Chapter VII: Part 7

_Obs._ 24. When the two Object-glasses were lay'd upon one another, so as to make the Rings of the Colours appear, though with my naked Eye I could not discern above eight or nine of those Rings, yet by viewing them through a Prism I have seen a far greater Multitude, insomuch that I could number more than forty, besides many others, that were so very small and close together, that I could not keep my Eye steady on them severally so as to number them, but by their Extent I have sometimes estimated them to be more than an hundred. And I believe the Experiment may be improved to the Discovery of far greater Numbers. For they seem to be really unlimited, though visible only so far as they can be separated by the Refraction of the Prism, as I shall hereafter explain.

But it was but one side of these Rings, namely, that towards which the Refraction was made, which by that Refraction was render'd distinct, and the other side became more confused than when view'd by the naked Eye, insomuch that there I could not discern above one or two, and sometimes none of those Rings, of which I could discern eight or nine with my naked Eye. And their Segments or Arcs, which on the other side appear'd so numerous, for the most part exceeded not the third Part of a Circle. If the Refraction was very great, or the Prism very distant from the Object-glasses, the middle Part of those Arcs became also confused, so as to disappear and constitute an even Whiteness, whilst on either side their Ends, as also the whole Arcs farthest from the Center, became distincter than before, appearing in the Form as you see them design'd in the fifth Figure.

The Arcs, where they seem'd distinctest, were only white and black successively, without any other Colours intermix'd. But in other Places there appeared Colours, whose Order was inverted by the refraction in such manner, that if I first held the Prism very near the Object-glasses, and then gradually removed it farther off towards my Eye, the Colours of the 2d, 3d, 4th, and following Rings, shrunk towards the white that emerged between them, until they wholly vanish'd into it at the middle of the Arcs, and afterwards emerged again in a contrary Order. But at the Ends of the Arcs they retain'd their Order unchanged.

I have sometimes so lay'd one Object-glass upon the other, that to the naked Eye they have all over seem'd uniformly white, without the least Appearance of any of the colour'd Rings; and yet by viewing them through a Prism, great Multitudes of those Rings have discover'd themselves. And in like manner Plates of _Muscovy_ Glass, and Bubbles of Glass blown at a Lamp-Furnace, which were not so thin as to exhibit any Colours to the naked Eye, have through the Prism exhibited a great Variety of them ranged irregularly up and down in the Form of Waves. And so Bubbles of Water, before they began to exhibit their Colours to the naked Eye of a Bystander, have appeared through a Prism, girded about with many parallel and horizontal Rings; to produce which Effect, it was necessary to hold the Prism parallel, or very nearly parallel to the Horizon, and to dispose it so that the Rays might be refracted upwards.

THE

SECOND BOOK

OF

OPTICKS

_PART II._

_Remarks upon the foregoing Observations._

Having given my Observations of these Colours, before I make use of them to unfold the Causes of the Colours of natural Bodies, it is convenient that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th, 18th, 20th, and 24th, I first explain the more compounded. And first to shew how the Colours in the fourth and eighteenth Observations are produced, let there be taken in any Right Line from the Point Y, [in _Fig._ 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16, 3/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to sound all the Notes in an eighth are represented; that is, in the Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243, 10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent of the several Colours set underneath against them, is to be represented. Then divide the Line _A[Greek: a]_ in such Proportion as the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of Division denote. And through those Divisions from Y draw Lines 1I, 2K, 3L, 5M, 6N, 7O, &c.

Now, if A2 be supposed to represent the Thickness of any thin transparent Body, at which the outmost Violet is most copiously reflected in the first Ring, or Series of Colours, then by the 13th Observation, HK will represent its Thickness, at which the utmost Red is most copiously reflected in the same Series. Also by the 5th and 16th Observations, A6 and HN will denote the Thicknesses at which those extreme Colours are most copiously reflected in the second Series, and A10 and HQ the Thicknesses at which they are most copiously reflected in the third Series, and so on. And the Thickness at which any of the intermediate Colours are reflected most copiously, will, according to the 14th Observation, be defined by the distance of the Line AH from the intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names of those Colours are written below.

But farther, to define the Latitude of these Colours in each Ring or Series, let A1 design the least thickness, and A3 the greatest thickness, at which the extreme violet in the first Series is reflected, and let HI, and HL, design the like limits for the extreme red, and let the intermediate Colours be limited by the intermediate parts of the Lines 1I, and 3L, against which the Names of those Colours are written, and so on: But yet with this caution, that the Reflexions be supposed strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on either side; where you must not conceive them to be precisely limited, but to decay indefinitely. And whereas I have assign'd the same Latitude to every Series, I did it, because although the Colours in the first Series seem to be a little broader than the rest, by reason of a stronger Reflexion there, yet that inequality is so insensible as scarcely to be determin'd by Observation.

Now according to this Description, conceiving that the Rays originally of several Colours are by turns reflected at the Spaces 1I, L3, 5M, O7, 9PR11, &c. and transmitted at the Spaces AHI1, 3LM5, 7OP9, &c. it is easy to know what Colour must in the open Air be exhibited at any thickness of a transparent thin Body. For if a Ruler be applied parallel to AH, at that distance from it by which the thickness of the Body is represented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth will denote the reflected original Colours, of which the Colour exhibited in the open Air is compounded. Thus if the constitution of the green in the third Series of Colours be desired, apply the Ruler as you see at [Greek: prsph], and by its passing through some of the blue at [Greek: p] and yellow at [Greek: s], as well as through the green at [Greek: r], you may conclude that the green exhibited at that thickness of the Body is principally constituted of original green, but not without a mixture of some blue and yellow.

By this means you may know how the Colours from the center of the Rings outward ought to succeed in order as they were described in the 4th and 18th Observations. For if you move the Ruler gradually from AH through all distances, having pass'd over the first Space which denotes little or no Reflexion to be made by thinnest Substances, it will first arrive at 1 the violet, and then very quickly at the blue and green, which together with that violet compound blue, and then at the yellow and red, by whose farther addition that blue is converted into whiteness, which whiteness continues during the transit of the edge of the Ruler from I to 3, and after that by the successive deficience of its component Colours, turns first to compound yellow, and then to red, and last of all the red ceaseth at L. Then begin the Colours of the second Series, which succeed in order during the transit of the edge of the Ruler from 5 to O, and are more lively than before, because more expanded and severed. And for the same reason instead of the former white there intercedes between the blue and yellow a mixture of orange, yellow, green, blue and indigo, all which together ought to exhibit a dilute and imperfect green. So the Colours of the third Series all succeed in order; first, the violet, which a little interferes with the red of the second order, and is thereby inclined to a reddish purple; then the blue and green, which are less mix'd with other Colours, and consequently more lively than before, especially the green: Then follows the yellow, some of which towards the green is distinct and good, but that part of it towards the succeeding red, as also that red is mix'd with the violet and blue of the fourth Series, whereby various degrees of red very much inclining to purple are compounded. This violet and blue, which should succeed this red, being mixed with, and hidden in it, there succeeds a green. And this at first is much inclined to blue, but soon becomes a good green, the only unmix'd and lively Colour in this fourth Series. For as it verges towards the yellow, it begins to interfere with the Colours of the fifth Series, by whose mixture the succeeding yellow and red are very much diluted and made dirty, especially the yellow, which being the weaker Colour is scarce able to shew it self. After this the several Series interfere more and more, and their Colours become more and more intermix'd, till after three or four more revolutions (in which the red and blue predominate by turns) all sorts of Colours are in all places pretty equally blended, and compound an even whiteness.

And since by the 15th Observation the Rays endued with one Colour are transmitted, where those of another Colour are reflected, the reason of the Colours made by the transmitted Light in the 9th and 20th Observations is from hence evident.

If not only the Order and Species of these Colours, but also the precise thickness of the Plate, or thin Body at which they are exhibited, be desired in parts of an Inch, that may be also obtained by assistance of the 6th or 16th Observations. For according to those Observations the thickness of the thinned Air, which between two Glasses exhibited the most luminous parts of the first six Rings were 1/178000, 3/178000, 5/178000, 7/178000, 9/178000, 11/178000 parts of an Inch. Suppose the Light reflected most copiously at these thicknesses be the bright citrine yellow, or confine of yellow and orange, and these thicknesses will be F[Greek: l], F[Greek: m], F[Greek: u], F[Greek: x], F[Greek: o], F[Greek: t]. And this being known, it is easy to determine what thickness of Air is represented by G[Greek: ph], or by any other distance of the Ruler from AH.

But farther, since by the 10th Observation the thickness of Air was to the thickness of Water, which between the same Glasses exhibited the same Colour, as 4 to 3, and by the 21st Observation the Colours of thin Bodies are not varied by varying the ambient Medium; the thickness of a Bubble of Water, exhibiting any Colour, will be 3/4 of the thickness of Air producing the same Colour. And so according to the same 10th and 21st Observations, the thickness of a Plate of Glass, whose Refraction of the mean refrangible Ray, is measured by the proportion of the Sines 31 to 20, may be 20/31 of the thickness of Air producing the same Colours; and the like of other Mediums. I do not affirm, that this proportion of 20 to 31, holds in all the Rays; for the Sines of other sorts of Rays have other Proportions. But the differences of those Proportions are so little that I do not here consider them. On these Grounds I have composed the following Table, wherein the thickness of Air, Water, and Glass, at which each Colour is most intense and specifick, is expressed in parts of an Inch divided into ten hundred thousand equal parts.

Now if this Table be compared with the 6th Scheme, you will there see the constitution of each Colour, as to its Ingredients, or the original Colours of which it is compounded, and thence be enabled to judge of its Intenseness or Imperfection; which may suffice in explication of the 4th and 18th Observations, unless it be farther desired to delineate the manner how the Colours appear, when the two Object-glasses are laid upon one another. To do which, let there be described a large Arc of a Circle, and a streight Line which may touch that Arc, and parallel to that Tangent several occult Lines, at such distances from it, as the Numbers set against the several Colours in the Table denote. For the Arc, and its Tangent, will represent the Superficies of the Glasses terminating the interjacent Air; and the places where the occult Lines cut the Arc will show at what distances from the center, or Point of contact, each Colour is reflected.

_The thickness of colour'd Plates and Particles of_
_____________|_______________
/ \
Air. Water. Glass.
|---------+----------+----------+
{Very black | 1/2 | 3/8 | 10/31 |
{Black | 1 | 3/4 | 20/31 |
{Beginning of | | | |
{ Black | 2 | 1-1/2 | 1-2/7 |
Their Colours of the {Blue | 2-2/5 | 1-4/5 | 1-11/22 |
first Order, {White | 5-1/4 | 3-7/8 | 3-2/5 |
{Yellow | 7-1/9 | 5-1/3 | 4-3/5 |
{Orange | 8 | 6 | 5-1/6 |
{Red | 9 | 6-3/4 | 5-4/5 |
|---------+----------+----------|
{Violet | 11-1/6 | 8-3/8 | 7-1/5 |
{Indigo | 12-5/6 | 9-5/8 | 8-2/11 |
{Blue | 14 | 10-1/2 | 9 |
{Green | 15-1/8 | 11-2/3 | 9-5/7 |
Of the second order, {Yellow | 16-2/7 | 12-1/5 | 10-2/5 |
{Orange | 17-2/9 | 13 | 11-1/9 |
{Bright red | 18-1/3 | 13-3/4 | 11-5/6 |
{Scarlet | 19-2/3 | 14-3/4 | 12-2/3 |
|---------+----------+----------|
{Purple | 21 | 15-3/4 | 13-11/20 |
{Indigo | 22-1/10 | 16-4/7 | 14-1/4 |
{Blue | 23-2/5 | 17-11/20 | 15-1/10 |
Of the third Order, {Green | 25-1/5 | 18-9/10 | 16-1/4 |
{Yellow | 27-1/7 | 20-1/3 | 17-1/2 |
{Red | 29 | 21-3/4 | 18-5/7 |
{Bluish red | 32 | 24 | 20-2/3 |
|---------+----------+----------|
{Bluish green | 34 | 25-1/2 | 22 |
{Green | 35-2/7 | 26-1/2 | 22-3/4 |
Of the fourth Order, {Yellowish green | 36 | 27 | 23-2/9 |
{Red | 40-1/3 | 30-1/4 | 26 |
|---------+----------+----------|
{Greenish blue | 46 | 34-1/2 | 29-2/3 |
Of the fifth Order, {Red | 52-1/2 | 39-3/8 | 34 |
|---------+----------+----------|
{Greenish blue | 58-3/4 | 44 | 38 |
Of the sixth Order, {Red | 65 | 48-3/4 | 42 |
|---------+----------+----------|
Of the seventh Order, {Greenish blue | 71 | 53-1/4 | 45-4/5 |
{Ruddy White | 77 | 57-3/4 | 49-2/3 |
|---------+----------+----------|

There are also other Uses of this Table: For by its assistance the thickness of the Bubble in the 19th Observation was determin'd by the Colours which it exhibited. And so the bigness of the parts of natural Bodies may be conjectured by their Colours, as shall be hereafter shewn. Also, if two or more very thin Plates be laid one upon another, so as to compose one Plate equalling them all in thickness, the resulting Colour may be hereby determin'd. For instance, Mr. _Hook_ observed, as is mentioned in his _Micrographia_, that a faint yellow Plate of _Muscovy_ Glass laid upon a blue one, constituted a very deep purple. The yellow of the first Order is a faint one, and the thickness of the Plate exhibiting it, according to the Table is 4-3/5, to which add 9, the thickness exhibiting blue of the second Order, and the Sum will be 13-3/5, which is the thickness exhibiting the purple of the third Order.

To explain, in the next place, the circumstances of the 2d and 3d Observations; that is, how the Rings of the Colours may (by turning the Prisms about their common Axis the contrary way to that expressed in those Observations) be converted into white and black Rings, and afterwards into Rings of Colours again, the Colours of each Ring lying now in an inverted order; it must be remember'd, that those Rings of Colours are dilated by the obliquation of the Rays to the Air which intercedes the Glasses, and that according to the Table in the 7th Observation, their Dilatation or Increase of their Diameter is most manifest and speedy when they are obliquest. Now the Rays of yellow being more refracted by the first Superficies of the said Air than those of red, are thereby made more oblique to the second Superficies, at which they are reflected to produce the colour'd Rings, and consequently the yellow Circle in each Ring will be more dilated than the red; and the Excess of its Dilatation will be so much the greater, by how much the greater is the obliquity of the Rays, until at last it become of equal extent with the red of the same Ring. And for the same reason the green, blue and violet, will be also so much dilated by the still greater obliquity of their Rays, as to become all very nearly of equal extent with the red, that is, equally distant from the center of the Rings. And then all the Colours of the same Ring must be co-incident, and by their mixture exhibit a white Ring. And these white Rings must have black and dark Rings between them, because they do not spread and interfere with one another, as before. And for that reason also they must become distincter, and visible to far greater numbers. But yet the violet being obliquest will be something more dilated, in proportion to its extent, than the other Colours, and so very apt to appear at the exterior Verges of the white.

Afterwards, by a greater obliquity of the Rays, the violet and blue become more sensibly dilated than the red and yellow, and so being farther removed from the center of the Rings, the Colours must emerge out of the white in an order contrary to that which they had before; the violet and blue at the exterior Limbs of each Ring, and the red and yellow at the interior. And the violet, by reason of the greatest obliquity of its Rays, being in proportion most of all expanded, will soonest appear at the exterior Limb of each white Ring, and become more conspicuous than the rest. And the several Series of Colours belonging to the several Rings, will, by their unfolding and spreading, begin again to interfere, and thereby render the Rings less distinct, and not visible to so great numbers.

If instead of the Prisms the Object-glasses 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 passage through that Air which intercedes the Glasses are very nearly parallel to those Lines in which they were first incident on the Glasses, 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 circumstance 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 Glasses, 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 Glasses. 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 constitute an even and uniform whiteness.

Among all the Observations there is none accompanied with so odd circumstances as the twenty-fourth. Of those the principal 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 Circumferences they so much interfere and are blended together, that they seem to constitute an uniform whiteness. But when the Rays pass 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 circumference 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 constituent 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.

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, constitute 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 pass 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 constitute 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-glasses: 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-glasses: 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 assistant 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-glasses, (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 Glass 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 Glass, by which these Waves for the most part are caused, yet they may seem to extend themselves over the whole Glass, 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 constitute so many several Waves, as there were divers orders of Colours promiscuously reflected from that part of the Glass.

These are the principal 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 circumstances; 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 associated 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 Glass; 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 multitude 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 constitute 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 circumstances 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 Analogy 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 Constitutions, 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 quantity 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 Analogy between Reflexion and Refraction will appear by considering, that when Light passeth 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 passing 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 passing out of Glass 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 passing 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 Glass, Crystal, metalline Glasses, Island Glasses, white transparent Arsenick, 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 Glass 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 Glass, 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 Glass and Crystal, there ought to be a weak Reflexion, and a stronger Reflexion in the Confine of common and metalline Glass; though I have not yet tried this. But in the Confine of two Glasses 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, Glass, 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 multitude 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 Spaces, 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 constitute Clouds or Mists; and for the most part Spaces 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 principal 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 scraped, Glass 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-glasses, 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, Glass, 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 constitute a Mass 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 Peacocks 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 Glass, the Infusion of _Lignum Nephriticum_, 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 associate into one cluster, 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 constitute Globules of all intermediate sizes, those Globules, when they become of convenient size to reflect some Colours and transmit others, may constitute 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._

This will appear by considering, that the Colour of a Body depends not only on the Rays which are incident perpendicularly on its parts, but on those also which are incident at all other Angles. And that according to the 7th Observation, a very little variation of obliquity will change the reflected Colour, where the thin Body or small Particles is rarer than the ambient Medium, insomuch that such a small Particle will at diversly oblique Incidences reflect all sorts of Colours, in so great a variety that the Colour resulting from them all, confusedly reflected from a heap of such Particles, must rather be a white or grey than any other Colour, or at best it must be but a very imperfect and dirty Colour. Whereas if the thin Body or small Particle be much denser than the ambient Medium, the Colours, according to the 19th Observation, are so little changed by the variation of obliquity, that the Rays which are reflected least obliquely may predominate over the rest, so much as to cause a heap of such Particles to appear very intensely of their Colour.

It conduces also something to the confirmation of this Proposition, that, according to the 22d Observation, the Colours exhibited by the denser thin Body within the rarer, are more brisk than those exhibited by the rarer within the denser.

PROP. VII.

_The bigness of the component parts of natural Bodies may be conjectured by their Colours._

For since the parts of these Bodies, by _Prop._ 5. do most probably exhibit the same Colours with a Plate of equal thickness, provided they have the same refractive density; and since their parts seem for the most part to have much the same density with Water or Glass, as by many circumstances is obvious to collect; to determine the sizes of those parts, you need only have recourse to the precedent Tables, in which the thickness of Water or Glass exhibiting any Colour is expressed. Thus if it be desired to know the diameter of a Corpuscle, which being of equal density with Glass shall reflect green of the third Order; the Number 16-1/4 shews it to be (16-1/4)/10000 parts of an Inch.

The greatest difficulty is here to know of what Order the Colour of any Body is. And for this end we must have recourse to the 4th and 18th Observations; from whence may be collected these particulars.

_Scarlets_, and other _reds_, _oranges_, and _yellows_, if they be pure and intense, are most probably of the second order. Those of the first and third order also may be pretty good; only the yellow of the first order is faint, and the orange and red of the third Order have a great Mixture of violet and blue.

There may be good _Greens_ of the fourth Order, but the purest are of the third. And of this Order the green of all Vegetables seems to be, partly by reason of the Intenseness of their Colours, and partly because when they wither some of them turn to a greenish yellow, and others to a more perfect yellow or orange, or perhaps to red, passing first through all the aforesaid intermediate Colours. Which Changes seem to be effected by the exhaling of the Moisture which may leave the tinging Corpuscles more dense, and something augmented by the Accretion of the oily and earthy Part of that Moisture. Now the green, without doubt, is of the same Order with those Colours into which it changeth, because the Changes are gradual, and those Colours, though usually not very full, yet are often too full and lively to be of the fourth Order.

_Blues_ and _Purples_ may be either of the second or third Order, but the best are of the third. Thus the Colour of Violets seems to be of that Order, because their Syrup by acid Liquors turns red, and by urinous and alcalizate turns green. For since it is of the Nature of Acids to dissolve or attenuate, and of Alcalies to precipitate or incrassate, if the Purple Colour of the Syrup was of the second Order, an acid Liquor by attenuating its tinging Corpuscles would change it to a red of the first Order, and an Alcali by incrassating them would change it to a green of the second Order; which red and green, especially the green, seem too imperfect to be the Colours produced by these Changes. But if the said Purple be supposed of the third Order, its Change to red of the second, and green of the third, may without any Inconvenience be allow'd.

If there be found any Body of a deeper and less reddish Purple than that of the Violets, its Colour most probably is of the second Order. But yet there being no Body commonly known whose Colour is constantly more deep than theirs, I have made use of their Name to denote the deepest and least reddish Purples, such as manifestly transcend their Colour in purity.

The _blue_ of the first Order, though very faint and little, may possibly be the Colour of some Substances; and particularly the azure Colour of the Skies seems to be of this Order. For all Vapours when they begin to condense and coalesce into small Parcels, become first of that Bigness, whereby such an Azure must be reflected before they can constitute Clouds of other Colours. And so this being the first Colour which Vapours begin to reflect, it ought to be the Colour of the finest and most transparent Skies, in which Vapours are not arrived to that Grossness requisite to reflect other Colours, as we find it is by Experience.