compress: move benchmark text from src/testdata to src/compress/testdata

This text is used mainly for benchmark compression testing, and in one
net test. The text was prevoiusly in a src/testdata directory, but since
that directory would only include one file, the text is moved to the
existing src/compression/testdata directory.

This does not cause any change to the benchmark results.

Updates #27151

Change-Id: I38ab5089dfe744189a970947d15be50ef1d48517
Reviewed-on: https://go-review.googlesource.com/138495
Run-TryBot: Katie Hockman <katie@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

1 files changed, 0 insertions, 9286 deletions

diff --git a/src/testdata/Isaac.Newton-Opticks.txt b/src/testdata/Isaac.Newton-Opticks.txt
deleted file mode 100644
index 15bb4c54d0..0000000000
--- a/src/testdata/Isaac.Newton-Opticks.txt
+++ /dev/null
@@ -1,9286 +0,0 @@
-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.
\ No newline at end of file