conspires with its Motion, it easily breaks through a refracting Surface, but when it is in the contrary part of the vibration which impedes its Motion, it is easily reflected; and, by consequence, that every Ray is successively disposed to be easily reflected, or easily transmitted, by every vibration which overtakes it. But whether this Hypothesis be true or false I do not here consider. I content my self with the bare Discovery, that the Rays of Light are by some cause or other alternately disposed to be reflected or refracted for many vicissitudes.

PG33504.B00535
DEFINITION.

PG33504.B00536
_The returns of the disposition of any Ray to be reflected I will call its_ Fits of easy Reflexion, _and those of its disposition to be transmitted its_ Fits of easy Transmission, _and the space it passes between every return and the next return, the_ Interval of its Fits.

PG33504.B00537
PROP. XIII.

PG33504.B00538
_The reason why the Surfaces of all thick transparent Bodies reflect part of the Light incident on them, and refract the rest, is, that some Rays at their Incidence are in Fits of easy Reflexion, and others in Fits of easy Transmission._

PG33504.B00539
This may be gather'd from the 24th Observation, where the Light reflected by thin Plates of Air and Glass, which to the naked Eye appear'd evenly white all over the Plate, did through a Prism appear waved with many Successions of Light and Darkness made by alternate Fits of easy Reflexion and easy Transmission, the Prism severing and distinguishing the Waves of which the white reflected Light was composed, as was explain'd above.

PG33504.B00540
And hence Light is in Fits of easy Reflexion and easy Transmission, before its Incidence on transparent Bodies. And probably it is put into such fits at its first emission from luminous Bodies, and continues in them during all its progress. For these Fits are of a lasting nature, as will appear by the next part of this Book.

PG33504.B00541
In this Proposition I suppose the transparent Bodies to be thick; because if the thickness of the Body be much less than the Interval of the Fits of easy Reflexion and Transmission of the Rays, the Body loseth its reflecting power. For if the Rays, which at their entering into the Body are put into Fits of easy Transmission, arrive at the farthest Surface of the Body before they be out of those Fits, they must be transmitted. And this is the reason why Bubbles of Water lose their reflecting power when they grow very thin; and why all opake Bodies, when reduced into very small parts, become transparent.

PG33504.B00542
PROP. XIV.

PG33504.B00543
_Those Surfaces of transparent Bodies, which if the Ray be in a Fit of Refraction do refract it most strongly, if the Ray be in a Fit of Reflexion do reflect it most easily._

PG33504.B00544
For we shewed above, in _Prop._ 8. that the cause of Reflexion is not the impinging of Light on the solid impervious parts of Bodies, but some other power by which those solid parts act on Light at a distance. We shewed also in _Prop._ 9. that Bodies reflect and refract Light by one and the same power, variously exercised in various circumstances; and in _Prop._ 1. that the most strongly refracting Surfaces reflect the most Light: All which compared together evince and rarify both this and the last Proposition.

PG33504.B00545
PROP. XV.

PG33504.B00546
_In any one and the same sort of Rays, emerging in any Angle out of any refracting Surface into one and the same Medium, the Interval of the following Fits of easy Reflexion and Transmission are either accurately or very nearly, as the Rectangle of the Secant of the Angle of Refraction, and of the Secant of another Angle, whose Sine is the first of 106 arithmetical mean Proportionals, between the Sines of Incidence and Refraction, counted from the Sine of Refraction._

PG33504.B00547
This is manifest by the 7th and 19th Observations.

PG33504.B00548
PROP. XVI.

PG33504.B00549
_In several sorts of Rays emerging in equal Angles out of any refracting Surface into the same Medium, the Intervals of the following Fits of easy Reflexion and easy Transmission are either accurately, or very nearly, as the Cube-Roots of the Squares of the lengths of a Chord, which found the Notes in an Eight_, sol, la, fa, sol, la, mi, fa, sol, _with all their intermediate degrees answering to the Colours of those Rays, according to the Analogy described in the seventh Experiment of the second Part of the first Book._

PG33504.B00550
This is manifest by the 13th and 14th Observations.

PG33504.B00551
PROP. XVII.

PG33504.B00552
_If Rays of any sort pass perpendicularly into several Mediums, the Intervals of the Fits of easy Reflexion and Transmission in any one Medium, are to those Intervals in any other, as the Sine of Incidence to the Sine of Refraction, when the Rays pass out of the first of those two Mediums into the second._

PG33504.B00553
This is manifest by the 10th Observation.

PG33504.B00554
PROP. XVIII.

PG33504.B00555
_If the Rays which paint the Colour in the Confine of yellow and orange pass perpendicularly out of any Medium into Air, the Intervals of their Fits of easy Reflexion are the 1/89000th part of an Inch. And of the same length are the Intervals of their Fits of easy Transmission._

PG33504.B00556
This is manifest by the 6th Observation. From these Propositions it is easy to collect the Intervals of the Fits of easy Reflexion and easy Transmission of any sort of Rays refracted in any angle into any Medium; and thence to know, whether the Rays shall be reflected or transmitted at their subsequent Incidence upon any other pellucid Medium. Which thing, being useful for understanding the next part of this Book, was here to be set down. And for the same reason I add the two following Propositions.

PG33504.B00557
PROP. XIX.

PG33504.B00558
_If any sort of Rays falling on the polite Surface of any pellucid Medium be reflected back, the Fits of easy Reflexion, which they have at the point of Reflexion, shall still continue to return; and the Returns shall be at distances from the point of Reflexion in the arithmetical progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these Fits the Rays shall be in Fits of easy Transmission._
