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diff --git a/src/testdata/Isaac.Newton-Opticks.txt b/src/testdata/Isaac.Newton-Opticks.txt new file mode 100644 index 0000000..15bb4c5 --- /dev/null +++ b/src/testdata/Isaac.Newton-Opticks.txt @@ -0,0 +1,9286 @@ +Produced by Suzanne Lybarger, steve harris, Josephine +Paolucci and the Online Distributed Proofreading Team at +http://www.pgdp.net. + + + + + + +OPTICKS: + +OR, A + +TREATISE + +OF THE + +_Reflections_, _Refractions_, +_Inflections_ and _Colours_ + +OF + +LIGHT. + +_The_ FOURTH EDITION, _corrected_. + +By Sir _ISAAC NEWTON_, Knt. + +LONDON: + +Printed for WILLIAM INNYS at the West-End of St. _Paul's_. MDCCXXX. + +TITLE PAGE OF THE 1730 EDITION + + + + +SIR ISAAC NEWTON'S ADVERTISEMENTS + + + + +Advertisement I + + +_Part of the ensuing Discourse about Light was written at the Desire of +some Gentlemen of the_ Royal-Society, _in the Year 1675, and then sent +to their Secretary, and read at their Meetings, and the rest was added +about twelve Years after to complete the Theory; except the third Book, +and the last Proposition of the Second, which were since put together +out of scatter'd Papers. To avoid being engaged in Disputes about these +Matters, I have hitherto delayed the printing, and should still have +delayed it, had not the Importunity of Friends prevailed upon me. If any +other Papers writ on this Subject are got out of my Hands they are +imperfect, and were perhaps written before I had tried all the +Experiments here set down, and fully satisfied my self about the Laws of +Refractions and Composition of Colours. I have here publish'd what I +think proper to come abroad, wishing that it may not be translated into +another Language without my Consent._ + +_The Crowns of Colours, which sometimes appear about the Sun and Moon, I +have endeavoured to give an Account of; but for want of sufficient +Observations leave that Matter to be farther examined. The Subject of +the Third Book I have also left imperfect, not having tried all the +Experiments which I intended when I was about these Matters, nor +repeated some of those which I did try, until I had satisfied my self +about all their Circumstances. To communicate what I have tried, and +leave the rest to others for farther Enquiry, is all my Design in +publishing these Papers._ + +_In a Letter written to Mr._ Leibnitz _in the year 1679, and published +by Dr._ Wallis, _I mention'd a Method by which I had found some general +Theorems about squaring Curvilinear Figures, or comparing them with the +Conic Sections, or other the simplest Figures with which they may be +compared. And some Years ago I lent out a Manuscript containing such +Theorems, and having since met with some Things copied out of it, I have +on this Occasion made it publick, prefixing to it an_ Introduction, _and +subjoining a_ Scholium _concerning that Method. And I have joined with +it another small Tract concerning the Curvilinear Figures of the Second +Kind, which was also written many Years ago, and made known to some +Friends, who have solicited the making it publick._ + + _I. N._ + +April 1, 1704. + + +Advertisement II + +_In this Second Edition of these Opticks I have omitted the Mathematical +Tracts publish'd at the End of the former Edition, as not belonging to +the Subject. And at the End of the Third Book I have added some +Questions. And to shew that I do not take Gravity for an essential +Property of Bodies, I have added one Question concerning its Cause, +chusing to propose it by way of a Question, because I am not yet +satisfied about it for want of Experiments._ + + _I. N._ + +July 16, 1717. + + +Advertisement to this Fourth Edition + +_This new Edition of Sir_ Isaac Newton's Opticks _is carefully printed +from the Third Edition, as it was corrected by the Author's own Hand, +and left before his Death with the Bookseller. Since Sir_ Isaac's +Lectiones Opticæ, _which he publickly read in the University of_ +Cambridge _in the Years 1669, 1670, and 1671, are lately printed, it has +been thought proper to make at the bottom of the Pages several Citations +from thence, where may be found the Demonstrations, which the Author +omitted in these_ Opticks. + + * * * * * + +Transcriber's Note: There are several greek letters used in the +descriptions of the illustrations. They are signified by [Greek: +letter]. Square roots are noted by the letters sqrt before the equation. + + * * * * * + +THE FIRST BOOK OF OPTICKS + + + + +_PART I._ + + +My Design in this Book is not to explain the Properties of Light by +Hypotheses, but to propose and prove them by Reason and Experiments: In +order 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 well +Successive in the same Lines, as Contemporary in several Lines._ For it +is manifest that Light consists of Parts, both Successive and +Contemporary; because in the same place you may stop that which comes +one moment, and let pass that which comes presently after; and in the +same time you may stop it in any one place, and let it pass in any +other. For that part of Light which is stopp'd cannot be the same with +that which is let pass. The least Light or part of Light, which may be +stopp'd alone without the rest of the Light, or propagated alone, or do +or suffer any thing alone, which the rest of the Light doth not or +suffers not, I call a Ray of Light. + + +DEFIN. II. + +_Refrangibility of the Rays of Light, is their Disposition to be +refracted or turned out of their Way in passing out of one transparent +Body or Medium into another. And a greater or less Refrangibility of +Rays, is their Disposition to be turned more or less out of their Way in +like Incidences on the same Medium._ Mathematicians usually consider the +Rays of Light to be Lines reaching from the luminous Body to the Body +illuminated, and the refraction of those Rays to be the bending or +breaking of those lines in their passing out of one Medium into another. +And thus may Rays and Refractions be considered, if Light be propagated +in an instant. But by an Argument taken from the Æquations of the times +of the Eclipses of _Jupiter's Satellites_, it seems that Light is +propagated in time, spending in its passage from the Sun to us about +seven Minutes of time: And therefore I have chosen to define Rays and +Refractions in such general terms as may agree to Light in both cases. + + +DEFIN. III. + +_Reflexibility of Rays, is their Disposition to be reflected or turned +back into the same Medium from any other Medium upon whose Surface they +fall. And Rays are more or less reflexible, which are turned back more +or less easily._ As if Light pass out of a Glass into Air, and by being +inclined more and more to the common Surface of the Glass and Air, +begins at length to be totally reflected by that Surface; those sorts of +Rays which at like Incidences are reflected most copiously, or by +inclining the Rays begin soonest to be totally reflected, are most +reflexible. + + +DEFIN. IV. + +_The Angle of Incidence is that Angle, which the Line described by the +incident Ray contains with the Perpendicular to the reflecting or +refracting Surface at the Point of Incidence._ + + +DEFIN. V. + +_The Angle of Reflexion or Refraction, is the Angle which the line +described by the reflected or refracted Ray containeth with the +Perpendicular to the reflecting or refracting Surface at the Point of +Incidence._ + + +DEFIN. VI. + +_The Sines of Incidence, Reflexion, and Refraction, are the Sines of the +Angles of Incidence, Reflexion, and Refraction._ + + +DEFIN. VII + +_The Light whose Rays are all alike Refrangible, I call Simple, +Homogeneal and Similar; and that whose Rays are some more Refrangible +than others, I call Compound, Heterogeneal and Dissimilar._ The former +Light I call Homogeneal, not because I would affirm it so in all +respects, but because the Rays which agree in Refrangibility, agree at +least in all those their other Properties which I consider in the +following Discourse. + + +DEFIN. VIII. + +_The Colours of Homogeneal Lights, I call Primary, Homogeneal and +Simple; and those of Heterogeneal Lights, Heterogeneal and Compound._ +For these are always compounded of the colours of Homogeneal Lights; as +will appear in the following Discourse. + + + + +_AXIOMS._ + + +AX. I. + +_The Angles of Reflexion and Refraction, lie in one and the same Plane +with the Angle of Incidence._ + + +AX. II. + +_The Angle of Reflexion is equal to the Angle of Incidence._ + + +AX. III. + +_If the refracted Ray be returned directly back to the Point of +Incidence, it shall be refracted into the Line before described by the +incident Ray._ + + +AX. IV. + +_Refraction out of the rarer Medium into the denser, is made towards the +Perpendicular; that is, so that the Angle of Refraction be less than the +Angle of Incidence._ + + +AX. V. + +_The Sine of Incidence is either accurately or very nearly in a given +Ratio to the Sine of Refraction._ + +Whence if that Proportion be known in any one Inclination of the +incident Ray, 'tis known in all the Inclinations, and thereby the +Refraction in all cases of Incidence on the same refracting Body may be +determined. Thus if the Refraction be made out of Air into Water, the +Sine of Incidence of the red Light is to the Sine of its Refraction as 4 +to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of +other Colours the Sines have other Proportions: but the difference is so +little that it need seldom be considered. + +[Illustration: FIG. 1] + +Suppose therefore, that RS [in _Fig._ 1.] represents the Surface of +stagnating Water, and that C is the point of Incidence in which any Ray +coming in the Air from A in the Line AC is reflected or refracted, and I +would know whither this Ray shall go after Reflexion or Refraction: I +erect upon the Surface of the Water from the point of Incidence the +Perpendicular CP and produce it downwards to Q, and conclude by the +first Axiom, that the Ray after Reflexion and Refraction, shall be +found somewhere in the Plane of the Angle of Incidence ACP produced. I +let 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 be +equal 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 and +Sine of Incidence, as they ought to be by the second Axiom, But if the +refracted Ray be desired, I produce AD to H, so that DH may be to AD as +the Sine of Refraction to the Sine of Incidence, that is, (if the Light +be red) as 3 to 4; and about the Center C and in the Plane ACP with the +Radius CA describing a Circle ABE, I draw a parallel to the +Perpendicular CPQ, the Line HE cutting the Circumference in E, and +joining CE, this Line CE shall be the Line of the refracted Ray. For if +EF be let fall perpendicularly on the Line PQ, this Line EF shall be the +Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and +this Sine EF is equal to DH, and consequently in Proportion to the Sine +of Incidence AD as 3 to 4. + +In like manner, if there be a Prism of Glass (that is, a Glass bounded +with two Equal and Parallel Triangular ends, and three plain and well +polished Sides, which meet in three Parallel Lines running from the +three Angles of one end to the three Angles of the other end) and if the +Refraction of the Light in passing cross this Prism be desired: Let ACB +[in _Fig._ 2.] represent a Plane cutting this Prism transversly to its +three Parallel lines or edges there where the Light passeth through it, +and let DE be the Ray incident upon the first side of the Prism AC where +the Light goes into the Glass; and by putting the Proportion of the Sine +of Incidence to the Sine of Refraction as 17 to 11 find EF the first +refracted Ray. Then taking this Ray for the Incident Ray upon the second +side of the Glass BC where the Light goes out, find the next refracted +Ray FG by putting the Proportion of the Sine of Incidence to the Sine of +Refraction as 11 to 17. For if the Sine of Incidence out of Air into +Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence +out of Glass into Air must on the contrary be to the Sine of Refraction +as 11 to 17, by the third Axiom. + +[Illustration: FIG. 2.] + +Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass +spherically convex on both sides (usually called a _Lens_, such as is a +Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope) +and it be required to know how Light falling upon it from any lucid +point Q shall be refracted, let QM represent a Ray falling upon any +point M of its first spherical Surface ACB, and by erecting a +Perpendicular to the Glass at the point M, find the first refracted Ray +MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of +the Glass be incident upon N, and then find the second refracted Ray +N_q_ by the Proportion of the Sines 11 to 17. And after the same manner +may the Refraction be found when the Lens is convex on one side and +plane or concave on the other, or concave on both sides. + +[Illustration: FIG. 3.] + + +AX. VI. + +_Homogeneal Rays which flow from several Points of any Object, and fall +perpendicularly or almost perpendicularly on any reflecting or +refracting Plane or spherical Surface, shall afterwards diverge from so +many other Points, or be parallel to so many other Lines, or converge to +so many other Points, either accurately or without any sensible Error. +And the same thing will happen, if the Rays be reflected or refracted +successively by two or three or more Plane or Spherical Surfaces._ + +The Point from which Rays diverge or to which they converge may be +called their _Focus_. And the Focus of the incident Rays being given, +that of the reflected or refracted ones may be found by finding the +Refraction of any two Rays, as above; or more readily thus. + +_Cas._ 1. Let ACB [in _Fig._ 4.] be a reflecting or refracting Plane, +and Q the Focus of the incident Rays, and Q_q_C a Perpendicular to that +Plane. And if this Perpendicular be produced to _q_, so that _q_C be +equal to QC, the Point _q_ shall be the Focus of the reflected Rays: Or +if _q_C be taken on the same side of the Plane with QC, and in +proportion to QC as the Sine of Incidence to the Sine of Refraction, the +Point _q_ shall be the Focus of the refracted Rays. + +[Illustration: FIG. 4.] + +_Cas._ 2. Let ACB [in _Fig._ 5.] be the reflecting Surface of any Sphere +whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if +in that Radius on the same side the Point T you take the Points Q and +_q_, so that TQ, TE, and T_q_, be continual Proportionals, and the Point +Q be the Focus of the incident Rays, the Point _q_ shall be the Focus of +the reflected ones. + +[Illustration: FIG. 5.] + +_Cas._ 3. Let ACB [in _Fig._ 6.] be the refracting Surface of any Sphere +whose Centre is E. In any Radius thereof EC produced both ways take ET +and C_t_ equal to one another and severally in such Proportion to that +Radius as the lesser of the Sines of Incidence and Refraction hath to +the difference of those Sines. And then if in the same Line you find any +two Points Q and _q_, so that TQ be to ET as E_t_ to _tq_, taking _tq_ +the contrary way from _t_ which TQ lieth from T, and if the Point Q be +the Focus of any incident Rays, the Point _q_ shall be the Focus of the +refracted ones. + +[Illustration: FIG. 6.] + +And by the same means the Focus of the Rays after two or more Reflexions +or Refractions may be found. + +[Illustration: FIG. 7.] + +_Cas._ 4. Let ACBD [in _Fig._ 7.] be any refracting Lens, spherically +Convex or Concave or Plane on either side, and let CD be its Axis (that +is, the Line which cuts both its Surfaces perpendicularly, and passes +through the Centres of the Spheres,) and in this Axis produced let F and +_f_ be the Foci of the refracted Rays found as above, when the incident +Rays on both sides the Lens are parallel to the same Axis; and upon the +Diameter F_f_ bisected in E, describe a Circle. Suppose now that any +Point Q be the Focus of any incident Rays. Draw QE cutting the said +Circle in T and _t_, and therein take _tq_ in such proportion to _t_E as +_t_E or TE hath to TQ. Let _tq_ lie the contrary way from _t_ which TQ +doth from T, and _q_ shall be the Focus of the refracted Rays without +any 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 on +the refracting Surfaces.[A] + +And by the like Operations may the reflecting or refracting Surfaces be +found when the two Foci are given, and thereby a Lens be formed, which +shall 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 Plane +or Spherical Surface or Lens, and before their Incidence flow from or +towards any Point Q, they shall after Reflexion or Refraction flow from +or towards the Point _q_ found by the foregoing Rules. And if the +incident Rays flow from or towards several points Q, the reflected or +refracted Rays shall flow from or towards so many other Points _q_ +found by the same Rules. Whether the reflected and refracted Rays flow +from or towards the Point _q_ is easily known by the situation of that +Point. For if that Point be on the same side of the reflecting or +refracting Surface or Lens with the Point Q, and the incident Rays flow +from the Point Q, the reflected flow towards the Point _q_ and the +refracted from it; and if the incident Rays flow towards Q, the +reflected flow from _q_, and the refracted towards it. And the contrary +happens when _q_ is on the other side of the Surface. + + +AX. VII. + +_Wherever the Rays which come from all the Points of any Object meet +again in so many Points after they have been made to converge by +Reflection or Refraction, there they will make a Picture of the Object +upon any white Body on which they fall._ + +So if PR [in _Fig._ 3.] represent any Object without Doors, and AB be a +Lens placed at a hole in the Window-shut of a dark Chamber, whereby the +Rays that come from any Point Q of that Object are made to converge and +meet again in the Point _q_; and if a Sheet of white Paper be held at +_q_ for the Light there to fall upon it, the Picture of that Object PR +will appear upon the Paper in its proper shape and Colours. For as the +Light which comes from the Point Q goes to the Point _q_, so the Light +which comes from other Points P and R of the Object, will go to so many +other correspondent Points _p_ and _r_ (as is manifest by the sixth +Axiom;) so that every Point of the Object shall illuminate a +correspondent Point of the Picture, and thereby make a Picture like the +Object in Shape and Colour, this only excepted, that the Picture shall +be inverted. And this is the Reason of that vulgar Experiment of casting +the Species of Objects from abroad upon a Wall or Sheet of white Paper +in a dark Room. + +In like manner, when a Man views any Object PQR, [in _Fig._ 8.] the +Light which comes from the several Points of the Object is so refracted +by the transparent skins and humours of the Eye, (that is, by the +outward coat EFG, called the _Tunica Cornea_, and by the crystalline +humour AB which is beyond the Pupil _mk_) as to converge and meet again +in so many Points in the bottom of the Eye, and there to paint the +Picture of the Object upon that skin (called the _Tunica Retina_) with +which the bottom of the Eye is covered. For Anatomists, when they have +taken off from the bottom of the Eye that outward and most thick Coat +called the _Dura Mater_, can then see through the thinner Coats, the +Pictures of Objects lively painted thereon. And these Pictures, +propagated by Motion along the Fibres of the Optick Nerves into the +Brain, are the cause of Vision. For accordingly as these Pictures are +perfect or imperfect, the Object is seen perfectly or imperfectly. If +the Eye be tinged with any colour (as in the Disease of the _Jaundice_) +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 of +the Eye by old Age decay, so as by shrinking to make the _Cornea_ and +Coat of the _Crystalline Humour_ grow flatter than before, the Light +will not be refracted enough, and for want of a sufficient Refraction +will 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 will +appear confused. This is the reason of the decay of sight in old Men, +and shews why their Sight is mended by Spectacles. For those Convex +glasses supply the defect of plumpness in the Eye, and by increasing the +Refraction make the Rays converge sooner, so as to convene distinctly at +the bottom of the Eye if the Glass have a due degree of convexity. And +the contrary happens in short-sighted Men whose Eyes are too plump. For +the Refraction being now too great, the Rays converge and convene in the +Eyes before they come at the bottom; and therefore the Picture made in +the bottom and the Vision caused thereby will not be distinct, unless +the Object be brought so near the Eye as that the place where the +converging Rays convene may be removed to the bottom, or that the +plumpness of the Eye be taken off and the Refractions diminished by a +Concave-glass of a due degree of Concavity, or lastly that by Age the +Eye grow flatter till it come to a due Figure: For short-sighted Men see +remote Objects best in Old Age, and therefore they are accounted to have +the most lasting Eyes. + +[Illustration: FIG. 8.] + + +AX. VIII. + +_An Object seen by Reflexion or Refraction, appears in that place from +whence the Rays after their last Reflexion or Refraction diverge in +falling on the Spectator's Eye._ + +[Illustration: FIG. 9.] + +If the Object A [in FIG. 9.] be seen by Reflexion of a Looking-glass +_mn_, it shall appear, not in its proper place A, but behind the Glass +at _a_, from whence any Rays AB, AC, AD, which flow from one and the +same 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 are +incident on the Spectator's Eyes. For these Rays do make the same +Picture in the bottom of the Eyes as if they had come from the Object +really placed at _a_ without the Interposition of the Looking-glass; and +all Vision is made according to the place and shape of that Picture. + +In like manner the Object D [in FIG. 2.] seen through a Prism, appears +not in its proper place D, but is thence translated to some other place +_d_ situated in the last refracted Ray FG drawn backward from F to _d_. + +[Illustration: FIG. 10.] + +And so the Object Q [in FIG. 10.] seen through the Lens AB, appears at +the place _q_ from whence the Rays diverge in passing from the Lens to +the Eye. Now it is to be noted, that the Image of the Object at _q_ is +so much bigger or lesser than the Object it self at Q, as the distance +of the Image at _q_ from the Lens AB is bigger or less than the distance +of the Object at Q from the same Lens. And if the Object be seen through +two or more such Convex or Concave-glasses, every Glass shall make a new +Image, and the Object shall appear in the place of the bigness of the +last Image. Which consideration unfolds the Theory of Microscopes and +Telescopes. For that Theory consists in almost nothing else than the +describing such Glasses as shall make the last Image of any Object as +distinct and large and luminous as it can conveniently be made. + +I have now given in Axioms and their Explications the sum of what hath +hitherto been treated of in Opticks. For what hath been generally +agreed on I content my self to assume under the notion of Principles, in +order to what I have farther to write. And this may suffice for an +Introduction to Readers of quick Wit and good Understanding not yet +versed in Opticks: Although those who are already acquainted with this +Science, and have handled Glasses, will more readily apprehend what +followeth. + +FOOTNOTES: + +[A] In our Author's _Lectiones Opticæ_, Part I. Sect. IV. Prop 29, 30, +there is an elegant Method of determining these _Foci_; not only in +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 the +Axis. + +[B] _Ibid._ Prop. 34. + + + + +_PROPOSITIONS._ + + + +_PROP._ I. THEOR. I. + +_Lights which differ in Colour, differ also in Degrees of +Refrangibility._ + +The PROOF by Experiments. + +_Exper._ 1. + +I took a black oblong stiff Paper terminated by Parallel Sides, and with +a Perpendicular right Line drawn cross from one Side to the other, +distinguished it into two equal Parts. One of these parts I painted with +a red colour and the other with a blue. The Paper was very black, and +the Colours intense and thickly laid on, that the Phænomenon might be +more 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 and +well polished, and contained an Angle of about sixty degrees; which +Angle I call the refracting Angle of the Prism. And whilst I view'd it, +I held it and the Prism before a Window in such manner that the Sides of +the Paper were parallel to the Prism, and both those Sides and the Prism +were parallel to the Horizon, and the cross Line was also parallel to +it: and that the Light which fell from the Window upon the Paper made an +Angle with the Paper, equal to that Angle which was made with the same +Paper by the Light reflected from it to the Eye. Beyond the Prism was +the Wall of the Chamber under the Window covered over with black Cloth, +and the Cloth was involved in Darkness that no Light might be reflected +from thence, which in passing by the Edges of the Paper to the Eye, +might mingle itself with the Light of the Paper, and obscure the +Phænomenon thereof. These things being thus ordered, I found that if the +refracting Angle of the Prism be turned upwards, so that the Paper may +seem to be lifted upwards by the Refraction, its blue half will be +lifted higher by the Refraction than its red half. But if the refracting +Angle of the Prism be turned downward, so that the Paper may seem to be +carried lower by the Refraction, its blue half will be carried something +lower thereby than its red half. Wherefore in both Cases the Light which +comes from the blue half of the Paper through the Prism to the Eye, does +in like Circumstances suffer a greater Refraction than the Light which +comes from the red half, and by consequence is more refrangible. + +_Illustration._ In the eleventh Figure, MN represents the Window, and DE +the Paper terminated with parallel Sides DJ and HE, and by the +transverse Line FG distinguished into two halfs, the one DG of an +intensely blue Colour, the other FE of an intensely red. And BAC_cab_ +represents the Prism whose refracting Planes AB_ba_ and AC_ca_ meet in +the Edge of the refracting Angle A_a_. This Edge A_a_ being upward, is +parallel both to the Horizon, and to the Parallel-Edges of the Paper DJ +and HE, and the transverse Line FG is perpendicular to the Plane of the +Window. And _de_ represents the Image of the Paper seen by Refraction +upwards in such manner, that the blue half DG is carried higher to _dg_ +than the red half FE is to _fe_, and therefore suffers a greater +Refraction. If the Edge of the refracting Angle be turned downward, the +Image of the Paper will be refracted downward; suppose to [Greek: de], +and the blue half will be refracted lower to [Greek: dg] than the red +half is to [Greek: pe]. + +[Illustration: FIG. 11.] + +_Exper._ 2. About the aforesaid Paper, whose two halfs were painted over +with red and blue, and which was stiff like thin Pasteboard, I lapped +several times a slender Thred of very black Silk, in such manner that +the several parts of the Thred might appear upon the Colours like so +many black Lines drawn over them, or like long and slender dark Shadows +cast upon them. I might have drawn black Lines with a Pen, but the +Threds were smaller and better defined. This Paper thus coloured and +lined I set against a Wall perpendicularly to the Horizon, so that one +of 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 a +Candle to illuminate the Paper strongly: For the Experiment was tried in +the Night. The Flame of the Candle reached up to the lower edge of the +Paper, or a very little higher. Then at the distance of six Feet, and +one or two Inches from the Paper upon the Floor I erected a Glass Lens +four Inches and a quarter broad, which might collect the Rays coming +from the several Points of the Paper, and make them converge towards so +many other Points at the same distance of six Feet, and one or two +Inches on the other side of the Lens, and so form the Image of the +coloured Paper upon a white Paper placed there, after the same manner +that a Lens at a Hole in a Window casts the Images of Objects abroad +upon 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 it +from the Lens, I moved sometimes towards the Lens, sometimes from it, to +find the Places where the Images of the blue and red Parts of the +coloured Paper appeared most distinct. Those Places I easily knew by the +Images of the black Lines which I had made by winding the Silk about the +Paper. For the Images of those fine and slender Lines (which by reason +of their Blackness were like Shadows on the Colours) were confused and +scarce visible, unless when the Colours on either side of each Line were +terminated most distinctly, Noting therefore, as diligently as I could, +the Places where the Images of the red and blue halfs of the coloured +Paper appeared most distinct, I found that where the red half of the +Paper appeared distinct, the blue half appeared confused, so that the +black Lines drawn upon it could scarce be seen; and on the contrary, +where the blue half appeared most distinct, the red half appeared +confused, so that the black Lines upon it were scarce visible. And +between the two Places where these Images appeared distinct there was +the distance of an Inch and a half; the distance of the white Paper from +the Lens, when the Image of the red half of the coloured Paper appeared +most distinct, being greater by an Inch and an half than the distance of +the same white Paper from the Lens, when the Image of the blue half +appeared most distinct. In like Incidences therefore of the blue and red +upon the Lens, the blue was refracted more by the Lens than the red, so +as to converge sooner by an Inch and a half, and therefore is more +refrangible. + +_Illustration._ In the twelfth Figure (p. 27), DE signifies the coloured +Paper, DG the blue half, FE the red half, MN the Lens, HJ the white +Paper in that Place where the red half with its black Lines appeared +distinct, and _hi_ the same Paper in that Place where the blue half +appeared distinct. The Place _hi_ was nearer to the Lens MN than the +Place HJ by an Inch and an half. + +_Scholium._ The same Things succeed, notwithstanding that some of the +Circumstances be varied; as in the first Experiment when the Prism and +Paper are any ways inclined to the Horizon, and in both when coloured +Lines are drawn upon very black Paper. But in the Description of these +Experiments, I have set down such Circumstances, by which either the +Phænomenon might be render'd more conspicuous, or a Novice might more +easily try them, or by which I did try them only. The same Thing, I have +often done in the following Experiments: Concerning all which, this one +Admonition may suffice. Now from these Experiments it follows not, that +all the Light of the blue is more refrangible than all the Light of the +red: For both Lights are mixed of Rays differently refrangible, so that +in the red there are some Rays not less refrangible than those of the +blue, and in the blue there are some Rays not more refrangible than +those of the red: But these Rays, in proportion to the whole Light, are +but few, and serve to diminish the Event of the Experiment, but are not +able to destroy it. For, if the red and blue Colours were more dilute +and weak, the distance of the Images would be less than an Inch and a +half; and if they were more intense and full, that distance would be +greater, as will appear hereafter. These Experiments may suffice for the +Colours of Natural Bodies. For in the Colours made by the Refraction of +Prisms, this Proposition will appear by the Experiments which are now to +follow in the next Proposition. + + +_PROP._ II. THEOR. II. + +_The Light of the Sun consists of Rays differently Refrangible._ + +The PROOF by Experiments. + +[Illustration: FIG. 12.] + +[Illustration: FIG. 13.] + +_Exper._ 3. + +In a very dark Chamber, at a round Hole, about one third Part of an Inch +broad, made in the Shut of a Window, I placed a Glass Prism, whereby the +Beam of the Sun's Light, which came in at that Hole, might be refracted +upwards toward the opposite Wall of the Chamber, and there form a +colour'd Image of the Sun. The Axis of the Prism (that is, the Line +passing through the middle of the Prism from one end of it to the other +end parallel to the edge of the Refracting Angle) was in this and the +following Experiments perpendicular to the incident Rays. About this +Axis 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, I +stopp'd the Prism, and fix'd it in that Posture, that it should be moved +no more. For in that Posture the Refractions of the Light at the two +Sides of the refracting Angle, that is, at the Entrance of the Rays into +the 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 Refractions +on both sides the Prism to be equal to one another, I noted the Place +where the Image of the Sun formed by the refracted Light stood still +between its two contrary Motions, in the common Period of its Progress +and Regress; and when the Image fell upon that Place, I made fast the +Prism. And in this Posture, as the most convenient, it is to be +understood that all the Prisms are placed in the following Experiments, +unless where some other Posture is described. The Prism therefore being +placed in this Posture, I let the refracted Light fall perpendicularly +upon a Sheet of white Paper at the opposite Wall of the Chamber, and +observed the Figure and Dimensions of the Solar Image formed on the +Paper by that Light. This Image was Oblong and not Oval, but terminated +with two Rectilinear and Parallel Sides, and two Semicircular Ends. On +its Sides it was bounded pretty distinctly, but on its Ends very +confusedly and indistinctly, the Light there decaying and vanishing by +degrees. The Breadth of this Image answered to the Sun's Diameter, and +was about two Inches and the eighth Part of an Inch, including the +Penumbra. For the Image was eighteen Feet and an half distant from the +Prism, and at this distance that Breadth, if diminished by the Diameter +of 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 the +Sun's apparent Diameter. But the Length of the Image was about ten +Inches and a quarter, and the Length of the Rectilinear Sides about +eight Inches; and the refracting Angle of the Prism, whereby so great a +Length was made, was 64 degrees. With a less Angle the Length of the +Image was less, the Breadth remaining the same. If the Prism was turned +about its Axis that way which made the Rays emerge more obliquely out of +the second refracting Surface of the Prism, the Image soon became an +Inch or two longer, or more; and if the Prism was turned about the +contrary way, so as to make the Rays fall more obliquely on the first +refracting Surface, the Image soon became an Inch or two shorter. And +therefore in trying this Experiment, I was as curious as I could be in +placing 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 Prism +might be equal to that at their Incidence on it. This Prism had some +Veins running along within the Glass from one end to the other, which +scattered some of the Sun's Light irregularly, but had no sensible +Effect in increasing the Length of the coloured Spectrum. For I tried +the same Experiment with other Prisms with the same Success. And +particularly with a Prism which seemed free from such Veins, and whose +refracting Angle was 62-1/2 Degrees, I found the Length of the Image +9-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, the +Breadth 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 its +due Posture, I repeated the Experiment four or five Times, and always +found the Length of the Image that which is set down above. With another +Prism of clearer Glass and better Polish, which seemed free from Veins, +and whose refracting Angle was 63-1/2 Degrees, the Length of this Image +at 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 of +the Spectrum the Light of the Clouds seemed to be a little tinged with +red and violet, but so very faintly, that I suspected that Tincture +might either wholly, or in great Measure arise from some Rays of the +Spectrum scattered irregularly by some Inequalities in the Substance and +Polish of the Glass, and therefore I did not include it in these +Measures. 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 sensible +changes in the length of the Image. Neither did the different matter of +the Prisms make any: for in a Vessel made of polished Plates of Glass +cemented together in the shape of a Prism and filled with Water, there +is the like Success of the Experiment according to the quantity of the +Refraction. It is farther to be observed, that the Rays went on in right +Lines from the Prism to the Image, and therefore at their very going out +of the Prism had all that Inclination to one another from which the +length of the Image proceeded, that is, the Inclination of more than two +degrees and an half. And yet according to the Laws of Opticks vulgarly +received, 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 hole +made therein through which a beam of the Sun's Light was transmitted +into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby +the Prism is feigned to be cut transversely through the middle of the +Light. Or if you please, let ABC represent the Prism it self, looking +directly towards the Spectator's Eye with its nearer end: And let XY be +the Sun, MN the Paper upon which the Solar Image or Spectrum is cast, +and PT the Image it self whose sides towards _v_ and _w_ are Rectilinear +and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are +two Rays, the first of which comes from the lower part of the Sun to the +higher part of the Image, and is refracted in the Prism at K and H, and +the latter comes from the higher part of the Sun to the lower part of +the Image, and is refracted at L and J. Since the Refractions on both +sides the Prism are equal to one another, that is, the Refraction at K +equal to the Refraction at J, and the Refraction at L equal to the +Refraction at H, so that the Refractions of the incident Rays at K and L +taken together, are equal to the Refractions of the emergent Rays at H +and J taken together: it follows by adding equal things to equal things, +that the Refractions at K and H taken together, are equal to the +Refractions at J and L taken together, and therefore the two Rays being +equally refracted, have the same Inclination to one another after +Refraction which they had before; that is, the Inclination of half a +Degree answering to the Sun's Diameter. For so great was the inclination +of the Rays to one another before Refraction. So then, the length of the +Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a +Degree at the Prism, and by Consequence be equal to the breadth _vw_; +and therefore the Image would be round. Thus it would be were the two +Rays XLJT and YKHP, and all the rest which form the Image P_w_T_v_, +alike refrangible. And therefore seeing by Experience it is found that +the Image is not round, but about five times longer than broad, the Rays +which going to the upper end P of the Image suffer the greatest +Refraction, must be more refrangible than those which go to the lower +end T, unless the Inequality of Refraction be casual. + +This Image or Spectrum PT was coloured, being red at its least refracted +end T, and violet at its most refracted end P, and yellow green and +blue in the intermediate Spaces. Which agrees with the first +Proposition, that Lights which differ in Colour, do also differ in +Refrangibility. The length of the Image in the foregoing Experiments, I +measured from the faintest and outmost red at one end, to the faintest +and 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 through +the 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 perpendicular +to that Beam. Then I looked through the Prism upon the hole, and turning +the Prism to and fro about its Axis, to make the Image of the Hole +ascend and descend, when between its two contrary Motions it seemed +Stationary, I stopp'd the Prism, that the Refractions of both sides of +the refracting Angle might be equal to each other, as in the former +Experiment. In this situation of the Prism viewing through it the said +Hole, I observed the length of its refracted Image to be many times +greater than its breadth, and that the most refracted part thereof +appeared violet, the least refracted red, the middle parts blue, green +and yellow in order. The same thing happen'd when I removed the Prism +out of the Sun's Light, and looked through it upon the hole shining by +the Light of the Clouds beyond it. And yet if the Refraction were done +regularly according to one certain Proportion of the Sines of Incidence +and Refraction as is vulgarly supposed, the refracted Image ought to +have appeared round. + +So then, by these two Experiments it appears, that in Equal Incidences +there is a considerable inequality of Refractions. But whence this +inequality arises, whether it be that some of the incident Rays are +refracted more, and others less, constantly, or by chance, or that one +and the same Ray is by Refraction disturbed, shatter'd, dilated, and as +it were split and spread into many diverging Rays, as _Grimaldo_ +supposes, does not yet appear by these Experiments, but will appear by +those that follow. + +_Exper._ 5. Considering therefore, that if in the third Experiment the +Image of the Sun should be drawn out into an oblong Form, either by a +Dilatation of every Ray, or by any other casual inequality of the +Refractions, the same oblong Image would by a second Refraction made +sideways be drawn out as much in breadth by the like Dilatation of the +Rays, or other casual inequality of the Refractions sideways, I tried +what would be the Effects of such a second Refraction. For this end I +ordered all things as in the third Experiment, and then placed a second +Prism immediately after the first in a cross Position to it, that it +might again refract the beam of the Sun's Light which came to it through +the first Prism. In the first Prism this beam was refracted upwards, and +in the second sideways. And I found that by the Refraction of the second +Prism, the breadth of the Image was not increased, but its superior +part, which in the first Prism suffered the greater Refraction, and +appeared violet and blue, did again in the second Prism suffer a greater +Refraction than its inferior part, which appeared red and yellow, and +this without any Dilatation of the Image in breadth. + +[Illustration: FIG. 14] + +_Illustration._ Let S [_Fig._ 14, 15.] represent the Sun, F the hole in +the Window, ABC the first Prism, DH the second Prism, Y the round Image +of the Sun made by a direct beam of Light when the Prisms are taken +away, PT the oblong Image of the Sun made by that beam passing through +the first Prism alone, when the second Prism is taken away, and _pt_ the +Image made by the cross Refractions of both Prisms together. Now if the +Rays which tend towards the several Points of the round Image Y were +dilated and spread by the Refraction of the first Prism, so that they +should not any longer go in single Lines to single Points, but that +every Ray being split, shattered, and changed from a Linear Ray to a +Superficies of Rays diverging from the Point of Refraction, and lying in +the Plane of the Angles of Incidence and Refraction, they should go in +those Planes to so many Lines reaching almost from one end of the Image +PT to the other, and if that Image should thence become oblong: those +Rays and their several parts tending towards the several Points of the +Image PT ought to be again dilated and spread sideways by the transverse +Refraction of the second Prism, so as to compose a four square Image, +such as is represented at [Greek: pt]. For the better understanding of +which, let the Image PT be distinguished into five equal parts PQK, +KQRL, LRSM, MSVN, NVT. And by the same irregularity that the orbicular +Light Y is by the Refraction of the first Prism dilated and drawn out +into a long Image PT, the Light PQK which takes up a space of the same +length and breadth with the Light Y ought to be by the Refraction of the +second Prism dilated and drawn out into the long Image _[Greek: p]qkp_, +and the Light KQRL into the long Image _kqrl_, and the Lights LRSM, +MSVN, NVT, into so many other long Images _lrsm_, _msvn_, _nvt[Greek: +t]_; and all these long Images would compose the four square Images +_[Greek: pt]_. Thus it ought to be were every Ray dilated by Refraction, +and spread into a triangular Superficies of Rays diverging from the +Point of Refraction. For the second Refraction would spread the Rays one +way as much as the first doth another, and so dilate the Image in +breadth as much as the first doth in length. And the same thing ought to +happen, were some rays casually refracted more than others. But the +Event is otherwise. The Image PT was not made broader by the Refraction +of the second Prism, but only became oblique, as 'tis represented at +_pt_, its upper end P being by the Refraction translated to a greater +distance than its lower end T. So then the Light which went towards the +upper end P of the Image, was (at equal Incidences) more refracted in +the second Prism, than the Light which tended towards the lower end T, +that is the blue and violet, than the red and yellow; and therefore was +more refrangible. The same Light was by the Refraction of the first +Prism translated farther from the place Y to which it tended before +Refraction; and therefore suffered as well in the first Prism as in the +second a greater Refraction than the rest of the Light, and by +consequence was more refrangible than the rest, even before its +incidence on the first Prism. + +Sometimes I placed a third Prism after the second, and sometimes also a +fourth after the third, by all which the Image might be often refracted +sideways: but the Rays which were more refracted than the rest in the +first Prism were also more refracted in all the rest, and that without +any Dilatation of the Image sideways: and therefore those Rays for their +constancy of a greater Refraction are deservedly reputed more +refrangible. + +[Illustration: FIG. 15] + +But that the meaning of this Experiment may more clearly appear, it is +to be considered that the Rays which are equally refrangible do fall +upon a Circle answering to the Sun's Disque. For this was proved in the +third Experiment. By a Circle I understand not here a perfect +geometrical Circle, but any orbicular Figure whose length is equal to +its breadth, and which, as to Sense, may seem circular. Let therefore AG +[in _Fig._ 15.] represent the Circle which all the most refrangible Rays +propagated from the whole Disque of the Sun, would illuminate and paint +upon the opposite Wall if they were alone; EL the Circle which all the +least refrangible Rays would in like manner illuminate and paint if they +were alone; BH, CJ, DK, the Circles which so many intermediate sorts of +Rays would successively paint upon the Wall, if they were singly +propagated from the Sun in successive order, the rest being always +intercepted; and conceive that there are other intermediate Circles +without Number, which innumerable other intermediate sorts of Rays would +successively paint upon the Wall if the Sun should successively emit +every sort apart. And seeing the Sun emits all these sorts at once, they +must all together illuminate and paint innumerable equal Circles, of all +which, being according to their degrees of Refrangibility placed in +order in a continual Series, that oblong Spectrum PT is composed which I +described in the third Experiment. Now if the Sun's circular Image Y [in +_Fig._ 15.] which is made by an unrefracted beam of Light was by any +Dilation of the single Rays, or by any other irregularity in the +Refraction of the first Prism, converted into the oblong Spectrum, PT: +then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the cross +Refraction of the second Prism again dilating or otherwise scattering +the Rays as before, to be in like manner drawn out and transformed into +an oblong Figure, and thereby the breadth of the Image PT would be now +as much augmented as the length of the Image Y was before by the +Refraction of the first Prism; and thus by the Refractions of both +Prisms together would be formed a four square Figure _p[Greek: +p]t[Greek: t]_, as I described above. Wherefore since the breadth of the +Spectrum PT is not increased by the Refraction sideways, it is certain +that the Rays are not split or dilated, or otherways irregularly +scatter'd by that Refraction, but that every Circle is by a regular and +uniform Refraction translated entire into another Place, as the Circle +AG by the greatest Refraction into the place _ag_, the Circle BH by a +less Refraction into the place _bh_, the Circle CJ by a Refraction still +less into the place _ci_, and so of the rest; by which means a new +Spectrum _pt_ inclined to the former PT is in like manner composed of +Circles lying in a right Line; and these Circles must be of the same +bigness with the former, because the breadths of all the Spectrums Y, PT +and _pt_ at equal distances from the Prisms are equal. + +I considered farther, that by the breadth of the hole F through which +the Light enters into the dark Chamber, there is a Penumbra made in the +Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear +Sides of the Spectrums PT and _pt_. I placed therefore at that hole a +Lens or Object-glass of a Telescope which might cast the Image of the +Sun distinctly on Y without any Penumbra at all, and found that the +Penumbra of the rectilinear Sides of the oblong Spectrums PT and _pt_ +was also thereby taken away, so that those Sides appeared as distinctly +defined as did the Circumference of the first Image Y. Thus it happens +if the Glass of the Prisms be free from Veins, and their sides be +accurately plane and well polished without those numberless Waves or +Curles which usually arise from Sand-holes a little smoothed in +polishing with Putty. If the Glass be only well polished and free from +Veins, and the Sides not accurately plane, but a little Convex or +Concave, as it frequently happens; yet may the three Spectrums Y, PT and +_pt_ want Penumbras, but not in equal distances from the Prisms. Now +from this want of Penumbras, I knew more certainly that every one of the +Circles was refracted according to some most regular, uniform and +constant Law. For if there were any irregularity in the Refraction, the +right Lines AE and GL, which all the Circles in the Spectrum PT do +touch, could not by that Refraction be translated into the Lines _ae_ +and _gl_ as distinct and straight as they were before, but there would +arise in those translated Lines some Penumbra or Crookedness or +Undulation, or other sensible Perturbation contrary to what is found by +Experience. Whatsoever Penumbra or Perturbation should be made in the +Circles by the cross Refraction of the second Prism, all that Penumbra +or Perturbation would be conspicuous in the right Lines _ae_ and _gl_ +which touch those Circles. And therefore since there is no such Penumbra +or Perturbation in those right Lines, there must be none in the +Circles. Since the distance between those Tangents or breadth of the +Spectrum is not increased by the Refractions, the Diameters of the +Circles are not increased thereby. Since those Tangents continue to be +right Lines, every Circle which in the first Prism is more or less +refracted, is exactly in the same proportion more or less refracted in +the second. And seeing all these things continue to succeed after the +same manner when the Rays are again in a third Prism, and again in a +fourth refracted sideways, it is evident that the Rays of one and the +same Circle, as to their degree of Refrangibility, continue always +uniform and homogeneal to one another, and that those of several Circles +do differ in degree of Refrangibility, and that in some certain and +constant Proportion. Which is the thing I was to prove. + +There is yet another Circumstance or two of this Experiment by which it +becomes still more plain and convincing. Let the second Prism DH [in +_Fig._ 16.] be placed not immediately after the first, but at some +distance from it; suppose in the mid-way between it and the Wall on +which the oblong Spectrum PT is cast, so that the Light from the first +Prism may fall upon it in the form of an oblong Spectrum [Greek: pt] +parallel to this second Prism, and be refracted sideways to form the +oblong Spectrum _pt_ upon the Wall. And you will find as before, that +this Spectrum _pt_ is inclined to that Spectrum PT, which the first +Prism forms alone without the second; the blue ends P and _p_ being +farther distant from one another than the red ones T and _t_, and by +consequence that the Rays which go to the blue end [Greek: p] of the +Image [Greek: pt], and which therefore suffer the greatest Refraction in +the first Prism, are again in the second Prism more refracted than the +rest. + +[Illustration: FIG. 16.] + +[Illustration: FIG. 17.] + +The same thing I try'd also by letting the Sun's Light into a dark Room +through two little round holes F and [Greek: ph] [in _Fig._ 17.] made in +the Window, and with two parallel Prisms ABC and [Greek: abg] placed at +those holes (one at each) refracting those two beams of Light to the +opposite Wall of the Chamber, in such manner that the two colour'd +Images PT and MN which they there painted were joined end to end and lay +in one straight Line, the red end T of the one touching the blue end M +of the other. For if these two refracted Beams were again by a third +Prism DH placed cross to the two first, refracted sideways, and the +Spectrums thereby translated to some other part of the Wall of the +Chamber, suppose the Spectrum PT to _pt_ and the Spectrum MN to _mn_, +these translated Spectrums _pt_ and _mn_ would not lie in one straight +Line with their ends contiguous as before, but be broken off from one +another and become parallel, the blue end _m_ of the Image _mn_ being by +a greater Refraction translated farther from its former place MT, than +the red end _t_ of the other Image _pt_ from the same place MT; which +puts the Proposition past Dispute. And this happens whether the third +Prism DH be placed immediately after the two first, or at a great +distance from them, so that the Light refracted in the two first Prisms +be either white and circular, or coloured and oblong when it falls on +the third. + +_Exper._ 6. In the middle of two thin Boards I made round holes a third +part of an Inch in diameter, and in the Window-shut a much broader hole +being made to let into my darkned Chamber a large Beam of the Sun's +Light; I placed a Prism behind the Shut in that beam to refract it +towards the opposite Wall, and close behind the Prism I fixed one of the +Boards, in such manner that the middle of the refracted Light might pass +through 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 fixed +the other Board in such manner that the middle of the refracted Light +which came through the hole in the first Board, and fell upon the +opposite Wall, might pass through the hole in this other Board, and the +rest being intercepted by the Board might paint upon it the coloured +Spectrum of the Sun. And close behind this Board I fixed another Prism +to refract the Light which came through the hole. Then I returned +speedily to the first Prism, and by turning it slowly to and fro about +its Axis, I caused the Image which fell upon the second Board to move up +and down upon that Board, that all its parts might successively pass +through the hole in that Board and fall upon the Prism behind it. And in +the mean time, I noted the places on the opposite Wall to which that +Light after its Refraction in the second Prism did pass; and by the +difference of the places I found that the Light which being most +refracted in the first Prism did go to the blue end of the Image, was +again more refracted in the second Prism than the Light which went to +the red end of that Image, which proves as well the first Proposition as +the second. And this happened whether the Axis of the two Prisms were +parallel, or inclined to one another, and to the Horizon in any given +Angles. + +_Illustration._ Let F [in _Fig._ 18.] be the wide hole in the +Window-shut, through which the Sun shines upon the first Prism ABC, and +let the refracted Light fall upon the middle of the Board DE, and the +middle part of that Light upon the hole G made in the middle part of +that Board. Let this trajected part of that Light fall again upon the +middle of the second Board _de_, and there paint such an oblong coloured +Image of the Sun as was described in the third Experiment. By turning +the Prism ABC slowly to and fro about its Axis, this Image will be made +to move up and down the Board _de_, and by this means all its parts from +one end to the other may be made to pass successively through the hole +_g_ which is made in the middle of that Board. In the mean while another +Prism _abc_ is to be fixed next after that hole _g_, to refract the +trajected Light a second time. And these things being thus ordered, I +marked the places M and N of the opposite Wall upon which the refracted +Light fell, and found that whilst the two Boards and second Prism +remained unmoved, those places by turning the first Prism about its Axis +were changed perpetually. For when the lower part of the Light which +fell upon the second Board _de_ was cast through the hole _g_, it went +to a lower place M on the Wall and when the higher part of that Light +was cast through the same hole _g_, it went to a higher place N on the +Wall, and when any intermediate part of the Light was cast through that +hole, it went to some place on the Wall between M and N. The unchanged +Position of the holes in the Boards, made the Incidence of the Rays upon +the second Prism to be the same in all cases. And yet in that common +Incidence some of the Rays were more refracted, and others less. And +those were more refracted in this Prism, which by a greater Refraction +in the first Prism were more turned out of the way, and therefore for +their Constancy of being more refracted are deservedly called more +refrangible. + +[Illustration: FIG. 18.] + +[Illustration: FIG. 20.] + +_Exper._ 7. At two holes made near one another in my Window-shut I +placed two Prisms, one at each, which might cast upon the opposite Wall +(after the manner of the third Experiment) two oblong coloured Images of +the Sun. And at a little distance from the Wall I placed a long slender +Paper with straight and parallel edges, and ordered the Prisms and Paper +so, that the red Colour of one Image might fall directly upon one half +of the Paper, and the violet Colour of the other Image upon the other +half of the same Paper; so that the Paper appeared of two Colours, red +and violet, much after the manner of the painted Paper in the first and +second Experiments. Then with a black Cloth I covered the Wall behind +the Paper, that no Light might be reflected from it to disturb the +Experiment, and viewing the Paper through a third Prism held parallel +to it, I saw that half of it which was illuminated by the violet Light +to be divided from the other half by a greater Refraction, especially +when I went a good way off from the Paper. For when I viewed it too near +at hand, the two halfs of the Paper did not appear fully divided from +one another, but seemed contiguous at one of their Angles like the +painted Paper in the first Experiment. Which also happened when the +Paper was too broad. + +[Illustration: FIG. 19.] + +Sometimes instead of the Paper I used a white Thred, and this appeared +through the Prism divided into two parallel Threds as is represented in +the nineteenth Figure, where DG denotes the Thred illuminated with +violet Light from D to E and with red Light from F to G, and _defg_ are +the parts of the Thred seen by Refraction. If one half of the Thred be +constantly illuminated with red, and the other half be illuminated with +all the Colours successively, (which may be done by causing one of the +Prisms to be turned about its Axis whilst the other remains unmoved) +this other half in viewing the Thred through the Prism, will appear in +a 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 still +farther when with green, and farther when with blue, and go yet farther +off when illuminated with Indigo, and farthest when with deep violet. +Which plainly shews, that the Lights of several Colours are more and +more refrangible one than another, in this Order of their Colours, red, +orange, yellow, green, blue, indigo, deep violet; and so proves as well +the first Proposition as the second. + +I caused also the coloured Spectrums PT [in _Fig._ 17.] and MN made in a +dark Chamber by the Refractions of two Prisms to lie in a Right Line end +to end, as was described above in the fifth Experiment, and viewing them +through a third Prism held parallel to their Length, they appeared no +longer in a Right Line, but became broken from one another, as they are +represented at _pt_ and _mn_, the violet end _m_ of the Spectrum _mn_ +being by a greater Refraction translated farther from its former Place +MT than the red end _t_ of the other Spectrum _pt_. + +I farther caused those two Spectrums PT [in _Fig._ 20.] and MN to become +co-incident in an inverted Order of their Colours, the red end of each +falling on the violet end of the other, as they are represented in the +oblong Figure PTMN; and then viewing them through a Prism DH held +parallel to their Length, they appeared not co-incident, as when view'd +with the naked Eye, but in the form of two distinct Spectrums _pt_ and +_mn_ crossing one another in the middle after the manner of the Letter +X. 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 a +greater Refraction of the violet to _p_ and _m_ than of the red to _n_ +and _t_, do differ in degrees of Refrangibility. + +I illuminated also a little Circular Piece of white Paper all over with +the Lights of both Prisms intermixed, and when it was illuminated with +the red of one Spectrum, and deep violet of the other, so as by the +Mixture 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 more +and more divided by the unequal Refraction of the two mixed Colours, and +at length parted into two distinct Images, a red one and a violet one, +whereof the violet was farthest from the Paper, and therefore suffered +the greatest Refraction. And when that Prism at the Window, which cast +the 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 two +Prisms, which had been intermixed on the purple Paper, but were parted +again by their unequal Refractions made in the third Prism, through +which the Paper was view'd. This also was observable, that if one of the +Prisms at the Window, suppose that which cast the violet on the Paper, +was turned about its Axis to make all the Colours in this order, +violet, indigo, blue, green, yellow, orange, red, fall successively on +the Paper from that Prism, the violet Image changed Colour accordingly, +turning successively to indigo, blue, green, yellow and red, and in +changing Colour came nearer and nearer to the red Image made by the +other Prism, until when it was also red both Images became fully +co-incident. + +I placed also two Paper Circles very near one another, the one in the +red 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 the +Wall was dark, that the Experiment might not be disturbed by any Light +coming from thence. These Circles thus illuminated, I viewed through a +Prism, so held, that the Refraction might be made towards the red +Circle, and as I went from them they came nearer and nearer together, +and at length became co-incident; and afterwards when I went still +farther off, they parted again in a contrary Order, the violet by a +greater Refraction being carried beyond the red. + +_Exper._ 8. In Summer, when the Sun's Light uses to be strongest, I +placed a Prism at the Hole of the Window-shut, as in the third +Experiment, yet so that its Axis might be parallel to the Axis of the +World, and at the opposite Wall in the Sun's refracted Light, I placed +an open Book. Then going six Feet and two Inches from the Book, I placed +there the above-mentioned Lens, by which the Light reflected from the +Book might be made to converge and meet again at the distance of six +Feet and two Inches behind the Lens, and there paint the Species of the +Book upon a Sheet of white Paper much after the manner of the second +Experiment. The Book and Lens being made fast, I noted the Place where +the Paper was, when the Letters of the Book, illuminated by the fullest +red Light of the Solar Image falling upon it, did cast their Species on +that Paper most distinctly: And then I stay'd till by the Motion of the +Sun, and consequent Motion of his Image on the Book, all the Colours +from that red to the middle of the blue pass'd over those Letters; and +when those Letters were illuminated by that blue, I noted again the +Place 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 Lens +than its former Place by about two Inches and an half, or two and three +quarters. So much sooner therefore did the Light in the violet end of +the Image by a greater Refraction converge and meet, than the Light in +the red end. But in trying this, the Chamber was as dark as I could make +it. For, if these Colours be diluted and weakned by the Mixture of any +adventitious Light, the distance between the Places of the Paper will +not be so great. This distance in the second Experiment, where the +Colours 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 of +the Prism, which are manifestly more full, intense, and lively than +those of natural Bodies, the distance is two Inches and three quarters. +And were the Colours still more full, I question not but that the +distance would be considerably greater. For the coloured Light of the +Prism, by the interfering of the Circles described in the second Figure +of the fifth Experiment, and also by the Light of the very bright Clouds +next the Sun's Body intermixing with these Colours, and by the Light +scattered by the Inequalities in the Polish of the Prism, was so very +much compounded, that the Species which those faint and dark Colours, +the indigo and violet, cast upon the Paper were not distinct enough to +be well observed. + +_Exper._ 9. A Prism, whose two Angles at its Base were equal to one +another, and half right ones, and the third a right one, I placed in a +Beam of the Sun's Light let into a dark Chamber through a Hole in the +Window-shut, as in the third Experiment. And turning the Prism slowly +about its Axis, until all the Light which went through one of its +Angles, and was refracted by it began to be reflected by its Base, at +which till then it went out of the Glass, I observed that those Rays +which had suffered the greatest Refraction were sooner reflected than +the rest. I conceived therefore, that those Rays of the reflected Light, +which were most refrangible, did first of all by a total Reflexion +become more copious in that Light than the rest, and that afterwards the +rest also, by a total Reflexion, became as copious as these. To try +this, I made the reflected Light pass through another Prism, and being +refracted by it to fall afterwards upon a Sheet of white Paper placed +at some distance behind it, and there by that Refraction to paint the +usual Colours of the Prism. And then causing the first Prism to be +turned about its Axis as above, I observed that when those Rays, which +in this Prism had suffered the greatest Refraction, and appeared of a +blue and violet Colour began to be totally reflected, the blue and +violet Light on the Paper, which was most refracted in the second Prism, +received a sensible Increase above that of the red and yellow, which was +least refracted; and afterwards, when the rest of the Light which was +green, yellow, and red, began to be totally reflected in the first +Prism, the Light of those Colours on the Paper received as great an +Increase as the violet and blue had done before. Whence 'tis manifest, +that the Beam of Light reflected by the Base of the Prism, being +augmented first by the more refrangible Rays, and afterwards by the less +refrangible ones, is compounded of Rays differently refrangible. And +that all such reflected Light is of the same Nature with the Sun's Light +before its Incidence on the Base of the Prism, no Man ever doubted; it +being generally allowed, that Light by such Reflexions suffers no +Alteration in its Modifications and Properties. I do not here take +Notice of any Refractions made in the sides of the first Prism, because +the Light enters it perpendicularly at the first side, and goes out +perpendicularly at the second side, and therefore suffers none. So then, +the Sun's incident Light being of the same Temper and Constitution with +his emergent Light, and the last being compounded of Rays differently +refrangible, the first must be in like manner compounded. + +[Illustration: FIG. 21.] + +_Illustration._ In the twenty-first Figure, ABC is the first Prism, BC +its Base, B and C its equal Angles at the Base, each of 45 Degrees, A +its rectangular Vertex, FM a beam of the Sun's Light let into a dark +Room through a hole F one third part of an Inch broad, M its Incidence +on the Base of the Prism, MG a less refracted Ray, MH a more refracted +Ray, MN the beam of Light reflected from the Base, VXY the second Prism +by which this beam in passing through it is refracted, N_t_ the less +refracted Light of this beam, and N_p_ the more refracted part thereof. +When the first Prism ABC is turned about its Axis according to the order +of the Letters ABC, the Rays MH emerge more and more obliquely out of +that Prism, and at length after their most oblique Emergence are +reflected towards N, and going on to _p_ do increase the Number of the +Rays N_p_. Afterwards by continuing the Motion of the first Prism, the +Rays MG are also reflected to N and increase the number of the Rays +N_t_. And therefore the Light MN admits into its Composition, first the +more refrangible Rays, and then the less refrangible Rays, and yet after +this Composition is of the same Nature with the Sun's immediate Light +FM, 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 a +Parallelopiped. And, the Sun shining into my dark Chamber through a +little hole in the Window-shut, I placed that Parallelopiped in his beam +at some distance from the hole, in such a Posture, that the Axes of the +Prisms might be perpendicular to the incident Rays, and that those Rays +being incident upon the first Side of one Prism, might go on through the +two contiguous Sides of both Prisms, and emerge out of the last Side of +the second Prism. This Side being parallel to the first Side of the +first Prism, caused the emerging Light to be parallel to the incident. +Then, beyond these two Prisms I placed a third, which might refract that +emergent Light, and by that Refraction cast the usual Colours of the +Prism upon the opposite Wall, or upon a sheet of white Paper held at a +convenient Distance behind the Prism for that refracted Light to fall +upon it. After this I turned the Parallelopiped about its Axis, and +found that when the contiguous Sides of the two Prisms became so oblique +to the incident Rays, that those Rays began all of them to be +reflected, those Rays which in the third Prism had suffered the greatest +Refraction, and painted the Paper with violet and blue, were first of +all by a total Reflexion taken out of the transmitted Light, the rest +remaining and on the Paper painting their Colours of green, yellow, +orange and red, as before; and afterwards by continuing the Motion of +the two Prisms, the rest of the Rays also by a total Reflexion vanished +in order, according to their degrees of Refrangibility. The Light +therefore which emerged out of the two Prisms is compounded of Rays +differently refrangible, seeing the more refrangible Rays may be taken +out of it, while the less refrangible remain. But this Light being +trajected only through the parallel Superficies of the two Prisms, if it +suffer'd any change by the Refraction of one Superficies it lost that +Impression by the contrary Refraction of the other Superficies, and so +being restor'd to its pristine Constitution, became of the same Nature +and Condition as at first before its Incidence on those Prisms; and +therefore, before its Incidence, was as much compounded of Rays +differently refrangible, as afterwards. + +[Illustration: FIG. 22.] + +_Illustration._ In the twenty second Figure ABC and BCD are the two +Prisms tied together in the form of a Parallelopiped, their Sides BC and +CB being contiguous, and their Sides AB and CD parallel. And HJK is the +third Prism, by which the Sun's Light propagated through the hole F into +the dark Chamber, and there passing through those sides of the Prisms +AB, BC, CB and CD, is refracted at O to the white Paper PT, falling +there partly upon P by a greater Refraction, partly upon T by a less +Refraction, and partly upon R and other intermediate places by +intermediate Refractions. By turning the Parallelopiped ACBD about its +Axis, according to the order of the Letters A, C, D, B, at length when +the contiguous Planes BC and CB become sufficiently oblique to the Rays +FM, which are incident upon them at M, there will vanish totally out of +the refracted Light OPT, first of all the most refracted Rays OP, (the +rest OR and OT remaining as before) then the Rays OR and other +intermediate ones, and lastly, the least refracted Rays OT. For when +the Plane BC becomes sufficiently oblique to the Rays incident upon it, +those Rays will begin to be totally reflected by it towards N; and first +the most refrangible Rays will be totally reflected (as was explained in +the 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 which +at O suffer the greatest Refraction, may be taken out of the Light MO +whilst the rest of the Rays remain in it, and therefore that Light MO is +compounded of Rays differently refrangible. And because the Planes AB +and CD are parallel, and therefore by equal and contrary Refractions +destroy one anothers Effects, the incident Light FM must be of the same +Kind and Nature with the emergent Light MO, and therefore doth also +consist of Rays differently refrangible. These two Lights FM and MO, +before the most refrangible Rays are separated out of the emergent Light +MO, agree in Colour, and in all other Properties so far as my +Observation reaches, and therefore are deservedly reputed of the same +Nature and Constitution, and by Consequence the one is compounded as +well as the other. But after the most refrangible Rays begin to be +totally reflected, and thereby separated out of the emergent Light MO, +that Light changes its Colour from white to a dilute and faint yellow, a +pretty good orange, a very full red successively, and then totally +vanishes. For after the most refrangible Rays which paint the Paper at +P with a purple Colour, are by a total Reflexion taken out of the beam +of Light MO, the rest of the Colours which appear on the Paper at R and +T being mix'd in the Light MO compound there a faint yellow, and after +the blue and part of the green which appear on the Paper between P and R +are taken away, the rest which appear between R and T (that is the +yellow, orange, red and a little green) being mixed in the beam MO +compound there an orange; and when all the Rays are by Reflexion taken +out of the beam MO, except the least refrangible, which at T appear of a +full 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 differently +refrangible Rays, without making any Alteration in their Colours, as +shall be more fully proved hereafter. All which confirms as well the +first Proposition as the second. + +_Scholium._ If this Experiment and the former be conjoined and made one +by applying a fourth Prism VXY [in _Fig._ 22.] to refract the reflected +beam MN towards _tp_, the Conclusion will be clearer. For then the Light +N_p_ which in the fourth Prism is more refracted, will become fuller and +stronger when the Light OP, which in the third Prism HJK is more +refracted, vanishes at P; and afterwards when the less refracted Light +OT vanishes at T, the less refracted Light N_t_ will become increased +whilst the more refracted Light at _p_ receives no farther increase. And +as the trajected beam MO in vanishing is always of such a Colour as +ought to result from the mixture of the Colours which fall upon the +Paper PT, so is the reflected beam MN always of such a Colour as ought +to result from the mixture of the Colours which fall upon the Paper +_pt_. For when the most refrangible Rays are by a total Reflexion taken +out of the beam MO, and leave that beam of an orange Colour, the Excess +of those Rays in the reflected Light, does not only make the violet, +indigo and blue at _p_ more full, but also makes the beam MN change from +the yellowish Colour of the Sun's Light, to a pale white inclining to +blue, and afterward recover its yellowish Colour again, so soon as all +the rest of the transmitted Light MOT is reflected. + +Now seeing that in all this variety of Experiments, whether the Trial be +made in Light reflected, and that either from natural Bodies, as in the +first and second Experiment, or specular, as in the ninth; or in Light +refracted, and that either before the unequally refracted Rays are by +diverging separated from one another, and losing their whiteness which +they have altogether, appear severally of several Colours, as in the +fifth Experiment; or after they are separated from one another, and +appear colour'd as in the sixth, seventh, and eighth Experiments; or in +Light trajected through parallel Superficies, destroying each others +Effects, as in the tenth Experiment; there are always found Rays, which +at equal Incidences on the same Medium suffer unequal Refractions, and +that without any splitting or dilating of single Rays, or contingence in +the inequality of the Refractions, as is proved in the fifth and sixth +Experiments. And seeing the Rays which differ in Refrangibility may be +parted and sorted from one another, and that either by Refraction as in +the third Experiment, or by Reflexion as in the tenth, and then the +several sorts apart at equal Incidences suffer unequal Refractions, and +those sorts are more refracted than others after Separation, which were +more refracted before it, as in the sixth and following Experiments, and +if the Sun's Light be trajected through three or more cross Prisms +successively, those Rays which in the first Prism are refracted more +than others, are in all the following Prisms refracted more than others +in 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 was +proposed. + + +_PROP._ III. THEOR. III. + +_The Sun's Light consists of Rays differing in Reflexibility, and those +Rays are more reflexible than others which are more refrangible._ + +This is manifest by the ninth and tenth Experiments: For in the ninth +Experiment, by turning the Prism about its Axis, until the Rays within +it which in going out into the Air were refracted by its Base, became so +oblique to that Base, as to begin to be totally reflected thereby; those +Rays became first of all totally reflected, which before at equal +Incidences with the rest had suffered the greatest Refraction. And the +same thing happens in the Reflexion made by the common Base of the two +Prisms in the tenth Experiment. + + +_PROP._ IV. PROB. I. + +_To separate from one another the heterogeneous Rays of compound Light._ + +[Illustration: FIG. 23.] + +The heterogeneous Rays are in some measure separated from one another by +the Refraction of the Prism in the third Experiment, and in the fifth +Experiment, by taking away the Penumbra from the rectilinear sides of +the coloured Image, that Separation in those very rectilinear sides or +straight edges of the Image becomes perfect. But in all places between +those rectilinear edges, those innumerable Circles there described, +which are severally illuminated by homogeneal Rays, by interfering with +one another, and being every where commix'd, do render the Light +sufficiently compound. But if these Circles, whilst their Centers keep +their Distances and Positions, could be made less in Diameter, their +interfering one with another, and by Consequence the Mixture of the +heterogeneous Rays would be proportionally diminish'd. In the twenty +third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many +sorts of Rays flowing from the same disque of the Sun, do in the third +Experiment illuminate; of all which and innumerable other intermediate +ones lying in a continual Series between the two rectilinear and +parallel edges of the Sun's oblong Image PT, that Image is compos'd, as +was explained in the fifth Experiment. And let _ag_, _bh_, _ci_, _dk_, +_el_, _fm_ be so many less Circles lying in a like continual Series +between two parallel right Lines _af_ and _gm_ with the same distances +between their Centers, and illuminated by the same sorts of Rays, that +is the Circle _ag_ with the same sort by which the corresponding Circle +AG was illuminated, and the Circle _bh_ with the same sort by which the +corresponding Circle BH was illuminated, and the rest of the Circles +_ci_, _dk_, _el_, _fm_ respectively, with the same sorts of Rays by +which the several corresponding Circles CJ, DK, EL, FM were illuminated. +In the Figure PT composed of the greater Circles, three of those Circles +AG, BH, CJ, are so expanded into one another, that the three sorts of +Rays by which those Circles are illuminated, together with other +innumerable sorts of intermediate Rays, are mixed at QR in the middle +of the Circle BH. And the like Mixture happens throughout almost the +whole length of the Figure PT. But in the Figure _pt_ composed of the +less Circles, the three less Circles _ag_, _bh_, _ci_, which answer to +those three greater, do not extend into one another; nor are there any +where mingled so much as any two of the three sorts of Rays by which +those Circles are illuminated, and which in the Figure PT are all of +them intermingled at BH. + +Now he that shall thus consider it, will easily understand that the +Mixture is diminished in the same Proportion with the Diameters of the +Circles. If the Diameters of the Circles whilst their Centers remain the +same, be made three times less than before, the Mixture will be also +three 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 the +greater Figure PT will be to their Mixture in the less _pt_, as the +Latitude of the greater Figure is to the Latitude of the less. For the +Latitudes of these Figures are equal to the Diameters of their Circles. +And hence it easily follows, that the Mixture of the Rays in the +refracted Spectrum _pt_ is to the Mixture of the Rays in the direct and +immediate Light of the Sun, as the breadth of that Spectrum is to the +difference between the length and breadth of the same Spectrum. + +So then, if we would diminish the Mixture of the Rays, we are to +diminish the Diameters of the Circles. Now these would be diminished if +the Sun's Diameter to which they answer could be made less than it is, +or (which comes to the same Purpose) if without Doors, at a great +distance 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 pass +through 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 to +that 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 Lens +is 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 of +Objects abroad are cast distinctly upon a Paper within the Room, and the +rectilinear Sides of the oblong Solar Image in the fifth Experiment +became distinct without any Penumbra. If this be done, it will not be +necessary to place that Hole very far off, no not beyond the Window. And +therefore instead of that Hole, I used the Hole in the Window-shut, as +follows. + +_Exper._ 11. In the Sun's Light let into my darken'd Chamber through a +small round Hole in my Window-shut, at about ten or twelve Feet from the +Window, I placed a Lens, by which the Image of the Hole might be +distinctly cast upon a Sheet of white Paper, placed at the distance of +six, eight, ten, or twelve Feet from the Lens. For, according to the +difference of the Lenses I used various distances, which I think not +worth the while to describe. Then immediately after the Lens I placed a +Prism, by which the trajected Light might be refracted either upwards or +sideways, and thereby the round Image, which the Lens alone did cast +upon 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 another +Paper at about the same distance from the Prism as before, moving the +Paper either towards the Prism or from it, until I found the just +distance where the Rectilinear Sides of the Image became most distinct. +For in this Case, the Circular Images of the Hole, which compose that +Image after the same manner that the Circles _ag_, _bh_, _ci_, &c. do +the Figure _pt_ [in _Fig._ 23.] were terminated most distinctly without +any Penumbra, and therefore extended into one another the least that +they could, and by consequence the Mixture of the heterogeneous Rays was +now the least of all. By this means I used to form an oblong Image (such +as is _pt_) [in _Fig._ 23, and 24.] of Circular Images of the Hole, +(such as are _ag_, _bh_, _ci_, &c.) and by using a greater or less Hole +in the Window-shut, I made the Circular Images _ag_, _bh_, _ci_, &c. of +which it was formed, to become greater or less at pleasure, and thereby +the Mixture of the Rays in the Image _pt_ to be as much, or as little as +I desired. + +[Illustration: FIG. 24.] + +_Illustration._ In the twenty-fourth Figure, F represents the Circular +Hole in the Window-shut, MN the Lens, whereby the Image or Species of +that Hole is cast distinctly upon a Paper at J, ABC the Prism, whereby +the Rays are at their emerging out of the Lens refracted from J towards +another Paper at _pt_, and the round Image at J is turned into an oblong +Image _pt_ falling on that other Paper. This Image _pt_ consists of +Circles placed one after another in a Rectilinear Order, as was +sufficiently explained in the fifth Experiment; and these Circles are +equal to the Circle J, and consequently answer in magnitude to the Hole +F; and therefore by diminishing that Hole they may be at pleasure +diminished, whilst their Centers remain in their Places. By this means I +made the Breadth of the Image _pt_ to be forty times, and sometimes +sixty or seventy times less than its Length. As for instance, if the +Breadth of the Hole F be one tenth of an Inch, and MF the distance of +the Lens from the Hole be 12 Feet; and if _p_B or _p_M the distance of +the Image _pt_ from the Prism or Lens be 10 Feet, and the refracting +Angle of the Prism be 62 Degrees, the Breadth of the Image _pt_ will be +one twelfth of an Inch, and the Length about six Inches, and therefore +the Length to the Breadth as 72 to 1, and by consequence the Light of +this Image 71 times less compound than the Sun's direct Light. And Light +thus far simple and homogeneal, is sufficient for trying all the +Experiments in this Book about simple Light. For the Composition of +heterogeneal Rays is in this Light so little, that it is scarce to be +discovered and perceiv'd by Sense, except perhaps in the indigo and +violet. For these being dark Colours do easily suffer a sensible Allay +by that little scattering Light which uses to be refracted irregularly +by the Inequalities of the Prism. + +Yet instead of the Circular Hole F, 'tis better to substitute an oblong +Hole shaped like a long Parallelogram with its Length parallel to the +Prism ABC. For if this Hole be an Inch or two long, and but a tenth or +twentieth Part of an Inch broad, or narrower; the Light of the Image +_pt_ will be as simple as before, or simpler, and the Image will become +much broader, and therefore more fit to have Experiments try'd in its +Light than before. + +Instead of this Parallelogram Hole may be substituted a triangular one +of equal Sides, whose Base, for instance, is about the tenth Part of an +Inch, and its Height an Inch or more. For by this means, if the Axis of +the Prism be parallel to the Perpendicular of the Triangle, the Image +_pt_ [in _Fig._ 25.] will now be form'd of equicrural Triangles _ag_, +_bh_, _ci_, _dk_, _el_, _fm_, &c. and innumerable other intermediate +ones answering to the triangular Hole in Shape and Bigness, and lying +one after another in a continual Series between two Parallel Lines _af_ +and _gm_. These Triangles are a little intermingled at their Bases, but +not at their Vertices; and therefore the Light on the brighter Side _af_ +of the Image, where the Bases of the Triangles are, is a little +compounded, but on the darker Side _gm_ is altogether uncompounded, and +in all Places between the Sides the Composition is proportional to the +distances of the Places from that obscurer Side _gm_. And having a +Spectrum _pt_ of such a Composition, we may try Experiments either in +its stronger and less simple Light near the Side _af_, or in its weaker +and simpler Light near the other Side _gm_, as it shall seem most +convenient. + +[Illustration: FIG. 25.] + +But in making Experiments of this kind, the Chamber ought to be made as +dark as can be, lest any Foreign Light mingle it self with the Light of +the Spectrum _pt_, and render it compound; especially if we would try +Experiments in the more simple Light next the Side _gm_ 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 troubled, and made more +compound. The Lens also ought to be good, such as may serve for optical +Uses, and the Prism ought to have a large Angle, suppose of 65 or 70 +Degrees, and to be well wrought, being made of Glass free from Bubbles +and Veins, with its Sides not a little convex or concave, as usually +happens, but truly plane, and its Polish elaborate, as in working +Optick-glasses, and not such as is usually wrought with Putty, whereby +the edges of the Sand-holes being worn away, there are left all over the +Glass a numberless Company of very little convex polite Risings like +Waves. The edges also of the Prism and Lens, so far as they may make any +irregular Refraction, must be covered with a black Paper glewed on. And +all the Light of the Sun's Beam let into the Chamber, which is useless +and unprofitable to the Experiment, ought to be intercepted with black +Paper, or other black Obstacles. For otherwise the useless Light being +reflected every way in the Chamber, will mix with the oblong Spectrum, +and help to disturb it. In trying these Things, so much diligence is not +altogether necessary, but it will promote the Success of the +Experiments, and by a very scrupulous Examiner of Things deserves to be +apply'd. It's difficult to get Glass Prisms fit for this Purpose, and +therefore I used sometimes prismatick Vessels made with pieces of broken +Looking-glasses, and filled with Rain Water. And to increase the +Refraction, I sometimes impregnated the Water strongly with _Saccharum +Saturni_. + + +_PROP._ V. THEOR. IV. + +_Homogeneal Light is refracted regularly without any Dilatation +splitting or shattering of the Rays, and the confused Vision of Objects +seen through refracting Bodies by heterogeneal Light arises from the +different Refrangibility of several sorts of Rays._ + +The first Part of this Proposition has been already sufficiently proved +in the fifth Experiment, and will farther appear by the Experiments +which follow. + +_Exper._ 12. In the middle of a black Paper I made a round Hole about a +fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the +Spectrum of homogeneal Light described in the former Proposition, so to +fall, that some part of the Light might pass through the Hole of the +Paper. This transmitted part of the Light I refracted with a Prism +placed behind the Paper, and letting this refracted Light fall +perpendicularly upon a white Paper two or three Feet distant from the +Prism, I found that the Spectrum formed on the Paper by this Light was +not oblong, as when 'tis made (in the third Experiment) by refracting +the 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. Which +shews, that this Light is refracted regularly without any Dilatation of +the Rays. + +_Exper._ 13. In the homogeneal Light I placed a Paper Circle of a +quarter of an Inch in diameter, and in the Sun's unrefracted +heterogeneal white Light I placed another Paper Circle of the same +Bigness. And going from the Papers to the distance of some Feet, I +viewed both Circles through a Prism. The Circle illuminated by the Sun's +heterogeneal Light appeared very oblong, as in the fourth Experiment, +the Length being many times greater than the Breadth; but the other +Circle, illuminated with homogeneal Light, appeared circular and +distinctly defined, as when 'tis view'd with the naked Eye. Which proves +the whole Proposition. + +_Exper._ 14. In the homogeneal Light I placed Flies, and such-like +minute Objects, and viewing them through a Prism, I saw their Parts as +distinctly defined, as if I had viewed them with the naked Eye. The same +Objects placed in the Sun's unrefracted heterogeneal Light, which was +white, I viewed also through a Prism, and saw them most confusedly +defined, so that I could not distinguish their smaller Parts from one +another. I placed also the Letters of a small print, one while in the +homogeneal Light, and then in the heterogeneal, and viewing them through +a 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 I +view'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 same +Situation. There was no difference, but in the Light by which the +Objects were illuminated, and which in one Case was simple, and in the +other compound; and therefore, the distinct Vision in the former Case, +and confused in the latter, could arise from nothing else than from that +difference of the Lights. Which proves the whole Proposition. + +And in these three Experiments it is farther very remarkable, that the +Colour 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 of +Refraction in a given Ratio._ + +That every Ray consider'd apart, is constant to it self in some degree +of Refrangibility, is sufficiently manifest out of what has been said. +Those Rays, which in the first Refraction, are at equal Incidences most +refracted, are also in the following Refractions at equal Incidences +most refracted; and so of the least refrangible, and the rest which have +any mean Degree of Refrangibility, as is manifest by the fifth, sixth, +seventh, eighth, and ninth Experiments. And those which the first Time +at like Incidences are equally refracted, are again at like Incidences +equally and uniformly refracted, and that whether they be refracted +before they be separated from one another, as in the fifth Experiment, +or whether they be refracted apart, as in the twelfth, thirteenth and +fourteenth Experiments. The Refraction therefore of every Ray apart is +regular, 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 a +given Proportion to the Sines of Refraction, as was explained in the +fifth Axiom, and some by Instruments fitted for measuring of +Refractions, or otherwise experimentally examining this Proportion, do +acquaint us that they have found it accurate. But whilst they, not +understanding the different Refrangibility of several Rays, conceived +them all to be refracted according to one and the same Proportion, 'tis +to be presumed that they adapted their Measures only to the middle of +the refracted Light; so that from their Measures we may conclude only +that the Rays which have a mean Degree of Refrangibility, that is, those +which when separated from the rest appear green, are refracted according +to 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 should +be so is very reasonable, Nature being ever conformable to her self; but +an experimental Proof is desired. And such a Proof will be had, if we +can shew that the Sines of Refraction of Rays differently refrangible +are one to another in a given Proportion when their Sines of Incidence +are equal. For, if the Sines of Refraction of all the Rays are in given +Proportions to the Sine of Refractions of a Ray which has a mean Degree +of Refrangibility, and this Sine is in a given Proportion to the equal +Sines of Incidence, those other Sines of Refraction will also be in +given Proportions to the equal Sines of Incidence. Now, when the Sines +of Incidence are equal, it will appear by the following Experiment, that +the Sines of Refraction are in a given Proportion to one another. + +[Illustration: FIG. 26.] + +_Exper._ 15. The Sun shining into a dark Chamber through a little round +Hole in the Window-shut, let S [in _Fig._ 26.] represent his round white +Image painted on the opposite Wall by his direct Light, PT his oblong +coloured Image made by refracting that Light with a Prism placed at the +Window; and _pt_, or _2p 2t_, _3p 3t_, his oblong colour'd Image made by +refracting again the same Light sideways with a second Prism placed +immediately after the first in a cross Position to it, as was explained +in the fifth Experiment; that is to say, _pt_ when the Refraction of the +second Prism is small, _2p 2t_ when its Refraction is greater, and _3p +3t_ when it is greatest. For such will be the diversity of the +Refractions, if the refracting Angle of the second Prism be of various +Magnitudes; suppose of fifteen or twenty Degrees to make the Image _pt_, +of thirty or forty to make the Image _2p 2t_, and of sixty to make the +Image _3p 3t_. But for want of solid Glass Prisms with Angles of +convenient Bignesses, there may be Vessels made of polished Plates of +Glass cemented together in the form of Prisms and filled with Water. +These things being thus ordered, I observed that all the solar Images or +coloured Spectrums PT, _pt_, _2p 2t_, _3p 3t_ did very nearly converge +to the place S on which the direct Light of the Sun fell and painted his +white round Image when the Prisms were taken away. The Axis of the +Spectrum PT, that is the Line drawn through the middle of it parallel to +its rectilinear Sides, did when produced pass exactly through the middle +of that white round Image S. And when the Refraction of the second Prism +was equal to the Refraction of the first, the refracting Angles of them +both being about 60 Degrees, the Axis of the Spectrum _3p 3t_ made by +that Refraction, did when produced pass also through the middle of the +same white round Image S. But when the Refraction of the second Prism +was less than that of the first, the produced Axes of the Spectrums _tp_ +or _2t 2p_ made by that Refraction did cut the produced Axis of the +Spectrum TP in the points _m_ and _n_, a little beyond the Center of +that white round Image S. Whence the proportion of the Line 3_t_T to the +Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P, +and this Proportion a little greater than that of _t_T to _p_P. Now when +the Light of the Spectrum PT falls perpendicularly upon the Wall, those +Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the +Tangents of the Refractions, and therefore by this Experiment the +Proportions of the Tangents of the Refractions are obtained, from whence +the Proportions of the Sines being derived, they come out equal, so far +as by viewing the Spectrums, and using some mathematical Reasoning I +could estimate. For I did not make an accurate Computation. So then the +Proposition holds true in every Ray apart, so far as appears by +Experiment. And that it is accurately true, may be demonstrated upon +this Supposition. _That Bodies refract Light by acting upon its Rays in +Lines perpendicular to their Surfaces._ But in order to this +Demonstration, I must distinguish the Motion of every Ray into two +Motions, the one perpendicular to the refracting Surface, the other +parallel to it, and concerning the perpendicular Motion lay down the +following Proposition. + +If any Motion or moving thing whatsoever be incident with any Velocity +on any broad and thin space terminated on both sides by two parallel +Planes, and in its Passage through that space be urged perpendicularly +towards the farther Plane by any force which at given distances from the +Plane is of given Quantities; the perpendicular velocity of that Motion +or Thing, at its emerging out of that space, shall be always equal to +the square Root of the sum of the square of the perpendicular velocity +of that Motion or Thing at its Incidence on that space; and of the +square of the perpendicular velocity which that Motion or Thing would +have at its Emergence, if at its Incidence its perpendicular velocity +was infinitely little. + +And the same Proposition holds true of any Motion or Thing +perpendicularly retarded in its passage through that space, if instead +of the sum of the two Squares you take their difference. The +Demonstration Mathematicians will easily find out, and therefore I shall +not trouble the Reader with it. + +Suppose now that a Ray coming most obliquely in the Line MC [in _Fig._ +1.] be refracted at C by the Plane RS into the Line CN, and if it be +required to find the Line CE, into which any other Ray AC shall be +refracted; let MC, AD, be the Sines of Incidence of the two Rays, and +NG, EF, their Sines of Refraction, and let the equal Motions of the +incident Rays be represented by the equal Lines MC and AC, and the +Motion MC being considered as parallel to the refracting Plane, let the +other Motion AC be distinguished into two Motions AD and DC, one of +which AD is parallel, and the other DC perpendicular to the refracting +Surface. In like manner, let the Motions of the emerging Rays be +distinguish'd into two, whereof the perpendicular ones are MC/NG × CG +and AD/EF × CF. And if the force of the refracting Plane begins to act +upon the Rays either in that Plane or at a certain distance from it on +the 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 Lines +perpendicular to that refracting Plane, and the Actions upon the Rays at +equal distances from the refracting Plane be equal, and at unequal ones +either equal or unequal according to any rate whatever; that Motion of +the Ray which is parallel to the refracting Plane, will suffer no +Alteration by that Force; and that Motion which is perpendicular to it +will be altered according to the rule of the foregoing Proposition. If +therefore for the perpendicular velocity of the emerging Ray CN you +write MC/NG × CG as above, then the perpendicular velocity of any other +emerging Ray CE which was AD/EF × CF, will be equal to the square Root +of CD_q_ + (_MCq/NGq_ × CG_q_). And by squaring these Equals, and adding +to them the Equals AD_q_ and MC_q_ - CD_q_, and dividing the Sums by the +Equals CF_q_ + EF_q_ and CG_q_ + NG_q_, you will have _MCq/NGq_ equal to +_ADq/EFq_. Whence AD, the Sine of Incidence, is to EF the Sine of +Refraction, as MC to NG, that is, in a given _ratio_. And this +Demonstration being general, without determining what Light is, or by +what kind of Force it is refracted, or assuming any thing farther than +that the refracting Body acts upon the Rays in Lines perpendicular to +its Surface; I take it to be a very convincing Argument of the full +truth of this Proposition. + +So then, if the _ratio_ of the Sines of Incidence and Refraction of any +sort of Rays be found in any one case, 'tis given in all cases; and this +may be readily found by the Method in the following Proposition. + + +_PROP._ VII. THEOR. VI. + +_The Perfection of Telescopes is impeded by the different Refrangibility +of the Rays of Light._ + +The Imperfection of Telescopes is vulgarly attributed to the spherical +Figures of the Glasses, and therefore Mathematicians have propounded to +figure them by the conical Sections. To shew that they are mistaken, I +have inserted this Proposition; the truth of which will appear by the +measure of the Refractions of the several sorts of Rays; and these +measures I thus determine. + +In the third Experiment of this first Part, where the refracting Angle +of 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 Glass +into the Air[F]; and the Sine of this Angle is 5188, the Radius being +10000. When the Axis of this Prism was parallel to the Horizon, and the +Refraction of the Rays at their Incidence on this Prism equal to that at +their Emergence out of it, I observed with a Quadrant the Angle which +the mean refrangible Rays, (that is those which went to the middle of +the Sun's coloured Image) made with the Horizon, and by this Angle and +the Sun's altitude observed at the same time, I found the Angle which +the 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. 15 +min. makes the Angle of Refraction, which is therefore 53 deg. 35 min. +and its Sine 8047. These are the Sines of Incidence and Refraction of +the mean refrangible Rays, and their Proportion in round Numbers is 20 +to 31. This Glass was of a Colour inclining to green. The last of the +Prisms mentioned in the third Experiment was of clear white Glass. Its +refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays +contained, with the incident 45 deg. 50 min. The Sine of half the first +Angle 5262. The Sine of half the Sum of the Angles 8157. And their +Proportion 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 7-3/4 +Inches would be the Length of the Image were the Sun but a Point, and +therefore subtends the Angle which the most and least refrangible Rays, +when incident on the Prism in the same Lines, do contain with one +another after their Emergence. Whence this Angle is 2 deg. 0´. 7´´. For +the 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 an +Angle of 2 deg. 0´. 7´´. Now half this Angle is the Angle which these +emergent Rays contain with the emergent mean refrangible Rays, and a +quarter thereof, that is 30´. 2´´. may be accounted the Angle which they +would contain with the same emergent mean refrangible Rays, were they +co-incident to them within the Glass, and suffered no other Refraction +than that at their Emergence. For, if two equal Refractions, the one at +the 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 will +make about a quarter of that Angle, and this quarter added to, and +subducted from the Angle of Refraction of the mean refrangible Rays, +which was 53 deg. 35´, gives the Angles of Refraction of the most and +least refrangible Rays 54 deg. 5´ 2´´, and 53 deg. 4´ 58´´, whose Sines +are 8099 and 7995, the common Angle of Incidence being 31 deg. 15´, and +its Sine 5188; and these Sines in the least round Numbers are in +proportion to one another, as 78 and 77 to 50. + +Now, if you subduct the common Sine of Incidence 50 from the Sines of +Refraction 77 and 78, the Remainders 27 and 28 shew, that in small +Refractions the Refraction of the least refrangible Rays is to the +Refraction of the most refrangible ones, as 27 to 28 very nearly, and +that the difference of the Refractions of the least refrangible and most +refrangible Rays is about the 27-1/2th Part of the whole Refraction of +the mean refrangible Rays. + +Whence they that are skilled in Opticks will easily understand,[G] that +the Breadth of the least circular Space, into which Object-glasses of +Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th +Part of half the Aperture of the Glass, or 55th Part of the whole +Aperture; and that the Focus of the most refrangible Rays is nearer to +the Object-glass than the Focus of the least refrangible ones, by about +the 27-1/2th Part of the distance between the Object-glass and the Focus +of the mean refrangible ones. + +And if Rays of all sorts, flowing from any one lucid Point in the Axis +of any convex Lens, be made by the Refraction of the Lens to converge to +Points not too remote from the Lens, the Focus of the most refrangible +Rays shall be nearer to the Lens than the Focus of the least refrangible +ones, by a distance which is to the 27-1/2th Part of the distance of the +Focus of the mean refrangible Rays from the Lens, as the distance +between that Focus and the lucid Point, from whence the Rays flow, is to +the distance between that lucid Point and the Lens very nearly. + +Now to examine whether the Difference between the Refractions, which the +most refrangible and the least refrangible Rays flowing from the same +Point suffer in the Object-glasses of Telescopes and such-like Glasses, +be so great as is here described, I contrived the following Experiment. + +_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 the +Species of that Object by the mean refrangible Rays at the distance of +six Feet and an Inch from the Lens on the other side. And therefore by +the foregoing Rule, it ought to collect the Species of that Object by +the least refrangible Rays at the distance of six Feet and 3-2/3 Inches +from the Lens, and by the most refrangible ones at the distance of five +Feet and 10-1/3 Inches from it: So that between the two Places, where +these least and most refrangible Rays collect the Species, there may be +the distance of about 5-1/3 Inches. For by that Rule, as six Feet and an +Inch (the distance of the Lens from the lucid Object) is to twelve Feet +and two Inches (the distance of the lucid Object from the Focus of the +mean refrangible Rays) that is, as One is to Two; so is the 27-1/2th +Part of six Feet and an Inch (the distance between the Lens and the same +Focus) to the distance between the Focus of the most refrangible Rays +and the Focus of the least refrangible ones, which is therefore 5-17/55 +Inches, that is very nearly 5-1/3 Inches. Now to know whether this +Measure was true, I repeated the second and eighth Experiment with +coloured Light, which was less compounded than that I there made use of: +For I now separated the heterogeneous Rays from one another by the +Method I described in the eleventh Experiment, so as to make a coloured +Spectrum about twelve or fifteen Times longer than broad. This Spectrum +I cast on a printed Book, and placing the above-mentioned Lens at the +distance of six Feet and an Inch from this Spectrum to collect the +Species of the illuminated Letters at the same distance on the other +side, I found that the Species of the Letters illuminated with blue were +nearer to the Lens than those illuminated with deep red by about three +Inches, or three and a quarter; but the Species of the Letters +illuminated with indigo and violet appeared so confused and indistinct, +that I could not read them: Whereupon viewing the Prism, I found it was +full of Veins running from one end of the Glass to the other; so that +the Refraction could not be regular. I took another Prism therefore +which was free from Veins, and instead of the Letters I used two or +three Parallel black Lines a little broader than the Strokes of the +Letters, and casting the Colours upon these Lines in such manner, that +the Lines ran along the Colours from one end of the Spectrum to the +other, I found that the Focus where the indigo, or confine of this +Colour 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 most +distinctly. The violet was so faint and dark, that I could not discern +the Species of the Lines distinctly by that Colour; and therefore +considering that the Prism was made of a dark coloured Glass inclining +to green, I took another Prism of clear white Glass; but the Spectrum of +Colours which this Prism made had long white Streams of faint Light +shooting out from both ends of the Colours, which made me conclude that +something was amiss; and viewing the Prism, I found two or three little +Bubbles in the Glass, which refracted the Light irregularly. Wherefore I +covered that Part of the Glass with black Paper, and letting the Light +pass through another Part of it which was free from such Bubbles, the +Spectrum 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 and +faint, 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 the +Spectrum. I suspected therefore, that this faint and dark Colour might +be allayed by that scattering Light which was refracted, and reflected +irregularly, partly by some very small Bubbles in the Glasses, and +partly by the Inequalities of their Polish; which Light, tho' it was but +little, yet it being of a white Colour, might suffice to affect the +Sense so strongly as to disturb the Phænomena of that weak and dark +Colour the violet, and therefore I tried, as in the 12th, 13th, and 14th +Experiments, whether the Light of this Colour did not consist of a +sensible Mixture of heterogeneous Rays, but found it did not. Nor did +the Refractions cause any other sensible Colour than violet to emerge +out of this Light, as they would have done out of white Light, and by +consequence out of this violet Light had it been sensibly compounded +with white Light. And therefore I concluded, that the reason why I could +not see the Species of the Lines distinctly by this Colour, was only +the Darkness of this Colour, and Thinness of its Light, and its distance +from the Axis of the Lens; I divided therefore those Parallel black +Lines into equal Parts, by which I might readily know the distances of +the Colours in the Spectrum from one another, and noted the distances of +the Lens from the Foci of such Colours, as cast the Species of the Lines +distinctly, and then considered whether the difference of those +distances bear such proportion to 5-1/3 Inches, the greatest Difference +of the distances, which the Foci of the deepest red and violet ought to +have from the Lens, as the distance of the observed Colours from one +another in the Spectrum bear to the greatest distance of the deepest red +and violet measured in the Rectilinear Sides of the Spectrum, that is, +to the Length of those Sides, or Excess of the Length of the Spectrum +above its Breadth. And my Observations were as follows. + +When I observed and compared the deepest sensible red, and the Colour in +the Confine of green and blue, which at the Rectilinear Sides of the +Spectrum was distant from it half the Length of those Sides, the Focus +where the Confine of green and blue cast the Species of the Lines +distinctly on the Paper, was nearer to the Lens than the Focus, where +the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4 +Inches. For sometimes the Measures were a little greater, sometimes a +little 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 some +little Errors. Now, if the Colours distant half the Length of the +Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4 +Difference of the distances of their Foci from the Lens, then the +Colours distant the whole Length ought to give 5 or 5-1/2 Inches +difference of those distances. + +But here it's to be noted, that I could not see the red to the full end +of the Spectrum, but only to the Center of the Semicircle which bounded +that end, or a little farther; and therefore I compared this red not +with that Colour which was exactly in the middle of the Spectrum, or +Confine of green and blue, but with that which verged a little more to +the blue than to the green: And as I reckoned the whole Length of the +Colours not to be the whole Length of the Spectrum, but the Length of +its Rectilinear Sides, so compleating the semicircular Ends into +Circles, when either of the observed Colours fell within those Circles, +I measured the distance of that Colour from the semicircular End of the +Spectrum, and subducting half this distance from the measured distance +of the two Colours, I took the Remainder for their corrected distance; +and in these Observations set down this corrected distance for the +difference of the distances of their Foci from the Lens. For, as the +Length of the Rectilinear Sides of the Spectrum would be the whole +Length of all the Colours, were the Circles of which (as we shewed) that +Spectrum consists contracted and reduced to Physical Points, so in that +Case this corrected distance would be the real distance of the two +observed Colours. + +When therefore I farther observed the deepest sensible red, and that +blue whose corrected distance from it was 7/12 Parts of the Length of +the Rectilinear Sides of the Spectrum, the difference of the distances +of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so +is 3-1/4 to 5-4/7. + +When I observed the deepest sensible red, and that indigo whose +corrected distance was 8/12 or 2/3 of the Length of the Rectilinear +Sides of the Spectrum, the difference of the distances of their Foci +from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to +5-1/2. + +When I observed the deepest sensible red, and that deep indigo whose +corrected distance from one another was 9/12 or 3/4 of the Length of the +Rectilinear Sides of the Spectrum, the difference of the distances of +their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to +5-1/3. + +When I observed the deepest sensible red, and that Part of the violet +next the indigo, whose corrected distance from the red was 10/12 or 5/6 +of the Length of the Rectilinear Sides of the Spectrum, the difference +of the distances of their Foci from the Lens was about 4-1/2 Inches, and +as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was +advantageously placed, so that its Axis respected the blue, and all +Things else were well ordered, and the Sun shone clear, and I held my +Eye very near to the Paper on which the Lens cast the Species of the +Lines, I could see pretty distinctly the Species of those Lines by that +Part of the violet which was next the indigo; and sometimes I could see +them by above half the violet, For in making these Experiments I had +observed, that the Species of those Colours only appear distinct, which +were in or near the Axis of the Lens: So that if the blue or indigo were +in the Axis, I could see their Species distinctly; and then the red +appeared much less distinct than before. Wherefore I contrived to make +the Spectrum of Colours shorter than before, so that both its Ends might +be nearer to the Axis of the Lens. And now its Length was about 2-1/2 +Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the +black Lines on which the Spectrum was cast, I made one black Line +broader than those, that I might see its Species more easily; and this +Line I divided by short cross Lines into equal Parts, for measuring the +distances of the observed Colours. And now I could sometimes see the +Species of this Line with its Divisions almost as far as the Center of +the semicircular violet End of the Spectrum, and made these farther +Observations. + +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 Rectilinear +Sides of the Spectrum, the Difference of the distances of the Foci of +those 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, to +5-1/4, 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 ordered +to the best Advantage, and the Sun shone very clear, was about 11/12 or +15/16 Parts of the Length of the Rectilinear Sides of the coloured +Spectrum) I found the Difference of the distances of their Foci from the +Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or +thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or +5-1/3 Inches. + +And by this Progression of Experiments I satisfied my self, that had the +Light at the very Ends of the Spectrum been strong enough to make the +Species of the black Lines appear plainly on the Paper, the Focus of the +deepest violet would have been found nearer to the Lens, than the Focus +of the deepest red, by about 5-1/3 Inches at least. And this is a +farther Evidence, that the Sines of Incidence and Refraction of the +several sorts of Rays, hold the same Proportion to one another in the +smallest Refractions which they do in the greatest. + +My Progress in making this nice and troublesome Experiment I have set +down more at large, that they that shall try it after me may be aware of +the Circumspection requisite to make it succeed well. And if they cannot +make it succeed so well as I did, they may notwithstanding collect by +the Proportion of the distance of the Colours of the Spectrum, to the +Difference of the distances of their Foci from the Lens, what would be +the Success in the more distant Colours by a better trial. And yet, if +they 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 Colour +whose Focus is desired, I question not but the Experiment will succeed +better with them than it did with me. For I directed the Axis as nearly +as I could to the middle of the Colours, and then the faint Ends of the +Spectrum being remote from the Axis, cast their Species less distinctly +on the Paper than they would have done, had the Axis been successively +directed to them. + +Now by what has been said, it's certain that the Rays which differ in +Refrangibility do not converge to the same Focus; but if they flow from +a lucid Point, as far from the Lens on one side as their Foci are on the +other, the Focus of the most refrangible Rays shall be nearer to the +Lens than that of the least refrangible, by above the fourteenth Part of +the whole distance; and if they flow from a lucid Point, so very remote +from the Lens, that before their Incidence they may be accounted +parallel, the Focus of the most refrangible Rays shall be nearer to the +Lens than the Focus of the least refrangible, by about the 27th or 28th +Part of their whole distance from it. And the Diameter of the Circle in +the middle Space between those two Foci which they illuminate, when they +fall there on any Plane, perpendicular to the Axis (which Circle is the +least into which they can all be gathered) is about the 55th Part of the +Diameter of the Aperture of the Glass. So that 'tis a wonder, that +Telescopes represent Objects so distinct as they do. But were all the +Rays of Light equally refrangible, the Error arising only from the +Sphericalness of the Figures of Glasses would be many hundred times +less. For, if the Object-glass of a Telescope be Plano-convex, and the +Plane side be turned towards the Object, and the Diameter of the +Sphere, whereof this Glass is a Segment, be called D, and the +Semi-diameter of the Aperture of the Glass be called S, and the Sine of +Incidence 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 the +Place where the Image of the Object is most distinctly made, be +scattered all over a little Circle, whose Diameter is _(Rq/Iq) × (S +cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of +the Rays by the Method of infinite Series, and rejecting the Terms, +whose Quantities are inconsiderable. As for instance, if the Sine of +Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the +Diameter 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 be +two Inches, the Diameter of the little Circle, (that is (_Rq × S +cub.)/(Iq × D quad._)) will be (31 × 31 × 8)/(20 × 20 × 1200 × 1200) (or +961/72000000) Parts of an Inch. But the Diameter of the little Circle, +through which these Rays are scattered by unequal Refrangibility, will +be about the 55th Part of the Aperture of the Object-glass, which here +is four Inches. And therefore, the Error arising from the Spherical +Figure of the Glass, is to the Error arising from the different +Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to +5449; and therefore being in comparison so very little, deserves not to +be considered. + +[Illustration: FIG. 27.] + +But you will say, if the Errors caused by the different Refrangibility +be so very great, how comes it to pass, that Objects appear through +Telescopes so distinct as they do? I answer, 'tis because the erring +Rays are not scattered uniformly over all that Circular Space, but +collected infinitely more densely in the Center than in any other Part +of the Circle, and in the Way from the Center to the Circumference, grow +continually rarer and rarer, so as at the Circumference to become +infinitely rare; and by reason of their Rarity are not strong enough to +be visible, unless in the Center and very near it. Let ADE [in _Fig._ +27.] represent one of those Circles described with the Center C, and +Semi-diameter AC, and let BFG be a smaller Circle concentrick to the +former, cutting with its Circumference the Diameter AC in B, and bisect +AC 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 the +lesser Circle BFG, will be to the whole Light within the greater AED, as +the Excess of the Square of AC above the Square of AB, is to the Square +of AC. As if BC be the fifth Part of AC, the Light will be four times +denser in B than in N, and the whole Light within the less Circle, will +be to the whole Light within the greater, as nine to twenty-five. Whence +it's evident, that the Light within the less Circle, must strike the +Sense much more strongly, than that faint and dilated Light round about +between it and the Circumference of the greater. + +But it's farther to be noted, that the most luminous of the Prismatick +Colours are the yellow and orange. These affect the Senses more strongly +than all the rest together, and next to these in strength are the red +and green. The blue compared with these is a faint and dark Colour, and +the indigo and violet are much darker and fainter, so that these +compared with the stronger Colours are little to be regarded. The Images +of Objects are therefore to be placed, not in the Focus of the mean +refrangible Rays, which are in the Confine of green and blue, but in the +Focus 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 the +brightest yellow, that yellow which inclines more to orange than to +green. And by the Refraction of these Rays (whose Sines of Incidence and +Refraction in Glass are as 17 and 11) the Refraction of Glass and +Crystal for Optical Uses is to be measured. Let us therefore place the +Image of the Object in the Focus of these Rays, and all the yellow and +orange will fall within a Circle, whose Diameter is about the 250th +Part of the Diameter of the Aperture of the Glass. And if you add the +brighter half of the red, (that half which is next the orange) and the +brighter half of the green, (that half which is next the yellow) about +three fifth Parts of the Light of these two Colours will fall within the +same Circle, and two fifth Parts will fall without it round about; and +that which falls without will be spread through almost as much more +space as that which falls within, and so in the gross be almost three +times rarer. Of the other half of the red and green, (that is of the +deep dark red and willow green) about one quarter will fall within this +Circle, and three quarters without, and that which falls without will be +spread through about four or five times more space than that which falls +within; and so in the gross be rarer, and if compared with the whole +Light within it, will be about 25 times rarer than all that taken in the +gross; or rather more than 30 or 40 times rarer, because the deep red in +the end of the Spectrum of Colours made by a Prism is very thin and +rare, and the willow green is something rarer than the orange and +yellow. The Light of these Colours therefore being so very much rarer +than that within the Circle, will scarce affect the Sense, especially +since the deep red and willow green of this Light, are much darker +Colours than the rest. And for the same reason the blue and violet being +much darker Colours than these, and much more rarified, may be +neglected. For the dense and bright Light of the Circle, will obscure +the rare and weak Light of these dark Colours round about it, and +render them almost insensible. The sensible Image of a lucid Point is +therefore scarce broader than a Circle, whose Diameter is the 250th Part +of 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 round +about it, which a Spectator will scarce regard. And therefore in a +Telescope, whose Aperture is four Inches, and Length an hundred Feet, it +exceeds not 2´´ 45´´´, or 3´´. And in a Telescope whose Aperture is two +Inches, and Length 20 or 30 Feet, it may be 5´´ or 6´´, and scarce +above. And this answers well to Experience: For some Astronomers have +found the Diameters of the fix'd Stars, in Telescopes of between 20 and +60 Feet in length, to be about 5´´ or 6´´, or at most 8´´ or 10´´ in +diameter. But if the Eye-Glass be tincted faintly with the Smoak of a +Lamp or Torch, to obscure the Light of the Star, the fainter Light in +the Circumference of the Star ceases to be visible, and the Star (if the +Glass be sufficiently soiled with Smoak) appears something more like a +mathematical Point. And for the same Reason, the enormous Part of the +Light in the Circumference of every lucid Point ought to be less +discernible in shorter Telescopes than in longer, because the shorter +transmit less Light to the Eye. + +Now, that the fix'd Stars, by reason of their immense Distance, appear +like Points, unless so far as their Light is dilated by Refraction, may +appear from hence; that when the Moon passes over them and eclipses +them, their Light vanishes, not gradually like that of the Planets, but +all at once; and in the end of the Eclipse it returns into Sight all at +once, or certainly in less time than the second of a Minute; the +Refraction of the Moon's Atmosphere a little protracting the time in +which the Light of the Star first vanishes, and afterwards returns into +Sight. + +Now, if we suppose the sensible Image of a lucid Point, to be even 250 +times narrower than the Aperture of the Glass; yet this Image would be +still much greater than if it were only from the spherical Figure of the +Glass. For were it not for the different Refrangibility of the Rays, its +breadth in an 100 Foot Telescope whose aperture is 4 Inches, would be +but 961/72000000 parts of an Inch, as is manifest by the foregoing +Computation. And therefore in this case the greatest Errors arising from +the spherical Figure of the Glass, would be to the greatest sensible +Errors arising from the different Refrangibility of the Rays as +961/72000000 to 4/250 at most, that is only as 1 to 1200. And this +sufficiently shews that it is not the spherical Figures of Glasses, but +the different Refrangibility of the Rays which hinders the perfection of +Telescopes. + +There is another Argument by which it may appear that the different +Refrangibility of Rays, is the true cause of the imperfection of +Telescopes. For the Errors of the Rays arising from the spherical +Figures of Object-glasses, are as the Cubes of the Apertures of the +Object Glasses; and thence to make Telescopes of various Lengths magnify +with equal distinctness, the Apertures of the Object-glasses, and the +Charges or magnifying Powers ought to be as the Cubes of the square +Roots of their lengths; which doth not answer to Experience. But the +Errors of the Rays arising from the different Refrangibility, are as the +Apertures of the Object-glasses; and thence to make Telescopes of +various lengths, magnify with equal distinctness, their Apertures and +Charges ought to be as the square Roots of their lengths; and this +answers to Experience, as is well known. For Instance, a Telescope of 64 +Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120 +times, with as much distinctness as one of a Foot in length, with 1/3 of +an Inch aperture, magnifies 15 times. + +[Illustration: FIG. 28.] + +Now were it not for this different Refrangibility of Rays, Telescopes +might be brought to a greater perfection than we have yet describ'd, by +composing the Object-glass of two Glasses with Water between them. Let +ADFC [in _Fig._ 28.] represent the Object-glass composed of two Glasses +ABED and BEFC, alike convex on the outsides AGD and CHF, and alike +concave on the insides BME, BNE, with Water in the concavity BMEN. Let +the Sine of Incidence out of Glass into Air be as I to R, and out of +Water 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 sides +AGD and CHF are ground be D, and the Diameter of the Sphere to which the +concave sides BME and BNE, are ground be to D, as the Cube Root of +KK--KI to the Cube Root of RK--RI: and the Refractions on the concave +sides of the Glasses, will very much correct the Errors of the +Refractions on the convex sides, so far as they arise from the +sphericalness of the Figure. And by this means might Telescopes be +brought to sufficient perfection, were it not for the different +Refrangibility of several sorts of Rays. But by reason of this different +Refrangibility, I do not yet see any other means of improving Telescopes +by Refractions alone, than that of increasing their lengths, for which +end the late Contrivance of _Hugenius_ seems well accommodated. For very +long Tubes are cumbersome, and scarce to be readily managed, and by +reason of their length are very apt to bend, and shake by bending, so as +to cause a continual trembling in the Objects, whereby it becomes +difficult to see them distinctly: whereas by his Contrivance the Glasses +are readily manageable, and the Object-glass being fix'd upon a strong +upright Pole becomes more steady. + +Seeing therefore the Improvement of Telescopes of given lengths by +Refractions is desperate; I contrived heretofore a Perspective by +Reflexion, using instead of an Object-glass a concave Metal. The +diameter of the Sphere to which the Metal was ground concave was about +25 _English_ Inches, and by consequence the length of the Instrument +about six Inches and a quarter. The Eye-glass was Plano-convex, and the +diameter of the Sphere to which the convex side was ground was about 1/5 +of an Inch, or a little less, and by consequence it magnified between 30 +and 40 times. By another way of measuring I found that it magnified +about 35 times. The concave Metal bore an Aperture of an Inch and a +third part; but the Aperture was limited not by an opake Circle, +covering the Limb of the Metal round about, but by an opake Circle +placed between the Eyeglass and the Eye, and perforated in the middle +with a little round hole for the Rays to pass through to the Eye. For +this Circle by being placed here, stopp'd much of the erroneous Light, +which otherwise would have disturbed the Vision. By comparing it with a +pretty good Perspective of four Feet in length, made with a concave +Eye-glass, I could read at a greater distance with my own Instrument +than with the Glass. Yet Objects appeared much darker in it than in the +Glass, and that partly because more Light was lost by Reflexion in the +Metal, than by Refraction in the Glass, and partly because my Instrument +was overcharged. Had it magnified but 30 or 25 times, it would have made +the Object appear more brisk and pleasant. Two of these I made about 16 +Years ago, and have one of them still by me, by which I can prove the +truth of what I write. Yet it is not so good as at the first. For the +concave has been divers times tarnished and cleared again, by rubbing +it with very soft Leather. When I made these an Artist in _London_ +undertook to imitate it; but using another way of polishing them than I +did, he fell much short of what I had attained to, as I afterwards +understood by discoursing the Under-workman he had employed. The Polish +I used was in this manner. I had two round Copper Plates, each six +Inches in Diameter, the one convex, the other concave, ground very true +to one another. On the convex I ground the Object-Metal or Concave which +was to be polish'd, 'till it had taken the Figure of the Convex and was +ready for a Polish. Then I pitched over the convex very thinly, by +dropping melted Pitch upon it, and warming it to keep the Pitch soft, +whilst I ground it with the concave Copper wetted to make it spread +eavenly all over the convex. Thus by working it well I made it as thin +as a Groat, and after the convex was cold I ground it again to give it +as true a Figure as I could. Then I took Putty which I had made very +fine by washing it from all its grosser Particles, and laying a little +of this upon the Pitch, I ground it upon the Pitch with the concave +Copper, till it had done making a Noise; and then upon the Pitch I +ground the Object-Metal with a brisk motion, for about two or three +Minutes of time, leaning hard upon it. Then I put fresh Putty upon the +Pitch, and ground it again till it had done making a noise, and +afterwards ground the Object-Metal upon it as before. And this Work I +repeated till the Metal was polished, grinding it the last time with all +my strength for a good while together, and frequently breathing upon +the Pitch, to keep it moist without laying on any more fresh Putty. The +Object-Metal was two Inches broad, and about one third part of an Inch +thick, to keep it from bending. I had two of these Metals, and when I +had polished them both, I tried which was best, and ground the other +again, to see if I could make it better than that which I kept. And thus +by many Trials I learn'd the way of polishing, till I made those two +reflecting Perspectives I spake of above. For this Art of polishing will +be better learn'd by repeated Practice than by my Description. Before I +ground the Object-Metal on the Pitch, I always ground the Putty on it +with the concave Copper, till it had done making a noise, because if the +Particles of the Putty were not by this means made to stick fast in the +Pitch, they would by rolling up and down grate and fret the Object-Metal +and fill it full of little holes. + +But because Metal is more difficult to polish than Glass, and is +afterwards very apt to be spoiled by tarnishing, and reflects not so +much Light as Glass quick-silver'd over does: I would propound to use +instead of the Metal, a Glass ground concave on the foreside, and as +much convex on the backside, and quick-silver'd over on the convex side. +The Glass must be every where of the same thickness exactly. Otherwise +it will make Objects look colour'd and indistinct. By such a Glass I +tried about five or six Years ago to make a reflecting Telescope of four +Feet in length to magnify about 150 times, and I satisfied my self that +there wants nothing but a good Artist to bring the Design to +perfection. For the Glass being wrought by one of our _London_ Artists +after such a manner as they grind Glasses for Telescopes, though it +seemed as well wrought as the Object-glasses use to be, yet when it was +quick-silver'd, the Reflexion discovered innumerable Inequalities all +over the Glass. And by reason of these Inequalities, Objects appeared +indistinct in this Instrument. For the Errors of reflected Rays caused +by any Inequality of the Glass, are about six times greater than the +Errors of refracted Rays caused by the like Inequalities. Yet by this +Experiment I satisfied my self that the Reflexion on the concave side of +the Glass, which I feared would disturb the Vision, did no sensible +prejudice to it, and by consequence that nothing is wanting to perfect +these Telescopes, but good Workmen who can grind and polish Glasses +truly spherical. An Object-glass of a fourteen Foot Telescope, made by +an Artificer at _London_, I once mended considerably, by grinding it on +Pitch with Putty, and leaning very easily on it in the grinding, lest +the Putty should scratch it. Whether this way may not do well enough for +polishing these reflecting Glasses, I have not yet tried. But he that +shall try either this or any other way of polishing which he may think +better, may do well to make his Glasses ready for polishing, by grinding +them without that Violence, wherewith our _London_ Workmen press their +Glasses in grinding. For by such violent pressure, Glasses are apt to +bend a little in the grinding, and such bending will certainly spoil +their Figure. To recommend therefore the consideration of these +reflecting Glasses to such Artists as are curious in figuring Glasses, I +shall describe this optical Instrument in the following Proposition. + + +_PROP._ VIII. PROB. II. + +_To shorten Telescopes._ + +Let ABCD [in _Fig._ 29.] represent a Glass spherically concave on the +foreside AB, and as much convex on the backside CD, so that it be every +where of an equal thickness. Let it not be thicker on one side than on +the other, lest it make Objects appear colour'd and indistinct, and let +it be very truly wrought and quick-silver'd over on the backside; and +set in the Tube VXYZ which must be very black within. Let EFG represent +a Prism of Glass or Crystal placed near the other end of the Tube, in +the middle of it, by means of a handle of Brass or Iron FGK, to the end +of 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 each +other, and by consequence equal to half right ones, and let the plane +sides FE and GE be square, and by consequence the third side FG a +rectangular Parallelogram, whose length is to its breadth in a +subduplicate 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 square +side EF perpendicularly and by consequence through the middle of the +side FG at an Angle of 45 Degrees, and let the side EF be turned towards +the Speculum, and the distance of this Prism from the Speculum be such +that the Rays of the Light PQ, RS, &c. which are incident upon the +Speculum in Lines parallel to the Axis thereof, may enter the Prism at +the side EF, and be reflected by the side FG, and thence go out of it +through the side GE, to the Point T, which must be the common Focus of +the Speculum ABDC, and of a Plano-convex Eye-glass H, through which +those Rays must pass to the Eye. And let the Rays at their coming out of +the Glass pass through a small round hole, or aperture made in a little +plate 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 pass +through. For so it will render the Object distinct, the Plate in which +'tis made intercepting all the erroneous part of the Light which comes +from the verges of the Speculum AB. Such an Instrument well made, if it +be 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 the +Speculum, and magnify between two and three hundred times. But the hole +H here limits the aperture with more advantage, than if the aperture was +placed at the Speculum. If the Instrument be made longer or shorter, the +aperture must be in proportion as the Cube of the square-square Root of +the length, and the magnifying as the aperture. But it's convenient that +the 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 the +working. The Prism EFG must be no bigger than is necessary, and its back +side FG must not be quick-silver'd over. For without quicksilver it will +reflect all the Light incident on it from the Speculum. + +[Illustration: FIG. 29.] + +In this Instrument the Object will be inverted, but may be erected by +making the square sides FF and EG of the Prism EFG not plane but +spherically convex, that the Rays may cross as well before they come at +it as afterwards between it and the Eye-glass. If it be desired that the +Instrument bear a larger aperture, that may be also done by composing +the Speculum of two Glasses with Water between them. + +If the Theory of making Telescopes could at length be fully brought into +Practice, yet there would be certain Bounds beyond which Telescopes +could not perform. For the Air through which we look upon the Stars, is +in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows +cast from high Towers, and by the twinkling of the fix'd Stars. But +these Stars do not twinkle when viewed through Telescopes which have +large apertures. For the Rays of Light which pass through divers parts +of the aperture, tremble each of them apart, and by means of their +various and sometimes contrary Tremors, fall at one and the same time +upon different points in the bottom of the Eye, and their trembling +Motions are too quick and confused to be perceived severally. And all +these illuminated Points constitute one broad lucid Point, composed of +those many trembling Points confusedly and insensibly mixed with one +another by very short and swift Tremors, and thereby cause the Star to +appear broader than it is, and without any trembling of the whole. Long +Telescopes may cause Objects to appear brighter and larger than short +ones can do, but they cannot be so formed as to take away that confusion +of the Rays which arises from the Tremors of the Atmosphere. The only +Remedy is a most serene and quiet Air, such as may perhaps be found on +the 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's _Lectiones 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. _Part_ I. +_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 caused +by new Modifications of the Light variously impress'd, according to the +various Terminations of the Light and Shadow_. + +The PROOF by Experiments. + +_Exper._ 1. For if the Sun shine into a very dark Chamber through an +oblong hole F, [in _Fig._ 1.] whose breadth is the sixth or eighth part +of an Inch, or something less; and his beam FH do afterwards pass first +through a very large Prism ABC, distant about 20 Feet from the hole, and +parallel to it, and then (with its white part) through an oblong hole H, +whose breadth is about the fortieth or sixtieth part of an Inch, and +which is made in a black opake Body GI, and placed at the distance of +two or three Feet from the Prism, in a parallel Situation both to the +Prism and to the former hole, and if this white Light thus transmitted +through the hole H, fall afterwards upon a white Paper _pt_, placed +after that hole H, at the distance of three or four Feet from it, and +there paint the usual Colours of the Prism, suppose red at _t_, yellow +at _s_, green at _r_, blue at _q_, and violet at _p_; you may with an +Iron Wire, or any such like slender opake Body, whose breadth is about +the tenth part of an Inch, by intercepting the Rays at _k_, _l_, _m_, +_n_ or _o_, take away any one of the Colours at _t_, _s_, _r_, _q_ or +_p_, whilst the other Colours remain upon the Paper as before; or with +an Obstacle something bigger you may take away any two, or three, or +four Colours together, the rest remaining: So that any one of the +Colours as well as violet may become outmost in the Confine of the +Shadow towards _p_, and any one of them as well as red may become +outmost in the Confine of the Shadow towards _t_, and any one of them +may also border upon the Shadow made within the Colours by the Obstacle +R intercepting some intermediate part of the Light; and, lastly, any one +of 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 not +arise from the different Confines of Shadow, whereby Light is variously +modified, as has hitherto been the Opinion of Philosophers. In trying +these things 'tis to be observed, that by how much the holes F and H are +narrower, and the Intervals between them and the Prism greater, and the +Chamber darker, by so much the better doth the Experiment succeed; +provided the Light be not so far diminished, but that the Colours at +_pt_ be sufficiently visible. To procure a Prism of solid Glass large +enough for this Experiment will be difficult, and therefore a prismatick +Vessel must be made of polish'd Glass Plates cemented together, and +filled with salt Water or clear Oil. + +[Illustration: FIG. 1.] + +_Exper._ 2. The Sun's Light let into a dark Chamber through the round +hole F, [in _Fig._ 2.] half an Inch wide, passed first through the Prism +ABC placed at the hole, and then through a Lens PT something more than +four Inches broad, and about eight Feet distant from the Prism, and +thence converged to O the Focus of the Lens distant from it about three +Feet, and there fell upon a white Paper DE. If that Paper was +perpendicular to that Light incident upon it, as 'tis represented in the +posture DE, all the Colours upon it at O appeared white. But if the +Paper being turned about an Axis parallel to the Prism, became very much +inclined to the Light, as 'tis represented in the Positions _de_ and +_[Greek: de]_; 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 and +the 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 Prism +in all these cases remained the same. + +[Illustration: FIG. 2.] + +[Illustration: FIG. 3.] + +_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 a +hole in the Window-shut be refracted by a large Prism ABC, [in _Fig._ +3.] whose refracting Angle C is more than 60 Degrees, and so soon as it +comes out of the Prism, let it fall upon the white Paper DE glewed upon +a stiff Plane; and this Light, when the Paper is perpendicular to it, as +'tis represented in DE, will appear perfectly white upon the Paper; but +when the Paper is very much inclin'd to it in such a manner as to keep +always parallel to the Axis of the Prism, the whiteness of the whole +Light upon the Paper will according to the inclination of the Paper this +way or that way, change either into yellow and red, as in the posture +_de_, or into blue and violet, as in the posture [Greek: de]. And if the +Light before it fall upon the Paper be twice refracted the same way by +two parallel Prisms, these Colours will become the more conspicuous. +Here all the middle parts of the broad beam of white Light which fell +upon the Paper, did without any Confine of Shadow to modify it, become +colour'd all over with one uniform Colour, the Colour being always the +same in the middle of the Paper as at the edges, and this Colour changed +according to the various Obliquity of the reflecting Paper, without any +change in the Refractions or Shadow, or in the Light which fell upon the +Paper. And therefore these Colours are to be derived from some other +Cause than the new Modifications of Light by Refractions and Shadows. + +If it be asked, what then is their Cause? I answer, That the Paper in +the posture _de_, being more oblique to the more refrangible Rays than +to the less refrangible ones, is more strongly illuminated by the latter +than by the former, and therefore the less refrangible Rays are +predominant in the reflected Light. And where-ever they are predominant +in any Light, they tinge it with red or yellow, as may in some measure +appear by the first Proposition of the first Part of this Book, and will +more fully appear hereafter. And the contrary happens in the posture of +the Paper [Greek: de], the more refrangible Rays being then predominant +which 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 Confine +or Shadow. If such a Bubble be cover'd with a concave Glass, to keep it +from being agitated by any Wind or Motion of the Air, the Colours will +slowly and regularly change their situation, even whilst the Eye and the +Bubble, and all Bodies which emit any Light, or cast any Shadow, remain +unmoved. And therefore their Colours arise from some regular Cause which +depends not on any Confine of Shadow. What this Cause is will be shewed +in the next Book. + +To these Experiments may be added the tenth Experiment of the first Part +of this first Book, where the Sun's Light in a dark Room being +trajected through the parallel Superficies of two Prisms tied together +in the form of a Parallelopipede, became totally of one uniform yellow +or red Colour, at its emerging out of the Prisms. Here, in the +production of these Colours, the Confine of Shadow can have nothing to +do. For the Light changes from white to yellow, orange and red +successively, without any alteration of the Confine of Shadow: And at +both edges of the emerging Light where the contrary Confines of Shadow +ought to produce different Effects, the Colour is one and the same, +whether it be white, yellow, orange or red: And in the middle of the +emerging Light, where there is no Confine of Shadow at all, the Colour +is the very same as at the edges, the whole Light at its very first +Emergence being of one uniform Colour, whether white, yellow, orange or +red, and going on thence perpetually without any change of Colour, such +as the Confine of Shadow is vulgarly supposed to work in refracted Light +after its Emergence. Neither can these Colours arise from any new +Modifications of the Light by Refractions, because they change +successively from white to yellow, orange and red, while the Refractions +remain the same, and also because the Refractions are made contrary ways +by parallel Superficies which destroy one another's Effects. They arise +not therefore from any Modifications of Light made by Refractions and +Shadows, but have some other Cause. What that Cause is we shewed above +in this tenth Experiment, and need not here repeat it. + +There is yet another material Circumstance of this Experiment. For this +emerging Light being by a third Prism HIK [in _Fig._ 22. _Part_ I.][I] +refracted towards the Paper PT, and there painting the usual Colours of +the Prism, red, yellow, green, blue, violet: If these Colours arose from +the Refractions of that Prism modifying the Light, they would not be in +the Light before its Incidence on that Prism. And yet in that Experiment +we found, that when by turning the two first Prisms about their common +Axis all the Colours were made to vanish but the red; the Light which +makes that red being left alone, appeared of the very same red Colour +before its Incidence on the third Prism. And in general we find by other +Experiments, that when the Rays which differ in Refrangibility are +separated from one another, and any one Sort of them is considered +apart, the Colour of the Light which they compose cannot be changed by +any Refraction or Reflexion whatever, as it ought to be were Colours +nothing else than Modifications of Light caused by Refractions, and +Reflexions, and Shadows. This Unchangeableness of Colour I am now to +describe in the following Proposition. + + +_PROP._ II. THEOR. II. + +_All homogeneal Light has its proper Colour answering to its Degree of +Refrangibility, and that Colour cannot be changed by Reflexions and +Refractions._ + +In the Experiments of the fourth Proposition of the first Part of this +first Book, when I had separated the heterogeneous Rays from one +another, the Spectrum _pt_ formed by the separated Rays, did in the +Progress from its End _p_, on which the most refrangible Rays fell, unto +its other End _t_, on which the least refrangible Rays fell, appear +tinged with this Series of Colours, violet, indigo, blue, green, yellow, +orange, red, together with all their intermediate Degrees in a continual +Succession perpetually varying. So that there appeared as many Degrees +of 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 this +Light, sometimes another very little Part, as is described in the +twelfth Experiment of the first Part of this Book. For by this +Refraction the Colour of the Light was never changed in the least. If +any Part of the red Light was refracted, it remained totally of the same +red Colour as before. No orange, no yellow, no green or blue, no other +new Colour was produced by that Refraction. Neither did the Colour any +ways change by repeated Refractions, but continued always the same red +entirely as at first. The like Constancy and Immutability I found also +in the blue, green, and other Colours. So also, if I looked through a +Prism upon any Body illuminated with any part of this homogeneal Light, +as in the fourteenth Experiment of the first Part of this Book is +described; I could not perceive any new Colour generated this way. All +Bodies illuminated with compound Light appear through Prisms confused, +(as was said above) and tinged with various new Colours, but those +illuminated with homogeneal Light appeared through Prisms neither less +distinct, nor otherwise colour'd, than when viewed with the naked Eyes. +Their Colours were not in the least changed by the Refraction of the +interposed Prism. I speak here of a sensible Change of Colour: For the +Light which I here call homogeneal, being not absolutely homogeneal, +there ought to arise some little Change of Colour from its +Heterogeneity. But, if that Heterogeneity was so little as it might be +made by the said Experiments of the fourth Proposition, that Change was +not sensible, and therefore in Experiments, where Sense is Judge, ought +to be accounted none at all. + +_Exper._ 6. And as these Colours were not changeable by Refractions, so +neither were they by Reflexions. For all white, grey, red, yellow, +green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, Indico +Bise, Gold, Silver, Copper, Grass, blue Flowers, Violets, Bubbles of +Water tinged with various Colours, Peacock's Feathers, the Tincture of +_Lignum Nephriticum_, and such-like, in red homogeneal Light appeared +totally red, in blue Light totally blue, in green Light totally green, +and so of other Colours. In the homogeneal Light of any Colour they all +appeared totally of that same Colour, with this only Difference, that +some of them reflected that Light more strongly, others more faintly. I +never yet found any Body, which by reflecting homogeneal Light could +sensibly change its Colour. + +From all which it is manifest, that if the Sun's Light consisted of but +one sort of Rays, there would be but one Colour in the whole World, nor +would it be possible to produce any new Colour by Reflexions and +Refractions, and by consequence that the variety of Colours depends upon +the Composition of Light. + + +_DEFINITION._ + +The homogeneal Light and Rays which appear red, or rather make Objects +appear so, I call Rubrifick or Red-making; those which make Objects +appear yellow, green, blue, and violet, I call Yellow-making, +Green-making, Blue-making, Violet-making, and so of the rest. And if at +any time I speak of Light and Rays as coloured or endued with Colours, I +would be understood to speak not philosophically and properly, but +grossly, and accordingly to such Conceptions as vulgar People in seeing +all these Experiments would be apt to frame. For the Rays to speak +properly are not coloured. In them there is nothing else than a certain +Power and Disposition to stir up a Sensation of this or that Colour. +For as Sound in a Bell or musical String, or other sounding Body, is +nothing but a trembling Motion, and in the Air nothing but that Motion +propagated from the Object, and in the Sensorium 'tis a Sense of that +Motion under the Form of Sound; so Colours in the Object are nothing but +a Disposition to reflect this or that sort of Rays more copiously than +the rest; in the Rays they are nothing but their Dispositions to +propagate this or that Motion into the Sensorium, and in the Sensorium +they are Sensations of those Motions under the Forms of Colours. + + +_PROP._ III. PROB. I. + +_To define the Refrangibility of the several sorts of homogeneal Light +answering to the several Colours._ + +For determining this Problem I made the following Experiment.[J] + +_Exper._ 7. When I had caused the Rectilinear Sides AF, GM, [in _Fig._ +4.] of the Spectrum of Colours made by the Prism to be distinctly +defined, as in the fifth Experiment of the first Part of this Book is +described, there were found in it all the homogeneal Colours in the same +Order and Situation one among another as in the Spectrum of simple +Light, described in the fourth Proposition of that Part. For the Circles +of which the Spectrum of compound Light PT is composed, and which in +the middle Parts of the Spectrum interfere, and are intermix'd with one +another, are not intermix'd in their outmost Parts where they touch +those Rectilinear Sides AF and GM. And therefore, in those Rectilinear +Sides when distinctly defined, there is no new Colour generated by +Refraction. I observed also, that if any where between the two outmost +Circles TMF and PGA a Right Line, as [Greek: gd], was cross to the +Spectrum, so as both Ends to fall perpendicularly upon its Rectilinear +Sides, there appeared one and the same Colour, and degree of Colour from +one End of this Line to the other. I delineated therefore in a Paper the +Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of +the first Part of this Book, I held the Paper so that the Spectrum might +fall upon this delineated Figure, and agree with it exactly, whilst an +Assistant, whose Eyes for distinguishing Colours were more critical than +mine, did by Right Lines [Greek: ab, gd, ez,] &c. drawn cross the +Spectrum, note the Confines of the Colours, that is of the red M[Greek: +ab]F, of the orange [Greek: agdb], of the yellow [Greek: gezd], of the +green [Greek: eêthz], of the blue [Greek: êikth], of the indico [Greek: +ilmk], and of the violet [Greek: l]GA[Greek: m]. And this Operation +being divers times repeated both in the same, and in several Papers, I +found that the Observations agreed well enough with one another, and +that the Rectilinear Sides MG and FA were by the said cross Lines +divided after the manner of a Musical Chord. Let GM be produced to X, +that MX may be equal to GM, and conceive GX, [Greek: l]X, [Greek: i]X, +[Greek: ê]X, [Greek: e]X, [Greek: g]X, [Greek: a]X, MX, to be in +proportion 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, a +third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth +above that Key: And the Intervals M[Greek: a], [Greek: ag], [Greek: ge], +[Greek: eê], [Greek: êi], [Greek: il], and [Greek: l]G, will be the +Spaces which the several Colours (red, orange, yellow, green, blue, +indigo, violet) take up. + +[Illustration: FIG. 4.] + +[Illustration: FIG. 5.] + +Now these Intervals or Spaces subtending the Differences of the +Refractions of the Rays going to the Limits of those Colours, that is, +to the Points M, [Greek: a], [Greek: g], [Greek: e], [Greek: ê], [Greek: +i], [Greek: l], G, may without any sensible Error be accounted +proportional to the Differences of the Sines of Refraction of those Rays +having one common Sine of Incidence, and therefore since the common Sine +of Incidence of the most and least refrangible Rays out of Glass into +Air was (by a Method described above) found in proportion to their Sines +of Refraction, as 50 to 77 and 78, divide the Difference between the +Sines of Refraction 77 and 78, as the Line GM is divided by those +Intervals, 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 the +Incidences of all the red-making Rays out of Glass into Air, were to the +Sines of their Refractions, not greater than 50 to 77, nor less than 50 +to 77-1/8, but they varied from one another according to all +intermediate Proportions. And the Sines of the Incidences of the +green-making Rays were to the Sines of their Refractions in all +Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And +by the like Limits above-mentioned were the Refractions of the Rays +belonging to the rest of the Colours defined, the Sines of the +red-making Rays extending from 77 to 77-1/8, those of the orange-making +from 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 the +blue-making from 77-1/2 to 77-2/3, those of the indigo-making from +77-2/3 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, and +thence by the third Axiom of the first Part of this Book, the Laws of +the Refractions made out of Air into Glass are easily derived. + +_Exper._ 8. I found moreover, that when Light goes out of Air through +several contiguous refracting Mediums as through Water and Glass, and +thence goes out again into Air, whether the refracting Superficies be +parallel or inclin'd to one another, that Light as often as by contrary +Refractions 'tis so corrected, that it emergeth in Lines parallel to +those in which it was incident, continues ever after to be white. But if +the emergent Rays be inclined to the incident, the Whiteness of the +emerging Light will by degrees in passing on from the Place of +Emergence, become tinged in its Edges with Colours. This I try'd by +refracting Light with Prisms of Glass placed within a Prismatick Vessel +of Water. Now those Colours argue a diverging and separation of the +heterogeneous Rays from one another by means of their unequal +Refractions, as in what follows will more fully appear. And, on the +contrary, the permanent whiteness argues, that in like Incidences of the +Rays there is no such separation of the emerging Rays, and by +consequence no inequality of their whole Refractions. Whence I seem to +gather the two following Theorems. + +1. The Excesses of the Sines of Refraction of several sorts of Rays +above their common Sine of Incidence when the Refractions are made out +of 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 of +one and the same sort of Rays out of one Medium into another, is +composed of the Proportion of the Sine of Incidence to the Sine of +Refraction out of the first Medium into any third Medium, and of the +Proportion of the Sine of Incidence to the Sine of Refraction out of +that third Medium into the second Medium. + +By the first Theorem the Refractions of the Rays of every sort made out +of any Medium into Air are known by having the Refraction of the Rays of +any one sort. As for instance, if the Refractions of the Rays of every +sort out of Rain-water into Air be desired, let the common Sine of +Incidence out of Glass into Air be subducted from the Sines of +Refraction, 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 least +refrangible Rays be to their Sine of Refraction out of Rain-water into +Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the +Sine of Incidence, so is 27 the least of the Excesses above-mentioned to +a fourth Number 81; and 81 will be the common Sine of Incidence out of +Rain-water into Air, to which Sine if you add all the above-mentioned +Excesses, 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 is +gathered as often as you have the Refractions out of them both into any +third Medium. As if the Sine of Incidence of any Ray out of Glass into +Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence +of the same Ray out of Air into Water, be to its Sine of Refraction as 4 +to 3; the Sine of Incidence of that Ray out of Glass into Water will be +to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as +the 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 scope +enough of handling that Science voluminously after a new manner,[K] not +only by teaching those things which tend to the perfection of Vision, +but also by determining mathematically all kinds of Phænomena of Colours +which could be produced by Refractions. For to do this, there is nothing +else requisite than to find out the Separations of heterogeneous Rays, +and their various Mixtures and Proportions in every Mixture. By this +way of arguing I invented almost all the Phænomena described in these +Books, beside some others less necessary to the Argument; and by the +successes I met with in the Trials, I dare promise, that to him who +shall argue truly, and then try all things with good Glasses and +sufficient Circumspection, the expected Event will not be wanting. But +he is first to know what Colours will arise from any others mix'd in any +assigned Proportion. + + +_PROP._ IV. THEOR. III. + +_Colours may be produced by Composition which shall be like to the +Colours of homogeneal Light as to the Appearance of Colour, but not as +to the Immutability of Colour and Constitution of Light. And those +Colours by how much they are more compounded by so much are they less +full and intense, and by too much Composition they maybe diluted and +weaken'd till they cease, and the Mixture becomes white or grey. There +may be also Colours produced by Composition, which are not fully like +any of the Colours of homogeneal Light._ + +For a Mixture of homogeneal red and yellow compounds an Orange, like in +appearance of Colour to that orange which in the series of unmixed +prismatick Colours lies between them; but the Light of one orange is +homogeneal as to Refrangibility, 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 red +and yellow. And after the same manner other neighbouring homogeneal +Colours may compound new Colours, like the intermediate homogeneal ones, +as yellow and green, the Colour between them both, and afterwards, if +blue be added, there will be made a green the middle Colour of the three +which enter the Composition. For the yellow and blue on either hand, if +they are equal in quantity they draw the intermediate green equally +towards themselves in Composition, and so keep it as it were in +Æquilibrion, that it verge not more to the yellow on the one hand, and +to the blue on the other, but by their mix'd Actions remain still a +middle Colour. To this mix'd green there may be farther added some red +and violet, and yet the green will not presently cease, but only grow +less full and vivid, and by increasing the red and violet, it will grow +more and more dilute, until by the prevalence of the added Colours it be +overcome and turned into whiteness, or some other Colour. So if to the +Colour of any homogeneal Light, the Sun's white Light composed of all +sorts of Rays be added, that Colour will not vanish or change its +Species, but be diluted, and by adding more and more white it will be +diluted more and more perpetually. Lastly, If red and violet be mingled, +there will be generated according to their various Proportions various +Purples, such as are not like in appearance to the Colour of any +homogeneal Light, and of these Purples mix'd with yellow and blue may be +made other new Colours. + + +_PROP._ V. THEOR. IV. + +_Whiteness and all grey Colours between white and black, may be +compounded of Colours, and the whiteness of the Sun's Light is +compounded of all the primary Colours mix'd in a due Proportion._ + +The PROOF by Experiments. + +_Exper._ 9. The Sun shining into a dark Chamber through a little round +hole in the Window-shut, and his Light being there refracted by a Prism +to cast his coloured Image PT [in _Fig._ 5.] upon the opposite Wall: I +held a white Paper V to that image in such manner that it might be +illuminated by the colour'd Light reflected from thence, and yet not +intercept any part of that Light in its passage from the Prism to the +Spectrum. And I found that when the Paper was held nearer to any Colour +than to the rest, it appeared of that Colour to which it approached +nearest; but when it was equally or almost equally distant from all the +Colours, so that it might be equally illuminated by them all it appeared +white. And in this last situation of the Paper, if some Colours were +intercepted, the Paper lost its white Colour, and appeared of the Colour +of the rest of the Light which was not intercepted. So then the Paper +was illuminated with Lights of various Colours, namely, red, yellow, +green, blue and violet, and every part of the Light retained its proper +Colour, until it was incident on the Paper, and became reflected thence +to the Eye; so that if it had been either alone (the rest of the Light +being intercepted) or if it had abounded most, and been predominant in +the Light reflected from the Paper, it would have tinged the Paper with +its own Colour; and yet being mixed with the rest of the Colours in a +due proportion, it made the Paper look white, and therefore by a +Composition with the rest produced that Colour. The several parts of the +coloured Light reflected from the Spectrum, whilst they are propagated +from thence through the Air, do perpetually retain their proper Colours, +because wherever they fall upon the Eyes of any Spectator, they make the +several parts of the Spectrum to appear under their proper Colours. They +retain therefore their proper Colours when they fall upon the Paper V, +and so by the confusion and perfect mixture of those Colours compound +the whiteness of the Light reflected from thence. + +_Exper._ 10. Let that Spectrum or solar Image PT [in _Fig._ 6.] fall now +upon the Lens MN above four Inches broad, and about six Feet distant +from the Prism ABC and so figured that it may cause the coloured Light +which divergeth from the Prism to converge and meet again at its Focus +G, about six or eight Feet distant from the Lens, and there to fall +perpendicularly upon a white Paper DE. And if you move this Paper to and +fro, you will perceive that near the Lens, as at _de_, the whole solar +Image (suppose at _pt_) will appear upon it intensely coloured after the +manner above-explained, and that by receding from the Lens those Colours +will perpetually come towards one another, and by mixing more and more +dilute one another continually, until at length the Paper come to the +Focus G, where by a perfect mixture they will wholly vanish and be +converted into whiteness, the whole Light appearing now upon the Paper +like a little white Circle. And afterwards by receding farther from the +Lens, the Rays which before converged will now cross one another in the +Focus G, and diverge from thence, and thereby make the Colours to appear +again, but yet in a contrary order; suppose at [Greek: de], where the +red _t_ is now above which before was below, and the violet _p_ is below +which before was above. + +Let us now stop the Paper at the Focus G, where the Light appears +totally white and circular, and let us consider its whiteness. I say, +that this is composed of the converging Colours. For if any of those +Colours be intercepted at the Lens, the whiteness will cease and +degenerate into that Colour which ariseth from the composition of the +other Colours which are not intercepted. And then if the intercepted +Colours be let pass and fall upon that compound Colour, they mix with +it, and by their mixture restore the whiteness. So if the violet, blue +and green be intercepted, the remaining yellow, orange and red will +compound upon the Paper an orange, and then if the intercepted Colours +be let pass, they will fall upon this compounded orange, and together +with it decompound a white. So also if the red and violet be +intercepted, the remaining yellow, green and blue, will compound a green +upon the Paper, and then the red and violet being let pass will fall +upon this green, and together with it decompound a white. And that in +this Composition of white the several Rays do not suffer any Change in +their colorific Qualities by acting upon one another, but are only +mixed, and by a mixture of their Colours produce white, may farther +appear by these Arguments. + +[Illustration: FIG. 6.] + +If the Paper be placed beyond the Focus G, suppose at [Greek: de], and +then the red Colour at the Lens be alternately intercepted, and let pass +again, the violet Colour on the Paper will not suffer any Change +thereby, as it ought to do if the several sorts of Rays acted upon one +another in the Focus G, where they cross. Neither will the red upon the +Paper be changed by any alternate stopping, and letting pass the violet +which crosseth it. + +And if the Paper be placed at the Focus G, and the white round Image at +G be viewed through the Prism HIK, and by the Refraction of that Prism +be translated to the place _rv_, and there appear tinged with various +Colours, namely, the violet at _v_ and red at _r_, and others between, +and then the red Colours at the Lens be often stopp'd and let pass by +turns, the red at _r_ will accordingly disappear, and return as often, +but the violet at _v_ will not thereby suffer any Change. And so by +stopping and letting pass alternately the blue at the Lens, the blue at +_v_ will accordingly disappear and return, without any Change made in +the red at _r_. The red therefore depends on one sort of Rays, and the +blue on another sort, which in the Focus G where they are commix'd, do +not act on one another. And there is the same Reason of the other +Colours. + +I considered farther, that when the most refrangible Rays P_p_, and the +least refrangible ones T_t_, are by converging inclined to one another, +the Paper, if held very oblique to those Rays in the Focus G, might +reflect one sort of them more copiously than the other sort, and by that +Means the reflected Light would be tinged in that Focus with the Colour +of the predominant Rays, provided those Rays severally retained their +Colours, or colorific Qualities in the Composition of White made by them +in that Focus. But if they did not retain them in that White, but became +all of them severally endued there with a Disposition to strike the +Sense with the Perception of White, then they could never lose their +Whiteness by such Reflexions. I inclined therefore the Paper to the Rays +very obliquely, as in the second Experiment of this second Part of the +first Book, that the most refrangible Rays, might be more copiously +reflected than the rest, and the Whiteness at Length changed +successively into blue, indigo, and violet. Then I inclined it the +contrary Way, that the least refrangible Rays might be more copious in +the reflected Light than the rest, and the Whiteness turned successively +to yellow, orange, and red. + +Lastly, I made an Instrument XY in fashion of a Comb, whose Teeth being +in number sixteen, were about an Inch and a half broad, and the +Intervals of the Teeth about two Inches wide. Then by interposing +successively the Teeth of this Instrument near the Lens, I intercepted +Part of the Colours by the interposed Tooth, whilst the rest of them +went on through the Interval of the Teeth to the Paper DE, and there +painted a round Solar Image. But the Paper I had first placed so, that +the Image might appear white as often as the Comb was taken away; and +then the Comb being as was said interposed, that Whiteness by reason of +the intercepted Part of the Colours at the Lens did always change into +the Colour compounded of those Colours which were not intercepted, and +that Colour was by the Motion of the Comb perpetually varied so, that in +the passing of every Tooth over the Lens all these Colours, red, yellow, +green, blue, and purple, did always succeed one another. I caused +therefore all the Teeth to pass successively over the Lens, and when the +Motion was slow, there appeared a perpetual Succession of the Colours +upon the Paper: But if I so much accelerated the Motion, that the +Colours by reason of their quick Succession could not be distinguished +from one another, the Appearance of the single Colours ceased. There was +no 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 +third green, a fourth blue, a fifth purple, and every Part retains its +proper Colour till it strike the Sensorium. If the Impressions follow +one another slowly, so that they may be severally perceived, there is +made a distinct Sensation of all the Colours one after another in a +continual Succession. But if the Impressions follow one another so +quickly, that they cannot be severally perceived, there ariseth out of +them all one common Sensation, which is neither of this Colour alone nor +of that alone, but hath it self indifferently to 'em all, and this is a +Sensation of Whiteness. By the Quickness of the Successions, the +Impressions of the several Colours are confounded in the Sensorium, and +out of that Confusion ariseth a mix'd Sensation. If a burning Coal be +nimbly moved round in a Circle with Gyrations continually repeated, the +whole Circle will appear like Fire; the reason of which is, that the +Sensation of the Coal in the several Places of that Circle remains +impress'd on the Sensorium, until the Coal return again to the same +Place. And so in a quick Consecution of the Colours the Impression of +every Colour remains in the Sensorium, until a Revolution of all the +Colours be compleated, and that first Colour return again. The +Impressions therefore of all the successive Colours are at once in the +Sensorium, and jointly stir up a Sensation of them all; and so it is +manifest by this Experiment, that the commix'd Impressions of all the +Colours do stir up and beget a Sensation of white, that is, that +Whiteness is compounded of all the Colours. + +And if the Comb be now taken away, that all the Colours may at once pass +from the Lens to the Paper, and be there intermixed, and together +reflected thence to the Spectator's Eyes; their Impressions on the +Sensorium being now more subtilly and perfectly commixed there, ought +much more to stir up a Sensation of Whiteness. + +You may instead of the Lens use two Prisms HIK and LMN, which by +refracting the coloured Light the contrary Way to that of the first +Refraction, may make the diverging Rays converge and meet again in G, as +you 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 [in _Fig._ 8.] fall upon +the Wall of a dark Chamber, as in the third Experiment of the first +Book, and let the same be viewed through a Prism _abc_, held parallel to +the Prism ABC, by whose Refraction that Image was made, and let it now +appear lower than before, suppose in the Place S over-against the red +Colour T. And if you go near to the Image PT, the Spectrum S will appear +oblong and coloured like the Image PT; but if you recede from it, the +Colours of the spectrum S will be contracted more and more, and at +length vanish, that Spectrum S becoming perfectly round and white; and +if you recede yet farther, the Colours will emerge again, but in a +contrary Order. Now that Spectrum S appears white in that Case, when the +Rays of several sorts which converge from the several Parts of the Image +PT, to the Prism _abc_, are so refracted unequally by it, that in their +Passage from the Prism to the Eye they may diverge from one and the same +Point of the Spectrum S, and so fall afterwards upon one and the same +Point in the bottom of the Eye, and there be mingled. + +[Illustration: FIG. 7.] + +[Illustration: FIG. 8.] + +And farther, if the Comb be here made use of, by whose Teeth the Colours +at the Image PT may be successively intercepted; the Spectrum S, when +the Comb is moved slowly, will be perpetually tinged with successive +Colours: But when by accelerating the Motion of the Comb, the Succession +of the Colours is so quick that they cannot be severally seen, that +Spectrum S, by a confused and mix'd Sensation of them all, will appear +white. + +_Exper._ 12. The Sun shining through a large Prism ABC [in _Fig._ 9.] +upon a Comb XY, placed immediately behind the Prism, his Light which +passed through the Interstices of the Teeth fell upon a white Paper DE. +The Breadths of the Teeth were equal to their Interstices, and seven +Teeth together with their Interstices took up an Inch in Breadth. Now, +when the Paper was about two or three Inches distant from the Comb, the +Light which passed through its several Interstices painted so many +Ranges of Colours, _kl_, _mn_, _op_, _qr_, &c. which were parallel to +one another, and contiguous, and without any Mixture of white. And these +Ranges of Colours, if the Comb was moved continually up and down with a +reciprocal Motion, ascended and descended in the Paper, and when the +Motion of the Comb was so quick, that the Colours could not be +distinguished from one another, the whole Paper by their Confusion and +Mixture in the Sensorium appeared white. + +[Illustration: FIG. 9.] + +Let the Comb now rest, and let the Paper be removed farther from the +Prism, and the several Ranges of Colours will be dilated and expanded +into one another more and more, and by mixing their Colours will dilute +one another, and at length, when the distance of the Paper from the Comb +is about a Foot, or a little more (suppose in the Place 2D 2E) they will +so far dilute one another, as to become white. + +With any Obstacle, let all the Light be now stopp'd which passes through +any one Interval of the Teeth, so that the Range of Colours which comes +from thence may be taken away, and you will see the Light of the rest of +the Ranges to be expanded into the Place of the Range taken away, and +there to be coloured. Let the intercepted Range pass on as before, and +its Colours falling upon the Colours of the other Ranges, and mixing +with them, will restore the Whiteness. + +Let the Paper 2D 2E be now very much inclined to the Rays, so that the +most refrangible Rays may be more copiously reflected than the rest, and +the white Colour of the Paper through the Excess of those Rays will be +changed into blue and violet. Let the Paper be as much inclined the +contrary way, that the least refrangible Rays may be now more copiously +reflected than the rest, and by their Excess the Whiteness will be +changed into yellow and red. The several Rays therefore in that white +Light do retain their colorific Qualities, by which those of any sort, +whenever they become more copious than the rest, do by their Excess and +Predominance cause their proper Colour to appear. + +And by the same way of arguing, applied to the third Experiment of this +second Part of the first Book, it may be concluded, that the white +Colour of all refracted Light at its very first Emergence, where it +appears as white as before its Incidence, is compounded of various +Colours. + +[Illustration: FIG. 10.] + +_Exper._ 13. In the foregoing Experiment the several Intervals of the +Teeth of the Comb do the Office of so many Prisms, every Interval +producing the Phænomenon of one Prism. Whence instead of those Intervals +using several Prisms, I try'd to compound Whiteness by mixing their +Colours, and did it by using only three Prisms, as also by using only +two as follows. Let two Prisms ABC and _abc_, [in _Fig._ 10.] whose +refracting Angles B and _b_ are equal, be so placed parallel to one +another, that the refracting Angle B of the one may touch the Angle _c_ +at the Base of the other, and their Planes CB and _cb_, at which the +Rays emerge, may lie in Directum. Then let the Light trajected through +them fall upon the Paper MN, distant about 8 or 12 Inches from the +Prisms. And the Colours generated by the interior Limits B and _c_ of +the two Prisms, will be mingled at PT, and there compound white. For if +either Prism be taken away, the Colours made by the other will appear in +that Place PT, and when the Prism is restored to its Place again, so +that its Colours may there fall upon the Colours of the other, the +Mixture of them both will restore the Whiteness. + +This Experiment succeeds also, as I have tried, when the Angle _b_ of +the lower Prism, is a little greater than the Angle B of the upper, and +between the interior Angles B and _c_, there intercedes some Space B_c_, +as is represented in the Figure, and the refracting Planes BC and _bc_, +are neither in Directum, nor parallel to one another. For there is +nothing more requisite to the Success of this Experiment, than that the +Rays 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 all +the Space from M to P, the Rays of the same sort which come from the +inferior Prism ought to begin at P, and take up all the rest of the +Space from thence towards N. If the least refrangible Rays coming from +the superior Prism take up the Space MT, the Rays of the same kind which +come from the other Prism ought to begin at T, and take up the +remaining Space TN. If one sort of the Rays which have intermediate +Degrees of Refrangibility, and come from the superior Prism be extended +through the Space MQ, and another sort of those Rays through the Space +MR, and a third sort of them through the Space MS, the same sorts of +Rays coming from the lower Prism, ought to illuminate the remaining +Spaces QN, RN, SN, respectively. And the same is to be understood of all +the other sorts of Rays. For thus the Rays of every sort will be +scattered uniformly and evenly through the whole Space MN, and so being +every where mix'd in the same Proportion, they must every where produce +the same Colour. And therefore, since by this Mixture they produce white +in the Exterior Spaces MP and TN, they must also produce white in the +Interior Space PT. This is the reason of the Composition by which +Whiteness was produced in this Experiment, and by what other way soever +I made the like Composition, the Result was Whiteness. + +Lastly, If with the Teeth of a Comb of a due Size, the coloured Lights +of the two Prisms which fall upon the Space PT be alternately +intercepted, that Space PT, when the Motion of the Comb is slow, will +always appear coloured, but by accelerating the Motion of the Comb so +much that the successive Colours cannot be distinguished from one +another, it will appear white. + +_Exper._ 14. Hitherto I have produced Whiteness by mixing the Colours of +Prisms. If now the Colours of natural Bodies are to be mingled, let +Water a little thicken'd with Soap be agitated to raise a Froth, and +after that Froth has stood a little, there will appear to one that shall +view it intently various Colours every where in the Surfaces of the +several Bubbles; but to one that shall go so far off, that he cannot +distinguish the Colours from one another, the whole Froth will grow +white with a perfect Whiteness. + +_Exper._ 15. Lastly, In attempting to compound a white, by mixing the +coloured Powders which Painters use, I consider'd that all colour'd +Powders do suppress and stop in them a very considerable Part of the +Light by which they are illuminated. For they become colour'd by +reflecting the Light of their own Colours more copiously, and that of +all other Colours more sparingly, and yet they do not reflect the Light +of their own Colours so copiously as white Bodies do. If red Lead, for +instance, and a white Paper, be placed in the red Light of the colour'd +Spectrum made in a dark Chamber by the Refraction of a Prism, as is +described in the third Experiment of the first Part of this Book; the +Paper will appear more lucid than the red Lead, and therefore reflects +the red-making Rays more copiously than red Lead doth. And if they be +held in the Light of any other Colour, the Light reflected by the Paper +will exceed the Light reflected by the red Lead in a much greater +Proportion. And the like happens in Powders of other Colours. And +therefore by mixing such Powders, we are not to expect a strong and +full White, such as is that of Paper, but some dusky obscure one, such +as might arise from a Mixture of Light and Darkness, or from white and +black, that is, a grey, or dun, or russet brown, such as are the Colours +of a Man's Nail, of a Mouse, of Ashes, of ordinary Stones, of Mortar, of +Dust and Dirt in High-ways, and the like. And such a dark white I have +often produced by mixing colour'd Powders. For thus one Part of red +Lead, and five Parts of _Viride Æris_, composed a dun Colour like that +of a Mouse. For these two Colours were severally so compounded of +others, that in both together were a Mixture of all Colours; and there +was less red Lead used than _Viride Æris_, because of the Fulness of its +Colour. 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 this +a certain Mixture of Orpiment and _Viride Æris_ in a due Proportion, the +Mixture lost its purple Tincture, and became perfectly dun. But the +Experiment succeeded best without Minium thus. To Orpiment I added by +little and little a certain full bright purple, which Painters use, +until the Orpiment ceased to be yellow, and became of a pale red. Then I +diluted that red by adding a little _Viride Æris_, and a little more +blue Bise than _Viride Æris_, until it became of such a grey or pale +white, as verged to no one of the Colours more than to another. For thus +it became of a Colour equal in Whiteness to that of Ashes, or of Wood +newly cut, or of a Man's Skin. The Orpiment reflected more Light than +did any other of the Powders, and therefore conduced more to the +Whiteness of the compounded Colour than they. To assign the Proportions +accurately may be difficult, by reason of the different Goodness of +Powders of the same kind. Accordingly, as the Colour of any Powder is +more or less full and luminous, it ought to be used in a less or greater +Proportion. + +Now, considering that these grey and dun Colours may be also produced by +mixing Whites and Blacks, and by consequence differ from perfect Whites, +not in Species of Colours, but only in degree of Luminousness, it is +manifest that there is nothing more requisite to make them perfectly +white 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 Colour +with the best Whites, and differ from them only in the Quantity of +Light. And this I tried as follows. I took the third of the +above-mention'd grey Mixtures, (that which was compounded of Orpiment, +Purple, Bise, and _Viride Æris_) and rubbed it thickly upon the Floor of +my Chamber, where the Sun shone upon it through the opened Casement; and +by 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 could +not discern the Unevenness of the Surface of the Powder, nor the little +Shadows let fall from the gritty Particles thereof; the Powder appeared +intensely white, so as to transcend even the Paper it self in Whiteness, +especially if the Paper were a little shaded from the Light of the +Clouds, and then the Paper compared with the Powder appeared of such a +grey Colour as the Powder had done before. But by laying the Paper where +the Sun shines through the Glass of the Window, or by shutting the +Window that the Sun might shine through the Glass upon the Powder, and +by such other fit Means of increasing or decreasing the Lights wherewith +the Powder and Paper were illuminated, the Light wherewith the Powder is +illuminated may be made stronger in such a due Proportion than the Light +wherewith the Paper is illuminated, that they shall both appear exactly +alike in Whiteness. For when I was trying this, a Friend coming to visit +me, I stopp'd him at the Door, and before I told him what the Colours +were, or what I was doing; I asked him, Which of the two Whites were the +best, and wherein they differed? And after he had at that distance +viewed them well, he answer'd, that they were both good Whites, and that +he 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 was +compounded of the Colours which the component Powders (Orpiment, Purple, +Bise, and _Viride Æris_) have in the same Sun-shine, you must +acknowledge by this Experiment, as well as by the former, that perfect +Whiteness may be compounded of Colours. + +From what has been said it is also evident, that the Whiteness of the +Sun's Light is compounded of all the Colours wherewith the several sorts +of Rays whereof that Light consists, when by their several +Refrangibilities they are separated from one another, do tinge Paper or +any other white Body whereon they fall. For those Colours (by _Prop._ +II. _Part_ 2.) are unchangeable, and whenever all those Rays with those +their Colours are mix'd again, they reproduce the same white Light as +before. + + +_PROP._ VI. PROB. II. + +_In a mixture of Primary Colours, the Quantity and Quality of each being +given, to know the Colour of the Compound._ + +[Illustration: FIG. 11.] + +With the Center O [in _Fig._ 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 the +eight 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 red +Colour, 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. And +conceive that these are all the Colours of uncompounded Light gradually +passing into one another, as they do when made by Prisms; the +Circumference DEFGABCD, representing the whole Series of Colours from +one end of the Sun's colour'd Image to the other, so that from D to E be +all degrees of red, at E the mean Colour between red and orange, from E +to F all degrees of orange, at F the mean between orange and yellow, +from F to G all degrees of yellow, and so on. Let _p_ be the Center of +Gravity of the Arch DE, and _q_, _r_, _s_, _t_, _u_, _x_, the Centers of +Gravity of the Arches EF, FG, GA, AB, BC, and CD respectively, and about +those Centers of Gravity let Circles proportional to the Number of Rays +of each Colour in the given Mixture be describ'd: that is, the Circle +_p_ proportional to the Number of the red-making Rays in the Mixture, +the Circle _q_ proportional to the Number of the orange-making Rays in +the Mixture, and so of the rest. Find the common Center of Gravity of +all those Circles, _p_, _q_, _r_, _s_, _t_, _u_, _x_. Let that Center be +Z; and from the Center of the Circle ADF, through Z to the +Circumference, drawing the Right Line OY, the Place of the Point Y in +the Circumference shall shew the Colour arising from the Composition of +all the Colours in the given Mixture, and the Line OZ shall be +proportional to the Fulness or Intenseness of the Colour, that is, to +its 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 the +middle towards F or G, the compound Colour shall accordingly be a +yellow, verging towards orange or green. If Z fall upon the +Circumference, the Colour shall be intense and florid in the highest +Degree; 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 as +would be made by diluting the intensest yellow with an equal quantity of +whiteness; and if it fall upon the center O, the Colour shall have lost +all its intenseness, and become a white. But it is to be noted, That if +the point Z fall in or near the line OD, the main ingredients being the +red and violet, the Colour compounded shall not be any of the prismatick +Colours, but a purple, inclining to red or violet, accordingly as the +point Z lieth on the side of the line DO towards E or towards C, and in +general the compounded violet is more bright and more fiery than the +uncompounded. Also if only two of the primary Colours which in the +circle are opposite to one another be mixed in an equal proportion, the +point Z shall fall upon the center O, and yet the Colour compounded of +those two shall not be perfectly white, but some faint anonymous Colour. +For I could never yet by mixing only two primary Colours produce a +perfect white. Whether it may be compounded of a mixture of three taken +at equal distances in the circumference I do not know, but of four or +five I do not much question but it may. But these are Curiosities of +little or no moment to the understanding the Phænomena of Nature. For in +all whites produced by Nature, there uses to be a mixture of all sorts +of Rays, and by consequence a composition of all Colours. + +To give an instance of this Rule; suppose a Colour is compounded of +these homogeneal Colours, of violet one part, of indigo one part, of +blue two parts, of green three parts, of yellow five parts, of orange +six parts, and of red ten parts. Proportional to these parts describe +the Circles _x_, _v_, _t_, _s_, _r_, _q_, _p_, respectively, that is, so +that if the Circle _x_ be one, the Circle _v_ may be one, the Circle _t_ +two, the Circle _s_ three, and the Circles _r_, _q_ and _p_, five, six +and 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 the +circumference between E and F, something nearer to E than to F, and +thence I conclude, that the Colour compounded of these Ingredients will +be an orange, verging a little more to red than to yellow. Also I find +that 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 intenseness +of an uncompounded orange; that is to say, that it is such an orange as +may be made by mixing an homogeneal orange with a good white in the +proportion of the Line OZ to the Line ZY, this Proportion being not of +the quantities of mixed orange and white Powders, but of the quantities +of the Lights reflected from them. + +This Rule I conceive accurate enough for practice, though not +mathematically accurate; and the truth of it may be sufficiently proved +to Sense, by stopping any of the Colours at the Lens in the tenth +Experiment of this Book. For the rest of the Colours which are not +stopp'd, but pass on to the Focus of the Lens, will there compound +either accurately or very nearly such a Colour, as by this Rule ought to +result from their Mixture. + + +_PROP._ VII. THEOR. V. + +_All the Colours in the Universe which are made by Light, and depend not +on the Power of Imagination, are either the Colours of homogeneal +Lights, or compounded of these, and that either accurately or very +nearly, according to the Rule of the foregoing Problem._ + +For it has been proved (in _Prop. 1. Part 2._) that the changes of +Colours made by Refractions do not arise from any new Modifications of +the Rays impress'd by those Refractions, and by the various Terminations +of Light and Shadow, as has been the constant and general Opinion of +Philosophers. It has also been proved that the several Colours of the +homogeneal Rays do constantly answer to their degrees of Refrangibility, +(_Prop._ 1. _Part_ 1. and _Prop._ 2. _Part_ 2.) and that their degrees +of Refrangibility cannot be changed by Refractions and Reflexions +(_Prop._ 2. _Part_ 1.) and by consequence that those their Colours are +likewise immutable. It has also been proved directly by refracting and +reflecting homogeneal Lights apart, that their Colours cannot be +changed, (_Prop._ 2. _Part_ 2.) It has been proved also, that when the +several sorts of Rays are mixed, and in crossing pass through the same +space, they do not act on one another so as to change each others +colorific qualities. (_Exper._ 10. _Part_ 2.) but by mixing their +Actions in the Sensorium beget a Sensation differing from what either +would do apart, that is a Sensation of a mean Colour between their +proper Colours; and particularly when by the concourse and mixtures of +all sorts of Rays, a white Colour is produced, the white is a mixture of +all the Colours which the Rays would have apart, (_Prop._ 5. _Part_ 2.) +The Rays in that mixture do not lose or alter their several colorific +qualities, but by all their various kinds of Actions mix'd in the +Sensorium, beget a Sensation of a middling Colour between all their +Colours, which is whiteness. For whiteness is a mean between all +Colours, having it self indifferently to them all, so as with equal +facility to be tinged with any of them. A red Powder mixed with a little +blue, 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 that +Colour, 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 sorts +of Rays, so its whiteness is a mixture of the Colours of all sorts of +Rays; those Rays having from the beginning their several colorific +qualities as well as their several Refrangibilities, and retaining them +perpetually unchanged notwithstanding any Refractions or Reflexions they +may at any time suffer, and that whenever any sort of the Sun's Rays is +by any means (as by Reflexion in _Exper._ 9, and 10. _Part_ 1. or by +Refraction as happens in all Refractions) separated from the rest, they +then manifest their proper Colours. These things have been prov'd, and +the sum of all this amounts to the Proposition here to be proved. For if +the Sun's Light is mix'd of several sorts of Rays, each of which have +originally their several Refrangibilities and colorific Qualities, and +notwithstanding their Refractions and Reflexions, and their various +Separations or Mixtures, keep those their original Properties +perpetually the same without alteration; then all the Colours in the +World must be such as constantly ought to arise from the original +colorific qualities of the Rays whereof the Lights consist by which +those Colours are seen. And therefore if the reason of any Colour +whatever be required, we have nothing else to do than to consider how +the Rays in the Sun's Light have by Reflexions or Refractions, or other +causes, been parted from one another, or mixed together; or otherwise to +find out what sorts of Rays are in the Light by which that Colour is +made, and in what Proportion; and then by the last Problem to learn the +Colour which ought to arise by mixing those Rays (or their Colours) in +that proportion. I speak here of Colours so far as they arise from +Light. For they appear sometimes by other Causes, as when by the power +of Phantasy we see Colours in a Dream, or a Mad-man sees things before +him which are not there; or when we see Fire by striking the Eye, or see +Colours like the Eye of a Peacock's Feather, by pressing our Eyes in +either corner whilst we look the other way. Where these and such like +Causes interpose not, the Colour always answers to the sort or sorts of +the Rays whereof the Light consists, as I have constantly found in +whatever Phænomena of Colours I have hitherto been able to examine. I +shall in the following Propositions give instances of this in the +Phænomena of chiefest note. + + +_PROP._ VIII. PROB. III. + +_By the discovered Properties of Light to explain the Colours made by +Prisms._ + +Let ABC [in _Fig._ 12.] represent a Prism refracting the Light of the +Sun, which comes into a dark Chamber through a hole F[Greek: ph] almost +as broad as the Prism, and let MN represent a white Paper on which the +refracted Light is cast, and suppose the most refrangible or deepest +violet-making Rays fall upon the Space P[Greek: p], the least +refrangible or deepest red-making Rays upon the Space T[Greek: t], the +middle sort between the indigo-making and blue-making Rays upon the +Space Q[Greek: ch], the middle sort of the green-making Rays upon the +Space R, the middle sort between the yellow-making and orange-making +Rays upon the Space S[Greek: s], and other intermediate sorts upon +intermediate Spaces. For so the Spaces upon which the several sorts +adequately fall will by reason of the different Refrangibility of those +sorts be one lower than another. Now if the Paper MN be so near the +Prism that the Spaces PT and [Greek: pt] do not interfere with one +another, the distance between them T[Greek: p] will be illuminated by +all the sorts of Rays in that proportion to one another which they have +at their very first coming out of the Prism, and consequently be white. +But the Spaces PT and [Greek: pt] on either hand, will not be +illuminated by them all, and therefore will appear coloured. And +particularly at P, where the outmost violet-making Rays fall alone, the +Colour must be the deepest violet. At Q where the violet-making and +indigo-making Rays are mixed, it must be a violet inclining much to +indigo. At R where the violet-making, indigo-making, blue-making, and +one half of the green-making Rays are mixed, their Colours must (by the +construction of the second Problem) compound a middle Colour between +indigo and blue. At S where all the Rays are mixed, except the +red-making and orange-making, their Colours ought by the same Rule to +compound a faint blue, verging more to green than indigo. And in the +progress from S to T, this blue will grow more and more faint and +dilute, till at T, where all the Colours begin to be mixed, it ends in +whiteness. + +[Illustration: FIG. 12.] + +So again, on the other side of the white at [Greek: t], where the least +refrangible or utmost red-making Rays are alone, the Colour must be the +deepest red. At [Greek: s] the mixture of red and orange will compound a +red inclining to orange. At [Greek: r] the mixture of red, orange, +yellow, and one half of the green must compound a middle Colour between +orange and yellow. At [Greek: ch] the mixture of all Colours but violet +and indigo will compound a faint yellow, verging more to green than to +orange. And this yellow will grow more faint and dilute continually in +its progress from [Greek: ch] to [Greek: p], where by a mixture of all +sorts of Rays it will become white. + +These Colours ought to appear were the Sun's Light perfectly white: But +because it inclines to yellow, the Excess of the yellow-making Rays +whereby 'tis tinged with that Colour, being mixed with the faint blue +between S and T, will draw it to a faint green. And so the Colours in +order from P to [Greek: t] ought to be violet, indigo, blue, very faint +green, 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 so +in Nature. + +These are the Colours on both sides the white when the Paper is held +between the Prism and the Point X where the Colours meet, and the +interjacent white vanishes. For if the Paper be held still farther off +from the Prism, the most refrangible and least refrangible Rays will be +wanting in the middle of the Light, and the rest of the Rays which are +found there, will by mixture produce a fuller green than before. Also +the yellow and blue will now become less compounded, and by consequence +more intense than before. And this also agrees with experience. + +And if one look through a Prism upon a white Object encompassed with +blackness or darkness, the reason of the Colours arising on the edges is +much the same, as will appear to one that shall a little consider it. If +a black Object be encompassed with a white one, the Colours which appear +through 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 a +contrary order to that, when a white Object is surrounded with black. +And the same is to be understood when an Object is viewed, whose parts +are some of them less luminous than others. For in the borders of the +more and less luminous Parts, Colours ought always by the same +Principles 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 to +be more faint and dilute. + +What is said of Colours made by Prisms may be easily applied to Colours +made by the Glasses of Telescopes or Microscopes, or by the Humours of +the Eye. For if the Object-glass of a Telescope be thicker on one side +than on the other, or if one half of the Glass, or one half of the Pupil +of the Eye be cover'd with any opake substance; the Object-glass, or +that part of it or of the Eye which is not cover'd, may be consider'd as +a Wedge with crooked Sides, and every Wedge of Glass or other pellucid +Substance has the effect of a Prism in refracting the Light which passes +through it.[L] + +How the Colours in the ninth and tenth Experiments of the first Part +arise from the different Reflexibility of Light, is evident by what was +there said. But it is observable in the ninth Experiment, that whilst +the Sun's direct Light is yellow, the Excess of the blue-making Rays in +the reflected beam of Light MN, suffices only to bring that yellow to a +pale white inclining to blue, and not to tinge it with a manifestly blue +Colour. To obtain therefore a better blue, I used instead of the yellow +Light of the Sun the white Light of the Clouds, by varying a little the +Experiment, as follows. + +[Illustration: FIG. 13.] + +_Exper._ 16 Let HFG [in _Fig._ 13.] represent a Prism in the open Air, +and S the Eye of the Spectator, viewing the Clouds by their Light coming +into the Prism at the Plane Side FIGK, and reflected in it by its Base +HEIG, and thence going out through its Plane Side HEFK to the Eye. And +when the Prism and Eye are conveniently placed, so that the Angles of +Incidence and Reflexion at the Base may be about 40 Degrees, the +Spectator will see a Bow MN of a blue Colour, running from one End of +the Base to the other, with the Concave Side towards him, and the Part +of the Base IMNG beyond this Bow will be brighter than the other Part +EMNH on the other Side of it. This blue Colour MN being made by nothing +else than by Reflexion of a specular Superficies, seems so odd a +Phænomenon, and so difficult to be explained by the vulgar Hypothesis of +Philosophers, that I could not but think it deserved to be taken Notice +of. Now for understanding the Reason of it, suppose the Plane ABC to cut +the Plane Sides and Base of the Prism perpendicularly. From the Eye to +the Line BC, wherein that Plane cuts the Base, draw the Lines S_p_ and +S_t_, in the Angles S_pc_ 50 degr. 1/9, and S_tc_ 49 degr. 1/28, and the +Point _p_ will be the Limit beyond which none of the most refrangible +Rays can pass through the Base of the Prism, and be refracted, whose +Incidence is such that they may be reflected to the Eye; and the Point +_t_ will be the like Limit for the least refrangible Rays, that is, +beyond which none of them can pass through the Base, whose Incidence is +such that by Reflexion they may come to the Eye. And the Point _r_ taken +in the middle Way between _p_ and _t_, will be the like Limit for the +meanly refrangible Rays. And therefore all the least refrangible Rays +which fall upon the Base beyond _t_, that is, between _t_ and B, and can +come from thence to the Eye, will be reflected thither: But on this side +_t_, that is, between _t_ and _c_, many of these Rays will be +transmitted through the Base. And all the most refrangible Rays which +fall upon the Base beyond _p_, that is, between, _p_ and B, and can by +Reflexion come from thence to the Eye, will be reflected thither, but +every where between _p_ and _c_, many of these Rays will get through the +Base, and be refracted; and the same is to be understood of the meanly +refrangible Rays on either side of the Point _r_. Whence it follows, +that the Base of the Prism must every where between _t_ and B, by a +total Reflexion of all sorts of Rays to the Eye, look white and bright. +And every where between _p_ and C, by reason of the Transmission of many +Rays of every sort, look more pale, obscure, and dark. But at _r_, and +in other Places between _p_ and _t_, where all the more refrangible Rays +are reflected to the Eye, and many of the less refrangible are +transmitted, the Excess of the most refrangible in the reflected Light +will tinge that Light with their Colour, which is violet and blue. And +this happens by taking the Line C _prt_ B any where between the Ends of +the Prism HG and EI. + + +_PROP._ IX. PROB. IV. + +_By the discovered Properties of Light to explain the Colours of the +Rain-bow._ + +[Illustration: FIG. 14.] + +This Bow never appears, but where it rains in the Sun-shine, and may be +made artificially by spouting up Water which may break aloft, and +scatter into Drops, and fall down like Rain. For the Sun shining upon +these Drops certainly causes the Bow to appear to a Spectator standing +in 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 of +falling Rain. This was understood by some of the Antients, and of late +more fully discover'd and explain'd by the famous _Antonius de Dominis_ +Archbishop of _Spalato_, in his book _De Radiis Visûs & Lucis_, +published by his Friend _Bartolus_ at _Venice_, in the Year 1611, and +written above 20 Years before. For he teaches there how the interior Bow +is 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, and +two sorts of Reflexions between them in each Drop of Water, and proves +his Explications by Experiments made with a Phial full of Water, and +with Globes of Glass filled with Water, and placed in the Sun to make +the Colours of the two Bows appear in them. The same Explication +_Des-Cartes_ hath pursued in his Meteors, and mended that of the +exterior Bow. But whilst they understood not the true Origin of Colours, +it's necessary to pursue it here a little farther. For understanding +therefore how the Bow is made, let a Drop of Rain, or any other +spherical transparent Body be represented by the Sphere BNFG, [in _Fig._ +14.] described with the Center C, and Semi-diameter CN. And let AN be +one 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 be +reflected to G; and at G let it either go out by Refraction to R, or be +reflected to H; and at H let it go out by Refraction towards S, cutting +the incident Ray in Y. Produce AN and RG, till they meet in X, and upon +AX and NF, let fall the Perpendiculars CD and CE, and produce CD till it +fall upon the Circumference at L. Parallel to the incident Ray AN draw +the Diameter BQ, and let the Sine of Incidence out of Air into Water be +to the Sine of Refraction as I to R. Now, if you suppose the Point of +Incidence N to move from the Point B, continually till it come to L, the +Arch QF will first increase and then decrease, and so will the Angle AXR +which the Rays AN and GR contain; and the Arch QF and Angle AXR will be +biggest when ND is to CN as sqrt(II - RR) to sqrt(3)RR, in which +case NE will be to ND as 2R to I. Also the Angle AYS, which the Rays AN +and HS contain will first decrease, and then increase and grow least +when ND is to CN as sqrt(II - RR) to sqrt(8)RR, in which case NE +will 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 the +incident Ray AN will come to its Limit when ND is to CN as sqrt(II - +RR) to sqrt(15)RR, in which case NE will be to ND as 4R to I. And the +Angle which the Ray next after that Emergent, that is, the Ray emergent +after four Reflexions, contains with the Incident, will come to its +Limit, when ND is to CN as sqrt(II - RR) to sqrt(24)RR, in which +case 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 the +arithmetical Progression 3, 5, 7, 9, &c. The Truth of all this +Mathematicians 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 their +Limits, they vary their quantity but very little for some time together, +and therefore a far greater number of the Rays which fall upon all the +Points 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, that +the Rays which differ in Refrangibility will have different Limits of +their Angles of Emergence, and by consequence according to their +different Degrees of Refrangibility emerge most copiously in different +Angles, and being separated from one another appear each in their proper +Colours. And what those Angles are may be easily gather'd from the +foregoing 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 be +found 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and +57 Minutes. And in the most refrangible Rays the Sines I and R are 109 +and 81, and thence by Computation the greatest Angle AXR will be found +40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7 +Minutes. + +Suppose now that O [in _Fig._ 15.] is the Spectator's Eye, and OP a Line +drawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Angles +of 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, shall +with their other Sides OE, OF; OG, OH, describe the Verges of two +Rain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any where +in the conical Superficies described by OE, OF, OG, OH, and be +illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being equal +to the Angle POE, or 40 Degr. 17 Min. shall be the greatest Angle in +which the most refrangible Rays can after one Reflexion be refracted to +the Eye, and therefore all the Drops in the Line OE shall send the most +refrangible Rays most copiously to the Eye, and thereby strike the +Senses with the deepest violet Colour in that Region. And in like +manner 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 one +Reflexion can emerge out of the Drops, and therefore those Rays shall +come most copiously to the Eye from the Drops in the Line OF, and strike +the Senses with the deepest red Colour in that Region. And by the same +Argument, the Rays which have intermediate Degrees of Refrangibility +shall come most copiously from Drops between E and F, and strike the +Senses with the intermediate Colours, in the Order which their Degrees +of Refrangibility require, that is in the Progress from E to F, or from +the inside of the Bow to the outside in this order, violet, indigo, +blue, green, yellow, orange, red. But the violet, by the mixture of the +white Light of the Clouds, will appear faint and incline to purple. + +[Illustration: FIG. 15.] + +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 after +two Reflexions emerge out of the Drops, and therefore the least +refrangible Rays shall come most copiously to the Eye from the Drops in +the 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. shall +be the least Angle, in which the most refrangible Rays after two +Reflexions can emerge out of the Drops; and therefore those Rays shall +come most copiously to the Eye from the Drops in the Line OH, and strike +the Senses with the deepest violet in that Region. And by the same +Argument, the Drops in the Regions between G and H shall strike the +Sense with the intermediate Colours in the Order which their Degrees of +Refrangibility require, that is, in the Progress from G to H, or from +the 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 understood +of 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; for +the Light becomes fainter by every Reflexion. And their Colours shall +lie in a contrary Order to one another, the red of both Bows bordering +upon the Space GF, which is between the Bows. The Breadth of the +interior Bow EOF measured cross the Colours shall be 1 Degr. 45 Min. and +the Breadth of the exterior GOH shall be 3 Degr. 10 Min. and the +distance between them GOF shall be 8 Gr. 15 Min. the greatest +Semi-diameter of the innermost, that is, the Angle POF being 42 Gr. 2 +Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57 +Min. These are the Measures of the Bows, as they would be were the Sun +but a Point; for by the Breadth of his Body, the Breadth of the Bows +will be increased, and their Distance decreased by half a Degree, and so +the breadth of the interior Iris will be 2 Degr. 15 Min. that of the +exterior 3 Degr. 40 Min. their distance 8 Degr. 25 Min. the greatest +Semi-diameter of the interior Bow 42 Degr. 17 Min. and the least of the +exterior 50 Degr. 42 Min. And such are the Dimensions of the Bows in the +Heavens found to be very nearly, when their Colours appear strong and +perfect. For once, by such means as I then had, I measured the greatest +Semi-diameter of the interior Iris about 42 Degrees, and the breadth of +the red, yellow and green in that Iris 63 or 64 Minutes, besides the +outmost faint red obscured by the brightness of the Clouds, for which we +may allow 3 or 4 Minutes more. The breadth of the blue was about 40 +Minutes more besides the violet, which was so much obscured by the +brightness of the Clouds, that I could not measure its breadth. But +supposing the breadth of the blue and violet together to equal that of +the red, yellow and green together, the whole breadth of this Iris will +be about 2-1/4 Degrees, as above. The least distance between this Iris +and the exterior Iris was about 8 Degrees and 30 Minutes. The exterior +Iris was broader than the interior, but so faint, especially on the blue +side, that I could not measure its breadth distinctly. At another time +when both Bows appeared more distinct, I measured the breadth of the +interior Iris 2 Gr. 10´, and the breadth of the red, yellow and green in +the exterior Iris, was to the breadth of the same Colours in the +interior as 3 to 2. + +This Explication of the Rain-bow is yet farther confirmed by the known +Experiment (made by _Antonius de Dominis_ and _Des-Cartes_) of hanging +up any where in the Sun-shine a Glass Globe filled with Water, and +viewing it in such a posture, that the Rays which come from the Globe to +the Eye may contain with the Sun's Rays an Angle of either 42 or 50 +Degrees. 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 Globe +opposed to the Sun as 'tis represented at F, and if that Angle become +less (suppose by depressing the Globe to E) there will appear other +Colours, yellow, green and blue successive in the same side of the +Globe. But if the Angle be made about 50 Degrees (suppose by lifting up +the Globe to G) there will appear a red Colour in that side of the Globe +towards the Sun, and if the Angle be made greater (suppose by lifting +up 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 Globe +rest, and raising or depressing the Eye, or otherwise moving it to make +the Angle of a just magnitude. + +I have heard it represented, that if the Light of a Candle be refracted +by a Prism to the Eye; when the blue Colour falls upon the Eye, the +Spectator shall see red in the Prism, and when the red falls upon the +Eye he shall see blue; and if this were certain, the Colours of the +Globe 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 to +arise from the difficulty of discerning what Colours fall on the Eye. +For, on the contrary, I have sometimes had occasion to observe in the +Sun's Light refracted by a Prism, that the Spectator always sees that +Colour in the Prism which falls upon his Eye. And the same I have found +true also in Candle-light. For when the Prism is moved slowly from the +Line which is drawn directly from the Candle to the Eye, the red appears +first in the Prism and then the blue, and therefore each of them is seen +when it falls upon the Eye. For the red passes over the Eye first, and +then the blue. + +The Light which comes through drops of Rain by two Refractions without +any Reflexion, ought to appear strongest at the distance of about 26 +Degrees from the Sun, and to decay gradually both ways as the distance +from him increases and decreases. And the same is to be understood of +Light transmitted through spherical Hail-stones. And if the Hail be a +little flatted, as it often is, the Light transmitted may grow so strong +at a little less distance than that of 26 Degrees, as to form a Halo +about the Sun or Moon; which Halo, as often as the Hail-stones are duly +figured may be colour'd, and then it must be red within by the least +refrangible Rays, and blue without by the most refrangible ones, +especially if the Hail-stones have opake Globules of Snow in their +center to intercept the Light within the Halo (as _Hugenius_ has +observ'd) and make the inside thereof more distinctly defined than it +would otherwise be. For such Hail-stones, though spherical, by +terminating the Light by the Snow, may make a Halo red within and +colourless without, and darker in the red than without, as Halos used to +be. For of those Rays which pass close by the Snow the Rubriform will be +least refracted, and so come to the Eye in the directest Lines. + +The Light which passes through a drop of Rain after two Refractions, and +three or more Reflexions, is scarce strong enough to cause a sensible +Bow; but in those Cylinders of Ice by which _Hugenius_ explains the +_Parhelia_, it may perhaps be sensible. + + +_PROP._ X. PROB. V. + +_By the discovered Properties of Light to explain the permanent Colours +of Natural Bodies._ + +These Colours arise from hence, that some natural Bodies reflect some +sorts of Rays, others other sorts more copiously than the rest. Minium +reflects the least refrangible or red-making Rays most copiously, and +thence appears red. Violets reflect the most refrangible most copiously, +and thence have their Colour, and so of other Bodies. Every Body +reflects the Rays of its own Colour more copiously than the rest, and +from their excess and predominance in the reflected Light has its +Colour. + +_Exper._ 17. For if in the homogeneal Lights obtained by the solution of +the Problem proposed in the fourth Proposition of the first Part of this +Book, you place Bodies of several Colours, you will find, as I have +done, that every Body looks most splendid and luminous in the Light of +its own Colour. Cinnaber in the homogeneal red Light is most +resplendent, in the green Light it is manifestly less resplendent, and +in the blue Light still less. Indigo in the violet blue Light is most +resplendent, and its splendor is gradually diminish'd, as it is removed +thence by degrees through the green and yellow Light to the red. By a +Leek the green Light, and next that the blue and yellow which compound +green, are more strongly reflected than the other Colours red and +violet, and so of the rest. But to make these Experiments the more +manifest, such Bodies ought to be chosen as have the fullest and most +vivid Colours, and two of those Bodies are to be compared together. +Thus, for instance, if Cinnaber and _ultra_-marine blue, or some other +full blue be held together in the red homogeneal Light, they will both +appear red, but the Cinnaber will appear of a strongly luminous and +resplendent red, and the _ultra_-marine blue of a faint obscure and dark +red; and if they be held together in the blue homogeneal Light, they +will both appear blue, but the _ultra_-marine will appear of a strongly +luminous and resplendent blue, and the Cinnaber of a faint and dark +blue. Which puts it out of dispute that the Cinnaber reflects the red +Light much more copiously than the _ultra_-marine doth, and the +_ultra_-marine reflects the blue Light much more copiously than the +Cinnaber doth. The same Experiment may be tried successfully with red +Lead and Indigo, or with any other two colour'd Bodies, if due allowance +be made for the different strength or weakness of their Colour and +Light. + +And as the reason of the Colours of natural Bodies is evident by these +Experiments, so it is farther confirmed and put past dispute by the two +first Experiments of the first Part, whereby 'twas proved in such Bodies +that the reflected Lights which differ in Colours do differ also in +degrees of Refrangibility. For thence it's certain, that some Bodies +reflect the more refrangible, others the less refrangible Rays more +copiously. + +And that this is not only a true reason of these Colours, but even the +only reason, may appear farther from this Consideration, that the Colour +of homogeneal Light cannot be changed by the Reflexion of natural +Bodies. + +For if Bodies by Reflexion cannot in the least change the Colour of any +one sort of Rays, they cannot appear colour'd by any other means than by +reflecting those which either are of their own Colour, or which by +mixture must produce it. + +But in trying Experiments of this kind care must be had that the Light +be sufficiently homogeneal. For if Bodies be illuminated by the ordinary +prismatick Colours, they will appear neither of their own Day-light +Colours, nor of the Colour of the Light cast on them, but of some middle +Colour between both, as I have found by Experience. Thus red Lead (for +instance) illuminated with the ordinary prismatick green will not appear +either red or green, but orange or yellow, or between yellow and green, +accordingly as the green Light by which 'tis illuminated is more or less +compounded. For because red Lead appears red when illuminated with white +Light, wherein all sorts of Rays are equally mix'd, and in the green +Light all sorts of Rays are not equally mix'd, the Excess of the +yellow-making, green-making and blue-making Rays in the incident green +Light, 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 red +Lead reflects the red-making Rays most copiously in proportion to their +number, and next after them the orange-making and yellow-making Rays; +these Rays in the reflected Light will be more in proportion to the +Light than they were in the incident green Light, and thereby will draw +the reflected Light from green towards their Colour. And therefore the +red Lead will appear neither red nor green, but of a Colour between +both. + +In transparently colour'd Liquors 'tis observable, that their Colour +uses to vary with their thickness. Thus, for instance, a red Liquor in a +conical Glass held between the Light and the Eye, looks of a pale and +dilute yellow at the bottom where 'tis thin, and a little higher where +'tis thicker grows orange, and where 'tis still thicker becomes red, and +where 'tis thickest the red is deepest and darkest. For it is to be +conceiv'd that such a Liquor stops the indigo-making and violet-making +Rays most easily, the blue-making Rays more difficultly, the +green-making Rays still more difficultly, and the red-making most +difficultly: And that if the thickness of the Liquor be only so much as +suffices to stop a competent number of the violet-making and +indigo-making Rays, without diminishing much the number of the rest, the +rest must (by _Prop._ 6. _Part_ 2.) compound a pale yellow. But if the +Liquor be so much thicker as to stop also a great number of the +blue-making Rays, and some of the green-making, the rest must compound +an orange; and where it is so thick as to stop also a great number of +the green-making and a considerable number of the yellow-making, the +rest must begin to compound a red, and this red must grow deeper and +darker as the yellow-making and orange-making Rays are more and more +stopp'd by increasing the thickness of the Liquor, so that few Rays +besides 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 clear +Sun-shine Day, that when he was sunk many Fathoms deep into the Water +the upper part of his Hand on which the Sun shone directly through the +Water and through a small Glass Window in the Vessel appeared of a red +Colour, like that of a Damask Rose, and the Water below and the under +part of his Hand illuminated by Light reflected from the Water below +look'd green. For thence it may be gather'd, that the Sea-Water reflects +back the violet and blue-making Rays most easily, and lets the +red-making Rays pass most freely and copiously to great Depths. For +thereby the Sun's direct Light at all great Depths, by reason of the +predominating red-making Rays, must appear red; and the greater the +Depth is, the fuller and intenser must that red be. And at such Depths +as the violet-making Rays scarce penetrate unto, the blue-making, +green-making, and yellow-making Rays being reflected from below more +copiously 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 sufficiently +full; though either Liquor be sufficiently transparent apart, yet will +you not be able to see through both together. For, if only the +red-making Rays pass through one Liquor, and only the blue-making +through the other, no Rays can pass through both. This Mr. _Hook_ tried +casually with Glass Wedges filled with red and blue Liquors, and was +surprized at the unexpected Event, the reason of it being then unknown; +which makes me trust the more to his Experiment, though I have not tried +it my self. But he that would repeat it, must take care the Liquors be +of very good and full Colours. + +Now, whilst Bodies become coloured by reflecting or transmitting this or +that sort of Rays more copiously than the rest, it is to be conceived +that they stop and stifle in themselves the Rays which they do not +reflect or transmit. For, if Gold be foliated and held between your Eye +and the Light, the Light looks of a greenish blue, and therefore massy +Gold lets into its Body the blue-making Rays to be reflected to and fro +within it till they be stopp'd and stifled, whilst it reflects the +yellow-making outwards, and thereby looks yellow. And much after the +same manner that Leaf Gold is yellow by reflected, and blue by +transmitted Light, and massy Gold is yellow in all Positions of the Eye; +there are some Liquors, as the Tincture of _Lignum Nephriticum_, and +some sorts of Glass which transmit one sort of Light most copiously, and +reflect another sort, and thereby look of several Colours, according to +the Position of the Eye to the Light. But, if these Liquors or Glasses +were so thick and massy that no Light could get through them, I question +not but they would like all other opake Bodies appear of one and the +same Colour in all Positions of the Eye, though this I cannot yet affirm +by Experience. For all colour'd Bodies, so far as my Observation +reaches, may be seen through if made sufficiently thin, and therefore +are in some measure transparent, and differ only in degrees of +Transparency from tinged transparent Liquors; these Liquors, as well as +those Bodies, by a sufficient Thickness becoming opake. A transparent +Body which looks of any Colour by transmitted Light, may also look of +the same Colour by reflected Light, the Light of that Colour being +reflected by the farther Surface of the Body, or by the Air beyond it. +And then the reflected Colour will be diminished, and perhaps cease, by +making the Body very thick, and pitching it on the backside to diminish +the Reflexion of its farther Surface, so that the Light reflected from +the tinging Particles may predominate. In such Cases, the Colour of the +reflected Light will be apt to vary from that of the Light transmitted. +But whence it is that tinged Bodies and Liquors reflect some sort of +Rays, and intromit or transmit other sorts, shall be said in the next +Book. In this Proposition I content my self to have put it past dispute, +that Bodies have such Properties, and thence appear colour'd. + + +_PROP._ XI. PROB. VI. + +_By mixing colour'd Lights to compound a beam of Light of the same +Colour and Nature with a beam of the Sun's direct Light, and therein to +experience the Truth of the foregoing Propositions._ + +[Illustration: FIG. 16.] + +Let ABC _abc_ [in _Fig._ 16.] represent a Prism, by which the Sun's +Light let into a dark Chamber through the Hole F, may be refracted +towards the Lens MN, and paint upon it at _p_, _q_, _r_, _s_, and _t_, +the usual Colours violet, blue, green, yellow, and red, and let the +diverging Rays by the Refraction of this Lens converge again towards X, +and there, by the mixture of all those their Colours, compound a white +according to what was shewn above. Then let another Prism DEG _deg_, +parallel to the former, be placed at X, to refract that white Light +upwards towards Y. Let the refracting Angles of the Prisms, and their +distances from the Lens be equal, so that the Rays which converged from +the Lens towards X, and without Refraction, would there have crossed and +diverged again, may by the Refraction of the second Prism be reduced +into Parallelism and diverge no more. For then those Rays will recompose +a beam of white Light XY. If the refracting Angle of either Prism be the +bigger, that Prism must be so much the nearer to the Lens. You will know +when the Prisms and the Lens are well set together, by observing if the +beam of Light XY, which comes out of the second Prism be perfectly white +to the very edges of the Light, and at all distances from the Prism +continue perfectly and totally white like a beam of the Sun's Light. For +till this happens, the Position of the Prisms and Lens to one another +must be corrected; and then if by the help of a long beam of Wood, as is +represented 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 try +all the same Experiments in this compounded beam of Light XY, which have +been made in the Sun's direct Light. For this compounded beam of Light +has the same appearance, and is endow'd with all the same Properties +with 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 the +Colours, _p_, _q_, _r_, _s_, and _t_, at the Lens, see how the Colours +produced in the Experiments are no other than those which the Rays had +at the Lens before they entered the Composition of this Beam: And by +consequence, that they arise not from any new Modifications of the Light +by Refractions and Reflexions, but from the various Separations and +Mixtures of the Rays originally endow'd with their colour-making +Qualities. + +So, for instance, having with a Lens 4-1/4 Inches broad, and two Prisms +on either hand 6-1/4 Feet distant from the Lens, made such a beam of +compounded Light; to examine the reason of the Colours made by Prisms, I +refracted this compounded beam of Light XY with another Prism HIK _kh_, +and thereby cast the usual Prismatick Colours PQRST upon the Paper LV +placed behind. And then by stopping any of the Colours _p_, _q_, _r_, +_s_, _t_, at the Lens, I found that the same Colour would vanish at the +Paper. So if the Purple _p_ was stopp'd at the Lens, the Purple P upon +the Paper would vanish, and the rest of the Colours would remain +unalter'd, unless perhaps the blue, so far as some purple latent in it +at the Lens might be separated from it by the following Refractions. And +so by intercepting the green upon the Lens, the green R upon the Paper +would vanish, and so of the rest; which plainly shews, that as the white +beam of Light XY was compounded of several Lights variously colour'd at +the Lens, so the Colours which afterwards emerge out of it by new +Refractions are no other than those of which its Whiteness was +compounded. The Refraction of the Prism HIK _kh_ generates the Colours +PQRST upon the Paper, not by changing the colorific Qualities of the +Rays, but by separating the Rays which had the very same colorific +Qualities before they enter'd the Composition of the refracted beam of +white Light XY. For otherwise the Rays which were of one Colour at the +Lens might be of another upon the Paper, contrary to what we find. + +So again, to examine the reason of the Colours of natural Bodies, I +placed such Bodies in the Beam of Light XY, and found that they all +appeared there of those their own Colours which they have in Day-light, +and that those Colours depend upon the Rays which had the same Colours +at the Lens before they enter'd the Composition of that beam. Thus, for +instance, Cinnaber illuminated by this beam appears of the same red +Colour as in Day-light; and if at the Lens you intercept the +green-making and blue-making Rays, its redness will become more full and +lively: But if you there intercept the red-making Rays, it will not any +longer 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 in +this Light XY appears of the same yellow Colour as in Day-light, but by +intercepting at the Lens a due Quantity of the yellow-making Rays it +will appear white like Silver (as I have tried) which shews that its +yellowness arises from the Excess of the intercepted Rays tinging that +Whiteness with their Colour when they are let pass. So the Infusion of +_Lignum Nephriticum_ (as I have also tried) when held in this beam of +Light XY, looks blue by the reflected Part of the Light, and red by the +transmitted Part of it, as when 'tis view'd in Day-light; but if you +intercept the blue at the Lens the Infusion will lose its reflected blue +Colour, whilst its transmitted red remains perfect, and by the loss of +some blue-making Rays, wherewith it was allay'd, becomes more intense +and full. And, on the contrary, if the red and orange-making Rays be +intercepted at the Lens, the Infusion will lose its transmitted red, +whilst its blue will remain and become more full and perfect. Which +shews, that the Infusion does not tinge the Rays with blue and red, but +only transmits those most copiously which were red-making before, and +reflects those most copiously which were blue-making before. And after +the same manner may the Reasons of other Phænomena be examined, by +trying 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. _Part_ I. +_Sect._ IV. _Prop._ 35 _and_ 36. + + + + +THE + +SECOND BOOK + +OF + +OPTICKS + + + + +_PART I._ + +_Observations concerning the Reflexions, Refractions, and Colours of +thin 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, or +otherwise formed into Plates, do exhibit various Colours according to +their various thinness, altho' at a greater thickness they appear very +clear and colourless. In the former Book I forbore to treat of these +Colours, because they seemed of a more difficult Consideration, and were +not necessary for establishing the Properties of Light there discoursed +of. But because they may conduce to farther Discoveries for compleating +the Theory of Light, especially as to the constitution of the parts of +natural Bodies, on which their Colours or Transparency depend; I have +here set down an account of them. To render this Discourse short and +distinct, I have first described the principal of my Observations, and +then consider'd and made use of them. The Observations are these. + +_Obs._ 1. Compressing two Prisms hard together that their sides (which +by chance were a very little convex) might somewhere touch one another: +I found the place in which they touched to become absolutely +transparent, as if they had there been one continued piece of Glass. For +when the Light fell so obliquely on the Air, which in other places was +between them, as to be all reflected; it seemed in that place of contact +to be wholly transmitted, insomuch that when look'd upon, it appeared +like a black or dark spot, by reason that little or no sensible Light +was reflected from thence, as from other places; and when looked through +it seemed (as it were) a hole in that Air which was formed into a thin +Plate, by being compress'd between the Glasses. And through this hole +Objects that were beyond might be seen distinctly, which could not at +all be seen through other parts of the Glasses where the Air was +interjacent. Although the Glasses were a little convex, yet this +transparent spot was of a considerable breadth, which breadth seemed +principally to proceed from the yielding inwards of the parts of the +Glasses, by reason of their mutual pressure. For by pressing them very +hard together it would become much broader than otherwise. + +_Obs._ 2. When the Plate of Air, by turning the Prisms about their +common Axis, became so little inclined to the incident Rays, that some +of them began to be transmitted, there arose in it many slender Arcs of +Colours which at first were shaped almost like the Conchoid, as you see +them delineated in the first Figure. And by continuing the Motion of the +Prisms, these Arcs increased and bended more and more about the said +transparent spot, till they were compleated into Circles or Rings +incompassing it, and afterwards continually grew more and more +contracted. + +[Illustration: FIG. 1.] + +These Arcs at their first appearance were of a violet and blue Colour, +and between them were white Arcs of Circles, which presently by +continuing the Motion of the Prisms became a little tinged in their +inward Limbs with red and yellow, and to their outward Limbs the blue +was adjacent. So that the order of these Colours from the central dark +spot, was at that time white, blue, violet; black, red, orange, yellow, +white, blue, violet, &c. But the yellow and red were much fainter than +the blue and violet. + +The Motion of the Prisms about their Axis being continued, these Colours +contracted more and more, shrinking towards the whiteness on either +side of it, until they totally vanished into it. And then the Circles in +those parts appear'd black and white, without any other Colours +intermix'd. But by farther moving the Prisms about, the Colours again +emerged 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 from +the 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 and +white, they were very distinct and well defined, and the blackness +seemed as intense as that of the central Spot. Also in the Borders of +the Rings, where the Colours began to emerge out of the whiteness, they +were pretty distinct, which made them visible to a very great multitude. +I have sometimes number'd above thirty Successions (reckoning every +black and white Ring for one Succession) and seen more of them, which by +reason of their smalness I could not number. But in other Positions of +the Prisms, at which the Rings appeared of many Colours, I could not +distinguish above eight or nine of them, and the Exterior of those were +very confused and dilute. + +In these two Observations to see the Rings distinct, and without any +other Colour than Black and white, I found it necessary to hold my Eye +at a good distance from them. For by approaching nearer, although in the +same inclination of my Eye to the Plane of the Rings, there emerged a +bluish Colour out of the white, which by dilating it self more and more +into the black, render'd the Circles less distinct, and left the white a +little tinged with red and yellow. I found also by looking through a +slit or oblong hole, which was narrower than the pupil of my Eye, and +held close to it parallel to the Prisms, I could see the Circles much +distincter and visible to a far greater number than otherwise. + +_Obs._ 4. To observe more nicely the order of the Colours which arose +out of the white Circles as the Rays became less and less inclined to +the Plate of Air; I took two Object-glasses, the one a Plano-convex for +a fourteen Foot Telescope, and the other a large double Convex for one +of about fifty Foot; and upon this, laying the other with its plane side +downwards, I pressed them slowly together, to make the Colours +successively emerge in the middle of the Circles, and then slowly lifted +the upper Glass from the lower to make them successively vanish again in +the same place. The Colour, which by pressing the Glasses together, +emerged last in the middle of the other Colours, would upon its first +appearance look like a Circle of a Colour almost uniform from the +circumference to the center and by compressing the Glasses still more, +grow continually broader until a new Colour emerged in its center, and +thereby it became a Ring encompassing that new Colour. And by +compressing the Glasses still more, the diameter of this Ring would +increase, and the breadth of its Orbit or Perimeter decrease until +another new Colour emerged in the center of the last: And so on until a +third, a fourth, a fifth, and other following new Colours successively +emerged there, and became Rings encompassing the innermost Colour, the +last of which was the black Spot. And, on the contrary, by lifting up +the upper Glass from the lower, the diameter of the Rings would +decrease, and the breadth of their Orbit increase, until their Colours +reached successively to the center; and then they being of a +considerable breadth, I could more easily discern and distinguish their +Species than before. And by this means I observ'd their Succession and +Quantity to be as followeth. + +Next to the pellucid central Spot made by the contact of the Glasses +succeeded blue, white, yellow, and red. The blue was so little in +quantity, 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 red +were 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 of +Colours immediately encompassing these were violet, blue, green, yellow, +and red: and these were all of them copious and vivid, excepting the +green, which was very little in quantity, and seemed much more faint and +dilute than the other Colours. Of the other four, the violet was the +least in extent, and the blue less than the yellow or red. The third +Circuit or Order was purple, blue, green, yellow, and red; in which the +purple seemed more reddish than the violet in the former Circuit, and +the green was much more conspicuous, being as brisk and copious as any +of the other Colours, except the yellow, but the red began to be a +little faded, inclining very much to purple. After this succeeded the +fourth 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. But +in this fourth Circuit there was neither violet, blue, nor yellow, and +the red was very imperfect and dirty. Also the succeeding Colours became +more and more imperfect and dilute, till after three or four revolutions +they ended in perfect whiteness. Their form, when the Glasses were most +compress'd so as to make the black Spot appear in the center, is +delineated in the second Figure; where _a_, _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, red: +purple, blue, green, yellow, red: green, red: greenish blue, red: +greenish blue, pale red: greenish blue, reddish white. + +[Illustration: FIG. 2.] + +_Obs._ 5. To determine the interval of the Glasses, or thickness of the +interjacent Air, by which each Colour was produced, I measured the +Diameters of the first six Rings at the most lucid part of their Orbits, +and squaring them, I found their Squares to be in the arithmetical +Progression of the odd Numbers, 1, 3, 5, 7, 9, 11. And since one of +these Glasses was plane, and the other spherical, their Intervals at +those Rings must be in the same Progression. I measured also the +Diameters of the dark or faint Rings between the more lucid Colours, and +found their Squares to be in the arithmetical Progression of the even +Numbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult to +take these measures exactly; I repeated them divers times at divers +parts of the Glasses, that by their Agreement I might be confirmed in +them. And the same method I used in determining some others of the +following Observations. + +_Obs._ 6. The Diameter of the sixth Ring at the most lucid part of its +Orbit was 58/100 parts of an Inch, and the Diameter of the Sphere on +which the double convex Object-glass was ground was about 102 Feet, and +hence I gathered the thickness of the Air or Aereal Interval of the +Glasses at that Ring. But some time after, suspecting that in making +this Observation I had not determined the Diameter of the Sphere with +sufficient accurateness, and being uncertain whether the Plano-convex +Glass was truly plane, and not something concave or convex on that side +which I accounted plane; and whether I had not pressed the Glasses +together, as I often did, to make them touch; (For by pressing such +Glasses together their parts easily yield inwards, and the Rings thereby +become sensibly broader than they would be, did the Glasses keep their +Figures.) I repeated the Experiment, and found the Diameter of the sixth +lucid Ring about 55/100 parts of an Inch. I repeated the Experiment also +with such an Object-glass of another Telescope as I had at hand. This +was a double Convex ground on both sides to one and the same Sphere, and +its Focus was distant from it 83-2/5 Inches. And thence, if the Sines of +Incidence and Refraction of the bright yellow Light be assumed in +proportion as 11 to 17, the Diameter of the Sphere to which the Glass +was figured will by computation be found 182 Inches. This Glass I laid +upon a flat one, so that the black Spot appeared in the middle of the +Rings of Colours without any other Pressure than that of the weight of +the Glass. And now measuring the Diameter of the fifth dark Circle as +accurately 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 the +upper Surface on the upper Glass, and my Eye was about eight or nine +Inches distance from the Glass, almost perpendicularly over it, and the +Glass was 1/6 of an Inch thick, and thence it is easy to collect that +the true Diameter of the Ring between the Glasses was greater than its +measur'd Diameter above the Glasses in the Proportion of 80 to 79, or +thereabouts, and by consequence equal to 16/79 parts of an Inch, and its +true Semi-diameter equal to 8/79 parts. Now as the Diameter of the +Sphere (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 the +Air at this fifth dark Ring; which is therefore 32/567931 or +100/1774784. Parts of an Inch; and the fifth Part thereof, _viz._ the +1/88739 Part of an Inch, is the Thickness of the Air at the first of +these dark Rings. + +The same Experiment I repeated with another double convex Object-glass +ground on both sides to one and the same Sphere. Its Focus was distant +from it 168-1/2 Inches, and therefore the Diameter of that Sphere was +184 Inches. This Glass being laid upon the same plain Glass, the +Diameter of the fifth of the dark Rings, when the black Spot in their +Center appear'd plainly without pressing the Glasses, was by the measure +of the Compasses upon the upper Glass 121/600 Parts of an Inch, and by +consequence between the Glasses it was 1222/6000: For the upper Glass +was 1/8 of an Inch thick, and my Eye was distant from it 8 Inches. And a +third proportional to half this from the Diameter of the Sphere is +5/88850 Parts of an Inch. This is therefore the Thickness of the Air at +this Ring, and a fifth Part thereof, _viz._ the 1/88850th Part of an +Inch is the Thickness thereof at the first of the Rings, as above. + +I tried the same Thing, by laying these Object-glasses upon flat Pieces +of a broken Looking-glass, and found the same Measures of the Rings: +Which makes me rely upon them till they can be determin'd more +accurately by Glasses ground to larger Spheres, though in such Glasses +greater care must be taken of a true Plane. + +These Dimensions were taken, when my Eye was placed almost +perpendicularly over the Glasses, being about an Inch, or an Inch and a +quarter, distant from the incident Rays, and eight Inches distant from +the Glass; so that the Rays were inclined to the Glass in an Angle of +about four Degrees. Whence by the following Observation you will +understand, that had the Rays been perpendicular to the Glasses, the +Thickness of the Air at these Rings would have been less in the +Proportion of the Radius to the Secant of four Degrees, that is, of +10000 to 10024. Let the Thicknesses found be therefore diminish'd in +this Proportion, and they will become 1/88952 and 1/89063, or (to use +the nearest round Number) the 1/89000th Part of an Inch. This is the +Thickness of the Air at the darkest Part of the first dark Ring made by +perpendicular Rays; and half this Thickness multiplied by the +Progression, 1, 3, 5, 7, 9, 11, &c. gives the Thicknesses of the Air at +the 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 of +all the dark ones. + +_Obs._ 7. The Rings were least, when my Eye was placed perpendicularly +over the Glasses in the Axis of the Rings: And when I view'd them +obliquely they became bigger, continually swelling as I removed my Eye +farther from the Axis. And partly by measuring the Diameter of the same +Circle at several Obliquities of my Eye, partly by other Means, as also +by making use of the two Prisms for very great Obliquities, I found its +Diameter, and consequently the Thickness of the Air at its Perimeter in +all those Obliquities to be very nearly in the Proportions express'd in +this Table. + +-------------------+--------------------+----------+---------- +Angle of Incidence |Angle of Refraction |Diameter |Thickness + on | into | of the | of the + the Air. | the Air. | Ring. | 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 incident +and emergent Rays to the Plate of the Air, that is, their Angles of +Incidence and Refraction. In the third Column the Diameter of any +colour'd Ring at those Obliquities is expressed in Parts, of which ten +constitute that Diameter when the Rays are perpendicular. And in the +fourth Column the Thickness of the Air at the Circumference of that Ring +is expressed in Parts, of which also ten constitute its Thickness when +the Rays are perpendicular. + +And from these Measures I seem to gather this Rule: That the Thickness +of the Air is proportional to the Secant of an Angle, whose Sine is a +certain mean Proportional between the Sines of Incidence and Refraction. +And that mean Proportional, so far as by these Measures I can determine +it, is the first of an hundred and six arithmetical mean Proportionals +between those Sines counted from the bigger Sine, that is, from the Sine +of Refraction when the Refraction is made out of the Glass into the +Plate of Air, or from the Sine of Incidence when the Refraction is made +out of the Plate of Air into the Glass. + +_Obs._ 8. The dark Spot in the middle of the Rings increased also by the +Obliquation of the Eye, although almost insensibly. But, if instead of +the Object-glasses the Prisms were made use of, its Increase was more +manifest when viewed so obliquely that no Colours appear'd about it. It +was least when the Rays were incident most obliquely on the interjacent +Air, and as the obliquity decreased it increased more and more until the +colour'd Rings appear'd, and then decreased again, but not so much as it +increased before. And hence it is evident, that the Transparency was +not only at the absolute Contact of the Glasses, but also where they had +some little Interval. I have sometimes observed the Diameter of that +Spot to be between half and two fifth parts of the Diameter of the +exterior Circumference of the red in the first Circuit or Revolution of +Colours when view'd almost perpendicularly; whereas when view'd +obliquely it hath wholly vanish'd and become opake and white like the +other parts of the Glass; whence it may be collected that the Glasses +did then scarcely, or not at all, touch one another, and that their +Interval at the perimeter of that Spot when view'd perpendicularly was +about a fifth or sixth part of their Interval at the circumference of +the said red. + +_Obs._ 9. By looking through the two contiguous Object-glasses, I found +that the interjacent Air exhibited Rings of Colours, as well by +transmitting 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. But +these Colours were very faint and dilute, unless when the Light was +trajected very obliquely through the Glasses: For by that means they +became pretty vivid. Only the first yellowish red, like the blue in the +fourth Observation, was so little and faint as scarcely to be discern'd. +Comparing the colour'd Rings made by Reflexion, with these made by +transmission of the Light; I found that white was opposite to black, red +to blue, yellow to violet, and green to a Compound of red and violet. +That is, those parts of the Glass were black when looked through, which +when looked upon appeared white, and on the contrary. And so those which +in one case exhibited blue, did in the other case exhibit red. And the +like of the other Colours. The manner you have represented in the third +Figure, where AB, CD, are the Surfaces of the Glasses contiguous at E, +and the black Lines between them are their Distances in arithmetical +Progression, 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 Water +crept in slowly between them, and the Circles thereby became less and +the Colours more faint: Insomuch that as the Water crept along, one half +of them at which it first arrived would appear broken off from the other +half, and contracted into a less Room. By measuring them I found the +Proportions of their Diameters to the Diameters of the like Circles made +by Air to be about seven to eight, and consequently the Intervals of the +Glasses at like Circles, caused by those two Mediums Water and Air, are +as about three to four. Perhaps it may be a general Rule, That if any +other Medium more or less dense than Water be compress'd between the +Glasses, their Intervals at the Rings caused thereby will be to their +Intervals caused by interjacent Air, as the Sines are which measure the +Refraction made out of that Medium into Air. + +_Obs._ 11. When the Water was between the Glasses, if I pressed the +upper Glass variously at its edges to make the Rings move nimbly from +one place to another, a little white Spot would immediately follow the +center of them, which upon creeping in of the ambient Water into that +place would presently vanish. Its appearance was such as interjacent Air +would have caused, and it exhibited the same Colours. But it was not +air, for where any Bubbles of Air were in the Water they would not +vanish. 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 to +examine the Effects of colour'd Light falling on the Glasses, I darken'd +the Room, and view'd them by Reflexion of the Colours of a Prism cast on +a Sheet of white Paper, my Eye being so placed that I could see the +colour'd Paper by Reflexion in the Glasses, as in a Looking-glass. And +by this means the Rings became distincter and visible to a far greater +number than in the open Air. I have sometimes seen more than twenty of +them, whereas in the open Air I could not discern above eight or nine. + +[Illustration: FIG. 3.] + +_Obs._ 13. Appointing an Assistant to move the Prism to and fro about +its Axis, that all the Colours might successively fall on that part of +the Paper which I saw by Reflexion from that part of the Glasses, where +the Circles appear'd, so that all the Colours might be successively +reflected from the Circles to my Eye, whilst I held it immovable, I +found the Circles which the red Light made to be manifestly bigger than +those which were made by the blue and violet. And it was very pleasant +to see them gradually swell or contract accordingly as the Colour of the +Light was changed. The Interval of the Glasses at any of the Rings when +they were made by the utmost red Light, was to their Interval at the +same Ring when made by the utmost violet, greater than as 3 to 2, and +less 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 my +Eye; unless when two Prisms were made use of instead of the +Object-glasses. For then at a certain great obliquity of my Eye, the +Rings made by the several Colours seem'd equal, and at a greater +obliquity those made by the violet would be greater than the same Rings +made by the red: the Refraction of the Prism in this case causing the +most refrangible Rays to fall more obliquely on that plate of the Air +than the least refrangible ones. Thus the Experiment succeeded in the +colour'd Light, which was sufficiently strong and copious to make the +Rings sensible. And thence it may be gather'd, that if the most +refrangible and least refrangible Rays had been copious enough to make +the Rings sensible without the mixture of other Rays, the Proportion +which here was 14 to 9 would have been a little greater, suppose 14-1/4 +or 14-1/3 to 9. + +_Obs._ 14. Whilst the Prism was turn'd about its Axis with an uniform +Motion, to make all the several Colours fall successively upon the +Object-glasses, and thereby to make the Rings contract and dilate: The +Contraction or Dilatation of each Ring thus made by the variation of its +Colour was swiftest in the red, and slowest in the violet, and in the +intermediate Colours it had intermediate degrees of Celerity. Comparing +the quantity of Contraction and Dilatation made by all the degrees of +each Colour, I found that it was greatest in the red; less in the +yellow, still less in the blue, and least in the violet. And to make as +just an Estimation as I could of the Proportions of their Contractions +or Dilatations, I observ'd that the whole Contraction or Dilatation of +the Diameter of any Ring made by all the degrees of red, was to that of +the Diameter of the same Ring made by all the degrees of violet, as +about four to three, or five to four, and that when the Light was of the +middle Colour between yellow and green, the Diameter of the Ring was +very nearly an arithmetical Mean between the greatest Diameter of the +same Ring made by the outmost red, and the least Diameter thereof made +by the outmost violet: Contrary to what happens in the Colours of the +oblong Spectrum made by the Refraction of a Prism, where the red is most +contracted, the violet most expanded, and in the midst of all the +Colours is the Confine of green and blue. And hence I seem to collect +that the thicknesses of the Air between the Glasses there, where the +Ring is successively made by the limits of the five principal Colours +(red, yellow, green, blue, violet) in order (that is, by the extreme +red, by the limit of red and yellow in the middle of the orange, by the +limit of yellow and green, by the limit of green and blue, by the limit +of blue and violet in the middle of the indigo, and by the extreme +violet) are to one another very nearly as the sixth lengths of a Chord +which found the Notes in a sixth Major, _sol_, _la_, _mi_, _fa_, _sol_, +_la_. But it agrees something better with the Observation to say, that +the thicknesses of the Air between the Glasses there, where the Rings +are successively made by the limits of the seven Colours, red, orange, +yellow, green, blue, indigo, violet in order, are to one another as the +Cube Roots of the Squares of the eight lengths of a Chord, which found +the 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 in +the open Air, but appeared all over of that prismatick Colour only with +which they were illuminated. And by projecting the prismatick Colours +immediately upon the Glasses, I found that the Light which fell on the +dark Spaces which were between the Colour'd Rings was transmitted +through the Glasses without any variation of Colour. For on a white +Paper placed behind, it would paint Rings of the same Colour with those +which were reflected, and of the bigness of their immediate Spaces. And +from thence the origin of these Rings is manifest; namely, that the Air +between the Glasses, according to its various thickness, is disposed in +some places to reflect, and in others to transmit the Light of any one +Colour (as you may see represented in the fourth Figure) and in the same +place to reflect that of one Colour where it transmits that of another. + +[Illustration: FIG. 4.] + +_Obs._ 16. The Squares of the Diameters of these Rings made by any +prismatick Colour were in arithmetical Progression, as in the fifth +Observation. And the Diameter of the sixth Circle, when made by the +citrine yellow, and viewed almost perpendicularly was about 58/100 parts +of 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 two +Glasses. In those that follow are set down the Appearances of a denser +Medium thin'd within a rarer, such as are Plates of Muscovy Glass, +Bubbles of Water, and some other thin Substances terminated on all sides +with air. + +_Obs._ 17. If a Bubble be blown with Water first made tenacious by +dissolving a little Soap in it, 'tis a common Observation, that after a +while it will appear tinged with a great variety of Colours. To defend +these Bubbles from being agitated by the external Air (whereby their +Colours are irregularly moved one among another, so that no accurate +Observation can be made of them,) as soon as I had blown any of them I +cover'd it with a clear Glass, and by that means its Colours emerged in +a very regular order, like so many concentrick Rings encompassing the +top of the Bubble. And as the Bubble grew thinner by the continual +subsiding of the Water, these Rings dilated slowly and overspread the +whole Bubble, descending in order to the bottom of it, where they +vanish'd successively. In the mean while, after all the Colours were +emerged at the top, there grew in the center of the Rings a small round +black Spot, like that in the first Observation, which continually +dilated it self till it became sometimes more than 1/2 or 3/4 of an Inch +in breadth before the Bubble broke. At first I thought there had been no +Light reflected from the Water in that place, but observing it more +curiously, I saw within it several smaller round Spots, which appeared +much blacker and darker than the rest, whereby I knew that there was +some Reflexion at the other places which were not so dark as those +Spots. And by farther Tryal I found that I could see the Images of some +things (as of a Candle or the Sun) very faintly reflected, not only from +the great black Spot, but also from the little darker Spots which were +within it. + +Besides the aforesaid colour'd Rings there would often appear small +Spots of Colours, ascending and descending up and down the sides of the +Bubble, by reason of some Inequalities in the subsiding of the Water. +And sometimes small black Spots generated at the sides would ascend up +to the larger black Spot at the top of the Bubble, and unite with it. + +_Obs._ 18. Because the Colours of these Bubbles were more extended and +lively than those of the Air thinn'd between two Glasses, and so more +easy to be distinguish'd, I shall here give you a farther description of +their order, as they were observ'd in viewing them by Reflexion of the +Skies when of a white Colour, whilst a black substance was placed +behind the Bubble. And they were these, red, blue; red, blue; red, blue; +red, green; red, yellow, green, blue, purple; red, yellow, green, blue, +violet; red, yellow, white, blue, black. + +The three first Successions of red and blue were very dilute and dirty, +especially the first, where the red seem'd in a manner to be white. +Among these there was scarce any other Colour sensible besides red and +blue, only the blues (and principally the second blue) inclined a little +to green. + +The fourth red was also dilute and dirty, but not so much as the former +three; after that succeeded little or no yellow, but a copious green, +which at first inclined a little to yellow, and then became a pretty +brisk and good willow green, and afterwards changed to a bluish Colour; +but there succeeded neither blue nor violet. + +The fifth red at first inclined very much to purple, and afterwards +became more bright and brisk, but yet not very pure. This was succeeded +with a very bright and intense yellow, which was but little in quantity, +and soon chang'd to green: But that green was copious and something more +pure, deep and lively, than the former green. After that follow'd an +excellent blue of a bright Sky-colour, and then a purple, which was less +in quantity than the blue, and much inclined to red. + +The sixth red was at first of a very fair and lively scarlet, and soon +after of a brighter Colour, being very pure and brisk, and the best of +all the reds. Then after a lively orange follow'd an intense bright and +copious yellow, which was also the best of all the yellows, and this +changed first to a greenish yellow, and then to a greenish blue; but the +green between the yellow and the blue, was very little and dilute, +seeming rather a greenish white than a green. The blue which succeeded +became very good, and of a very bright Sky-colour, but yet something +inferior to the former blue; and the violet was intense and deep with +little or no redness in it. And less in quantity than the blue. + +In the last red appeared a tincture of scarlet next to violet, which +soon changed to a brighter Colour, inclining to an orange; and the +yellow which follow'd was at first pretty good and lively, but +afterwards it grew more dilute until by degrees it ended in perfect +whiteness. And this whiteness, if the Water was very tenacious and +well-temper'd, would slowly spread and dilate it self over the greater +part of the Bubble; continually growing paler at the top, where at +length it would crack in many places, and those cracks, as they dilated, +would appear of a pretty good, but yet obscure and dark Sky-colour; the +white between the blue Spots diminishing, until it resembled the Threds +of an irregular Net-work, and soon after vanish'd, and left all the +upper part of the Bubble of the said dark blue Colour. And this Colour, +after the aforesaid manner, dilated it self downwards, until sometimes +it hath overspread the whole Bubble. In the mean while at the top, which +was of a darker blue than the bottom, and appear'd also full of many +round blue Spots, something darker than the rest, there would emerge +one or more very black Spots, and within those, other Spots of an +intenser blackness, which I mention'd in the former Observation; and +these continually dilated themselves until the Bubble broke. + +If the Water was not very tenacious, the black Spots would break forth +in the white, without any sensible intervention of the blue. And +sometimes they would break forth within the precedent yellow, or red, or +perhaps within the blue of the second order, before the intermediate +Colours had time to display themselves. + +By this description you may perceive how great an affinity these Colours +have with those of Air described in the fourth Observation, although set +down in a contrary order, by reason that they begin to appear when the +Bubble is thickest, and are most conveniently reckon'd from the lowest +and thickest part of the Bubble upwards. + +_Obs._ 19. Viewing in several oblique Positions of my Eye the Rings of +Colours emerging on the top of the Bubble, I found that they were +sensibly dilated by increasing the obliquity, but yet not so much by far +as those made by thinn'd Air in the seventh Observation. For there they +were dilated so much as, when view'd most obliquely, to arrive at a part +of the Plate more than twelve times thicker than that where they +appear'd when viewed perpendicularly; whereas in this case the thickness +of the Water, at which they arrived when viewed most obliquely, was to +that thickness which exhibited them by perpendicular Rays, something +less than as 8 to 5. By the best of my Observations it was between 15 +and 15-1/2 to 10; an increase about 24 times less than in the other +case. + +Sometimes the Bubble would become of an uniform thickness all over, +except at the top of it near the black Spot, as I knew, because it would +exhibit the same appearance of Colours in all Positions of the Eye. And +then the Colours which were seen at its apparent circumference by the +obliquest Rays, would be different from those that were seen in other +places, by Rays less oblique to it. And divers Spectators might see the +same part of it of differing Colours, by viewing it at very differing +Obliquities. Now observing how much the Colours at the same places of +the Bubble, or at divers places of equal thickness, were varied by the +several Obliquities of the Rays; by the assistance of the 4th, 14th, +16th and 18th Observations, as they are hereafter explain'd, I collect +the thickness of the Water requisite to exhibit any one and the same +Colour, at several Obliquities, to be very nearly in the Proportion +expressed in this Table. + +-----------------+------------------+---------------- + Incidence on | Refraction into | Thickness of + the Water. | the Water. | the Water. +-----------------+------------------+---------------- + Deg. Min. | Deg. Min. | + | | + 00 00 | 00 00 | 10 + | | + 15 00 | 11 11 | 10-1/4 + | | + 30 00 | 22 1 | 10-4/5 + | | + 45 00 | 32 2 | 11-4/5 + | | + 60 00 | 40 30 | 13 + | | + 75 00 | 46 25 | 14-1/2 + | | + 90 00 | 48 35 | 15-1/5 +-----------------+------------------+---------------- + +In the two first Columns are express'd the Obliquities of the Rays to +the Superficies of the Water, that is, their Angles of Incidence and +Refraction. Where I suppose, that the Sines which measure them are in +round Numbers, as 3 to 4, though probably the Dissolution of Soap in the +Water, may a little alter its refractive Virtue. In the third Column, +the Thickness of the Bubble, at which any one Colour is exhibited in +those several Obliquities, is express'd in Parts, of which ten +constitute its Thickness when the Rays are perpendicular. And the Rule +found by the seventh Observation agrees well with these Measures, if +duly apply'd; namely, that the Thickness of a Plate of Water requisite +to exhibit one and the same Colour at several Obliquities of the Eye, is +proportional to the Secant of an Angle, whose Sine is the first of an +hundred and six arithmetical mean Proportionals between the Sines of +Incidence and Refraction counted from the lesser Sine, that is, from the +Sine of Refraction when the Refraction is made out of Air into Water, +otherwise from the Sine of Incidence. + +I have sometimes observ'd, that the Colours which arise on polish'd +Steel by heating it, or on Bell-metal, and some other metalline +Substances, when melted and pour'd on the Ground, where they may cool in +the open Air, have, like the Colours of Water-bubbles, been a little +changed by viewing them at divers Obliquities, and particularly that a +deep blue, or violet, when view'd very obliquely, hath been changed to a +deep red. But the Changes of these Colours are not so great and +sensible as of those made by Water. For the Scoria, or vitrified Part of +the Metal, which most Metals when heated or melted do continually +protrude, and send out to their Surface, and which by covering the +Metals in form of a thin glassy Skin, causes these Colours, is much +denser than Water; and I find that the Change made by the Obliquation of +the Eye is least in Colours of the densest thin Substances. + +_Obs._ 20. As in the ninth Observation, so here, the Bubble, by +transmitted Light, appear'd of a contrary Colour to that, which it +exhibited by Reflexion. Thus when the Bubble being look'd on by the +Light of the Clouds reflected from it, seemed red at its apparent +Circumference, 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 would +appear red by transmitted Light. + +_Obs._ 21. By wetting very thin Plates of _Muscovy_ Glass, whose +thinness made the like Colours appear, the Colours became more faint and +languid, especially by wetting the Plates on that side opposite to the +Eye: But I could not perceive any variation of their Species. So then +the thickness of a Plate requisite to produce any Colour, depends only +on the density of the Plate, and not on that of the ambient Medium. And +hence, by the 10th and 16th Observations, may be known the thickness +which Bubbles of Water, or Plates of _Muscovy_ Glass, or other +Substances, have at any Colour produced by them. + +_Obs._ 22. A thin transparent Body, which is denser than its ambient +Medium, exhibits more brisk and vivid Colours than that which is so much +rarer; as I have particularly observed in the Air and Glass. For blowing +Glass very thin at a Lamp Furnace, those Plates encompassed with Air did +exhibit Colours much more vivid than those of Air made thin between two +Glasses. + +_Obs._ 23. Comparing the quantity of Light reflected from the several +Rings, I found that it was most copious from the first or inmost, and in +the exterior Rings became gradually less and less. Also the whiteness of +the first Ring was stronger than that reflected from those parts of the +thin Medium or Plate which were without the Rings; as I could manifestly +perceive by viewing at a distance the Rings made by the two +Object-glasses; or by comparing two Bubbles of Water blown at distant +Times, in the first of which the Whiteness appear'd, which succeeded all +the Colours, and in the other, the Whiteness which preceded them all. + +_Obs._ 24. When the two Object-glasses were lay'd upon one another, so +as to make the Rings of the Colours appear, though with my naked Eye I +could not discern above eight or nine of those Rings, yet by viewing +them through a Prism I have seen a far greater Multitude, insomuch that +I could number more than forty, besides many others, that were so very +small and close together, that I could not keep my Eye steady on them +severally so as to number them, but by their Extent I have sometimes +estimated them to be more than an hundred. And I believe the Experiment +may be improved to the Discovery of far greater Numbers. For they seem +to be really unlimited, though visible only so far as they can be +separated by the Refraction of the Prism, as I shall hereafter explain. + +[Illustration: FIG. 5.] + +But it was but one side of these Rings, namely, that towards which the +Refraction was made, which by that Refraction was render'd distinct, and +the other side became more confused than when view'd by the naked Eye, +insomuch that there I could not discern above one or two, and sometimes +none of those Rings, of which I could discern eight or nine with my +naked Eye. And their Segments or Arcs, which on the other side appear'd +so numerous, for the most part exceeded not the third Part of a Circle. +If the Refraction was very great, or the Prism very distant from the +Object-glasses, the middle Part of those Arcs became also confused, so +as to disappear and constitute an even Whiteness, whilst on either side +their Ends, as also the whole Arcs farthest from the Center, became +distincter than before, appearing in the Form as you see them design'd +in the fifth Figure. + +The Arcs, where they seem'd distinctest, were only white and black +successively, without any other Colours intermix'd. But in other Places +there appeared Colours, whose Order was inverted by the refraction in +such manner, that if I first held the Prism very near the +Object-glasses, and then gradually removed it farther off towards my +Eye, the Colours of the 2d, 3d, 4th, and following Rings, shrunk towards +the white that emerged between them, until they wholly vanish'd into it +at the middle of the Arcs, and afterwards emerged again in a contrary +Order. But at the Ends of the Arcs they retain'd their Order unchanged. + +I have sometimes so lay'd one Object-glass upon the other, that to the +naked Eye they have all over seem'd uniformly white, without the least +Appearance of any of the colour'd Rings; and yet by viewing them through +a Prism, great Multitudes of those Rings have discover'd themselves. And +in like manner Plates of _Muscovy_ Glass, and Bubbles of Glass blown at +a Lamp-Furnace, which were not so thin as to exhibit any Colours to the +naked Eye, have through the Prism exhibited a great Variety of them +ranged irregularly up and down in the Form of Waves. And so Bubbles of +Water, before they began to exhibit their Colours to the naked Eye of a +Bystander, have appeared through a Prism, girded about with many +parallel and horizontal Rings; to produce which Effect, it was necessary +to hold the Prism parallel, or very nearly parallel to the Horizon, and +to dispose it so that the Rays might be refracted upwards. + + + + +THE + +SECOND BOOK + +OF + +OPTICKS + + +_PART II._ + +_Remarks upon the foregoing Observations._ + + +Having given my Observations of these Colours, before I make use of them +to unfold the Causes of the Colours of natural Bodies, it is convenient +that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th, +18th, 20th, and 24th, I first explain the more compounded. And first to +shew how the Colours in the fourth and eighteenth Observations are +produced, let there be taken in any Right Line from the Point Y, [in +_Fig._ 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to +one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16, +3/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to +sound all the Notes in an eighth are represented; that is, in the +Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243, +10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars +A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent +of the several Colours set underneath against them, is to be +represented. Then divide the Line _A[Greek: a]_ in such Proportion as +the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of +Division denote. And through those Divisions from Y draw Lines 1I, 2K, +3L, 5M, 6N, 7O, &c. + +Now, if A2 be supposed to represent the Thickness of any thin +transparent Body, at which the outmost Violet is most copiously +reflected in the first Ring, or Series of Colours, then by the 13th +Observation, HK will represent its Thickness, at which the utmost Red is +most copiously reflected in the same Series. Also by the 5th and 16th +Observations, A6 and HN will denote the Thicknesses at which those +extreme Colours are most copiously reflected in the second Series, and +A10 and HQ the Thicknesses at which they are most copiously reflected in +the third Series, and so on. And the Thickness at which any of the +intermediate Colours are reflected most copiously, will, according to +the 14th Observation, be defined by the distance of the Line AH from the +intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names +of those Colours are written below. + +[Illustration: FIG. 6.] + +But farther, to define the Latitude of these Colours in each Ring or +Series, let A1 design the least thickness, and A3 the greatest +thickness, at which the extreme violet in the first Series is reflected, +and let HI, and HL, design the like limits for the extreme red, and let +the intermediate Colours be limited by the intermediate parts of the +Lines 1I, and 3L, against which the Names of those Colours are written, +and so on: But yet with this caution, that the Reflexions be supposed +strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence +to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on +either side; where you must not conceive them to be precisely limited, +but to decay indefinitely. And whereas I have assign'd the same Latitude +to every Series, I did it, because although the Colours in the first +Series seem to be a little broader than the rest, by reason of a +stronger Reflexion there, yet that inequality is so insensible as +scarcely to be determin'd by Observation. + +Now according to this Description, conceiving that the Rays originally +of several Colours are by turns reflected at the Spaces 1I, L3, 5M, O7, +9PR11, &c. and transmitted at the Spaces AHI1, 3LM5, 7OP9, &c. it is +easy to know what Colour must in the open Air be exhibited at any +thickness of a transparent thin Body. For if a Ruler be applied parallel +to AH, at that distance from it by which the thickness of the Body is +represented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth will +denote the reflected original Colours, of which the Colour exhibited in +the open Air is compounded. Thus if the constitution of the green in the +third Series of Colours be desired, apply the Ruler as you see at +[Greek: prsph], and by its passing through some of the blue at [Greek: +p] and yellow at [Greek: s], as well as through the green at [Greek: r], +you may conclude that the green exhibited at that thickness of the Body +is principally constituted of original green, but not without a mixture +of some blue and yellow. + +By this means you may know how the Colours from the center of the Rings +outward ought to succeed in order as they were described in the 4th and +18th Observations. For if you move the Ruler gradually from AH through +all distances, having pass'd over the first Space which denotes little +or no Reflexion to be made by thinnest Substances, it will first arrive +at 1 the violet, and then very quickly at the blue and green, which +together with that violet compound blue, and then at the yellow and red, +by whose farther addition that blue is converted into whiteness, which +whiteness continues during the transit of the edge of the Ruler from I +to 3, and after that by the successive deficience of its component +Colours, turns first to compound yellow, and then to red, and last of +all the red ceaseth at L. Then begin the Colours of the second Series, +which succeed in order during the transit of the edge of the Ruler from +5 to O, and are more lively than before, because more expanded and +severed. And for the same reason instead of the former white there +intercedes between the blue and yellow a mixture of orange, yellow, +green, blue and indigo, all which together ought to exhibit a dilute and +imperfect green. So the Colours of the third Series all succeed in +order; first, the violet, which a little interferes with the red of the +second order, and is thereby inclined to a reddish purple; then the blue +and green, which are less mix'd with other Colours, and consequently +more lively than before, especially the green: Then follows the yellow, +some of which towards the green is distinct and good, but that part of +it towards the succeeding red, as also that red is mix'd with the violet +and blue of the fourth Series, whereby various degrees of red very much +inclining to purple are compounded. This violet and blue, which should +succeed this red, being mixed with, and hidden in it, there succeeds a +green. And this at first is much inclined to blue, but soon becomes a +good green, the only unmix'd and lively Colour in this fourth Series. +For as it verges towards the yellow, it begins to interfere with the +Colours of the fifth Series, by whose mixture the succeeding yellow and +red are very much diluted and made dirty, especially the yellow, which +being the weaker Colour is scarce able to shew it self. After this the +several Series interfere more and more, and their Colours become more +and more intermix'd, till after three or four more revolutions (in which +the red and blue predominate by turns) all sorts of Colours are in all +places pretty equally blended, and compound an even whiteness. + +And since by the 15th Observation the Rays endued with one Colour are +transmitted, where those of another Colour are reflected, the reason of +the Colours made by the transmitted Light in the 9th and 20th +Observations is from hence evident. + +If not only the Order and Species of these Colours, but also the precise +thickness of the Plate, or thin Body at which they are exhibited, be +desired in parts of an Inch, that may be also obtained by assistance of +the 6th or 16th Observations. For according to those Observations the +thickness of the thinned Air, which between two Glasses exhibited the +most luminous parts of the first six Rings were 1/178000, 3/178000, +5/178000, 7/178000, 9/178000, 11/178000 parts of an Inch. Suppose the +Light reflected most copiously at these thicknesses be the bright +citrine yellow, or confine of yellow and orange, and these thicknesses +will be F[Greek: l], F[Greek: m], F[Greek: u], F[Greek: x], F[Greek: o], +F[Greek: t]. And this being known, it is easy to determine what +thickness of Air is represented by G[Greek: ph], or by any other +distance of the Ruler from AH. + +But farther, since by the 10th Observation the thickness of Air was to +the thickness of Water, which between the same Glasses exhibited the +same Colour, as 4 to 3, and by the 21st Observation the Colours of thin +Bodies are not varied by varying the ambient Medium; the thickness of a +Bubble of Water, exhibiting any Colour, will be 3/4 of the thickness of +Air producing the same Colour. And so according to the same 10th and +21st Observations, the thickness of a Plate of Glass, whose Refraction +of the mean refrangible Ray, is measured by the proportion of the Sines +31 to 20, may be 20/31 of the thickness of Air producing the same +Colours; and the like of other Mediums. I do not affirm, that this +proportion of 20 to 31, holds in all the Rays; for the Sines of other +sorts of Rays have other Proportions. But the differences of those +Proportions are so little that I do not here consider them. On these +Grounds I have composed the following Table, wherein the thickness of +Air, Water, and Glass, at which each Colour is most intense and +specifick, is expressed in parts of an Inch divided into ten hundred +thousand equal parts. + +Now if this Table be compared with the 6th Scheme, you will there see +the constitution of each Colour, as to its Ingredients, or the original +Colours of which it is compounded, and thence be enabled to judge of its +Intenseness or Imperfection; which may suffice in explication of the 4th +and 18th Observations, unless it be farther desired to delineate the +manner how the Colours appear, when the two Object-glasses are laid upon +one another. To do which, let there be described a large Arc of a +Circle, and a streight Line which may touch that Arc, and parallel to +that Tangent several occult Lines, at such distances from it, as the +Numbers set against the several Colours in the Table denote. For the +Arc, and its Tangent, will represent the Superficies of the Glasses +terminating the interjacent Air; and the places where the occult Lines +cut the Arc will show at what distances from the center, or Point of +contact, each Colour is reflected. + +_The thickness of colour'd Plates and Particles of_ + _____________|_______________ + / \ + Air. Water. Glass. + |---------+----------+----------+ + {Very black | 1/2 | 3/8 | 10/31 | + {Black | 1 | 3/4 | 20/31 | + {Beginning of | | | | + { Black | 2 | 1-1/2 | 1-2/7 | +Their Colours of the {Blue | 2-2/5 | 1-4/5 | 1-11/22 | +first Order, {White | 5-1/4 | 3-7/8 | 3-2/5 | + {Yellow | 7-1/9 | 5-1/3 | 4-3/5 | + {Orange | 8 | 6 | 5-1/6 | + {Red | 9 | 6-3/4 | 5-4/5 | + |---------+----------+----------| + {Violet | 11-1/6 | 8-3/8 | 7-1/5 | + {Indigo | 12-5/6 | 9-5/8 | 8-2/11 | + {Blue | 14 | 10-1/2 | 9 | + {Green | 15-1/8 | 11-2/3 | 9-5/7 | +Of the second order, {Yellow | 16-2/7 | 12-1/5 | 10-2/5 | + {Orange | 17-2/9 | 13 | 11-1/9 | + {Bright red | 18-1/3 | 13-3/4 | 11-5/6 | + {Scarlet | 19-2/3 | 14-3/4 | 12-2/3 | + |---------+----------+----------| + {Purple | 21 | 15-3/4 | 13-11/20 | + {Indigo | 22-1/10 | 16-4/7 | 14-1/4 | + {Blue | 23-2/5 | 17-11/20 | 15-1/10 | +Of the third Order, {Green | 25-1/5 | 18-9/10 | 16-1/4 | + {Yellow | 27-1/7 | 20-1/3 | 17-1/2 | + {Red | 29 | 21-3/4 | 18-5/7 | + {Bluish red | 32 | 24 | 20-2/3 | + |---------+----------+----------| + {Bluish green | 34 | 25-1/2 | 22 | + {Green | 35-2/7 | 26-1/2 | 22-3/4 | +Of the fourth Order, {Yellowish green | 36 | 27 | 23-2/9 | + {Red | 40-1/3 | 30-1/4 | 26 | + |---------+----------+----------| + {Greenish blue | 46 | 34-1/2 | 29-2/3 | +Of the fifth Order, {Red | 52-1/2 | 39-3/8 | 34 | + |---------+----------+----------| + {Greenish blue | 58-3/4 | 44 | 38 | +Of the sixth Order, {Red | 65 | 48-3/4 | 42 | + |---------+----------+----------| +Of the seventh Order, {Greenish blue | 71 | 53-1/4 | 45-4/5 | + {Ruddy White | 77 | 57-3/4 | 49-2/3 | + |---------+----------+----------| + +There are also other Uses of this Table: For by its assistance the +thickness of the Bubble in the 19th Observation was determin'd by the +Colours which it exhibited. And so the bigness of the parts of natural +Bodies may be conjectured by their Colours, as shall be hereafter shewn. +Also, if two or more very thin Plates be laid one upon another, so as to +compose one Plate equalling them all in thickness, the resulting Colour +may be hereby determin'd. For instance, Mr. _Hook_ observed, as is +mentioned in his _Micrographia_, that a faint yellow Plate of _Muscovy_ +Glass laid upon a blue one, constituted a very deep purple. The yellow +of the first Order is a faint one, and the thickness of the Plate +exhibiting it, according to the Table is 4-3/5, to which add 9, the +thickness exhibiting blue of the second Order, and the Sum will be +13-3/5, which is the thickness exhibiting the purple of the third Order. + +To explain, in the next place, the circumstances of the 2d and 3d +Observations; that is, how the Rings of the Colours may (by turning the +Prisms about their common Axis the contrary way to that expressed in +those Observations) be converted into white and black Rings, and +afterwards into Rings of Colours again, the Colours of each Ring lying +now in an inverted order; it must be remember'd, that those Rings of +Colours are dilated by the obliquation of the Rays to the Air which +intercedes the Glasses, and that according to the Table in the 7th +Observation, their Dilatation or Increase of their Diameter is most +manifest and speedy when they are obliquest. Now the Rays of yellow +being more refracted by the first Superficies of the said Air than those +of red, are thereby made more oblique to the second Superficies, at +which they are reflected to produce the colour'd Rings, and consequently +the yellow Circle in each Ring will be more dilated than the red; and +the Excess of its Dilatation will be so much the greater, by how much +the greater is the obliquity of the Rays, until at last it become of +equal extent with the red of the same Ring. And for the same reason the +green, blue and violet, will be also so much dilated by the still +greater obliquity of their Rays, as to become all very nearly of equal +extent with the red, that is, equally distant from the center of the +Rings. And then all the Colours of the same Ring must be co-incident, +and by their mixture exhibit a white Ring. And these white Rings must +have black and dark Rings between them, because they do not spread and +interfere with one another, as before. And for that reason also they +must become distincter, and visible to far greater numbers. But yet the +violet being obliquest will be something more dilated, in proportion to +its extent, than the other Colours, and so very apt to appear at the +exterior Verges of the white. + +Afterwards, by a greater obliquity of the Rays, the violet and blue +become more sensibly dilated than the red and yellow, and so being +farther removed from the center of the Rings, the Colours must emerge +out of the white in an order contrary to that which they had before; the +violet and blue at the exterior Limbs of each Ring, and the red and +yellow at the interior. And the violet, by reason of the greatest +obliquity of its Rays, being in proportion most of all expanded, will +soonest appear at the exterior Limb of each white Ring, and become more +conspicuous than the rest. And the several Series of Colours belonging +to the several Rings, will, by their unfolding and spreading, begin +again to interfere, and thereby render the Rings less distinct, and not +visible to so great numbers. + +If instead of the Prisms the Object-glasses be made use of, the Rings +which they exhibit become not white and distinct by the obliquity of the +Eye, by reason that the Rays in their passage through that Air which +intercedes the Glasses are very nearly parallel to those Lines in which +they were first incident on the Glasses, and consequently the Rays +endued with several Colours are not inclined one more than another to +that Air, as it happens in the Prisms. + +There is yet another circumstance of these Experiments to be consider'd, +and that is why the black and white Rings which when view'd at a +distance appear distinct, should not only become confused by viewing +them near at hand, but also yield a violet Colour at both the edges of +every white Ring. And the reason is, that the Rays which enter the Eye +at several parts of the Pupil, have several Obliquities to the Glasses, +and those which are most oblique, if consider'd apart, would represent +the Rings bigger than those which are the least oblique. Whence the +breadth of the Perimeter of every white Ring is expanded outwards by the +obliquest Rays, and inwards by the least oblique. And this Expansion is +so much the greater by how much the greater is the difference of the +Obliquity; that is, by how much the Pupil is wider, or the Eye nearer to +the Glasses. And the breadth of the violet must be most expanded, +because the Rays apt to excite a Sensation of that Colour are most +oblique to a second or farther Superficies of the thinn'd Air at which +they are reflected, and have also the greatest variation of Obliquity, +which makes that Colour soonest emerge out of the edges of the white. +And as the breadth of every Ring is thus augmented, the dark Intervals +must be diminish'd, until the neighbouring Rings become continuous, and +are blended, the exterior first, and then those nearer the center; so +that they can no longer be distinguish'd apart, but seem to constitute +an even and uniform whiteness. + +Among all the Observations there is none accompanied with so odd +circumstances as the twenty-fourth. Of those the principal are, that in +thin Plates, which to the naked Eye seem of an even and uniform +transparent whiteness, without any terminations of Shadows, the +Refraction of a Prism should make Rings of Colours appear, whereas it +usually makes Objects appear colour'd only there where they are +terminated with Shadows, or have parts unequally luminous; and that it +should make those Rings exceedingly distinct and white, although it +usually renders Objects confused and coloured. The Cause of these things +you will understand by considering, that all the Rings of Colours are +really in the Plate, when view'd with the naked Eye, although by reason +of the great breadth of their Circumferences they so much interfere and +are blended together, that they seem to constitute an uniform whiteness. +But when the Rays pass through the Prism to the Eye, the Orbits of the +several Colours in every Ring are refracted, some more than others, +according to their degrees of Refrangibility: By which means the Colours +on one side of the Ring (that is in the circumference on one side of its +center), become more unfolded and dilated, and those on the other side +more complicated and contracted. And where by a due Refraction they are +so much contracted, that the several Rings become narrower than to +interfere with one another, they must appear distinct, and also white, +if the constituent Colours be so much contracted as to be wholly +co-incident. But on the other side, where the Orbit of every Ring is +made broader by the farther unfolding of its Colours, it must interfere +more with other Rings than before, and so become less distinct. + +[Illustration: FIG. 7.] + +To explain this a little farther, suppose the concentrick Circles AV, +and BX, [in _Fig._ 7.] represent the red and violet of any Order, which, +together with the intermediate Colours, constitute any one of these +Rings. Now these being view'd through a Prism, the violet Circle BX, +will, by a greater Refraction, be farther translated from its place than +the red AV, and so approach nearer to it on that side of the Circles, +towards which the Refractions are made. For instance, if the red be +translated to _av_, the violet may be translated to _bx_, so as to +approach nearer to it at _x_ than before; and if the red be farther +translated to av, the violet may be so much farther translated to bx as +to convene with it at x; and if the red be yet farther translated to +[Greek: aY], the violet may be still so much farther translated to +[Greek: bx] as to pass beyond it at [Greek: x], and convene with it at +_e_ and _f_. And this being understood not only of the red and violet, +but of all the other intermediate Colours, and also of every revolution +of those Colours, you will easily perceive how those of the same +revolution or order, by their nearness at _xv_ and [Greek: Yx], and +their coincidence at xv, _e_ and _f_, ought to constitute pretty +distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that +they will appear severally at _x_[Greek: u] and at xv exhibit whiteness +by their coincidence, and again appear severally at [Greek: Yx], but yet +in a contrary order to that which they had before, and still retain +beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab], +these Colours must become much more confused by being dilated and spread +so as to interfere with those of other Orders. And the same confusion +will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be +very great, or the Prism very distant from the Object-glasses: In which +case no parts of the Rings will be seen, save only two little Arcs at +_e_ and _f_, whose distance from one another will be augmented by +removing the Prism still farther from the Object-glasses: And these +little Arcs must be distinctest and whitest at their middle, and at +their ends, where they begin to grow confused, they must be colour'd. +And the Colours at one end of every Arc must be in a contrary order to +those at the other end, by reason that they cross in the intermediate +white; namely, their ends, which verge towards [Greek: Ux], will be red +and yellow on that side next the center, and blue and violet on the +other side. But their other ends which verge from [Greek: Ux], will on +the contrary be blue and violet on that side towards the center, and on +the other side red and yellow. + +Now as all these things follow from the properties of Light by a +mathematical way of reasoning, so the truth of them may be manifested by +Experiments. For in a dark Room, by viewing these Rings through a Prism, +by reflexion of the several prismatick Colours, which an assistant +causes to move to and fro upon a Wall or Paper from whence they are +reflected, whilst the Spectator's Eye, the Prism, and the +Object-glasses, (as in the 13th Observation,) are placed steady; the +Position of the Circles made successively by the several Colours, will +be found such, in respect of one another, as I have described in the +Figures _abxv_, or abxv, or _[Greek: abxU]_. And by the same method the +truth of the Explications of other Observations may be examined. + +By what hath been said, the like Phænomena of Water and thin Plates of +Glass may be understood. But in small fragments of those Plates there is +this farther observable, that where they lie flat upon a Table, and are +turned about their centers whilst they are view'd through a Prism, they +will in some postures exhibit Waves of various Colours; and some of them +exhibit these Waves in one or two Positions only, but the most of them +do in all Positions exhibit them, and make them for the most part appear +almost all over the Plates. The reason is, that the Superficies of such +Plates are not even, but have many Cavities and Swellings, which, how +shallow soever, do a little vary the thickness of the Plate. For at the +several sides of those Cavities, for the Reasons newly described, there +ought to be produced Waves in several postures of the Prism. Now though +it be but some very small and narrower parts of the Glass, by which +these Waves for the most part are caused, yet they may seem to extend +themselves over the whole Glass, because from the narrowest of those +parts there are Colours of several Orders, that is, of several Rings, +confusedly reflected, which by Refraction of the Prism are unfolded, +separated, and, according to their degrees of Refraction, dispersed to +several places, so as to constitute so many several Waves, as there were +divers orders of Colours promiscuously reflected from that part of the +Glass. + +These are the principal Phænomena of thin Plates or Bubbles, whose +Explications depend on the properties of Light, which I have heretofore +deliver'd. And these you see do necessarily follow from them, and agree +with them, even to their very least circumstances; and not only so, but +do very much tend to their proof. Thus, by the 24th Observation it +appears, that the Rays of several Colours, made as well by thin Plates +or Bubbles, as by Refractions of a Prism, have several degrees of +Refrangibility; whereby those of each order, which at the reflexion from +the Plate or Bubble are intermix'd with those of other orders, are +separated from them by Refraction, and associated together so as to +become visible by themselves like Arcs of Circles. For if the Rays were +all alike refrangible, 'tis impossible that the whiteness, which to the +naked Sense appears uniform, should by Refraction have its parts +transposed and ranged into those black and white Arcs. + +It appears also that the unequal Refractions of difform Rays proceed not +from any contingent irregularities; such as are Veins, an uneven Polish, +or fortuitous Position of the Pores of Glass; unequal and casual Motions +in the Air or Æther, the spreading, breaking, or dividing the same Ray +into many diverging parts; or the like. For, admitting any such +irregularities, it would be impossible for Refractions to render those +Rings so very distinct, and well defined, as they do in the 24th +Observation. It is necessary therefore that every Ray have its proper +and constant degree of Refrangibility connate with it, according to +which its refraction is ever justly and regularly perform'd; and that +several Rays have several of those degrees. + +And what is said of their Refrangibility may be also understood of their +Reflexibility, that is, of their Dispositions to be reflected, some at a +greater, and others at a less thickness of thin Plates or Bubbles; +namely, that those Dispositions are also connate with the Rays, and +immutable; as may appear by the 13th, 14th, and 15th Observations, +compared with the fourth and eighteenth. + +By the Precedent Observations it appears also, that whiteness is a +dissimilar mixture of all Colours, and that Light is a mixture of Rays +endued with all those Colours. For, considering the multitude of the +Rings of Colours in the 3d, 12th, and 24th Observations, it is manifest, +that although in the 4th and 18th Observations there appear no more than +eight or nine of those Rings, yet there are really a far greater number, +which so much interfere and mingle with one another, as after those +eight or nine revolutions to dilute one another wholly, and constitute +an even and sensibly uniform whiteness. And consequently that whiteness +must be allow'd a mixture of all Colours, and the Light which conveys it +to the Eye must be a mixture of Rays endued with all those Colours. + +But farther; by the 24th Observation it appears, that there is a +constant relation between Colours and Refrangibility; the most +refrangible Rays being violet, the least refrangible red, and those of +intermediate Colours having proportionably intermediate degrees of +Refrangibility. And by the 13th, 14th, and 15th Observations, compared +with the 4th or 18th there appears to be the same constant relation +between Colour and Reflexibility; the violet being in like circumstances +reflected at least thicknesses of any thin Plate or Bubble, the red at +greatest thicknesses, and the intermediate Colours at intermediate +thicknesses. Whence it follows, that the colorifick Dispositions of +Rays are also connate with them, and immutable; and by consequence, that +all the Productions and Appearances of Colours in the World are derived, +not from any physical Change caused in Light by Refraction or Reflexion, +but only from the various Mixtures or Separations of Rays, by virtue of +their different Refrangibility or Reflexibility. And in this respect the +Science of Colours becomes a Speculation as truly mathematical as any +other part of Opticks. I mean, so far as they depend on the Nature of +Light, and are not produced or alter'd by the Power of Imagination, or +by striking or pressing the Eye. + + + + +THE + +SECOND BOOK + +OF + +OPTICKS + + +_PART III._ + +_Of the permanent Colours of natural Bodies, and the Analogy between +them and the Colours of thin transparent Plates._ + +I am now come to another part of this Design, which is to consider how +the Phænomena of thin transparent Plates stand related to those of all +other natural Bodies. Of these Bodies I have already told you that they +appear of divers Colours, accordingly as they are disposed to reflect +most copiously the Rays originally endued with those Colours. But their +Constitutions, whereby they reflect some Rays more copiously than +others, remain to be discover'd; and these I shall endeavour to manifest +in the following Propositions. + + +PROP. I. + +_Those Superficies of transparent Bodies reflect the greatest quantity +of Light, which have the greatest refracting Power; that is, which +intercede Mediums that differ most in their refractive Densities. And in +the Confines of equally refracting Mediums there is no Reflexion._ + +The Analogy between Reflexion and Refraction will appear by considering, +that when Light passeth obliquely out of one Medium into another which +refracts from the perpendicular, the greater is the difference of their +refractive Density, the less Obliquity of Incidence is requisite to +cause a total Reflexion. For as the Sines are which measure the +Refraction, so is the Sine of Incidence at which the total Reflexion +begins, to the Radius of the Circle; and consequently that Angle of +Incidence is least where there is the greatest difference of the Sines. +Thus in the passing of Light out of Water into Air, where the Refraction +is measured by the Ratio of the Sines 3 to 4, the total Reflexion begins +when the Angle of Incidence is about 48 Degrees 35 Minutes. In passing +out of Glass into Air, where the Refraction is measured by the Ratio of +the Sines 20 to 31, the total Reflexion begins when the Angle of +Incidence is 40 Degrees 10 Minutes; and so in passing out of Crystal, or +more strongly refracting Mediums into Air, there is still a less +obliquity requisite to cause a total reflexion. Superficies therefore +which refract most do soonest reflect all the Light which is incident on +them, and so must be allowed most strongly reflexive. + +But the truth of this Proposition will farther appear by observing, that +in the Superficies interceding two transparent Mediums, (such as are +Air, Water, Oil, common Glass, Crystal, metalline Glasses, Island +Glasses, white transparent Arsenick, Diamonds, &c.) the Reflexion is +stronger or weaker accordingly, as the Superficies hath a greater or +less refracting Power. For in the Confine of Air and Sal-gem 'tis +stronger than in the Confine of Air and Water, and still stronger in the +Confine of Air and common Glass or Crystal, and stronger in the Confine +of Air and a Diamond. If any of these, and such like transparent Solids, +be immerged in Water, its Reflexion becomes, much weaker than before; +and still weaker if they be immerged in the more strongly refracting +Liquors of well rectified Oil of Vitriol or Spirit of Turpentine. If +Water be distinguish'd into two parts by any imaginary Surface, the +Reflexion in the Confine of those two parts is none at all. In the +Confine of Water and Ice 'tis very little; in that of Water and Oil 'tis +something greater; in that of Water and Sal-gem still greater; and in +that of Water and Glass, or Crystal or other denser Substances still +greater, accordingly as those Mediums differ more or less in their +refracting Powers. Hence in the Confine of common Glass and Crystal, +there ought to be a weak Reflexion, and a stronger Reflexion in the +Confine of common and metalline Glass; though I have not yet tried +this. But in the Confine of two Glasses of equal density, there is not +any sensible Reflexion; as was shewn in the first Observation. And the +same may be understood of the Superficies interceding two Crystals, or +two Liquors, or any other Substances in which no Refraction is caused. +So then the reason why uniform pellucid Mediums (such as Water, Glass, +or Crystal,) have no sensible Reflexion but in their external +Superficies, where they are adjacent to other Mediums of a different +density, is because all their contiguous parts have one and the same +degree of density. + + +PROP. II. + +_The least parts of almost all natural Bodies are in some measure +transparent: And the Opacity of those Bodies ariseth from the multitude +of Reflexions caused in their internal Parts._ + +That this is so has been observed by others, and will easily be granted +by them that have been conversant with Microscopes. And it may be also +tried by applying any substance to a hole through which some Light is +immitted into a dark Room. For how opake soever that Substance may seem +in the open Air, it will by that means appear very manifestly +transparent, if it be of a sufficient thinness. Only white metalline +Bodies must be excepted, which by reason of their excessive density seem +to reflect almost all the Light incident on their first Superficies; +unless by solution in Menstruums they be reduced into very small +Particles, and then they become transparent. + + +PROP. III. + +_Between the parts of opake and colour'd Bodies are many Spaces, either +empty, or replenish'd with Mediums of other Densities; as Water between +the tinging Corpuscles wherewith any Liquor is impregnated, Air between +the aqueous Globules that constitute Clouds or Mists; and for the most +part Spaces void of both Air and Water, but yet perhaps not wholly void +of all Substance, between the parts of hard Bodies._ + +The truth of this is evinced by the two precedent Propositions: For by +the second Proposition there are many Reflexions made by the internal +parts of Bodies, which, by the first Proposition, would not happen if +the parts of those Bodies were continued without any such Interstices +between them; because Reflexions are caused only in Superficies, which +intercede Mediums of a differing density, by _Prop._ 1. + +But farther, that this discontinuity of parts is the principal Cause of +the opacity of Bodies, will appear by considering, that opake Substances +become transparent by filling their Pores with any Substance of equal or +almost equal density with their parts. Thus Paper dipped in Water or +Oil, the _Oculus Mundi_ Stone steep'd in Water, Linnen Cloth oiled or +varnish'd, and many other Substances soaked in such Liquors as will +intimately pervade their little Pores, become by that means more +transparent than otherwise; so, on the contrary, the most transparent +Substances, may, by evacuating their Pores, or separating their parts, +be render'd sufficiently opake; as Salts or wet Paper, or the _Oculus +Mundi_ Stone by being dried, Horn by being scraped, Glass by being +reduced to Powder, or otherwise flawed; Turpentine by being stirred +about with Water till they mix imperfectly, and Water by being form'd +into many small Bubbles, either alone in the form of Froth, or by +shaking it together with Oil of Turpentine, or Oil Olive, or with some +other convenient Liquor, with which it will not perfectly incorporate. +And to the increase of the opacity of these Bodies, it conduces +something, that by the 23d Observation the Reflexions of very thin +transparent Substances are considerably stronger than those made by the +same Substances of a greater thickness. + + +PROP. IV. + +_The Parts of Bodies and their Interstices must not be less than of some +definite bigness, to render them opake and colour'd._ + +For the opakest Bodies, if their parts be subtilly divided, (as Metals, +by being dissolved in acid Menstruums, &c.) become perfectly +transparent. And you may also remember, that in the eighth Observation +there was no sensible reflexion at the Superficies of the +Object-glasses, where they were very near one another, though they did +not absolutely touch. And in the 17th Observation the Reflexion of the +Water-bubble where it became thinnest was almost insensible, so as to +cause very black Spots to appear on the top of the Bubble, by the want +of reflected Light. + +On these grounds I perceive it is that Water, Salt, Glass, Stones, and +such like Substances, are transparent. For, upon divers Considerations, +they seem to be as full of Pores or Interstices between their parts as +other Bodies are, but yet their Parts and Interstices to be too small to +cause Reflexions in their common Surfaces. + + +PROP. V. + +_The transparent parts of Bodies, according to their several sizes, +reflect Rays of one Colour, and transmit those of another, on the same +grounds that thin Plates or Bubbles do reflect or transmit those Rays. +And this I take to be the ground of all their Colours._ + +For if a thinn'd or plated Body, which being of an even thickness, +appears all over of one uniform Colour, should be slit into Threads, or +broken into Fragments, of the same thickness with the Plate; I see no +reason why every Thread or Fragment should not keep its Colour, and by +consequence why a heap of those Threads or Fragments should not +constitute a Mass or Powder of the same Colour, which the Plate +exhibited before it was broken. And the parts of all natural Bodies +being like so many Fragments of a Plate, must on the same grounds +exhibit the same Colours. + +Now, that they do so will appear by the affinity of their Properties. +The finely colour'd Feathers of some Birds, and particularly those of +Peacocks Tails, do, in the very same part of the Feather, appear of +several Colours in several Positions of the Eye, after the very same +manner that thin Plates were found to do in the 7th and 19th +Observations, and therefore their Colours arise from the thinness of the +transparent parts of the Feathers; that is, from the slenderness of the +very fine Hairs, or _Capillamenta_, which grow out of the sides of the +grosser lateral Branches or Fibres of those Feathers. And to the same +purpose it is, that the Webs of some Spiders, by being spun very fine, +have appeared colour'd, as some have observ'd, and that the colour'd +Fibres of some Silks, by varying the Position of the Eye, do vary their +Colour. Also the Colours of Silks, Cloths, and other Substances, which +Water or Oil can intimately penetrate, become more faint and obscure by +being immerged in those Liquors, and recover their Vigor again by being +dried; much after the manner declared of thin Bodies in the 10th and +21st Observations. Leaf-Gold, some sorts of painted Glass, the Infusion +of _Lignum Nephriticum_, and some other Substances, reflect one Colour, +and transmit another; like thin Bodies in the 9th and 20th Observations. +And some of those colour'd Powders which Painters use, may have their +Colours a little changed, by being very elaborately and finely ground. +Where I see not what can be justly pretended for those changes, besides +the breaking of their parts into less parts by that contrition, after +the same manner that the Colour of a thin Plate is changed by varying +its thickness. For which reason also it is that the colour'd Flowers of +Plants and Vegetables, by being bruised, usually become more transparent +than before, or at least in some degree or other change their Colours. +Nor is it much less to my purpose, that, by mixing divers Liquors, very +odd and remarkable Productions and Changes of Colours may be effected, +of which no cause can be more obvious and rational than that the saline +Corpuscles of one Liquor do variously act upon or unite with the tinging +Corpuscles of another, so as to make them swell, or shrink, (whereby not +only their bulk but their density also may be changed,) or to divide +them into smaller Corpuscles, (whereby a colour'd Liquor may become +transparent,) or to make many of them associate into one cluster, +whereby two transparent Liquors may compose a colour'd one. For we see +how apt those saline Menstruums are to penetrate and dissolve Substances +to which they are applied, and some of them to precipitate what others +dissolve. In like manner, if we consider the various Phænomena of the +Atmosphere, we may observe, that when Vapours are first raised, they +hinder not the transparency of the Air, being divided into parts too +small to cause any Reflexion in their Superficies. But when in order to +compose drops of Rain they begin to coalesce and constitute Globules of +all intermediate sizes, those Globules, when they become of convenient +size to reflect some Colours and transmit others, may constitute Clouds +of various Colours according to their sizes. And I see not what can be +rationally conceived in so transparent a Substance as Water for the +production of these Colours, besides the various sizes of its fluid and +globular Parcels. + + +PROP. VI. + +_The parts of Bodies on which their Colours depend, are denser than the +Medium which pervades their Interstices._ + +This will appear by considering, that the Colour of a Body depends not +only on the Rays which are incident perpendicularly on its parts, but on +those also which are incident at all other Angles. And that according to +the 7th Observation, a very little variation of obliquity will change +the reflected Colour, where the thin Body or small Particles is rarer +than the ambient Medium, insomuch that such a small Particle will at +diversly oblique Incidences reflect all sorts of Colours, in so great a +variety that the Colour resulting from them all, confusedly reflected +from a heap of such Particles, must rather be a white or grey than any +other Colour, or at best it must be but a very imperfect and dirty +Colour. Whereas if the thin Body or small Particle be much denser than +the ambient Medium, the Colours, according to the 19th Observation, are +so little changed by the variation of obliquity, that the Rays which +are reflected least obliquely may predominate over the rest, so much as +to cause a heap of such Particles to appear very intensely of their +Colour. + +It conduces also something to the confirmation of this Proposition, +that, according to the 22d Observation, the Colours exhibited by the +denser thin Body within the rarer, are more brisk than those exhibited +by the rarer within the denser. + + +PROP. VII. + +_The bigness of the component parts of natural Bodies may be conjectured +by their Colours._ + +For since the parts of these Bodies, by _Prop._ 5. do most probably +exhibit the same Colours with a Plate of equal thickness, provided they +have the same refractive density; and since their parts seem for the +most part to have much the same density with Water or Glass, as by many +circumstances is obvious to collect; to determine the sizes of those +parts, you need only have recourse to the precedent Tables, in which the +thickness of Water or Glass exhibiting any Colour is expressed. Thus if +it be desired to know the diameter of a Corpuscle, which being of equal +density with Glass shall reflect green of the third Order; the Number +16-1/4 shews it to be (16-1/4)/10000 parts of an Inch. + +The greatest difficulty is here to know of what Order the Colour of any +Body is. And for this end we must have recourse to the 4th and 18th +Observations; from whence may be collected these particulars. + +_Scarlets_, and other _reds_, _oranges_, and _yellows_, if they be pure +and intense, are most probably of the second order. Those of the first +and third order also may be pretty good; only the yellow of the first +order is faint, and the orange and red of the third Order have a great +Mixture of violet and blue. + +There may be good _Greens_ of the fourth Order, but the purest are of +the third. And of this Order the green of all Vegetables seems to be, +partly by reason of the Intenseness of their Colours, and partly because +when they wither some of them turn to a greenish yellow, and others to a +more perfect yellow or orange, or perhaps to red, passing first through +all the aforesaid intermediate Colours. Which Changes seem to be +effected by the exhaling of the Moisture which may leave the tinging +Corpuscles more dense, and something augmented by the Accretion of the +oily and earthy Part of that Moisture. Now the green, without doubt, is +of the same Order with those Colours into which it changeth, because the +Changes are gradual, and those Colours, though usually not very full, +yet are often too full and lively to be of the fourth Order. + +_Blues_ and _Purples_ may be either of the second or third Order, but +the best are of the third. Thus the Colour of Violets seems to be of +that Order, because their Syrup by acid Liquors turns red, and by +urinous and alcalizate turns green. For since it is of the Nature of +Acids to dissolve or attenuate, and of Alcalies to precipitate or +incrassate, if the Purple Colour of the Syrup was of the second Order, +an acid Liquor by attenuating its tinging Corpuscles would change it to +a red of the first Order, and an Alcali by incrassating them would +change it to a green of the second Order; which red and green, +especially the green, seem too imperfect to be the Colours produced by +these Changes. But if the said Purple be supposed of the third Order, +its Change to red of the second, and green of the third, may without any +Inconvenience be allow'd. + +If there be found any Body of a deeper and less reddish Purple than that +of the Violets, its Colour most probably is of the second Order. But yet +there being no Body commonly known whose Colour is constantly more deep +than theirs, I have made use of their Name to denote the deepest and +least reddish Purples, such as manifestly transcend their Colour in +purity. + +The _blue_ of the first Order, though very faint and little, may +possibly be the Colour of some Substances; and particularly the azure +Colour of the Skies seems to be of this Order. For all Vapours when they +begin to condense and coalesce into small Parcels, become first of that +Bigness, whereby such an Azure must be reflected before they can +constitute Clouds of other Colours. And so this being the first Colour +which Vapours begin to reflect, it ought to be the Colour of the finest +and most transparent Skies, in which Vapours are not arrived to that +Grossness requisite to reflect other Colours, as we find it is by +Experience. + +_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 most +white Substances; of the former I reckon that of white Metals to be. For +whilst the densest of Metals, Gold, if foliated, is transparent, and all +Metals become transparent if dissolved in Menstruums or vitrified, the +Opacity of white Metals ariseth not from their Density alone. They being +less dense than Gold would be more transparent than it, did not some +other Cause concur with their Density to make them opake. And this Cause +I take to be such a Bigness of their Particles as fits them to reflect +the white of the first order. For, if they be of other Thicknesses they +may reflect other Colours, as is manifest by the Colours which appear +upon hot Steel in tempering it, and sometimes upon the Surface of melted +Metals 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 made +by Plates of transparent Substances, so it ought to be stronger in the +denser 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 may +fit them to reflect the white of the first order, may, by reason of +their great Density (according to the Tenor of the first of these +Propositions) reflect all the Light incident upon them, and so be as +opake and splendent as it's possible for any Body to be. Gold, or Copper +mix'd with less than half their Weight of Silver, or Tin, or Regulus of +Antimony, in fusion, or amalgamed with a very little Mercury, become +white; which shews both that the Particles of white Metals have much +more Superficies, and so are smaller, than those of Gold and Copper, and +also that they are so opake as not to suffer the Particles of Gold or +Copper to shine through them. Now it is scarce to be doubted but that +the Colours of Gold and Copper are of the second and third order, and +therefore the Particles of white Metals cannot be much bigger than is +requisite to make them reflect the white of the first order. The +Volatility of Mercury argues that they are not much bigger, nor may they +be much less, lest they lose their Opacity, and become either +transparent as they do when attenuated by Vitrification, or by Solution +in Menstruums, or black as they do when ground smaller, by rubbing +Silver, or Tin, or Lead, upon other Substances to draw black Lines. The +first and only Colour which white Metals take by grinding their +Particles smaller, is black, and therefore their white ought to be that +which 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 gather +the Bigness of metallick Particles, you must allow for their Density. +For were Mercury transparent, its Density is such that the Sine of +Incidence upon it (by my Computation) would be to the Sine of its +Refraction, as 71 to 20, or 7 to 2. And therefore the Thickness of its +Particles, that they may exhibit the same Colours with those of Bubbles +of Water, ought to be less than the Thickness of the Skin of those +Bubbles in the Proportion of 2 to 7. Whence it's possible, that the +Particles of Mercury may be as little as the Particles of some +transparent and volatile Fluids, and yet reflect the white of the first +order. + +Lastly, for the production of _black_, the Corpuscles must be less than +any of those which exhibit Colours. For at all greater sizes there is +too much Light reflected to constitute this Colour. But if they be +supposed a little less than is requisite to reflect the white and very +faint blue of the first order, they will, according to the 4th, 8th, +17th and 18th Observations, reflect so very little Light as to appear +intensely black, and yet may perhaps variously refract it to and fro +within themselves so long, until it happen to be stifled and lost, by +which means they will appear black in all positions of the Eye without +any transparency. And from hence may be understood why Fire, and the +more subtile dissolver Putrefaction, by dividing the Particles of +Substances, turn them to black, why small quantities of black Substances +impart their Colour very freely and intensely to other Substances to +which they are applied; the minute Particles of these, by reason of +their very great number, easily overspreading the gross Particles of +others; why Glass ground very elaborately with Sand on a Copper Plate, +'till it be well polish'd, makes the Sand, together with what is worn +off from the Glass and Copper, become very black: why black Substances +do soonest of all others become hot in the Sun's Light and burn, (which +Effect may proceed partly from the multitude of Refractions in a little +room, and partly from the easy Commotion of so very small Corpuscles;) +and why blacks are usually a little inclined to a bluish Colour. For +that they are so may be seen by illuminating white Paper by Light +reflected from black Substances. For the Paper will usually appear of a +bluish white; and the reason is, that black borders in the obscure blue +of the order described in the 18th Observation, and therefore reflects +more Rays of that Colour than of any other. + +In these Descriptions I have been the more particular, because it is not +impossible but that Microscopes may at length be improved to the +discovery of the Particles of Bodies on which their Colours depend, if +they are not already in some measure arrived to that degree of +perfection. For if those Instruments are or can be so far improved as +with sufficient distinctness to represent Objects five or six hundred +times bigger than at a Foot distance they appear to our naked Eyes, I +should hope that we might be able to discover some of the greatest of +those Corpuscles. And by one that would magnify three or four thousand +times perhaps they might all be discover'd, but those which produce +blackness. In the mean while I see nothing material in this Discourse +that may rationally be doubted of, excepting this Position: That +transparent Corpuscles of the same thickness and density with a Plate, +do exhibit the same Colour. And this I would have understood not without +some Latitude, as well because those Corpuscles may be of irregular +Figures, and many Rays must be obliquely incident on them, and so have +a shorter way through them than the length of their Diameters, as +because the straitness of the Medium put in on all sides within such +Corpuscles may a little alter its Motions or other qualities on which +the Reflexion depends. But yet I cannot much suspect the last, because I +have observed of some small Plates of Muscovy Glass which were of an +even thickness, that through a Microscope they have appeared of the same +Colour at their edges and corners where the included Medium was +terminated, which they appeared of in other places. However it will add +much to our Satisfaction, if those Corpuscles can be discover'd with +Microscopes; which if we shall at length attain to, I fear it will be +the utmost improvement of this Sense. For it seems impossible to see the +more secret and noble Works of Nature within the Corpuscles by reason of +their transparency. + + +PROP. VIII. + +_The Cause of Reflexion is not the impinging of Light on the solid or +impervious parts of Bodies, as is commonly believed._ + +This will appear by the following Considerations. First, That in the +passage of Light out of Glass into Air there is a Reflexion as strong as +in its passage out of Air into Glass, or rather a little stronger, and +by many degrees stronger than in its passage out of Glass into Water. +And it seems not probable that Air should have more strongly reflecting +parts than Water or Glass. But if that should possibly be supposed, yet +it will avail nothing; for the Reflexion is as strong or stronger when +the Air is drawn away from the Glass, (suppose by the Air-Pump invented +by _Otto Gueriet_, and improved and made useful by Mr. _Boyle_) as when +it is adjacent to it. Secondly, If Light in its passage out of Glass +into Air be incident more obliquely than at an Angle of 40 or 41 Degrees +it is wholly reflected, if less obliquely it is in great measure +transmitted. Now it is not to be imagined that Light at one degree of +obliquity should meet with Pores enough in the Air to transmit the +greater part of it, and at another degree of obliquity should meet with +nothing but parts to reflect it wholly, especially considering that in +its 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. If +any Man suppose that it is not reflected by the Air, but by the outmost +superficial parts of the Glass, there is still the same difficulty: +Besides, that such a Supposition is unintelligible, and will also appear +to be false by applying Water behind some part of the Glass instead of +Air. For so in a convenient obliquity of the Rays, suppose of 45 or 46 +Degrees, at which they are all reflected where the Air is adjacent to +the Glass, they shall be in great measure transmitted where the Water is +adjacent to it; which argues, that their Reflexion or Transmission +depends on the constitution of the Air and Water behind the Glass, and +not on the striking of the Rays upon the parts of the Glass. Thirdly, +If the Colours made by a Prism placed at the entrance of a Beam of Light +into a darken'd Room be successively cast on a second Prism placed at a +greater distance from the former, in such manner that they are all alike +incident upon it, the second Prism may be so inclined to the incident +Rays, that those which are of a blue Colour shall be all reflected by +it, and yet those of a red Colour pretty copiously transmitted. Now if +the Reflexion be caused by the parts of Air or Glass, I would ask, why +at the same Obliquity of Incidence the blue should wholly impinge on +those parts, so as to be all reflected, and yet the red find Pores +enough to be in a great measure transmitted. Fourthly, Where two Glasses +touch one another, there is no sensible Reflexion, as was declared in +the first Observation; and yet I see no reason why the Rays should not +impinge on the parts of Glass, as much when contiguous to other Glass as +when contiguous to Air. Fifthly, When the top of a Water-Bubble (in the +17th Observation,) by the continual subsiding and exhaling of the Water +grew very thin, there was such a little and almost insensible quantity +of Light reflected from it, that it appeared intensely black; whereas +round about that black Spot, where the Water was thicker, the Reflexion +was so strong as to make the Water seem very white. Nor is it only at +the least thickness of thin Plates or Bubbles, that there is no manifest +Reflexion, but at many other thicknesses continually greater and +greater. For in the 15th Observation the Rays of the same Colour were by +turns transmitted at one thickness, and reflected at another thickness, +for an indeterminate number of Successions. And yet in the Superficies +of the thinned Body, where it is of any one thickness, there are as many +parts 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, it +would be impossible for thin Plates or Bubbles, at one and the same +place, 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 to +be imagined that at one place the Rays which, for instance, exhibit a +blue Colour, should have the fortune to dash upon the parts, and those +which exhibit a red to hit upon the Pores of the Body; and then at +another place, where the Body is either a little thicker or a little +thinner, that on the contrary the blue should hit upon its pores, and +the red upon its parts. Lastly, Were the Rays of Light reflected by +impinging on the solid parts of Bodies, their Reflexions from polish'd +Bodies could not be so regular as they are. For in polishing Glass with +Sand, Putty, or Tripoly, it is not to be imagined that those Substances +can, by grating and fretting the Glass, bring all its least Particles to +an accurate Polish; so that all their Surfaces shall be truly plain or +truly spherical, and look all the same way, so as together to compose +one even Surface. The smaller the Particles of those Substances are, the +smaller will be the Scratches by which they continually fret and wear +away the Glass until it be polish'd; but be they never so small they can +wear away the Glass no otherwise than by grating and scratching it, and +breaking the Protuberances; and therefore polish it no otherwise than by +bringing its roughness to a very fine Grain, so that the Scratches and +Frettings of the Surface become too small to be visible. And therefore +if 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 the +roughest. So then it remains a Problem, how Glass polish'd by fretting +Substances can reflect Light so regularly as it does. And this Problem +is scarce otherwise to be solved, than by saying, that the Reflexion of +a Ray is effected, not by a single point of the reflecting Body, but by +some power of the Body which is evenly diffused all over its Surface, +and by which it acts upon the Ray without immediate Contact. For that +the parts of Bodies do act upon Light at a distance shall be shewn +hereafter. + +Now if Light be reflected, not by impinging on the solid parts of +Bodies, but by some other principle; it's probable that as many of its +Rays as impinge on the solid parts of Bodies are not reflected but +stifled and lost in the Bodies. For otherwise we must allow two sorts of +Reflexions. Should all the Rays be reflected which impinge on the +internal parts of clear Water or Crystal, those Substances would rather +have a cloudy Colour than a clear Transparency. To make Bodies look +black, it's necessary that many Rays be stopp'd, retained, and lost in +them; and it seems not probable that any Rays can be stopp'd and +stifled in them which do not impinge on their parts. + +And hence we may understand that Bodies are much more rare and porous +than is commonly believed. Water is nineteen times lighter, and by +consequence nineteen times rarer than Gold; and Gold is so rare as very +readily and without the least opposition to transmit the magnetick +Effluvia, and easily to admit Quicksilver into its Pores, and to let +Water pass through it. For a concave Sphere of Gold filled with Water, +and solder'd up, has, upon pressing the Sphere with great force, let the +Water squeeze through it, and stand all over its outside in multitudes +of small Drops, like Dew, without bursting or cracking the Body of the +Gold, as I have been inform'd by an Eye witness. From all which we may +conclude, that Gold has more Pores than solid parts, and by consequence +that Water has above forty times more Pores than Parts. And he that +shall find out an Hypothesis, by which Water may be so rare, and yet not +be capable of compression by force, may doubtless by the same Hypothesis +make Gold, and Water, and all other Bodies, as much rarer as he pleases; +so that Light may find a ready passage through transparent Substances. + +The Magnet acts upon Iron through all dense Bodies not magnetick nor red +hot, without any diminution of its Virtue; as for instance, through +Gold, Silver, Lead, Glass, Water. The gravitating Power of the Sun is +transmitted through the vast Bodies of the Planets without any +diminution, so as to act upon all their parts to their very centers +with the same Force and according to the same Laws, as if the part upon +which it acts were not surrounded with the Body of the Planet, The Rays +of Light, whether they be very small Bodies projected, or only Motion or +Force propagated, are moved in right Lines; and whenever a Ray of Light +is by any Obstacle turned out of its rectilinear way, it will never +return into the same rectilinear way, unless perhaps by very great +accident. And yet Light is transmitted through pellucid solid Bodies in +right Lines to very great distances. How Bodies can have a sufficient +quantity of Pores for producing these Effects is very difficult to +conceive, but perhaps not altogether impossible. For the Colours of +Bodies arise from the Magnitudes of the Particles which reflect them, as +was explained above. Now if we conceive these Particles of Bodies to be +so disposed amongst themselves, that the Intervals or empty Spaces +between them may be equal in magnitude to them all; and that these +Particles may be composed of other Particles much smaller, which have as +much empty Space between them as equals all the Magnitudes of these +smaller Particles: And that in like manner these smaller Particles are +again composed of others much smaller, all which together are equal to +all the Pores or empty Spaces between them; and so on perpetually till +you come to solid Particles, such as have no Pores or empty Spaces +within them: And if in any gross Body there be, for instance, three such +degrees of Particles, the least of which are solid; this Body will have +seven times more Pores than solid Parts. But if there be four such +degrees of Particles, the least of which are solid, the Body will have +fifteen times more Pores than solid Parts. If there be five degrees, the +Body will have one and thirty times more Pores than solid Parts. If six +degrees, the Body will have sixty and three times more Pores than solid +Parts. And so on perpetually. And there are other ways of conceiving how +Bodies may be exceeding porous. But what is really their inward Frame is +not yet known to us. + + +PROP. IX. + +_Bodies reflect and refract Light by one and the same power, variously +exercised in various Circumstances._ + +This appears by several Considerations. First, Because when Light goes +out of Glass into Air, as obliquely as it can possibly do. If its +Incidence be made still more oblique, it becomes totally reflected. For +the power of the Glass after it has refracted the Light as obliquely as +is possible, if the Incidence be still made more oblique, becomes too +strong to let any of its Rays go through, and by consequence causes +total Reflexions. Secondly, Because Light is alternately reflected and +transmitted by thin Plates of Glass for many Successions, accordingly as +the thickness of the Plate increases in an arithmetical Progression. For +here the thickness of the Glass determines whether that Power by which +Glass acts upon Light shall cause it to be reflected, or suffer it to +be transmitted. And, Thirdly, because those Surfaces of transparent +Bodies which have the greatest refracting power, reflect the greatest +quantity of Light, as was shewn in the first Proposition. + + +PROP. X. + +_If Light be swifter in Bodies than in Vacuo, in the proportion of the +Sines which measure the Refraction of the Bodies, the Forces of the +Bodies to reflect and refract Light, are very nearly proportional to the +densities of the same Bodies; excepting that unctuous and sulphureous +Bodies refract more than others of this same density._ + +[Illustration: FIG. 8.] + +Let AB represent the refracting plane Surface of any Body, and IC a Ray +incident very obliquely upon the Body in C, so that the Angle ACI may be +infinitely little, and let CR be the refracted Ray. From a given Point B +perpendicular to the refracting Surface erect BR meeting with the +refracting Ray CR in R, and if CR represent the Motion of the refracted +Ray, and this Motion be distinguish'd into two Motions CB and BR, +whereof CB is parallel to the refracting Plane, and BR perpendicular to +it: CB shall represent the Motion of the incident Ray, and BR the +Motion generated by the Refraction, as Opticians have of late explain'd. + +Now if any Body or Thing, in moving through any Space of a given breadth +terminated on both sides by two parallel Planes, be urged forward in all +parts of that Space by Forces tending directly forwards towards the last +Plane, and before its Incidence on the first Plane, had no Motion +towards it, or but an infinitely little one; and if the Forces in all +parts of that Space, between the Planes, be at equal distances from the +Planes equal to one another, but at several distances be bigger or less +in any given Proportion, the Motion generated by the Forces in the whole +passage of the Body or thing through that Space shall be in a +subduplicate Proportion of the Forces, as Mathematicians will easily +understand. And therefore, if the Space of activity of the refracting +Superficies of the Body be consider'd as such a Space, the Motion of the +Ray generated by the refracting Force of the Body, during its passage +through that Space, that is, the Motion BR, must be in subduplicate +Proportion of that refracting Force. I say therefore, that the Square of +the Line BR, and by consequence the refracting Force of the Body, is +very nearly as the density of the same Body. For this will appear by the +following Table, wherein the Proportion of the Sines which measure the +Refractions of several Bodies, the Square of BR, supposing CB an unite, +the Densities of the Bodies estimated by their Specifick Gravities, and +their Refractive Power in respect of their Densities are set down in +several Columns. + +---------------------+----------------+----------------+----------+----------- + | | | | + | | The Square | The | The + | | of BR, to | density | refractive + | The Proportion | which the | and | Power of + | of the Sines of| refracting | specifick| the Body + | Incidence and | force of the | gravity | in respect + The refracting | Refraction of | Body is | of the | of its + Bodies. | yellow Light. | proportionate. | Body. | density. +---------------------+----------------+----------------+----------+----------- +A Pseudo-Topazius, | | | | + being a natural, | | | | + pellucid, brittle, | 23 to 14 | 1'699 | 4'27 | 3979 + hairy Stone, of a | | | | + yellow Colour. | | | | +Air. | 3201 to 3200 | 0'000625 | 0'0012 | 5208 +Glass of Antimony. | 17 to 9 | 2'568 | 5'28 | 4864 +A Selenitis. | 61 to 41 | 1'213 | 2'252 | 5386 +Glass vulgar. | 31 to 20 | 1'4025 | 2'58 | 5436 +Crystal of the Rock. | 25 to 16 | 1'445 | 2'65 | 5450 +Island Crystal. | 5 to 3 | 1'778 | 2'72 | 6536 +Sal 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 by that of the +Atmosphere observed by Astronomers. For, if Light pass through many +refracting Substances or Mediums gradually denser and denser, and +terminated with parallel Surfaces, the Sum of all the Refractions will +be equal to the single Refraction which it would have suffer'd in +passing immediately out of the first Medium into the last. And this +holds true, though the Number of the refracting Substances be increased +to Infinity, and the Distances from one another as much decreased, so +that the Light may be refracted in every Point of its Passage, and by +continual Refractions bent into a Curve-Line. And therefore the whole +Refraction of Light in passing through the Atmosphere from the highest +and rarest Part thereof down to the lowest and densest Part, must be +equal to the Refraction which it would suffer in passing at like +Obliquity out of a Vacuum immediately into Air of equal Density with +that in the lowest Part of the Atmosphere. + +Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal, +Vulgar Glass (that is, Sand melted together) and Glass of Antimony, +which are terrestrial stony alcalizate Concretes, and Air which probably +arises from such Substances by Fermentation, be Substances very +differing from one another in Density, yet by this Table, they have +their refractive Powers almost in the same Proportion to one another as +their Densities are, excepting that the Refraction of that strange +Substance, Island Crystal is a little bigger than the rest. And +particularly Air, which is 3500 Times rarer than the Pseudo-Topaz, and +4400 Times rarer than Glass of Antimony, and 2000 Times rarer than the +Selenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding its +rarity the same refractive Power in respect of its Density which those +very dense Substances have in respect of theirs, excepting so far as +those differ from one another. + +Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit of +Turpentine and Amber, which are fat sulphureous unctuous Bodies, and a +Diamond, which probably is an unctuous Substance coagulated, have their +refractive Powers in Proportion to one another as their Densities +without any considerable Variation. But the refractive Powers of these +unctuous Substances are two or three Times greater in respect of their +Densities than the refractive Powers of the former Substances in respect +of theirs. + +Water has a refractive Power in a middle degree between those two sorts +of Substances, and probably is of a middle nature. For out of it grow +all vegetable and animal Substances, which consist as well of +sulphureous fat and inflamable Parts, as of earthy lean and alcalizate +ones. + +Salts and Vitriols have refractive Powers in a middle degree between +those of earthy Substances and Water, and accordingly are composed of +those two sorts of Substances. For by distillation and rectification of +their Spirits a great Part of them goes into Water, and a great Part +remains behind in the form of a dry fix'd Earth capable of +Vitrification. + +Spirit of Wine has a refractive Power in a middle degree between those +of Water and oily Substances, and accordingly seems to be composed of +both, united by Fermentation; the Water, by means of some saline Spirits +with which 'tis impregnated, dissolving the Oil, and volatizing it by +the Action. For Spirit of Wine is inflamable by means of its oily Parts, +and being distilled often from Salt of Tartar, grow by every +distillation more and more aqueous and phlegmatick. And Chymists +observe, that Vegetables (as Lavender, Rue, Marjoram, &c.) distilled +_per se_, before fermentation yield Oils without any burning Spirits, +but after fermentation yield ardent Spirits without Oils: Which shews, +that their Oil is by fermentation converted into Spirit. They find also, +that if Oils be poured in a small quantity upon fermentating Vegetables, +they distil over after fermentation in the form of Spirits. + +So then, by the foregoing Table, all Bodies seem to have their +refractive Powers proportional to their Densities, (or very nearly;) +excepting so far as they partake more or less of sulphureous oily +Particles, and thereby have their refractive Power made greater or less. +Whence it seems rational to attribute the refractive Power of all Bodies +chiefly, if not wholly, to the sulphureous Parts with which they abound. +For it's probable that all Bodies abound more or less with Sulphurs. And +as Light congregated by a Burning-glass acts most upon sulphureous +Bodies, to turn them into Fire and Flame; so, since all Action is +mutual, Sulphurs ought to act most upon Light. For that the action +between Light and Bodies is mutual, may appear from this Consideration; +That the densest Bodies which refract and reflect Light most strongly, +grow hottest in the Summer Sun, by the action of the refracted or +reflected Light. + +I have hitherto explain'd the power of Bodies to reflect and refract, +and shew'd, that thin transparent Plates, Fibres, and Particles, do, +according to their several thicknesses and densities, reflect several +sorts of Rays, and thereby appear of several Colours; and by consequence +that nothing more is requisite for producing all the Colours of natural +Bodies, than the several sizes and densities of their transparent +Particles. But whence it is that these Plates, Fibres, and Particles, +do, according to their several thicknesses and densities, reflect +several sorts of Rays, I have not yet explain'd. To give some insight +into this matter, and make way for understanding the next part of this +Book, I shall conclude this part with a few more Propositions. Those +which preceded respect the nature of Bodies, these the nature of Light: +For both must be understood, before the reason of their Actions upon one +another can be known. And because the last Proposition depended upon the +velocity of Light, I will begin with a Proposition of that kind. + + +PROP. XI. + +_Light is propagated from luminous Bodies in time, and spends about +seven or eight Minutes of an Hour in passing from the Sun to the Earth._ + +This was observed first by _Roemer_, and then by others, by means of the +Eclipses of the Satellites of _Jupiter_. For these Eclipses, when the +Earth is between the Sun and _Jupiter_, happen about seven or eight +Minutes sooner than they ought to do by the Tables, and when the Earth +is beyond the Sun they happen about seven or eight Minutes later than +they ought to do; the reason being, that the Light of the Satellites has +farther to go in the latter case than in the former by the Diameter of +the Earth's Orbit. Some inequalities of time may arise from the +Excentricities of the Orbs of the Satellites; but those cannot answer in +all the Satellites, and at all times to the Position and Distance of the +Earth from the Sun. The mean motions of _Jupiter_'s Satellites is also +swifter in his descent from his Aphelium to his Perihelium, than in his +ascent in the other half of his Orb. But this inequality has no respect +to the position of the Earth, and in the three interior Satellites is +insensible, as I find by computation from the Theory of their Gravity. + + +PROP. XII. + +_Every Ray of Light in its passage through any refracting Surface is put +into a certain transient Constitution or State, which in the progress of +the Ray returns at equal Intervals, and disposes the Ray at every return +to be easily transmitted through the next refracting Surface, and +between the returns to be easily reflected by it._ + +This is manifest by the 5th, 9th, 12th, and 15th Observations. For by +those Observations it appears, that one and the same sort of Rays at +equal Angles of Incidence on any thin transparent Plate, is alternately +reflected and transmitted for many Successions accordingly as the +thickness of the Plate increases in arithmetical Progression of the +Numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, &c. so that if the first Reflexion +(that which makes the first or innermost of the Rings of Colours there +described) be made at the thickness 1, the Rays shall be transmitted at +the thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the central +Spot and Rings of Light, which appear by transmission, and be reflected +at the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings which +appear by Reflexion. And this alternate Reflexion and Transmission, as I +gather by the 24th Observation, continues for above an hundred +vicissitudes, and by the Observations in the next part of this Book, for +many thousands, being propagated from one Surface of a Glass Plate to +the other, though the thickness of the Plate be a quarter of an Inch or +above: So that this alternation seems to be propagated from every +refracting Surface to all distances without end or limitation. + +This alternate Reflexion and Refraction depends on both the Surfaces of +every thin Plate, because it depends on their distance. By the 21st +Observation, if either Surface of a thin Plate of _Muscovy_ Glass be +wetted, the Colours caused by the alternate Reflexion and Refraction +grow faint, and therefore it depends on them both. + +It is therefore perform'd at the second Surface; for if it were +perform'd at the first, before the Rays arrive at the second, it would +not depend on the second. + +It is also influenced by some action or disposition, propagated from the +first to the second, because otherwise at the second it would not depend +on the first. And this action or disposition, in its propagation, +intermits and returns by equal Intervals, because in all its progress it +inclines the Ray at one distance from the first Surface to be reflected +by the second, at another to be transmitted by it, and that by equal +Intervals for innumerable vicissitudes. And because the Ray is disposed +to Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission at +the distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through the +first Surface, is at the distance 0, and it is transmitted through both +together, if their distance be infinitely little or much less than 1) +the disposition to be transmitted at the distances 2, 4, 6, 8, 10, &c. +is to be accounted a return of the same disposition which the Ray first +had at the distance 0, that is at its transmission through the first +refracting Surface. All which is the thing I would prove. + +What kind of action or disposition this is; Whether it consists in a +circulating or a vibrating motion of the Ray, or of the Medium, or +something else, I do not here enquire. Those that are averse from +assenting to any new Discoveries, but such as they can explain by an +Hypothesis, may for the present suppose, that as Stones by falling upon +Water put the Water into an undulating Motion, and all Bodies by +percussion excite vibrations in the Air; so the Rays of Light, by +impinging on any refracting or reflecting Surface, excite vibrations in +the refracting or reflecting Medium or Substance, and by exciting them +agitate the solid parts of the refracting or reflecting Body, and by +agitating them cause the Body to grow warm or hot; that the vibrations +thus excited are propagated in the refracting or reflecting Medium or +Substance, much after the manner that vibrations are propagated in the +Air for causing Sound, and move faster than the Rays so as to overtake +them; and that when any Ray is in that part of the vibration which +conspires with its Motion, it easily breaks through a refracting +Surface, but when it is in the contrary part of the vibration which +impedes its Motion, it is easily reflected; and, by consequence, that +every Ray is successively disposed to be easily reflected, or easily +transmitted, by every vibration which overtakes it. But whether this +Hypothesis be true or false I do not here consider. I content my self +with the bare Discovery, that the Rays of Light are by some cause or +other alternately disposed to be reflected or refracted for many +vicissitudes. + + +DEFINITION. + +_The returns of the disposition of any Ray to be reflected I will call +its_ Fits of easy Reflexion, _and those of its disposition to be +transmitted its_ Fits of easy Transmission, _and the space it passes +between every return and the next return, the_ Interval of its Fits. + + +PROP. XIII. + +_The reason why the Surfaces of all thick transparent Bodies reflect +part of the Light incident on them, and refract the rest, is, that some +Rays at their Incidence are in Fits of easy Reflexion, and others in +Fits of easy Transmission._ + +This may be gather'd from the 24th Observation, where the Light +reflected by thin Plates of Air and Glass, which to the naked Eye +appear'd evenly white all over the Plate, did through a Prism appear +waved with many Successions of Light and Darkness made by alternate Fits +of easy Reflexion and easy Transmission, the Prism severing and +distinguishing the Waves of which the white reflected Light was +composed, as was explain'd above. + +And hence Light is in Fits of easy Reflexion and easy Transmission, +before its Incidence on transparent Bodies. And probably it is put into +such fits at its first emission from luminous Bodies, and continues in +them during all its progress. For these Fits are of a lasting nature, as +will appear by the next part of this Book. + +In this Proposition I suppose the transparent Bodies to be thick; +because if the thickness of the Body be much less than the Interval of +the Fits of easy Reflexion and Transmission of the Rays, the Body loseth +its reflecting power. For if the Rays, which at their entering into the +Body are put into Fits of easy Transmission, arrive at the farthest +Surface of the Body before they be out of those Fits, they must be +transmitted. And this is the reason why Bubbles of Water lose their +reflecting power when they grow very thin; and why all opake Bodies, +when reduced into very small parts, become transparent. + + +PROP. XIV. + +_Those Surfaces of transparent Bodies, which if the Ray be in a Fit of +Refraction do refract it most strongly, if the Ray be in a Fit of +Reflexion do reflect it most easily._ + +For we shewed above, in _Prop._ 8. that the cause of Reflexion is not +the impinging of Light on the solid impervious parts of Bodies, but some +other power by which those solid parts act on Light at a distance. We +shewed also in _Prop._ 9. that Bodies reflect and refract Light by one +and the same power, variously exercised in various circumstances; and in +_Prop._ 1. that the most strongly refracting Surfaces reflect the most +Light: All which compared together evince and rarify both this and the +last Proposition. + + +PROP. XV. + +_In any one and the same sort of Rays, emerging in any Angle out of any +refracting Surface into one and the same Medium, the Interval of the +following Fits of easy Reflexion and Transmission are either accurately +or very nearly, as the Rectangle of the Secant of the Angle of +Refraction, and of the Secant of another Angle, whose Sine is the first +of 106 arithmetical mean Proportionals, between the Sines of Incidence +and Refraction, counted from the Sine of Refraction._ + +This is manifest by the 7th and 19th Observations. + + +PROP. XVI. + +_In several sorts of Rays emerging in equal Angles out of any refracting +Surface into the same Medium, the Intervals of the following Fits of +easy Reflexion and easy Transmission are either accurately, or very +nearly, as the Cube-Roots of the Squares of the lengths of a Chord, +which found the Notes in an Eight_, sol, la, fa, sol, la, mi, fa, sol, +_with all their intermediate degrees answering to the Colours of those +Rays, according to the Analogy described in the seventh Experiment of +the second Part of the first Book._ + +This is manifest by the 13th and 14th Observations. + + +PROP. XVII. + +_If Rays of any sort pass perpendicularly into several Mediums, the +Intervals of the Fits of easy Reflexion and Transmission in any one +Medium, are to those Intervals in any other, as the Sine of Incidence to +the Sine of Refraction, when the Rays pass out of the first of those two +Mediums into the second._ + +This is manifest by the 10th Observation. + + +PROP. XVIII. + +_If the Rays which paint the Colour in the Confine of yellow and orange +pass perpendicularly out of any Medium into Air, the Intervals of their +Fits of easy Reflexion are the 1/89000th part of an Inch. And of the +same length are the Intervals of their Fits of easy Transmission._ + +This is manifest by the 6th Observation. From these Propositions it is +easy to collect the Intervals of the Fits of easy Reflexion and easy +Transmission of any sort of Rays refracted in any angle into any Medium; +and thence to know, whether the Rays shall be reflected or transmitted +at their subsequent Incidence upon any other pellucid Medium. Which +thing, being useful for understanding the next part of this Book, was +here to be set down. And for the same reason I add the two following +Propositions. + + +PROP. XIX. + +_If any sort of Rays falling on the polite Surface of any pellucid +Medium be reflected back, the Fits of easy Reflexion, which they have at +the point of Reflexion, shall still continue to return; and the Returns +shall be at distances from the point of Reflexion in the arithmetical +progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these +Fits the Rays shall be in Fits of easy Transmission._ + +For since the Fits of easy Reflexion and easy Transmission are of a +returning nature, there is no reason why these Fits, which continued +till the Ray arrived at the reflecting Medium, and there inclined the +Ray to Reflexion, should there cease. And if the Ray at the point of +Reflexion was in a Fit of easy Reflexion, the progression of the +distances of these Fits from that point must begin from 0, and so be of +the Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of the +distances of the intermediate Fits of easy Transmission, reckon'd from +the 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 from +points of Refraction. + + +PROP. XX. + +_The Intervals of the Fits of easy Reflexion and easy Transmission, +propagated from points of Reflexion into any Medium, are equal to the +Intervals of the like Fits, which the same Rays would have, if refracted +into the same Medium in Angles of Refraction equal to their Angles of +Reflexion._ + +For when Light is reflected by the second Surface of thin Plates, it +goes out afterwards freely at the first Surface to make the Rings of +Colours which appear by Reflexion; and, by the freedom of its egress, +makes the Colours of these Rings more vivid and strong than those which +appear on the other side of the Plates by the transmitted Light. The +reflected Rays are therefore in Fits of easy Transmission at their +egress; which would not always happen, if the Intervals of the Fits +within the Plate after Reflexion were not equal, both in length and +number, to their Intervals before it. And this confirms also the +proportions set down in the former Proposition. For if the Rays both in +going 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 second +Surface, before and after Reflexion, be equal, the distances of the Fits +of easy Transmission from either Surface, must be in the same +progression after Reflexion as before; that is, from the first Surface +which transmitted them in the progression of the even Numbers 0, 2, 4, +6, 8, &c. and from the second which reflected them, in that of the odd +Numbers 1, 3, 5, 7, &c. But these two Propositions will become much more +evident by the Observations in the following part of this Book. + + + + +THE + +SECOND BOOK + +OF + +OPTICKS + + +_PART IV._ + +_Observations concerning the Reflexions and Colours of thick transparent +polish'd Plates._ + +There is no Glass or Speculum how well soever polished, but, besides the +Light which it refracts or reflects regularly, scatters every way +irregularly a faint Light, by means of which the polish'd Surface, when +illuminated in a dark room by a beam of the Sun's Light, may be easily +seen in all positions of the Eye. There are certain Phænomena of this +scatter'd Light, which when I first observed them, seem'd very strange +and surprizing to me. My Observations were as follows. + +_Obs._ 1. The Sun shining into my darken'd Chamber through a hole one +third of an Inch wide, I let the intromitted beam of Light fall +perpendicularly upon a Glass Speculum ground concave on one side and +convex 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 opake +Chart, or a Quire of Paper at the center of the Spheres to which the +Speculum was ground, that is, at the distance of about five Feet and +eleven Inches from the Speculum, in such manner, that the beam of Light +might pass through a little hole made in the middle of the Chart to the +Speculum, and thence be reflected back to the same hole: I observed upon +the Chart four or five concentric Irises or Rings of Colours, like +Rain-bows, encompassing the hole much after the manner that those, which +in the fourth and following Observations of the first part of this Book +appear'd between the Object-glasses, encompassed the black Spot, but yet +larger and fainter than those. These Rings as they grew larger and +larger became diluter and fainter, so that the fifth was scarce visible. +Yet sometimes, when the Sun shone very clear, there appear'd faint +Lineaments of a sixth and seventh. If the distance of the Chart from the +Speculum was much greater or much less than that of six Feet, the Rings +became dilute and vanish'd. And if the distance of the Speculum from the +Window was much greater than that of six Feet, the reflected beam of +Light would be so broad at the distance of six Feet from the Speculum +where the Rings appear'd, as to obscure one or two of the innermost +Rings. And therefore I usually placed the Speculum at about six Feet +from the Window; so that its Focus might there fall in with the center +of its concavity at the Rings upon the Chart. And this Posture is always +to be understood in the following Observations where no other is +express'd. + +_Obs._ 2. The Colours of these Rain-bows succeeded one another from the +center outwards, in the same form and order with those which were made +in the ninth Observation of the first Part of this Book by Light not +reflected, 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 sometimes +fell upon the middle of the Spot, and sometimes by a little inclination +of the Speculum receded from the middle, and left the Spot white to the +center. + +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 on +the inside next the dark grey were a little violet and indigo, and next +to that a blue, which on the outside grew pale, and then succeeded a +little greenish yellow, and after that a brighter yellow, and then on +the outward edge of the Iris a red which on the outside inclined to +purple. + +This Iris was immediately encompassed with a second, whose Colours were +in order from the inside outwards, purple, blue, green, yellow, light +red, a red mix'd with purple. + +Then immediately follow'd the Colours of the third Iris, which were in +order outwards a green inclining to purple, a good green, and a red more +bright than that of the former Iris. + +The fourth and fifth Iris seem'd of a bluish green within, and red +without, but so faintly that it was difficult to discern the Colours. + +_Obs._ 3. Measuring the Diameters of these Rings upon the Chart as +accurately as I could, I found them also in the same proportion to one +another with the Rings made by Light transmitted through the two +Object-glasses. For the Diameters of the four first of the bright Rings +measured between the brightest parts of their Orbits, at the distance of +six 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 put +equipollent to an infinitely little Ring; the Squares of the Diameters +of the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measured +also the Diameters of the dark Circles between these luminous ones, and +found 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 Feet +from the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If the +distance of the Chart from the Speculum was increased or diminished, the +Diameters of the Circles were increased or diminished proportionally. + +_Obs._ 4. By the analogy between these Rings and those described in the +Observations of the first Part of this Book, I suspected that there +were many more of them which spread into one another, and by interfering +mix'd their Colours, and diluted one another so that they could not be +seen apart. I viewed them therefore through a Prism, as I did those in +the 24th Observation of the first Part of this Book. And when the Prism +was so placed as by refracting the Light of their mix'd Colours to +separate them, and distinguish the Rings from one another, as it did +those in that Observation, I could then see them distincter than before, +and easily number eight or nine of them, and sometimes twelve or +thirteen. And had not their Light been so very faint, I question not but +that I might have seen many more. + +_Obs._ 5. Placing a Prism at the Window to refract the intromitted beam +of Light, and cast the oblong Spectrum of Colours on the Speculum: I +covered the Speculum with a black Paper which had in the middle of it a +hole to let any one of the Colours pass through to the Speculum, whilst +the rest were intercepted by the Paper. And now I found Rings of that +Colour only which fell upon the Speculum. If the Speculum was +illuminated with red, the Rings were totally red with dark Intervals, if +with blue they were totally blue, and so of the other Colours. And when +they were illuminated with any one Colour, the Squares of their +Diameters measured between their most luminous Parts, were in the +arithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squares +of the Diameters of their dark Intervals in the Progression of the +intermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2. But if the Colour was +varied, they varied their Magnitude. In the red they were largest, in +the indigo and violet least, and in the intermediate Colours yellow, +green, and blue, they were of several intermediate Bignesses answering +to the Colour, that is, greater in yellow than in green, and greater in +green than in blue. And hence I knew, that when the Speculum was +illuminated with white Light, the red and yellow on the outside of the +Rings were produced by the least refrangible Rays, and the blue and +violet by the most refrangible, and that the Colours of each Ring spread +into the Colours of the neighbouring Rings on either side, after the +manner explain'd in the first and second Part of this Book, and by +mixing diluted one another so that they could not be distinguish'd, +unless near the Center where they were least mix'd. For in this +Observation I could see the Rings more distinctly, and to a greater +Number than before, being able in the yellow Light to number eight or +nine of them, besides a faint shadow of a tenth. To satisfy my self how +much the Colours of the several Rings spread into one another, I +measured the Diameters of the second and third Rings, and found them +when made by the Confine of the red and orange to be to the same +Diameters when made by the Confine of blue and indigo, as 9 to 8, or +thereabouts. 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 the +green, blue, and indigo. For the Circle made by the violet was too dark +to be seen. To carry on the Computation, let us therefore suppose that +the Differences of the Diameters of the Circles made by the outmost red, +the Confine of red and orange, the Confine of orange and yellow, the +Confine of yellow and green, the Confine of green and blue, the Confine +of blue and indigo, the Confine of indigo and violet, and outmost +violet, are in proportion as the Differences of the Lengths of a +Monochord 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 Confine +of red and orange be 9A, and that of the Circle made by the Confine of +blue and indigo be 8A as above; their difference 9A-8A will be to the +difference of the Diameters of the Circles made by the outmost red, and +by 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 Circles +made by the outmost violet, and by the Confine of blue and indigo, as +1/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, or +as 16 to 5. And therefore these differences will be 3/8A and 5/16A. Add +the first to 9A and subduct the last from 8A, and you will have the +Diameters of the Circles made by the least and most refrangible Rays +75/8A and ((61-1/2)/8)A. These diameters are therefore to one another as +75 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as +3 to 2 very nearly. Which proportion differs not much from the +proportion of the Diameters of the Circles made by the outmost red and +outmost 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 the +Speculum tinged all over with Waves of Colours, (red, yellow, green, +blue;) like those which in the Observations of the first part of this +Book appeared between the Object-glasses, and upon Bubbles of Water, but +much larger. And after the manner of those, they were of various +magnitudes in various Positions of the Eye, swelling and shrinking as I +moved my Eye this way and that way. They were formed like Arcs of +concentrick Circles, as those were; and when my Eye was over against the +center of the concavity of the Speculum, (that is, 5 Feet and 10 Inches +distant from the Speculum,) their common center was in a right Line with +that center of concavity, and with the hole in the Window. But in other +postures of my Eye their center had other positions. They appear'd by +the Light of the Clouds propagated to the Speculum through the hole in +the 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 by +its splendor obscured the Rings made by the Light of the Clouds, unless +when the Speculum was removed to a great distance from the Window, so +that his Light upon it might be broad and faint. By varying the position +of my Eye, and moving it nearer to or farther from the direct beam of +the Sun's Light, the Colour of the Sun's reflected Light constantly +varied upon the Speculum, as it did upon my Eye, the same Colour always +appearing to a Bystander upon my Eye which to me appear'd upon the +Speculum. And thence I knew that the Rings of Colours upon the Chart +were made by these reflected Colours, propagated thither from the +Speculum in several Angles, and that their production depended not upon +the termination of Light and Shadow. + +_Obs._ 7. By the Analogy of all these Phænomena with those of the like +Rings of Colours described in the first part of this Book, it seemed to +me that these Colours were produced by this thick Plate of Glass, much +after the manner that those were produced by very thin Plates. For, upon +trial, I found that if the Quick-silver were rubb'd off from the +backside of the Speculum, the Glass alone would cause the same Rings of +Colours, but much more faint than before; and therefore the Phænomenon +depends not upon the Quick-silver, unless so far as the Quick-silver by +increasing the Reflexion of the backside of the Glass increases the +Light of the Rings of Colours. I found also that a Speculum of Metal +without Glass made some Years since for optical uses, and very well +wrought, produced none of those Rings; and thence I understood that +these Rings arise not from one specular Surface alone, but depend upon +the 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 and +19th Observations of the first part of this Book a thin Plate of Air, +Water, or Glass of an even thickness appeared of one Colour when the +Rays were perpendicular to it, of another when they were a little +oblique, of another when more oblique, of another when still more +oblique, and so on; so here, in the sixth Observation, the Light which +emerged out of the Glass in several Obliquities, made the Glass appear +of several Colours, and being propagated in those Obliquities to the +Chart, there painted Rings of those Colours. And as the reason why a +thin Plate appeared of several Colours in several Obliquities of the +Rays, was, that the Rays of one and the same sort are reflected by the +thin Plate at one obliquity and transmitted at another, and those of +other sorts transmitted where these are reflected, and reflected where +these are transmitted: So the reason why the thick Plate of Glass +whereof the Speculum was made did appear of various Colours in various +Obliquities, and in those Obliquities propagated those Colours to the +Chart, was, that the Rays of one and the same sort did at one Obliquity +emerge out of the Glass, at another did not emerge, but were reflected +back towards the Quick-silver by the hither Surface of the Glass, and +accordingly as the Obliquity became greater and greater, emerged and +were reflected alternately for many Successions; and that in one and the +same Obliquity the Rays of one sort were reflected, and those of another +transmitted. This is manifest by the fifth Observation of this part of +this Book. For in that Observation, when the Speculum was illuminated by +any one of the prismatick Colours, that Light made many Rings of the +same Colour upon the Chart with dark Intervals, and therefore at its +emergence out of the Speculum was alternately transmitted and not +transmitted from the Speculum to the Chart for many Successions, +according to the various Obliquities of its Emergence. And when the +Colour cast on the Speculum by the Prism was varied, the Rings became of +the Colour cast on it, and varied their bigness with their Colour, and +therefore the Light was now alternately transmitted and not transmitted +from the Speculum to the Chart at other Obliquities than before. It +seemed to me therefore that these Rings were of one and the same +original with those of thin Plates, but yet with this difference, that +those of thin Plates are made by the alternate Reflexions and +Transmissions of the Rays at the second Surface of the Plate, after one +passage through it; but here the Rays go twice through the Plate before +they are alternately reflected and transmitted. First, they go through +it from the first Surface to the Quick-silver, and then return through +it from the Quick-silver to the first Surface, and there are either +transmitted to the Chart or reflected back to the Quick-silver, +accordingly as they are in their Fits of easy Reflexion or Transmission +when they arrive at that Surface. For the Intervals of the Fits of the +Rays which fall perpendicularly on the Speculum, and are reflected back +in the same perpendicular Lines, by reason of the equality of these +Angles and Lines, are of the same length and number within the Glass +after Reflexion as before, by the 19th Proposition of the third part of +this Book. And therefore since all the Rays that enter through the +first 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 of +easy Reflexion there, all these must be again in their Fits of easy +Transmission at their return to the first, and by consequence there go +out of the Glass to the Chart, and form upon it the white Spot of Light +in the center of the Rings. For the reason holds good in all sorts of +Rays, 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 Fits +of those Rays which are reflected more obliquely than they enter, must +be greater after Reflexion than before, by the 15th and 20th +Propositions. And thence it may happen that the Rays at their return to +the first Surface, may in certain Obliquities be in Fits of easy +Reflexion, and return back to the Quick-silver, and in other +intermediate Obliquities be again in Fits of easy Transmission, and so +go out to the Chart, and paint on it the Rings of Colours about the +white Spot. And because the Intervals of the Fits at equal obliquities +are greater and fewer in the less refrangible Rays, and less and more +numerous in the more refrangible, therefore the less refrangible at +equal obliquities shall make fewer Rings than the more refrangible, and +the Rings made by those shall be larger than the like number of Rings +made 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 than +the violet, as they were really found to be in the fifth Observation. +And therefore the first Ring of all Colours encompassing the white Spot +of 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; and +these Colours in the second Ring, and those that follow, shall be more +expanded, till they spread into one another, and blend one another by +interfering. + +These seem to be the reasons of these Rings in general; and this put me +upon observing the thickness of the Glass, and considering whether the +dimensions and proportions of the Rings may be truly derived from it by +computation. + +_Obs._ 8. I measured therefore the thickness of this concavo-convex +Plate 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 of +Air transmits the brightest Light of the first Ring, that is, the bright +yellow, when its thickness is the 1/89000th part of an Inch; and by the +tenth Observation of the same Part, a thin Plate of Glass transmits the +same Light of the same Ring, when its thickness is less in proportion of +the Sine of Refraction to the Sine of Incidence, that is, when its +thickness is the 11/1513000th or 1/137545th part of an Inch, supposing +the Sines are as 11 to 17. And if this thickness be doubled, it +transmits the same bright Light of the second Ring; if tripled, it +transmits that of the third, and so on; the bright yellow Light in all +these cases being in its Fits of Transmission. And therefore if its +thickness be multiplied 34386 times, so as to become 1/4 of an Inch, it +transmits the same bright Light of the 34386th Ring. Suppose this be the +bright yellow Light transmitted perpendicularly from the reflecting +convex side of the Glass through the concave side to the white Spot in +the center of the Rings of Colours on the Chart: And by a Rule in the +7th and 19th Observations in the first Part of this Book, and by the +15th and 20th Propositions of the third Part of this Book, if the Rays +be made oblique to the Glass, the thickness of the Glass requisite to +transmit the same bright Light of the same Ring in any obliquity, is to +this thickness of 1/4 of an Inch, as the Secant of a certain Angle to +the Radius, the Sine of which Angle is the first of an hundred and six +arithmetical Means between the Sines of Incidence and Refraction, +counted from the Sine of Incidence when the Refraction is made out of +any 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 by +degrees, so as to bear to its first thickness, (_viz._ that of a quarter +of an Inch,) the Proportions which 34386 (the number of Fits of the +perpendicular Rays in going through the Glass towards the white Spot in +the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the +numbers of the Fits of the oblique Rays in going through the Glass +towards the first, second, third, and fourth Rings of Colours,) and if +the first thickness be divided into 100000000 equal parts, the increased +thicknesses will be 100002908, 100005816, 100008725, and 100011633, and +the Angles of which these thicknesses are Secants will be 26´ 13´´, 37´ +5´´, 45´ 6´´, and 52´ 26´´, the Radius being 100000000; and the Sines of +these Angles are 762, 1079, 1321, and 1525, and the proportional Sines +of Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. For +since the Sines of Incidence out of Glass into Air are to the Sines of +Refraction as 11 to 17, and to the above-mentioned Secants as 11 to the +first of 106 arithmetical Means between 11 and 17, that is, as 11 to +11-6/106, 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 the +obliquities of the Rays to the concave Surface of the Glass be such that +the Sines of their Refraction in passing out of the Glass through that +Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the +34386th Ring shall emerge at the thicknesses of the Glass, which are to +1/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. And +therefore, if the thickness in all these Cases be 1/4 of an Inch (as it +is in the Glass of which the Speculum was made) the bright Light of the +34385th Ring shall emerge where the Sine of Refraction is 1172, and that +of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031, +and 2345 respectively. And in these Angles of Refraction the Light of +these Rings shall be propagated from the Speculum to the Chart, and +there paint Rings about the white central round Spot of Light which we +said was the Light of the 34386th Ring. And the Semidiameters of these +Rings shall subtend the Angles of Refraction made at the +Concave-Surface of the Speculum, and by consequence their Diameters +shall be to the distance of the Chart from the Speculum as those Sines +of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031, +and 2345, doubled are to 100000. And therefore, if the distance of the +Chart from the Concave-Surface of the Speculum be six Feet (as it was in +the third of these Observations) the Diameters of the Rings of this +bright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375 +Inches: For these Diameters are to six Feet, as the above-mention'd +Sines doubled are to the Radius. Now, these Diameters of the bright +yellow Rings, thus found by Computation are the very same with those +found in the third of these Observations by measuring them, _viz._ with +1-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory of +deriving these Rings from the thickness of the Plate of Glass of which +the Speculum was made, and from the Obliquity of the emerging Rays +agrees with the Observation. In this Computation I have equalled the +Diameters of the bright Rings made by Light of all Colours, to the +Diameters of the Rings made by the bright yellow. For this yellow makes +the brightest Part of the Rings of all Colours. If you desire the +Diameters 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 bright +yellow ones in a subduplicate Proportion of the Intervals of the Fits of +the Rays of those Colours when equally inclined to the refracting or +reflecting Surface which caused those Fits, that is, by putting the +Diameters of the Rings made by the Rays in the Extremities and Limits of +the 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 the +Notes in an Eighth: For by this means the Diameters of the Rings of +these Colours will be found pretty nearly in the same Proportion to one +another, 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 and +Original with those of thin Plates, and by consequence that the Fits or +alternate Dispositions of the Rays to be reflected and transmitted are +propagated to great distances from every reflecting and refracting +Surface. But yet to put the matter out of doubt, I added the following +Observation. + +_Obs._ 9. If these Rings thus depend on the thickness of the Plate of +Glass, their Diameters at equal distances from several Speculums made of +such concavo-convex Plates of Glass as are ground on the same Sphere, +ought to be reciprocally in a subduplicate Proportion of the thicknesses +of the Plates of Glass. And if this Proportion be found true by +experience it will amount to a demonstration that these Rings (like +those formed in thin Plates) do depend on the thickness of the Glass. I +procured therefore another concavo-convex Plate of Glass ground on both +sides to the same Sphere with the former Plate. Its thickness was 5/62 +Parts of an Inch; and the Diameters of the three first bright Rings +measured between the brightest Parts of their Orbits at the distance of +six Feet from the Glass were 3·4-1/6·5-1/8· Inches. Now, the thickness +of the other Glass being 1/4 of an Inch was to the thickness of this +Glass 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 the +Proportion of the first of these Roots to the second are the Diameters +of 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 of +these Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, that +is, the Diameters of the Rings are reciprocally in a subduplicate +Proportion of the thicknesses of the Plates of Glass. + +So then in Plates of Glass which are alike concave on one side, and +alike convex on the other side, and alike quick-silver'd on the convex +sides, and differ in nothing but their thickness, the Diameters of the +Rings are reciprocally in a subduplicate Proportion of the thicknesses +of the Plates. And this shews sufficiently that the Rings depend on both +the Surfaces of the Glass. They depend on the convex Surface, because +they are more luminous when that Surface is quick-silver'd over than +when it is without Quick-silver. They depend also upon the concave +Surface, because without that Surface a Speculum makes them not. They +depend on both Surfaces, and on the distances between them, because +their bigness is varied by varying only that distance. And this +dependence is of the same kind with that which the Colours of thin +Plates have on the distance of the Surfaces of those Plates, because the +bigness of the Rings, and their Proportion to one another, and the +variation of their bigness arising from the variation of the thickness +of the Glass, and the Orders of their Colours, is such as ought to +result 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 the +first Part. + +There are yet other Phænomena of these Rings of Colours, but such as +follow from the same Propositions, and therefore confirm both the Truth +of those Propositions, and the Analogy between these Rings and the Rings +of 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 the +Speculum not directly to the hole in the Window, but to a place a little +distant from it, the common center of that Spot, and of all the Rings of +Colours 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 of +the spherical concavity of the Speculum, whenever the Chart on which the +Rings of Colours fell was placed at that center. And as the beam of +reflected Light by inclining the Speculum receded more and more from the +beam of incident Light and from the common center of the colour'd Rings +between them, those Rings grew bigger and bigger, and so also did the +white round Spot, and new Rings of Colours emerged successively out of +their common center, and the white Spot became a white Ring +encompassing them; and the incident and reflected beams of Light always +fell upon the opposite parts of this white Ring, illuminating its +Perimeter like two mock Suns in the opposite parts of an Iris. So then +the Diameter of this Ring, measured from the middle of its Light on one +side to the middle of its Light on the other side, was always equal to +the distance between the middle of the incident beam of Light, and the +middle of the reflected beam measured at the Chart on which the Rings +appeared: And the Rays which form'd this Ring were reflected by the +Speculum in Angles equal to their Angles of Incidence, and by +consequence to their Angles of Refraction at their entrance into the +Glass, but yet their Angles of Reflexion were not in the same Planes +with their Angles of Incidence. + +_Obs._ 11. The Colours of the new Rings were in a contrary order to +those of the former, and arose after this manner. The white round Spot +of Light in the middle of the Rings continued white to the center till +the distance of the incident and reflected beams at the Chart was about +7/8 parts of an Inch, and then it began to grow dark in the middle. And +when that distance was about 1-3/16 of an Inch, the white Spot was +become a Ring encompassing a dark round Spot which in the middle +inclined to violet and indigo. And the luminous Rings encompassing it +were grown equal to those dark ones which in the four first Observations +encompassed them, that is to say, the white Spot was grown a white Ring +equal to the first of those dark Rings, and the first of those luminous +Rings was now grown equal to the second of those dark ones, and the +second of those luminous ones to the third of those dark ones, and so +on. 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 Light +became a little bigger, there emerged out of the middle of the dark Spot +after the indigo a blue, and then out of that blue a pale green, and +soon after a yellow and red. And when the Colour at the center was +brightest, being between yellow and red, the bright Rings were grown +equal to those Rings which in the four first Observations next +encompassed them; that is to say, the white Spot in the middle of those +Rings was now become a white Ring equal to the first of those bright +Rings, and the first of those bright ones was now become equal to the +second of those, and so on. For the Diameters of the white Ring, and of +the 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 little +more 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, the +former indigo, blue, green, yellow and red, were become an Iris or Ring +of Colours equal to the first of those luminous Rings which appeared in +the four first Observations, and the white Ring which was now become +the 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 become +equal to the third of those, and so on. For their Diameters were +1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams of +Light, and the Diameter of the white Ring being 2-3/8 Inches. + +When these two beams became more distant there emerged out of the middle +of the purplish red, first a darker round Spot, and then out of the +middle of that Spot a brighter. And now the former Colours (purple, +blue, green, yellow, and purplish red) were become a Ring equal to the +first of the bright Rings mentioned in the four first Observations, and +the Rings about this Ring were grown equal to the Rings about that +respectively; the distance between the two beams of Light and the +Diameter of the white Ring (which was now become the third Ring) being +about 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, or +an Inch more, they vanish'd whilst the white Ring, with one or two of +the Rings next it on either side, continued still visible. But if the +distance of the two beams of Light was still more increased, these also +vanished: For the Light which coming from several parts of the hole in +the Window fell upon the Speculum in several Angles of Incidence, made +Rings of several bignesses, which diluted and blotted out one another, +as I knew by intercepting some part of that Light. For if I intercepted +that part which was nearest to the Axis of the Speculum the Rings would +be less, if the other part which was remotest from it they would be +bigger. + +_Obs._ 12. When the Colours of the Prism were cast successively on the +Speculum, that Ring which in the two last Observations was white, was of +the same bigness in all the Colours, but the Rings without it were +greater 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 that +white Circle were less in the green than in the blue, and still less in +the yellow, and least in the red. For the Angles of Reflexion of those +Rays which made this Ring, being equal to their Angles of Incidence, the +Fits of every reflected Ray within the Glass after Reflexion are equal +in length and number to the Fits of the same Ray within the Glass before +its Incidence on the reflecting Surface. And therefore since all the +Rays of all sorts at their entrance into the Glass were in a Fit of +Transmission, they were also in a Fit of Transmission at their returning +to the same Surface after Reflexion; and by consequence were +transmitted, and went out to the white Ring on the Chart. This is the +reason why that Ring was of the same bigness in all the Colours, and why +in a mixture of all it appears white. But in Rays which are reflected in +other Angles, the Intervals of the Fits of the least refrangible being +greatest, make the Rings of their Colour in their progress from this +white Ring, either outwards or inwards, increase or decrease by the +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 Rings +made by all Colours appeared red without and blue within, and the +interior blue without and red within. + +These are the Phænomena of thick convexo-concave Plates of Glass, which +are every where of the same thickness. There are yet other Phænomena +when 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, or +plano-convex, or double-convex. For in all these cases the Plates make +Rings of Colours, but after various manners; all which, so far as I have +yet observed, follow from the Propositions in the end of the third part +of this Book, and so conspire to confirm the truth of those +Propositions. But the Phænomena are too various, and the Calculations +whereby they follow from those Propositions too intricate to be here +prosecuted. I content my self with having prosecuted this kind of +Phænomena so far as to discover their Cause, and by discovering it to +ratify the Propositions in the third Part of this Book. + +_Obs._ 13. As Light reflected by a Lens quick-silver'd on the backside +makes the Rings of Colours above described, so it ought to make the like +Rings of Colours in passing through a drop of Water. At the first +Reflexion of the Rays within the drop, some Colours ought to be +transmitted, as in the case of a Lens, and others to be reflected back +to the Eye. For instance, if the Diameter of a small drop or globule of +Water be about the 500th part of an Inch, so that a red-making Ray in +passing through the middle of this globule has 250 Fits of easy +Transmission within the globule, and that all the red-making Rays which +are at a certain distance from this middle Ray round about it have 249 +Fits within the globule, and all the like Rays at a certain farther +distance round about it have 248 Fits, and all those at a certain +farther distance 247 Fits, and so on; these concentrick Circles of Rays +after their transmission, falling on a white Paper, will make +concentrick Rings of red upon the Paper, supposing the Light which +passes through one single globule, strong enough to be sensible. And, in +like 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 of +such globules of Water or Hail, and that the globules are all of the +same bigness; and the Sun seen through this Cloud shall appear +encompassed with the like concentrick Rings of Colours, and the Diameter +of the first Ring of red shall be 7-1/4 Degrees, that of the second +10-1/4 Degrees, that of the third 12 Degrees 33 Minutes. And accordingly +as the Globules of Water are bigger or less, the Rings shall be less or +bigger. This is the Theory, and Experience answers it. For in _June_ +1692, 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 first or innermost Crown +were blue next the Sun, red without, and white in the middle between the +blue and red. Those of the second Crown were purple and blue within, and +pale red without, and green in the middle. And those of the third were +pale blue within, and pale red without; these Crowns enclosed one +another immediately, so that their Colours proceeded in this continual +order from the Sun outward: blue, white, red; purple, blue, green, pale +yellow and red; pale blue, pale red. The Diameter of the second Crown +measured 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, or +thereabouts. The Diameters of the first and third I had not time to +measure, but that of the first seemed to be about five or six Degrees, +and that of the third about twelve. The like Crowns appear sometimes +about the Moon; for in the beginning of the Year 1664, _Febr._ 19th at +Night, I saw two such Crowns about her. The Diameter of the first or +innermost was about three Degrees, and that of the second about five +Degrees and an half. Next about the Moon was a Circle of white, and next +about that the inner Crown, which was of a bluish green within next the +white, and of a yellow and red without, and next about these Colours +were blue and green on the inside of the outward Crown, and red on the +outside of it. At the same time there appear'd a Halo about 22 Degrees +35´ distant from the center of the Moon. It was elliptical, and its long +Diameter was perpendicular to the Horizon, verging below farthest from +the Moon. I am told that the Moon has sometimes three or more +concentrick Crowns of Colours encompassing one another next about her +Body. 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 more +lively. The Halo at the distance of 22-1/2 Degrees from the Moon is of +another sort. By its being oval and remoter from the Moon below than +above, I conclude, that it was made by Refraction in some sort of Hail +or Snow floating in the Air in an horizontal posture, the refracting +Angle being about 58 or 60 Degrees. + + + + +THE + +THIRD BOOK + +OF + +OPTICKS + + +_PART I._ + +_Observations concerning the Inflexions of the Rays of Light, and the +Colours made thereby._ + +Grimaldo has inform'd us, that if a beam of the Sun's Light be let into +a dark Room through a very small hole, the Shadows of things in this +Light will be larger than they ought to be if the Rays went on by the +Bodies in straight Lines, and that these Shadows have three parallel +Fringes, Bands or Ranks of colour'd Light adjacent to them. But if the +Hole be enlarged the Fringes grow broad and run into one another, so +that they cannot be distinguish'd. These broad Shadows and Fringes have +been reckon'd by some to proceed from the ordinary refraction of the +Air, but without due examination of the Matter. For the circumstances of +the Phænomenon, so far as I have observed them, are as follows. + +_Obs._ 1. I made in a piece of Lead a small Hole with a Pin, whose +breadth was the 42d part of an Inch. For 21 of those Pins laid together +took up the breadth of half an Inch. Through this Hole I let into my +darken'd Chamber a beam of the Sun's Light, and found that the Shadows +of Hairs, Thred, Pins, Straws, and such like slender Substances placed +in 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. And +particularly a Hair of a Man's Head, whose breadth was but the 280th +part of an Inch, being held in this Light, at the distance of about +twelve Feet from the Hole, did cast a Shadow which at the distance of +four Inches from the Hair was the sixtieth part of an Inch broad, that +is, above four times broader than the Hair, and at the distance of two +Feet from the Hair was about the eight and twentieth part of an Inch +broad, that is, ten times broader than the Hair, and at the distance of +ten 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 any +other pellucid Substance. For I wetted a polish'd Plate of Glass, and +laid the Hair in the Water upon the Glass, and then laying another +polish'd Plate of Glass upon it, so that the Water might fill up the +space between the Glasses, I held them in the aforesaid beam of Light, +so that the Light might pass through them perpendicularly, and the +Shadow of the Hair was at the same distances as big as before. The +Shadows of Scratches made in polish'd Plates of Glass were also much +broader than they ought to be, and the Veins in polish'd Plates of Glass +did also cast the like broad Shadows. And therefore the great breadth of +these Shadows proceeds from some other cause than the Refraction of the +Air. + +Let the Circle X [in _Fig._ 1.] represent the middle of the Hair; ADG, +BEH, CFI, three Rays passing by one side of the Hair at several +distances; KNQ, LOR, MPS, three other Rays passing by the other side of +the Hair at the like distances; D, E, F, and N, O, P, the places where +the 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 the +Shadow of the Hair cast on the Paper, and TI, VS, two Rays passing to +the Points I and S without bending when the Hair is taken away. And it's +manifest that all the Light between these two Rays TI and VS is bent in +passing by the Hair, and turned aside from the Shadow IS, because if any +part of this Light were not bent it would fall on the Paper within the +Shadow, and there illuminate the Paper, contrary to experience. And +because when the Paper is at a great distance from the Hair, the Shadow +is broad, and therefore the Rays TI and VS are at a great distance from +one another, it follows that the Hair acts upon the Rays of Light at a +good distance in their passing by it. But the Action is strongest on the +Rays which pass by at least distances, and grows weaker and weaker +accordingly as the Rays pass by at distances greater and greater, as is +represented in the Scheme: For thence it comes to pass, that the Shadow +of the Hair is much broader in proportion to the distance of the Paper +from the Hair, when the Paper is nearer the Hair, than when it is at a +great 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 or +Bands of colour'd Light, whereof that which was contiguous to the Shadow +was broadest and most luminous, and that which was remotest from it was +narrowest, and so faint, as not easily to be visible. It was difficult +to distinguish the Colours, unless when the Light fell very obliquely +upon a smooth Paper, or some other smooth white Body, so as to make them +appear much broader than they would otherwise do. And then the Colours +were plainly visible in this Order: The first or innermost Fringe was +violet and deep blue next the Shadow, and then light blue, green, and +yellow in the middle, and red without. The second Fringe was almost +contiguous to the first, and the third to the second, and both were blue +within, and yellow and red without, but their Colours were very faint, +especially those of the third. The Colours therefore proceeded in this +order from the Shadow; violet, indigo, pale blue, green, yellow, red; +blue, yellow, red; pale blue, pale yellow and red. The Shadows made by +Scratches and Bubbles in polish'd Plates of Glass were border'd with the +like Fringes of colour'd Light. And if Plates of Looking-glass sloop'd +off near the edges with a Diamond-cut, be held in the same beam of +Light, the Light which passes through the parallel Planes of the Glass +will be border'd with the like Fringes of Colours where those Planes +meet with the Diamond-cut, and by this means there will sometimes appear +four or five Fringes of Colours. Let AB, CD [in _Fig._ 2.] represent the +parallel 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 Light +between the Rays ENI and FBM pass directly through the parallel Planes +of the Glass, and fall upon the Paper between I and M, and all the Light +between the Rays GO and HD be refracted by the oblique Plane of the +Diamond-cut BD, and fall upon the Paper between K and L; and the Light +which passes directly through the parallel Planes of the Glass, and +falls upon the Paper between I and M, will be border'd with three or +more Fringes at M. + +[Illustration: FIG. 1.] + +[Illustration: FIG. 2.] + +So by looking on the Sun through a Feather or black Ribband held close +to the Eye, several Rain-bows will appear; the Shadows which the Fibres +or Threds cast on the _Tunica Retina_, being border'd with the like +Fringes of Colours. + +_Obs._ 3. When the Hair was twelve Feet distant from this Hole, and its +Shadow fell obliquely upon a flat white Scale of Inches and Parts of an +Inch placed half a Foot beyond it, and also when the Shadow fell +perpendicularly upon the same Scale placed nine Feet beyond it; I +measured the breadth of the Shadow and Fringes as accurately as I could, +and found them in Parts of an Inch as follows. + +-------------------------------------------+-----------+-------- + | half a | Nine + At the Distance of | Foot | Feet +-------------------------------------------+-----------+-------- +The breadth of the Shadow | 1/54 | 1/9 +-------------------------------------------+-----------+-------- +The breadth between the Middles of the | 1/38 | + brightest Light of the innermost Fringes | or | + on either side the Shadow | 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 | 1/18 | + brightest Light of the outmost Fringes | or | + on either side the Shadow | 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 Foot +distance, fall so obliquely on the Scale, as to appear twelve times +broader than when it fell perpendicularly on it at the same distance, +and setting down in this Table the twelfth part of the Measures I then +took. + +_Obs._ 4. When the Shadow and Fringes were cast obliquely upon a smooth +white 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 the +Light 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 to +appear at a less distance from the Hair than that of the third part of +an Inch. The second Fringe began to appear at a distance from the Hair +of less than half an Inch, and the Shadow between that and the third +Fringe at a distance less than an inch, and the third Fringe at a +distance less than three Inches. At greater distances they became much +more sensible, but kept very nearly the same proportion of their +breadths and intervals which they had at their first appearing. For the +distance between the middle of the first, and middle of the second +Fringe, was to the distance between the middle of the second and middle +of the third Fringe, as three to two, or ten to seven. And the last of +these two distances was equal to the breadth of the bright Light or +luminous part of the first Fringe. And this breadth was to the breadth +of the bright Light of the second Fringe as seven to four, and to the +dark Interval of the first and second Fringe as three to two, and to +the like dark Interval between the second and third as two to one. For +the breadths of the Fringes seem'd to be in the progression of the +Numbers 1, sqrt(1/3), sqrt(1/5), and their Intervals to be in the +same progression with them; that is, the Fringes and their Intervals +together to be in the continual progression of the Numbers 1, +sqrt(1/2), sqrt(1/3), sqrt(1/4), sqrt(1/5), or thereabouts. And +these Proportions held the same very nearly at all distances from the +Hair; the dark Intervals of the Fringes being as broad in proportion to +the breadth of the Fringes at their first appearance as afterwards at +great distances from the Hair, though not so dark and distinct. + +_Obs._ 5. The Sun shining into my darken'd Chamber through a hole a +quarter of an Inch broad, I placed at the distance of two or three Feet +from the Hole a Sheet of Pasteboard, which was black'd all over on both +sides, and in the middle of it had a hole about three quarters of an +Inch square for the Light to pass through. And behind the hole I +fasten'd to the Pasteboard with Pitch the blade of a sharp Knife, to +intercept some part of the Light which passed through the hole. The +Planes of the Pasteboard and blade of the Knife were parallel to one +another, and perpendicular to the Rays. And when they were so placed +that none of the Sun's Light fell on the Pasteboard, but all of it +passed through the hole to the Knife, and there part of it fell upon the +blade of the Knife, and part of it passed by its edge; I let this part +of the Light which passed by, fall on a white Paper two or three Feet +beyond the Knife, and there saw two streams of faint Light shoot out +both ways from the beam of Light into the shadow, like the Tails of +Comets. But because the Sun's direct Light by its brightness upon the +Paper obscured these faint streams, so that I could scarce see them, I +made a little hole in the midst of the Paper for that Light to pass +through and fall on a black Cloth behind it; and then I saw the two +streams plainly. They were like one another, and pretty nearly equal in +length, and breadth, and quantity of Light. Their Light at that end next +the Sun's direct Light was pretty strong for the space of about a +quarter of an Inch, or half an Inch, and in all its progress from that +direct Light decreased gradually till it became insensible. The whole +length of either of these streams measured upon the paper at the +distance of three Feet from the Knife was about six or eight Inches; so +that 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 or +four Degrees farther, but with a Light so very faint that I could scarce +perceive it, and suspected it might (in some measure at least) arise +from some other cause than the two streams did. For placing my Eye in +that Light beyond the end of that stream which was behind the Knife, and +looking 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 also +when it was without that line either towards the point of the Knife, or +towards the handle. This line of Light appear'd contiguous to the edge +of the Knife, and was narrower than the Light of the innermost Fringe, +and narrowest when my Eye was farthest from the direct Light, and +therefore seem'd to pass between the Light of that Fringe and the edge +of 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 be +parallel, and look towards one another, and that the beam of Light might +fall 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 an +Inch, the stream parted in the middle, and left a Shadow between the two +parts. This Shadow was so black and dark that all the Light which passed +between the Knives seem'd to be bent, and turn'd aside to the one hand +or to the other. And as the Knives still approach'd one another the +Shadow grew broader, and the streams shorter at their inward ends which +were next the Shadow, until upon the contact of the Knives the whole +Light vanish'd, leaving its place to the Shadow. + +And hence I gather that the Light which is least bent, and goes to the +inward ends of the streams, passes by the edges of the Knives at the +greatest distance, and this distance when the Shadow begins to appear +between the streams, is about the 800th part of an Inch. And the Light +which passes by the edges of the Knives at distances still less and +less, is more and more bent, and goes to those parts of the streams +which are farther and farther from the direct Light; because when the +Knives approach one another till they touch, those parts of the streams +vanish last which are farthest from the direct Light. + +_Obs._ 7. In the fifth Observation the Fringes did not appear, but by +reason of the breadth of the hole in the Window became so broad as to +run into one another, and by joining, to make one continued Light in the +beginning of the streams. But in the sixth, as the Knives approached one +another, a little before the Shadow appeared between the two streams, +the Fringes began to appear on the inner ends of the Streams on either +side of the direct Light; three on one side made by the edge of one +Knife, and three on the other side made by the edge of the other Knife. +They were distinctest when the Knives were placed at the greatest +distance from the hole in the Window, and still became more distinct by +making the hole less, insomuch that I could sometimes see a faint +lineament of a fourth Fringe beyond the three above mention'd. And as +the Knives continually approach'd one another, the Fringes grew +distincter and larger, until they vanish'd. The outmost Fringe vanish'd +first, and the middlemost next, and the innermost last. And after they +were all vanish'd, and the line of Light which was in the middle between +them was grown very broad, enlarging it self on both sides into the +streams of Light described in the fifth Observation, the above-mention'd +Shadow began to appear in the middle of this line, and divide it along +the middle into two lines of Light, and increased until the whole Light +vanish'd. This enlargement of the Fringes was so great that the Rays +which go to the innermost Fringe seem'd to be bent above twenty times +more when this Fringe was ready to vanish, than when one of the Knives +was taken away. + +And from this and the former Observation compared, I gather, that the +Light of the first Fringe passed by the edge of the Knife at a distance +greater than the 800th part of an Inch, and the Light of the second +Fringe passed by the edge of the Knife at a greater distance than the +Light of the first Fringe did, and that of the third at a greater +distance than that of the second, and that of the streams of Light +described in the fifth and sixth Observations passed by the edges of the +Knives 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 look +towards one another, and meeting near their points contain a rectilinear +Angle, I fasten'd their Handles together with Pitch to make this Angle +invariable. The distance of the edges of the Knives from one another at +the distance of four Inches from the angular Point, where the edges of +the Knives met, was the eighth part of an Inch; and therefore the Angle +contain'd by the edges was about one Degree 54: The Knives thus fix'd +together I placed in a beam of the Sun's Light, let into my darken'd +Chamber through a Hole the 42d Part of an Inch wide, at the distance of +10 or 15 Feet from the Hole, and let the Light which passed between +their edges fall very obliquely upon a smooth white Ruler at the +distance of half an Inch, or an Inch from the Knives, and there saw the +Fringes by the two edges of the Knives run along the edges of the +Shadows of the Knives in Lines parallel to those edges without growing +sensibly broader, till they met in Angles equal to the Angle contained +by the edges of the Knives, and where they met and joined they ended +without crossing one another. But if the Ruler was held at a much +greater distance from the Knives, the Fringes where they were farther +from the Place of their Meeting, were a little narrower, and became +something broader and broader as they approach'd nearer and nearer to +one another, and after they met they cross'd one another, and then +became much broader than before. + +Whence I gather that the distances at which the Fringes pass by the +Knives are not increased nor alter'd by the approach of the Knives, but +the Angles in which the Rays are there bent are much increased by that +approach; and that the Knife which is nearest any Ray determines which +way the Ray shall be bent, and the other Knife increases the bent. + +_Obs._ 9. When the Rays fell very obliquely upon the Ruler at the +distance of the third Part of an Inch from the Knives, the dark Line +between the first and second Fringe of the Shadow of one Knife, and the +dark Line between the first and second Fringe of the Shadow of the other +knife met with one another, at the distance of the fifth Part of an Inch +from the end of the Light which passed between the Knives at the +concourse of their edges. And therefore the distance of the edges of the +Knives 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 of +the edges of the Knives measured from the point of their concourse to +the distance of the edges of the Knives at the end of that Length, and +so is the fifth Part of an Inch to the 160th Part. So then the dark +Lines above-mention'd meet in the middle of the Light which passes +between the Knives where they are distant the 160th Part of an Inch, and +the one half of that Light passes by the edge of one Knife at a distance +not greater than the 320th Part of an Inch, and falling upon the Paper +makes the Fringes of the Shadow of that Knife, and the other half passes +by the edge of the other Knife, at a distance not greater than the 320th +Part of an Inch, and falling upon the Paper makes the Fringes of the +Shadow of the other Knife. But if the Paper be held at a distance from +the Knives greater than the third Part of an Inch, the dark Lines +above-mention'd meet at a greater distance than the fifth Part of an +Inch from the end of the Light which passed between the Knives at the +concourse of their edges; and therefore the Light which falls upon the +Paper where those dark Lines meet passes between the Knives where the +edges are distant above the 160th part of an Inch. + +For at another time, when the two Knives were distant eight Feet and +five Inches from the little hole in the Window, made with a small Pin as +above, the Light which fell upon the Paper where the aforesaid dark +lines met, passed between the Knives, where the distance between their +edges was as in the following Table, when the distance of the Paper from +the Knives was also as follows. + +-----------------------------+------------------------------ + | Distances between the edges + Distances of the Paper | of the Knives in millesimal + from the Knives in Inches. | 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 the +Paper is not the same Light at all distances of the Paper from the +Knives, but when the Paper is held near the Knives, the Fringes are made +by Light which passes by the edges of the Knives at a less distance, and +is more bent than when the Paper is held at a greater distance from the +Knives. + +[Illustration: FIG. 3.] + +_Obs._ 10. When the Fringes of the Shadows of the Knives fell +perpendicularly upon a Paper at a great distance from the Knives, they +were in the form of Hyperbola's, and their Dimensions were as follows. +Let CA, CB [in _Fig._ 3.] represent Lines drawn upon the Paper parallel +to 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 a +Right Line drawn through C making the Angles ACD, BCE, equal to one +another, and terminating all the Light which falls upon the Paper from +the point where the edges of the Knives meet; _eis_, _fkt_, and _glv_, +three hyperbolical Lines representing the Terminus of the Shadow of one +of the Knives, the dark Line between the first and second Fringes of +that Shadow, and the dark Line between the second and third Fringes of +the same Shadow; _xip_, _ykq_, and _zlr_, three other hyperbolical Lines +representing the Terminus of the Shadow of the other Knife, the dark +Line between the first and second Fringes of that Shadow, and the dark +line between the second and third Fringes of the same Shadow. And +conceive that these three Hyperbola's are like and equal to the former +three, and cross them in the points _i_, _k_, and _l_, and that the +Shadows of the Knives are terminated and distinguish'd from the first +luminous Fringes by the lines _eis_ and _xip_, until the meeting and +crossing of the Fringes, and then those lines cross the Fringes in the +form of dark lines, terminating the first luminous Fringes within side, +and distinguishing them from another Light which begins to appear at +_i_, and illuminates all the triangular space _ip_DE_s_ comprehended by +these dark lines, and the right line DE. Of these Hyperbola's one +Asymptote is the line DE, and their other Asymptotes are parallel to the +lines CA and CB. Let _rv_ represent a line drawn any where upon the +Paper parallel to the Asymptote DE, and let this line cross the right +lines AC in _m_, and BC in _n_, and the six dark hyperbolical lines in +_p_, _q_, _r_; _s_, _t_, _v_; and by measuring the distances _ps_, _qt_, +_rv_, and thence collecting the lengths of the Ordinates _np_, _nq_, +_nr_ or _ms_, _mt_, _mv_, and doing this at several distances of the +line _rv_ from the Asymptote DD, you may find as many points of these +Hyperbola's as you please, and thereby know that these curve lines are +Hyperbola's differing little from the conical Hyperbola. And by +measuring the lines C_i_, C_k_, C_l_, you may find other points of these +Curves. + +For instance; when the Knives were distant from the hole in the Window +ten Feet, and the Paper from the Knives nine Feet, and the Angle +contained 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 the +distance of the line _rv_ from the Asymptote DE was half an Inch: I +measured the lines _ps_, _qt_, _rv_, and found them 0'35, 0'65, 0'98 +Inches respectively; and by adding to their halfs the line 1/2 _mn_, +(which here was the 128th part of an Inch, or 0'0078 Inches,) the Sums +_np_, _nq_, _nr_, were 0'1828, 0'3328, 0'4978 Inches. I measured also +the distances of the brightest parts of the Fringes which run between +_pq_ and _st_, _qr_ and _tv_, and next beyond _r_ and _v_, and found +them 0'5, 0'8, and 1'17 Inches. + +_Obs._ 11. The Sun shining into my darken'd Room through a small round +hole made in a Plate of Lead with a slender Pin, as above; I placed at +the hole a Prism to refract the Light, and form on the opposite Wall the +Spectrum of Colours, described in the third Experiment of the first +Book. And then I found that the Shadows of all Bodies held in the +colour'd Light between the Prism and the Wall, were border'd with +Fringes of the Colour of that Light in which they were held. In the full +red Light they were totally red without any sensible blue or violet, and +in the deep blue Light they were totally blue without any sensible red +or yellow; and so in the green Light they were totally green, excepting +a little yellow and blue, which were mixed in the green Light of the +Prism. And comparing the Fringes made in the several colour'd Lights, I +found that those made in the red Light were largest, those made in the +violet 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 the +Hair, the distance between the middle and most luminous part of the +first or innermost Fringe on one side of the Shadow, and that of the +like Fringe on the other side of the Shadow, was in the full red Light +1/37-1/4 of an Inch, and in the full violet 7/46. And the like distance +between the middle and most luminous parts of the second Fringes on +either side the Shadow was in the full red Light 1/22, and in the violet +1/27 of an Inch. And these distances of the Fringes held the same +proportion at all distances from the Hair without any sensible +variation. + +So then the Rays which made these Fringes in the red Light passed by the +Hair at a greater distance than those did which made the like Fringes in +the violet; and therefore the Hair in causing these Fringes acted alike +upon the red Light or least refrangible Rays at a greater distance, and +upon the violet or most refrangible Rays at a less distance, and by +those actions disposed the red Light into Larger Fringes, and the violet +into smaller, and the Lights of intermediate Colours into Fringes of +intermediate bignesses without changing the Colour of any sort of Light. + +When therefore the Hair in the first and second of these Observations +was held in the white beam of the Sun's Light, and cast a Shadow which +was border'd with three Fringes of coloured Light, those Colours arose +not from any new modifications impress'd upon the Rays of Light by the +Hair, but only from the various inflexions whereby the several Sorts of +Rays were separated from one another, which before separation, by the +mixture of all their Colours, composed the white beam of the Sun's +Light, but whenever separated compose Lights of the several Colours +which they are originally disposed to exhibit. In this 11th Observation, +where the Colours are separated before the Light passes by the Hair, the +least refrangible Rays, which when separated from the rest make red, +were inflected at a greater distance from the Hair, so as to make three +red Fringes at a greater distance from the middle of the Shadow of the +Hair; and the most refrangible Rays which when separated make violet, +were inflected at a less distance from the Hair, so as to make three +violet Fringes at a less distance from the middle of the Shadow of the +Hair. And other Rays of intermediate degrees of Refrangibility were +inflected at intermediate distances from the Hair, so as to make Fringes +of intermediate Colours at intermediate distances from the middle of the +Shadow of the Hair. And in the second Observation, where all the Colours +are mix'd in the white Light which passes by the Hair, these Colours are +separated by the various inflexions of the Rays, and the Fringes which +they make appear all together, and the innermost Fringes being +contiguous make one broad Fringe composed of all the Colours in due +order, the violet lying on the inside of the Fringe next the Shadow, the +red on the outside farthest from the Shadow, and the blue, green, and +yellow, in the middle. And, in like manner, the middlemost Fringes of +all the Colours lying in order, and being contiguous, make another broad +Fringe composed of all the Colours; and the outmost Fringes of all the +Colours lying in order, and being contiguous, make a third broad Fringe +composed of all the Colours. These are the three Fringes of colour'd +Light with which the Shadows of all Bodies are border'd in the second +Observation. + +When I made the foregoing Observations, I design'd to repeat most of +them with more care and exactness, and to make some new ones for +determining the manner how the Rays of Light are bent in their passage +by Bodies, for making the Fringes of Colours with the dark lines between +them. But I was then interrupted, and cannot now think of taking these +things into farther Consideration. And since I have not finish'd this +part of my Design, I shall conclude with proposing only some Queries, in +order to a farther search to be made by others. + +_Query_ 1. Do not Bodies act upon Light at a distance, and by their +action 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 in +Flexibity; and are they not by their different Inflexions separated from +one another, so as after separation to make the Colours in the three +Fringes above described? And after what manner are they inflected to +make those Fringes? + +_Qu._ 3. Are not the Rays of Light in passing by the edges and sides of +Bodies, bent several times backwards and forwards, with a motion like +that of an Eel? And do not the three Fringes of colour'd Light +above-mention'd arise from three such bendings? + +_Qu._ 4. Do not the Rays of Light which fall upon Bodies, and are +reflected or refracted, begin to bend before they arrive at the Bodies; +and are they not reflected, refracted, and inflected, by one and the +same Principle, acting variously in various Circumstances? + +_Qu._ 5. Do not Bodies and Light act mutually upon one another; that is +to say, Bodies upon Light in emitting, reflecting, refracting and +inflecting it, and Light upon Bodies for heating them, and putting their +parts into a vibrating motion wherein heat consists? + +_Qu._ 6. Do not black Bodies conceive heat more easily from Light than +those of other Colours do, by reason that the Light falling on them is +not reflected outwards, but enters the Bodies, and is often reflected +and refracted within them, until it be stifled and lost? + +_Qu._ 7. Is not the strength and vigor of the action between Light and +sulphureous Bodies observed above, one reason why sulphureous Bodies +take 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 the +vibrating motions of their parts? And do not all Bodies which abound +with terrestrial parts, and especially with sulphureous ones, emit Light +as often as those parts are sufficiently agitated; whether that +agitation be made by Heat, or by Friction, or Percussion, or +Putrefaction, or by any vital Motion, or any other Cause? As for +instance; Sea-Water in a raging Storm; Quick-silver agitated in _vacuo_; +the Back of a Cat, or Neck of a Horse, obliquely struck or rubbed in a +dark place; Wood, Flesh and Fish while they putrefy; Vapours arising +from putrefy'd Waters, usually call'd _Ignes Fatui_; Stacks of moist Hay +or Corn growing hot by fermentation; Glow-worms and the Eyes of some +Animals by vital Motions; the vulgar _Phosphorus_ agitated by the +attrition of any Body, or by the acid Particles of the Air; Amber and +some Diamonds by striking, pressing or rubbing them; Scrapings of Steel +struck off with a Flint; Iron hammer'd very nimbly till it become so hot +as to kindle Sulphur thrown upon it; the Axletrees of Chariots taking +fire by the rapid rotation of the Wheels; and some Liquors mix'd with +one another whose Particles come together with an Impetus, as Oil of +Vitriol distilled from its weight of Nitre, and then mix'd with twice +its weight of Oil of Anniseeds. So also a Globe of Glass about 8 or 10 +Inches in diameter, being put into a Frame where it may be swiftly +turn'd round its Axis, will in turning shine where it rubs against the +palm of ones Hand apply'd to it: And if at the same time a piece of +white Paper or white Cloth, or the end of ones Finger be held at the +distance of about a quarter of an Inch or half an Inch from that part of +the Glass where it is most in motion, the electrick Vapour which is +excited by the friction of the Glass against the Hand, will by dashing +against the white Paper, Cloth or Finger, be put into such an agitation +as to emit Light, and make the white Paper, Cloth or Finger, appear +lucid like a Glowworm; and in rushing out of the Glass will sometimes +push against the finger so as to be felt. And the same things have been +found by rubbing a long and large Cylinder or Glass or Amber with a +Paper held in ones hand, and continuing the friction till the Glass grew +warm. + +_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 burning +Coal than red hot Wood? + +_Qu._ 10. Is not Flame a Vapour, Fume or Exhalation heated red hot, that +is, so hot as to shine? For Bodies do not flame without emitting a +copious Fume, and this Fume burns in the Flame. The _Ignis Fatuus_ is a +Vapour shining without heat, and is there not the same difference +between this Vapour and Flame, as between rotten Wood shining without +heat and burning Coals of Fire? In distilling hot Spirits, if the Head +of the Still be taken off, the Vapour which ascends out of the Still +will take fire at the Flame of a Candle, and turn into Flame, and the +Flame will run along the Vapour from the Candle to the Still. Some +Bodies heated by Motion, or Fermentation, if the heat grow intense, fume +copiously, and if the heat be great enough the Fumes will shine and +become Flame. Metals in fusion do not flame for want of a copious Fume, +except Spelter, which fumes copiously, and thereby flames. All flaming +Bodies, as Oil, Tallow, Wax, Wood, fossil Coals, Pitch, Sulphur, by +flaming waste and vanish into burning Smoke, which Smoke, if the Flame +be put out, is very thick and visible, and sometimes smells strongly, +but in the Flame loses its smell by burning, and according to the nature +of 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, that +of Camphire white. Smoke passing through Flame cannot but grow red hot, +and red hot Smoke can have no other appearance than that of Flame. When +Gun-powder takes fire, it goes away into Flaming Smoke. For the Charcoal +and Sulphur easily take fire, and set fire to the Nitre, and the Spirit +of the Nitre being thereby rarified into Vapour, rushes out with +Explosion much after the manner that the Vapour of Water rushes out of +an Æolipile; the Sulphur also being volatile is converted into Vapour, +and augments the Explosion. And the acid Vapour of the Sulphur (namely +that which distils under a Bell into Oil of Sulphur,) entring violently +into 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 the +Explosion is thereby made more vehement and quick. For if Salt of Tartar +be 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-powder +alone; which cannot proceed from any other cause than the action of the +Vapour of the Gun-powder upon the Salt of Tartar, whereby that Salt is +rarified. The Explosion of Gun-powder arises therefore from the violent +action whereby all the Mixture being quickly and vehemently heated, is +rarified and converted into Fume and Vapour: which Vapour, by the +violence of that action, becoming so hot as to shine, appears in the +form of Flame. + +_Qu._ 11. Do not great Bodies conserve their heat the longest, their +parts heating one another, and may not great dense and fix'd Bodies, +when heated beyond a certain degree, emit Light so copiously, as by the +Emission and Re-action of its Light, and the Reflexions and Refractions +of its Rays within its Pores to grow still hotter, till it comes to a +certain period of heat, such as is that of the Sun? And are not the Sun +and fix'd Stars great Earths vehemently hot, whose heat is conserved by +the greatness of the Bodies, and the mutual Action and Reaction between +them, and the Light which they emit, and whose parts are kept from +fuming away, not only by their fixity, but also by the vast weight and +density of the Atmospheres incumbent upon them; and very strongly +compressing them, and condensing the Vapours and Exhalations which arise +from them? For if Water be made warm in any pellucid Vessel emptied of +Air, that Water in the _Vacuum_ will bubble and boil as vehemently as it +would in the open Air in a Vessel set upon the Fire till it conceives a +much greater heat. For the weight of the incumbent Atmosphere keeps down +the Vapours, and hinders the Water from boiling, until it grow much +hotter than is requisite to make it boil _in vacuo_. Also a mixture of +Tin and Lead being put upon a red hot Iron _in vacuo_ emits a Fume and +Flame, but the same Mixture in the open Air, by reason of the incumbent +Atmosphere, does not so much as emit any Fume which can be perceived by +Sight. In like manner the great weight of the Atmosphere which lies upon +the Globe of the Sun may hinder Bodies there from rising up and going +away from the Sun in the form of Vapours and Fumes, unless by means of a +far greater heat than that which on the Surface of our Earth would very +easily turn them into Vapours and Fumes. And the same great weight may +condense those Vapours and Exhalations as soon as they shall at any time +begin to ascend from the Sun, and make them presently fall back again +into him, and by that action increase his Heat much after the manner +that in our Earth the Air increases the Heat of a culinary Fire. And the +same weight may hinder the Globe of the Sun from being diminish'd, +unless by the Emission of Light, and a very small quantity of Vapours +and Exhalations. + +_Qu._ 12. Do not the Rays of Light in falling upon the bottom of the Eye +excite Vibrations in the _Tunica Retina_? Which Vibrations, being +propagated along the solid Fibres of the optick Nerves into the Brain, +cause the Sense of seeing. For because dense Bodies conserve their Heat +a long time, and the densest Bodies conserve their Heat the longest, the +Vibrations of their parts are of a lasting nature, and therefore may be +propagated along solid Fibres of uniform dense Matter to a great +distance, for conveying into the Brain the impressions made upon all the +Organs of Sense. For that Motion which can continue long in one and the +same part of a Body, can be propagated a long way from one part to +another, supposing the Body homogeneal, so that the Motion may not be +reflected, refracted, interrupted or disorder'd by any unevenness of the +Body. + +_Qu._ 13. Do not several sorts of Rays make Vibrations of several +bignesses, which according to their bignesses excite Sensations of +several Colours, much after the manner that the Vibrations of the Air, +according to their several bignesses excite Sensations of several +Sounds? And particularly do not the most refrangible Rays excite the +shortest Vibrations for making a Sensation of deep violet, the least +refrangible the largest for making a Sensation of deep red, and the +several intermediate sorts of Rays, Vibrations of several intermediate +bignesses to make Sensations of the several intermediate Colours? + +_Qu._ 14. May not the harmony and discord of Colours arise from the +proportions of the Vibrations propagated through the Fibres of the +optick Nerves into the Brain, as the harmony and discord of Sounds arise +from the proportions of the Vibrations of the Air? For some Colours, if +they be view'd together, are agreeable to one another, as those of Gold +and Indigo, and others disagree. + +_Qu._ 15. Are not the Species of Objects seen with both Eyes united +where the optick Nerves meet before they come into the Brain, the Fibres +on the right side of both Nerves uniting there, and after union going +thence into the Brain in the Nerve which is on the right side of the +Head, and the Fibres on the left side of both Nerves uniting in the same +place, and after union going into the Brain in the Nerve which is on the +left side of the Head, and these two Nerves meeting in the Brain in such +a manner that their Fibres make but one entire Species or Picture, half +of which on the right side of the Sensorium comes from the right side of +both Eyes through the right side of both optick Nerves to the place +where the Nerves meet, and from thence on the right side of the Head +into the Brain, and the other half on the left side of the Sensorium +comes in like manner from the left side of both Eyes. For the optick +Nerves 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 the +optick 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 rightly +inform'd. + +_Qu._ 16. When a Man in the dark presses either corner of his Eye with +his Finger, and turns his Eye away from his Finger, he will see a Circle +of Colours like those in the Feather of a Peacock's Tail. If the Eye and +the 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. Do +not these Colours arise from such Motions excited in the bottom of the +Eye by the Pressure and Motion of the Finger, as, at other times are +excited there by Light for causing Vision? And do not the Motions once +excited continue about a Second of Time before they cease? And when a +Man by a stroke upon his Eye sees a flash of Light, are not the like +Motions excited in the _Retina_ by the stroke? And when a Coal of Fire +moved nimbly in the circumference of a Circle, makes the whole +circumference appear like a Circle of Fire; is it not because the +Motions excited in the bottom of the Eye by the Rays of Light are of a +lasting nature, and continue till the Coal of Fire in going round +returns to its former place? And considering the lastingness of the +Motions excited in the bottom of the Eye by Light, are they not of a +vibrating nature? + +_Qu._ 17. If a stone be thrown into stagnating Water, the Waves excited +thereby continue some time to arise in the place where the Stone fell +into the Water, and are propagated from thence in concentrick Circles +upon the Surface of the Water to great distances. And the Vibrations or +Tremors excited in the Air by percussion, continue a little time to move +from the place of percussion in concentrick Spheres to great distances. +And in like manner, when a Ray of Light falls upon the Surface of any +pellucid Body, and is there refracted or reflected, may not Waves of +Vibrations, or Tremors, be thereby excited in the refracting or +reflecting Medium at the point of Incidence, and continue to arise +there, and to be propagated from thence as long as they continue to +arise and be propagated, when they are excited in the bottom of the Eye +by the Pressure or Motion of the Finger, or by the Light which comes +from the Coal of Fire in the Experiments above-mention'd? and are not +these Vibrations propagated from the point of Incidence to great +distances? And do they not overtake the Rays of Light, and by overtaking +them successively, do they not put them into the Fits of easy Reflexion +and easy Transmission described above? For if the Rays endeavour to +recede from the densest part of the Vibration, they may be alternately +accelerated 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, and +the Air be drawn out of one of these Vessels, and these Vessels thus +prepared be carried out of a cold place into a warm one; the Thermometer +_in vacuo_ will grow warm as much, and almost as soon as the Thermometer +which is not _in vacuo_. And when the Vessels are carried back into the +cold place, the Thermometer _in vacuo_ will grow cold almost as soon as +the other Thermometer. Is not the Heat of the warm Room convey'd through +the _Vacuum_ by the Vibrations of a much subtiler Medium than Air, which +after the Air was drawn out remained in the _Vacuum_? And is not this +Medium the same with that Medium by which Light is refracted and +reflected, and by whose Vibrations Light communicates Heat to Bodies, +and is put into Fits of easy Reflexion and easy Transmission? And do not +the Vibrations of this Medium in hot Bodies contribute to the +intenseness and duration of their Heat? And do not hot Bodies +communicate their Heat to contiguous cold ones, by the Vibrations of +this Medium propagated from them into the cold ones? And is not this +Medium exceedingly more rare and subtile than the Air, and exceedingly +more 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 different +density of this Æthereal Medium in different places, the Light receding +always from the denser parts of the Medium? And is not the density +thereof greater in free and open Spaces void of Air and other grosser +Bodies, than within the Pores of Water, Glass, Crystal, Gems, and other +compact Bodies? For when Light passes through Glass or Crystal, and +falling very obliquely upon the farther Surface thereof is totally +reflected, the total Reflexion ought to proceed rather from the density +and vigour of the Medium without and beyond the Glass, than from the +rarity 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, grow +denser and denser by degrees, and by that means refract the Rays of +Light not in a point, but by bending them gradually in curve Lines? And +doth not the gradual condensation of this Medium extend to some distance +from the Bodies, and thereby cause the Inflexions of the Rays of Light, +which pass by the edges of dense Bodies, at some distance from the +Bodies? + +_Qu._ 21. Is not this Medium much rarer within the dense Bodies of the +Sun, Stars, Planets and Comets, than in the empty celestial Spaces +between them? And in passing from them to great distances, doth it not +grow denser and denser perpetually, and thereby cause the gravity of +those great Bodies towards one another, and of their parts towards the +Bodies; every Body endeavouring to go from the denser parts of the +Medium towards the rarer? For if this Medium be rarer within the Sun's +Body than at its Surface, and rarer there than at the hundredth part of +an Inch from its Body, and rarer there than at the fiftieth part of an +Inch from its Body, and rarer there than at the Orb of _Saturn_; I see +no reason why the Increase of density should stop any where, and not +rather be continued through all distances from the Sun to _Saturn_, and +beyond. And though this Increase of density may at great distances be +exceeding slow, yet if the elastick force of this Medium be exceeding +great, it may suffice to impel Bodies from the denser parts of the +Medium towards the rarer, with all that power which we call Gravity. And +that the elastick force of this Medium is exceeding great, may be +gather'd from the swiftness of its Vibrations. Sounds move about 1140 +_English_ Feet in a second Minute of Time, and in seven or eight Minutes +of Time they move about one hundred _English_ Miles. Light moves from +the Sun to us in about seven or eight Minutes of Time, which distance is +about 70,000,000 _English_ Miles, supposing the horizontal Parallax of +the Sun to be about 12´´. And the Vibrations or Pulses of this Medium, +that they may cause the alternate Fits of easy Transmission and easy +Reflexion, must be swifter than Light, and by consequence above 700,000 +times swifter than Sounds. And therefore the elastick force of this +Medium, in proportion to its density, must be above 700000 x 700000 +(that is, above 490,000,000,000) times greater than the elastick force +of the Air is in proportion to its density. For the Velocities of the +Pulses of elastick Mediums are in a subduplicate _Ratio_ of the +Elasticities and the Rarities of the Mediums taken together. + +As Attraction is stronger in small Magnets than in great ones in +proportion to their Bulk, and Gravity is greater in the Surfaces of +small Planets than in those of great ones in proportion to their bulk, +and small Bodies are agitated much more by electric attraction than +great ones; so the smallness of the Rays of Light may contribute very +much to the power of the Agent by which they are refracted. And so if +any one should suppose that _Æther_ (like our Air) may contain Particles +which endeavour to recede from one another (for I do not know what this +_Æther_ is) and that its Particles are exceedingly smaller than those of +Air, or even than those of Light: The exceeding smallness of its +Particles may contribute to the greatness of the force by which those +Particles may recede from one another, and thereby make that Medium +exceedingly more rare and elastick than Air, and by consequence +exceedingly less able to resist the motions of Projectiles, and +exceedingly more able to press upon gross Bodies, by endeavouring to +expand it self. + +_Qu._ 22. May not Planets and Comets, and all gross Bodies, perform +their Motions more freely, and with less resistance in this Æthereal +Medium than in any Fluid, which fills all Space adequately without +leaving any Pores, and by consequence is much denser than Quick-silver +or Gold? And may not its resistance be so small, as to be +inconsiderable? For instance; If this _Æther_ (for so I will call it) +should be supposed 700000 times more elastick than our Air, and above +700000 times more rare; its resistance would be above 600,000,000 times +less than that of Water. And so small a resistance would scarce make any +sensible alteration in the Motions of the Planets in ten thousand +Years. If any one would ask how a Medium can be so rare, let him tell me +how the Air, in the upper parts of the Atmosphere, can be above an +hundred thousand thousand times rarer than Gold. Let him also tell me, +how an electrick Body can by Friction emit an Exhalation so rare and +subtile, and yet so potent, as by its Emission to cause no sensible +Diminution of the weight of the electrick Body, and to be expanded +through a Sphere, whose Diameter is above two Feet, and yet to be able +to agitate and carry up Leaf Copper, or Leaf Gold, at the distance of +above a Foot from the electrick Body? And how the Effluvia of a Magnet +can be so rare and subtile, as to pass through a Plate of Glass without +any Resistance or Diminution of their Force, and yet so potent as to +turn a magnetick Needle beyond the Glass? + +_Qu._ 23. Is not Vision perform'd chiefly by the Vibrations of this +Medium, excited in the bottom of the Eye by the Rays of Light, and +propagated through the solid, pellucid and uniform Capillamenta of the +optick Nerves into the place of Sensation? And is not Hearing perform'd +by the Vibrations either of this or some other Medium, excited in the +auditory Nerves by the Tremors of the Air, and propagated through the +solid, pellucid and uniform Capillamenta of those Nerves into the place +of Sensation? And so of the other Senses. + +_Qu._ 24. Is not Animal Motion perform'd by the Vibrations of this +Medium, excited in the Brain by the power of the Will, and propagated +from thence through the solid, pellucid and uniform Capillamenta of the +Nerves into the Muscles, for contracting and dilating them? I suppose +that the Capillamenta of the Nerves are each of them solid and uniform, +that the vibrating Motion of the Æthereal Medium may be propagated along +them from one end to the other uniformly, and without interruption: For +Obstructions in the Nerves create Palsies. And that they may be +sufficiently uniform, I suppose them to be pellucid when view'd singly, +tho' the Reflexions in their cylindrical Surfaces may make the whole +Nerve (composed of many Capillamenta) appear opake and white. For +opacity arises from reflecting Surfaces, such as may disturb and +interrupt the Motions of this Medium. + +[Sidenote: _See the following Scheme, p. 356._] + +_Qu._ 25. Are there not other original Properties of the Rays of Light, +besides those already described? An instance of another original +Property we have in the Refraction of Island Crystal, described first by +_Erasmus Bartholine_, and afterwards more exactly by _Hugenius_, in his +Book _De la Lumiere_. This Crystal is a pellucid fissile Stone, clear as +Water or Crystal of the Rock, and without Colour; enduring a red Heat +without losing its transparency, and in a very strong Heat calcining +without Fusion. Steep'd a Day or two in Water, it loses its natural +Polish. Being rubb'd on Cloth, it attracts pieces of Straws and other +light things, like Ambar or Glass; and with _Aqua fortis_ it makes an +Ebullition. It seems to be a sort of Talk, and is found in form of an +oblique Parallelopiped, with six parallelogram Sides and eight solid +Angles. The obtuse Angles of the Parallelograms are each of them 101 +Degrees and 52 Minutes; the acute ones 78 Degrees and 8 Minutes. Two of +the solid Angles opposite to one another, as C and E, are compassed each +of them with three of these obtuse Angles, and each of the other six +with one obtuse and two acute ones. It cleaves easily in planes parallel +to any of its Sides, and not in any other Planes. It cleaves with a +glossy polite Surface not perfectly plane, but with some little +unevenness. It is easily scratch'd, and by reason of its softness it +takes a Polish very difficultly. It polishes better upon polish'd +Looking-glass than upon Metal, and perhaps better upon Pitch, Leather or +Parchment. Afterwards it must be rubb'd with a little Oil or white of an +Egg, to fill up its Scratches; whereby it will become very transparent +and polite. But for several Experiments, it is not necessary to polish +it. If a piece of this crystalline Stone be laid upon a Book, every +Letter of the Book seen through it will appear double, by means of a +double Refraction. And if any beam of Light falls either +perpendicularly, or in any oblique Angle upon any Surface of this +Crystal, it becomes divided into two beams by means of the same double +Refraction. Which beams are of the same Colour with the incident beam of +Light, and seem equal to one another in the quantity of their Light, or +very nearly equal. One of these Refractions is perform'd by the usual +Rule of Opticks, the Sine of Incidence out of Air into this Crystal +being to the Sine of Refraction, as five to three. The other +Refraction, which may be called the unusual Refraction, is perform'd by +the following Rule. + +[Illustration: FIG. 4.] + +Let ADBC represent the refracting Surface of the Crystal, C the biggest +solid Angle at that Surface, GEHF the opposite Surface, and CK a +perpendicular on that Surface. This perpendicular makes with the edge of +the Crystal CF, an Angle of 19 Degr. 3'. Join KF, and in it take KL, so +that the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. And +if ST represent any beam of Light incident at T in any Angle upon the +refracting Surface ADBC, let TV be the refracted beam determin'd by the +given Portion of the Sines 5 to 3, according to the usual Rule of +Opticks. Draw VX parallel and equal to KL. Draw it the same way from V +in which L lieth from K; and joining TX, this line TX shall be the other +refracted beam carried from T to X, by the unusual Refraction. + +If therefore the incident beam ST be perpendicular to the refracting +Surface, 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 going +through the Crystal perpendicularly, as it ought to do by the usual Laws +of Opticks, and the other TX by an unusual Refraction diverging from the +perpendicular, 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 like +Planes which are parallel to the Plane CFK, may be called the Planes of +perpendicular Refraction. And the Coast towards which the lines KL and +VX are drawn, may be call'd the Coast of unusual Refraction. + +In like manner Crystal of the Rock has a double Refraction: But the +difference of the two Refractions is not so great and manifest as in +Island Crystal. + +When the beam ST incident on Island Crystal is divided into two beams TV +and 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 usual +manner, shall be again refracted entirely after the usual manner at the +second Surface; and the beam TX, which was refracted after the unusual +manner in the first Surface, shall be again refracted entirely after the +unusual manner in the second Surface; so that both these beams shall +emerge out of the second Surface in lines parallel to the first incident +beam ST. + +And if two pieces of Island Crystal be placed one after another, in such +manner that all the Surfaces of the latter be parallel to all the +corresponding Surfaces of the former: The Rays which are refracted after +the usual manner in the first Surface of the first Crystal, shall be +refracted after the usual manner in all the following Surfaces; and the +Rays which are refracted after the unusual manner in the first Surface, +shall be refracted after the unusual manner in all the following +Surfaces. And the same thing happens, though the Surfaces of the +Crystals be any ways inclined to one another, provided that their Planes +of perpendicular Refraction be parallel to one another. + +And therefore there is an original difference in the Rays of Light, by +means of which some Rays are in this Experiment constantly refracted +after the usual manner, and others constantly after the unusual manner: +For if the difference be not original, but arises from new Modifications +impress'd on the Rays at their first Refraction, it would be alter'd by +new Modifications in the three following Refractions; whereas it suffers +no alteration, but is constant, and has the same effect upon the Rays in +all the Refractions. The unusual Refraction is therefore perform'd by an +original property of the Rays. And it remains to be enquired, whether +the Rays have not more original Properties than are yet discover'd. + +_Qu._ 26. Have not the Rays of Light several sides, endued with several +original Properties? For if the Planes of perpendicular Refraction of +the second Crystal be at right Angles with the Planes of perpendicular +Refraction of the first Crystal, the Rays which are refracted after the +usual manner in passing through the first Crystal, will be all of them +refracted after the unusual manner in passing through the second +Crystal; and the Rays which are refracted after the unusual manner in +passing through the first Crystal, will be all of them refracted after +the usual manner in passing through the second Crystal. And therefore +there are not two sorts of Rays differing in their nature from one +another, one of which is constantly and in all Positions refracted after +the usual manner, and the other constantly and in all Positions after +the unusual manner. The difference between the two sorts of Rays in the +Experiment mention'd in the 25th Question, was only in the Positions of +the Sides of the Rays to the Planes of perpendicular Refraction. For one +and the same Ray is here refracted sometimes after the usual, and +sometimes after the unusual manner, according to the Position which its +Sides have to the Crystals. If the Sides of the Ray are posited the same +way to both Crystals, it is refracted after the same manner in them +both: But if that side of the Ray which looks towards the Coast of the +unusual Refraction of the first Crystal, be 90 Degrees from that side of +the same Ray which looks toward the Coast of the unusual Refraction of +the second Crystal, (which may be effected by varying the Position of +the second Crystal to the first, and by consequence to the Rays of +Light,) the Ray shall be refracted after several manners in the several +Crystals. There is nothing more required to determine whether the Rays +of Light which fall upon the second Crystal shall be refracted after +the 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 or +on that side of the Ray. And therefore every Ray may be consider'd as +having four Sides or Quarters, two of which opposite to one another +incline the Ray to be refracted after the unusual manner, as often as +either of them are turn'd towards the Coast of unusual Refraction; and +the other two, whenever either of them are turn'd towards the Coast of +unusual Refraction, do not incline it to be otherwise refracted than +after the usual manner. The two first may therefore be call'd the Sides +of unusual Refraction. And since these Dispositions were in the Rays +before their Incidence on the second, third, and fourth Surfaces of the +two Crystals, and suffered no alteration (so far as appears,) by the +Refraction of the Rays in their passage through those Surfaces, and the +Rays were refracted by the same Laws in all the four Surfaces; it +appears that those Dispositions were in the Rays originally, and +suffer'd no alteration by the first Refraction, and that by means of +those Dispositions the Rays were refracted at their Incidence on the +first Surface of the first Crystal, some of them after the usual, and +some of them after the unusual manner, accordingly as their Sides of +unusual Refraction were then turn'd towards the Coast of the unusual +Refraction of that Crystal, or sideways from it. + +Every Ray of Light has therefore two opposite Sides, originally endued +with a Property on which the unusual Refraction depends, and the other +two opposite Sides not endued with that Property. And it remains to be +enquired, whether there are not more Properties of Light by which the +Sides of the Rays differ, and are distinguished from one another. + +In explaining the difference of the Sides of the Rays above mention'd, I +have supposed that the Rays fall perpendicularly on the first Crystal. +But if they fall obliquely on it, the Success is the same. Those Rays +which are refracted after the usual manner in the first Crystal, will be +refracted after the unusual manner in the second Crystal, supposing the +Planes of perpendicular Refraction to be at right Angles with one +another, as above; and on the contrary. + +If the Planes of the perpendicular Refraction of the two Crystals be +neither parallel nor perpendicular to one another, but contain an acute +Angle: 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 the +second Crystal. For in this case the Rays in each of the two beams will +some of them have their Sides of unusual Refraction, and some of them +their other Sides turn'd towards the Coast of the unusual Refraction of +the second Crystal. + +_Qu._ 27. Are not all Hypotheses erroneous which have hitherto been +invented for explaining the Phænomena of Light, by new Modifications of +the Rays? For those Phænomena depend not upon new Modifications, as has +been supposed, but upon the original and unchangeable Properties of the +Rays. + +_Qu._ 28. Are not all Hypotheses erroneous, in which Light is supposed +to consist in Pression or Motion, propagated through a fluid Medium? For +in all these Hypotheses the Phænomena of Light have been hitherto +explain'd by supposing that they arise from new Modifications of the +Rays; which is an erroneous Supposition. + +If Light consisted only in Pression propagated without actual Motion, it +would not be able to agitate and heat the Bodies which refract and +reflect it. If it consisted in Motion propagated to all distances in an +instant, it would require an infinite force every moment, in every +shining Particle, to generate that Motion. And if it consisted in +Pression or Motion, propagated either in an instant or in time, it would +bend into the Shadow. For Pression or Motion cannot be propagated in a +Fluid in right Lines, beyond an Obstacle which stops part of the Motion, +but will bend and spread every way into the quiescent Medium which lies +beyond the Obstacle. Gravity tends downwards, but the Pressure of Water +arising from Gravity tends every way with equal Force, and is propagated +as readily, and with as much force sideways as downwards, and through +crooked passages as through strait ones. The Waves on the Surface of +stagnating Water, passing by the sides of a broad Obstacle which stops +part of them, bend afterwards and dilate themselves gradually into the +quiet Water behind the Obstacle. The Waves, Pulses or Vibrations of the +Air, wherein Sounds consist, bend manifestly, though not so much as the +Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which +intercepts the sight of the sounding Body, and Sounds are propagated as +readily through crooked Pipes as through streight ones. But Light is +never known to follow crooked Passages nor to bend into the Shadow. For +the fix'd Stars by the Interposition of any of the Planets cease to be +seen. And so do the Parts of the Sun by the Interposition of the Moon, +_Mercury_ or _Venus_. The Rays which pass very near to the edges of any +Body, 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'd +only in the passage of the Ray by the Body, and at a very small distance +from it. So soon as the Ray is past the Body, it goes right on. + +[Sidenote: _Mais pour dire comment cela se fait, je n'ay rien trove +jusqu' ici qui me satisfasse._ C. H. de la lumiere, c. 5, p. 91.] + +To explain the unusual Refraction of Island Crystal by Pression or +Motion propagated, has not hitherto been attempted (to my knowledge) +except by _Huygens_, who for that end supposed two several vibrating +Mediums within that Crystal. But when he tried the Refractions in two +successive pieces of that Crystal, and found them such as is mention'd +above; he confessed himself at a loss for explaining them. For Pressions +or 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 different +Sides. He suspected that the Pulses of _Æther_ in passing through the +first Crystal might receive certain new Modifications, which might +determine them to be propagated in this or that Medium within the +second Crystal, according to the Position of that Crystal. But what +Modifications those might be he could not say, nor think of any thing +satisfactory in that Point. And if he had known that the unusual +Refraction depends not on new Modifications, but on the original and +unchangeable Dispositions of the Rays, he would have found it as +difficult to explain how those Dispositions which he supposed to be +impress'd on the Rays by the first Crystal, could be in them before +their Incidence on that Crystal, and in general, how all Rays emitted by +shining Bodies, can have those Dispositions in them from the beginning. +To me, at least, this seems inexplicable, if Light be nothing else than +Pression or Motion propagated through _Æther_. + +And it is as difficult to explain by these Hypotheses, how Rays can be +alternately in Fits of easy Reflexion and easy Transmission; unless +perhaps one might suppose that there are in all Space two Æthereal +vibrating Mediums, and that the Vibrations of one of them constitute +Light, and the Vibrations of the other are swifter, and as often as they +overtake the Vibrations of the first, put them into those Fits. But how +two _Æthers_ can be diffused through all Space, one of which acts upon +the other, and by consequence is re-acted upon, without retarding, +shattering, dispersing and confounding one anothers Motions, is +inconceivable. And against filling the Heavens with fluid Mediums, +unless they be exceeding rare, a great Objection arises from the regular +and very lasting Motions of the Planets and Comets in all manner of +Courses through the Heavens. For thence it is manifest, that the Heavens +are void of all sensible Resistance, and by consequence of all sensible +Matter. + +For the resisting Power of fluid Mediums arises partly from the +Attrition of the Parts of the Medium, and partly from the _Vis inertiæ_ +of the Matter. That part of the Resistance of a spherical Body which +arises from the Attrition of the Parts of the Medium is very nearly as +the Diameter, or, at the most, as the _Factum_ of the Diameter, and the +Velocity of the spherical Body together. And that part of the Resistance +which arises from the _Vis inertiæ_ of the Matter, is as the Square of +that _Factum_. And by this difference the two sorts of Resistance may be +distinguish'd from one another in any Medium; and these being +distinguish'd, it will be found that almost all the Resistance of Bodies +of a competent Magnitude moving in Air, Water, Quick-silver, and such +like Fluids with a competent Velocity, arises from the _Vis inertiæ_ of +the Parts of the Fluid. + +Now that part of the resisting Power of any Medium which arises from the +Tenacity, Friction or Attrition of the Parts of the Medium, may be +diminish'd by dividing the Matter into smaller Parts, and making the +Parts more smooth and slippery: But that part of the Resistance which +arises from the _Vis inertiæ_, is proportional to the Density of the +Matter, and cannot be diminish'd by dividing the Matter into smaller +Parts, nor by any other means than by decreasing the Density of the +Medium. And for these Reasons the Density of fluid Mediums is very +nearly proportional to their Resistance. Liquors which differ not much +in Density, as Water, Spirit of Wine, Spirit of Turpentine, hot Oil, +differ not much in Resistance. Water is thirteen or fourteen times +lighter than Quick-silver and by consequence thirteen or fourteen times +rarer, and its Resistance is less than that of Quick-silver in the same +Proportion, or thereabouts, as I have found by Experiments made with +Pendulums. The open Air in which we breathe is eight or nine hundred +times lighter than Water, and by consequence eight or nine hundred times +rarer, and accordingly its Resistance is less than that of Water in the +same Proportion, or thereabouts; as I have also found by Experiments +made with Pendulums. And in thinner Air the Resistance is still less, +and at length, by ratifying the Air, becomes insensible. For small +Feathers falling in the open Air meet with great Resistance, but in a +tall Glass well emptied of Air, they fall as fast as Lead or Gold, as I +have seen tried several times. Whence the Resistance seems still to +decrease in proportion to the Density of the Fluid. For I do not find by +any Experiments, that Bodies moving in Quick-silver, Water or Air, meet +with any other sensible Resistance than what arises from the Density and +Tenacity of those sensible Fluids, as they would do if the Pores of +those Fluids, and all other Spaces, were filled with a dense and +subtile 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 a +million of times less than in Quick-silver. But it seems to be much less +in such a Vessel, and still much less in the Heavens, at the height of +three or four hundred Miles from the Earth, or above. For Mr. _Boyle_ +has shew'd that Air may be rarified above ten thousand times in Vessels +of Glass; and the Heavens are much emptier of Air than any _Vacuum_ we +can make below. For since the Air is compress'd by the Weight of the +incumbent Atmosphere, and the Density of Air is proportional to the +Force compressing it, it follows by Computation, that at the height of +about seven and a half _English_ Miles from the Earth, the Air is four +times rarer than at the Surface of the Earth; and at the height of 15 +Miles 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 1000000000000000000 +times 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 increases +the Fluidity of tenacious Liquids, as of Oil, Balsam, and Honey, and +thereby decreases their Resistance. But it decreases not the Resistance +of Water considerably, as it would do if any considerable part of the +Resistance of Water arose from the Attrition or Tenacity of its Parts. +And therefore the Resistance of Water arises principally and almost +entirely from the _Vis inertiæ_ of its Matter; and by consequence, if +the Heavens were as dense as Water, they would not have much less +Resistance than Water; if as dense as Quick-silver, they would not have +much less Resistance than Quick-silver; if absolutely dense, or full of +Matter without any _Vacuum_, let the Matter be never so subtil and +fluid, they would have a greater Resistance than Quick-silver. A solid +Globe in such a Medium would lose above half its Motion in moving three +times the length of its Diameter, and a Globe not solid (such as are the +Planets,) would be retarded sooner. And therefore to make way for the +regular and lasting Motions of the Planets and Comets, it's necessary to +empty 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 we +described above. A dense Fluid can be of no use for explaining the +Phænomena of Nature, the Motions of the Planets and Comets being better +explain'd without it. It serves only to disturb and retard the Motions +of those great Bodies, and make the Frame of Nature languish: And in the +Pores of Bodies, it serves only to stop the vibrating Motions of their +Parts, wherein their Heat and Activity consists. And as it is of no use, +and hinders the Operations of Nature, and makes her languish, so there +is no evidence for its Existence, and therefore it ought to be rejected. +And if it be rejected, the Hypotheses that Light consists in Pression +or Motion, propagated through such a Medium, are rejected with it. + +And for rejecting such a Medium, we have the Authority of those the +oldest and most celebrated Philosophers of _Greece_ and _Phoenicia_, +who made a _Vacuum_, and Atoms, and the Gravity of Atoms, the first +Principles of their Philosophy; tacitly attributing Gravity to some +other Cause than dense Matter. Later Philosophers banish the +Consideration of such a Cause out of natural Philosophy, feigning +Hypotheses for explaining all things mechanically, and referring other +Causes to Metaphysicks: Whereas the main Business of natural Philosophy +is to argue from Phænomena without feigning Hypotheses, and to deduce +Causes from Effects, till we come to the very first Cause, which +certainly is not mechanical; and not only to unfold the Mechanism of the +World, but chiefly to resolve these and such like Questions. What is +there in places almost empty of Matter, and whence is it that the Sun +and Planets gravitate towards one another, without dense Matter between +them? Whence is it that Nature doth nothing in vain; and whence arises +all that Order and Beauty which we see in the World? To what end are +Comets, and whence is it that Planets move all one and the same way in +Orbs concentrick, while Comets move all manner of ways in Orbs very +excentrick; and what hinders the fix'd Stars from falling upon one +another? How came the Bodies of Animals to be contrived with so much +Art, and for what ends were their several Parts? Was the Eye contrived +without Skill in Opticks, and the Ear without Knowledge of Sounds? How +do the Motions of the Body follow from the Will, and whence is the +Instinct in Animals? Is not the Sensory of Animals that place to which +the sensitive Substance is present, and into which the sensible Species +of Things are carried through the Nerves and Brain, that there they may +be perceived by their immediate presence to that Substance? And these +things being rightly dispatch'd, does it not appear from Phænomena that +there is a Being incorporeal, living, intelligent, omnipresent, who in +infinite Space, as it were in his Sensory, sees the things themselves +intimately, and throughly perceives them, and comprehends them wholly by +their immediate presence to himself: Of which things the Images only +carried through the Organs of Sense into our little Sensoriums, are +there seen and beheld by that which in us perceives and thinks. And +though every true Step made in this Philosophy brings us not immediately +to the Knowledge of the first Cause, yet it brings us nearer to it, and +on that account is to be highly valued. + +_Qu._ 29. Are not the Rays of Light very small Bodies emitted from +shining Substances? For such Bodies will pass through uniform Mediums in +right Lines without bending into the Shadow, which is the Nature of the +Rays of Light. They will also be capable of several Properties, and be +able to conserve their Properties unchanged in passing through several +Mediums, which is another Condition of the Rays of Light. Pellucid +Substances act upon the Rays of Light at a distance in refracting, +reflecting, and inflecting them, and the Rays mutually agitate the Parts +of those Substances at a distance for heating them; and this Action and +Re-action at a distance very much resembles an attractive Force between +Bodies. If Refraction be perform'd by Attraction of the Rays, the Sines +of 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 by +Experience. The Rays of Light in going out of Glass into a _Vacuum_, are +bent towards the Glass; and if they fall too obliquely on the _Vacuum_, +they are bent backwards into the Glass, and totally reflected; and this +Reflexion cannot be ascribed to the Resistance of an absolute _Vacuum_, +but must be caused by the Power of the Glass attracting the Rays at +their going out of it into the _Vacuum_, and bringing them back. For if +the farther Surface of the Glass be moisten'd with Water or clear Oil, +or liquid and clear Honey, the Rays which would otherwise be reflected +will go into the Water, Oil, or Honey; and therefore are not reflected +before they arrive at the farther Surface of the Glass, and begin to go +out of it. If they go out of it into the Water, Oil, or Honey, they go +on, because the Attraction of the Glass is almost balanced and rendered +ineffectual by the contrary Attraction of the Liquor. But if they go out +of it into a _Vacuum_ which has no Attraction to balance that of the +Glass, the Attraction of the Glass either bends and refracts them, or +brings them back and reflects them. And this is still more evident by +laying together two Prisms of Glass, or two Object-glasses of very long +Telescopes, the one plane, the other a little convex, and so compressing +them that they do not fully touch, nor are too far asunder. For the +Light which falls upon the farther Surface of the first Glass where the +Interval between the Glasses is not above the ten hundred thousandth +Part of an Inch, will go through that Surface, and through the Air or +_Vacuum_ between the Glasses, and enter into the second Glass, as was +explain'd in the first, fourth, and eighth Observations of the first +Part of the second Book. But, if the second Glass be taken away, the +Light which goes out of the second Surface of the first Glass into the +Air or _Vacuum_, will not go on forwards, but turns back into the first +Glass, and is reflected; and therefore it is drawn back by the Power of +the first Glass, there being nothing else to turn it back. Nothing more +is requisite for producing all the variety of Colours, and degrees of +Refrangibility, than that the Rays of Light be Bodies of different +Sizes, the least of which may take violet the weakest and darkest of the +Colours, and be more easily diverted by refracting Surfaces from the +right Course; and the rest as they are bigger and bigger, may make the +stronger and more lucid Colours, blue, green, yellow, and red, and be +more and more difficultly diverted. Nothing more is requisite for +putting the Rays of Light into Fits of easy Reflexion and easy +Transmission, than that they be small Bodies which by their attractive +Powers, or some other Force, stir up Vibrations in what they act upon, +which Vibrations being swifter than the Rays, overtake them +successively, and agitate them so as by turns to increase and decrease +their Velocities, and thereby put them into those Fits. And lastly, the +unusual Refraction of Island-Crystal looks very much as if it were +perform'd by some kind of attractive virtue lodged in certain Sides both +of the Rays, and of the Particles of the Crystal. For were it not for +some kind of Disposition or Virtue lodged in some Sides of the Particles +of the Crystal, and not in their other Sides, and which inclines and +bends the Rays towards the Coast of unusual Refraction, the Rays which +fall perpendicularly on the Crystal, would not be refracted towards that +Coast rather than towards any other Coast, both at their Incidence and +at their Emergence, so as to emerge perpendicularly by a contrary +Situation of the Coast of unusual Refraction at the second Surface; the +Crystal acting upon the Rays after they have pass'd through it, and are +emerging into the Air; or, if you please, into a _Vacuum_. And since the +Crystal by this Disposition or Virtue does not act upon the Rays, unless +when one of their Sides of unusual Refraction looks towards that Coast, +this argues a Virtue or Disposition in those Sides of the Rays, which +answers to, and sympathizes with that Virtue or Disposition of the +Crystal, as the Poles of two Magnets answer to one another. And as +Magnetism may be intended and remitted, and is found only in the Magnet +and in Iron: So this Virtue of refracting the perpendicular Rays is +greater in Island-Crystal, less in Crystal of the Rock, and is not yet +found in other Bodies. I do not say that this Virtue is magnetical: It +seems to be of another kind. I only say, that whatever it be, it's +difficult to conceive how the Rays of Light, unless they be Bodies, can +have a permanent Virtue in two of their Sides which is not in their +other Sides, and this without any regard to their Position to the Space +or Medium through which they pass. + +What I mean in this Question by a _Vacuum_, and by the Attractions of +the Rays of Light towards Glass or Crystal, may be understood by what +was said in the 18th, 19th, and 20th Questions. + +_Quest._ 30. Are not gross Bodies and Light convertible into one +another, and may not Bodies receive much of their Activity from the +Particles of Light which enter their Composition? For all fix'd Bodies +being heated emit Light so long as they continue sufficiently hot, and +Light mutually stops in Bodies as often as its Rays strike upon their +Parts, 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 a +sufficient Heat, shines by Heat like other Bodies. + +The changing of Bodies into Light, and Light into Bodies, is very +conformable to the Course of Nature, which seems delighted with +Transmutations. Water, which is a very fluid tasteless Salt, she changes +by Heat into Vapour, which is a sort of Air, and by Cold into Ice, which +is a hard, pellucid, brittle, fusible Stone; and this Stone returns into +Water by Heat, and Vapour returns into Water by Cold. Earth by Heat +becomes Fire, and by Cold returns into Earth. Dense Bodies by +Fermentation rarify into several sorts of Air, and this Air by +Fermentation, and sometimes without it, returns into dense Bodies. +Mercury appears sometimes in the form of a fluid Metal, sometimes in the +form of a hard brittle Metal, sometimes in the form of a corrosive +pellucid Salt call'd Sublimate, sometimes in the form of a tasteless, +pellucid, volatile white Earth, call'd _Mercurius Dulcis_; or in that of +a red opake volatile Earth, call'd Cinnaber; or in that of a red or +white Precipitate, or in that of a fluid Salt; and in Distillation it +turns into Vapour, and being agitated _in Vacuo_, it shines like Fire. +And after all these Changes it returns again into its first form of +Mercury. 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 out +of Water and watry Tinctures and Salts, and by Putrefaction return again +into watry Substances. And Water standing a few Days in the open Air, +yields a Tincture, which (like that of Malt) by standing longer yields a +Sediment and a Spirit, but before Putrefaction is fit Nourishment for +Animals and Vegetables. And among such various and strange +Transmutations, why may not Nature change Bodies into Light, and Light +into Bodies? + +_Quest._ 31. Have not the small Particles of Bodies certain Powers, +Virtues, or Forces, by which they act at a distance, not only upon the +Rays of Light for reflecting, refracting, and inflecting them, but also +upon 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 Attractions +of Gravity, Magnetism, and Electricity; and these Instances shew the +Tenor and Course of Nature, and make it not improbable but that there +may be more attractive Powers than these. For Nature is very consonant +and conformable to her self. How these Attractions may be perform'd, I +do not here consider. What I call Attraction may be perform'd by +impulse, or by some other means unknown to me. I use that Word here to +signify only in general any Force by which Bodies tend towards one +another, whatsoever be the Cause. For we must learn from the Phænomena +of Nature what Bodies attract one another, and what are the Laws and +Properties of the Attraction, before we enquire the Cause by which the +Attraction is perform'd. The Attractions of Gravity, Magnetism, and +Electricity, reach to very sensible distances, and so have been observed +by vulgar Eyes, and there may be others which reach to so small +distances as hitherto escape Observation; and perhaps electrical +Attraction may reach to such small distances, even without being excited +by Friction. + +For when Salt of Tartar runs _per Deliquium_, is not this done by an +Attraction between the Particles of the Salt of Tartar, and the +Particles of the Water which float in the Air in the form of Vapours? +And why does not common Salt, or Salt-petre, or Vitriol, run _per +Deliquium_, but for want of such an Attraction? Or why does not Salt of +Tartar draw more Water out of the Air than in a certain Proportion to +its quantity, but for want of an attractive Force after it is satiated +with Water? And whence is it but from this attractive Power that Water +which alone distils with a gentle luke-warm Heat, will not distil from +Salt of Tartar without a great Heat? And is it not from the like +attractive Power between the Particles of Oil of Vitriol and the +Particles of Water, that Oil of Vitriol draws to it a good quantity of +Water out of the Air, and after it is satiated draws no more, and in +Distillation lets go the Water very difficultly? And when Water and Oil +of Vitriol poured successively into the same Vessel grow very hot in the +mixing, does not this Heat argue a great Motion in the Parts of the +Liquors? And does not this Motion argue, that the Parts of the two +Liquors in mixing coalesce with Violence, and by consequence rush +towards one another with an accelerated Motion? And when _Aqua fortis_, +or Spirit of Vitriol poured upon Filings of Iron dissolves the Filings +with a great Heat and Ebullition, is not this Heat and Ebullition +effected by a violent Motion of the Parts, and does not that Motion +argue that the acid Parts of the Liquor rush towards the Parts of the +Metal with violence, and run forcibly into its Pores till they get +between its outmost Particles, and the main Mass of the Metal, and +surrounding those Particles loosen them from the main Mass, and set them +at liberty to float off into the Water? And when the acid Particles, +which alone would distil with an easy Heat, will not separate from the +Particles of the Metal without a very violent Heat, does not this +confirm the Attraction between them? + +When Spirit of Vitriol poured upon common Salt or Salt-petre makes an +Ebullition with the Salt, and unites with it, and in Distillation the +Spirit of the common Salt or Salt-petre comes over much easier than it +would do before, and the acid part of the Spirit of Vitriol stays +behind; does not this argue that the fix'd Alcaly of the Salt attracts +the acid Spirit of the Vitriol more strongly than its own Spirit, and +not being able to hold them both, lets go its own? And when Oil of +Vitriol is drawn off from its weight of Nitre, and from both the +Ingredients a compound Spirit of Nitre is distilled, and two parts of +this 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 of +Turpentine thicken'd with a little Balsam of Sulphur, and the Liquors +grow 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 mix +with violence, and that their Parts in mixing run towards one another +with an accelerated Motion, and clash with the greatest Force? And is it +not for the same reason that well rectified Spirit of Wine poured on the +same compound Spirit flashes; and that the _Pulvis fulminans_, composed +of Sulphur, Nitre, and Salt of Tartar, goes off with a more sudden and +violent Explosion than Gun-powder, the acid Spirits of the Sulphur and +Nitre rushing towards one another, and towards the Salt of Tartar, with +so great a violence, as by the shock to turn the whole at once into +Vapour and Flame? Where the Dissolution is slow, it makes a slow +Ebullition and a gentle Heat; and where it is quicker, it makes a +greater Ebullition with more heat; and where it is done at once, the +Ebullition is contracted into a sudden Blast or violent Explosion, with +a heat equal to that of Fire and Flame. So when a Drachm of the +above-mention'd compound Spirit of Nitre was poured upon half a Drachm +of Oil of Carraway Seeds _in vacuo_, the Mixture immediately made a +flash like Gun-powder, and burst the exhausted Receiver, which was a +Glass six Inches wide, and eight Inches deep. And even the gross Body of +Sulphur powder'd, and with an equal weight of Iron Filings and a little +Water made into Paste, acts upon the Iron, and in five or six hours +grows too hot to be touch'd, and emits a Flame. And by these Experiments +compared with the great quantity of Sulphur with which the Earth +abounds, and the warmth of the interior Parts of the Earth, and hot +Springs, and burning Mountains, and with Damps, mineral Coruscations, +Earthquakes, hot suffocating Exhalations, Hurricanes, and Spouts; we may +learn that sulphureous Steams abound in the Bowels of the Earth and +ferment with Minerals, and sometimes take fire with a sudden Coruscation +and Explosion; and if pent up in subterraneous Caverns, burst the +Caverns with a great shaking of the Earth, as in springing of a Mine. +And then the Vapour generated by the Explosion, expiring through the +Pores of the Earth, feels hot and suffocates, and makes Tempests and +Hurricanes, and sometimes causes the Land to slide, or the Sea to boil, +and carries up the Water thereof in Drops, which by their weight fall +down again in Spouts. Also some sulphureous Steams, at all times when +the Earth is dry, ascending into the Air, ferment there with nitrous +Acids, and sometimes taking fire cause Lightning and Thunder, and fiery +Meteors. For the Air abounds with acid Vapours fit to promote +Fermentations, as appears by the rusting of Iron and Copper in it, the +kindling of Fire by blowing, and the beating of the Heart by means of +Respiration. Now the above-mention'd Motions are so great and violent as +to shew that in Fermentations the Particles of Bodies which almost rest, +are put into new Motions by a very potent Principle, which acts upon +them only when they approach one another, and causes them to meet and +clash with great violence, and grow hot with the motion, and dash one +another into pieces, and vanish into Air, and Vapour, and Flame. + +When Salt of Tartar _per deliquium_, being poured into the Solution of +any Metal, precipitates the Metal and makes it fall down to the bottom +of the Liquor in the form of Mud: Does not this argue that the acid +Particles are attracted more strongly by the Salt of Tartar than by the +Metal, and by the stronger Attraction go from the Metal to the Salt of +Tartar? And so when a Solution of Iron in _Aqua fortis_ dissolves the +_Lapis Calaminaris_, and lets go the Iron, or a Solution of Copper +dissolves Iron immersed in it and lets go the Copper, or a Solution of +Silver dissolves Copper and lets go the Silver, or a Solution of Mercury +in _Aqua fortis_ being poured upon Iron, Copper, Tin, or Lead, dissolves +the Metal and lets go the Mercury; does not this argue that the acid +Particles of the _Aqua fortis_ are attracted more strongly by the _Lapis +Calaminaris_ than by Iron, and more strongly by Iron than by Copper, and +more strongly by Copper than by Silver, and more strongly by Iron, +Copper, Tin, and Lead, than by Mercury? And is it not for the same +reason that Iron requires more _Aqua fortis_ to dissolve it than Copper, +and Copper more than the other Metals; and that of all Metals, Iron is +dissolved 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 run _per +deliquium_, and in Distillation the Water ascends difficultly, and +brings over with it some part of the Oil of Vitriol in the form of +Spirit of Vitriol, and this Spirit being poured upon Iron, Copper, or +Salt of Tartar, unites with the Body and lets go the Water; doth not +this shew that the acid Spirit is attracted by the Water, and more +attracted by the fix'd Body than by the Water, and therefore lets go the +Water to close with the fix'd Body? And is it not for the same reason +that the Water and acid Spirits which are mix'd together in Vinegar, +_Aqua fortis_, and Spirit of Salt, cohere and rise together in +Distillation; but if the _Menstruum_ be poured on Salt of Tartar, or on +Lead, or Iron, or any fix'd Body which it can dissolve, the Acid by a +stronger Attraction adheres to the Body, and lets go the Water? And is +it not also from a mutual Attraction that the Spirits of Soot and +Sea-Salt unite and compose the Particles of Sal-armoniac, which are less +volatile than before, because grosser and freer from Water; and that the +Particles of Sal-armoniac in Sublimation carry up the Particles of +Antimony, which will not sublime alone; and that the Particles of +Mercury uniting with the acid Particles of Spirit of Salt compose +Mercury sublimate, and with the Particles of Sulphur, compose Cinnaber; +and that the Particles of Spirit of Wine and Spirit of Urine well +rectified unite, and letting go the Water which dissolved them, compose +a consistent Body; and that in subliming Cinnaber from Salt of Tartar, +or from quick Lime, the Sulphur by a stronger Attraction of the Salt or +Lime lets go the Mercury, and stays with the fix'd Body; and that when +Mercury sublimate is sublimed from Antimony, or from Regulus of +Antimony, the Spirit of Salt lets go the Mercury, and unites with the +antimonial metal which attracts it more strongly, and stays with it till +the Heat be great enough to make them both ascend together, and then +carries up the Metal with it in the form of a very fusible Salt, called +Butter of Antimony, although the Spirit of Salt alone be almost as +volatile as Water, and the Antimony alone as fix'd as Lead? + +When _Aqua fortis_ dissolves Silver and not Gold, and _Aqua regia_ +dissolves Gold and not Silver, may it not be said that _Aqua fortis_ is +subtil enough to penetrate Gold as well as Silver, but wants the +attractive Force to give it Entrance; and that _Aqua regia_ is subtil +enough to penetrate Silver as well as Gold, but wants the attractive +Force to give it Entrance? For _Aqua regia_ is nothing else than _Aqua +fortis_ mix'd with some Spirit of Salt, or with Sal-armoniac; and even +common Salt dissolved in _Aqua fortis_, enables the _Menstruum_ to +dissolve Gold, though the Salt be a gross Body. When therefore Spirit of +Salt precipitates Silver out of _Aqua fortis_, is it not done by +attracting and mixing with the _Aqua fortis_, and not attracting, or +perhaps repelling Silver? And when Water precipitates Antimony out of +the Sublimate of Antimony and Sal-armoniac, or out of Butter of +Antimony, is it not done by its dissolving, mixing with, and weakening +the Sal-armoniac or Spirit of Salt, and its not attracting, or perhaps +repelling the Antimony? And is it not for want of an attractive virtue +between the Parts of Water and Oil, of Quick-silver and Antimony, of +Lead and Iron, that these Substances do not mix; and by a weak +Attraction, that Quick-silver and Copper mix difficultly; and from a +strong one, that Quick-silver and Tin, Antimony and Iron, Water and +Salts, mix readily? And in general, is it not from the same Principle +that Heat congregates homogeneal Bodies, and separates heterogeneal +ones? + +When Arsenick with Soap gives a Regulus, and with Mercury sublimate a +volatile fusible Salt, like Butter of Antimony, doth not this shew that +Arsenick, which is a Substance totally volatile, is compounded of fix'd +and volatile Parts, strongly cohering by a mutual Attraction, so that +the volatile will not ascend without carrying up the fixed? And so, when +an equal weight of Spirit of Wine and Oil of Vitriol are digested +together, and in Distillation yield two fragrant and volatile Spirits +which will not mix with one another, and a fix'd black Earth remains +behind; doth not this shew that Oil of Vitriol is composed of volatile +and fix'd Parts strongly united by Attraction, so as to ascend together +in form of a volatile, acid, fluid Salt, until the Spirit of Wine +attracts and separates the volatile Parts from the fixed? And therefore, +since Oil of Sulphur _per Campanam_ is of the same Nature with Oil of +Vitriol, may it not be inferred, that Sulphur is also a mixture of +volatile and fix'd Parts so strongly cohering by Attraction, as to +ascend together in Sublimation. By dissolving Flowers of Sulphur in Oil +of Turpentine, and distilling the Solution, it is found that Sulphur is +composed of an inflamable thick Oil or fat Bitumen, an acid Salt, a very +fix'd Earth, and a little Metal. The three first were found not much +unequal to one another, the fourth in so small a quantity as scarce to +be worth considering. The acid Salt dissolved in Water, is the same with +Oil of Sulphur _per Campanam_, and abounding much in the Bowels of the +Earth, and particularly in Markasites, unites it self to the other +Ingredients of the Markasite, which are, Bitumen, Iron, Copper, and +Earth, and with them compounds Allum, Vitriol, and Sulphur. With the +Earth alone it compounds Allum; with the Metal alone, or Metal and +Earth together, it compounds Vitriol; and with the Bitumen and Earth it +compounds Sulphur. Whence it comes to pass that Markasites abound with +those three Minerals. And is it not from the mutual Attraction of the +Ingredients that they stick together for compounding these Minerals, and +that the Bitumen carries up the other Ingredients of the Sulphur, which +without it would not sublime? And the same Question may be put +concerning all, or almost all the gross Bodies in Nature. For all the +Parts of Animals and Vegetables are composed of Substances volatile and +fix'd, fluid and solid, as appears by their Analysis; and so are Salts +and Minerals, so far as Chymists have been hitherto able to examine +their Composition. + +When Mercury sublimate is re-sublimed with fresh Mercury, and becomes +_Mercurius Dulcis_, which is a white tasteless Earth scarce dissolvable +in Water, and _Mercurius Dulcis_ re-sublimed with Spirit of Salt returns +into Mercury sublimate; and when Metals corroded with a little acid turn +into rust, which is an Earth tasteless and indissolvable in Water, and +this Earth imbibed with more acid becomes a metallick Salt; and when +some Stones, as Spar of Lead, dissolved in proper _Menstruums_ become +Salts; do not these things shew that Salts are dry Earth and watry Acid +united by Attraction, and that the Earth will not become a Salt without +so much acid as makes it dissolvable in Water? Do not the sharp and +pungent Tastes of Acids arise from the strong Attraction whereby the +acid Particles rush upon and agitate the Particles of the Tongue? And +when Metals are dissolved in acid _Menstruums_, and the Acids in +conjunction with the Metal act after a different manner, so that the +Compound has a different Taste much milder than before, and sometimes a +sweet one; is it not because the Acids adhere to the metallick +Particles, and thereby lose much of their Activity? And if the Acid be +in too small a Proportion to make the Compound dissolvable in Water, +will it not by adhering strongly to the Metal become unactive and lose +its Taste, and the Compound be a tasteless Earth? For such things as are +not dissolvable by the Moisture of the Tongue, act not upon the Taste. + +As Gravity makes the Sea flow round the denser and weightier Parts of +the Globe of the Earth, so the Attraction may make the watry Acid flow +round the denser and compacter Particles of Earth for composing the +Particles of Salt. For otherwise the Acid would not do the Office of a +Medium between the Earth and common Water, for making Salts dissolvable +in the Water; nor would Salt of Tartar readily draw off the Acid from +dissolved Metals, nor Metals the Acid from Mercury. Now, as in the great +Globe of the Earth and Sea, the densest Bodies by their Gravity sink +down in Water, and always endeavour to go towards the Center of the +Globe; so in Particles of Salt, the densest Matter may always endeavour +to approach the Center of the Particle: So that a Particle of Salt may +be compared to a Chaos; being dense, hard, dry, and earthy in the +Center; and rare, soft, moist, and watry in the Circumference. And +hence it seems to be that Salts are of a lasting Nature, being scarce +destroy'd, unless by drawing away their watry Parts by violence, or by +letting them soak into the Pores of the central Earth by a gentle Heat +in Putrefaction, until the Earth be dissolved by the Water, and +separated into smaller Particles, which by reason of their Smallness +make 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 easily +changing its Texture by a gentle Heat and Motion, till it becomes like +the dense, hard, dry, and durable Earth in the Center of each Particle. +But when the Nourishment grows unfit to be assimilated, or the central +Earth 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 great +quantity of Water, the Particles of the Salt or Vitriol will not sink to +the bottom, though they be heavier in Specie than the Water, but will +evenly diffuse themselves into all the Water, so as to make it as saline +at the top as at the bottom. And does not this imply that the Parts of +the Salt or Vitriol recede from one another, and endeavour to expand +themselves, and get as far asunder as the quantity of Water in which +they float, will allow? And does not this Endeavour imply that they have +a repulsive Force by which they fly from one another, or at least, that +they attract the Water more strongly than they do one another? For as +all things ascend in Water which are less attracted than Water, by the +gravitating Power of the Earth; so all the Particles of Salt which float +in Water, and are less attracted than Water by any one Particle of Salt, +must recede from that Particle, and give way to the more attracted +Water. + +When any saline Liquor is evaporated to a Cuticle and let cool, the Salt +concretes in regular Figures; which argues, that the Particles of the +Salt before they concreted, floated in the Liquor at equal distances in +rank and file, and by consequence that they acted upon one another by +some Power which at equal distances is equal, at unequal distances +unequal. For by such a Power they will range themselves uniformly, and +without it they will float irregularly, and come together as +irregularly. And since the Particles of Island-Crystal act all the same +way upon the Rays of Light for causing the unusual Refraction, may it +not be supposed that in the Formation of this Crystal, the Particles not +only ranged themselves in rank and file for concreting in regular +Figures, but also by some kind of polar Virtue turned their homogeneal +Sides 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, some +have invented hooked Atoms, which is begging the Question; and others +tell us that Bodies are glued together by rest, that is, by an occult +Quality, or rather by nothing; and others, that they stick together by +conspiring Motions, that is, by relative rest amongst themselves. I had +rather infer from their Cohesion, that their Particles attract one +another by some Force, which in immediate Contact is exceeding strong, +at small distances performs the chymical Operations above-mention'd, and +reaches not far from the Particles with any sensible Effect. + +All Bodies seem to be composed of hard Particles: For otherwise Fluids +would not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitriol +do by freezing; Mercury by Fumes of Lead; Spirit of Nitre and Mercury, +by dissolving the Mercury and evaporating the Flegm; Spirit of Wine and +Spirit of Urine, by deflegming and mixing them; and Spirit of Urine and +Spirit of Salt, by subliming them together to make Sal-armoniac. Even +the Rays of Light seem to be hard Bodies; for otherwise they would not +retain different Properties in their different Sides. And therefore +Hardness may be reckon'd the Property of all uncompounded Matter. At +least, this seems to be as evident as the universal Impenetrability of +Matter. For all Bodies, so far as Experience reaches, are either hard, +or may be harden'd; and we have no other Evidence of universal +Impenetrability, besides a large Experience without an experimental +Exception. Now if compound Bodies are so very hard as we find some of +them to be, and yet are very porous, and consist of Parts which are only +laid together; the simple Particles which are void of Pores, and were +never yet divided, must be much harder. For such hard Particles being +heaped up together, can scarce touch one another in more than a few +Points, and therefore must be separable by much less Force than is +requisite to break a solid Particle, whose Parts touch in all the Space +between them, without any Pores or Interstices to weaken their Cohesion. +And how such very hard Particles which are only laid together and touch +only 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 or +press'd towards one another, is very difficult to conceive. + +The same thing I infer also from the cohering of two polish'd Marbles +_in vacuo_, and from the standing of Quick-silver in the Barometer at +the height of 50, 60 or 70 Inches, or above, when ever it is well-purged +of Air and carefully poured in, so that its Parts be every where +contiguous both to one another and to the Glass. The Atmosphere by its +weight presses the Quick-silver into the Glass, to the height of 29 or +30 Inches. And some other Agent raises it higher, not by pressing it +into the Glass, but by making its Parts stick to the Glass, and to one +another. For upon any discontinuation of Parts, made either by Bubbles +or by shaking the Glass, the whole Mercury falls down to the height of +29 or 30 Inches. + +And of the same kind with these Experiments are those that follow. If +two plane polish'd Plates of Glass (suppose two pieces of a polish'd +Looking-glass) be laid together, so that their sides be parallel and at +a very small distance from one another, and then their lower edges be +dipped into Water, the Water will rise up between them. And the less +the distance of the Glasses is, the greater will be the height to which +the Water will rise. If the distance be about the hundredth part of an +Inch, the Water will rise to the height of about an Inch; and if the +distance be greater or less in any Proportion, the height will be +reciprocally proportional to the distance very nearly. For the +attractive Force of the Glasses is the same, whether the distance +between them be greater or less; and the weight of the Water drawn up is +the same, if the height of it be reciprocally proportional to the +distance of the Glasses. And in like manner, Water ascends between two +Marbles polish'd plane, when their polish'd sides are parallel, and at a +very little distance from one another, And if slender Pipes of Glass be +dipped at one end into stagnating Water, the Water will rise up within +the Pipe, and the height to which it rises will be reciprocally +proportional to the Diameter of the Cavity of the Pipe, and will equal +the height to which it rises between two Planes of Glass, if the +Semi-diameter of the Cavity of the Pipe be equal to the distance between +the Planes, or thereabouts. And these Experiments succeed after the same +manner _in vacuo_ as in the open Air, (as hath been tried before the +Royal Society,) and therefore are not influenced by the Weight or +Pressure of the Atmosphere. + +And if a large Pipe of Glass be filled with sifted Ashes well pressed +together in the Glass, and one end of the Pipe be dipped into stagnating +Water, the Water will rise up slowly in the Ashes, so as in the space +of a Week or Fortnight to reach up within the Glass, to the height of 30 +or 40 Inches above the stagnating Water. And the Water rises up to this +height by the Action only of those Particles of the Ashes which are upon +the Surface of the elevated Water; the Particles which are within the +Water, attracting or repelling it as much downwards as upwards. And +therefore the Action of the Particles is very strong. But the Particles +of 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-silver +suspended to the height of 60 or 70 Inches, and therefore acts with a +Force 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 the +Bodies 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, and +twenty 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 one +another, and contain an Angle of about 10 or 15 Minutes, and the same be +first moisten'd on their inward sides with a clean Cloth dipp'd into Oil +of Oranges or Spirit of Turpentine, and a Drop or two of the Oil or +Spirit be let fall upon the lower Glass at the other; so soon as the +upper Glass is laid down upon the lower, so as to touch it at one end as +above, and to touch the Drop at the other end, making with the lower +Glass an Angle of about 10 or 15 Minutes; the Drop will begin to move +towards the Concourse of the Glasses, and will continue to move with an +accelerated Motion, till it arrives at that Concourse of the Glasses. +For the two Glasses attract the Drop, and make it run that way towards +which the Attractions incline. And if when the Drop is in motion you +lift up that end of the Glasses where they meet, and towards which the +Drop moves, the Drop will ascend between the Glasses, and therefore is +attracted. And as you lift up the Glasses more and more, the Drop will +ascend slower and slower, and at length rest, being then carried +downward by its Weight, as much as upwards by the Attraction. And by +this means you may know the Force by which the Drop is attracted at all +distances from the Concourse of the Glasses. + +Now by some Experiments of this kind, (made by Mr. _Hauksbee_) it has +been found that the Attraction is almost reciprocally in a duplicate +Proportion of the distance of the middle of the Drop from the Concourse +of the Glasses, _viz._ reciprocally in a simple Proportion, by reason of +the spreading of the Drop, and its touching each Glass in a larger +Surface; and again reciprocally in a simple Proportion, by reason of the +Attractions growing stronger within the same quantity of attracting +Surface. The Attraction therefore within the same quantity of attracting +Surface, is reciprocally as the distance between the Glasses. And +therefore where the distance is exceeding small, the Attraction must be +exceeding great. By the Table in the second Part of the second Book, +wherein the thicknesses of colour'd Plates of Water between two Glasses +are set down, the thickness of the Plate where it appears very black, is +three eighths of the ten hundred thousandth part of an Inch. And where +the Oil of Oranges between the Glasses is of this thickness, the +Attraction collected by the foregoing Rule, seems to be so strong, as +within a Circle of an Inch in diameter, to suffice to hold up a Weight +equal to that of a Cylinder of Water of an Inch in diameter, and two or +three Furlongs in length. And where it is of a less thickness the +Attraction 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 of +Bodies stick together by very strong Attractions. And it is the Business +of experimental Philosophy to find them out. + +Now the smallest Particles of Matter may cohere by the strongest +Attractions, and compose bigger Particles of weaker Virtue; and many of +these may cohere and compose bigger Particles whose Virtue is still +weaker, and so on for divers Successions, until the Progression end in +the biggest Particles on which the Operations in Chymistry, and the +Colours of natural Bodies depend, and which by cohering compose Bodies +of a sensible Magnitude. If the Body is compact, and bends or yields +inward to Pression without any sliding of its Parts, it is hard and +elastick, returning to its Figure with a Force rising from the mutual +Attraction of its Parts. If the Parts slide upon one another, the Body +is malleable or soft. If they slip easily, and are of a fit Size to be +agitated 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; and +the Drops of every fluid affect a round Figure by the mutual Attraction +of their Parts, as the Globe of the Earth and Sea affects a round Figure +by the mutual Attraction of its Parts by Gravity. + +Since Metals dissolved in Acids attract but a small quantity of the +Acid, their attractive Force can reach but to a small distance from +them. 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 a +Virtue, seems to follow from the Reflexions and Inflexions of the Rays +of Light. For the Rays are repelled by Bodies in both these Cases, +without the immediate Contact of the reflecting or inflecting Body. It +seems also to follow from the Emission of Light; the Ray so soon as it +is shaken off from a shining Body by the vibrating Motion of the Parts +of the Body, and gets beyond the reach of Attraction, being driven away +with exceeding great Velocity. For that Force which is sufficient to +turn it back in Reflexion, may be sufficient to emit it. It seems also +to follow from the Production of Air and Vapour. The Particles when they +are shaken off from Bodies by Heat or Fermentation, so soon as they are +beyond the reach of the Attraction of the Body, receding from it, and +also from one another with great Strength, and keeping at a distance, +so as sometimes to take up above a Million of Times more space than they +did before in the form of a dense Body. Which vast Contraction and +Expansion seems unintelligible, by feigning the Particles of Air to be +springy and ramous, or rolled up like Hoops, or by any other means than +a repulsive Power. The Particles of Fluids which do not cohere too +strongly, and are of such a Smallness as renders them most susceptible +of those Agitations which keep Liquors in a Fluor, are most easily +separated and rarified into Vapour, and in the Language of the Chymists, +they are volatile, rarifying with an easy Heat, and condensing with +Cold. But those which are grosser, and so less susceptible of Agitation, +or cohere by a stronger Attraction, are not separated without a stronger +Heat, or perhaps not without Fermentation. And these last are the Bodies +which Chymists call fix'd, and being rarified by Fermentation, become +true permanent Air; those Particles receding from one another with the +greatest Force, and being most difficultly brought together, which upon +Contact cohere most strongly. And because the Particles of permanent Air +are grosser, and arise from denser Substances than those of Vapours, +thence it is that true Air is more ponderous than Vapour, and that a +moist Atmosphere is lighter than a dry one, quantity for quantity. From +the same repelling Power it seems to be that Flies walk upon the Water +without wetting their Feet; and that the Object-glasses of long +Telescopes lie upon one another without touching; and that dry Powders +are difficultly made to touch one another so as to stick together, +unless by melting them, or wetting them with Water, which by exhaling +may bring them together; and that two polish'd Marbles, which by +immediate Contact stick together, are difficultly brought so close +together 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 the +Attraction of Gravity which intercedes those Bodies, and almost all the +small ones of their Particles by some other attractive and repelling +Powers which intercede the Particles. The _Vis inertiæ_ is a passive +Principle by which Bodies persist in their Motion or Rest, receive +Motion in proportion to the Force impressing it, and resist as much as +they are resisted. By this Principle alone there never could have been +any Motion in the World. Some other Principle was necessary for putting +Bodies into Motion; and now they are in Motion, some other Principle is +necessary for conserving the Motion. For from the various Composition of +two Motions, 'tis very certain that there is not always the same +quantity of Motion in the World. For if two Globes joined by a slender +Rod, revolve about their common Center of Gravity with an uniform +Motion, while that Center moves on uniformly in a right Line drawn in +the Plane of their circular Motion; the Sum of the Motions of the two +Globes, as often as the Globes are in the right Line described by their +common Center of Gravity, will be bigger than the Sum of their Motions, +when they are in a Line perpendicular to that right Line. By this +Instance it appears that Motion may be got or lost. But by reason of the +Tenacity of Fluids, and Attrition of their Parts, and the Weakness of +Elasticity in Solids, Motion is much more apt to be lost than got, and +is always upon the Decay. For Bodies which are either absolutely hard, +or so soft as to be void of Elasticity, will not rebound from one +another. Impenetrability makes them only stop. If two equal Bodies meet +directly _in vacuo_, they will by the Laws of Motion stop where they +meet, and lose all their Motion, and remain in rest, unless they be +elastick, and receive new Motion from their Spring. If they have so much +Elasticity as suffices to make them re-bound with a quarter, or half, or +three quarters of the Force with which they come together, they will +lose three quarters, or half, or a quarter of their Motion. And this may +be try'd, by letting two equal Pendulums fall against one another from +equal heights. If the Pendulums be of Lead or soft Clay, they will lose +all or almost all their Motions: If of elastick Bodies they will lose +all but what they recover from their Elasticity. If it be said, that +they can lose no Motion but what they communicate to other Bodies, the +consequence is, that _in vacuo_ they can lose no Motion, but when they +meet they must go on and penetrate one another's Dimensions. If three +equal round Vessels be filled, the one with Water, the other with Oil, +the third with molten Pitch, and the Liquors be stirred about alike to +give them a vortical Motion; the Pitch by its Tenacity will lose its +Motion quickly, the Oil being less tenacious will keep it longer, and +the Water being less tenacious will keep it longest, but yet will lose +it in a short time. Whence it is easy to understand, that if many +contiguous Vortices of molten Pitch were each of them as large as those +which some suppose to revolve about the Sun and fix'd Stars, yet these +and all their Parts would, by their Tenacity and Stiffness, communicate +their Motion to one another till they all rested among themselves. +Vortices of Oil or Water, or some fluider Matter, might continue longer +in Motion; but unless the Matter were void of all Tenacity and Attrition +of Parts, and Communication of Motion, (which is not to be supposed,) +the Motion would constantly decay. Seeing therefore the variety of +Motion which we find in the World is always decreasing, there is a +necessity of conserving and recruiting it by active Principles, such as +are the cause of Gravity, by which Planets and Comets keep their Motions +in their Orbs, and Bodies acquire great Motion in falling; and the cause +of Fermentation, by which the Heart and Blood of Animals are kept in +perpetual Motion and Heat; the inward Parts of the Earth are constantly +warm'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 Sun +continues violently hot and lucid, and warms all things by his Light. +For we meet with very little Motion in the World, besides what is owing +to these active Principles. And if it were not for these Principles, the +Bodies of the Earth, Planets, Comets, Sun, and all things in them, +would grow cold and freeze, and become inactive Masses; and all +Putrefaction, Generation, Vegetation and Life would cease, and the +Planets and Comets would not remain in their Orbs. + +All these things being consider'd, it seems probable to me, that God in +the Beginning form'd Matter in solid, massy, hard, impenetrable, +moveable Particles, of such Sizes and Figures, and with such other +Properties, and in such Proportion to Space, as most conduced to the End +for which he form'd them; and that these primitive Particles being +Solids, are incomparably harder than any porous Bodies compounded of +them; even so very hard, as never to wear or break in pieces; no +ordinary Power being able to divide what God himself made one in the +first Creation. While the Particles continue entire, they may compose +Bodies of one and the same Nature and Texture in all Ages: But should +they wear away, or break in pieces, the Nature of Things depending on +them, would be changed. Water and Earth, composed of old worn Particles +and Fragments of Particles, would not be of the same Nature and Texture +now, with Water and Earth composed of entire Particles in the Beginning. +And therefore, that Nature may be lasting, the Changes of corporeal +Things are to be placed only in the various Separations and new +Associations and Motions of these permanent Particles; compound Bodies +being apt to break, not in the midst of solid Particles, but where those +Particles are laid together, and only touch in a few Points. + +It seems to me farther, that these Particles have not only a _Vis +inertiæ_, accompanied with such passive Laws of Motion as naturally +result from that Force, but also that they are moved by certain active +Principles, such as is that of Gravity, and that which causes +Fermentation, and the Cohesion of Bodies. These Principles I consider, +not as occult Qualities, supposed to result from the specifick Forms of +Things, but as general Laws of Nature, by which the Things themselves +are form'd; their Truth appearing to us by Phænomena, though their +Causes be not yet discover'd. For these are manifest Qualities, and +their Causes only are occult. And the _Aristotelians_ gave the Name of +occult Qualities, not to manifest Qualities, but to such Qualities only +as they supposed to lie hid in Bodies, and to be the unknown Causes of +manifest Effects: Such as would be the Causes of Gravity, and of +magnetick and electrick Attractions, and of Fermentations, if we should +suppose that these Forces or Actions arose from Qualities unknown to us, +and uncapable of being discovered and made manifest. Such occult +Qualities put a stop to the Improvement of natural Philosophy, and +therefore of late Years have been rejected. To tell us that every +Species of Things is endow'd with an occult specifick Quality by which +it acts and produces manifest Effects, is to tell us nothing: But to +derive two or three general Principles of Motion from Phænomena, and +afterwards to tell us how the Properties and Actions of all corporeal +Things follow from those manifest Principles, would be a very great step +in Philosophy, though the Causes of those Principles were not yet +discover'd: And therefore I scruple not to propose the Principles of +Motion above-mention'd, they being of very general Extent, and leave +their Causes to be found out. + +Now by the help of these Principles, all material Things seem to have +been composed of the hard and solid Particles above-mention'd, variously +associated 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 did +so, it's unphilosophical to seek for any other Origin of the World, or +to pretend that it might arise out of a Chaos by the mere Laws of +Nature; though being once form'd, it may continue by those Laws for many +Ages. For while Comets move in very excentrick Orbs in all manner of +Positions, blind Fate could never make all the Planets move one and the +same way in Orbs concentrick, some inconsiderable Irregularities +excepted, which may have risen from the mutual Actions of Comets and +Planets upon one another, and which will be apt to increase, till this +System wants a Reformation. Such a wonderful Uniformity in the Planetary +System must be allowed the Effect of Choice. And so must the Uniformity +in the Bodies of Animals, they having generally a right and a left side +shaped alike, and on either side of their Bodies two Legs behind, and +either 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 a +Head upon it; and in the Head two Ears, two Eyes, a Nose, a Mouth, and +a Tongue, alike situated. Also the first Contrivance of those very +artificial Parts of Animals, the Eyes, Ears, Brain, Muscles, Heart, +Lungs, Midriff, Glands, Larynx, Hands, Wings, swimming Bladders, natural +Spectacles, and other Organs of Sense and Motion; and the Instinct of +Brutes and Insects, can be the effect of nothing else than the Wisdom +and Skill of a powerful ever-living Agent, who being in all Places, is +more able by his Will to move the Bodies within his boundless uniform +Sensorium, 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 we +are not to consider the World as the Body of God, or the several Parts +thereof, as the Parts of God. He is an uniform Being, void of Organs, +Members or Parts, and they are his Creatures subordinate to him, and +subservient to his Will; and he is no more the Soul of them, than the +Soul of Man is the Soul of the Species of Things carried through the +Organs of Sense into the place of its Sensation, where it perceives them +by means of its immediate Presence, without the Intervention of any +third thing. The Organs of Sense are not for enabling the Soul to +perceive the Species of Things in its Sensorium, but only for conveying +them thither; and God has no need of such Organs, he being every where +present to the Things themselves. And since Space is divisible _in +infinitum_, and Matter is not necessarily in all places, it may be also +allow'd that God is able to create Particles of Matter of several Sizes +and Figures, and in several Proportions to Space, and perhaps of +different Densities and Forces, and thereby to vary the Laws of Nature, +and make Worlds of several sorts in several Parts of the Universe. At +least, I see nothing of Contradiction in all this. + +As in Mathematicks, so in Natural Philosophy, the Investigation of +difficult Things by the Method of Analysis, ought ever to precede the +Method of Composition. This Analysis consists in making Experiments and +Observations, and in drawing general Conclusions from them by Induction, +and admitting of no Objections against the Conclusions, but such as are +taken from Experiments, or other certain Truths. For Hypotheses are not +to be regarded in experimental Philosophy. And although the arguing from +Experiments and Observations by Induction be no Demonstration of general +Conclusions; yet it is the best way of arguing which the Nature of +Things admits of, and may be looked upon as so much the stronger, by how +much the Induction is more general. And if no Exception occur from +Phænomena, the Conclusion may be pronounced generally. But if at any +time afterwards any Exception shall occur from Experiments, it may then +begin to be pronounced with such Exceptions as occur. By this way of +Analysis we may proceed from Compounds to Ingredients, and from Motions +to the Forces producing them; and in general, from Effects to their +Causes, and from particular Causes to more general ones, till the +Argument end in the most general. This is the Method of Analysis: And +the Synthesis consists in assuming the Causes discover'd, and +establish'd as Principles, and by them explaining the Phænomena +proceeding from them, and proving the Explanations. + +In the two first Books of these Opticks, I proceeded by this Analysis to +discover and prove the original Differences of the Rays of Light in +respect of Refrangibility, Reflexibility, and Colour, and their +alternate Fits of easy Reflexion and easy Transmission, and the +Properties of Bodies, both opake and pellucid, on which their Reflexions +and Colours depend. And these Discoveries being proved, may be assumed +in the Method of Composition for explaining the Phænomena arising from +them: 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 be +discover'd about Light and its Effects upon the Frame of Nature, hinting +several things about it, and leaving the Hints to be examin'd and +improv'd by the farther Experiments and Observations of such as are +inquisitive. And if natural Philosophy in all its Parts, by pursuing +this Method, shall at length be perfected, the Bounds of Moral +Philosophy will be also enlarged. For so far as we can know by natural +Philosophy what is the first Cause, what Power he has over us, and what +Benefits we receive from him, so far our Duty towards him, as well as +that towards one another, will appear to us by the Light of Nature. And +no doubt, if the Worship of false Gods had not blinded the Heathen, +their moral Philosophy would have gone farther than to the four +Cardinal Virtues; and instead of teaching the Transmigration of Souls, +and to worship the Sun and Moon, and dead Heroes, they would have taught +us to worship our true Author and Benefactor, as their Ancestors did +under the Government of _Noah_ and his Sons before they corrupted +themselves.
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