Opticks Part 9

Besides the aforesaid colour'd Rings there would often appear small Spots of Colours, ascending and descending up and down the sides of the Bubble, by reason of some Inequalities in the subsiding of the Water.

And sometimes small black Spots generated at the sides would ascend up to the larger black Spot at the top of the Bubble, and unite with it.

_Obs._ 18. Because the Colours of these Bubbles were more extended and lively than those of the Air thinn'd between two Gla.s.ses, and so more easy to be distinguish'd, I shall here give you a farther description of their order, as they were observ'd in viewing them by Reflexion of the Skies when of a white Colour, whilst a black substance was placed behind the Bubble. And they were these, red, blue; red, blue; red, blue; red, green; red, yellow, green, blue, purple; red, yellow, green, blue, violet; red, yellow, white, blue, black.

The three first Successions of red and blue were very dilute and dirty, especially the first, where the red seem'd in a manner to be white.

Among these there was scarce any other Colour sensible besides red and blue, only the blues (and princ.i.p.ally the second blue) inclined a little to green.

The fourth red was also dilute and dirty, but not so much as the former three; after that succeeded little or no yellow, but a copious green, which at first inclined a little to yellow, and then became a pretty brisk and good willow green, and afterwards changed to a bluish Colour; but there succeeded neither blue nor violet.

The fifth red at first inclined very much to purple, and afterwards became more bright and brisk, but yet not very pure. This was succeeded with a very bright and intense yellow, which was but little in quant.i.ty, and soon chang'd to green: But that green was copious and something more pure, deep and lively, than the former green. After that follow'd an excellent blue of a bright Sky-colour, and then a purple, which was less in quant.i.ty than the blue, and much inclined to red.

The sixth red was at first of a very fair and lively scarlet, and soon after of a brighter Colour, being very pure and brisk, and the best of all the reds. Then after a lively orange follow'd an intense bright and copious yellow, which was also the best of all the yellows, and this changed first to a greenish yellow, and then to a greenish blue; but the green between the yellow and the blue, was very little and dilute, seeming rather a greenish white than a green. The blue which succeeded became very good, and of a very bright Sky-colour, but yet something inferior to the former blue; and the violet was intense and deep with little or no redness in it. And less in quant.i.ty than the blue.

In the last red appeared a tincture of scarlet next to violet, which soon changed to a brighter Colour, inclining to an orange; and the yellow which follow'd was at first pretty good and lively, but afterwards it grew more dilute until by degrees it ended in perfect whiteness. And this whiteness, if the Water was very tenacious and well-temper'd, would slowly spread and dilate it self over the greater part of the Bubble; continually growing paler at the top, where at length it would crack in many places, and those cracks, as they dilated, would appear of a pretty good, but yet obscure and dark Sky-colour; the white between the blue Spots diminis.h.i.+ng, until it resembled the Threds of an irregular Net-work, and soon after vanish'd, and left all the upper part of the Bubble of the said dark blue Colour. And this Colour, after the aforesaid manner, dilated it self downwards, until sometimes it hath overspread the whole Bubble. In the mean while at the top, which was of a darker blue than the bottom, and appear'd also full of many round blue Spots, something darker than the rest, there would emerge one or more very black Spots, and within those, other Spots of an intenser blackness, which I mention'd in the former Observation; and these continually dilated themselves until the Bubble broke.

If the Water was not very tenacious, the black Spots would break forth in the white, without any sensible intervention of the blue. And sometimes they would break forth within the precedent yellow, or red, or perhaps within the blue of the second order, before the intermediate Colours had time to display themselves.

By this description you may perceive how great an affinity these Colours have with those of Air described in the fourth Observation, although set down in a contrary order, by reason that they begin to appear when the Bubble is thickest, and are most conveniently reckon'd from the lowest and thickest part of the Bubble upwards.

_Obs._ 19. Viewing in several oblique Positions of my Eye the Rings of Colours emerging on the top of the Bubble, I found that they were sensibly dilated by increasing the obliquity, but yet not so much by far as those made by thinn'd Air in the seventh Observation. For there they were dilated so much as, when view'd most obliquely, to arrive at a part of the Plate more than twelve times thicker than that where they appear'd when viewed perpendicularly; whereas in this case the thickness of the Water, at which they arrived when viewed most obliquely, was to that thickness which exhibited them by perpendicular Rays, something less than as 8 to 5. By the best of my Observations it was between 15 and 15-1/2 to 10; an increase about 24 times less than in the other case.

Sometimes the Bubble would become of an uniform thickness all over, except at the top of it near the black Spot, as I knew, because it would exhibit the same appearance of Colours in all Positions of the Eye. And then the Colours which were seen at its apparent circ.u.mference by the obliquest Rays, would be different from those that were seen in other places, by Rays less oblique to it. And divers Spectators might see the same part of it of differing Colours, by viewing it at very differing Obliquities. Now observing how much the Colours at the same places of the Bubble, or at divers places of equal thickness, were varied by the several Obliquities of the Rays; by the a.s.sistance of the 4th, 14th, 16th and 18th Observations, as they are hereafter explain'd, I collect the thickness of the Water requisite to exhibit any one and the same Colour, at several Obliquities, to be very nearly in the Proportion expressed in this Table.

-----------------+------------------+---------------- Incidence on | Refraction into | Thickness of the Water. | the Water. | the Water.

-----------------+------------------+---------------- Deg. Min. | Deg. Min. | | | 00 00 | 00 00 | 10 | | 15 00 | 11 11 | 10-1/4 | | 30 00 | 22 1 | 10-4/5 | | 45 00 | 32 2 | 11-4/5 | | 60 00 | 40 30 | 13 | | 75 00 | 46 25 | 14-1/2 | | 90 00 | 48 35 | 15-1/5 -----------------+------------------+----------------

In the two first Columns are express'd the Obliquities of the Rays to the Superficies of the Water, that is, their Angles of Incidence and Refraction. Where I suppose, that the Sines which measure them are in round Numbers, as 3 to 4, though probably the Dissolution of Soap in the Water, may a little alter its refractive Virtue. In the third Column, the Thickness of the Bubble, at which any one Colour is exhibited in those several Obliquities, is express'd in Parts, of which ten const.i.tute its Thickness when the Rays are perpendicular. And the Rule found by the seventh Observation agrees well with these Measures, if duly apply'd; namely, that the Thickness of a Plate of Water requisite to exhibit one and the same Colour at several Obliquities of the Eye, is proportional to the Secant of an Angle, whose Sine is the first of an hundred and six arithmetical mean Proportionals between the Sines of Incidence and Refraction counted from the lesser Sine, that is, from the Sine of Refraction when the Refraction is made out of Air into Water, otherwise from the Sine of Incidence.

I have sometimes observ'd, that the Colours which arise on polish'd Steel by heating it, or on Bell-metal, and some other metalline Substances, when melted and pour'd on the Ground, where they may cool in the open Air, have, like the Colours of Water-bubbles, been a little changed by viewing them at divers Obliquities, and particularly that a deep blue, or violet, when view'd very obliquely, hath been changed to a deep red. But the Changes of these Colours are not so great and sensible as of those made by Water. For the Scoria, or vitrified Part of the Metal, which most Metals when heated or melted do continually protrude, and send out to their Surface, and which by covering the Metals in form of a thin gla.s.sy Skin, causes these Colours, is much denser than Water; and I find that the Change made by the Obliquation of the Eye is least in Colours of the densest thin Substances.

_Obs._ 20. As in the ninth Observation, so here, the Bubble, by transmitted Light, appear'd of a contrary Colour to that, which it exhibited by Reflexion. Thus when the Bubble being look'd on by the Light of the Clouds reflected from it, seemed red at its apparent Circ.u.mference, if the Clouds at the same time, or immediately after, were view'd through it, the Colour at its Circ.u.mference would be blue.

And, on the contrary, when by reflected Light it appeared blue, it would appear red by transmitted Light.

_Obs._ 21. By wetting very thin Plates of _Muscovy_ Gla.s.s, whose thinness made the like Colours appear, the Colours became more faint and languid, especially by wetting the Plates on that side opposite to the Eye: But I could not perceive any variation of their Species. So then the thickness of a Plate requisite to produce any Colour, depends only on the density of the Plate, and not on that of the ambient Medium. And hence, by the 10th and 16th Observations, may be known the thickness which Bubbles of Water, or Plates of _Muscovy_ Gla.s.s, or other Substances, have at any Colour produced by them.

_Obs._ 22. A thin transparent Body, which is denser than its ambient Medium, exhibits more brisk and vivid Colours than that which is so much rarer; as I have particularly observed in the Air and Gla.s.s. For blowing Gla.s.s very thin at a Lamp Furnace, those Plates encompa.s.sed with Air did exhibit Colours much more vivid than those of Air made thin between two Gla.s.ses.

_Obs._ 23. Comparing the quant.i.ty of Light reflected from the several Rings, I found that it was most copious from the first or inmost, and in the exterior Rings became gradually less and less. Also the whiteness of the first Ring was stronger than that reflected from those parts of the thin Medium or Plate which were without the Rings; as I could manifestly perceive by viewing at a distance the Rings made by the two Object-gla.s.ses; or by comparing two Bubbles of Water blown at distant Times, in the first of which the Whiteness appear'd, which succeeded all the Colours, and in the other, the Whiteness which preceded them all.

_Obs._ 24. When the two Object-gla.s.ses 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 Mult.i.tude, 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.

[Ill.u.s.tration: FIG. 5.]

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-gla.s.ses, the middle Part of those Arcs became also confused, so as to disappear and const.i.tute 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-gla.s.ses, 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-gla.s.s 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 Mult.i.tudes of those Rings have discover'd themselves. And in like manner Plates of _Muscovy_ Gla.s.s, and Bubbles of Gla.s.s 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.

[Ill.u.s.tration: FIG. 6.]

But farther, to define the Lat.i.tude 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 s.p.a.ces, 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 a.s.sign'd the same Lat.i.tude 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 s.p.a.ces 1I, L3, 5M, O7, 9PR11, &c. and transmitted at the s.p.a.ces 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 s.p.a.ces 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 const.i.tution of the green in the third Series of Colours be desired, apply the Ruler as you see at [Greek: prsph], and by its pa.s.sing 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 princ.i.p.ally const.i.tuted 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 pa.s.s'd over the first s.p.a.ce 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 a.s.sistance of the 6th or 16th Observations. For according to those Observations the thickness of the thinned Air, which between two Gla.s.ses 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 Gla.s.ses 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 Gla.s.s, 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 Gla.s.s, 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 const.i.tution 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-gla.s.ses 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 Gla.s.ses 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. Gla.s.s.

|---------+----------+----------+ {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 a.s.sistance 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_ Gla.s.s laid upon a blue one, const.i.tuted 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 circ.u.mstances 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 Gla.s.ses, 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.