If instead of the Prisms the Object-gla.s.ses be made use of, the Rings which they exhibit become not white and distinct by the obliquity of the Eye, by reason that the Rays in their pa.s.sage through that Air which intercedes the Gla.s.ses are very nearly parallel to those Lines in which they were first incident on the Gla.s.ses, and consequently the Rays endued with several Colours are not inclined one more than another to that Air, as it happens in the Prisms.

There is yet another circ.u.mstance of these Experiments to be consider'd, and that is why the black and white Rings which when view'd at a distance appear distinct, should not only become confused by viewing them near at hand, but also yield a violet Colour at both the edges of every white Ring. And the reason is, that the Rays which enter the Eye at several parts of the Pupil, have several Obliquities to the Gla.s.ses, and those which are most oblique, if consider'd apart, would represent the Rings bigger than those which are the least oblique. Whence the breadth of the Perimeter of every white Ring is expanded outwards by the obliquest Rays, and inwards by the least oblique. And this Expansion is so much the greater by how much the greater is the difference of the Obliquity; that is, by how much the Pupil is wider, or the Eye nearer to the Gla.s.ses. And the breadth of the violet must be most expanded, because the Rays apt to excite a Sensation of that Colour are most oblique to a second or farther Superficies of the thinn'd Air at which they are reflected, and have also the greatest variation of Obliquity, which makes that Colour soonest emerge out of the edges of the white.

And as the breadth of every Ring is thus augmented, the dark Intervals must be diminish'd, until the neighbouring Rings become continuous, and are blended, the exterior first, and then those nearer the center; so that they can no longer be distinguish'd apart, but seem to const.i.tute an even and uniform whiteness.

Among all the Observations there is none accompanied with so odd circ.u.mstances as the twenty-fourth. Of those the princ.i.p.al are, that in thin Plates, which to the naked Eye seem of an even and uniform transparent whiteness, without any terminations of Shadows, the Refraction of a Prism should make Rings of Colours appear, whereas it usually makes Objects appear colour'd only there where they are terminated with Shadows, or have parts unequally luminous; and that it should make those Rings exceedingly distinct and white, although it usually renders Objects confused and coloured. The Cause of these things you will understand by considering, that all the Rings of Colours are really in the Plate, when view'd with the naked Eye, although by reason of the great breadth of their Circ.u.mferences they so much interfere and are blended together, that they seem to const.i.tute an uniform whiteness.

But when the Rays pa.s.s through the Prism to the Eye, the Orbits of the several Colours in every Ring are refracted, some more than others, according to their degrees of Refrangibility: By which means the Colours on one side of the Ring (that is in the circ.u.mference on one side of its center), become more unfolded and dilated, and those on the other side more complicated and contracted. And where by a due Refraction they are so much contracted, that the several Rings become narrower than to interfere with one another, they must appear distinct, and also white, if the const.i.tuent Colours be so much contracted as to be wholly co-incident. But on the other side, where the Orbit of every Ring is made broader by the farther unfolding of its Colours, it must interfere more with other Rings than before, and so become less distinct.

[Ill.u.s.tration: FIG. 7.]

To explain this a little farther, suppose the concentrick Circles AV, and BX, [in _Fig._ 7.] represent the red and violet of any Order, which, together with the intermediate Colours, const.i.tute any one of these Rings. Now these being view'd through a Prism, the violet Circle BX, will, by a greater Refraction, be farther translated from its place than the red AV, and so approach nearer to it on that side of the Circles, towards which the Refractions are made. For instance, if the red be translated to _av_, the violet may be translated to _bx_, so as to approach nearer to it at _x_ than before; and if the red be farther translated to av, the violet may be so much farther translated to bx as to convene with it at x; and if the red be yet farther translated to [Greek: aY], the violet may be still so much farther translated to [Greek: bx] as to pa.s.s beyond it at [Greek: x], and convene with it at _e_ and _f_. And this being understood not only of the red and violet, but of all the other intermediate Colours, and also of every revolution of those Colours, you will easily perceive how those of the same revolution or order, by their nearness at _xv_ and [Greek: Yx], and their coincidence at xv, _e_ and _f_, ought to const.i.tute pretty distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that they will appear severally at _x_[Greek: u] and at xv exhibit whiteness by their coincidence, and again appear severally at [Greek: Yx], but yet in a contrary order to that which they had before, and still retain beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab], these Colours must become much more confused by being dilated and spread so as to interfere with those of other Orders. And the same confusion will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be very great, or the Prism very distant from the Object-gla.s.ses: In which case no parts of the Rings will be seen, save only two little Arcs at _e_ and _f_, whose distance from one another will be augmented by removing the Prism still farther from the Object-gla.s.ses: And these little Arcs must be distinctest and whitest at their middle, and at their ends, where they begin to grow confused, they must be colour'd.

And the Colours at one end of every Arc must be in a contrary order to those at the other end, by reason that they cross in the intermediate white; namely, their ends, which verge towards [Greek: Ux], will be red and yellow on that side next the center, and blue and violet on the other side. But their other ends which verge from [Greek: Ux], will on the contrary be blue and violet on that side towards the center, and on the other side red and yellow.

Now as all these things follow from the properties of Light by a mathematical way of reasoning, so the truth of them may be manifested by Experiments. For in a dark Room, by viewing these Rings through a Prism, by reflexion of the several prismatick Colours, which an a.s.sistant causes to move to and fro upon a Wall or Paper from whence they are reflected, whilst the Spectator's Eye, the Prism, and the Object-gla.s.ses, (as in the 13th Observation,) are placed steady; the Position of the Circles made successively by the several Colours, will be found such, in respect of one another, as I have described in the Figures _abxv_, or abxv, or _[Greek: abxU]_. And by the same method the truth of the Explications of other Observations may be examined.

By what hath been said, the like Phaenomena of Water and thin Plates of Gla.s.s may be understood. But in small fragments of those Plates there is this farther observable, that where they lie flat upon a Table, and are turned about their centers whilst they are view'd through a Prism, they will in some postures exhibit Waves of various Colours; and some of them exhibit these Waves in one or two Positions only, but the most of them do in all Positions exhibit them, and make them for the most part appear almost all over the Plates. The reason is, that the Superficies of such Plates are not even, but have many Cavities and Swellings, which, how shallow soever, do a little vary the thickness of the Plate. For at the several sides of those Cavities, for the Reasons newly described, there ought to be produced Waves in several postures of the Prism. Now though it be but some very small and narrower parts of the Gla.s.s, by which these Waves for the most part are caused, yet they may seem to extend themselves over the whole Gla.s.s, because from the narrowest of those parts there are Colours of several Orders, that is, of several Rings, confusedly reflected, which by Refraction of the Prism are unfolded, separated, and, according to their degrees of Refraction, dispersed to several places, so as to const.i.tute so many several Waves, as there were divers orders of Colours promiscuously reflected from that part of the Gla.s.s.

These are the princ.i.p.al Phaenomena of thin Plates or Bubbles, whose Explications depend on the properties of Light, which I have heretofore deliver'd. And these you see do necessarily follow from them, and agree with them, even to their very least circ.u.mstances; and not only so, but do very much tend to their proof. Thus, by the 24th Observation it appears, that the Rays of several Colours, made as well by thin Plates or Bubbles, as by Refractions of a Prism, have several degrees of Refrangibility; whereby those of each order, which at the reflexion from the Plate or Bubble are intermix'd with those of other orders, are separated from them by Refraction, and a.s.sociated together so as to become visible by themselves like Arcs of Circles. For if the Rays were all alike refrangible, 'tis impossible that the whiteness, which to the naked Sense appears uniform, should by Refraction have its parts transposed and ranged into those black and white Arcs.

It appears also that the unequal Refractions of difform Rays proceed not from any contingent irregularities; such as are Veins, an uneven Polish, or fortuitous Position of the Pores of Gla.s.s; unequal and casual Motions in the Air or aether, the spreading, breaking, or dividing the same Ray into many diverging parts; or the like. For, admitting any such irregularities, it would be impossible for Refractions to render those Rings so very distinct, and well defined, as they do in the 24th Observation. It is necessary therefore that every Ray have its proper and constant degree of Refrangibility connate with it, according to which its refraction is ever justly and regularly perform'd; and that several Rays have several of those degrees.

And what is said of their Refrangibility may be also understood of their Reflexibility, that is, of their Dispositions to be reflected, some at a greater, and others at a less thickness of thin Plates or Bubbles; namely, that those Dispositions are also connate with the Rays, and immutable; as may appear by the 13th, 14th, and 15th Observations, compared with the fourth and eighteenth.

By the Precedent Observations it appears also, that whiteness is a dissimilar mixture of all Colours, and that Light is a mixture of Rays endued with all those Colours. For, considering the mult.i.tude of the Rings of Colours in the 3d, 12th, and 24th Observations, it is manifest, that although in the 4th and 18th Observations there appear no more than eight or nine of those Rings, yet there are really a far greater number, which so much interfere and mingle with one another, as after those eight or nine revolutions to dilute one another wholly, and const.i.tute an even and sensibly uniform whiteness. And consequently that whiteness must be allow'd a mixture of all Colours, and the Light which conveys it to the Eye must be a mixture of Rays endued with all those Colours.

But farther; by the 24th Observation it appears, that there is a constant relation between Colours and Refrangibility; the most refrangible Rays being violet, the least refrangible red, and those of intermediate Colours having proportionably intermediate degrees of Refrangibility. And by the 13th, 14th, and 15th Observations, compared with the 4th or 18th there appears to be the same constant relation between Colour and Reflexibility; the violet being in like circ.u.mstances reflected at least thicknesses of any thin Plate or Bubble, the red at greatest thicknesses, and the intermediate Colours at intermediate thicknesses. Whence it follows, that the colorifick Dispositions of Rays are also connate with them, and immutable; and by consequence, that all the Productions and Appearances of Colours in the World are derived, not from any physical Change caused in Light by Refraction or Reflexion, but only from the various Mixtures or Separations of Rays, by virtue of their different Refrangibility or Reflexibility. And in this respect the Science of Colours becomes a Speculation as truly mathematical as any other part of Opticks. I mean, so far as they depend on the Nature of Light, and are not produced or alter'd by the Power of Imagination, or by striking or pressing the Eye.

THE

SECOND BOOK

OF

OPTICKS

_PART III._

_Of the permanent Colours of natural Bodies, and the a.n.a.logy between them and the Colours of thin transparent Plates._

I am now come to another part of this Design, which is to consider how the Phaenomena of thin transparent Plates stand related to those of all other natural Bodies. Of these Bodies I have already told you that they appear of divers Colours, accordingly as they are disposed to reflect most copiously the Rays originally endued with those Colours. But their Const.i.tutions, whereby they reflect some Rays more copiously than others, remain to be discover'd; and these I shall endeavour to manifest in the following Propositions.

PROP. I.

_Those Superficies of transparent Bodies reflect the greatest quant.i.ty of Light, which have the greatest refracting Power; that is, which intercede Mediums that differ most in their refractive Densities. And in the Confines of equally refracting Mediums there is no Reflexion._

The a.n.a.logy between Reflexion and Refraction will appear by considering, that when Light pa.s.seth obliquely out of one Medium into another which refracts from the perpendicular, the greater is the difference of their refractive Density, the less Obliquity of Incidence is requisite to cause a total Reflexion. For as the Sines are which measure the Refraction, so is the Sine of Incidence at which the total Reflexion begins, to the Radius of the Circle; and consequently that Angle of Incidence is least where there is the greatest difference of the Sines.

Thus in the pa.s.sing of Light out of Water into Air, where the Refraction is measured by the Ratio of the Sines 3 to 4, the total Reflexion begins when the Angle of Incidence is about 48 Degrees 35 Minutes. In pa.s.sing out of Gla.s.s into Air, where the Refraction is measured by the Ratio of the Sines 20 to 31, the total Reflexion begins when the Angle of Incidence is 40 Degrees 10 Minutes; and so in pa.s.sing out of Crystal, or more strongly refracting Mediums into Air, there is still a less obliquity requisite to cause a total reflexion. Superficies therefore which refract most do soonest reflect all the Light which is incident on them, and so must be allowed most strongly reflexive.

But the truth of this Proposition will farther appear by observing, that in the Superficies interceding two transparent Mediums, (such as are Air, Water, Oil, common Gla.s.s, Crystal, metalline Gla.s.ses, Island Gla.s.ses, white transparent a.r.s.enick, Diamonds, &c.) the Reflexion is stronger or weaker accordingly, as the Superficies hath a greater or less refracting Power. For in the Confine of Air and Sal-gem 'tis stronger than in the Confine of Air and Water, and still stronger in the Confine of Air and common Gla.s.s or Crystal, and stronger in the Confine of Air and a Diamond. If any of these, and such like transparent Solids, be immerged in Water, its Reflexion becomes, much weaker than before; and still weaker if they be immerged in the more strongly refracting Liquors of well rectified Oil of Vitriol or Spirit of Turpentine. If Water be distinguish'd into two parts by any imaginary Surface, the Reflexion in the Confine of those two parts is none at all. In the Confine of Water and Ice 'tis very little; in that of Water and Oil 'tis something greater; in that of Water and Sal-gem still greater; and in that of Water and Gla.s.s, or Crystal or other denser Substances still greater, accordingly as those Mediums differ more or less in their refracting Powers. Hence in the Confine of common Gla.s.s and Crystal, there ought to be a weak Reflexion, and a stronger Reflexion in the Confine of common and metalline Gla.s.s; though I have not yet tried this. But in the Confine of two Gla.s.ses of equal density, there is not any sensible Reflexion; as was shewn in the first Observation. And the same may be understood of the Superficies interceding two Crystals, or two Liquors, or any other Substances in which no Refraction is caused.

So then the reason why uniform pellucid Mediums (such as Water, Gla.s.s, or Crystal,) have no sensible Reflexion but in their external Superficies, where they are adjacent to other Mediums of a different density, is because all their contiguous parts have one and the same degree of density.

PROP. II.

_The least parts of almost all natural Bodies are in some measure transparent: And the Opacity of those Bodies ariseth from the mult.i.tude of Reflexions caused in their internal Parts._

That this is so has been observed by others, and will easily be granted by them that have been conversant with Microscopes. And it may be also tried by applying any substance to a hole through which some Light is immitted into a dark Room. For how opake soever that Substance may seem in the open Air, it will by that means appear very manifestly transparent, if it be of a sufficient thinness. Only white metalline Bodies must be excepted, which by reason of their excessive density seem to reflect almost all the Light incident on their first Superficies; unless by solution in Menstruums they be reduced into very small Particles, and then they become transparent.

PROP. III.

_Between the parts of opake and colour'd Bodies are many s.p.a.ces, either empty, or replenish'd with Mediums of other Densities; as Water between the tinging Corpuscles wherewith any Liquor is impregnated, Air between the aqueous Globules that const.i.tute Clouds or Mists; and for the most part s.p.a.ces void of both Air and Water, but yet perhaps not wholly void of all Substance, between the parts of hard Bodies._

The truth of this is evinced by the two precedent Propositions: For by the second Proposition there are many Reflexions made by the internal parts of Bodies, which, by the first Proposition, would not happen if the parts of those Bodies were continued without any such Interstices between them; because Reflexions are caused only in Superficies, which intercede Mediums of a differing density, by _Prop._ 1.

But farther, that this discontinuity of parts is the princ.i.p.al Cause of the opacity of Bodies, will appear by considering, that opake Substances become transparent by filling their Pores with any Substance of equal or almost equal density with their parts. Thus Paper dipped in Water or Oil, the _Oculus Mundi_ Stone steep'd in Water, Linnen Cloth oiled or varnish'd, and many other Substances soaked in such Liquors as will intimately pervade their little Pores, become by that means more transparent than otherwise; so, on the contrary, the most transparent Substances, may, by evacuating their Pores, or separating their parts, be render'd sufficiently opake; as Salts or wet Paper, or the _Oculus Mundi_ Stone by being dried, Horn by being sc.r.a.ped, Gla.s.s by being reduced to Powder, or otherwise flawed; Turpentine by being stirred about with Water till they mix imperfectly, and Water by being form'd into many small Bubbles, either alone in the form of Froth, or by shaking it together with Oil of Turpentine, or Oil Olive, or with some other convenient Liquor, with which it will not perfectly incorporate.

And to the increase of the opacity of these Bodies, it conduces something, that by the 23d Observation the Reflexions of very thin transparent Substances are considerably stronger than those made by the same Substances of a greater thickness.

PROP. IV.

_The Parts of Bodies and their Interstices must not be less than of some definite bigness, to render them opake and colour'd._

For the opakest Bodies, if their parts be subtilly divided, (as Metals, by being dissolved in acid Menstruums, &c.) become perfectly transparent. And you may also remember, that in the eighth Observation there was no sensible reflexion at the Superficies of the Object-gla.s.ses, where they were very near one another, though they did not absolutely touch. And in the 17th Observation the Reflexion of the Water-bubble where it became thinnest was almost insensible, so as to cause very black Spots to appear on the top of the Bubble, by the want of reflected Light.

On these grounds I perceive it is that Water, Salt, Gla.s.s, Stones, and such like Substances, are transparent. For, upon divers Considerations, they seem to be as full of Pores or Interstices between their parts as other Bodies are, but yet their Parts and Interstices to be too small to cause Reflexions in their common Surfaces.

PROP. V.

_The transparent parts of Bodies, according to their several sizes, reflect Rays of one Colour, and transmit those of another, on the same grounds that thin Plates or Bubbles do reflect or transmit those Rays.

And this I take to be the ground of all their Colours._

For if a thinn'd or plated Body, which being of an even thickness, appears all over of one uniform Colour, should be slit into Threads, or broken into Fragments, of the same thickness with the Plate; I see no reason why every Thread or Fragment should not keep its Colour, and by consequence why a heap of those Threads or Fragments should not const.i.tute a Ma.s.s or Powder of the same Colour, which the Plate exhibited before it was broken. And the parts of all natural Bodies being like so many Fragments of a Plate, must on the same grounds exhibit the same Colours.

Now, that they do so will appear by the affinity of their Properties.

The finely colour'd Feathers of some Birds, and particularly those of Peac.o.c.ks Tails, do, in the very same part of the Feather, appear of several Colours in several Positions of the Eye, after the very same manner that thin Plates were found to do in the 7th and 19th Observations, and therefore their Colours arise from the thinness of the transparent parts of the Feathers; that is, from the slenderness of the very fine Hairs, or _Capillamenta_, which grow out of the sides of the grosser lateral Branches or Fibres of those Feathers. And to the same purpose it is, that the Webs of some Spiders, by being spun very fine, have appeared colour'd, as some have observ'd, and that the colour'd Fibres of some Silks, by varying the Position of the Eye, do vary their Colour. Also the Colours of Silks, Cloths, and other Substances, which Water or Oil can intimately penetrate, become more faint and obscure by being immerged in those Liquors, and recover their Vigor again by being dried; much after the manner declared of thin Bodies in the 10th and 21st Observations. Leaf-Gold, some sorts of painted Gla.s.s, the Infusion of _Lignum Nephritic.u.m_, and some other Substances, reflect one Colour, and transmit another; like thin Bodies in the 9th and 20th Observations.

And some of those colour'd Powders which Painters use, may have their Colours a little changed, by being very elaborately and finely ground.

Where I see not what can be justly pretended for those changes, besides the breaking of their parts into less parts by that contrition, after the same manner that the Colour of a thin Plate is changed by varying its thickness. For which reason also it is that the colour'd Flowers of Plants and Vegetables, by being bruised, usually become more transparent than before, or at least in some degree or other change their Colours.

Nor is it much less to my purpose, that, by mixing divers Liquors, very odd and remarkable Productions and Changes of Colours may be effected, of which no cause can be more obvious and rational than that the saline Corpuscles of one Liquor do variously act upon or unite with the tinging Corpuscles of another, so as to make them swell, or shrink, (whereby not only their bulk but their density also may be changed,) or to divide them into smaller Corpuscles, (whereby a colour'd Liquor may become transparent,) or to make many of them a.s.sociate into one cl.u.s.ter, whereby two transparent Liquors may compose a colour'd one. For we see how apt those saline Menstruums are to penetrate and dissolve Substances to which they are applied, and some of them to precipitate what others dissolve. In like manner, if we consider the various Phaenomena of the Atmosphere, we may observe, that when Vapours are first raised, they hinder not the transparency of the Air, being divided into parts too small to cause any Reflexion in their Superficies. But when in order to compose drops of Rain they begin to coalesce and const.i.tute Globules of all intermediate sizes, those Globules, when they become of convenient size to reflect some Colours and transmit others, may const.i.tute Clouds of various Colours according to their sizes. And I see not what can be rationally conceived in so transparent a Substance as Water for the production of these Colours, besides the various sizes of its fluid and globular Parcels.

PROP. VI.

_The parts of Bodies on which their Colours depend, are denser than the Medium which pervades their Interstices._