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SIR ISAAC NEWTON'S ADVERTISEMENTS

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Part of the ensuing Discourse about Light was written at the Desire ofsome Gentlemen of the Royal-Society,in the Year 1675, and then sentto their Secretary, and read at their Meetings, and the rest was addedabout twelve Years after to complete the Theory; except the third Book,and the last Proposition of the Second, which were since put togetherout of scatter'd Papers. To avoid being engaged in Disputes about theseMatters, I have hitherto delayed the printing, and should still havedelayed it, had not the Importunity of Friends prevailed upon me. If anyother Papers writ on this Subject are got out of my Hands they areimperfect, and were perhaps written before I had tried all theExperiments here set down, and fully satisfied my self about the Laws ofRefractions and Composition of Colours. I have here publish'd what Ithink proper to come abroad, wishing that it may not be translated intoanother Language without my Consent.

The Crowns of Colours, which sometimes appear about the Sun and Moon, Ihave endeavoured to give an Account of; but for want of sufficientObservations leave that Matter to be farther examined. The Subject ofthe Third Book I have also left imperfect, not having tried all theExperiments which I intended when I was about these Matters, norrepeated some of those which I did try, until I had satisfied my selfabout all their Circumstances. To communicate what I have tried, andleave the rest to others for farther Enquiry, is all my Design inpublishing these Papers.

In a Letter written to Mr. Leibnitzin the year 1679, and publishedby Dr. Wallis,I mention'd a Method by which I had found some generalTheorems about squaring Curvilinear Figures, or comparing them with theConic Sections, or other the simplest Figures with which they may becompared. And some Years ago I lent out a Manuscript containing suchTheorems, and having since met with some Things copied out of it, I haveon this Occasion made it publick, prefixing to it an Introduction,andsubjoining a Scholiumconcerning that Method. And I have joined withit another small Tract concerning the Curvilinear Figures of the SecondKind, which was also written many Years ago, and made known to someFriends, who have solicited the making it publick.

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In this Second Edition of these Opticks I have omitted the MathematicalTracts publish'd at the End of the former Edition, as not belonging tothe Subject. And at the End of the Third Book I have added someQuestions. And to shew that I do not take Gravity for an essentialProperty of Bodies, I have added one Question concerning its Cause,chusing to propose it by way of a Question, because I am not yetsatisfied about it for want of Experiments.

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This new Edition of Sir Isaac Newton's Opticksis carefully printedfrom the Third Edition, as it was corrected by the Author's own Hand,and left before his Death with the Bookseller. Since Sir Isaac'sLectiones Opticæ,which he publickly read in the University ofCambridgein the Years 1669, 1670, and 1671, are lately printed, it hasbeen thought proper to make at the bottom of the Pages several Citationsfrom thence, where may be found the Demonstrations, which the Authoromitted in these Opticks.

THE FIRST BOOK OF OPTICKS

PART I.

My Design in this Book is not to explain the Properties of Light byHypotheses, but to propose and prove them by Reason and Experiments: Inorder to which I shall premise the following Definitions and Axioms.

DEFINITIONS

DEFIN. I.

By the Rays of Light I understand its least Parts, and those as wellSuccessive in the same Lines, as Contemporary in several Lines. For itis manifest that Light consists of Parts, both Successive andContemporary; because in the same place you may stop[Pg 2] that which comesone moment, and let pass that which comes presently after; and in thesame time you may stop it in any one place, and let it pass in anyother. For that part of Light which is stopp'd cannot be the same withthat which is let pass. The least Light or part of Light, which may bestopp'd alone without the rest of the Light, or propagated alone, or door suffer any thing alone, which the rest of the Light doth not orsuffers not, I call a Ray of Light.

DEFIN. II.

Refrangibility of the Rays of Light, is their Disposition to berefracted or turned out of their Way in passing out of one transparentBody or Medium into another. And a greater or less Refrangibility ofRays, is their Disposition to be turned more or less out of their Way inlike Incidences on the same Medium. Mathematicians usually consider theRays of Light to be Lines reaching from the luminous Body to the Bodyilluminated, and the refraction of those Rays to be the bending orbreaking of those lines in their passing out of one Medium into another.And thus may Rays and Refractions be considered, if Light be propagatedin an instant. But by an Argument taken from the Æquations of the timesof the Eclipses ofJupiter's Satellites, it seems that Light ispropagated in time, spending in its passage from the Sun to us aboutseven Minutes of time: And therefore I have chosen to define Rays andRefractions in such general terms as may agree to Light in both cases.[Pg 3]

DEFIN. III.

Reflexibility of Rays, is their Disposition to be reflected or turnedback into the same Medium from any other Medium upon whose Surface theyfall. And Rays are more or less reflexible, which are turned back moreor less easily. As if Light pass out of a Glass into Air, and by beinginclined more and more to the common Surface of the Glass and Air,begins at length to be totally reflected by that Surface; those sorts ofRays which at like Incidences are reflected most copiously, or byinclining the Rays begin soonest to be totally reflected, are mostreflexible.

DEFIN. IV.

The Angle of Incidence is that Angle, which the Line described by theincident Ray contains with the Perpendicular to the reflecting orrefracting Surface at the Point of Incidence.

DEFIN. V.

The Angle of Reflexion or Refraction, is the Angle which the linedescribed by the reflected or refracted Ray containeth with thePerpendicular to the reflecting or refracting Surface at the Point ofIncidence.

DEFIN. VI.

The Sines of Incidence, Reflexion, and Refraction, are the Sines of theAngles of Incidence, Reflexion, and Refraction.[Pg 4]

DEFIN. VII

The Light whose Rays are all alike Refrangible, I call Simple,Homogeneal and Similar; and that whose Rays are some more Refrangiblethan others, I call Compound, Heterogeneal and Dissimilar. The formerLight I call Homogeneal, not because I would affirm it so in allrespects, but because the Rays which agree in Refrangibility, agree atleast in all those their other Properties which I consider in thefollowing Discourse.

DEFIN. VIII.

The Colours of Homogeneal Lights, I call Primary, Homogeneal andSimple; and those of Heterogeneal Lights, Heterogeneal and Compound.For these are always compounded of the colours of Homogeneal Lights; aswill appear in the following Discourse.

AXIOMS.

AX. I.

The Angles of Reflexion and Refraction, lie in one and the same Planewith the Angle of Incidence.

AX. II.

AX. III.

If the refracted Ray be returned directly back to the Point ofIncidence, it shall be refracted into the Line before described by theincident Ray.

AX. IV.

Refraction out of the rarer Medium into the denser, is made towards thePerpendicular; that is, so that the Angle of Refraction be less than theAngle of Incidence.

AX. V.

The Sine of Incidence is either accurately or very nearly in a givenRatio to the Sine of Refraction.

Whence if that Proportion be known in any one Inclination of theincident Ray, 'tis known in all the Inclinations, and thereby theRefraction in all cases[Pg 6] of Incidence on the same refracting Body may bedetermined. Thus if the Refraction be made out of Air into Water, theSine of Incidence of the red Light is to the Sine of its Refraction as 4to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light ofother Colours the Sines have other Proportions: but the difference is solittle that it need seldom be considered.

Suppose therefore, that RS [inFig. 1.] represents the Surface ofstagnating Water, and that C is the point of Incidence in which any Raycoming in the Air from A in the Line AC is reflected or refracted, and Iwould know whither this Ray shall go after Reflexion or Refraction: Ierect upon the Surface of the Water from the point of Incidence thePerpendicular CP and produce it downwards to Q, and conclude by thefirst Axiom, that the Ray after Reflexion and[Pg 7] Refraction, shall befound somewhere in the Plane of the Angle of Incidence ACP produced. Ilet fall therefore upon the Perpendicular CP the Sine of Incidence AD;and if the reflected Ray be desired, I produce AD to B so that DB beequal to AD, and draw CB. For this Line CB shall be the reflected Ray;the Angle of Reflexion BCP and its Sine BD being equal to the Angle andSine of Incidence, as they ought to be by the second Axiom, But if therefracted Ray be desired, I produce AD to H, so that DH may be to AD asthe Sine of Refraction to the Sine of Incidence, that is, (if the Lightbe red) as 3 to 4; and about the Center C and in the Plane ACP with theRadius CA describing a Circle ABE, I draw a parallel to thePerpendicular CPQ, the Line HE cutting the Circumference in E, andjoining CE, this Line CE shall be the Line of the refracted Ray. For ifEF be let fall perpendicularly on the Line PQ, this Line EF shall be theSine of Refraction of the Ray CE, the Angle of Refraction being ECQ; andthis Sine EF is equal to DH, and consequently in Proportion to the Sineof Incidence AD as 3 to 4.

In like manner, if there be a Prism of Glass (that is, a Glass boundedwith two Equal and Parallel Triangular ends, and three plain and wellpolished Sides, which meet in three Parallel Lines running from thethree Angles of one end to the three Angles of the other end) and if theRefraction of the Light in passing cross this Prism be desired: Let ACB[inFig. 2.] represent a Plane cutting this Prism transversly to itsthree Parallel lines or edges there where[Pg 8] the Light passeth through it,and let DE be the Ray incident upon the first side of the Prism AC wherethe Light goes into the Glass; and by putting the Proportion of the Sineof Incidence to the Sine of Refraction as 17 to 11 find EF the firstrefracted Ray. Then taking this Ray for the Incident Ray upon the secondside of the Glass BC where the Light goes out, find the next refractedRay FG by putting the Proportion of the Sine of Incidence to the Sine ofRefraction as 11 to 17. For if the Sine of Incidence out of Air intoGlass be to the Sine of Refraction as 17 to 11, the Sine of Incidenceout of Glass into Air must on the contrary be to the Sine of Refractionas 11 to 17, by the third Axiom.

Much after the same manner, if ACBD [inFig. 3.] represent a Glassspherically convex on both sides (usually called aLens, such as is aBurning-glass, or Spectacle-glass, or an Object-glass of a Telescope)and it be required to know how Light falling upon it from any lucidpoint Q shall be refracted, let QM represent a Ray falling upon anypoint M of its first spherical Surface ACB, and by erecting aPerpendicular to the Glass at the point M, find the first refracted RayMN by the Proportion of the Sines 17 to 11. Let that Ray in going out ofthe Glass be incident upon N, and then find the second refracted RayNq by the Proportion of the Sines 11 to 17. And after the same mannermay the Refraction be found when the Lens is convex on one side andplane or concave on the other, or concave on both sides.[Pg 9]

AX. VI.

Homogeneal Rays which flow from several Points of any Object, and fallperpendicularly or almost perpendicularly on any reflecting orrefracting Plane or spherical Surface, shall afterwards diverge from somany other Points, or be parallel to so many other Lines, or converge toso many other Points, either accurately or without any sensible Error.And the same thing will happen, if the Rays be reflected or refractedsuccessively by two or three or more Plane or Spherical Surfaces.

The Point from which Rays diverge or to which they converge may becalled theirFocus. And the Focus of the incident Rays being given,that of the reflected or refracted ones may be found by finding theRefraction of any two Rays, as above; or more readily thus.

Cas. 1. Let ACB [inFig. 4.] be a reflecting or refracting Plane,and Q the Focus of the incident Rays, and QqC a Perpendicular to thatPlane. And if this Perpendicular be produced toq, so thatqC beequal[Pg 11] to QC, the Pointq shall be the Focus of the reflected Rays: OrifqC be taken on the same side of the Plane with QC, and inproportion to QC as the Sine of Incidence to the Sine of Refraction, thePointq shall be the Focus of the refracted Rays.

Cas. 2. Let ACB [inFig. 5.] be the reflecting Surface of any Spherewhose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and ifin that Radius on the same side the Point T you take the Points Q andq, so that TQ, TE, and Tq, be continual Proportionals, and the PointQ be the Focus of the incident Rays, the Pointq shall be the Focus ofthe reflected ones.

Cas. 3. Let ACB [inFig. 6.] be the refracting Surface of any Spherewhose Centre is E. In any Radius thereof EC produced both ways take ETand Ct[Pg 12] equal to one another and severally in such Proportion to thatRadius as the lesser of the Sines of Incidence and Refraction hath tothe difference of those Sines. And then if in the same Line you find anytwo Points Q andq, so that TQ be to ET as Et totq, takingtqthe contrary way fromt which TQ lieth from T, and if the Point Q bethe Focus of any incident Rays, the Pointq shall be the Focus of therefracted ones.

And by the same means the Focus of the Rays after two or more Reflexionsor Refractions may be found.

Cas. 4. Let ACBD [inFig. 7.] be any refracting Lens, sphericallyConvex or Concave or Plane on either side, and let CD be its Axis (thatis, the Line which cuts both its Surfaces perpendicularly, and passesthrough the Centres of the Spheres,) and in this Axis produced let F andf be the Foci of the refracted[Pg 13] Rays found as above, when the incidentRays on both sides the Lens are parallel to the same Axis; and upon theDiameter Ff bisected in E, describe a Circle. Suppose now that anyPoint Q be the Focus of any incident Rays. Draw QE cutting the saidCircle in T andt, and therein taketq in such proportion totE astE or TE hath to TQ. Lettq lie the contrary way fromt which TQdoth from T, andq shall be the Focus of the refracted Rays withoutany sensible Error, provided the Point Q be not so remote from the Axis,nor the Lens so broad as to make any of the Rays fall too obliquely onthe refracting Surfaces.[A]

And by the like Operations may the reflecting or refracting Surfaces befound when the two Foci are given, and thereby a Lens be formed, whichshall make the Rays flow towards or from what Place you please.[B]

So then the Meaning of this Axiom is, that if Rays fall upon any Planeor Spherical Surface or Lens, and before their Incidence flow from ortowards any Point Q, they shall after Reflexion or Refraction flow fromor towards the Pointq found by the foregoing Rules. And if theincident Rays flow from or towards several points Q, the reflected orrefracted Rays shall flow from or towards so many other Points[Pg 14]qfound by the same Rules. Whether the reflected and refracted Rays flowfrom or towards the Pointq is easily known by the situation of thatPoint. For if that Point be on the same side of the reflecting orrefracting Surface or Lens with the Point Q, and the incident Rays flowfrom the Point Q, the reflected flow towards the Pointq and therefracted from it; and if the incident Rays flow towards Q, thereflected flow fromq, and the refracted towards it. And the contraryhappens whenq is on the other side of the Surface.

AX. VII.

Wherever the Rays which come from all the Points of any Object meetagain in so many Points after they have been made to converge byReflection or Refraction, there they will make a Picture of the Objectupon any white Body on which they fall.

So if PR [inFig. 3.] represent any Object without Doors, and AB be aLens placed at a hole in the Window-shut of a dark Chamber, whereby theRays that come from any Point Q of that Object are made to converge andmeet again in the Pointq; and if a Sheet of white Paper be held atq for the Light there to fall upon it, the Picture of that Object PRwill appear upon the Paper in its proper shape and Colours. For as theLight which comes from the Point Q goes to the Pointq, so the Lightwhich comes from other Points P and R of the Object, will go to so manyother correspondent Pointsp andr (as is manifest by the sixthAxiom;) so that every Point of the Object[Pg 15] shall illuminate acorrespondent Point of the Picture, and thereby make a Picture like theObject in Shape and Colour, this only excepted, that the Picture shallbe inverted. And this is the Reason of that vulgar Experiment of castingthe Species of Objects from abroad upon a Wall or Sheet of white Paperin a dark Room.

In like manner, when a Man views any Object PQR, [inFig. 8.] theLight which comes from the several Points of the Object is so refractedby the transparent skins and humours of the Eye, (that is, by theoutward coat EFG, called theTunica Cornea, and by the crystallinehumour AB which is beyond the Pupilmk) as to converge and meet againin so many Points in the bottom of the Eye, and there to paint thePicture of the Object upon that skin (called theTunica Retina) withwhich the bottom of the Eye is covered. For Anatomists, when they havetaken off from the bottom of the Eye that outward and most thick Coatcalled theDura Mater, can then see through the thinner Coats, thePictures of Objects lively painted thereon. And these Pictures,propagated by Motion along the Fibres of the Optick Nerves into theBrain, are the cause of Vision. For accordingly as these Pictures areperfect or imperfect, the Object is seen perfectly or imperfectly. Ifthe Eye be tinged with any colour (as in the Disease of theJaundice)so as to tinge the Pictures in the bottom of the Eye with that Colour,then all Objects appear tinged with the same Colour. If the Humours ofthe Eye by old Age decay, so as by shrinking to[Pg 16] make theCornea andCoat of theCrystalline Humour grow flatter than before, the Lightwill not be refracted enough, and for want of a sufficient Refractionwill not converge to the bottom of the Eye but to some place beyond it,and by consequence paint in the bottom of the Eye a confused Picture,and according to the Indistinctness of this Picture the Object willappear confused. This is the reason of the decay of sight in old Men,and shews why their Sight is mended by Spectacles. For those Convexglasses supply the defect of plumpness in the Eye, and by increasing theRefraction make the Rays converge sooner, so as to convene distinctly atthe bottom of the Eye if the Glass have a due degree of convexity. Andthe contrary happens in short-sighted Men whose Eyes are too plump. Forthe Refraction being now too great, the Rays converge and convene in theEyes before they come at the bottom; and therefore the Picture made inthe bottom and the Vision caused thereby will not be distinct, unlessthe Object be brought so near the Eye as that the place where theconverging Rays convene may be removed to the bottom, or that theplumpness of the Eye be taken off and the Refractions diminished by aConcave-glass of a due degree of Concavity, or lastly that by Age theEye grow flatter till it come to a due Figure: For short-sighted Men seeremote Objects best in Old Age, and therefore they are accounted to havethe most lasting Eyes.[Pg 17]

AX. VIII.

An Object seen by Reflexion or Refraction, appears in that place fromwhence the Rays after their last Reflexion or Refraction diverge infalling on the Spectator's Eye.

If the Object A [inFig. 9.] be seen by Reflexion of a Looking-glassmn, it shall appear, not in its proper place A, but behind the Glassata, from whence any Rays AB, AC, AD, which flow from one and thesame Point of the Object, do after their Reflexion made in the Points B,C, D, diverge in going from the Glass to E, F, G, where they areincident on the Spectator's Eyes. For these Rays do make the samePicture in the bottom of the Eyes as if they had come from the Objectreally placed ata without the Interposition of the Looking-glass; andall Vision is made according to the place and shape of that Picture.[Pg 19]

In like manner the Object D [inFig. 2.] seen through a Prism, appearsnot in its proper place D, but is thence translated to some other placed situated in the last refracted Ray FG drawn backward from F tod.

And so the Object Q [inFig. 10.] seen through the Lens AB, appears atthe placeq from whence the Rays diverge in passing from the Lens tothe Eye. Now it is to be noted, that the Image of the Object atq isso much bigger or lesser than the Object it self at Q, as the distanceof the Image atq from the Lens AB is bigger or less than the distanceof the Object at Q from the same Lens. And if the Object be seen throughtwo or more such Convex or Concave-glasses, every Glass shall make a newImage, and the Object shall appear in the place of the bigness of thelast Image. Which consideration unfolds the Theory of Microscopes andTelescopes. For that Theory consists in almost nothing else than thedescribing such Glasses as shall make the last Image of any Object asdistinct and large and luminous as it can conveniently be made.

I have now given in Axioms and their Explications the sum of what hathhitherto been treated of in[Pg 20] Opticks. For what hath been generallyagreed on I content my self to assume under the notion of Principles, inorder to what I have farther to write. And this may suffice for anIntroduction to Readers of quick Wit and good Understanding not yetversed in Opticks: Although those who are already acquainted with thisScience, and have handled Glasses, will more readily apprehend whatfolloweth.

FOOTNOTES:

[A] In our Author'sLectiones Opticæ, Part I. Sect. IV. Prop29, 30, there is an elegant Method of determining theseFoci; not onlyin spherical Surfaces, but likewise in any other curved Figure whatever:And in Prop. 32, 33, the same thing is done for any Ray lying out of theAxis.

[B]Ibid. Prop. 34.

PROPOSITIONS.

PROP. I.Theor. I.

Exper. 1. I took a black oblong stiff Paper terminated by Parallel Sides, and witha Perpendicular right Line drawn cross from one Side to the other,distinguished it into two equal Parts. One of these parts I painted witha red colour and the other with a blue. The Paper was very black, andthe Colours intense and thickly laid on, that the Phænomenon might bemore conspicuous. This Paper I view'd through a Prism of solid Glass,whose two Sides through which the Light passed to the Eye were plane andwell polished, and contained an Angle of about sixty degrees; whichAngle I call the refracting Angle of the Prism. And whilst I view'd it,[Pg 21]I held it and the Prism before a Window in such manner that the Sides ofthe Paper were parallel to the Prism, and both those Sides and the Prismwere parallel to the Horizon, and the cross Line was also parallel toit: and that the Light which fell from the Window upon the Paper made anAngle with the Paper, equal to that Angle which was made with the samePaper by the Light reflected from it to the Eye. Beyond the Prism wasthe Wall of the Chamber under the Window covered over with black Cloth,and the Cloth was involved in Darkness that no Light might be reflectedfrom thence, which in passing by the Edges of the Paper to the Eye,might mingle itself with the Light of the Paper, and obscure thePhænomenon thereof. These things being thus ordered, I found that if therefracting Angle of the Prism be turned upwards, so that the Paper mayseem to be lifted upwards by the Refraction, its blue half will belifted higher by the Refraction than its red half. But if the refractingAngle of the Prism be turned downward, so that the Paper may seem to becarried lower by the Refraction, its blue half will be carried somethinglower thereby than its red half. Wherefore in both Cases the Light whichcomes from the blue half of the Paper through the Prism to the Eye, doesin like Circumstances suffer a greater Refraction than the Light whichcomes from the red half, and by consequence is more refrangible.

Illustration. In the eleventh Figure, MN represents the Window, and DEthe Paper terminated with parallel Sides DJ and HE, and by thetransverse[Pg 22] Line FG distinguished into two halfs, the one DG of anintensely blue Colour, the other FE of an intensely red. And BACcabrepresents the Prism whose refracting Planes ABba and ACca meet inthe Edge of the refracting Angle Aa. This Edge Aa being upward, isparallel both to the Horizon, and to the Parallel-Edges of the Paper DJand HE, and the transverse Line FG is perpendicular to the Plane of theWindow. Andde represents the Image of the Paper seen by Refractionupwards in such manner, that the blue half DG is carried higher todgthan the[Pg 23] red half FE is tofe, and therefore suffers a greaterRefraction. If the Edge of the refracting Angle be turned downward, theImage of the Paper will be refracted downward; suppose to δε,and the blue half will be refracted lower to δγ than the redhalf is to πε.

Exper. 2. About the aforesaid Paper, whose two halfs were painted overwith red and blue, and which was stiff like thin Pasteboard, I lappedseveral times a slender Thred of very black Silk, in such manner thatthe several parts of the Thred might appear upon the Colours like somany black Lines drawn over them, or like long and slender dark Shadowscast upon them. I might have drawn black Lines with a Pen, but theThreds were smaller and better defined. This Paper thus coloured andlined I set against a Wall perpendicularly to the Horizon, so that oneof the Colours might stand to the Right Hand, and the other to the Left.Close before the Paper, at the Confine of the Colours below, I placed aCandle to illuminate the Paper strongly: For the Experiment was tried inthe Night. The Flame of the Candle reached up to the lower edge of thePaper, or a very little higher. Then at the distance of six Feet, andone or two Inches from the Paper upon the Floor I erected a Glass Lensfour Inches and a quarter broad, which might collect the Rays comingfrom the several Points of the Paper, and make them converge towards somany other Points at the same distance of six Feet, and one or twoInches on the other side of the Lens, and so form the Image of the[Pg 24]coloured Paper upon a white Paper placed there, after the same mannerthat a Lens at a Hole in a Window casts the Images of Objects abroadupon a Sheet of white Paper in a dark Room. The aforesaid white Paper,erected perpendicular to the Horizon, and to the Rays which fell upon itfrom the Lens, I moved sometimes towards the Lens, sometimes from it, tofind the Places where the Images of the blue and red Parts of thecoloured Paper appeared most distinct. Those Places I easily knew by theImages of the black Lines which I had made by winding the Silk about thePaper. For the Images of those fine and slender Lines (which by reasonof their Blackness were like Shadows on the Colours) were confused andscarce visible, unless when the Colours on either side of each Line wereterminated most distinctly, Noting therefore, as diligently as I could,the Places where the Images of the red and blue halfs of the colouredPaper appeared most distinct, I found that where the red half of thePaper appeared distinct, the blue half appeared confused, so that theblack Lines drawn upon it could scarce be seen; and on the contrary,where the blue half appeared most distinct, the red half appearedconfused, so that the black Lines upon it were scarce visible. Andbetween the two Places where these Images appeared distinct there wasthe distance of an Inch and a half; the distance of the white Paper fromthe Lens, when the Image of the red half of the coloured Paper appearedmost distinct, being greater by an Inch and an half than the distance ofthe same white Paper from the[Pg 25] Lens, when the Image of the blue halfappeared most distinct. In like Incidences therefore of the blue and redupon the Lens, the blue was refracted more by the Lens than the red, soas to converge sooner by an Inch and a half, and therefore is morerefrangible.

Illustration. In the twelfth Figure (p. 27), DE signifies the colouredPaper, DG the blue half, FE the red half, MN the Lens, HJ the whitePaper in that Place where the red half with its black Lines appeareddistinct, andhi the same Paper in that Place where the blue halfappeared distinct. The Placehi was nearer to the Lens MN than thePlace HJ by an Inch and an half.

Scholium. The same Things succeed, notwithstanding that some of theCircumstances be varied; as in the first Experiment when the Prism andPaper are any ways inclined to the Horizon, and in both when colouredLines are drawn upon very black Paper. But in the Description of theseExperiments, I have set down such Circumstances, by which either thePhænomenon might be render'd more conspicuous, or a Novice might moreeasily try them, or by which I did try them only. The same Thing, I haveoften done in the following Experiments: Concerning all which, this oneAdmonition may suffice. Now from these Experiments it follows not, thatall the Light of the blue is more refrangible than all the Light of thered: For both Lights are mixed of Rays differently refrangible, so thatin the red there are some Rays not less refrangible than those of theblue,[Pg 26] and in the blue there are some Rays not more refrangible thanthose of the red: But these Rays, in proportion to the whole Light, arebut few, and serve to diminish the Event of the Experiment, but are notable to destroy it. For, if the red and blue Colours were more diluteand weak, the distance of the Images would be less than an Inch and ahalf; and if they were more intense and full, that distance would begreater, as will appear hereafter. These Experiments may suffice for theColours of Natural Bodies. For in the Colours made by the Refraction ofPrisms, this Proposition will appear by the Experiments which are now tofollow in the next Proposition.

PROP. II.Theor. II.

In a very dark Chamber, at a round Hole, about one third Part of an Inchbroad, made in the Shut of a Window, I placed a Glass Prism, whereby theBeam of the Sun's Light, which came in at that Hole, might be refractedupwards toward the opposite Wall of the Chamber, and there form acolour'd Image of the Sun. The Axis of the Prism (that is, the Linepassing through the middle of the Prism from one end of it to the otherend parallel to the edge of the Refracting Angle) was in this and thefollowing Experiments perpendicular to the incident Rays. About thisAxis I turned the Prism slowly, and saw the refracted Light on the Wall,or coloured Image of the Sun, first to descend, and then to ascend.Between the Descent and Ascent, when the Image seemed Stationary, Istopp'd the Prism, and fix'd it in that Posture, that it should be movedno more. For in that Posture the Refractions of the Light at the twoSides of the refracting Angle, that is, at the Entrance of the Rays intothe Prism, and at their going out of it, were equal to one another.[C]So also in other Experiments, as often as I would have the Refractionson both sides the Prism to be equal to one another, I noted the Placewhere the Image of the Sun formed by the refracted Light stood stillbetween its two contrary Motions, in the common Period of its Progressand Regress; and when the Image fell upon that Place, I made fast thePrism. And in this Posture, as the most convenient, it is to beunderstood that all the Prisms are placed in the following Experiments,unless where some other Posture is described. The Prism therefore beingplaced in this Posture, I let the refracted Light fall perpendicularlyupon a Sheet of white Paper at the opposite Wall of the Chamber, andobserved the Figure and Dimensions of the Solar Image formed on thePaper by that Light. This Image was Oblong and not Oval, but terminatedwith two Rectilinear and Parallel Sides, and two Semicircular Ends. On[Pg 29]its Sides it was bounded pretty distinctly, but on its Ends veryconfusedly and indistinctly, the Light there decaying and vanishing bydegrees. The Breadth of this Image answered to the Sun's Diameter, andwas about two Inches and the eighth Part of an Inch, including thePenumbra. For the Image was eighteen Feet and an half distant from thePrism, and at this distance that Breadth, if diminished by the Diameterof the Hole in the Window-shut, that is by a quarter of an Inch,subtended an Angle at the Prism of about half a Degree, which is theSun's apparent Diameter. But the Length of the Image was about tenInches and a quarter, and the Length of the Rectilinear Sides abouteight Inches; and the refracting Angle of the Prism, whereby so great aLength was made, was 64 degrees. With a less Angle the Length of theImage was less, the Breadth remaining the same. If the Prism was turnedabout its Axis that way which made the Rays emerge more obliquely out ofthe second refracting Surface of the Prism, the Image soon became anInch or two longer, or more; and if the Prism was turned about thecontrary way, so as to make the Rays fall more obliquely on the firstrefracting Surface, the Image soon became an Inch or two shorter. Andtherefore in trying this Experiment, I was as curious as I could be inplacing the Prism by the above-mention'd Rule exactly in such a Posture,that the Refractions of the Rays at their Emergence out of the Prismmight be equal to that at their Incidence on it. This Prism had someVeins running along within the Glass from one[Pg 30] end to the other, whichscattered some of the Sun's Light irregularly, but had no sensibleEffect in increasing the Length of the coloured Spectrum. For I triedthe same Experiment with other Prisms with the same Success. Andparticularly with a Prism which seemed free from such Veins, and whoserefracting Angle was 62-1/2 Degrees, I found the Length of the Image9-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, theBreadth of the Hole in the Window-shut being 1/4 of an Inch, as before.And because it is easy to commit a Mistake in placing the Prism in itsdue Posture, I repeated the Experiment four or five Times, and alwaysfound the Length of the Image that which is set down above. With anotherPrism of clearer Glass and better Polish, which seemed free from Veins,and whose refracting Angle was 63-1/2 Degrees, the Length of this Imageat the same distance of 18-1/2 Feet was also about 10 Inches, or 10-1/8.Beyond these Measures for about a 1/4 or 1/3 of an Inch at either end ofthe Spectrum the Light of the Clouds seemed to be a little tinged withred and violet, but so very faintly, that I suspected that Tincturemight either wholly, or in great Measure arise from some Rays of theSpectrum scattered irregularly by some Inequalities in the Substance andPolish of the Glass, and therefore I did not include it in theseMeasures. Now the different Magnitude of the hole in the Window-shut,and different thickness of the Prism where the Rays passed through it,and different inclinations of the Prism to the Horizon, made no sensiblechanges in[Pg 31] the length of the Image. Neither did the different matter ofthe Prisms make any: for in a Vessel made of polished Plates of Glasscemented together in the shape of a Prism and filled with Water, thereis the like Success of the Experiment according to the quantity of theRefraction. It is farther to be observed, that the Rays went on in rightLines from the Prism to the Image, and therefore at their very going outof the Prism had all that Inclination to one another from which thelength of the Image proceeded, that is, the Inclination of more than twodegrees and an half. And yet according to the Laws of Opticks vulgarlyreceived, they could not possibly be so much inclined to one another.[D]For let EG [Fig. 13. (p. 27)] represent the Window-shut, F the holemade therein through which a beam of the Sun's Light was transmittedinto the darkened Chamber, and ABC a Triangular Imaginary Plane wherebythe Prism is feigned to be cut transversely through the middle of theLight. Or if you please, let ABC represent the Prism it self, lookingdirectly towards the Spectator's Eye with its nearer end: And let XY bethe Sun, MN the Paper upon which the Solar Image or Spectrum is cast,and PT the Image it self whose sides towardsv andw are Rectilinearand Parallel, and ends towards P and T Semicircular. YKHP and XLJT aretwo Rays, the first of which comes from the lower part of the Sun to thehigher part of the Image, and is refracted in the Prism at K and H, andthe latter comes from the higher part of[Pg 32] the Sun to the lower part ofthe Image, and is refracted at L and J. Since the Refractions on bothsides the Prism are equal to one another, that is, the Refraction at Kequal to the Refraction at J, and the Refraction at L equal to theRefraction at H, so that the Refractions of the incident Rays at K and Ltaken together, are equal to the Refractions of the emergent Rays at Hand J taken together: it follows by adding equal things to equal things,that the Refractions at K and H taken together, are equal to theRefractions at J and L taken together, and therefore the two Rays beingequally refracted, have the same Inclination to one another afterRefraction which they had before; that is, the Inclination of half aDegree answering to the Sun's Diameter. For so great was the inclinationof the Rays to one another before Refraction. So then, the length of theImage PT would by the Rules of Vulgar Opticks subtend an Angle of half aDegree at the Prism, and by Consequence be equal to the breadthvw;and therefore the Image would be round. Thus it would be were the twoRays XLJT and YKHP, and all the rest which form the Image PwTv,alike refrangible. And therefore seeing by Experience it is found thatthe Image is not round, but about five times longer than broad, the Rayswhich going to the upper end P of the Image suffer the greatestRefraction, must be more refrangible than those which go to the lowerend T, unless the Inequality of Refraction be casual.

This Image or Spectrum PT was coloured, being red at its least refractedend T, and violet at its most[Pg 33] refracted end P, and yellow green andblue in the intermediate Spaces. Which agrees with the firstProposition, that Lights which differ in Colour, do also differ inRefrangibility. The length of the Image in the foregoing Experiments, Imeasured from the faintest and outmost red at one end, to the faintestand outmost blue at the other end, excepting only a little Penumbra,whose breadth scarce exceeded a quarter of an Inch, as was said above.

Exper. 4. In the Sun's Beam which was propagated into the Room throughthe hole in the Window-shut, at the distance of some Feet from the hole,I held the Prism in such a Posture, that its Axis might be perpendicularto that Beam. Then I looked through the Prism upon the hole, and turningthe Prism to and fro about its Axis, to make the Image of the Holeascend and descend, when between its two contrary Motions it seemedStationary, I stopp'd the Prism, that the Refractions of both sides ofthe refracting Angle might be equal to each other, as in the formerExperiment. In this situation of the Prism viewing through it the saidHole, I observed the length of its refracted Image to be many timesgreater than its breadth, and that the most refracted part thereofappeared violet, the least refracted red, the middle parts blue, greenand yellow in order. The same thing happen'd when I removed the Prismout of the Sun's Light, and looked through it upon the hole shining bythe Light of the Clouds beyond it. And yet if the Refraction were doneregularly according to one certain Proportion of the[Pg 34] Sines of Incidenceand Refraction as is vulgarly supposed, the refracted Image ought tohave appeared round.

So then, by these two Experiments it appears, that in Equal Incidencesthere is a considerable inequality of Refractions. But whence thisinequality arises, whether it be that some of the incident Rays arerefracted more, and others less, constantly, or by chance, or that oneand the same Ray is by Refraction disturbed, shatter'd, dilated, and asit were split and spread into many diverging Rays, asGrimaldosupposes, does not yet appear by these Experiments, but will appear bythose that follow.

Exper. 5. Considering therefore, that if in the third Experiment theImage of the Sun should be drawn out into an oblong Form, either by aDilatation of every Ray, or by any other casual inequality of theRefractions, the same oblong Image would by a second Refraction madesideways be drawn out as much in breadth by the like Dilatation of theRays, or other casual inequality of the Refractions sideways, I triedwhat would be the Effects of such a second Refraction. For this end Iordered all things as in the third Experiment, and then placed a secondPrism immediately after the first in a cross Position to it, that itmight again refract the beam of the Sun's Light which came to it throughthe first Prism. In the first Prism this beam was refracted upwards, andin the second sideways. And I found that by the Refraction of the secondPrism, the breadth of the Image was not increased, but its superiorpart,[Pg 35] which in the first Prism suffered the greater Refraction, andappeared violet and blue, did again in the second Prism suffer a greaterRefraction than its inferior part, which appeared red and yellow, andthis without any Dilatation of the Image in breadth.

Illustration. Let S [Fig. 14, 15.] represent the Sun, F the hole inthe Window, ABC the first Prism, DH the second Prism, Y the round Imageof the Sun made by a direct beam of Light when the Prisms are takenaway, PT the oblong Image of the Sun made by that beam passing throughthe first Prism alone, when the second Prism is taken away, andpt theImage made by the cross Refractions of both Prisms together. Now if theRays which tend towards the several Points of the round Image Y weredilated and spread by the Refraction of the first Prism, so that theyshould not any longer go in single Lines to single Points, but thatevery Ray being split, shattered, and changed from a Linear Ray to aSuperficies of Rays diverging from the Point of Refraction, and lying inthe Plane of the Angles of Incidence and Refraction, they should go inthose Planes to so many Lines reaching almost from one end of the ImagePT to the other, and if that Image should thence become oblong: thoseRays and their several parts tending towards the several Points of theImage PT ought to be again dilated and spread sideways by the transverseRefraction of the second Prism, so as to compose a four square Image,such as is represented at πτ. For the better understanding ofwhich, let the Image PT be distinguished into five[Pg 36]

[Pg 37]equal parts PQK, KQRL, LRSM, MSVN, NVT. And by the same irregularitythat the orbicular Light Y is by the Refraction of the first Prismdilated and drawn out into a long Image PT, the Light PQK which takes upa space of the same length and breadth with the Light Y ought to be bythe Refraction of the second Prism dilated and drawn out into the longImageπqkp, and the Light KQRL into the long Imagekqrl,and the Lights LRSM, MSVN, NVT, into so many other long Imageslrsm,msvn,nvtτ; and all these long Images would compose thefour square Imagesπτ. Thus it ought to be were every Raydilated by Refraction, and spread into a triangular Superficies of Raysdiverging from the Point of Refraction. For the second Refraction wouldspread the Rays one way as much as the first doth another, and so dilatethe Image in breadth as much as the first doth in length. And the samething ought to happen, were some rays casually refracted more thanothers. But the Event is otherwise. The Image PT was not made broader bythe Refraction of the second Prism, but only became oblique, as 'tisrepresented atpt, its upper end P being by the Refraction translatedto a greater distance than its lower end T. So then the Light which wenttowards the upper end P of the Image, was (at equal Incidences) morerefracted in the second Prism, than the Light which tended towards thelower end T, that is the blue and violet, than the red and yellow; andtherefore was more refrangible. The same Light was by the Refraction ofthe first Prism translated[Pg 38] farther from the place Y to which it tendedbefore Refraction; and therefore suffered as well in the first Prism asin the second a greater Refraction than the rest of the Light, and byconsequence was more refrangible than the rest, even before itsincidence on the first Prism.

Sometimes I placed a third Prism after the second, and sometimes also afourth after the third, by all which the Image might be often refractedsideways: but the Rays which were more refracted than the rest in thefirst Prism were also more refracted in all the rest, and that withoutany Dilatation of the Image sideways: and therefore those Rays for theirconstancy of a greater Refraction are deservedly reputed morerefrangible.

But that the meaning of this Experiment may more clearly appear, it isto be considered that the Rays which are equally refrangible do fallupon a Circle answering to the Sun's Disque. For this was proved in thethird Experiment. By a Circle I understand not here a perfectgeometrical Circle, but any orbicular Figure whose length is equal toits breadth, and which, as to Sense, may seem circular. Let therefore AG[inFig. 15.] represent the Circle which all the most refrangible Rayspropagated from the whole Disque of the Sun, would illuminate and paintupon the opposite Wall if they were alone; EL the Circle which all theleast refrangible Rays would in like manner illuminate and paint if theywere alone; BH, CJ, DK, the Circles which so many intermediate sorts ofRays would successively paint upon the[Pg 39] Wall, if they were singlypropagated from the Sun in successive order, the rest being alwaysintercepted; and conceive that there are other intermediate Circleswithout Number, which innumerable other intermediate sorts of Rays wouldsuccessively paint upon the Wall if the Sun should successively emitevery sort apart. And seeing the Sun emits all these sorts at once, theymust all together illuminate and paint innumerable equal Circles, of allwhich, being according to their degrees of Refrangibility placed inorder in a continual Series, that oblong Spectrum PT is composed which Idescribed in the third Experiment. Now if the Sun's circular Image Y [inFig. 15.] which is made by an unrefracted beam of Light was by anyDilation of the single Rays, or by any other irregularity in theRefraction of the first Prism, converted into the oblong Spectrum, PT:then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the crossRefraction of the second[Pg 40] Prism again dilating or otherwise scatteringthe Rays as before, to be in like manner drawn out and transformed intoan oblong Figure, and thereby the breadth of the Image PT would be nowas much augmented as the length of the Image Y was before by theRefraction of the first Prism; and thus by the Refractions of bothPrisms together would be formed a four square Figurepπtτ, as I described above. Wherefore since the breadth of theSpectrum PT is not increased by the Refraction sideways, it is certainthat the Rays are not split or dilated, or otherways irregularlyscatter'd by that Refraction, but that every Circle is by a regular anduniform Refraction translated entire into another Place, as the CircleAG by the greatest Refraction into the placeag, the Circle BH by aless Refraction into the placebh, the Circle CJ by a Refraction stillless into the placeci, and so of the rest; by which means a newSpectrumpt inclined to the former PT is in like manner composed ofCircles lying in a right Line; and these Circles must be of the samebigness with the former, because the breadths of all the Spectrums Y, PTandpt at equal distances from the Prisms are equal.

I considered farther, that by the breadth of the hole F through whichthe Light enters into the dark Chamber, there is a Penumbra made in theCircuit of the Spectrum Y, and that Penumbra remains in the rectilinearSides of the Spectrums PT andpt. I placed therefore at that hole aLens or Object-glass of a Telescope which might cast the Image of theSun distinctly on Y without any Penumbra at all,[Pg 41] and found that thePenumbra of the rectilinear Sides of the oblong Spectrums PT andptwas also thereby taken away, so that those Sides appeared as distinctlydefined as did the Circumference of the first Image Y. Thus it happensif the Glass of the Prisms be free from Veins, and their sides beaccurately plane and well polished without those numberless Waves orCurles which usually arise from Sand-holes a little smoothed inpolishing with Putty. If the Glass be only well polished and free fromVeins, and the Sides not accurately plane, but a little Convex orConcave, as it frequently happens; yet may the three Spectrums Y, PT andpt want Penumbras, but not in equal distances from the Prisms. Nowfrom this want of Penumbras, I knew more certainly that every one of theCircles was refracted according to some most regular, uniform andconstant Law. For if there were any irregularity in the Refraction, theright Lines AE and GL, which all the Circles in the Spectrum PT dotouch, could not by that Refraction be translated into the Linesaeandgl as distinct and straight as they were before, but there wouldarise in those translated Lines some Penumbra or Crookedness orUndulation, or other sensible Perturbation contrary to what is found byExperience. Whatsoever Penumbra or Perturbation should be made in theCircles by the cross Refraction of the second Prism, all that Penumbraor Perturbation would be conspicuous in the right Linesae andglwhich touch those Circles. And therefore since there is no such Penumbraor Perturbation in[Pg 42] those right Lines, there must be none in theCircles. Since the distance between those Tangents or breadth of theSpectrum is not increased by the Refractions, the Diameters of theCircles are not increased thereby. Since those Tangents continue to beright Lines, every Circle which in the first Prism is more or lessrefracted, is exactly in the same proportion more or less refracted inthe second. And seeing all these things continue to succeed after thesame manner when the Rays are again in a third Prism, and again in afourth refracted sideways, it is evident that the Rays of one and thesame Circle, as to their degree of Refrangibility, continue alwaysuniform and homogeneal to one another, and that those of several Circlesdo differ in degree of Refrangibility, and that in some certain andconstant Proportion. Which is the thing I was to prove.

There is yet another Circumstance or two of this Experiment by which itbecomes still more plain and convincing. Let the second Prism DH [inFig. 16.] be placed not immediately after the first, but at somedistance from it; suppose in the mid-way between it and the Wall onwhich the oblong Spectrum PT is cast, so that the Light from the firstPrism may fall upon it in the form of an oblong Spectrum πτparallel to this second Prism, and be refracted sideways to form theoblong Spectrumpt upon the Wall. And you will find as before, thatthis Spectrumpt is inclined to that Spectrum PT, which the firstPrism forms alone without the second; the blue ends P andp beingfarther distant from one another than the red ones T andt, and byconsequence that the Rays which go to the blue end π of theImage πτ, and which therefore suffer the greatest Refraction inthe first Prism, are again in the second Prism more refracted than therest.[Pg 43]

The same thing I try'd also by letting the Sun's Light into a dark Roomthrough two little round holes F and φ [inFig. 17.] made inthe Window, and with two parallel Prisms ABC and αβγ placed atthose holes (one at each) refracting those two beams of Light to theopposite Wall of the Chamber, in such manner that the two colour'dImages PT and MN which they there painted were joined end to end and layin one straight Line, the red end T of the one touching the blue end Mof the other. For if these two refracted Beams were again by a thirdPrism DH placed cross to the two first, refracted sideways, and theSpectrums thereby translated to some other part of the Wall of theChamber, suppose the Spectrum PT topt and the Spectrum MN tomn,these translated Spectrumspt andmn would not lie in one straightLine with their ends contiguous as before, but be broken off from oneanother and become parallel, the blue endm of the Imagemn being bya greater Refraction translated farther from its former place MT, thanthe red endt of the other Imagept from the same place MT; whichputs the Proposition past Dispute. And this happens whether the thirdPrism DH be placed immediately after the two first, or at a greatdistance from them, so that the Light refracted in the two first Prismsbe either[Pg 45] white and circular, or coloured and oblong when it falls onthe third.

Exper. 6. In the middle of two thin Boards I made round holes a thirdpart of an Inch in diameter, and in the Window-shut a much broader holebeing made to let into my darkned Chamber a large Beam of the Sun'sLight; I placed a Prism behind the Shut in that beam to refract ittowards the opposite Wall, and close behind the Prism I fixed one of theBoards, in such manner that the middle of the refracted Light might passthrough the hole made in it, and the rest be intercepted by the Board.Then at the distance of about twelve Feet from the first Board I fixedthe other Board in such manner that the middle of the refracted Lightwhich came through the hole in the first Board, and fell upon theopposite Wall, might pass through the hole in this other Board, and therest being intercepted by the Board might paint upon it the colouredSpectrum of the Sun. And close behind this Board I fixed another Prismto refract the Light which came through the hole. Then I returnedspeedily to the first Prism, and by turning it slowly to and fro aboutits Axis, I caused the Image which fell upon the second Board to move upand down upon that Board, that all its parts might successively passthrough the hole in that Board and fall upon the Prism behind it. And inthe mean time, I noted the places on the opposite Wall to which thatLight after its Refraction in the second Prism did pass; and by thedifference of the places I found that the Light which being mostrefracted in the first[Pg 46] Prism did go to the blue end of the Image, wasagain more refracted in the second Prism than the Light which went tothe red end of that Image, which proves as well the first Proposition asthe second. And this happened whether the Axis of the two Prisms wereparallel, or inclined to one another, and to the Horizon in any givenAngles.

Illustration. Let F [inFig. 18.] be the wide hole in theWindow-shut, through which the Sun shines upon the first Prism ABC, andlet the refracted Light fall upon the middle of the Board DE, and themiddle part of that Light upon the hole G made in the middle part ofthat Board. Let this trajected part of that Light fall again upon themiddle of the second Boardde, and there paint such an oblong colouredImage of the Sun as was described in the third Experiment. By turningthe Prism ABC slowly to and fro about its Axis, this Image will be madeto move up and down the Boardde, and by this means all its parts fromone end to the other may be made to pass successively through the holeg which is made in the middle of that Board. In the mean while anotherPrismabc is to be fixed next after that holeg, to refract thetrajected Light a second time. And these things being thus ordered, Imarked the places M and N of the opposite Wall upon which the refractedLight fell, and found that whilst the two Boards and second Prismremained unmoved, those places by turning the first Prism about its Axiswere changed perpetually. For when the lower part of the Light whichfell upon the second Boardde was cast through the holeg, it wentto a lower place M on the Wall and when the higher part of that Lightwas cast through the same holeg, it went to a higher place N on theWall, and when any intermediate part of the Light was cast through thathole, it went to some place on the Wall between M and N. The unchangedPosition of the holes in the Boards, made the Incidence of the Rays uponthe second Prism to be the same in all cases. And yet in that commonIncidence some of the Rays were more refracted, and others less. Andthose were more refracted in this Prism, which by a greater Refractionin the first Prism were more turned out of the way, and therefore fortheir Constancy of being more refracted are deservedly called morerefrangible.[Pg 47]

Exper. 7. At two holes made near one another in my Window-shut Iplaced two Prisms, one at each, which might cast upon the opposite Wall(after the manner of the third Experiment) two oblong coloured Images ofthe Sun. And at a little distance from the Wall I placed a long slenderPaper with straight and parallel edges, and ordered the Prisms and Paperso, that the red Colour of one Image might fall directly upon one halfof the Paper, and the violet Colour of the other Image upon the otherhalf of the same Paper; so that the Paper appeared of two Colours, redand violet, much after the manner of the painted Paper in the first andsecond Experiments. Then with a black Cloth I covered the Wall behindthe Paper, that no Light might be reflected from it to disturb theExperiment, and viewing the[Pg 49] Paper through a third Prism held parallelto it, I saw that half of it which was illuminated by the violet Lightto be divided from the other half by a greater Refraction, especiallywhen I went a good way off from the Paper. For when I viewed it too nearat hand, the two halfs of the Paper did not appear fully divided fromone another, but seemed contiguous at one of their Angles like thepainted Paper in the first Experiment. Which also happened when thePaper was too broad.

Sometimes instead of the Paper I used a white Thred, and this appearedthrough the Prism divided into two parallel Threds as is represented inthe nineteenth Figure, where DG denotes the Thred illuminated withviolet Light from D to E and with red Light from F to G, anddefg arethe parts of the Thred seen by Refraction. If one half of the Thred beconstantly illuminated with red, and the other half be illuminated withall the Colours successively, (which may be done by causing one of thePrisms to be turned about its Axis whilst the other remains unmoved)this other half in viewing the Thred through[Pg 50] the Prism, will appear ina continual right Line with the first half when illuminated with red,and begin to be a little divided from it when illuminated with Orange,and remove farther from it when illuminated with yellow, and stillfarther when with green, and farther when with blue, and go yet fartheroff when illuminated with Indigo, and farthest when with deep violet.Which plainly shews, that the Lights of several Colours are more andmore refrangible one than another, in this Order of their Colours, red,orange, yellow, green, blue, indigo, deep violet; and so proves as wellthe first Proposition as the second.

I caused also the coloured Spectrums PT [inFig. 17.] and MN made in adark Chamber by the Refractions of two Prisms to lie in a Right Line endto end, as was described above in the fifth Experiment, and viewing themthrough a third Prism held parallel to their Length, they appeared nolonger in a Right Line, but became broken from one another, as they arerepresented atpt andmn, the violet endm of the Spectrummnbeing by a greater Refraction translated farther from its former PlaceMT than the red endt of the other Spectrumpt.

I farther caused those two Spectrums PT [inFig. 20.] and MN to becomeco-incident in an inverted Order of their Colours, the red end of eachfalling on the violet end of the other, as they are represented in theoblong Figure PTMN; and then viewing them through a Prism DH heldparallel to their Length, they appeared not co-incident, as when view'dwith the naked Eye, but in the form of two distinct Spectrums[Pg 51]pt andmn crossing one another in the middle after the manner of the LetterX. Which shews that the red of the one Spectrum and violet of the other,which were co-incident at PN and MT, being parted from one another by agreater Refraction of the violet top andm than of the red tonandt, do differ in degrees of Refrangibility.

I illuminated also a little Circular Piece of white Paper all over withthe Lights of both Prisms intermixed, and when it was illuminated withthe red of one Spectrum, and deep violet of the other, so as by theMixture of those Colours to appear all over purple, I viewed the Paper,first at a less distance, and then at a greater, through a third Prism;and as I went from the Paper, the refracted Image thereof became moreand more divided by the unequal Refraction of the two mixed Colours, andat length parted into two distinct Images, a red one and a violet one,whereof the violet was farthest from the Paper, and therefore sufferedthe greatest Refraction. And when that Prism at the Window, which castthe violet on the Paper was taken away, the violet Image disappeared;but when the other Prism was taken away the red vanished; which shews,that these two Images were nothing else than the Lights of the twoPrisms, which had been intermixed on the purple Paper, but were partedagain by their unequal Refractions made in the third Prism, throughwhich the Paper was view'd. This also was observable, that if one of thePrisms at the Window, suppose that which cast the violet on the Paper,was[Pg 52] turned about its Axis to make all the Colours in this order,violet, indigo, blue, green, yellow, orange, red, fall successively onthe Paper from that Prism, the violet Image changed Colour accordingly,turning successively to indigo, blue, green, yellow and red, and inchanging Colour came nearer and nearer to the red Image made by theother Prism, until when it was also red both Images became fullyco-incident.

I placed also two Paper Circles very near one another, the one in thered Light of one Prism, and the other in the violet Light of the other.The Circles were each of them an Inch in diameter, and behind them theWall was dark, that the Experiment might not be disturbed by any Lightcoming from thence. These Circles thus illuminated, I viewed through aPrism, so held, that the Refraction might be made towards the redCircle, and as I went from them they came nearer and nearer together,and at length became co-incident; and afterwards when I went stillfarther off, they parted again in a contrary Order, the violet by agreater Refraction being carried beyond the red.

Exper. 8. In Summer, when the Sun's Light uses to be strongest, Iplaced a Prism at the Hole of the Window-shut, as in the thirdExperiment, yet so that its Axis might be parallel to the Axis of theWorld, and at the opposite Wall in the Sun's refracted Light, I placedan open Book. Then going six Feet and two Inches from the Book, I placedthere the above-mentioned Lens, by which the Light reflected from theBook might be made to converge[Pg 53] and meet again at the distance of sixFeet and two Inches behind the Lens, and there paint the Species of theBook upon a Sheet of white Paper much after the manner of the secondExperiment. The Book and Lens being made fast, I noted the Place wherethe Paper was, when the Letters of the Book, illuminated by the fullestred Light of the Solar Image falling upon it, did cast their Species onthat Paper most distinctly: And then I stay'd till by the Motion of theSun, and consequent Motion of his Image on the Book, all the Coloursfrom that red to the middle of the blue pass'd over those Letters; andwhen those Letters were illuminated by that blue, I noted again thePlace of the Paper when they cast their Species most distinctly upon it:And I found that this last Place of the Paper was nearer to the Lensthan its former Place by about two Inches and an half, or two and threequarters. So much sooner therefore did the Light in the violet end ofthe Image by a greater Refraction converge and meet, than the Light inthe red end. But in trying this, the Chamber was as dark as I could makeit. For, if these Colours be diluted and weakned by the Mixture of anyadventitious Light, the distance between the Places of the Paper willnot be so great. This distance in the second Experiment, where theColours of natural Bodies were made use of, was but an Inch and an half,by reason of the Imperfection of those Colours. Here in the Colours ofthe Prism, which are manifestly more full, intense, and lively thanthose of natural Bodies, the distance is two Inches and three quarters.And were[Pg 54] the Colours still more full, I question not but that thedistance would be considerably greater. For the coloured Light of thePrism, by the interfering of the Circles described in the second Figureof the fifth Experiment, and also by the Light of the very bright Cloudsnext the Sun's Body intermixing with these Colours, and by the Lightscattered by the Inequalities in the Polish of the Prism, was so verymuch compounded, that the Species which those faint and dark Colours,the indigo and violet, cast upon the Paper were not distinct enough tobe well observed.

Exper. 9. A Prism, whose two Angles at its Base were equal to oneanother, and half right ones, and the third a right one, I placed in aBeam of the Sun's Light let into a dark Chamber through a Hole in theWindow-shut, as in the third Experiment. And turning the Prism slowlyabout its Axis, until all the Light which went through one of itsAngles, and was refracted by it began to be reflected by its Base, atwhich till then it went out of the Glass, I observed that those Rayswhich had suffered the greatest Refraction were sooner reflected thanthe rest. I conceived therefore, that those Rays of the reflected Light,which were most refrangible, did first of all by a total Reflexionbecome more copious in that Light than the rest, and that afterwards therest also, by a total Reflexion, became as copious as these. To trythis, I made the reflected Light pass through another Prism, and beingrefracted by it to fall afterwards upon a Sheet of white Paper placed[Pg 55]at some distance behind it, and there by that Refraction to paint theusual Colours of the Prism. And then causing the first Prism to beturned about its Axis as above, I observed that when those Rays, whichin this Prism had suffered the greatest Refraction, and appeared of ablue and violet Colour began to be totally reflected, the blue andviolet Light on the Paper, which was most refracted in the second Prism,received a sensible Increase above that of the red and yellow, which wasleast refracted; and afterwards, when the rest of the Light which wasgreen, yellow, and red, began to be totally reflected in the firstPrism, the Light of those Colours on the Paper received as great anIncrease as the violet and blue had done before. Whence 'tis manifest,that the Beam of Light reflected by the Base of the Prism, beingaugmented first by the more refrangible Rays, and afterwards by the lessrefrangible ones, is compounded of Rays differently refrangible. Andthat all such reflected Light is of the same Nature with the Sun's Lightbefore its Incidence on the Base of the Prism, no Man ever doubted; itbeing generally allowed, that Light by such Reflexions suffers noAlteration in its Modifications and Properties. I do not here takeNotice of any Refractions made in the sides of the first Prism, becausethe Light enters it perpendicularly at the first side, and goes outperpendicularly at the second side, and therefore suffers none. So then,the Sun's incident Light being of the same Temper and Constitution withhis emergent Light, and the last being compounded[Pg 56] of Rays differentlyrefrangible, the first must be in like manner compounded.

Illustration. In the twenty-first Figure, ABC is the first Prism, BCits Base, B and C its equal Angles at the Base, each of 45 Degrees, Aits rectangular Vertex, FM a beam of the Sun's Light let into a darkRoom through a hole F one third part of an Inch broad, M its Incidenceon the Base of the Prism, MG a less refracted Ray, MH a more refractedRay, MN the beam of Light reflected from the Base, VXY the second Prismby which this beam in passing through it is refracted, Nt the lessrefracted Light of this beam, and Np the more refracted part thereof.When the first Prism ABC is turned about its Axis according to the orderof the Letters ABC, the Rays MH emerge more and more obliquely out ofthat Prism, and at length after their most oblique Emergence arereflected towards N, and going on top do increase the Number of the[Pg 57]Rays Np. Afterwards by continuing the Motion of the first Prism, theRays MG are also reflected to N and increase the number of the RaysNt. And therefore the Light MN admits into its Composition, first themore refrangible Rays, and then the less refrangible Rays, and yet afterthis Composition is of the same Nature with the Sun's immediate LightFM, the Reflexion of the specular Base BC causing no Alteration therein.

Exper. 10. Two Prisms, which were alike in Shape, I tied so together,that their Axis and opposite Sides being parallel, they composed aParallelopiped. And, the Sun shining into my dark Chamber through alittle hole in the Window-shut, I placed that Parallelopiped in his beamat some distance from the hole, in such a Posture, that the Axes of thePrisms might be perpendicular to the incident Rays, and that those Raysbeing incident upon the first Side of one Prism, might go on through thetwo contiguous Sides of both Prisms, and emerge out of the last Side ofthe second Prism. This Side being parallel to the first Side of thefirst Prism, caused the emerging Light to be parallel to the incident.Then, beyond these two Prisms I placed a third, which might refract thatemergent Light, and by that Refraction cast the usual Colours of thePrism upon the opposite Wall, or upon a sheet of white Paper held at aconvenient Distance behind the Prism for that refracted Light to fallupon it. After this I turned the Parallelopiped about its Axis, andfound that when the contiguous Sides of the two Prisms became so obliqueto the[Pg 58] incident Rays, that those Rays began all of them to bereflected, those Rays which in the third Prism had suffered the greatestRefraction, and painted the Paper with violet and blue, were first ofall by a total Reflexion taken out of the transmitted Light, the restremaining and on the Paper painting their Colours of green, yellow,orange and red, as before; and afterwards by continuing the Motion ofthe two Prisms, the rest of the Rays also by a total Reflexion vanishedin order, according to their degrees of Refrangibility. The Lighttherefore which emerged out of the two Prisms is compounded of Raysdifferently refrangible, seeing the more refrangible Rays may be takenout of it, while the less refrangible remain. But this Light beingtrajected only through the parallel Superficies of the two Prisms, if itsuffer'd any change by the Refraction of one Superficies it lost thatImpression by the contrary Refraction of the other Superficies, and sobeing restor'd to its pristine Constitution, became of the same Natureand Condition as at first before its Incidence on those Prisms; andtherefore, before its Incidence, was as much compounded of Raysdifferently refrangible, as afterwards.

Illustration. In the twenty second Figure ABC and BCD are the twoPrisms tied together in the form of a Parallelopiped, their Sides BC andCB being contiguous, and their Sides AB and CD parallel. And HJK is thethird Prism, by which the Sun's Light propagated through the hole F intothe dark Chamber, and there passing through those sides[Pg 59] of the PrismsAB, BC, CB and CD, is refracted at O to the white Paper PT, fallingthere partly upon P by a greater Refraction, partly upon T by a lessRefraction, and partly upon R and other intermediate places byintermediate Refractions. By turning the Parallelopiped ACBD about itsAxis, according to the order of the Letters A, C, D, B, at length whenthe contiguous Planes BC and CB become sufficiently oblique to the RaysFM, which are incident upon them at M, there will vanish totally out ofthe refracted Light OPT, first of all the most refracted Rays OP, (therest OR and OT remaining as before) then the Rays OR and otherintermediate ones, and[Pg 60] lastly, the least refracted Rays OT. For whenthe Plane BC becomes sufficiently oblique to the Rays incident upon it,those Rays will begin to be totally reflected by it towards N; and firstthe most refrangible Rays will be totally reflected (as was explained inthe preceding Experiment) and by Consequence must first disappear at P,and afterwards the rest as they are in order totally reflected to N,they must disappear in the same order at R and T. So then the Rays whichat O suffer the greatest Refraction, may be taken out of the Light MOwhilst the rest of the Rays remain in it, and therefore that Light MO iscompounded of Rays differently refrangible. And because the Planes ABand CD are parallel, and therefore by equal and contrary Refractionsdestroy one anothers Effects, the incident Light FM must be of the sameKind and Nature with the emergent Light MO, and therefore doth alsoconsist of Rays differently refrangible. These two Lights FM and MO,before the most refrangible Rays are separated out of the emergent LightMO, agree in Colour, and in all other Properties so far as myObservation reaches, and therefore are deservedly reputed of the sameNature and Constitution, and by Consequence the one is compounded aswell as the other. But after the most refrangible Rays begin to betotally reflected, and thereby separated out of the emergent Light MO,that Light changes its Colour from white to a dilute and faint yellow, apretty good orange, a very full red successively, and then totallyvanishes. For after the most refrangible Rays which paint the[Pg 61] Paper atP with a purple Colour, are by a total Reflexion taken out of the beamof Light MO, the rest of the Colours which appear on the Paper at R andT being mix'd in the Light MO compound there a faint yellow, and afterthe blue and part of the green which appear on the Paper between P and Rare taken away, the rest which appear between R and T (that is theyellow, orange, red and a little green) being mixed in the beam MOcompound there an orange; and when all the Rays are by Reflexion takenout of the beam MO, except the least refrangible, which at T appear of afull red, their Colour is the same in that beam MO as afterwards at T,the Refraction of the Prism HJK serving only to separate the differentlyrefrangible Rays, without making any Alteration in their Colours, asshall be more fully proved hereafter. All which confirms as well thefirst Proposition as the second.

Scholium. If this Experiment and the former be conjoined and made oneby applying a fourth Prism VXY [inFig. 22.] to refract the reflectedbeam MN towardstp, the Conclusion will be clearer. For then the LightNp which in the fourth Prism is more refracted, will become fuller andstronger when the Light OP, which in the third Prism HJK is morerefracted, vanishes at P; and afterwards when the less refracted LightOT vanishes at T, the less refracted Light Nt will become increasedwhilst the more refracted Light atp receives no farther increase. Andas the trajected beam MO in vanishing is always of such a Colour asought to result from the mixture of the[Pg 62] Colours which fall upon thePaper PT, so is the reflected beam MN always of such a Colour as oughtto result from the mixture of the Colours which fall upon the Paperpt. For when the most refrangible Rays are by a total Reflexion takenout of the beam MO, and leave that beam of an orange Colour, the Excessof those Rays in the reflected Light, does not only make the violet,indigo and blue atp more full, but also makes the beam MN change fromthe yellowish Colour of the Sun's Light, to a pale white inclining toblue, and afterward recover its yellowish Colour again, so soon as allthe rest of the transmitted Light MOT is reflected.

Now seeing that in all this variety of Experiments, whether the Trial bemade in Light reflected, and that either from natural Bodies, as in thefirst and second Experiment, or specular, as in the ninth; or in Lightrefracted, and that either before the unequally refracted Rays are bydiverging separated from one another, and losing their whiteness whichthey have altogether, appear severally of several Colours, as in thefifth Experiment; or after they are separated from one another, andappear colour'd as in the sixth, seventh, and eighth Experiments; or inLight trajected through parallel Superficies, destroying each othersEffects, as in the tenth Experiment; there are always found Rays, whichat equal Incidences on the same Medium suffer unequal Refractions, andthat without any splitting or dilating of single Rays, or contingence inthe inequality of the Refractions, as is proved in the fifth and sixth[Pg 63]Experiments. And seeing the Rays which differ in Refrangibility may beparted and sorted from one another, and that either by Refraction as inthe third Experiment, or by Reflexion as in the tenth, and then theseveral sorts apart at equal Incidences suffer unequal Refractions, andthose sorts are more refracted than others after Separation, which weremore refracted before it, as in the sixth and following Experiments, andif the Sun's Light be trajected through three or more cross Prismssuccessively, those Rays which in the first Prism are refracted morethan others, are in all the following Prisms refracted more than othersin the same Rate and Proportion, as appears by the fifth Experiment;it's manifest that the Sun's Light is an heterogeneous Mixture of Rays,some of which are constantly more refrangible than others, as wasproposed.

PROP. III.Theor. III.

The Sun's Light consists of Rays differing in Reflexibility, and thoseRays are more reflexible than others which are more refrangible.

This is manifest by the ninth and tenth Experiments: For in the ninthExperiment, by turning the Prism about its Axis, until the Rays withinit which in going out into the Air were refracted by its Base, became sooblique to that Base, as to begin to be totally reflected thereby; thoseRays became[Pg 64] first of all totally reflected, which before at equalIncidences with the rest had suffered the greatest Refraction. And thesame thing happens in the Reflexion made by the common Base of the twoPrisms in the tenth Experiment.

PROP. IV.Prob. I.

The heterogeneous Rays are in some measure separated from one another bythe Refraction of the Prism in the third Experiment, and in the fifthExperiment, by taking away the Penumbra from the rectilinear sides ofthe coloured Image, that Separation in those very rectilinear sides orstraight edges of the Image becomes perfect. But in all places betweenthose rectilinear edges, those innumerable Circles there described,which are severally illuminated by homogeneal Rays, by interfering withone another, and being every where commix'd, do render the Lightsufficiently compound. But if these Circles, whilst their Centers keeptheir Distances and Positions, could be made less in Diameter, theirinterfering one with another, and by Consequence the Mixture of theheterogeneous Rays would be proportionally diminish'd. In the twentythird Figure let AG, BH, CJ, DK, EL, FM be the Circles which so manysorts of Rays flowing from the same disque of[Pg 65] the Sun, do in the thirdExperiment illuminate; of all which and innumerable other intermediateones lying in a continual Series between the two rectilinear andparallel edges of the Sun's oblong Image PT, that Image is compos'd, aswas explained in the fifth Experiment. And letag,bh,ci,dk,el,fm be so many less Circles lying in a like continual Seriesbetween two parallel right Linesaf andgm with the same distancesbetween their Centers, and illuminated by the same sorts of Rays, thatis the Circleag with the same sort by which the corresponding CircleAG was illuminated, and the Circlebh with the same sort by which thecorresponding Circle BH was illuminated, and the rest of the Circlesci,dk,el,fm respectively, with the same sorts of Rays bywhich the several corresponding Circles CJ, DK, EL, FM were illuminated.In the Figure PT composed of the greater Circles, three of those CirclesAG, BH, CJ, are so expanded into one another, that the three sorts ofRays by which those Circles are illuminated, together with otherinnumerable sorts of intermediate[Pg 66] Rays, are mixed at QR in the middleof the Circle BH. And the like Mixture happens throughout almost thewhole length of the Figure PT. But in the Figurept composed of theless Circles, the three less Circlesag,bh,ci, which answer tothose three greater, do not extend into one another; nor are there anywhere mingled so much as any two of the three sorts of Rays by whichthose Circles are illuminated, and which in the Figure PT are all ofthem intermingled at BH.

Now he that shall thus consider it, will easily understand that theMixture is diminished in the same Proportion with the Diameters of theCircles. If the Diameters of the Circles whilst their Centers remain thesame, be made three times less than before, the Mixture will be alsothree times less; if ten times less, the Mixture will be ten times less,and so of other Proportions. That is, the Mixture of the Rays in thegreater Figure PT will be to their Mixture in the lesspt, as theLatitude of the greater Figure is to the Latitude of the less. For theLatitudes of these Figures are equal to the Diameters of their Circles.And hence it easily follows, that the Mixture of the Rays in therefracted Spectrumpt is to the Mixture of the Rays in the direct andimmediate Light of the Sun, as the breadth of that Spectrum is to thedifference between the length and breadth of the same Spectrum.

So then, if we would diminish the Mixture of the Rays, we are todiminish the Diameters of the Circles. Now these would be diminished ifthe Sun's Diameter[Pg 67] to which they answer could be made less than it is,or (which comes to the same Purpose) if without Doors, at a greatdistance from the Prism towards the Sun, some opake Body were placed,with a round hole in the middle of it, to intercept all the Sun's Light,excepting so much as coming from the middle of his Body could passthrough that Hole to the Prism. For so the Circles AG, BH, and the rest,would not any longer answer to the whole Disque of the Sun, but only tothat Part of it which could be seen from the Prism through that Hole,that it is to the apparent Magnitude of that Hole view'd from the Prism.But that these Circles may answer more distinctly to that Hole, a Lensis to be placed by the Prism to cast the Image of the Hole, (that is,every one of the Circles AG, BH, &c.) distinctly upon the Paper at PT,after such a manner, as by a Lens placed at a Window, the Species ofObjects abroad are cast distinctly upon a Paper within the Room, and therectilinear Sides of the oblong Solar Image in the fifth Experimentbecame distinct without any Penumbra. If this be done, it will not benecessary to place that Hole very far off, no not beyond the Window. Andtherefore instead of that Hole, I used the Hole in the Window-shut, asfollows.

Exper. 11. In the Sun's Light let into my darken'd Chamber through asmall round Hole in my Window-shut, at about ten or twelve Feet from theWindow, I placed a Lens, by which the Image of the Hole might bedistinctly cast upon a Sheet of white Paper, placed at the distance ofsix, eight, ten, or twelve[Pg 68] Feet from the Lens. For, according to thedifference of the Lenses I used various distances, which I think notworth the while to describe. Then immediately after the Lens I placed aPrism, by which the trajected Light might be refracted either upwards orsideways, and thereby the round Image, which the Lens alone did castupon the Paper might be drawn out into a long one with Parallel Sides,as in the third Experiment. This oblong Image I let fall upon anotherPaper at about the same distance from the Prism as before, moving thePaper either towards the Prism or from it, until I found the justdistance where the Rectilinear Sides of the Image became most distinct.For in this Case, the Circular Images of the Hole, which compose thatImage after the same manner that the Circlesag,bh,ci, &c. dothe Figurept [inFig. 23.] were terminated most distinctly withoutany Penumbra, and therefore extended into one another the least thatthey could, and by consequence the Mixture of the heterogeneous Rays wasnow the least of all. By this means I used to form an oblong Image (suchas ispt) [inFig. 23, and 24.] of Circular Images of the Hole,(such as areag,bh,ci, &c.) and by using a greater or less Holein the Window-shut, I made the Circular Imagesag,bh,ci, &c. ofwhich it was formed, to become greater or less at pleasure, and therebythe Mixture of the Rays in the Imagept to be as much, or as little asI desired.

Illustration. In the twenty-fourth Figure, F represents the CircularHole in the Window-shut, MN[Pg 69] the Lens, whereby the Image or Species ofthat Hole is cast distinctly upon a Paper at J, ABC the Prism, wherebythe Rays are at their emerging out of the Lens refracted from J towardsanother Paper atpt, and the round Image at J is turned into an oblongImagept falling on that other Paper. This Imagept consists ofCircles placed one after another in a Rectilinear Order, as wassufficiently explained in the fifth Experiment; and these Circles areequal to the Circle J, and consequently answer in magnitude to the HoleF; and therefore by diminishing that Hole they may be at pleasurediminished, whilst their Centers remain in their Places. By this means Imade the Breadth of the Imagept to be forty times, and sometimessixty or seventy times less than its Length. As for instance, if theBreadth of the Hole F be one tenth of an Inch, and MF the distance ofthe Lens from the Hole be 12 Feet; and ifpB orpM the distance ofthe Imagept from the Prism or Lens be 10 Feet, and the refractingAngle of the Prism be 62[Pg 70] Degrees, the Breadth of the Imagept will beone twelfth of an Inch, and the Length about six Inches, and thereforethe Length to the Breadth as 72 to 1, and by consequence the Light ofthis Image 71 times less compound than the Sun's direct Light. And Lightthus far simple and homogeneal, is sufficient for trying all theExperiments in this Book about simple Light. For the Composition ofheterogeneal Rays is in this Light so little, that it is scarce to bediscovered and perceiv'd by Sense, except perhaps in the indigo andviolet. For these being dark Colours do easily suffer a sensible Allayby that little scattering Light which uses to be refracted irregularlyby the Inequalities of the Prism.

Yet instead of the Circular Hole F, 'tis better to substitute an oblongHole shaped like a long Parallelogram with its Length parallel to thePrism ABC. For if this Hole be an Inch or two long, and but a tenth ortwentieth Part of an Inch broad, or narrower; the Light of the Imagept will be as simple as before, or simpler, and the Image will becomemuch broader, and therefore more fit to have Experiments try'd in itsLight than before.

Instead of this Parallelogram Hole may be substituted a triangular oneof equal Sides, whose Base, for instance, is about the tenth Part of anInch, and its Height an Inch or more. For by this means, if the Axis ofthe Prism be parallel to the Perpendicular of the Triangle, the Imagept [inFig. 25.] will now be form'd of equicrural Trianglesag,bh,ci,dk,el,fm, &c. and innumerable other intermediateones answering[Pg 71] to the triangular Hole in Shape and Bigness, and lyingone after another in a continual Series between two Parallel Linesafandgm. These Triangles are a little intermingled at their Bases, butnot at their Vertices; and therefore the Light on the brighter Sideafof the Image, where the Bases of the Triangles are, is a littlecompounded, but on the darker Sidegm is altogether uncompounded, andin all Places between the Sides the Composition is proportional to thedistances of the Places from that obscurer Sidegm. And having aSpectrumpt of such a Composition, we may try Experiments either inits stronger and less simple Light near the Sideaf, or in its weakerand simpler Light near the other Sidegm, as it shall seem mostconvenient.

But in making Experiments of this kind, the Chamber ought to be made asdark as can be, lest any Foreign Light mingle it self with the Light ofthe Spectrumpt, and render it compound; especially if we would tryExperiments in the more simple Light next the Sidegm of the Spectrum;which being fainter, will have a less proportion to the Foreign Light;and so by the mixture of that Light be more[Pg 72] troubled, and made morecompound. The Lens also ought to be good, such as may serve for opticalUses, and the Prism ought to have a large Angle, suppose of 65 or 70Degrees, and to be well wrought, being made of Glass free from Bubblesand Veins, with its Sides not a little convex or concave, as usuallyhappens, but truly plane, and its Polish elaborate, as in workingOptick-glasses, and not such as is usually wrought with Putty, wherebythe edges of the Sand-holes being worn away, there are left all over theGlass a numberless Company of very little convex polite Risings likeWaves. The edges also of the Prism and Lens, so far as they may make anyirregular Refraction, must be covered with a black Paper glewed on. Andall the Light of the Sun's Beam let into the Chamber, which is uselessand unprofitable to the Experiment, ought to be intercepted with blackPaper, or other black Obstacles. For otherwise the useless Light beingreflected every way in the Chamber, will mix with the oblong Spectrum,and help to disturb it. In trying these Things, so much diligence is notaltogether necessary, but it will promote the Success of theExperiments, and by a very scrupulous Examiner of Things deserves to beapply'd. It's difficult to get Glass Prisms fit for this Purpose, andtherefore I used sometimes prismatick Vessels made with pieces of brokenLooking-glasses, and filled with Rain Water. And to increase theRefraction, I sometimes impregnated the Water strongly withSaccharumSaturni.[Pg 73]

PROP. V.Theor. IV.

Homogeneal Light is refracted regularly without any Dilatationsplitting or shattering of the Rays, and the confused Vision of Objectsseen through refracting Bodies by heterogeneal Light arises from thedifferent Refrangibility of several sorts of Rays.

The first Part of this Proposition has been already sufficiently provedin the fifth Experiment, and will farther appear by the Experimentswhich follow.

Exper. 12. In the middle of a black Paper I made a round Hole about afifth or sixth Part of an Inch in diameter. Upon this Paper I caused theSpectrum of homogeneal Light described in the former Proposition, so tofall, that some part of the Light might pass through the Hole of thePaper. This transmitted part of the Light I refracted with a Prismplaced behind the Paper, and letting this refracted Light fallperpendicularly upon a white Paper two or three Feet distant from thePrism, I found that the Spectrum formed on the Paper by this Light wasnot oblong, as when 'tis made (in the third Experiment) by refractingthe Sun's compound Light, but was (so far as I could judge by my Eye)perfectly circular, the Length being no greater than the Breadth. Whichshews, that this Light is refracted regularly without any Dilatation ofthe Rays.

Exper. 13. In the homogeneal Light I placed a Paper Circle of aquarter of an Inch in diameter, and[Pg 74] in the Sun's unrefractedheterogeneal white Light I placed another Paper Circle of the sameBigness. And going from the Papers to the distance of some Feet, Iviewed both Circles through a Prism. The Circle illuminated by the Sun'sheterogeneal Light appeared very oblong, as in the fourth Experiment,the Length being many times greater than the Breadth; but the otherCircle, illuminated with homogeneal Light, appeared circular anddistinctly defined, as when 'tis view'd with the naked Eye. Which provesthe whole Proposition.

Exper. 14. In the homogeneal Light I placed Flies, and such-likeminute Objects, and viewing them through a Prism, I saw their Parts asdistinctly defined, as if I had viewed them with the naked Eye. The sameObjects placed in the Sun's unrefracted heterogeneal Light, which waswhite, I viewed also through a Prism, and saw them most confusedlydefined, so that I could not distinguish their smaller Parts from oneanother. I placed also the Letters of a small print, one while in thehomogeneal Light, and then in the heterogeneal, and viewing them througha Prism, they appeared in the latter Case so confused and indistinct,that I could not read them; but in the former they appeared so distinct,that I could read readily, and thought I saw them as distinct, as when Iview'd them with my naked Eye. In both Cases I view'd the same Objects,through the same Prism at the same distance from me, and in the sameSituation. There was no difference, but in the Light by which theObjects were illuminated,[Pg 75] and which in one Case was simple, and in theother compound; and therefore, the distinct Vision in the former Case,and confused in the latter, could arise from nothing else than from thatdifference of the Lights. Which proves the whole Proposition.

And in these three Experiments it is farther very remarkable, that theColour of homogeneal Light was never changed by the Refraction.

PROP. VI.Theor. V.

The Sine of Incidence of every Ray considered apart, is to its Sine ofRefraction in a given Ratio.

That every Ray consider'd apart, is constant to it self in some degreeof Refrangibility, is sufficiently manifest out of what has been said.Those Rays, which in the first Refraction, are at equal Incidences mostrefracted, are also in the following Refractions at equal Incidencesmost refracted; and so of the least refrangible, and the rest which haveany mean Degree of Refrangibility, as is manifest by the fifth, sixth,seventh, eighth, and ninth Experiments. And those which the first Timeat like Incidences are equally refracted, are again at like Incidencesequally and uniformly refracted, and that whether they be refractedbefore they be separated from one another, as in the fifth Experiment,or whether they be refracted apart, as in the twelfth, thirteenth andfourteenth Experiments. The Refraction therefore[Pg 76] of every Ray apart isregular, and what Rule that Refraction observes we are now to shew.[E]

The late Writers in Opticks teach, that the Sines of Incidence are in agiven Proportion to the Sines of Refraction, as was explained in thefifth Axiom, and some by Instruments fitted for measuring ofRefractions, or otherwise experimentally examining this Proportion, doacquaint us that they have found it accurate. But whilst they, notunderstanding the different Refrangibility of several Rays, conceivedthem all to be refracted according to one and the same Proportion, 'tisto be presumed that they adapted their Measures only to the middle ofthe refracted Light; so that from their Measures we may conclude onlythat the Rays which have a mean Degree of Refrangibility, that is, thosewhich when separated from the rest appear green, are refracted accordingto a given Proportion of their Sines. And therefore we are now to shew,that the like given Proportions obtain in all the rest. That it shouldbe so is very reasonable, Nature being ever conformable to her self; butan experimental Proof is desired. And such a Proof will be had, if wecan shew that the Sines of Refraction of Rays differently refrangibleare one to another in a given Proportion when their Sines of Incidenceare equal. For, if the Sines of Refraction of all the Rays are in givenProportions to the Sine of Refractions of a Ray which has a mean Degreeof Refrangibility, and this Sine is in a given[Pg 77] Proportion to the equalSines of Incidence, those other Sines of Refraction will also be ingiven Proportions to the equal Sines of Incidence. Now, when the Sinesof Incidence are equal, it will appear by the following Experiment, thatthe Sines of Refraction are in a given Proportion to one another.

Exper. 15. The Sun shining into a dark Chamber through a little roundHole in the Window-shut, let S [inFig. 26.] represent his round whiteImage painted on the opposite Wall by his direct Light, PT his oblongcoloured Image made by refracting that Light with a Prism placed at theWindow; andpt, or2p 2t,3p 3t, his oblong colour'd Image made byrefracting again the same Light sideways with a[Pg 78] second Prism placedimmediately after the first in a cross Position to it, as was explainedin the fifth Experiment; that is to say,pt when the Refraction of thesecond Prism is small,2p 2t when its Refraction is greater, and3p3t when it is greatest. For such will be the diversity of theRefractions, if the refracting Angle of the second Prism be of variousMagnitudes; suppose of fifteen or twenty Degrees to make the Imagept,of thirty or forty to make the Image2p 2t, and of sixty to make theImage3p 3t. But for want of solid Glass Prisms with Angles ofconvenient Bignesses, there may be Vessels made of polished Plates ofGlass cemented together in the form of Prisms and filled with Water.These things being thus ordered, I observed that all the solar Images orcoloured Spectrums PT,pt,2p 2t,3p 3t did very nearly convergeto the place S on which the direct Light of the Sun fell and painted hiswhite round Image when the Prisms were taken away. The Axis of theSpectrum PT, that is the Line drawn through the middle of it parallel toits rectilinear Sides, did when produced pass exactly through the middleof that white round Image S. And when the Refraction of the second Prismwas equal to the Refraction of the first, the refracting Angles of themboth being about 60 Degrees, the Axis of the Spectrum3p 3t made bythat Refraction, did when produced pass also through the middle of thesame white round Image S. But when the Refraction of the second Prismwas less than that of the first, the produced Axes of the Spectrumstpor2t 2p made by that Refraction[Pg 79] did cut the produced Axis of theSpectrum TP in the pointsm andn, a little beyond the Center ofthat white round Image S. Whence the proportion of the Line 3tT to theLine 3pP was a little greater than the Proportion of 2tT or 2pP,and this Proportion a little greater than that oftT topP. Now whenthe Light of the Spectrum PT falls perpendicularly upon the Wall, thoseLines 3tT, 3pP, and 2tT, and 2pP, andtT,pP, are theTangents of the Refractions, and therefore by this Experiment theProportions of the Tangents of the Refractions are obtained, from whencethe Proportions of the Sines being derived, they come out equal, so faras by viewing the Spectrums, and using some mathematical Reasoning Icould estimate. For I did not make an accurate Computation. So then theProposition holds true in every Ray apart, so far as appears byExperiment. And that it is accurately true, may be demonstrated uponthis Supposition.That Bodies refract Light by acting upon its Rays inLines perpendicular to their Surfaces. But in order to thisDemonstration, I must distinguish the Motion of every Ray into twoMotions, the one perpendicular to the refracting Surface, the otherparallel to it, and concerning the perpendicular Motion lay down thefollowing Proposition.

If any Motion or moving thing whatsoever be incident with any Velocityon any broad and thin space terminated on both sides by two parallelPlanes, and in its Passage through that space be urged perpendicularlytowards the farther Plane by any force which at given distances from thePlane is of given[Pg 80] Quantities; the perpendicular velocity of that Motionor Thing, at its emerging out of that space, shall be always equal tothe square Root of the sum of the square of the perpendicular velocityof that Motion or Thing at its Incidence on that space; and of thesquare of the perpendicular velocity which that Motion or Thing wouldhave at its Emergence, if at its Incidence its perpendicular velocitywas infinitely little.

And the same Proposition holds true of any Motion or Thingperpendicularly retarded in its passage through that space, if insteadof the sum of the two Squares you take their difference. TheDemonstration Mathematicians will easily find out, and therefore I shallnot trouble the Reader with it.

Suppose now that a Ray coming most obliquely in the Line MC [inFig.1.] be refracted at C by the Plane RS into the Line CN, and if it berequired to find the Line CE, into which any other Ray AC shall berefracted; let MC, AD, be the Sines of Incidence of the two Rays, andNG, EF, their Sines of Refraction, and let the equal Motions of theincident Rays be represented by the equal Lines MC and AC, and theMotion MC being considered as parallel to the refracting Plane, let theother Motion AC be distinguished into two Motions AD and DC, one ofwhich AD is parallel, and the other DC perpendicular to the refractingSurface. In like manner, let the Motions of the emerging Rays bedistinguish'd into two, whereof the perpendicular ones are MC/NG × CG[Pg 81]and AD/EF × CF. And if the force of the refracting Plane begins to actupon the Rays either in that Plane or at a certain distance from it onthe one side, and ends at a certain distance from it on the other side,and in all places between those two limits acts upon the Rays in Linesperpendicular to that refracting Plane, and the Actions upon the Rays atequal distances from the refracting Plane be equal, and at unequal oneseither equal or unequal according to any rate whatever; that Motion ofthe Ray which is parallel to the refracting Plane, will suffer noAlteration by that Force; and that Motion which is perpendicular to itwill be altered according to the rule of the foregoing Proposition. Iftherefore for the perpendicular velocity of the emerging Ray CN youwrite MC/NG × CG as above, then the perpendicular velocity of any otheremerging Ray CE which was AD/EF × CF, will be equal to the square Rootof CDq + (MCq/NGq × CGq). And by squaring these Equals, and addingto them the Equals ADq and MCq - CDq, and dividing the Sums by theEquals CFq + EFq and CGq + NGq, you will haveMCq/NGq equal toADq/EFq. Whence AD, the Sine of Incidence, is to EF the Sine ofRefraction, as MC to NG, that is, in a givenratio. And thisDemonstration being general, without determining what Light[Pg 82] is, or bywhat kind of Force it is refracted, or assuming any thing farther thanthat the refracting Body acts upon the Rays in Lines perpendicular toits Surface; I take it to be a very convincing Argument of the fulltruth of this Proposition.

So then, if theratio of the Sines of Incidence and Refraction of anysort of Rays be found in any one case, 'tis given in all cases; and thismay be readily found by the Method in the following Proposition.

PROP. VII.Theor. VI.

The Perfection of Telescopes is impeded by the different Refrangibilityof the Rays of Light.

The Imperfection of Telescopes is vulgarly attributed to the sphericalFigures of the Glasses, and therefore Mathematicians have propounded tofigure them by the conical Sections. To shew that they are mistaken, Ihave inserted this Proposition; the truth of which will appear by themeasure of the Refractions of the several sorts of Rays; and thesemeasures I thus determine.

In the third Experiment of this first Part, where the refracting Angleof the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min.is the Angle of Incidence of the Rays at their going out of the Glassinto the Air [F]; and the Sine of this Angle is 5188, the Radius being10000. When the Axis of this[Pg 83] Prism was parallel to the Horizon, and theRefraction of the Rays at their Incidence on this Prism equal to that attheir Emergence out of it, I observed with a Quadrant the Angle whichthe mean refrangible Rays, (that is those which went to the middle ofthe Sun's coloured Image) made with the Horizon, and by this Angle andthe Sun's altitude observed at the same time, I found the Angle whichthe emergent Rays contained with the incident to be 44 deg. and 40 min.and the half of this Angle added to the Angle of Incidence 31 deg. 15min. makes the Angle of Refraction, which is therefore 53 deg. 35 min.and its Sine 8047. These are the Sines of Incidence and Refraction ofthe mean refrangible Rays, and their Proportion in round Numbers is 20to 31. This Glass was of a Colour inclining to green. The last of thePrisms mentioned in the third Experiment was of clear white Glass. Itsrefracting Angle 63-1/2 Degrees. The Angle which the emergent Rayscontained, with the incident 45 deg. 50 min. The Sine of half the firstAngle 5262. The Sine of half the Sum of the Angles 8157. And theirProportion in round Numbers 20 to 31, as before.

From the Length of the Image, which was about 9-3/4 or 10 Inches,subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4Inches would be the Length of the Image were the Sun but a Point, andtherefore subtends the Angle which the most and least refrangible Rays,when incident on the Prism in the same Lines, do contain with oneanother after their Emergence. Whence this Angle is 2 deg. 0´. 7´´.[Pg 84] Forthe distance between the Image and the Prism where this Angle is made,was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends anAngle of 2 deg. 0´. 7´´. Now half this Angle is the Angle which theseemergent Rays contain with the emergent mean refrangible Rays, and aquarter thereof, that is 30´. 2´´. may be accounted the Angle which theywould contain with the same emergent mean refrangible Rays, were theyco-incident to them within the Glass, and suffered no other Refractionthan that at their Emergence. For, if two equal Refractions, the one atthe Incidence of the Rays on the Prism, the other at their Emergence,make half the Angle 2 deg. 0´. 7´´. then one of those Refractions willmake about a quarter of that Angle, and this quarter added to, andsubducted from the Angle of Refraction of the mean refrangible Rays,which was 53 deg. 35´, gives the Angles of Refraction of the most andleast refrangible Rays 54 deg. 5´ 2´´, and 53 deg. 4´ 58´´, whose Sinesare 8099 and 7995, the common Angle of Incidence being 31 deg. 15´, andits Sine 5188; and these Sines in the least round Numbers are inproportion to one another, as 78 and 77 to 50.

Now, if you subduct the common Sine of Incidence 50 from the Sines ofRefraction 77 and 78, the Remainders 27 and 28 shew, that in smallRefractions the Refraction of the least refrangible Rays is to theRefraction of the most refrangible ones, as 27 to 28 very nearly, andthat the difference of the Refractions of the least refrangible and mostrefrangible Rays is[Pg 85] about the 27-1/2th Part of the whole Refraction ofthe mean refrangible Rays.

Whence they that are skilled in Opticks will easily understand,[G] thatthe Breadth of the least circular Space, into which Object-glasses ofTelescopes can collect all sorts of Parallel Rays, is about the 27-1/2thPart of half the Aperture of the Glass, or 55th Part of the wholeAperture; and that the Focus of the most refrangible Rays is nearer tothe Object-glass than the Focus of the least refrangible ones, by aboutthe 27-1/2th Part of the distance between the Object-glass and the Focusof the mean refrangible ones.

And if Rays of all sorts, flowing from any one lucid Point in the Axisof any convex Lens, be made by the Refraction of the Lens to converge toPoints not too remote from the Lens, the Focus of the most refrangibleRays shall be nearer to the Lens than the Focus of the least refrangibleones, by a distance which is to the 27-1/2th Part of the distance of theFocus of the mean refrangible Rays from the Lens, as the distancebetween that Focus and the lucid Point, from whence the Rays flow, is tothe distance between that lucid Point and the Lens very nearly.

Now to examine whether the Difference between the Refractions, which themost refrangible and the least refrangible Rays flowing from the samePoint suffer in the Object-glasses of Telescopes and such-like Glasses,be so great as is here described, I contrived the following Experiment.[Pg 86]

Exper. 16. The Lens which I used in the second and eighth Experiments,being placed six Feet and an Inch distant from any Object, collected theSpecies of that Object by the mean refrangible Rays at the distance ofsix Feet and an Inch from the Lens on the other side. And therefore bythe foregoing Rule, it ought to collect the Species of that Object bythe least refrangible Rays at the distance of six Feet and 3-2/3 Inchesfrom the Lens, and by the most refrangible ones at the distance of fiveFeet and 10-1/3 Inches from it: So that between the two Places, wherethese least and most refrangible Rays collect the Species, there may bethe distance of about 5-1/3 Inches. For by that Rule, as six Feet and anInch (the distance of the Lens from the lucid Object) is to twelve Feetand two Inches (the distance of the lucid Object from the Focus of themean refrangible Rays) that is, as One is to Two; so is the 27-1/2thPart of six Feet and an Inch (the distance between the Lens and the sameFocus) to the distance between the Focus of the most refrangible Raysand the Focus of the least refrangible ones, which is therefore 5-17/55Inches, that is very nearly 5-1/3 Inches. Now to know whether thisMeasure was true, I repeated the second and eighth Experiment withcoloured Light, which was less compounded than that I there made use of:For I now separated the heterogeneous Rays from one another by theMethod I described in the eleventh Experiment, so as to make a colouredSpectrum about twelve or fifteen Times longer than broad. This SpectrumI cast on a printed Book, and[Pg 87] placing the above-mentioned Lens at thedistance of six Feet and an Inch from this Spectrum to collect theSpecies of the illuminated Letters at the same distance on the otherside, I found that the Species of the Letters illuminated with blue werenearer to the Lens than those illuminated with deep red by about threeInches, or three and a quarter; but the Species of the Lettersilluminated with indigo and violet appeared so confused and indistinct,that I could not read them: Whereupon viewing the Prism, I found it wasfull of Veins running from one end of the Glass to the other; so thatthe Refraction could not be regular. I took another Prism thereforewhich was free from Veins, and instead of the Letters I used two orthree Parallel black Lines a little broader than the Strokes of theLetters, and casting the Colours upon these Lines in such manner, thatthe Lines ran along the Colours from one end of the Spectrum to theother, I found that the Focus where the indigo, or confine of thisColour and violet cast the Species of the black Lines most distinctly,to be about four Inches, or 4-1/4 nearer to the Lens than the Focus,where the deepest red cast the Species of the same black Lines mostdistinctly. The violet was so faint and dark, that I could not discernthe Species of the Lines distinctly by that Colour; and thereforeconsidering that the Prism was made of a dark coloured Glass incliningto green, I took another Prism of clear white Glass; but the Spectrum ofColours which this Prism made had long white Streams of faint Lightshooting out from[Pg 88] both ends of the Colours, which made me conclude thatsomething was amiss; and viewing the Prism, I found two or three littleBubbles in the Glass, which refracted the Light irregularly. Wherefore Icovered that Part of the Glass with black Paper, and letting the Lightpass through another Part of it which was free from such Bubbles, theSpectrum of Colours became free from those irregular Streams of Light,and was now such as I desired. But still I found the violet so dark andfaint, that I could scarce see the Species of the Lines by the violet,and not at all by the deepest Part of it, which was next the end of theSpectrum. I suspected therefore, that this faint and dark Colour mightbe allayed by that scattering Light which was refracted, and reflectedirregularly, partly by some very small Bubbles in the Glasses, andpartly by the Inequalities of their Polish; which Light, tho' it was butlittle, yet it being of a white Colour, might suffice to affect theSense so strongly as to disturb the Phænomena of that weak and darkColour the violet, and therefore I tried, as in the 12th, 13th, and 14thExperiments, whether the Light of this Colour did not consist of asensible Mixture of heterogeneous Rays, but found it did not. Nor didthe Refractions cause any other sensible Colour than violet to emergeout of this Light, as they would have done out of white Light, and byconsequence out of this violet Light had it been sensibly compoundedwith white Light. And therefore I concluded, that the reason why I couldnot see the Species of the Lines distinctly by this[Pg 89] Colour, was onlythe Darkness of this Colour, and Thinness of its Light, and its distancefrom the Axis of the Lens; I divided therefore those Parallel blackLines into equal Parts, by which I might readily know the distances ofthe Colours in the Spectrum from one another, and noted the distances ofthe Lens from the Foci of such Colours, as cast the Species of the Linesdistinctly, and then considered whether the difference of thosedistances bear such proportion to 5-1/3 Inches, the greatest Differenceof the distances, which the Foci of the deepest red and violet ought tohave from the Lens, as the distance of the observed Colours from oneanother in the Spectrum bear to the greatest distance of the deepest redand violet measured in the Rectilinear Sides of the Spectrum, that is,to the Length of those Sides, or Excess of the Length of the Spectrumabove its Breadth. And my Observations were as follows.

When I observed and compared the deepest sensible red, and the Colour inthe Confine of green and blue, which at the Rectilinear Sides of theSpectrum was distant from it half the Length of those Sides, the Focuswhere the Confine of green and blue cast the Species of the Linesdistinctly on the Paper, was nearer to the Lens than the Focus, wherethe red cast those Lines distinctly on it by about 2-1/2 or 2-3/4Inches. For sometimes the Measures were a little greater, sometimes alittle less, but seldom varied from one another above 1/3 of an Inch.For it was very difficult to define the Places of the Foci, without somelittle Errors. Now, if the Colours distant half[Pg 90] the Length of theImage, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4Difference of the distances of their Foci from the Lens, then theColours distant the whole Length ought to give 5 or 5-1/2 Inchesdifference of those distances.

But here it's to be noted, that I could not see the red to the full endof the Spectrum, but only to the Center of the Semicircle which boundedthat end, or a little farther; and therefore I compared this red notwith that Colour which was exactly in the middle of the Spectrum, orConfine of green and blue, but with that which verged a little more tothe blue than to the green: And as I reckoned the whole Length of theColours not to be the whole Length of the Spectrum, but the Length ofits Rectilinear Sides, so compleating the semicircular Ends intoCircles, when either of the observed Colours fell within those Circles,I measured the distance of that Colour from the semicircular End of theSpectrum, and subducting half this distance from the measured distanceof the two Colours, I took the Remainder for their corrected distance;and in these Observations set down this corrected distance for thedifference of the distances of their Foci from the Lens. For, as theLength of the Rectilinear Sides of the Spectrum would be the wholeLength of all the Colours, were the Circles of which (as we shewed) thatSpectrum consists contracted and reduced to Physical Points, so in thatCase this corrected distance would be the real distance of the twoobserved Colours.

When therefore I farther observed the deepest[Pg 91] sensible red, and thatblue whose corrected distance from it was 7/12 Parts of the Length ofthe Rectilinear Sides of the Spectrum, the difference of the distancesof their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, sois 3-1/4 to 5-4/7.

When I observed the deepest sensible red, and that indigo whosecorrected distance was 8/12 or 2/3 of the Length of the RectilinearSides of the Spectrum, the difference of the distances of their Focifrom the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to5-1/2.

When I observed the deepest sensible red, and that deep indigo whosecorrected distance from one another was 9/12 or 3/4 of the Length of theRectilinear Sides of the Spectrum, the difference of the distances oftheir Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to5-1/3.

When I observed the deepest sensible red, and that Part of the violetnext the indigo, whose corrected distance from the red was 10/12 or 5/6of the Length of the Rectilinear Sides of the Spectrum, the differenceof the distances of their Foci from the Lens was about 4-1/2 Inches, andas 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens wasadvantageously placed, so that its Axis respected the blue, and allThings else were well ordered, and the Sun shone clear, and I held myEye very near to the Paper on which the Lens cast the Species of theLines, I could see pretty distinctly the Species of those Lines by thatPart of the violet which was next the indigo; and sometimes I could seethem by above half the violet,[Pg 92] For in making these Experiments I hadobserved, that the Species of those Colours only appear distinct, whichwere in or near the Axis of the Lens: So that if the blue or indigo werein the Axis, I could see their Species distinctly; and then the redappeared much less distinct than before. Wherefore I contrived to makethe Spectrum of Colours shorter than before, so that both its Ends mightbe nearer to the Axis of the Lens. And now its Length was about 2-1/2Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of theblack Lines on which the Spectrum was cast, I made one black Linebroader than those, that I might see its Species more easily; and thisLine I divided by short cross Lines into equal Parts, for measuring thedistances of the observed Colours. And now I could sometimes see theSpecies of this Line with its Divisions almost as far as the Center ofthe semicircular violet End of the Spectrum, and made these fartherObservations.

When I observed the deepest sensible red, and that Part of the violet,whose corrected distance from it was about 8/9 Parts of the RectilinearSides of the Spectrum, the Difference of the distances of the Foci ofthose Colours from the Lens, was one time 4-2/3, another time 4-3/4,another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to5-1/4, 5-11/32, 5-31/64 respectively.

When I observed the deepest sensible red, and deepest sensible violet,(the corrected distance of which Colours, when all Things were orderedto the best Advantage, and the Sun shone very clear, was about 11/12 or15/16 Parts of the Length of the Rectilinear[Pg 93] Sides of the colouredSpectrum) I found the Difference of the distances of their Foci from theLens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches orthereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or5-1/3 Inches.

And by this Progression of Experiments I satisfied my self, that had theLight at the very Ends of the Spectrum been strong enough to make theSpecies of the black Lines appear plainly on the Paper, the Focus of thedeepest violet would have been found nearer to the Lens, than the Focusof the deepest red, by about 5-1/3 Inches at least. And this is afarther Evidence, that the Sines of Incidence and Refraction of theseveral sorts of Rays, hold the same Proportion to one another in thesmallest Refractions which they do in the greatest.

My Progress in making this nice and troublesome Experiment I have setdown more at large, that they that shall try it after me may be aware ofthe Circumspection requisite to make it succeed well. And if they cannotmake it succeed so well as I did, they may notwithstanding collect bythe Proportion of the distance of the Colours of the Spectrum, to theDifference of the distances of their Foci from the Lens, what would bethe Success in the more distant Colours by a better trial. And yet, ifthey use a broader Lens than I did, and fix it to a long strait Staff,by means of which it may be readily and truly directed to the Colourwhose Focus is desired, I question not but the Experiment will succeedbetter with them than it did with me. For I directed the[Pg 94] Axis as nearlyas I could to the middle of the Colours, and then the faint Ends of theSpectrum being remote from the Axis, cast their Species less distinctlyon the Paper than they would have done, had the Axis been successivelydirected to them.

Now by what has been said, it's certain that the Rays which differ inRefrangibility do not converge to the same Focus; but if they flow froma lucid Point, as far from the Lens on one side as their Foci are on theother, the Focus of the most refrangible Rays shall be nearer to theLens than that of the least refrangible, by above the fourteenth Part ofthe whole distance; and if they flow from a lucid Point, so very remotefrom the Lens, that before their Incidence they may be accountedparallel, the Focus of the most refrangible Rays shall be nearer to theLens than the Focus of the least refrangible, by about the 27th or 28thPart of their whole distance from it. And the Diameter of the Circle inthe middle Space between those two Foci which they illuminate, when theyfall there on any Plane, perpendicular to the Axis (which Circle is theleast into which they can all be gathered) is about the 55th Part of theDiameter of the Aperture of the Glass. So that 'tis a wonder, thatTelescopes represent Objects so distinct as they do. But were all theRays of Light equally refrangible, the Error arising only from theSphericalness of the Figures of Glasses would be many hundred timesless. For, if the Object-glass of a Telescope be Plano-convex, and thePlane side be turned towards the Object, and the Diameter of the[Pg 95]Sphere, whereof this Glass is a Segment, be called D, and theSemi-diameter of the Aperture of the Glass be called S, and the Sine ofIncidence out of Glass into Air, be to the Sine of Refraction as I to R;the Rays which come parallel to the Axis of the Glass, shall in thePlace where the Image of the Object is most distinctly made, bescattered all over a little Circle, whose Diameter is(Rq/Iq) × (Scub./D quad.) very nearly,[H] as I gather by computing the Errors ofthe Rays by the Method of infinite Series, and rejecting the Terms,whose Quantities are inconsiderable. As for instance, if the Sine ofIncidence I, be to the Sine of Refraction R, as 20 to 31, and if D theDiameter of the Sphere, to which the Convex-side of the Glass is ground,be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture betwo Inches, the Diameter of the little Circle, (that is (Rq × Scub.)/(Iq × D quad.)) will be (31 × 31 × 8)/(20 × 20 × 1200 × 1200) (or961/72000000) Parts of an Inch. But the Diameter of the little Circle,through which these Rays are scattered by unequal Refrangibility, willbe about the 55th Part of the Aperture of the Object-glass, which hereis four Inches. And therefore, the Error arising from the SphericalFigure of the Glass, is to the Error arising from the differentRefrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to5449; and therefore[Pg 96] being in comparison so very little, deserves not tobe considered.

But you will say, if the Errors caused by the different Refrangibilitybe so very great, how comes it to pass, that Objects appear throughTelescopes so distinct as they do? I answer, 'tis because the erringRays are not scattered uniformly over all that Circular Space, butcollected infinitely more densely in the Center than in any other Partof the Circle, and in the Way from the Center to the Circumference, growcontinually rarer and rarer, so as at the Circumference to becomeinfinitely rare; and by reason of their Rarity are not strong enough tobe visible, unless in the Center and very near it. Let ADE [inFig.27.] represent one of those Circles described with the Center C, andSemi-diameter AC, and let BFG be a smaller Circle concentrick to theformer, cutting with its Circumference the Diameter AC in B, and bisectAC in N; and by my reckoning, the Density of the Light in any Place B,will be to its Density in N, as AB to BC; and the whole Light within thelesser Circle BFG, will be to the whole Light within the greater AED, asthe Excess of the[Pg 97] Square of AC above the Square of AB, is to the Squareof AC. As if BC be the fifth Part of AC, the Light will be four timesdenser in B than in N, and the whole Light within the less Circle, willbe to the whole Light within the greater, as nine to twenty-five. Whenceit's evident, that the Light within the less Circle, must strike theSense much more strongly, than that faint and dilated Light round aboutbetween it and the Circumference of the greater.

But it's farther to be noted, that the most luminous of the PrismatickColours are the yellow and orange. These affect the Senses more stronglythan all the rest together, and next to these in strength are the redand green. The blue compared with these is a faint and dark Colour, andthe indigo and violet are much darker and fainter, so that thesecompared with the stronger Colours are little to be regarded. The Imagesof Objects are therefore to be placed, not in the Focus of the meanrefrangible Rays, which are in the Confine of green and blue, but in theFocus of those Rays which are in the middle of the orange and yellow;there where the Colour is most luminous and fulgent, that is in thebrightest yellow, that yellow which inclines more to orange than togreen. And by the Refraction of these Rays (whose Sines of Incidence andRefraction in Glass are as 17 and 11) the Refraction of Glass andCrystal for Optical Uses is to be measured. Let us therefore place theImage of the Object in the Focus of these Rays, and all the yellow andorange will fall within a[Pg 98] Circle, whose Diameter is about the 250thPart of the Diameter of the Aperture of the Glass. And if you add thebrighter half of the red, (that half which is next the orange) and thebrighter half of the green, (that half which is next the yellow) aboutthree fifth Parts of the Light of these two Colours will fall within thesame Circle, and two fifth Parts will fall without it round about; andthat which falls without will be spread through almost as much morespace as that which falls within, and so in the gross be almost threetimes rarer. Of the other half of the red and green, (that is of thedeep dark red and willow green) about one quarter will fall within thisCircle, and three quarters without, and that which falls without will bespread through about four or five times more space than that which fallswithin; and so in the gross be rarer, and if compared with the wholeLight within it, will be about 25 times rarer than all that taken in thegross; or rather more than 30 or 40 times rarer, because the deep red inthe end of the Spectrum of Colours made by a Prism is very thin andrare, and the willow green is something rarer than the orange andyellow. The Light of these Colours therefore being so very much rarerthan that within the Circle, will scarce affect the Sense, especiallysince the deep red and willow green of this Light, are much darkerColours than the rest. And for the same reason the blue and violet beingmuch darker Colours than these, and much more rarified, may beneglected. For the dense and bright Light of the Circle, will obscurethe rare and weak Light of these dark[Pg 99] Colours round about it, andrender them almost insensible. The sensible Image of a lucid Point istherefore scarce broader than a Circle, whose Diameter is the 250th Partof the Diameter of the Aperture of the Object-glass of a good Telescope,or not much broader, if you except a faint and dark misty Light roundabout it, which a Spectator will scarce regard. And therefore in aTelescope, whose Aperture is four Inches, and Length an hundred Feet, itexceeds not 2´´ 45´´´, or 3´´. And in a Telescope whose Aperture is twoInches, and Length 20 or 30 Feet, it may be 5´´ or 6´´, and scarceabove. And this answers well to Experience: For some Astronomers havefound the Diameters of the fix'd Stars, in Telescopes of between 20 and60 Feet in length, to be about 5´´ or 6´´, or at most 8´´ or 10´´ indiameter. But if the Eye-Glass be tincted faintly with the Smoak of aLamp or Torch, to obscure the Light of the Star, the fainter Light inthe Circumference of the Star ceases to be visible, and the Star (if theGlass be sufficiently soiled with Smoak) appears something more like amathematical Point. And for the same Reason, the enormous Part of theLight in the Circumference of every lucid Point ought to be lessdiscernible in shorter Telescopes than in longer, because the shortertransmit less Light to the Eye.

Now, that the fix'd Stars, by reason of their immense Distance, appearlike Points, unless so far as their Light is dilated by Refraction, mayappear from hence; that when the Moon passes over them and eclipsesthem, their Light vanishes, not gradually[Pg 100] like that of the Planets, butall at once; and in the end of the Eclipse it returns into Sight all atonce, or certainly in less time than the second of a Minute; theRefraction of the Moon's Atmosphere a little protracting the time inwhich the Light of the Star first vanishes, and afterwards returns intoSight.

Now, if we suppose the sensible Image of a lucid Point, to be even 250times narrower than the Aperture of the Glass; yet this Image would bestill much greater than if it were only from the spherical Figure of theGlass. For were it not for the different Refrangibility of the Rays, itsbreadth in an 100 Foot Telescope whose aperture is 4 Inches, would bebut 961/72000000 parts of an Inch, as is manifest by the foregoingComputation. And therefore in this case the greatest Errors arising fromthe spherical Figure of the Glass, would be to the greatest sensibleErrors arising from the different Refrangibility of the Rays as961/72000000 to 4/250 at most, that is only as 1 to 1200. And thissufficiently shews that it is not the spherical Figures of Glasses, butthe different Refrangibility of the Rays which hinders the perfection ofTelescopes.

There is another Argument by which it may appear that the differentRefrangibility of Rays, is the true cause of the imperfection ofTelescopes. For the Errors of the Rays arising from the sphericalFigures of Object-glasses, are as the Cubes of the Apertures of theObject Glasses; and thence to make Telescopes of various Lengths magnifywith equal distinctness, the Apertures of the Object-glasses, and theCharges or magnifying Powers ought to be as the[Pg 101] Cubes of the squareRoots of their lengths; which doth not answer to Experience. But theErrors of the Rays arising from the different Refrangibility, are as theApertures of the Object-glasses; and thence to make Telescopes ofvarious lengths, magnify with equal distinctness, their Apertures andCharges ought to be as the square Roots of their lengths; and thisanswers to Experience, as is well known. For Instance, a Telescope of 64Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120times, with as much distinctness as one of a Foot in length, with 1/3 ofan Inch aperture, magnifies 15 times.

Now were it not for this different Refrangibility of Rays, Telescopesmight be brought to a greater perfection than we have yet describ'd, bycomposing the Object-glass of two Glasses with Water between them. LetADFC [inFig. 28.] represent the Object-glass composed of two GlassesABED and BEFC, alike convex on the outsides AGD and CHF, and alikeconcave on the insides BME, BNE, with Water in the concavity BMEN. Letthe Sine of Incidence[Pg 102] out of Glass into Air be as I to R, and out ofWater into Air, as K to R, and by consequence out of Glass into Water,as I to K: and let the Diameter of the Sphere to which the convex sidesAGD and CHF are ground be D, and the Diameter of the Sphere to which theconcave sides BME and BNE, are ground be to D, as the Cube Root ofKK—KI to the Cube Root of RK—RI: and the Refractions on the concavesides of the Glasses, will very much correct the Errors of theRefractions on the convex sides, so far as they arise from thesphericalness of the Figure. And by this means might Telescopes bebrought to sufficient perfection, were it not for the differentRefrangibility of several sorts of Rays. But by reason of this differentRefrangibility, I do not yet see any other means of improving Telescopesby Refractions alone, than that of increasing their lengths, for whichend the late Contrivance ofHugenius seems well accommodated. For verylong Tubes are cumbersome, and scarce to be readily managed, and byreason of their length are very apt to bend, and shake by bending, so asto cause a continual trembling in the Objects, whereby it becomesdifficult to see them distinctly: whereas by his Contrivance the Glassesare readily manageable, and the Object-glass being fix'd upon a strongupright Pole becomes more steady.

Seeing therefore the Improvement of Telescopes of given lengths byRefractions is desperate; I contrived heretofore a Perspective byReflexion, using instead of an Object-glass a concave Metal. Thediameter[Pg 103] of the Sphere to which the Metal was ground concave was about25English Inches, and by consequence the length of the Instrumentabout six Inches and a quarter. The Eye-glass was Plano-convex, and thediameter of the Sphere to which the convex side was ground was about 1/5of an Inch, or a little less, and by consequence it magnified between 30and 40 times. By another way of measuring I found that it magnifiedabout 35 times. The concave Metal bore an Aperture of an Inch and athird part; but the Aperture was limited not by an opake Circle,covering the Limb of the Metal round about, but by an opake Circleplaced between the Eyeglass and the Eye, and perforated in the middlewith a little round hole for the Rays to pass through to the Eye. Forthis Circle by being placed here, stopp'd much of the erroneous Light,which otherwise would have disturbed the Vision. By comparing it with apretty good Perspective of four Feet in length, made with a concaveEye-glass, I could read at a greater distance with my own Instrumentthan with the Glass. Yet Objects appeared much darker in it than in theGlass, and that partly because more Light was lost by Reflexion in theMetal, than by Refraction in the Glass, and partly because my Instrumentwas overcharged. Had it magnified but 30 or 25 times, it would have madethe Object appear more brisk and pleasant. Two of these I made about 16Years ago, and have one of them still by me, by which I can prove thetruth of what I write. Yet it is not so good as at the first. For theconcave has been divers times tarnished[Pg 104] and cleared again, by rubbingit with very soft Leather. When I made these an Artist inLondonundertook to imitate it; but using another way of polishing them than Idid, he fell much short of what I had attained to, as I afterwardsunderstood by discoursing the Under-workman he had employed. The PolishI used was in this manner. I had two round Copper Plates, each sixInches in Diameter, the one convex, the other concave, ground very trueto one another. On the convex I ground the Object-Metal or Concave whichwas to be polish'd, 'till it had taken the Figure of the Convex and wasready for a Polish. Then I pitched over the convex very thinly, bydropping melted Pitch upon it, and warming it to keep the Pitch soft,whilst I ground it with the concave Copper wetted to make it spreadeavenly all over the convex. Thus by working it well I made it as thinas a Groat, and after the convex was cold I ground it again to give itas true a Figure as I could. Then I took Putty which I had made veryfine by washing it from all its grosser Particles, and laying a littleof this upon the Pitch, I ground it upon the Pitch with the concaveCopper, till it had done making a Noise; and then upon the Pitch Iground the Object-Metal with a brisk motion, for about two or threeMinutes of time, leaning hard upon it. Then I put fresh Putty upon thePitch, and ground it again till it had done making a noise, andafterwards ground the Object-Metal upon it as before. And this Work Irepeated till the Metal was polished, grinding it the last time with allmy strength for a good while[Pg 105] together, and frequently breathing uponthe Pitch, to keep it moist without laying on any more fresh Putty. TheObject-Metal was two Inches broad, and about one third part of an Inchthick, to keep it from bending. I had two of these Metals, and when Ihad polished them both, I tried which was best, and ground the otheragain, to see if I could make it better than that which I kept. And thusby many Trials I learn'd the way of polishing, till I made those tworeflecting Perspectives I spake of above. For this Art of polishing willbe better learn'd by repeated Practice than by my Description. Before Iground the Object-Metal on the Pitch, I always ground the Putty on itwith the concave Copper, till it had done making a noise, because if theParticles of the Putty were not by this means made to stick fast in thePitch, they would by rolling up and down grate and fret the Object-Metaland fill it full of little holes.

But because Metal is more difficult to polish than Glass, and isafterwards very apt to be spoiled by tarnishing, and reflects not somuch Light as Glass quick-silver'd over does: I would propound to useinstead of the Metal, a Glass ground concave on the foreside, and asmuch convex on the backside, and quick-silver'd over on the convex side.The Glass must be every where of the same thickness exactly. Otherwiseit will make Objects look colour'd and indistinct. By such a Glass Itried about five or six Years ago to make a reflecting Telescope of fourFeet in length to magnify about 150 times, and I satisfied my self thatthere wants nothing but a good[Pg 106] Artist to bring the Design toperfection. For the Glass being wrought by one of ourLondon Artistsafter such a manner as they grind Glasses for Telescopes, though itseemed as well wrought as the Object-glasses use to be, yet when it wasquick-silver'd, the Reflexion discovered innumerable Inequalities allover the Glass. And by reason of these Inequalities, Objects appearedindistinct in this Instrument. For the Errors of reflected Rays causedby any Inequality of the Glass, are about six times greater than theErrors of refracted Rays caused by the like Inequalities. Yet by thisExperiment I satisfied my self that the Reflexion on the concave side ofthe Glass, which I feared would disturb the Vision, did no sensibleprejudice to it, and by consequence that nothing is wanting to perfectthese Telescopes, but good Workmen who can grind and polish Glassestruly spherical. An Object-glass of a fourteen Foot Telescope, made byan Artificer atLondon, I once mended considerably, by grinding it onPitch with Putty, and leaning very easily on it in the grinding, lestthe Putty should scratch it. Whether this way may not do well enough forpolishing these reflecting Glasses, I have not yet tried. But he thatshall try either this or any other way of polishing which he may thinkbetter, may do well to make his Glasses ready for polishing, by grindingthem without that Violence, wherewith ourLondon Workmen press theirGlasses in grinding. For by such violent pressure, Glasses are apt tobend a little in the grinding, and such bending will certainly spoiltheir[Pg 107] Figure. To recommend therefore the consideration of thesereflecting Glasses to such Artists as are curious in figuring Glasses, Ishall describe this optical Instrument in the following Proposition.

PROP. VIII.Prob. II.

Let ABCD [inFig. 29.] represent a Glass spherically concave on theforeside AB, and as much convex on the backside CD, so that it be everywhere of an equal thickness. Let it not be thicker on one side than onthe other, lest it make Objects appear colour'd and indistinct, and letit be very truly wrought and quick-silver'd over on the backside; andset in the Tube VXYZ which must be very black within. Let EFG representa Prism of Glass or Crystal placed near the other end of the Tube, inthe middle of it, by means of a handle of Brass or Iron FGK, to the endof which made flat it is cemented. Let this Prism be rectangular at E,and let the other two Angles at F and G be accurately equal to eachother, and by consequence equal to half right ones, and let the planesides FE and GE be square, and by consequence the third side FG arectangular Parallelogram, whose length is to its breadth in asubduplicate proportion of two to one. Let it be so placed in the Tube,that the Axis of the Speculum may pass through the middle of the squareside EF perpendicularly[Pg 108] and by consequence through the middle of theside FG at an Angle of 45 Degrees, and let the side EF be turned towardsthe Speculum, and the distance of this Prism from the Speculum be suchthat the Rays of the Light PQ, RS, &c. which are incident upon theSpeculum in Lines parallel to the Axis thereof, may enter the Prism atthe side EF, and be reflected by the side FG, and thence go out of itthrough the side GE, to the Point T, which must be the common Focus ofthe Speculum ABDC, and of a Plano-convex Eye-glass H, through whichthose Rays must pass to the Eye. And let the Rays at their coming out ofthe Glass pass through a small round hole, or aperture made in a littleplate of Lead, Brass, or Silver, wherewith the Glass is to be covered,which hole must be no bigger than is necessary for Light enough to passthrough. For so it will render the Object distinct, the Plate in which'tis made intercepting all the erroneous part of the Light which comesfrom the verges of the Speculum AB. Such an Instrument well made, if itbe six Foot long, (reckoning the length from the Speculum to the Prism,and thence to the Focus T) will bear an aperture of six Inches at theSpeculum, and magnify between two and three hundred times. But the holeH here limits the aperture with more advantage, than if the aperture wasplaced at the Speculum. If the Instrument be made longer or shorter, theaperture must be in proportion as the Cube of the square-square Root ofthe length, and the magnifying as the aperture. But it's convenient thatthe Speculum be an Inch or two broader than the aperture at the least,and that the Glass of the Speculum be thick, that it bend not in theworking. The Prism EFG must be no bigger than is necessary, and its backside FG must not be quick-silver'd over. For without quicksilver it willreflect all the Light incident on it from the Speculum.[Pg 109]

In this Instrument the Object will be inverted, but may be erected bymaking the square sides FF and EG of the Prism EFG not plane butspherically convex, that the Rays may cross as well before they come atit as afterwards between it and the Eye-glass. If it be desired that theInstrument bear a larger aperture, that may be also done by composingthe Speculum of two Glasses with Water between them.

If the Theory of making Telescopes could at length be fully brought intoPractice, yet there would be certain Bounds beyond which Telescopescould not perform. For the Air through which we look upon the Stars, isin a perpetual Tremor; as may be seen by the tremulous Motion of Shadowscast from high Towers, and by the twinkling of the fix'd Stars. Butthese Stars do not twinkle when viewed through Telescopes which havelarge apertures. For the Rays of Light which pass through divers partsof the aperture, tremble each of them apart, and by means of theirvarious and sometimes contrary Tremors, fall at one and the same timeupon different points in the bottom of the Eye, and their tremblingMotions are too quick and confused to be perceived severally. And allthese illuminated Points constitute[Pg 111] one broad lucid Point, composed ofthose many trembling Points confusedly and insensibly mixed with oneanother by very short and swift Tremors, and thereby cause the Star toappear broader than it is, and without any trembling of the whole. LongTelescopes may cause Objects to appear brighter and larger than shortones can do, but they cannot be so formed as to take away that confusionof the Rays which arises from the Tremors of the Atmosphere. The onlyRemedy is a most serene and quiet Air, such as may perhaps be found onthe tops of the highest Mountains above the grosser Clouds.

FOOTNOTES:

[C]See our Author's Lectiones Opticæ § 10.Sect. II. § 29.and Sect. III. Prop. 25.

[D] See our Author'sLectiones Opticæ, Part. I. Sect. 1. §5.

[E]This is very fully treated of in our Author's Lect.Optic.Part I.Sect. II.

[F]See our Author's Lect. Optic. Part I. Sect. II. § 29.

[G]This is demonstrated in our Author's Lect. Optic.PartI.Sect. IV.Prop. 37.

[H]How to do this, is shewn in our Author's Lect. Optic.Part I.Sect. IV.Prop. 31.

THE FIRST BOOK OF OPTICKS

PART II.

PROP. I.Theor. I.

The Phænomena of Colours in refracted or reflected Light are not causedby new Modifications of the Light variously impress'd, according to thevarious Terminations of the Light and Shadow.

Exper. 1. For if the Sun shine into a very dark Chamber through anoblong hole F, [inFig. 1.] whose breadth is the sixth or eighth partof an Inch, or something less; and his beam FH do afterwards pass firstthrough a very large Prism ABC, distant about 20 Feet from the hole, andparallel to it, and then (with its white part) through an oblong hole H,whose breadth is about the fortieth or sixtieth[Pg 114] part of an Inch, andwhich is made in a black opake Body GI, and placed at the distance oftwo or three Feet from the Prism, in a parallel Situation both to thePrism and to the former hole, and if this white Light thus transmittedthrough the hole H, fall afterwards upon a white Paperpt, placedafter that hole H, at the distance of three or four Feet from it, andthere paint the usual Colours of the Prism, suppose red att, yellowats, green atr, blue atq, and violet atp; you may with anIron Wire, or any such like slender opake Body, whose breadth is aboutthe tenth part of an Inch, by intercepting the Rays atk,l,m,n oro, take away any one of the Colours att,s,r,q orp, whilst the other Colours remain upon the Paper as before; or withan Obstacle something bigger you may take away any two, or three, orfour Colours together, the rest remaining: So that any one of theColours as well as violet may become outmost in the Confine of theShadow towardsp, and any one of them as well as red may becomeoutmost in the Confine of the Shadow towardst, and any one of themmay also border upon the Shadow made within the Colours by the ObstacleR intercepting some intermediate part of the Light; and, lastly, any oneof them by being left alone, may border upon the Shadow on either hand.All the Colours have themselves indifferently to any Confines of Shadow,and therefore the differences of these Colours from one another, do notarise from the different Confines of Shadow, whereby Light is variouslymodified, as has hitherto been the Opinion of Philosophers. In tryingthese things 'tis to be observed, that by how much the holes F and H arenarrower, and the Intervals between them and the Prism greater, and theChamber darker, by so much the better doth the Experiment succeed;provided the Light be not so far diminished, but that the Colours atpt be sufficiently visible. To procure a Prism of solid Glass largeenough for this Experiment will be difficult, and therefore a prismatickVessel must be made of polish'd Glass Plates cemented together, andfilled with salt Water or clear Oil.[Pg 115]

Exper. 2. The Sun's Light let into a dark Chamber through the roundhole F, [inFig. 2.] half an Inch wide, passed first through the PrismABC placed at the hole, and then through a Lens PT something more thanfour Inches broad, and about eight Feet distant from the Prism, andthence converged to O the Focus of the Lens distant from it about threeFeet, and there fell upon a white Paper DE. If that Paper wasperpendicular to that Light incident upon it, as 'tis represented in theposture DE, all the Colours upon it at O appeared white. But if thePaper being turned about an Axis parallel to the Prism, became very muchinclined to the Light, as 'tis represented in the Positionsde andδε; the same Light in the one case appeared yellow and red,in the other blue. Here one and the same part of the Light in one andthe same place, according to the various Inclinations of the Paper,appeared in one case white, in another yellow or red, in a third blue,whilst the Confine of Light and shadow, and the Refractions of the Prismin all these cases remained the same.[Pg 117]

Exper. 3. Such another Experiment may be more easily tried as follows.Let a broad beam of the Sun's Light coming into a dark Chamber through ahole in the Window-shut be refracted by a large Prism ABC, [inFig.3.] whose refracting Angle C is more than 60 Degrees, and so soon as itcomes out of the Prism, let it fall upon the white Paper DE glewed upona stiff Plane; and this Light, when the Paper is perpendicular to it, as'tis represented in DE, will appear perfectly white upon the Paper; butwhen the Paper is very much inclin'd to it in such a manner as to keepalways parallel to the Axis of the Prism, the whiteness of the wholeLight upon the Paper will according to the inclination of the Paper thisway or that way, change either into yellow and red, as in the posturede, or into blue and violet, as in the posture δε. And if theLight before it fall upon the Paper be twice refracted the same way bytwo parallel Prisms, these Colours will become the more conspicuous.Here all the middle parts of the broad beam of white Light which fellupon the Paper, did without any Confine of Shadow to modify it, becomecolour'd all over with one uniform Colour, the Colour being always thesame in the middle of the Paper as at the edges, and this Colour changedaccording to the various Obliquity of the reflecting Paper, without anychange in the Refractions or Shadow, or in the Light which fell upon thePaper. And therefore these Colours are to be derived from[Pg 119] some otherCause than the new Modifications of Light by Refractions and Shadows.

If it be asked, what then is their Cause? I answer, That the Paper inthe posturede, being more oblique to the more refrangible Rays thanto the less refrangible ones, is more strongly illuminated by the latterthan by the former, and therefore the less refrangible Rays arepredominant in the reflected Light. And where-ever they are predominantin any Light, they tinge it with red or yellow, as may in some measureappear by the first Proposition of the first Part of this Book, and willmore fully appear hereafter. And the contrary happens in the posture ofthe Paper δε, the more refrangible Rays being then predominantwhich always tinge Light with blues and violets.

Exper. 4. The Colours of Bubbles with which Children play are various,and change their Situation variously, without any respect to any Confineor Shadow. If such a Bubble be cover'd with a concave Glass, to keep itfrom being agitated by any Wind or Motion of the Air, the Colours willslowly and regularly change their situation, even whilst the Eye and theBubble, and all Bodies which emit any Light, or cast any Shadow, remainunmoved. And therefore their Colours arise from some regular Cause whichdepends not on any Confine of Shadow. What this Cause is will be shewedin the next Book.

To these Experiments may be added the tenth Experiment of the first Partof this first Book, where the Sun's Light in a dark Room beingtrajected[Pg 120] through the parallel Superficies of two Prisms tied togetherin the form of a Parallelopipede, became totally of one uniform yellowor red Colour, at its emerging out of the Prisms. Here, in theproduction of these Colours, the Confine of Shadow can have nothing todo. For the Light changes from white to yellow, orange and redsuccessively, without any alteration of the Confine of Shadow: And atboth edges of the emerging Light where the contrary Confines of Shadowought to produce different Effects, the Colour is one and the same,whether it be white, yellow, orange or red: And in the middle of theemerging Light, where there is no Confine of Shadow at all, the Colouris the very same as at the edges, the whole Light at its very firstEmergence being of one uniform Colour, whether white, yellow, orange orred, and going on thence perpetually without any change of Colour, suchas the Confine of Shadow is vulgarly supposed to work in refracted Lightafter its Emergence. Neither can these Colours arise from any newModifications of the Light by Refractions, because they changesuccessively from white to yellow, orange and red, while the Refractionsremain the same, and also because the Refractions are made contrary waysby parallel Superficies which destroy one another's Effects. They arisenot therefore from any Modifications of Light made by Refractions andShadows, but have some other Cause. What that Cause is we shewed abovein this tenth Experiment, and need not here repeat it.[Pg 121]

There is yet another material Circumstance of this Experiment. For thisemerging Light being by a third Prism HIK [inFig. 22.Part I.][I]refracted towards the Paper PT, and there painting the usual Colours ofthe Prism, red, yellow, green, blue, violet: If these Colours arose fromthe Refractions of that Prism modifying the Light, they would not be inthe Light before its Incidence on that Prism. And yet in that Experimentwe found, that when by turning the two first Prisms about their commonAxis all the Colours were made to vanish but the red; the Light whichmakes that red being left alone, appeared of the very same red Colourbefore its Incidence on the third Prism. And in general we find by otherExperiments, that when the Rays which differ in Refrangibility areseparated from one another, and any one Sort of them is consideredapart, the Colour of the Light which they compose cannot be changed byany Refraction or Reflexion whatever, as it ought to be were Coloursnothing else than Modifications of Light caused by Refractions, andReflexions, and Shadows. This Unchangeableness of Colour I am now todescribe in the following Proposition.

PROP. II.Theor. II.

All homogeneal Light has its proper Colour answering to its Degree ofRefrangibility, and that Colour cannot be changed by Reflexions andRefractions.

In the Experiments of the fourth Proposition of the first Part of thisfirst Book, when I had separated the heterogeneous Rays from oneanother, the Spectrumpt formed by the separated Rays, did in theProgress from its Endp, on which the most refrangible Rays fell, untoits other Endt, on which the least refrangible Rays fell, appeartinged with this Series of Colours, violet, indigo, blue, green, yellow,orange, red, together with all their intermediate Degrees in a continualSuccession perpetually varying. So that there appeared as many Degreesof Colours, as there were sorts of Rays differing in Refrangibility.

Exper. 5. Now, that these Colours could not be changed by Refraction,I knew by refracting with a Prism sometimes one very little Part of thisLight, sometimes another very little Part, as is described in thetwelfth Experiment of the first Part of this Book. For by thisRefraction the Colour of the Light was never changed in the least. Ifany Part of the red Light was refracted, it remained totally of the samered Colour as before. No orange, no yellow, no green or blue, no othernew Colour was produced by that Refraction. Neither did the Colour anyways change by repeated Refractions, but continued always the[Pg 123] same redentirely as at first. The like Constancy and Immutability I found alsoin the blue, green, and other Colours. So also, if I looked through aPrism upon any Body illuminated with any part of this homogeneal Light,as in the fourteenth Experiment of the first Part of this Book isdescribed; I could not perceive any new Colour generated this way. AllBodies illuminated with compound Light appear through Prisms confused,(as was said above) and tinged with various new Colours, but thoseilluminated with homogeneal Light appeared through Prisms neither lessdistinct, nor otherwise colour'd, than when viewed with the naked Eyes.Their Colours were not in the least changed by the Refraction of theinterposed Prism. I speak here of a sensible Change of Colour: For theLight which I here call homogeneal, being not absolutely homogeneal,there ought to arise some little Change of Colour from itsHeterogeneity. But, if that Heterogeneity was so little as it might bemade by the said Experiments of the fourth Proposition, that Change wasnot sensible, and therefore in Experiments, where Sense is Judge, oughtto be accounted none at all.

Exper. 6. And as these Colours were not changeable by Refractions, soneither were they by Reflexions. For all white, grey, red, yellow,green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, IndicoBise, Gold, Silver, Copper, Grass, blue Flowers, Violets, Bubbles ofWater tinged with various Colours, Peacock's Feathers, the Tincture of[Pg 124]Lignum Nephriticum, and such-like, in red homogeneal Light appearedtotally red, in blue Light totally blue, in green Light totally green,and so of other Colours. In the homogeneal Light of any Colour they allappeared totally of that same Colour, with this only Difference, thatsome of them reflected that Light more strongly, others more faintly. Inever yet found any Body, which by reflecting homogeneal Light couldsensibly change its Colour.

From all which it is manifest, that if the Sun's Light consisted of butone sort of Rays, there would be but one Colour in the whole World, norwould it be possible to produce any new Colour by Reflexions andRefractions, and by consequence that the variety of Colours depends uponthe Composition of Light.

DEFINITION.

The homogeneal Light and Rays which appear red, or rather make Objectsappear so, I call Rubrifick or Red-making; those which make Objectsappear yellow, green, blue, and violet, I call Yellow-making,Green-making, Blue-making, Violet-making, and so of the rest. And if atany time I speak of Light and Rays as coloured or endued with Colours, Iwould be understood to speak not philosophically and properly, butgrossly, and accordingly to such Conceptions as vulgar People in seeingall these Experiments would be apt to frame. For the Rays to speakproperly are not coloured. In them there is nothing else than a certainPower and Disposition to[Pg 125] stir up a Sensation of this or that Colour.For as Sound in a Bell or musical String, or other sounding Body, isnothing but a trembling Motion, and in the Air nothing but that Motionpropagated from the Object, and in the Sensorium 'tis a Sense of thatMotion under the Form of Sound; so Colours in the Object are nothing buta Disposition to reflect this or that sort of Rays more copiously thanthe rest; in the Rays they are nothing but their Dispositions topropagate this or that Motion into the Sensorium, and in the Sensoriumthey are Sensations of those Motions under the Forms of Colours.

PROP. III.Prob. I.

To define the Refrangibility of the several sorts of homogeneal Lightanswering to the several Colours.

Exper. 7. When I had caused the Rectilinear Sides AF, GM, [inFig.4.] of the Spectrum of Colours made by the Prism to be distinctlydefined, as in the fifth Experiment of the first Part of this Book isdescribed, there were found in it all the homogeneal Colours in the sameOrder and Situation one among another as in the Spectrum of simpleLight, described in the fourth Proposition of that Part. For the Circlesof which the Spectrum of compound Light[Pg 126] PT is composed, and which inthe middle Parts of the Spectrum interfere, and are intermix'd with oneanother, are not intermix'd in their outmost Parts where they touchthose Rectilinear Sides AF and GM. And therefore, in those RectilinearSides when distinctly defined, there is no new Colour generated byRefraction. I observed also, that if any where between the two outmostCircles TMF and PGA a Right Line, as γδ, was cross to theSpectrum, so as both Ends to fall perpendicularly upon its RectilinearSides, there appeared one and the same Colour, and degree of Colour fromone End of this Line to the other. I delineated therefore in a Paper thePerimeter of the Spectrum FAP GMT, and in trying the third Experiment ofthe first Part of this Book, I held the Paper so that the Spectrum mightfall upon this delineated Figure, and agree with it exactly, whilst anAssistant, whose Eyes for distinguishing Colours were more critical thanmine, did by Right Lines αβ, γδ, εζ, &c. drawn cross theSpectrum, note the Confines of the Colours, that is of the red MαβF, of the orange αγδβ, of the yellow γεζδ, of thegreen ηθζ, of the blue ηικθ, of the indico ιλμκ,and of the violet λGAμ. And this Operationbeing divers times repeated both in the same, and in several Papers, Ifound that the Observations agreed well enough with one another, andthat the Rectilinear Sides MG and FA were by the said cross Linesdivided after the manner of a Musical Chord. Let GM be produced to X,that MX may be equal to GM, and conceive GX, λX, ιX,ηX, εX, γX, αX, MX, to be inproportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5,9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, athird Minor, a fourth, a fifth, a sixth Major, a seventh and an eighthabove that Key: And the Intervals Mα, αγ, γε,εη, ηι, ιλ, and λG, will be theSpaces which the several Colours (red, orange, yellow, green, blue,indigo, violet) take up.[Pg 127]

Now these Intervals or Spaces subtending the Differences of theRefractions of the Rays going to the Limits of those Colours, that is,to the Points M, α, γ, ε, η, ι, λ, G, may without any sensible Error be accountedproportional to the Differences of the Sines of Refraction of those Rayshaving one common Sine of Incidence, and therefore since the common Sineof Incidence of the most and least refrangible Rays out of Glass intoAir was (by a Method described above) found in proportion to their Sinesof Refraction, as 50 to 77 and 78, divide the Difference between theSines of Refraction 77 and 78, as the Line GM is divided by thoseIntervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3,77-7/9, 78, the Sines of Refraction of those Rays out of Glass into Air,their common Sine of Incidence being 50. So then the Sines of theIncidences of all the red-making Rays out of Glass into Air, were to theSines of their Refractions, not greater than 50 to 77, nor less than 50to 77-1/8, but they varied from one another according to allintermediate Proportions. And the Sines of the Incidences of thegreen-making Rays were to the Sines of their Refractions in allProportions[Pg 129] from that of 50 to 77-1/3, unto that of 50 to 77-1/2. Andby the like Limits above-mentioned were the Refractions of the Raysbelonging to the rest of the Colours defined, the Sines of thered-making Rays extending from 77 to 77-1/8, those of the orange-makingfrom 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3,those of the green-making from 77-1/3 to 77-1/2, those of theblue-making from 77-1/2 to 77-2/3, those of the indigo-making from77-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.

These are the Laws of the Refractions made out of Glass into Air, andthence by the third Axiom of the first Part of this Book, the Laws ofthe Refractions made out of Air into Glass are easily derived.

Exper. 8. I found moreover, that when Light goes out of Air throughseveral contiguous refracting Mediums as through Water and Glass, andthence goes out again into Air, whether the refracting Superficies beparallel or inclin'd to one another, that Light as often as by contraryRefractions 'tis so corrected, that it emergeth in Lines parallel tothose in which it was incident, continues ever after to be white. But ifthe emergent Rays be inclined to the incident, the Whiteness of theemerging Light will by degrees in passing on from the Place ofEmergence, become tinged in its Edges with Colours. This I try'd byrefracting Light with Prisms of Glass placed within a Prismatick Vesselof Water. Now those Colours argue a diverging and separation of theheterogeneous Rays from one another by means of their unequalRefractions, as in what follows will[Pg 130] more fully appear. And, on thecontrary, the permanent whiteness argues, that in like Incidences of theRays there is no such separation of the emerging Rays, and byconsequence no inequality of their whole Refractions. Whence I seem togather the two following Theorems.

1. The Excesses of the Sines of Refraction of several sorts of Raysabove their common Sine of Incidence when the Refractions are made outof divers denser Mediums immediately into one and the same rarer Medium,suppose of Air, are to one another in a given Proportion.

2. The Proportion of the Sine of Incidence to the Sine of Refraction ofone and the same sort of Rays out of one Medium into another, iscomposed of the Proportion of the Sine of Incidence to the Sine ofRefraction out of the first Medium into any third Medium, and of theProportion of the Sine of Incidence to the Sine of Refraction out ofthat third Medium into the second Medium.

By the first Theorem the Refractions of the Rays of every sort made outof any Medium into Air are known by having the Refraction of the Rays ofany one sort. As for instance, if the Refractions of the Rays of everysort out of Rain-water into Air be desired, let the common Sine ofIncidence out of Glass into Air be subducted from the Sines ofRefraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2,27-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the leastrefrangible Rays be to their Sine of Refraction out of Rain-water intoAir as 3 to 4,[Pg 131] and say as 1 the difference of those Sines is to 3 theSine of Incidence, so is 27 the least of the Excesses above-mentioned toa fourth Number 81; and 81 will be the common Sine of Incidence out ofRain-water into Air, to which Sine if you add all the above-mentionedExcesses, you will have the desired Sines of the Refractions 108,108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.

By the latter Theorem the Refraction out of one Medium into another isgathered as often as you have the Refractions out of them both into anythird Medium. As if the Sine of Incidence of any Ray out of Glass intoAir be to its Sine of Refraction, as 20 to 31, and the Sine of Incidenceof the same Ray out of Air into Water, be to its Sine of Refraction as 4to 3; the Sine of Incidence of that Ray out of Glass into Water will beto its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, asthe Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.

And these Theorems being admitted into Opticks, there would be scopeenough of handling that Science voluminously after a new manner,[K] notonly by teaching those things which tend to the perfection of Vision,but also by determining mathematically all kinds of Phænomena of Colourswhich could be produced by Refractions. For to do this, there is nothingelse requisite than to find out the Separations of heterogeneous Rays,and their various Mixtures and Proportions in every Mixture. By this[Pg 132]way of arguing I invented almost all the Phænomena described in theseBooks, beside some others less necessary to the Argument; and by thesuccesses I met with in the Trials, I dare promise, that to him whoshall argue truly, and then try all things with good Glasses andsufficient Circumspection, the expected Event will not be wanting. Buthe is first to know what Colours will arise from any others mix'd in anyassigned Proportion.

PROP. IV.Theor. III.

Colours may be produced by Composition which shall be like to theColours of homogeneal Light as to the Appearance of Colour, but not asto the Immutability of Colour and Constitution of Light. And thoseColours by how much they are more compounded by so much are they lessfull and intense, and by too much Composition they maybe diluted andweaken'd till they cease, and the Mixture becomes white or grey. Theremay be also Colours produced by Composition, which are not fully likeany of the Colours of homogeneal Light.

For a Mixture of homogeneal red and yellow compounds an Orange, like inappearance of Colour to that orange which in the series of unmixedprismatick Colours lies between them; but the Light of one orange ishomogeneal as to Refrangibility,[Pg 133] and that of the other is heterogeneal,and the Colour of the one, if viewed through a Prism, remains unchanged,that of the other is changed and resolved into its component Colours redand yellow. And after the same manner other neighbouring homogenealColours may compound new Colours, like the intermediate homogeneal ones,as yellow and green, the Colour between them both, and afterwards, ifblue be added, there will be made a green the middle Colour of the threewhich enter the Composition. For the yellow and blue on either hand, ifthey are equal in quantity they draw the intermediate green equallytowards themselves in Composition, and so keep it as it were inÆquilibrion, that it verge not more to the yellow on the one hand, andto the blue on the other, but by their mix'd Actions remain still amiddle Colour. To this mix'd green there may be farther added some redand violet, and yet the green will not presently cease, but only growless full and vivid, and by increasing the red and violet, it will growmore and more dilute, until by the prevalence of the added Colours it beovercome and turned into whiteness, or some other Colour. So if to theColour of any homogeneal Light, the Sun's white Light composed of allsorts of Rays be added, that Colour will not vanish or change itsSpecies, but be diluted, and by adding more and more white it will bediluted more and more perpetually. Lastly, If red and violet be mingled,there will be generated according to their various Proportions variousPurples, such as are not like in appearance to the Colour of any[Pg 134]homogeneal Light, and of these Purples mix'd with yellow and blue may bemade other new Colours.

PROP. V.Theor. IV.

Whiteness and all grey Colours between white and black, may becompounded of Colours, and the whiteness of the Sun's Light iscompounded of all the primary Colours mix'd in a due Proportion.

Exper. 9. The Sun shining into a dark Chamber through a little roundhole in the Window-shut, and his Light being there refracted by a Prismto cast his coloured Image PT [inFig. 5.] upon the opposite Wall: Iheld a white Paper V to that image in such manner that it might beilluminated by the colour'd Light reflected from thence, and yet notintercept any part of that Light in its passage from the Prism to theSpectrum. And I found that when the Paper was held nearer to any Colourthan to the rest, it appeared of that Colour to which it approachednearest; but when it was equally or almost equally distant from all theColours, so that it might be equally illuminated by them all it appearedwhite. And in this last situation of the Paper, if some Colours wereintercepted, the Paper lost its white Colour, and appeared of the Colourof the rest of the Light which was not intercepted. So then the Paperwas illuminated with Lights of various[Pg 135] Colours, namely, red, yellow,green, blue and violet, and every part of the Light retained its properColour, until it was incident on the Paper, and became reflected thenceto the Eye; so that if it had been either alone (the rest of the Lightbeing intercepted) or if it had abounded most, and been predominant inthe Light reflected from the Paper, it would have tinged the Paper withits own Colour; and yet being mixed with the rest of the Colours in adue proportion, it made the Paper look white, and therefore by aComposition with the rest produced that Colour. The several parts of thecoloured Light reflected from the Spectrum, whilst they are propagatedfrom thence through the Air, do perpetually retain their proper Colours,because wherever they fall upon the Eyes of any Spectator, they make theseveral parts of the Spectrum to appear under their proper Colours. Theyretain therefore their proper Colours when they fall upon the Paper V,and so by the confusion and perfect mixture of those Colours compoundthe whiteness of the Light reflected from thence.

Exper. 10. Let that Spectrum or solar Image PT [inFig. 6.] fall nowupon the Lens MN above four Inches broad, and about six Feet distantfrom the Prism ABC and so figured that it may cause the coloured Lightwhich divergeth from the Prism to converge and meet again at its FocusG, about six or eight Feet distant from the Lens, and there to fallperpendicularly upon a white Paper DE. And if you move this Paper to andfro, you will perceive that[Pg 136] near the Lens, as atde, the whole solarImage (suppose atpt) will appear upon it intensely coloured after themanner above-explained, and that by receding from the Lens those Colourswill perpetually come towards one another, and by mixing more and moredilute one another continually, until at length the Paper come to theFocus G, where by a perfect mixture they will wholly vanish and beconverted into whiteness, the whole Light appearing now upon the Paperlike a little white Circle. And afterwards by receding farther from theLens, the Rays which before converged will now cross one another in theFocus G, and diverge from thence, and thereby make the Colours to appearagain, but yet in a contrary order; suppose at δε, where theredt is now above which before was below, and the violetp is belowwhich before was above.

Let us now stop the Paper at the Focus G, where the Light appearstotally white and circular, and let us consider its whiteness. I say,that this is composed of the converging Colours. For if any of thoseColours be intercepted at the Lens, the whiteness will cease anddegenerate into that Colour which ariseth from the composition of theother Colours which are not intercepted. And then if the interceptedColours be let pass and fall upon that compound Colour, they mix withit, and by their mixture restore the whiteness. So if the violet, blueand green be intercepted, the remaining yellow, orange and red willcompound upon the Paper an orange, and then if the intercepted Coloursbe let pass, they will fall upon this compounded orange, and togetherwith it decompound a white. So also if the red and violet beintercepted, the remaining yellow, green and blue, will compound a greenupon the Paper, and then the red and violet being let pass will fallupon this green, and together with it decompound a white. And that inthis Composition of white the several Rays do not suffer any Change intheir colorific Qualities by acting upon one another, but are onlymixed, and by a mixture of their Colours produce white, may fartherappear by these Arguments.[Pg 137]

If the Paper be placed beyond the Focus G, suppose at δε, andthen the red Colour at the Lens be alternately intercepted, and let passagain, the violet Colour on the Paper will not suffer any Changethereby, as it ought to do if the several sorts of Rays acted upon oneanother in the Focus G, where they cross. Neither will the red upon thePaper be changed by any alternate stopping, and letting pass the violetwhich crosseth it.

And if the Paper be placed at the Focus G, and the white round Image atG be viewed through the Prism HIK, and by the Refraction of that Prismbe translated to the placerv, and there appear tinged with variousColours, namely, the violet atv and red atr, and others between,and then the red Colours at the Lens be often stopp'd and let pass byturns, the red atr will accordingly disappear, and return as often,but the violet atv will not thereby suffer any Change. And so bystopping and letting pass alternately the blue at the Lens, the blue atv will accordingly[Pg 139] disappear and return, without any Change made inthe red atr. The red therefore depends on one sort of Rays, and theblue on another sort, which in the Focus G where they are commix'd, donot act on one another. And there is the same Reason of the otherColours.

I considered farther, that when the most refrangible Rays Pp, and theleast refrangible ones Tt, are by converging inclined to one another,the Paper, if held very oblique to those Rays in the Focus G, mightreflect one sort of them more copiously than the other sort, and by thatMeans the reflected Light would be tinged in that Focus with the Colourof the predominant Rays, provided those Rays severally retained theirColours, or colorific Qualities in the Composition of White made by themin that Focus. But if they did not retain them in that White, but becameall of them severally endued there with a Disposition to strike theSense with the Perception of White, then they could never lose theirWhiteness by such Reflexions. I inclined therefore the Paper to the Raysvery obliquely, as in the second Experiment of this second Part of thefirst Book, that the most refrangible Rays, might be more copiouslyreflected than the rest, and the Whiteness at Length changedsuccessively into blue, indigo, and violet. Then I inclined it thecontrary Way, that the least refrangible Rays might be more copious inthe reflected Light than the rest, and the Whiteness turned successivelyto yellow, orange, and red.

Lastly, I made an Instrument XY in fashion of a[Pg 140] Comb, whose Teeth beingin number sixteen, were about an Inch and a half broad, and theIntervals of the Teeth about two Inches wide. Then by interposingsuccessively the Teeth of this Instrument near the Lens, I interceptedPart of the Colours by the interposed Tooth, whilst the rest of themwent on through the Interval of the Teeth to the Paper DE, and therepainted a round Solar Image. But the Paper I had first placed so, thatthe Image might appear white as often as the Comb was taken away; andthen the Comb being as was said interposed, that Whiteness by reason ofthe intercepted Part of the Colours at the Lens did always change intothe Colour compounded of those Colours which were not intercepted, andthat Colour was by the Motion of the Comb perpetually varied so, that inthe passing of every Tooth over the Lens all these Colours, red, yellow,green, blue, and purple, did always succeed one another. I causedtherefore all the Teeth to pass successively over the Lens, and when theMotion was slow, there appeared a perpetual Succession of the Coloursupon the Paper: But if I so much accelerated the Motion, that theColours by reason of their quick Succession could not be distinguishedfrom one another, the Appearance of the single Colours ceased. There wasno red, no yellow, no green, no blue, nor purple to be seen any longer,but from a Confusion of them all there arose one uniform white Colour.Of the Light which now by the Mixture of all the Colours appeared white,there was no Part really white. One Part was red, another yellow, a[Pg 141]third green, a fourth blue, a fifth purple, and every Part retains itsproper Colour till it strike the Sensorium. If the Impressions followone another slowly, so that they may be severally perceived, there ismade a distinct Sensation of all the Colours one after another in acontinual Succession. But if the Impressions follow one another soquickly, that they cannot be severally perceived, there ariseth out ofthem all one common Sensation, which is neither of this Colour alone norof that alone, but hath it self indifferently to 'em all, and this is aSensation of Whiteness. By the Quickness of the Successions, theImpressions of the several Colours are confounded in the Sensorium, andout of that Confusion ariseth a mix'd Sensation. If a burning Coal benimbly moved round in a Circle with Gyrations continually repeated, thewhole Circle will appear like Fire; the reason of which is, that theSensation of the Coal in the several Places of that Circle remainsimpress'd on the Sensorium, until the Coal return again to the samePlace. And so in a quick Consecution of the Colours the Impression ofevery Colour remains in the Sensorium, until a Revolution of all theColours be compleated, and that first Colour return again. TheImpressions therefore of all the successive Colours are at once in theSensorium, and jointly stir up a Sensation of them all; and so it ismanifest by this Experiment, that the commix'd Impressions of all theColours do stir up and beget a Sensation of white, that is, thatWhiteness is compounded of all the Colours.[Pg 142]

And if the Comb be now taken away, that all the Colours may at once passfrom the Lens to the Paper, and be there intermixed, and togetherreflected thence to the Spectator's Eyes; their Impressions on theSensorium being now more subtilly and perfectly commixed there, oughtmuch more to stir up a Sensation of Whiteness.

You may instead of the Lens use two Prisms HIK and LMN, which byrefracting the coloured Light the contrary Way to that of the firstRefraction, may make the diverging Rays converge and meet again in G, asyou see represented in the seventh Figure. For where they meet and mix,they will compose a white Light, as when a Lens is used.

Exper. 11. Let the Sun's coloured Image PT [inFig. 8.] fall uponthe Wall of a dark Chamber, as in the third Experiment of the firstBook, and let the same be viewed through a Prismabc, held parallel tothe Prism ABC, by whose Refraction that Image was made, and let it nowappear lower than before, suppose in the Place S over-against the redColour T. And if you go near to the Image PT, the Spectrum S will appearoblong and coloured like the Image PT; but if you recede from it, theColours of the spectrum S will be contracted more and more, and atlength vanish, that Spectrum S becoming perfectly round and white; andif you recede yet farther, the Colours will emerge again, but in acontrary Order. Now that Spectrum S appears white in that Case, when theRays of several sorts which converge from the several Parts of the ImagePT, to the Prismabc, are so refracted unequally by it, that in theirPassage from the Prism to the Eye they may diverge from one and the samePoint of the Spectrum S, and so fall afterwards upon one and the samePoint in the bottom of the Eye, and there be mingled.[Pg 143]

And farther, if the Comb be here made use of, by whose Teeth the Coloursat the Image PT may be successively intercepted; the Spectrum S, whenthe Comb is moved slowly, will be perpetually tinged with successiveColours: But when by accelerating the Motion of the Comb, the Successionof the Colours is so quick that they cannot be severally seen, thatSpectrum S, by a confused and mix'd Sensation of them all, will appearwhite.

Exper. 12. The Sun shining through a large Prism ABC [inFig. 9.]upon a Comb XY, placed immediately behind the Prism, his Light whichpassed through the Interstices of the Teeth fell upon a white Paper DE.The Breadths of the Teeth were equal to their Interstices, and sevenTeeth together with their Interstices took up an Inch in Breadth. Now,when the Paper was about two or three Inches distant from the Comb, theLight which passed through its several Interstices painted so manyRanges of Colours,kl,mn,op,qr, &c. which were parallel toone another, and contiguous, and without any Mixture of white. And theseRanges of Colours, if the Comb was moved continually up and down with areciprocal Motion, ascended and descended in the Paper, and when theMotion of the Comb was so quick, that the Colours could not bedistinguished from one another, the whole Paper by their Confusion andMixture in the Sensorium appeared white.[Pg 145]

Let the Comb now rest, and let the Paper be removed farther from thePrism, and the several Ranges of Colours will be dilated and expandedinto one another more and more, and by mixing their Colours will diluteone another, and at length, when the distance of the Paper from the Combis about a Foot, or a little more (suppose in the Place 2D 2E) they willso far dilute one another, as to become white.

With any Obstacle, let all the Light be now stopp'd which passes throughany one Interval of the Teeth, so that the Range of Colours which comesfrom thence may be taken away, and you will see the Light of the rest ofthe Ranges to be expanded into the Place of the Range taken away, andthere to be coloured. Let the intercepted Range pass on as before, andits Colours falling upon the Colours of the other Ranges, and mixingwith them, will restore the Whiteness.

Let the Paper 2D 2E be now very much inclined to the Rays, so that themost refrangible Rays may be more copiously reflected than the rest, andthe white Colour of the Paper through the Excess of those Rays will bechanged into blue and violet. Let the Paper be as much inclined thecontrary way, that the least refrangible Rays may be now more copiouslyreflected than the rest, and by their Excess the Whiteness will bechanged into yellow and red. The several Rays therefore in that whiteLight do retain their colorific Qualities, by which those of any sort,whenever[Pg 147] they become more copious than the rest, do by their Excess andPredominance cause their proper Colour to appear.

And by the same way of arguing, applied to the third Experiment of thissecond Part of the first Book, it may be concluded, that the whiteColour of all refracted Light at its very first Emergence, where itappears as white as before its Incidence, is compounded of variousColours.

Exper. 13. In the foregoing Experiment the several Intervals of theTeeth of the Comb do the Office of so many Prisms, every Intervalproducing the Phænomenon of one Prism. Whence instead of those Intervalsusing several Prisms, I try'd to compound Whiteness by mixing theirColours, and did it by using only three Prisms, as also by using onlytwo as follows. Let two Prisms ABC andabc, [inFig. 10.] whoserefracting Angles B andb are equal, be so[Pg 148] placed parallel to oneanother, that the refracting Angle B of the one may touch the Anglecat the Base of the other, and their Planes CB andcb, at which theRays emerge, may lie in Directum. Then let the Light trajected throughthem fall upon the Paper MN, distant about 8 or 12 Inches from thePrisms. And the Colours generated by the interior Limits B andc ofthe two Prisms, will be mingled at PT, and there compound white. For ifeither Prism be taken away, the Colours made by the other will appear inthat Place PT, and when the Prism is restored to its Place again, sothat its Colours may there fall upon the Colours of the other, theMixture of them both will restore the Whiteness.

This Experiment succeeds also, as I have tried, when the Angleb ofthe lower Prism, is a little greater than the Angle B of the upper, andbetween the interior Angles B andc, there intercedes some Space Bc,as is represented in the Figure, and the refracting Planes BC andbc,are neither in Directum, nor parallel to one another. For there isnothing more requisite to the Success of this Experiment, than that theRays of all sorts may be uniformly mixed upon the Paper in the Place PT.If the most refrangible Rays coming from the superior Prism take up allthe Space from M to P, the Rays of the same sort which come from theinferior Prism ought to begin at P, and take up all the rest of theSpace from thence towards N. If the least refrangible Rays coming fromthe superior Prism take up the Space MT, the Rays of the same kind whichcome from the other Prism[Pg 149] ought to begin at T, and take up theremaining Space TN. If one sort of the Rays which have intermediateDegrees of Refrangibility, and come from the superior Prism be extendedthrough the Space MQ, and another sort of those Rays through the SpaceMR, and a third sort of them through the Space MS, the same sorts ofRays coming from the lower Prism, ought to illuminate the remainingSpaces QN, RN, SN, respectively. And the same is to be understood of allthe other sorts of Rays. For thus the Rays of every sort will bescattered uniformly and evenly through the whole Space MN, and so beingevery where mix'd in the same Proportion, they must every where producethe same Colour. And therefore, since by this Mixture they produce whitein the Exterior Spaces MP and TN, they must also produce white in theInterior Space PT. This is the reason of the Composition by whichWhiteness was produced in this Experiment, and by what other way soeverI made the like Composition, the Result was Whiteness.

Lastly, If with the Teeth of a Comb of a due Size, the coloured Lightsof the two Prisms which fall upon the Space PT be alternatelyintercepted, that Space PT, when the Motion of the Comb is slow, willalways appear coloured, but by accelerating the Motion of the Comb somuch that the successive Colours cannot be distinguished from oneanother, it will appear white.

Exper. 14. Hitherto I have produced Whiteness by mixing the Colours ofPrisms. If now the Colours[Pg 150] of natural Bodies are to be mingled, letWater a little thicken'd with Soap be agitated to raise a Froth, andafter that Froth has stood a little, there will appear to one that shallview it intently various Colours every where in the Surfaces of theseveral Bubbles; but to one that shall go so far off, that he cannotdistinguish the Colours from one another, the whole Froth will growwhite with a perfect Whiteness.

Exper. 15. Lastly, In attempting to compound a white, by mixing thecoloured Powders which Painters use, I consider'd that all colour'dPowders do suppress and stop in them a very considerable Part of theLight by which they are illuminated. For they become colour'd byreflecting the Light of their own Colours more copiously, and that ofall other Colours more sparingly, and yet they do not reflect the Lightof their own Colours so copiously as white Bodies do. If red Lead, forinstance, and a white Paper, be placed in the red Light of the colour'dSpectrum made in a dark Chamber by the Refraction of a Prism, as isdescribed in the third Experiment of the first Part of this Book; thePaper will appear more lucid than the red Lead, and therefore reflectsthe red-making Rays more copiously than red Lead doth. And if they beheld in the Light of any other Colour, the Light reflected by the Paperwill exceed the Light reflected by the red Lead in a much greaterProportion. And the like happens in Powders of other Colours. Andtherefore by mixing such Powders, we are not to expect a strong andfull[Pg 151] White, such as is that of Paper, but some dusky obscure one, suchas might arise from a Mixture of Light and Darkness, or from white andblack, that is, a grey, or dun, or russet brown, such as are the Coloursof a Man's Nail, of a Mouse, of Ashes, of ordinary Stones, of Mortar, ofDust and Dirt in High-ways, and the like. And such a dark white I haveoften produced by mixing colour'd Powders. For thus one Part of redLead, and five Parts ofViride Æris, composed a dun Colour like thatof a Mouse. For these two Colours were severally so compounded ofothers, that in both together were a Mixture of all Colours; and therewas less red Lead used thanViride Æris, because of the Fulness of itsColour. Again, one Part of red Lead, and four Parts of blue Bise,composed a dun Colour verging a little to purple, and by adding to thisa certain Mixture of Orpiment andViride Æris in a due Proportion, theMixture lost its purple Tincture, and became perfectly dun. But theExperiment succeeded best without Minium thus. To Orpiment I added bylittle and little a certain full bright purple, which Painters use,until the Orpiment ceased to be yellow, and became of a pale red. Then Idiluted that red by adding a littleViride Æris, and a little moreblue Bise thanViride Æris, until it became of such a grey or palewhite, as verged to no one of the Colours more than to another. For thusit became of a Colour equal in Whiteness to that of Ashes, or of Woodnewly cut, or of a Man's Skin. The Orpiment reflected more Light thandid any other of the Powders, and therefore[Pg 152] conduced more to theWhiteness of the compounded Colour than they. To assign the Proportionsaccurately may be difficult, by reason of the different Goodness ofPowders of the same kind. Accordingly, as the Colour of any Powder ismore or less full and luminous, it ought to be used in a less or greaterProportion.

Now, considering that these grey and dun Colours may be also produced bymixing Whites and Blacks, and by consequence differ from perfect Whites,not in Species of Colours, but only in degree of Luminousness, it ismanifest that there is nothing more requisite to make them perfectlywhite than to increase their Light sufficiently; and, on the contrary,if by increasing their Light they can be brought to perfect Whiteness,it will thence also follow, that they are of the same Species of Colourwith the best Whites, and differ from them only in the Quantity ofLight. And this I tried as follows. I took the third of theabove-mention'd grey Mixtures, (that which was compounded of Orpiment,Purple, Bise, andViride Æris) and rubbed it thickly upon the Floor ofmy Chamber, where the Sun shone upon it through the opened Casement; andby it, in the shadow, I laid a Piece of white Paper of the same Bigness.Then going from them to the distance of 12 or 18 Feet, so that I couldnot discern the Unevenness of the Surface of the Powder, nor the littleShadows let fall from the gritty Particles thereof; the Powder appearedintensely white, so as to transcend even the Paper it self in Whiteness,especially if the Paper were a little[Pg 153] shaded from the Light of theClouds, and then the Paper compared with the Powder appeared of such agrey Colour as the Powder had done before. But by laying the Paper wherethe Sun shines through the Glass of the Window, or by shutting theWindow that the Sun might shine through the Glass upon the Powder, andby such other fit Means of increasing or decreasing the Lights wherewiththe Powder and Paper were illuminated, the Light wherewith the Powder isilluminated may be made stronger in such a due Proportion than the Lightwherewith the Paper is illuminated, that they shall both appear exactlyalike in Whiteness. For when I was trying this, a Friend coming to visitme, I stopp'd him at the Door, and before I told him what the Colourswere, or what I was doing; I asked him, Which of the two Whites were thebest, and wherein they differed? And after he had at that distanceviewed them well, he answer'd, that they were both good Whites, and thathe could not say which was best, nor wherein their Colours differed.Now, if you consider, that this White of the Powder in the Sun-shine wascompounded of the Colours which the component Powders (Orpiment, Purple,Bise, andViride Æris) have in the same Sun-shine, you mustacknowledge by this Experiment, as well as by the former, that perfectWhiteness may be compounded of Colours.

From what has been said it is also evident, that the Whiteness of theSun's Light is compounded of all the Colours wherewith the several sortsof Rays whereof that Light consists, when by their several[Pg 154]Refrangibilities they are separated from one another, do tinge Paper orany other white Body whereon they fall. For those Colours (byProp.II.Part 2.) are unchangeable, and whenever all those Rays with thosetheir Colours are mix'd again, they reproduce the same white Light asbefore.

PROP. VI.Prob. II.

In a mixture of Primary Colours, the Quantity and Quality of each beinggiven, to know the Colour of the Compound.

With the Center O [inFig. 11.] and Radius OD describe a Circle ADF,and distinguish its Circumference into seven Parts DE, EF, FG, GA, AB,BC, CD, proportional to the seven Musical Tones or Intervals of theeight Sounds,Sol,la,fa,sol,la,mi,fa,sol,contained in an eight, that is, proportional to the Number 1/9, 1/16,1/10, 1/9, 1/16, 1/16, 1/9. Let the first Part DE represent a redColour, the second EF orange, the third FG yellow, the fourth CA green,the fifth AB blue, the sixth BC indigo, and the seventh CD violet. Andconceive that these are all the Colours of uncompounded Light graduallypassing into one another, as they do when made by Prisms; theCircumference DEFGABCD, representing the whole Series of Colours fromone end of the Sun's colour'd Image to the other, so that from D to E beall degrees of red, at E the mean Colour[Pg 155] between red and orange, from Eto F all degrees of orange, at F the mean between orange and yellow,from F to G all degrees of yellow, and so on. Letp be the Center ofGravity of the Arch DE, andq,r,s,t,u,x, the Centers ofGravity of the Arches EF, FG, GA, AB, BC, and CD respectively, and aboutthose Centers of Gravity let Circles proportional to the Number of Raysof each Colour in the given Mixture be describ'd: that is, the Circlep proportional to the Number of the red-making Rays in the Mixture,the Circleq proportional to the Number of the orange-making Rays inthe Mixture, and so of the rest. Find the common Center of Gravity ofall those Circles,p,q,r,s,t,u,x. Let that Center beZ; and from the Center of the Circle ADF, through Z to theCircumference, drawing the Right Line OY, the Place of the Point Y inthe Circumference shall shew the Colour arising from the Composition ofall the Colours in the given Mixture, and the Line OZ shall[Pg 156] beproportional to the Fulness or Intenseness of the Colour, that is, toits distance from Whiteness. As if Y fall in the middle between F and G,the compounded Colour shall be the best yellow; if Y verge from themiddle towards F or G, the compound Colour shall accordingly be ayellow, verging towards orange or green. If Z fall upon theCircumference, the Colour shall be intense and florid in the highestDegree; if it fall in the mid-way between the Circumference and Center,it shall be but half so intense, that is, it shall be such a Colour aswould be made by diluting the intensest yellow with an equal quantity ofwhiteness; and if it fall upon the center O, the Colour shall have lostall its intenseness, and become a white. But it is to be noted, That ifthe point Z fall in or near the line OD, the main ingredients being thered and violet, the Colour compounded shall not be any of the prismatickColours, but a purple, inclining to red or violet, accordingly as thepoint Z lieth on the side of the line DO towards E or towards C, and ingeneral the compounded violet is more bright and more fiery than theuncompounded. Also if only two of the primary Colours which in thecircle are opposite to one another be mixed in an equal proportion, thepoint Z shall fall upon the center O, and yet the Colour compounded ofthose two shall not be perfectly white, but some faint anonymous Colour.For I could never yet by mixing only two primary Colours produce aperfect white. Whether it may be compounded of a mixture of three takenat equal distances in the circumference[Pg 157] I do not know, but of four orfive I do not much question but it may. But these are Curiosities oflittle or no moment to the understanding the Phænomena of Nature. For inall whites produced by Nature, there uses to be a mixture of all sortsof Rays, and by consequence a composition of all Colours.

To give an instance of this Rule; suppose a Colour is compounded ofthese homogeneal Colours, of violet one part, of indigo one part, ofblue two parts, of green three parts, of yellow five parts, of orangesix parts, and of red ten parts. Proportional to these parts describethe Circlesx,v,t,s,r,q,p, respectively, that is, sothat if the Circlex be one, the Circlev may be one, the Circlettwo, the Circles three, and the Circlesr,q andp, five, sixand ten. Then I find Z the common center of gravity of these Circles,and through Z drawing the Line OY, the Point Y falls upon thecircumference between E and F, something nearer to E than to F, andthence I conclude, that the Colour compounded of these Ingredients willbe an orange, verging a little more to red than to yellow. Also I findthat OZ is a little less than one half of OY, and thence I conclude,that this orange hath a little less than half the fulness or intensenessof an uncompounded orange; that is to say, that it is such an orange asmay be made by mixing an homogeneal orange with a good white in theproportion of the Line OZ to the Line ZY, this Proportion being not ofthe quantities of mixed orange and white Powders, but of the quantitiesof the Lights reflected from them.[Pg 158]

This Rule I conceive accurate enough for practice, though notmathematically accurate; and the truth of it may be sufficiently provedto Sense, by stopping any of the Colours at the Lens in the tenthExperiment of this Book. For the rest of the Colours which are notstopp'd, but pass on to the Focus of the Lens, will there compoundeither accurately or very nearly such a Colour, as by this Rule ought toresult from their Mixture.

PROP. VII.Theor. V.

All the Colours in the Universe which are made by Light, and depend noton the Power of Imagination, are either the Colours of homogenealLights, or compounded of these, and that either accurately or verynearly, according to the Rule of the foregoing Problem.

For it has been proved (inProp. 1. Part 2.) that the changes ofColours made by Refractions do not arise from any new Modifications ofthe Rays impress'd by those Refractions, and by the various Terminationsof Light and Shadow, as has been the constant and general Opinion ofPhilosophers. It has also been proved that the several Colours of thehomogeneal Rays do constantly answer to their degrees of Refrangibility,(Prop. 1.Part 1. andProp. 2.Part 2.) and that their degreesof Refrangibility cannot be changed by Refractions and Reflexions(Prop.[Pg 159] 2.Part 1.) and by consequence that those their Colours arelikewise immutable. It has also been proved directly by refracting andreflecting homogeneal Lights apart, that their Colours cannot bechanged, (Prop. 2.Part 2.) It has been proved also, that when theseveral sorts of Rays are mixed, and in crossing pass through the samespace, they do not act on one another so as to change each otherscolorific qualities. (Exper. 10.Part 2.) but by mixing theirActions in the Sensorium beget a Sensation differing from what eitherwould do apart, that is a Sensation of a mean Colour between theirproper Colours; and particularly when by the concourse and mixtures ofall sorts of Rays, a white Colour is produced, the white is a mixture ofall the Colours which the Rays would have apart, (Prop. 5.Part 2.)The Rays in that mixture do not lose or alter their several colorificqualities, but by all their various kinds of Actions mix'd in theSensorium, beget a Sensation of a middling Colour between all theirColours, which is whiteness. For whiteness is a mean between allColours, having it self indifferently to them all, so as with equalfacility to be tinged with any of them. A red Powder mixed with a littleblue, or a blue with a little red, doth not presently lose its Colour,but a white Powder mix'd with any Colour is presently tinged with thatColour, and is equally capable of being tinged with any Colour whatever.It has been shewed also, that as the Sun's Light is mix'd of all sortsof Rays, so its whiteness is a mixture of the Colours of all sorts ofRays; those Rays having from the beginning their[Pg 160] several colorificqualities as well as their several Refrangibilities, and retaining themperpetually unchanged notwithstanding any Refractions or Reflexions theymay at any time suffer, and that whenever any sort of the Sun's Rays isby any means (as by Reflexion inExper. 9, and 10.Part 1. or byRefraction as happens in all Refractions) separated from the rest, theythen manifest their proper Colours. These things have been prov'd, andthe sum of all this amounts to the Proposition here to be proved. For ifthe Sun's Light is mix'd of several sorts of Rays, each of which haveoriginally their several Refrangibilities and colorific Qualities, andnotwithstanding their Refractions and Reflexions, and their variousSeparations or Mixtures, keep those their original Propertiesperpetually the same without alteration; then all the Colours in theWorld must be such as constantly ought to arise from the originalcolorific qualities of the Rays whereof the Lights consist by whichthose Colours are seen. And therefore if the reason of any Colourwhatever be required, we have nothing else to do than to consider howthe Rays in the Sun's Light have by Reflexions or Refractions, or othercauses, been parted from one another, or mixed together; or otherwise tofind out what sorts of Rays are in the Light by which that Colour ismade, and in what Proportion; and then by the last Problem to learn theColour which ought to arise by mixing those Rays (or their Colours) inthat proportion. I speak here of Colours so far as they arise fromLight. For they appear sometimes by other Causes, as when[Pg 161] by the powerof Phantasy we see Colours in a Dream, or a Mad-man sees things beforehim which are not there; or when we see Fire by striking the Eye, or seeColours like the Eye of a Peacock's Feather, by pressing our Eyes ineither corner whilst we look the other way. Where these and such likeCauses interpose not, the Colour always answers to the sort or sorts ofthe Rays whereof the Light consists, as I have constantly found inwhatever Phænomena of Colours I have hitherto been able to examine. Ishall in the following Propositions give instances of this in thePhænomena of chiefest note.

PROP. VIII.Prob. III.

Let ABC [inFig. 12.] represent a Prism refracting the Light of theSun, which comes into a dark Chamber through a hole Fφ almostas broad as the Prism, and let MN represent a white Paper on which therefracted Light is cast, and suppose the most refrangible or deepestviolet-making Rays fall upon the Space Pπ, the leastrefrangible or deepest red-making Rays upon the Space Tτ, themiddle sort between the indigo-making and blue-making Rays upon theSpace Qχ, the middle sort of the green-making Rays upon theSpace R, the middle sort between the yellow-making and orange-makingRays[Pg 162] upon the Space Sσ, and other intermediate sorts uponintermediate Spaces. For so the Spaces upon which the several sortsadequately fall will by reason of the different Refrangibility of thosesorts be one lower than another. Now if the Paper MN be so near thePrism that the Spaces PT and πτ do not interfere with oneanother, the distance between them Tπ will be illuminated byall the sorts of Rays in that proportion to one another which they haveat their very first coming out of the Prism, and consequently be white.But the Spaces PT and πτ on either hand, will not beilluminated by them all, and therefore will appear coloured. Andparticularly at P, where the outmost violet-making Rays fall alone, theColour must be the deepest violet. At Q where the violet-making andindigo-making Rays are mixed, it must be a violet inclining much toindigo. At R where the violet-making, indigo-making, blue-making, andone half of the green-making Rays are mixed, their Colours must (by theconstruction of the second Problem) compound a middle Colour betweenindigo and blue. At S where all the Rays are mixed, except thered-making and orange-making, their Colours ought by the same Rule tocompound a faint blue, verging more to green than indigo. And in theprogress from S to T, this blue will grow more and more faint anddilute, till at T, where all the Colours begin to be mixed, it ends inwhiteness.[Pg 163]

So again, on the other side of the white at τ, where the leastrefrangible or utmost red-making Rays are alone, the Colour must be thedeepest red. At σ the mixture of red and orange will compound ared inclining to orange. At ρ the mixture of red, orange,yellow, and one half of the green must compound a middle Colour betweenorange and yellow. At χ the mixture of all Colours but violetand indigo will compound a faint yellow, verging more to green than toorange. And this yellow will grow more faint and dilute continually inits progress from χ to π, where by a mixture of allsorts of Rays it will become white.

These Colours ought to appear were the Sun's Light perfectly white: Butbecause it inclines to yellow, the Excess of the yellow-making Rayswhereby 'tis tinged with that Colour, being mixed with the faint bluebetween S and T, will draw it to a faint green. And so the Colours inorder from P to τ ought to be violet, indigo, blue, very faintgreen, white, faint yellow, orange, red. Thus it is by the computation:And they that please to view the Colours made by a Prism will find it soin Nature.

These are the Colours on both sides the white when the Paper is heldbetween the Prism and the Point X where the Colours meet, and theinterjacent white vanishes. For if the Paper be held still farther offfrom the Prism, the most refrangible and least refrangible Rays will bewanting in the middle of the Light, and the rest of the Rays which arefound there, will by mixture produce a fuller green than before. Alsothe yellow and blue will now become less compounded, and by consequencemore intense than before. And this also agrees with experience.[Pg 165]

And if one look through a Prism upon a white Object encompassed withblackness or darkness, the reason of the Colours arising on the edges ismuch the same, as will appear to one that shall a little consider it. Ifa black Object be encompassed with a white one, the Colours which appearthrough the Prism are to be derived from the Light of the white one,spreading into the Regions of the black, and therefore they appear in acontrary order to that, when a white Object is surrounded with black.And the same is to be understood when an Object is viewed, whose partsare some of them less luminous than others. For in the borders of themore and less luminous Parts, Colours ought always by the samePrinciples to arise from the Excess of the Light of the more luminous,and to be of the same kind as if the darker parts were black, but yet tobe more faint and dilute.

What is said of Colours made by Prisms may be easily applied to Coloursmade by the Glasses of Telescopes or Microscopes, or by the Humours ofthe Eye. For if the Object-glass of a Telescope be thicker on one sidethan on the other, or if one half of the Glass, or one half of the Pupilof the Eye be cover'd with any opake substance; the Object-glass, orthat part of it or of the Eye which is not cover'd, may be consider'd asa Wedge with crooked Sides, and every Wedge of Glass or other pellucidSubstance has the effect of a Prism in refracting the Light which passesthrough it.[L]

How the Colours in the ninth and tenth Experiments of the first Partarise from the different Reflexibility of Light, is evident by what wasthere said. But it is observable in the ninth Experiment, that whilstthe Sun's direct Light is yellow, the Excess of the blue-making Rays inthe reflected beam of Light MN, suffices only to bring that yellow to apale white inclining to blue, and not to tinge it with a manifestly blueColour. To obtain therefore a better blue, I used instead of the yellowLight of the Sun the white Light of the Clouds, by varying a little theExperiment, as follows.

Exper. 16 Let HFG [inFig. 13.] represent a Prism in the open Air,and S the Eye of the Spectator, viewing the Clouds by their Light cominginto the Prism at the Plane Side FIGK, and reflected in it by its BaseHEIG, and thence going out through its Plane Side HEFK to the Eye. Andwhen the Prism and Eye are conveniently placed, so that the Angles ofIncidence and Reflexion at the Base may be about[Pg 167] 40 Degrees, theSpectator will see a Bow MN of a blue Colour, running from one End ofthe Base to the other, with the Concave Side towards him, and the Partof the Base IMNG beyond this Bow will be brighter than the other PartEMNH on the other Side of it. This blue Colour MN being made by nothingelse than by Reflexion of a specular Superficies, seems so odd aPhænomenon, and so difficult to be explained by the vulgar Hypothesis ofPhilosophers, that I could not but think it deserved to be taken Noticeof. Now for understanding the Reason of it, suppose the Plane ABC to cutthe Plane Sides and Base of the Prism perpendicularly. From the Eye tothe Line BC, wherein that Plane cuts the Base, draw the Lines Sp andSt, in the Angles Spc 50 degr. 1/9, and Stc 49 degr. 1/28, and thePointp will be the Limit beyond which none of the most refrangibleRays can pass through the Base of the Prism, and be refracted, whoseIncidence is such that they may be reflected to the Eye; and the Pointt will be the like Limit for the least refrangible Rays, that is,beyond which none of them can pass through the Base, whose Incidence issuch that by Reflexion they may come to the Eye. And the Pointr takenin the middle Way betweenp andt, will be the like Limit for themeanly refrangible Rays. And therefore all the least refrangible Rayswhich fall upon the Base beyondt, that is, betweent and B, and cancome from thence to the Eye, will be reflected thither: But on this sidet, that is, betweent andc, many of these Rays will betransmitted through the Base. And all the most refrangible[Pg 168] Rays whichfall upon the Base beyondp, that is, between,p and B, and can byReflexion come from thence to the Eye, will be reflected thither, butevery where betweenp andc, many of these Rays will get through theBase, and be refracted; and the same is to be understood of the meanlyrefrangible Rays on either side of the Pointr. Whence it follows,that the Base of the Prism must every where betweent and B, by atotal Reflexion of all sorts of Rays to the Eye, look white and bright.And every where betweenp and C, by reason of the Transmission of manyRays of every sort, look more pale, obscure, and dark. But atr, andin other Places betweenp andt, where all the more refrangible Raysare reflected to the Eye, and many of the less refrangible aretransmitted, the Excess of the most refrangible in the reflected Lightwill tinge that Light with their Colour, which is violet and blue. Andthis happens by taking the Line Cprt B any where between the Ends ofthe Prism HG and EI.

PROP. IX.Prob. IV.

This Bow never appears, but where it rains in the Sun-shine, and may bemade artificially by spouting up Water which may break aloft, andscatter into Drops, and fall down like Rain. For the[Pg 169] Sun shining uponthese Drops certainly causes the Bow to appear to a Spectator standingin a due Position to the Rain and Sun. And hence it is now agreed upon,that this Bow is made by Refraction of the Sun's Light in drops offalling Rain. This was understood by some of the Antients, and of latemore fully discover'd and explain'd by the famousAntonius de DominisArchbishop ofSpalato, in his bookDe Radiis Visûs & Lucis,published by his FriendBartolus atVenice, in the Year 1611, andwritten above 20 Years before. For he teaches there how the interior Bowis made in round Drops of Rain by two Refractions of the Sun's Light,and one Reflexion between them, and the exterior by two Refractions, andtwo sorts of Reflexions between them in each Drop of Water, and proveshis Explications by Experiments made with a Phial full of Water, andwith Globes of Glass filled with Water, and placed in the Sun to makethe Colours of the two Bows appear in them. The same ExplicationDes-Cartes hath pursued in his Meteors, and mended that of theexterior Bow. But whilst they understood not the true Origin of Colours,it's necessary to pursue it here a little farther. For understandingtherefore how the Bow is made, let a Drop of Rain, or any otherspherical transparent Body be represented by the Sphere BNFG, [inFig.14.] described with the Center C, and Semi-diameter CN. And let AN beone of the Sun's Rays incident upon it at N, and thence refracted to F,where let it either go out of the Sphere by Refraction towards V, or bereflected to G; and at G let it either go out by Refraction[Pg 170] to R, or bereflected to H; and at H let it go out by Refraction towards S, cuttingthe incident Ray in Y. Produce AN and RG, till they meet in X, and uponAX and NF, let fall the Perpendiculars CD and CE, and produce CD till itfall upon the Circumference at L. Parallel to the incident Ray AN drawthe Diameter BQ, and let the Sine of Incidence out of Air into Water beto the Sine of Refraction as I to R. Now, if you suppose the Point ofIncidence N to move from the Point B, continually till it come to L, theArch QF will first increase and then decrease, and so will the Angle AXRwhich the Rays AN and GR contain; and the Arch QF and Angle AXR will bebiggest when ND is to CN as √(II - RR) to √(3)RR, in whichcase NE will be to ND as 2R to I. Also the Angle AYS, which the Rays ANand HS contain will first decrease, and then increase and grow leastwhen ND is to CN as √(II - RR) to √(8)RR,[Pg 171] in which case NEwill be to ND, as 3R to I. And so the Angle which the next emergent Ray(that is, the emergent Ray after three Reflexions) contains with theincident Ray AN will come to its Limit when ND is to CN as √(II -RR) to √(15)RR, in which case NE will be to ND as 4R to I. And theAngle which the Ray next after that Emergent, that is, the Ray emergentafter four Reflexions, contains with the Incident, will come to itsLimit, when ND is to CN as √(II - RR) to √(24)RR, in whichcase NE will be to ND as 5R to I; and so on infinitely, the Numbers 3,8, 15, 24, &c. being gather'd by continual Addition of the Terms of thearithmetical Progression 3, 5, 7, 9, &c. The Truth of all thisMathematicians will easily examine.[M]

Now it is to be observed, that as when the Sun comes to his Tropicks,Days increase and decrease but a very little for a great while together;so when by increasing the distance CD, these Angles come to theirLimits, they vary their quantity but very little for some time together,and therefore a far greater number of the Rays which fall upon all thePoints N in the Quadrant BL, shall emerge in the Limits of these Angles,than in any other Inclinations. And farther it is to be observed, thatthe Rays which differ in Refrangibility will have different Limits oftheir Angles of Emergence, and by consequence according to theirdifferent Degrees of Refrangibility emerge most copiously in different[Pg 172]Angles, and being separated from one another appear each in their properColours. And what those Angles are may be easily gather'd from theforegoing Theorem by Computation.

For in the least refrangible Rays the Sines I and R (as was found above)are 108 and 81, and thence by Computation the greatest Angle AXR will befound 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and57 Minutes. And in the most refrangible Rays the Sines I and R are 109and 81, and thence by Computation the greatest Angle AXR will be found40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7Minutes.

Suppose now that O [inFig. 15.] is the Spectator's Eye, and OP a Linedrawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Anglesof 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min.respectively, and these Angles turned about their common Side OP, shallwith their other Sides OE, OF; OG, OH, describe the Verges of twoRain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any wherein the conical Superficies described by OE, OF, OG, OH, and beilluminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being equalto the Angle POE, or 40 Degr. 17 Min. shall be the greatest Angle inwhich the most refrangible Rays can after one Reflexion be refracted tothe Eye, and therefore all the Drops in the Line OE shall send the mostrefrangible Rays most copiously to the Eye, and thereby strike theSenses with the deepest violet Colour in that Region.[Pg 173] And in likemanner the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min.shall be the greatest in which the least refrangible Rays after oneReflexion can emerge out of the Drops, and therefore those Rays shallcome most copiously to the Eye from the Drops in the Line OF, and strikethe Senses with the deepest red Colour in that Region. And by the sameArgument, the Rays which have intermediate Degrees of Refrangibilityshall come most copiously from Drops between E and F, and strike theSenses with the intermediate Colours, in the Order which their Degreesof Refrangibility require, that is in the Progress from E to F, or fromthe inside of the Bow to the outside in this order, violet, indigo,[Pg 174]blue, green, yellow, orange, red. But the violet, by the mixture of thewhite Light of the Clouds, will appear faint and incline to purple.

Again, the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min.shall be the least Angle in which the least refrangible Rays can aftertwo Reflexions emerge out of the Drops, and therefore the leastrefrangible Rays shall come most copiously to the Eye from the Drops inthe Line OG, and strike the Sense with the deepest red in that Region.And the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min. shallbe the least Angle, in which the most refrangible Rays after twoReflexions can emerge out of the Drops; and therefore those Rays shallcome most copiously to the Eye from the Drops in the Line OH, and strikethe Senses with the deepest violet in that Region. And by the sameArgument, the Drops in the Regions between G and H shall strike theSense with the intermediate Colours in the Order which their Degrees ofRefrangibility require, that is, in the Progress from G to H, or fromthe inside of the Bow to the outside in this order, red, orange, yellow,green, blue, indigo, violet. And since these four Lines OE, OF, OG, OH,may be situated any where in the above-mention'd conical Superficies;what is said of the Drops and Colours in these Lines is to be understoodof the Drops and Colours every where in those Superficies.

Thus shall there be made two Bows of Colours, an interior and stronger,by one Reflexion in the Drops, and an exterior and fainter by two; forthe Light becomes[Pg 175] fainter by every Reflexion. And their Colours shalllie in a contrary Order to one another, the red of both Bows borderingupon the Space GF, which is between the Bows. The Breadth of theinterior Bow EOF measured cross the Colours shall be 1 Degr. 45 Min. andthe Breadth of the exterior GOH shall be 3 Degr. 10 Min. and thedistance between them GOF shall be 8 Gr. 15 Min. the greatestSemi-diameter of the innermost, that is, the Angle POF being 42 Gr. 2Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57Min. These are the Measures of the Bows, as they would be were the Sunbut a Point; for by the Breadth of his Body, the Breadth of the Bowswill be increased, and their Distance decreased by half a Degree, and sothe breadth of the interior Iris will be 2 Degr. 15 Min. that of theexterior 3 Degr. 40 Min. their distance 8 Degr. 25 Min. the greatestSemi-diameter of the interior Bow 42 Degr. 17 Min. and the least of theexterior 50 Degr. 42 Min. And such are the Dimensions of the Bows in theHeavens found to be very nearly, when their Colours appear strong andperfect. For once, by such means as I then had, I measured the greatestSemi-diameter of the interior Iris about 42 Degrees, and the breadth ofthe red, yellow and green in that Iris 63 or 64 Minutes, besides theoutmost faint red obscured by the brightness of the Clouds, for which wemay allow 3 or 4 Minutes more. The breadth of the blue was about 40Minutes more besides the violet, which was so much obscured by thebrightness of the Clouds, that[Pg 176] I could not measure its breadth. Butsupposing the breadth of the blue and violet together to equal that ofthe red, yellow and green together, the whole breadth of this Iris willbe about 2-1/4 Degrees, as above. The least distance between this Irisand the exterior Iris was about 8 Degrees and 30 Minutes. The exteriorIris was broader than the interior, but so faint, especially on the blueside, that I could not measure its breadth distinctly. At another timewhen both Bows appeared more distinct, I measured the breadth of theinterior Iris 2 Gr. 10´, and the breadth of the red, yellow and green inthe exterior Iris, was to the breadth of the same Colours in theinterior as 3 to 2.

This Explication of the Rain-bow is yet farther confirmed by the knownExperiment (made byAntonius de Dominis andDes-Cartes) of hangingup any where in the Sun-shine a Glass Globe filled with Water, andviewing it in such a posture, that the Rays which come from the Globe tothe Eye may contain with the Sun's Rays an Angle of either 42 or 50Degrees. For if the Angle be about 42 or 43 Degrees, the Spectator(suppose at O) shall see a full red Colour in that side of the Globeopposed to the Sun as 'tis represented at F, and if that Angle becomeless (suppose by depressing the Globe to E) there will appear otherColours, yellow, green and blue successive in the same side of theGlobe. But if the Angle be made about 50 Degrees (suppose by lifting upthe Globe to G) there will appear a red Colour in that side of the Globetowards the Sun,[Pg 177] and if the Angle be made greater (suppose by liftingup the Globe to H) the red will turn successively to the other Colours,yellow, green and blue. The same thing I have tried, by letting a Globerest, and raising or depressing the Eye, or otherwise moving it to makethe Angle of a just magnitude.

I have heard it represented, that if the Light of a Candle be refractedby a Prism to the Eye; when the blue Colour falls upon the Eye, theSpectator shall see red in the Prism, and when the red falls upon theEye he shall see blue; and if this were certain, the Colours of theGlobe and Rain-bow ought to appear in a contrary order to what we find.But the Colours of the Candle being very faint, the mistake seems toarise from the difficulty of discerning what Colours fall on the Eye.For, on the contrary, I have sometimes had occasion to observe in theSun's Light refracted by a Prism, that the Spectator always sees thatColour in the Prism which falls upon his Eye. And the same I have foundtrue also in Candle-light. For when the Prism is moved slowly from theLine which is drawn directly from the Candle to the Eye, the red appearsfirst in the Prism and then the blue, and therefore each of them is seenwhen it falls upon the Eye. For the red passes over the Eye first, andthen the blue.

The Light which comes through drops of Rain by two Refractions withoutany Reflexion, ought to appear strongest at the distance of about 26Degrees from the Sun, and to decay gradually both ways as the distancefrom him increases and decreases. And[Pg 178] the same is to be understood ofLight transmitted through spherical Hail-stones. And if the Hail be alittle flatted, as it often is, the Light transmitted may grow so strongat a little less distance than that of 26 Degrees, as to form a Haloabout the Sun or Moon; which Halo, as often as the Hail-stones are dulyfigured may be colour'd, and then it must be red within by the leastrefrangible Rays, and blue without by the most refrangible ones,especially if the Hail-stones have opake Globules of Snow in theircenter to intercept the Light within the Halo (asHugenius hasobserv'd) and make the inside thereof more distinctly defined than itwould otherwise be. For such Hail-stones, though spherical, byterminating the Light by the Snow, may make a Halo red within andcolourless without, and darker in the red than without, as Halos used tobe. For of those Rays which pass close by the Snow the Rubriform will beleast refracted, and so come to the Eye in the directest Lines.

The Light which passes through a drop of Rain after two Refractions, andthree or more Reflexions, is scarce strong enough to cause a sensibleBow; but in those Cylinders of Ice by whichHugenius explains theParhelia, it may perhaps be sensible.[Pg 179]

PROP. X.Prob. V.

By the discovered Properties of Light to explain the permanent Coloursof Natural Bodies.

These Colours arise from hence, that some natural Bodies reflect somesorts of Rays, others other sorts more copiously than the rest. Miniumreflects the least refrangible or red-making Rays most copiously, andthence appears red. Violets reflect the most refrangible most copiously,and thence have their Colour, and so of other Bodies. Every Bodyreflects the Rays of its own Colour more copiously than the rest, andfrom their excess and predominance in the reflected Light has itsColour.

Exper. 17. For if in the homogeneal Lights obtained by the solution ofthe Problem proposed in the fourth Proposition of the first Part of thisBook, you place Bodies of several Colours, you will find, as I havedone, that every Body looks most splendid and luminous in the Light ofits own Colour. Cinnaber in the homogeneal red Light is mostresplendent, in the green Light it is manifestly less resplendent, andin the blue Light still less. Indigo in the violet blue Light is mostresplendent, and its splendor is gradually diminish'd, as it is removedthence by degrees through the green and yellow Light to the red. By aLeek the green Light, and next that the blue and yellow which compoundgreen, are more strongly reflected than the other Colours red andviolet, and so of the rest. But to make these Experiments the more[Pg 180]manifest, such Bodies ought to be chosen as have the fullest and mostvivid Colours, and two of those Bodies are to be compared together.Thus, for instance, if Cinnaber andultra-marine blue, or some otherfull blue be held together in the red homogeneal Light, they will bothappear red, but the Cinnaber will appear of a strongly luminous andresplendent red, and theultra-marine blue of a faint obscure and darkred; and if they be held together in the blue homogeneal Light, theywill both appear blue, but theultra-marine will appear of a stronglyluminous and resplendent blue, and the Cinnaber of a faint and darkblue. Which puts it out of dispute that the Cinnaber reflects the redLight much more copiously than theultra-marine doth, and theultra-marine reflects the blue Light much more copiously than theCinnaber doth. The same Experiment may be tried successfully with redLead and Indigo, or with any other two colour'd Bodies, if due allowancebe made for the different strength or weakness of their Colour andLight.

And as the reason of the Colours of natural Bodies is evident by theseExperiments, so it is farther confirmed and put past dispute by the twofirst Experiments of the first Part, whereby 'twas proved in such Bodiesthat the reflected Lights which differ in Colours do differ also indegrees of Refrangibility. For thence it's certain, that some Bodiesreflect the more refrangible, others the less refrangible Rays morecopiously.

And that this is not only a true reason of these[Pg 181] Colours, but even theonly reason, may appear farther from this Consideration, that the Colourof homogeneal Light cannot be changed by the Reflexion of naturalBodies.

For if Bodies by Reflexion cannot in the least change the Colour of anyone sort of Rays, they cannot appear colour'd by any other means than byreflecting those which either are of their own Colour, or which bymixture must produce it.

But in trying Experiments of this kind care must be had that the Lightbe sufficiently homogeneal. For if Bodies be illuminated by the ordinaryprismatick Colours, they will appear neither of their own Day-lightColours, nor of the Colour of the Light cast on them, but of some middleColour between both, as I have found by Experience. Thus red Lead (forinstance) illuminated with the ordinary prismatick green will not appeareither red or green, but orange or yellow, or between yellow and green,accordingly as the green Light by which 'tis illuminated is more or lesscompounded. For because red Lead appears red when illuminated with whiteLight, wherein all sorts of Rays are equally mix'd, and in the greenLight all sorts of Rays are not equally mix'd, the Excess of theyellow-making, green-making and blue-making Rays in the incident greenLight, will cause those Rays to abound so much in the reflected Light,as to draw the Colour from red towards their Colour. And because the redLead reflects the red-making Rays most copiously in proportion to theirnumber, and next after them the[Pg 182] orange-making and yellow-making Rays;these Rays in the reflected Light will be more in proportion to theLight than they were in the incident green Light, and thereby will drawthe reflected Light from green towards their Colour. And therefore thered Lead will appear neither red nor green, but of a Colour betweenboth.

In transparently colour'd Liquors 'tis observable, that their Colouruses to vary with their thickness. Thus, for instance, a red Liquor in aconical Glass held between the Light and the Eye, looks of a pale anddilute yellow at the bottom where 'tis thin, and a little higher where'tis thicker grows orange, and where 'tis still thicker becomes red, andwhere 'tis thickest the red is deepest and darkest. For it is to beconceiv'd that such a Liquor stops the indigo-making and violet-makingRays most easily, the blue-making Rays more difficultly, thegreen-making Rays still more difficultly, and the red-making mostdifficultly: And that if the thickness of the Liquor be only so much assuffices to stop a competent number of the violet-making andindigo-making Rays, without diminishing much the number of the rest, therest must (byProp. 6.Part 2.) compound a pale yellow. But if theLiquor be so much thicker as to stop also a great number of theblue-making Rays, and some of the green-making, the rest must compoundan orange; and where it is so thick as to stop also a great number ofthe green-making and a considerable number of the yellow-making, therest must begin to compound a red, and this red must[Pg 183] grow deeper anddarker as the yellow-making and orange-making Rays are more and morestopp'd by increasing the thickness of the Liquor, so that few Raysbesides the red-making can get through.

Of this kind is an Experiment lately related to me by Mr.Halley, who,in diving deep into the Sea in a diving Vessel, found in a clearSun-shine Day, that when he was sunk many Fathoms deep into the Waterthe upper part of his Hand on which the Sun shone directly through theWater and through a small Glass Window in the Vessel appeared of a redColour, like that of a Damask Rose, and the Water below and the underpart of his Hand illuminated by Light reflected from the Water belowlook'd green. For thence it may be gather'd, that the Sea-Water reflectsback the violet and blue-making Rays most easily, and lets thered-making Rays pass most freely and copiously to great Depths. Forthereby the Sun's direct Light at all great Depths, by reason of thepredominating red-making Rays, must appear red; and the greater theDepth is, the fuller and intenser must that red be. And at such Depthsas the violet-making Rays scarce penetrate unto, the blue-making,green-making, and yellow-making Rays being reflected from below morecopiously than the red-making ones, must compound a green.

Now, if there be two Liquors of full Colours, suppose a red and blue,and both of them so thick as suffices to make their Colours sufficientlyfull; though either Liquor be sufficiently transparent apart, yet willyou not be able to see through both[Pg 184] together. For, if only thered-making Rays pass through one Liquor, and only the blue-makingthrough the other, no Rays can pass through both. This Mr.Hook triedcasually with Glass Wedges filled with red and blue Liquors, and wassurprized at the unexpected Event, the reason of it being then unknown;which makes me trust the more to his Experiment, though I have not triedit my self. But he that would repeat it, must take care the Liquors beof very good and full Colours.

Now, whilst Bodies become coloured by reflecting or transmitting this orthat sort of Rays more copiously than the rest, it is to be conceivedthat they stop and stifle in themselves the Rays which they do notreflect or transmit. For, if Gold be foliated and held between your Eyeand the Light, the Light looks of a greenish blue, and therefore massyGold lets into its Body the blue-making Rays to be reflected to and frowithin it till they be stopp'd and stifled, whilst it reflects theyellow-making outwards, and thereby looks yellow. And much after thesame manner that Leaf Gold is yellow by reflected, and blue bytransmitted Light, and massy Gold is yellow in all Positions of the Eye;there are some Liquors, as the Tincture ofLignum Nephriticum, andsome sorts of Glass which transmit one sort of Light most copiously, andreflect another sort, and thereby look of several Colours, according tothe Position of the Eye to the Light. But, if these Liquors or Glasseswere so thick and massy that no Light could get through them, I questionnot but they would like all[Pg 185] other opake Bodies appear of one and thesame Colour in all Positions of the Eye, though this I cannot yet affirmby Experience. For all colour'd Bodies, so far as my Observationreaches, may be seen through if made sufficiently thin, and thereforeare in some measure transparent, and differ only in degrees ofTransparency from tinged transparent Liquors; these Liquors, as well asthose Bodies, by a sufficient Thickness becoming opake. A transparentBody which looks of any Colour by transmitted Light, may also look ofthe same Colour by reflected Light, the Light of that Colour beingreflected by the farther Surface of the Body, or by the Air beyond it.And then the reflected Colour will be diminished, and perhaps cease, bymaking the Body very thick, and pitching it on the backside to diminishthe Reflexion of its farther Surface, so that the Light reflected fromthe tinging Particles may predominate. In such Cases, the Colour of thereflected Light will be apt to vary from that of the Light transmitted.But whence it is that tinged Bodies and Liquors reflect some sort ofRays, and intromit or transmit other sorts, shall be said in the nextBook. In this Proposition I content my self to have put it past dispute,that Bodies have such Properties, and thence appear colour'd.[Pg 186]

PROP. XI.Prob. VI.

By mixing colour'd Lights to compound a beam of Light of the sameColour and Nature with a beam of the Sun's direct Light, and therein toexperience the Truth of the foregoing Propositions.

Let ABCabc [inFig. 16.] represent a Prism, by which the Sun'sLight let into a dark Chamber through the Hole F, may be refractedtowards the Lens MN, and paint upon it atp,q,r,s, andt,the usual Colours violet, blue, green, yellow, and red, and let thediverging Rays by the Refraction of this Lens converge again towards X,and there, by the mixture of all those their Colours, compound a whiteaccording to what was shewn above. Then let another Prism DEGdeg,parallel to the former, be placed at X, to refract that white Lightupwards towards Y. Let the refracting Angles of the Prisms, and theirdistances from the Lens be equal, so that the Rays which converged fromthe Lens towards X, and without Refraction, would there have crossed anddiverged again, may by the Refraction of the second Prism be reducedinto Parallelism and diverge no more. For then those Rays will recomposea beam of white Light XY. If the refracting Angle of either Prism be thebigger, that Prism must be so much the nearer to the Lens. You will knowwhen the Prisms and the Lens are well set together, by observing if thebeam of Light XY, which comes out of the second Prism be perfectly whiteto the very[Pg 188]edges of the Light, and at all distances from the Prismcontinue perfectly and totally white like a beam of the Sun's Light. Fortill this happens, the Position of the Prisms and Lens to one anothermust be corrected; and then if by the help of a long beam of Wood, as isrepresented in the Figure, or by a Tube, or some other such Instrument,made for that Purpose, they be made fast in that Situation, you may tryall the same Experiments in this compounded beam of Light XY, which havebeen made in the Sun's direct Light. For this compounded beam of Lighthas the same appearance, and is endow'd with all the same Propertieswith a direct beam of the Sun's Light, so far as my Observation reaches.And in trying Experiments in this beam you may by stopping any of theColours,p,q,r,s, andt, at the Lens, see how the Coloursproduced in the Experiments are no other than those which the Rays hadat the Lens before they entered the Composition of this Beam: And byconsequence, that they arise not from any new Modifications of the Lightby Refractions and Reflexions, but from the various Separations andMixtures of the Rays originally endow'd with their colour-makingQualities.

So, for instance, having with a Lens 4-1/4 Inches broad, and two Prismson either hand 6-1/4 Feet distant from the Lens, made such a beam ofcompounded Light; to examine the reason of the Colours made by Prisms, Irefracted this compounded beam of Light XY with another Prism[Pg 189] HIKkh,and thereby cast the usual Prismatick Colours PQRST upon the Paper LVplaced behind. And then by stopping any of the Coloursp,q,r,s,t, at the Lens, I found that the same Colour would vanish at thePaper. So if the Purplep was stopp'd at the Lens, the Purple P uponthe Paper would vanish, and the rest of the Colours would remainunalter'd, unless perhaps the blue, so far as some purple latent in itat the Lens might be separated from it by the following Refractions. Andso by intercepting the green upon the Lens, the green R upon the Paperwould vanish, and so of the rest; which plainly shews, that as the whitebeam of Light XY was compounded of several Lights variously colour'd atthe Lens, so the Colours which afterwards emerge out of it by newRefractions are no other than those of which its Whiteness wascompounded. The Refraction of the Prism HIKkh generates the ColoursPQRST upon the Paper, not by changing the colorific Qualities of theRays, but by separating the Rays which had the very same colorificQualities before they enter'd the Composition of the refracted beam ofwhite Light XY. For otherwise the Rays which were of one Colour at theLens might be of another upon the Paper, contrary to what we find.

So again, to examine the reason of the Colours of natural Bodies, Iplaced such Bodies in the Beam of Light XY, and found that they allappeared there of those their own Colours which they have in Day-light,and that those Colours depend upon the Rays which had the same Coloursat the Lens before they[Pg 190] enter'd the Composition of that beam. Thus, forinstance, Cinnaber illuminated by this beam appears of the same redColour as in Day-light; and if at the Lens you intercept thegreen-making and blue-making Rays, its redness will become more full andlively: But if you there intercept the red-making Rays, it will not anylonger appear red, but become yellow or green, or of some other Colour,according to the sorts of Rays which you do not intercept. So Gold inthis Light XY appears of the same yellow Colour as in Day-light, but byintercepting at the Lens a due Quantity of the yellow-making Rays itwill appear white like Silver (as I have tried) which shews that itsyellowness arises from the Excess of the intercepted Rays tinging thatWhiteness with their Colour when they are let pass. So the Infusion ofLignum Nephriticum (as I have also tried) when held in this beam ofLight XY, looks blue by the reflected Part of the Light, and red by thetransmitted Part of it, as when 'tis view'd in Day-light; but if youintercept the blue at the Lens the Infusion will lose its reflected blueColour, whilst its transmitted red remains perfect, and by the loss ofsome blue-making Rays, wherewith it was allay'd, becomes more intenseand full. And, on the contrary, if the red and orange-making Rays beintercepted at the Lens, the Infusion will lose its transmitted red,whilst its blue will remain and become more full and perfect. Whichshews, that the Infusion does not tinge the Rays with blue and red, butonly transmits those most copiously which were red-making[Pg 191] before, andreflects those most copiously which were blue-making before. And afterthe same manner may the Reasons of other Phænomena be examined, bytrying them in this artificial beam of Light XY.

FOOTNOTES:

[I] See p. 59.

[J]See our Author's Lect. Optic.Part II.Sect. II.p.239.

[K]As is done in our Author's Lect. Optic.Part I.Sect.III.and IV.and Part II.Sect. II.

[L]See our Author's Lect. Optic.Part II.Sect. II.pag. 269, &c.

[M]This is demonstrated in our Author's Lect. Optic.PartI.Sect. IV.Prop. 35and 36.

THE

SECOND BOOK

OPTICKS

PART I.

Observations concerning the Reflexions, Refractions, and Colours ofthin transparent Bodies.

It has been observed by others, that transparent Substances, as Glass,Water, Air, &c. when made very thin by being blown into Bubbles, orotherwise formed into Plates, do exhibit various Colours according totheir various thinness, altho' at a greater thickness they appear veryclear and colourless. In the former Book I forbore to treat of theseColours, because they seemed of a more difficult Consideration, and werenot necessary for establishing the Properties of Light there discoursedof. But because they may conduce to farther Discoveries for compleatingthe Theory of Light, especially as to the constitution of the parts ofnatural Bodies, on which[Pg 194] their Colours or Transparency depend; I havehere set down an account of them. To render this Discourse short anddistinct, I have first described the principal of my Observations, andthen consider'd and made use of them. The Observations are these.

Obs. 1. Compressing two Prisms hard together that their sides (whichby chance were a very little convex) might somewhere touch one another:I found the place in which they touched to become absolutelytransparent, as if they had there been one continued piece of Glass. Forwhen the Light fell so obliquely on the Air, which in other places wasbetween them, as to be all reflected; it seemed in that place of contactto be wholly transmitted, insomuch that when look'd upon, it appearedlike a black or dark spot, by reason that little or no sensible Lightwas reflected from thence, as from other places; and when looked throughit seemed (as it were) a hole in that Air which was formed into a thinPlate, by being compress'd between the Glasses. And through this holeObjects that were beyond might be seen distinctly, which could not atall be seen through other parts of the Glasses where the Air wasinterjacent. Although the Glasses were a little convex, yet thistransparent spot was of a considerable breadth, which breadth seemedprincipally to proceed from the yielding inwards of the parts of theGlasses, by reason of their mutual pressure. For by pressing them veryhard together it would become much broader than otherwise.

Obs. 2. When the Plate of Air, by turning the[Pg 195] Prisms about theircommon Axis, became so little inclined to the incident Rays, that someof them began to be transmitted, there arose in it many slender Arcs ofColours which at first were shaped almost like the Conchoid, as you seethem delineated in the first Figure. And by continuing the Motion of thePrisms, these Arcs increased and bended more and more about the saidtransparent spot, till they were compleated into Circles or Ringsincompassing it, and afterwards continually grew more and morecontracted.

These Arcs at their first appearance were of a violet and blue Colour,and between them were white Arcs of Circles, which presently bycontinuing the Motion of the Prisms became a little tinged in theirinward Limbs with red and yellow, and to their outward Limbs the bluewas adjacent. So that the order of these Colours from the central darkspot, was at that time white, blue, violet; black, red, orange, yellow,white, blue, violet, &c. But the yellow and red were much fainter thanthe blue and violet.

The Motion of the Prisms about their Axis being continued, these Colourscontracted more and more,[Pg 196] shrinking towards the whiteness on eitherside of it, until they totally vanished into it. And then the Circles inthose parts appear'd black and white, without any other Coloursintermix'd. But by farther moving the Prisms about, the Colours againemerged out of the whiteness, the violet and blue at its inward Limb,and at its outward Limb the red and yellow. So that now their order fromthe central Spot was white, yellow, red; black; violet, blue, white,yellow, red, &c. contrary to what it was before.

Obs. 3. When the Rings or some parts of them appeared only black andwhite, they were very distinct and well defined, and the blacknessseemed as intense as that of the central Spot. Also in the Borders ofthe Rings, where the Colours began to emerge out of the whiteness, theywere pretty distinct, which made them visible to a very great multitude.I have sometimes number'd above thirty Successions (reckoning everyblack and white Ring for one Succession) and seen more of them, which byreason of their smalness I could not number. But in other Positions ofthe Prisms, at which the Rings appeared of many Colours, I could notdistinguish above eight or nine of them, and the Exterior of those werevery confused and dilute.

In these two Observations to see the Rings distinct, and without anyother Colour than Black and white, I found it necessary to hold my Eyeat a good distance from them. For by approaching nearer, although in thesame inclination of my Eye to the Plane of the Rings, there emerged abluish Colour[Pg 197] out of the white, which by dilating it self more and moreinto the black, render'd the Circles less distinct, and left the white alittle tinged with red and yellow. I found also by looking through aslit or oblong hole, which was narrower than the pupil of my Eye, andheld close to it parallel to the Prisms, I could see the Circles muchdistincter and visible to a far greater number than otherwise.

Obs. 4. To observe more nicely the order of the Colours which aroseout of the white Circles as the Rays became less and less inclined tothe Plate of Air; I took two Object-glasses, the one a Plano-convex fora fourteen Foot Telescope, and the other a large double Convex for oneof about fifty Foot; and upon this, laying the other with its plane sidedownwards, I pressed them slowly together, to make the Colourssuccessively emerge in the middle of the Circles, and then slowly liftedthe upper Glass from the lower to make them successively vanish again inthe same place. The Colour, which by pressing the Glasses together,emerged last in the middle of the other Colours, would upon its firstappearance look like a Circle of a Colour almost uniform from thecircumference to the center and by compressing the Glasses still more,grow continually broader until a new Colour emerged in its center, andthereby it became a Ring encompassing that new Colour. And bycompressing the Glasses still more, the diameter of this Ring wouldincrease, and the breadth of its Orbit or Perimeter decrease untilanother new Colour emerged in the center of the last: And so on[Pg 198] until athird, a fourth, a fifth, and other following new Colours successivelyemerged there, and became Rings encompassing the innermost Colour, thelast of which was the black Spot. And, on the contrary, by lifting upthe upper Glass from the lower, the diameter of the Rings woulddecrease, and the breadth of their Orbit increase, until their Coloursreached successively to the center; and then they being of aconsiderable breadth, I could more easily discern and distinguish theirSpecies than before. And by this means I observ'd their Succession andQuantity to be as followeth.

Next to the pellucid central Spot made by the contact of the Glassessucceeded blue, white, yellow, and red. The blue was so little inquantity, that I could not discern it in the Circles made by the Prisms,nor could I well distinguish any violet in it, but the yellow and redwere pretty copious, and seemed about as much in extent as the white,and four or five times more than the blue. The next Circuit in order ofColours immediately encompassing these were violet, blue, green, yellow,and red: and these were all of them copious and vivid, excepting thegreen, which was very little in quantity, and seemed much more faint anddilute than the other Colours. Of the other four, the violet was theleast in extent, and the blue less than the yellow or red. The thirdCircuit or Order was purple, blue, green, yellow, and red; in which thepurple seemed more reddish than the violet in the former Circuit, andthe green was much more conspicuous, being[Pg 199] as brisk and copious as anyof the other Colours, except the yellow, but the red began to be alittle faded, inclining very much to purple. After this succeeded thefourth Circuit of green and red. The green was very copious and lively,inclining on the one side to blue, and on the other side to yellow. Butin this fourth Circuit there was neither violet, blue, nor yellow, andthe red was very imperfect and dirty. Also the succeeding Colours becamemore and more imperfect and dilute, till after three or four revolutionsthey ended in perfect whiteness. Their form, when the Glasses were mostcompress'd so as to make the black Spot appear in the center, isdelineated in the second Figure; wherea,b,c,d,e:f,g,h,i,k:l,m,n,o,p:q,r:s,t:v,x:y,z, denote the Colours reckon'd in order from the center,black, blue, white, yellow, red: violet, blue, green, yellow,[Pg 200] red:purple, blue, green, yellow, red: green, red: greenish blue, red:greenish blue, pale red: greenish blue, reddish white.

Obs. 5. To determine the interval of the Glasses, or thickness of theinterjacent Air, by which each Colour was produced, I measured theDiameters of the first six Rings at the most lucid part of their Orbits,and squaring them, I found their Squares to be in the arithmeticalProgression of the odd Numbers, 1, 3, 5, 7, 9, 11. And since one ofthese Glasses was plane, and the other spherical, their Intervals atthose Rings must be in the same Progression. I measured also theDiameters of the dark or faint Rings between the more lucid Colours, andfound their Squares to be in the arithmetical Progression of the evenNumbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult totake these measures exactly; I repeated them divers times at diversparts of the Glasses, that by their Agreement I might be confirmed inthem. And the same method I used in determining some others of thefollowing Observations.

Obs. 6. The Diameter of the sixth Ring at the most lucid part of itsOrbit was 58/100 parts of an Inch, and the Diameter of the Sphere onwhich the double convex Object-glass was ground was about 102 Feet, andhence I gathered the thickness of the Air or Aereal Interval of theGlasses at that Ring. But some time after, suspecting that in makingthis Observation I had not determined the Diameter of the Sphere withsufficient accurateness, and being uncertain[Pg 201] whether the Plano-convexGlass was truly plane, and not something concave or convex on that sidewhich I accounted plane; and whether I had not pressed the Glassestogether, as I often did, to make them touch; (For by pressing suchGlasses together their parts easily yield inwards, and the Rings therebybecome sensibly broader than they would be, did the Glasses keep theirFigures.) I repeated the Experiment, and found the Diameter of the sixthlucid Ring about 55/100 parts of an Inch. I repeated the Experiment alsowith such an Object-glass of another Telescope as I had at hand. Thiswas a double Convex ground on both sides to one and the same Sphere, andits Focus was distant from it 83-2/5 Inches. And thence, if the Sines ofIncidence and Refraction of the bright yellow Light be assumed inproportion as 11 to 17, the Diameter of the Sphere to which the Glasswas figured will by computation be found 182 Inches. This Glass I laidupon a flat one, so that the black Spot appeared in the middle of theRings of Colours without any other Pressure than that of the weight ofthe Glass. And now measuring the Diameter of the fifth dark Circle asaccurately as I could, I found it the fifth part of an Inch precisely.This Measure was taken with the points of a pair of Compasses on theupper Surface on the upper Glass, and my Eye was about eight or nineInches distance from the Glass, almost perpendicularly over it, and theGlass was 1/6 of an Inch thick, and thence it is easy to collect thatthe true Diameter of the Ring between the Glasses was greater than itsmeasur'd Diameter[Pg 202] above the Glasses in the Proportion of 80 to 79, orthereabouts, and by consequence equal to 16/79 parts of an Inch, and itstrue Semi-diameter equal to 8/79 parts. Now as the Diameter of theSphere (182 Inches) is to the Semi-diameter of this fifth dark Ring(8/79 parts of an Inch) so is this Semi-diameter to the thickness of theAir at this fifth dark Ring; which is therefore 32/567931 or100/1774784. Parts of an Inch; and the fifth Part thereof,viz. the1/88739 Part of an Inch, is the Thickness of the Air at the first ofthese dark Rings.

The same Experiment I repeated with another double convex Object-glassground on both sides to one and the same Sphere. Its Focus was distantfrom it 168-1/2 Inches, and therefore the Diameter of that Sphere was184 Inches. This Glass being laid upon the same plain Glass, theDiameter of the fifth of the dark Rings, when the black Spot in theirCenter appear'd plainly without pressing the Glasses, was by the measureof the Compasses upon the upper Glass 121/600 Parts of an Inch, and byconsequence between the Glasses it was 1222/6000: For the upper Glasswas 1/8 of an Inch thick, and my Eye was distant from it 8 Inches. And athird proportional to half this from the Diameter of the Sphere is5/88850 Parts of an Inch. This is therefore the Thickness of the Air atthis Ring, and a fifth Part thereof,viz. the 1/88850th Part of anInch is the Thickness thereof at the first of the Rings, as above.

I tried the same Thing, by laying these Object-glasses upon flat Piecesof a broken Looking-glass,[Pg 203] and found the same Measures of the Rings:Which makes me rely upon them till they can be determin'd moreaccurately by Glasses ground to larger Spheres, though in such Glassesgreater care must be taken of a true Plane.

These Dimensions were taken, when my Eye was placed almostperpendicularly over the Glasses, being about an Inch, or an Inch and aquarter, distant from the incident Rays, and eight Inches distant fromthe Glass; so that the Rays were inclined to the Glass in an Angle ofabout four Degrees. Whence by the following Observation you willunderstand, that had the Rays been perpendicular to the Glasses, theThickness of the Air at these Rings would have been less in theProportion of the Radius to the Secant of four Degrees, that is, of10000 to 10024. Let the Thicknesses found be therefore diminish'd inthis Proportion, and they will become 1/88952 and 1/89063, or (to usethe nearest round Number) the 1/89000th Part of an Inch. This is theThickness of the Air at the darkest Part of the first dark Ring made byperpendicular Rays; and half this Thickness multiplied by theProgression, 1, 3, 5, 7, 9, 11, &c. gives the Thicknesses of the Air atthe most luminous Parts of all the brightest Rings,viz. 1/178000,3/178000, 5/178000, 7/178000, &c. their arithmetical Means 2/178000,4/178000, 6/178000, &c. being its Thicknesses at the darkest Parts ofall the dark ones.

Obs. 7. The Rings were least, when my Eye was placed perpendicularlyover the Glasses in the Axis[Pg 204] of the Rings: And when I view'd themobliquely they became bigger, continually swelling as I removed my Eyefarther from the Axis. And partly by measuring the Diameter of the sameCircle at several Obliquities of my Eye, partly by other Means, as alsoby making use of the two Prisms for very great Obliquities, I found itsDiameter, and consequently the Thickness of the Air at its Perimeter inall those Obliquities to be very nearly in the Proportions express'd inthis Table.

Angle of Incidence on the Air.	Angle of Refraction into the Air.	Diameter of the Ring.	Thickness of the Air.
Deg. Min.
00 00	00 00	10	10
06 26	10 00	10-1/13	10-2/13
12 45	20 00	10-1/3	10-2/3
18 49	30 00	10-3/4	11-1/2
24 30	40 00	11-2/5	13
29 37	50 00	12-1/2	15-1/2
33 58	60 00	14	20
35 47	65 00	15-1/4	23-1/4
37 19	70 00	16-4/5	28-1/4
38 33	75 00	19-1/4	37
39 27	80 00	22-6/7	52-1/4
40 00	85 00	29	84-1/12
40 11	90 00	35	122-1/2

In the two first Columns are express'd the Obliquities of the incidentand emergent Rays to the Plate of the Air, that is, their Angles ofIncidence[Pg 205] and Refraction. In the third Column the Diameter of anycolour'd Ring at those Obliquities is expressed in Parts, of which tenconstitute that Diameter when the Rays are perpendicular. And in thefourth Column the Thickness of the Air at the Circumference of that Ringis expressed in Parts, of which also ten constitute its Thickness whenthe Rays are perpendicular.

And from these Measures I seem to gather this Rule: That the Thicknessof the Air is proportional to the Secant of an Angle, whose Sine is acertain mean Proportional between the Sines of Incidence and Refraction.And that mean Proportional, so far as by these Measures I can determineit, is the first of an hundred and six arithmetical mean Proportionalsbetween those Sines counted from the bigger Sine, that is, from the Sineof Refraction when the Refraction is made out of the Glass into thePlate of Air, or from the Sine of Incidence when the Refraction is madeout of the Plate of Air into the Glass.

Obs. 8. The dark Spot in the middle of the Rings increased also by theObliquation of the Eye, although almost insensibly. But, if instead ofthe Object-glasses the Prisms were made use of, its Increase was moremanifest when viewed so obliquely that no Colours appear'd about it. Itwas least when the Rays were incident most obliquely on the interjacentAir, and as the obliquity decreased it increased more and more until thecolour'd Rings appear'd, and then decreased again, but not so much as itincreased before. And hence it is evident, that the Transparency[Pg 206] wasnot only at the absolute Contact of the Glasses, but also where they hadsome little Interval. I have sometimes observed the Diameter of thatSpot to be between half and two fifth parts of the Diameter of theexterior Circumference of the red in the first Circuit or Revolution ofColours when view'd almost perpendicularly; whereas when view'dobliquely it hath wholly vanish'd and become opake and white like theother parts of the Glass; whence it may be collected that the Glassesdid then scarcely, or not at all, touch one another, and that theirInterval at the perimeter of that Spot when view'd perpendicularly wasabout a fifth or sixth part of their Interval at the circumference ofthe said red.

Obs. 9. By looking through the two contiguous Object-glasses, I foundthat the interjacent Air exhibited Rings of Colours, as well bytransmitting Light as by reflecting it. The central Spot was now white,and from it the order of the Colours were yellowish red; black, violet,blue, white, yellow, red; violet, blue, green, yellow, red, &c. Butthese Colours were very faint and dilute, unless when the Light wastrajected very obliquely through the Glasses: For by that means theybecame pretty vivid. Only the first yellowish red, like the blue in thefourth Observation, was so little and faint as scarcely to be discern'd.Comparing the colour'd Rings made by Reflexion, with these made bytransmission of the Light; I found that white was opposite to black, redto blue, yellow to violet, and green to a Compound of red and violet.That is,[Pg 207] those parts of the Glass were black when looked through, whichwhen looked upon appeared white, and on the contrary. And so those whichin one case exhibited blue, did in the other case exhibit red. And thelike of the other Colours. The manner you have represented in the thirdFigure, where AB, CD, are the Surfaces of the Glasses contiguous at E,and the black Lines between them are their Distances in arithmeticalProgression, and the Colours written above are seen by reflected Light,and those below by Light transmitted (p. 209).

Obs. 10. Wetting the Object-glasses a little at their edges, the Watercrept in slowly between them, and the Circles thereby became less andthe Colours more faint: Insomuch that as the Water crept along, one halfof them at which it first arrived would appear broken off from the otherhalf, and contracted into a less Room. By measuring them I found theProportions of their Diameters to the Diameters of the like Circles madeby Air to be about seven to eight, and consequently the Intervals of theGlasses at like Circles, caused by those two Mediums Water and Air, areas about three to four. Perhaps it may be a general Rule, That if anyother Medium more or less dense than Water be compress'd between theGlasses, their Intervals at the Rings caused thereby will be to theirIntervals caused by interjacent Air, as the Sines are which measure theRefraction made out of that Medium into Air.

Obs. 11. When the Water was between the Glasses, if I pressed theupper Glass variously at its edges to[Pg 208] make the Rings move nimbly fromone place to another, a little white Spot would immediately follow thecenter of them, which upon creeping in of the ambient Water into thatplace would presently vanish. Its appearance was such as interjacent Airwould have caused, and it exhibited the same Colours. But it was notair, for where any Bubbles of Air were in the Water they would notvanish. The Reflexion must have rather been caused by a subtiler Medium,which could recede through the Glasses at the creeping in of the Water.

Obs. 12. These Observations were made in the open Air. But farther toexamine the Effects of colour'd Light falling on the Glasses, I darken'dthe Room, and view'd them by Reflexion of the Colours of a Prism cast ona Sheet of white Paper, my Eye being so placed that I could see thecolour'd Paper by Reflexion in the Glasses, as in a Looking-glass. Andby this means the Rings became distincter and visible to a far greaternumber than in the open Air. I have sometimes seen more than twenty ofthem, whereas in the open Air I could not discern above eight or nine.[Pg 209]

Obs. 13. Appointing an Assistant to move the Prism to and fro aboutits Axis, that all the Colours might successively fall on that part ofthe Paper which I saw by Reflexion from that part of the Glasses, wherethe Circles appear'd, so that all the Colours might be successivelyreflected from the Circles to my Eye, whilst I held it immovable, Ifound the Circles which the red Light made to be manifestly bigger thanthose which were made by the blue and violet. And it was very pleasantto see them gradually swell or contract accordingly as the Colour of theLight was changed. The Interval of the Glasses at any of the Rings whenthey were made by the utmost red Light, was to their Interval at thesame Ring when made by the utmost violet, greater than as 3 to 2, andless than as 13 to 8. By the most of my Observations it was as 14 to 9.And this Proportion seem'd very nearly the same in all Obliquities of myEye; unless when two Prisms were made use of instead of theObject-glasses. For then at a certain great obliquity of my Eye, theRings made by the several Colours seem'd equal, and at a greaterobliquity those made by the violet would be greater than the same Ringsmade by the red: the Refraction of the Prism in this case causing themost refrangible Rays to fall more obliquely on that plate of the Airthan the least refrangible ones. Thus the Experiment succeeded in thecolour'd Light, which was sufficiently strong and copious to make theRings sensible. And thence it may be gather'd, that if the mostrefrangible and least refrangible Rays had been copious enough to makethe Rings sensible without the mixture of other Rays, the Proportionwhich here was 14 to 9 would have been a little greater, suppose 14-1/4or 14-1/3 to 9.

Obs. 14. Whilst the Prism was turn'd about its Axis with an uniformMotion, to make all the several Colours fall successively upon theObject-glasses, and thereby to make the Rings contract and[Pg 211] dilate: TheContraction or Dilatation of each Ring thus made by the variation of itsColour was swiftest in the red, and slowest in the violet, and in theintermediate Colours it had intermediate degrees of Celerity. Comparingthe quantity of Contraction and Dilatation made by all the degrees ofeach Colour, I found that it was greatest in the red; less in theyellow, still less in the blue, and least in the violet. And to make asjust an Estimation as I could of the Proportions of their Contractionsor Dilatations, I observ'd that the whole Contraction or Dilatation ofthe Diameter of any Ring made by all the degrees of red, was to that ofthe Diameter of the same Ring made by all the degrees of violet, asabout four to three, or five to four, and that when the Light was of themiddle Colour between yellow and green, the Diameter of the Ring wasvery nearly an arithmetical Mean between the greatest Diameter of thesame Ring made by the outmost red, and the least Diameter thereof madeby the outmost violet: Contrary to what happens in the Colours of theoblong Spectrum made by the Refraction of a Prism, where the red is mostcontracted, the violet most expanded, and in the midst of all theColours is the Confine of green and blue. And hence I seem to collectthat the thicknesses of the Air between the Glasses there, where theRing is successively made by the limits of the five principal Colours(red, yellow, green, blue, violet) in order (that is, by the extremered, by the limit of red and yellow in the middle of the orange, by thelimit of yellow and green, by the limit of green[Pg 212] and blue, by the limitof blue and violet in the middle of the indigo, and by the extremeviolet) are to one another very nearly as the sixth lengths of a Chordwhich found the Notes in a sixth Major,sol,la,mi,fa,sol,la. But it agrees something better with the Observation to say, thatthe thicknesses of the Air between the Glasses there, where the Ringsare successively made by the limits of the seven Colours, red, orange,yellow, green, blue, indigo, violet in order, are to one another as theCube Roots of the Squares of the eight lengths of a Chord, which foundthe Notes in an eighth,sol,la,fa,sol,la,mi,fa,sol; that is, as the Cube Roots of the Squares of the Numbers, 1, 8/9,5/6, 3/4, 2/3, 3/5, 9/16, 1/2.

Obs. 15. These Rings were not of various Colours like those made inthe open Air, but appeared all over of that prismatick Colour only withwhich they were illuminated. And by projecting the prismatick Coloursimmediately upon the Glasses, I found that the Light which fell on thedark Spaces which were between the Colour'd Rings was transmittedthrough the Glasses without any variation of Colour. For on a whitePaper placed behind, it would paint Rings of the same Colour with thosewhich were reflected, and of the bigness of their immediate Spaces. Andfrom thence the origin of these Rings is manifest; namely, that the Airbetween the Glasses, according to its various thickness, is disposed insome places to reflect, and in others to transmit the Light of any oneColour (as you may see represented in the fourth Figure) and in the sameplace to reflect that of one Colour where it transmits that of another.[Pg 213]

Obs. 16. The Squares of the Diameters of these Rings made by anyprismatick Colour were in arithmetical Progression, as in the fifthObservation. And the Diameter of the sixth Circle, when made by thecitrine yellow, and viewed almost perpendicularly was about 58/100 partsof an Inch, or a little less, agreeable to the sixth Observation.

The precedent Observations were made with a rarer thin Medium,terminated by a denser, such as was Air or Water compress'd between twoGlasses. In those that follow are set down the Appearances of a denserMedium thin'd within a rarer, such as are Plates of Muscovy Glass,Bubbles of Water, and some other thin Substances terminated on all sideswith air.

Obs. 17. If a Bubble be blown with Water first made tenacious bydissolving a little Soap in it, 'tis a common Observation, that after awhile it will appear tinged with a great variety of Colours. To defendthese Bubbles from being agitated by the external Air (whereby theirColours are irregularly moved one among another, so that no accurateObservation can be made of them,) as soon as I had blown any of them Icover'd it with a clear Glass, and by that means its Colours emerged ina very regular order, like so many concentrick Rings encompassing thetop of the Bubble. And as the Bubble grew thinner by the continualsubsiding of the Water, these Rings dilated slowly and overspread thewhole Bubble, descending in order to the bottom of it,[Pg 215] where theyvanish'd successively. In the mean while, after all the Colours wereemerged at the top, there grew in the center of the Rings a small roundblack Spot, like that in the first Observation, which continuallydilated it self till it became sometimes more than 1/2 or 3/4 of an Inchin breadth before the Bubble broke. At first I thought there had been noLight reflected from the Water in that place, but observing it morecuriously, I saw within it several smaller round Spots, which appearedmuch blacker and darker than the rest, whereby I knew that there wassome Reflexion at the other places which were not so dark as thoseSpots. And by farther Tryal I found that I could see the Images of somethings (as of a Candle or the Sun) very faintly reflected, not only fromthe great black Spot, but also from the little darker Spots which werewithin it.

Besides the aforesaid colour'd Rings there would often appear smallSpots of Colours, ascending and descending up and down the sides of theBubble, by reason of some Inequalities in the subsiding of the Water.And sometimes small black Spots generated at the sides would ascend upto 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 andlively than those of the Air thinn'd between two Glasses, and so moreeasy to be distinguish'd, I shall here give you a farther description oftheir order, as they were observ'd in viewing them by Reflexion of theSkies when of a white Colour, whilst a black substance was placed[Pg 216]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 andblue, only the blues (and principally the second blue) inclined a littleto green.

The fourth red was also dilute and dirty, but not so much as the formerthree; after that succeeded little or no yellow, but a copious green,which at first inclined a little to yellow, and then became a prettybrisk 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 afterwardsbecame more bright and brisk, but yet not very pure. This was succeededwith a very bright and intense yellow, which was but little in quantity,and soon chang'd to green: But that green was copious and something morepure, deep and lively, than the former green. After that follow'd anexcellent blue of a bright Sky-colour, and then a purple, which was lessin quantity than the blue, and much inclined to red.

The sixth red was at first of a very fair and lively scarlet, and soonafter of a brighter Colour, being very pure and brisk, and the best ofall the reds. Then after a lively orange follow'd an intense bright[Pg 217] andcopious yellow, which was also the best of all the yellows, and thischanged first to a greenish yellow, and then to a greenish blue; but thegreen between the yellow and the blue, was very little and dilute,seeming rather a greenish white than a green. The blue which succeededbecame very good, and of a very bright Sky-colour, but yet somethinginferior to the former blue; and the violet was intense and deep withlittle or no redness in it. And less in quantity than the blue.

In the last red appeared a tincture of scarlet next to violet, whichsoon changed to a brighter Colour, inclining to an orange; and theyellow which follow'd was at first pretty good and lively, butafterwards it grew more dilute until by degrees it ended in perfectwhiteness. And this whiteness, if the Water was very tenacious andwell-temper'd, would slowly spread and dilate it self over the greaterpart of the Bubble; continually growing paler at the top, where atlength 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; thewhite between the blue Spots diminishing, until it resembled the Thredsof an irregular Net-work, and soon after vanish'd, and left all theupper part of the Bubble of the said dark blue Colour. And this Colour,after the aforesaid manner, dilated it self downwards, until sometimesit hath overspread the whole Bubble. In the mean while at the top, whichwas of a darker blue than the bottom, and appear'd also full of manyround blue Spots, something darker than the rest, there would[Pg 218] emergeone or more very black Spots, and within those, other Spots of anintenser blackness, which I mention'd in the former Observation; andthese continually dilated themselves until the Bubble broke.

If the Water was not very tenacious, the black Spots would break forthin the white, without any sensible intervention of the blue. Andsometimes they would break forth within the precedent yellow, or red, orperhaps within the blue of the second order, before the intermediateColours had time to display themselves.

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

Obs. 19. Viewing in several oblique Positions of my Eye the Rings ofColours emerging on the top of the Bubble, I found that they weresensibly dilated by increasing the obliquity, but yet not so much by faras those made by thinn'd Air in the seventh Observation. For there theywere dilated so much as, when view'd most obliquely, to arrive at a partof the Plate more than twelve times thicker than that where theyappear'd when viewed perpendicularly; whereas in this case the thicknessof the Water, at which they arrived when viewed most obliquely, was tothat thickness which exhibited them by perpendicular Rays, somethingless than as 8 to 5. By the best of[Pg 219] my Observations it was between 15and 15-1/2 to 10; an increase about 24 times less than in the othercase.

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 wouldexhibit the same appearance of Colours in all Positions of the Eye. Andthen the Colours which were seen at its apparent circumference by theobliquest Rays, would be different from those that were seen in otherplaces, by Rays less oblique to it. And divers Spectators might see thesame part of it of differing Colours, by viewing it at very differingObliquities. Now observing how much the Colours at the same places ofthe Bubble, or at divers places of equal thickness, were varied by theseveral Obliquities of the Rays; by the assistance of the 4th, 14th,16th and 18th Observations, as they are hereafter explain'd, I collectthe thickness of the Water requisite to exhibit any one and the sameColour, at several Obliquities, to be very nearly in the Proportionexpressed in this Table.

Incidence on the Water.	Refraction into the Water.	Thickness of 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 tothe Superficies of the Water, that is, their Angles of Incidence andRefraction. Where I suppose, that the Sines which measure them are inround Numbers, as 3 to 4, though probably the Dissolution of Soap in theWater, may a little alter its refractive Virtue. In the third Column,the Thickness of the Bubble, at which any one Colour is exhibited inthose several Obliquities, is express'd in Parts, of which tenconstitute its Thickness when the Rays are perpendicular. And the Rulefound by the seventh Observation agrees well with these Measures, ifduly apply'd; namely, that the Thickness of a Plate of Water requisiteto exhibit one and the same Colour at several Obliquities of the Eye, isproportional to the Secant of an Angle, whose Sine is the first of anhundred and six arithmetical mean Proportionals between the Sines ofIncidence and Refraction counted from the lesser Sine, that is, from theSine 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'dSteel by heating it, or on Bell-metal, and some other metallineSubstances, when melted and pour'd on the Ground, where they may cool inthe open Air, have, like the Colours of Water-bubbles, been a littlechanged by viewing them at divers Obliquities, and particularly that adeep blue, or violet, when view'd very obliquely, hath been changed to adeep red. But the Changes of these[Pg 221] Colours are not so great andsensible as of those made by Water. For the Scoria, or vitrified Part ofthe Metal, which most Metals when heated or melted do continuallyprotrude, and send out to their Surface, and which by covering theMetals in form of a thin glassy Skin, causes these Colours, is muchdenser than Water; and I find that the Change made by the Obliquation ofthe Eye is least in Colours of the densest thin Substances.

Obs. 20. As in the ninth Observation, so here, the Bubble, bytransmitted Light, appear'd of a contrary Colour to that, which itexhibited by Reflexion. Thus when the Bubble being look'd on by theLight of the Clouds reflected from it, seemed red at its apparentCircumference, if the Clouds at the same time, or immediately after,were view'd through it, the Colour at its Circumference would be blue.And, on the contrary, when by reflected Light it appeared blue, it wouldappear red by transmitted Light.

Obs. 21. By wetting very thin Plates ofMuscovy Glass, whosethinness made the like Colours appear, the Colours became more faint andlanguid, especially by wetting the Plates on that side opposite to theEye: But I could not perceive any variation of their Species. So thenthe thickness of a Plate requisite to produce any Colour, depends onlyon the density of the Plate, and not on that of the ambient Medium. Andhence, by the 10th and 16th Observations, may be known the thicknesswhich Bubbles of Water, or Plates ofMuscovy Glass, or otherSubstances, have at any Colour produced by them.[Pg 222]

Obs. 22. A thin transparent Body, which is denser than its ambientMedium, exhibits more brisk and vivid Colours than that which is so muchrarer; as I have particularly observed in the Air and Glass. For blowingGlass very thin at a Lamp Furnace, those Plates encompassed with Air didexhibit Colours much more vivid than those of Air made thin between twoGlasses.

Obs. 23. Comparing the quantity of Light reflected from the severalRings, I found that it was most copious from the first or inmost, and inthe exterior Rings became gradually less and less. Also the whiteness ofthe first Ring was stronger than that reflected from those parts of thethin Medium or Plate which were without the Rings; as I could manifestlyperceive by viewing at a distance the Rings made by the twoObject-glasses; or by comparing two Bubbles of Water blown at distantTimes, in the first of which the Whiteness appear'd, which succeeded allthe Colours, and in the other, the Whiteness which preceded them all.

Obs. 24. When the two Object-glasses were lay'd upon one another, soas to make the Rings of the Colours appear, though with my naked Eye Icould not discern above eight or nine of those Rings, yet by viewingthem through a Prism I have seen a far greater Multitude, insomuch thatI could number more than forty, besides many others, that were so verysmall and close together, that I could not keep my Eye steady on themseverally so as to number them, but by their Extent I have sometimesestimated[Pg 223] them to be more than an hundred. And I believe the Experimentmay be improved to the Discovery of far greater Numbers. For they seemto be really unlimited, though visible only so far as they can beseparated by the Refraction of the Prism, as I shall hereafter explain.

But it was but one side of these Rings, namely, that towards which theRefraction was made, which by that Refraction was render'd distinct, andthe 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 sometimesnone of those Rings, of which I could discern eight or nine with mynaked Eye. And their Segments or Arcs, which on the other side appear'dso 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 theObject-glasses, the middle Part of those Arcs became also confused, soas to disappear and constitute an even Whiteness, whilst on either sidetheir Ends, as also the whole Arcs farthest from the Center, becamedistincter than before, appearing in the Form as you see them design'din the fifth Figure.

The Arcs, where they seem'd distinctest, were only white and blacksuccessively, without any other Colours intermix'd. But in other Placesthere[Pg 224] appeared Colours, whose Order was inverted by the refraction insuch manner, that if I first held the Prism very near theObject-glasses, and then gradually removed it farther off towards myEye, the Colours of the 2d, 3d, 4th, and following Rings, shrunk towardsthe white that emerged between them, until they wholly vanish'd into itat the middle of the Arcs, and afterwards emerged again in a contraryOrder. 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 thenaked Eye they have all over seem'd uniformly white, without the leastAppearance of any of the colour'd Rings; and yet by viewing them througha Prism, great Multitudes of those Rings have discover'd themselves. Andin like manner Plates ofMuscovy Glass, and Bubbles of Glass blown ata Lamp-Furnace, which were not so thin as to exhibit any Colours to thenaked Eye, have through the Prism exhibited a great Variety of themranged irregularly up and down in the Form of Waves. And so Bubbles ofWater, before they began to exhibit their Colours to the naked Eye of aBystander, have appeared through a Prism, girded about with manyparallel and horizontal Rings; to produce which Effect, it was necessaryto hold the Prism parallel, or very nearly parallel to the Horizon, andto dispose it so that the Rays might be refracted upwards.

THE

SECOND BOOK

OPTICKS

PART II.

Remarks upon the foregoing Observations.

Having given my Observations of these Colours, before I make use of themto unfold the Causes of the Colours of natural Bodies, it is convenientthat 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 toshew how the Colours in the fourth and eighteenth Observations areproduced, let there be taken in any Right Line from the Point Y, [inFig. 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion toone 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 tosound all the Notes in an eighth are represented; that is, in theProportion[Pg 226] of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243,10000. And at the Points A, B, C, D, E, F, G, H, let PerpendicularsAα, Bβ, &c. be erected, by whose Intervals the Extentof the several Colours set underneath against them, is to berepresented. Then divide the LineAα in such Proportion asthe Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points ofDivision 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 thintransparent Body, at which the outmost Violet is most copiouslyreflected in the first Ring, or Series of Colours, then by the 13thObservation, HK will represent its Thickness, at which the utmost Red ismost copiously reflected in the same Series. Also by the 5th and 16thObservations, A6 and HN will denote the Thicknesses at which thoseextreme Colours are most copiously reflected in the second Series, andA10 and HQ the Thicknesses at which they are most copiously reflected inthe third Series, and so on. And the Thickness at which any of theintermediate Colours are reflected most copiously, will, according tothe 14th Observation, be defined by the distance of the Line AH from theintermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Namesof those Colours are written below.[Pg 227]

But farther, to define the Latitude of these Colours in each Ring orSeries, let A1 design the least thickness, and A3 the greatestthickness, 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 letthe intermediate Colours be limited by the intermediate parts of theLines 1I, and 3L, against which the Names of those Colours are written,and so on: But yet with this caution, that the Reflexions be supposedstrongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thenceto decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. oneither side; where you must not conceive them to be precisely limited,but to decay indefinitely. And whereas I have assign'd the same Latitudeto every Series, I did it, because although the Colours in the firstSeries seem to be a little broader than the rest, by reason of astronger Reflexion there, yet that inequality is so insensible asscarcely to be determin'd by Observation.

Now according to this Description, conceiving that the Rays originallyof 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 iseasy to know what Colour must in the open Air be exhibited at anythickness of a transparent thin Body. For if a Ruler be applied parallelto AH, at that distance from it by which the thickness of the Body isrepresented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth willdenote the reflected original Colours, of which the Colour exhibited inthe open Air is compounded. Thus if the constitution of the green in thethird Series of Colours be desired, apply the Ruler as you[Pg 229] see atπρσφ, and by its passing through some of the blue at π and yellow at σ, as well as through the green at ρ,you may conclude that the green exhibited at that thickness of the Bodyis principally constituted of original green, but not without a mixtureof some blue and yellow.

By this means you may know how the Colours from the center of the Ringsoutward ought to succeed in order as they were described in the 4th and18th Observations. For if you move the Ruler gradually from AH throughall distances, having pass'd over the first Space which denotes littleor no Reflexion to be made by thinnest Substances, it will first arriveat 1 the violet, and then very quickly at the blue and green, whichtogether with that violet compound blue, and then at the yellow and red,by whose farther addition that blue is converted into whiteness, whichwhiteness continues during the transit of the edge of the Ruler from Ito 3, and after that by the successive deficience of its componentColours, turns first to compound yellow, and then to red, and last ofall 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 from5 to O, and are more lively than before, because more expanded andsevered. And for the same reason instead of the former white thereintercedes between the blue and yellow a mixture of orange, yellow,green, blue and indigo, all which together ought to exhibit a dilute andimperfect green. So the Colours of the third Series all succeed inorder; first, the[Pg 230] violet, which a little interferes with the red of thesecond order, and is thereby inclined to a reddish purple; then the blueand green, which are less mix'd with other Colours, and consequentlymore lively than before, especially the green: Then follows the yellow,some of which towards the green is distinct and good, but that part ofit towards the succeeding red, as also that red is mix'd with the violetand blue of the fourth Series, whereby various degrees of red very muchinclining to purple are compounded. This violet and blue, which shouldsucceed this red, being mixed with, and hidden in it, there succeeds agreen. And this at first is much inclined to blue, but soon becomes agood green, the only unmix'd and lively Colour in this fourth Series.For as it verges towards the yellow, it begins to interfere with theColours of the fifth Series, by whose mixture the succeeding yellow andred are very much diluted and made dirty, especially the yellow, whichbeing the weaker Colour is scarce able to shew it self. After this theseveral Series interfere more and more, and their Colours become moreand more intermix'd, till after three or four more revolutions (in whichthe red and blue predominate by turns) all sorts of Colours are in allplaces pretty equally blended, and compound an even whiteness.

And since by the 15th Observation the Rays endued with one Colour aretransmitted, where those of another Colour are reflected, the reason ofthe Colours made by the transmitted Light in the 9th and 20thObservations is from hence evident.[Pg 231]

If not only the Order and Species of these Colours, but also the precisethickness of the Plate, or thin Body at which they are exhibited, bedesired in parts of an Inch, that may be also obtained by assistance ofthe 6th or 16th Observations. For according to those Observations thethickness of the thinned Air, which between two Glasses exhibited themost 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 theLight reflected most copiously at these thicknesses be the brightcitrine yellow, or confine of yellow and orange, and these thicknesseswill be Fλ, Fμ, Fυ, Fξ, Fο,Fτ. And this being known, it is easy to determine whatthickness of Air is represented by Gφ, or by any otherdistance of the Ruler from AH.

But farther, since by the 10th Observation the thickness of Air was tothe thickness of Water, which between the same Glasses exhibited thesame Colour, as 4 to 3, and by the 21st Observation the Colours of thinBodies are not varied by varying the ambient Medium; the thickness of aBubble of Water, exhibiting any Colour, will be 3/4 of the thickness ofAir producing the same Colour. And so according to the same 10th and21st Observations, the thickness of a Plate of Glass, whose Refractionof the mean refrangible Ray, is measured by the proportion of the Sines31 to 20, may be 20/31 of the thickness of Air producing the sameColours; and the like of other Mediums. I do not affirm, that thisproportion of 20 to 31, holds in all the Rays; for the Sines of othersorts of Rays[Pg 232] have other Proportions. But the differences of thoseProportions are so little that I do not here consider them. On theseGrounds I have composed the following Table, wherein the thickness ofAir, Water, and Glass, at which each Colour is most intense andspecifick, is expressed in parts of an Inch divided into ten hundredthousand equal parts.

Now if this Table be compared with the 6th Scheme, you will there seethe constitution of each Colour, as to its Ingredients, or the originalColours of which it is compounded, and thence be enabled to judge of itsIntenseness or Imperfection; which may suffice in explication of the 4thand 18th Observations, unless it be farther desired to delineate themanner how the Colours appear, when the two Object-glasses are laid uponone another. To do which, let there be described a large Arc of aCircle, and a streight Line which may touch that Arc, and parallel tothat Tangent several occult Lines, at such distances from it, as theNumbers set against the several Colours in the Table denote. For theArc, and its Tangent, will represent the Superficies of the Glassesterminating the interjacent Air; and the places where the occult Linescut the Arc will show at what distances from the center, or Point ofcontact, each Colour is reflected.[Pg 233]

The thickness of colour'd Plates and Particles of

		Air.	Water.	Glass.

Their Colours of the first Order,	Very black	1/2	3/8	10/31
	Black	1	3/4	20/31
	Beginning of Black	2	1-1/2	1-2/7
	Blue	2-2/5	1-4/5	1-11/22
	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

Of the second order,	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
	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

Of the third Order,	Indigo	22-1/10	16-4/7	14-1/4
	Blue	23-2/5	17-11/20	15-1/10
	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

Of the fourth Order,	Green	35-2/7	26-1/2	22-3/4
	Yellowish green	36	27	23-2/9
	Red	40-1/3	30-1/4	26

Of the fifth Order,	Greenish blue	46	34-1/2	29-2/3
Of the fifth Order,	Red	52-1/2	39-3/8	34

Of the sixth Order,	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
Of the seventh Order,	Ruddy White	77	57-3/4	49-2/3

There are also other Uses of this Table: For by its assistance thethickness of the Bubble in the 19th Observation was determin'd by theColours which it exhibited. And so the bigness of the parts of naturalBodies 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 tocompose one Plate equalling them all in thickness, the resulting Colourmay be hereby determin'd. For instance, Mr.Hook observed, as ismentioned in hisMicrographia, that a faint yellow Plate ofMuscovyGlass laid upon a blue one, constituted a very deep purple. The yellowof the first Order is a faint one, and the thickness of the Plateexhibiting it, according to the Table is 4-3/5, to which add 9, thethickness exhibiting blue of the second Order, and the Sum will be13-3/5, which is the thickness exhibiting the purple of the third Order.

To explain, in the next place, the circumstances of the 2d and 3dObservations; that is, how the Rings of the Colours may (by turning thePrisms about their common Axis the contrary way to that expressed inthose Observations) be converted into white and black Rings, andafterwards into Rings of Colours again, the Colours of each Ring lyingnow in an inverted order; it must be remember'd, that those Rings ofColours are dilated by the obliquation of the Rays to the Air whichintercedes the Glasses, and that according to the Table in the 7thObservation, their Dilatation or Increase of their Diameter is mostmanifest and speedy when they are obliquest. Now the Rays of yellowbeing more refracted by the first Superficies of the said Air than thoseof red, are thereby made more oblique to the second Superficies, atwhich they are reflected to produce the colour'd Rings, and consequentlythe yellow Circle in each Ring will be more dilated than the red; and[Pg 235]the Excess of its Dilatation will be so much the greater, by how muchthe greater is the obliquity of the Rays, until at last it become ofequal extent with the red of the same Ring. And for the same reason thegreen, blue and violet, will be also so much dilated by the stillgreater obliquity of their Rays, as to become all very nearly of equalextent with the red, that is, equally distant from the center of theRings. 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 musthave black and dark Rings between them, because they do not spread andinterfere with one another, as before. And for that reason also theymust become distincter, and visible to far greater numbers. But yet theviolet being obliquest will be something more dilated, in proportion toits extent, than the other Colours, and so very apt to appear at theexterior Verges of the white.

Afterwards, by a greater obliquity of the Rays, the violet and bluebecome more sensibly dilated than the red and yellow, and so beingfarther removed from the center of the Rings, the Colours must emergeout of the white in an order contrary to that which they had before; theviolet and blue at the exterior Limbs of each Ring, and the red andyellow at the interior. And the violet, by reason of the greatestobliquity of its Rays, being in proportion most of all expanded, willsoonest appear at the exterior Limb of each white Ring, and become moreconspicuous than the rest. And the several Series of Colours belongingto the several Rings, will, by their unfolding[Pg 236] and spreading, beginagain to interfere, and thereby render the Rings less distinct, and notvisible to so great numbers.

If instead of the Prisms the Object-glasses be made use of, the Ringswhich they exhibit become not white and distinct by the obliquity of theEye, by reason that the Rays in their passage through that Air whichintercedes the Glasses are very nearly parallel to those Lines in whichthey were first incident on the Glasses, and consequently the Raysendued with several Colours are not inclined one more than another tothat 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 adistance appear distinct, should not only become confused by viewingthem near at hand, but also yield a violet Colour at both the edges ofevery white Ring. And the reason is, that the Rays which enter the Eyeat several parts of the Pupil, have several Obliquities to the Glasses,and those which are most oblique, if consider'd apart, would representthe Rings bigger than those which are the least oblique. Whence thebreadth of the Perimeter of every white Ring is expanded outwards by theobliquest Rays, and inwards by the least oblique. And this Expansion isso much the greater by how much the greater is the difference of theObliquity; that is, by how much the Pupil is wider, or the Eye nearer tothe Glasses. And the breadth of the violet must be most expanded,because the Rays apt to[Pg 237] excite a Sensation of that Colour are mostoblique to a second or farther Superficies of the thinn'd Air at whichthey 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 Intervalsmust be diminish'd, until the neighbouring Rings become continuous, andare blended, the exterior first, and then those nearer the center; sothat they can no longer be distinguish'd apart, but seem to constitutean even and uniform whiteness.

Among all the Observations there is none accompanied with so oddcircumstances as the twenty-fourth. Of those the principal are, that inthin Plates, which to the naked Eye seem of an even and uniformtransparent whiteness, without any terminations of Shadows, theRefraction of a Prism should make Rings of Colours appear, whereas itusually makes Objects appear colour'd only there where they areterminated with Shadows, or have parts unequally luminous; and that itshould make those Rings exceedingly distinct and white, although itusually renders Objects confused and coloured. The Cause of these thingsyou will understand by considering, that all the Rings of Colours arereally in the Plate, when view'd with the naked Eye, although by reasonof the great breadth of their Circumferences they so much interfere andare blended together, that they seem to constitute an uniform whiteness.But when the Rays pass through the Prism to the Eye, the[Pg 238] Orbits of theseveral Colours in every Ring are refracted, some more than others,according to their degrees of Refrangibility: By which means the Colourson one side of the Ring (that is in the circumference on one side of itscenter), become more unfolded and dilated, and those on the other sidemore complicated and contracted. And where by a due Refraction they areso much contracted, that the several Rings become narrower than tointerfere with one another, they must appear distinct, and also white,if the constituent Colours be so much contracted as to be whollyco-incident. But on the other side, where the Orbit of every Ring ismade broader by the farther unfolding of its Colours, it must interferemore with other Rings than before, and so become less distinct.

To explain this a little farther, suppose the concentrick Circles AV,and BX, [inFig. 7.] represent the red and violet of any Order, which,together with the intermediate Colours, constitute any one of theseRings. Now these being view'd through a Prism, the violet Circle BX,will, by a greater Refraction, be farther translated from its place thanthe red AV, and so[Pg 239] approach nearer to it on that side of the Circles,towards which the Refractions are made. For instance, if the red betranslated toav, the violet may be translated tobx, so as toapproach nearer to it atx than before; and if the red be farthertranslated to av, the violet may be so much farther translated to bx asto convene with it at x; and if the red be yet farther translated toαΥ, the violet may be still so much farther translated toβξ as to pass beyond it at ξ, and convene with it ate andf. And this being understood not only of the red and violet,but of all the other intermediate Colours, and also of every revolutionof those Colours, you will easily perceive how those of the samerevolution or order, by their nearness atxv and Υξ, andtheir coincidence at xv,e andf, ought to constitute prettydistinct Arcs of Circles, especially at xv, or ate andf; and thatthey will appear severally atxυ and at xv exhibit whitenessby their coincidence, and again appear severally at Υξ, but yetin a contrary order to that which they had before, and still retainbeyonde andf. But on the other side, atab, ab, or αβ,these Colours must become much more confused by being dilated and spreadso as to interfere with those of other Orders. And the same confusionwill happen at Υξ betweene andf, if the Refraction bevery great, or the Prism very distant from the Object-glasses: In whichcase no parts of the Rings will be seen, save only two little Arcs ate andf, whose distance from one another will be augmented byremoving the Prism still farther from the Object-glasses: And theselittle Arcs must be distinctest and[Pg 240] whitest at their middle, and attheir 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 tothose at the other end, by reason that they cross in the intermediatewhite; namely, their ends, which verge towards Υξ, will be redand yellow on that side next the center, and blue and violet on theother side. But their other ends which verge from Υξ, will onthe contrary be blue and violet on that side towards the center, and onthe other side red and yellow.

Now as all these things follow from the properties of Light by amathematical way of reasoning, so the truth of them may be manifested byExperiments. For in a dark Room, by viewing these Rings through a Prism,by reflexion of the several prismatick Colours, which an assistantcauses to move to and fro upon a Wall or Paper from whence they arereflected, whilst the Spectator's Eye, the Prism, and theObject-glasses, (as in the 13th Observation,) are placed steady; thePosition of the Circles made successively by the several Colours, willbe found such, in respect of one another, as I have described in theFiguresabxv, or abxv, orαβξΥ. And by the same method thetruth of the Explications of other Observations may be examined.

By what hath been said, the like Phænomena of Water and thin Plates ofGlass may be understood. But in small fragments of those Plates there isthis farther observable, that where they lie flat upon a Table, and areturned about their centers whilst they[Pg 241] are view'd through a Prism, theywill in some postures exhibit Waves of various Colours; and some of themexhibit these Waves in one or two Positions only, but the most of themdo in all Positions exhibit them, and make them for the most part appearalmost all over the Plates. The reason is, that the Superficies of suchPlates are not even, but have many Cavities and Swellings, which, howshallow soever, do a little vary the thickness of the Plate. For at theseveral sides of those Cavities, for the Reasons newly described, thereought to be produced Waves in several postures of the Prism. Now thoughit be but some very small and narrower parts of the Glass, by whichthese Waves for the most part are caused, yet they may seem to extendthemselves over the whole Glass, because from the narrowest of thoseparts 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 toseveral places, so as to constitute so many several Waves, as there weredivers orders of Colours promiscuously reflected from that part of theGlass.

These are the principal Phænomena of thin Plates or Bubbles, whoseExplications depend on the properties of Light, which I have heretoforedeliver'd. And these you see do necessarily follow from them, and agreewith them, even to their very least circumstances; and not only so, butdo very much tend to their proof. Thus, by the 24th Observation itappears, that the Rays of several Colours, made as well by[Pg 242] thin Platesor Bubbles, as by Refractions of a Prism, have several degrees ofRefrangibility; whereby those of each order, which at the reflexion fromthe Plate or Bubble are intermix'd with those of other orders, areseparated from them by Refraction, and associated together so as tobecome visible by themselves like Arcs of Circles. For if the Rays wereall alike refrangible, 'tis impossible that the whiteness, which to thenaked Sense appears uniform, should by Refraction have its partstransposed and ranged into those black and white Arcs.

It appears also that the unequal Refractions of difform Rays proceed notfrom any contingent irregularities; such as are Veins, an uneven Polish,or fortuitous Position of the Pores of Glass; unequal and casual Motionsin the Air or Æther, the spreading, breaking, or dividing the same Rayinto many diverging parts; or the like. For, admitting any suchirregularities, it would be impossible for Refractions to render thoseRings so very distinct, and well defined, as they do in the 24thObservation. It is necessary therefore that every Ray have its properand constant degree of Refrangibility connate with it, according towhich its refraction is ever justly and regularly perform'd; and thatseveral Rays have several of those degrees.

And what is said of their Refrangibility may be also understood of theirReflexibility, that is, of their Dispositions to be reflected, some at agreater, and others at a less thickness of thin Plates or Bubbles;namely, that those Dispositions are also connate with[Pg 243] the Rays, andimmutable; 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 adissimilar mixture of all Colours, and that Light is a mixture of Raysendued with all those Colours. For, considering the multitude of theRings of Colours in the 3d, 12th, and 24th Observations, it is manifest,that although in the 4th and 18th Observations there appear no more thaneight or nine of those Rings, yet there are really a far greater number,which so much interfere and mingle with one another, as after thoseeight or nine revolutions to dilute one another wholly, and constitutean even and sensibly uniform whiteness. And consequently that whitenessmust be allow'd a mixture of all Colours, and the Light which conveys itto the Eye must be a mixture of Rays endued with all those Colours.

But farther; by the 24th Observation it appears, that there is aconstant relation between Colours and Refrangibility; the mostrefrangible Rays being violet, the least refrangible red, and those ofintermediate Colours having proportionably intermediate degrees ofRefrangibility. And by the 13th, 14th, and 15th Observations, comparedwith the 4th or 18th there appears to be the same constant relationbetween Colour and Reflexibility; the violet being in like circumstancesreflected at least thicknesses of any thin Plate or Bubble, the red atgreatest thicknesses, and the intermediate Colours at intermediatethicknesses.[Pg 244] Whence it follows, that the colorifick Dispositions ofRays are also connate with them, and immutable; and by consequence, thatall 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 oftheir different Refrangibility or Reflexibility. And in this respect theScience of Colours becomes a Speculation as truly mathematical as anyother part of Opticks. I mean, so far as they depend on the Nature ofLight, and are not produced or alter'd by the Power of Imagination, orby striking or pressing the Eye.

THE

SECOND BOOK

OPTICKS

PART III.

Of the permanent Colours of natural Bodies, and the Analogy betweenthem and the Colours of thin transparent Plates.

I am now come to another part of this Design, which is to consider howthe Phænomena of thin transparent Plates stand related to those of allother natural Bodies. Of these Bodies I have already told you that theyappear of divers Colours, accordingly as they are disposed to reflectmost copiously the Rays originally endued with those Colours. But theirConstitutions, whereby they reflect some Rays more copiously thanothers, remain to be discover'd; and these I shall endeavour to manifestin the following Propositions.[Pg 246]

Prop. I.

Those Superficies of transparent Bodies reflect the greatest quantityof Light, which have the greatest refracting Power; that is, whichintercede Mediums that differ most in their refractive Densities. And inthe 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 whichrefracts from the perpendicular, the greater is the difference of theirrefractive Density, the less Obliquity of Incidence is requisite tocause a total Reflexion. For as the Sines are which measure theRefraction, so is the Sine of Incidence at which the total Reflexionbegins, to the Radius of the Circle; and consequently that Angle ofIncidence is least where there is the greatest difference of the Sines.Thus in the passing of Light out of Water into Air, where the Refractionis measured by the Ratio of the Sines 3 to 4, the total Reflexion beginswhen the Angle of Incidence is about 48 Degrees 35 Minutes. In passingout of Glass into Air, where the Refraction is measured by the Ratio ofthe Sines 20 to 31, the total Reflexion begins when the Angle ofIncidence is 40 Degrees 10 Minutes; and so in passing out of Crystal, ormore strongly refracting Mediums into Air, there is still a lessobliquity requisite to cause a total reflexion. Superficies therefore[Pg 247]which refract most do soonest reflect all the Light which is incident onthem, and so must be allowed most strongly reflexive.

But the truth of this Proposition will farther appear by observing, thatin the Superficies interceding two transparent Mediums, (such as areAir, Water, Oil, common Glass, Crystal, metalline Glasses, IslandGlasses, white transparent Arsenick, Diamonds, &c.) the Reflexion isstronger or weaker accordingly, as the Superficies hath a greater orless refracting Power. For in the Confine of Air and Sal-gem 'tisstronger than in the Confine of Air and Water, and still stronger in theConfine of Air and common Glass or Crystal, and stronger in the Confineof 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 refractingLiquors of well rectified Oil of Vitriol or Spirit of Turpentine. IfWater be distinguish'd into two parts by any imaginary Surface, theReflexion in the Confine of those two parts is none at all. In theConfine of Water and Ice 'tis very little; in that of Water and Oil 'tissomething greater; in that of Water and Sal-gem still greater; and inthat of Water and Glass, or Crystal or other denser Substances stillgreater, accordingly as those Mediums differ more or less in theirrefracting Powers. Hence in the Confine of common Glass and Crystal,there ought to be a weak Reflexion, and a stronger Reflexion in theConfine of common and metalline Glass; though[Pg 248] I have not yet triedthis. But in the Confine of two Glasses of equal density, there is notany sensible Reflexion; as was shewn in the first Observation. And thesame may be understood of the Superficies interceding two Crystals, ortwo 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 externalSuperficies, where they are adjacent to other Mediums of a differentdensity, is because all their contiguous parts have one and the samedegree of density.

Prop. II.

The least parts of almost all natural Bodies are in some measuretransparent: And the Opacity of those Bodies ariseth from the multitudeof Reflexions caused in their internal Parts.

That this is so has been observed by others, and will easily be grantedby them that have been conversant with Microscopes. And it may be alsotried by applying any substance to a hole through which some Light isimmitted into a dark Room. For how opake soever that Substance may seemin the open Air, it will by that means appear very manifestlytransparent, if it be of a sufficient thinness. Only white metallineBodies must be excepted, which by reason of their excessive density seemto reflect almost all the Light incident on their first Superficies;unless by solution in Menstruums they[Pg 249] be reduced into very smallParticles, and then they become transparent.

Prop. III.

Between the parts of opake and colour'd Bodies are many Spaces, eitherempty, or replenish'd with Mediums of other Densities; as Water betweenthe tinging Corpuscles wherewith any Liquor is impregnated, Air betweenthe aqueous Globules that constitute Clouds or Mists; and for the mostpart Spaces void of both Air and Water, but yet perhaps not wholly voidof all Substance, between the parts of hard Bodies.

The truth of this is evinced by the two precedent Propositions: For bythe second Proposition there are many Reflexions made by the internalparts of Bodies, which, by the first Proposition, would not happen ifthe parts of those Bodies were continued without any such Intersticesbetween them; because Reflexions are caused only in Superficies, whichintercede Mediums of a differing density, byProp. 1.

But farther, that this discontinuity of parts is the principal Cause ofthe opacity of Bodies, will appear by considering, that opake Substancesbecome transparent by filling their Pores with any Substance of equal oralmost equal density with their parts. Thus Paper dipped in Water orOil, theOculus Mundi Stone steep'd in Water, Linnen Cloth oiled orvarnish'd, and many other Substances soaked in such[Pg 250] Liquors as willintimately pervade their little Pores, become by that means moretransparent than otherwise; so, on the contrary, the most transparentSubstances, may, by evacuating their Pores, or separating their parts,be render'd sufficiently opake; as Salts or wet Paper, or theOculusMundi Stone by being dried, Horn by being scraped, Glass by beingreduced to Powder, or otherwise flawed; Turpentine by being stirredabout with Water till they mix imperfectly, and Water by being form'dinto many small Bubbles, either alone in the form of Froth, or byshaking it together with Oil of Turpentine, or Oil Olive, or with someother convenient Liquor, with which it will not perfectly incorporate.And to the increase of the opacity of these Bodies, it conducessomething, that by the 23d Observation the Reflexions of very thintransparent Substances are considerably stronger than those made by thesame Substances of a greater thickness.

Prop. IV.

The Parts of Bodies and their Interstices must not be less than of somedefinite 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 perfectlytransparent. And you may also remember, that in the eighth Observationthere was no sensible reflexion at the Superficies of theObject-glasses, where they were very[Pg 251] near one another, though they didnot absolutely touch. And in the 17th Observation the Reflexion of theWater-bubble where it became thinnest was almost insensible, so as tocause very black Spots to appear on the top of the Bubble, by the wantof reflected Light.

On these grounds I perceive it is that Water, Salt, Glass, Stones, andsuch like Substances, are transparent. For, upon divers Considerations,they seem to be as full of Pores or Interstices between their parts asother Bodies are, but yet their Parts and Interstices to be too small tocause 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 samegrounds 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, orbroken into Fragments, of the same thickness with the Plate; I see noreason why every Thread or Fragment should not keep its Colour, and byconsequence why a heap of those Threads or Fragments should notconstitute a Mass or Powder of the same Colour, which the Plateexhibited before it was broken. And the parts of all natural Bodiesbeing like so many[Pg 252] Fragments of a Plate, must on the same groundsexhibit 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 ofPeacocks Tails, do, in the very same part of the Feather, appear ofseveral Colours in several Positions of the Eye, after the very samemanner that thin Plates were found to do in the 7th and 19thObservations, and therefore their Colours arise from the thinness of thetransparent parts of the Feathers; that is, from the slenderness of thevery fine Hairs, orCapillamenta, which grow out of the sides of thegrosser lateral Branches or Fibres of those Feathers. And to the samepurpose 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'dFibres of some Silks, by varying the Position of the Eye, do vary theirColour. Also the Colours of Silks, Cloths, and other Substances, whichWater or Oil can intimately penetrate, become more faint and obscure bybeing immerged in those Liquors, and recover their Vigor again by beingdried; much after the manner declared of thin Bodies in the 10th and21st Observations. Leaf-Gold, some sorts of painted Glass, the InfusionofLignum 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 theirColours a little changed, by being very elaborately and finely ground.Where I see not[Pg 253] what can be justly pretended for those changes, besidesthe breaking of their parts into less parts by that contrition, afterthe same manner that the Colour of a thin Plate is changed by varyingits thickness. For which reason also it is that the colour'd Flowers ofPlants and Vegetables, by being bruised, usually become more transparentthan 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, veryodd and remarkable Productions and Changes of Colours may be effected,of which no cause can be more obvious and rational than that the salineCorpuscles of one Liquor do variously act upon or unite with the tingingCorpuscles of another, so as to make them swell, or shrink, (whereby notonly their bulk but their density also may be changed,) or to dividethem into smaller Corpuscles, (whereby a colour'd Liquor may becometransparent,) or to make many of them associate into one cluster,whereby two transparent Liquors may compose a colour'd one. For we seehow apt those saline Menstruums are to penetrate and dissolve Substancesto which they are applied, and some of them to precipitate what othersdissolve. In like manner, if we consider the various Phænomena of theAtmosphere, we may observe, that when Vapours are first raised, theyhinder not the transparency of the Air, being divided into parts toosmall to cause any Reflexion in their Superficies. But when in order tocompose drops of Rain they begin to coalesce and constitute Globules ofall intermediate[Pg 254] sizes, those Globules, when they become of convenientsize to reflect some Colours and transmit others, may constitute Cloudsof various Colours according to their sizes. And I see not what can berationally conceived in so transparent a Substance as Water for theproduction of these Colours, besides the various sizes of its fluid andglobular Parcels.

Prop. VI.

The parts of Bodies on which their Colours depend, are denser than theMedium which pervades their Interstices.

This will appear by considering, that the Colour of a Body depends notonly on the Rays which are incident perpendicularly on its parts, but onthose also which are incident at all other Angles. And that according tothe 7th Observation, a very little variation of obliquity will changethe reflected Colour, where the thin Body or small Particles is rarerthan the ambient Medium, insomuch that such a small Particle will atdiversly oblique Incidences reflect all sorts of Colours, in so great avariety that the Colour resulting from them all, confusedly reflectedfrom a heap of such Particles, must rather be a white or grey than anyother Colour, or at best it must be but a very imperfect and dirtyColour. Whereas if the thin Body or small Particle be much denser thanthe ambient Medium, the Colours, according to the 19th Observation, areso little changed by the variation of obliquity, that the Rays which[Pg 255]are reflected least obliquely may predominate over the rest, so much asto cause a heap of such Particles to appear very intensely of theirColour.

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

Prop. VII.

The bigness of the component parts of natural Bodies may be conjecturedby their Colours.

For since the parts of these Bodies, byProp. 5. do most probablyexhibit the same Colours with a Plate of equal thickness, provided theyhave the same refractive density; and since their parts seem for themost part to have much the same density with Water or Glass, as by manycircumstances is obvious to collect; to determine the sizes of thoseparts, you need only have recourse to the precedent Tables, in which thethickness of Water or Glass exhibiting any Colour is expressed. Thus ifit be desired to know the diameter of a Corpuscle, which being of equaldensity with Glass shall reflect green of the third Order; the Number16-1/4 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 anyBody is. And for this end we must have recourse to the 4th and 18th[Pg 256]Observations; from whence may be collected these particulars.

Scarlets, and otherreds,oranges, andyellows, if they be pureand intense, are most probably of the second order. Those of the firstand third order also may be pretty good; only the yellow of the firstorder is faint, and the orange and red of the third Order have a greatMixture of violet and blue.

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

Blues andPurples may be either of the second or third Order, butthe best are of the third. Thus the Colour of Violets seems to be ofthat Order, because their Syrup by acid Liquors turns red, and byurinous and alcalizate turns green. For since it is of the Nature ofAcids to dissolve or attenuate, and of[Pg 257] Alcalies to precipitate orincrassate, if the Purple Colour of the Syrup was of the second Order,an acid Liquor by attenuating its tinging Corpuscles would change it toa red of the first Order, and an Alcali by incrassating them wouldchange it to a green of the second Order; which red and green,especially the green, seem too imperfect to be the Colours produced bythese 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 anyInconvenience be allow'd.

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

Theblue of the first Order, though very faint and little, maypossibly be the Colour of some Substances; and particularly the azureColour of the Skies seems to be of this Order. For all Vapours when theybegin to condense and coalesce into small Parcels, become first of thatBigness, whereby such an Azure must be reflected before they canconstitute Clouds of other Colours. And so this being the first Colourwhich Vapours begin to reflect, it ought to be the Colour of the finestand most transparent Skies, in which Vapours are not arrived to thatGrossness requisite to reflect other Colours, as we find it is byExperience.[Pg 258]

Whiteness, if most intense and luminous, is that of the first Order,if less strong and luminous, a Mixture of the Colours of several Orders.Of this last kind is the Whiteness of Froth, Paper, Linnen, and mostwhite Substances; of the former I reckon that of white Metals to be. Forwhilst the densest of Metals, Gold, if foliated, is transparent, and allMetals become transparent if dissolved in Menstruums or vitrified, theOpacity of white Metals ariseth not from their Density alone. They beingless dense than Gold would be more transparent than it, did not someother Cause concur with their Density to make them opake. And this CauseI take to be such a Bigness of their Particles as fits them to reflectthe white of the first order. For, if they be of other Thicknesses theymay reflect other Colours, as is manifest by the Colours which appearupon hot Steel in tempering it, and sometimes upon the Surface of meltedMetals in the Skin or Scoria which arises upon them in their cooling.And as the white of the first order is the strongest which can be madeby Plates of transparent Substances, so it ought to be stronger in thedenser Substances of Metals than in the rarer of Air, Water, and Glass.Nor do I see but that metallick Substances of such a Thickness as mayfit them to reflect the white of the first order, may, by reason oftheir great Density (according to the Tenor of the first of thesePropositions) reflect all the Light incident upon them, and so be asopake and splendent as it's possible for any Body to be. Gold, or Coppermix'd with less than half their Weight of[Pg 259] Silver, or Tin, or Regulus ofAntimony, in fusion, or amalgamed with a very little Mercury, becomewhite; which shews both that the Particles of white Metals have muchmore Superficies, and so are smaller, than those of Gold and Copper, andalso that they are so opake as not to suffer the Particles of Gold orCopper to shine through them. Now it is scarce to be doubted but thatthe Colours of Gold and Copper are of the second and third order, andtherefore the Particles of white Metals cannot be much bigger than isrequisite to make them reflect the white of the first order. TheVolatility of Mercury argues that they are not much bigger, nor may theybe much less, lest they lose their Opacity, and become eithertransparent as they do when attenuated by Vitrification, or by Solutionin Menstruums, or black as they do when ground smaller, by rubbingSilver, or Tin, or Lead, upon other Substances to draw black Lines. Thefirst and only Colour which white Metals take by grinding theirParticles smaller, is black, and therefore their white ought to be thatwhich borders upon the black Spot in the Center of the Rings of Colours,that is, the white of the first order. But, if you would hence gatherthe Bigness of metallick Particles, you must allow for their Density.For were Mercury transparent, its Density is such that the Sine ofIncidence upon it (by my Computation) would be to the Sine of itsRefraction, as 71 to 20, or 7 to 2. And therefore the Thickness of itsParticles, that they may exhibit the same Colours with those of Bubblesof Water, ought to be less than the Thickness of the[Pg 260] Skin of thoseBubbles in the Proportion of 2 to 7. Whence it's possible, that theParticles of Mercury may be as little as the Particles of sometransparent and volatile Fluids, and yet reflect the white of the firstorder.

Lastly, for the production ofblack, the Corpuscles must be less thanany of those which exhibit Colours. For at all greater sizes there istoo much Light reflected to constitute this Colour. But if they besupposed a little less than is requisite to reflect the white and veryfaint blue of the first order, they will, according to the 4th, 8th,17th and 18th Observations, reflect so very little Light as to appearintensely black, and yet may perhaps variously refract it to and frowithin themselves so long, until it happen to be stifled and lost, bywhich means they will appear black in all positions of the Eye withoutany transparency. And from hence may be understood why Fire, and themore subtile dissolver Putrefaction, by dividing the Particles ofSubstances, turn them to black, why small quantities of black Substancesimpart their Colour very freely and intensely to other Substances towhich they are applied; the minute Particles of these, by reason oftheir very great number, easily overspreading the gross Particles ofothers; why Glass ground very elaborately with Sand on a Copper Plate,'till it be well polish'd, makes the Sand, together with what is wornoff from the Glass and Copper, become very black: why black Substancesdo soonest of all others become hot in the Sun's Light and burn, (whichEffect may proceed[Pg 261] partly from the multitude of Refractions in a littleroom, and partly from the easy Commotion of so very small Corpuscles;)and why blacks are usually a little inclined to a bluish Colour. Forthat they are so may be seen by illuminating white Paper by Lightreflected from black Substances. For the Paper will usually appear of abluish white; and the reason is, that black borders in the obscure blueof the order described in the 18th Observation, and therefore reflectsmore Rays of that Colour than of any other.

In these Descriptions I have been the more particular, because it is notimpossible but that Microscopes may at length be improved to thediscovery of the Particles of Bodies on which their Colours depend, ifthey are not already in some measure arrived to that degree ofperfection. For if those Instruments are or can be so far improved aswith sufficient distinctness to represent Objects five or six hundredtimes bigger than at a Foot distance they appear to our naked Eyes, Ishould hope that we might be able to discover some of the greatest ofthose Corpuscles. And by one that would magnify three or four thousandtimes perhaps they might all be discover'd, but those which produceblackness. In the mean while I see nothing material in this Discoursethat may rationally be doubted of, excepting this Position: Thattransparent Corpuscles of the same thickness and density with a Plate,do exhibit the same Colour. And this I would have understood not withoutsome Latitude, as well because those Corpuscles may be of irregularFigures, and many Rays[Pg 262] must be obliquely incident on them, and so havea shorter way through them than the length of their Diameters, asbecause the straitness of the Medium put in on all sides within suchCorpuscles may a little alter its Motions or other qualities on whichthe Reflexion depends. But yet I cannot much suspect the last, because Ihave observed of some small Plates of Muscovy Glass which were of aneven thickness, that through a Microscope they have appeared of the sameColour at their edges and corners where the included Medium wasterminated, which they appeared of in other places. However it will addmuch to our Satisfaction, if those Corpuscles can be discover'd withMicroscopes; which if we shall at length attain to, I fear it will bethe utmost improvement of this Sense. For it seems impossible to see themore secret and noble Works of Nature within the Corpuscles by reason oftheir transparency.

Prop. VIII.

The Cause of Reflexion is not the impinging of Light on the solid orimpervious parts of Bodies, as is commonly believed.

This will appear by the following Considerations. First, That in thepassage of Light out of Glass into Air there is a Reflexion as strong asin its passage out of Air into Glass, or rather a little stronger, andby many degrees stronger than in its passage out of Glass into Water.And it seems not probable that Air should have more strongly reflecting[Pg 263]parts than Water or Glass. But if that should possibly be supposed, yetit will avail nothing; for the Reflexion is as strong or stronger whenthe Air is drawn away from the Glass, (suppose by the Air-Pump inventedbyOtto Gueriet, and improved and made useful by Mr.Boyle) as whenit is adjacent to it. Secondly, If Light in its passage out of Glassinto Air be incident more obliquely than at an Angle of 40 or 41 Degreesit is wholly reflected, if less obliquely it is in great measuretransmitted. Now it is not to be imagined that Light at one degree ofobliquity should meet with Pores enough in the Air to transmit thegreater part of it, and at another degree of obliquity should meet withnothing but parts to reflect it wholly, especially considering that inits passage out of Air into Glass, how oblique soever be its Incidence,it finds Pores enough in the Glass to transmit a great part of it. Ifany Man suppose that it is not reflected by the Air, but by the outmostsuperficial parts of the Glass, there is still the same difficulty:Besides, that such a Supposition is unintelligible, and will also appearto be false by applying Water behind some part of the Glass instead ofAir. For so in a convenient obliquity of the Rays, suppose of 45 or 46Degrees, at which they are all reflected where the Air is adjacent tothe Glass, they shall be in great measure transmitted where the Water isadjacent to it; which argues, that their Reflexion or Transmissiondepends on the constitution of the Air and Water behind the Glass, andnot on the striking of the Rays upon the parts of the Glass.[Pg 264] Thirdly,If the Colours made by a Prism placed at the entrance of a Beam of Lightinto a darken'd Room be successively cast on a second Prism placed at agreater distance from the former, in such manner that they are all alikeincident upon it, the second Prism may be so inclined to the incidentRays, that those which are of a blue Colour shall be all reflected byit, and yet those of a red Colour pretty copiously transmitted. Now ifthe Reflexion be caused by the parts of Air or Glass, I would ask, whyat the same Obliquity of Incidence the blue should wholly impinge onthose parts, so as to be all reflected, and yet the red find Poresenough to be in a great measure transmitted. Fourthly, Where two Glassestouch one another, there is no sensible Reflexion, as was declared inthe first Observation; and yet I see no reason why the Rays should notimpinge on the parts of Glass, as much when contiguous to other Glass aswhen contiguous to Air. Fifthly, When the top of a Water-Bubble (in the17th Observation,) by the continual subsiding and exhaling of the Watergrew very thin, there was such a little and almost insensible quantityof Light reflected from it, that it appeared intensely black; whereasround about that black Spot, where the Water was thicker, the Reflexionwas so strong as to make the Water seem very white. Nor is it only atthe least thickness of thin Plates or Bubbles, that there is no manifestReflexion, but at many other thicknesses continually greater andgreater. For in the 15th Observation the Rays of the same Colour were byturns transmitted at one thickness,[Pg 265] and reflected at another thickness,for an indeterminate number of Successions. And yet in the Superficiesof the thinned Body, where it is of any one thickness, there are as manyparts for the Rays to impinge on, as where it is of any other thickness.Sixthly, If Reflexion were caused by the parts of reflecting Bodies, itwould be impossible for thin Plates or Bubbles, at one and the sameplace, to reflect the Rays of one Colour, and transmit those of another,as they do according to the 13th and 15th Observations. For it is not tobe imagined that at one place the Rays which, for instance, exhibit ablue Colour, should have the fortune to dash upon the parts, and thosewhich exhibit a red to hit upon the Pores of the Body; and then atanother place, where the Body is either a little thicker or a littlethinner, that on the contrary the blue should hit upon its pores, andthe red upon its parts. Lastly, Were the Rays of Light reflected byimpinging on the solid parts of Bodies, their Reflexions from polish'dBodies could not be so regular as they are. For in polishing Glass withSand, Putty, or Tripoly, it is not to be imagined that those Substancescan, by grating and fretting the Glass, bring all its least Particles toan accurate Polish; so that all their Surfaces shall be truly plain ortruly spherical, and look all the same way, so as together to composeone even Surface. The smaller the Particles of those Substances are, thesmaller will be the Scratches by which they continually fret and wearaway the Glass until it be polish'd; but be they never so small they canwear away the Glass no[Pg 266] otherwise than by grating and scratching it, andbreaking the Protuberances; and therefore polish it no otherwise than bybringing its roughness to a very fine Grain, so that the Scratches andFrettings of the Surface become too small to be visible. And thereforeif Light were reflected by impinging upon the solid parts of the Glass,it would be scatter'd as much by the most polish'd Glass as by theroughest. So then it remains a Problem, how Glass polish'd by frettingSubstances can reflect Light so regularly as it does. And this Problemis scarce otherwise to be solved, than by saying, that the Reflexion ofa Ray is effected, not by a single point of the reflecting Body, but bysome power of the Body which is evenly diffused all over its Surface,and by which it acts upon the Ray without immediate Contact. For thatthe parts of Bodies do act upon Light at a distance shall be shewnhereafter.

Now if Light be reflected, not by impinging on the solid parts ofBodies, but by some other principle; it's probable that as many of itsRays as impinge on the solid parts of Bodies are not reflected butstifled and lost in the Bodies. For otherwise we must allow two sorts ofReflexions. Should all the Rays be reflected which impinge on theinternal parts of clear Water or Crystal, those Substances would ratherhave a cloudy Colour than a clear Transparency. To make Bodies lookblack, it's necessary that many Rays be stopp'd, retained, and lost inthem; and it seems not probable that any Rays can be[Pg 267] stopp'd andstifled in them which do not impinge on their parts.

And hence we may understand that Bodies are much more rare and porousthan is commonly believed. Water is nineteen times lighter, and byconsequence nineteen times rarer than Gold; and Gold is so rare as veryreadily and without the least opposition to transmit the magnetickEffluvia, and easily to admit Quicksilver into its Pores, and to letWater pass through it. For a concave Sphere of Gold filled with Water,and solder'd up, has, upon pressing the Sphere with great force, let theWater squeeze through it, and stand all over its outside in multitudesof small Drops, like Dew, without bursting or cracking the Body of theGold, as I have been inform'd by an Eye witness. From all which we mayconclude, that Gold has more Pores than solid parts, and by consequencethat Water has above forty times more Pores than Parts. And he thatshall find out an Hypothesis, by which Water may be so rare, and yet notbe capable of compression by force, may doubtless by the same Hypothesismake Gold, and Water, and all other Bodies, as much rarer as he pleases;so that Light may find a ready passage through transparent Substances.

The Magnet acts upon Iron through all dense Bodies not magnetick nor redhot, without any diminution of its Virtue; as for instance, throughGold, Silver, Lead, Glass, Water. The gravitating Power of the Sun istransmitted through the vast Bodies of the Planets without anydiminution, so as to act upon[Pg 268] all their parts to their very centerswith the same Force and according to the same Laws, as if the part uponwhich it acts were not surrounded with the Body of the Planet, The Raysof Light, whether they be very small Bodies projected, or only Motion orForce propagated, are moved in right Lines; and whenever a Ray of Lightis by any Obstacle turned out of its rectilinear way, it will neverreturn into the same rectilinear way, unless perhaps by very greataccident. And yet Light is transmitted through pellucid solid Bodies inright Lines to very great distances. How Bodies can have a sufficientquantity of Pores for producing these Effects is very difficult toconceive, but perhaps not altogether impossible. For the Colours ofBodies arise from the Magnitudes of the Particles which reflect them, aswas explained above. Now if we conceive these Particles of Bodies to beso disposed amongst themselves, that the Intervals or empty Spacesbetween them may be equal in magnitude to them all; and that theseParticles may be composed of other Particles much smaller, which have asmuch empty Space between them as equals all the Magnitudes of thesesmaller Particles: And that in like manner these smaller Particles areagain composed of others much smaller, all which together are equal toall the Pores or empty Spaces between them; and so on perpetually tillyou come to solid Particles, such as have no Pores or empty Spaceswithin them: And if in any gross Body there be, for instance, three suchdegrees of Particles, the least of which are solid; this Body will haveseven[Pg 269] times more Pores than solid Parts. But if there be four suchdegrees of Particles, the least of which are solid, the Body will havefifteen times more Pores than solid Parts. If there be five degrees, theBody will have one and thirty times more Pores than solid Parts. If sixdegrees, the Body will have sixty and three times more Pores than solidParts. And so on perpetually. And there are other ways of conceiving howBodies may be exceeding porous. But what is really their inward Frame isnot yet known to us.

Prop. IX.

Bodies reflect and refract Light by one and the same power, variouslyexercised in various Circumstances.

This appears by several Considerations. First, Because when Light goesout of Glass into Air, as obliquely as it can possibly do. If itsIncidence be made still more oblique, it becomes totally reflected. Forthe power of the Glass after it has refracted the Light as obliquely asis possible, if the Incidence be still made more oblique, becomes toostrong to let any of its Rays go through, and by consequence causestotal Reflexions. Secondly, Because Light is alternately reflected andtransmitted by thin Plates of Glass for many Successions, accordingly asthe thickness of the Plate increases in an arithmetical Progression. Forhere the thickness of the Glass determines whether that Power by whichGlass acts upon Light shall cause it to be reflected, or[Pg 270] suffer it tobe transmitted. And, Thirdly, because those Surfaces of transparentBodies which have the greatest refracting power, reflect the greatestquantity of Light, as was shewn in the first Proposition.

Prop. X.

If Light be swifter in Bodies than in Vacuo, in the proportion of theSines which measure the Refraction of the Bodies, the Forces of theBodies to reflect and refract Light, are very nearly proportional to thedensities of the same Bodies; excepting that unctuous and sulphureousBodies refract more than others of this same density.

Let AB represent the refracting plane Surface of any Body, and IC a Rayincident very obliquely upon the Body in C, so that the Angle ACI may beinfinitely little, and let CR be the refracted Ray. From a given Point Bperpendicular to the refracting Surface erect BR meeting with therefracting Ray CR in R, and if CR represent the Motion of the refractedRay, and this Motion be distinguish'd into two Motions CB and BR,whereof CB is parallel to the refracting Plane, and BR perpendicular toit: CB[Pg 271] shall represent the Motion of the incident Ray, and BR theMotion generated by the Refraction, as Opticians have of late explain'd.

Now if any Body or Thing, in moving through any Space of a given breadthterminated on both sides by two parallel Planes, be urged forward in allparts of that Space by Forces tending directly forwards towards the lastPlane, and before its Incidence on the first Plane, had no Motiontowards it, or but an infinitely little one; and if the Forces in allparts of that Space, between the Planes, be at equal distances from thePlanes equal to one another, but at several distances be bigger or lessin any given Proportion, the Motion generated by the Forces in the wholepassage of the Body or thing through that Space shall be in asubduplicate Proportion of the Forces, as Mathematicians will easilyunderstand. And therefore, if the Space of activity of the refractingSuperficies of the Body be consider'd as such a Space, the Motion of theRay generated by the refracting Force of the Body, during its passagethrough that Space, that is, the Motion BR, must be in subduplicateProportion of that refracting Force. I say therefore, that the Square ofthe Line BR, and by consequence the refracting Force of the Body, isvery nearly as the density of the same Body. For this will appear by thefollowing Table, wherein the Proportion of the Sines which measure theRefractions of several Bodies, the Square of BR, supposing CB an unite,the Densities of the Bodies estimated by their Specifick Gravities, andtheir Refractive Power in[Pg 272] respect of their Densities are set down inseveral Columns.

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

The Refraction of the Air in this Table is determin'd[Pg 273] by that of theAtmosphere observed by Astronomers. For, if Light pass through manyrefracting Substances or Mediums gradually denser and denser, andterminated with parallel Surfaces, the Sum of all the Refractions willbe equal to the single Refraction which it would have suffer'd inpassing immediately out of the first Medium into the last. And thisholds true, though the Number of the refracting Substances be increasedto Infinity, and the Distances from one another as much decreased, sothat the Light may be refracted in every Point of its Passage, and bycontinual Refractions bent into a Curve-Line. And therefore the wholeRefraction of Light in passing through the Atmosphere from the highestand rarest Part thereof down to the lowest and densest Part, must beequal to the Refraction which it would suffer in passing at likeObliquity out of a Vacuum immediately into Air of equal Density withthat in the lowest Part of the Atmosphere.

Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal,Vulgar Glass (that is, Sand melted together) and Glass of Antimony,which are terrestrial stony alcalizate Concretes, and Air which probablyarises from such Substances by Fermentation, be Substances verydiffering from one another in Density, yet by this Table, they havetheir refractive Powers almost in the same Proportion to one another astheir Densities are, excepting that the Refraction of that strangeSubstance, Island Crystal is a little bigger than the rest. Andparticularly Air, which is 3500 Times rarer than the Pseudo-Topaz,[Pg 274] and4400 Times rarer than Glass of Antimony, and 2000 Times rarer than theSelenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding itsrarity the same refractive Power in respect of its Density which thosevery dense Substances have in respect of theirs, excepting so far asthose differ from one another.

Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit ofTurpentine and Amber, which are fat sulphureous unctuous Bodies, and aDiamond, which probably is an unctuous Substance coagulated, have theirrefractive Powers in Proportion to one another as their Densitieswithout any considerable Variation. But the refractive Powers of theseunctuous Substances are two or three Times greater in respect of theirDensities than the refractive Powers of the former Substances in respectof theirs.

Water has a refractive Power in a middle degree between those two sortsof Substances, and probably is of a middle nature. For out of it growall vegetable and animal Substances, which consist as well ofsulphureous fat and inflamable Parts, as of earthy lean and alcalizateones.

Salts and Vitriols have refractive Powers in a middle degree betweenthose of earthy Substances and Water, and accordingly are composed ofthose two sorts of Substances. For by distillation and rectification oftheir Spirits a great Part of them goes into Water, and a great Partremains behind in the form of a dry fix'd Earth capable ofVitrification.

Spirit of Wine has a refractive Power in a middle[Pg 275] degree between thoseof Water and oily Substances, and accordingly seems to be composed ofboth, united by Fermentation; the Water, by means of some saline Spiritswith which 'tis impregnated, dissolving the Oil, and volatizing it bythe Action. For Spirit of Wine is inflamable by means of its oily Parts,and being distilled often from Salt of Tartar, grow by everydistillation more and more aqueous and phlegmatick. And Chymistsobserve, that Vegetables (as Lavender, Rue, Marjoram, &c.) distilledper se, before fermentation yield Oils without any burning Spirits,but after fermentation yield ardent Spirits without Oils: Which shews,that their Oil is by fermentation converted into Spirit. They find also,that if Oils be poured in a small quantity upon fermentating Vegetables,they distil over after fermentation in the form of Spirits.

So then, by the foregoing Table, all Bodies seem to have theirrefractive Powers proportional to their Densities, (or very nearly;)excepting so far as they partake more or less of sulphureous oilyParticles, and thereby have their refractive Power made greater or less.Whence it seems rational to attribute the refractive Power of all Bodieschiefly, if not wholly, to the sulphureous Parts with which they abound.For it's probable that all Bodies abound more or less with Sulphurs. Andas Light congregated by a Burning-glass acts most upon sulphureousBodies, to turn them into Fire and Flame; so, since all Action ismutual, Sulphurs ought to act most upon Light. For that the actionbetween Light and[Pg 276] Bodies is mutual, may appear from this Consideration;That the densest Bodies which refract and reflect Light most strongly,grow hottest in the Summer Sun, by the action of the refracted orreflected Light.

I have hitherto explain'd the power of Bodies to reflect and refract,and shew'd, that thin transparent Plates, Fibres, and Particles, do,according to their several thicknesses and densities, reflect severalsorts of Rays, and thereby appear of several Colours; and by consequencethat nothing more is requisite for producing all the Colours of naturalBodies, than the several sizes and densities of their transparentParticles. But whence it is that these Plates, Fibres, and Particles,do, according to their several thicknesses and densities, reflectseveral sorts of Rays, I have not yet explain'd. To give some insightinto this matter, and make way for understanding the next part of thisBook, I shall conclude this part with a few more Propositions. Thosewhich preceded respect the nature of Bodies, these the nature of Light:For both must be understood, before the reason of their Actions upon oneanother can be known. And because the last Proposition depended upon thevelocity of Light, I will begin with a Proposition of that kind.[Pg 277]

Prop. XI.

Light is propagated from luminous Bodies in time, and spends aboutseven or eight Minutes of an Hour in passing from the Sun to the Earth.

This was observed first byRoemer, and then by others, by means of theEclipses of the Satellites ofJupiter. For these Eclipses, when theEarth is between the Sun andJupiter, happen about seven or eightMinutes sooner than they ought to do by the Tables, and when the Earthis beyond the Sun they happen about seven or eight Minutes later thanthey ought to do; the reason being, that the Light of the Satellites hasfarther to go in the latter case than in the former by the Diameter ofthe Earth's Orbit. Some inequalities of time may arise from theExcentricities of the Orbs of the Satellites; but those cannot answer inall the Satellites, and at all times to the Position and Distance of theEarth from the Sun. The mean motions ofJupiter's Satellites is alsoswifter in his descent from his Aphelium to his Perihelium, than in hisascent in the other half of his Orb. But this inequality has no respectto the position of the Earth, and in the three interior Satellites isinsensible, as I find by computation from the Theory of their Gravity.[Pg 278]

Prop. XII.

Every Ray of Light in its passage through any refracting Surface is putinto a certain transient Constitution or State, which in the progress ofthe Ray returns at equal Intervals, and disposes the Ray at every returnto be easily transmitted through the next refracting Surface, andbetween the returns to be easily reflected by it.

This is manifest by the 5th, 9th, 12th, and 15th Observations. For bythose Observations it appears, that one and the same sort of Rays atequal Angles of Incidence on any thin transparent Plate, is alternatelyreflected and transmitted for many Successions accordingly as thethickness of the Plate increases in arithmetical Progression of theNumbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, &c. so that if the first Reflexion(that which makes the first or innermost of the Rings of Colours theredescribed) be made at the thickness 1, the Rays shall be transmitted atthe thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the centralSpot and Rings of Light, which appear by transmission, and be reflectedat the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings whichappear by Reflexion. And this alternate Reflexion and Transmission, as Igather by the 24th Observation, continues for above an hundredvicissitudes, and by the Observations in the next part of this Book, formany thousands, being propagated from one Surface of a Glass Plate tothe other, though the thickness[Pg 279] of the Plate be a quarter of an Inch orabove: So that this alternation seems to be propagated from everyrefracting Surface to all distances without end or limitation.

This alternate Reflexion and Refraction depends on both the Surfaces ofevery thin Plate, because it depends on their distance. By the 21stObservation, if either Surface of a thin Plate ofMuscovy Glass bewetted, the Colours caused by the alternate Reflexion and Refractiongrow faint, and therefore it depends on them both.

It is therefore perform'd at the second Surface; for if it wereperform'd at the first, before the Rays arrive at the second, it wouldnot depend on the second.

It is also influenced by some action or disposition, propagated from thefirst to the second, because otherwise at the second it would not dependon the first. And this action or disposition, in its propagation,intermits and returns by equal Intervals, because in all its progress itinclines the Ray at one distance from the first Surface to be reflectedby the second, at another to be transmitted by it, and that by equalIntervals for innumerable vicissitudes. And because the Ray is disposedto Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission atthe distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through thefirst Surface, is at the distance 0, and it is transmitted through bothtogether, if their distance be infinitely little or much less than 1)the disposition to be transmitted at the distances 2, 4, 6, 8, 10,[Pg 280] &c.is to be accounted a return of the same disposition which the Ray firsthad at the distance 0, that is at its transmission through the firstrefracting Surface. All which is the thing I would prove.

What kind of action or disposition this is; Whether it consists in acirculating or a vibrating motion of the Ray, or of the Medium, orsomething else, I do not here enquire. Those that are averse fromassenting to any new Discoveries, but such as they can explain by anHypothesis, may for the present suppose, that as Stones by falling uponWater put the Water into an undulating Motion, and all Bodies bypercussion excite vibrations in the Air; so the Rays of Light, byimpinging on any refracting or reflecting Surface, excite vibrations inthe refracting or reflecting Medium or Substance, and by exciting themagitate the solid parts of the refracting or reflecting Body, and byagitating them cause the Body to grow warm or hot; that the vibrationsthus excited are propagated in the refracting or reflecting Medium orSubstance, much after the manner that vibrations are propagated in theAir for causing Sound, and move faster than the Rays so as to overtakethem; and that when any Ray is in that part of the vibration whichconspires with its Motion, it easily breaks through a refractingSurface, but when it is in the contrary part of the vibration whichimpedes its Motion, it is easily reflected; and, by consequence, thatevery Ray is successively disposed to be easily reflected, or easilytransmitted, by every vibration which overtakes it. But whether thisHypothesis be true or false[Pg 281] I do not here consider. I content my selfwith the bare Discovery, that the Rays of Light are by some cause orother alternately disposed to be reflected or refracted for manyvicissitudes.

DEFINITION.

The returns of the disposition of any Ray to be reflected I will callits Fits of easy Reflexion,and those of its disposition to betransmitted its Fits of easy Transmission,and the space it passesbetween every return and the next return, the Interval of its Fits.

Prop. XIII.

The reason why the Surfaces of all thick transparent Bodies reflectpart of the Light incident on them, and refract the rest, is, that someRays at their Incidence are in Fits of easy Reflexion, and others inFits of easy Transmission.

This may be gather'd from the 24th Observation, where the Lightreflected by thin Plates of Air and Glass, which to the naked Eyeappear'd evenly white all over the Plate, did through a Prism appearwaved with many Successions of Light and Darkness made by alternate Fitsof easy Reflexion and easy Transmission, the Prism severing anddistinguishing the Waves of which the white reflected Light wascomposed, as was explain'd above.[Pg 282]

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

In this Proposition I suppose the transparent Bodies to be thick;because if the thickness of the Body be much less than the Interval ofthe Fits of easy Reflexion and Transmission of the Rays, the Body losethits reflecting power. For if the Rays, which at their entering into theBody are put into Fits of easy Transmission, arrive at the farthestSurface of the Body before they be out of those Fits, they must betransmitted. And this is the reason why Bubbles of Water lose theirreflecting power when they grow very thin; and why all opake Bodies,when reduced into very small parts, become transparent.[Pg 283]

Prop. XIV.

Those Surfaces of transparent Bodies, which if the Ray be in a Fit ofRefraction do refract it most strongly, if the Ray be in a Fit ofReflexion do reflect it most easily.

For we shewed above, inProp. 8. that the cause of Reflexion is notthe impinging of Light on the solid impervious parts of Bodies, but someother power by which those solid parts act on Light at a distance. Weshewed also inProp. 9. that Bodies reflect and refract Light by oneand the same power, variously exercised in various circumstances; and inProp. 1. that the most strongly refracting Surfaces reflect the mostLight: All which compared together evince and rarify both this and thelast Proposition.

Prop. XV.

In any one and the same sort of Rays, emerging in any Angle out of anyrefracting Surface into one and the same Medium, the Interval of thefollowing Fits of easy Reflexion and Transmission are either accuratelyor very nearly, as the Rectangle of the Secant of the Angle ofRefraction, and of the Secant of another Angle, whose Sine is the firstof 106 arithmetical mean Proportionals, between the Sines of Incidenceand Refraction, counted from the Sine of Refraction.

Prop. XVI.

In several sorts of Rays emerging in equal Angles out of any refractingSurface into the same Medium, the Intervals of the following Fits ofeasy Reflexion and easy Transmission are either accurately, or verynearly, as the Cube-Roots of the Squares of the lengths of a Chord,which found the Notes in an Eight, sol, la, fa, sol, la, mi, fa, sol,with all their intermediate degrees answering to the Colours of thoseRays, according to the Analogy described in the seventh Experiment ofthe second Part of the first Book.

Prop. XVII.

If Rays of any sort pass perpendicularly into several Mediums, theIntervals of the Fits of easy Reflexion and Transmission in any oneMedium, are to those Intervals in any other, as the Sine of Incidence tothe Sine of Refraction, when the Rays pass out of the first of those twoMediums into the second.

Prop. XVIII.

If the Rays which paint the Colour in the Confine of yellow and orangepass perpendicularly out of any Medium into Air, the Intervals of theirFits of easy Reflexion are the 1/89000th part of an Inch. And of thesame length are the Intervals of their Fits of easy Transmission.

This is manifest by the 6th Observation. From these Propositions it iseasy to collect the Intervals of the Fits of easy Reflexion and easyTransmission of any sort of Rays refracted in any angle into any Medium;and thence to know, whether the Rays shall be reflected or transmittedat their subsequent Incidence upon any other pellucid Medium. Whichthing, being useful for understanding the next part of this Book, washere to be set down. And for the same reason I add the two followingPropositions.[Pg 286]

Prop. XIX.

If any sort of Rays falling on the polite Surface of any pellucidMedium be reflected back, the Fits of easy Reflexion, which they have atthe point of Reflexion, shall still continue to return; and the Returnsshall be at distances from the point of Reflexion in the arithmeticalprogression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between theseFits the Rays shall be in Fits of easy Transmission.

For since the Fits of easy Reflexion and easy Transmission are of areturning nature, there is no reason why these Fits, which continuedtill the Ray arrived at the reflecting Medium, and there inclined theRay to Reflexion, should there cease. And if the Ray at the point ofReflexion was in a Fit of easy Reflexion, the progression of thedistances of these Fits from that point must begin from 0, and so be ofthe Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of thedistances of the intermediate Fits of easy Transmission, reckon'd fromthe same point, must be in the progression of the odd Numbers 1, 3, 5,7, 9, &c. contrary to what happens when the Fits are propagated frompoints of Refraction.[Pg 287]

Prop. XX.

The Intervals of the Fits of easy Reflexion and easy Transmission,propagated from points of Reflexion into any Medium, are equal to theIntervals of the like Fits, which the same Rays would have, if refractedinto the same Medium in Angles of Refraction equal to their Angles ofReflexion.

For when Light is reflected by the second Surface of thin Plates, itgoes out afterwards freely at the first Surface to make the Rings ofColours which appear by Reflexion; and, by the freedom of its egress,makes the Colours of these Rings more vivid and strong than those whichappear on the other side of the Plates by the transmitted Light. Thereflected Rays are therefore in Fits of easy Transmission at theiregress; which would not always happen, if the Intervals of the Fitswithin the Plate after Reflexion were not equal, both in length andnumber, to their Intervals before it. And this confirms also theproportions set down in the former Proposition. For if the Rays both ingoing in and out at the first Surface be in Fits of easy Transmission,and the Intervals and Numbers of those Fits between the first and secondSurface, before and after Reflexion, be equal, the distances of the Fitsof easy Transmission from either Surface, must be in the sameprogression after Reflexion as before; that is, from the first Surfacewhich transmitted them in the progression of the even Numbers 0, 2, 4,6,[Pg 288] 8, &c. and from the second which reflected them, in that of the oddNumbers 1, 3, 5, 7, &c. But these two Propositions will become much moreevident by the Observations in the following part of this Book.

THE

SECOND BOOK

OPTICKS

PART IV.

Observations concerning the Reflexions and Colours of thick transparentpolish'd Plates.

There is no Glass or Speculum how well soever polished, but, besides theLight which it refracts or reflects regularly, scatters every wayirregularly a faint Light, by means of which the polish'd Surface, whenilluminated in a dark room by a beam of the Sun's Light, may be easilyseen in all positions of the Eye. There are certain Phænomena of thisscatter'd Light, which when I first observed them, seem'd very strangeand surprizing to me. My Observations were as follows.

Obs. 1. The Sun shining into my darken'd Chamber through a hole onethird of an Inch wide,[Pg 290] I let the intromitted beam of Light fallperpendicularly upon a Glass Speculum ground concave on one side andconvex on the other, to a Sphere of five Feet and eleven Inches Radius,and Quick-silver'd over on the convex side. And holding a white opakeChart, or a Quire of Paper at the center of the Spheres to which theSpeculum was ground, that is, at the distance of about five Feet andeleven Inches from the Speculum, in such manner, that the beam of Lightmight pass through a little hole made in the middle of the Chart to theSpeculum, and thence be reflected back to the same hole: I observed uponthe Chart four or five concentric Irises or Rings of Colours, likeRain-bows, encompassing the hole much after the manner that those, whichin the fourth and following Observations of the first part of this Bookappear'd between the Object-glasses, encompassed the black Spot, but yetlarger and fainter than those. These Rings as they grew larger andlarger became diluter and fainter, so that the fifth was scarce visible.Yet sometimes, when the Sun shone very clear, there appear'd faintLineaments of a sixth and seventh. If the distance of the Chart from theSpeculum was much greater or much less than that of six Feet, the Ringsbecame dilute and vanish'd. And if the distance of the Speculum from theWindow was much greater than that of six Feet, the reflected beam ofLight would be so broad at the distance of six Feet from the Speculumwhere the Rings appear'd, as to obscure one or two of the innermostRings. And therefore I usually placed the Speculum[Pg 291] at about six Feetfrom the Window; so that its Focus might there fall in with the centerof its concavity at the Rings upon the Chart. And this Posture is alwaysto be understood in the following Observations where no other isexpress'd.

Obs. 2. The Colours of these Rain-bows succeeded one another from thecenter outwards, in the same form and order with those which were madein the ninth Observation of the first Part of this Book by Light notreflected, but transmitted through the two Object-glasses. For, first,there was in their common center a white round Spot of faint Light,something broader than the reflected beam of Light, which beam sometimesfell upon the middle of the Spot, and sometimes by a little inclinationof the Speculum receded from the middle, and left the Spot white to thecenter.

This white Spot was immediately encompassed with a dark grey or russet,and that dark grey with the Colours of the first Iris; which Colours onthe inside next the dark grey were a little violet and indigo, and nextto that a blue, which on the outside grew pale, and then succeeded alittle greenish yellow, and after that a brighter yellow, and then onthe outward edge of the Iris a red which on the outside inclined topurple.

This Iris was immediately encompassed with a second, whose Colours werein order from the inside outwards, purple, blue, green, yellow, lightred, a red mix'd with purple.

Then immediately follow'd the Colours of the[Pg 292] third Iris, which were inorder outwards a green inclining to purple, a good green, and a red morebright than that of the former Iris.

The fourth and fifth Iris seem'd of a bluish green within, and redwithout, but so faintly that it was difficult to discern the Colours.

Obs. 3. Measuring the Diameters of these Rings upon the Chart asaccurately as I could, I found them also in the same proportion to oneanother with the Rings made by Light transmitted through the twoObject-glasses. For the Diameters of the four first of the bright Ringsmeasured between the brightest parts of their Orbits, at the distance ofsix Feet from the Speculum were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches,whose Squares are in arithmetical progression of the numbers 1, 2, 3, 4.If the white circular Spot in the middle be reckon'd amongst the Rings,and its central Light, where it seems to be most luminous, be putequipollent to an infinitely little Ring; the Squares of the Diametersof the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measuredalso the Diameters of the dark Circles between these luminous ones, andfound their Squares in the progression of the numbers 1/2, 1-1/2, 2-1/2,3-1/2, &c. the Diameters of the first four at the distance of six Feetfrom the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If thedistance of the Chart from the Speculum was increased or diminished, theDiameters of the Circles were increased or diminished proportionally.

Obs. 4. By the analogy between these Rings and those described in theObservations of the first Part[Pg 293] of this Book, I suspected that therewere many more of them which spread into one another, and by interferingmix'd their Colours, and diluted one another so that they could not beseen apart. I viewed them therefore through a Prism, as I did those inthe 24th Observation of the first Part of this Book. And when the Prismwas so placed as by refracting the Light of their mix'd Colours toseparate them, and distinguish the Rings from one another, as it didthose in that Observation, I could then see them distincter than before,and easily number eight or nine of them, and sometimes twelve orthirteen. And had not their Light been so very faint, I question not butthat I might have seen many more.

Obs. 5. Placing a Prism at the Window to refract the intromitted beamof Light, and cast the oblong Spectrum of Colours on the Speculum: Icovered the Speculum with a black Paper which had in the middle of it ahole to let any one of the Colours pass through to the Speculum, whilstthe rest were intercepted by the Paper. And now I found Rings of thatColour only which fell upon the Speculum. If the Speculum wasilluminated with red, the Rings were totally red with dark Intervals, ifwith blue they were totally blue, and so of the other Colours. And whenthey were illuminated with any one Colour, the Squares of theirDiameters measured between their most luminous Parts, were in thearithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squaresof the Diameters of their dark Intervals in the Progression of theintermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2.[Pg 294] But if the Colour wasvaried, they varied their Magnitude. In the red they were largest, inthe indigo and violet least, and in the intermediate Colours yellow,green, and blue, they were of several intermediate Bignesses answeringto the Colour, that is, greater in yellow than in green, and greater ingreen than in blue. And hence I knew, that when the Speculum wasilluminated with white Light, the red and yellow on the outside of theRings were produced by the least refrangible Rays, and the blue andviolet by the most refrangible, and that the Colours of each Ring spreadinto the Colours of the neighbouring Rings on either side, after themanner explain'd in the first and second Part of this Book, and bymixing diluted one another so that they could not be distinguish'd,unless near the Center where they were least mix'd. For in thisObservation I could see the Rings more distinctly, and to a greaterNumber than before, being able in the yellow Light to number eight ornine of them, besides a faint shadow of a tenth. To satisfy my self howmuch the Colours of the several Rings spread into one another, Imeasured the Diameters of the second and third Rings, and found themwhen made by the Confine of the red and orange to be to the sameDiameters when made by the Confine of blue and indigo, as 9 to 8, orthereabouts. For it was hard to determine this Proportion accurately.Also the Circles made successively by the red, yellow, and green,differ'd more from one another than those made successively by thegreen, blue, and indigo. For the Circle made by the violet[Pg 295] was too darkto be seen. To carry on the Computation, let us therefore suppose thatthe Differences of the Diameters of the Circles made by the outmost red,the Confine of red and orange, the Confine of orange and yellow, theConfine of yellow and green, the Confine of green and blue, the Confineof blue and indigo, the Confine of indigo and violet, and outmostviolet, are in proportion as the Differences of the Lengths of aMonochord which sound the Tones in an Eight;sol,la,fa,sol,la,mi,fa,sol, that is, as the Numbers 1/9, 1/18, 1/12, 1/12,2/27, 1/27, 1/18. And if the Diameter of the Circle made by the Confineof red and orange be 9A, and that of the Circle made by the Confine ofblue and indigo be 8A as above; their difference 9A-8A will be to thedifference of the Diameters of the Circles made by the outmost red, andby the Confine of red and orange, as 1/18 + 1/12 + 1/12 + 2/27 to 1/9,that is as 8/27 to 1/9, or 8 to 3, and to the difference of the Circlesmade by the outmost violet, and by the Confine of blue and indigo, as1/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, oras 16 to 5. And therefore these differences will be 3/8A and 5/16A. Addthe first to 9A and subduct the last from 8A, and you will have theDiameters of the Circles made by the least and most refrangible Rays75/8A and ((61-1/2)/8)A. These diameters are therefore to one another as75 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as3 to 2 very nearly. Which proportion differs not much from theproportion of the Diameters of the Circles made by the outmost red[Pg 296] andoutmost violet, in the 13th Observation of the first part of this Book.

Obs. 6. Placing my Eye where these Rings appear'd plainest, I saw theSpeculum tinged all over with Waves of Colours, (red, yellow, green,blue;) like those which in the Observations of the first part of thisBook appeared between the Object-glasses, and upon Bubbles of Water, butmuch larger. And after the manner of those, they were of variousmagnitudes in various Positions of the Eye, swelling and shrinking as Imoved my Eye this way and that way. They were formed like Arcs ofconcentrick Circles, as those were; and when my Eye was over against thecenter of the concavity of the Speculum, (that is, 5 Feet and 10 Inchesdistant from the Speculum,) their common center was in a right Line withthat center of concavity, and with the hole in the Window. But in otherpostures of my Eye their center had other positions. They appear'd bythe Light of the Clouds propagated to the Speculum through the hole inthe Window; and when the Sun shone through that hole upon the Speculum,his Light upon it was of the Colour of the Ring whereon it fell, but byits splendor obscured the Rings made by the Light of the Clouds, unlesswhen the Speculum was removed to a great distance from the Window, sothat his Light upon it might be broad and faint. By varying the positionof my Eye, and moving it nearer to or farther from the direct beam ofthe Sun's Light, the Colour of the Sun's reflected Light constantlyvaried upon the Speculum, as it did upon my[Pg 297] Eye, the same Colour alwaysappearing to a Bystander upon my Eye which to me appear'd upon theSpeculum. And thence I knew that the Rings of Colours upon the Chartwere made by these reflected Colours, propagated thither from theSpeculum in several Angles, and that their production depended not uponthe termination of Light and Shadow.

Obs. 7. By the Analogy of all these Phænomena with those of the likeRings of Colours described in the first part of this Book, it seemed tome that these Colours were produced by this thick Plate of Glass, muchafter the manner that those were produced by very thin Plates. For, upontrial, I found that if the Quick-silver were rubb'd off from thebackside of the Speculum, the Glass alone would cause the same Rings ofColours, but much more faint than before; and therefore the Phænomenondepends not upon the Quick-silver, unless so far as the Quick-silver byincreasing the Reflexion of the backside of the Glass increases theLight of the Rings of Colours. I found also that a Speculum of Metalwithout Glass made some Years since for optical uses, and very wellwrought, produced none of those Rings; and thence I understood thatthese Rings arise not from one specular Surface alone, but depend uponthe two Surfaces of the Plate of Glass whereof the Speculum was made,and upon the thickness of the Glass between them. For as in the 7th and19th Observations of the first part of this Book a thin Plate of Air,Water, or Glass of an even thickness appeared of one[Pg 298] Colour when theRays were perpendicular to it, of another when they were a littleoblique, of another when more oblique, of another when still moreoblique, and so on; so here, in the sixth Observation, the Light whichemerged out of the Glass in several Obliquities, made the Glass appearof several Colours, and being propagated in those Obliquities to theChart, there painted Rings of those Colours. And as the reason why athin Plate appeared of several Colours in several Obliquities of theRays, was, that the Rays of one and the same sort are reflected by thethin Plate at one obliquity and transmitted at another, and those ofother sorts transmitted where these are reflected, and reflected wherethese are transmitted: So the reason why the thick Plate of Glasswhereof the Speculum was made did appear of various Colours in variousObliquities, and in those Obliquities propagated those Colours to theChart, was, that the Rays of one and the same sort did at one Obliquityemerge out of the Glass, at another did not emerge, but were reflectedback towards the Quick-silver by the hither Surface of the Glass, andaccordingly as the Obliquity became greater and greater, emerged andwere reflected alternately for many Successions; and that in one and thesame Obliquity the Rays of one sort were reflected, and those of anothertransmitted. This is manifest by the fifth Observation of this part ofthis Book. For in that Observation, when the Speculum was illuminated byany one of the prismatick Colours, that Light made many Rings of thesame Colour[Pg 299] upon the Chart with dark Intervals, and therefore at itsemergence out of the Speculum was alternately transmitted and nottransmitted from the Speculum to the Chart for many Successions,according to the various Obliquities of its Emergence. And when theColour cast on the Speculum by the Prism was varied, the Rings became ofthe Colour cast on it, and varied their bigness with their Colour, andtherefore the Light was now alternately transmitted and not transmittedfrom the Speculum to the Chart at other Obliquities than before. Itseemed to me therefore that these Rings were of one and the sameoriginal with those of thin Plates, but yet with this difference, thatthose of thin Plates are made by the alternate Reflexions andTransmissions of the Rays at the second Surface of the Plate, after onepassage through it; but here the Rays go twice through the Plate beforethey are alternately reflected and transmitted. First, they go throughit from the first Surface to the Quick-silver, and then return throughit from the Quick-silver to the first Surface, and there are eithertransmitted to the Chart or reflected back to the Quick-silver,accordingly as they are in their Fits of easy Reflexion or Transmissionwhen they arrive at that Surface. For the Intervals of the Fits of theRays which fall perpendicularly on the Speculum, and are reflected backin the same perpendicular Lines, by reason of the equality of theseAngles and Lines, are of the same length and number within the Glassafter Reflexion as before, by the 19th Proposition of the third part ofthis Book.[Pg 300] And therefore since all the Rays that enter through thefirst Surface are in their Fits of easy Transmission at their entrance,and as many of these as are reflected by the second are in their Fits ofeasy Reflexion there, all these must be again in their Fits of easyTransmission at their return to the first, and by consequence there goout of the Glass to the Chart, and form upon it the white Spot of Lightin the center of the Rings. For the reason holds good in all sorts ofRays, and therefore all sorts must go out promiscuously to that Spot,and by their mixture cause it to be white. But the Intervals of the Fitsof those Rays which are reflected more obliquely than they enter, mustbe greater after Reflexion than before, by the 15th and 20thPropositions. And thence it may happen that the Rays at their return tothe first Surface, may in certain Obliquities be in Fits of easyReflexion, and return back to the Quick-silver, and in otherintermediate Obliquities be again in Fits of easy Transmission, and sogo out to the Chart, and paint on it the Rings of Colours about thewhite Spot. And because the Intervals of the Fits at equal obliquitiesare greater and fewer in the less refrangible Rays, and less and morenumerous in the more refrangible, therefore the less refrangible atequal obliquities shall make fewer Rings than the more refrangible, andthe Rings made by those shall be larger than the like number of Ringsmade by these; that is, the red Rings shall be larger than the yellow,the yellow than the green, the green than the blue, and the blue thanthe violet, as they were really[Pg 301] found to be in the fifth Observation.And therefore the first Ring of all Colours encompassing the white Spotof Light shall be red without any violet within, and yellow, and green,and blue in the middle, as it was found in the second Observation; andthese Colours in the second Ring, and those that follow, shall be moreexpanded, till they spread into one another, and blend one another byinterfering.

These seem to be the reasons of these Rings in general; and this put meupon observing the thickness of the Glass, and considering whether thedimensions and proportions of the Rings may be truly derived from it bycomputation.

Obs. 8. I measured therefore the thickness of this concavo-convexPlate of Glass, and found it every where 1/4 of an Inch precisely. Now,by the sixth Observation of the first Part of this Book, a thin Plate ofAir transmits the brightest Light of the first Ring, that is, the brightyellow, when its thickness is the 1/89000th part of an Inch; and by thetenth Observation of the same Part, a thin Plate of Glass transmits thesame Light of the same Ring, when its thickness is less in proportion ofthe Sine of Refraction to the Sine of Incidence, that is, when itsthickness is the 11/1513000th or 1/137545th part of an Inch, supposingthe Sines are as 11 to 17. And if this thickness be doubled, ittransmits the same bright Light of the second Ring; if tripled, ittransmits that of the third, and so on; the bright yellow Light in allthese cases being in its Fits of Transmission. And therefore if itsthickness be multiplied 34386 times, so as[Pg 302] to become 1/4 of an Inch, ittransmits the same bright Light of the 34386th Ring. Suppose this be thebright yellow Light transmitted perpendicularly from the reflectingconvex side of the Glass through the concave side to the white Spot inthe center of the Rings of Colours on the Chart: And by a Rule in the7th and 19th Observations in the first Part of this Book, and by the15th and 20th Propositions of the third Part of this Book, if the Raysbe made oblique to the Glass, the thickness of the Glass requisite totransmit the same bright Light of the same Ring in any obliquity, is tothis thickness of 1/4 of an Inch, as the Secant of a certain Angle tothe Radius, the Sine of which Angle is the first of an hundred and sixarithmetical Means between the Sines of Incidence and Refraction,counted from the Sine of Incidence when the Refraction is made out ofany plated Body into any Medium encompassing it; that is, in this case,out of Glass into Air. Now if the thickness of the Glass be increased bydegrees, so as to bear to its first thickness, (viz. that of a quarterof an Inch,) the Proportions which 34386 (the number of Fits of theperpendicular Rays in going through the Glass towards the white Spot inthe center of the Rings,) hath to 34385, 34384, 34383, and 34382, (thenumbers of the Fits of the oblique Rays in going through the Glasstowards the first, second, third, and fourth Rings of Colours,) and ifthe first thickness be divided into 100000000 equal parts, the increasedthicknesses will be 100002908, 100005816, 100008725, and 100011633, andthe Angles of which[Pg 303] these thicknesses are Secants will be 26´ 13´´, 37´5´´, 45´ 6´´, and 52´ 26´´, the Radius being 100000000; and the Sines ofthese Angles are 762, 1079, 1321, and 1525, and the proportional Sinesof Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. Forsince the Sines of Incidence out of Glass into Air are to the Sines ofRefraction as 11 to 17, and to the above-mentioned Secants as 11 to thefirst of 106 arithmetical Means between 11 and 17, that is, as 11 to11-6/106, those Secants will be to the Sines of Refraction as 11-6/106,to 17, and by this Analogy will give these Sines. So then, if theobliquities of the Rays to the concave Surface of the Glass be such thatthe Sines of their Refraction in passing out of the Glass through thatSurface into the Air be 1172, 1659, 2031, 2345, the bright Light of the34386th Ring shall emerge at the thicknesses of the Glass, which are to1/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. Andtherefore, if the thickness in all these Cases be 1/4 of an Inch (as itis in the Glass of which the Speculum was made) the bright Light of the34385th Ring shall emerge where the Sine of Refraction is 1172, and thatof the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031,and 2345 respectively. And in these Angles of Refraction the Light ofthese Rings shall be propagated from the Speculum to the Chart, andthere paint Rings about the white central round Spot of Light which wesaid was the Light of the 34386th Ring. And the Semidiameters of theseRings shall subtend the Angles of Refraction made at theConcave-Surface[Pg 304] of the Speculum, and by consequence their Diametersshall be to the distance of the Chart from the Speculum as those Sinesof Refraction doubled are to the Radius, that is, as 1172, 1659, 2031,and 2345, doubled are to 100000. And therefore, if the distance of theChart from the Concave-Surface of the Speculum be six Feet (as it was inthe third of these Observations) the Diameters of the Rings of thisbright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375Inches: For these Diameters are to six Feet, as the above-mention'dSines doubled are to the Radius. Now, these Diameters of the brightyellow Rings, thus found by Computation are the very same with thosefound in the third of these Observations by measuring them,viz. with1-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory ofderiving these Rings from the thickness of the Plate of Glass of whichthe Speculum was made, and from the Obliquity of the emerging Raysagrees with the Observation. In this Computation I have equalled theDiameters of the bright Rings made by Light of all Colours, to theDiameters of the Rings made by the bright yellow. For this yellow makesthe brightest Part of the Rings of all Colours. If you desire theDiameters of the Rings made by the Light of any other unmix'd Colour,you may find them readily by putting them to the Diameters of the brightyellow ones in a subduplicate Proportion of the Intervals of the Fits ofthe Rays of those Colours when equally inclined to the refracting orreflecting Surface which caused those Fits, that is,[Pg 305] by putting theDiameters of the Rings made by the Rays in the Extremities and Limits ofthe seven Colours, red, orange, yellow, green, blue, indigo, violet,proportional to the Cube-roots of the Numbers, 1, 8/9, 5/6, 3/4, 2/3,3/5, 9/16, 1/2, which express the Lengths of a Monochord sounding theNotes in an Eighth: For by this means the Diameters of the Rings ofthese Colours will be found pretty nearly in the same Proportion to oneanother, which they ought to have by the fifth of these Observations.

And thus I satisfy'd my self, that these Rings were of the same kind andOriginal with those of thin Plates, and by consequence that the Fits oralternate Dispositions of the Rays to be reflected and transmitted arepropagated to great distances from every reflecting and refractingSurface. But yet to put the matter out of doubt, I added the followingObservation.

Obs. 9. If these Rings thus depend on the thickness of the Plate ofGlass, their Diameters at equal distances from several Speculums made ofsuch concavo-convex Plates of Glass as are ground on the same Sphere,ought to be reciprocally in a subduplicate Proportion of the thicknessesof the Plates of Glass. And if this Proportion be found true byexperience it will amount to a demonstration that these Rings (likethose formed in thin Plates) do depend on the thickness of the Glass. Iprocured therefore another concavo-convex Plate of Glass ground on bothsides to the same Sphere with the former Plate. Its thickness was 5/62Parts of an Inch; and the Diameters[Pg 306] of the three first bright Ringsmeasured between the brightest Parts of their Orbits at the distance ofsix Feet from the Glass were 3·4-1/6·5-1/8· Inches. Now, the thicknessof the other Glass being 1/4 of an Inch was to the thickness of thisGlass as 1/4 to 5/62, that is as 31 to 10, or 310000000 to 100000000,and the Roots of these Numbers are 17607 and 10000, and in theProportion of the first of these Roots to the second are the Diametersof the bright Rings made in this Observation by the thinner Glass,3·4-1/6·5-1/8, to the Diameters of the same Rings made in the third ofthese Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, thatis, the Diameters of the Rings are reciprocally in a subduplicateProportion of the thicknesses of the Plates of Glass.

So then in Plates of Glass which are alike concave on one side, andalike convex on the other side, and alike quick-silver'd on the convexsides, and differ in nothing but their thickness, the Diameters of theRings are reciprocally in a subduplicate Proportion of the thicknessesof the Plates. And this shews sufficiently that the Rings depend on boththe Surfaces of the Glass. They depend on the convex Surface, becausethey are more luminous when that Surface is quick-silver'd over thanwhen it is without Quick-silver. They depend also upon the concaveSurface, because without that Surface a Speculum makes them not. Theydepend on both Surfaces, and on the distances between them, becausetheir bigness is varied by varying only that distance. And thisdependence is of the same kind with that which the Colours[Pg 307] of thinPlates have on the distance of the Surfaces of those Plates, because thebigness of the Rings, and their Proportion to one another, and thevariation of their bigness arising from the variation of the thicknessof the Glass, and the Orders of their Colours, is such as ought toresult from the Propositions in the end of the third Part of this Book,derived from the Phænomena of the Colours of thin Plates set down in thefirst Part.

There are yet other Phænomena of these Rings of Colours, but such asfollow from the same Propositions, and therefore confirm both the Truthof those Propositions, and the Analogy between these Rings and the Ringsof Colours made by very thin Plates. I shall subjoin some of them.

Obs. 10. When the beam of the Sun's Light was reflected back from theSpeculum not directly to the hole in the Window, but to a place a littledistant from it, the common center of that Spot, and of all the Rings ofColours fell in the middle way between the beam of the incident Light,and the beam of the reflected Light, and by consequence in the center ofthe spherical concavity of the Speculum, whenever the Chart on which theRings of Colours fell was placed at that center. And as the beam ofreflected Light by inclining the Speculum receded more and more from thebeam of incident Light and from the common center of the colour'd Ringsbetween them, those Rings grew bigger and bigger, and so also did thewhite round Spot, and new Rings of Colours emerged successively out oftheir common center,[Pg 308] and the white Spot became a white Ringencompassing them; and the incident and reflected beams of Light alwaysfell upon the opposite parts of this white Ring, illuminating itsPerimeter like two mock Suns in the opposite parts of an Iris. So thenthe Diameter of this Ring, measured from the middle of its Light on oneside to the middle of its Light on the other side, was always equal tothe distance between the middle of the incident beam of Light, and themiddle of the reflected beam measured at the Chart on which the Ringsappeared: And the Rays which form'd this Ring were reflected by theSpeculum in Angles equal to their Angles of Incidence, and byconsequence to their Angles of Refraction at their entrance into theGlass, but yet their Angles of Reflexion were not in the same Planeswith their Angles of Incidence.

Obs. 11. The Colours of the new Rings were in a contrary order tothose of the former, and arose after this manner. The white round Spotof Light in the middle of the Rings continued white to the center tillthe distance of the incident and reflected beams at the Chart was about7/8 parts of an Inch, and then it began to grow dark in the middle. Andwhen that distance was about 1-3/16 of an Inch, the white Spot wasbecome a Ring encompassing a dark round Spot which in the middleinclined to violet and indigo. And the luminous Rings encompassing itwere grown equal to those dark ones which in the four first Observationsencompassed them, that is to say, the white Spot was grown a white Ringequal to the[Pg 309] first of those dark Rings, and the first of those luminousRings was now grown equal to the second of those dark ones, and thesecond of those luminous ones to the third of those dark ones, and soon. For the Diameters of the luminous Rings were now 1-3/16, 2-1/16,2-2/3, 3-3/20, &c. Inches.

When the distance between the incident and reflected beams of Lightbecame a little bigger, there emerged out of the middle of the dark Spotafter the indigo a blue, and then out of that blue a pale green, andsoon after a yellow and red. And when the Colour at the center wasbrightest, being between yellow and red, the bright Rings were grownequal to those Rings which in the four first Observations nextencompassed them; that is to say, the white Spot in the middle of thoseRings was now become a white Ring equal to the first of those brightRings, and the first of those bright ones was now become equal to thesecond of those, and so on. For the Diameters of the white Ring, and ofthe other luminous Rings encompassing it, were now 1-11/16, 2-3/8,2-11/12, 3-3/8, &c. or thereabouts.

When the distance of the two beams of Light at the Chart was a littlemore increased, there emerged out of the middle in order after the red,a purple, a blue, a green, a yellow, and a red inclining much to purple,and when the Colour was brightest being between yellow and red, theformer indigo, blue, green, yellow and red, were become an Iris or Ringof Colours equal to the first of those luminous Rings which appeared inthe four first Observations, and[Pg 310] the white Ring which was now becomethe second of the luminous Rings was grown equal to the second of those,and the first of those which was now become the third Ring was becomeequal to the third of those, and so on. For their Diameters were1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams ofLight, and the Diameter of the white Ring being 2-3/8 Inches.

When these two beams became more distant there emerged out of the middleof the purplish red, first a darker round Spot, and then out of themiddle of that Spot a brighter. And now the former Colours (purple,blue, green, yellow, and purplish red) were become a Ring equal to thefirst of the bright Rings mentioned in the four first Observations, andthe Rings about this Ring were grown equal to the Rings about thatrespectively; the distance between the two beams of Light and theDiameter of the white Ring (which was now become the third Ring) beingabout 3 Inches.

The Colours of the Rings in the middle began now to grow very dilute,and if the distance between the two Beams was increased half an Inch, oran Inch more, they vanish'd whilst the white Ring, with one or two ofthe Rings next it on either side, continued still visible. But if thedistance of the two beams of Light was still more increased, these alsovanished: For the Light which coming from several parts of the hole inthe Window fell upon the Speculum in several Angles of Incidence, madeRings of several bignesses, which diluted and blotted out one another,as I knew by intercepting some part of[Pg 311] that Light. For if I interceptedthat part which was nearest to the Axis of the Speculum the Rings wouldbe less, if the other part which was remotest from it they would bebigger.

Obs. 12. When the Colours of the Prism were cast successively on theSpeculum, that Ring which in the two last Observations was white, was ofthe same bigness in all the Colours, but the Rings without it weregreater in the green than in the blue, and still greater in the yellow,and greatest in the red. And, on the contrary, the Rings within thatwhite Circle were less in the green than in the blue, and still less inthe yellow, and least in the red. For the Angles of Reflexion of thoseRays which made this Ring, being equal to their Angles of Incidence, theFits of every reflected Ray within the Glass after Reflexion are equalin length and number to the Fits of the same Ray within the Glass beforeits Incidence on the reflecting Surface. And therefore since all theRays of all sorts at their entrance into the Glass were in a Fit ofTransmission, they were also in a Fit of Transmission at their returningto the same Surface after Reflexion; and by consequence weretransmitted, and went out to the white Ring on the Chart. This is thereason why that Ring was of the same bigness in all the Colours, and whyin a mixture of all it appears white. But in Rays which are reflected inother Angles, the Intervals of the Fits of the least refrangible beinggreatest, make the Rings of their Colour in their progress from thiswhite Ring, either outwards or inwards, increase or decrease by the[Pg 312]greatest steps; so that the Rings of this Colour without are greatest,and within least. And this is the reason why in the last Observation,when the Speculum was illuminated with white Light, the exterior Ringsmade by all Colours appeared red without and blue within, and theinterior blue without and red within.

These are the Phænomena of thick convexo-concave Plates of Glass, whichare every where of the same thickness. There are yet other Phænomenawhen these Plates are a little thicker on one side than on the other,and others when the Plates are more or less concave than convex, orplano-convex, or double-convex. For in all these cases the Plates makeRings of Colours, but after various manners; all which, so far as I haveyet observed, follow from the Propositions in the end of the third partof this Book, and so conspire to confirm the truth of thosePropositions. But the Phænomena are too various, and the Calculationswhereby they follow from those Propositions too intricate to be hereprosecuted. I content my self with having prosecuted this kind ofPhænomena so far as to discover their Cause, and by discovering it toratify the Propositions in the third Part of this Book.

Obs. 13. As Light reflected by a Lens quick-silver'd on the backsidemakes the Rings of Colours above described, so it ought to make the likeRings of Colours in passing through a drop of Water. At the firstReflexion of the Rays within the drop, some Colours ought to betransmitted, as in the case of a[Pg 313] Lens, and others to be reflected backto the Eye. For instance, if the Diameter of a small drop or globule ofWater be about the 500th part of an Inch, so that a red-making Ray inpassing through the middle of this globule has 250 Fits of easyTransmission within the globule, and that all the red-making Rays whichare at a certain distance from this middle Ray round about it have 249Fits within the globule, and all the like Rays at a certain fartherdistance round about it have 248 Fits, and all those at a certainfarther distance 247 Fits, and so on; these concentrick Circles of Raysafter their transmission, falling on a white Paper, will makeconcentrick Rings of red upon the Paper, supposing the Light whichpasses through one single globule, strong enough to be sensible. And, inlike manner, the Rays of other Colours will make Rings of other Colours.Suppose now that in a fair Day the Sun shines through a thin Cloud ofsuch globules of Water or Hail, and that the globules are all of thesame bigness; and the Sun seen through this Cloud shall appearencompassed with the like concentrick Rings of Colours, and the Diameterof the first Ring of red shall be 7-1/4 Degrees, that of the second10-1/4 Degrees, that of the third 12 Degrees 33 Minutes. And accordinglyas the Globules of Water are bigger or less, the Rings shall be less orbigger. This is the Theory, and Experience answers it. For inJune1692, I saw by reflexion in a Vessel of stagnating Water three Halos,Crowns, or Rings of Colours about the Sun, like three little Rain-bows,concentrick to his Body. The Colours of the[Pg 314] first or innermost Crownwere blue next the Sun, red without, and white in the middle between theblue and red. Those of the second Crown were purple and blue within, andpale red without, and green in the middle. And those of the third werepale blue within, and pale red without; these Crowns enclosed oneanother immediately, so that their Colours proceeded in this continualorder from the Sun outward: blue, white, red; purple, blue, green, paleyellow and red; pale blue, pale red. The Diameter of the second Crownmeasured from the middle of the yellow and red on one side of the Sun,to the middle of the same Colour on the other side was 9-1/3 Degrees, orthereabouts. The Diameters of the first and third I had not time tomeasure, but that of the first seemed to be about five or six Degrees,and that of the third about twelve. The like Crowns appear sometimesabout the Moon; for in the beginning of the Year 1664,Febr. 19th atNight, I saw two such Crowns about her. The Diameter of the first orinnermost was about three Degrees, and that of the second about fiveDegrees and an half. Next about the Moon was a Circle of white, and nextabout that the inner Crown, which was of a bluish green within next thewhite, and of a yellow and red without, and next about these Colourswere blue and green on the inside of the outward Crown, and red on theoutside of it. At the same time there appear'd a Halo about 22 Degrees35´ distant from the center of the Moon. It was elliptical, and its longDiameter was perpendicular to the Horizon, verging below farthest from[Pg 315]the Moon. I am told that the Moon has sometimes three or moreconcentrick Crowns of Colours encompassing one another next about herBody. The more equal the globules of Water or Ice are to one another,the more Crowns of Colours will appear, and the Colours will be the morelively. The Halo at the distance of 22-1/2 Degrees from the Moon is ofanother sort. By its being oval and remoter from the Moon below thanabove, I conclude, that it was made by Refraction in some sort of Hailor Snow floating in the Air in an horizontal posture, the refractingAngle being about 58 or 60 Degrees.

THE

THIRD BOOK

OPTICKS

PART I.

Observations concerning the Inflexions of the Rays of Light, and theColours made thereby.

Grimaldo has inform'd us, that if a beam of the Sun's Light be let intoa dark Room through a very small hole, the Shadows of things in thisLight will be larger than they ought to be if the Rays went on by theBodies in straight Lines, and that these Shadows have three parallelFringes, Bands or Ranks of colour'd Light adjacent to them. But if theHole be enlarged the Fringes grow broad and run into one another, sothat they cannot be distinguish'd. These broad Shadows and Fringes havebeen reckon'd by some to proceed from the ordinary refraction of theAir, but without due examination of the Matter. For the circumstances ofthe Phænomenon, so far as I have observed them, are as follows.[Pg 318]

Obs. 1. I made in a piece of Lead a small Hole with a Pin, whosebreadth was the 42d part of an Inch. For 21 of those Pins laid togethertook up the breadth of half an Inch. Through this Hole I let into mydarken'd Chamber a beam of the Sun's Light, and found that the Shadowsof Hairs, Thred, Pins, Straws, and such like slender Substances placedin this beam of Light, were considerably broader than they ought to be,if the Rays of Light passed on by these Bodies in right Lines. Andparticularly a Hair of a Man's Head, whose breadth was but the 280thpart of an Inch, being held in this Light, at the distance of abouttwelve Feet from the Hole, did cast a Shadow which at the distance offour Inches from the Hair was the sixtieth part of an Inch broad, thatis, above four times broader than the Hair, and at the distance of twoFeet from the Hair was about the eight and twentieth part of an Inchbroad, that is, ten times broader than the Hair, and at the distance often Feet was the eighth part of an Inch broad, that is 35 times broader.

Nor is it material whether the Hair be encompassed with Air, or with anyother pellucid Substance. For I wetted a polish'd Plate of Glass, andlaid the Hair in the Water upon the Glass, and then laying anotherpolish'd Plate of Glass upon it, so that the Water might fill up thespace between the Glasses, I held them in the aforesaid beam of Light,so that the Light might pass through them perpendicularly, and theShadow of the Hair was at the same distances as big as before. TheShadows of[Pg 319] Scratches made in polish'd Plates of Glass were also muchbroader than they ought to be, and the Veins in polish'd Plates of Glassdid also cast the like broad Shadows. And therefore the great breadth ofthese Shadows proceeds from some other cause than the Refraction of theAir.

Let the Circle X [inFig. 1.] represent the middle of the Hair; ADG,BEH, CFI, three Rays passing by one side of the Hair at severaldistances; KNQ, LOR, MPS, three other Rays passing by the other side ofthe Hair at the like distances; D, E, F, and N, O, P, the places wherethe Rays are bent in their passage by the Hair; G, H, I, and Q, R, S,the places where the Rays fall on a Paper GQ; IS the breadth of theShadow of the Hair cast on the Paper, and TI, VS, two Rays passing tothe Points I and S without bending when the Hair is taken away. And it'smanifest that all the Light between these two Rays TI and VS is bent inpassing by the Hair, and turned aside from the Shadow IS, because if anypart of this Light were not bent it would fall on the Paper within theShadow, and there illuminate the Paper, contrary to experience. Andbecause when the Paper is at a great distance from the Hair, the Shadowis broad, and therefore the Rays TI and VS are at a great distance fromone another, it follows that the Hair acts upon the Rays of Light at agood distance in their passing by it. But the Action is strongest on theRays which pass by at least distances, and grows weaker and weakeraccordingly as the Rays pass by at distances greater and greater, as isrepresented[Pg 320] in the Scheme: For thence it comes to pass, that the Shadowof the Hair is much broader in proportion to the distance of the Paperfrom the Hair, when the Paper is nearer the Hair, than when it is at agreat distance from it.

Obs. 2. The Shadows of all Bodies (Metals, Stones, Glass, Wood, Horn,Ice, &c.) in this Light were border'd with three Parallel Fringes orBands of colour'd Light, whereof that which was contiguous to the Shadowwas broadest and most luminous, and that which was remotest from it wasnarrowest, and so faint, as not easily to be visible. It was difficultto distinguish the Colours, unless when the Light fell very obliquelyupon a smooth Paper, or some other smooth white Body, so as to make themappear much broader than they would otherwise do. And then the Colourswere plainly visible in this Order: The first or innermost Fringe wasviolet and deep blue next the Shadow, and then light blue, green, andyellow in the middle, and red without. The second Fringe was almostcontiguous to the first, and the third to the second, and both were bluewithin, and yellow and red without, but their Colours were very faint,especially those of the third. The Colours therefore proceeded in thisorder from the Shadow; violet, indigo, pale blue, green, yellow, red;blue, yellow, red; pale blue, pale yellow and red. The Shadows made byScratches and Bubbles in polish'd Plates of Glass were border'd with thelike Fringes of colour'd Light. And if Plates of Looking-glass sloop'doff near the edges with a Diamond-cut, be held in the same beam ofLight, the Light which passes through the parallel Planes of the Glasswill be border'd with the like Fringes of Colours where those Planesmeet with the Diamond-cut, and by this means there will sometimes appearfour or five Fringes of Colours. Let AB, CD [inFig. 2.] represent theparallel Planes of a Looking-glass, and BD the Plane of the Diamond-cut,making at B a very obtuse Angle with the Plane AB. And let all the Lightbetween the Rays ENI and FBM pass directly through the parallel Planesof the Glass, and fall upon the Paper between I and M, and all the Lightbetween the Rays GO and HD be refracted by the oblique Plane of theDiamond-cut BD, and fall upon the Paper between K and L; and the Lightwhich passes directly through the parallel Planes of the Glass, andfalls upon the Paper between I and M, will be border'd with three ormore Fringes at M.[Pg 321]

So by looking on the Sun through a Feather or black Ribband held closeto the Eye, several Rain-bows will appear; the Shadows which the Fibresor Threds cast on theTunica Retina, being border'd with the likeFringes of Colours.

Obs. 3. When the Hair was twelve Feet distant from this Hole, and itsShadow fell obliquely upon a flat white Scale of Inches and Parts of anInch placed half a Foot beyond it, and also when the Shadow fellperpendicularly upon the same Scale placed nine Feet beyond it; Imeasured the breadth of the Shadow and Fringes as accurately as I could,and found them in Parts of an Inch as follows.[Pg 323]

At the Distance of	half a Foot	Nine Feet
The breadth of the Shadow	1/54	1/9
The breadth between the Middles of the brightest Light of the innermost Fringes on either side the Shadow	1/38 or 1/39	7/50
The breadth between the Middles of the brightest Light of the middlemost Fringes on either side the Shadow	1/23-1/2	4/17
The breadth between the Middles of the brightest Light of the outmost Fringes on either side the Shadow	1/18 or 1/18-1/2	3/10
The distance between the Middles of the brightest Light of the first and second Fringes	1/120	1/21
The distance between the Middles of the brightest Light of the second and third Fringes	1/170	1/31
The breadth of the luminous Part (green, white, yellow, and red) of the first Fringe	1/170	1/32
The breadth of the darker Space between the first and second Fringes	1/240	1/45
The breadth of the luminous Part of the second Fringe	1/290	1/55
The breadth of the darker Space between the second and third Fringes	1/340	1/63

These Measures I took by letting the Shadow of the Hair, at half a Footdistance, fall so obliquely on the Scale, as to appear twelve timesbroader than when it fell perpendicularly on it at the same distance,and setting down in this Table the twelfth part of the Measures I thentook.

Obs. 4. When the Shadow and Fringes were cast obliquely upon a smoothwhite Body, and that Body was removed farther and farther from the Hair,the first Fringe began to appear and look brighter than the rest of theLight at the distance of less than a quarter of an Inch from the Hair,and the dark Line or Shadow between that and the second Fringe began toappear at a less distance from the Hair than that of the third part ofan Inch. The second Fringe began to appear at a distance from the Hairof less than half an Inch, and the Shadow between that and the thirdFringe at a distance less than an inch, and the third Fringe at adistance less than three Inches. At greater distances they became muchmore sensible, but kept very nearly the same proportion of theirbreadths and intervals which they had at their first appearing. For thedistance between the middle of the first, and middle of the secondFringe, was to the distance between the middle of the second and middleof the third Fringe, as three to two, or ten to seven. And the last ofthese two distances was equal to the breadth of the bright Light orluminous part of the first Fringe. And this breadth was to the breadthof the bright Light of the second Fringe as seven to four, and to thedark Interval of the first[Pg 325] and second Fringe as three to two, and tothe like dark Interval between the second and third as two to one. Forthe breadths of the Fringes seem'd to be in the progression of theNumbers 1, √(1/3), √(1/5), and their Intervals to be in thesame progression with them; that is, the Fringes and their Intervalstogether to be in the continual progression of the Numbers 1,√(1/2), √(1/3), √(1/4), √(1/5), or thereabouts. Andthese Proportions held the same very nearly at all distances from theHair; the dark Intervals of the Fringes being as broad in proportion tothe breadth of the Fringes at their first appearance as afterwards atgreat distances from the Hair, though not so dark and distinct.

Obs. 5. The Sun shining into my darken'd Chamber through a hole aquarter of an Inch broad, I placed at the distance of two or three Feetfrom the Hole a Sheet of Pasteboard, which was black'd all over on bothsides, and in the middle of it had a hole about three quarters of anInch square for the Light to pass through. And behind the hole Ifasten'd to the Pasteboard with Pitch the blade of a sharp Knife, tointercept some part of the Light which passed through the hole. ThePlanes of the Pasteboard and blade of the Knife were parallel to oneanother, and perpendicular to the Rays. And when they were so placedthat none of the Sun's Light fell on the Pasteboard, but all of itpassed through the hole to the Knife, and there part of it fell upon theblade of the Knife, and part of it passed by its edge; I let this partof the Light which passed[Pg 326] by, fall on a white Paper two or three Feetbeyond the Knife, and there saw two streams of faint Light shoot outboth ways from the beam of Light into the shadow, like the Tails ofComets. But because the Sun's direct Light by its brightness upon thePaper obscured these faint streams, so that I could scarce see them, Imade a little hole in the midst of the Paper for that Light to passthrough and fall on a black Cloth behind it; and then I saw the twostreams plainly. They were like one another, and pretty nearly equal inlength, and breadth, and quantity of Light. Their Light at that end nextthe Sun's direct Light was pretty strong for the space of about aquarter of an Inch, or half an Inch, and in all its progress from thatdirect Light decreased gradually till it became insensible. The wholelength of either of these streams measured upon the paper at thedistance of three Feet from the Knife was about six or eight Inches; sothat it subtended an Angle at the edge of the Knife of about 10 or 12,or at most 14 Degrees. Yet sometimes I thought I saw it shoot three orfour Degrees farther, but with a Light so very faint that I could scarceperceive it, and suspected it might (in some measure at least) arisefrom some other cause than the two streams did. For placing my Eye inthat Light beyond the end of that stream which was behind the Knife, andlooking towards the Knife, I could see a line of Light upon its edge,and that not only when my Eye was in the line of the Streams, but alsowhen it was without that line either towards the point of the Knife, or[Pg 327]towards the handle. This line of Light appear'd contiguous to the edgeof the Knife, and was narrower than the Light of the innermost Fringe,and narrowest when my Eye was farthest from the direct Light, andtherefore seem'd to pass between the Light of that Fringe and the edgeof the Knife, and that which passed nearest the edge to be most bent,though not all of it.

Obs. 6. I placed another Knife by this, so that their edges might beparallel, and look towards one another, and that the beam of Light mightfall upon both the Knives, and some part of it pass between their edges.And when the distance of their edges was about the 400th part of anInch, the stream parted in the middle, and left a Shadow between the twoparts. This Shadow was so black and dark that all the Light which passedbetween the Knives seem'd to be bent, and turn'd aside to the one handor to the other. And as the Knives still approach'd one another theShadow grew broader, and the streams shorter at their inward ends whichwere next the Shadow, until upon the contact of the Knives the wholeLight vanish'd, leaving its place to the Shadow.

And hence I gather that the Light which is least bent, and goes to theinward ends of the streams, passes by the edges of the Knives at thegreatest distance, and this distance when the Shadow begins to appearbetween the streams, is about the 800th part of an Inch. And the Lightwhich passes by the edges of the Knives at distances still less andless, is more and more bent, and goes to those parts of the[Pg 328] streamswhich are farther and farther from the direct Light; because when theKnives approach one another till they touch, those parts of the streamsvanish last which are farthest from the direct Light.

Obs. 7. In the fifth Observation the Fringes did not appear, but byreason of the breadth of the hole in the Window became so broad as torun into one another, and by joining, to make one continued Light in thebeginning of the streams. But in the sixth, as the Knives approached oneanother, a little before the Shadow appeared between the two streams,the Fringes began to appear on the inner ends of the Streams on eitherside of the direct Light; three on one side made by the edge of oneKnife, and three on the other side made by the edge of the other Knife.They were distinctest when the Knives were placed at the greatestdistance from the hole in the Window, and still became more distinct bymaking the hole less, insomuch that I could sometimes see a faintlineament of a fourth Fringe beyond the three above mention'd. And asthe Knives continually approach'd one another, the Fringes grewdistincter and larger, until they vanish'd. The outmost Fringe vanish'dfirst, and the middlemost next, and the innermost last. And after theywere all vanish'd, and the line of Light which was in the middle betweenthem was grown very broad, enlarging it self on both sides into thestreams of Light described in the fifth Observation, the above-mention'dShadow began to appear in the middle of this line, and divide it alongthe middle into two lines of Light, and increased[Pg 329] until the whole Lightvanish'd. This enlargement of the Fringes was so great that the Rayswhich go to the innermost Fringe seem'd to be bent above twenty timesmore when this Fringe was ready to vanish, than when one of the Kniveswas taken away.

And from this and the former Observation compared, I gather, that theLight of the first Fringe passed by the edge of the Knife at a distancegreater than the 800th part of an Inch, and the Light of the secondFringe passed by the edge of the Knife at a greater distance than theLight of the first Fringe did, and that of the third at a greaterdistance than that of the second, and that of the streams of Lightdescribed in the fifth and sixth Observations passed by the edges of theKnives at less distances than that of any of the Fringes.

Obs. 8. I caused the edges of two Knives to be ground truly strait,and pricking their points into a Board so that their edges might looktowards one another, and meeting near their points contain a rectilinearAngle, I fasten'd their Handles together with Pitch to make this Angleinvariable. The distance of the edges of the Knives from one another atthe distance of four Inches from the angular Point, where the edges ofthe Knives met, was the eighth part of an Inch; and therefore the Anglecontain'd by the edges was about one Degree 54: The Knives thus fix'dtogether I placed in a beam of the Sun's Light, let into my darken'dChamber through a Hole the 42d Part of an Inch wide, at the distance of10 or 15 Feet from the Hole, and let the Light which[Pg 330] passed betweentheir edges fall very obliquely upon a smooth white Ruler at thedistance of half an Inch, or an Inch from the Knives, and there saw theFringes by the two edges of the Knives run along the edges of theShadows of the Knives in Lines parallel to those edges without growingsensibly broader, till they met in Angles equal to the Angle containedby the edges of the Knives, and where they met and joined they endedwithout crossing one another. But if the Ruler was held at a muchgreater distance from the Knives, the Fringes where they were fartherfrom the Place of their Meeting, were a little narrower, and becamesomething broader and broader as they approach'd nearer and nearer toone another, and after they met they cross'd one another, and thenbecame much broader than before.

Whence I gather that the distances at which the Fringes pass by theKnives are not increased nor alter'd by the approach of the Knives, butthe Angles in which the Rays are there bent are much increased by thatapproach; and that the Knife which is nearest any Ray determines whichway the Ray shall be bent, and the other Knife increases the bent.

Obs. 9. When the Rays fell very obliquely upon the Ruler at thedistance of the third Part of an Inch from the Knives, the dark Linebetween the first and second Fringe of the Shadow of one Knife, and thedark Line between the first and second Fringe of the Shadow of the otherknife met with one another, at the distance of the fifth Part of an Inchfrom the end of the Light which passed between the Knives at the[Pg 331]concourse of their edges. And therefore the distance of the edges of theKnives at the meeting of these dark Lines was the 160th Part of an Inch.For as four Inches to the eighth Part of an Inch, so is any Length ofthe edges of the Knives measured from the point of their concourse tothe distance of the edges of the Knives at the end of that Length, andso is the fifth Part of an Inch to the 160th Part. So then the darkLines above-mention'd meet in the middle of the Light which passesbetween the Knives where they are distant the 160th Part of an Inch, andthe one half of that Light passes by the edge of one Knife at a distancenot greater than the 320th Part of an Inch, and falling upon the Papermakes the Fringes of the Shadow of that Knife, and the other half passesby the edge of the other Knife, at a distance not greater than the 320thPart of an Inch, and falling upon the Paper makes the Fringes of theShadow of the other Knife. But if the Paper be held at a distance fromthe Knives greater than the third Part of an Inch, the dark Linesabove-mention'd meet at a greater distance than the fifth Part of anInch from the end of the Light which passed between the Knives at theconcourse of their edges; and therefore the Light which falls upon thePaper where those dark Lines meet passes between the Knives where theedges are distant above the 160th part of an Inch.

For at another time, when the two Knives were distant eight Feet andfive Inches from the little hole in the Window, made with a small Pin asabove, the[Pg 332] Light which fell upon the Paper where the aforesaid darklines met, passed between the Knives, where the distance between theiredges was as in the following Table, when the distance of the Paper fromthe Knives was also as follows.

Distances of the Paper from the Knives in Inches.	Distances between the edges of the Knives in millesimal parts of an Inch.
1-1/2.	0'012
3-1/3.	0'020
8-3/5.	0'034
32.	0'057
96.	0'081
131.	0'087

And hence I gather, that the Light which makes the Fringes upon thePaper is not the same Light at all distances of the Paper from theKnives, but when the Paper is held near the Knives, the Fringes are madeby Light which passes by the edges of the Knives at a less distance, andis more bent than when the Paper is held at a greater distance from theKnives.[Pg 333]

Obs. 10. When the Fringes of the Shadows of the Knives fellperpendicularly upon a Paper at a great distance from the Knives, theywere in the form of Hyperbola's, and their Dimensions were as follows.Let CA, CB [inFig. 3.] represent Lines drawn upon the Paper parallelto the edges of the Knives, and between which all the Light would fall,if it passed between the edges of the Knives without inflexion; DE aRight Line drawn through C making the Angles ACD, BCE, equal to oneanother, and terminating all the Light which falls upon the Paper fromthe point where the edges of the Knives meet;eis,fkt, andglv,three hyperbolical Lines representing the Terminus of the Shadow of oneof the Knives, the dark Line between the first and second Fringes ofthat Shadow, and the dark Line between the second and third Fringes ofthe same Shadow;xip,ykq, andzlr, three other hyperbolical Linesrepresenting the Terminus of the Shadow of the other Knife, the darkLine between the first and second Fringes of that Shadow, and the darkline between the second and third Fringes of the same Shadow. Andconceive that these three Hyperbola's are like and equal to the formerthree, and cross them in the pointsi,k, andl, and that theShadows of the Knives are terminated and distinguish'd from the firstluminous Fringes by the lineseis andxip, until the meeting andcrossing of the Fringes, and then those lines cross the Fringes in theform of dark lines, terminating the first luminous Fringes within side,and distinguishing them from another Light which begins to appear ati, and illuminates all the triangular spaceipDEs comprehended bythese dark lines, and the right line DE. Of these Hyperbola's oneAsymptote is the line DE, and their other Asymptotes are parallel to thelines CA and CB. Letrv represent a line drawn any where upon thePaper parallel to the Asymptote DE, and let this line cross the rightlines AC inm, and BC inn, and the six dark hyperbolical[Pg 335] lines inp,q,r;s,t,v; and by measuring the distancesps,qt,rv, and thence collecting the lengths of the Ordinatesnp,nq,nr orms,mt,mv, and doing this at several distances of thelinerv from the Asymptote DD, you may find as many points of theseHyperbola's as you please, and thereby know that these curve lines areHyperbola's differing little from the conical Hyperbola. And bymeasuring the lines Ci, Ck, Cl, you may find other points of theseCurves.

For instance; when the Knives were distant from the hole in the Windowten Feet, and the Paper from the Knives nine Feet, and the Anglecontained by the edges of the Knives to which the Angle ACB is equal,was subtended by a Chord which was to the Radius as 1 to 32, and thedistance of the linerv from the Asymptote DE was half an Inch: Imeasured the linesps,qt,rv, and found them 0'35, 0'65, 0'98Inches respectively; and by adding to their halfs the line 1/2mn,(which here was the 128th part of an Inch, or 0'0078 Inches,) the Sumsnp,nq,nr, were 0'1828, 0'3328, 0'4978 Inches. I measured alsothe distances of the brightest parts of the Fringes which run betweenpq andst,qr andtv, and next beyondr andv, and foundthem 0'5, 0'8, and 1'17 Inches.

Obs. 11. The Sun shining into my darken'd Room through a small roundhole made in a Plate of Lead with a slender Pin, as above; I placed atthe hole a Prism to refract the Light, and form on the opposite Wall theSpectrum of Colours, described in the third Experiment of the firstBook. And then I found that the Shadows of all Bodies held in thecolour'd[Pg 336] Light between the Prism and the Wall, were border'd withFringes of the Colour of that Light in which they were held. In the fullred Light they were totally red without any sensible blue or violet, andin the deep blue Light they were totally blue without any sensible redor yellow; and so in the green Light they were totally green, exceptinga little yellow and blue, which were mixed in the green Light of thePrism. And comparing the Fringes made in the several colour'd Lights, Ifound that those made in the red Light were largest, those made in theviolet were least, and those made in the green were of a middle bigness.For the Fringes with which the Shadow of a Man's Hair were bordered,being measured cross the Shadow at the distance of six Inches from theHair, the distance between the middle and most luminous part of thefirst or innermost Fringe on one side of the Shadow, and that of thelike Fringe on the other side of the Shadow, was in the full red Light1/37-1/4 of an Inch, and in the full violet 7/46. And the like distancebetween the middle and most luminous parts of the second Fringes oneither side the Shadow was in the full red Light 1/22, and in the violet1/27 of an Inch. And these distances of the Fringes held the sameproportion at all distances from the Hair without any sensiblevariation.

So then the Rays which made these Fringes in the red Light passed by theHair at a greater distance than those did which made the like Fringes inthe violet; and therefore the Hair in causing these[Pg 337] Fringes acted alikeupon the red Light or least refrangible Rays at a greater distance, andupon the violet or most refrangible Rays at a less distance, and bythose actions disposed the red Light into Larger Fringes, and the violetinto smaller, and the Lights of intermediate Colours into Fringes ofintermediate bignesses without changing the Colour of any sort of Light.

When therefore the Hair in the first and second of these Observationswas held in the white beam of the Sun's Light, and cast a Shadow whichwas border'd with three Fringes of coloured Light, those Colours arosenot from any new modifications impress'd upon the Rays of Light by theHair, but only from the various inflexions whereby the several Sorts ofRays were separated from one another, which before separation, by themixture of all their Colours, composed the white beam of the Sun'sLight, but whenever separated compose Lights of the several Colourswhich they are originally disposed to exhibit. In this 11th Observation,where the Colours are separated before the Light passes by the Hair, theleast refrangible Rays, which when separated from the rest make red,were inflected at a greater distance from the Hair, so as to make threered Fringes at a greater distance from the middle of the Shadow of theHair; and the most refrangible Rays which when separated make violet,were inflected at a less distance from the Hair, so as to make threeviolet Fringes at a less distance from the middle of the Shadow of theHair. And other Rays[Pg 338] of intermediate degrees of Refrangibility wereinflected at intermediate distances from the Hair, so as to make Fringesof intermediate Colours at intermediate distances from the middle of theShadow of the Hair. And in the second Observation, where all the Coloursare mix'd in the white Light which passes by the Hair, these Colours areseparated by the various inflexions of the Rays, and the Fringes whichthey make appear all together, and the innermost Fringes beingcontiguous make one broad Fringe composed of all the Colours in dueorder, the violet lying on the inside of the Fringe next the Shadow, thered on the outside farthest from the Shadow, and the blue, green, andyellow, in the middle. And, in like manner, the middlemost Fringes ofall the Colours lying in order, and being contiguous, make another broadFringe composed of all the Colours; and the outmost Fringes of all theColours lying in order, and being contiguous, make a third broad Fringecomposed of all the Colours. These are the three Fringes of colour'dLight with which the Shadows of all Bodies are border'd in the secondObservation.

When I made the foregoing Observations, I design'd to repeat most ofthem with more care and exactness, and to make some new ones fordetermining the manner how the Rays of Light are bent in their passageby Bodies, for making the Fringes of Colours with the dark lines betweenthem. But I was then interrupted, and cannot now think of taking thesethings into farther Consideration. And since I[Pg 339] have not finish'd thispart of my Design, I shall conclude with proposing only some Queries, inorder to a farther search to be made by others.

Query 1. Do not Bodies act upon Light at a distance, and by theiraction bend its Rays; and is not this action (cæteris paribus)strongest at the least distance?

Qu. 2. Do not the Rays which differ in Refrangibility differ also inFlexibity; and are they not by their different Inflexions separated fromone another, so as after separation to make the Colours in the threeFringes above described? And after what manner are they inflected tomake those Fringes?

Qu. 3. Are not the Rays of Light in passing by the edges and sides ofBodies, bent several times backwards and forwards, with a motion likethat of an Eel? And do not the three Fringes of colour'd Lightabove-mention'd arise from three such bendings?

Qu. 4. Do not the Rays of Light which fall upon Bodies, and arereflected or refracted, begin to bend before they arrive at the Bodies;and are they not reflected, refracted, and inflected, by one and thesame Principle, acting variously in various Circumstances?

Qu. 5. Do not Bodies and Light act mutually upon one another; that isto say, Bodies upon Light in emitting, reflecting, refracting andinflecting it, and Light upon Bodies for heating them, and putting theirparts into a vibrating motion wherein heat consists?

Qu. 6. Do not black Bodies conceive heat more easily from Light thanthose of other Colours do, by[Pg 340] reason that the Light falling on them isnot reflected outwards, but enters the Bodies, and is often reflectedand refracted within them, until it be stifled and lost?

Qu. 7. Is not the strength and vigor of the action between Light andsulphureous Bodies observed above, one reason why sulphureous Bodiestake fire more readily, and burn more vehemently than other Bodies do?

Qu. 8. Do not all fix'd Bodies, when heated beyond a certain degree,emit Light and shine; and is not this Emission perform'd by thevibrating motions of their parts? And do not all Bodies which aboundwith terrestrial parts, and especially with sulphureous ones, emit Lightas often as those parts are sufficiently agitated; whether thatagitation be made by Heat, or by Friction, or Percussion, orPutrefaction, or by any vital Motion, or any other Cause? As forinstance; Sea-Water in a raging Storm; Quick-silver agitated invacuo;the Back of a Cat, or Neck of a Horse, obliquely struck or rubbed in adark place; Wood, Flesh and Fish while they putrefy; Vapours arisingfrom putrefy'd Waters, usually call'dIgnes Fatui; Stacks of moist Hayor Corn growing hot by fermentation; Glow-worms and the Eyes of someAnimals by vital Motions; the vulgarPhosphorus agitated by theattrition of any Body, or by the acid Particles of the Air; Amber andsome Diamonds by striking, pressing or rubbing them; Scrapings of Steelstruck off with a Flint; Iron hammer'd very nimbly till it become so hotas to kindle Sulphur[Pg 341] thrown upon it; the Axletrees of Chariots takingfire by the rapid rotation of the Wheels; and some Liquors mix'd withone another whose Particles come together with an Impetus, as Oil ofVitriol distilled from its weight of Nitre, and then mix'd with twiceits weight of Oil of Anniseeds. So also a Globe of Glass about 8 or 10Inches in diameter, being put into a Frame where it may be swiftlyturn'd round its Axis, will in turning shine where it rubs against thepalm of ones Hand apply'd to it: And if at the same time a piece ofwhite Paper or white Cloth, or the end of ones Finger be held at thedistance of about a quarter of an Inch or half an Inch from that part ofthe Glass where it is most in motion, the electrick Vapour which isexcited by the friction of the Glass against the Hand, will by dashingagainst the white Paper, Cloth or Finger, be put into such an agitationas to emit Light, and make the white Paper, Cloth or Finger, appearlucid like a Glowworm; and in rushing out of the Glass will sometimespush against the finger so as to be felt. And the same things have beenfound by rubbing a long and large Cylinder or Glass or Amber with aPaper held in ones hand, and continuing the friction till the Glass grewwarm.

Qu. 9. Is not Fire a Body heated so hot as to emit Light copiously?For what else is a red hot Iron than Fire? And what else is a burningCoal than red hot Wood?

Qu. 10. Is not Flame a Vapour, Fume or Exhalation heated red hot, thatis, so hot as to shine? For[Pg 342] Bodies do not flame without emitting acopious Fume, and this Fume burns in the Flame. TheIgnis Fatuus is aVapour shining without heat, and is there not the same differencebetween this Vapour and Flame, as between rotten Wood shining withoutheat and burning Coals of Fire? In distilling hot Spirits, if the Headof the Still be taken off, the Vapour which ascends out of the Stillwill take fire at the Flame of a Candle, and turn into Flame, and theFlame will run along the Vapour from the Candle to the Still. SomeBodies heated by Motion, or Fermentation, if the heat grow intense, fumecopiously, and if the heat be great enough the Fumes will shine andbecome Flame. Metals in fusion do not flame for want of a copious Fume,except Spelter, which fumes copiously, and thereby flames. All flamingBodies, as Oil, Tallow, Wax, Wood, fossil Coals, Pitch, Sulphur, byflaming waste and vanish into burning Smoke, which Smoke, if the Flamebe put out, is very thick and visible, and sometimes smells strongly,but in the Flame loses its smell by burning, and according to the natureof the Smoke the Flame is of several Colours, as that of Sulphur blue,that of Copper open'd with sublimate green, that of Tallow yellow, thatof Camphire white. Smoke passing through Flame cannot but grow red hot,and red hot Smoke can have no other appearance than that of Flame. WhenGun-powder takes fire, it goes away into Flaming Smoke. For the Charcoaland Sulphur easily take fire, and set fire to the Nitre, and the Spiritof the Nitre being thereby rarified into Vapour,[Pg 343] rushes out withExplosion much after the manner that the Vapour of Water rushes out ofan Æolipile; the Sulphur also being volatile is converted into Vapour,and augments the Explosion. And the acid Vapour of the Sulphur (namelythat which distils under a Bell into Oil of Sulphur,) entring violentlyinto the fix'd Body of the Nitre, sets loose the Spirit of the Nitre,and excites a great Fermentation, whereby the Heat is farther augmented,and the fix'd Body of the Nitre is also rarified into Fume, and theExplosion is thereby made more vehement and quick. For if Salt of Tartarbe mix'd with Gun-powder, and that Mixture be warm'd till it takes fire,the Explosion will be more violent and quick than that of Gun-powderalone; which cannot proceed from any other cause than the action of theVapour of the Gun-powder upon the Salt of Tartar, whereby that Salt israrified. The Explosion of Gun-powder arises therefore from the violentaction whereby all the Mixture being quickly and vehemently heated, israrified and converted into Fume and Vapour: which Vapour, by theviolence of that action, becoming so hot as to shine, appears in theform of Flame.

Qu. 11. Do not great Bodies conserve their heat the longest, theirparts heating one another, and may not great dense and fix'd Bodies,when heated beyond a certain degree, emit Light so copiously, as by theEmission and Re-action of its Light, and the Reflexions and Refractionsof its Rays within its Pores to grow still hotter, till it comes to acertain period of heat, such as is that of the Sun? And are not the[Pg 344] Sunand fix'd Stars great Earths vehemently hot, whose heat is conserved bythe greatness of the Bodies, and the mutual Action and Reaction betweenthem, and the Light which they emit, and whose parts are kept fromfuming away, not only by their fixity, but also by the vast weight anddensity of the Atmospheres incumbent upon them; and very stronglycompressing them, and condensing the Vapours and Exhalations which arisefrom them? For if Water be made warm in any pellucid Vessel emptied ofAir, that Water in theVacuum will bubble and boil as vehemently as itwould in the open Air in a Vessel set upon the Fire till it conceives amuch greater heat. For the weight of the incumbent Atmosphere keeps downthe Vapours, and hinders the Water from boiling, until it grow muchhotter than is requisite to make it boilin vacuo. Also a mixture ofTin and Lead being put upon a red hot Ironin vacuo emits a Fume andFlame, but the same Mixture in the open Air, by reason of the incumbentAtmosphere, does not so much as emit any Fume which can be perceived bySight. In like manner the great weight of the Atmosphere which lies uponthe Globe of the Sun may hinder Bodies there from rising up and goingaway from the Sun in the form of Vapours and Fumes, unless by means of afar greater heat than that which on the Surface of our Earth would veryeasily turn them into Vapours and Fumes. And the same great weight maycondense those Vapours and Exhalations as soon as they shall at any timebegin to ascend from the Sun, and make them[Pg 345] presently fall back againinto him, and by that action increase his Heat much after the mannerthat in our Earth the Air increases the Heat of a culinary Fire. And thesame weight may hinder the Globe of the Sun from being diminish'd,unless by the Emission of Light, and a very small quantity of Vapoursand Exhalations.

Qu. 12. Do not the Rays of Light in falling upon the bottom of the Eyeexcite Vibrations in theTunica Retina? Which Vibrations, beingpropagated along the solid Fibres of the optick Nerves into the Brain,cause the Sense of seeing. For because dense Bodies conserve their Heata long time, and the densest Bodies conserve their Heat the longest, theVibrations of their parts are of a lasting nature, and therefore may bepropagated along solid Fibres of uniform dense Matter to a greatdistance, for conveying into the Brain the impressions made upon all theOrgans of Sense. For that Motion which can continue long in one and thesame part of a Body, can be propagated a long way from one part toanother, supposing the Body homogeneal, so that the Motion may not bereflected, refracted, interrupted or disorder'd by any unevenness of theBody.

Qu. 13. Do not several sorts of Rays make Vibrations of severalbignesses, which according to their bignesses excite Sensations ofseveral Colours, much after the manner that the Vibrations of the Air,according to their several bignesses excite Sensations of severalSounds? And particularly do not the most refrangible Rays excite theshortest Vibrations for[Pg 346] making a Sensation of deep violet, the leastrefrangible the largest for making a Sensation of deep red, and theseveral intermediate sorts of Rays, Vibrations of several intermediatebignesses to make Sensations of the several intermediate Colours?

Qu. 14. May not the harmony and discord of Colours arise from theproportions of the Vibrations propagated through the Fibres of theoptick Nerves into the Brain, as the harmony and discord of Sounds arisefrom the proportions of the Vibrations of the Air? For some Colours, ifthey be view'd together, are agreeable to one another, as those of Goldand Indigo, and others disagree.

Qu. 15. Are not the Species of Objects seen with both Eyes unitedwhere the optick Nerves meet before they come into the Brain, the Fibreson the right side of both Nerves uniting there, and after union goingthence into the Brain in the Nerve which is on the right side of theHead, and the Fibres on the left side of both Nerves uniting in the sameplace, and after union going into the Brain in the Nerve which is on theleft side of the Head, and these two Nerves meeting in the Brain in sucha manner that their Fibres make but one entire Species or Picture, halfof which on the right side of the Sensorium comes from the right side ofboth Eyes through the right side of both optick Nerves to the placewhere the Nerves meet, and from thence on the right side of the Headinto the Brain, and the other half on the left side of the Sensoriumcomes in like manner from the left side of both Eyes. For[Pg 347] the optickNerves of such Animals as look the same way with both Eyes (as of Men,Dogs, Sheep, Oxen, &c.) meet before they come into the Brain, but theoptick Nerves of such Animals as do not look the same way with both Eyes(as of Fishes, and of the Chameleon,) do not meet, if I am rightlyinform'd.

Qu. 16. When a Man in the dark presses either corner of his Eye withhis Finger, and turns his Eye away from his Finger, he will see a Circleof Colours like those in the Feather of a Peacock's Tail. If the Eye andthe Finger remain quiet these Colours vanish in a second Minute of Time,but if the Finger be moved with a quavering Motion they appear again. Donot these Colours arise from such Motions excited in the bottom of theEye by the Pressure and Motion of the Finger, as, at other times areexcited there by Light for causing Vision? And do not the Motions onceexcited continue about a Second of Time before they cease? And when aMan by a stroke upon his Eye sees a flash of Light, are not the likeMotions excited in theRetina by the stroke? And when a Coal of Firemoved nimbly in the circumference of a Circle, makes the wholecircumference appear like a Circle of Fire; is it not because theMotions excited in the bottom of the Eye by the Rays of Light are of alasting nature, and continue till the Coal of Fire in going roundreturns to its former place? And considering the lastingness of theMotions excited in the bottom of the Eye by Light, are they not of avibrating nature?

Qu. 17. If a stone be thrown into stagnating Water,[Pg 348] the Waves excitedthereby continue some time to arise in the place where the Stone fellinto the Water, and are propagated from thence in concentrick Circlesupon the Surface of the Water to great distances. And the Vibrations orTremors excited in the Air by percussion, continue a little time to movefrom the place of percussion in concentrick Spheres to great distances.And in like manner, when a Ray of Light falls upon the Surface of anypellucid Body, and is there refracted or reflected, may not Waves ofVibrations, or Tremors, be thereby excited in the refracting orreflecting Medium at the point of Incidence, and continue to arisethere, and to be propagated from thence as long as they continue toarise and be propagated, when they are excited in the bottom of the Eyeby the Pressure or Motion of the Finger, or by the Light which comesfrom the Coal of Fire in the Experiments above-mention'd? and are notthese Vibrations propagated from the point of Incidence to greatdistances? And do they not overtake the Rays of Light, and by overtakingthem successively, do they not put them into the Fits of easy Reflexionand easy Transmission described above? For if the Rays endeavour torecede from the densest part of the Vibration, they may be alternatelyaccelerated and retarded by the Vibrations overtaking them.

Qu. 18. If in two large tall cylindrical Vessels of Glass inverted,two little Thermometers be suspended so as not to touch the Vessels, andthe Air be drawn out of one of these Vessels, and these Vessels[Pg 349] thusprepared be carried out of a cold place into a warm one; the Thermometerin vacuo will grow warm as much, and almost as soon as the Thermometerwhich is notin vacuo. And when the Vessels are carried back into thecold place, the Thermometerin vacuo will grow cold almost as soon asthe other Thermometer. Is not the Heat of the warm Room convey'd throughtheVacuum by the Vibrations of a much subtiler Medium than Air, whichafter the Air was drawn out remained in theVacuum? And is not thisMedium the same with that Medium by which Light is refracted andreflected, and by whose Vibrations Light communicates Heat to Bodies,and is put into Fits of easy Reflexion and easy Transmission? And do notthe Vibrations of this Medium in hot Bodies contribute to theintenseness and duration of their Heat? And do not hot Bodiescommunicate their Heat to contiguous cold ones, by the Vibrations ofthis Medium propagated from them into the cold ones? And is not thisMedium exceedingly more rare and subtile than the Air, and exceedinglymore elastick and active? And doth it not readily pervade all Bodies?And is it not (by its elastick force) expanded through all the Heavens?

Qu. 19. Doth not the Refraction of Light proceed from the differentdensity of this Æthereal Medium in different places, the Light recedingalways from the denser parts of the Medium? And is not the densitythereof greater in free and open Spaces void of Air and other grosserBodies, than within the Pores of Water, Glass, Crystal, Gems, and othercompact[Pg 350] Bodies? For when Light passes through Glass or Crystal, andfalling very obliquely upon the farther Surface thereof is totallyreflected, the total Reflexion ought to proceed rather from the densityand vigour of the Medium without and beyond the Glass, than from therarity and weakness thereof.

Qu. 20. Doth not this Æthereal Medium in passing out of Water, Glass,Crystal, and other compact and dense Bodies into empty Spaces, growdenser and denser by degrees, and by that means refract the Rays ofLight not in a point, but by bending them gradually in curve Lines? Anddoth not the gradual condensation of this Medium extend to some distancefrom the Bodies, and thereby cause the Inflexions of the Rays of Light,which pass by the edges of dense Bodies, at some distance from theBodies?

Qu. 21. Is not this Medium much rarer within the dense Bodies of theSun, Stars, Planets and Comets, than in the empty celestial Spacesbetween them? And in passing from them to great distances, doth it notgrow denser and denser perpetually, and thereby cause the gravity ofthose great Bodies towards one another, and of their parts towards theBodies; every Body endeavouring to go from the denser parts of theMedium towards the rarer? For if this Medium be rarer within the Sun'sBody than at its Surface, and rarer there than at the hundredth part ofan Inch from its Body, and rarer there than at the fiftieth part of anInch from its Body, and rarer there than at the Orb ofSaturn; I seeno reason why the Increase of[Pg 351] density should stop any where, and notrather be continued through all distances from the Sun toSaturn, andbeyond. And though this Increase of density may at great distances beexceeding slow, yet if the elastick force of this Medium be exceedinggreat, it may suffice to impel Bodies from the denser parts of theMedium towards the rarer, with all that power which we call Gravity. Andthat the elastick force of this Medium is exceeding great, may begather'd from the swiftness of its Vibrations. Sounds move about 1140English Feet in a second Minute of Time, and in seven or eight Minutesof Time they move about one hundredEnglish Miles. Light moves fromthe Sun to us in about seven or eight Minutes of Time, which distance isabout 70,000,000English Miles, supposing the horizontal Parallax ofthe Sun to be about 12´´. And the Vibrations or Pulses of this Medium,that they may cause the alternate Fits of easy Transmission and easyReflexion, must be swifter than Light, and by consequence above 700,000times swifter than Sounds. And therefore the elastick force of thisMedium, in proportion to its density, must be above 700000 x 700000(that is, above 490,000,000,000) times greater than the elastick forceof the Air is in proportion to its density. For the Velocities of thePulses of elastick Mediums are in a subduplicateRatio of theElasticities and the Rarities of the Mediums taken together.

As Attraction is stronger in small Magnets than in great ones inproportion to their Bulk, and Gravity is greater in the Surfaces ofsmall Planets than in[Pg 352] those of great ones in proportion to their bulk,and small Bodies are agitated much more by electric attraction thangreat ones; so the smallness of the Rays of Light may contribute verymuch to the power of the Agent by which they are refracted. And so ifany one should suppose thatÆther (like our Air) may contain Particleswhich endeavour to recede from one another (for I do not know what thisÆther is) and that its Particles are exceedingly smaller than those ofAir, or even than those of Light: The exceeding smallness of itsParticles may contribute to the greatness of the force by which thoseParticles may recede from one another, and thereby make that Mediumexceedingly more rare and elastick than Air, and by consequenceexceedingly less able to resist the motions of Projectiles, andexceedingly more able to press upon gross Bodies, by endeavouring toexpand it self.

Qu. 22. May not Planets and Comets, and all gross Bodies, performtheir Motions more freely, and with less resistance in this ÆtherealMedium than in any Fluid, which fills all Space adequately withoutleaving any Pores, and by consequence is much denser than Quick-silveror Gold? And may not its resistance be so small, as to beinconsiderable? For instance; If thisÆther (for so I will call it)should be supposed 700000 times more elastick than our Air, and above700000 times more rare; its resistance would be above 600,000,000 timesless than that of Water. And so small a resistance would scarce make anysensible alteration in the Motions of the Planets[Pg 353] in ten thousandYears. If any one would ask how a Medium can be so rare, let him tell mehow the Air, in the upper parts of the Atmosphere, can be above anhundred thousand thousand times rarer than Gold. Let him also tell me,how an electrick Body can by Friction emit an Exhalation so rare andsubtile, and yet so potent, as by its Emission to cause no sensibleDiminution of the weight of the electrick Body, and to be expandedthrough a Sphere, whose Diameter is above two Feet, and yet to be ableto agitate and carry up Leaf Copper, or Leaf Gold, at the distance ofabove a Foot from the electrick Body? And how the Effluvia of a Magnetcan be so rare and subtile, as to pass through a Plate of Glass withoutany Resistance or Diminution of their Force, and yet so potent as toturn a magnetick Needle beyond the Glass?

Qu. 23. Is not Vision perform'd chiefly by the Vibrations of thisMedium, excited in the bottom of the Eye by the Rays of Light, andpropagated through the solid, pellucid and uniform Capillamenta of theoptick Nerves into the place of Sensation? And is not Hearing perform'dby the Vibrations either of this or some other Medium, excited in theauditory Nerves by the Tremors of the Air, and propagated through thesolid, pellucid and uniform Capillamenta of those Nerves into the placeof Sensation? And so of the other Senses.

Qu. 24. Is not Animal Motion perform'd by the Vibrations of thisMedium, excited in the Brain by the power of the Will, and propagatedfrom thence[Pg 354] through the solid, pellucid and uniform Capillamenta of theNerves into the Muscles, for contracting and dilating them? I supposethat the Capillamenta of the Nerves are each of them solid and uniform,that the vibrating Motion of the Æthereal Medium may be propagated alongthem from one end to the other uniformly, and without interruption: ForObstructions in the Nerves create Palsies. And that they may besufficiently uniform, I suppose them to be pellucid when view'd singly,tho' the Reflexions in their cylindrical Surfaces may make the wholeNerve (composed of many Capillamenta) appear opake and white. Foropacity arises from reflecting Surfaces, such as may disturb andinterrupt the Motions of this Medium.

Qu. 25. Are there not other original Properties of the Rays of Light,besides those already described? An instance of another originalProperty we have in the Refraction of Island Crystal, described first byErasmus Bartholine, and afterwards more exactly byHugenius, in hisBookDe la Lumiere. This Crystal is a pellucid fissile Stone, clear asWater or Crystal of the Rock, and without Colour; enduring a red Heatwithout losing its transparency, and in a very strong Heat calciningwithout Fusion. Steep'd a Day or two in Water, it loses its naturalPolish. Being rubb'd on Cloth, it attracts pieces of Straws and otherlight things, like Ambar or Glass; and withAqua fortis it makes anEbullition. It seems to be a sort of Talk, and is found in form of anoblique Parallelopiped, with six parallelogram Sides and eight solidAngles.[Pg 355] The obtuse Angles of the Parallelograms are each of them 101Degrees and 52 Minutes; the acute ones 78 Degrees and 8 Minutes. Two ofthe solid Angles opposite to one another, as C and E, are compassed eachof them with three of these obtuse Angles, and each of the other sixwith one obtuse and two acute ones. It cleaves easily in planes parallelto any of its Sides, and not in any other Planes. It cleaves with aglossy polite Surface not perfectly plane, but with some littleunevenness. It is easily scratch'd, and by reason of its softness ittakes a Polish very difficultly. It polishes better upon polish'dLooking-glass than upon Metal, and perhaps better upon Pitch, Leather orParchment. Afterwards it must be rubb'd with a little Oil or white of anEgg, to fill up its Scratches; whereby it will become very transparentand polite. But for several Experiments, it is not necessary to polishit. If a piece of this crystalline Stone be laid upon a Book, everyLetter of the Book seen through it will appear double, by means of adouble Refraction. And if any beam of Light falls eitherperpendicularly, or in any oblique Angle upon any Surface of thisCrystal, it becomes divided into two beams by means of the same doubleRefraction. Which beams are of the same Colour with the incident beam ofLight, and seem equal to one another in the quantity of their Light, orvery nearly equal. One of these Refractions is perform'd by the usualRule of Opticks, the Sine of Incidence out of Air into this Crystalbeing to the Sine of Refraction, as five to three. The[Pg 356] otherRefraction, which may be called the unusual Refraction, is perform'd bythe following Rule.

Let ADBC represent the refracting Surface of the Crystal, C the biggestsolid Angle at that Surface, GEHF the opposite Surface, and CK aperpendicular on that Surface. This perpendicular makes with the edge ofthe Crystal CF, an Angle of 19 Degr. 3'. Join KF, and in it take KL, sothat the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. Andif ST represent any beam of Light incident at T in any Angle upon therefracting Surface ADBC, let TV be the refracted beam determin'd by thegiven Portion of the Sines 5 to 3, according to the usual Rule ofOpticks. Draw VX parallel and equal to KL. Draw it the same way from Vin which L lieth from K; and joining TX, this line TX shall be the otherrefracted beam carried from T to X, by the unusual Refraction.[Pg 357]

If therefore the incident beam ST be perpendicular to the refractingSurface, the two beams TV and TX, into which it shall become divided,shall be parallel to the lines CK and CL; one of those beams goingthrough the Crystal perpendicularly, as it ought to do by the usual Lawsof Opticks, and the other TX by an unusual Refraction diverging from theperpendicular, and making with it an Angle VTX of about 6-2/3 Degrees,as is found by Experience. And hence, the Plane VTX, and such likePlanes which are parallel to the Plane CFK, may be called the Planes ofperpendicular Refraction. And the Coast towards which the lines KL andVX are drawn, may be call'd the Coast of unusual Refraction.

In like manner Crystal of the Rock has a double Refraction: But thedifference of the two Refractions is not so great and manifest as inIsland Crystal.

When the beam ST incident on Island Crystal is divided into two beams TVand TX, and these two beams arrive at the farther Surface of the Glass;the beam TV, which was refracted at the first Surface after the usualmanner, shall be again refracted entirely after the usual manner at thesecond Surface; and the beam TX, which was refracted after the unusualmanner in the first Surface, shall be again refracted entirely after theunusual manner in the second Surface; so that both these beams shallemerge out of the second Surface in lines parallel to the first incidentbeam ST.

And if two pieces of Island Crystal be placed one after another, in suchmanner that all the Surfaces[Pg 358] of the latter be parallel to all thecorresponding Surfaces of the former: The Rays which are refracted afterthe usual manner in the first Surface of the first Crystal, shall berefracted after the usual manner in all the following Surfaces; and theRays which are refracted after the unusual manner in the first Surface,shall be refracted after the unusual manner in all the followingSurfaces. And the same thing happens, though the Surfaces of theCrystals be any ways inclined to one another, provided that their Planesof perpendicular Refraction be parallel to one another.

And therefore there is an original difference in the Rays of Light, bymeans of which some Rays are in this Experiment constantly refractedafter the usual manner, and others constantly after the unusual manner:For if the difference be not original, but arises from new Modificationsimpress'd on the Rays at their first Refraction, it would be alter'd bynew Modifications in the three following Refractions; whereas it suffersno alteration, but is constant, and has the same effect upon the Rays inall the Refractions. The unusual Refraction is therefore perform'd by anoriginal property of the Rays. And it remains to be enquired, whetherthe Rays have not more original Properties than are yet discover'd.

Qu. 26. Have not the Rays of Light several sides, endued with severaloriginal Properties? For if the Planes of perpendicular Refraction ofthe second Crystal be at right Angles with the Planes of perpendicularRefraction of the first Crystal, the Rays which[Pg 359] are refracted after theusual manner in passing through the first Crystal, will be all of themrefracted after the unusual manner in passing through the secondCrystal; and the Rays which are refracted after the unusual manner inpassing through the first Crystal, will be all of them refracted afterthe usual manner in passing through the second Crystal. And thereforethere are not two sorts of Rays differing in their nature from oneanother, one of which is constantly and in all Positions refracted afterthe usual manner, and the other constantly and in all Positions afterthe unusual manner. The difference between the two sorts of Rays in theExperiment mention'd in the 25th Question, was only in the Positions ofthe Sides of the Rays to the Planes of perpendicular Refraction. For oneand the same Ray is here refracted sometimes after the usual, andsometimes after the unusual manner, according to the Position which itsSides have to the Crystals. If the Sides of the Ray are posited the sameway to both Crystals, it is refracted after the same manner in themboth: But if that side of the Ray which looks towards the Coast of theunusual Refraction of the first Crystal, be 90 Degrees from that side ofthe same Ray which looks toward the Coast of the unusual Refraction ofthe second Crystal, (which may be effected by varying the Position ofthe second Crystal to the first, and by consequence to the Rays ofLight,) the Ray shall be refracted after several manners in the severalCrystals. There is nothing more required to determine whether the Raysof Light[Pg 360] which fall upon the second Crystal shall be refracted afterthe usual or after the unusual manner, but to turn about this Crystal,so that the Coast of this Crystal's unusual Refraction may be on this oron that side of the Ray. And therefore every Ray may be consider'd ashaving four Sides or Quarters, two of which opposite to one anotherincline the Ray to be refracted after the unusual manner, as often aseither of them are turn'd towards the Coast of unusual Refraction; andthe other two, whenever either of them are turn'd towards the Coast ofunusual Refraction, do not incline it to be otherwise refracted thanafter the usual manner. The two first may therefore be call'd the Sidesof unusual Refraction. And since these Dispositions were in the Raysbefore their Incidence on the second, third, and fourth Surfaces of thetwo Crystals, and suffered no alteration (so far as appears,) by theRefraction of the Rays in their passage through those Surfaces, and theRays were refracted by the same Laws in all the four Surfaces; itappears that those Dispositions were in the Rays originally, andsuffer'd no alteration by the first Refraction, and that by means ofthose Dispositions the Rays were refracted at their Incidence on thefirst Surface of the first Crystal, some of them after the usual, andsome of them after the unusual manner, accordingly as their Sides ofunusual Refraction were then turn'd towards the Coast of the unusualRefraction of that Crystal, or sideways from it.

Every Ray of Light has therefore two opposite Sides, originally enduedwith a Property on which the[Pg 361] unusual Refraction depends, and the othertwo opposite Sides not endued with that Property. And it remains to beenquired, whether there are not more Properties of Light by which theSides of the Rays differ, and are distinguished from one another.

In explaining the difference of the Sides of the Rays above mention'd, Ihave supposed that the Rays fall perpendicularly on the first Crystal.But if they fall obliquely on it, the Success is the same. Those Rayswhich are refracted after the usual manner in the first Crystal, will berefracted after the unusual manner in the second Crystal, supposing thePlanes of perpendicular Refraction to be at right Angles with oneanother, as above; and on the contrary.

If the Planes of the perpendicular Refraction of the two Crystals beneither parallel nor perpendicular to one another, but contain an acuteAngle: The two beams of Light which emerge out of the first Crystal,will be each of them divided into two more at their Incidence on thesecond Crystal. For in this case the Rays in each of the two beams willsome of them have their Sides of unusual Refraction, and some of themtheir other Sides turn'd towards the Coast of the unusual Refraction ofthe second Crystal.

Qu. 27. Are not all Hypotheses erroneous which have hitherto beeninvented for explaining the Phænomena of Light, by new Modifications ofthe Rays? For those Phænomena depend not upon new Modifications, as hasbeen supposed, but upon the original and unchangeable Properties of theRays.[Pg 362]

Qu. 28. Are not all Hypotheses erroneous, in which Light is supposedto consist in Pression or Motion, propagated through a fluid Medium? Forin all these Hypotheses the Phænomena of Light have been hithertoexplain'd by supposing that they arise from new Modifications of theRays; which is an erroneous Supposition.

If Light consisted only in Pression propagated without actual Motion, itwould not be able to agitate and heat the Bodies which refract andreflect it. If it consisted in Motion propagated to all distances in aninstant, it would require an infinite force every moment, in everyshining Particle, to generate that Motion. And if it consisted inPression or Motion, propagated either in an instant or in time, it wouldbend into the Shadow. For Pression or Motion cannot be propagated in aFluid in right Lines, beyond an Obstacle which stops part of the Motion,but will bend and spread every way into the quiescent Medium which liesbeyond the Obstacle. Gravity tends downwards, but the Pressure of Waterarising from Gravity tends every way with equal Force, and is propagatedas readily, and with as much force sideways as downwards, and throughcrooked passages as through strait ones. The Waves on the Surface ofstagnating Water, passing by the sides of a broad Obstacle which stopspart of them, bend afterwards and dilate themselves gradually into thequiet Water behind the Obstacle. The Waves, Pulses or Vibrations of theAir, wherein Sounds consist, bend manifestly, though not so much as theWaves of Water.[Pg 363] For a Bell or a Cannon may be heard beyond a Hill whichintercepts the sight of the sounding Body, and Sounds are propagated asreadily through crooked Pipes as through streight ones. But Light isnever known to follow crooked Passages nor to bend into the Shadow. Forthe fix'd Stars by the Interposition of any of the Planets cease to beseen. And so do the Parts of the Sun by the Interposition of the Moon,Mercury orVenus. The Rays which pass very near to the edges of anyBody, are bent a little by the action of the Body, as we shew'd above;but this bending is not towards but from the Shadow, and is perform'donly in the passage of the Ray by the Body, and at a very small distancefrom it. So soon as the Ray is past the Body, it goes right on.

To explain the unusual Refraction of Island Crystal by Pression orMotion propagated, has not hitherto been attempted (to my knowledge)except byHuygens, who for that end supposed two several vibratingMediums within that Crystal. But when he tried the Refractions in twosuccessive pieces of that Crystal, and found them such as is mention'dabove; he confessed himself at a loss for explaining them. For Pressionsor Motions, propagated from a shining Body through an uniform Medium,must be on all sides alike; whereas by those Experiments it appears,that the Rays of Light have different Properties in their differentSides. He suspected that the Pulses ofÆther in passing through thefirst Crystal might receive certain new Modifications, which mightdetermine them to be propagated in this or that Medium[Pg 364] within thesecond Crystal, according to the Position of that Crystal. But whatModifications those might be he could not say, nor think of any thingsatisfactory in that Point. And if he had known that the unusualRefraction depends not on new Modifications, but on the original andunchangeable Dispositions of the Rays, he would have found it asdifficult to explain how those Dispositions which he supposed to beimpress'd on the Rays by the first Crystal, could be in them beforetheir Incidence on that Crystal, and in general, how all Rays emitted byshining Bodies, can have those Dispositions in them from the beginning.To me, at least, this seems inexplicable, if Light be nothing else thanPression or Motion propagated throughÆther.

And it is as difficult to explain by these Hypotheses, how Rays can bealternately in Fits of easy Reflexion and easy Transmission; unlessperhaps one might suppose that there are in all Space two Ætherealvibrating Mediums, and that the Vibrations of one of them constituteLight, and the Vibrations of the other are swifter, and as often as theyovertake the Vibrations of the first, put them into those Fits. But howtwoÆthers can be diffused through all Space, one of which acts uponthe other, and by consequence is re-acted upon, without retarding,shattering, dispersing and confounding one anothers Motions, isinconceivable. And against filling the[Pg 365] Heavens with fluid Mediums,unless they be exceeding rare, a great Objection arises from the regularand very lasting Motions of the Planets and Comets in all manner ofCourses through the Heavens. For thence it is manifest, that the Heavensare void of all sensible Resistance, and by consequence of all sensibleMatter.

For the resisting Power of fluid Mediums arises partly from theAttrition of the Parts of the Medium, and partly from theVis inertiæof the Matter. That part of the Resistance of a spherical Body whicharises from the Attrition of the Parts of the Medium is very nearly asthe Diameter, or, at the most, as theFactum of the Diameter, and theVelocity of the spherical Body together. And that part of the Resistancewhich arises from theVis inertiæ of the Matter, is as the Square ofthatFactum. And by this difference the two sorts of Resistance may bedistinguish'd from one another in any Medium; and these beingdistinguish'd, it will be found that almost all the Resistance of Bodiesof a competent Magnitude moving in Air, Water, Quick-silver, and suchlike Fluids with a competent Velocity, arises from theVis inertiæ ofthe Parts of the Fluid.

Now that part of the resisting Power of any Medium which arises from theTenacity, Friction or Attrition of the Parts of the Medium, may bediminish'd by dividing the Matter into smaller Parts, and making theParts more smooth and slippery: But that part of the Resistance whicharises from theVis inertiæ, is proportional to the Density of theMatter,[Pg 366] and cannot be diminish'd by dividing the Matter into smallerParts, nor by any other means than by decreasing the Density of theMedium. And for these Reasons the Density of fluid Mediums is verynearly proportional to their Resistance. Liquors which differ not muchin Density, as Water, Spirit of Wine, Spirit of Turpentine, hot Oil,differ not much in Resistance. Water is thirteen or fourteen timeslighter than Quick-silver and by consequence thirteen or fourteen timesrarer, and its Resistance is less than that of Quick-silver in the sameProportion, or thereabouts, as I have found by Experiments made withPendulums. The open Air in which we breathe is eight or nine hundredtimes lighter than Water, and by consequence eight or nine hundred timesrarer, and accordingly its Resistance is less than that of Water in thesame Proportion, or thereabouts; as I have also found by Experimentsmade with Pendulums. And in thinner Air the Resistance is still less,and at length, by ratifying the Air, becomes insensible. For smallFeathers falling in the open Air meet with great Resistance, but in atall Glass well emptied of Air, they fall as fast as Lead or Gold, as Ihave seen tried several times. Whence the Resistance seems still todecrease in proportion to the Density of the Fluid. For I do not find byany Experiments, that Bodies moving in Quick-silver, Water or Air, meetwith any other sensible Resistance than what arises from the Density andTenacity of those sensible Fluids, as they would do if the Pores ofthose Fluids, and all other Spaces, were filled with a dense[Pg 367] andsubtile Fluid. Now if the Resistance in a Vessel well emptied of Air,was but an hundred times less than in the open Air, it would be about amillion of times less than in Quick-silver. But it seems to be much lessin such a Vessel, and still much less in the Heavens, at the height ofthree or four hundred Miles from the Earth, or above. For Mr.Boylehas shew'd that Air may be rarified above ten thousand times in Vesselsof Glass; and the Heavens are much emptier of Air than anyVacuum wecan make below. For since the Air is compress'd by the Weight of theincumbent Atmosphere, and the Density of Air is proportional to theForce compressing it, it follows by Computation, that at the height ofabout seven and a halfEnglish Miles from the Earth, the Air is fourtimes rarer than at the Surface of the Earth; and at the height of 15Miles it is sixteen times rarer than that at the Surface of the Earth;and at the height of 22-1/2, 30, or 38 Miles, it is respectively 64,256, or 1024 times rarer, or thereabouts; and at the height of 76, 152,228 Miles, it is about 1000000, 1000000000000, or 1000000000000000000times rarer; and so on.

Heat promotes Fluidity very much by diminishing the Tenacity of Bodies.It makes many Bodies fluid which are not fluid in cold, and increasesthe Fluidity of tenacious Liquids, as of Oil, Balsam, and Honey, andthereby decreases their Resistance. But it decreases not the Resistanceof Water considerably, as it would do if any considerable part of theResistance of Water arose from the Attrition or Tenacity of its Parts.And therefore the Resistance of Water arises[Pg 368] principally and almostentirely from theVis inertiæ of its Matter; and by consequence, ifthe Heavens were as dense as Water, they would not have much lessResistance than Water; if as dense as Quick-silver, they would not havemuch less Resistance than Quick-silver; if absolutely dense, or full ofMatter without anyVacuum, let the Matter be never so subtil andfluid, they would have a greater Resistance than Quick-silver. A solidGlobe in such a Medium would lose above half its Motion in moving threetimes the length of its Diameter, and a Globe not solid (such as are thePlanets,) would be retarded sooner. And therefore to make way for theregular and lasting Motions of the Planets and Comets, it's necessary toempty the Heavens of all Matter, except perhaps some very thin Vapours,Steams, or Effluvia, arising from the Atmospheres of the Earth, Planets,and Comets, and from such an exceedingly rare Æthereal Medium as wedescribed above. A dense Fluid can be of no use for explaining thePhænomena of Nature, the Motions of the Planets and Comets being betterexplain'd without it. It serves only to disturb and retard the Motionsof those great Bodies, and make the Frame of Nature languish: And in thePores of Bodies, it serves only to stop the vibrating Motions of theirParts, wherein their Heat and Activity consists. And as it is of no use,and hinders the Operations of Nature, and makes her languish, so thereis no evidence for its Existence, and therefore it ought to be rejected.And if it be rejected, the Hypotheses that Light consists in Pression[Pg 369]or Motion, propagated through such a Medium, are rejected with it.

And for rejecting such a Medium, we have the Authority of those theoldest and most celebrated Philosophers ofGreece andPhœnicia,who made aVacuum, and Atoms, and the Gravity of Atoms, the firstPrinciples of their Philosophy; tacitly attributing Gravity to someother Cause than dense Matter. Later Philosophers banish theConsideration of such a Cause out of natural Philosophy, feigningHypotheses for explaining all things mechanically, and referring otherCauses to Metaphysicks: Whereas the main Business of natural Philosophyis to argue from Phænomena without feigning Hypotheses, and to deduceCauses from Effects, till we come to the very first Cause, whichcertainly is not mechanical; and not only to unfold the Mechanism of theWorld, but chiefly to resolve these and such like Questions. What isthere in places almost empty of Matter, and whence is it that the Sunand Planets gravitate towards one another, without dense Matter betweenthem? Whence is it that Nature doth nothing in vain; and whence arisesall that Order and Beauty which we see in the World? To what end areComets, and whence is it that Planets move all one and the same way inOrbs concentrick, while Comets move all manner of ways in Orbs veryexcentrick; and what hinders the fix'd Stars from falling upon oneanother? How came the Bodies of Animals to be contrived with so muchArt, and for what ends were their several Parts? Was the Eye contrivedwithout Skill[Pg 370] in Opticks, and the Ear without Knowledge of Sounds? Howdo the Motions of the Body follow from the Will, and whence is theInstinct in Animals? Is not the Sensory of Animals that place to whichthe sensitive Substance is present, and into which the sensible Speciesof Things are carried through the Nerves and Brain, that there they maybe perceived by their immediate presence to that Substance? And thesethings being rightly dispatch'd, does it not appear from Phænomena thatthere is a Being incorporeal, living, intelligent, omnipresent, who ininfinite Space, as it were in his Sensory, sees the things themselvesintimately, and throughly perceives them, and comprehends them wholly bytheir immediate presence to himself: Of which things the Images onlycarried through the Organs of Sense into our little Sensoriums, arethere seen and beheld by that which in us perceives and thinks. Andthough every true Step made in this Philosophy brings us not immediatelyto the Knowledge of the first Cause, yet it brings us nearer to it, andon that account is to be highly valued.

Qu. 29. Are not the Rays of Light very small Bodies emitted fromshining Substances? For such Bodies will pass through uniform Mediums inright Lines without bending into the Shadow, which is the Nature of theRays of Light. They will also be capable of several Properties, and beable to conserve their Properties unchanged in passing through severalMediums, which is another Condition of the Rays of Light. PellucidSubstances act upon the Rays of[Pg 371] Light at a distance in refracting,reflecting, and inflecting them, and the Rays mutually agitate the Partsof those Substances at a distance for heating them; and this Action andRe-action at a distance very much resembles an attractive Force betweenBodies. If Refraction be perform'd by Attraction of the Rays, the Sinesof Incidence must be to the Sines of Refraction in a given Proportion,as we shew'd in our Principles of Philosophy: And this Rule is true byExperience. The Rays of Light in going out of Glass into aVacuum, arebent towards the Glass; and if they fall too obliquely on theVacuum,they are bent backwards into the Glass, and totally reflected; and thisReflexion cannot be ascribed to the Resistance of an absoluteVacuum,but must be caused by the Power of the Glass attracting the Rays attheir going out of it into theVacuum, and bringing them back. For ifthe farther Surface of the Glass be moisten'd with Water or clear Oil,or liquid and clear Honey, the Rays which would otherwise be reflectedwill go into the Water, Oil, or Honey; and therefore are not reflectedbefore they arrive at the farther Surface of the Glass, and begin to goout of it. If they go out of it into the Water, Oil, or Honey, they goon, because the Attraction of the Glass is almost balanced and renderedineffectual by the contrary Attraction of the Liquor. But if they go outof it into aVacuum which has no Attraction to balance that of theGlass, the Attraction of the Glass either bends and refracts them, orbrings them back and reflects them. And this is still more evident bylaying together[Pg 372] two Prisms of Glass, or two Object-glasses of very longTelescopes, the one plane, the other a little convex, and so compressingthem that they do not fully touch, nor are too far asunder. For theLight which falls upon the farther Surface of the first Glass where theInterval between the Glasses is not above the ten hundred thousandthPart of an Inch, will go through that Surface, and through the Air orVacuum between the Glasses, and enter into the second Glass, as wasexplain'd in the first, fourth, and eighth Observations of the firstPart of the second Book. But, if the second Glass be taken away, theLight which goes out of the second Surface of the first Glass into theAir orVacuum, will not go on forwards, but turns back into the firstGlass, and is reflected; and therefore it is drawn back by the Power ofthe first Glass, there being nothing else to turn it back. Nothing moreis requisite for producing all the variety of Colours, and degrees ofRefrangibility, than that the Rays of Light be Bodies of differentSizes, the least of which may take violet the weakest and darkest of theColours, and be more easily diverted by refracting Surfaces from theright Course; and the rest as they are bigger and bigger, may make thestronger and more lucid Colours, blue, green, yellow, and red, and bemore and more difficultly diverted. Nothing more is requisite forputting the Rays of Light into Fits of easy Reflexion and easyTransmission, than that they be small Bodies which by their attractivePowers, or some other Force, stir up Vibrations in what they act upon,which Vibrations[Pg 373] being swifter than the Rays, overtake themsuccessively, and agitate them so as by turns to increase and decreasetheir Velocities, and thereby put them into those Fits. And lastly, theunusual Refraction of Island-Crystal looks very much as if it wereperform'd by some kind of attractive virtue lodged in certain Sides bothof the Rays, and of the Particles of the Crystal. For were it not forsome kind of Disposition or Virtue lodged in some Sides of the Particlesof the Crystal, and not in their other Sides, and which inclines andbends the Rays towards the Coast of unusual Refraction, the Rays whichfall perpendicularly on the Crystal, would not be refracted towards thatCoast rather than towards any other Coast, both at their Incidence andat their Emergence, so as to emerge perpendicularly by a contrarySituation of the Coast of unusual Refraction at the second Surface; theCrystal acting upon the Rays after they have pass'd through it, and areemerging into the Air; or, if you please, into aVacuum. And since theCrystal by this Disposition or Virtue does not act upon the Rays, unlesswhen one of their Sides of unusual Refraction looks towards that Coast,this argues a Virtue or Disposition in those Sides of the Rays, whichanswers to, and sympathizes with that Virtue or Disposition of theCrystal, as the Poles of two Magnets answer to one another. And asMagnetism may be intended and remitted, and is found only in the Magnetand in Iron: So this Virtue of refracting the perpendicular Rays isgreater in Island-Crystal, less in Crystal of[Pg 374] the Rock, and is not yetfound in other Bodies. I do not say that this Virtue is magnetical: Itseems to be of another kind. I only say, that whatever it be, it'sdifficult to conceive how the Rays of Light, unless they be Bodies, canhave a permanent Virtue in two of their Sides which is not in theirother Sides, and this without any regard to their Position to the Spaceor Medium through which they pass.

What I mean in this Question by aVacuum, and by the Attractions ofthe Rays of Light towards Glass or Crystal, may be understood by whatwas said in the 18th, 19th, and 20th Questions.

Quest. 30. Are not gross Bodies and Light convertible into oneanother, and may not Bodies receive much of their Activity from theParticles of Light which enter their Composition? For all fix'd Bodiesbeing heated emit Light so long as they continue sufficiently hot, andLight mutually stops in Bodies as often as its Rays strike upon theirParts, as we shew'd above. I know no Body less apt to shine than Water;and yet Water by frequent Distillations changes into fix'd Earth, as Mr.Boyle has try'd; and then this Earth being enabled to endure asufficient Heat, shines by Heat like other Bodies.

The changing of Bodies into Light, and Light into Bodies, is veryconformable to the Course of Nature, which seems delighted withTransmutations. Water, which is a very fluid tasteless Salt, she changesby Heat into Vapour, which is a sort of Air, and by Cold into Ice, whichis a hard, pellucid, brittle, fusible Stone; and this Stone returns intoWater by Heat,[Pg 375] and Vapour returns into Water by Cold. Earth by Heatbecomes Fire, and by Cold returns into Earth. Dense Bodies byFermentation rarify into several sorts of Air, and this Air byFermentation, and sometimes without it, returns into dense Bodies.Mercury appears sometimes in the form of a fluid Metal, sometimes in theform of a hard brittle Metal, sometimes in the form of a corrosivepellucid Salt call'd Sublimate, sometimes in the form of a tasteless,pellucid, volatile white Earth, call'dMercurius Dulcis; or in that ofa red opake volatile Earth, call'd Cinnaber; or in that of a red orwhite Precipitate, or in that of a fluid Salt; and in Distillation itturns into Vapour, and being agitatedin Vacuo, it shines like Fire.And after all these Changes it returns again into its first form ofMercury. Eggs grow from insensible Magnitudes, and change into Animals;Tadpoles into Frogs; and Worms into Flies. All Birds, Beasts and Fishes,Insects, Trees, and other Vegetables, with their several Parts, grow outof Water and watry Tinctures and Salts, and by Putrefaction return againinto watry Substances. And Water standing a few Days in the open Air,yields a Tincture, which (like that of Malt) by standing longer yields aSediment and a Spirit, but before Putrefaction is fit Nourishment forAnimals and Vegetables. And among such various and strangeTransmutations, why may not Nature change Bodies into Light, and Lightinto Bodies?

Quest. 31. Have not the small Particles of Bodies certain Powers,Virtues, or Forces, by which they[Pg 376] act at a distance, not only upon theRays of Light for reflecting, refracting, and inflecting them, but alsoupon one another for producing a great Part of the Phænomena of Nature?For it's well known, that Bodies act one upon another by the Attractionsof Gravity, Magnetism, and Electricity; and these Instances shew theTenor and Course of Nature, and make it not improbable but that theremay be more attractive Powers than these. For Nature is very consonantand conformable to her self. How these Attractions may be perform'd, Ido not here consider. What I call Attraction may be perform'd byimpulse, or by some other means unknown to me. I use that Word here tosignify only in general any Force by which Bodies tend towards oneanother, whatsoever be the Cause. For we must learn from the Phænomenaof Nature what Bodies attract one another, and what are the Laws andProperties of the Attraction, before we enquire the Cause by which theAttraction is perform'd. The Attractions of Gravity, Magnetism, andElectricity, reach to very sensible distances, and so have been observedby vulgar Eyes, and there may be others which reach to so smalldistances as hitherto escape Observation; and perhaps electricalAttraction may reach to such small distances, even without being excitedby Friction.

For when Salt of Tartar runsper Deliquium, is not this done by anAttraction between the Particles of the Salt of Tartar, and theParticles of the Water which float in the Air in the form of Vapours?And why does not common Salt, or Salt-petre, or Vitriol,[Pg 377] runperDeliquium, but for want of such an Attraction? Or why does not Salt ofTartar draw more Water out of the Air than in a certain Proportion toits quantity, but for want of an attractive Force after it is satiatedwith Water? And whence is it but from this attractive Power that Waterwhich alone distils with a gentle luke-warm Heat, will not distil fromSalt of Tartar without a great Heat? And is it not from the likeattractive Power between the Particles of Oil of Vitriol and theParticles of Water, that Oil of Vitriol draws to it a good quantity ofWater out of the Air, and after it is satiated draws no more, and inDistillation lets go the Water very difficultly? And when Water and Oilof Vitriol poured successively into the same Vessel grow very hot in themixing, does not this Heat argue a great Motion in the Parts of theLiquors? And does not this Motion argue, that the Parts of the twoLiquors in mixing coalesce with Violence, and by consequence rushtowards one another with an accelerated Motion? And whenAqua fortis,or Spirit of Vitriol poured upon Filings of Iron dissolves the Filingswith a great Heat and Ebullition, is not this Heat and Ebullitioneffected by a violent Motion of the Parts, and does not that Motionargue that the acid Parts of the Liquor rush towards the Parts of theMetal with violence, and run forcibly into its Pores till they getbetween its outmost Particles, and the main Mass of the Metal, andsurrounding those Particles loosen them from the main Mass, and set themat liberty to float off into the Water? And when the acid Particles,which alone[Pg 378] would distil with an easy Heat, will not separate from theParticles of the Metal without a very violent Heat, does not thisconfirm the Attraction between them?

When Spirit of Vitriol poured upon common Salt or Salt-petre makes anEbullition with the Salt, and unites with it, and in Distillation theSpirit of the common Salt or Salt-petre comes over much easier than itwould do before, and the acid part of the Spirit of Vitriol staysbehind; does not this argue that the fix'd Alcaly of the Salt attractsthe acid Spirit of the Vitriol more strongly than its own Spirit, andnot being able to hold them both, lets go its own? And when Oil ofVitriol is drawn off from its weight of Nitre, and from both theIngredients a compound Spirit of Nitre is distilled, and two parts ofthis Spirit are poured on one part of Oil of Cloves or Carraway Seeds,or of any ponderous Oil of vegetable or animal Substances, or Oil ofTurpentine thicken'd with a little Balsam of Sulphur, and the Liquorsgrow so very hot in mixing, as presently to send up a burning Flame;does not this very great and sudden Heat argue that the two Liquors mixwith violence, and that their Parts in mixing run towards one anotherwith an accelerated Motion, and clash with the greatest Force? And is itnot for the same reason that well rectified Spirit of Wine poured on thesame compound Spirit flashes; and that thePulvis fulminans, composedof Sulphur, Nitre, and Salt of Tartar, goes off with a more sudden andviolent Explosion than Gun-powder, the acid Spirits of the[Pg 379] Sulphur andNitre rushing towards one another, and towards the Salt of Tartar, withso great a violence, as by the shock to turn the whole at once intoVapour and Flame? Where the Dissolution is slow, it makes a slowEbullition and a gentle Heat; and where it is quicker, it makes agreater Ebullition with more heat; and where it is done at once, theEbullition is contracted into a sudden Blast or violent Explosion, witha heat equal to that of Fire and Flame. So when a Drachm of theabove-mention'd compound Spirit of Nitre was poured upon half a Drachmof Oil of Carraway Seedsin vacuo, the Mixture immediately made aflash like Gun-powder, and burst the exhausted Receiver, which was aGlass six Inches wide, and eight Inches deep. And even the gross Body ofSulphur powder'd, and with an equal weight of Iron Filings and a littleWater made into Paste, acts upon the Iron, and in five or six hoursgrows too hot to be touch'd, and emits a Flame. And by these Experimentscompared with the great quantity of Sulphur with which the Earthabounds, and the warmth of the interior Parts of the Earth, and hotSprings, and burning Mountains, and with Damps, mineral Coruscations,Earthquakes, hot suffocating Exhalations, Hurricanes, and Spouts; we maylearn that sulphureous Steams abound in the Bowels of the Earth andferment with Minerals, and sometimes take fire with a sudden Coruscationand Explosion; and if pent up in subterraneous Caverns, burst theCaverns with a great shaking of the Earth, as in springing of a Mine.And then the Vapour[Pg 380] generated by the Explosion, expiring through thePores of the Earth, feels hot and suffocates, and makes Tempests andHurricanes, and sometimes causes the Land to slide, or the Sea to boil,and carries up the Water thereof in Drops, which by their weight falldown again in Spouts. Also some sulphureous Steams, at all times whenthe Earth is dry, ascending into the Air, ferment there with nitrousAcids, and sometimes taking fire cause Lightning and Thunder, and fieryMeteors. For the Air abounds with acid Vapours fit to promoteFermentations, as appears by the rusting of Iron and Copper in it, thekindling of Fire by blowing, and the beating of the Heart by means ofRespiration. Now the above-mention'd Motions are so great and violent asto shew that in Fermentations the Particles of Bodies which almost rest,are put into new Motions by a very potent Principle, which acts uponthem only when they approach one another, and causes them to meet andclash with great violence, and grow hot with the motion, and dash oneanother into pieces, and vanish into Air, and Vapour, and Flame.

When Salt of Tartarper deliquium, being poured into the Solution ofany Metal, precipitates the Metal and makes it fall down to the bottomof the Liquor in the form of Mud: Does not this argue that the acidParticles are attracted more strongly by the Salt of Tartar than by theMetal, and by the stronger Attraction go from the Metal to the Salt ofTartar? And so when a Solution of Iron inAqua fortis dissolves theLapis Calaminaris, and lets go the Iron, or a Solution[Pg 381] of Copperdissolves Iron immersed in it and lets go the Copper, or a Solution ofSilver dissolves Copper and lets go the Silver, or a Solution of MercuryinAqua fortis being poured upon Iron, Copper, Tin, or Lead, dissolvesthe Metal and lets go the Mercury; does not this argue that the acidParticles of theAqua fortis are attracted more strongly by theLapisCalaminaris than by Iron, and more strongly by Iron than by Copper, andmore strongly by Copper than by Silver, and more strongly by Iron,Copper, Tin, and Lead, than by Mercury? And is it not for the samereason that Iron requires moreAqua fortis to dissolve it than Copper,and Copper more than the other Metals; and that of all Metals, Iron isdissolved most easily, and is most apt to rust; and next after Iron,Copper?

When Oil of Vitriol is mix'd with a little Water, or is runperdeliquium, and in Distillation the Water ascends difficultly, andbrings over with it some part of the Oil of Vitriol in the form ofSpirit of Vitriol, and this Spirit being poured upon Iron, Copper, orSalt of Tartar, unites with the Body and lets go the Water; doth notthis shew that the acid Spirit is attracted by the Water, and moreattracted by the fix'd Body than by the Water, and therefore lets go theWater to close with the fix'd Body? And is it not for the same reasonthat the Water and acid Spirits which are mix'd together in Vinegar,Aqua fortis, and Spirit of Salt, cohere and rise together inDistillation; but if theMenstruum be poured on Salt of Tartar, or onLead, or Iron, or any fix'd Body which[Pg 382] it can dissolve, the Acid by astronger Attraction adheres to the Body, and lets go the Water? And isit not also from a mutual Attraction that the Spirits of Soot andSea-Salt unite and compose the Particles of Sal-armoniac, which are lessvolatile than before, because grosser and freer from Water; and that theParticles of Sal-armoniac in Sublimation carry up the Particles ofAntimony, which will not sublime alone; and that the Particles ofMercury uniting with the acid Particles of Spirit of Salt composeMercury sublimate, and with the Particles of Sulphur, compose Cinnaber;and that the Particles of Spirit of Wine and Spirit of Urine wellrectified unite, and letting go the Water which dissolved them, composea consistent Body; and that in subliming Cinnaber from Salt of Tartar,or from quick Lime, the Sulphur by a stronger Attraction of the Salt orLime lets go the Mercury, and stays with the fix'd Body; and that whenMercury sublimate is sublimed from Antimony, or from Regulus ofAntimony, the Spirit of Salt lets go the Mercury, and unites with theantimonial metal which attracts it more strongly, and stays with it tillthe Heat be great enough to make them both ascend together, and thencarries up the Metal with it in the form of a very fusible Salt, calledButter of Antimony, although the Spirit of Salt alone be almost asvolatile as Water, and the Antimony alone as fix'd as Lead?

WhenAqua fortis dissolves Silver and not Gold, andAqua regiadissolves Gold and not Silver, may it not be said thatAqua fortis issubtil enough to[Pg 383] penetrate Gold as well as Silver, but wants theattractive Force to give it Entrance; and thatAqua regia is subtilenough to penetrate Silver as well as Gold, but wants the attractiveForce to give it Entrance? ForAqua regia is nothing else thanAquafortis mix'd with some Spirit of Salt, or with Sal-armoniac; and evencommon Salt dissolved inAqua fortis, enables theMenstruum todissolve Gold, though the Salt be a gross Body. When therefore Spirit ofSalt precipitates Silver out ofAqua fortis, is it not done byattracting and mixing with theAqua fortis, and not attracting, orperhaps repelling Silver? And when Water precipitates Antimony out ofthe Sublimate of Antimony and Sal-armoniac, or out of Butter ofAntimony, is it not done by its dissolving, mixing with, and weakeningthe Sal-armoniac or Spirit of Salt, and its not attracting, or perhapsrepelling the Antimony? And is it not for want of an attractive virtuebetween the Parts of Water and Oil, of Quick-silver and Antimony, ofLead and Iron, that these Substances do not mix; and by a weakAttraction, that Quick-silver and Copper mix difficultly; and from astrong one, that Quick-silver and Tin, Antimony and Iron, Water andSalts, mix readily? And in general, is it not from the same Principlethat Heat congregates homogeneal Bodies, and separates heterogenealones?

When Arsenick with Soap gives a Regulus, and with Mercury sublimate avolatile fusible Salt, like Butter of Antimony, doth not this shew thatArsenick, which is a Substance totally volatile, is compounded[Pg 384] of fix'dand volatile Parts, strongly cohering by a mutual Attraction, so thatthe volatile will not ascend without carrying up the fixed? And so, whenan equal weight of Spirit of Wine and Oil of Vitriol are digestedtogether, and in Distillation yield two fragrant and volatile Spiritswhich will not mix with one another, and a fix'd black Earth remainsbehind; doth not this shew that Oil of Vitriol is composed of volatileand fix'd Parts strongly united by Attraction, so as to ascend togetherin form of a volatile, acid, fluid Salt, until the Spirit of Wineattracts and separates the volatile Parts from the fixed? And therefore,since Oil of Sulphurper Campanam is of the same Nature with Oil ofVitriol, may it not be inferred, that Sulphur is also a mixture ofvolatile and fix'd Parts so strongly cohering by Attraction, as toascend together in Sublimation. By dissolving Flowers of Sulphur in Oilof Turpentine, and distilling the Solution, it is found that Sulphur iscomposed of an inflamable thick Oil or fat Bitumen, an acid Salt, a veryfix'd Earth, and a little Metal. The three first were found not muchunequal to one another, the fourth in so small a quantity as scarce tobe worth considering. The acid Salt dissolved in Water, is the same withOil of Sulphurper Campanam, and abounding much in the Bowels of theEarth, and particularly in Markasites, unites it self to the otherIngredients of the Markasite, which are, Bitumen, Iron, Copper, andEarth, and with them compounds Allum, Vitriol, and Sulphur. With theEarth alone it compounds Allum; with the Metal alone, or Metal[Pg 385] andEarth together, it compounds Vitriol; and with the Bitumen and Earth itcompounds Sulphur. Whence it comes to pass that Markasites abound withthose three Minerals. And is it not from the mutual Attraction of theIngredients that they stick together for compounding these Minerals, andthat the Bitumen carries up the other Ingredients of the Sulphur, whichwithout it would not sublime? And the same Question may be putconcerning all, or almost all the gross Bodies in Nature. For all theParts of Animals and Vegetables are composed of Substances volatile andfix'd, fluid and solid, as appears by their Analysis; and so are Saltsand Minerals, so far as Chymists have been hitherto able to examinetheir Composition.

When Mercury sublimate is re-sublimed with fresh Mercury, and becomesMercurius Dulcis, which is a white tasteless Earth scarce dissolvablein Water, andMercurius Dulcis re-sublimed with Spirit of Salt returnsinto Mercury sublimate; and when Metals corroded with a little acid turninto rust, which is an Earth tasteless and indissolvable in Water, andthis Earth imbibed with more acid becomes a metallick Salt; and whensome Stones, as Spar of Lead, dissolved in properMenstruums becomeSalts; do not these things shew that Salts are dry Earth and watry Acidunited by Attraction, and that the Earth will not become a Salt withoutso much acid as makes it dissolvable in Water? Do not the sharp andpungent Tastes of Acids arise from the strong Attraction whereby theacid Particles rush upon and agitate the[Pg 386] Particles of the Tongue? Andwhen Metals are dissolved in acidMenstruums, and the Acids inconjunction with the Metal act after a different manner, so that theCompound has a different Taste much milder than before, and sometimes asweet one; is it not because the Acids adhere to the metallickParticles, and thereby lose much of their Activity? And if the Acid bein too small a Proportion to make the Compound dissolvable in Water,will it not by adhering strongly to the Metal become unactive and loseits Taste, and the Compound be a tasteless Earth? For such things as arenot dissolvable by the Moisture of the Tongue, act not upon the Taste.

As Gravity makes the Sea flow round the denser and weightier Parts ofthe Globe of the Earth, so the Attraction may make the watry Acid flowround the denser and compacter Particles of Earth for composing theParticles of Salt. For otherwise the Acid would not do the Office of aMedium between the Earth and common Water, for making Salts dissolvablein the Water; nor would Salt of Tartar readily draw off the Acid fromdissolved Metals, nor Metals the Acid from Mercury. Now, as in the greatGlobe of the Earth and Sea, the densest Bodies by their Gravity sinkdown in Water, and always endeavour to go towards the Center of theGlobe; so in Particles of Salt, the densest Matter may always endeavourto approach the Center of the Particle: So that a Particle of Salt maybe compared to a Chaos; being dense, hard, dry, and earthy in theCenter; and rare, soft, moist, and watry in the Circumference.[Pg 387] Andhence it seems to be that Salts are of a lasting Nature, being scarcedestroy'd, unless by drawing away their watry Parts by violence, or byletting them soak into the Pores of the central Earth by a gentle Heatin Putrefaction, until the Earth be dissolved by the Water, andseparated into smaller Particles, which by reason of their Smallnessmake the rotten Compound appear of a black Colour. Hence also it may be,that the Parts of Animals and Vegetables preserve their several Forms,and assimilate their Nourishment; the soft and moist Nourishment easilychanging its Texture by a gentle Heat and Motion, till it becomes likethe dense, hard, dry, and durable Earth in the Center of each Particle.But when the Nourishment grows unfit to be assimilated, or the centralEarth grows too feeble to assimilate it, the Motion ends in Confusion,Putrefaction, and Death.

If a very small quantity of any Salt or Vitriol be dissolved in a greatquantity of Water, the Particles of the Salt or Vitriol will not sink tothe bottom, though they be heavier in Specie than the Water, but willevenly diffuse themselves into all the Water, so as to make it as salineat the top as at the bottom. And does not this imply that the Parts ofthe Salt or Vitriol recede from one another, and endeavour to expandthemselves, and get as far asunder as the quantity of Water in whichthey float, will allow? And does not this Endeavour imply that they havea repulsive Force by which they fly from one another, or at least, thatthey attract the Water more strongly[Pg 388] than they do one another? For asall things ascend in Water which are less attracted than Water, by thegravitating Power of the Earth; so all the Particles of Salt which floatin Water, and are less attracted than Water by any one Particle of Salt,must recede from that Particle, and give way to the more attractedWater.

When any saline Liquor is evaporated to a Cuticle and let cool, the Saltconcretes in regular Figures; which argues, that the Particles of theSalt before they concreted, floated in the Liquor at equal distances inrank and file, and by consequence that they acted upon one another bysome Power which at equal distances is equal, at unequal distancesunequal. For by such a Power they will range themselves uniformly, andwithout it they will float irregularly, and come together asirregularly. And since the Particles of Island-Crystal act all the sameway upon the Rays of Light for causing the unusual Refraction, may itnot be supposed that in the Formation of this Crystal, the Particles notonly ranged themselves in rank and file for concreting in regularFigures, but also by some kind of polar Virtue turned their homogenealSides the same way.

The Parts of all homogeneal hard Bodies which fully touch one another,stick together very strongly. And for explaining how this may be, somehave invented hooked Atoms, which is begging the Question; and otherstell us that Bodies are glued together by rest, that is, by an occultQuality, or rather by nothing; and others, that they stick together byconspiring[Pg 389] Motions, that is, by relative rest amongst themselves. I hadrather infer from their Cohesion, that their Particles attract oneanother by some Force, which in immediate Contact is exceeding strong,at small distances performs the chymical Operations above-mention'd, andreaches not far from the Particles with any sensible Effect.

All Bodies seem to be composed of hard Particles: For otherwise Fluidswould not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitrioldo by freezing; Mercury by Fumes of Lead; Spirit of Nitre and Mercury,by dissolving the Mercury and evaporating the Flegm; Spirit of Wine andSpirit of Urine, by deflegming and mixing them; and Spirit of Urine andSpirit of Salt, by subliming them together to make Sal-armoniac. Eventhe Rays of Light seem to be hard Bodies; for otherwise they would notretain different Properties in their different Sides. And thereforeHardness may be reckon'd the Property of all uncompounded Matter. Atleast, this seems to be as evident as the universal Impenetrability ofMatter. For all Bodies, so far as Experience reaches, are either hard,or may be harden'd; and we have no other Evidence of universalImpenetrability, besides a large Experience without an experimentalException. Now if compound Bodies are so very hard as we find some ofthem to be, and yet are very porous, and consist of Parts which are onlylaid together; the simple Particles which are void of Pores, and werenever yet divided, must be much harder. For such hard Particles beingheaped up together, can scarce[Pg 390] touch one another in more than a fewPoints, and therefore must be separable by much less Force than isrequisite to break a solid Particle, whose Parts touch in all the Spacebetween them, without any Pores or Interstices to weaken their Cohesion.And how such very hard Particles which are only laid together and touchonly in a few Points, can stick together, and that so firmly as they do,without the assistance of something which causes them to be attracted orpress'd towards one another, is very difficult to conceive.

The same thing I infer also from the cohering of two polish'd Marblesin vacuo, and from the standing of Quick-silver in the Barometer atthe height of 50, 60 or 70 Inches, or above, when ever it is well-purgedof Air and carefully poured in, so that its Parts be every wherecontiguous both to one another and to the Glass. The Atmosphere by itsweight presses the Quick-silver into the Glass, to the height of 29 or30 Inches. And some other Agent raises it higher, not by pressing itinto the Glass, but by making its Parts stick to the Glass, and to oneanother. For upon any discontinuation of Parts, made either by Bubblesor by shaking the Glass, the whole Mercury falls down to the height of29 or 30 Inches.

And of the same kind with these Experiments are those that follow. Iftwo plane polish'd Plates of Glass (suppose two pieces of a polish'dLooking-glass) be laid together, so that their sides be parallel and ata very small distance from one another, and then their lower edges bedipped into Water, the[Pg 391] Water will rise up between them. And the lessthe distance of the Glasses is, the greater will be the height to whichthe Water will rise. If the distance be about the hundredth part of anInch, the Water will rise to the height of about an Inch; and if thedistance be greater or less in any Proportion, the height will bereciprocally proportional to the distance very nearly. For theattractive Force of the Glasses is the same, whether the distancebetween them be greater or less; and the weight of the Water drawn up isthe same, if the height of it be reciprocally proportional to thedistance of the Glasses. And in like manner, Water ascends between twoMarbles polish'd plane, when their polish'd sides are parallel, and at avery little distance from one another, And if slender Pipes of Glass bedipped at one end into stagnating Water, the Water will rise up withinthe Pipe, and the height to which it rises will be reciprocallyproportional to the Diameter of the Cavity of the Pipe, and will equalthe height to which it rises between two Planes of Glass, if theSemi-diameter of the Cavity of the Pipe be equal to the distance betweenthe Planes, or thereabouts. And these Experiments succeed after the samemannerin vacuo as in the open Air, (as hath been tried before theRoyal Society,) and therefore are not influenced by the Weight orPressure of the Atmosphere.

And if a large Pipe of Glass be filled with sifted Ashes well pressedtogether in the Glass, and one end of the Pipe be dipped into stagnatingWater, the Water will rise up slowly in the Ashes, so as in[Pg 392] the spaceof a Week or Fortnight to reach up within the Glass, to the height of 30or 40 Inches above the stagnating Water. And the Water rises up to thisheight by the Action only of those Particles of the Ashes which are uponthe Surface of the elevated Water; the Particles which are within theWater, attracting or repelling it as much downwards as upwards. Andtherefore the Action of the Particles is very strong. But the Particlesof the Ashes being not so dense and close together as those of Glass,their Action is not so strong as that of Glass, which keeps Quick-silversuspended to the height of 60 or 70 Inches, and therefore acts with aForce which would keep Water suspended to the height of above 60 Feet.

By the same Principle, a Sponge sucks in Water, and the Glands in theBodies of Animals, according to their several Natures and Dispositions,suck in various Juices from the Blood.

If two plane polish'd Plates of Glass three or four Inches broad, andtwenty or twenty five long, be laid one of them parallel to the Horizon,the other upon the first, so as at one of their ends to touch oneanother, and contain an Angle of about 10 or 15 Minutes, and the same befirst moisten'd on their inward sides with a clean Cloth dipp'd into Oilof Oranges or Spirit of Turpentine, and a Drop or two of the Oil orSpirit be let fall upon the lower Glass at the other; so soon as theupper Glass is laid down upon the lower, so as to touch it at one end asabove, and to touch the Drop at the other end, making with the lowerGlass an Angle of about 10 or 15[Pg 393] Minutes; the Drop will begin to movetowards the Concourse of the Glasses, and will continue to move with anaccelerated Motion, till it arrives at that Concourse of the Glasses.For the two Glasses attract the Drop, and make it run that way towardswhich the Attractions incline. And if when the Drop is in motion youlift up that end of the Glasses where they meet, and towards which theDrop moves, the Drop will ascend between the Glasses, and therefore isattracted. And as you lift up the Glasses more and more, the Drop willascend slower and slower, and at length rest, being then carrieddownward by its Weight, as much as upwards by the Attraction. And bythis means you may know the Force by which the Drop is attracted at alldistances from the Concourse of the Glasses.

Now by some Experiments of this kind, (made by Mr.Hauksbee) it hasbeen found that the Attraction is almost reciprocally in a duplicateProportion of the distance of the middle of the Drop from the Concourseof the Glasses,viz. reciprocally in a simple Proportion, by reason ofthe spreading of the Drop, and its touching each Glass in a largerSurface; and again reciprocally in a simple Proportion, by reason of theAttractions growing stronger within the same quantity of attractingSurface. The Attraction therefore within the same quantity of attractingSurface, is reciprocally as the distance between the Glasses. Andtherefore where the distance is exceeding small, the Attraction must beexceeding great. By the Table in the second Part of the second Book,wherein the[Pg 394] thicknesses of colour'd Plates of Water between two Glassesare set down, the thickness of the Plate where it appears very black, isthree eighths of the ten hundred thousandth part of an Inch. And wherethe Oil of Oranges between the Glasses is of this thickness, theAttraction collected by the foregoing Rule, seems to be so strong, aswithin a Circle of an Inch in diameter, to suffice to hold up a Weightequal to that of a Cylinder of Water of an Inch in diameter, and two orthree Furlongs in length. And where it is of a less thickness theAttraction may be proportionally greater, and continue to increase,until the thickness do not exceed that of a single Particle of the Oil.There are therefore Agents in Nature able to make the Particles ofBodies stick together by very strong Attractions. And it is the Businessof experimental Philosophy to find them out.

Now the smallest Particles of Matter may cohere by the strongestAttractions, and compose bigger Particles of weaker Virtue; and many ofthese may cohere and compose bigger Particles whose Virtue is stillweaker, and so on for divers Successions, until the Progression end inthe biggest Particles on which the Operations in Chymistry, and theColours of natural Bodies depend, and which by cohering compose Bodiesof a sensible Magnitude. If the Body is compact, and bends or yieldsinward to Pression without any sliding of its Parts, it is hard andelastick, returning to its Figure with a Force rising from the mutualAttraction of its Parts. If the Parts slide upon one another, the Bodyis malleable or soft. If they[Pg 395] slip easily, and are of a fit Size to beagitated by Heat, and the Heat is big enough to keep them in Agitation,the Body is fluid; and if it be apt to stick to things, it is humid; andthe Drops of every fluid affect a round Figure by the mutual Attractionof their Parts, as the Globe of the Earth and Sea affects a round Figureby the mutual Attraction of its Parts by Gravity.

Since Metals dissolved in Acids attract but a small quantity of theAcid, their attractive Force can reach but to a small distance fromthem. And as in Algebra, where affirmative Quantities vanish and cease,there negative ones begin; so in Mechanicks, where Attraction ceases,there a repulsive Virtue ought to succeed. And that there is such aVirtue, seems to follow from the Reflexions and Inflexions of the Raysof Light. For the Rays are repelled by Bodies in both these Cases,without the immediate Contact of the reflecting or inflecting Body. Itseems also to follow from the Emission of Light; the Ray so soon as itis shaken off from a shining Body by the vibrating Motion of the Partsof the Body, and gets beyond the reach of Attraction, being driven awaywith exceeding great Velocity. For that Force which is sufficient toturn it back in Reflexion, may be sufficient to emit it. It seems alsoto follow from the Production of Air and Vapour. The Particles when theyare shaken off from Bodies by Heat or Fermentation, so soon as they arebeyond the reach of the Attraction of the Body, receding from it, andalso from one another with great Strength, and keeping at a distance,[Pg 396]so as sometimes to take up above a Million of Times more space than theydid before in the form of a dense Body. Which vast Contraction andExpansion seems unintelligible, by feigning the Particles of Air to bespringy and ramous, or rolled up like Hoops, or by any other means thana repulsive Power. The Particles of Fluids which do not cohere toostrongly, and are of such a Smallness as renders them most susceptibleof those Agitations which keep Liquors in a Fluor, are most easilyseparated and rarified into Vapour, and in the Language of the Chymists,they are volatile, rarifying with an easy Heat, and condensing withCold. But those which are grosser, and so less susceptible of Agitation,or cohere by a stronger Attraction, are not separated without a strongerHeat, or perhaps not without Fermentation. And these last are the Bodieswhich Chymists call fix'd, and being rarified by Fermentation, becometrue permanent Air; those Particles receding from one another with thegreatest Force, and being most difficultly brought together, which uponContact cohere most strongly. And because the Particles of permanent Airare grosser, and arise from denser Substances than those of Vapours,thence it is that true Air is more ponderous than Vapour, and that amoist Atmosphere is lighter than a dry one, quantity for quantity. Fromthe same repelling Power it seems to be that Flies walk upon the Waterwithout wetting their Feet; and that the Object-glasses of longTelescopes lie upon one another without touching; and that dry Powdersare difficultly[Pg 397] made to touch one another so as to stick together,unless by melting them, or wetting them with Water, which by exhalingmay bring them together; and that two polish'd Marbles, which byimmediate Contact stick together, are difficultly brought so closetogether as to stick.

And thus Nature will be very conformable to her self and very simple,performing all the great Motions of the heavenly Bodies by theAttraction of Gravity which intercedes those Bodies, and almost all thesmall ones of their Particles by some other attractive and repellingPowers which intercede the Particles. TheVis inertiæ is a passivePrinciple by which Bodies persist in their Motion or Rest, receiveMotion in proportion to the Force impressing it, and resist as much asthey are resisted. By this Principle alone there never could have beenany Motion in the World. Some other Principle was necessary for puttingBodies into Motion; and now they are in Motion, some other Principle isnecessary for conserving the Motion. For from the various Composition oftwo Motions, 'tis very certain that there is not always the samequantity of Motion in the World. For if two Globes joined by a slenderRod, revolve about their common Center of Gravity with an uniformMotion, while that Center moves on uniformly in a right Line drawn inthe Plane of their circular Motion; the Sum of the Motions of the twoGlobes, as often as the Globes are in the right Line described by theircommon Center of Gravity, will be bigger than the Sum of their Motions,when they are in a Line perpendicular[Pg 398] to that right Line. By thisInstance it appears that Motion may be got or lost. But by reason of theTenacity of Fluids, and Attrition of their Parts, and the Weakness ofElasticity in Solids, Motion is much more apt to be lost than got, andis always upon the Decay. For Bodies which are either absolutely hard,or so soft as to be void of Elasticity, will not rebound from oneanother. Impenetrability makes them only stop. If two equal Bodies meetdirectlyin vacuo, they will by the Laws of Motion stop where theymeet, and lose all their Motion, and remain in rest, unless they beelastick, and receive new Motion from their Spring. If they have so muchElasticity as suffices to make them re-bound with a quarter, or half, orthree quarters of the Force with which they come together, they willlose three quarters, or half, or a quarter of their Motion. And this maybe try'd, by letting two equal Pendulums fall against one another fromequal heights. If the Pendulums be of Lead or soft Clay, they will loseall or almost all their Motions: If of elastick Bodies they will loseall but what they recover from their Elasticity. If it be said, thatthey can lose no Motion but what they communicate to other Bodies, theconsequence is, thatin vacuo they can lose no Motion, but when theymeet they must go on and penetrate one another's Dimensions. If threeequal round Vessels be filled, the one with Water, the other with Oil,the third with molten Pitch, and the Liquors be stirred about alike togive them a vortical Motion; the Pitch by its Tenacity will lose itsMotion quickly, the Oil[Pg 399] being less tenacious will keep it longer, andthe Water being less tenacious will keep it longest, but yet will loseit in a short time. Whence it is easy to understand, that if manycontiguous Vortices of molten Pitch were each of them as large as thosewhich some suppose to revolve about the Sun and fix'd Stars, yet theseand all their Parts would, by their Tenacity and Stiffness, communicatetheir Motion to one another till they all rested among themselves.Vortices of Oil or Water, or some fluider Matter, might continue longerin Motion; but unless the Matter were void of all Tenacity and Attritionof Parts, and Communication of Motion, (which is not to be supposed,)the Motion would constantly decay. Seeing therefore the variety ofMotion which we find in the World is always decreasing, there is anecessity of conserving and recruiting it by active Principles, such asare the cause of Gravity, by which Planets and Comets keep their Motionsin their Orbs, and Bodies acquire great Motion in falling; and the causeof Fermentation, by which the Heart and Blood of Animals are kept inperpetual Motion and Heat; the inward Parts of the Earth are constantlywarm'd, and in some places grow very hot; Bodies burn and shine,Mountains take fire, the Caverns of the Earth are blown up, and the Suncontinues violently hot and lucid, and warms all things by his Light.For we meet with very little Motion in the World, besides what is owingto these active Principles. And if it were not for these Principles, theBodies of the Earth, Planets, Comets, Sun, and all things in them,[Pg 400]would grow cold and freeze, and become inactive Masses; and allPutrefaction, Generation, Vegetation and Life would cease, and thePlanets and Comets would not remain in their Orbs.

All these things being consider'd, it seems probable to me, that God inthe Beginning form'd Matter in solid, massy, hard, impenetrable,moveable Particles, of such Sizes and Figures, and with such otherProperties, and in such Proportion to Space, as most conduced to the Endfor which he form'd them; and that these primitive Particles beingSolids, are incomparably harder than any porous Bodies compounded ofthem; even so very hard, as never to wear or break in pieces; noordinary Power being able to divide what God himself made one in thefirst Creation. While the Particles continue entire, they may composeBodies of one and the same Nature and Texture in all Ages: But shouldthey wear away, or break in pieces, the Nature of Things depending onthem, would be changed. Water and Earth, composed of old worn Particlesand Fragments of Particles, would not be of the same Nature and Texturenow, with Water and Earth composed of entire Particles in the Beginning.And therefore, that Nature may be lasting, the Changes of corporealThings are to be placed only in the various Separations and newAssociations and Motions of these permanent Particles; compound Bodiesbeing apt to break, not in the midst of solid Particles, but where thoseParticles are laid together, and only touch in a few Points.[Pg 401]

It seems to me farther, that these Particles have not only aVisinertiæ, accompanied with such passive Laws of Motion as naturallyresult from that Force, but also that they are moved by certain activePrinciples, such as is that of Gravity, and that which causesFermentation, and the Cohesion of Bodies. These Principles I consider,not as occult Qualities, supposed to result from the specifick Forms ofThings, but as general Laws of Nature, by which the Things themselvesare form'd; their Truth appearing to us by Phænomena, though theirCauses be not yet discover'd. For these are manifest Qualities, andtheir Causes only are occult. And theAristotelians gave the Name ofoccult Qualities, not to manifest Qualities, but to such Qualities onlyas they supposed to lie hid in Bodies, and to be the unknown Causes ofmanifest Effects: Such as would be the Causes of Gravity, and ofmagnetick and electrick Attractions, and of Fermentations, if we shouldsuppose that these Forces or Actions arose from Qualities unknown to us,and uncapable of being discovered and made manifest. Such occultQualities put a stop to the Improvement of natural Philosophy, andtherefore of late Years have been rejected. To tell us that everySpecies of Things is endow'd with an occult specifick Quality by whichit acts and produces manifest Effects, is to tell us nothing: But toderive two or three general Principles of Motion from Phænomena, andafterwards to tell us how the Properties and Actions of all corporealThings follow from those manifest Principles, would be a very great stepin[Pg 402] Philosophy, though the Causes of those Principles were not yetdiscover'd: And therefore I scruple not to propose the Principles ofMotion above-mention'd, they being of very general Extent, and leavetheir Causes to be found out.

Now by the help of these Principles, all material Things seem to havebeen composed of the hard and solid Particles above-mention'd, variouslyassociated in the first Creation by the Counsel of an intelligent Agent.For it became him who created them to set them in order. And if he didso, it's unphilosophical to seek for any other Origin of the World, orto pretend that it might arise out of a Chaos by the mere Laws ofNature; though being once form'd, it may continue by those Laws for manyAges. For while Comets move in very excentrick Orbs in all manner ofPositions, blind Fate could never make all the Planets move one and thesame way in Orbs concentrick, some inconsiderable Irregularitiesexcepted, which may have risen from the mutual Actions of Comets andPlanets upon one another, and which will be apt to increase, till thisSystem wants a Reformation. Such a wonderful Uniformity in the PlanetarySystem must be allowed the Effect of Choice. And so must the Uniformityin the Bodies of Animals, they having generally a right and a left sideshaped alike, and on either side of their Bodies two Legs behind, andeither two Arms, or two Legs, or two Wings before upon their Shoulders,and between their Shoulders a Neck running down into a Back-bone, and aHead upon it; and in the Head two[Pg 403] Ears, two Eyes, a Nose, a Mouth, anda Tongue, alike situated. Also the first Contrivance of those veryartificial Parts of Animals, the Eyes, Ears, Brain, Muscles, Heart,Lungs, Midriff, Glands, Larynx, Hands, Wings, swimming Bladders, naturalSpectacles, and other Organs of Sense and Motion; and the Instinct ofBrutes and Insects, can be the effect of nothing else than the Wisdomand Skill of a powerful ever-living Agent, who being in all Places, ismore able by his Will to move the Bodies within his boundless uniformSensorium, and thereby to form and reform the Parts of the Universe,than we are by our Will to move the Parts of our own Bodies. And yet weare not to consider the World as the Body of God, or the several Partsthereof, as the Parts of God. He is an uniform Being, void of Organs,Members or Parts, and they are his Creatures subordinate to him, andsubservient to his Will; and he is no more the Soul of them, than theSoul of Man is the Soul of the Species of Things carried through theOrgans of Sense into the place of its Sensation, where it perceives themby means of its immediate Presence, without the Intervention of anythird thing. The Organs of Sense are not for enabling the Soul toperceive the Species of Things in its Sensorium, but only for conveyingthem thither; and God has no need of such Organs, he being every wherepresent to the Things themselves. And since Space is divisibleininfinitum, and Matter is not necessarily in all places, it may be alsoallow'd that God is able to create Particles of Matter of several Sizesand[Pg 404] Figures, and in several Proportions to Space, and perhaps ofdifferent Densities and Forces, and thereby to vary the Laws of Nature,and make Worlds of several sorts in several Parts of the Universe. Atleast, I see nothing of Contradiction in all this.

As in Mathematicks, so in Natural Philosophy, the Investigation ofdifficult Things by the Method of Analysis, ought ever to precede theMethod of Composition. This Analysis consists in making Experiments andObservations, and in drawing general Conclusions from them by Induction,and admitting of no Objections against the Conclusions, but such as aretaken from Experiments, or other certain Truths. For Hypotheses are notto be regarded in experimental Philosophy. And although the arguing fromExperiments and Observations by Induction be no Demonstration of generalConclusions; yet it is the best way of arguing which the Nature ofThings admits of, and may be looked upon as so much the stronger, by howmuch the Induction is more general. And if no Exception occur fromPhænomena, the Conclusion may be pronounced generally. But if at anytime afterwards any Exception shall occur from Experiments, it may thenbegin to be pronounced with such Exceptions as occur. By this way ofAnalysis we may proceed from Compounds to Ingredients, and from Motionsto the Forces producing them; and in general, from Effects to theirCauses, and from particular Causes to more general ones, till theArgument end in the most general. This is the Method of Analysis: Andthe[Pg 405] Synthesis consists in assuming the Causes discover'd, andestablish'd as Principles, and by them explaining the Phænomenaproceeding from them, and proving the Explanations.

In the two first Books of these Opticks, I proceeded by this Analysis todiscover and prove the original Differences of the Rays of Light inrespect of Refrangibility, Reflexibility, and Colour, and theiralternate Fits of easy Reflexion and easy Transmission, and theProperties of Bodies, both opake and pellucid, on which their Reflexionsand Colours depend. And these Discoveries being proved, may be assumedin the Method of Composition for explaining the Phænomena arising fromthem: An Instance of which Method I gave in the End of the first Book.In this third Book I have only begun the Analysis of what remains to bediscover'd about Light and its Effects upon the Frame of Nature, hintingseveral things about it, and leaving the Hints to be examin'd andimprov'd by the farther Experiments and Observations of such as areinquisitive. And if natural Philosophy in all its Parts, by pursuingthis Method, shall at length be perfected, the Bounds of MoralPhilosophy will be also enlarged. For so far as we can know by naturalPhilosophy what is the first Cause, what Power he has over us, and whatBenefits we receive from him, so far our Duty towards him, as well asthat towards one another, will appear to us by the Light of Nature. Andno doubt, if the Worship of false Gods had not blinded the Heathen,their moral Philosophy would have gone farther than[Pg 406] to the fourCardinal Virtues; and instead of teaching the Transmigration of Souls,and to worship the Sun and Moon, and dead Heroes, they would have taughtus to worship our true Author and Benefactor, as their Ancestors didunder the Government ofNoah and his Sons before they corruptedthemselves.

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OPTICKS:

OR, A

TREATISE

OF THE

Reflections,Refractions,Inflections andColours

OF

LIGHT.

TheFourth Edition,corrected.

By SirISAAC NEWTON, Knt.

SIR ISAAC NEWTON'S ADVERTISEMENTS

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THE FIRST BOOK OF OPTICKS

PART I.

DEFINITIONS

DEFIN. I.

DEFIN. II.

DEFIN. III.

DEFIN. IV.

DEFIN. V.

DEFIN. VI.

DEFIN. VII

DEFIN. VIII.

AXIOMS.

AX. I.

AX. II.

AX. III.

AX. IV.

AX. V.

AX. VI.

AX. VII.

AX. VIII.

FOOTNOTES:

PROPOSITIONS.

PROP. I.Theor. I.

PROP. II.Theor. II.

PROP. III.Theor. III.

PROP. IV.Prob. I.

PROP. V.Theor. IV.

PROP. VI.Theor. V.

PROP. VII.Theor. VI.

PROP. VIII.Prob. II.

FOOTNOTES:

THE FIRST BOOK OF OPTICKS

PART II.

PROP. I.Theor. I.

PROP. II.Theor. II.

DEFINITION.

PROP. III.Prob. I.

PROP. IV.Theor. III.

PROP. V.Theor. IV.

PROP. VI.Prob. II.

PROP. VII.Theor. V.

PROP. VIII.Prob. III.

PROP. IX.Prob. IV.

PROP. X.Prob. V.

PROP. XI.Prob. VI.

FOOTNOTES:

THE

SECOND BOOK

OF

OPTICKS

PART I.

Observations concerning the Reflexions, Refractions, and Colours ofthin transparent Bodies.

THE

SECOND BOOK

OF

OPTICKS

PART II.

Remarks upon the foregoing Observations.

The thickness of colour'd Plates and Particles of

THE

SECOND BOOK

OF

OPTICKS

PART III.

Of the permanent Colours of natural Bodies, and the Analogy betweenthem and the Colours of thin transparent Plates.

Prop. I.

Reflections,Refractions,
Inflections andColours