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>

3 files changed, 9289 insertions, 3 deletions

diff --git a/src/compress/flate/deflate_test.go b/src/compress/flate/deflate_test.go
index 831be2198c..46d917c01e 100644
--- a/src/compress/flate/deflate_test.go
+++ b/src/compress/flate/deflate_test.go
@@ -371,7 +371,7 @@ var deflateInflateStringTests = []deflateInflateStringTest{
 		[...]int{100018, 50650, 50960, 51150, 50930, 50790, 50790, 50790, 50790, 50790, 43683},
 	},
 	{
-		"../../testdata/Isaac.Newton-Opticks.txt",
+		"../testdata/Isaac.Newton-Opticks.txt",
 		"Isaac.Newton-Opticks",
 		[...]int{567248, 218338, 198211, 193152, 181100, 175427, 175427, 173597, 173422, 173422, 325240},
 	},
@@ -654,7 +654,7 @@ func (w *failWriter) Write(b []byte) (int, error) {
 
 func TestWriterPersistentError(t *testing.T) {
 	t.Parallel()
-	d, err := ioutil.ReadFile("../../testdata/Isaac.Newton-Opticks.txt")
+	d, err := ioutil.ReadFile("../testdata/Isaac.Newton-Opticks.txt")
 	if err != nil {
 		t.Fatalf("ReadFile: %v", err)
 	}
diff --git a/src/compress/flate/reader_test.go b/src/compress/flate/reader_test.go
index 9d2943a540..e1c3dff11b 100644
--- a/src/compress/flate/reader_test.go
+++ b/src/compress/flate/reader_test.go
@@ -28,7 +28,7 @@ var suites = []struct{ name, file string }{
 	// reasonably compressible.
 	{"Digits", "../testdata/e.txt"},
 	// Newton is Isaac Newtons's educational text on Opticks.
-	{"Newton", "../../testdata/Isaac.Newton-Opticks.txt"},
+	{"Newton", "../testdata/Isaac.Newton-Opticks.txt"},
 }
 
 func BenchmarkDecode(b *testing.B) {
diff --git a/src/compress/testdata/Isaac.Newton-Opticks.txt b/src/compress/testdata/Isaac.Newton-Opticks.txt
new file mode 100644
index 0000000000..15bb4c54d0
--- /dev/null
+++ b/src/compress/testdata/Isaac.Newton-Opticks.txt
@@ -0,0 +1,9286 @@
+Produced by Suzanne Lybarger, steve harris, Josephine
+Paolucci and the Online Distributed Proofreading Team at
+http://www.pgdp.net.
+
+
+
+
+
+
+OPTICKS:
+
+OR, A
+
+TREATISE
+
+OF THE
+
+_Reflections_, _Refractions_,
+_Inflections_ and _Colours_
+
+OF
+
+LIGHT.
+
+_The_ FOURTH EDITION, _corrected_.
+
+By Sir _ISAAC NEWTON_, Knt.
+
+LONDON:
+
+Printed for WILLIAM INNYS at the West-End of St. _Paul's_. MDCCXXX.
+
+TITLE PAGE OF THE 1730 EDITION
+
+
+
+
+SIR ISAAC NEWTON'S ADVERTISEMENTS
+
+
+
+
+Advertisement I
+
+
+_Part of the ensuing Discourse about Light was written at the Desire of
+some Gentlemen of the_ Royal-Society, _in the Year 1675, and then sent
+to their Secretary, and read at their Meetings, and the rest was added
+about twelve Years after to complete the Theory; except the third Book,
+and the last Proposition of the Second, which were since put together
+out of scatter'd Papers. To avoid being engaged in Disputes about these
+Matters, I have hitherto delayed the printing, and should still have
+delayed it, had not the Importunity of Friends prevailed upon me. If any
+other Papers writ on this Subject are got out of my Hands they are
+imperfect, and were perhaps written before I had tried all the
+Experiments here set down, and fully satisfied my self about the Laws of
+Refractions and Composition of Colours. I have here publish'd what I
+think proper to come abroad, wishing that it may not be translated into
+another Language without my Consent._
+
+_The Crowns of Colours, which sometimes appear about the Sun and Moon, I
+have endeavoured to give an Account of; but for want of sufficient
+Observations leave that Matter to be farther examined. The Subject of
+the Third Book I have also left imperfect, not having tried all the
+Experiments which I intended when I was about these Matters, nor
+repeated some of those which I did try, until I had satisfied my self
+about all their Circumstances. To communicate what I have tried, and
+leave the rest to others for farther Enquiry, is all my Design in
+publishing these Papers._
+
+_In a Letter written to Mr._ Leibnitz _in the year 1679, and published
+by Dr._ Wallis, _I mention'd a Method by which I had found some general
+Theorems about squaring Curvilinear Figures, or comparing them with the
+Conic Sections, or other the simplest Figures with which they may be
+compared. And some Years ago I lent out a Manuscript containing such
+Theorems, and having since met with some Things copied out of it, I have
+on this Occasion made it publick, prefixing to it an_ Introduction, _and
+subjoining a_ Scholium _concerning that Method. And I have joined with
+it another small Tract concerning the Curvilinear Figures of the Second
+Kind, which was also written many Years ago, and made known to some
+Friends, who have solicited the making it publick._
+
+                                        _I. N._
+
+April 1, 1704.
+
+
+Advertisement II
+
+_In this Second Edition of these Opticks I have omitted the Mathematical
+Tracts publish'd at the End of the former Edition, as not belonging to
+the Subject. And at the End of the Third Book I have added some
+Questions. And to shew that I do not take Gravity for an essential
+Property of Bodies, I have added one Question concerning its Cause,
+chusing to propose it by way of a Question, because I am not yet
+satisfied about it for want of Experiments._
+
+                                        _I. N._
+
+July 16, 1717.
+
+
+Advertisement to this Fourth Edition
+
+_This new Edition of Sir_ Isaac Newton's Opticks _is carefully printed
+from the Third Edition, as it was corrected by the Author's own Hand,
+and left before his Death with the Bookseller. Since Sir_ Isaac's
+Lectiones Opticæ, _which he publickly read in the University of_
+Cambridge _in the Years 1669, 1670, and 1671, are lately printed, it has
+been thought proper to make at the bottom of the Pages several Citations
+from thence, where may be found the Demonstrations, which the Author
+omitted in these_ Opticks.
+
+       *       *       *       *       *
+
+Transcriber's Note: There are several greek letters used in the
+descriptions of the illustrations. They are signified by [Greek:
+letter]. Square roots are noted by the letters sqrt before the equation.
+
+       *       *       *       *       *
+
+THE FIRST BOOK OF OPTICKS
+
+
+
+
+_PART I._
+
+
+My Design in this Book is not to explain the Properties of Light by
+Hypotheses, but to propose and prove them by Reason and Experiments: In
+order to which I shall premise the following Definitions and Axioms.
+
+
+
+
+_DEFINITIONS_
+
+
+DEFIN. I.
+
+_By the Rays of Light I understand its least Parts, and those as well
+Successive in the same Lines, as Contemporary in several Lines._ For it
+is manifest that Light consists of Parts, both Successive and
+Contemporary; because in the same place you may stop that which comes
+one moment, and let pass that which comes presently after; and in the
+same time you may stop it in any one place, and let it pass in any
+other. For that part of Light which is stopp'd cannot be the same with
+that which is let pass. The least Light or part of Light, which may be
+stopp'd alone without the rest of the Light, or propagated alone, or do
+or suffer any thing alone, which the rest of the Light doth not or
+suffers not, I call a Ray of Light.
+
+
+DEFIN. II.
+
+_Refrangibility of the Rays of Light, is their Disposition to be
+refracted or turned out of their Way in passing out of one transparent
+Body or Medium into another. And a greater or less Refrangibility of
+Rays, is their Disposition to be turned more or less out of their Way in
+like Incidences on the same Medium._ Mathematicians usually consider the
+Rays of Light to be Lines reaching from the luminous Body to the Body
+illuminated, and the refraction of those Rays to be the bending or
+breaking of those lines in their passing out of one Medium into another.
+And thus may Rays and Refractions be considered, if Light be propagated
+in an instant. But by an Argument taken from the Æquations of the times
+of the Eclipses of _Jupiter's Satellites_, it seems that Light is
+propagated in time, spending in its passage from the Sun to us about
+seven Minutes of time: And therefore I have chosen to define Rays and
+Refractions in such general terms as may agree to Light in both cases.
+
+
+DEFIN. III.
+
+_Reflexibility of Rays, is their Disposition to be reflected or turned
+back into the same Medium from any other Medium upon whose Surface they
+fall. And Rays are more or less reflexible, which are turned back more
+or less easily._ As if Light pass out of a Glass into Air, and by being
+inclined more and more to the common Surface of the Glass and Air,
+begins at length to be totally reflected by that Surface; those sorts of
+Rays which at like Incidences are reflected most copiously, or by
+inclining the Rays begin soonest to be totally reflected, are most
+reflexible.
+
+
+DEFIN. IV.
+
+_The Angle of Incidence is that Angle, which the Line described by the
+incident Ray contains with the Perpendicular to the reflecting or
+refracting Surface at the Point of Incidence._
+
+
+DEFIN. V.
+
+_The Angle of Reflexion or Refraction, is the Angle which the line
+described by the reflected or refracted Ray containeth with the
+Perpendicular to the reflecting or refracting Surface at the Point of
+Incidence._
+
+
+DEFIN. VI.
+
+_The Sines of Incidence, Reflexion, and Refraction, are the Sines of the
+Angles of Incidence, Reflexion, and Refraction._
+
+
+DEFIN. VII
+
+_The Light whose Rays are all alike Refrangible, I call Simple,
+Homogeneal and Similar; and that whose Rays are some more Refrangible
+than others, I call Compound, Heterogeneal and Dissimilar._ The former
+Light I call Homogeneal, not because I would affirm it so in all
+respects, but because the Rays which agree in Refrangibility, agree at
+least in all those their other Properties which I consider in the
+following Discourse.
+
+
+DEFIN. VIII.
+
+_The Colours of Homogeneal Lights, I call Primary, Homogeneal and
+Simple; and those of Heterogeneal Lights, Heterogeneal and Compound._
+For these are always compounded of the colours of Homogeneal Lights; as
+will appear in the following Discourse.
+
+
+
+
+_AXIOMS._
+
+
+AX. I.
+
+_The Angles of Reflexion and Refraction, lie in one and the same Plane
+with the Angle of Incidence._
+
+
+AX. II.
+
+_The Angle of Reflexion is equal to the Angle of Incidence._
+
+
+AX. III.
+
+_If the refracted Ray be returned directly back to the Point of
+Incidence, it shall be refracted into the Line before described by the
+incident Ray._
+
+
+AX. IV.
+
+_Refraction out of the rarer Medium into the denser, is made towards the
+Perpendicular; that is, so that the Angle of Refraction be less than the
+Angle of Incidence._
+
+
+AX. V.
+
+_The Sine of Incidence is either accurately or very nearly in a given
+Ratio to the Sine of Refraction._
+
+Whence if that Proportion be known in any one Inclination of the
+incident Ray, 'tis known in all the Inclinations, and thereby the
+Refraction in all cases of Incidence on the same refracting Body may be
+determined. Thus if the Refraction be made out of Air into Water, the
+Sine of Incidence of the red Light is to the Sine of its Refraction as 4
+to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of
+other Colours the Sines have other Proportions: but the difference is so
+little that it need seldom be considered.
+
+[Illustration: FIG. 1]
+
+Suppose therefore, that RS [in _Fig._ 1.] represents the Surface of
+stagnating Water, and that C is the point of Incidence in which any Ray
+coming in the Air from A in the Line AC is reflected or refracted, and I
+would know whither this Ray shall go after Reflexion or Refraction: I
+erect upon the Surface of the Water from the point of Incidence the
+Perpendicular CP and produce it downwards to Q, and conclude by the
+first Axiom, that the Ray after Reflexion and Refraction, shall be
+found somewhere in the Plane of the Angle of Incidence ACP produced. I
+let fall therefore upon the Perpendicular CP the Sine of Incidence AD;
+and if the reflected Ray be desired, I produce AD to B so that DB be
+equal to AD, and draw CB. For this Line CB shall be the reflected Ray;
+the Angle of Reflexion BCP and its Sine BD being equal to the Angle and
+Sine of Incidence, as they ought to be by the second Axiom, But if the
+refracted Ray be desired, I produce AD to H, so that DH may be to AD as
+the Sine of Refraction to the Sine of Incidence, that is, (if the Light
+be red) as 3 to 4; and about the Center C and in the Plane ACP with the
+Radius CA describing a Circle ABE, I draw a parallel to the
+Perpendicular CPQ, the Line HE cutting the Circumference in E, and
+joining CE, this Line CE shall be the Line of the refracted Ray. For if
+EF be let fall perpendicularly on the Line PQ, this Line EF shall be the
+Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and
+this Sine EF is equal to DH, and consequently in Proportion to the Sine
+of Incidence AD as 3 to 4.
+
+In like manner, if there be a Prism of Glass (that is, a Glass bounded
+with two Equal and Parallel Triangular ends, and three plain and well
+polished Sides, which meet in three Parallel Lines running from the
+three Angles of one end to the three Angles of the other end) and if the
+Refraction of the Light in passing cross this Prism be desired: Let ACB
+[in _Fig._ 2.] represent a Plane cutting this Prism transversly to its
+three Parallel lines or edges there where the Light passeth through it,
+and let DE be the Ray incident upon the first side of the Prism AC where
+the Light goes into the Glass; and by putting the Proportion of the Sine
+of Incidence to the Sine of Refraction as 17 to 11 find EF the first
+refracted Ray. Then taking this Ray for the Incident Ray upon the second
+side of the Glass BC where the Light goes out, find the next refracted
+Ray FG by putting the Proportion of the Sine of Incidence to the Sine of
+Refraction as 11 to 17. For if the Sine of Incidence out of Air into
+Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence
+out of Glass into Air must on the contrary be to the Sine of Refraction
+as 11 to 17, by the third Axiom.
+
+[Illustration: FIG. 2.]
+
+Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass
+spherically convex on both sides (usually called a _Lens_, such as is a
+Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope)
+and it be required to know how Light falling upon it from any lucid
+point Q shall be refracted, let QM represent a Ray falling upon any
+point M of its first spherical Surface ACB, and by erecting a
+Perpendicular to the Glass at the point M, find the first refracted Ray
+MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of
+the Glass be incident upon N, and then find the second refracted Ray
+N_q_ by the Proportion of the Sines 11 to 17. And after the same manner
+may the Refraction be found when the Lens is convex on one side and
+plane or concave on the other, or concave on both sides.
+
+[Illustration: FIG. 3.]
+
+
+AX. VI.
+
+_Homogeneal Rays which flow from several Points of any Object, and fall
+perpendicularly or almost perpendicularly on any reflecting or
+refracting Plane or spherical Surface, shall afterwards diverge from so
+many other Points, or be parallel to so many other Lines, or converge to
+so many other Points, either accurately or without any sensible Error.
+And the same thing will happen, if the Rays be reflected or refracted
+successively by two or three or more Plane or Spherical Surfaces._
+
+The Point from which Rays diverge or to which they converge may be
+called their _Focus_. And the Focus of the incident Rays being given,
+that of the reflected or refracted ones may be found by finding the
+Refraction of any two Rays, as above; or more readily thus.
+
+_Cas._ 1. Let ACB [in _Fig._ 4.] be a reflecting or refracting Plane,
+and Q the Focus of the incident Rays, and Q_q_C a Perpendicular to that
+Plane. And if this Perpendicular be produced to _q_, so that _q_C be
+equal to QC, the Point _q_ shall be the Focus of the reflected Rays: Or
+if _q_C be taken on the same side of the Plane with QC, and in
+proportion to QC as the Sine of Incidence to the Sine of Refraction, the
+Point _q_ shall be the Focus of the refracted Rays.
+
+[Illustration: FIG. 4.]
+
+_Cas._ 2. Let ACB [in _Fig._ 5.] be the reflecting Surface of any Sphere
+whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if
+in that Radius on the same side the Point T you take the Points Q and
+_q_, so that TQ, TE, and T_q_, be continual Proportionals, and the Point
+Q be the Focus of the incident Rays, the Point _q_ shall be the Focus of
+the reflected ones.
+
+[Illustration: FIG. 5.]
+
+_Cas._ 3. Let ACB [in _Fig._ 6.] be the refracting Surface of any Sphere
+whose Centre is E. In any Radius thereof EC produced both ways take ET
+and C_t_ equal to one another and severally in such Proportion to that
+Radius as the lesser of the Sines of Incidence and Refraction hath to
+the difference of those Sines. And then if in the same Line you find any
+two Points Q and _q_, so that TQ be to ET as E_t_ to _tq_, taking _tq_
+the contrary way from _t_ which TQ lieth from T, and if the Point Q be
+the Focus of any incident Rays, the Point _q_ shall be the Focus of the
+refracted ones.
+
+[Illustration: FIG. 6.]
+
+And by the same means the Focus of the Rays after two or more Reflexions
+or Refractions may be found.
+
+[Illustration: FIG. 7.]
+
+_Cas._ 4. Let ACBD [in _Fig._ 7.] be any refracting Lens, spherically
+Convex or Concave or Plane on either side, and let CD be its Axis (that
+is, the Line which cuts both its Surfaces perpendicularly, and passes
+through the Centres of the Spheres,) and in this Axis produced let F and
+_f_ be the Foci of the refracted Rays found as above, when the incident
+Rays on both sides the Lens are parallel to the same Axis; and upon the
+Diameter F_f_ bisected in E, describe a Circle. Suppose now that any
+Point Q be the Focus of any incident Rays. Draw QE cutting the said
+Circle in T and _t_, and therein take _tq_ in such proportion to _t_E as
+_t_E or TE hath to TQ. Let _tq_ lie the contrary way from _t_ which TQ
+doth from T, and _q_ shall be the Focus of the refracted Rays without
+any sensible Error, provided the Point Q be not so remote from the Axis,
+nor the Lens so broad as to make any of the Rays fall too obliquely on
+the refracting Surfaces.[A]
+
+And by the like Operations may the reflecting or refracting Surfaces be
+found when the two Foci are given, and thereby a Lens be formed, which
+shall make the Rays flow towards or from what Place you please.[B]
+
+So then the Meaning of this Axiom is, that if Rays fall upon any Plane
+or Spherical Surface or Lens, and before their Incidence flow from or
+towards any Point Q, they shall after Reflexion or Refraction flow from
+or towards the Point _q_ found by the foregoing Rules. And if the
+incident Rays flow from or towards several points Q, the reflected or
+refracted Rays shall flow from or towards so many other Points _q_
+found by the same Rules. Whether the reflected and refracted Rays flow
+from or towards the Point _q_ is easily known by the situation of that
+Point. For if that Point be on the same side of the reflecting or
+refracting Surface or Lens with the Point Q, and the incident Rays flow
+from the Point Q, the reflected flow towards the Point _q_ and the
+refracted from it; and if the incident Rays flow towards Q, the
+reflected flow from _q_, and the refracted towards it. And the contrary
+happens when _q_ is on the other side of the Surface.
+
+
+AX. VII.
+
+_Wherever the Rays which come from all the Points of any Object meet
+again in so many Points after they have been made to converge by
+Reflection or Refraction, there they will make a Picture of the Object
+upon any white Body on which they fall._
+
+So if PR [in _Fig._ 3.] represent any Object without Doors, and AB be a
+Lens placed at a hole in the Window-shut of a dark Chamber, whereby the
+Rays that come from any Point Q of that Object are made to converge and
+meet again in the Point _q_; and if a Sheet of white Paper be held at
+_q_ for the Light there to fall upon it, the Picture of that Object PR
+will appear upon the Paper in its proper shape and Colours. For as the
+Light which comes from the Point Q goes to the Point _q_, so the Light
+which comes from other Points P and R of the Object, will go to so many
+other correspondent Points _p_ and _r_ (as is manifest by the sixth
+Axiom;) so that every Point of the Object shall illuminate a
+correspondent Point of the Picture, and thereby make a Picture like the
+Object in Shape and Colour, this only excepted, that the Picture shall
+be inverted. And this is the Reason of that vulgar Experiment of casting
+the Species of Objects from abroad upon a Wall or Sheet of white Paper
+in a dark Room.
+
+In like manner, when a Man views any Object PQR, [in _Fig._ 8.] the
+Light which comes from the several Points of the Object is so refracted
+by the transparent skins and humours of the Eye, (that is, by the
+outward coat EFG, called the _Tunica Cornea_, and by the crystalline
+humour AB which is beyond the Pupil _mk_) as to converge and meet again
+in so many Points in the bottom of the Eye, and there to paint the
+Picture of the Object upon that skin (called the _Tunica Retina_) with
+which the bottom of the Eye is covered. For Anatomists, when they have
+taken off from the bottom of the Eye that outward and most thick Coat
+called the _Dura Mater_, can then see through the thinner Coats, the
+Pictures of Objects lively painted thereon. And these Pictures,
+propagated by Motion along the Fibres of the Optick Nerves into the
+Brain, are the cause of Vision. For accordingly as these Pictures are
+perfect or imperfect, the Object is seen perfectly or imperfectly. If
+the Eye be tinged with any colour (as in the Disease of the _Jaundice_)
+so as to tinge the Pictures in the bottom of the Eye with that Colour,
+then all Objects appear tinged with the same Colour. If the Humours of
+the Eye by old Age decay, so as by shrinking to make the _Cornea_ and
+Coat of the _Crystalline Humour_ grow flatter than before, the Light
+will not be refracted enough, and for want of a sufficient Refraction
+will not converge to the bottom of the Eye but to some place beyond it,
+and by consequence paint in the bottom of the Eye a confused Picture,
+and according to the Indistinctness of this Picture the Object will
+appear confused. This is the reason of the decay of sight in old Men,
+and shews why their Sight is mended by Spectacles. For those Convex
+glasses supply the defect of plumpness in the Eye, and by increasing the
+Refraction make the Rays converge sooner, so as to convene distinctly at
+the bottom of the Eye if the Glass have a due degree of convexity. And
+the contrary happens in short-sighted Men whose Eyes are too plump. For
+the Refraction being now too great, the Rays converge and convene in the
+Eyes before they come at the bottom; and therefore the Picture made in
+the bottom and the Vision caused thereby will not be distinct, unless
+the Object be brought so near the Eye as that the place where the
+converging Rays convene may be removed to the bottom, or that the
+plumpness of the Eye be taken off and the Refractions diminished by a
+Concave-glass of a due degree of Concavity, or lastly that by Age the
+Eye grow flatter till it come to a due Figure: For short-sighted Men see
+remote Objects best in Old Age, and therefore they are accounted to have
+the most lasting Eyes.
+
+[Illustration: FIG. 8.]
+
+
+AX. VIII.
+
+_An Object seen by Reflexion or Refraction, appears in that place from
+whence the Rays after their last Reflexion or Refraction diverge in
+falling on the Spectator's Eye._
+
+[Illustration: FIG. 9.]
+
+If the Object A [in FIG. 9.] be seen by Reflexion of a Looking-glass
+_mn_, it shall appear, not in its proper place A, but behind the Glass
+at _a_, from whence any Rays AB, AC, AD, which flow from one and the
+same Point of the Object, do after their Reflexion made in the Points B,
+C, D, diverge in going from the Glass to E, F, G, where they are
+incident on the Spectator's Eyes. For these Rays do make the same
+Picture in the bottom of the Eyes as if they had come from the Object
+really placed at _a_ without the Interposition of the Looking-glass; and
+all Vision is made according to the place and shape of that Picture.
+
+In like manner the Object D [in FIG. 2.] seen through a Prism, appears
+not in its proper place D, but is thence translated to some other place
+_d_ situated in the last refracted Ray FG drawn backward from F to _d_.
+
+[Illustration: FIG. 10.]
+
+And so the Object Q [in FIG. 10.] seen through the Lens AB, appears at
+the place _q_ from whence the Rays diverge in passing from the Lens to
+the Eye. Now it is to be noted, that the Image of the Object at _q_ is
+so much bigger or lesser than the Object it self at Q, as the distance
+of the Image at _q_ from the Lens AB is bigger or less than the distance
+of the Object at Q from the same Lens. And if the Object be seen through
+two or more such Convex or Concave-glasses, every Glass shall make a new
+Image, and the Object shall appear in the place of the bigness of the
+last Image. Which consideration unfolds the Theory of Microscopes and
+Telescopes. For that Theory consists in almost nothing else than the
+describing such Glasses as shall make the last Image of any Object as
+distinct and large and luminous as it can conveniently be made.
+
+I have now given in Axioms and their Explications the sum of what hath
+hitherto been treated of in Opticks. For what hath been generally
+agreed on I content my self to assume under the notion of Principles, in
+order to what I have farther to write. And this may suffice for an
+Introduction to Readers of quick Wit and good Understanding not yet
+versed in Opticks: Although those who are already acquainted with this
+Science, and have handled Glasses, will more readily apprehend what
+followeth.
+
+FOOTNOTES:
+
+[A] In our Author's _Lectiones Opticæ_, Part I. Sect. IV. Prop 29, 30,
+there is an elegant Method of determining these _Foci_; not only in
+spherical Surfaces, but likewise in any other curved Figure whatever:
+And in Prop. 32, 33, the same thing is done for any Ray lying out of the
+Axis.
+
+[B] _Ibid._ Prop. 34.
+
+
+
+
+_PROPOSITIONS._
+
+
+
+_PROP._ I. THEOR. I.
+
+_Lights which differ in Colour, differ also in Degrees of
+Refrangibility._
+
+The PROOF by Experiments.
+
+_Exper._ 1.
+
+I took a black oblong stiff Paper terminated by Parallel Sides, and with
+a Perpendicular right Line drawn cross from one Side to the other,
+distinguished it into two equal Parts. One of these parts I painted with
+a red colour and the other with a blue. The Paper was very black, and
+the Colours intense and thickly laid on, that the Phænomenon might be
+more conspicuous. This Paper I view'd through a Prism of solid Glass,
+whose two Sides through which the Light passed to the Eye were plane and
+well polished, and contained an Angle of about sixty degrees; which
+Angle I call the refracting Angle of the Prism. And whilst I view'd it,
+I held it and the Prism before a Window in such manner that the Sides of
+the Paper were parallel to the Prism, and both those Sides and the Prism
+were parallel to the Horizon, and the cross Line was also parallel to
+it: and that the Light which fell from the Window upon the Paper made an
+Angle with the Paper, equal to that Angle which was made with the same
+Paper by the Light reflected from it to the Eye. Beyond the Prism was
+the Wall of the Chamber under the Window covered over with black Cloth,
+and the Cloth was involved in Darkness that no Light might be reflected
+from thence, which in passing by the Edges of the Paper to the Eye,
+might mingle itself with the Light of the Paper, and obscure the
+Phænomenon thereof. These things being thus ordered, I found that if the
+refracting Angle of the Prism be turned upwards, so that the Paper may
+seem to be lifted upwards by the Refraction, its blue half will be
+lifted higher by the Refraction than its red half. But if the refracting
+Angle of the Prism be turned downward, so that the Paper may seem to be
+carried lower by the Refraction, its blue half will be carried something
+lower thereby than its red half. Wherefore in both Cases the Light which
+comes from the blue half of the Paper through the Prism to the Eye, does
+in like Circumstances suffer a greater Refraction than the Light which
+comes from the red half, and by consequence is more refrangible.
+
+_Illustration._ In the eleventh Figure, MN represents the Window, and DE
+the Paper terminated with parallel Sides DJ and HE, and by the
+transverse Line FG distinguished into two halfs, the one DG of an
+intensely blue Colour, the other FE of an intensely red. And BAC_cab_
+represents the Prism whose refracting Planes AB_ba_ and AC_ca_ meet in
+the Edge of the refracting Angle A_a_. This Edge A_a_ being upward, is
+parallel both to the Horizon, and to the Parallel-Edges of the Paper DJ
+and HE, and the transverse Line FG is perpendicular to the Plane of the
+Window. And _de_ represents the Image of the Paper seen by Refraction
+upwards in such manner, that the blue half DG is carried higher to _dg_
+than the red half FE is to _fe_, and therefore suffers a greater
+Refraction. If the Edge of the refracting Angle be turned downward, the
+Image of the Paper will be refracted downward; suppose to [Greek: de],
+and the blue half will be refracted lower to [Greek: dg] than the red
+half is to [Greek: pe].
+
+[Illustration: FIG. 11.]
+
+_Exper._ 2. About the aforesaid Paper, whose two halfs were painted over
+with red and blue, and which was stiff like thin Pasteboard, I lapped
+several times a slender Thred of very black Silk, in such manner that
+the several parts of the Thred might appear upon the Colours like so
+many black Lines drawn over them, or like long and slender dark Shadows
+cast upon them. I might have drawn black Lines with a Pen, but the
+Threds were smaller and better defined. This Paper thus coloured and
+lined I set against a Wall perpendicularly to the Horizon, so that one
+of the Colours might stand to the Right Hand, and the other to the Left.
+Close before the Paper, at the Confine of the Colours below, I placed a
+Candle to illuminate the Paper strongly: For the Experiment was tried in
+the Night. The Flame of the Candle reached up to the lower edge of the
+Paper, or a very little higher. Then at the distance of six Feet, and
+one or two Inches from the Paper upon the Floor I erected a Glass Lens
+four Inches and a quarter broad, which might collect the Rays coming
+from the several Points of the Paper, and make them converge towards so
+many other Points at the same distance of six Feet, and one or two
+Inches on the other side of the Lens, and so form the Image of the
+coloured Paper upon a white Paper placed there, after the same manner
+that a Lens at a Hole in a Window casts the Images of Objects abroad
+upon a Sheet of white Paper in a dark Room. The aforesaid white Paper,
+erected perpendicular to the Horizon, and to the Rays which fell upon it
+from the Lens, I moved sometimes towards the Lens, sometimes from it, to
+find the Places where the Images of the blue and red Parts of the
+coloured Paper appeared most distinct. Those Places I easily knew by the
+Images of the black Lines which I had made by winding the Silk about the
+Paper. For the Images of those fine and slender Lines (which by reason
+of their Blackness were like Shadows on the Colours) were confused and
+scarce visible, unless when the Colours on either side of each Line were
+terminated most distinctly, Noting therefore, as diligently as I could,
+the Places where the Images of the red and blue halfs of the coloured
+Paper appeared most distinct, I found that where the red half of the
+Paper appeared distinct, the blue half appeared confused, so that the
+black Lines drawn upon it could scarce be seen; and on the contrary,
+where the blue half appeared most distinct, the red half appeared
+confused, so that the black Lines upon it were scarce visible. And
+between the two Places where these Images appeared distinct there was
+the distance of an Inch and a half; the distance of the white Paper from
+the Lens, when the Image of the red half of the coloured Paper appeared
+most distinct, being greater by an Inch and an half than the distance of
+the same white Paper from the Lens, when the Image of the blue half
+appeared most distinct. In like Incidences therefore of the blue and red
+upon the Lens, the blue was refracted more by the Lens than the red, so
+as to converge sooner by an Inch and a half, and therefore is more
+refrangible.
+
+_Illustration._ In the twelfth Figure (p. 27), DE signifies the coloured
+Paper, DG the blue half, FE the red half, MN the Lens, HJ the white
+Paper in that Place where the red half with its black Lines appeared
+distinct, and _hi_ the same Paper in that Place where the blue half
+appeared distinct. The Place _hi_ was nearer to the Lens MN than the
+Place HJ by an Inch and an half.
+
+_Scholium._ The same Things succeed, notwithstanding that some of the
+Circumstances be varied; as in the first Experiment when the Prism and
+Paper are any ways inclined to the Horizon, and in both when coloured
+Lines are drawn upon very black Paper. But in the Description of these
+Experiments, I have set down such Circumstances, by which either the
+Phænomenon might be render'd more conspicuous, or a Novice might more
+easily try them, or by which I did try them only. The same Thing, I have
+often done in the following Experiments: Concerning all which, this one
+Admonition may suffice. Now from these Experiments it follows not, that
+all the Light of the blue is more refrangible than all the Light of the
+red: For both Lights are mixed of Rays differently refrangible, so that
+in the red there are some Rays not less refrangible than those of the
+blue, and in the blue there are some Rays not more refrangible than
+those of the red: But these Rays, in proportion to the whole Light, are
+but few, and serve to diminish the Event of the Experiment, but are not
+able to destroy it. For, if the red and blue Colours were more dilute
+and weak, the distance of the Images would be less than an Inch and a
+half; and if they were more intense and full, that distance would be
+greater, as will appear hereafter. These Experiments may suffice for the
+Colours of Natural Bodies. For in the Colours made by the Refraction of
+Prisms, this Proposition will appear by the Experiments which are now to
+follow in the next Proposition.
+
+
+_PROP._ II. THEOR. II.
+
+_The Light of the Sun consists of Rays differently Refrangible._
+
+The PROOF by Experiments.
+
+[Illustration: FIG. 12.]
+
+[Illustration: FIG. 13.]
+
+_Exper._ 3.
+
+In a very dark Chamber, at a round Hole, about one third Part of an Inch
+broad, made in the Shut of a Window, I placed a Glass Prism, whereby the
+Beam of the Sun's Light, which came in at that Hole, might be refracted
+upwards toward the opposite Wall of the Chamber, and there form a
+colour'd Image of the Sun. The Axis of the Prism (that is, the Line
+passing through the middle of the Prism from one end of it to the other
+end parallel to the edge of the Refracting Angle) was in this and the
+following Experiments perpendicular to the incident Rays. About this
+Axis I turned the Prism slowly, and saw the refracted Light on the Wall,
+or coloured Image of the Sun, first to descend, and then to ascend.
+Between the Descent and Ascent, when the Image seemed Stationary, I
+stopp'd the Prism, and fix'd it in that Posture, that it should be moved
+no more. For in that Posture the Refractions of the Light at the two
+Sides of the refracting Angle, that is, at the Entrance of the Rays into
+the Prism, and at their going out of it, were equal to one another.[C]
+So also in other Experiments, as often as I would have the Refractions
+on both sides the Prism to be equal to one another, I noted the Place
+where the Image of the Sun formed by the refracted Light stood still
+between its two contrary Motions, in the common Period of its Progress
+and Regress; and when the Image fell upon that Place, I made fast the
+Prism. And in this Posture, as the most convenient, it is to be
+understood that all the Prisms are placed in the following Experiments,
+unless where some other Posture is described. The Prism therefore being
+placed in this Posture, I let the refracted Light fall perpendicularly
+upon a Sheet of white Paper at the opposite Wall of the Chamber, and
+observed the Figure and Dimensions of the Solar Image formed on the
+Paper by that Light. This Image was Oblong and not Oval, but terminated
+with two Rectilinear and Parallel Sides, and two Semicircular Ends. On
+its Sides it was bounded pretty distinctly, but on its Ends very
+confusedly and indistinctly, the Light there decaying and vanishing by
+degrees. The Breadth of this Image answered to the Sun's Diameter, and
+was about two Inches and the eighth Part of an Inch, including the
+Penumbra. For the Image was eighteen Feet and an half distant from the
+Prism, and at this distance that Breadth, if diminished by the Diameter
+of the Hole in the Window-shut, that is by a quarter of an Inch,
+subtended an Angle at the Prism of about half a Degree, which is the
+Sun's apparent Diameter. But the Length of the Image was about ten
+Inches and a quarter, and the Length of the Rectilinear Sides about
+eight Inches; and the refracting Angle of the Prism, whereby so great a
+Length was made, was 64 degrees. With a less Angle the Length of the
+Image was less, the Breadth remaining the same. If the Prism was turned
+about its Axis that way which made the Rays emerge more obliquely out of
+the second refracting Surface of the Prism, the Image soon became an
+Inch or two longer, or more; and if the Prism was turned about the
+contrary way, so as to make the Rays fall more obliquely on the first
+refracting Surface, the Image soon became an Inch or two shorter. And
+therefore in trying this Experiment, I was as curious as I could be in
+placing the Prism by the above-mention'd Rule exactly in such a Posture,
+that the Refractions of the Rays at their Emergence out of the Prism
+might be equal to that at their Incidence on it. This Prism had some
+Veins running along within the Glass from one end to the other, which
+scattered some of the Sun's Light irregularly, but had no sensible
+Effect in increasing the Length of the coloured Spectrum. For I tried
+the same Experiment with other Prisms with the same Success. And
+particularly with a Prism which seemed free from such Veins, and whose
+refracting Angle was 62-1/2 Degrees, I found the Length of the Image
+9-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, the
+Breadth of the Hole in the Window-shut being 1/4 of an Inch, as before.
+And because it is easy to commit a Mistake in placing the Prism in its
+due Posture, I repeated the Experiment four or five Times, and always
+found the Length of the Image that which is set down above. With another
+Prism of clearer Glass and better Polish, which seemed free from Veins,
+and whose refracting Angle was 63-1/2 Degrees, the Length of this Image
+at the same distance of 18-1/2 Feet was also about 10 Inches, or 10-1/8.
+Beyond these Measures for about a 1/4 or 1/3 of an Inch at either end of
+the Spectrum the Light of the Clouds seemed to be a little tinged with
+red and violet, but so very faintly, that I suspected that Tincture
+might either wholly, or in great Measure arise from some Rays of the
+Spectrum scattered irregularly by some Inequalities in the Substance and
+Polish of the Glass, and therefore I did not include it in these
+Measures. Now the different Magnitude of the hole in the Window-shut,
+and different thickness of the Prism where the Rays passed through it,
+and different inclinations of the Prism to the Horizon, made no sensible
+changes in the length of the Image. Neither did the different matter of
+the Prisms make any: for in a Vessel made of polished Plates of Glass
+cemented together in the shape of a Prism and filled with Water, there
+is the like Success of the Experiment according to the quantity of the
+Refraction. It is farther to be observed, that the Rays went on in right
+Lines from the Prism to the Image, and therefore at their very going out
+of the Prism had all that Inclination to one another from which the
+length of the Image proceeded, that is, the Inclination of more than two
+degrees and an half. And yet according to the Laws of Opticks vulgarly
+received, they could not possibly be so much inclined to one another.[D]
+For let EG [_Fig._ 13. (p. 27)] represent the Window-shut, F the hole
+made therein through which a beam of the Sun's Light was transmitted
+into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby
+the Prism is feigned to be cut transversely through the middle of the
+Light. Or if you please, let ABC represent the Prism it self, looking
+directly towards the Spectator's Eye with its nearer end: And let XY be
+the Sun, MN the Paper upon which the Solar Image or Spectrum is cast,
+and PT the Image it self whose sides towards _v_ and _w_ are Rectilinear
+and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are
+two Rays, the first of which comes from the lower part of the Sun to the
+higher part of the Image, and is refracted in the Prism at K and H, and
+the latter comes from the higher part of the Sun to the lower part of
+the Image, and is refracted at L and J. Since the Refractions on both
+sides the Prism are equal to one another, that is, the Refraction at K
+equal to the Refraction at J, and the Refraction at L equal to the
+Refraction at H, so that the Refractions of the incident Rays at K and L
+taken together, are equal to the Refractions of the emergent Rays at H
+and J taken together: it follows by adding equal things to equal things,
+that the Refractions at K and H taken together, are equal to the
+Refractions at J and L taken together, and therefore the two Rays being
+equally refracted, have the same Inclination to one another after
+Refraction which they had before; that is, the Inclination of half a
+Degree answering to the Sun's Diameter. For so great was the inclination
+of the Rays to one another before Refraction. So then, the length of the
+Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a
+Degree at the Prism, and by Consequence be equal to the breadth _vw_;
+and therefore the Image would be round. Thus it would be were the two
+Rays XLJT and YKHP, and all the rest which form the Image P_w_T_v_,
+alike refrangible. And therefore seeing by Experience it is found that
+the Image is not round, but about five times longer than broad, the Rays
+which going to the upper end P of the Image suffer the greatest
+Refraction, must be more refrangible than those which go to the lower
+end T, unless the Inequality of Refraction be casual.
+
+This Image or Spectrum PT was coloured, being red at its least refracted
+end T, and violet at its most refracted end P, and yellow green and
+blue in the intermediate Spaces. Which agrees with the first
+Proposition, that Lights which differ in Colour, do also differ in
+Refrangibility. The length of the Image in the foregoing Experiments, I
+measured from the faintest and outmost red at one end, to the faintest
+and outmost blue at the other end, excepting only a little Penumbra,
+whose breadth scarce exceeded a quarter of an Inch, as was said above.
+
+_Exper._ 4. In the Sun's Beam which was propagated into the Room through
+the hole in the Window-shut, at the distance of some Feet from the hole,
+I held the Prism in such a Posture, that its Axis might be perpendicular
+to that Beam. Then I looked through the Prism upon the hole, and turning
+the Prism to and fro about its Axis, to make the Image of the Hole
+ascend and descend, when between its two contrary Motions it seemed
+Stationary, I stopp'd the Prism, that the Refractions of both sides of
+the refracting Angle might be equal to each other, as in the former
+Experiment. In this situation of the Prism viewing through it the said
+Hole, I observed the length of its refracted Image to be many times
+greater than its breadth, and that the most refracted part thereof
+appeared violet, the least refracted red, the middle parts blue, green
+and yellow in order. The same thing happen'd when I removed the Prism
+out of the Sun's Light, and looked through it upon the hole shining by
+the Light of the Clouds beyond it. And yet if the Refraction were done
+regularly according to one certain Proportion of the Sines of Incidence
+and Refraction as is vulgarly supposed, the refracted Image ought to
+have appeared round.
+
+So then, by these two Experiments it appears, that in Equal Incidences
+there is a considerable inequality of Refractions. But whence this
+inequality arises, whether it be that some of the incident Rays are
+refracted more, and others less, constantly, or by chance, or that one
+and the same Ray is by Refraction disturbed, shatter'd, dilated, and as
+it were split and spread into many diverging Rays, as _Grimaldo_
+supposes, does not yet appear by these Experiments, but will appear by
+those that follow.
+
+_Exper._ 5. Considering therefore, that if in the third Experiment the
+Image of the Sun should be drawn out into an oblong Form, either by a
+Dilatation of every Ray, or by any other casual inequality of the
+Refractions, the same oblong Image would by a second Refraction made
+sideways be drawn out as much in breadth by the like Dilatation of the
+Rays, or other casual inequality of the Refractions sideways, I tried
+what would be the Effects of such a second Refraction. For this end I
+ordered all things as in the third Experiment, and then placed a second
+Prism immediately after the first in a cross Position to it, that it
+might again refract the beam of the Sun's Light which came to it through
+the first Prism. In the first Prism this beam was refracted upwards, and
+in the second sideways. And I found that by the Refraction of the second
+Prism, the breadth of the Image was not increased, but its superior
+part, which in the first Prism suffered the greater Refraction, and
+appeared violet and blue, did again in the second Prism suffer a greater
+Refraction than its inferior part, which appeared red and yellow, and
+this without any Dilatation of the Image in breadth.
+
+[Illustration: FIG. 14]
+
+_Illustration._ Let S [_Fig._ 14, 15.] represent the Sun, F the hole in
+the Window, ABC the first Prism, DH the second Prism, Y the round Image
+of the Sun made by a direct beam of Light when the Prisms are taken
+away, PT the oblong Image of the Sun made by that beam passing through
+the first Prism alone, when the second Prism is taken away, and _pt_ the
+Image made by the cross Refractions of both Prisms together. Now if the
+Rays which tend towards the several Points of the round Image Y were
+dilated and spread by the Refraction of the first Prism, so that they
+should not any longer go in single Lines to single Points, but that
+every Ray being split, shattered, and changed from a Linear Ray to a
+Superficies of Rays diverging from the Point of Refraction, and lying in
+the Plane of the Angles of Incidence and Refraction, they should go in
+those Planes to so many Lines reaching almost from one end of the Image
+PT to the other, and if that Image should thence become oblong: those
+Rays and their several parts tending towards the several Points of the
+Image PT ought to be again dilated and spread sideways by the transverse
+Refraction of the second Prism, so as to compose a four square Image,
+such as is represented at [Greek: pt]. For the better understanding of
+which, let the Image PT be distinguished into five equal parts PQK,
+KQRL, LRSM, MSVN, NVT. And by the same irregularity that the orbicular
+Light Y is by the Refraction of the first Prism dilated and drawn out
+into a long Image PT, the Light PQK which takes up a space of the same
+length and breadth with the Light Y ought to be by the Refraction of the
+second Prism dilated and drawn out into the long Image _[Greek: p]qkp_,
+and the Light KQRL into the long Image _kqrl_, and the Lights LRSM,
+MSVN, NVT, into so many other long Images _lrsm_, _msvn_, _nvt[Greek:
+t]_; and all these long Images would compose the four square Images
+_[Greek: pt]_. Thus it ought to be were every Ray dilated by Refraction,
+and spread into a triangular Superficies of Rays diverging from the
+Point of Refraction. For the second Refraction would spread the Rays one
+way as much as the first doth another, and so dilate the Image in
+breadth as much as the first doth in length. And the same thing ought to
+happen, were some rays casually refracted more than others. But the
+Event is otherwise. The Image PT was not made broader by the Refraction
+of the second Prism, but only became oblique, as 'tis represented at
+_pt_, its upper end P being by the Refraction translated to a greater
+distance than its lower end T. So then the Light which went towards the
+upper end P of the Image, was (at equal Incidences) more refracted in
+the second Prism, than the Light which tended towards the lower end T,
+that is the blue and violet, than the red and yellow; and therefore was
+more refrangible. The same Light was by the Refraction of the first
+Prism translated farther from the place Y to which it tended before
+Refraction; and therefore suffered as well in the first Prism as in the
+second a greater Refraction than the rest of the Light, and by
+consequence was more refrangible than the rest, even before its
+incidence on the first Prism.
+
+Sometimes I placed a third Prism after the second, and sometimes also a
+fourth after the third, by all which the Image might be often refracted
+sideways: but the Rays which were more refracted than the rest in the
+first Prism were also more refracted in all the rest, and that without
+any Dilatation of the Image sideways: and therefore those Rays for their
+constancy of a greater Refraction are deservedly reputed more
+refrangible.
+
+[Illustration: FIG. 15]
+
+But that the meaning of this Experiment may more clearly appear, it is
+to be considered that the Rays which are equally refrangible do fall
+upon a Circle answering to the Sun's Disque. For this was proved in the
+third Experiment. By a Circle I understand not here a perfect
+geometrical Circle, but any orbicular Figure whose length is equal to
+its breadth, and which, as to Sense, may seem circular. Let therefore AG
+[in _Fig._ 15.] represent the Circle which all the most refrangible Rays
+propagated from the whole Disque of the Sun, would illuminate and paint
+upon the opposite Wall if they were alone; EL the Circle which all the
+least refrangible Rays would in like manner illuminate and paint if they
+were alone; BH, CJ, DK, the Circles which so many intermediate sorts of
+Rays would successively paint upon the Wall, if they were singly
+propagated from the Sun in successive order, the rest being always
+intercepted; and conceive that there are other intermediate Circles
+without Number, which innumerable other intermediate sorts of Rays would
+successively paint upon the Wall if the Sun should successively emit
+every sort apart. And seeing the Sun emits all these sorts at once, they
+must all together illuminate and paint innumerable equal Circles, of all
+which, being according to their degrees of Refrangibility placed in
+order in a continual Series, that oblong Spectrum PT is composed which I
+described in the third Experiment. Now if the Sun's circular Image Y [in
+_Fig._ 15.] which is made by an unrefracted beam of Light was by any
+Dilation of the single Rays, or by any other irregularity in the
+Refraction of the first Prism, converted into the oblong Spectrum, PT:
+then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the cross
+Refraction of the second Prism again dilating or otherwise scattering
+the Rays as before, to be in like manner drawn out and transformed into
+an oblong Figure, and thereby the breadth of the Image PT would be now
+as much augmented as the length of the Image Y was before by the
+Refraction of the first Prism; and thus by the Refractions of both
+Prisms together would be formed a four square Figure _p[Greek:
+p]t[Greek: t]_, as I described above. Wherefore since the breadth of the
+Spectrum PT is not increased by the Refraction sideways, it is certain
+that the Rays are not split or dilated, or otherways irregularly
+scatter'd by that Refraction, but that every Circle is by a regular and
+uniform Refraction translated entire into another Place, as the Circle
+AG by the greatest Refraction into the place _ag_, the Circle BH by a
+less Refraction into the place _bh_, the Circle CJ by a Refraction still
+less into the place _ci_, and so of the rest; by which means a new
+Spectrum _pt_ inclined to the former PT is in like manner composed of
+Circles lying in a right Line; and these Circles must be of the same
+bigness with the former, because the breadths of all the Spectrums Y, PT
+and _pt_ at equal distances from the Prisms are equal.
+
+I considered farther, that by the breadth of the hole F through which
+the Light enters into the dark Chamber, there is a Penumbra made in the
+Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear
+Sides of the Spectrums PT and _pt_. I placed therefore at that hole a
+Lens or Object-glass of a Telescope which might cast the Image of the
+Sun distinctly on Y without any Penumbra at all, and found that the
+Penumbra of the rectilinear Sides of the oblong Spectrums PT and _pt_
+was also thereby taken away, so that those Sides appeared as distinctly
+defined as did the Circumference of the first Image Y. Thus it happens
+if the Glass of the Prisms be free from Veins, and their sides be
+accurately plane and well polished without those numberless Waves or
+Curles which usually arise from Sand-holes a little smoothed in
+polishing with Putty. If the Glass be only well polished and free from
+Veins, and the Sides not accurately plane, but a little Convex or
+Concave, as it frequently happens; yet may the three Spectrums Y, PT and
+_pt_ want Penumbras, but not in equal distances from the Prisms. Now
+from this want of Penumbras, I knew more certainly that every one of the
+Circles was refracted according to some most regular, uniform and
+constant Law. For if there were any irregularity in the Refraction, the
+right Lines AE and GL, which all the Circles in the Spectrum PT do
+touch, could not by that Refraction be translated into the Lines _ae_
+and _gl_ as distinct and straight as they were before, but there would
+arise in those translated Lines some Penumbra or Crookedness or
+Undulation, or other sensible Perturbation contrary to what is found by
+Experience. Whatsoever Penumbra or Perturbation should be made in the
+Circles by the cross Refraction of the second Prism, all that Penumbra
+or Perturbation would be conspicuous in the right Lines _ae_ and _gl_
+which touch those Circles. And therefore since there is no such Penumbra
+or Perturbation in those right Lines, there must be none in the
+Circles. Since the distance between those Tangents or breadth of the
+Spectrum is not increased by the Refractions, the Diameters of the
+Circles are not increased thereby. Since those Tangents continue to be
+right Lines, every Circle which in the first Prism is more or less
+refracted, is exactly in the same proportion more or less refracted in
+the second. And seeing all these things continue to succeed after the
+same manner when the Rays are again in a third Prism, and again in a
+fourth refracted sideways, it is evident that the Rays of one and the
+same Circle, as to their degree of Refrangibility, continue always
+uniform and homogeneal to one another, and that those of several Circles
+do differ in degree of Refrangibility, and that in some certain and
+constant Proportion. Which is the thing I was to prove.
+
+There is yet another Circumstance or two of this Experiment by which it
+becomes still more plain and convincing. Let the second Prism DH [in
+_Fig._ 16.] be placed not immediately after the first, but at some
+distance from it; suppose in the mid-way between it and the Wall on
+which the oblong Spectrum PT is cast, so that the Light from the first
+Prism may fall upon it in the form of an oblong Spectrum [Greek: pt]
+parallel to this second Prism, and be refracted sideways to form the
+oblong Spectrum _pt_ upon the Wall. And you will find as before, that
+this Spectrum _pt_ is inclined to that Spectrum PT, which the first
+Prism forms alone without the second; the blue ends P and _p_ being
+farther distant from one another than the red ones T and _t_, and by
+consequence that the Rays which go to the blue end [Greek: p] of the
+Image [Greek: pt], and which therefore suffer the greatest Refraction in
+the first Prism, are again in the second Prism more refracted than the
+rest.
+
+[Illustration: FIG. 16.]
+
+[Illustration: FIG. 17.]
+
+The same thing I try'd also by letting the Sun's Light into a dark Room
+through two little round holes F and [Greek: ph] [in _Fig._ 17.] made in
+the Window, and with two parallel Prisms ABC and [Greek: abg] placed at
+those holes (one at each) refracting those two beams of Light to the
+opposite Wall of the Chamber, in such manner that the two colour'd
+Images PT and MN which they there painted were joined end to end and lay
+in one straight Line, the red end T of the one touching the blue end M
+of the other. For if these two refracted Beams were again by a third
+Prism DH placed cross to the two first, refracted sideways, and the
+Spectrums thereby translated to some other part of the Wall of the
+Chamber, suppose the Spectrum PT to _pt_ and the Spectrum MN to _mn_,
+these translated Spectrums _pt_ and _mn_ would not lie in one straight
+Line with their ends contiguous as before, but be broken off from one
+another and become parallel, the blue end _m_ of the Image _mn_ being by
+a greater Refraction translated farther from its former place MT, than
+the red end _t_ of the other Image _pt_ from the same place MT; which
+puts the Proposition past Dispute. And this happens whether the third
+Prism DH be placed immediately after the two first, or at a great
+distance from them, so that the Light refracted in the two first Prisms
+be either white and circular, or coloured and oblong when it falls on
+the third.
+
+_Exper._ 6. In the middle of two thin Boards I made round holes a third
+part of an Inch in diameter, and in the Window-shut a much broader hole
+being made to let into my darkned Chamber a large Beam of the Sun's
+Light; I placed a Prism behind the Shut in that beam to refract it
+towards the opposite Wall, and close behind the Prism I fixed one of the
+Boards, in such manner that the middle of the refracted Light might pass
+through the hole made in it, and the rest be intercepted by the Board.
+Then at the distance of about twelve Feet from the first Board I fixed
+the other Board in such manner that the middle of the refracted Light
+which came through the hole in the first Board, and fell upon the
+opposite Wall, might pass through the hole in this other Board, and the
+rest being intercepted by the Board might paint upon it the coloured
+Spectrum of the Sun. And close behind this Board I fixed another Prism
+to refract the Light which came through the hole. Then I returned
+speedily to the first Prism, and by turning it slowly to and fro about
+its Axis, I caused the Image which fell upon the second Board to move up
+and down upon that Board, that all its parts might successively pass
+through the hole in that Board and fall upon the Prism behind it. And in
+the mean time, I noted the places on the opposite Wall to which that
+Light after its Refraction in the second Prism did pass; and by the
+difference of the places I found that the Light which being most
+refracted in the first Prism did go to the blue end of the Image, was
+again more refracted in the second Prism than the Light which went to
+the red end of that Image, which proves as well the first Proposition as
+the second. And this happened whether the Axis of the two Prisms were
+parallel, or inclined to one another, and to the Horizon in any given
+Angles.
+
+_Illustration._ Let F [in _Fig._ 18.] be the wide hole in the
+Window-shut, through which the Sun shines upon the first Prism ABC, and
+let the refracted Light fall upon the middle of the Board DE, and the
+middle part of that Light upon the hole G made in the middle part of
+that Board. Let this trajected part of that Light fall again upon the
+middle of the second Board _de_, and there paint such an oblong coloured
+Image of the Sun as was described in the third Experiment. By turning
+the Prism ABC slowly to and fro about its Axis, this Image will be made
+to move up and down the Board _de_, and by this means all its parts from
+one end to the other may be made to pass successively through the hole
+_g_ which is made in the middle of that Board. In the mean while another
+Prism _abc_ is to be fixed next after that hole _g_, to refract the
+trajected Light a second time. And these things being thus ordered, I
+marked the places M and N of the opposite Wall upon which the refracted
+Light fell, and found that whilst the two Boards and second Prism
+remained unmoved, those places by turning the first Prism about its Axis
+were changed perpetually. For when the lower part of the Light which
+fell upon the second Board _de_ was cast through the hole _g_, it went
+to a lower place M on the Wall and when the higher part of that Light
+was cast through the same hole _g_, it went to a higher place N on the
+Wall, and when any intermediate part of the Light was cast through that
+hole, it went to some place on the Wall between M and N. The unchanged
+Position of the holes in the Boards, made the Incidence of the Rays upon
+the second Prism to be the same in all cases. And yet in that common
+Incidence some of the Rays were more refracted, and others less. And
+those were more refracted in this Prism, which by a greater Refraction
+in the first Prism were more turned out of the way, and therefore for
+their Constancy of being more refracted are deservedly called more
+refrangible.
+
+[Illustration: FIG. 18.]
+
+[Illustration: FIG. 20.]
+
+_Exper._ 7. At two holes made near one another in my Window-shut I
+placed two Prisms, one at each, which might cast upon the opposite Wall
+(after the manner of the third Experiment) two oblong coloured Images of
+the Sun. And at a little distance from the Wall I placed a long slender
+Paper with straight and parallel edges, and ordered the Prisms and Paper
+so, that the red Colour of one Image might fall directly upon one half
+of the Paper, and the violet Colour of the other Image upon the other
+half of the same Paper; so that the Paper appeared of two Colours, red
+and violet, much after the manner of the painted Paper in the first and
+second Experiments. Then with a black Cloth I covered the Wall behind
+the Paper, that no Light might be reflected from it to disturb the
+Experiment, and viewing the Paper through a third Prism held parallel
+to it, I saw that half of it which was illuminated by the violet Light
+to be divided from the other half by a greater Refraction, especially
+when I went a good way off from the Paper. For when I viewed it too near
+at hand, the two halfs of the Paper did not appear fully divided from
+one another, but seemed contiguous at one of their Angles like the
+painted Paper in the first Experiment. Which also happened when the
+Paper was too broad.
+
+[Illustration: FIG. 19.]
+
+Sometimes instead of the Paper I used a white Thred, and this appeared
+through the Prism divided into two parallel Threds as is represented in
+the nineteenth Figure, where DG denotes the Thred illuminated with
+violet Light from D to E and with red Light from F to G, and _defg_ are
+the parts of the Thred seen by Refraction. If one half of the Thred be
+constantly illuminated with red, and the other half be illuminated with
+all the Colours successively, (which may be done by causing one of the
+Prisms to be turned about its Axis whilst the other remains unmoved)
+this other half in viewing the Thred through the Prism, will appear in
+a continual right Line with the first half when illuminated with red,
+and begin to be a little divided from it when illuminated with Orange,
+and remove farther from it when illuminated with yellow, and still
+farther when with green, and farther when with blue, and go yet farther
+off when illuminated with Indigo, and farthest when with deep violet.
+Which plainly shews, that the Lights of several Colours are more and
+more refrangible one than another, in this Order of their Colours, red,
+orange, yellow, green, blue, indigo, deep violet; and so proves as well
+the first Proposition as the second.
+
+I caused also the coloured Spectrums PT [in _Fig._ 17.] and MN made in a
+dark Chamber by the Refractions of two Prisms to lie in a Right Line end
+to end, as was described above in the fifth Experiment, and viewing them
+through a third Prism held parallel to their Length, they appeared no
+longer in a Right Line, but became broken from one another, as they are
+represented at _pt_ and _mn_, the violet end _m_ of the Spectrum _mn_
+being by a greater Refraction translated farther from its former Place
+MT than the red end _t_ of the other Spectrum _pt_.
+
+I farther caused those two Spectrums PT [in _Fig._ 20.] and MN to become
+co-incident in an inverted Order of their Colours, the red end of each
+falling on the violet end of the other, as they are represented in the
+oblong Figure PTMN; and then viewing them through a Prism DH held
+parallel to their Length, they appeared not co-incident, as when view'd
+with the naked Eye, but in the form of two distinct Spectrums _pt_ and
+_mn_ crossing one another in the middle after the manner of the Letter
+X. Which shews that the red of the one Spectrum and violet of the other,
+which were co-incident at PN and MT, being parted from one another by a
+greater Refraction of the violet to _p_ and _m_ than of the red to _n_
+and _t_, do differ in degrees of Refrangibility.
+
+I illuminated also a little Circular Piece of white Paper all over with
+the Lights of both Prisms intermixed, and when it was illuminated with
+the red of one Spectrum, and deep violet of the other, so as by the
+Mixture of those Colours to appear all over purple, I viewed the Paper,
+first at a less distance, and then at a greater, through a third Prism;
+and as I went from the Paper, the refracted Image thereof became more
+and more divided by the unequal Refraction of the two mixed Colours, and
+at length parted into two distinct Images, a red one and a violet one,
+whereof the violet was farthest from the Paper, and therefore suffered
+the greatest Refraction. And when that Prism at the Window, which cast
+the violet on the Paper was taken away, the violet Image disappeared;
+but when the other Prism was taken away the red vanished; which shews,
+that these two Images were nothing else than the Lights of the two
+Prisms, which had been intermixed on the purple Paper, but were parted
+again by their unequal Refractions made in the third Prism, through
+which the Paper was view'd. This also was observable, that if one of the
+Prisms at the Window, suppose that which cast the violet on the Paper,
+was turned about its Axis to make all the Colours in this order,
+violet, indigo, blue, green, yellow, orange, red, fall successively on
+the Paper from that Prism, the violet Image changed Colour accordingly,
+turning successively to indigo, blue, green, yellow and red, and in
+changing Colour came nearer and nearer to the red Image made by the
+other Prism, until when it was also red both Images became fully
+co-incident.
+
+I placed also two Paper Circles very near one another, the one in the
+red Light of one Prism, and the other in the violet Light of the other.
+The Circles were each of them an Inch in diameter, and behind them the
+Wall was dark, that the Experiment might not be disturbed by any Light
+coming from thence. These Circles thus illuminated, I viewed through a
+Prism, so held, that the Refraction might be made towards the red
+Circle, and as I went from them they came nearer and nearer together,
+and at length became co-incident; and afterwards when I went still
+farther off, they parted again in a contrary Order, the violet by a
+greater Refraction being carried beyond the red.
+
+_Exper._ 8. In Summer, when the Sun's Light uses to be strongest, I
+placed a Prism at the Hole of the Window-shut, as in the third
+Experiment, yet so that its Axis might be parallel to the Axis of the
+World, and at the opposite Wall in the Sun's refracted Light, I placed
+an open Book. Then going six Feet and two Inches from the Book, I placed
+there the above-mentioned Lens, by which the Light reflected from the
+Book might be made to converge and meet again at the distance of six
+Feet and two Inches behind the Lens, and there paint the Species of the
+Book upon a Sheet of white Paper much after the manner of the second
+Experiment. The Book and Lens being made fast, I noted the Place where
+the Paper was, when the Letters of the Book, illuminated by the fullest
+red Light of the Solar Image falling upon it, did cast their Species on
+that Paper most distinctly: And then I stay'd till by the Motion of the
+Sun, and consequent Motion of his Image on the Book, all the Colours
+from that red to the middle of the blue pass'd over those Letters; and
+when those Letters were illuminated by that blue, I noted again the
+Place of the Paper when they cast their Species most distinctly upon it:
+And I found that this last Place of the Paper was nearer to the Lens
+than its former Place by about two Inches and an half, or two and three
+quarters. So much sooner therefore did the Light in the violet end of
+the Image by a greater Refraction converge and meet, than the Light in
+the red end. But in trying this, the Chamber was as dark as I could make
+it. For, if these Colours be diluted and weakned by the Mixture of any
+adventitious Light, the distance between the Places of the Paper will
+not be so great. This distance in the second Experiment, where the
+Colours of natural Bodies were made use of, was but an Inch and an half,
+by reason of the Imperfection of those Colours. Here in the Colours of
+the Prism, which are manifestly more full, intense, and lively than
+those of natural Bodies, the distance is two Inches and three quarters.
+And were the Colours still more full, I question not but that the
+distance would be considerably greater. For the coloured Light of the
+Prism, by the interfering of the Circles described in the second Figure
+of the fifth Experiment, and also by the Light of the very bright Clouds
+next the Sun's Body intermixing with these Colours, and by the Light
+scattered by the Inequalities in the Polish of the Prism, was so very
+much compounded, that the Species which those faint and dark Colours,
+the indigo and violet, cast upon the Paper were not distinct enough to
+be well observed.
+
+_Exper._ 9. A Prism, whose two Angles at its Base were equal to one
+another, and half right ones, and the third a right one, I placed in a
+Beam of the Sun's Light let into a dark Chamber through a Hole in the
+Window-shut, as in the third Experiment. And turning the Prism slowly
+about its Axis, until all the Light which went through one of its
+Angles, and was refracted by it began to be reflected by its Base, at
+which till then it went out of the Glass, I observed that those Rays
+which had suffered the greatest Refraction were sooner reflected than
+the rest. I conceived therefore, that those Rays of the reflected Light,
+which were most refrangible, did first of all by a total Reflexion
+become more copious in that Light than the rest, and that afterwards the
+rest also, by a total Reflexion, became as copious as these. To try
+this, I made the reflected Light pass through another Prism, and being
+refracted by it to fall afterwards upon a Sheet of white Paper placed
+at some distance behind it, and there by that Refraction to paint the
+usual Colours of the Prism. And then causing the first Prism to be
+turned about its Axis as above, I observed that when those Rays, which
+in this Prism had suffered the greatest Refraction, and appeared of a
+blue and violet Colour began to be totally reflected, the blue and
+violet Light on the Paper, which was most refracted in the second Prism,
+received a sensible Increase above that of the red and yellow, which was
+least refracted; and afterwards, when the rest of the Light which was
+green, yellow, and red, began to be totally reflected in the first
+Prism, the Light of those Colours on the Paper received as great an
+Increase as the violet and blue had done before. Whence 'tis manifest,
+that the Beam of Light reflected by the Base of the Prism, being
+augmented first by the more refrangible Rays, and afterwards by the less
+refrangible ones, is compounded of Rays differently refrangible. And
+that all such reflected Light is of the same Nature with the Sun's Light
+before its Incidence on the Base of the Prism, no Man ever doubted; it
+being generally allowed, that Light by such Reflexions suffers no
+Alteration in its Modifications and Properties. I do not here take
+Notice of any Refractions made in the sides of the first Prism, because
+the Light enters it perpendicularly at the first side, and goes out
+perpendicularly at the second side, and therefore suffers none. So then,
+the Sun's incident Light being of the same Temper and Constitution with
+his emergent Light, and the last being compounded of Rays differently
+refrangible, the first must be in like manner compounded.
+
+[Illustration: FIG. 21.]
+
+_Illustration._ In the twenty-first Figure, ABC is the first Prism, BC
+its Base, B and C its equal Angles at the Base, each of 45 Degrees, A
+its rectangular Vertex, FM a beam of the Sun's Light let into a dark
+Room through a hole F one third part of an Inch broad, M its Incidence
+on the Base of the Prism, MG a less refracted Ray, MH a more refracted
+Ray, MN the beam of Light reflected from the Base, VXY the second Prism
+by which this beam in passing through it is refracted, N_t_ the less
+refracted Light of this beam, and N_p_ the more refracted part thereof.
+When the first Prism ABC is turned about its Axis according to the order
+of the Letters ABC, the Rays MH emerge more and more obliquely out of
+that Prism, and at length after their most oblique Emergence are
+reflected towards N, and going on to _p_ do increase the Number of the
+Rays N_p_. Afterwards by continuing the Motion of the first Prism, the
+Rays MG are also reflected to N and increase the number of the Rays
+N_t_. And therefore the Light MN admits into its Composition, first the
+more refrangible Rays, and then the less refrangible Rays, and yet after
+this Composition is of the same Nature with the Sun's immediate Light
+FM, the Reflexion of the specular Base BC causing no Alteration therein.
+
+_Exper._ 10. Two Prisms, which were alike in Shape, I tied so together,
+that their Axis and opposite Sides being parallel, they composed a
+Parallelopiped. And, the Sun shining into my dark Chamber through a
+little hole in the Window-shut, I placed that Parallelopiped in his beam
+at some distance from the hole, in such a Posture, that the Axes of the
+Prisms might be perpendicular to the incident Rays, and that those Rays
+being incident upon the first Side of one Prism, might go on through the
+two contiguous Sides of both Prisms, and emerge out of the last Side of
+the second Prism. This Side being parallel to the first Side of the
+first Prism, caused the emerging Light to be parallel to the incident.
+Then, beyond these two Prisms I placed a third, which might refract that
+emergent Light, and by that Refraction cast the usual Colours of the
+Prism upon the opposite Wall, or upon a sheet of white Paper held at a
+convenient Distance behind the Prism for that refracted Light to fall
+upon it. After this I turned the Parallelopiped about its Axis, and
+found that when the contiguous Sides of the two Prisms became so oblique
+to the incident Rays, that those Rays began all of them to be
+reflected, those Rays which in the third Prism had suffered the greatest
+Refraction, and painted the Paper with violet and blue, were first of
+all by a total Reflexion taken out of the transmitted Light, the rest
+remaining and on the Paper painting their Colours of green, yellow,
+orange and red, as before; and afterwards by continuing the Motion of
+the two Prisms, the rest of the Rays also by a total Reflexion vanished
+in order, according to their degrees of Refrangibility. The Light
+therefore which emerged out of the two Prisms is compounded of Rays
+differently refrangible, seeing the more refrangible Rays may be taken
+out of it, while the less refrangible remain. But this Light being
+trajected only through the parallel Superficies of the two Prisms, if it
+suffer'd any change by the Refraction of one Superficies it lost that
+Impression by the contrary Refraction of the other Superficies, and so
+being restor'd to its pristine Constitution, became of the same Nature
+and Condition as at first before its Incidence on those Prisms; and
+therefore, before its Incidence, was as much compounded of Rays
+differently refrangible, as afterwards.
+
+[Illustration: FIG. 22.]
+
+_Illustration._ In the twenty second Figure ABC and BCD are the two
+Prisms tied together in the form of a Parallelopiped, their Sides BC and
+CB being contiguous, and their Sides AB and CD parallel. And HJK is the
+third Prism, by which the Sun's Light propagated through the hole F into
+the dark Chamber, and there passing through those sides of the Prisms
+AB, BC, CB and CD, is refracted at O to the white Paper PT, falling
+there partly upon P by a greater Refraction, partly upon T by a less
+Refraction, and partly upon R and other intermediate places by
+intermediate Refractions. By turning the Parallelopiped ACBD about its
+Axis, according to the order of the Letters A, C, D, B, at length when
+the contiguous Planes BC and CB become sufficiently oblique to the Rays
+FM, which are incident upon them at M, there will vanish totally out of
+the refracted Light OPT, first of all the most refracted Rays OP, (the
+rest OR and OT remaining as before) then the Rays OR and other
+intermediate ones, and lastly, the least refracted Rays OT. For when
+the Plane BC becomes sufficiently oblique to the Rays incident upon it,
+those Rays will begin to be totally reflected by it towards N; and first
+the most refrangible Rays will be totally reflected (as was explained in
+the preceding Experiment) and by Consequence must first disappear at P,
+and afterwards the rest as they are in order totally reflected to N,
+they must disappear in the same order at R and T. So then the Rays which
+at O suffer the greatest Refraction, may be taken out of the Light MO
+whilst the rest of the Rays remain in it, and therefore that Light MO is
+compounded of Rays differently refrangible. And because the Planes AB
+and CD are parallel, and therefore by equal and contrary Refractions
+destroy one anothers Effects, the incident Light FM must be of the same
+Kind and Nature with the emergent Light MO, and therefore doth also
+consist of Rays differently refrangible. These two Lights FM and MO,
+before the most refrangible Rays are separated out of the emergent Light
+MO, agree in Colour, and in all other Properties so far as my
+Observation reaches, and therefore are deservedly reputed of the same
+Nature and Constitution, and by Consequence the one is compounded as
+well as the other. But after the most refrangible Rays begin to be
+totally reflected, and thereby separated out of the emergent Light MO,
+that Light changes its Colour from white to a dilute and faint yellow, a
+pretty good orange, a very full red successively, and then totally
+vanishes. For after the most refrangible Rays which paint the Paper at
+P with a purple Colour, are by a total Reflexion taken out of the beam
+of Light MO, the rest of the Colours which appear on the Paper at R and
+T being mix'd in the Light MO compound there a faint yellow, and after
+the blue and part of the green which appear on the Paper between P and R
+are taken away, the rest which appear between R and T (that is the
+yellow, orange, red and a little green) being mixed in the beam MO
+compound there an orange; and when all the Rays are by Reflexion taken
+out of the beam MO, except the least refrangible, which at T appear of a
+full red, their Colour is the same in that beam MO as afterwards at T,
+the Refraction of the Prism HJK serving only to separate the differently
+refrangible Rays, without making any Alteration in their Colours, as
+shall be more fully proved hereafter. All which confirms as well the
+first Proposition as the second.
+
+_Scholium._ If this Experiment and the former be conjoined and made one
+by applying a fourth Prism VXY [in _Fig._ 22.] to refract the reflected
+beam MN towards _tp_, the Conclusion will be clearer. For then the Light
+N_p_ which in the fourth Prism is more refracted, will become fuller and
+stronger when the Light OP, which in the third Prism HJK is more
+refracted, vanishes at P; and afterwards when the less refracted Light
+OT vanishes at T, the less refracted Light N_t_ will become increased
+whilst the more refracted Light at _p_ receives no farther increase. And
+as the trajected beam MO in vanishing is always of such a Colour as
+ought to result from the mixture of the Colours which fall upon the
+Paper PT, so is the reflected beam MN always of such a Colour as ought
+to result from the mixture of the Colours which fall upon the Paper
+_pt_. For when the most refrangible Rays are by a total Reflexion taken
+out of the beam MO, and leave that beam of an orange Colour, the Excess
+of those Rays in the reflected Light, does not only make the violet,
+indigo and blue at _p_ more full, but also makes the beam MN change from
+the yellowish Colour of the Sun's Light, to a pale white inclining to
+blue, and afterward recover its yellowish Colour again, so soon as all
+the rest of the transmitted Light MOT is reflected.
+
+Now seeing that in all this variety of Experiments, whether the Trial be
+made in Light reflected, and that either from natural Bodies, as in the
+first and second Experiment, or specular, as in the ninth; or in Light
+refracted, and that either before the unequally refracted Rays are by
+diverging separated from one another, and losing their whiteness which
+they have altogether, appear severally of several Colours, as in the
+fifth Experiment; or after they are separated from one another, and
+appear colour'd as in the sixth, seventh, and eighth Experiments; or in
+Light trajected through parallel Superficies, destroying each others
+Effects, as in the tenth Experiment; there are always found Rays, which
+at equal Incidences on the same Medium suffer unequal Refractions, and
+that without any splitting or dilating of single Rays, or contingence in
+the inequality of the Refractions, as is proved in the fifth and sixth
+Experiments. And seeing the Rays which differ in Refrangibility may be
+parted and sorted from one another, and that either by Refraction as in
+the third Experiment, or by Reflexion as in the tenth, and then the
+several sorts apart at equal Incidences suffer unequal Refractions, and
+those sorts are more refracted than others after Separation, which were
+more refracted before it, as in the sixth and following Experiments, and
+if the Sun's Light be trajected through three or more cross Prisms
+successively, those Rays which in the first Prism are refracted more
+than others, are in all the following Prisms refracted more than others
+in the same Rate and Proportion, as appears by the fifth Experiment;
+it's manifest that the Sun's Light is an heterogeneous Mixture of Rays,
+some of which are constantly more refrangible than others, as was
+proposed.
+
+
+_PROP._ III. THEOR. III.
+
+_The Sun's Light consists of Rays differing in Reflexibility, and those
+Rays are more reflexible than others which are more refrangible._
+
+This is manifest by the ninth and tenth Experiments: For in the ninth
+Experiment, by turning the Prism about its Axis, until the Rays within
+it which in going out into the Air were refracted by its Base, became so
+oblique to that Base, as to begin to be totally reflected thereby; those
+Rays became first of all totally reflected, which before at equal
+Incidences with the rest had suffered the greatest Refraction. And the
+same thing happens in the Reflexion made by the common Base of the two
+Prisms in the tenth Experiment.
+
+
+_PROP._ IV. PROB. I.
+
+_To separate from one another the heterogeneous Rays of compound Light._
+
+[Illustration: FIG. 23.]
+
+The heterogeneous Rays are in some measure separated from one another by
+the Refraction of the Prism in the third Experiment, and in the fifth
+Experiment, by taking away the Penumbra from the rectilinear sides of
+the coloured Image, that Separation in those very rectilinear sides or
+straight edges of the Image becomes perfect. But in all places between
+those rectilinear edges, those innumerable Circles there described,
+which are severally illuminated by homogeneal Rays, by interfering with
+one another, and being every where commix'd, do render the Light
+sufficiently compound. But if these Circles, whilst their Centers keep
+their Distances and Positions, could be made less in Diameter, their
+interfering one with another, and by Consequence the Mixture of the
+heterogeneous Rays would be proportionally diminish'd. In the twenty
+third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many
+sorts of Rays flowing from the same disque of the Sun, do in the third
+Experiment illuminate; of all which and innumerable other intermediate
+ones lying in a continual Series between the two rectilinear and
+parallel edges of the Sun's oblong Image PT, that Image is compos'd, as
+was explained in the fifth Experiment. And let _ag_, _bh_, _ci_, _dk_,
+_el_, _fm_ be so many less Circles lying in a like continual Series
+between two parallel right Lines _af_ and _gm_ with the same distances
+between their Centers, and illuminated by the same sorts of Rays, that
+is the Circle _ag_ with the same sort by which the corresponding Circle
+AG was illuminated, and the Circle _bh_ with the same sort by which the
+corresponding Circle BH was illuminated, and the rest of the Circles
+_ci_, _dk_, _el_, _fm_ respectively, with the same sorts of Rays by
+which the several corresponding Circles CJ, DK, EL, FM were illuminated.
+In the Figure PT composed of the greater Circles, three of those Circles
+AG, BH, CJ, are so expanded into one another, that the three sorts of
+Rays by which those Circles are illuminated, together with other
+innumerable sorts of intermediate Rays, are mixed at QR in the middle
+of the Circle BH. And the like Mixture happens throughout almost the
+whole length of the Figure PT. But in the Figure _pt_ composed of the
+less Circles, the three less Circles _ag_, _bh_, _ci_, which answer to
+those three greater, do not extend into one another; nor are there any
+where mingled so much as any two of the three sorts of Rays by which
+those Circles are illuminated, and which in the Figure PT are all of
+them intermingled at BH.
+
+Now he that shall thus consider it, will easily understand that the
+Mixture is diminished in the same Proportion with the Diameters of the
+Circles. If the Diameters of the Circles whilst their Centers remain the
+same, be made three times less than before, the Mixture will be also
+three times less; if ten times less, the Mixture will be ten times less,
+and so of other Proportions. That is, the Mixture of the Rays in the
+greater Figure PT will be to their Mixture in the less _pt_, as the
+Latitude of the greater Figure is to the Latitude of the less. For the
+Latitudes of these Figures are equal to the Diameters of their Circles.
+And hence it easily follows, that the Mixture of the Rays in the
+refracted Spectrum _pt_ is to the Mixture of the Rays in the direct and
+immediate Light of the Sun, as the breadth of that Spectrum is to the
+difference between the length and breadth of the same Spectrum.
+
+So then, if we would diminish the Mixture of the Rays, we are to
+diminish the Diameters of the Circles. Now these would be diminished if
+the Sun's Diameter to which they answer could be made less than it is,
+or (which comes to the same Purpose) if without Doors, at a great
+distance from the Prism towards the Sun, some opake Body were placed,
+with a round hole in the middle of it, to intercept all the Sun's Light,
+excepting so much as coming from the middle of his Body could pass
+through that Hole to the Prism. For so the Circles AG, BH, and the rest,
+would not any longer answer to the whole Disque of the Sun, but only to
+that Part of it which could be seen from the Prism through that Hole,
+that it is to the apparent Magnitude of that Hole view'd from the Prism.
+But that these Circles may answer more distinctly to that Hole, a Lens
+is to be placed by the Prism to cast the Image of the Hole, (that is,
+every one of the Circles AG, BH, &c.) distinctly upon the Paper at PT,
+after such a manner, as by a Lens placed at a Window, the Species of
+Objects abroad are cast distinctly upon a Paper within the Room, and the
+rectilinear Sides of the oblong Solar Image in the fifth Experiment
+became distinct without any Penumbra. If this be done, it will not be
+necessary to place that Hole very far off, no not beyond the Window. And
+therefore instead of that Hole, I used the Hole in the Window-shut, as
+follows.
+
+_Exper._ 11. In the Sun's Light let into my darken'd Chamber through a
+small round Hole in my Window-shut, at about ten or twelve Feet from the
+Window, I placed a Lens, by which the Image of the Hole might be
+distinctly cast upon a Sheet of white Paper, placed at the distance of
+six, eight, ten, or twelve Feet from the Lens. For, according to the
+difference of the Lenses I used various distances, which I think not
+worth the while to describe. Then immediately after the Lens I placed a
+Prism, by which the trajected Light might be refracted either upwards or
+sideways, and thereby the round Image, which the Lens alone did cast
+upon the Paper might be drawn out into a long one with Parallel Sides,
+as in the third Experiment. This oblong Image I let fall upon another
+Paper at about the same distance from the Prism as before, moving the
+Paper either towards the Prism or from it, until I found the just
+distance where the Rectilinear Sides of the Image became most distinct.
+For in this Case, the Circular Images of the Hole, which compose that
+Image after the same manner that the Circles _ag_, _bh_, _ci_, &c. do
+the Figure _pt_ [in _Fig._ 23.] were terminated most distinctly without
+any Penumbra, and therefore extended into one another the least that
+they could, and by consequence the Mixture of the heterogeneous Rays was
+now the least of all. By this means I used to form an oblong Image (such
+as is _pt_) [in _Fig._ 23, and 24.] of Circular Images of the Hole,
+(such as are _ag_, _bh_, _ci_, &c.) and by using a greater or less Hole
+in the Window-shut, I made the Circular Images _ag_, _bh_, _ci_, &c. of
+which it was formed, to become greater or less at pleasure, and thereby
+the Mixture of the Rays in the Image _pt_ to be as much, or as little as
+I desired.
+
+[Illustration: FIG. 24.]
+
+_Illustration._ In the twenty-fourth Figure, F represents the Circular
+Hole in the Window-shut, MN the Lens, whereby the Image or Species of
+that Hole is cast distinctly upon a Paper at J, ABC the Prism, whereby
+the Rays are at their emerging out of the Lens refracted from J towards
+another Paper at _pt_, and the round Image at J is turned into an oblong
+Image _pt_ falling on that other Paper. This Image _pt_ consists of
+Circles placed one after another in a Rectilinear Order, as was
+sufficiently explained in the fifth Experiment; and these Circles are
+equal to the Circle J, and consequently answer in magnitude to the Hole
+F; and therefore by diminishing that Hole they may be at pleasure
+diminished, whilst their Centers remain in their Places. By this means I
+made the Breadth of the Image _pt_ to be forty times, and sometimes
+sixty or seventy times less than its Length. As for instance, if the
+Breadth of the Hole F be one tenth of an Inch, and MF the distance of
+the Lens from the Hole be 12 Feet; and if _p_B or _p_M the distance of
+the Image _pt_ from the Prism or Lens be 10 Feet, and the refracting
+Angle of the Prism be 62 Degrees, the Breadth of the Image _pt_ will be
+one twelfth of an Inch, and the Length about six Inches, and therefore
+the Length to the Breadth as 72 to 1, and by consequence the Light of
+this Image 71 times less compound than the Sun's direct Light. And Light
+thus far simple and homogeneal, is sufficient for trying all the
+Experiments in this Book about simple Light. For the Composition of
+heterogeneal Rays is in this Light so little, that it is scarce to be
+discovered and perceiv'd by Sense, except perhaps in the indigo and
+violet. For these being dark Colours do easily suffer a sensible Allay
+by that little scattering Light which uses to be refracted irregularly
+by the Inequalities of the Prism.
+
+Yet instead of the Circular Hole F, 'tis better to substitute an oblong
+Hole shaped like a long Parallelogram with its Length parallel to the
+Prism ABC. For if this Hole be an Inch or two long, and but a tenth or
+twentieth Part of an Inch broad, or narrower; the Light of the Image
+_pt_ will be as simple as before, or simpler, and the Image will become
+much broader, and therefore more fit to have Experiments try'd in its
+Light than before.
+
+Instead of this Parallelogram Hole may be substituted a triangular one
+of equal Sides, whose Base, for instance, is about the tenth Part of an
+Inch, and its Height an Inch or more. For by this means, if the Axis of
+the Prism be parallel to the Perpendicular of the Triangle, the Image
+_pt_ [in _Fig._ 25.] will now be form'd of equicrural Triangles _ag_,
+_bh_, _ci_, _dk_, _el_, _fm_, &c. and innumerable other intermediate
+ones answering to the triangular Hole in Shape and Bigness, and lying
+one after another in a continual Series between two Parallel Lines _af_
+and _gm_. These Triangles are a little intermingled at their Bases, but
+not at their Vertices; and therefore the Light on the brighter Side _af_
+of the Image, where the Bases of the Triangles are, is a little
+compounded, but on the darker Side _gm_ is altogether uncompounded, and
+in all Places between the Sides the Composition is proportional to the
+distances of the Places from that obscurer Side _gm_. And having a
+Spectrum _pt_ of such a Composition, we may try Experiments either in
+its stronger and less simple Light near the Side _af_, or in its weaker
+and simpler Light near the other Side _gm_, as it shall seem most
+convenient.
+
+[Illustration: FIG. 25.]
+
+But in making Experiments of this kind, the Chamber ought to be made as
+dark as can be, lest any Foreign Light mingle it self with the Light of
+the Spectrum _pt_, and render it compound; especially if we would try
+Experiments in the more simple Light next the Side _gm_ of the Spectrum;
+which being fainter, will have a less proportion to the Foreign Light;
+and so by the mixture of that Light be more troubled, and made more
+compound. The Lens also ought to be good, such as may serve for optical
+Uses, and the Prism ought to have a large Angle, suppose of 65 or 70
+Degrees, and to be well wrought, being made of Glass free from Bubbles
+and Veins, with its Sides not a little convex or concave, as usually
+happens, but truly plane, and its Polish elaborate, as in working
+Optick-glasses, and not such as is usually wrought with Putty, whereby
+the edges of the Sand-holes being worn away, there are left all over the
+Glass a numberless Company of very little convex polite Risings like
+Waves. The edges also of the Prism and Lens, so far as they may make any
+irregular Refraction, must be covered with a black Paper glewed on. And
+all the Light of the Sun's Beam let into the Chamber, which is useless
+and unprofitable to the Experiment, ought to be intercepted with black
+Paper, or other black Obstacles. For otherwise the useless Light being
+reflected every way in the Chamber, will mix with the oblong Spectrum,
+and help to disturb it. In trying these Things, so much diligence is not
+altogether necessary, but it will promote the Success of the
+Experiments, and by a very scrupulous Examiner of Things deserves to be
+apply'd. It's difficult to get Glass Prisms fit for this Purpose, and
+therefore I used sometimes prismatick Vessels made with pieces of broken
+Looking-glasses, and filled with Rain Water. And to increase the
+Refraction, I sometimes impregnated the Water strongly with _Saccharum
+Saturni_.
+
+
+_PROP._ V. THEOR. IV.
+
+_Homogeneal Light is refracted regularly without any Dilatation
+splitting or shattering of the Rays, and the confused Vision of Objects
+seen through refracting Bodies by heterogeneal Light arises from the
+different Refrangibility of several sorts of Rays._
+
+The first Part of this Proposition has been already sufficiently proved
+in the fifth Experiment, and will farther appear by the Experiments
+which follow.
+
+_Exper._ 12. In the middle of a black Paper I made a round Hole about a
+fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the
+Spectrum of homogeneal Light described in the former Proposition, so to
+fall, that some part of the Light might pass through the Hole of the
+Paper. This transmitted part of the Light I refracted with a Prism
+placed behind the Paper, and letting this refracted Light fall
+perpendicularly upon a white Paper two or three Feet distant from the
+Prism, I found that the Spectrum formed on the Paper by this Light was
+not oblong, as when 'tis made (in the third Experiment) by refracting
+the Sun's compound Light, but was (so far as I could judge by my Eye)
+perfectly circular, the Length being no greater than the Breadth. Which
+shews, that this Light is refracted regularly without any Dilatation of
+the Rays.
+
+_Exper._ 13. In the homogeneal Light I placed a Paper Circle of a
+quarter of an Inch in diameter, and in the Sun's unrefracted
+heterogeneal white Light I placed another Paper Circle of the same
+Bigness. And going from the Papers to the distance of some Feet, I
+viewed both Circles through a Prism. The Circle illuminated by the Sun's
+heterogeneal Light appeared very oblong, as in the fourth Experiment,
+the Length being many times greater than the Breadth; but the other
+Circle, illuminated with homogeneal Light, appeared circular and
+distinctly defined, as when 'tis view'd with the naked Eye. Which proves
+the whole Proposition.
+
+_Exper._ 14. In the homogeneal Light I placed Flies, and such-like
+minute Objects, and viewing them through a Prism, I saw their Parts as
+distinctly defined, as if I had viewed them with the naked Eye. The same
+Objects placed in the Sun's unrefracted heterogeneal Light, which was
+white, I viewed also through a Prism, and saw them most confusedly
+defined, so that I could not distinguish their smaller Parts from one
+another. I placed also the Letters of a small print, one while in the
+homogeneal Light, and then in the heterogeneal, and viewing them through
+a Prism, they appeared in the latter Case so confused and indistinct,
+that I could not read them; but in the former they appeared so distinct,
+that I could read readily, and thought I saw them as distinct, as when I
+view'd them with my naked Eye. In both Cases I view'd the same Objects,
+through the same Prism at the same distance from me, and in the same
+Situation. There was no difference, but in the Light by which the
+Objects were illuminated, and which in one Case was simple, and in the
+other compound; and therefore, the distinct Vision in the former Case,
+and confused in the latter, could arise from nothing else than from that
+difference of the Lights. Which proves the whole Proposition.
+
+And in these three Experiments it is farther very remarkable, that the
+Colour of homogeneal Light was never changed by the Refraction.
+
+
+_PROP._ VI. THEOR. V.
+
+_The Sine of Incidence of every Ray considered apart, is to its Sine of
+Refraction in a given Ratio._
+
+That every Ray consider'd apart, is constant to it self in some degree
+of Refrangibility, is sufficiently manifest out of what has been said.
+Those Rays, which in the first Refraction, are at equal Incidences most
+refracted, are also in the following Refractions at equal Incidences
+most refracted; and so of the least refrangible, and the rest which have
+any mean Degree of Refrangibility, as is manifest by the fifth, sixth,
+seventh, eighth, and ninth Experiments. And those which the first Time
+at like Incidences are equally refracted, are again at like Incidences
+equally and uniformly refracted, and that whether they be refracted
+before they be separated from one another, as in the fifth Experiment,
+or whether they be refracted apart, as in the twelfth, thirteenth and
+fourteenth Experiments. The Refraction therefore of every Ray apart is
+regular, and what Rule that Refraction observes we are now to shew.[E]
+
+The late Writers in Opticks teach, that the Sines of Incidence are in a
+given Proportion to the Sines of Refraction, as was explained in the
+fifth Axiom, and some by Instruments fitted for measuring of
+Refractions, or otherwise experimentally examining this Proportion, do
+acquaint us that they have found it accurate. But whilst they, not
+understanding the different Refrangibility of several Rays, conceived
+them all to be refracted according to one and the same Proportion, 'tis
+to be presumed that they adapted their Measures only to the middle of
+the refracted Light; so that from their Measures we may conclude only
+that the Rays which have a mean Degree of Refrangibility, that is, those
+which when separated from the rest appear green, are refracted according
+to a given Proportion of their Sines. And therefore we are now to shew,
+that the like given Proportions obtain in all the rest. That it should
+be so is very reasonable, Nature being ever conformable to her self; but
+an experimental Proof is desired. And such a Proof will be had, if we
+can shew that the Sines of Refraction of Rays differently refrangible
+are one to another in a given Proportion when their Sines of Incidence
+are equal. For, if the Sines of Refraction of all the Rays are in given
+Proportions to the Sine of Refractions of a Ray which has a mean Degree
+of Refrangibility, and this Sine is in a given Proportion to the equal
+Sines of Incidence, those other Sines of Refraction will also be in
+given Proportions to the equal Sines of Incidence. Now, when the Sines
+of Incidence are equal, it will appear by the following Experiment, that
+the Sines of Refraction are in a given Proportion to one another.
+
+[Illustration: FIG. 26.]
+
+_Exper._ 15. The Sun shining into a dark Chamber through a little round
+Hole in the Window-shut, let S [in _Fig._ 26.] represent his round white
+Image painted on the opposite Wall by his direct Light, PT his oblong
+coloured Image made by refracting that Light with a Prism placed at the
+Window; and _pt_, or _2p 2t_, _3p 3t_, his oblong colour'd Image made by
+refracting again the same Light sideways with a second Prism placed
+immediately after the first in a cross Position to it, as was explained
+in the fifth Experiment; that is to say, _pt_ when the Refraction of the
+second Prism is small, _2p 2t_ when its Refraction is greater, and _3p
+3t_ when it is greatest. For such will be the diversity of the
+Refractions, if the refracting Angle of the second Prism be of various
+Magnitudes; suppose of fifteen or twenty Degrees to make the Image _pt_,
+of thirty or forty to make the Image _2p 2t_, and of sixty to make the
+Image _3p 3t_. But for want of solid Glass Prisms with Angles of
+convenient Bignesses, there may be Vessels made of polished Plates of
+Glass cemented together in the form of Prisms and filled with Water.
+These things being thus ordered, I observed that all the solar Images or
+coloured Spectrums PT, _pt_, _2p 2t_, _3p 3t_ did very nearly converge
+to the place S on which the direct Light of the Sun fell and painted his
+white round Image when the Prisms were taken away. The Axis of the
+Spectrum PT, that is the Line drawn through the middle of it parallel to
+its rectilinear Sides, did when produced pass exactly through the middle
+of that white round Image S. And when the Refraction of the second Prism
+was equal to the Refraction of the first, the refracting Angles of them
+both being about 60 Degrees, the Axis of the Spectrum _3p 3t_ made by
+that Refraction, did when produced pass also through the middle of the
+same white round Image S. But when the Refraction of the second Prism
+was less than that of the first, the produced Axes of the Spectrums _tp_
+or _2t 2p_ made by that Refraction did cut the produced Axis of the
+Spectrum TP in the points _m_ and _n_, a little beyond the Center of
+that white round Image S. Whence the proportion of the Line 3_t_T to the
+Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P,
+and this Proportion a little greater than that of _t_T to _p_P. Now when
+the Light of the Spectrum PT falls perpendicularly upon the Wall, those
+Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the
+Tangents of the Refractions, and therefore by this Experiment the
+Proportions of the Tangents of the Refractions are obtained, from whence
+the Proportions of the Sines being derived, they come out equal, so far
+as by viewing the Spectrums, and using some mathematical Reasoning I
+could estimate. For I did not make an accurate Computation. So then the
+Proposition holds true in every Ray apart, so far as appears by
+Experiment. And that it is accurately true, may be demonstrated upon
+this Supposition. _That Bodies refract Light by acting upon its Rays in
+Lines perpendicular to their Surfaces._ But in order to this
+Demonstration, I must distinguish the Motion of every Ray into two
+Motions, the one perpendicular to the refracting Surface, the other
+parallel to it, and concerning the perpendicular Motion lay down the
+following Proposition.
+
+If any Motion or moving thing whatsoever be incident with any Velocity
+on any broad and thin space terminated on both sides by two parallel
+Planes, and in its Passage through that space be urged perpendicularly
+towards the farther Plane by any force which at given distances from the
+Plane is of given Quantities; the perpendicular velocity of that Motion
+or Thing, at its emerging out of that space, shall be always equal to
+the square Root of the sum of the square of the perpendicular velocity
+of that Motion or Thing at its Incidence on that space; and of the
+square of the perpendicular velocity which that Motion or Thing would
+have at its Emergence, if at its Incidence its perpendicular velocity
+was infinitely little.
+
+And the same Proposition holds true of any Motion or Thing
+perpendicularly retarded in its passage through that space, if instead
+of the sum of the two Squares you take their difference. The
+Demonstration Mathematicians will easily find out, and therefore I shall
+not trouble the Reader with it.
+
+Suppose now that a Ray coming most obliquely in the Line MC [in _Fig._
+1.] be refracted at C by the Plane RS into the Line CN, and if it be
+required to find the Line CE, into which any other Ray AC shall be
+refracted; let MC, AD, be the Sines of Incidence of the two Rays, and
+NG, EF, their Sines of Refraction, and let the equal Motions of the
+incident Rays be represented by the equal Lines MC and AC, and the
+Motion MC being considered as parallel to the refracting Plane, let the
+other Motion AC be distinguished into two Motions AD and DC, one of
+which AD is parallel, and the other DC perpendicular to the refracting
+Surface. In like manner, let the Motions of the emerging Rays be
+distinguish'd into two, whereof the perpendicular ones are MC/NG × CG
+and AD/EF × CF. And if the force of the refracting Plane begins to act
+upon the Rays either in that Plane or at a certain distance from it on
+the one side, and ends at a certain distance from it on the other side,
+and in all places between those two limits acts upon the Rays in Lines
+perpendicular to that refracting Plane, and the Actions upon the Rays at
+equal distances from the refracting Plane be equal, and at unequal ones
+either equal or unequal according to any rate whatever; that Motion of
+the Ray which is parallel to the refracting Plane, will suffer no
+Alteration by that Force; and that Motion which is perpendicular to it
+will be altered according to the rule of the foregoing Proposition. If
+therefore for the perpendicular velocity of the emerging Ray CN you
+write MC/NG × CG as above, then the perpendicular velocity of any other
+emerging Ray CE which was AD/EF × CF, will be equal to the square Root
+of CD_q_ + (_MCq/NGq_ × CG_q_). And by squaring these Equals, and adding
+to them the Equals AD_q_ and MC_q_ - CD_q_, and dividing the Sums by the
+Equals CF_q_ + EF_q_ and CG_q_ + NG_q_, you will have _MCq/NGq_ equal to
+_ADq/EFq_. Whence AD, the Sine of Incidence, is to EF the Sine of
+Refraction, as MC to NG, that is, in a given _ratio_. And this
+Demonstration being general, without determining what Light is, or by
+what kind of Force it is refracted, or assuming any thing farther than
+that the refracting Body acts upon the Rays in Lines perpendicular to
+its Surface; I take it to be a very convincing Argument of the full
+truth of this Proposition.
+
+So then, if the _ratio_ of the Sines of Incidence and Refraction of any
+sort of Rays be found in any one case, 'tis given in all cases; and this
+may be readily found by the Method in the following Proposition.
+
+
+_PROP._ VII. THEOR. VI.
+
+_The Perfection of Telescopes is impeded by the different Refrangibility
+of the Rays of Light._
+
+The Imperfection of Telescopes is vulgarly attributed to the spherical
+Figures of the Glasses, and therefore Mathematicians have propounded to
+figure them by the conical Sections. To shew that they are mistaken, I
+have inserted this Proposition; the truth of which will appear by the
+measure of the Refractions of the several sorts of Rays; and these
+measures I thus determine.
+
+In the third Experiment of this first Part, where the refracting Angle
+of the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min.
+is the Angle of Incidence of the Rays at their going out of the Glass
+into the Air[F]; and the Sine of this Angle is 5188, the Radius being
+10000. When the Axis of this Prism was parallel to the Horizon, and the
+Refraction of the Rays at their Incidence on this Prism equal to that at
+their Emergence out of it, I observed with a Quadrant the Angle which
+the mean refrangible Rays, (that is those which went to the middle of
+the Sun's coloured Image) made with the Horizon, and by this Angle and
+the Sun's altitude observed at the same time, I found the Angle which
+the emergent Rays contained with the incident to be 44 deg. and 40 min.
+and the half of this Angle added to the Angle of Incidence 31 deg. 15
+min. makes the Angle of Refraction, which is therefore 53 deg. 35 min.
+and its Sine 8047. These are the Sines of Incidence and Refraction of
+the mean refrangible Rays, and their Proportion in round Numbers is 20
+to 31. This Glass was of a Colour inclining to green. The last of the
+Prisms mentioned in the third Experiment was of clear white Glass. Its
+refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays
+contained, with the incident 45 deg. 50 min. The Sine of half the first
+Angle 5262. The Sine of half the Sum of the Angles 8157. And their
+Proportion in round Numbers 20 to 31, as before.
+
+From the Length of the Image, which was about 9-3/4 or 10 Inches,
+subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4
+Inches would be the Length of the Image were the Sun but a Point, and
+therefore subtends the Angle which the most and least refrangible Rays,
+when incident on the Prism in the same Lines, do contain with one
+another after their Emergence. Whence this Angle is 2 deg. 0´. 7´´. For
+the distance between the Image and the Prism where this Angle is made,
+was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends an
+Angle of 2 deg. 0´. 7´´. Now half this Angle is the Angle which these
+emergent Rays contain with the emergent mean refrangible Rays, and a
+quarter thereof, that is 30´. 2´´. may be accounted the Angle which they
+would contain with the same emergent mean refrangible Rays, were they
+co-incident to them within the Glass, and suffered no other Refraction
+than that at their Emergence. For, if two equal Refractions, the one at
+the Incidence of the Rays on the Prism, the other at their Emergence,
+make half the Angle 2 deg. 0´. 7´´. then one of those Refractions will
+make about a quarter of that Angle, and this quarter added to, and
+subducted from the Angle of Refraction of the mean refrangible Rays,
+which was 53 deg. 35´, gives the Angles of Refraction of the most and
+least refrangible Rays 54 deg. 5´ 2´´, and 53 deg. 4´ 58´´, whose Sines
+are 8099 and 7995, the common Angle of Incidence being 31 deg. 15´, and
+its Sine 5188; and these Sines in the least round Numbers are in
+proportion to one another, as 78 and 77 to 50.
+
+Now, if you subduct the common Sine of Incidence 50 from the Sines of
+Refraction 77 and 78, the Remainders 27 and 28 shew, that in small
+Refractions the Refraction of the least refrangible Rays is to the
+Refraction of the most refrangible ones, as 27 to 28 very nearly, and
+that the difference of the Refractions of the least refrangible and most
+refrangible Rays is about the 27-1/2th Part of the whole Refraction of
+the mean refrangible Rays.
+
+Whence they that are skilled in Opticks will easily understand,[G] that
+the Breadth of the least circular Space, into which Object-glasses of
+Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th
+Part of half the Aperture of the Glass, or 55th Part of the whole
+Aperture; and that the Focus of the most refrangible Rays is nearer to
+the Object-glass than the Focus of the least refrangible ones, by about
+the 27-1/2th Part of the distance between the Object-glass and the Focus
+of the mean refrangible ones.
+
+And if Rays of all sorts, flowing from any one lucid Point in the Axis
+of any convex Lens, be made by the Refraction of the Lens to converge to
+Points not too remote from the Lens, the Focus of the most refrangible
+Rays shall be nearer to the Lens than the Focus of the least refrangible
+ones, by a distance which is to the 27-1/2th Part of the distance of the
+Focus of the mean refrangible Rays from the Lens, as the distance
+between that Focus and the lucid Point, from whence the Rays flow, is to
+the distance between that lucid Point and the Lens very nearly.
+
+Now to examine whether the Difference between the Refractions, which the
+most refrangible and the least refrangible Rays flowing from the same
+Point suffer in the Object-glasses of Telescopes and such-like Glasses,
+be so great as is here described, I contrived the following Experiment.
+
+_Exper._ 16. The Lens which I used in the second and eighth Experiments,
+being placed six Feet and an Inch distant from any Object, collected the
+Species of that Object by the mean refrangible Rays at the distance of
+six Feet and an Inch from the Lens on the other side. And therefore by
+the foregoing Rule, it ought to collect the Species of that Object by
+the least refrangible Rays at the distance of six Feet and 3-2/3 Inches
+from the Lens, and by the most refrangible ones at the distance of five
+Feet and 10-1/3 Inches from it: So that between the two Places, where
+these least and most refrangible Rays collect the Species, there may be
+the distance of about 5-1/3 Inches. For by that Rule, as six Feet and an
+Inch (the distance of the Lens from the lucid Object) is to twelve Feet
+and two Inches (the distance of the lucid Object from the Focus of the
+mean refrangible Rays) that is, as One is to Two; so is the 27-1/2th
+Part of six Feet and an Inch (the distance between the Lens and the same
+Focus) to the distance between the Focus of the most refrangible Rays
+and the Focus of the least refrangible ones, which is therefore 5-17/55
+Inches, that is very nearly 5-1/3 Inches. Now to know whether this
+Measure was true, I repeated the second and eighth Experiment with
+coloured Light, which was less compounded than that I there made use of:
+For I now separated the heterogeneous Rays from one another by the
+Method I described in the eleventh Experiment, so as to make a coloured
+Spectrum about twelve or fifteen Times longer than broad. This Spectrum
+I cast on a printed Book, and placing the above-mentioned Lens at the
+distance of six Feet and an Inch from this Spectrum to collect the
+Species of the illuminated Letters at the same distance on the other
+side, I found that the Species of the Letters illuminated with blue were
+nearer to the Lens than those illuminated with deep red by about three
+Inches, or three and a quarter; but the Species of the Letters
+illuminated with indigo and violet appeared so confused and indistinct,
+that I could not read them: Whereupon viewing the Prism, I found it was
+full of Veins running from one end of the Glass to the other; so that
+the Refraction could not be regular. I took another Prism therefore
+which was free from Veins, and instead of the Letters I used two or
+three Parallel black Lines a little broader than the Strokes of the
+Letters, and casting the Colours upon these Lines in such manner, that
+the Lines ran along the Colours from one end of the Spectrum to the
+other, I found that the Focus where the indigo, or confine of this
+Colour and violet cast the Species of the black Lines most distinctly,
+to be about four Inches, or 4-1/4 nearer to the Lens than the Focus,
+where the deepest red cast the Species of the same black Lines most
+distinctly. The violet was so faint and dark, that I could not discern
+the Species of the Lines distinctly by that Colour; and therefore
+considering that the Prism was made of a dark coloured Glass inclining
+to green, I took another Prism of clear white Glass; but the Spectrum of
+Colours which this Prism made had long white Streams of faint Light
+shooting out from both ends of the Colours, which made me conclude that
+something was amiss; and viewing the Prism, I found two or three little
+Bubbles in the Glass, which refracted the Light irregularly. Wherefore I
+covered that Part of the Glass with black Paper, and letting the Light
+pass through another Part of it which was free from such Bubbles, the
+Spectrum of Colours became free from those irregular Streams of Light,
+and was now such as I desired. But still I found the violet so dark and
+faint, that I could scarce see the Species of the Lines by the violet,
+and not at all by the deepest Part of it, which was next the end of the
+Spectrum. I suspected therefore, that this faint and dark Colour might
+be allayed by that scattering Light which was refracted, and reflected
+irregularly, partly by some very small Bubbles in the Glasses, and
+partly by the Inequalities of their Polish; which Light, tho' it was but
+little, yet it being of a white Colour, might suffice to affect the
+Sense so strongly as to disturb the Phænomena of that weak and dark
+Colour the violet, and therefore I tried, as in the 12th, 13th, and 14th
+Experiments, whether the Light of this Colour did not consist of a
+sensible Mixture of heterogeneous Rays, but found it did not. Nor did
+the Refractions cause any other sensible Colour than violet to emerge
+out of this Light, as they would have done out of white Light, and by
+consequence out of this violet Light had it been sensibly compounded
+with white Light. And therefore I concluded, that the reason why I could
+not see the Species of the Lines distinctly by this Colour, was only
+the Darkness of this Colour, and Thinness of its Light, and its distance
+from the Axis of the Lens; I divided therefore those Parallel black
+Lines into equal Parts, by which I might readily know the distances of
+the Colours in the Spectrum from one another, and noted the distances of
+the Lens from the Foci of such Colours, as cast the Species of the Lines
+distinctly, and then considered whether the difference of those
+distances bear such proportion to 5-1/3 Inches, the greatest Difference
+of the distances, which the Foci of the deepest red and violet ought to
+have from the Lens, as the distance of the observed Colours from one
+another in the Spectrum bear to the greatest distance of the deepest red
+and violet measured in the Rectilinear Sides of the Spectrum, that is,
+to the Length of those Sides, or Excess of the Length of the Spectrum
+above its Breadth. And my Observations were as follows.
+
+When I observed and compared the deepest sensible red, and the Colour in
+the Confine of green and blue, which at the Rectilinear Sides of the
+Spectrum was distant from it half the Length of those Sides, the Focus
+where the Confine of green and blue cast the Species of the Lines
+distinctly on the Paper, was nearer to the Lens than the Focus, where
+the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4
+Inches. For sometimes the Measures were a little greater, sometimes a
+little less, but seldom varied from one another above 1/3 of an Inch.
+For it was very difficult to define the Places of the Foci, without some
+little Errors. Now, if the Colours distant half the Length of the
+Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4
+Difference of the distances of their Foci from the Lens, then the
+Colours distant the whole Length ought to give 5 or 5-1/2 Inches
+difference of those distances.
+
+But here it's to be noted, that I could not see the red to the full end
+of the Spectrum, but only to the Center of the Semicircle which bounded
+that end, or a little farther; and therefore I compared this red not
+with that Colour which was exactly in the middle of the Spectrum, or
+Confine of green and blue, but with that which verged a little more to
+the blue than to the green: And as I reckoned the whole Length of the
+Colours not to be the whole Length of the Spectrum, but the Length of
+its Rectilinear Sides, so compleating the semicircular Ends into
+Circles, when either of the observed Colours fell within those Circles,
+I measured the distance of that Colour from the semicircular End of the
+Spectrum, and subducting half this distance from the measured distance
+of the two Colours, I took the Remainder for their corrected distance;
+and in these Observations set down this corrected distance for the
+difference of the distances of their Foci from the Lens. For, as the
+Length of the Rectilinear Sides of the Spectrum would be the whole
+Length of all the Colours, were the Circles of which (as we shewed) that
+Spectrum consists contracted and reduced to Physical Points, so in that
+Case this corrected distance would be the real distance of the two
+observed Colours.
+
+When therefore I farther observed the deepest sensible red, and that
+blue whose corrected distance from it was 7/12 Parts of the Length of
+the Rectilinear Sides of the Spectrum, the difference of the distances
+of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so
+is 3-1/4 to 5-4/7.
+
+When I observed the deepest sensible red, and that indigo whose
+corrected distance was 8/12 or 2/3 of the Length of the Rectilinear
+Sides of the Spectrum, the difference of the distances of their Foci
+from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to
+5-1/2.
+
+When I observed the deepest sensible red, and that deep indigo whose
+corrected distance from one another was 9/12 or 3/4 of the Length of the
+Rectilinear Sides of the Spectrum, the difference of the distances of
+their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to
+5-1/3.
+
+When I observed the deepest sensible red, and that Part of the violet
+next the indigo, whose corrected distance from the red was 10/12 or 5/6
+of the Length of the Rectilinear Sides of the Spectrum, the difference
+of the distances of their Foci from the Lens was about 4-1/2 Inches, and
+as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was
+advantageously placed, so that its Axis respected the blue, and all
+Things else were well ordered, and the Sun shone clear, and I held my
+Eye very near to the Paper on which the Lens cast the Species of the
+Lines, I could see pretty distinctly the Species of those Lines by that
+Part of the violet which was next the indigo; and sometimes I could see
+them by above half the violet, For in making these Experiments I had
+observed, that the Species of those Colours only appear distinct, which
+were in or near the Axis of the Lens: So that if the blue or indigo were
+in the Axis, I could see their Species distinctly; and then the red
+appeared much less distinct than before. Wherefore I contrived to make
+the Spectrum of Colours shorter than before, so that both its Ends might
+be nearer to the Axis of the Lens. And now its Length was about 2-1/2
+Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the
+black Lines on which the Spectrum was cast, I made one black Line
+broader than those, that I might see its Species more easily; and this
+Line I divided by short cross Lines into equal Parts, for measuring the
+distances of the observed Colours. And now I could sometimes see the
+Species of this Line with its Divisions almost as far as the Center of
+the semicircular violet End of the Spectrum, and made these farther
+Observations.
+
+When I observed the deepest sensible red, and that Part of the violet,
+whose corrected distance from it was about 8/9 Parts of the Rectilinear
+Sides of the Spectrum, the Difference of the distances of the Foci of
+those Colours from the Lens, was one time 4-2/3, another time 4-3/4,
+another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to
+5-1/4, 5-11/32, 5-31/64 respectively.
+
+When I observed the deepest sensible red, and deepest sensible violet,
+(the corrected distance of which Colours, when all Things were ordered
+to the best Advantage, and the Sun shone very clear, was about 11/12 or
+15/16 Parts of the Length of the Rectilinear Sides of the coloured
+Spectrum) I found the Difference of the distances of their Foci from the
+Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or
+thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or
+5-1/3 Inches.
+
+And by this Progression of Experiments I satisfied my self, that had the
+Light at the very Ends of the Spectrum been strong enough to make the
+Species of the black Lines appear plainly on the Paper, the Focus of the
+deepest violet would have been found nearer to the Lens, than the Focus
+of the deepest red, by about 5-1/3 Inches at least. And this is a
+farther Evidence, that the Sines of Incidence and Refraction of the
+several sorts of Rays, hold the same Proportion to one another in the
+smallest Refractions which they do in the greatest.
+
+My Progress in making this nice and troublesome Experiment I have set
+down more at large, that they that shall try it after me may be aware of
+the Circumspection requisite to make it succeed well. And if they cannot
+make it succeed so well as I did, they may notwithstanding collect by
+the Proportion of the distance of the Colours of the Spectrum, to the
+Difference of the distances of their Foci from the Lens, what would be
+the Success in the more distant Colours by a better trial. And yet, if
+they use a broader Lens than I did, and fix it to a long strait Staff,
+by means of which it may be readily and truly directed to the Colour
+whose Focus is desired, I question not but the Experiment will succeed
+better with them than it did with me. For I directed the Axis as nearly
+as I could to the middle of the Colours, and then the faint Ends of the
+Spectrum being remote from the Axis, cast their Species less distinctly
+on the Paper than they would have done, had the Axis been successively
+directed to them.
+
+Now by what has been said, it's certain that the Rays which differ in
+Refrangibility do not converge to the same Focus; but if they flow from
+a lucid Point, as far from the Lens on one side as their Foci are on the
+other, the Focus of the most refrangible Rays shall be nearer to the
+Lens than that of the least refrangible, by above the fourteenth Part of
+the whole distance; and if they flow from a lucid Point, so very remote
+from the Lens, that before their Incidence they may be accounted
+parallel, the Focus of the most refrangible Rays shall be nearer to the
+Lens than the Focus of the least refrangible, by about the 27th or 28th
+Part of their whole distance from it. And the Diameter of the Circle in
+the middle Space between those two Foci which they illuminate, when they
+fall there on any Plane, perpendicular to the Axis (which Circle is the
+least into which they can all be gathered) is about the 55th Part of the
+Diameter of the Aperture of the Glass. So that 'tis a wonder, that
+Telescopes represent Objects so distinct as they do. But were all the
+Rays of Light equally refrangible, the Error arising only from the
+Sphericalness of the Figures of Glasses would be many hundred times
+less. For, if the Object-glass of a Telescope be Plano-convex, and the
+Plane side be turned towards the Object, and the Diameter of the
+Sphere, whereof this Glass is a Segment, be called D, and the
+Semi-diameter of the Aperture of the Glass be called S, and the Sine of
+Incidence out of Glass into Air, be to the Sine of Refraction as I to R;
+the Rays which come parallel to the Axis of the Glass, shall in the
+Place where the Image of the Object is most distinctly made, be
+scattered all over a little Circle, whose Diameter is _(Rq/Iq) × (S
+cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of
+the Rays by the Method of infinite Series, and rejecting the Terms,
+whose Quantities are inconsiderable. As for instance, if the Sine of
+Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the
+Diameter of the Sphere, to which the Convex-side of the Glass is ground,
+be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be
+two Inches, the Diameter of the little Circle, (that is (_Rq × S
+cub.)/(Iq × D quad._)) will be (31 × 31 × 8)/(20 × 20 × 1200 × 1200) (or
+961/72000000) Parts of an Inch. But the Diameter of the little Circle,
+through which these Rays are scattered by unequal Refrangibility, will
+be about the 55th Part of the Aperture of the Object-glass, which here
+is four Inches. And therefore, the Error arising from the Spherical
+Figure of the Glass, is to the Error arising from the different
+Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to
+5449; and therefore being in comparison so very little, deserves not to
+be considered.
+
+[Illustration: FIG. 27.]
+
+But you will say, if the Errors caused by the different Refrangibility
+be so very great, how comes it to pass, that Objects appear through
+Telescopes so distinct as they do? I answer, 'tis because the erring
+Rays are not scattered uniformly over all that Circular Space, but
+collected infinitely more densely in the Center than in any other Part
+of the Circle, and in the Way from the Center to the Circumference, grow
+continually rarer and rarer, so as at the Circumference to become
+infinitely rare; and by reason of their Rarity are not strong enough to
+be visible, unless in the Center and very near it. Let ADE [in _Fig._
+27.] represent one of those Circles described with the Center C, and
+Semi-diameter AC, and let BFG be a smaller Circle concentrick to the
+former, cutting with its Circumference the Diameter AC in B, and bisect
+AC in N; and by my reckoning, the Density of the Light in any Place B,
+will be to its Density in N, as AB to BC; and the whole Light within the
+lesser Circle BFG, will be to the whole Light within the greater AED, as
+the Excess of the Square of AC above the Square of AB, is to the Square
+of AC. As if BC be the fifth Part of AC, the Light will be four times
+denser in B than in N, and the whole Light within the less Circle, will
+be to the whole Light within the greater, as nine to twenty-five. Whence
+it's evident, that the Light within the less Circle, must strike the
+Sense much more strongly, than that faint and dilated Light round about
+between it and the Circumference of the greater.
+
+But it's farther to be noted, that the most luminous of the Prismatick
+Colours are the yellow and orange. These affect the Senses more strongly
+than all the rest together, and next to these in strength are the red
+and green. The blue compared with these is a faint and dark Colour, and
+the indigo and violet are much darker and fainter, so that these
+compared with the stronger Colours are little to be regarded. The Images
+of Objects are therefore to be placed, not in the Focus of the mean
+refrangible Rays, which are in the Confine of green and blue, but in the
+Focus of those Rays which are in the middle of the orange and yellow;
+there where the Colour is most luminous and fulgent, that is in the
+brightest yellow, that yellow which inclines more to orange than to
+green. And by the Refraction of these Rays (whose Sines of Incidence and
+Refraction in Glass are as 17 and 11) the Refraction of Glass and
+Crystal for Optical Uses is to be measured. Let us therefore place the
+Image of the Object in the Focus of these Rays, and all the yellow and
+orange will fall within a Circle, whose Diameter is about the 250th
+Part of the Diameter of the Aperture of the Glass. And if you add the
+brighter half of the red, (that half which is next the orange) and the
+brighter half of the green, (that half which is next the yellow) about
+three fifth Parts of the Light of these two Colours will fall within the
+same Circle, and two fifth Parts will fall without it round about; and
+that which falls without will be spread through almost as much more
+space as that which falls within, and so in the gross be almost three
+times rarer. Of the other half of the red and green, (that is of the
+deep dark red and willow green) about one quarter will fall within this
+Circle, and three quarters without, and that which falls without will be
+spread through about four or five times more space than that which falls
+within; and so in the gross be rarer, and if compared with the whole
+Light within it, will be about 25 times rarer than all that taken in the
+gross; or rather more than 30 or 40 times rarer, because the deep red in
+the end of the Spectrum of Colours made by a Prism is very thin and
+rare, and the willow green is something rarer than the orange and
+yellow. The Light of these Colours therefore being so very much rarer
+than that within the Circle, will scarce affect the Sense, especially
+since the deep red and willow green of this Light, are much darker
+Colours than the rest. And for the same reason the blue and violet being
+much darker Colours than these, and much more rarified, may be
+neglected. For the dense and bright Light of the Circle, will obscure
+the rare and weak Light of these dark Colours round about it, and
+render them almost insensible. The sensible Image of a lucid Point is
+therefore scarce broader than a Circle, whose Diameter is the 250th Part
+of the Diameter of the Aperture of the Object-glass of a good Telescope,
+or not much broader, if you except a faint and dark misty Light round
+about it, which a Spectator will scarce regard. And therefore in a
+Telescope, whose Aperture is four Inches, and Length an hundred Feet, it
+exceeds not 2´´ 45´´´, or 3´´. And in a Telescope whose Aperture is two
+Inches, and Length 20 or 30 Feet, it may be 5´´ or 6´´, and scarce
+above. And this answers well to Experience: For some Astronomers have
+found the Diameters of the fix'd Stars, in Telescopes of between 20 and
+60 Feet in length, to be about 5´´ or 6´´, or at most 8´´ or 10´´ in
+diameter. But if the Eye-Glass be tincted faintly with the Smoak of a
+Lamp or Torch, to obscure the Light of the Star, the fainter Light in
+the Circumference of the Star ceases to be visible, and the Star (if the
+Glass be sufficiently soiled with Smoak) appears something more like a
+mathematical Point. And for the same Reason, the enormous Part of the
+Light in the Circumference of every lucid Point ought to be less
+discernible in shorter Telescopes than in longer, because the shorter
+transmit less Light to the Eye.
+
+Now, that the fix'd Stars, by reason of their immense Distance, appear
+like Points, unless so far as their Light is dilated by Refraction, may
+appear from hence; that when the Moon passes over them and eclipses
+them, their Light vanishes, not gradually like that of the Planets, but
+all at once; and in the end of the Eclipse it returns into Sight all at
+once, or certainly in less time than the second of a Minute; the
+Refraction of the Moon's Atmosphere a little protracting the time in
+which the Light of the Star first vanishes, and afterwards returns into
+Sight.
+
+Now, if we suppose the sensible Image of a lucid Point, to be even 250
+times narrower than the Aperture of the Glass; yet this Image would be
+still much greater than if it were only from the spherical Figure of the
+Glass. For were it not for the different Refrangibility of the Rays, its
+breadth in an 100 Foot Telescope whose aperture is 4 Inches, would be
+but 961/72000000 parts of an Inch, as is manifest by the foregoing
+Computation. And therefore in this case the greatest Errors arising from
+the spherical Figure of the Glass, would be to the greatest sensible
+Errors arising from the different Refrangibility of the Rays as
+961/72000000 to 4/250 at most, that is only as 1 to 1200. And this
+sufficiently shews that it is not the spherical Figures of Glasses, but
+the different Refrangibility of the Rays which hinders the perfection of
+Telescopes.
+
+There is another Argument by which it may appear that the different
+Refrangibility of Rays, is the true cause of the imperfection of
+Telescopes. For the Errors of the Rays arising from the spherical
+Figures of Object-glasses, are as the Cubes of the Apertures of the
+Object Glasses; and thence to make Telescopes of various Lengths magnify
+with equal distinctness, the Apertures of the Object-glasses, and the
+Charges or magnifying Powers ought to be as the Cubes of the square
+Roots of their lengths; which doth not answer to Experience. But the
+Errors of the Rays arising from the different Refrangibility, are as the
+Apertures of the Object-glasses; and thence to make Telescopes of
+various lengths, magnify with equal distinctness, their Apertures and
+Charges ought to be as the square Roots of their lengths; and this
+answers to Experience, as is well known. For Instance, a Telescope of 64
+Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120
+times, with as much distinctness as one of a Foot in length, with 1/3 of
+an Inch aperture, magnifies 15 times.
+
+[Illustration: FIG. 28.]
+
+Now were it not for this different Refrangibility of Rays, Telescopes
+might be brought to a greater perfection than we have yet describ'd, by
+composing the Object-glass of two Glasses with Water between them. Let
+ADFC [in _Fig._ 28.] represent the Object-glass composed of two Glasses
+ABED and BEFC, alike convex on the outsides AGD and CHF, and alike
+concave on the insides BME, BNE, with Water in the concavity BMEN. Let
+the Sine of Incidence out of Glass into Air be as I to R, and out of
+Water into Air, as K to R, and by consequence out of Glass into Water,
+as I to K: and let the Diameter of the Sphere to which the convex sides
+AGD and CHF are ground be D, and the Diameter of the Sphere to which the
+concave sides BME and BNE, are ground be to D, as the Cube Root of
+KK--KI to the Cube Root of RK--RI: and the Refractions on the concave
+sides of the Glasses, will very much correct the Errors of the
+Refractions on the convex sides, so far as they arise from the
+sphericalness of the Figure. And by this means might Telescopes be
+brought to sufficient perfection, were it not for the different
+Refrangibility of several sorts of Rays. But by reason of this different
+Refrangibility, I do not yet see any other means of improving Telescopes
+by Refractions alone, than that of increasing their lengths, for which
+end the late Contrivance of _Hugenius_ seems well accommodated. For very
+long Tubes are cumbersome, and scarce to be readily managed, and by
+reason of their length are very apt to bend, and shake by bending, so as
+to cause a continual trembling in the Objects, whereby it becomes
+difficult to see them distinctly: whereas by his Contrivance the Glasses
+are readily manageable, and the Object-glass being fix'd upon a strong
+upright Pole becomes more steady.
+
+Seeing therefore the Improvement of Telescopes of given lengths by
+Refractions is desperate; I contrived heretofore a Perspective by
+Reflexion, using instead of an Object-glass a concave Metal. The
+diameter of the Sphere to which the Metal was ground concave was about
+25 _English_ Inches, and by consequence the length of the Instrument
+about six Inches and a quarter. The Eye-glass was Plano-convex, and the
+diameter of the Sphere to which the convex side was ground was about 1/5
+of an Inch, or a little less, and by consequence it magnified between 30
+and 40 times. By another way of measuring I found that it magnified
+about 35 times. The concave Metal bore an Aperture of an Inch and a
+third part; but the Aperture was limited not by an opake Circle,
+covering the Limb of the Metal round about, but by an opake Circle
+placed between the Eyeglass and the Eye, and perforated in the middle
+with a little round hole for the Rays to pass through to the Eye. For
+this Circle by being placed here, stopp'd much of the erroneous Light,
+which otherwise would have disturbed the Vision. By comparing it with a
+pretty good Perspective of four Feet in length, made with a concave
+Eye-glass, I could read at a greater distance with my own Instrument
+than with the Glass. Yet Objects appeared much darker in it than in the
+Glass, and that partly because more Light was lost by Reflexion in the
+Metal, than by Refraction in the Glass, and partly because my Instrument
+was overcharged. Had it magnified but 30 or 25 times, it would have made
+the Object appear more brisk and pleasant. Two of these I made about 16
+Years ago, and have one of them still by me, by which I can prove the
+truth of what I write. Yet it is not so good as at the first. For the
+concave has been divers times tarnished and cleared again, by rubbing
+it with very soft Leather. When I made these an Artist in _London_
+undertook to imitate it; but using another way of polishing them than I
+did, he fell much short of what I had attained to, as I afterwards
+understood by discoursing the Under-workman he had employed. The Polish
+I used was in this manner. I had two round Copper Plates, each six
+Inches in Diameter, the one convex, the other concave, ground very true
+to one another. On the convex I ground the Object-Metal or Concave which
+was to be polish'd, 'till it had taken the Figure of the Convex and was
+ready for a Polish. Then I pitched over the convex very thinly, by
+dropping melted Pitch upon it, and warming it to keep the Pitch soft,
+whilst I ground it with the concave Copper wetted to make it spread
+eavenly all over the convex. Thus by working it well I made it as thin
+as a Groat, and after the convex was cold I ground it again to give it
+as true a Figure as I could. Then I took Putty which I had made very
+fine by washing it from all its grosser Particles, and laying a little
+of this upon the Pitch, I ground it upon the Pitch with the concave
+Copper, till it had done making a Noise; and then upon the Pitch I
+ground the Object-Metal with a brisk motion, for about two or three
+Minutes of time, leaning hard upon it. Then I put fresh Putty upon the
+Pitch, and ground it again till it had done making a noise, and
+afterwards ground the Object-Metal upon it as before. And this Work I
+repeated till the Metal was polished, grinding it the last time with all
+my strength for a good while together, and frequently breathing upon
+the Pitch, to keep it moist without laying on any more fresh Putty. The
+Object-Metal was two Inches broad, and about one third part of an Inch
+thick, to keep it from bending. I had two of these Metals, and when I
+had polished them both, I tried which was best, and ground the other
+again, to see if I could make it better than that which I kept. And thus
+by many Trials I learn'd the way of polishing, till I made those two
+reflecting Perspectives I spake of above. For this Art of polishing will
+be better learn'd by repeated Practice than by my Description. Before I
+ground the Object-Metal on the Pitch, I always ground the Putty on it
+with the concave Copper, till it had done making a noise, because if the
+Particles of the Putty were not by this means made to stick fast in the
+Pitch, they would by rolling up and down grate and fret the Object-Metal
+and fill it full of little holes.
+
+But because Metal is more difficult to polish than Glass, and is
+afterwards very apt to be spoiled by tarnishing, and reflects not so
+much Light as Glass quick-silver'd over does: I would propound to use
+instead of the Metal, a Glass ground concave on the foreside, and as
+much convex on the backside, and quick-silver'd over on the convex side.
+The Glass must be every where of the same thickness exactly. Otherwise
+it will make Objects look colour'd and indistinct. By such a Glass I
+tried about five or six Years ago to make a reflecting Telescope of four
+Feet in length to magnify about 150 times, and I satisfied my self that
+there wants nothing but a good Artist to bring the Design to
+perfection. For the Glass being wrought by one of our _London_ Artists
+after such a manner as they grind Glasses for Telescopes, though it
+seemed as well wrought as the Object-glasses use to be, yet when it was
+quick-silver'd, the Reflexion discovered innumerable Inequalities all
+over the Glass. And by reason of these Inequalities, Objects appeared
+indistinct in this Instrument. For the Errors of reflected Rays caused
+by any Inequality of the Glass, are about six times greater than the
+Errors of refracted Rays caused by the like Inequalities. Yet by this
+Experiment I satisfied my self that the Reflexion on the concave side of
+the Glass, which I feared would disturb the Vision, did no sensible
+prejudice to it, and by consequence that nothing is wanting to perfect
+these Telescopes, but good Workmen who can grind and polish Glasses
+truly spherical. An Object-glass of a fourteen Foot Telescope, made by
+an Artificer at _London_, I once mended considerably, by grinding it on
+Pitch with Putty, and leaning very easily on it in the grinding, lest
+the Putty should scratch it. Whether this way may not do well enough for
+polishing these reflecting Glasses, I have not yet tried. But he that
+shall try either this or any other way of polishing which he may think
+better, may do well to make his Glasses ready for polishing, by grinding
+them without that Violence, wherewith our _London_ Workmen press their
+Glasses in grinding. For by such violent pressure, Glasses are apt to
+bend a little in the grinding, and such bending will certainly spoil
+their Figure. To recommend therefore the consideration of these
+reflecting Glasses to such Artists as are curious in figuring Glasses, I
+shall describe this optical Instrument in the following Proposition.
+
+
+_PROP._ VIII. PROB. II.
+
+_To shorten Telescopes._
+
+Let ABCD [in _Fig._ 29.] represent a Glass spherically concave on the
+foreside AB, and as much convex on the backside CD, so that it be every
+where of an equal thickness. Let it not be thicker on one side than on
+the other, lest it make Objects appear colour'd and indistinct, and let
+it be very truly wrought and quick-silver'd over on the backside; and
+set in the Tube VXYZ which must be very black within. Let EFG represent
+a Prism of Glass or Crystal placed near the other end of the Tube, in
+the middle of it, by means of a handle of Brass or Iron FGK, to the end
+of which made flat it is cemented. Let this Prism be rectangular at E,
+and let the other two Angles at F and G be accurately equal to each
+other, and by consequence equal to half right ones, and let the plane
+sides FE and GE be square, and by consequence the third side FG a
+rectangular Parallelogram, whose length is to its breadth in a
+subduplicate proportion of two to one. Let it be so placed in the Tube,
+that the Axis of the Speculum may pass through the middle of the square
+side EF perpendicularly and by consequence through the middle of the
+side FG at an Angle of 45 Degrees, and let the side EF be turned towards
+the Speculum, and the distance of this Prism from the Speculum be such
+that the Rays of the Light PQ, RS, &c. which are incident upon the
+Speculum in Lines parallel to the Axis thereof, may enter the Prism at
+the side EF, and be reflected by the side FG, and thence go out of it
+through the side GE, to the Point T, which must be the common Focus of
+the Speculum ABDC, and of a Plano-convex Eye-glass H, through which
+those Rays must pass to the Eye. And let the Rays at their coming out of
+the Glass pass through a small round hole, or aperture made in a little
+plate of Lead, Brass, or Silver, wherewith the Glass is to be covered,
+which hole must be no bigger than is necessary for Light enough to pass
+through. For so it will render the Object distinct, the Plate in which
+'tis made intercepting all the erroneous part of the Light which comes
+from the verges of the Speculum AB. Such an Instrument well made, if it
+be six Foot long, (reckoning the length from the Speculum to the Prism,
+and thence to the Focus T) will bear an aperture of six Inches at the
+Speculum, and magnify between two and three hundred times. But the hole
+H here limits the aperture with more advantage, than if the aperture was
+placed at the Speculum. If the Instrument be made longer or shorter, the
+aperture must be in proportion as the Cube of the square-square Root of
+the length, and the magnifying as the aperture. But it's convenient that
+the Speculum be an Inch or two broader than the aperture at the least,
+and that the Glass of the Speculum be thick, that it bend not in the
+working. The Prism EFG must be no bigger than is necessary, and its back
+side FG must not be quick-silver'd over. For without quicksilver it will
+reflect all the Light incident on it from the Speculum.
+
+[Illustration: FIG. 29.]
+
+In this Instrument the Object will be inverted, but may be erected by
+making the square sides FF and EG of the Prism EFG not plane but
+spherically convex, that the Rays may cross as well before they come at
+it as afterwards between it and the Eye-glass. If it be desired that the
+Instrument bear a larger aperture, that may be also done by composing
+the Speculum of two Glasses with Water between them.
+
+If the Theory of making Telescopes could at length be fully brought into
+Practice, yet there would be certain Bounds beyond which Telescopes
+could not perform. For the Air through which we look upon the Stars, is
+in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows
+cast from high Towers, and by the twinkling of the fix'd Stars. But
+these Stars do not twinkle when viewed through Telescopes which have
+large apertures. For the Rays of Light which pass through divers parts
+of the aperture, tremble each of them apart, and by means of their
+various and sometimes contrary Tremors, fall at one and the same time
+upon different points in the bottom of the Eye, and their trembling
+Motions are too quick and confused to be perceived severally. And all
+these illuminated Points constitute one broad lucid Point, composed of
+those many trembling Points confusedly and insensibly mixed with one
+another by very short and swift Tremors, and thereby cause the Star to
+appear broader than it is, and without any trembling of the whole. Long
+Telescopes may cause Objects to appear brighter and larger than short
+ones can do, but they cannot be so formed as to take away that confusion
+of the Rays which arises from the Tremors of the Atmosphere. The only
+Remedy is a most serene and quiet Air, such as may perhaps be found on
+the tops of the highest Mountains above the grosser Clouds.
+
+FOOTNOTES:
+
+[C] _See our_ Author's Lectiones Opticæ § 10. _Sect. II. § 29. and Sect.
+III. Prop. 25._
+
+[D] See our Author's _Lectiones Opticæ_, Part. I. Sect. 1. §5.
+
+[E] _This is very fully treated of in our_ Author's Lect. Optic. _Part_
+I. _Sect._ II.
+
+[F] _See our_ Author's Lect. Optic. Part I. Sect. II. § 29.
+
+[G] _This is demonstrated in our_ Author's Lect. Optic. _Part_ I.
+_Sect._ IV. _Prop._ 37.
+
+[H] _How to do this, is shewn in our_ Author's Lect. Optic. _Part_ I.
+_Sect._ IV. _Prop._ 31.
+
+
+
+
+THE FIRST BOOK OF OPTICKS
+
+
+
+
+_PART II._
+
+
+_PROP._ I. THEOR. I.
+
+_The Phænomena of Colours in refracted or reflected Light are not caused
+by new Modifications of the Light variously impress'd, according to the
+various Terminations of the Light and Shadow_.
+
+The PROOF by Experiments.
+
+_Exper._ 1. For if the Sun shine into a very dark Chamber through an
+oblong hole F, [in _Fig._ 1.] whose breadth is the sixth or eighth part
+of an Inch, or something less; and his beam FH do afterwards pass first
+through a very large Prism ABC, distant about 20 Feet from the hole, and
+parallel to it, and then (with its white part) through an oblong hole H,
+whose breadth is about the fortieth or sixtieth part of an Inch, and
+which is made in a black opake Body GI, and placed at the distance of
+two or three Feet from the Prism, in a parallel Situation both to the
+Prism and to the former hole, and if this white Light thus transmitted
+through the hole H, fall afterwards upon a white Paper _pt_, placed
+after that hole H, at the distance of three or four Feet from it, and
+there paint the usual Colours of the Prism, suppose red at _t_, yellow
+at _s_, green at _r_, blue at _q_, and violet at _p_; you may with an
+Iron Wire, or any such like slender opake Body, whose breadth is about
+the tenth part of an Inch, by intercepting the Rays at _k_, _l_, _m_,
+_n_ or _o_, take away any one of the Colours at _t_, _s_, _r_, _q_ or
+_p_, whilst the other Colours remain upon the Paper as before; or with
+an Obstacle something bigger you may take away any two, or three, or
+four Colours together, the rest remaining: So that any one of the
+Colours as well as violet may become outmost in the Confine of the
+Shadow towards _p_, and any one of them as well as red may become
+outmost in the Confine of the Shadow towards _t_, and any one of them
+may also border upon the Shadow made within the Colours by the Obstacle
+R intercepting some intermediate part of the Light; and, lastly, any one
+of them by being left alone, may border upon the Shadow on either hand.
+All the Colours have themselves indifferently to any Confines of Shadow,
+and therefore the differences of these Colours from one another, do not
+arise from the different Confines of Shadow, whereby Light is variously
+modified, as has hitherto been the Opinion of Philosophers. In trying
+these things 'tis to be observed, that by how much the holes F and H are
+narrower, and the Intervals between them and the Prism greater, and the
+Chamber darker, by so much the better doth the Experiment succeed;
+provided the Light be not so far diminished, but that the Colours at
+_pt_ be sufficiently visible. To procure a Prism of solid Glass large
+enough for this Experiment will be difficult, and therefore a prismatick
+Vessel must be made of polish'd Glass Plates cemented together, and
+filled with salt Water or clear Oil.
+
+[Illustration: FIG. 1.]
+
+_Exper._ 2. The Sun's Light let into a dark Chamber through the round
+hole F, [in _Fig._ 2.] half an Inch wide, passed first through the Prism
+ABC placed at the hole, and then through a Lens PT something more than
+four Inches broad, and about eight Feet distant from the Prism, and
+thence converged to O the Focus of the Lens distant from it about three
+Feet, and there fell upon a white Paper DE. If that Paper was
+perpendicular to that Light incident upon it, as 'tis represented in the
+posture DE, all the Colours upon it at O appeared white. But if the
+Paper being turned about an Axis parallel to the Prism, became very much
+inclined to the Light, as 'tis represented in the Positions _de_ and
+_[Greek: de]_; the same Light in the one case appeared yellow and red,
+in the other blue. Here one and the same part of the Light in one and
+the same place, according to the various Inclinations of the Paper,
+appeared in one case white, in another yellow or red, in a third blue,
+whilst the Confine of Light and shadow, and the Refractions of the Prism
+in all these cases remained the same.
+
+[Illustration: FIG. 2.]
+
+[Illustration: FIG. 3.]
+
+_Exper._ 3. Such another Experiment may be more easily tried as follows.
+Let a broad beam of the Sun's Light coming into a dark Chamber through a
+hole in the Window-shut be refracted by a large Prism ABC, [in _Fig._
+3.] whose refracting Angle C is more than 60 Degrees, and so soon as it
+comes out of the Prism, let it fall upon the white Paper DE glewed upon
+a stiff Plane; and this Light, when the Paper is perpendicular to it, as
+'tis represented in DE, will appear perfectly white upon the Paper; but
+when the Paper is very much inclin'd to it in such a manner as to keep
+always parallel to the Axis of the Prism, the whiteness of the whole
+Light upon the Paper will according to the inclination of the Paper this
+way or that way, change either into yellow and red, as in the posture
+_de_, or into blue and violet, as in the posture [Greek: de]. And if the
+Light before it fall upon the Paper be twice refracted the same way by
+two parallel Prisms, these Colours will become the more conspicuous.
+Here all the middle parts of the broad beam of white Light which fell
+upon the Paper, did without any Confine of Shadow to modify it, become
+colour'd all over with one uniform Colour, the Colour being always the
+same in the middle of the Paper as at the edges, and this Colour changed
+according to the various Obliquity of the reflecting Paper, without any
+change in the Refractions or Shadow, or in the Light which fell upon the
+Paper. And therefore these Colours are to be derived from some other
+Cause than the new Modifications of Light by Refractions and Shadows.
+
+If it be asked, what then is their Cause? I answer, That the Paper in
+the posture _de_, being more oblique to the more refrangible Rays than
+to the less refrangible ones, is more strongly illuminated by the latter
+than by the former, and therefore the less refrangible Rays are
+predominant in the reflected Light. And where-ever they are predominant
+in any Light, they tinge it with red or yellow, as may in some measure
+appear by the first Proposition of the first Part of this Book, and will
+more fully appear hereafter. And the contrary happens in the posture of
+the Paper [Greek: de], the more refrangible Rays being then predominant
+which always tinge Light with blues and violets.
+
+_Exper._ 4. The Colours of Bubbles with which Children play are various,
+and change their Situation variously, without any respect to any Confine
+or Shadow. If such a Bubble be cover'd with a concave Glass, to keep it
+from being agitated by any Wind or Motion of the Air, the Colours will
+slowly and regularly change their situation, even whilst the Eye and the
+Bubble, and all Bodies which emit any Light, or cast any Shadow, remain
+unmoved. And therefore their Colours arise from some regular Cause which
+depends not on any Confine of Shadow. What this Cause is will be shewed
+in the next Book.
+
+To these Experiments may be added the tenth Experiment of the first Part
+of this first Book, where the Sun's Light in a dark Room being
+trajected through the parallel Superficies of two Prisms tied together
+in the form of a Parallelopipede, became totally of one uniform yellow
+or red Colour, at its emerging out of the Prisms. Here, in the
+production of these Colours, the Confine of Shadow can have nothing to
+do. For the Light changes from white to yellow, orange and red
+successively, without any alteration of the Confine of Shadow: And at
+both edges of the emerging Light where the contrary Confines of Shadow
+ought to produce different Effects, the Colour is one and the same,
+whether it be white, yellow, orange or red: And in the middle of the
+emerging Light, where there is no Confine of Shadow at all, the Colour
+is the very same as at the edges, the whole Light at its very first
+Emergence being of one uniform Colour, whether white, yellow, orange or
+red, and going on thence perpetually without any change of Colour, such
+as the Confine of Shadow is vulgarly supposed to work in refracted Light
+after its Emergence. Neither can these Colours arise from any new
+Modifications of the Light by Refractions, because they change
+successively from white to yellow, orange and red, while the Refractions
+remain the same, and also because the Refractions are made contrary ways
+by parallel Superficies which destroy one another's Effects. They arise
+not therefore from any Modifications of Light made by Refractions and
+Shadows, but have some other Cause. What that Cause is we shewed above
+in this tenth Experiment, and need not here repeat it.
+
+There is yet another material Circumstance of this Experiment. For this
+emerging Light being by a third Prism HIK [in _Fig._ 22. _Part_ I.][I]
+refracted towards the Paper PT, and there painting the usual Colours of
+the Prism, red, yellow, green, blue, violet: If these Colours arose from
+the Refractions of that Prism modifying the Light, they would not be in
+the Light before its Incidence on that Prism. And yet in that Experiment
+we found, that when by turning the two first Prisms about their common
+Axis all the Colours were made to vanish but the red; the Light which
+makes that red being left alone, appeared of the very same red Colour
+before its Incidence on the third Prism. And in general we find by other
+Experiments, that when the Rays which differ in Refrangibility are
+separated from one another, and any one Sort of them is considered
+apart, the Colour of the Light which they compose cannot be changed by
+any Refraction or Reflexion whatever, as it ought to be were Colours
+nothing else than Modifications of Light caused by Refractions, and
+Reflexions, and Shadows. This Unchangeableness of Colour I am now to
+describe in the following Proposition.
+
+
+_PROP._ II. THEOR. II.
+
+_All homogeneal Light has its proper Colour answering to its Degree of
+Refrangibility, and that Colour cannot be changed by Reflexions and
+Refractions._
+
+In the Experiments of the fourth Proposition of the first Part of this
+first Book, when I had separated the heterogeneous Rays from one
+another, the Spectrum _pt_ formed by the separated Rays, did in the
+Progress from its End _p_, on which the most refrangible Rays fell, unto
+its other End _t_, on which the least refrangible Rays fell, appear
+tinged with this Series of Colours, violet, indigo, blue, green, yellow,
+orange, red, together with all their intermediate Degrees in a continual
+Succession perpetually varying. So that there appeared as many Degrees
+of Colours, as there were sorts of Rays differing in Refrangibility.
+
+_Exper._ 5. Now, that these Colours could not be changed by Refraction,
+I knew by refracting with a Prism sometimes one very little Part of this
+Light, sometimes another very little Part, as is described in the
+twelfth Experiment of the first Part of this Book. For by this
+Refraction the Colour of the Light was never changed in the least. If
+any Part of the red Light was refracted, it remained totally of the same
+red Colour as before. No orange, no yellow, no green or blue, no other
+new Colour was produced by that Refraction. Neither did the Colour any
+ways change by repeated Refractions, but continued always the same red
+entirely as at first. The like Constancy and Immutability I found also
+in the blue, green, and other Colours. So also, if I looked through a
+Prism upon any Body illuminated with any part of this homogeneal Light,
+as in the fourteenth Experiment of the first Part of this Book is
+described; I could not perceive any new Colour generated this way. All
+Bodies illuminated with compound Light appear through Prisms confused,
+(as was said above) and tinged with various new Colours, but those
+illuminated with homogeneal Light appeared through Prisms neither less
+distinct, nor otherwise colour'd, than when viewed with the naked Eyes.
+Their Colours were not in the least changed by the Refraction of the
+interposed Prism. I speak here of a sensible Change of Colour: For the
+Light which I here call homogeneal, being not absolutely homogeneal,
+there ought to arise some little Change of Colour from its
+Heterogeneity. But, if that Heterogeneity was so little as it might be
+made by the said Experiments of the fourth Proposition, that Change was
+not sensible, and therefore in Experiments, where Sense is Judge, ought
+to be accounted none at all.
+
+_Exper._ 6. And as these Colours were not changeable by Refractions, so
+neither were they by Reflexions. For all white, grey, red, yellow,
+green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, Indico
+Bise, Gold, Silver, Copper, Grass, blue Flowers, Violets, Bubbles of
+Water tinged with various Colours, Peacock's Feathers, the Tincture of
+_Lignum Nephriticum_, and such-like, in red homogeneal Light appeared
+totally red, in blue Light totally blue, in green Light totally green,
+and so of other Colours. In the homogeneal Light of any Colour they all
+appeared totally of that same Colour, with this only Difference, that
+some of them reflected that Light more strongly, others more faintly. I
+never yet found any Body, which by reflecting homogeneal Light could
+sensibly change its Colour.
+
+From all which it is manifest, that if the Sun's Light consisted of but
+one sort of Rays, there would be but one Colour in the whole World, nor
+would it be possible to produce any new Colour by Reflexions and
+Refractions, and by consequence that the variety of Colours depends upon
+the Composition of Light.
+
+
+_DEFINITION._
+
+The homogeneal Light and Rays which appear red, or rather make Objects
+appear so, I call Rubrifick or Red-making; those which make Objects
+appear yellow, green, blue, and violet, I call Yellow-making,
+Green-making, Blue-making, Violet-making, and so of the rest. And if at
+any time I speak of Light and Rays as coloured or endued with Colours, I
+would be understood to speak not philosophically and properly, but
+grossly, and accordingly to such Conceptions as vulgar People in seeing
+all these Experiments would be apt to frame. For the Rays to speak
+properly are not coloured. In them there is nothing else than a certain
+Power and Disposition to stir up a Sensation of this or that Colour.
+For as Sound in a Bell or musical String, or other sounding Body, is
+nothing but a trembling Motion, and in the Air nothing but that Motion
+propagated from the Object, and in the Sensorium 'tis a Sense of that
+Motion under the Form of Sound; so Colours in the Object are nothing but
+a Disposition to reflect this or that sort of Rays more copiously than
+the rest; in the Rays they are nothing but their Dispositions to
+propagate this or that Motion into the Sensorium, and in the Sensorium
+they are Sensations of those Motions under the Forms of Colours.
+
+
+_PROP._ III. PROB. I.
+
+_To define the Refrangibility of the several sorts of homogeneal Light
+answering to the several Colours._
+
+For determining this Problem I made the following Experiment.[J]
+
+_Exper._ 7. When I had caused the Rectilinear Sides AF, GM, [in _Fig._
+4.] of the Spectrum of Colours made by the Prism to be distinctly
+defined, as in the fifth Experiment of the first Part of this Book is
+described, there were found in it all the homogeneal Colours in the same
+Order and Situation one among another as in the Spectrum of simple
+Light, described in the fourth Proposition of that Part. For the Circles
+of which the Spectrum of compound Light PT is composed, and which in
+the middle Parts of the Spectrum interfere, and are intermix'd with one
+another, are not intermix'd in their outmost Parts where they touch
+those Rectilinear Sides AF and GM. And therefore, in those Rectilinear
+Sides when distinctly defined, there is no new Colour generated by
+Refraction. I observed also, that if any where between the two outmost
+Circles TMF and PGA a Right Line, as [Greek: gd], was cross to the
+Spectrum, so as both Ends to fall perpendicularly upon its Rectilinear
+Sides, there appeared one and the same Colour, and degree of Colour from
+one End of this Line to the other. I delineated therefore in a Paper the
+Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of
+the first Part of this Book, I held the Paper so that the Spectrum might
+fall upon this delineated Figure, and agree with it exactly, whilst an
+Assistant, whose Eyes for distinguishing Colours were more critical than
+mine, did by Right Lines [Greek: ab, gd, ez,] &c. drawn cross the
+Spectrum, note the Confines of the Colours, that is of the red M[Greek:
+ab]F, of the orange [Greek: agdb], of the yellow [Greek: gezd], of the
+green [Greek: eêthz], of the blue [Greek: êikth], of the indico [Greek:
+ilmk], and of the violet [Greek: l]GA[Greek: m]. And this Operation
+being divers times repeated both in the same, and in several Papers, I
+found that the Observations agreed well enough with one another, and
+that the Rectilinear Sides MG and FA were by the said cross Lines
+divided after the manner of a Musical Chord. Let GM be produced to X,
+that MX may be equal to GM, and conceive GX, [Greek: l]X, [Greek: i]X,
+[Greek: ê]X, [Greek: e]X, [Greek: g]X, [Greek: a]X, MX, to be in
+proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5,
+9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a
+third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth
+above that Key: And the Intervals M[Greek: a], [Greek: ag], [Greek: ge],
+[Greek: eê], [Greek: êi], [Greek: il], and [Greek: l]G, will be the
+Spaces which the several Colours (red, orange, yellow, green, blue,
+indigo, violet) take up.
+
+[Illustration: FIG. 4.]
+
+[Illustration: FIG. 5.]
+
+Now these Intervals or Spaces subtending the Differences of the
+Refractions of the Rays going to the Limits of those Colours, that is,
+to the Points M, [Greek: a], [Greek: g], [Greek: e], [Greek: ê], [Greek:
+i], [Greek: l], G, may without any sensible Error be accounted
+proportional to the Differences of the Sines of Refraction of those Rays
+having one common Sine of Incidence, and therefore since the common Sine
+of Incidence of the most and least refrangible Rays out of Glass into
+Air was (by a Method described above) found in proportion to their Sines
+of Refraction, as 50 to 77 and 78, divide the Difference between the
+Sines of Refraction 77 and 78, as the Line GM is divided by those
+Intervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3,
+77-7/9, 78, the Sines of Refraction of those Rays out of Glass into Air,
+their common Sine of Incidence being 50. So then the Sines of the
+Incidences of all the red-making Rays out of Glass into Air, were to the
+Sines of their Refractions, not greater than 50 to 77, nor less than 50
+to 77-1/8, but they varied from one another according to all
+intermediate Proportions. And the Sines of the Incidences of the
+green-making Rays were to the Sines of their Refractions in all
+Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And
+by the like Limits above-mentioned were the Refractions of the Rays
+belonging to the rest of the Colours defined, the Sines of the
+red-making Rays extending from 77 to 77-1/8, those of the orange-making
+from 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3,
+those of the green-making from 77-1/3 to 77-1/2, those of the
+blue-making from 77-1/2 to 77-2/3, those of the indigo-making from
+77-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.
+
+These are the Laws of the Refractions made out of Glass into Air, and
+thence by the third Axiom of the first Part of this Book, the Laws of
+the Refractions made out of Air into Glass are easily derived.
+
+_Exper._ 8. I found moreover, that when Light goes out of Air through
+several contiguous refracting Mediums as through Water and Glass, and
+thence goes out again into Air, whether the refracting Superficies be
+parallel or inclin'd to one another, that Light as often as by contrary
+Refractions 'tis so corrected, that it emergeth in Lines parallel to
+those in which it was incident, continues ever after to be white. But if
+the emergent Rays be inclined to the incident, the Whiteness of the
+emerging Light will by degrees in passing on from the Place of
+Emergence, become tinged in its Edges with Colours. This I try'd by
+refracting Light with Prisms of Glass placed within a Prismatick Vessel
+of Water. Now those Colours argue a diverging and separation of the
+heterogeneous Rays from one another by means of their unequal
+Refractions, as in what follows will more fully appear. And, on the
+contrary, the permanent whiteness argues, that in like Incidences of the
+Rays there is no such separation of the emerging Rays, and by
+consequence no inequality of their whole Refractions. Whence I seem to
+gather the two following Theorems.
+
+1. The Excesses of the Sines of Refraction of several sorts of Rays
+above their common Sine of Incidence when the Refractions are made out
+of divers denser Mediums immediately into one and the same rarer Medium,
+suppose of Air, are to one another in a given Proportion.
+
+2. The Proportion of the Sine of Incidence to the Sine of Refraction of
+one and the same sort of Rays out of one Medium into another, is
+composed of the Proportion of the Sine of Incidence to the Sine of
+Refraction out of the first Medium into any third Medium, and of the
+Proportion of the Sine of Incidence to the Sine of Refraction out of
+that third Medium into the second Medium.
+
+By the first Theorem the Refractions of the Rays of every sort made out
+of any Medium into Air are known by having the Refraction of the Rays of
+any one sort. As for instance, if the Refractions of the Rays of every
+sort out of Rain-water into Air be desired, let the common Sine of
+Incidence out of Glass into Air be subducted from the Sines of
+Refraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2,
+27-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the least
+refrangible Rays be to their Sine of Refraction out of Rain-water into
+Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the
+Sine of Incidence, so is 27 the least of the Excesses above-mentioned to
+a fourth Number 81; and 81 will be the common Sine of Incidence out of
+Rain-water into Air, to which Sine if you add all the above-mentioned
+Excesses, you will have the desired Sines of the Refractions 108,
+108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.
+
+By the latter Theorem the Refraction out of one Medium into another is
+gathered as often as you have the Refractions out of them both into any
+third Medium. As if the Sine of Incidence of any Ray out of Glass into
+Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence
+of the same Ray out of Air into Water, be to its Sine of Refraction as 4
+to 3; the Sine of Incidence of that Ray out of Glass into Water will be
+to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as
+the Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.
+
+And these Theorems being admitted into Opticks, there would be scope
+enough of handling that Science voluminously after a new manner,[K] not
+only by teaching those things which tend to the perfection of Vision,
+but also by determining mathematically all kinds of Phænomena of Colours
+which could be produced by Refractions. For to do this, there is nothing
+else requisite than to find out the Separations of heterogeneous Rays,
+and their various Mixtures and Proportions in every Mixture. By this
+way of arguing I invented almost all the Phænomena described in these
+Books, beside some others less necessary to the Argument; and by the
+successes I met with in the Trials, I dare promise, that to him who
+shall argue truly, and then try all things with good Glasses and
+sufficient Circumspection, the expected Event will not be wanting. But
+he is first to know what Colours will arise from any others mix'd in any
+assigned Proportion.
+
+
+_PROP._ IV. THEOR. III.
+
+_Colours may be produced by Composition which shall be like to the
+Colours of homogeneal Light as to the Appearance of Colour, but not as
+to the Immutability of Colour and Constitution of Light. And those
+Colours by how much they are more compounded by so much are they less
+full and intense, and by too much Composition they maybe diluted and
+weaken'd till they cease, and the Mixture becomes white or grey. There
+may be also Colours produced by Composition, which are not fully like
+any of the Colours of homogeneal Light._
+
+For a Mixture of homogeneal red and yellow compounds an Orange, like in
+appearance of Colour to that orange which in the series of unmixed
+prismatick Colours lies between them; but the Light of one orange is
+homogeneal as to Refrangibility, and that of the other is heterogeneal,
+and the Colour of the one, if viewed through a Prism, remains unchanged,
+that of the other is changed and resolved into its component Colours red
+and yellow. And after the same manner other neighbouring homogeneal
+Colours may compound new Colours, like the intermediate homogeneal ones,
+as yellow and green, the Colour between them both, and afterwards, if
+blue be added, there will be made a green the middle Colour of the three
+which enter the Composition. For the yellow and blue on either hand, if
+they are equal in quantity they draw the intermediate green equally
+towards themselves in Composition, and so keep it as it were in
+Æquilibrion, that it verge not more to the yellow on the one hand, and
+to the blue on the other, but by their mix'd Actions remain still a
+middle Colour. To this mix'd green there may be farther added some red
+and violet, and yet the green will not presently cease, but only grow
+less full and vivid, and by increasing the red and violet, it will grow
+more and more dilute, until by the prevalence of the added Colours it be
+overcome and turned into whiteness, or some other Colour. So if to the
+Colour of any homogeneal Light, the Sun's white Light composed of all
+sorts of Rays be added, that Colour will not vanish or change its
+Species, but be diluted, and by adding more and more white it will be
+diluted more and more perpetually. Lastly, If red and violet be mingled,
+there will be generated according to their various Proportions various
+Purples, such as are not like in appearance to the Colour of any
+homogeneal Light, and of these Purples mix'd with yellow and blue may be
+made other new Colours.
+
+
+_PROP._ V. THEOR. IV.
+
+_Whiteness and all grey Colours between white and black, may be
+compounded of Colours, and the whiteness of the Sun's Light is
+compounded of all the primary Colours mix'd in a due Proportion._
+
+The PROOF by Experiments.
+
+_Exper._ 9. The Sun shining into a dark Chamber through a little round
+hole in the Window-shut, and his Light being there refracted by a Prism
+to cast his coloured Image PT [in _Fig._ 5.] upon the opposite Wall: I
+held a white Paper V to that image in such manner that it might be
+illuminated by the colour'd Light reflected from thence, and yet not
+intercept any part of that Light in its passage from the Prism to the
+Spectrum. And I found that when the Paper was held nearer to any Colour
+than to the rest, it appeared of that Colour to which it approached
+nearest; but when it was equally or almost equally distant from all the
+Colours, so that it might be equally illuminated by them all it appeared
+white. And in this last situation of the Paper, if some Colours were
+intercepted, the Paper lost its white Colour, and appeared of the Colour
+of the rest of the Light which was not intercepted. So then the Paper
+was illuminated with Lights of various Colours, namely, red, yellow,
+green, blue and violet, and every part of the Light retained its proper
+Colour, until it was incident on the Paper, and became reflected thence
+to the Eye; so that if it had been either alone (the rest of the Light
+being intercepted) or if it had abounded most, and been predominant in
+the Light reflected from the Paper, it would have tinged the Paper with
+its own Colour; and yet being mixed with the rest of the Colours in a
+due proportion, it made the Paper look white, and therefore by a
+Composition with the rest produced that Colour. The several parts of the
+coloured Light reflected from the Spectrum, whilst they are propagated
+from thence through the Air, do perpetually retain their proper Colours,
+because wherever they fall upon the Eyes of any Spectator, they make the
+several parts of the Spectrum to appear under their proper Colours. They
+retain therefore their proper Colours when they fall upon the Paper V,
+and so by the confusion and perfect mixture of those Colours compound
+the whiteness of the Light reflected from thence.
+
+_Exper._ 10. Let that Spectrum or solar Image PT [in _Fig._ 6.] fall now
+upon the Lens MN above four Inches broad, and about six Feet distant
+from the Prism ABC and so figured that it may cause the coloured Light
+which divergeth from the Prism to converge and meet again at its Focus
+G, about six or eight Feet distant from the Lens, and there to fall
+perpendicularly upon a white Paper DE. And if you move this Paper to and
+fro, you will perceive that near the Lens, as at _de_, the whole solar
+Image (suppose at _pt_) will appear upon it intensely coloured after the
+manner above-explained, and that by receding from the Lens those Colours
+will perpetually come towards one another, and by mixing more and more
+dilute one another continually, until at length the Paper come to the
+Focus G, where by a perfect mixture they will wholly vanish and be
+converted into whiteness, the whole Light appearing now upon the Paper
+like a little white Circle. And afterwards by receding farther from the
+Lens, the Rays which before converged will now cross one another in the
+Focus G, and diverge from thence, and thereby make the Colours to appear
+again, but yet in a contrary order; suppose at [Greek: de], where the
+red _t_ is now above which before was below, and the violet _p_ is below
+which before was above.
+
+Let us now stop the Paper at the Focus G, where the Light appears
+totally white and circular, and let us consider its whiteness. I say,
+that this is composed of the converging Colours. For if any of those
+Colours be intercepted at the Lens, the whiteness will cease and
+degenerate into that Colour which ariseth from the composition of the
+other Colours which are not intercepted. And then if the intercepted
+Colours be let pass and fall upon that compound Colour, they mix with
+it, and by their mixture restore the whiteness. So if the violet, blue
+and green be intercepted, the remaining yellow, orange and red will
+compound upon the Paper an orange, and then if the intercepted Colours
+be let pass, they will fall upon this compounded orange, and together
+with it decompound a white. So also if the red and violet be
+intercepted, the remaining yellow, green and blue, will compound a green
+upon the Paper, and then the red and violet being let pass will fall
+upon this green, and together with it decompound a white. And that in
+this Composition of white the several Rays do not suffer any Change in
+their colorific Qualities by acting upon one another, but are only
+mixed, and by a mixture of their Colours produce white, may farther
+appear by these Arguments.
+
+[Illustration: FIG. 6.]
+
+If the Paper be placed beyond the Focus G, suppose at [Greek: de], and
+then the red Colour at the Lens be alternately intercepted, and let pass
+again, the violet Colour on the Paper will not suffer any Change
+thereby, as it ought to do if the several sorts of Rays acted upon one
+another in the Focus G, where they cross. Neither will the red upon the
+Paper be changed by any alternate stopping, and letting pass the violet
+which crosseth it.
+
+And if the Paper be placed at the Focus G, and the white round Image at
+G be viewed through the Prism HIK, and by the Refraction of that Prism
+be translated to the place _rv_, and there appear tinged with various
+Colours, namely, the violet at _v_ and red at _r_, and others between,
+and then the red Colours at the Lens be often stopp'd and let pass by
+turns, the red at _r_ will accordingly disappear, and return as often,
+but the violet at _v_ will not thereby suffer any Change. And so by
+stopping and letting pass alternately the blue at the Lens, the blue at
+_v_ will accordingly disappear and return, without any Change made in
+the red at _r_. The red therefore depends on one sort of Rays, and the
+blue on another sort, which in the Focus G where they are commix'd, do
+not act on one another. And there is the same Reason of the other
+Colours.
+
+I considered farther, that when the most refrangible Rays P_p_, and the
+least refrangible ones T_t_, are by converging inclined to one another,
+the Paper, if held very oblique to those Rays in the Focus G, might
+reflect one sort of them more copiously than the other sort, and by that
+Means the reflected Light would be tinged in that Focus with the Colour
+of the predominant Rays, provided those Rays severally retained their
+Colours, or colorific Qualities in the Composition of White made by them
+in that Focus. But if they did not retain them in that White, but became
+all of them severally endued there with a Disposition to strike the
+Sense with the Perception of White, then they could never lose their
+Whiteness by such Reflexions. I inclined therefore the Paper to the Rays
+very obliquely, as in the second Experiment of this second Part of the
+first Book, that the most refrangible Rays, might be more copiously
+reflected than the rest, and the Whiteness at Length changed
+successively into blue, indigo, and violet. Then I inclined it the
+contrary Way, that the least refrangible Rays might be more copious in
+the reflected Light than the rest, and the Whiteness turned successively
+to yellow, orange, and red.
+
+Lastly, I made an Instrument XY in fashion of a Comb, whose Teeth being
+in number sixteen, were about an Inch and a half broad, and the
+Intervals of the Teeth about two Inches wide. Then by interposing
+successively the Teeth of this Instrument near the Lens, I intercepted
+Part of the Colours by the interposed Tooth, whilst the rest of them
+went on through the Interval of the Teeth to the Paper DE, and there
+painted a round Solar Image. But the Paper I had first placed so, that
+the Image might appear white as often as the Comb was taken away; and
+then the Comb being as was said interposed, that Whiteness by reason of
+the intercepted Part of the Colours at the Lens did always change into
+the Colour compounded of those Colours which were not intercepted, and
+that Colour was by the Motion of the Comb perpetually varied so, that in
+the passing of every Tooth over the Lens all these Colours, red, yellow,
+green, blue, and purple, did always succeed one another. I caused
+therefore all the Teeth to pass successively over the Lens, and when the
+Motion was slow, there appeared a perpetual Succession of the Colours
+upon the Paper: But if I so much accelerated the Motion, that the
+Colours by reason of their quick Succession could not be distinguished
+from one another, the Appearance of the single Colours ceased. There was
+no red, no yellow, no green, no blue, nor purple to be seen any longer,
+but from a Confusion of them all there arose one uniform white Colour.
+Of the Light which now by the Mixture of all the Colours appeared white,
+there was no Part really white. One Part was red, another yellow, a
+third green, a fourth blue, a fifth purple, and every Part retains its
+proper Colour till it strike the Sensorium. If the Impressions follow
+one another slowly, so that they may be severally perceived, there is
+made a distinct Sensation of all the Colours one after another in a
+continual Succession. But if the Impressions follow one another so
+quickly, that they cannot be severally perceived, there ariseth out of
+them all one common Sensation, which is neither of this Colour alone nor
+of that alone, but hath it self indifferently to 'em all, and this is a
+Sensation of Whiteness. By the Quickness of the Successions, the
+Impressions of the several Colours are confounded in the Sensorium, and
+out of that Confusion ariseth a mix'd Sensation. If a burning Coal be
+nimbly moved round in a Circle with Gyrations continually repeated, the
+whole Circle will appear like Fire; the reason of which is, that the
+Sensation of the Coal in the several Places of that Circle remains
+impress'd on the Sensorium, until the Coal return again to the same
+Place. And so in a quick Consecution of the Colours the Impression of
+every Colour remains in the Sensorium, until a Revolution of all the
+Colours be compleated, and that first Colour return again. The
+Impressions therefore of all the successive Colours are at once in the
+Sensorium, and jointly stir up a Sensation of them all; and so it is
+manifest by this Experiment, that the commix'd Impressions of all the
+Colours do stir up and beget a Sensation of white, that is, that
+Whiteness is compounded of all the Colours.
+
+And if the Comb be now taken away, that all the Colours may at once pass
+from the Lens to the Paper, and be there intermixed, and together
+reflected thence to the Spectator's Eyes; their Impressions on the
+Sensorium being now more subtilly and perfectly commixed there, ought
+much more to stir up a Sensation of Whiteness.
+
+You may instead of the Lens use two Prisms HIK and LMN, which by
+refracting the coloured Light the contrary Way to that of the first
+Refraction, may make the diverging Rays converge and meet again in G, as
+you see represented in the seventh Figure. For where they meet and mix,
+they will compose a white Light, as when a Lens is used.
+
+_Exper._ 11. Let the Sun's coloured Image PT [in _Fig._ 8.] fall upon
+the Wall of a dark Chamber, as in the third Experiment of the first
+Book, and let the same be viewed through a Prism _abc_, held parallel to
+the Prism ABC, by whose Refraction that Image was made, and let it now
+appear lower than before, suppose in the Place S over-against the red
+Colour T. And if you go near to the Image PT, the Spectrum S will appear
+oblong and coloured like the Image PT; but if you recede from it, the
+Colours of the spectrum S will be contracted more and more, and at
+length vanish, that Spectrum S becoming perfectly round and white; and
+if you recede yet farther, the Colours will emerge again, but in a
+contrary Order. Now that Spectrum S appears white in that Case, when the
+Rays of several sorts which converge from the several Parts of the Image
+PT, to the Prism _abc_, are so refracted unequally by it, that in their
+Passage from the Prism to the Eye they may diverge from one and the same
+Point of the Spectrum S, and so fall afterwards upon one and the same
+Point in the bottom of the Eye, and there be mingled.
+
+[Illustration: FIG. 7.]
+
+[Illustration: FIG. 8.]
+
+And farther, if the Comb be here made use of, by whose Teeth the Colours
+at the Image PT may be successively intercepted; the Spectrum S, when
+the Comb is moved slowly, will be perpetually tinged with successive
+Colours: But when by accelerating the Motion of the Comb, the Succession
+of the Colours is so quick that they cannot be severally seen, that
+Spectrum S, by a confused and mix'd Sensation of them all, will appear
+white.
+
+_Exper._ 12. The Sun shining through a large Prism ABC [in _Fig._ 9.]
+upon a Comb XY, placed immediately behind the Prism, his Light which
+passed through the Interstices of the Teeth fell upon a white Paper DE.
+The Breadths of the Teeth were equal to their Interstices, and seven
+Teeth together with their Interstices took up an Inch in Breadth. Now,
+when the Paper was about two or three Inches distant from the Comb, the
+Light which passed through its several Interstices painted so many
+Ranges of Colours, _kl_, _mn_, _op_, _qr_, &c. which were parallel to
+one another, and contiguous, and without any Mixture of white. And these
+Ranges of Colours, if the Comb was moved continually up and down with a
+reciprocal Motion, ascended and descended in the Paper, and when the
+Motion of the Comb was so quick, that the Colours could not be
+distinguished from one another, the whole Paper by their Confusion and
+Mixture in the Sensorium appeared white.
+
+[Illustration: FIG. 9.]
+
+Let the Comb now rest, and let the Paper be removed farther from the
+Prism, and the several Ranges of Colours will be dilated and expanded
+into one another more and more, and by mixing their Colours will dilute
+one another, and at length, when the distance of the Paper from the Comb
+is about a Foot, or a little more (suppose in the Place 2D 2E) they will
+so far dilute one another, as to become white.
+
+With any Obstacle, let all the Light be now stopp'd which passes through
+any one Interval of the Teeth, so that the Range of Colours which comes
+from thence may be taken away, and you will see the Light of the rest of
+the Ranges to be expanded into the Place of the Range taken away, and
+there to be coloured. Let the intercepted Range pass on as before, and
+its Colours falling upon the Colours of the other Ranges, and mixing
+with them, will restore the Whiteness.
+
+Let the Paper 2D 2E be now very much inclined to the Rays, so that the
+most refrangible Rays may be more copiously reflected than the rest, and
+the white Colour of the Paper through the Excess of those Rays will be
+changed into blue and violet. Let the Paper be as much inclined the
+contrary way, that the least refrangible Rays may be now more copiously
+reflected than the rest, and by their Excess the Whiteness will be
+changed into yellow and red. The several Rays therefore in that white
+Light do retain their colorific Qualities, by which those of any sort,
+whenever they become more copious than the rest, do by their Excess and
+Predominance cause their proper Colour to appear.
+
+And by the same way of arguing, applied to the third Experiment of this
+second Part of the first Book, it may be concluded, that the white
+Colour of all refracted Light at its very first Emergence, where it
+appears as white as before its Incidence, is compounded of various
+Colours.
+
+[Illustration: FIG. 10.]
+
+_Exper._ 13. In the foregoing Experiment the several Intervals of the
+Teeth of the Comb do the Office of so many Prisms, every Interval
+producing the Phænomenon of one Prism. Whence instead of those Intervals
+using several Prisms, I try'd to compound Whiteness by mixing their
+Colours, and did it by using only three Prisms, as also by using only
+two as follows. Let two Prisms ABC and _abc_, [in _Fig._ 10.] whose
+refracting Angles B and _b_ are equal, be so placed parallel to one
+another, that the refracting Angle B of the one may touch the Angle _c_
+at the Base of the other, and their Planes CB and _cb_, at which the
+Rays emerge, may lie in Directum. Then let the Light trajected through
+them fall upon the Paper MN, distant about 8 or 12 Inches from the
+Prisms. And the Colours generated by the interior Limits B and _c_ of
+the two Prisms, will be mingled at PT, and there compound white. For if
+either Prism be taken away, the Colours made by the other will appear in
+that Place PT, and when the Prism is restored to its Place again, so
+that its Colours may there fall upon the Colours of the other, the
+Mixture of them both will restore the Whiteness.
+
+This Experiment succeeds also, as I have tried, when the Angle _b_ of
+the lower Prism, is a little greater than the Angle B of the upper, and
+between the interior Angles B and _c_, there intercedes some Space B_c_,
+as is represented in the Figure, and the refracting Planes BC and _bc_,
+are neither in Directum, nor parallel to one another. For there is
+nothing more requisite to the Success of this Experiment, than that the
+Rays of all sorts may be uniformly mixed upon the Paper in the Place PT.
+If the most refrangible Rays coming from the superior Prism take up all
+the Space from M to P, the Rays of the same sort which come from the
+inferior Prism ought to begin at P, and take up all the rest of the
+Space from thence towards N. If the least refrangible Rays coming from
+the superior Prism take up the Space MT, the Rays of the same kind which
+come from the other Prism ought to begin at T, and take up the
+remaining Space TN. If one sort of the Rays which have intermediate
+Degrees of Refrangibility, and come from the superior Prism be extended
+through the Space MQ, and another sort of those Rays through the Space
+MR, and a third sort of them through the Space MS, the same sorts of
+Rays coming from the lower Prism, ought to illuminate the remaining
+Spaces QN, RN, SN, respectively. And the same is to be understood of all
+the other sorts of Rays. For thus the Rays of every sort will be
+scattered uniformly and evenly through the whole Space MN, and so being
+every where mix'd in the same Proportion, they must every where produce
+the same Colour. And therefore, since by this Mixture they produce white
+in the Exterior Spaces MP and TN, they must also produce white in the
+Interior Space PT. This is the reason of the Composition by which
+Whiteness was produced in this Experiment, and by what other way soever
+I made the like Composition, the Result was Whiteness.
+
+Lastly, If with the Teeth of a Comb of a due Size, the coloured Lights
+of the two Prisms which fall upon the Space PT be alternately
+intercepted, that Space PT, when the Motion of the Comb is slow, will
+always appear coloured, but by accelerating the Motion of the Comb so
+much that the successive Colours cannot be distinguished from one
+another, it will appear white.
+
+_Exper._ 14. Hitherto I have produced Whiteness by mixing the Colours of
+Prisms. If now the Colours of natural Bodies are to be mingled, let
+Water a little thicken'd with Soap be agitated to raise a Froth, and
+after that Froth has stood a little, there will appear to one that shall
+view it intently various Colours every where in the Surfaces of the
+several Bubbles; but to one that shall go so far off, that he cannot
+distinguish the Colours from one another, the whole Froth will grow
+white with a perfect Whiteness.
+
+_Exper._ 15. Lastly, In attempting to compound a white, by mixing the
+coloured Powders which Painters use, I consider'd that all colour'd
+Powders do suppress and stop in them a very considerable Part of the
+Light by which they are illuminated. For they become colour'd by
+reflecting the Light of their own Colours more copiously, and that of
+all other Colours more sparingly, and yet they do not reflect the Light
+of their own Colours so copiously as white Bodies do. If red Lead, for
+instance, and a white Paper, be placed in the red Light of the colour'd
+Spectrum made in a dark Chamber by the Refraction of a Prism, as is
+described in the third Experiment of the first Part of this Book; the
+Paper will appear more lucid than the red Lead, and therefore reflects
+the red-making Rays more copiously than red Lead doth. And if they be
+held in the Light of any other Colour, the Light reflected by the Paper
+will exceed the Light reflected by the red Lead in a much greater
+Proportion. And the like happens in Powders of other Colours. And
+therefore by mixing such Powders, we are not to expect a strong and
+full White, such as is that of Paper, but some dusky obscure one, such
+as might arise from a Mixture of Light and Darkness, or from white and
+black, that is, a grey, or dun, or russet brown, such as are the Colours
+of a Man's Nail, of a Mouse, of Ashes, of ordinary Stones, of Mortar, of
+Dust and Dirt in High-ways, and the like. And such a dark white I have
+often produced by mixing colour'd Powders. For thus one Part of red
+Lead, and five Parts of _Viride Æris_, composed a dun Colour like that
+of a Mouse. For these two Colours were severally so compounded of
+others, that in both together were a Mixture of all Colours; and there
+was less red Lead used than _Viride Æris_, because of the Fulness of its
+Colour. Again, one Part of red Lead, and four Parts of blue Bise,
+composed a dun Colour verging a little to purple, and by adding to this
+a certain Mixture of Orpiment and _Viride Æris_ in a due Proportion, the
+Mixture lost its purple Tincture, and became perfectly dun. But the
+Experiment succeeded best without Minium thus. To Orpiment I added by
+little and little a certain full bright purple, which Painters use,
+until the Orpiment ceased to be yellow, and became of a pale red. Then I
+diluted that red by adding a little _Viride Æris_, and a little more
+blue Bise than _Viride Æris_, until it became of such a grey or pale
+white, as verged to no one of the Colours more than to another. For thus
+it became of a Colour equal in Whiteness to that of Ashes, or of Wood
+newly cut, or of a Man's Skin. The Orpiment reflected more Light than
+did any other of the Powders, and therefore conduced more to the
+Whiteness of the compounded Colour than they. To assign the Proportions
+accurately may be difficult, by reason of the different Goodness of
+Powders of the same kind. Accordingly, as the Colour of any Powder is
+more or less full and luminous, it ought to be used in a less or greater
+Proportion.
+
+Now, considering that these grey and dun Colours may be also produced by
+mixing Whites and Blacks, and by consequence differ from perfect Whites,
+not in Species of Colours, but only in degree of Luminousness, it is
+manifest that there is nothing more requisite to make them perfectly
+white than to increase their Light sufficiently; and, on the contrary,
+if by increasing their Light they can be brought to perfect Whiteness,
+it will thence also follow, that they are of the same Species of Colour
+with the best Whites, and differ from them only in the Quantity of
+Light. And this I tried as follows. I took the third of the
+above-mention'd grey Mixtures, (that which was compounded of Orpiment,
+Purple, Bise, and _Viride Æris_) and rubbed it thickly upon the Floor of
+my Chamber, where the Sun shone upon it through the opened Casement; and
+by it, in the shadow, I laid a Piece of white Paper of the same Bigness.
+Then going from them to the distance of 12 or 18 Feet, so that I could
+not discern the Unevenness of the Surface of the Powder, nor the little
+Shadows let fall from the gritty Particles thereof; the Powder appeared
+intensely white, so as to transcend even the Paper it self in Whiteness,
+especially if the Paper were a little shaded from the Light of the
+Clouds, and then the Paper compared with the Powder appeared of such a
+grey Colour as the Powder had done before. But by laying the Paper where
+the Sun shines through the Glass of the Window, or by shutting the
+Window that the Sun might shine through the Glass upon the Powder, and
+by such other fit Means of increasing or decreasing the Lights wherewith
+the Powder and Paper were illuminated, the Light wherewith the Powder is
+illuminated may be made stronger in such a due Proportion than the Light
+wherewith the Paper is illuminated, that they shall both appear exactly
+alike in Whiteness. For when I was trying this, a Friend coming to visit
+me, I stopp'd him at the Door, and before I told him what the Colours
+were, or what I was doing; I asked him, Which of the two Whites were the
+best, and wherein they differed? And after he had at that distance
+viewed them well, he answer'd, that they were both good Whites, and that
+he could not say which was best, nor wherein their Colours differed.
+Now, if you consider, that this White of the Powder in the Sun-shine was
+compounded of the Colours which the component Powders (Orpiment, Purple,
+Bise, and _Viride Æris_) have in the same Sun-shine, you must
+acknowledge by this Experiment, as well as by the former, that perfect
+Whiteness may be compounded of Colours.
+
+From what has been said it is also evident, that the Whiteness of the
+Sun's Light is compounded of all the Colours wherewith the several sorts
+of Rays whereof that Light consists, when by their several
+Refrangibilities they are separated from one another, do tinge Paper or
+any other white Body whereon they fall. For those Colours (by _Prop._
+II. _Part_ 2.) are unchangeable, and whenever all those Rays with those
+their Colours are mix'd again, they reproduce the same white Light as
+before.
+
+
+_PROP._ VI. PROB. II.
+
+_In a mixture of Primary Colours, the Quantity and Quality of each being
+given, to know the Colour of the Compound._
+
+[Illustration: FIG. 11.]
+
+With the Center O [in _Fig._ 11.] and Radius OD describe a Circle ADF,
+and distinguish its Circumference into seven Parts DE, EF, FG, GA, AB,
+BC, CD, proportional to the seven Musical Tones or Intervals of the
+eight Sounds, _Sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_, _sol_,
+contained in an eight, that is, proportional to the Number 1/9, 1/16,
+1/10, 1/9, 1/16, 1/16, 1/9. Let the first Part DE represent a red
+Colour, the second EF orange, the third FG yellow, the fourth CA green,
+the fifth AB blue, the sixth BC indigo, and the seventh CD violet. And
+conceive that these are all the Colours of uncompounded Light gradually
+passing into one another, as they do when made by Prisms; the
+Circumference DEFGABCD, representing the whole Series of Colours from
+one end of the Sun's colour'd Image to the other, so that from D to E be
+all degrees of red, at E the mean Colour between red and orange, from E
+to F all degrees of orange, at F the mean between orange and yellow,
+from F to G all degrees of yellow, and so on. Let _p_ be the Center of
+Gravity of the Arch DE, and _q_, _r_, _s_, _t_, _u_, _x_, the Centers of
+Gravity of the Arches EF, FG, GA, AB, BC, and CD respectively, and about
+those Centers of Gravity let Circles proportional to the Number of Rays
+of each Colour in the given Mixture be describ'd: that is, the Circle
+_p_ proportional to the Number of the red-making Rays in the Mixture,
+the Circle _q_ proportional to the Number of the orange-making Rays in
+the Mixture, and so of the rest. Find the common Center of Gravity of
+all those Circles, _p_, _q_, _r_, _s_, _t_, _u_, _x_. Let that Center be
+Z; and from the Center of the Circle ADF, through Z to the
+Circumference, drawing the Right Line OY, the Place of the Point Y in
+the Circumference shall shew the Colour arising from the Composition of
+all the Colours in the given Mixture, and the Line OZ shall be
+proportional to the Fulness or Intenseness of the Colour, that is, to
+its distance from Whiteness. As if Y fall in the middle between F and G,
+the compounded Colour shall be the best yellow; if Y verge from the
+middle towards F or G, the compound Colour shall accordingly be a
+yellow, verging towards orange or green. If Z fall upon the
+Circumference, the Colour shall be intense and florid in the highest
+Degree; if it fall in the mid-way between the Circumference and Center,
+it shall be but half so intense, that is, it shall be such a Colour as
+would be made by diluting the intensest yellow with an equal quantity of
+whiteness; and if it fall upon the center O, the Colour shall have lost
+all its intenseness, and become a white. But it is to be noted, That if
+the point Z fall in or near the line OD, the main ingredients being the
+red and violet, the Colour compounded shall not be any of the prismatick
+Colours, but a purple, inclining to red or violet, accordingly as the
+point Z lieth on the side of the line DO towards E or towards C, and in
+general the compounded violet is more bright and more fiery than the
+uncompounded. Also if only two of the primary Colours which in the
+circle are opposite to one another be mixed in an equal proportion, the
+point Z shall fall upon the center O, and yet the Colour compounded of
+those two shall not be perfectly white, but some faint anonymous Colour.
+For I could never yet by mixing only two primary Colours produce a
+perfect white. Whether it may be compounded of a mixture of three taken
+at equal distances in the circumference I do not know, but of four or
+five I do not much question but it may. But these are Curiosities of
+little or no moment to the understanding the Phænomena of Nature. For in
+all whites produced by Nature, there uses to be a mixture of all sorts
+of Rays, and by consequence a composition of all Colours.
+
+To give an instance of this Rule; suppose a Colour is compounded of
+these homogeneal Colours, of violet one part, of indigo one part, of
+blue two parts, of green three parts, of yellow five parts, of orange
+six parts, and of red ten parts. Proportional to these parts describe
+the Circles _x_, _v_, _t_, _s_, _r_, _q_, _p_, respectively, that is, so
+that if the Circle _x_ be one, the Circle _v_ may be one, the Circle _t_
+two, the Circle _s_ three, and the Circles _r_, _q_ and _p_, five, six
+and ten. Then I find Z the common center of gravity of these Circles,
+and through Z drawing the Line OY, the Point Y falls upon the
+circumference between E and F, something nearer to E than to F, and
+thence I conclude, that the Colour compounded of these Ingredients will
+be an orange, verging a little more to red than to yellow. Also I find
+that OZ is a little less than one half of OY, and thence I conclude,
+that this orange hath a little less than half the fulness or intenseness
+of an uncompounded orange; that is to say, that it is such an orange as
+may be made by mixing an homogeneal orange with a good white in the
+proportion of the Line OZ to the Line ZY, this Proportion being not of
+the quantities of mixed orange and white Powders, but of the quantities
+of the Lights reflected from them.
+
+This Rule I conceive accurate enough for practice, though not
+mathematically accurate; and the truth of it may be sufficiently proved
+to Sense, by stopping any of the Colours at the Lens in the tenth
+Experiment of this Book. For the rest of the Colours which are not
+stopp'd, but pass on to the Focus of the Lens, will there compound
+either accurately or very nearly such a Colour, as by this Rule ought to
+result from their Mixture.
+
+
+_PROP._ VII. THEOR. V.
+
+_All the Colours in the Universe which are made by Light, and depend not
+on the Power of Imagination, are either the Colours of homogeneal
+Lights, or compounded of these, and that either accurately or very
+nearly, according to the Rule of the foregoing Problem._
+
+For it has been proved (in _Prop. 1. Part 2._) that the changes of
+Colours made by Refractions do not arise from any new Modifications of
+the Rays impress'd by those Refractions, and by the various Terminations
+of Light and Shadow, as has been the constant and general Opinion of
+Philosophers. It has also been proved that the several Colours of the
+homogeneal Rays do constantly answer to their degrees of Refrangibility,
+(_Prop._ 1. _Part_ 1. and _Prop._ 2. _Part_ 2.) and that their degrees
+of Refrangibility cannot be changed by Refractions and Reflexions
+(_Prop._ 2. _Part_ 1.) and by consequence that those their Colours are
+likewise immutable. It has also been proved directly by refracting and
+reflecting homogeneal Lights apart, that their Colours cannot be
+changed, (_Prop._ 2. _Part_ 2.) It has been proved also, that when the
+several sorts of Rays are mixed, and in crossing pass through the same
+space, they do not act on one another so as to change each others
+colorific qualities. (_Exper._ 10. _Part_ 2.) but by mixing their
+Actions in the Sensorium beget a Sensation differing from what either
+would do apart, that is a Sensation of a mean Colour between their
+proper Colours; and particularly when by the concourse and mixtures of
+all sorts of Rays, a white Colour is produced, the white is a mixture of
+all the Colours which the Rays would have apart, (_Prop._ 5. _Part_ 2.)
+The Rays in that mixture do not lose or alter their several colorific
+qualities, but by all their various kinds of Actions mix'd in the
+Sensorium, beget a Sensation of a middling Colour between all their
+Colours, which is whiteness. For whiteness is a mean between all
+Colours, having it self indifferently to them all, so as with equal
+facility to be tinged with any of them. A red Powder mixed with a little
+blue, or a blue with a little red, doth not presently lose its Colour,
+but a white Powder mix'd with any Colour is presently tinged with that
+Colour, and is equally capable of being tinged with any Colour whatever.
+It has been shewed also, that as the Sun's Light is mix'd of all sorts
+of Rays, so its whiteness is a mixture of the Colours of all sorts of
+Rays; those Rays having from the beginning their several colorific
+qualities as well as their several Refrangibilities, and retaining them
+perpetually unchanged notwithstanding any Refractions or Reflexions they
+may at any time suffer, and that whenever any sort of the Sun's Rays is
+by any means (as by Reflexion in _Exper._ 9, and 10. _Part_ 1. or by
+Refraction as happens in all Refractions) separated from the rest, they
+then manifest their proper Colours. These things have been prov'd, and
+the sum of all this amounts to the Proposition here to be proved. For if
+the Sun's Light is mix'd of several sorts of Rays, each of which have
+originally their several Refrangibilities and colorific Qualities, and
+notwithstanding their Refractions and Reflexions, and their various
+Separations or Mixtures, keep those their original Properties
+perpetually the same without alteration; then all the Colours in the
+World must be such as constantly ought to arise from the original
+colorific qualities of the Rays whereof the Lights consist by which
+those Colours are seen. And therefore if the reason of any Colour
+whatever be required, we have nothing else to do than to consider how
+the Rays in the Sun's Light have by Reflexions or Refractions, or other
+causes, been parted from one another, or mixed together; or otherwise to
+find out what sorts of Rays are in the Light by which that Colour is
+made, and in what Proportion; and then by the last Problem to learn the
+Colour which ought to arise by mixing those Rays (or their Colours) in
+that proportion. I speak here of Colours so far as they arise from
+Light. For they appear sometimes by other Causes, as when by the power
+of Phantasy we see Colours in a Dream, or a Mad-man sees things before
+him which are not there; or when we see Fire by striking the Eye, or see
+Colours like the Eye of a Peacock's Feather, by pressing our Eyes in
+either corner whilst we look the other way. Where these and such like
+Causes interpose not, the Colour always answers to the sort or sorts of
+the Rays whereof the Light consists, as I have constantly found in
+whatever Phænomena of Colours I have hitherto been able to examine. I
+shall in the following Propositions give instances of this in the
+Phænomena of chiefest note.
+
+
+_PROP._ VIII. PROB. III.
+
+_By the discovered Properties of Light to explain the Colours made by
+Prisms._
+
+Let ABC [in _Fig._ 12.] represent a Prism refracting the Light of the
+Sun, which comes into a dark Chamber through a hole F[Greek: ph] almost
+as broad as the Prism, and let MN represent a white Paper on which the
+refracted Light is cast, and suppose the most refrangible or deepest
+violet-making Rays fall upon the Space P[Greek: p], the least
+refrangible or deepest red-making Rays upon the Space T[Greek: t], the
+middle sort between the indigo-making and blue-making Rays upon the
+Space Q[Greek: ch], the middle sort of the green-making Rays upon the
+Space R, the middle sort between the yellow-making and orange-making
+Rays upon the Space S[Greek: s], and other intermediate sorts upon
+intermediate Spaces. For so the Spaces upon which the several sorts
+adequately fall will by reason of the different Refrangibility of those
+sorts be one lower than another. Now if the Paper MN be so near the
+Prism that the Spaces PT and [Greek: pt] do not interfere with one
+another, the distance between them T[Greek: p] will be illuminated by
+all the sorts of Rays in that proportion to one another which they have
+at their very first coming out of the Prism, and consequently be white.
+But the Spaces PT and [Greek: pt] on either hand, will not be
+illuminated by them all, and therefore will appear coloured. And
+particularly at P, where the outmost violet-making Rays fall alone, the
+Colour must be the deepest violet. At Q where the violet-making and
+indigo-making Rays are mixed, it must be a violet inclining much to
+indigo. At R where the violet-making, indigo-making, blue-making, and
+one half of the green-making Rays are mixed, their Colours must (by the
+construction of the second Problem) compound a middle Colour between
+indigo and blue. At S where all the Rays are mixed, except the
+red-making and orange-making, their Colours ought by the same Rule to
+compound a faint blue, verging more to green than indigo. And in the
+progress from S to T, this blue will grow more and more faint and
+dilute, till at T, where all the Colours begin to be mixed, it ends in
+whiteness.
+
+[Illustration: FIG. 12.]
+
+So again, on the other side of the white at [Greek: t], where the least
+refrangible or utmost red-making Rays are alone, the Colour must be the
+deepest red. At [Greek: s] the mixture of red and orange will compound a
+red inclining to orange. At [Greek: r] the mixture of red, orange,
+yellow, and one half of the green must compound a middle Colour between
+orange and yellow. At [Greek: ch] the mixture of all Colours but violet
+and indigo will compound a faint yellow, verging more to green than to
+orange. And this yellow will grow more faint and dilute continually in
+its progress from [Greek: ch] to [Greek: p], where by a mixture of all
+sorts of Rays it will become white.
+
+These Colours ought to appear were the Sun's Light perfectly white: But
+because it inclines to yellow, the Excess of the yellow-making Rays
+whereby 'tis tinged with that Colour, being mixed with the faint blue
+between S and T, will draw it to a faint green. And so the Colours in
+order from P to [Greek: t] ought to be violet, indigo, blue, very faint
+green, white, faint yellow, orange, red. Thus it is by the computation:
+And they that please to view the Colours made by a Prism will find it so
+in Nature.
+
+These are the Colours on both sides the white when the Paper is held
+between the Prism and the Point X where the Colours meet, and the
+interjacent white vanishes. For if the Paper be held still farther off
+from the Prism, the most refrangible and least refrangible Rays will be
+wanting in the middle of the Light, and the rest of the Rays which are
+found there, will by mixture produce a fuller green than before. Also
+the yellow and blue will now become less compounded, and by consequence
+more intense than before. And this also agrees with experience.
+
+And if one look through a Prism upon a white Object encompassed with
+blackness or darkness, the reason of the Colours arising on the edges is
+much the same, as will appear to one that shall a little consider it. If
+a black Object be encompassed with a white one, the Colours which appear
+through the Prism are to be derived from the Light of the white one,
+spreading into the Regions of the black, and therefore they appear in a
+contrary order to that, when a white Object is surrounded with black.
+And the same is to be understood when an Object is viewed, whose parts
+are some of them less luminous than others. For in the borders of the
+more and less luminous Parts, Colours ought always by the same
+Principles to arise from the Excess of the Light of the more luminous,
+and to be of the same kind as if the darker parts were black, but yet to
+be more faint and dilute.
+
+What is said of Colours made by Prisms may be easily applied to Colours
+made by the Glasses of Telescopes or Microscopes, or by the Humours of
+the Eye. For if the Object-glass of a Telescope be thicker on one side
+than on the other, or if one half of the Glass, or one half of the Pupil
+of the Eye be cover'd with any opake substance; the Object-glass, or
+that part of it or of the Eye which is not cover'd, may be consider'd as
+a Wedge with crooked Sides, and every Wedge of Glass or other pellucid
+Substance has the effect of a Prism in refracting the Light which passes
+through it.[L]
+
+How the Colours in the ninth and tenth Experiments of the first Part
+arise from the different Reflexibility of Light, is evident by what was
+there said. But it is observable in the ninth Experiment, that whilst
+the Sun's direct Light is yellow, the Excess of the blue-making Rays in
+the reflected beam of Light MN, suffices only to bring that yellow to a
+pale white inclining to blue, and not to tinge it with a manifestly blue
+Colour. To obtain therefore a better blue, I used instead of the yellow
+Light of the Sun the white Light of the Clouds, by varying a little the
+Experiment, as follows.
+
+[Illustration: FIG. 13.]
+
+_Exper._ 16 Let HFG [in _Fig._ 13.] represent a Prism in the open Air,
+and S the Eye of the Spectator, viewing the Clouds by their Light coming
+into the Prism at the Plane Side FIGK, and reflected in it by its Base
+HEIG, and thence going out through its Plane Side HEFK to the Eye. And
+when the Prism and Eye are conveniently placed, so that the Angles of
+Incidence and Reflexion at the Base may be about 40 Degrees, the
+Spectator will see a Bow MN of a blue Colour, running from one End of
+the Base to the other, with the Concave Side towards him, and the Part
+of the Base IMNG beyond this Bow will be brighter than the other Part
+EMNH on the other Side of it. This blue Colour MN being made by nothing
+else than by Reflexion of a specular Superficies, seems so odd a
+Phænomenon, and so difficult to be explained by the vulgar Hypothesis of
+Philosophers, that I could not but think it deserved to be taken Notice
+of. Now for understanding the Reason of it, suppose the Plane ABC to cut
+the Plane Sides and Base of the Prism perpendicularly. From the Eye to
+the Line BC, wherein that Plane cuts the Base, draw the Lines S_p_ and
+S_t_, in the Angles S_pc_ 50 degr. 1/9, and S_tc_ 49 degr. 1/28, and the
+Point _p_ will be the Limit beyond which none of the most refrangible
+Rays can pass through the Base of the Prism, and be refracted, whose
+Incidence is such that they may be reflected to the Eye; and the Point
+_t_ will be the like Limit for the least refrangible Rays, that is,
+beyond which none of them can pass through the Base, whose Incidence is
+such that by Reflexion they may come to the Eye. And the Point _r_ taken
+in the middle Way between _p_ and _t_, will be the like Limit for the
+meanly refrangible Rays. And therefore all the least refrangible Rays
+which fall upon the Base beyond _t_, that is, between _t_ and B, and can
+come from thence to the Eye, will be reflected thither: But on this side
+_t_, that is, between _t_ and _c_, many of these Rays will be
+transmitted through the Base. And all the most refrangible Rays which
+fall upon the Base beyond _p_, that is, between, _p_ and B, and can by
+Reflexion come from thence to the Eye, will be reflected thither, but
+every where between _p_ and _c_, many of these Rays will get through the
+Base, and be refracted; and the same is to be understood of the meanly
+refrangible Rays on either side of the Point _r_. Whence it follows,
+that the Base of the Prism must every where between _t_ and B, by a
+total Reflexion of all sorts of Rays to the Eye, look white and bright.
+And every where between _p_ and C, by reason of the Transmission of many
+Rays of every sort, look more pale, obscure, and dark. But at _r_, and
+in other Places between _p_ and _t_, where all the more refrangible Rays
+are reflected to the Eye, and many of the less refrangible are
+transmitted, the Excess of the most refrangible in the reflected Light
+will tinge that Light with their Colour, which is violet and blue. And
+this happens by taking the Line C _prt_ B any where between the Ends of
+the Prism HG and EI.
+
+
+_PROP._ IX. PROB. IV.
+
+_By the discovered Properties of Light to explain the Colours of the
+Rain-bow._
+
+[Illustration: FIG. 14.]
+
+This Bow never appears, but where it rains in the Sun-shine, and may be
+made artificially by spouting up Water which may break aloft, and
+scatter into Drops, and fall down like Rain. For the Sun shining upon
+these Drops certainly causes the Bow to appear to a Spectator standing
+in a due Position to the Rain and Sun. And hence it is now agreed upon,
+that this Bow is made by Refraction of the Sun's Light in drops of
+falling Rain. This was understood by some of the Antients, and of late
+more fully discover'd and explain'd by the famous _Antonius de Dominis_
+Archbishop of _Spalato_, in his book _De Radiis Visûs & Lucis_,
+published by his Friend _Bartolus_ at _Venice_, in the Year 1611, and
+written above 20 Years before. For he teaches there how the interior Bow
+is made in round Drops of Rain by two Refractions of the Sun's Light,
+and one Reflexion between them, and the exterior by two Refractions, and
+two sorts of Reflexions between them in each Drop of Water, and proves
+his Explications by Experiments made with a Phial full of Water, and
+with Globes of Glass filled with Water, and placed in the Sun to make
+the Colours of the two Bows appear in them. The same Explication
+_Des-Cartes_ hath pursued in his Meteors, and mended that of the
+exterior Bow. But whilst they understood not the true Origin of Colours,
+it's necessary to pursue it here a little farther. For understanding
+therefore how the Bow is made, let a Drop of Rain, or any other
+spherical transparent Body be represented by the Sphere BNFG, [in _Fig._
+14.] described with the Center C, and Semi-diameter CN. And let AN be
+one of the Sun's Rays incident upon it at N, and thence refracted to F,
+where let it either go out of the Sphere by Refraction towards V, or be
+reflected to G; and at G let it either go out by Refraction to R, or be
+reflected to H; and at H let it go out by Refraction towards S, cutting
+the incident Ray in Y. Produce AN and RG, till they meet in X, and upon
+AX and NF, let fall the Perpendiculars CD and CE, and produce CD till it
+fall upon the Circumference at L. Parallel to the incident Ray AN draw
+the Diameter BQ, and let the Sine of Incidence out of Air into Water be
+to the Sine of Refraction as I to R. Now, if you suppose the Point of
+Incidence N to move from the Point B, continually till it come to L, the
+Arch QF will first increase and then decrease, and so will the Angle AXR
+which the Rays AN and GR contain; and the Arch QF and Angle AXR will be
+biggest when ND is to CN as sqrt(II - RR) to sqrt(3)RR, in which
+case NE will be to ND as 2R to I. Also the Angle AYS, which the Rays AN
+and HS contain will first decrease, and then increase and grow least
+when ND is to CN as sqrt(II - RR) to sqrt(8)RR, in which case NE
+will be to ND, as 3R to I. And so the Angle which the next emergent Ray
+(that is, the emergent Ray after three Reflexions) contains with the
+incident Ray AN will come to its Limit when ND is to CN as sqrt(II -
+RR) to sqrt(15)RR, in which case NE will be to ND as 4R to I. And the
+Angle which the Ray next after that Emergent, that is, the Ray emergent
+after four Reflexions, contains with the Incident, will come to its
+Limit, when ND is to CN as sqrt(II - RR) to sqrt(24)RR, in which
+case NE will be to ND as 5R to I; and so on infinitely, the Numbers 3,
+8, 15, 24, &c. being gather'd by continual Addition of the Terms of the
+arithmetical Progression 3, 5, 7, 9, &c. The Truth of all this
+Mathematicians will easily examine.[M]
+
+Now it is to be observed, that as when the Sun comes to his Tropicks,
+Days increase and decrease but a very little for a great while together;
+so when by increasing the distance CD, these Angles come to their
+Limits, they vary their quantity but very little for some time together,
+and therefore a far greater number of the Rays which fall upon all the
+Points N in the Quadrant BL, shall emerge in the Limits of these Angles,
+than in any other Inclinations. And farther it is to be observed, that
+the Rays which differ in Refrangibility will have different Limits of
+their Angles of Emergence, and by consequence according to their
+different Degrees of Refrangibility emerge most copiously in different
+Angles, and being separated from one another appear each in their proper
+Colours. And what those Angles are may be easily gather'd from the
+foregoing Theorem by Computation.
+
+For in the least refrangible Rays the Sines I and R (as was found above)
+are 108 and 81, and thence by Computation the greatest Angle AXR will be
+found 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and
+57 Minutes. And in the most refrangible Rays the Sines I and R are 109
+and 81, and thence by Computation the greatest Angle AXR will be found
+40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7
+Minutes.
+
+Suppose now that O [in _Fig._ 15.] is the Spectator's Eye, and OP a Line
+drawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Angles
+of 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min.
+respectively, and these Angles turned about their common Side OP, shall
+with their other Sides OE, OF; OG, OH, describe the Verges of two
+Rain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any where
+in the conical Superficies described by OE, OF, OG, OH, and be
+illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being equal
+to the Angle POE, or 40 Degr. 17 Min. shall be the greatest Angle in
+which the most refrangible Rays can after one Reflexion be refracted to
+the Eye, and therefore all the Drops in the Line OE shall send the most
+refrangible Rays most copiously to the Eye, and thereby strike the
+Senses with the deepest violet Colour in that Region. And in like
+manner the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min.
+shall be the greatest in which the least refrangible Rays after one
+Reflexion can emerge out of the Drops, and therefore those Rays shall
+come most copiously to the Eye from the Drops in the Line OF, and strike
+the Senses with the deepest red Colour in that Region. And by the same
+Argument, the Rays which have intermediate Degrees of Refrangibility
+shall come most copiously from Drops between E and F, and strike the
+Senses with the intermediate Colours, in the Order which their Degrees
+of Refrangibility require, that is in the Progress from E to F, or from
+the inside of the Bow to the outside in this order, violet, indigo,
+blue, green, yellow, orange, red. But the violet, by the mixture of the
+white Light of the Clouds, will appear faint and incline to purple.
+
+[Illustration: FIG. 15.]
+
+Again, the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min.
+shall be the least Angle in which the least refrangible Rays can after
+two Reflexions emerge out of the Drops, and therefore the least
+refrangible Rays shall come most copiously to the Eye from the Drops in
+the Line OG, and strike the Sense with the deepest red in that Region.
+And the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min. shall
+be the least Angle, in which the most refrangible Rays after two
+Reflexions can emerge out of the Drops; and therefore those Rays shall
+come most copiously to the Eye from the Drops in the Line OH, and strike
+the Senses with the deepest violet in that Region. And by the same
+Argument, the Drops in the Regions between G and H shall strike the
+Sense with the intermediate Colours in the Order which their Degrees of
+Refrangibility require, that is, in the Progress from G to H, or from
+the inside of the Bow to the outside in this order, red, orange, yellow,
+green, blue, indigo, violet. And since these four Lines OE, OF, OG, OH,
+may be situated any where in the above-mention'd conical Superficies;
+what is said of the Drops and Colours in these Lines is to be understood
+of the Drops and Colours every where in those Superficies.
+
+Thus shall there be made two Bows of Colours, an interior and stronger,
+by one Reflexion in the Drops, and an exterior and fainter by two; for
+the Light becomes fainter by every Reflexion. And their Colours shall
+lie in a contrary Order to one another, the red of both Bows bordering
+upon the Space GF, which is between the Bows. The Breadth of the
+interior Bow EOF measured cross the Colours shall be 1 Degr. 45 Min. and
+the Breadth of the exterior GOH shall be 3 Degr. 10 Min. and the
+distance between them GOF shall be 8 Gr. 15 Min. the greatest
+Semi-diameter of the innermost, that is, the Angle POF being 42 Gr. 2
+Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57
+Min. These are the Measures of the Bows, as they would be were the Sun
+but a Point; for by the Breadth of his Body, the Breadth of the Bows
+will be increased, and their Distance decreased by half a Degree, and so
+the breadth of the interior Iris will be 2 Degr. 15 Min. that of the
+exterior 3 Degr. 40 Min. their distance 8 Degr. 25 Min. the greatest
+Semi-diameter of the interior Bow 42 Degr. 17 Min. and the least of the
+exterior 50 Degr. 42 Min. And such are the Dimensions of the Bows in the
+Heavens found to be very nearly, when their Colours appear strong and
+perfect. For once, by such means as I then had, I measured the greatest
+Semi-diameter of the interior Iris about 42 Degrees, and the breadth of
+the red, yellow and green in that Iris 63 or 64 Minutes, besides the
+outmost faint red obscured by the brightness of the Clouds, for which we
+may allow 3 or 4 Minutes more. The breadth of the blue was about 40
+Minutes more besides the violet, which was so much obscured by the
+brightness of the Clouds, that I could not measure its breadth. But
+supposing the breadth of the blue and violet together to equal that of
+the red, yellow and green together, the whole breadth of this Iris will
+be about 2-1/4 Degrees, as above. The least distance between this Iris
+and the exterior Iris was about 8 Degrees and 30 Minutes. The exterior
+Iris was broader than the interior, but so faint, especially on the blue
+side, that I could not measure its breadth distinctly. At another time
+when both Bows appeared more distinct, I measured the breadth of the
+interior Iris 2 Gr. 10´, and the breadth of the red, yellow and green in
+the exterior Iris, was to the breadth of the same Colours in the
+interior as 3 to 2.
+
+This Explication of the Rain-bow is yet farther confirmed by the known
+Experiment (made by _Antonius de Dominis_ and _Des-Cartes_) of hanging
+up any where in the Sun-shine a Glass Globe filled with Water, and
+viewing it in such a posture, that the Rays which come from the Globe to
+the Eye may contain with the Sun's Rays an Angle of either 42 or 50
+Degrees. For if the Angle be about 42 or 43 Degrees, the Spectator
+(suppose at O) shall see a full red Colour in that side of the Globe
+opposed to the Sun as 'tis represented at F, and if that Angle become
+less (suppose by depressing the Globe to E) there will appear other
+Colours, yellow, green and blue successive in the same side of the
+Globe. But if the Angle be made about 50 Degrees (suppose by lifting up
+the Globe to G) there will appear a red Colour in that side of the Globe
+towards the Sun, and if the Angle be made greater (suppose by lifting
+up the Globe to H) the red will turn successively to the other Colours,
+yellow, green and blue. The same thing I have tried, by letting a Globe
+rest, and raising or depressing the Eye, or otherwise moving it to make
+the Angle of a just magnitude.
+
+I have heard it represented, that if the Light of a Candle be refracted
+by a Prism to the Eye; when the blue Colour falls upon the Eye, the
+Spectator shall see red in the Prism, and when the red falls upon the
+Eye he shall see blue; and if this were certain, the Colours of the
+Globe and Rain-bow ought to appear in a contrary order to what we find.
+But the Colours of the Candle being very faint, the mistake seems to
+arise from the difficulty of discerning what Colours fall on the Eye.
+For, on the contrary, I have sometimes had occasion to observe in the
+Sun's Light refracted by a Prism, that the Spectator always sees that
+Colour in the Prism which falls upon his Eye. And the same I have found
+true also in Candle-light. For when the Prism is moved slowly from the
+Line which is drawn directly from the Candle to the Eye, the red appears
+first in the Prism and then the blue, and therefore each of them is seen
+when it falls upon the Eye. For the red passes over the Eye first, and
+then the blue.
+
+The Light which comes through drops of Rain by two Refractions without
+any Reflexion, ought to appear strongest at the distance of about 26
+Degrees from the Sun, and to decay gradually both ways as the distance
+from him increases and decreases. And the same is to be understood of
+Light transmitted through spherical Hail-stones. And if the Hail be a
+little flatted, as it often is, the Light transmitted may grow so strong
+at a little less distance than that of 26 Degrees, as to form a Halo
+about the Sun or Moon; which Halo, as often as the Hail-stones are duly
+figured may be colour'd, and then it must be red within by the least
+refrangible Rays, and blue without by the most refrangible ones,
+especially if the Hail-stones have opake Globules of Snow in their
+center to intercept the Light within the Halo (as _Hugenius_ has
+observ'd) and make the inside thereof more distinctly defined than it
+would otherwise be. For such Hail-stones, though spherical, by
+terminating the Light by the Snow, may make a Halo red within and
+colourless without, and darker in the red than without, as Halos used to
+be. For of those Rays which pass close by the Snow the Rubriform will be
+least refracted, and so come to the Eye in the directest Lines.
+
+The Light which passes through a drop of Rain after two Refractions, and
+three or more Reflexions, is scarce strong enough to cause a sensible
+Bow; but in those Cylinders of Ice by which _Hugenius_ explains the
+_Parhelia_, it may perhaps be sensible.
+
+
+_PROP._ X. PROB. V.
+
+_By the discovered Properties of Light to explain the permanent Colours
+of Natural Bodies._
+
+These Colours arise from hence, that some natural Bodies reflect some
+sorts of Rays, others other sorts more copiously than the rest. Minium
+reflects the least refrangible or red-making Rays most copiously, and
+thence appears red. Violets reflect the most refrangible most copiously,
+and thence have their Colour, and so of other Bodies. Every Body
+reflects the Rays of its own Colour more copiously than the rest, and
+from their excess and predominance in the reflected Light has its
+Colour.
+
+_Exper._ 17. For if in the homogeneal Lights obtained by the solution of
+the Problem proposed in the fourth Proposition of the first Part of this
+Book, you place Bodies of several Colours, you will find, as I have
+done, that every Body looks most splendid and luminous in the Light of
+its own Colour. Cinnaber in the homogeneal red Light is most
+resplendent, in the green Light it is manifestly less resplendent, and
+in the blue Light still less. Indigo in the violet blue Light is most
+resplendent, and its splendor is gradually diminish'd, as it is removed
+thence by degrees through the green and yellow Light to the red. By a
+Leek the green Light, and next that the blue and yellow which compound
+green, are more strongly reflected than the other Colours red and
+violet, and so of the rest. But to make these Experiments the more
+manifest, such Bodies ought to be chosen as have the fullest and most
+vivid Colours, and two of those Bodies are to be compared together.
+Thus, for instance, if Cinnaber and _ultra_-marine blue, or some other
+full blue be held together in the red homogeneal Light, they will both
+appear red, but the Cinnaber will appear of a strongly luminous and
+resplendent red, and the _ultra_-marine blue of a faint obscure and dark
+red; and if they be held together in the blue homogeneal Light, they
+will both appear blue, but the _ultra_-marine will appear of a strongly
+luminous and resplendent blue, and the Cinnaber of a faint and dark
+blue. Which puts it out of dispute that the Cinnaber reflects the red
+Light much more copiously than the _ultra_-marine doth, and the
+_ultra_-marine reflects the blue Light much more copiously than the
+Cinnaber doth. The same Experiment may be tried successfully with red
+Lead and Indigo, or with any other two colour'd Bodies, if due allowance
+be made for the different strength or weakness of their Colour and
+Light.
+
+And as the reason of the Colours of natural Bodies is evident by these
+Experiments, so it is farther confirmed and put past dispute by the two
+first Experiments of the first Part, whereby 'twas proved in such Bodies
+that the reflected Lights which differ in Colours do differ also in
+degrees of Refrangibility. For thence it's certain, that some Bodies
+reflect the more refrangible, others the less refrangible Rays more
+copiously.
+
+And that this is not only a true reason of these Colours, but even the
+only reason, may appear farther from this Consideration, that the Colour
+of homogeneal Light cannot be changed by the Reflexion of natural
+Bodies.
+
+For if Bodies by Reflexion cannot in the least change the Colour of any
+one sort of Rays, they cannot appear colour'd by any other means than by
+reflecting those which either are of their own Colour, or which by
+mixture must produce it.
+
+But in trying Experiments of this kind care must be had that the Light
+be sufficiently homogeneal. For if Bodies be illuminated by the ordinary
+prismatick Colours, they will appear neither of their own Day-light
+Colours, nor of the Colour of the Light cast on them, but of some middle
+Colour between both, as I have found by Experience. Thus red Lead (for
+instance) illuminated with the ordinary prismatick green will not appear
+either red or green, but orange or yellow, or between yellow and green,
+accordingly as the green Light by which 'tis illuminated is more or less
+compounded. For because red Lead appears red when illuminated with white
+Light, wherein all sorts of Rays are equally mix'd, and in the green
+Light all sorts of Rays are not equally mix'd, the Excess of the
+yellow-making, green-making and blue-making Rays in the incident green
+Light, will cause those Rays to abound so much in the reflected Light,
+as to draw the Colour from red towards their Colour. And because the red
+Lead reflects the red-making Rays most copiously in proportion to their
+number, and next after them the orange-making and yellow-making Rays;
+these Rays in the reflected Light will be more in proportion to the
+Light than they were in the incident green Light, and thereby will draw
+the reflected Light from green towards their Colour. And therefore the
+red Lead will appear neither red nor green, but of a Colour between
+both.
+
+In transparently colour'd Liquors 'tis observable, that their Colour
+uses to vary with their thickness. Thus, for instance, a red Liquor in a
+conical Glass held between the Light and the Eye, looks of a pale and
+dilute yellow at the bottom where 'tis thin, and a little higher where
+'tis thicker grows orange, and where 'tis still thicker becomes red, and
+where 'tis thickest the red is deepest and darkest. For it is to be
+conceiv'd that such a Liquor stops the indigo-making and violet-making
+Rays most easily, the blue-making Rays more difficultly, the
+green-making Rays still more difficultly, and the red-making most
+difficultly: And that if the thickness of the Liquor be only so much as
+suffices to stop a competent number of the violet-making and
+indigo-making Rays, without diminishing much the number of the rest, the
+rest must (by _Prop._ 6. _Part_ 2.) compound a pale yellow. But if the
+Liquor be so much thicker as to stop also a great number of the
+blue-making Rays, and some of the green-making, the rest must compound
+an orange; and where it is so thick as to stop also a great number of
+the green-making and a considerable number of the yellow-making, the
+rest must begin to compound a red, and this red must grow deeper and
+darker as the yellow-making and orange-making Rays are more and more
+stopp'd by increasing the thickness of the Liquor, so that few Rays
+besides the red-making can get through.
+
+Of this kind is an Experiment lately related to me by Mr. _Halley_, who,
+in diving deep into the Sea in a diving Vessel, found in a clear
+Sun-shine Day, that when he was sunk many Fathoms deep into the Water
+the upper part of his Hand on which the Sun shone directly through the
+Water and through a small Glass Window in the Vessel appeared of a red
+Colour, like that of a Damask Rose, and the Water below and the under
+part of his Hand illuminated by Light reflected from the Water below
+look'd green. For thence it may be gather'd, that the Sea-Water reflects
+back the violet and blue-making Rays most easily, and lets the
+red-making Rays pass most freely and copiously to great Depths. For
+thereby the Sun's direct Light at all great Depths, by reason of the
+predominating red-making Rays, must appear red; and the greater the
+Depth is, the fuller and intenser must that red be. And at such Depths
+as the violet-making Rays scarce penetrate unto, the blue-making,
+green-making, and yellow-making Rays being reflected from below more
+copiously than the red-making ones, must compound a green.
+
+Now, if there be two Liquors of full Colours, suppose a red and blue,
+and both of them so thick as suffices to make their Colours sufficiently
+full; though either Liquor be sufficiently transparent apart, yet will
+you not be able to see through both together. For, if only the
+red-making Rays pass through one Liquor, and only the blue-making
+through the other, no Rays can pass through both. This Mr. _Hook_ tried
+casually with Glass Wedges filled with red and blue Liquors, and was
+surprized at the unexpected Event, the reason of it being then unknown;
+which makes me trust the more to his Experiment, though I have not tried
+it my self. But he that would repeat it, must take care the Liquors be
+of very good and full Colours.
+
+Now, whilst Bodies become coloured by reflecting or transmitting this or
+that sort of Rays more copiously than the rest, it is to be conceived
+that they stop and stifle in themselves the Rays which they do not
+reflect or transmit. For, if Gold be foliated and held between your Eye
+and the Light, the Light looks of a greenish blue, and therefore massy
+Gold lets into its Body the blue-making Rays to be reflected to and fro
+within it till they be stopp'd and stifled, whilst it reflects the
+yellow-making outwards, and thereby looks yellow. And much after the
+same manner that Leaf Gold is yellow by reflected, and blue by
+transmitted Light, and massy Gold is yellow in all Positions of the Eye;
+there are some Liquors, as the Tincture of _Lignum Nephriticum_, and
+some sorts of Glass which transmit one sort of Light most copiously, and
+reflect another sort, and thereby look of several Colours, according to
+the Position of the Eye to the Light. But, if these Liquors or Glasses
+were so thick and massy that no Light could get through them, I question
+not but they would like all other opake Bodies appear of one and the
+same Colour in all Positions of the Eye, though this I cannot yet affirm
+by Experience. For all colour'd Bodies, so far as my Observation
+reaches, may be seen through if made sufficiently thin, and therefore
+are in some measure transparent, and differ only in degrees of
+Transparency from tinged transparent Liquors; these Liquors, as well as
+those Bodies, by a sufficient Thickness becoming opake. A transparent
+Body which looks of any Colour by transmitted Light, may also look of
+the same Colour by reflected Light, the Light of that Colour being
+reflected by the farther Surface of the Body, or by the Air beyond it.
+And then the reflected Colour will be diminished, and perhaps cease, by
+making the Body very thick, and pitching it on the backside to diminish
+the Reflexion of its farther Surface, so that the Light reflected from
+the tinging Particles may predominate. In such Cases, the Colour of the
+reflected Light will be apt to vary from that of the Light transmitted.
+But whence it is that tinged Bodies and Liquors reflect some sort of
+Rays, and intromit or transmit other sorts, shall be said in the next
+Book. In this Proposition I content my self to have put it past dispute,
+that Bodies have such Properties, and thence appear colour'd.
+
+
+_PROP._ XI. PROB. VI.
+
+_By mixing colour'd Lights to compound a beam of Light of the same
+Colour and Nature with a beam of the Sun's direct Light, and therein to
+experience the Truth of the foregoing Propositions._
+
+[Illustration: FIG. 16.]
+
+Let ABC _abc_ [in _Fig._ 16.] represent a Prism, by which the Sun's
+Light let into a dark Chamber through the Hole F, may be refracted
+towards the Lens MN, and paint upon it at _p_, _q_, _r_, _s_, and _t_,
+the usual Colours violet, blue, green, yellow, and red, and let the
+diverging Rays by the Refraction of this Lens converge again towards X,
+and there, by the mixture of all those their Colours, compound a white
+according to what was shewn above. Then let another Prism DEG _deg_,
+parallel to the former, be placed at X, to refract that white Light
+upwards towards Y. Let the refracting Angles of the Prisms, and their
+distances from the Lens be equal, so that the Rays which converged from
+the Lens towards X, and without Refraction, would there have crossed and
+diverged again, may by the Refraction of the second Prism be reduced
+into Parallelism and diverge no more. For then those Rays will recompose
+a beam of white Light XY. If the refracting Angle of either Prism be the
+bigger, that Prism must be so much the nearer to the Lens. You will know
+when the Prisms and the Lens are well set together, by observing if the
+beam of Light XY, which comes out of the second Prism be perfectly white
+to the very edges of the Light, and at all distances from the Prism
+continue perfectly and totally white like a beam of the Sun's Light. For
+till this happens, the Position of the Prisms and Lens to one another
+must be corrected; and then if by the help of a long beam of Wood, as is
+represented in the Figure, or by a Tube, or some other such Instrument,
+made for that Purpose, they be made fast in that Situation, you may try
+all the same Experiments in this compounded beam of Light XY, which have
+been made in the Sun's direct Light. For this compounded beam of Light
+has the same appearance, and is endow'd with all the same Properties
+with a direct beam of the Sun's Light, so far as my Observation reaches.
+And in trying Experiments in this beam you may by stopping any of the
+Colours, _p_, _q_, _r_, _s_, and _t_, at the Lens, see how the Colours
+produced in the Experiments are no other than those which the Rays had
+at the Lens before they entered the Composition of this Beam: And by
+consequence, that they arise not from any new Modifications of the Light
+by Refractions and Reflexions, but from the various Separations and
+Mixtures of the Rays originally endow'd with their colour-making
+Qualities.
+
+So, for instance, having with a Lens 4-1/4 Inches broad, and two Prisms
+on either hand 6-1/4 Feet distant from the Lens, made such a beam of
+compounded Light; to examine the reason of the Colours made by Prisms, I
+refracted this compounded beam of Light XY with another Prism HIK _kh_,
+and thereby cast the usual Prismatick Colours PQRST upon the Paper LV
+placed behind. And then by stopping any of the Colours _p_, _q_, _r_,
+_s_, _t_, at the Lens, I found that the same Colour would vanish at the
+Paper. So if the Purple _p_ was stopp'd at the Lens, the Purple P upon
+the Paper would vanish, and the rest of the Colours would remain
+unalter'd, unless perhaps the blue, so far as some purple latent in it
+at the Lens might be separated from it by the following Refractions. And
+so by intercepting the green upon the Lens, the green R upon the Paper
+would vanish, and so of the rest; which plainly shews, that as the white
+beam of Light XY was compounded of several Lights variously colour'd at
+the Lens, so the Colours which afterwards emerge out of it by new
+Refractions are no other than those of which its Whiteness was
+compounded. The Refraction of the Prism HIK _kh_ generates the Colours
+PQRST upon the Paper, not by changing the colorific Qualities of the
+Rays, but by separating the Rays which had the very same colorific
+Qualities before they enter'd the Composition of the refracted beam of
+white Light XY. For otherwise the Rays which were of one Colour at the
+Lens might be of another upon the Paper, contrary to what we find.
+
+So again, to examine the reason of the Colours of natural Bodies, I
+placed such Bodies in the Beam of Light XY, and found that they all
+appeared there of those their own Colours which they have in Day-light,
+and that those Colours depend upon the Rays which had the same Colours
+at the Lens before they enter'd the Composition of that beam. Thus, for
+instance, Cinnaber illuminated by this beam appears of the same red
+Colour as in Day-light; and if at the Lens you intercept the
+green-making and blue-making Rays, its redness will become more full and
+lively: But if you there intercept the red-making Rays, it will not any
+longer appear red, but become yellow or green, or of some other Colour,
+according to the sorts of Rays which you do not intercept. So Gold in
+this Light XY appears of the same yellow Colour as in Day-light, but by
+intercepting at the Lens a due Quantity of the yellow-making Rays it
+will appear white like Silver (as I have tried) which shews that its
+yellowness arises from the Excess of the intercepted Rays tinging that
+Whiteness with their Colour when they are let pass. So the Infusion of
+_Lignum Nephriticum_ (as I have also tried) when held in this beam of
+Light XY, looks blue by the reflected Part of the Light, and red by the
+transmitted Part of it, as when 'tis view'd in Day-light; but if you
+intercept the blue at the Lens the Infusion will lose its reflected blue
+Colour, whilst its transmitted red remains perfect, and by the loss of
+some blue-making Rays, wherewith it was allay'd, becomes more intense
+and full. And, on the contrary, if the red and orange-making Rays be
+intercepted at the Lens, the Infusion will lose its transmitted red,
+whilst its blue will remain and become more full and perfect. Which
+shews, that the Infusion does not tinge the Rays with blue and red, but
+only transmits those most copiously which were red-making before, and
+reflects those most copiously which were blue-making before. And after
+the same manner may the Reasons of other Phænomena be examined, by
+trying them in this artificial beam of Light XY.
+
+FOOTNOTES:
+
+[I] See p. 59.
+
+[J] _See our_ Author's Lect. Optic. _Part_ II. _Sect._ II. _p._ 239.
+
+[K] _As is done in our_ Author's Lect. Optic. _Part_ I. _Sect._ III.
+_and_ IV. _and Part_ II. _Sect._ II.
+
+[L] _See our_ Author's Lect. Optic. _Part_ II. _Sect._ II. _pag._ 269,
+&c.
+
+[M] _This is demonstrated in our_ Author's Lect. Optic. _Part_ I.
+_Sect._ IV. _Prop._ 35 _and_ 36.
+
+
+
+
+THE
+
+SECOND BOOK
+
+OF
+
+OPTICKS
+
+
+
+
+_PART I._
+
+_Observations concerning the Reflexions, Refractions, and Colours of
+thin transparent Bodies._
+
+
+It has been observed by others, that transparent Substances, as Glass,
+Water, Air, &c. when made very thin by being blown into Bubbles, or
+otherwise formed into Plates, do exhibit various Colours according to
+their various thinness, altho' at a greater thickness they appear very
+clear and colourless. In the former Book I forbore to treat of these
+Colours, because they seemed of a more difficult Consideration, and were
+not necessary for establishing the Properties of Light there discoursed
+of. But because they may conduce to farther Discoveries for compleating
+the Theory of Light, especially as to the constitution of the parts of
+natural Bodies, on which their Colours or Transparency depend; I have
+here set down an account of them. To render this Discourse short and
+distinct, I have first described the principal of my Observations, and
+then consider'd and made use of them. The Observations are these.
+
+_Obs._ 1. Compressing two Prisms hard together that their sides (which
+by chance were a very little convex) might somewhere touch one another:
+I found the place in which they touched to become absolutely
+transparent, as if they had there been one continued piece of Glass. For
+when the Light fell so obliquely on the Air, which in other places was
+between them, as to be all reflected; it seemed in that place of contact
+to be wholly transmitted, insomuch that when look'd upon, it appeared
+like a black or dark spot, by reason that little or no sensible Light
+was reflected from thence, as from other places; and when looked through
+it seemed (as it were) a hole in that Air which was formed into a thin
+Plate, by being compress'd between the Glasses. And through this hole
+Objects that were beyond might be seen distinctly, which could not at
+all be seen through other parts of the Glasses where the Air was
+interjacent. Although the Glasses were a little convex, yet this
+transparent spot was of a considerable breadth, which breadth seemed
+principally to proceed from the yielding inwards of the parts of the
+Glasses, by reason of their mutual pressure. For by pressing them very
+hard together it would become much broader than otherwise.
+
+_Obs._ 2. When the Plate of Air, by turning the Prisms about their
+common Axis, became so little inclined to the incident Rays, that some
+of them began to be transmitted, there arose in it many slender Arcs of
+Colours which at first were shaped almost like the Conchoid, as you see
+them delineated in the first Figure. And by continuing the Motion of the
+Prisms, these Arcs increased and bended more and more about the said
+transparent spot, till they were compleated into Circles or Rings
+incompassing it, and afterwards continually grew more and more
+contracted.
+
+[Illustration: FIG. 1.]
+
+These Arcs at their first appearance were of a violet and blue Colour,
+and between them were white Arcs of Circles, which presently by
+continuing the Motion of the Prisms became a little tinged in their
+inward Limbs with red and yellow, and to their outward Limbs the blue
+was adjacent. So that the order of these Colours from the central dark
+spot, was at that time white, blue, violet; black, red, orange, yellow,
+white, blue, violet, &c. But the yellow and red were much fainter than
+the blue and violet.
+
+The Motion of the Prisms about their Axis being continued, these Colours
+contracted more and more, shrinking towards the whiteness on either
+side of it, until they totally vanished into it. And then the Circles in
+those parts appear'd black and white, without any other Colours
+intermix'd. But by farther moving the Prisms about, the Colours again
+emerged out of the whiteness, the violet and blue at its inward Limb,
+and at its outward Limb the red and yellow. So that now their order from
+the central Spot was white, yellow, red; black; violet, blue, white,
+yellow, red, &c. contrary to what it was before.
+
+_Obs._ 3. When the Rings or some parts of them appeared only black and
+white, they were very distinct and well defined, and the blackness
+seemed as intense as that of the central Spot. Also in the Borders of
+the Rings, where the Colours began to emerge out of the whiteness, they
+were pretty distinct, which made them visible to a very great multitude.
+I have sometimes number'd above thirty Successions (reckoning every
+black and white Ring for one Succession) and seen more of them, which by
+reason of their smalness I could not number. But in other Positions of
+the Prisms, at which the Rings appeared of many Colours, I could not
+distinguish above eight or nine of them, and the Exterior of those were
+very confused and dilute.
+
+In these two Observations to see the Rings distinct, and without any
+other Colour than Black and white, I found it necessary to hold my Eye
+at a good distance from them. For by approaching nearer, although in the
+same inclination of my Eye to the Plane of the Rings, there emerged a
+bluish Colour out of the white, which by dilating it self more and more
+into the black, render'd the Circles less distinct, and left the white a
+little tinged with red and yellow. I found also by looking through a
+slit or oblong hole, which was narrower than the pupil of my Eye, and
+held close to it parallel to the Prisms, I could see the Circles much
+distincter and visible to a far greater number than otherwise.
+
+_Obs._ 4. To observe more nicely the order of the Colours which arose
+out of the white Circles as the Rays became less and less inclined to
+the Plate of Air; I took two Object-glasses, the one a Plano-convex for
+a fourteen Foot Telescope, and the other a large double Convex for one
+of about fifty Foot; and upon this, laying the other with its plane side
+downwards, I pressed them slowly together, to make the Colours
+successively emerge in the middle of the Circles, and then slowly lifted
+the upper Glass from the lower to make them successively vanish again in
+the same place. The Colour, which by pressing the Glasses together,
+emerged last in the middle of the other Colours, would upon its first
+appearance look like a Circle of a Colour almost uniform from the
+circumference to the center and by compressing the Glasses still more,
+grow continually broader until a new Colour emerged in its center, and
+thereby it became a Ring encompassing that new Colour. And by
+compressing the Glasses still more, the diameter of this Ring would
+increase, and the breadth of its Orbit or Perimeter decrease until
+another new Colour emerged in the center of the last: And so on until a
+third, a fourth, a fifth, and other following new Colours successively
+emerged there, and became Rings encompassing the innermost Colour, the
+last of which was the black Spot. And, on the contrary, by lifting up
+the upper Glass from the lower, the diameter of the Rings would
+decrease, and the breadth of their Orbit increase, until their Colours
+reached successively to the center; and then they being of a
+considerable breadth, I could more easily discern and distinguish their
+Species than before. And by this means I observ'd their Succession and
+Quantity to be as followeth.
+
+Next to the pellucid central Spot made by the contact of the Glasses
+succeeded blue, white, yellow, and red. The blue was so little in
+quantity, that I could not discern it in the Circles made by the Prisms,
+nor could I well distinguish any violet in it, but the yellow and red
+were pretty copious, and seemed about as much in extent as the white,
+and four or five times more than the blue. The next Circuit in order of
+Colours immediately encompassing these were violet, blue, green, yellow,
+and red: and these were all of them copious and vivid, excepting the
+green, which was very little in quantity, and seemed much more faint and
+dilute than the other Colours. Of the other four, the violet was the
+least in extent, and the blue less than the yellow or red. The third
+Circuit or Order was purple, blue, green, yellow, and red; in which the
+purple seemed more reddish than the violet in the former Circuit, and
+the green was much more conspicuous, being as brisk and copious as any
+of the other Colours, except the yellow, but the red began to be a
+little faded, inclining very much to purple. After this succeeded the
+fourth Circuit of green and red. The green was very copious and lively,
+inclining on the one side to blue, and on the other side to yellow. But
+in this fourth Circuit there was neither violet, blue, nor yellow, and
+the red was very imperfect and dirty. Also the succeeding Colours became
+more and more imperfect and dilute, till after three or four revolutions
+they ended in perfect whiteness. Their form, when the Glasses were most
+compress'd so as to make the black Spot appear in the center, is
+delineated in the second Figure; where _a_, _b_, _c_, _d_, _e_: _f_,
+_g_, _h_, _i_, _k_: _l_, _m_, _n_, _o_, _p_: _q_, _r_: _s_, _t_: _v_,
+_x_: _y_, _z_, denote the Colours reckon'd in order from the center,
+black, blue, white, yellow, red: violet, blue, green, yellow, red:
+purple, blue, green, yellow, red: green, red: greenish blue, red:
+greenish blue, pale red: greenish blue, reddish white.
+
+[Illustration: FIG. 2.]
+
+_Obs._ 5. To determine the interval of the Glasses, or thickness of the
+interjacent Air, by which each Colour was produced, I measured the
+Diameters of the first six Rings at the most lucid part of their Orbits,
+and squaring them, I found their Squares to be in the arithmetical
+Progression of the odd Numbers, 1, 3, 5, 7, 9, 11. And since one of
+these Glasses was plane, and the other spherical, their Intervals at
+those Rings must be in the same Progression. I measured also the
+Diameters of the dark or faint Rings between the more lucid Colours, and
+found their Squares to be in the arithmetical Progression of the even
+Numbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult to
+take these measures exactly; I repeated them divers times at divers
+parts of the Glasses, that by their Agreement I might be confirmed in
+them. And the same method I used in determining some others of the
+following Observations.
+
+_Obs._ 6. The Diameter of the sixth Ring at the most lucid part of its
+Orbit was 58/100 parts of an Inch, and the Diameter of the Sphere on
+which the double convex Object-glass was ground was about 102 Feet, and
+hence I gathered the thickness of the Air or Aereal Interval of the
+Glasses at that Ring. But some time after, suspecting that in making
+this Observation I had not determined the Diameter of the Sphere with
+sufficient accurateness, and being uncertain whether the Plano-convex
+Glass was truly plane, and not something concave or convex on that side
+which I accounted plane; and whether I had not pressed the Glasses
+together, as I often did, to make them touch; (For by pressing such
+Glasses together their parts easily yield inwards, and the Rings thereby
+become sensibly broader than they would be, did the Glasses keep their
+Figures.) I repeated the Experiment, and found the Diameter of the sixth
+lucid Ring about 55/100 parts of an Inch. I repeated the Experiment also
+with such an Object-glass of another Telescope as I had at hand. This
+was a double Convex ground on both sides to one and the same Sphere, and
+its Focus was distant from it 83-2/5 Inches. And thence, if the Sines of
+Incidence and Refraction of the bright yellow Light be assumed in
+proportion as 11 to 17, the Diameter of the Sphere to which the Glass
+was figured will by computation be found 182 Inches. This Glass I laid
+upon a flat one, so that the black Spot appeared in the middle of the
+Rings of Colours without any other Pressure than that of the weight of
+the Glass. And now measuring the Diameter of the fifth dark Circle as
+accurately as I could, I found it the fifth part of an Inch precisely.
+This Measure was taken with the points of a pair of Compasses on the
+upper Surface on the upper Glass, and my Eye was about eight or nine
+Inches distance from the Glass, almost perpendicularly over it, and the
+Glass was 1/6 of an Inch thick, and thence it is easy to collect that
+the true Diameter of the Ring between the Glasses was greater than its
+measur'd Diameter above the Glasses in the Proportion of 80 to 79, or
+thereabouts, and by consequence equal to 16/79 parts of an Inch, and its
+true Semi-diameter equal to 8/79 parts. Now as the Diameter of the
+Sphere (182 Inches) is to the Semi-diameter of this fifth dark Ring
+(8/79 parts of an Inch) so is this Semi-diameter to the thickness of the
+Air at this fifth dark Ring; which is therefore 32/567931 or
+100/1774784. Parts of an Inch; and the fifth Part thereof, _viz._ the
+1/88739 Part of an Inch, is the Thickness of the Air at the first of
+these dark Rings.
+
+The same Experiment I repeated with another double convex Object-glass
+ground on both sides to one and the same Sphere. Its Focus was distant
+from it 168-1/2 Inches, and therefore the Diameter of that Sphere was
+184 Inches. This Glass being laid upon the same plain Glass, the
+Diameter of the fifth of the dark Rings, when the black Spot in their
+Center appear'd plainly without pressing the Glasses, was by the measure
+of the Compasses upon the upper Glass 121/600 Parts of an Inch, and by
+consequence between the Glasses it was 1222/6000: For the upper Glass
+was 1/8 of an Inch thick, and my Eye was distant from it 8 Inches. And a
+third proportional to half this from the Diameter of the Sphere is
+5/88850 Parts of an Inch. This is therefore the Thickness of the Air at
+this Ring, and a fifth Part thereof, _viz._ the 1/88850th Part of an
+Inch is the Thickness thereof at the first of the Rings, as above.
+
+I tried the same Thing, by laying these Object-glasses upon flat Pieces
+of a broken Looking-glass, and found the same Measures of the Rings:
+Which makes me rely upon them till they can be determin'd more
+accurately by Glasses ground to larger Spheres, though in such Glasses
+greater care must be taken of a true Plane.
+
+These Dimensions were taken, when my Eye was placed almost
+perpendicularly over the Glasses, being about an Inch, or an Inch and a
+quarter, distant from the incident Rays, and eight Inches distant from
+the Glass; so that the Rays were inclined to the Glass in an Angle of
+about four Degrees. Whence by the following Observation you will
+understand, that had the Rays been perpendicular to the Glasses, the
+Thickness of the Air at these Rings would have been less in the
+Proportion of the Radius to the Secant of four Degrees, that is, of
+10000 to 10024. Let the Thicknesses found be therefore diminish'd in
+this Proportion, and they will become 1/88952 and 1/89063, or (to use
+the nearest round Number) the 1/89000th Part of an Inch. This is the
+Thickness of the Air at the darkest Part of the first dark Ring made by
+perpendicular Rays; and half this Thickness multiplied by the
+Progression, 1, 3, 5, 7, 9, 11, &c. gives the Thicknesses of the Air at
+the most luminous Parts of all the brightest Rings, _viz._ 1/178000,
+3/178000, 5/178000, 7/178000, &c. their arithmetical Means 2/178000,
+4/178000, 6/178000, &c. being its Thicknesses at the darkest Parts of
+all the dark ones.
+
+_Obs._ 7. The Rings were least, when my Eye was placed perpendicularly
+over the Glasses in the Axis of the Rings: And when I view'd them
+obliquely they became bigger, continually swelling as I removed my Eye
+farther from the Axis. And partly by measuring the Diameter of the same
+Circle at several Obliquities of my Eye, partly by other Means, as also
+by making use of the two Prisms for very great Obliquities, I found its
+Diameter, and consequently the Thickness of the Air at its Perimeter in
+all those Obliquities to be very nearly in the Proportions express'd in
+this Table.
+
+-------------------+--------------------+----------+----------
+Angle of Incidence |Angle of Refraction |Diameter  |Thickness
+        on         |         into       |  of the  |   of the
+      the Air.     |       the Air.     |   Ring.  |    Air.
+-------------------+--------------------+----------+----------
+    Deg.    Min.   |                    |          |
+                   |                    |          |
+    00      00     |     00      00     |  10      |  10
+                   |                    |          |
+    06      26     |     10      00     |  10-1/13 |  10-2/13
+                   |                    |          |
+    12      45     |     20      00     |  10-1/3  |  10-2/3
+                   |                    |          |
+    18      49     |     30      00     |  10-3/4  |  11-1/2
+                   |                    |          |
+    24      30     |     40      00     |  11-2/5  |  13
+                   |                    |          |
+    29      37     |     50      00     |  12-1/2  |  15-1/2
+                   |                    |          |
+    33      58     |     60      00     |  14      |  20
+                   |                    |          |
+    35      47     |     65      00     |  15-1/4  |  23-1/4
+                   |                    |          |
+    37      19     |     70      00     |  16-4/5  |  28-1/4
+                   |                    |          |
+    38      33     |     75      00     |  19-1/4  |  37
+                   |                    |          |
+    39      27     |     80      00     |  22-6/7  |  52-1/4
+                   |                    |          |
+    40      00     |     85      00     |  29      |  84-1/12
+                   |                    |          |
+    40      11     |     90      00     |  35      | 122-1/2
+-------------------+--------------------+----------+----------
+
+In the two first Columns are express'd the Obliquities of the incident
+and emergent Rays to the Plate of the Air, that is, their Angles of
+Incidence and Refraction. In the third Column the Diameter of any
+colour'd Ring at those Obliquities is expressed in Parts, of which ten
+constitute that Diameter when the Rays are perpendicular. And in the
+fourth Column the Thickness of the Air at the Circumference of that Ring
+is expressed in Parts, of which also ten constitute its Thickness when
+the Rays are perpendicular.
+
+And from these Measures I seem to gather this Rule: That the Thickness
+of the Air is proportional to the Secant of an Angle, whose Sine is a
+certain mean Proportional between the Sines of Incidence and Refraction.
+And that mean Proportional, so far as by these Measures I can determine
+it, is the first of an hundred and six arithmetical mean Proportionals
+between those Sines counted from the bigger Sine, that is, from the Sine
+of Refraction when the Refraction is made out of the Glass into the
+Plate of Air, or from the Sine of Incidence when the Refraction is made
+out of the Plate of Air into the Glass.
+
+_Obs._ 8. The dark Spot in the middle of the Rings increased also by the
+Obliquation of the Eye, although almost insensibly. But, if instead of
+the Object-glasses the Prisms were made use of, its Increase was more
+manifest when viewed so obliquely that no Colours appear'd about it. It
+was least when the Rays were incident most obliquely on the interjacent
+Air, and as the obliquity decreased it increased more and more until the
+colour'd Rings appear'd, and then decreased again, but not so much as it
+increased before. And hence it is evident, that the Transparency was
+not only at the absolute Contact of the Glasses, but also where they had
+some little Interval. I have sometimes observed the Diameter of that
+Spot to be between half and two fifth parts of the Diameter of the
+exterior Circumference of the red in the first Circuit or Revolution of
+Colours when view'd almost perpendicularly; whereas when view'd
+obliquely it hath wholly vanish'd and become opake and white like the
+other parts of the Glass; whence it may be collected that the Glasses
+did then scarcely, or not at all, touch one another, and that their
+Interval at the perimeter of that Spot when view'd perpendicularly was
+about a fifth or sixth part of their Interval at the circumference of
+the said red.
+
+_Obs._ 9. By looking through the two contiguous Object-glasses, I found
+that the interjacent Air exhibited Rings of Colours, as well by
+transmitting Light as by reflecting it. The central Spot was now white,
+and from it the order of the Colours were yellowish red; black, violet,
+blue, white, yellow, red; violet, blue, green, yellow, red, &c. But
+these Colours were very faint and dilute, unless when the Light was
+trajected very obliquely through the Glasses: For by that means they
+became pretty vivid. Only the first yellowish red, like the blue in the
+fourth Observation, was so little and faint as scarcely to be discern'd.
+Comparing the colour'd Rings made by Reflexion, with these made by
+transmission of the Light; I found that white was opposite to black, red
+to blue, yellow to violet, and green to a Compound of red and violet.
+That is, those parts of the Glass were black when looked through, which
+when looked upon appeared white, and on the contrary. And so those which
+in one case exhibited blue, did in the other case exhibit red. And the
+like of the other Colours. The manner you have represented in the third
+Figure, where AB, CD, are the Surfaces of the Glasses contiguous at E,
+and the black Lines between them are their Distances in arithmetical
+Progression, and the Colours written above are seen by reflected Light,
+and those below by Light transmitted (p. 209).
+
+_Obs._ 10. Wetting the Object-glasses a little at their edges, the Water
+crept in slowly between them, and the Circles thereby became less and
+the Colours more faint: Insomuch that as the Water crept along, one half
+of them at which it first arrived would appear broken off from the other
+half, and contracted into a less Room. By measuring them I found the
+Proportions of their Diameters to the Diameters of the like Circles made
+by Air to be about seven to eight, and consequently the Intervals of the
+Glasses at like Circles, caused by those two Mediums Water and Air, are
+as about three to four. Perhaps it may be a general Rule, That if any
+other Medium more or less dense than Water be compress'd between the
+Glasses, their Intervals at the Rings caused thereby will be to their
+Intervals caused by interjacent Air, as the Sines are which measure the
+Refraction made out of that Medium into Air.
+
+_Obs._ 11. When the Water was between the Glasses, if I pressed the
+upper Glass variously at its edges to make the Rings move nimbly from
+one place to another, a little white Spot would immediately follow the
+center of them, which upon creeping in of the ambient Water into that
+place would presently vanish. Its appearance was such as interjacent Air
+would have caused, and it exhibited the same Colours. But it was not
+air, for where any Bubbles of Air were in the Water they would not
+vanish. The Reflexion must have rather been caused by a subtiler Medium,
+which could recede through the Glasses at the creeping in of the Water.
+
+_Obs._ 12. These Observations were made in the open Air. But farther to
+examine the Effects of colour'd Light falling on the Glasses, I darken'd
+the Room, and view'd them by Reflexion of the Colours of a Prism cast on
+a Sheet of white Paper, my Eye being so placed that I could see the
+colour'd Paper by Reflexion in the Glasses, as in a Looking-glass. And
+by this means the Rings became distincter and visible to a far greater
+number than in the open Air. I have sometimes seen more than twenty of
+them, whereas in the open Air I could not discern above eight or nine.
+
+[Illustration: FIG. 3.]
+
+_Obs._ 13. Appointing an Assistant to move the Prism to and fro about
+its Axis, that all the Colours might successively fall on that part of
+the Paper which I saw by Reflexion from that part of the Glasses, where
+the Circles appear'd, so that all the Colours might be successively
+reflected from the Circles to my Eye, whilst I held it immovable, I
+found the Circles which the red Light made to be manifestly bigger than
+those which were made by the blue and violet. And it was very pleasant
+to see them gradually swell or contract accordingly as the Colour of the
+Light was changed. The Interval of the Glasses at any of the Rings when
+they were made by the utmost red Light, was to their Interval at the
+same Ring when made by the utmost violet, greater than as 3 to 2, and
+less than as 13 to 8. By the most of my Observations it was as 14 to 9.
+And this Proportion seem'd very nearly the same in all Obliquities of my
+Eye; unless when two Prisms were made use of instead of the
+Object-glasses. For then at a certain great obliquity of my Eye, the
+Rings made by the several Colours seem'd equal, and at a greater
+obliquity those made by the violet would be greater than the same Rings
+made by the red: the Refraction of the Prism in this case causing the
+most refrangible Rays to fall more obliquely on that plate of the Air
+than the least refrangible ones. Thus the Experiment succeeded in the
+colour'd Light, which was sufficiently strong and copious to make the
+Rings sensible. And thence it may be gather'd, that if the most
+refrangible and least refrangible Rays had been copious enough to make
+the Rings sensible without the mixture of other Rays, the Proportion
+which here was 14 to 9 would have been a little greater, suppose 14-1/4
+or 14-1/3 to 9.
+
+_Obs._ 14. Whilst the Prism was turn'd about its Axis with an uniform
+Motion, to make all the several Colours fall successively upon the
+Object-glasses, and thereby to make the Rings contract and dilate: The
+Contraction or Dilatation of each Ring thus made by the variation of its
+Colour was swiftest in the red, and slowest in the violet, and in the
+intermediate Colours it had intermediate degrees of Celerity. Comparing
+the quantity of Contraction and Dilatation made by all the degrees of
+each Colour, I found that it was greatest in the red; less in the
+yellow, still less in the blue, and least in the violet. And to make as
+just an Estimation as I could of the Proportions of their Contractions
+or Dilatations, I observ'd that the whole Contraction or Dilatation of
+the Diameter of any Ring made by all the degrees of red, was to that of
+the Diameter of the same Ring made by all the degrees of violet, as
+about four to three, or five to four, and that when the Light was of the
+middle Colour between yellow and green, the Diameter of the Ring was
+very nearly an arithmetical Mean between the greatest Diameter of the
+same Ring made by the outmost red, and the least Diameter thereof made
+by the outmost violet: Contrary to what happens in the Colours of the
+oblong Spectrum made by the Refraction of a Prism, where the red is most
+contracted, the violet most expanded, and in the midst of all the
+Colours is the Confine of green and blue. And hence I seem to collect
+that the thicknesses of the Air between the Glasses there, where the
+Ring is successively made by the limits of the five principal Colours
+(red, yellow, green, blue, violet) in order (that is, by the extreme
+red, by the limit of red and yellow in the middle of the orange, by the
+limit of yellow and green, by the limit of green and blue, by the limit
+of blue and violet in the middle of the indigo, and by the extreme
+violet) are to one another very nearly as the sixth lengths of a Chord
+which found the Notes in a sixth Major, _sol_, _la_, _mi_, _fa_, _sol_,
+_la_. But it agrees something better with the Observation to say, that
+the thicknesses of the Air between the Glasses there, where the Rings
+are successively made by the limits of the seven Colours, red, orange,
+yellow, green, blue, indigo, violet in order, are to one another as the
+Cube Roots of the Squares of the eight lengths of a Chord, which found
+the Notes in an eighth, _sol_, _la_, _fa_, _sol_, _la_, _mi_, _fa_,
+_sol_; that is, as the Cube Roots of the Squares of the Numbers, 1, 8/9,
+5/6, 3/4, 2/3, 3/5, 9/16, 1/2.
+
+_Obs._ 15. These Rings were not of various Colours like those made in
+the open Air, but appeared all over of that prismatick Colour only with
+which they were illuminated. And by projecting the prismatick Colours
+immediately upon the Glasses, I found that the Light which fell on the
+dark Spaces which were between the Colour'd Rings was transmitted
+through the Glasses without any variation of Colour. For on a white
+Paper placed behind, it would paint Rings of the same Colour with those
+which were reflected, and of the bigness of their immediate Spaces. And
+from thence the origin of these Rings is manifest; namely, that the Air
+between the Glasses, according to its various thickness, is disposed in
+some places to reflect, and in others to transmit the Light of any one
+Colour (as you may see represented in the fourth Figure) and in the same
+place to reflect that of one Colour where it transmits that of another.
+
+[Illustration: FIG. 4.]
+
+_Obs._ 16. The Squares of the Diameters of these Rings made by any
+prismatick Colour were in arithmetical Progression, as in the fifth
+Observation. And the Diameter of the sixth Circle, when made by the
+citrine yellow, and viewed almost perpendicularly was about 58/100 parts
+of an Inch, or a little less, agreeable to the sixth Observation.
+
+The precedent Observations were made with a rarer thin Medium,
+terminated by a denser, such as was Air or Water compress'd between two
+Glasses. In those that follow are set down the Appearances of a denser
+Medium thin'd within a rarer, such as are Plates of Muscovy Glass,
+Bubbles of Water, and some other thin Substances terminated on all sides
+with air.
+
+_Obs._ 17. If a Bubble be blown with Water first made tenacious by
+dissolving a little Soap in it, 'tis a common Observation, that after a
+while it will appear tinged with a great variety of Colours. To defend
+these Bubbles from being agitated by the external Air (whereby their
+Colours are irregularly moved one among another, so that no accurate
+Observation can be made of them,) as soon as I had blown any of them I
+cover'd it with a clear Glass, and by that means its Colours emerged in
+a very regular order, like so many concentrick Rings encompassing the
+top of the Bubble. And as the Bubble grew thinner by the continual
+subsiding of the Water, these Rings dilated slowly and overspread the
+whole Bubble, descending in order to the bottom of it, where they
+vanish'd successively. In the mean while, after all the Colours were
+emerged at the top, there grew in the center of the Rings a small round
+black Spot, like that in the first Observation, which continually
+dilated it self till it became sometimes more than 1/2 or 3/4 of an Inch
+in breadth before the Bubble broke. At first I thought there had been no
+Light reflected from the Water in that place, but observing it more
+curiously, I saw within it several smaller round Spots, which appeared
+much blacker and darker than the rest, whereby I knew that there was
+some Reflexion at the other places which were not so dark as those
+Spots. And by farther Tryal I found that I could see the Images of some
+things (as of a Candle or the Sun) very faintly reflected, not only from
+the great black Spot, but also from the little darker Spots which were
+within it.
+
+Besides the aforesaid colour'd Rings there would often appear small
+Spots of Colours, ascending and descending up and down the sides of the
+Bubble, by reason of some Inequalities in the subsiding of the Water.
+And sometimes small black Spots generated at the sides would ascend up
+to the larger black Spot at the top of the Bubble, and unite with it.
+
+_Obs._ 18. Because the Colours of these Bubbles were more extended and
+lively than those of the Air thinn'd between two Glasses, and so more
+easy to be distinguish'd, I shall here give you a farther description of
+their order, as they were observ'd in viewing them by Reflexion of the
+Skies when of a white Colour, whilst a black substance was placed
+behind the Bubble. And they were these, red, blue; red, blue; red, blue;
+red, green; red, yellow, green, blue, purple; red, yellow, green, blue,
+violet; red, yellow, white, blue, black.
+
+The three first Successions of red and blue were very dilute and dirty,
+especially the first, where the red seem'd in a manner to be white.
+Among these there was scarce any other Colour sensible besides red and
+blue, only the blues (and principally the second blue) inclined a little
+to green.
+
+The fourth red was also dilute and dirty, but not so much as the former
+three; after that succeeded little or no yellow, but a copious green,
+which at first inclined a little to yellow, and then became a pretty
+brisk and good willow green, and afterwards changed to a bluish Colour;
+but there succeeded neither blue nor violet.
+
+The fifth red at first inclined very much to purple, and afterwards
+became more bright and brisk, but yet not very pure. This was succeeded
+with a very bright and intense yellow, which was but little in quantity,
+and soon chang'd to green: But that green was copious and something more
+pure, deep and lively, than the former green. After that follow'd an
+excellent blue of a bright Sky-colour, and then a purple, which was less
+in quantity than the blue, and much inclined to red.
+
+The sixth red was at first of a very fair and lively scarlet, and soon
+after of a brighter Colour, being very pure and brisk, and the best of
+all the reds. Then after a lively orange follow'd an intense bright and
+copious yellow, which was also the best of all the yellows, and this
+changed first to a greenish yellow, and then to a greenish blue; but the
+green between the yellow and the blue, was very little and dilute,
+seeming rather a greenish white than a green. The blue which succeeded
+became very good, and of a very bright Sky-colour, but yet something
+inferior to the former blue; and the violet was intense and deep with
+little or no redness in it. And less in quantity than the blue.
+
+In the last red appeared a tincture of scarlet next to violet, which
+soon changed to a brighter Colour, inclining to an orange; and the
+yellow which follow'd was at first pretty good and lively, but
+afterwards it grew more dilute until by degrees it ended in perfect
+whiteness. And this whiteness, if the Water was very tenacious and
+well-temper'd, would slowly spread and dilate it self over the greater
+part of the Bubble; continually growing paler at the top, where at
+length it would crack in many places, and those cracks, as they dilated,
+would appear of a pretty good, but yet obscure and dark Sky-colour; the
+white between the blue Spots diminishing, until it resembled the Threds
+of an irregular Net-work, and soon after vanish'd, and left all the
+upper part of the Bubble of the said dark blue Colour. And this Colour,
+after the aforesaid manner, dilated it self downwards, until sometimes
+it hath overspread the whole Bubble. In the mean while at the top, which
+was of a darker blue than the bottom, and appear'd also full of many
+round blue Spots, something darker than the rest, there would emerge
+one or more very black Spots, and within those, other Spots of an
+intenser blackness, which I mention'd in the former Observation; and
+these continually dilated themselves until the Bubble broke.
+
+If the Water was not very tenacious, the black Spots would break forth
+in the white, without any sensible intervention of the blue. And
+sometimes they would break forth within the precedent yellow, or red, or
+perhaps within the blue of the second order, before the intermediate
+Colours had time to display themselves.
+
+By this description you may perceive how great an affinity these Colours
+have with those of Air described in the fourth Observation, although set
+down in a contrary order, by reason that they begin to appear when the
+Bubble is thickest, and are most conveniently reckon'd from the lowest
+and thickest part of the Bubble upwards.
+
+_Obs._ 19. Viewing in several oblique Positions of my Eye the Rings of
+Colours emerging on the top of the Bubble, I found that they were
+sensibly dilated by increasing the obliquity, but yet not so much by far
+as those made by thinn'd Air in the seventh Observation. For there they
+were dilated so much as, when view'd most obliquely, to arrive at a part
+of the Plate more than twelve times thicker than that where they
+appear'd when viewed perpendicularly; whereas in this case the thickness
+of the Water, at which they arrived when viewed most obliquely, was to
+that thickness which exhibited them by perpendicular Rays, something
+less than as 8 to 5. By the best of my Observations it was between 15
+and 15-1/2 to 10; an increase about 24 times less than in the other
+case.
+
+Sometimes the Bubble would become of an uniform thickness all over,
+except at the top of it near the black Spot, as I knew, because it would
+exhibit the same appearance of Colours in all Positions of the Eye. And
+then the Colours which were seen at its apparent circumference by the
+obliquest Rays, would be different from those that were seen in other
+places, by Rays less oblique to it. And divers Spectators might see the
+same part of it of differing Colours, by viewing it at very differing
+Obliquities. Now observing how much the Colours at the same places of
+the Bubble, or at divers places of equal thickness, were varied by the
+several Obliquities of the Rays; by the assistance of the 4th, 14th,
+16th and 18th Observations, as they are hereafter explain'd, I collect
+the thickness of the Water requisite to exhibit any one and the same
+Colour, at several Obliquities, to be very nearly in the Proportion
+expressed in this Table.
+
+-----------------+------------------+----------------
+  Incidence on   | Refraction into  | Thickness of
+   the Water.    |    the Water.    |   the Water.
+-----------------+------------------+----------------
+   Deg.    Min.  |    Deg.    Min.  |
+                 |                  |
+    00     00    |     00     00    |    10
+                 |                  |
+    15     00    |     11     11    |    10-1/4
+                 |                  |
+    30     00    |     22      1    |    10-4/5
+                 |                  |
+    45     00    |     32      2    |    11-4/5
+                 |                  |
+    60     00    |     40     30    |    13
+                 |                  |
+    75     00    |     46     25    |    14-1/2
+                 |                  |
+    90     00    |     48     35    |    15-1/5
+-----------------+------------------+----------------
+
+In the two first Columns are express'd the Obliquities of the Rays to
+the Superficies of the Water, that is, their Angles of Incidence and
+Refraction. Where I suppose, that the Sines which measure them are in
+round Numbers, as 3 to 4, though probably the Dissolution of Soap in the
+Water, may a little alter its refractive Virtue. In the third Column,
+the Thickness of the Bubble, at which any one Colour is exhibited in
+those several Obliquities, is express'd in Parts, of which ten
+constitute its Thickness when the Rays are perpendicular. And the Rule
+found by the seventh Observation agrees well with these Measures, if
+duly apply'd; namely, that the Thickness of a Plate of Water requisite
+to exhibit one and the same Colour at several Obliquities of the Eye, is
+proportional to the Secant of an Angle, whose Sine is the first of an
+hundred and six arithmetical mean Proportionals between the Sines of
+Incidence and Refraction counted from the lesser Sine, that is, from the
+Sine of Refraction when the Refraction is made out of Air into Water,
+otherwise from the Sine of Incidence.
+
+I have sometimes observ'd, that the Colours which arise on polish'd
+Steel by heating it, or on Bell-metal, and some other metalline
+Substances, when melted and pour'd on the Ground, where they may cool in
+the open Air, have, like the Colours of Water-bubbles, been a little
+changed by viewing them at divers Obliquities, and particularly that a
+deep blue, or violet, when view'd very obliquely, hath been changed to a
+deep red. But the Changes of these Colours are not so great and
+sensible as of those made by Water. For the Scoria, or vitrified Part of
+the Metal, which most Metals when heated or melted do continually
+protrude, and send out to their Surface, and which by covering the
+Metals in form of a thin glassy Skin, causes these Colours, is much
+denser than Water; and I find that the Change made by the Obliquation of
+the Eye is least in Colours of the densest thin Substances.
+
+_Obs._ 20. As in the ninth Observation, so here, the Bubble, by
+transmitted Light, appear'd of a contrary Colour to that, which it
+exhibited by Reflexion. Thus when the Bubble being look'd on by the
+Light of the Clouds reflected from it, seemed red at its apparent
+Circumference, if the Clouds at the same time, or immediately after,
+were view'd through it, the Colour at its Circumference would be blue.
+And, on the contrary, when by reflected Light it appeared blue, it would
+appear red by transmitted Light.
+
+_Obs._ 21. By wetting very thin Plates of _Muscovy_ Glass, whose
+thinness made the like Colours appear, the Colours became more faint and
+languid, especially by wetting the Plates on that side opposite to the
+Eye: But I could not perceive any variation of their Species. So then
+the thickness of a Plate requisite to produce any Colour, depends only
+on the density of the Plate, and not on that of the ambient Medium. And
+hence, by the 10th and 16th Observations, may be known the thickness
+which Bubbles of Water, or Plates of _Muscovy_ Glass, or other
+Substances, have at any Colour produced by them.
+
+_Obs._ 22. A thin transparent Body, which is denser than its ambient
+Medium, exhibits more brisk and vivid Colours than that which is so much
+rarer; as I have particularly observed in the Air and Glass. For blowing
+Glass very thin at a Lamp Furnace, those Plates encompassed with Air did
+exhibit Colours much more vivid than those of Air made thin between two
+Glasses.
+
+_Obs._ 23. Comparing the quantity of Light reflected from the several
+Rings, I found that it was most copious from the first or inmost, and in
+the exterior Rings became gradually less and less. Also the whiteness of
+the first Ring was stronger than that reflected from those parts of the
+thin Medium or Plate which were without the Rings; as I could manifestly
+perceive by viewing at a distance the Rings made by the two
+Object-glasses; or by comparing two Bubbles of Water blown at distant
+Times, in the first of which the Whiteness appear'd, which succeeded all
+the Colours, and in the other, the Whiteness which preceded them all.
+
+_Obs._ 24. When the two Object-glasses were lay'd upon one another, so
+as to make the Rings of the Colours appear, though with my naked Eye I
+could not discern above eight or nine of those Rings, yet by viewing
+them through a Prism I have seen a far greater Multitude, insomuch that
+I could number more than forty, besides many others, that were so very
+small and close together, that I could not keep my Eye steady on them
+severally so as to number them, but by their Extent I have sometimes
+estimated them to be more than an hundred. And I believe the Experiment
+may be improved to the Discovery of far greater Numbers. For they seem
+to be really unlimited, though visible only so far as they can be
+separated by the Refraction of the Prism, as I shall hereafter explain.
+
+[Illustration: FIG. 5.]
+
+But it was but one side of these Rings, namely, that towards which the
+Refraction was made, which by that Refraction was render'd distinct, and
+the other side became more confused than when view'd by the naked Eye,
+insomuch that there I could not discern above one or two, and sometimes
+none of those Rings, of which I could discern eight or nine with my
+naked Eye. And their Segments or Arcs, which on the other side appear'd
+so numerous, for the most part exceeded not the third Part of a Circle.
+If the Refraction was very great, or the Prism very distant from the
+Object-glasses, the middle Part of those Arcs became also confused, so
+as to disappear and constitute an even Whiteness, whilst on either side
+their Ends, as also the whole Arcs farthest from the Center, became
+distincter than before, appearing in the Form as you see them design'd
+in the fifth Figure.
+
+The Arcs, where they seem'd distinctest, were only white and black
+successively, without any other Colours intermix'd. But in other Places
+there appeared Colours, whose Order was inverted by the refraction in
+such manner, that if I first held the Prism very near the
+Object-glasses, and then gradually removed it farther off towards my
+Eye, the Colours of the 2d, 3d, 4th, and following Rings, shrunk towards
+the white that emerged between them, until they wholly vanish'd into it
+at the middle of the Arcs, and afterwards emerged again in a contrary
+Order. But at the Ends of the Arcs they retain'd their Order unchanged.
+
+I have sometimes so lay'd one Object-glass upon the other, that to the
+naked Eye they have all over seem'd uniformly white, without the least
+Appearance of any of the colour'd Rings; and yet by viewing them through
+a Prism, great Multitudes of those Rings have discover'd themselves. And
+in like manner Plates of _Muscovy_ Glass, and Bubbles of Glass blown at
+a Lamp-Furnace, which were not so thin as to exhibit any Colours to the
+naked Eye, have through the Prism exhibited a great Variety of them
+ranged irregularly up and down in the Form of Waves. And so Bubbles of
+Water, before they began to exhibit their Colours to the naked Eye of a
+Bystander, have appeared through a Prism, girded about with many
+parallel and horizontal Rings; to produce which Effect, it was necessary
+to hold the Prism parallel, or very nearly parallel to the Horizon, and
+to dispose it so that the Rays might be refracted upwards.
+
+
+
+
+THE
+
+SECOND BOOK
+
+OF
+
+OPTICKS
+
+
+_PART II._
+
+_Remarks upon the foregoing Observations._
+
+
+Having given my Observations of these Colours, before I make use of them
+to unfold the Causes of the Colours of natural Bodies, it is convenient
+that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th,
+18th, 20th, and 24th, I first explain the more compounded. And first to
+shew how the Colours in the fourth and eighteenth Observations are
+produced, let there be taken in any Right Line from the Point Y, [in
+_Fig._ 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to
+one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16,
+3/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to
+sound all the Notes in an eighth are represented; that is, in the
+Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243,
+10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars
+A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent
+of the several Colours set underneath against them, is to be
+represented. Then divide the Line _A[Greek: a]_ in such Proportion as
+the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of
+Division denote. And through those Divisions from Y draw Lines 1I, 2K,
+3L, 5M, 6N, 7O, &c.
+
+Now, if A2 be supposed to represent the Thickness of any thin
+transparent Body, at which the outmost Violet is most copiously
+reflected in the first Ring, or Series of Colours, then by the 13th
+Observation, HK will represent its Thickness, at which the utmost Red is
+most copiously reflected in the same Series. Also by the 5th and 16th
+Observations, A6 and HN will denote the Thicknesses at which those
+extreme Colours are most copiously reflected in the second Series, and
+A10 and HQ the Thicknesses at which they are most copiously reflected in
+the third Series, and so on. And the Thickness at which any of the
+intermediate Colours are reflected most copiously, will, according to
+the 14th Observation, be defined by the distance of the Line AH from the
+intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names
+of those Colours are written below.
+
+[Illustration: FIG. 6.]
+
+But farther, to define the Latitude of these Colours in each Ring or
+Series, let A1 design the least thickness, and A3 the greatest
+thickness, at which the extreme violet in the first Series is reflected,
+and let HI, and HL, design the like limits for the extreme red, and let
+the intermediate Colours be limited by the intermediate parts of the
+Lines 1I, and 3L, against which the Names of those Colours are written,
+and so on: But yet with this caution, that the Reflexions be supposed
+strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence
+to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on
+either side; where you must not conceive them to be precisely limited,
+but to decay indefinitely. And whereas I have assign'd the same Latitude
+to every Series, I did it, because although the Colours in the first
+Series seem to be a little broader than the rest, by reason of a
+stronger Reflexion there, yet that inequality is so insensible as
+scarcely to be determin'd by Observation.
+
+Now according to this Description, conceiving that the Rays originally
+of several Colours are by turns reflected at the Spaces 1I, L3, 5M, O7,
+9PR11, &c. and transmitted at the Spaces AHI1, 3LM5, 7OP9, &c. it is
+easy to know what Colour must in the open Air be exhibited at any
+thickness of a transparent thin Body. For if a Ruler be applied parallel
+to AH, at that distance from it by which the thickness of the Body is
+represented, the alternate Spaces 1IL3, 5MO7, &c. which it crosseth will
+denote the reflected original Colours, of which the Colour exhibited in
+the open Air is compounded. Thus if the constitution of the green in the
+third Series of Colours be desired, apply the Ruler as you see at
+[Greek: prsph], and by its passing through some of the blue at [Greek:
+p] and yellow at [Greek: s], as well as through the green at [Greek: r],
+you may conclude that the green exhibited at that thickness of the Body
+is principally constituted of original green, but not without a mixture
+of some blue and yellow.
+
+By this means you may know how the Colours from the center of the Rings
+outward ought to succeed in order as they were described in the 4th and
+18th Observations. For if you move the Ruler gradually from AH through
+all distances, having pass'd over the first Space which denotes little
+or no Reflexion to be made by thinnest Substances, it will first arrive
+at 1 the violet, and then very quickly at the blue and green, which
+together with that violet compound blue, and then at the yellow and red,
+by whose farther addition that blue is converted into whiteness, which
+whiteness continues during the transit of the edge of the Ruler from I
+to 3, and after that by the successive deficience of its component
+Colours, turns first to compound yellow, and then to red, and last of
+all the red ceaseth at L. Then begin the Colours of the second Series,
+which succeed in order during the transit of the edge of the Ruler from
+5 to O, and are more lively than before, because more expanded and
+severed. And for the same reason instead of the former white there
+intercedes between the blue and yellow a mixture of orange, yellow,
+green, blue and indigo, all which together ought to exhibit a dilute and
+imperfect green. So the Colours of the third Series all succeed in
+order; first, the violet, which a little interferes with the red of the
+second order, and is thereby inclined to a reddish purple; then the blue
+and green, which are less mix'd with other Colours, and consequently
+more lively than before, especially the green: Then follows the yellow,
+some of which towards the green is distinct and good, but that part of
+it towards the succeeding red, as also that red is mix'd with the violet
+and blue of the fourth Series, whereby various degrees of red very much
+inclining to purple are compounded. This violet and blue, which should
+succeed this red, being mixed with, and hidden in it, there succeeds a
+green. And this at first is much inclined to blue, but soon becomes a
+good green, the only unmix'd and lively Colour in this fourth Series.
+For as it verges towards the yellow, it begins to interfere with the
+Colours of the fifth Series, by whose mixture the succeeding yellow and
+red are very much diluted and made dirty, especially the yellow, which
+being the weaker Colour is scarce able to shew it self. After this the
+several Series interfere more and more, and their Colours become more
+and more intermix'd, till after three or four more revolutions (in which
+the red and blue predominate by turns) all sorts of Colours are in all
+places pretty equally blended, and compound an even whiteness.
+
+And since by the 15th Observation the Rays endued with one Colour are
+transmitted, where those of another Colour are reflected, the reason of
+the Colours made by the transmitted Light in the 9th and 20th
+Observations is from hence evident.
+
+If not only the Order and Species of these Colours, but also the precise
+thickness of the Plate, or thin Body at which they are exhibited, be
+desired in parts of an Inch, that may be also obtained by assistance of
+the 6th or 16th Observations. For according to those Observations the
+thickness of the thinned Air, which between two Glasses exhibited the
+most luminous parts of the first six Rings were 1/178000, 3/178000,
+5/178000, 7/178000, 9/178000, 11/178000 parts of an Inch. Suppose the
+Light reflected most copiously at these thicknesses be the bright
+citrine yellow, or confine of yellow and orange, and these thicknesses
+will be F[Greek: l], F[Greek: m], F[Greek: u], F[Greek: x], F[Greek: o],
+F[Greek: t]. And this being known, it is easy to determine what
+thickness of Air is represented by G[Greek: ph], or by any other
+distance of the Ruler from AH.
+
+But farther, since by the 10th Observation the thickness of Air was to
+the thickness of Water, which between the same Glasses exhibited the
+same Colour, as 4 to 3, and by the 21st Observation the Colours of thin
+Bodies are not varied by varying the ambient Medium; the thickness of a
+Bubble of Water, exhibiting any Colour, will be 3/4 of the thickness of
+Air producing the same Colour. And so according to the same 10th and
+21st Observations, the thickness of a Plate of Glass, whose Refraction
+of the mean refrangible Ray, is measured by the proportion of the Sines
+31 to 20, may be 20/31 of the thickness of Air producing the same
+Colours; and the like of other Mediums. I do not affirm, that this
+proportion of 20 to 31, holds in all the Rays; for the Sines of other
+sorts of Rays have other Proportions. But the differences of those
+Proportions are so little that I do not here consider them. On these
+Grounds I have composed the following Table, wherein the thickness of
+Air, Water, and Glass, at which each Colour is most intense and
+specifick, is expressed in parts of an Inch divided into ten hundred
+thousand equal parts.
+
+Now if this Table be compared with the 6th Scheme, you will there see
+the constitution of each Colour, as to its Ingredients, or the original
+Colours of which it is compounded, and thence be enabled to judge of its
+Intenseness or Imperfection; which may suffice in explication of the 4th
+and 18th Observations, unless it be farther desired to delineate the
+manner how the Colours appear, when the two Object-glasses are laid upon
+one another. To do which, let there be described a large Arc of a
+Circle, and a streight Line which may touch that Arc, and parallel to
+that Tangent several occult Lines, at such distances from it, as the
+Numbers set against the several Colours in the Table denote. For the
+Arc, and its Tangent, will represent the Superficies of the Glasses
+terminating the interjacent Air; and the places where the occult Lines
+cut the Arc will show at what distances from the center, or Point of
+contact, each Colour is reflected.
+
+_The thickness of colour'd Plates and Particles of_
+                                          _____________|_______________
+                                         /                             \
+                                            Air.      Water.     Glass.
+                                        |---------+----------+----------+
+                       {Very black      |    1/2  |    3/8   |  10/31   |
+                       {Black           |  1      |    3/4   |  20/31   |
+                       {Beginning of    |         |          |          |
+                       {  Black         |  2      |  1-1/2   |  1-2/7   |
+Their Colours of the   {Blue            |  2-2/5  |  1-4/5   |  1-11/22 |
+first Order,           {White           |  5-1/4  |  3-7/8   |  3-2/5   |
+                       {Yellow          |  7-1/9  |  5-1/3   |  4-3/5   |
+                       {Orange          |  8      |  6       |  5-1/6   |
+                       {Red             |  9      |  6-3/4   |  5-4/5   |
+                                        |---------+----------+----------|
+                       {Violet          | 11-1/6  |  8-3/8   |  7-1/5   |
+                       {Indigo          | 12-5/6  |  9-5/8   |  8-2/11  |
+                       {Blue            | 14      |  10-1/2  |  9       |
+                       {Green           | 15-1/8  | 11-2/3   |  9-5/7   |
+Of the second order,   {Yellow          | 16-2/7  | 12-1/5   | 10-2/5   |
+                       {Orange          | 17-2/9  | 13       | 11-1/9   |
+                       {Bright red      | 18-1/3  | 13-3/4   | 11-5/6   |
+                       {Scarlet         | 19-2/3  | 14-3/4   | 12-2/3   |
+                                        |---------+----------+----------|
+                       {Purple          | 21      | 15-3/4   | 13-11/20 |
+                       {Indigo          | 22-1/10 | 16-4/7   | 14-1/4   |
+                       {Blue            | 23-2/5  | 17-11/20 | 15-1/10  |
+Of the third Order,    {Green           | 25-1/5  | 18-9/10  | 16-1/4   |
+                       {Yellow          | 27-1/7  | 20-1/3   | 17-1/2   |
+                       {Red             | 29      | 21-3/4   | 18-5/7   |
+                       {Bluish red      | 32      | 24       | 20-2/3   |
+                                        |---------+----------+----------|
+                       {Bluish green    | 34      | 25-1/2   | 22       |
+                       {Green           | 35-2/7  | 26-1/2   | 22-3/4   |
+Of the fourth Order,   {Yellowish green | 36      | 27       | 23-2/9   |
+                       {Red             | 40-1/3  | 30-1/4   | 26       |
+                                        |---------+----------+----------|
+                       {Greenish blue   | 46      | 34-1/2   | 29-2/3   |
+Of the fifth Order,    {Red             | 52-1/2  | 39-3/8   | 34       |
+                                        |---------+----------+----------|
+                       {Greenish blue   | 58-3/4  | 44       | 38       |
+Of the sixth Order,    {Red             | 65      | 48-3/4   | 42       |
+                                        |---------+----------+----------|
+Of the seventh Order,  {Greenish blue   | 71      | 53-1/4   | 45-4/5   |
+                       {Ruddy White     | 77      | 57-3/4   | 49-2/3   |
+                                        |---------+----------+----------|
+
+There are also other Uses of this Table: For by its assistance the
+thickness of the Bubble in the 19th Observation was determin'd by the
+Colours which it exhibited. And so the bigness of the parts of natural
+Bodies may be conjectured by their Colours, as shall be hereafter shewn.
+Also, if two or more very thin Plates be laid one upon another, so as to
+compose one Plate equalling them all in thickness, the resulting Colour
+may be hereby determin'd. For instance, Mr. _Hook_ observed, as is
+mentioned in his _Micrographia_, that a faint yellow Plate of _Muscovy_
+Glass laid upon a blue one, constituted a very deep purple. The yellow
+of the first Order is a faint one, and the thickness of the Plate
+exhibiting it, according to the Table is 4-3/5, to which add 9, the
+thickness exhibiting blue of the second Order, and the Sum will be
+13-3/5, which is the thickness exhibiting the purple of the third Order.
+
+To explain, in the next place, the circumstances of the 2d and 3d
+Observations; that is, how the Rings of the Colours may (by turning the
+Prisms about their common Axis the contrary way to that expressed in
+those Observations) be converted into white and black Rings, and
+afterwards into Rings of Colours again, the Colours of each Ring lying
+now in an inverted order; it must be remember'd, that those Rings of
+Colours are dilated by the obliquation of the Rays to the Air which
+intercedes the Glasses, and that according to the Table in the 7th
+Observation, their Dilatation or Increase of their Diameter is most
+manifest and speedy when they are obliquest. Now the Rays of yellow
+being more refracted by the first Superficies of the said Air than those
+of red, are thereby made more oblique to the second Superficies, at
+which they are reflected to produce the colour'd Rings, and consequently
+the yellow Circle in each Ring will be more dilated than the red; and
+the Excess of its Dilatation will be so much the greater, by how much
+the greater is the obliquity of the Rays, until at last it become of
+equal extent with the red of the same Ring. And for the same reason the
+green, blue and violet, will be also so much dilated by the still
+greater obliquity of their Rays, as to become all very nearly of equal
+extent with the red, that is, equally distant from the center of the
+Rings. And then all the Colours of the same Ring must be co-incident,
+and by their mixture exhibit a white Ring. And these white Rings must
+have black and dark Rings between them, because they do not spread and
+interfere with one another, as before. And for that reason also they
+must become distincter, and visible to far greater numbers. But yet the
+violet being obliquest will be something more dilated, in proportion to
+its extent, than the other Colours, and so very apt to appear at the
+exterior Verges of the white.
+
+Afterwards, by a greater obliquity of the Rays, the violet and blue
+become more sensibly dilated than the red and yellow, and so being
+farther removed from the center of the Rings, the Colours must emerge
+out of the white in an order contrary to that which they had before; the
+violet and blue at the exterior Limbs of each Ring, and the red and
+yellow at the interior. And the violet, by reason of the greatest
+obliquity of its Rays, being in proportion most of all expanded, will
+soonest appear at the exterior Limb of each white Ring, and become more
+conspicuous than the rest. And the several Series of Colours belonging
+to the several Rings, will, by their unfolding and spreading, begin
+again to interfere, and thereby render the Rings less distinct, and not
+visible to so great numbers.
+
+If instead of the Prisms the Object-glasses be made use of, the Rings
+which they exhibit become not white and distinct by the obliquity of the
+Eye, by reason that the Rays in their passage through that Air which
+intercedes the Glasses are very nearly parallel to those Lines in which
+they were first incident on the Glasses, and consequently the Rays
+endued with several Colours are not inclined one more than another to
+that Air, as it happens in the Prisms.
+
+There is yet another circumstance of these Experiments to be consider'd,
+and that is why the black and white Rings which when view'd at a
+distance appear distinct, should not only become confused by viewing
+them near at hand, but also yield a violet Colour at both the edges of
+every white Ring. And the reason is, that the Rays which enter the Eye
+at several parts of the Pupil, have several Obliquities to the Glasses,
+and those which are most oblique, if consider'd apart, would represent
+the Rings bigger than those which are the least oblique. Whence the
+breadth of the Perimeter of every white Ring is expanded outwards by the
+obliquest Rays, and inwards by the least oblique. And this Expansion is
+so much the greater by how much the greater is the difference of the
+Obliquity; that is, by how much the Pupil is wider, or the Eye nearer to
+the Glasses. And the breadth of the violet must be most expanded,
+because the Rays apt to excite a Sensation of that Colour are most
+oblique to a second or farther Superficies of the thinn'd Air at which
+they are reflected, and have also the greatest variation of Obliquity,
+which makes that Colour soonest emerge out of the edges of the white.
+And as the breadth of every Ring is thus augmented, the dark Intervals
+must be diminish'd, until the neighbouring Rings become continuous, and
+are blended, the exterior first, and then those nearer the center; so
+that they can no longer be distinguish'd apart, but seem to constitute
+an even and uniform whiteness.
+
+Among all the Observations there is none accompanied with so odd
+circumstances as the twenty-fourth. Of those the principal are, that in
+thin Plates, which to the naked Eye seem of an even and uniform
+transparent whiteness, without any terminations of Shadows, the
+Refraction of a Prism should make Rings of Colours appear, whereas it
+usually makes Objects appear colour'd only there where they are
+terminated with Shadows, or have parts unequally luminous; and that it
+should make those Rings exceedingly distinct and white, although it
+usually renders Objects confused and coloured. The Cause of these things
+you will understand by considering, that all the Rings of Colours are
+really in the Plate, when view'd with the naked Eye, although by reason
+of the great breadth of their Circumferences they so much interfere and
+are blended together, that they seem to constitute an uniform whiteness.
+But when the Rays pass through the Prism to the Eye, the Orbits of the
+several Colours in every Ring are refracted, some more than others,
+according to their degrees of Refrangibility: By which means the Colours
+on one side of the Ring (that is in the circumference on one side of its
+center), become more unfolded and dilated, and those on the other side
+more complicated and contracted. And where by a due Refraction they are
+so much contracted, that the several Rings become narrower than to
+interfere with one another, they must appear distinct, and also white,
+if the constituent Colours be so much contracted as to be wholly
+co-incident. But on the other side, where the Orbit of every Ring is
+made broader by the farther unfolding of its Colours, it must interfere
+more with other Rings than before, and so become less distinct.
+
+[Illustration: FIG. 7.]
+
+To explain this a little farther, suppose the concentrick Circles AV,
+and BX, [in _Fig._ 7.] represent the red and violet of any Order, which,
+together with the intermediate Colours, constitute any one of these
+Rings. Now these being view'd through a Prism, the violet Circle BX,
+will, by a greater Refraction, be farther translated from its place than
+the red AV, and so approach nearer to it on that side of the Circles,
+towards which the Refractions are made. For instance, if the red be
+translated to _av_, the violet may be translated to _bx_, so as to
+approach nearer to it at _x_ than before; and if the red be farther
+translated to av, the violet may be so much farther translated to bx as
+to convene with it at x; and if the red be yet farther translated to
+[Greek: aY], the violet may be still so much farther translated to
+[Greek: bx] as to pass beyond it at [Greek: x], and convene with it at
+_e_ and _f_. And this being understood not only of the red and violet,
+but of all the other intermediate Colours, and also of every revolution
+of those Colours, you will easily perceive how those of the same
+revolution or order, by their nearness at _xv_ and [Greek: Yx], and
+their coincidence at xv, _e_ and _f_, ought to constitute pretty
+distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that
+they will appear severally at _x_[Greek: u] and at xv exhibit whiteness
+by their coincidence, and again appear severally at [Greek: Yx], but yet
+in a contrary order to that which they had before, and still retain
+beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab],
+these Colours must become much more confused by being dilated and spread
+so as to interfere with those of other Orders. And the same confusion
+will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be
+very great, or the Prism very distant from the Object-glasses: In which
+case no parts of the Rings will be seen, save only two little Arcs at
+_e_ and _f_, whose distance from one another will be augmented by
+removing the Prism still farther from the Object-glasses: And these
+little Arcs must be distinctest and whitest at their middle, and at
+their ends, where they begin to grow confused, they must be colour'd.
+And the Colours at one end of every Arc must be in a contrary order to
+those at the other end, by reason that they cross in the intermediate
+white; namely, their ends, which verge towards [Greek: Ux], will be red
+and yellow on that side next the center, and blue and violet on the
+other side. But their other ends which verge from [Greek: Ux], will on
+the contrary be blue and violet on that side towards the center, and on
+the other side red and yellow.
+
+Now as all these things follow from the properties of Light by a
+mathematical way of reasoning, so the truth of them may be manifested by
+Experiments. For in a dark Room, by viewing these Rings through a Prism,
+by reflexion of the several prismatick Colours, which an assistant
+causes to move to and fro upon a Wall or Paper from whence they are
+reflected, whilst the Spectator's Eye, the Prism, and the
+Object-glasses, (as in the 13th Observation,) are placed steady; the
+Position of the Circles made successively by the several Colours, will
+be found such, in respect of one another, as I have described in the
+Figures _abxv_, or abxv, or _[Greek: abxU]_. And by the same method the
+truth of the Explications of other Observations may be examined.
+
+By what hath been said, the like Phænomena of Water and thin Plates of
+Glass may be understood. But in small fragments of those Plates there is
+this farther observable, that where they lie flat upon a Table, and are
+turned about their centers whilst they are view'd through a Prism, they
+will in some postures exhibit Waves of various Colours; and some of them
+exhibit these Waves in one or two Positions only, but the most of them
+do in all Positions exhibit them, and make them for the most part appear
+almost all over the Plates. The reason is, that the Superficies of such
+Plates are not even, but have many Cavities and Swellings, which, how
+shallow soever, do a little vary the thickness of the Plate. For at the
+several sides of those Cavities, for the Reasons newly described, there
+ought to be produced Waves in several postures of the Prism. Now though
+it be but some very small and narrower parts of the Glass, by which
+these Waves for the most part are caused, yet they may seem to extend
+themselves over the whole Glass, because from the narrowest of those
+parts there are Colours of several Orders, that is, of several Rings,
+confusedly reflected, which by Refraction of the Prism are unfolded,
+separated, and, according to their degrees of Refraction, dispersed to
+several places, so as to constitute so many several Waves, as there were
+divers orders of Colours promiscuously reflected from that part of the
+Glass.
+
+These are the principal Phænomena of thin Plates or Bubbles, whose
+Explications depend on the properties of Light, which I have heretofore
+deliver'd. And these you see do necessarily follow from them, and agree
+with them, even to their very least circumstances; and not only so, but
+do very much tend to their proof. Thus, by the 24th Observation it
+appears, that the Rays of several Colours, made as well by thin Plates
+or Bubbles, as by Refractions of a Prism, have several degrees of
+Refrangibility; whereby those of each order, which at the reflexion from
+the Plate or Bubble are intermix'd with those of other orders, are
+separated from them by Refraction, and associated together so as to
+become visible by themselves like Arcs of Circles. For if the Rays were
+all alike refrangible, 'tis impossible that the whiteness, which to the
+naked Sense appears uniform, should by Refraction have its parts
+transposed and ranged into those black and white Arcs.
+
+It appears also that the unequal Refractions of difform Rays proceed not
+from any contingent irregularities; such as are Veins, an uneven Polish,
+or fortuitous Position of the Pores of Glass; unequal and casual Motions
+in the Air or Æther, the spreading, breaking, or dividing the same Ray
+into many diverging parts; or the like. For, admitting any such
+irregularities, it would be impossible for Refractions to render those
+Rings so very distinct, and well defined, as they do in the 24th
+Observation. It is necessary therefore that every Ray have its proper
+and constant degree of Refrangibility connate with it, according to
+which its refraction is ever justly and regularly perform'd; and that
+several Rays have several of those degrees.
+
+And what is said of their Refrangibility may be also understood of their
+Reflexibility, that is, of their Dispositions to be reflected, some at a
+greater, and others at a less thickness of thin Plates or Bubbles;
+namely, that those Dispositions are also connate with the Rays, and
+immutable; as may appear by the 13th, 14th, and 15th Observations,
+compared with the fourth and eighteenth.
+
+By the Precedent Observations it appears also, that whiteness is a
+dissimilar mixture of all Colours, and that Light is a mixture of Rays
+endued with all those Colours. For, considering the multitude of the
+Rings of Colours in the 3d, 12th, and 24th Observations, it is manifest,
+that although in the 4th and 18th Observations there appear no more than
+eight or nine of those Rings, yet there are really a far greater number,
+which so much interfere and mingle with one another, as after those
+eight or nine revolutions to dilute one another wholly, and constitute
+an even and sensibly uniform whiteness. And consequently that whiteness
+must be allow'd a mixture of all Colours, and the Light which conveys it
+to the Eye must be a mixture of Rays endued with all those Colours.
+
+But farther; by the 24th Observation it appears, that there is a
+constant relation between Colours and Refrangibility; the most
+refrangible Rays being violet, the least refrangible red, and those of
+intermediate Colours having proportionably intermediate degrees of
+Refrangibility. And by the 13th, 14th, and 15th Observations, compared
+with the 4th or 18th there appears to be the same constant relation
+between Colour and Reflexibility; the violet being in like circumstances
+reflected at least thicknesses of any thin Plate or Bubble, the red at
+greatest thicknesses, and the intermediate Colours at intermediate
+thicknesses. Whence it follows, that the colorifick Dispositions of
+Rays are also connate with them, and immutable; and by consequence, that
+all the Productions and Appearances of Colours in the World are derived,
+not from any physical Change caused in Light by Refraction or Reflexion,
+but only from the various Mixtures or Separations of Rays, by virtue of
+their different Refrangibility or Reflexibility. And in this respect the
+Science of Colours becomes a Speculation as truly mathematical as any
+other part of Opticks. I mean, so far as they depend on the Nature of
+Light, and are not produced or alter'd by the Power of Imagination, or
+by striking or pressing the Eye.
+
+
+
+
+THE
+
+SECOND BOOK
+
+OF
+
+OPTICKS
+
+
+_PART III._
+
+_Of the permanent Colours of natural Bodies, and the Analogy between
+them and the Colours of thin transparent Plates._
+
+I am now come to another part of this Design, which is to consider how
+the Phænomena of thin transparent Plates stand related to those of all
+other natural Bodies. Of these Bodies I have already told you that they
+appear of divers Colours, accordingly as they are disposed to reflect
+most copiously the Rays originally endued with those Colours. But their
+Constitutions, whereby they reflect some Rays more copiously than
+others, remain to be discover'd; and these I shall endeavour to manifest
+in the following Propositions.
+
+
+PROP. I.
+
+_Those Superficies of transparent Bodies reflect the greatest quantity
+of Light, which have the greatest refracting Power; that is, which
+intercede Mediums that differ most in their refractive Densities. And in
+the Confines of equally refracting Mediums there is no Reflexion._
+
+The Analogy between Reflexion and Refraction will appear by considering,
+that when Light passeth obliquely out of one Medium into another which
+refracts from the perpendicular, the greater is the difference of their
+refractive Density, the less Obliquity of Incidence is requisite to
+cause a total Reflexion. For as the Sines are which measure the
+Refraction, so is the Sine of Incidence at which the total Reflexion
+begins, to the Radius of the Circle; and consequently that Angle of
+Incidence is least where there is the greatest difference of the Sines.
+Thus in the passing of Light out of Water into Air, where the Refraction
+is measured by the Ratio of the Sines 3 to 4, the total Reflexion begins
+when the Angle of Incidence is about 48 Degrees 35 Minutes. In passing
+out of Glass into Air, where the Refraction is measured by the Ratio of
+the Sines 20 to 31, the total Reflexion begins when the Angle of
+Incidence is 40 Degrees 10 Minutes; and so in passing out of Crystal, or
+more strongly refracting Mediums into Air, there is still a less
+obliquity requisite to cause a total reflexion. Superficies therefore
+which refract most do soonest reflect all the Light which is incident on
+them, and so must be allowed most strongly reflexive.
+
+But the truth of this Proposition will farther appear by observing, that
+in the Superficies interceding two transparent Mediums, (such as are
+Air, Water, Oil, common Glass, Crystal, metalline Glasses, Island
+Glasses, white transparent Arsenick, Diamonds, &c.) the Reflexion is
+stronger or weaker accordingly, as the Superficies hath a greater or
+less refracting Power. For in the Confine of Air and Sal-gem 'tis
+stronger than in the Confine of Air and Water, and still stronger in the
+Confine of Air and common Glass or Crystal, and stronger in the Confine
+of Air and a Diamond. If any of these, and such like transparent Solids,
+be immerged in Water, its Reflexion becomes, much weaker than before;
+and still weaker if they be immerged in the more strongly refracting
+Liquors of well rectified Oil of Vitriol or Spirit of Turpentine. If
+Water be distinguish'd into two parts by any imaginary Surface, the
+Reflexion in the Confine of those two parts is none at all. In the
+Confine of Water and Ice 'tis very little; in that of Water and Oil 'tis
+something greater; in that of Water and Sal-gem still greater; and in
+that of Water and Glass, or Crystal or other denser Substances still
+greater, accordingly as those Mediums differ more or less in their
+refracting Powers. Hence in the Confine of common Glass and Crystal,
+there ought to be a weak Reflexion, and a stronger Reflexion in the
+Confine of common and metalline Glass; though I have not yet tried
+this. But in the Confine of two Glasses of equal density, there is not
+any sensible Reflexion; as was shewn in the first Observation. And the
+same may be understood of the Superficies interceding two Crystals, or
+two Liquors, or any other Substances in which no Refraction is caused.
+So then the reason why uniform pellucid Mediums (such as Water, Glass,
+or Crystal,) have no sensible Reflexion but in their external
+Superficies, where they are adjacent to other Mediums of a different
+density, is because all their contiguous parts have one and the same
+degree of density.
+
+
+PROP. II.
+
+_The least parts of almost all natural Bodies are in some measure
+transparent: And the Opacity of those Bodies ariseth from the multitude
+of Reflexions caused in their internal Parts._
+
+That this is so has been observed by others, and will easily be granted
+by them that have been conversant with Microscopes. And it may be also
+tried by applying any substance to a hole through which some Light is
+immitted into a dark Room. For how opake soever that Substance may seem
+in the open Air, it will by that means appear very manifestly
+transparent, if it be of a sufficient thinness. Only white metalline
+Bodies must be excepted, which by reason of their excessive density seem
+to reflect almost all the Light incident on their first Superficies;
+unless by solution in Menstruums they be reduced into very small
+Particles, and then they become transparent.
+
+
+PROP. III.
+
+_Between the parts of opake and colour'd Bodies are many Spaces, either
+empty, or replenish'd with Mediums of other Densities; as Water between
+the tinging Corpuscles wherewith any Liquor is impregnated, Air between
+the aqueous Globules that constitute Clouds or Mists; and for the most
+part Spaces void of both Air and Water, but yet perhaps not wholly void
+of all Substance, between the parts of hard Bodies._
+
+The truth of this is evinced by the two precedent Propositions: For by
+the second Proposition there are many Reflexions made by the internal
+parts of Bodies, which, by the first Proposition, would not happen if
+the parts of those Bodies were continued without any such Interstices
+between them; because Reflexions are caused only in Superficies, which
+intercede Mediums of a differing density, by _Prop._ 1.
+
+But farther, that this discontinuity of parts is the principal Cause of
+the opacity of Bodies, will appear by considering, that opake Substances
+become transparent by filling their Pores with any Substance of equal or
+almost equal density with their parts. Thus Paper dipped in Water or
+Oil, the _Oculus Mundi_ Stone steep'd in Water, Linnen Cloth oiled or
+varnish'd, and many other Substances soaked in such Liquors as will
+intimately pervade their little Pores, become by that means more
+transparent than otherwise; so, on the contrary, the most transparent
+Substances, may, by evacuating their Pores, or separating their parts,
+be render'd sufficiently opake; as Salts or wet Paper, or the _Oculus
+Mundi_ Stone by being dried, Horn by being scraped, Glass by being
+reduced to Powder, or otherwise flawed; Turpentine by being stirred
+about with Water till they mix imperfectly, and Water by being form'd
+into many small Bubbles, either alone in the form of Froth, or by
+shaking it together with Oil of Turpentine, or Oil Olive, or with some
+other convenient Liquor, with which it will not perfectly incorporate.
+And to the increase of the opacity of these Bodies, it conduces
+something, that by the 23d Observation the Reflexions of very thin
+transparent Substances are considerably stronger than those made by the
+same Substances of a greater thickness.
+
+
+PROP. IV.
+
+_The Parts of Bodies and their Interstices must not be less than of some
+definite bigness, to render them opake and colour'd._
+
+For the opakest Bodies, if their parts be subtilly divided, (as Metals,
+by being dissolved in acid Menstruums, &c.) become perfectly
+transparent. And you may also remember, that in the eighth Observation
+there was no sensible reflexion at the Superficies of the
+Object-glasses, where they were very near one another, though they did
+not absolutely touch. And in the 17th Observation the Reflexion of the
+Water-bubble where it became thinnest was almost insensible, so as to
+cause very black Spots to appear on the top of the Bubble, by the want
+of reflected Light.
+
+On these grounds I perceive it is that Water, Salt, Glass, Stones, and
+such like Substances, are transparent. For, upon divers Considerations,
+they seem to be as full of Pores or Interstices between their parts as
+other Bodies are, but yet their Parts and Interstices to be too small to
+cause Reflexions in their common Surfaces.
+
+
+PROP. V.
+
+_The transparent parts of Bodies, according to their several sizes,
+reflect Rays of one Colour, and transmit those of another, on the same
+grounds that thin Plates or Bubbles do reflect or transmit those Rays.
+And this I take to be the ground of all their Colours._
+
+For if a thinn'd or plated Body, which being of an even thickness,
+appears all over of one uniform Colour, should be slit into Threads, or
+broken into Fragments, of the same thickness with the Plate; I see no
+reason why every Thread or Fragment should not keep its Colour, and by
+consequence why a heap of those Threads or Fragments should not
+constitute a Mass or Powder of the same Colour, which the Plate
+exhibited before it was broken. And the parts of all natural Bodies
+being like so many Fragments of a Plate, must on the same grounds
+exhibit the same Colours.
+
+Now, that they do so will appear by the affinity of their Properties.
+The finely colour'd Feathers of some Birds, and particularly those of
+Peacocks Tails, do, in the very same part of the Feather, appear of
+several Colours in several Positions of the Eye, after the very same
+manner that thin Plates were found to do in the 7th and 19th
+Observations, and therefore their Colours arise from the thinness of the
+transparent parts of the Feathers; that is, from the slenderness of the
+very fine Hairs, or _Capillamenta_, which grow out of the sides of the
+grosser lateral Branches or Fibres of those Feathers. And to the same
+purpose it is, that the Webs of some Spiders, by being spun very fine,
+have appeared colour'd, as some have observ'd, and that the colour'd
+Fibres of some Silks, by varying the Position of the Eye, do vary their
+Colour. Also the Colours of Silks, Cloths, and other Substances, which
+Water or Oil can intimately penetrate, become more faint and obscure by
+being immerged in those Liquors, and recover their Vigor again by being
+dried; much after the manner declared of thin Bodies in the 10th and
+21st Observations. Leaf-Gold, some sorts of painted Glass, the Infusion
+of _Lignum Nephriticum_, and some other Substances, reflect one Colour,
+and transmit another; like thin Bodies in the 9th and 20th Observations.
+And some of those colour'd Powders which Painters use, may have their
+Colours a little changed, by being very elaborately and finely ground.
+Where I see not what can be justly pretended for those changes, besides
+the breaking of their parts into less parts by that contrition, after
+the same manner that the Colour of a thin Plate is changed by varying
+its thickness. For which reason also it is that the colour'd Flowers of
+Plants and Vegetables, by being bruised, usually become more transparent
+than before, or at least in some degree or other change their Colours.
+Nor is it much less to my purpose, that, by mixing divers Liquors, very
+odd and remarkable Productions and Changes of Colours may be effected,
+of which no cause can be more obvious and rational than that the saline
+Corpuscles of one Liquor do variously act upon or unite with the tinging
+Corpuscles of another, so as to make them swell, or shrink, (whereby not
+only their bulk but their density also may be changed,) or to divide
+them into smaller Corpuscles, (whereby a colour'd Liquor may become
+transparent,) or to make many of them associate into one cluster,
+whereby two transparent Liquors may compose a colour'd one. For we see
+how apt those saline Menstruums are to penetrate and dissolve Substances
+to which they are applied, and some of them to precipitate what others
+dissolve. In like manner, if we consider the various Phænomena of the
+Atmosphere, we may observe, that when Vapours are first raised, they
+hinder not the transparency of the Air, being divided into parts too
+small to cause any Reflexion in their Superficies. But when in order to
+compose drops of Rain they begin to coalesce and constitute Globules of
+all intermediate sizes, those Globules, when they become of convenient
+size to reflect some Colours and transmit others, may constitute Clouds
+of various Colours according to their sizes. And I see not what can be
+rationally conceived in so transparent a Substance as Water for the
+production of these Colours, besides the various sizes of its fluid and
+globular Parcels.
+
+
+PROP. VI.
+
+_The parts of Bodies on which their Colours depend, are denser than the
+Medium which pervades their Interstices._
+
+This will appear by considering, that the Colour of a Body depends not
+only on the Rays which are incident perpendicularly on its parts, but on
+those also which are incident at all other Angles. And that according to
+the 7th Observation, a very little variation of obliquity will change
+the reflected Colour, where the thin Body or small Particles is rarer
+than the ambient Medium, insomuch that such a small Particle will at
+diversly oblique Incidences reflect all sorts of Colours, in so great a
+variety that the Colour resulting from them all, confusedly reflected
+from a heap of such Particles, must rather be a white or grey than any
+other Colour, or at best it must be but a very imperfect and dirty
+Colour. Whereas if the thin Body or small Particle be much denser than
+the ambient Medium, the Colours, according to the 19th Observation, are
+so little changed by the variation of obliquity, that the Rays which
+are reflected least obliquely may predominate over the rest, so much as
+to cause a heap of such Particles to appear very intensely of their
+Colour.
+
+It conduces also something to the confirmation of this Proposition,
+that, according to the 22d Observation, the Colours exhibited by the
+denser thin Body within the rarer, are more brisk than those exhibited
+by the rarer within the denser.
+
+
+PROP. VII.
+
+_The bigness of the component parts of natural Bodies may be conjectured
+by their Colours._
+
+For since the parts of these Bodies, by _Prop._ 5. do most probably
+exhibit the same Colours with a Plate of equal thickness, provided they
+have the same refractive density; and since their parts seem for the
+most part to have much the same density with Water or Glass, as by many
+circumstances is obvious to collect; to determine the sizes of those
+parts, you need only have recourse to the precedent Tables, in which the
+thickness of Water or Glass exhibiting any Colour is expressed. Thus if
+it be desired to know the diameter of a Corpuscle, which being of equal
+density with Glass shall reflect green of the third Order; the Number
+16-1/4 shews it to be (16-1/4)/10000 parts of an Inch.
+
+The greatest difficulty is here to know of what Order the Colour of any
+Body is. And for this end we must have recourse to the 4th and 18th
+Observations; from whence may be collected these particulars.
+
+_Scarlets_, and other _reds_, _oranges_, and _yellows_, if they be pure
+and intense, are most probably of the second order. Those of the first
+and third order also may be pretty good; only the yellow of the first
+order is faint, and the orange and red of the third Order have a great
+Mixture of violet and blue.
+
+There may be good _Greens_ of the fourth Order, but the purest are of
+the third. And of this Order the green of all Vegetables seems to be,
+partly by reason of the Intenseness of their Colours, and partly because
+when they wither some of them turn to a greenish yellow, and others to a
+more perfect yellow or orange, or perhaps to red, passing first through
+all the aforesaid intermediate Colours. Which Changes seem to be
+effected by the exhaling of the Moisture which may leave the tinging
+Corpuscles more dense, and something augmented by the Accretion of the
+oily and earthy Part of that Moisture. Now the green, without doubt, is
+of the same Order with those Colours into which it changeth, because the
+Changes are gradual, and those Colours, though usually not very full,
+yet are often too full and lively to be of the fourth Order.
+
+_Blues_ and _Purples_ may be either of the second or third Order, but
+the best are of the third. Thus the Colour of Violets seems to be of
+that Order, because their Syrup by acid Liquors turns red, and by
+urinous and alcalizate turns green. For since it is of the Nature of
+Acids to dissolve or attenuate, and of Alcalies to precipitate or
+incrassate, if the Purple Colour of the Syrup was of the second Order,
+an acid Liquor by attenuating its tinging Corpuscles would change it to
+a red of the first Order, and an Alcali by incrassating them would
+change it to a green of the second Order; which red and green,
+especially the green, seem too imperfect to be the Colours produced by
+these Changes. But if the said Purple be supposed of the third Order,
+its Change to red of the second, and green of the third, may without any
+Inconvenience be allow'd.
+
+If there be found any Body of a deeper and less reddish Purple than that
+of the Violets, its Colour most probably is of the second Order. But yet
+there being no Body commonly known whose Colour is constantly more deep
+than theirs, I have made use of their Name to denote the deepest and
+least reddish Purples, such as manifestly transcend their Colour in
+purity.
+
+The _blue_ of the first Order, though very faint and little, may
+possibly be the Colour of some Substances; and particularly the azure
+Colour of the Skies seems to be of this Order. For all Vapours when they
+begin to condense and coalesce into small Parcels, become first of that
+Bigness, whereby such an Azure must be reflected before they can
+constitute Clouds of other Colours. And so this being the first Colour
+which Vapours begin to reflect, it ought to be the Colour of the finest
+and most transparent Skies, in which Vapours are not arrived to that
+Grossness requisite to reflect other Colours, as we find it is by
+Experience.
+
+_Whiteness_, if most intense and luminous, is that of the first Order,
+if less strong and luminous, a Mixture of the Colours of several Orders.
+Of this last kind is the Whiteness of Froth, Paper, Linnen, and most
+white Substances; of the former I reckon that of white Metals to be. For
+whilst the densest of Metals, Gold, if foliated, is transparent, and all
+Metals become transparent if dissolved in Menstruums or vitrified, the
+Opacity of white Metals ariseth not from their Density alone. They being
+less dense than Gold would be more transparent than it, did not some
+other Cause concur with their Density to make them opake. And this Cause
+I take to be such a Bigness of their Particles as fits them to reflect
+the white of the first order. For, if they be of other Thicknesses they
+may reflect other Colours, as is manifest by the Colours which appear
+upon hot Steel in tempering it, and sometimes upon the Surface of melted
+Metals in the Skin or Scoria which arises upon them in their cooling.
+And as the white of the first order is the strongest which can be made
+by Plates of transparent Substances, so it ought to be stronger in the
+denser Substances of Metals than in the rarer of Air, Water, and Glass.
+Nor do I see but that metallick Substances of such a Thickness as may
+fit them to reflect the white of the first order, may, by reason of
+their great Density (according to the Tenor of the first of these
+Propositions) reflect all the Light incident upon them, and so be as
+opake and splendent as it's possible for any Body to be. Gold, or Copper
+mix'd with less than half their Weight of Silver, or Tin, or Regulus of
+Antimony, in fusion, or amalgamed with a very little Mercury, become
+white; which shews both that the Particles of white Metals have much
+more Superficies, and so are smaller, than those of Gold and Copper, and
+also that they are so opake as not to suffer the Particles of Gold or
+Copper to shine through them. Now it is scarce to be doubted but that
+the Colours of Gold and Copper are of the second and third order, and
+therefore the Particles of white Metals cannot be much bigger than is
+requisite to make them reflect the white of the first order. The
+Volatility of Mercury argues that they are not much bigger, nor may they
+be much less, lest they lose their Opacity, and become either
+transparent as they do when attenuated by Vitrification, or by Solution
+in Menstruums, or black as they do when ground smaller, by rubbing
+Silver, or Tin, or Lead, upon other Substances to draw black Lines. The
+first and only Colour which white Metals take by grinding their
+Particles smaller, is black, and therefore their white ought to be that
+which borders upon the black Spot in the Center of the Rings of Colours,
+that is, the white of the first order. But, if you would hence gather
+the Bigness of metallick Particles, you must allow for their Density.
+For were Mercury transparent, its Density is such that the Sine of
+Incidence upon it (by my Computation) would be to the Sine of its
+Refraction, as 71 to 20, or 7 to 2. And therefore the Thickness of its
+Particles, that they may exhibit the same Colours with those of Bubbles
+of Water, ought to be less than the Thickness of the Skin of those
+Bubbles in the Proportion of 2 to 7. Whence it's possible, that the
+Particles of Mercury may be as little as the Particles of some
+transparent and volatile Fluids, and yet reflect the white of the first
+order.
+
+Lastly, for the production of _black_, the Corpuscles must be less than
+any of those which exhibit Colours. For at all greater sizes there is
+too much Light reflected to constitute this Colour. But if they be
+supposed a little less than is requisite to reflect the white and very
+faint blue of the first order, they will, according to the 4th, 8th,
+17th and 18th Observations, reflect so very little Light as to appear
+intensely black, and yet may perhaps variously refract it to and fro
+within themselves so long, until it happen to be stifled and lost, by
+which means they will appear black in all positions of the Eye without
+any transparency. And from hence may be understood why Fire, and the
+more subtile dissolver Putrefaction, by dividing the Particles of
+Substances, turn them to black, why small quantities of black Substances
+impart their Colour very freely and intensely to other Substances to
+which they are applied; the minute Particles of these, by reason of
+their very great number, easily overspreading the gross Particles of
+others; why Glass ground very elaborately with Sand on a Copper Plate,
+'till it be well polish'd, makes the Sand, together with what is worn
+off from the Glass and Copper, become very black: why black Substances
+do soonest of all others become hot in the Sun's Light and burn, (which
+Effect may proceed partly from the multitude of Refractions in a little
+room, and partly from the easy Commotion of so very small Corpuscles;)
+and why blacks are usually a little inclined to a bluish Colour. For
+that they are so may be seen by illuminating white Paper by Light
+reflected from black Substances. For the Paper will usually appear of a
+bluish white; and the reason is, that black borders in the obscure blue
+of the order described in the 18th Observation, and therefore reflects
+more Rays of that Colour than of any other.
+
+In these Descriptions I have been the more particular, because it is not
+impossible but that Microscopes may at length be improved to the
+discovery of the Particles of Bodies on which their Colours depend, if
+they are not already in some measure arrived to that degree of
+perfection. For if those Instruments are or can be so far improved as
+with sufficient distinctness to represent Objects five or six hundred
+times bigger than at a Foot distance they appear to our naked Eyes, I
+should hope that we might be able to discover some of the greatest of
+those Corpuscles. And by one that would magnify three or four thousand
+times perhaps they might all be discover'd, but those which produce
+blackness. In the mean while I see nothing material in this Discourse
+that may rationally be doubted of, excepting this Position: That
+transparent Corpuscles of the same thickness and density with a Plate,
+do exhibit the same Colour. And this I would have understood not without
+some Latitude, as well because those Corpuscles may be of irregular
+Figures, and many Rays must be obliquely incident on them, and so have
+a shorter way through them than the length of their Diameters, as
+because the straitness of the Medium put in on all sides within such
+Corpuscles may a little alter its Motions or other qualities on which
+the Reflexion depends. But yet I cannot much suspect the last, because I
+have observed of some small Plates of Muscovy Glass which were of an
+even thickness, that through a Microscope they have appeared of the same
+Colour at their edges and corners where the included Medium was
+terminated, which they appeared of in other places. However it will add
+much to our Satisfaction, if those Corpuscles can be discover'd with
+Microscopes; which if we shall at length attain to, I fear it will be
+the utmost improvement of this Sense. For it seems impossible to see the
+more secret and noble Works of Nature within the Corpuscles by reason of
+their transparency.
+
+
+PROP. VIII.
+
+_The Cause of Reflexion is not the impinging of Light on the solid or
+impervious parts of Bodies, as is commonly believed._
+
+This will appear by the following Considerations. First, That in the
+passage of Light out of Glass into Air there is a Reflexion as strong as
+in its passage out of Air into Glass, or rather a little stronger, and
+by many degrees stronger than in its passage out of Glass into Water.
+And it seems not probable that Air should have more strongly reflecting
+parts than Water or Glass. But if that should possibly be supposed, yet
+it will avail nothing; for the Reflexion is as strong or stronger when
+the Air is drawn away from the Glass, (suppose by the Air-Pump invented
+by _Otto Gueriet_, and improved and made useful by Mr. _Boyle_) as when
+it is adjacent to it. Secondly, If Light in its passage out of Glass
+into Air be incident more obliquely than at an Angle of 40 or 41 Degrees
+it is wholly reflected, if less obliquely it is in great measure
+transmitted. Now it is not to be imagined that Light at one degree of
+obliquity should meet with Pores enough in the Air to transmit the
+greater part of it, and at another degree of obliquity should meet with
+nothing but parts to reflect it wholly, especially considering that in
+its passage out of Air into Glass, how oblique soever be its Incidence,
+it finds Pores enough in the Glass to transmit a great part of it. If
+any Man suppose that it is not reflected by the Air, but by the outmost
+superficial parts of the Glass, there is still the same difficulty:
+Besides, that such a Supposition is unintelligible, and will also appear
+to be false by applying Water behind some part of the Glass instead of
+Air. For so in a convenient obliquity of the Rays, suppose of 45 or 46
+Degrees, at which they are all reflected where the Air is adjacent to
+the Glass, they shall be in great measure transmitted where the Water is
+adjacent to it; which argues, that their Reflexion or Transmission
+depends on the constitution of the Air and Water behind the Glass, and
+not on the striking of the Rays upon the parts of the Glass. Thirdly,
+If the Colours made by a Prism placed at the entrance of a Beam of Light
+into a darken'd Room be successively cast on a second Prism placed at a
+greater distance from the former, in such manner that they are all alike
+incident upon it, the second Prism may be so inclined to the incident
+Rays, that those which are of a blue Colour shall be all reflected by
+it, and yet those of a red Colour pretty copiously transmitted. Now if
+the Reflexion be caused by the parts of Air or Glass, I would ask, why
+at the same Obliquity of Incidence the blue should wholly impinge on
+those parts, so as to be all reflected, and yet the red find Pores
+enough to be in a great measure transmitted. Fourthly, Where two Glasses
+touch one another, there is no sensible Reflexion, as was declared in
+the first Observation; and yet I see no reason why the Rays should not
+impinge on the parts of Glass, as much when contiguous to other Glass as
+when contiguous to Air. Fifthly, When the top of a Water-Bubble (in the
+17th Observation,) by the continual subsiding and exhaling of the Water
+grew very thin, there was such a little and almost insensible quantity
+of Light reflected from it, that it appeared intensely black; whereas
+round about that black Spot, where the Water was thicker, the Reflexion
+was so strong as to make the Water seem very white. Nor is it only at
+the least thickness of thin Plates or Bubbles, that there is no manifest
+Reflexion, but at many other thicknesses continually greater and
+greater. For in the 15th Observation the Rays of the same Colour were by
+turns transmitted at one thickness, and reflected at another thickness,
+for an indeterminate number of Successions. And yet in the Superficies
+of the thinned Body, where it is of any one thickness, there are as many
+parts for the Rays to impinge on, as where it is of any other thickness.
+Sixthly, If Reflexion were caused by the parts of reflecting Bodies, it
+would be impossible for thin Plates or Bubbles, at one and the same
+place, to reflect the Rays of one Colour, and transmit those of another,
+as they do according to the 13th and 15th Observations. For it is not to
+be imagined that at one place the Rays which, for instance, exhibit a
+blue Colour, should have the fortune to dash upon the parts, and those
+which exhibit a red to hit upon the Pores of the Body; and then at
+another place, where the Body is either a little thicker or a little
+thinner, that on the contrary the blue should hit upon its pores, and
+the red upon its parts. Lastly, Were the Rays of Light reflected by
+impinging on the solid parts of Bodies, their Reflexions from polish'd
+Bodies could not be so regular as they are. For in polishing Glass with
+Sand, Putty, or Tripoly, it is not to be imagined that those Substances
+can, by grating and fretting the Glass, bring all its least Particles to
+an accurate Polish; so that all their Surfaces shall be truly plain or
+truly spherical, and look all the same way, so as together to compose
+one even Surface. The smaller the Particles of those Substances are, the
+smaller will be the Scratches by which they continually fret and wear
+away the Glass until it be polish'd; but be they never so small they can
+wear away the Glass no otherwise than by grating and scratching it, and
+breaking the Protuberances; and therefore polish it no otherwise than by
+bringing its roughness to a very fine Grain, so that the Scratches and
+Frettings of the Surface become too small to be visible. And therefore
+if Light were reflected by impinging upon the solid parts of the Glass,
+it would be scatter'd as much by the most polish'd Glass as by the
+roughest. So then it remains a Problem, how Glass polish'd by fretting
+Substances can reflect Light so regularly as it does. And this Problem
+is scarce otherwise to be solved, than by saying, that the Reflexion of
+a Ray is effected, not by a single point of the reflecting Body, but by
+some power of the Body which is evenly diffused all over its Surface,
+and by which it acts upon the Ray without immediate Contact. For that
+the parts of Bodies do act upon Light at a distance shall be shewn
+hereafter.
+
+Now if Light be reflected, not by impinging on the solid parts of
+Bodies, but by some other principle; it's probable that as many of its
+Rays as impinge on the solid parts of Bodies are not reflected but
+stifled and lost in the Bodies. For otherwise we must allow two sorts of
+Reflexions. Should all the Rays be reflected which impinge on the
+internal parts of clear Water or Crystal, those Substances would rather
+have a cloudy Colour than a clear Transparency. To make Bodies look
+black, it's necessary that many Rays be stopp'd, retained, and lost in
+them; and it seems not probable that any Rays can be stopp'd and
+stifled in them which do not impinge on their parts.
+
+And hence we may understand that Bodies are much more rare and porous
+than is commonly believed. Water is nineteen times lighter, and by
+consequence nineteen times rarer than Gold; and Gold is so rare as very
+readily and without the least opposition to transmit the magnetick
+Effluvia, and easily to admit Quicksilver into its Pores, and to let
+Water pass through it. For a concave Sphere of Gold filled with Water,
+and solder'd up, has, upon pressing the Sphere with great force, let the
+Water squeeze through it, and stand all over its outside in multitudes
+of small Drops, like Dew, without bursting or cracking the Body of the
+Gold, as I have been inform'd by an Eye witness. From all which we may
+conclude, that Gold has more Pores than solid parts, and by consequence
+that Water has above forty times more Pores than Parts. And he that
+shall find out an Hypothesis, by which Water may be so rare, and yet not
+be capable of compression by force, may doubtless by the same Hypothesis
+make Gold, and Water, and all other Bodies, as much rarer as he pleases;
+so that Light may find a ready passage through transparent Substances.
+
+The Magnet acts upon Iron through all dense Bodies not magnetick nor red
+hot, without any diminution of its Virtue; as for instance, through
+Gold, Silver, Lead, Glass, Water. The gravitating Power of the Sun is
+transmitted through the vast Bodies of the Planets without any
+diminution, so as to act upon all their parts to their very centers
+with the same Force and according to the same Laws, as if the part upon
+which it acts were not surrounded with the Body of the Planet, The Rays
+of Light, whether they be very small Bodies projected, or only Motion or
+Force propagated, are moved in right Lines; and whenever a Ray of Light
+is by any Obstacle turned out of its rectilinear way, it will never
+return into the same rectilinear way, unless perhaps by very great
+accident. And yet Light is transmitted through pellucid solid Bodies in
+right Lines to very great distances. How Bodies can have a sufficient
+quantity of Pores for producing these Effects is very difficult to
+conceive, but perhaps not altogether impossible. For the Colours of
+Bodies arise from the Magnitudes of the Particles which reflect them, as
+was explained above. Now if we conceive these Particles of Bodies to be
+so disposed amongst themselves, that the Intervals or empty Spaces
+between them may be equal in magnitude to them all; and that these
+Particles may be composed of other Particles much smaller, which have as
+much empty Space between them as equals all the Magnitudes of these
+smaller Particles: And that in like manner these smaller Particles are
+again composed of others much smaller, all which together are equal to
+all the Pores or empty Spaces between them; and so on perpetually till
+you come to solid Particles, such as have no Pores or empty Spaces
+within them: And if in any gross Body there be, for instance, three such
+degrees of Particles, the least of which are solid; this Body will have
+seven times more Pores than solid Parts. But if there be four such
+degrees of Particles, the least of which are solid, the Body will have
+fifteen times more Pores than solid Parts. If there be five degrees, the
+Body will have one and thirty times more Pores than solid Parts. If six
+degrees, the Body will have sixty and three times more Pores than solid
+Parts. And so on perpetually. And there are other ways of conceiving how
+Bodies may be exceeding porous. But what is really their inward Frame is
+not yet known to us.
+
+
+PROP. IX.
+
+_Bodies reflect and refract Light by one and the same power, variously
+exercised in various Circumstances._
+
+This appears by several Considerations. First, Because when Light goes
+out of Glass into Air, as obliquely as it can possibly do. If its
+Incidence be made still more oblique, it becomes totally reflected. For
+the power of the Glass after it has refracted the Light as obliquely as
+is possible, if the Incidence be still made more oblique, becomes too
+strong to let any of its Rays go through, and by consequence causes
+total Reflexions. Secondly, Because Light is alternately reflected and
+transmitted by thin Plates of Glass for many Successions, accordingly as
+the thickness of the Plate increases in an arithmetical Progression. For
+here the thickness of the Glass determines whether that Power by which
+Glass acts upon Light shall cause it to be reflected, or suffer it to
+be transmitted. And, Thirdly, because those Surfaces of transparent
+Bodies which have the greatest refracting power, reflect the greatest
+quantity of Light, as was shewn in the first Proposition.
+
+
+PROP. X.
+
+_If Light be swifter in Bodies than in Vacuo, in the proportion of the
+Sines which measure the Refraction of the Bodies, the Forces of the
+Bodies to reflect and refract Light, are very nearly proportional to the
+densities of the same Bodies; excepting that unctuous and sulphureous
+Bodies refract more than others of this same density._
+
+[Illustration: FIG. 8.]
+
+Let AB represent the refracting plane Surface of any Body, and IC a Ray
+incident very obliquely upon the Body in C, so that the Angle ACI may be
+infinitely little, and let CR be the refracted Ray. From a given Point B
+perpendicular to the refracting Surface erect BR meeting with the
+refracting Ray CR in R, and if CR represent the Motion of the refracted
+Ray, and this Motion be distinguish'd into two Motions CB and BR,
+whereof CB is parallel to the refracting Plane, and BR perpendicular to
+it: CB shall represent the Motion of the incident Ray, and BR the
+Motion generated by the Refraction, as Opticians have of late explain'd.
+
+Now if any Body or Thing, in moving through any Space of a given breadth
+terminated on both sides by two parallel Planes, be urged forward in all
+parts of that Space by Forces tending directly forwards towards the last
+Plane, and before its Incidence on the first Plane, had no Motion
+towards it, or but an infinitely little one; and if the Forces in all
+parts of that Space, between the Planes, be at equal distances from the
+Planes equal to one another, but at several distances be bigger or less
+in any given Proportion, the Motion generated by the Forces in the whole
+passage of the Body or thing through that Space shall be in a
+subduplicate Proportion of the Forces, as Mathematicians will easily
+understand. And therefore, if the Space of activity of the refracting
+Superficies of the Body be consider'd as such a Space, the Motion of the
+Ray generated by the refracting Force of the Body, during its passage
+through that Space, that is, the Motion BR, must be in subduplicate
+Proportion of that refracting Force. I say therefore, that the Square of
+the Line BR, and by consequence the refracting Force of the Body, is
+very nearly as the density of the same Body. For this will appear by the
+following Table, wherein the Proportion of the Sines which measure the
+Refractions of several Bodies, the Square of BR, supposing CB an unite,
+the Densities of the Bodies estimated by their Specifick Gravities, and
+their Refractive Power in respect of their Densities are set down in
+several Columns.
+
+---------------------+----------------+----------------+----------+-----------
+                     |                |                |          |
+                     |                | The Square     | The      | The
+                     |                | of BR, to      | density  | refractive
+                     | The Proportion | which the      | and      | Power of
+                     | of the Sines of| refracting     | specifick| the Body
+                     | Incidence and  | force of the   | gravity  | in respect
+   The refracting    | Refraction of  | Body is        | of the   | of its
+      Bodies.        | yellow Light.  | proportionate. | Body.    | density.
+---------------------+----------------+----------------+----------+-----------
+A Pseudo-Topazius,   |                |                |          |
+  being a natural,   |                |                |          |
+  pellucid, brittle, |   23 to   14   |    1'699       |  4'27    |   3979
+  hairy Stone, of a  |                |                |          |
+  yellow Colour.     |                |                |          |
+Air.                 | 3201 to 3200   |    0'000625    |  0'0012  |   5208
+Glass of Antimony.   |   17 to    9   |    2'568       |  5'28    |   4864
+A Selenitis.         |   61 to   41   |    1'213       |  2'252   |   5386
+Glass vulgar.        |   31 to   20   |    1'4025      |  2'58    |   5436
+Crystal of the Rock. |   25 to   16   |    1'445       |  2'65    |   5450
+Island Crystal.      |    5 to    3   |    1'778       |  2'72    |   6536
+Sal Gemmæ.           |   17 to   11   |    1'388       |  2'143   |   6477
+Alume.               |   35 to   24   |    1'1267      |  1'714   |   6570
+Borax.               |   22 to   15   |    1'1511      |  1'714   |   6716
+Niter.               |   32 to   21   |    1'345       |  1'9     |   7079
+Dantzick Vitriol.    |  303 to  200   |    1'295       |  1'715   |   7551
+Oil of Vitriol.      |   10 to    7   |    1'041       |  1'7     |   6124
+Rain Water.          |  529 to  396   |    0'7845      |  1'      |   7845
+Gum Arabick.         |   31 to   21   |    1'179       |  1'375   |   8574
+Spirit of Wine well  |                |                |          |
+  rectified.         |  100 to   73   |    0'8765      |  0'866   |  10121
+Camphire.            |    3 to    2   |    1'25        |  0'996   |  12551
+Oil Olive.           |   22 to   15   |    1'1511      |  0'913   |  12607
+Linseed Oil.         |   40 to   27   |    1'1948      |  0'932   |  12819
+Spirit of Turpentine.|   25 to   17   |    1'1626      |  0'874   |  13222
+Amber.               |   14 to    9   |    1'42        |  1'04    |  13654
+A Diamond.           |  100 to   41   |    4'949       |  3'4     |  14556
+---------------------+----------------+----------------+----------+-----------
+
+The Refraction of the Air in this Table is determin'd by that of the
+Atmosphere observed by Astronomers. For, if Light pass through many
+refracting Substances or Mediums gradually denser and denser, and
+terminated with parallel Surfaces, the Sum of all the Refractions will
+be equal to the single Refraction which it would have suffer'd in
+passing immediately out of the first Medium into the last. And this
+holds true, though the Number of the refracting Substances be increased
+to Infinity, and the Distances from one another as much decreased, so
+that the Light may be refracted in every Point of its Passage, and by
+continual Refractions bent into a Curve-Line. And therefore the whole
+Refraction of Light in passing through the Atmosphere from the highest
+and rarest Part thereof down to the lowest and densest Part, must be
+equal to the Refraction which it would suffer in passing at like
+Obliquity out of a Vacuum immediately into Air of equal Density with
+that in the lowest Part of the Atmosphere.
+
+Now, although a Pseudo-Topaz, a Selenitis, Rock Crystal, Island Crystal,
+Vulgar Glass (that is, Sand melted together) and Glass of Antimony,
+which are terrestrial stony alcalizate Concretes, and Air which probably
+arises from such Substances by Fermentation, be Substances very
+differing from one another in Density, yet by this Table, they have
+their refractive Powers almost in the same Proportion to one another as
+their Densities are, excepting that the Refraction of that strange
+Substance, Island Crystal is a little bigger than the rest. And
+particularly Air, which is 3500 Times rarer than the Pseudo-Topaz, and
+4400 Times rarer than Glass of Antimony, and 2000 Times rarer than the
+Selenitis, Glass vulgar, or Crystal of the Rock, has notwithstanding its
+rarity the same refractive Power in respect of its Density which those
+very dense Substances have in respect of theirs, excepting so far as
+those differ from one another.
+
+Again, the Refraction of Camphire, Oil Olive, Linseed Oil, Spirit of
+Turpentine and Amber, which are fat sulphureous unctuous Bodies, and a
+Diamond, which probably is an unctuous Substance coagulated, have their
+refractive Powers in Proportion to one another as their Densities
+without any considerable Variation. But the refractive Powers of these
+unctuous Substances are two or three Times greater in respect of their
+Densities than the refractive Powers of the former Substances in respect
+of theirs.
+
+Water has a refractive Power in a middle degree between those two sorts
+of Substances, and probably is of a middle nature. For out of it grow
+all vegetable and animal Substances, which consist as well of
+sulphureous fat and inflamable Parts, as of earthy lean and alcalizate
+ones.
+
+Salts and Vitriols have refractive Powers in a middle degree between
+those of earthy Substances and Water, and accordingly are composed of
+those two sorts of Substances. For by distillation and rectification of
+their Spirits a great Part of them goes into Water, and a great Part
+remains behind in the form of a dry fix'd Earth capable of
+Vitrification.
+
+Spirit of Wine has a refractive Power in a middle degree between those
+of Water and oily Substances, and accordingly seems to be composed of
+both, united by Fermentation; the Water, by means of some saline Spirits
+with which 'tis impregnated, dissolving the Oil, and volatizing it by
+the Action. For Spirit of Wine is inflamable by means of its oily Parts,
+and being distilled often from Salt of Tartar, grow by every
+distillation more and more aqueous and phlegmatick. And Chymists
+observe, that Vegetables (as Lavender, Rue, Marjoram, &c.) distilled
+_per se_, before fermentation yield Oils without any burning Spirits,
+but after fermentation yield ardent Spirits without Oils: Which shews,
+that their Oil is by fermentation converted into Spirit. They find also,
+that if Oils be poured in a small quantity upon fermentating Vegetables,
+they distil over after fermentation in the form of Spirits.
+
+So then, by the foregoing Table, all Bodies seem to have their
+refractive Powers proportional to their Densities, (or very nearly;)
+excepting so far as they partake more or less of sulphureous oily
+Particles, and thereby have their refractive Power made greater or less.
+Whence it seems rational to attribute the refractive Power of all Bodies
+chiefly, if not wholly, to the sulphureous Parts with which they abound.
+For it's probable that all Bodies abound more or less with Sulphurs. And
+as Light congregated by a Burning-glass acts most upon sulphureous
+Bodies, to turn them into Fire and Flame; so, since all Action is
+mutual, Sulphurs ought to act most upon Light. For that the action
+between Light and Bodies is mutual, may appear from this Consideration;
+That the densest Bodies which refract and reflect Light most strongly,
+grow hottest in the Summer Sun, by the action of the refracted or
+reflected Light.
+
+I have hitherto explain'd the power of Bodies to reflect and refract,
+and shew'd, that thin transparent Plates, Fibres, and Particles, do,
+according to their several thicknesses and densities, reflect several
+sorts of Rays, and thereby appear of several Colours; and by consequence
+that nothing more is requisite for producing all the Colours of natural
+Bodies, than the several sizes and densities of their transparent
+Particles. But whence it is that these Plates, Fibres, and Particles,
+do, according to their several thicknesses and densities, reflect
+several sorts of Rays, I have not yet explain'd. To give some insight
+into this matter, and make way for understanding the next part of this
+Book, I shall conclude this part with a few more Propositions. Those
+which preceded respect the nature of Bodies, these the nature of Light:
+For both must be understood, before the reason of their Actions upon one
+another can be known. And because the last Proposition depended upon the
+velocity of Light, I will begin with a Proposition of that kind.
+
+
+PROP. XI.
+
+_Light is propagated from luminous Bodies in time, and spends about
+seven or eight Minutes of an Hour in passing from the Sun to the Earth._
+
+This was observed first by _Roemer_, and then by others, by means of the
+Eclipses of the Satellites of _Jupiter_. For these Eclipses, when the
+Earth is between the Sun and _Jupiter_, happen about seven or eight
+Minutes sooner than they ought to do by the Tables, and when the Earth
+is beyond the Sun they happen about seven or eight Minutes later than
+they ought to do; the reason being, that the Light of the Satellites has
+farther to go in the latter case than in the former by the Diameter of
+the Earth's Orbit. Some inequalities of time may arise from the
+Excentricities of the Orbs of the Satellites; but those cannot answer in
+all the Satellites, and at all times to the Position and Distance of the
+Earth from the Sun. The mean motions of _Jupiter_'s Satellites is also
+swifter in his descent from his Aphelium to his Perihelium, than in his
+ascent in the other half of his Orb. But this inequality has no respect
+to the position of the Earth, and in the three interior Satellites is
+insensible, as I find by computation from the Theory of their Gravity.
+
+
+PROP. XII.
+
+_Every Ray of Light in its passage through any refracting Surface is put
+into a certain transient Constitution or State, which in the progress of
+the Ray returns at equal Intervals, and disposes the Ray at every return
+to be easily transmitted through the next refracting Surface, and
+between the returns to be easily reflected by it._
+
+This is manifest by the 5th, 9th, 12th, and 15th Observations. For by
+those Observations it appears, that one and the same sort of Rays at
+equal Angles of Incidence on any thin transparent Plate, is alternately
+reflected and transmitted for many Successions accordingly as the
+thickness of the Plate increases in arithmetical Progression of the
+Numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, &c. so that if the first Reflexion
+(that which makes the first or innermost of the Rings of Colours there
+described) be made at the thickness 1, the Rays shall be transmitted at
+the thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the central
+Spot and Rings of Light, which appear by transmission, and be reflected
+at the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings which
+appear by Reflexion. And this alternate Reflexion and Transmission, as I
+gather by the 24th Observation, continues for above an hundred
+vicissitudes, and by the Observations in the next part of this Book, for
+many thousands, being propagated from one Surface of a Glass Plate to
+the other, though the thickness of the Plate be a quarter of an Inch or
+above: So that this alternation seems to be propagated from every
+refracting Surface to all distances without end or limitation.
+
+This alternate Reflexion and Refraction depends on both the Surfaces of
+every thin Plate, because it depends on their distance. By the 21st
+Observation, if either Surface of a thin Plate of _Muscovy_ Glass be
+wetted, the Colours caused by the alternate Reflexion and Refraction
+grow faint, and therefore it depends on them both.
+
+It is therefore perform'd at the second Surface; for if it were
+perform'd at the first, before the Rays arrive at the second, it would
+not depend on the second.
+
+It is also influenced by some action or disposition, propagated from the
+first to the second, because otherwise at the second it would not depend
+on the first. And this action or disposition, in its propagation,
+intermits and returns by equal Intervals, because in all its progress it
+inclines the Ray at one distance from the first Surface to be reflected
+by the second, at another to be transmitted by it, and that by equal
+Intervals for innumerable vicissitudes. And because the Ray is disposed
+to Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission at
+the distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through the
+first Surface, is at the distance 0, and it is transmitted through both
+together, if their distance be infinitely little or much less than 1)
+the disposition to be transmitted at the distances 2, 4, 6, 8, 10, &c.
+is to be accounted a return of the same disposition which the Ray first
+had at the distance 0, that is at its transmission through the first
+refracting Surface. All which is the thing I would prove.
+
+What kind of action or disposition this is; Whether it consists in a
+circulating or a vibrating motion of the Ray, or of the Medium, or
+something else, I do not here enquire. Those that are averse from
+assenting to any new Discoveries, but such as they can explain by an
+Hypothesis, may for the present suppose, that as Stones by falling upon
+Water put the Water into an undulating Motion, and all Bodies by
+percussion excite vibrations in the Air; so the Rays of Light, by
+impinging on any refracting or reflecting Surface, excite vibrations in
+the refracting or reflecting Medium or Substance, and by exciting them
+agitate the solid parts of the refracting or reflecting Body, and by
+agitating them cause the Body to grow warm or hot; that the vibrations
+thus excited are propagated in the refracting or reflecting Medium or
+Substance, much after the manner that vibrations are propagated in the
+Air for causing Sound, and move faster than the Rays so as to overtake
+them; and that when any Ray is in that part of the vibration which
+conspires with its Motion, it easily breaks through a refracting
+Surface, but when it is in the contrary part of the vibration which
+impedes its Motion, it is easily reflected; and, by consequence, that
+every Ray is successively disposed to be easily reflected, or easily
+transmitted, by every vibration which overtakes it. But whether this
+Hypothesis be true or false I do not here consider. I content my self
+with the bare Discovery, that the Rays of Light are by some cause or
+other alternately disposed to be reflected or refracted for many
+vicissitudes.
+
+
+DEFINITION.
+
+_The returns of the disposition of any Ray to be reflected I will call
+its_ Fits of easy Reflexion, _and those of its disposition to be
+transmitted its_ Fits of easy Transmission, _and the space it passes
+between every return and the next return, the_ Interval of its Fits.
+
+
+PROP. XIII.
+
+_The reason why the Surfaces of all thick transparent Bodies reflect
+part of the Light incident on them, and refract the rest, is, that some
+Rays at their Incidence are in Fits of easy Reflexion, and others in
+Fits of easy Transmission._
+
+This may be gather'd from the 24th Observation, where the Light
+reflected by thin Plates of Air and Glass, which to the naked Eye
+appear'd evenly white all over the Plate, did through a Prism appear
+waved with many Successions of Light and Darkness made by alternate Fits
+of easy Reflexion and easy Transmission, the Prism severing and
+distinguishing the Waves of which the white reflected Light was
+composed, as was explain'd above.
+
+And hence Light is in Fits of easy Reflexion and easy Transmission,
+before its Incidence on transparent Bodies. And probably it is put into
+such fits at its first emission from luminous Bodies, and continues in
+them during all its progress. For these Fits are of a lasting nature, as
+will appear by the next part of this Book.
+
+In this Proposition I suppose the transparent Bodies to be thick;
+because if the thickness of the Body be much less than the Interval of
+the Fits of easy Reflexion and Transmission of the Rays, the Body loseth
+its reflecting power. For if the Rays, which at their entering into the
+Body are put into Fits of easy Transmission, arrive at the farthest
+Surface of the Body before they be out of those Fits, they must be
+transmitted. And this is the reason why Bubbles of Water lose their
+reflecting power when they grow very thin; and why all opake Bodies,
+when reduced into very small parts, become transparent.
+
+
+PROP. XIV.
+
+_Those Surfaces of transparent Bodies, which if the Ray be in a Fit of
+Refraction do refract it most strongly, if the Ray be in a Fit of
+Reflexion do reflect it most easily._
+
+For we shewed above, in _Prop._ 8. that the cause of Reflexion is not
+the impinging of Light on the solid impervious parts of Bodies, but some
+other power by which those solid parts act on Light at a distance. We
+shewed also in _Prop._ 9. that Bodies reflect and refract Light by one
+and the same power, variously exercised in various circumstances; and in
+_Prop._ 1. that the most strongly refracting Surfaces reflect the most
+Light: All which compared together evince and rarify both this and the
+last Proposition.
+
+
+PROP. XV.
+
+_In any one and the same sort of Rays, emerging in any Angle out of any
+refracting Surface into one and the same Medium, the Interval of the
+following Fits of easy Reflexion and Transmission are either accurately
+or very nearly, as the Rectangle of the Secant of the Angle of
+Refraction, and of the Secant of another Angle, whose Sine is the first
+of 106 arithmetical mean Proportionals, between the Sines of Incidence
+and Refraction, counted from the Sine of Refraction._
+
+This is manifest by the 7th and 19th Observations.
+
+
+PROP. XVI.
+
+_In several sorts of Rays emerging in equal Angles out of any refracting
+Surface into the same Medium, the Intervals of the following Fits of
+easy Reflexion and easy Transmission are either accurately, or very
+nearly, as the Cube-Roots of the Squares of the lengths of a Chord,
+which found the Notes in an Eight_, sol, la, fa, sol, la, mi, fa, sol,
+_with all their intermediate degrees answering to the Colours of those
+Rays, according to the Analogy described in the seventh Experiment of
+the second Part of the first Book._
+
+This is manifest by the 13th and 14th Observations.
+
+
+PROP. XVII.
+
+_If Rays of any sort pass perpendicularly into several Mediums, the
+Intervals of the Fits of easy Reflexion and Transmission in any one
+Medium, are to those Intervals in any other, as the Sine of Incidence to
+the Sine of Refraction, when the Rays pass out of the first of those two
+Mediums into the second._
+
+This is manifest by the 10th Observation.
+
+
+PROP. XVIII.
+
+_If the Rays which paint the Colour in the Confine of yellow and orange
+pass perpendicularly out of any Medium into Air, the Intervals of their
+Fits of easy Reflexion are the 1/89000th part of an Inch. And of the
+same length are the Intervals of their Fits of easy Transmission._
+
+This is manifest by the 6th Observation. From these Propositions it is
+easy to collect the Intervals of the Fits of easy Reflexion and easy
+Transmission of any sort of Rays refracted in any angle into any Medium;
+and thence to know, whether the Rays shall be reflected or transmitted
+at their subsequent Incidence upon any other pellucid Medium. Which
+thing, being useful for understanding the next part of this Book, was
+here to be set down. And for the same reason I add the two following
+Propositions.
+
+
+PROP. XIX.
+
+_If any sort of Rays falling on the polite Surface of any pellucid
+Medium be reflected back, the Fits of easy Reflexion, which they have at
+the point of Reflexion, shall still continue to return; and the Returns
+shall be at distances from the point of Reflexion in the arithmetical
+progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these
+Fits the Rays shall be in Fits of easy Transmission._
+
+For since the Fits of easy Reflexion and easy Transmission are of a
+returning nature, there is no reason why these Fits, which continued
+till the Ray arrived at the reflecting Medium, and there inclined the
+Ray to Reflexion, should there cease. And if the Ray at the point of
+Reflexion was in a Fit of easy Reflexion, the progression of the
+distances of these Fits from that point must begin from 0, and so be of
+the Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of the
+distances of the intermediate Fits of easy Transmission, reckon'd from
+the same point, must be in the progression of the odd Numbers 1, 3, 5,
+7, 9, &c. contrary to what happens when the Fits are propagated from
+points of Refraction.
+
+
+PROP. XX.
+
+_The Intervals of the Fits of easy Reflexion and easy Transmission,
+propagated from points of Reflexion into any Medium, are equal to the
+Intervals of the like Fits, which the same Rays would have, if refracted
+into the same Medium in Angles of Refraction equal to their Angles of
+Reflexion._
+
+For when Light is reflected by the second Surface of thin Plates, it
+goes out afterwards freely at the first Surface to make the Rings of
+Colours which appear by Reflexion; and, by the freedom of its egress,
+makes the Colours of these Rings more vivid and strong than those which
+appear on the other side of the Plates by the transmitted Light. The
+reflected Rays are therefore in Fits of easy Transmission at their
+egress; which would not always happen, if the Intervals of the Fits
+within the Plate after Reflexion were not equal, both in length and
+number, to their Intervals before it. And this confirms also the
+proportions set down in the former Proposition. For if the Rays both in
+going in and out at the first Surface be in Fits of easy Transmission,
+and the Intervals and Numbers of those Fits between the first and second
+Surface, before and after Reflexion, be equal, the distances of the Fits
+of easy Transmission from either Surface, must be in the same
+progression after Reflexion as before; that is, from the first Surface
+which transmitted them in the progression of the even Numbers 0, 2, 4,
+6, 8, &c. and from the second which reflected them, in that of the odd
+Numbers 1, 3, 5, 7, &c. But these two Propositions will become much more
+evident by the Observations in the following part of this Book.
+
+
+
+
+THE
+
+SECOND BOOK
+
+OF
+
+OPTICKS
+
+
+_PART IV._
+
+_Observations concerning the Reflexions and Colours of thick transparent
+polish'd Plates._
+
+There is no Glass or Speculum how well soever polished, but, besides the
+Light which it refracts or reflects regularly, scatters every way
+irregularly a faint Light, by means of which the polish'd Surface, when
+illuminated in a dark room by a beam of the Sun's Light, may be easily
+seen in all positions of the Eye. There are certain Phænomena of this
+scatter'd Light, which when I first observed them, seem'd very strange
+and surprizing to me. My Observations were as follows.
+
+_Obs._ 1. The Sun shining into my darken'd Chamber through a hole one
+third of an Inch wide, I let the intromitted beam of Light fall
+perpendicularly upon a Glass Speculum ground concave on one side and
+convex on the other, to a Sphere of five Feet and eleven Inches Radius,
+and Quick-silver'd over on the convex side. And holding a white opake
+Chart, or a Quire of Paper at the center of the Spheres to which the
+Speculum was ground, that is, at the distance of about five Feet and
+eleven Inches from the Speculum, in such manner, that the beam of Light
+might pass through a little hole made in the middle of the Chart to the
+Speculum, and thence be reflected back to the same hole: I observed upon
+the Chart four or five concentric Irises or Rings of Colours, like
+Rain-bows, encompassing the hole much after the manner that those, which
+in the fourth and following Observations of the first part of this Book
+appear'd between the Object-glasses, encompassed the black Spot, but yet
+larger and fainter than those. These Rings as they grew larger and
+larger became diluter and fainter, so that the fifth was scarce visible.
+Yet sometimes, when the Sun shone very clear, there appear'd faint
+Lineaments of a sixth and seventh. If the distance of the Chart from the
+Speculum was much greater or much less than that of six Feet, the Rings
+became dilute and vanish'd. And if the distance of the Speculum from the
+Window was much greater than that of six Feet, the reflected beam of
+Light would be so broad at the distance of six Feet from the Speculum
+where the Rings appear'd, as to obscure one or two of the innermost
+Rings. And therefore I usually placed the Speculum at about six Feet
+from the Window; so that its Focus might there fall in with the center
+of its concavity at the Rings upon the Chart. And this Posture is always
+to be understood in the following Observations where no other is
+express'd.
+
+_Obs._ 2. The Colours of these Rain-bows succeeded one another from the
+center outwards, in the same form and order with those which were made
+in the ninth Observation of the first Part of this Book by Light not
+reflected, but transmitted through the two Object-glasses. For, first,
+there was in their common center a white round Spot of faint Light,
+something broader than the reflected beam of Light, which beam sometimes
+fell upon the middle of the Spot, and sometimes by a little inclination
+of the Speculum receded from the middle, and left the Spot white to the
+center.
+
+This white Spot was immediately encompassed with a dark grey or russet,
+and that dark grey with the Colours of the first Iris; which Colours on
+the inside next the dark grey were a little violet and indigo, and next
+to that a blue, which on the outside grew pale, and then succeeded a
+little greenish yellow, and after that a brighter yellow, and then on
+the outward edge of the Iris a red which on the outside inclined to
+purple.
+
+This Iris was immediately encompassed with a second, whose Colours were
+in order from the inside outwards, purple, blue, green, yellow, light
+red, a red mix'd with purple.
+
+Then immediately follow'd the Colours of the third Iris, which were in
+order outwards a green inclining to purple, a good green, and a red more
+bright than that of the former Iris.
+
+The fourth and fifth Iris seem'd of a bluish green within, and red
+without, but so faintly that it was difficult to discern the Colours.
+
+_Obs._ 3. Measuring the Diameters of these Rings upon the Chart as
+accurately as I could, I found them also in the same proportion to one
+another with the Rings made by Light transmitted through the two
+Object-glasses. For the Diameters of the four first of the bright Rings
+measured between the brightest parts of their Orbits, at the distance of
+six Feet from the Speculum were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches,
+whose Squares are in arithmetical progression of the numbers 1, 2, 3, 4.
+If the white circular Spot in the middle be reckon'd amongst the Rings,
+and its central Light, where it seems to be most luminous, be put
+equipollent to an infinitely little Ring; the Squares of the Diameters
+of the Rings will be in the progression 0, 1, 2, 3, 4, &c. I measured
+also the Diameters of the dark Circles between these luminous ones, and
+found their Squares in the progression of the numbers 1/2, 1-1/2, 2-1/2,
+3-1/2, &c. the Diameters of the first four at the distance of six Feet
+from the Speculum, being 1-3/16, 2-1/16, 2-2/3, 3-3/20 Inches. If the
+distance of the Chart from the Speculum was increased or diminished, the
+Diameters of the Circles were increased or diminished proportionally.
+
+_Obs._ 4. By the analogy between these Rings and those described in the
+Observations of the first Part of this Book, I suspected that there
+were many more of them which spread into one another, and by interfering
+mix'd their Colours, and diluted one another so that they could not be
+seen apart. I viewed them therefore through a Prism, as I did those in
+the 24th Observation of the first Part of this Book. And when the Prism
+was so placed as by refracting the Light of their mix'd Colours to
+separate them, and distinguish the Rings from one another, as it did
+those in that Observation, I could then see them distincter than before,
+and easily number eight or nine of them, and sometimes twelve or
+thirteen. And had not their Light been so very faint, I question not but
+that I might have seen many more.
+
+_Obs._ 5. Placing a Prism at the Window to refract the intromitted beam
+of Light, and cast the oblong Spectrum of Colours on the Speculum: I
+covered the Speculum with a black Paper which had in the middle of it a
+hole to let any one of the Colours pass through to the Speculum, whilst
+the rest were intercepted by the Paper. And now I found Rings of that
+Colour only which fell upon the Speculum. If the Speculum was
+illuminated with red, the Rings were totally red with dark Intervals, if
+with blue they were totally blue, and so of the other Colours. And when
+they were illuminated with any one Colour, the Squares of their
+Diameters measured between their most luminous Parts, were in the
+arithmetical Progression of the Numbers, 0, 1, 2, 3, 4 and the Squares
+of the Diameters of their dark Intervals in the Progression of the
+intermediate Numbers 1/2, 1-1/2, 2-1/2, 3-1/2. But if the Colour was
+varied, they varied their Magnitude. In the red they were largest, in
+the indigo and violet least, and in the intermediate Colours yellow,
+green, and blue, they were of several intermediate Bignesses answering
+to the Colour, that is, greater in yellow than in green, and greater in
+green than in blue. And hence I knew, that when the Speculum was
+illuminated with white Light, the red and yellow on the outside of the
+Rings were produced by the least refrangible Rays, and the blue and
+violet by the most refrangible, and that the Colours of each Ring spread
+into the Colours of the neighbouring Rings on either side, after the
+manner explain'd in the first and second Part of this Book, and by
+mixing diluted one another so that they could not be distinguish'd,
+unless near the Center where they were least mix'd. For in this
+Observation I could see the Rings more distinctly, and to a greater
+Number than before, being able in the yellow Light to number eight or
+nine of them, besides a faint shadow of a tenth. To satisfy my self how
+much the Colours of the several Rings spread into one another, I
+measured the Diameters of the second and third Rings, and found them
+when made by the Confine of the red and orange to be to the same
+Diameters when made by the Confine of blue and indigo, as 9 to 8, or
+thereabouts. For it was hard to determine this Proportion accurately.
+Also the Circles made successively by the red, yellow, and green,
+differ'd more from one another than those made successively by the
+green, blue, and indigo. For the Circle made by the violet was too dark
+to be seen. To carry on the Computation, let us therefore suppose that
+the Differences of the Diameters of the Circles made by the outmost red,
+the Confine of red and orange, the Confine of orange and yellow, the
+Confine of yellow and green, the Confine of green and blue, the Confine
+of blue and indigo, the Confine of indigo and violet, and outmost
+violet, are in proportion as the Differences of the Lengths of a
+Monochord which sound the Tones in an Eight; _sol_, _la_, _fa_, _sol_,
+_la_, _mi_, _fa_, _sol_, that is, as the Numbers 1/9, 1/18, 1/12, 1/12,
+2/27, 1/27, 1/18. And if the Diameter of the Circle made by the Confine
+of red and orange be 9A, and that of the Circle made by the Confine of
+blue and indigo be 8A as above; their difference 9A-8A will be to the
+difference of the Diameters of the Circles made by the outmost red, and
+by the Confine of red and orange, as 1/18 + 1/12 + 1/12 + 2/27 to 1/9,
+that is as 8/27 to 1/9, or 8 to 3, and to the difference of the Circles
+made by the outmost violet, and by the Confine of blue and indigo, as
+1/18 + 1/12 + 1/12 + 2/27 to 1/27 + 1/18, that is, as 8/27 to 5/54, or
+as 16 to 5. And therefore these differences will be 3/8A and 5/16A. Add
+the first to 9A and subduct the last from 8A, and you will have the
+Diameters of the Circles made by the least and most refrangible Rays
+75/8A and ((61-1/2)/8)A. These diameters are therefore to one another as
+75 to 61-1/2 or 50 to 41, and their Squares as 2500 to 1681, that is, as
+3 to 2 very nearly. Which proportion differs not much from the
+proportion of the Diameters of the Circles made by the outmost red and
+outmost violet, in the 13th Observation of the first part of this Book.
+
+_Obs._ 6. Placing my Eye where these Rings appear'd plainest, I saw the
+Speculum tinged all over with Waves of Colours, (red, yellow, green,
+blue;) like those which in the Observations of the first part of this
+Book appeared between the Object-glasses, and upon Bubbles of Water, but
+much larger. And after the manner of those, they were of various
+magnitudes in various Positions of the Eye, swelling and shrinking as I
+moved my Eye this way and that way. They were formed like Arcs of
+concentrick Circles, as those were; and when my Eye was over against the
+center of the concavity of the Speculum, (that is, 5 Feet and 10 Inches
+distant from the Speculum,) their common center was in a right Line with
+that center of concavity, and with the hole in the Window. But in other
+postures of my Eye their center had other positions. They appear'd by
+the Light of the Clouds propagated to the Speculum through the hole in
+the Window; and when the Sun shone through that hole upon the Speculum,
+his Light upon it was of the Colour of the Ring whereon it fell, but by
+its splendor obscured the Rings made by the Light of the Clouds, unless
+when the Speculum was removed to a great distance from the Window, so
+that his Light upon it might be broad and faint. By varying the position
+of my Eye, and moving it nearer to or farther from the direct beam of
+the Sun's Light, the Colour of the Sun's reflected Light constantly
+varied upon the Speculum, as it did upon my Eye, the same Colour always
+appearing to a Bystander upon my Eye which to me appear'd upon the
+Speculum. And thence I knew that the Rings of Colours upon the Chart
+were made by these reflected Colours, propagated thither from the
+Speculum in several Angles, and that their production depended not upon
+the termination of Light and Shadow.
+
+_Obs._ 7. By the Analogy of all these Phænomena with those of the like
+Rings of Colours described in the first part of this Book, it seemed to
+me that these Colours were produced by this thick Plate of Glass, much
+after the manner that those were produced by very thin Plates. For, upon
+trial, I found that if the Quick-silver were rubb'd off from the
+backside of the Speculum, the Glass alone would cause the same Rings of
+Colours, but much more faint than before; and therefore the Phænomenon
+depends not upon the Quick-silver, unless so far as the Quick-silver by
+increasing the Reflexion of the backside of the Glass increases the
+Light of the Rings of Colours. I found also that a Speculum of Metal
+without Glass made some Years since for optical uses, and very well
+wrought, produced none of those Rings; and thence I understood that
+these Rings arise not from one specular Surface alone, but depend upon
+the two Surfaces of the Plate of Glass whereof the Speculum was made,
+and upon the thickness of the Glass between them. For as in the 7th and
+19th Observations of the first part of this Book a thin Plate of Air,
+Water, or Glass of an even thickness appeared of one Colour when the
+Rays were perpendicular to it, of another when they were a little
+oblique, of another when more oblique, of another when still more
+oblique, and so on; so here, in the sixth Observation, the Light which
+emerged out of the Glass in several Obliquities, made the Glass appear
+of several Colours, and being propagated in those Obliquities to the
+Chart, there painted Rings of those Colours. And as the reason why a
+thin Plate appeared of several Colours in several Obliquities of the
+Rays, was, that the Rays of one and the same sort are reflected by the
+thin Plate at one obliquity and transmitted at another, and those of
+other sorts transmitted where these are reflected, and reflected where
+these are transmitted: So the reason why the thick Plate of Glass
+whereof the Speculum was made did appear of various Colours in various
+Obliquities, and in those Obliquities propagated those Colours to the
+Chart, was, that the Rays of one and the same sort did at one Obliquity
+emerge out of the Glass, at another did not emerge, but were reflected
+back towards the Quick-silver by the hither Surface of the Glass, and
+accordingly as the Obliquity became greater and greater, emerged and
+were reflected alternately for many Successions; and that in one and the
+same Obliquity the Rays of one sort were reflected, and those of another
+transmitted. This is manifest by the fifth Observation of this part of
+this Book. For in that Observation, when the Speculum was illuminated by
+any one of the prismatick Colours, that Light made many Rings of the
+same Colour upon the Chart with dark Intervals, and therefore at its
+emergence out of the Speculum was alternately transmitted and not
+transmitted from the Speculum to the Chart for many Successions,
+according to the various Obliquities of its Emergence. And when the
+Colour cast on the Speculum by the Prism was varied, the Rings became of
+the Colour cast on it, and varied their bigness with their Colour, and
+therefore the Light was now alternately transmitted and not transmitted
+from the Speculum to the Chart at other Obliquities than before. It
+seemed to me therefore that these Rings were of one and the same
+original with those of thin Plates, but yet with this difference, that
+those of thin Plates are made by the alternate Reflexions and
+Transmissions of the Rays at the second Surface of the Plate, after one
+passage through it; but here the Rays go twice through the Plate before
+they are alternately reflected and transmitted. First, they go through
+it from the first Surface to the Quick-silver, and then return through
+it from the Quick-silver to the first Surface, and there are either
+transmitted to the Chart or reflected back to the Quick-silver,
+accordingly as they are in their Fits of easy Reflexion or Transmission
+when they arrive at that Surface. For the Intervals of the Fits of the
+Rays which fall perpendicularly on the Speculum, and are reflected back
+in the same perpendicular Lines, by reason of the equality of these
+Angles and Lines, are of the same length and number within the Glass
+after Reflexion as before, by the 19th Proposition of the third part of
+this Book. And therefore since all the Rays that enter through the
+first Surface are in their Fits of easy Transmission at their entrance,
+and as many of these as are reflected by the second are in their Fits of
+easy Reflexion there, all these must be again in their Fits of easy
+Transmission at their return to the first, and by consequence there go
+out of the Glass to the Chart, and form upon it the white Spot of Light
+in the center of the Rings. For the reason holds good in all sorts of
+Rays, and therefore all sorts must go out promiscuously to that Spot,
+and by their mixture cause it to be white. But the Intervals of the Fits
+of those Rays which are reflected more obliquely than they enter, must
+be greater after Reflexion than before, by the 15th and 20th
+Propositions. And thence it may happen that the Rays at their return to
+the first Surface, may in certain Obliquities be in Fits of easy
+Reflexion, and return back to the Quick-silver, and in other
+intermediate Obliquities be again in Fits of easy Transmission, and so
+go out to the Chart, and paint on it the Rings of Colours about the
+white Spot. And because the Intervals of the Fits at equal obliquities
+are greater and fewer in the less refrangible Rays, and less and more
+numerous in the more refrangible, therefore the less refrangible at
+equal obliquities shall make fewer Rings than the more refrangible, and
+the Rings made by those shall be larger than the like number of Rings
+made by these; that is, the red Rings shall be larger than the yellow,
+the yellow than the green, the green than the blue, and the blue than
+the violet, as they were really found to be in the fifth Observation.
+And therefore the first Ring of all Colours encompassing the white Spot
+of Light shall be red without any violet within, and yellow, and green,
+and blue in the middle, as it was found in the second Observation; and
+these Colours in the second Ring, and those that follow, shall be more
+expanded, till they spread into one another, and blend one another by
+interfering.
+
+These seem to be the reasons of these Rings in general; and this put me
+upon observing the thickness of the Glass, and considering whether the
+dimensions and proportions of the Rings may be truly derived from it by
+computation.
+
+_Obs._ 8. I measured therefore the thickness of this concavo-convex
+Plate of Glass, and found it every where 1/4 of an Inch precisely. Now,
+by the sixth Observation of the first Part of this Book, a thin Plate of
+Air transmits the brightest Light of the first Ring, that is, the bright
+yellow, when its thickness is the 1/89000th part of an Inch; and by the
+tenth Observation of the same Part, a thin Plate of Glass transmits the
+same Light of the same Ring, when its thickness is less in proportion of
+the Sine of Refraction to the Sine of Incidence, that is, when its
+thickness is the 11/1513000th or 1/137545th part of an Inch, supposing
+the Sines are as 11 to 17. And if this thickness be doubled, it
+transmits the same bright Light of the second Ring; if tripled, it
+transmits that of the third, and so on; the bright yellow Light in all
+these cases being in its Fits of Transmission. And therefore if its
+thickness be multiplied 34386 times, so as to become 1/4 of an Inch, it
+transmits the same bright Light of the 34386th Ring. Suppose this be the
+bright yellow Light transmitted perpendicularly from the reflecting
+convex side of the Glass through the concave side to the white Spot in
+the center of the Rings of Colours on the Chart: And by a Rule in the
+7th and 19th Observations in the first Part of this Book, and by the
+15th and 20th Propositions of the third Part of this Book, if the Rays
+be made oblique to the Glass, the thickness of the Glass requisite to
+transmit the same bright Light of the same Ring in any obliquity, is to
+this thickness of 1/4 of an Inch, as the Secant of a certain Angle to
+the Radius, the Sine of which Angle is the first of an hundred and six
+arithmetical Means between the Sines of Incidence and Refraction,
+counted from the Sine of Incidence when the Refraction is made out of
+any plated Body into any Medium encompassing it; that is, in this case,
+out of Glass into Air. Now if the thickness of the Glass be increased by
+degrees, so as to bear to its first thickness, (_viz._ that of a quarter
+of an Inch,) the Proportions which 34386 (the number of Fits of the
+perpendicular Rays in going through the Glass towards the white Spot in
+the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the
+numbers of the Fits of the oblique Rays in going through the Glass
+towards the first, second, third, and fourth Rings of Colours,) and if
+the first thickness be divided into 100000000 equal parts, the increased
+thicknesses will be 100002908, 100005816, 100008725, and 100011633, and
+the Angles of which these thicknesses are Secants will be 26´ 13´´, 37´
+5´´, 45´ 6´´, and 52´ 26´´, the Radius being 100000000; and the Sines of
+these Angles are 762, 1079, 1321, and 1525, and the proportional Sines
+of Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. For
+since the Sines of Incidence out of Glass into Air are to the Sines of
+Refraction as 11 to 17, and to the above-mentioned Secants as 11 to the
+first of 106 arithmetical Means between 11 and 17, that is, as 11 to
+11-6/106, those Secants will be to the Sines of Refraction as 11-6/106,
+to 17, and by this Analogy will give these Sines. So then, if the
+obliquities of the Rays to the concave Surface of the Glass be such that
+the Sines of their Refraction in passing out of the Glass through that
+Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the
+34386th Ring shall emerge at the thicknesses of the Glass, which are to
+1/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. And
+therefore, if the thickness in all these Cases be 1/4 of an Inch (as it
+is in the Glass of which the Speculum was made) the bright Light of the
+34385th Ring shall emerge where the Sine of Refraction is 1172, and that
+of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031,
+and 2345 respectively. And in these Angles of Refraction the Light of
+these Rings shall be propagated from the Speculum to the Chart, and
+there paint Rings about the white central round Spot of Light which we
+said was the Light of the 34386th Ring. And the Semidiameters of these
+Rings shall subtend the Angles of Refraction made at the
+Concave-Surface of the Speculum, and by consequence their Diameters
+shall be to the distance of the Chart from the Speculum as those Sines
+of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031,
+and 2345, doubled are to 100000. And therefore, if the distance of the
+Chart from the Concave-Surface of the Speculum be six Feet (as it was in
+the third of these Observations) the Diameters of the Rings of this
+bright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375
+Inches: For these Diameters are to six Feet, as the above-mention'd
+Sines doubled are to the Radius. Now, these Diameters of the bright
+yellow Rings, thus found by Computation are the very same with those
+found in the third of these Observations by measuring them, _viz._ with
+1-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory of
+deriving these Rings from the thickness of the Plate of Glass of which
+the Speculum was made, and from the Obliquity of the emerging Rays
+agrees with the Observation. In this Computation I have equalled the
+Diameters of the bright Rings made by Light of all Colours, to the
+Diameters of the Rings made by the bright yellow. For this yellow makes
+the brightest Part of the Rings of all Colours. If you desire the
+Diameters of the Rings made by the Light of any other unmix'd Colour,
+you may find them readily by putting them to the Diameters of the bright
+yellow ones in a subduplicate Proportion of the Intervals of the Fits of
+the Rays of those Colours when equally inclined to the refracting or
+reflecting Surface which caused those Fits, that is, by putting the
+Diameters of the Rings made by the Rays in the Extremities and Limits of
+the seven Colours, red, orange, yellow, green, blue, indigo, violet,
+proportional to the Cube-roots of the Numbers, 1, 8/9, 5/6, 3/4, 2/3,
+3/5, 9/16, 1/2, which express the Lengths of a Monochord sounding the
+Notes in an Eighth: For by this means the Diameters of the Rings of
+these Colours will be found pretty nearly in the same Proportion to one
+another, which they ought to have by the fifth of these Observations.
+
+And thus I satisfy'd my self, that these Rings were of the same kind and
+Original with those of thin Plates, and by consequence that the Fits or
+alternate Dispositions of the Rays to be reflected and transmitted are
+propagated to great distances from every reflecting and refracting
+Surface. But yet to put the matter out of doubt, I added the following
+Observation.
+
+_Obs._ 9. If these Rings thus depend on the thickness of the Plate of
+Glass, their Diameters at equal distances from several Speculums made of
+such concavo-convex Plates of Glass as are ground on the same Sphere,
+ought to be reciprocally in a subduplicate Proportion of the thicknesses
+of the Plates of Glass. And if this Proportion be found true by
+experience it will amount to a demonstration that these Rings (like
+those formed in thin Plates) do depend on the thickness of the Glass. I
+procured therefore another concavo-convex Plate of Glass ground on both
+sides to the same Sphere with the former Plate. Its thickness was 5/62
+Parts of an Inch; and the Diameters of the three first bright Rings
+measured between the brightest Parts of their Orbits at the distance of
+six Feet from the Glass were 3·4-1/6·5-1/8· Inches. Now, the thickness
+of the other Glass being 1/4 of an Inch was to the thickness of this
+Glass as 1/4 to 5/62, that is as 31 to 10, or 310000000 to 100000000,
+and the Roots of these Numbers are 17607 and 10000, and in the
+Proportion of the first of these Roots to the second are the Diameters
+of the bright Rings made in this Observation by the thinner Glass,
+3·4-1/6·5-1/8, to the Diameters of the same Rings made in the third of
+these Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, that
+is, the Diameters of the Rings are reciprocally in a subduplicate
+Proportion of the thicknesses of the Plates of Glass.
+
+So then in Plates of Glass which are alike concave on one side, and
+alike convex on the other side, and alike quick-silver'd on the convex
+sides, and differ in nothing but their thickness, the Diameters of the
+Rings are reciprocally in a subduplicate Proportion of the thicknesses
+of the Plates. And this shews sufficiently that the Rings depend on both
+the Surfaces of the Glass. They depend on the convex Surface, because
+they are more luminous when that Surface is quick-silver'd over than
+when it is without Quick-silver. They depend also upon the concave
+Surface, because without that Surface a Speculum makes them not. They
+depend on both Surfaces, and on the distances between them, because
+their bigness is varied by varying only that distance. And this
+dependence is of the same kind with that which the Colours of thin
+Plates have on the distance of the Surfaces of those Plates, because the
+bigness of the Rings, and their Proportion to one another, and the
+variation of their bigness arising from the variation of the thickness
+of the Glass, and the Orders of their Colours, is such as ought to
+result from the Propositions in the end of the third Part of this Book,
+derived from the Phænomena of the Colours of thin Plates set down in the
+first Part.
+
+There are yet other Phænomena of these Rings of Colours, but such as
+follow from the same Propositions, and therefore confirm both the Truth
+of those Propositions, and the Analogy between these Rings and the Rings
+of Colours made by very thin Plates. I shall subjoin some of them.
+
+_Obs._ 10. When the beam of the Sun's Light was reflected back from the
+Speculum not directly to the hole in the Window, but to a place a little
+distant from it, the common center of that Spot, and of all the Rings of
+Colours fell in the middle way between the beam of the incident Light,
+and the beam of the reflected Light, and by consequence in the center of
+the spherical concavity of the Speculum, whenever the Chart on which the
+Rings of Colours fell was placed at that center. And as the beam of
+reflected Light by inclining the Speculum receded more and more from the
+beam of incident Light and from the common center of the colour'd Rings
+between them, those Rings grew bigger and bigger, and so also did the
+white round Spot, and new Rings of Colours emerged successively out of
+their common center, and the white Spot became a white Ring
+encompassing them; and the incident and reflected beams of Light always
+fell upon the opposite parts of this white Ring, illuminating its
+Perimeter like two mock Suns in the opposite parts of an Iris. So then
+the Diameter of this Ring, measured from the middle of its Light on one
+side to the middle of its Light on the other side, was always equal to
+the distance between the middle of the incident beam of Light, and the
+middle of the reflected beam measured at the Chart on which the Rings
+appeared: And the Rays which form'd this Ring were reflected by the
+Speculum in Angles equal to their Angles of Incidence, and by
+consequence to their Angles of Refraction at their entrance into the
+Glass, but yet their Angles of Reflexion were not in the same Planes
+with their Angles of Incidence.
+
+_Obs._ 11. The Colours of the new Rings were in a contrary order to
+those of the former, and arose after this manner. The white round Spot
+of Light in the middle of the Rings continued white to the center till
+the distance of the incident and reflected beams at the Chart was about
+7/8 parts of an Inch, and then it began to grow dark in the middle. And
+when that distance was about 1-3/16 of an Inch, the white Spot was
+become a Ring encompassing a dark round Spot which in the middle
+inclined to violet and indigo. And the luminous Rings encompassing it
+were grown equal to those dark ones which in the four first Observations
+encompassed them, that is to say, the white Spot was grown a white Ring
+equal to the first of those dark Rings, and the first of those luminous
+Rings was now grown equal to the second of those dark ones, and the
+second of those luminous ones to the third of those dark ones, and so
+on. For the Diameters of the luminous Rings were now 1-3/16, 2-1/16,
+2-2/3, 3-3/20, &c. Inches.
+
+When the distance between the incident and reflected beams of Light
+became a little bigger, there emerged out of the middle of the dark Spot
+after the indigo a blue, and then out of that blue a pale green, and
+soon after a yellow and red. And when the Colour at the center was
+brightest, being between yellow and red, the bright Rings were grown
+equal to those Rings which in the four first Observations next
+encompassed them; that is to say, the white Spot in the middle of those
+Rings was now become a white Ring equal to the first of those bright
+Rings, and the first of those bright ones was now become equal to the
+second of those, and so on. For the Diameters of the white Ring, and of
+the other luminous Rings encompassing it, were now 1-11/16, 2-3/8,
+2-11/12, 3-3/8, &c. or thereabouts.
+
+When the distance of the two beams of Light at the Chart was a little
+more increased, there emerged out of the middle in order after the red,
+a purple, a blue, a green, a yellow, and a red inclining much to purple,
+and when the Colour was brightest being between yellow and red, the
+former indigo, blue, green, yellow and red, were become an Iris or Ring
+of Colours equal to the first of those luminous Rings which appeared in
+the four first Observations, and the white Ring which was now become
+the second of the luminous Rings was grown equal to the second of those,
+and the first of those which was now become the third Ring was become
+equal to the third of those, and so on. For their Diameters were
+1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams of
+Light, and the Diameter of the white Ring being 2-3/8 Inches.
+
+When these two beams became more distant there emerged out of the middle
+of the purplish red, first a darker round Spot, and then out of the
+middle of that Spot a brighter. And now the former Colours (purple,
+blue, green, yellow, and purplish red) were become a Ring equal to the
+first of the bright Rings mentioned in the four first Observations, and
+the Rings about this Ring were grown equal to the Rings about that
+respectively; the distance between the two beams of Light and the
+Diameter of the white Ring (which was now become the third Ring) being
+about 3 Inches.
+
+The Colours of the Rings in the middle began now to grow very dilute,
+and if the distance between the two Beams was increased half an Inch, or
+an Inch more, they vanish'd whilst the white Ring, with one or two of
+the Rings next it on either side, continued still visible. But if the
+distance of the two beams of Light was still more increased, these also
+vanished: For the Light which coming from several parts of the hole in
+the Window fell upon the Speculum in several Angles of Incidence, made
+Rings of several bignesses, which diluted and blotted out one another,
+as I knew by intercepting some part of that Light. For if I intercepted
+that part which was nearest to the Axis of the Speculum the Rings would
+be less, if the other part which was remotest from it they would be
+bigger.
+
+_Obs._ 12. When the Colours of the Prism were cast successively on the
+Speculum, that Ring which in the two last Observations was white, was of
+the same bigness in all the Colours, but the Rings without it were
+greater in the green than in the blue, and still greater in the yellow,
+and greatest in the red. And, on the contrary, the Rings within that
+white Circle were less in the green than in the blue, and still less in
+the yellow, and least in the red. For the Angles of Reflexion of those
+Rays which made this Ring, being equal to their Angles of Incidence, the
+Fits of every reflected Ray within the Glass after Reflexion are equal
+in length and number to the Fits of the same Ray within the Glass before
+its Incidence on the reflecting Surface. And therefore since all the
+Rays of all sorts at their entrance into the Glass were in a Fit of
+Transmission, they were also in a Fit of Transmission at their returning
+to the same Surface after Reflexion; and by consequence were
+transmitted, and went out to the white Ring on the Chart. This is the
+reason why that Ring was of the same bigness in all the Colours, and why
+in a mixture of all it appears white. But in Rays which are reflected in
+other Angles, the Intervals of the Fits of the least refrangible being
+greatest, make the Rings of their Colour in their progress from this
+white Ring, either outwards or inwards, increase or decrease by the
+greatest steps; so that the Rings of this Colour without are greatest,
+and within least. And this is the reason why in the last Observation,
+when the Speculum was illuminated with white Light, the exterior Rings
+made by all Colours appeared red without and blue within, and the
+interior blue without and red within.
+
+These are the Phænomena of thick convexo-concave Plates of Glass, which
+are every where of the same thickness. There are yet other Phænomena
+when these Plates are a little thicker on one side than on the other,
+and others when the Plates are more or less concave than convex, or
+plano-convex, or double-convex. For in all these cases the Plates make
+Rings of Colours, but after various manners; all which, so far as I have
+yet observed, follow from the Propositions in the end of the third part
+of this Book, and so conspire to confirm the truth of those
+Propositions. But the Phænomena are too various, and the Calculations
+whereby they follow from those Propositions too intricate to be here
+prosecuted. I content my self with having prosecuted this kind of
+Phænomena so far as to discover their Cause, and by discovering it to
+ratify the Propositions in the third Part of this Book.
+
+_Obs._ 13. As Light reflected by a Lens quick-silver'd on the backside
+makes the Rings of Colours above described, so it ought to make the like
+Rings of Colours in passing through a drop of Water. At the first
+Reflexion of the Rays within the drop, some Colours ought to be
+transmitted, as in the case of a Lens, and others to be reflected back
+to the Eye. For instance, if the Diameter of a small drop or globule of
+Water be about the 500th part of an Inch, so that a red-making Ray in
+passing through the middle of this globule has 250 Fits of easy
+Transmission within the globule, and that all the red-making Rays which
+are at a certain distance from this middle Ray round about it have 249
+Fits within the globule, and all the like Rays at a certain farther
+distance round about it have 248 Fits, and all those at a certain
+farther distance 247 Fits, and so on; these concentrick Circles of Rays
+after their transmission, falling on a white Paper, will make
+concentrick Rings of red upon the Paper, supposing the Light which
+passes through one single globule, strong enough to be sensible. And, in
+like manner, the Rays of other Colours will make Rings of other Colours.
+Suppose now that in a fair Day the Sun shines through a thin Cloud of
+such globules of Water or Hail, and that the globules are all of the
+same bigness; and the Sun seen through this Cloud shall appear
+encompassed with the like concentrick Rings of Colours, and the Diameter
+of the first Ring of red shall be 7-1/4 Degrees, that of the second
+10-1/4 Degrees, that of the third 12 Degrees 33 Minutes. And accordingly
+as the Globules of Water are bigger or less, the Rings shall be less or
+bigger. This is the Theory, and Experience answers it. For in _June_
+1692, I saw by reflexion in a Vessel of stagnating Water three Halos,
+Crowns, or Rings of Colours about the Sun, like three little Rain-bows,
+concentrick to his Body. The Colours of the first or innermost Crown
+were blue next the Sun, red without, and white in the middle between the
+blue and red. Those of the second Crown were purple and blue within, and
+pale red without, and green in the middle. And those of the third were
+pale blue within, and pale red without; these Crowns enclosed one
+another immediately, so that their Colours proceeded in this continual
+order from the Sun outward: blue, white, red; purple, blue, green, pale
+yellow and red; pale blue, pale red. The Diameter of the second Crown
+measured from the middle of the yellow and red on one side of the Sun,
+to the middle of the same Colour on the other side was 9-1/3 Degrees, or
+thereabouts. The Diameters of the first and third I had not time to
+measure, but that of the first seemed to be about five or six Degrees,
+and that of the third about twelve. The like Crowns appear sometimes
+about the Moon; for in the beginning of the Year 1664, _Febr._ 19th at
+Night, I saw two such Crowns about her. The Diameter of the first or
+innermost was about three Degrees, and that of the second about five
+Degrees and an half. Next about the Moon was a Circle of white, and next
+about that the inner Crown, which was of a bluish green within next the
+white, and of a yellow and red without, and next about these Colours
+were blue and green on the inside of the outward Crown, and red on the
+outside of it. At the same time there appear'd a Halo about 22 Degrees
+35´ distant from the center of the Moon. It was elliptical, and its long
+Diameter was perpendicular to the Horizon, verging below farthest from
+the Moon. I am told that the Moon has sometimes three or more
+concentrick Crowns of Colours encompassing one another next about her
+Body. The more equal the globules of Water or Ice are to one another,
+the more Crowns of Colours will appear, and the Colours will be the more
+lively. The Halo at the distance of 22-1/2 Degrees from the Moon is of
+another sort. By its being oval and remoter from the Moon below than
+above, I conclude, that it was made by Refraction in some sort of Hail
+or Snow floating in the Air in an horizontal posture, the refracting
+Angle being about 58 or 60 Degrees.
+
+
+
+
+THE
+
+THIRD BOOK
+
+OF
+
+OPTICKS
+
+
+_PART I._
+
+_Observations concerning the Inflexions of the Rays of Light, and the
+Colours made thereby._
+
+Grimaldo has inform'd us, that if a beam of the Sun's Light be let into
+a dark Room through a very small hole, the Shadows of things in this
+Light will be larger than they ought to be if the Rays went on by the
+Bodies in straight Lines, and that these Shadows have three parallel
+Fringes, Bands or Ranks of colour'd Light adjacent to them. But if the
+Hole be enlarged the Fringes grow broad and run into one another, so
+that they cannot be distinguish'd. These broad Shadows and Fringes have
+been reckon'd by some to proceed from the ordinary refraction of the
+Air, but without due examination of the Matter. For the circumstances of
+the Phænomenon, so far as I have observed them, are as follows.
+
+_Obs._ 1. I made in a piece of Lead a small Hole with a Pin, whose
+breadth was the 42d part of an Inch. For 21 of those Pins laid together
+took up the breadth of half an Inch. Through this Hole I let into my
+darken'd Chamber a beam of the Sun's Light, and found that the Shadows
+of Hairs, Thred, Pins, Straws, and such like slender Substances placed
+in this beam of Light, were considerably broader than they ought to be,
+if the Rays of Light passed on by these Bodies in right Lines. And
+particularly a Hair of a Man's Head, whose breadth was but the 280th
+part of an Inch, being held in this Light, at the distance of about
+twelve Feet from the Hole, did cast a Shadow which at the distance of
+four Inches from the Hair was the sixtieth part of an Inch broad, that
+is, above four times broader than the Hair, and at the distance of two
+Feet from the Hair was about the eight and twentieth part of an Inch
+broad, that is, ten times broader than the Hair, and at the distance of
+ten Feet was the eighth part of an Inch broad, that is 35 times broader.
+
+Nor is it material whether the Hair be encompassed with Air, or with any
+other pellucid Substance. For I wetted a polish'd Plate of Glass, and
+laid the Hair in the Water upon the Glass, and then laying another
+polish'd Plate of Glass upon it, so that the Water might fill up the
+space between the Glasses, I held them in the aforesaid beam of Light,
+so that the Light might pass through them perpendicularly, and the
+Shadow of the Hair was at the same distances as big as before. The
+Shadows of Scratches made in polish'd Plates of Glass were also much
+broader than they ought to be, and the Veins in polish'd Plates of Glass
+did also cast the like broad Shadows. And therefore the great breadth of
+these Shadows proceeds from some other cause than the Refraction of the
+Air.
+
+Let the Circle X [in _Fig._ 1.] represent the middle of the Hair; ADG,
+BEH, CFI, three Rays passing by one side of the Hair at several
+distances; KNQ, LOR, MPS, three other Rays passing by the other side of
+the Hair at the like distances; D, E, F, and N, O, P, the places where
+the Rays are bent in their passage by the Hair; G, H, I, and Q, R, S,
+the places where the Rays fall on a Paper GQ; IS the breadth of the
+Shadow of the Hair cast on the Paper, and TI, VS, two Rays passing to
+the Points I and S without bending when the Hair is taken away. And it's
+manifest that all the Light between these two Rays TI and VS is bent in
+passing by the Hair, and turned aside from the Shadow IS, because if any
+part of this Light were not bent it would fall on the Paper within the
+Shadow, and there illuminate the Paper, contrary to experience. And
+because when the Paper is at a great distance from the Hair, the Shadow
+is broad, and therefore the Rays TI and VS are at a great distance from
+one another, it follows that the Hair acts upon the Rays of Light at a
+good distance in their passing by it. But the Action is strongest on the
+Rays which pass by at least distances, and grows weaker and weaker
+accordingly as the Rays pass by at distances greater and greater, as is
+represented in the Scheme: For thence it comes to pass, that the Shadow
+of the Hair is much broader in proportion to the distance of the Paper
+from the Hair, when the Paper is nearer the Hair, than when it is at a
+great distance from it.
+
+_Obs._ 2. The Shadows of all Bodies (Metals, Stones, Glass, Wood, Horn,
+Ice, &c.) in this Light were border'd with three Parallel Fringes or
+Bands of colour'd Light, whereof that which was contiguous to the Shadow
+was broadest and most luminous, and that which was remotest from it was
+narrowest, and so faint, as not easily to be visible. It was difficult
+to distinguish the Colours, unless when the Light fell very obliquely
+upon a smooth Paper, or some other smooth white Body, so as to make them
+appear much broader than they would otherwise do. And then the Colours
+were plainly visible in this Order: The first or innermost Fringe was
+violet and deep blue next the Shadow, and then light blue, green, and
+yellow in the middle, and red without. The second Fringe was almost
+contiguous to the first, and the third to the second, and both were blue
+within, and yellow and red without, but their Colours were very faint,
+especially those of the third. The Colours therefore proceeded in this
+order from the Shadow; violet, indigo, pale blue, green, yellow, red;
+blue, yellow, red; pale blue, pale yellow and red. The Shadows made by
+Scratches and Bubbles in polish'd Plates of Glass were border'd with the
+like Fringes of colour'd Light. And if Plates of Looking-glass sloop'd
+off near the edges with a Diamond-cut, be held in the same beam of
+Light, the Light which passes through the parallel Planes of the Glass
+will be border'd with the like Fringes of Colours where those Planes
+meet with the Diamond-cut, and by this means there will sometimes appear
+four or five Fringes of Colours. Let AB, CD [in _Fig._ 2.] represent the
+parallel Planes of a Looking-glass, and BD the Plane of the Diamond-cut,
+making at B a very obtuse Angle with the Plane AB. And let all the Light
+between the Rays ENI and FBM pass directly through the parallel Planes
+of the Glass, and fall upon the Paper between I and M, and all the Light
+between the Rays GO and HD be refracted by the oblique Plane of the
+Diamond-cut BD, and fall upon the Paper between K and L; and the Light
+which passes directly through the parallel Planes of the Glass, and
+falls upon the Paper between I and M, will be border'd with three or
+more Fringes at M.
+
+[Illustration: FIG. 1.]
+
+[Illustration: FIG. 2.]
+
+So by looking on the Sun through a Feather or black Ribband held close
+to the Eye, several Rain-bows will appear; the Shadows which the Fibres
+or Threds cast on the _Tunica Retina_, being border'd with the like
+Fringes of Colours.
+
+_Obs._ 3. When the Hair was twelve Feet distant from this Hole, and its
+Shadow fell obliquely upon a flat white Scale of Inches and Parts of an
+Inch placed half a Foot beyond it, and also when the Shadow fell
+perpendicularly upon the same Scale placed nine Feet beyond it; I
+measured the breadth of the Shadow and Fringes as accurately as I could,
+and found them in Parts of an Inch as follows.
+
+-------------------------------------------+-----------+--------
+                                           |  half a   | Nine
+                      At the Distance of   |   Foot    |  Feet
+-------------------------------------------+-----------+--------
+The breadth of the Shadow                  |   1/54    |  1/9
+-------------------------------------------+-----------+--------
+The breadth between the Middles of the     |   1/38    |
+  brightest Light of the innermost Fringes |    or     |
+  on either side the Shadow                |   1/39    |  7/50
+-------------------------------------------+-----------+--------
+The breadth between the Middles of the     |           |
+  brightest Light of the middlemost Fringes|           |
+  on either side the Shadow                | 1/23-1/2  |  4/17
+-------------------------------------------+-----------+--------
+The breadth between the Middles of the     |  1/18     |
+  brightest Light of the outmost Fringes   |   or      |
+  on either side the Shadow                | 1/18-1/2  |  3/10
+-------------------------------------------+-----------+--------
+The distance between the Middles of the    |           |
+  brightest Light of the first and second  |           |
+  Fringes                                  |  1/120    |  1/21
+-------------------------------------------+-----------+--------
+The distance between the Middles of the    |           |
+  brightest Light of the second and third  |           |
+  Fringes                                  |  1/170    |  1/31
+-------------------------------------------+-----------+--------
+The breadth of the luminous Part (green,   |           |
+  white, yellow, and red) of the first     |           |
+  Fringe                                   |  1/170    |  1/32
+-------------------------------------------+-----------+--------
+The breadth of the darker Space between    |           |
+  the first and second Fringes             |  1/240    |  1/45
+-------------------------------------------+-----------+--------
+The breadth of the luminous Part of the    |           |
+  second Fringe                            |  1/290    |  1/55
+-------------------------------------------+-----------+--------
+The breadth of the darker Space between    |           |
+  the second and third Fringes             |  1/340    |  1/63
+-------------------------------------------+-----------+--------
+
+These Measures I took by letting the Shadow of the Hair, at half a Foot
+distance, fall so obliquely on the Scale, as to appear twelve times
+broader than when it fell perpendicularly on it at the same distance,
+and setting down in this Table the twelfth part of the Measures I then
+took.
+
+_Obs._ 4. When the Shadow and Fringes were cast obliquely upon a smooth
+white Body, and that Body was removed farther and farther from the Hair,
+the first Fringe began to appear and look brighter than the rest of the
+Light at the distance of less than a quarter of an Inch from the Hair,
+and the dark Line or Shadow between that and the second Fringe began to
+appear at a less distance from the Hair than that of the third part of
+an Inch. The second Fringe began to appear at a distance from the Hair
+of less than half an Inch, and the Shadow between that and the third
+Fringe at a distance less than an inch, and the third Fringe at a
+distance less than three Inches. At greater distances they became much
+more sensible, but kept very nearly the same proportion of their
+breadths and intervals which they had at their first appearing. For the
+distance between the middle of the first, and middle of the second
+Fringe, was to the distance between the middle of the second and middle
+of the third Fringe, as three to two, or ten to seven. And the last of
+these two distances was equal to the breadth of the bright Light or
+luminous part of the first Fringe. And this breadth was to the breadth
+of the bright Light of the second Fringe as seven to four, and to the
+dark Interval of the first and second Fringe as three to two, and to
+the like dark Interval between the second and third as two to one. For
+the breadths of the Fringes seem'd to be in the progression of the
+Numbers 1, sqrt(1/3), sqrt(1/5), and their Intervals to be in the
+same progression with them; that is, the Fringes and their Intervals
+together to be in the continual progression of the Numbers 1,
+sqrt(1/2), sqrt(1/3), sqrt(1/4), sqrt(1/5), or thereabouts. And
+these Proportions held the same very nearly at all distances from the
+Hair; the dark Intervals of the Fringes being as broad in proportion to
+the breadth of the Fringes at their first appearance as afterwards at
+great distances from the Hair, though not so dark and distinct.
+
+_Obs._ 5. The Sun shining into my darken'd Chamber through a hole a
+quarter of an Inch broad, I placed at the distance of two or three Feet
+from the Hole a Sheet of Pasteboard, which was black'd all over on both
+sides, and in the middle of it had a hole about three quarters of an
+Inch square for the Light to pass through. And behind the hole I
+fasten'd to the Pasteboard with Pitch the blade of a sharp Knife, to
+intercept some part of the Light which passed through the hole. The
+Planes of the Pasteboard and blade of the Knife were parallel to one
+another, and perpendicular to the Rays. And when they were so placed
+that none of the Sun's Light fell on the Pasteboard, but all of it
+passed through the hole to the Knife, and there part of it fell upon the
+blade of the Knife, and part of it passed by its edge; I let this part
+of the Light which passed by, fall on a white Paper two or three Feet
+beyond the Knife, and there saw two streams of faint Light shoot out
+both ways from the beam of Light into the shadow, like the Tails of
+Comets. But because the Sun's direct Light by its brightness upon the
+Paper obscured these faint streams, so that I could scarce see them, I
+made a little hole in the midst of the Paper for that Light to pass
+through and fall on a black Cloth behind it; and then I saw the two
+streams plainly. They were like one another, and pretty nearly equal in
+length, and breadth, and quantity of Light. Their Light at that end next
+the Sun's direct Light was pretty strong for the space of about a
+quarter of an Inch, or half an Inch, and in all its progress from that
+direct Light decreased gradually till it became insensible. The whole
+length of either of these streams measured upon the paper at the
+distance of three Feet from the Knife was about six or eight Inches; so
+that it subtended an Angle at the edge of the Knife of about 10 or 12,
+or at most 14 Degrees. Yet sometimes I thought I saw it shoot three or
+four Degrees farther, but with a Light so very faint that I could scarce
+perceive it, and suspected it might (in some measure at least) arise
+from some other cause than the two streams did. For placing my Eye in
+that Light beyond the end of that stream which was behind the Knife, and
+looking towards the Knife, I could see a line of Light upon its edge,
+and that not only when my Eye was in the line of the Streams, but also
+when it was without that line either towards the point of the Knife, or
+towards the handle. This line of Light appear'd contiguous to the edge
+of the Knife, and was narrower than the Light of the innermost Fringe,
+and narrowest when my Eye was farthest from the direct Light, and
+therefore seem'd to pass between the Light of that Fringe and the edge
+of the Knife, and that which passed nearest the edge to be most bent,
+though not all of it.
+
+_Obs._ 6. I placed another Knife by this, so that their edges might be
+parallel, and look towards one another, and that the beam of Light might
+fall upon both the Knives, and some part of it pass between their edges.
+And when the distance of their edges was about the 400th part of an
+Inch, the stream parted in the middle, and left a Shadow between the two
+parts. This Shadow was so black and dark that all the Light which passed
+between the Knives seem'd to be bent, and turn'd aside to the one hand
+or to the other. And as the Knives still approach'd one another the
+Shadow grew broader, and the streams shorter at their inward ends which
+were next the Shadow, until upon the contact of the Knives the whole
+Light vanish'd, leaving its place to the Shadow.
+
+And hence I gather that the Light which is least bent, and goes to the
+inward ends of the streams, passes by the edges of the Knives at the
+greatest distance, and this distance when the Shadow begins to appear
+between the streams, is about the 800th part of an Inch. And the Light
+which passes by the edges of the Knives at distances still less and
+less, is more and more bent, and goes to those parts of the streams
+which are farther and farther from the direct Light; because when the
+Knives approach one another till they touch, those parts of the streams
+vanish last which are farthest from the direct Light.
+
+_Obs._ 7. In the fifth Observation the Fringes did not appear, but by
+reason of the breadth of the hole in the Window became so broad as to
+run into one another, and by joining, to make one continued Light in the
+beginning of the streams. But in the sixth, as the Knives approached one
+another, a little before the Shadow appeared between the two streams,
+the Fringes began to appear on the inner ends of the Streams on either
+side of the direct Light; three on one side made by the edge of one
+Knife, and three on the other side made by the edge of the other Knife.
+They were distinctest when the Knives were placed at the greatest
+distance from the hole in the Window, and still became more distinct by
+making the hole less, insomuch that I could sometimes see a faint
+lineament of a fourth Fringe beyond the three above mention'd. And as
+the Knives continually approach'd one another, the Fringes grew
+distincter and larger, until they vanish'd. The outmost Fringe vanish'd
+first, and the middlemost next, and the innermost last. And after they
+were all vanish'd, and the line of Light which was in the middle between
+them was grown very broad, enlarging it self on both sides into the
+streams of Light described in the fifth Observation, the above-mention'd
+Shadow began to appear in the middle of this line, and divide it along
+the middle into two lines of Light, and increased until the whole Light
+vanish'd. This enlargement of the Fringes was so great that the Rays
+which go to the innermost Fringe seem'd to be bent above twenty times
+more when this Fringe was ready to vanish, than when one of the Knives
+was taken away.
+
+And from this and the former Observation compared, I gather, that the
+Light of the first Fringe passed by the edge of the Knife at a distance
+greater than the 800th part of an Inch, and the Light of the second
+Fringe passed by the edge of the Knife at a greater distance than the
+Light of the first Fringe did, and that of the third at a greater
+distance than that of the second, and that of the streams of Light
+described in the fifth and sixth Observations passed by the edges of the
+Knives at less distances than that of any of the Fringes.
+
+_Obs._ 8. I caused the edges of two Knives to be ground truly strait,
+and pricking their points into a Board so that their edges might look
+towards one another, and meeting near their points contain a rectilinear
+Angle, I fasten'd their Handles together with Pitch to make this Angle
+invariable. The distance of the edges of the Knives from one another at
+the distance of four Inches from the angular Point, where the edges of
+the Knives met, was the eighth part of an Inch; and therefore the Angle
+contain'd by the edges was about one Degree 54: The Knives thus fix'd
+together I placed in a beam of the Sun's Light, let into my darken'd
+Chamber through a Hole the 42d Part of an Inch wide, at the distance of
+10 or 15 Feet from the Hole, and let the Light which passed between
+their edges fall very obliquely upon a smooth white Ruler at the
+distance of half an Inch, or an Inch from the Knives, and there saw the
+Fringes by the two edges of the Knives run along the edges of the
+Shadows of the Knives in Lines parallel to those edges without growing
+sensibly broader, till they met in Angles equal to the Angle contained
+by the edges of the Knives, and where they met and joined they ended
+without crossing one another. But if the Ruler was held at a much
+greater distance from the Knives, the Fringes where they were farther
+from the Place of their Meeting, were a little narrower, and became
+something broader and broader as they approach'd nearer and nearer to
+one another, and after they met they cross'd one another, and then
+became much broader than before.
+
+Whence I gather that the distances at which the Fringes pass by the
+Knives are not increased nor alter'd by the approach of the Knives, but
+the Angles in which the Rays are there bent are much increased by that
+approach; and that the Knife which is nearest any Ray determines which
+way the Ray shall be bent, and the other Knife increases the bent.
+
+_Obs._ 9. When the Rays fell very obliquely upon the Ruler at the
+distance of the third Part of an Inch from the Knives, the dark Line
+between the first and second Fringe of the Shadow of one Knife, and the
+dark Line between the first and second Fringe of the Shadow of the other
+knife met with one another, at the distance of the fifth Part of an Inch
+from the end of the Light which passed between the Knives at the
+concourse of their edges. And therefore the distance of the edges of the
+Knives at the meeting of these dark Lines was the 160th Part of an Inch.
+For as four Inches to the eighth Part of an Inch, so is any Length of
+the edges of the Knives measured from the point of their concourse to
+the distance of the edges of the Knives at the end of that Length, and
+so is the fifth Part of an Inch to the 160th Part. So then the dark
+Lines above-mention'd meet in the middle of the Light which passes
+between the Knives where they are distant the 160th Part of an Inch, and
+the one half of that Light passes by the edge of one Knife at a distance
+not greater than the 320th Part of an Inch, and falling upon the Paper
+makes the Fringes of the Shadow of that Knife, and the other half passes
+by the edge of the other Knife, at a distance not greater than the 320th
+Part of an Inch, and falling upon the Paper makes the Fringes of the
+Shadow of the other Knife. But if the Paper be held at a distance from
+the Knives greater than the third Part of an Inch, the dark Lines
+above-mention'd meet at a greater distance than the fifth Part of an
+Inch from the end of the Light which passed between the Knives at the
+concourse of their edges; and therefore the Light which falls upon the
+Paper where those dark Lines meet passes between the Knives where the
+edges are distant above the 160th part of an Inch.
+
+For at another time, when the two Knives were distant eight Feet and
+five Inches from the little hole in the Window, made with a small Pin as
+above, the Light which fell upon the Paper where the aforesaid dark
+lines met, passed between the Knives, where the distance between their
+edges was as in the following Table, when the distance of the Paper from
+the Knives was also as follows.
+
+-----------------------------+------------------------------
+                             | Distances between the edges
+ Distances of the Paper      |  of the Knives in millesimal
+ from the Knives in Inches.  |      parts of an Inch.
+-----------------------------+------------------------------
+          1-1/2.             |             0'012
+          3-1/3.             |             0'020
+          8-3/5.             |             0'034
+         32.                 |             0'057
+         96.                 |             0'081
+        131.                 |             0'087
+_____________________________|______________________________
+
+And hence I gather, that the Light which makes the Fringes upon the
+Paper is not the same Light at all distances of the Paper from the
+Knives, but when the Paper is held near the Knives, the Fringes are made
+by Light which passes by the edges of the Knives at a less distance, and
+is more bent than when the Paper is held at a greater distance from the
+Knives.
+
+[Illustration: FIG. 3.]
+
+_Obs._ 10. When the Fringes of the Shadows of the Knives fell
+perpendicularly upon a Paper at a great distance from the Knives, they
+were in the form of Hyperbola's, and their Dimensions were as follows.
+Let CA, CB [in _Fig._ 3.] represent Lines drawn upon the Paper parallel
+to the edges of the Knives, and between which all the Light would fall,
+if it passed between the edges of the Knives without inflexion; DE a
+Right Line drawn through C making the Angles ACD, BCE, equal to one
+another, and terminating all the Light which falls upon the Paper from
+the point where the edges of the Knives meet; _eis_, _fkt_, and _glv_,
+three hyperbolical Lines representing the Terminus of the Shadow of one
+of the Knives, the dark Line between the first and second Fringes of
+that Shadow, and the dark Line between the second and third Fringes of
+the same Shadow; _xip_, _ykq_, and _zlr_, three other hyperbolical Lines
+representing the Terminus of the Shadow of the other Knife, the dark
+Line between the first and second Fringes of that Shadow, and the dark
+line between the second and third Fringes of the same Shadow. And
+conceive that these three Hyperbola's are like and equal to the former
+three, and cross them in the points _i_, _k_, and _l_, and that the
+Shadows of the Knives are terminated and distinguish'd from the first
+luminous Fringes by the lines _eis_ and _xip_, until the meeting and
+crossing of the Fringes, and then those lines cross the Fringes in the
+form of dark lines, terminating the first luminous Fringes within side,
+and distinguishing them from another Light which begins to appear at
+_i_, and illuminates all the triangular space _ip_DE_s_ comprehended by
+these dark lines, and the right line DE. Of these Hyperbola's one
+Asymptote is the line DE, and their other Asymptotes are parallel to the
+lines CA and CB. Let _rv_ represent a line drawn any where upon the
+Paper parallel to the Asymptote DE, and let this line cross the right
+lines AC in _m_, and BC in _n_, and the six dark hyperbolical lines in
+_p_, _q_, _r_; _s_, _t_, _v_; and by measuring the distances _ps_, _qt_,
+_rv_, and thence collecting the lengths of the Ordinates _np_, _nq_,
+_nr_ or _ms_, _mt_, _mv_, and doing this at several distances of the
+line _rv_ from the Asymptote DD, you may find as many points of these
+Hyperbola's as you please, and thereby know that these curve lines are
+Hyperbola's differing little from the conical Hyperbola. And by
+measuring the lines C_i_, C_k_, C_l_, you may find other points of these
+Curves.
+
+For instance; when the Knives were distant from the hole in the Window
+ten Feet, and the Paper from the Knives nine Feet, and the Angle
+contained by the edges of the Knives to which the Angle ACB is equal,
+was subtended by a Chord which was to the Radius as 1 to 32, and the
+distance of the line _rv_ from the Asymptote DE was half an Inch: I
+measured the lines _ps_, _qt_, _rv_, and found them 0'35, 0'65, 0'98
+Inches respectively; and by adding to their halfs the line 1/2 _mn_,
+(which here was the 128th part of an Inch, or 0'0078 Inches,) the Sums
+_np_, _nq_, _nr_, were 0'1828, 0'3328, 0'4978 Inches. I measured also
+the distances of the brightest parts of the Fringes which run between
+_pq_ and _st_, _qr_ and _tv_, and next beyond _r_ and _v_, and found
+them 0'5, 0'8, and 1'17 Inches.
+
+_Obs._ 11. The Sun shining into my darken'd Room through a small round
+hole made in a Plate of Lead with a slender Pin, as above; I placed at
+the hole a Prism to refract the Light, and form on the opposite Wall the
+Spectrum of Colours, described in the third Experiment of the first
+Book. And then I found that the Shadows of all Bodies held in the
+colour'd Light between the Prism and the Wall, were border'd with
+Fringes of the Colour of that Light in which they were held. In the full
+red Light they were totally red without any sensible blue or violet, and
+in the deep blue Light they were totally blue without any sensible red
+or yellow; and so in the green Light they were totally green, excepting
+a little yellow and blue, which were mixed in the green Light of the
+Prism. And comparing the Fringes made in the several colour'd Lights, I
+found that those made in the red Light were largest, those made in the
+violet were least, and those made in the green were of a middle bigness.
+For the Fringes with which the Shadow of a Man's Hair were bordered,
+being measured cross the Shadow at the distance of six Inches from the
+Hair, the distance between the middle and most luminous part of the
+first or innermost Fringe on one side of the Shadow, and that of the
+like Fringe on the other side of the Shadow, was in the full red Light
+1/37-1/4 of an Inch, and in the full violet 7/46. And the like distance
+between the middle and most luminous parts of the second Fringes on
+either side the Shadow was in the full red Light 1/22, and in the violet
+1/27 of an Inch. And these distances of the Fringes held the same
+proportion at all distances from the Hair without any sensible
+variation.
+
+So then the Rays which made these Fringes in the red Light passed by the
+Hair at a greater distance than those did which made the like Fringes in
+the violet; and therefore the Hair in causing these Fringes acted alike
+upon the red Light or least refrangible Rays at a greater distance, and
+upon the violet or most refrangible Rays at a less distance, and by
+those actions disposed the red Light into Larger Fringes, and the violet
+into smaller, and the Lights of intermediate Colours into Fringes of
+intermediate bignesses without changing the Colour of any sort of Light.
+
+When therefore the Hair in the first and second of these Observations
+was held in the white beam of the Sun's Light, and cast a Shadow which
+was border'd with three Fringes of coloured Light, those Colours arose
+not from any new modifications impress'd upon the Rays of Light by the
+Hair, but only from the various inflexions whereby the several Sorts of
+Rays were separated from one another, which before separation, by the
+mixture of all their Colours, composed the white beam of the Sun's
+Light, but whenever separated compose Lights of the several Colours
+which they are originally disposed to exhibit. In this 11th Observation,
+where the Colours are separated before the Light passes by the Hair, the
+least refrangible Rays, which when separated from the rest make red,
+were inflected at a greater distance from the Hair, so as to make three
+red Fringes at a greater distance from the middle of the Shadow of the
+Hair; and the most refrangible Rays which when separated make violet,
+were inflected at a less distance from the Hair, so as to make three
+violet Fringes at a less distance from the middle of the Shadow of the
+Hair. And other Rays of intermediate degrees of Refrangibility were
+inflected at intermediate distances from the Hair, so as to make Fringes
+of intermediate Colours at intermediate distances from the middle of the
+Shadow of the Hair. And in the second Observation, where all the Colours
+are mix'd in the white Light which passes by the Hair, these Colours are
+separated by the various inflexions of the Rays, and the Fringes which
+they make appear all together, and the innermost Fringes being
+contiguous make one broad Fringe composed of all the Colours in due
+order, the violet lying on the inside of the Fringe next the Shadow, the
+red on the outside farthest from the Shadow, and the blue, green, and
+yellow, in the middle. And, in like manner, the middlemost Fringes of
+all the Colours lying in order, and being contiguous, make another broad
+Fringe composed of all the Colours; and the outmost Fringes of all the
+Colours lying in order, and being contiguous, make a third broad Fringe
+composed of all the Colours. These are the three Fringes of colour'd
+Light with which the Shadows of all Bodies are border'd in the second
+Observation.
+
+When I made the foregoing Observations, I design'd to repeat most of
+them with more care and exactness, and to make some new ones for
+determining the manner how the Rays of Light are bent in their passage
+by Bodies, for making the Fringes of Colours with the dark lines between
+them. But I was then interrupted, and cannot now think of taking these
+things into farther Consideration. And since I have not finish'd this
+part of my Design, I shall conclude with proposing only some Queries, in
+order to a farther search to be made by others.
+
+_Query_ 1. Do not Bodies act upon Light at a distance, and by their
+action bend its Rays; and is not this action (_cæteris paribus_)
+strongest at the least distance?
+
+_Qu._ 2. Do not the Rays which differ in Refrangibility differ also in
+Flexibity; and are they not by their different Inflexions separated from
+one another, so as after separation to make the Colours in the three
+Fringes above described? And after what manner are they inflected to
+make those Fringes?
+
+_Qu._ 3. Are not the Rays of Light in passing by the edges and sides of
+Bodies, bent several times backwards and forwards, with a motion like
+that of an Eel? And do not the three Fringes of colour'd Light
+above-mention'd arise from three such bendings?
+
+_Qu._ 4. Do not the Rays of Light which fall upon Bodies, and are
+reflected or refracted, begin to bend before they arrive at the Bodies;
+and are they not reflected, refracted, and inflected, by one and the
+same Principle, acting variously in various Circumstances?
+
+_Qu._ 5. Do not Bodies and Light act mutually upon one another; that is
+to say, Bodies upon Light in emitting, reflecting, refracting and
+inflecting it, and Light upon Bodies for heating them, and putting their
+parts into a vibrating motion wherein heat consists?
+
+_Qu._ 6. Do not black Bodies conceive heat more easily from Light than
+those of other Colours do, by reason that the Light falling on them is
+not reflected outwards, but enters the Bodies, and is often reflected
+and refracted within them, until it be stifled and lost?
+
+_Qu._ 7. Is not the strength and vigor of the action between Light and
+sulphureous Bodies observed above, one reason why sulphureous Bodies
+take fire more readily, and burn more vehemently than other Bodies do?
+
+_Qu._ 8. Do not all fix'd Bodies, when heated beyond a certain degree,
+emit Light and shine; and is not this Emission perform'd by the
+vibrating motions of their parts? And do not all Bodies which abound
+with terrestrial parts, and especially with sulphureous ones, emit Light
+as often as those parts are sufficiently agitated; whether that
+agitation be made by Heat, or by Friction, or Percussion, or
+Putrefaction, or by any vital Motion, or any other Cause? As for
+instance; Sea-Water in a raging Storm; Quick-silver agitated in _vacuo_;
+the Back of a Cat, or Neck of a Horse, obliquely struck or rubbed in a
+dark place; Wood, Flesh and Fish while they putrefy; Vapours arising
+from putrefy'd Waters, usually call'd _Ignes Fatui_; Stacks of moist Hay
+or Corn growing hot by fermentation; Glow-worms and the Eyes of some
+Animals by vital Motions; the vulgar _Phosphorus_ agitated by the
+attrition of any Body, or by the acid Particles of the Air; Amber and
+some Diamonds by striking, pressing or rubbing them; Scrapings of Steel
+struck off with a Flint; Iron hammer'd very nimbly till it become so hot
+as to kindle Sulphur thrown upon it; the Axletrees of Chariots taking
+fire by the rapid rotation of the Wheels; and some Liquors mix'd with
+one another whose Particles come together with an Impetus, as Oil of
+Vitriol distilled from its weight of Nitre, and then mix'd with twice
+its weight of Oil of Anniseeds. So also a Globe of Glass about 8 or 10
+Inches in diameter, being put into a Frame where it may be swiftly
+turn'd round its Axis, will in turning shine where it rubs against the
+palm of ones Hand apply'd to it: And if at the same time a piece of
+white Paper or white Cloth, or the end of ones Finger be held at the
+distance of about a quarter of an Inch or half an Inch from that part of
+the Glass where it is most in motion, the electrick Vapour which is
+excited by the friction of the Glass against the Hand, will by dashing
+against the white Paper, Cloth or Finger, be put into such an agitation
+as to emit Light, and make the white Paper, Cloth or Finger, appear
+lucid like a Glowworm; and in rushing out of the Glass will sometimes
+push against the finger so as to be felt. And the same things have been
+found by rubbing a long and large Cylinder or Glass or Amber with a
+Paper held in ones hand, and continuing the friction till the Glass grew
+warm.
+
+_Qu._ 9. Is not Fire a Body heated so hot as to emit Light copiously?
+For what else is a red hot Iron than Fire? And what else is a burning
+Coal than red hot Wood?
+
+_Qu._ 10. Is not Flame a Vapour, Fume or Exhalation heated red hot, that
+is, so hot as to shine? For Bodies do not flame without emitting a
+copious Fume, and this Fume burns in the Flame. The _Ignis Fatuus_ is a
+Vapour shining without heat, and is there not the same difference
+between this Vapour and Flame, as between rotten Wood shining without
+heat and burning Coals of Fire? In distilling hot Spirits, if the Head
+of the Still be taken off, the Vapour which ascends out of the Still
+will take fire at the Flame of a Candle, and turn into Flame, and the
+Flame will run along the Vapour from the Candle to the Still. Some
+Bodies heated by Motion, or Fermentation, if the heat grow intense, fume
+copiously, and if the heat be great enough the Fumes will shine and
+become Flame. Metals in fusion do not flame for want of a copious Fume,
+except Spelter, which fumes copiously, and thereby flames. All flaming
+Bodies, as Oil, Tallow, Wax, Wood, fossil Coals, Pitch, Sulphur, by
+flaming waste and vanish into burning Smoke, which Smoke, if the Flame
+be put out, is very thick and visible, and sometimes smells strongly,
+but in the Flame loses its smell by burning, and according to the nature
+of the Smoke the Flame is of several Colours, as that of Sulphur blue,
+that of Copper open'd with sublimate green, that of Tallow yellow, that
+of Camphire white. Smoke passing through Flame cannot but grow red hot,
+and red hot Smoke can have no other appearance than that of Flame. When
+Gun-powder takes fire, it goes away into Flaming Smoke. For the Charcoal
+and Sulphur easily take fire, and set fire to the Nitre, and the Spirit
+of the Nitre being thereby rarified into Vapour, rushes out with
+Explosion much after the manner that the Vapour of Water rushes out of
+an Æolipile; the Sulphur also being volatile is converted into Vapour,
+and augments the Explosion. And the acid Vapour of the Sulphur (namely
+that which distils under a Bell into Oil of Sulphur,) entring violently
+into the fix'd Body of the Nitre, sets loose the Spirit of the Nitre,
+and excites a great Fermentation, whereby the Heat is farther augmented,
+and the fix'd Body of the Nitre is also rarified into Fume, and the
+Explosion is thereby made more vehement and quick. For if Salt of Tartar
+be mix'd with Gun-powder, and that Mixture be warm'd till it takes fire,
+the Explosion will be more violent and quick than that of Gun-powder
+alone; which cannot proceed from any other cause than the action of the
+Vapour of the Gun-powder upon the Salt of Tartar, whereby that Salt is
+rarified. The Explosion of Gun-powder arises therefore from the violent
+action whereby all the Mixture being quickly and vehemently heated, is
+rarified and converted into Fume and Vapour: which Vapour, by the
+violence of that action, becoming so hot as to shine, appears in the
+form of Flame.
+
+_Qu._ 11. Do not great Bodies conserve their heat the longest, their
+parts heating one another, and may not great dense and fix'd Bodies,
+when heated beyond a certain degree, emit Light so copiously, as by the
+Emission and Re-action of its Light, and the Reflexions and Refractions
+of its Rays within its Pores to grow still hotter, till it comes to a
+certain period of heat, such as is that of the Sun? And are not the Sun
+and fix'd Stars great Earths vehemently hot, whose heat is conserved by
+the greatness of the Bodies, and the mutual Action and Reaction between
+them, and the Light which they emit, and whose parts are kept from
+fuming away, not only by their fixity, but also by the vast weight and
+density of the Atmospheres incumbent upon them; and very strongly
+compressing them, and condensing the Vapours and Exhalations which arise
+from them? For if Water be made warm in any pellucid Vessel emptied of
+Air, that Water in the _Vacuum_ will bubble and boil as vehemently as it
+would in the open Air in a Vessel set upon the Fire till it conceives a
+much greater heat. For the weight of the incumbent Atmosphere keeps down
+the Vapours, and hinders the Water from boiling, until it grow much
+hotter than is requisite to make it boil _in vacuo_. Also a mixture of
+Tin and Lead being put upon a red hot Iron _in vacuo_ emits a Fume and
+Flame, but the same Mixture in the open Air, by reason of the incumbent
+Atmosphere, does not so much as emit any Fume which can be perceived by
+Sight. In like manner the great weight of the Atmosphere which lies upon
+the Globe of the Sun may hinder Bodies there from rising up and going
+away from the Sun in the form of Vapours and Fumes, unless by means of a
+far greater heat than that which on the Surface of our Earth would very
+easily turn them into Vapours and Fumes. And the same great weight may
+condense those Vapours and Exhalations as soon as they shall at any time
+begin to ascend from the Sun, and make them presently fall back again
+into him, and by that action increase his Heat much after the manner
+that in our Earth the Air increases the Heat of a culinary Fire. And the
+same weight may hinder the Globe of the Sun from being diminish'd,
+unless by the Emission of Light, and a very small quantity of Vapours
+and Exhalations.
+
+_Qu._ 12. Do not the Rays of Light in falling upon the bottom of the Eye
+excite Vibrations in the _Tunica Retina_? Which Vibrations, being
+propagated along the solid Fibres of the optick Nerves into the Brain,
+cause the Sense of seeing. For because dense Bodies conserve their Heat
+a long time, and the densest Bodies conserve their Heat the longest, the
+Vibrations of their parts are of a lasting nature, and therefore may be
+propagated along solid Fibres of uniform dense Matter to a great
+distance, for conveying into the Brain the impressions made upon all the
+Organs of Sense. For that Motion which can continue long in one and the
+same part of a Body, can be propagated a long way from one part to
+another, supposing the Body homogeneal, so that the Motion may not be
+reflected, refracted, interrupted or disorder'd by any unevenness of the
+Body.
+
+_Qu._ 13. Do not several sorts of Rays make Vibrations of several
+bignesses, which according to their bignesses excite Sensations of
+several Colours, much after the manner that the Vibrations of the Air,
+according to their several bignesses excite Sensations of several
+Sounds? And particularly do not the most refrangible Rays excite the
+shortest Vibrations for making a Sensation of deep violet, the least
+refrangible the largest for making a Sensation of deep red, and the
+several intermediate sorts of Rays, Vibrations of several intermediate
+bignesses to make Sensations of the several intermediate Colours?
+
+_Qu._ 14. May not the harmony and discord of Colours arise from the
+proportions of the Vibrations propagated through the Fibres of the
+optick Nerves into the Brain, as the harmony and discord of Sounds arise
+from the proportions of the Vibrations of the Air? For some Colours, if
+they be view'd together, are agreeable to one another, as those of Gold
+and Indigo, and others disagree.
+
+_Qu._ 15. Are not the Species of Objects seen with both Eyes united
+where the optick Nerves meet before they come into the Brain, the Fibres
+on the right side of both Nerves uniting there, and after union going
+thence into the Brain in the Nerve which is on the right side of the
+Head, and the Fibres on the left side of both Nerves uniting in the same
+place, and after union going into the Brain in the Nerve which is on the
+left side of the Head, and these two Nerves meeting in the Brain in such
+a manner that their Fibres make but one entire Species or Picture, half
+of which on the right side of the Sensorium comes from the right side of
+both Eyes through the right side of both optick Nerves to the place
+where the Nerves meet, and from thence on the right side of the Head
+into the Brain, and the other half on the left side of the Sensorium
+comes in like manner from the left side of both Eyes. For the optick
+Nerves of such Animals as look the same way with both Eyes (as of Men,
+Dogs, Sheep, Oxen, &c.) meet before they come into the Brain, but the
+optick Nerves of such Animals as do not look the same way with both Eyes
+(as of Fishes, and of the Chameleon,) do not meet, if I am rightly
+inform'd.
+
+_Qu._ 16. When a Man in the dark presses either corner of his Eye with
+his Finger, and turns his Eye away from his Finger, he will see a Circle
+of Colours like those in the Feather of a Peacock's Tail. If the Eye and
+the Finger remain quiet these Colours vanish in a second Minute of Time,
+but if the Finger be moved with a quavering Motion they appear again. Do
+not these Colours arise from such Motions excited in the bottom of the
+Eye by the Pressure and Motion of the Finger, as, at other times are
+excited there by Light for causing Vision? And do not the Motions once
+excited continue about a Second of Time before they cease? And when a
+Man by a stroke upon his Eye sees a flash of Light, are not the like
+Motions excited in the _Retina_ by the stroke? And when a Coal of Fire
+moved nimbly in the circumference of a Circle, makes the whole
+circumference appear like a Circle of Fire; is it not because the
+Motions excited in the bottom of the Eye by the Rays of Light are of a
+lasting nature, and continue till the Coal of Fire in going round
+returns to its former place? And considering the lastingness of the
+Motions excited in the bottom of the Eye by Light, are they not of a
+vibrating nature?
+
+_Qu._ 17. If a stone be thrown into stagnating Water, the Waves excited
+thereby continue some time to arise in the place where the Stone fell
+into the Water, and are propagated from thence in concentrick Circles
+upon the Surface of the Water to great distances. And the Vibrations or
+Tremors excited in the Air by percussion, continue a little time to move
+from the place of percussion in concentrick Spheres to great distances.
+And in like manner, when a Ray of Light falls upon the Surface of any
+pellucid Body, and is there refracted or reflected, may not Waves of
+Vibrations, or Tremors, be thereby excited in the refracting or
+reflecting Medium at the point of Incidence, and continue to arise
+there, and to be propagated from thence as long as they continue to
+arise and be propagated, when they are excited in the bottom of the Eye
+by the Pressure or Motion of the Finger, or by the Light which comes
+from the Coal of Fire in the Experiments above-mention'd? and are not
+these Vibrations propagated from the point of Incidence to great
+distances? And do they not overtake the Rays of Light, and by overtaking
+them successively, do they not put them into the Fits of easy Reflexion
+and easy Transmission described above? For if the Rays endeavour to
+recede from the densest part of the Vibration, they may be alternately
+accelerated and retarded by the Vibrations overtaking them.
+
+_Qu._ 18. If in two large tall cylindrical Vessels of Glass inverted,
+two little Thermometers be suspended so as not to touch the Vessels, and
+the Air be drawn out of one of these Vessels, and these Vessels thus
+prepared be carried out of a cold place into a warm one; the Thermometer
+_in vacuo_ will grow warm as much, and almost as soon as the Thermometer
+which is not _in vacuo_. And when the Vessels are carried back into the
+cold place, the Thermometer _in vacuo_ will grow cold almost as soon as
+the other Thermometer. Is not the Heat of the warm Room convey'd through
+the _Vacuum_ by the Vibrations of a much subtiler Medium than Air, which
+after the Air was drawn out remained in the _Vacuum_? And is not this
+Medium the same with that Medium by which Light is refracted and
+reflected, and by whose Vibrations Light communicates Heat to Bodies,
+and is put into Fits of easy Reflexion and easy Transmission? And do not
+the Vibrations of this Medium in hot Bodies contribute to the
+intenseness and duration of their Heat? And do not hot Bodies
+communicate their Heat to contiguous cold ones, by the Vibrations of
+this Medium propagated from them into the cold ones? And is not this
+Medium exceedingly more rare and subtile than the Air, and exceedingly
+more elastick and active? And doth it not readily pervade all Bodies?
+And is it not (by its elastick force) expanded through all the Heavens?
+
+_Qu._ 19. Doth not the Refraction of Light proceed from the different
+density of this Æthereal Medium in different places, the Light receding
+always from the denser parts of the Medium? And is not the density
+thereof greater in free and open Spaces void of Air and other grosser
+Bodies, than within the Pores of Water, Glass, Crystal, Gems, and other
+compact Bodies? For when Light passes through Glass or Crystal, and
+falling very obliquely upon the farther Surface thereof is totally
+reflected, the total Reflexion ought to proceed rather from the density
+and vigour of the Medium without and beyond the Glass, than from the
+rarity and weakness thereof.
+
+_Qu._ 20. Doth not this Æthereal Medium in passing out of Water, Glass,
+Crystal, and other compact and dense Bodies into empty Spaces, grow
+denser and denser by degrees, and by that means refract the Rays of
+Light not in a point, but by bending them gradually in curve Lines? And
+doth not the gradual condensation of this Medium extend to some distance
+from the Bodies, and thereby cause the Inflexions of the Rays of Light,
+which pass by the edges of dense Bodies, at some distance from the
+Bodies?
+
+_Qu._ 21. Is not this Medium much rarer within the dense Bodies of the
+Sun, Stars, Planets and Comets, than in the empty celestial Spaces
+between them? And in passing from them to great distances, doth it not
+grow denser and denser perpetually, and thereby cause the gravity of
+those great Bodies towards one another, and of their parts towards the
+Bodies; every Body endeavouring to go from the denser parts of the
+Medium towards the rarer? For if this Medium be rarer within the Sun's
+Body than at its Surface, and rarer there than at the hundredth part of
+an Inch from its Body, and rarer there than at the fiftieth part of an
+Inch from its Body, and rarer there than at the Orb of _Saturn_; I see
+no reason why the Increase of density should stop any where, and not
+rather be continued through all distances from the Sun to _Saturn_, and
+beyond. And though this Increase of density may at great distances be
+exceeding slow, yet if the elastick force of this Medium be exceeding
+great, it may suffice to impel Bodies from the denser parts of the
+Medium towards the rarer, with all that power which we call Gravity. And
+that the elastick force of this Medium is exceeding great, may be
+gather'd from the swiftness of its Vibrations. Sounds move about 1140
+_English_ Feet in a second Minute of Time, and in seven or eight Minutes
+of Time they move about one hundred _English_ Miles. Light moves from
+the Sun to us in about seven or eight Minutes of Time, which distance is
+about 70,000,000 _English_ Miles, supposing the horizontal Parallax of
+the Sun to be about 12´´. And the Vibrations or Pulses of this Medium,
+that they may cause the alternate Fits of easy Transmission and easy
+Reflexion, must be swifter than Light, and by consequence above 700,000
+times swifter than Sounds. And therefore the elastick force of this
+Medium, in proportion to its density, must be above 700000 x 700000
+(that is, above 490,000,000,000) times greater than the elastick force
+of the Air is in proportion to its density. For the Velocities of the
+Pulses of elastick Mediums are in a subduplicate _Ratio_ of the
+Elasticities and the Rarities of the Mediums taken together.
+
+As Attraction is stronger in small Magnets than in great ones in
+proportion to their Bulk, and Gravity is greater in the Surfaces of
+small Planets than in those of great ones in proportion to their bulk,
+and small Bodies are agitated much more by electric attraction than
+great ones; so the smallness of the Rays of Light may contribute very
+much to the power of the Agent by which they are refracted. And so if
+any one should suppose that _Æther_ (like our Air) may contain Particles
+which endeavour to recede from one another (for I do not know what this
+_Æther_ is) and that its Particles are exceedingly smaller than those of
+Air, or even than those of Light: The exceeding smallness of its
+Particles may contribute to the greatness of the force by which those
+Particles may recede from one another, and thereby make that Medium
+exceedingly more rare and elastick than Air, and by consequence
+exceedingly less able to resist the motions of Projectiles, and
+exceedingly more able to press upon gross Bodies, by endeavouring to
+expand it self.
+
+_Qu._ 22. May not Planets and Comets, and all gross Bodies, perform
+their Motions more freely, and with less resistance in this Æthereal
+Medium than in any Fluid, which fills all Space adequately without
+leaving any Pores, and by consequence is much denser than Quick-silver
+or Gold? And may not its resistance be so small, as to be
+inconsiderable? For instance; If this _Æther_ (for so I will call it)
+should be supposed 700000 times more elastick than our Air, and above
+700000 times more rare; its resistance would be above 600,000,000 times
+less than that of Water. And so small a resistance would scarce make any
+sensible alteration in the Motions of the Planets in ten thousand
+Years. If any one would ask how a Medium can be so rare, let him tell me
+how the Air, in the upper parts of the Atmosphere, can be above an
+hundred thousand thousand times rarer than Gold. Let him also tell me,
+how an electrick Body can by Friction emit an Exhalation so rare and
+subtile, and yet so potent, as by its Emission to cause no sensible
+Diminution of the weight of the electrick Body, and to be expanded
+through a Sphere, whose Diameter is above two Feet, and yet to be able
+to agitate and carry up Leaf Copper, or Leaf Gold, at the distance of
+above a Foot from the electrick Body? And how the Effluvia of a Magnet
+can be so rare and subtile, as to pass through a Plate of Glass without
+any Resistance or Diminution of their Force, and yet so potent as to
+turn a magnetick Needle beyond the Glass?
+
+_Qu._ 23. Is not Vision perform'd chiefly by the Vibrations of this
+Medium, excited in the bottom of the Eye by the Rays of Light, and
+propagated through the solid, pellucid and uniform Capillamenta of the
+optick Nerves into the place of Sensation? And is not Hearing perform'd
+by the Vibrations either of this or some other Medium, excited in the
+auditory Nerves by the Tremors of the Air, and propagated through the
+solid, pellucid and uniform Capillamenta of those Nerves into the place
+of Sensation? And so of the other Senses.
+
+_Qu._ 24. Is not Animal Motion perform'd by the Vibrations of this
+Medium, excited in the Brain by the power of the Will, and propagated
+from thence through the solid, pellucid and uniform Capillamenta of the
+Nerves into the Muscles, for contracting and dilating them? I suppose
+that the Capillamenta of the Nerves are each of them solid and uniform,
+that the vibrating Motion of the Æthereal Medium may be propagated along
+them from one end to the other uniformly, and without interruption: For
+Obstructions in the Nerves create Palsies. And that they may be
+sufficiently uniform, I suppose them to be pellucid when view'd singly,
+tho' the Reflexions in their cylindrical Surfaces may make the whole
+Nerve (composed of many Capillamenta) appear opake and white. For
+opacity arises from reflecting Surfaces, such as may disturb and
+interrupt the Motions of this Medium.
+
+[Sidenote: _See the following Scheme, p. 356._]
+
+_Qu._ 25. Are there not other original Properties of the Rays of Light,
+besides those already described? An instance of another original
+Property we have in the Refraction of Island Crystal, described first by
+_Erasmus Bartholine_, and afterwards more exactly by _Hugenius_, in his
+Book _De la Lumiere_. This Crystal is a pellucid fissile Stone, clear as
+Water or Crystal of the Rock, and without Colour; enduring a red Heat
+without losing its transparency, and in a very strong Heat calcining
+without Fusion. Steep'd a Day or two in Water, it loses its natural
+Polish. Being rubb'd on Cloth, it attracts pieces of Straws and other
+light things, like Ambar or Glass; and with _Aqua fortis_ it makes an
+Ebullition. It seems to be a sort of Talk, and is found in form of an
+oblique Parallelopiped, with six parallelogram Sides and eight solid
+Angles. The obtuse Angles of the Parallelograms are each of them 101
+Degrees and 52 Minutes; the acute ones 78 Degrees and 8 Minutes. Two of
+the solid Angles opposite to one another, as C and E, are compassed each
+of them with three of these obtuse Angles, and each of the other six
+with one obtuse and two acute ones. It cleaves easily in planes parallel
+to any of its Sides, and not in any other Planes. It cleaves with a
+glossy polite Surface not perfectly plane, but with some little
+unevenness. It is easily scratch'd, and by reason of its softness it
+takes a Polish very difficultly. It polishes better upon polish'd
+Looking-glass than upon Metal, and perhaps better upon Pitch, Leather or
+Parchment. Afterwards it must be rubb'd with a little Oil or white of an
+Egg, to fill up its Scratches; whereby it will become very transparent
+and polite. But for several Experiments, it is not necessary to polish
+it. If a piece of this crystalline Stone be laid upon a Book, every
+Letter of the Book seen through it will appear double, by means of a
+double Refraction. And if any beam of Light falls either
+perpendicularly, or in any oblique Angle upon any Surface of this
+Crystal, it becomes divided into two beams by means of the same double
+Refraction. Which beams are of the same Colour with the incident beam of
+Light, and seem equal to one another in the quantity of their Light, or
+very nearly equal. One of these Refractions is perform'd by the usual
+Rule of Opticks, the Sine of Incidence out of Air into this Crystal
+being to the Sine of Refraction, as five to three. The other
+Refraction, which may be called the unusual Refraction, is perform'd by
+the following Rule.
+
+[Illustration: FIG. 4.]
+
+Let ADBC represent the refracting Surface of the Crystal, C the biggest
+solid Angle at that Surface, GEHF the opposite Surface, and CK a
+perpendicular on that Surface. This perpendicular makes with the edge of
+the Crystal CF, an Angle of 19 Degr. 3'. Join KF, and in it take KL, so
+that the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. And
+if ST represent any beam of Light incident at T in any Angle upon the
+refracting Surface ADBC, let TV be the refracted beam determin'd by the
+given Portion of the Sines 5 to 3, according to the usual Rule of
+Opticks. Draw VX parallel and equal to KL. Draw it the same way from V
+in which L lieth from K; and joining TX, this line TX shall be the other
+refracted beam carried from T to X, by the unusual Refraction.
+
+If therefore the incident beam ST be perpendicular to the refracting
+Surface, the two beams TV and TX, into which it shall become divided,
+shall be parallel to the lines CK and CL; one of those beams going
+through the Crystal perpendicularly, as it ought to do by the usual Laws
+of Opticks, and the other TX by an unusual Refraction diverging from the
+perpendicular, and making with it an Angle VTX of about 6-2/3 Degrees,
+as is found by Experience. And hence, the Plane VTX, and such like
+Planes which are parallel to the Plane CFK, may be called the Planes of
+perpendicular Refraction. And the Coast towards which the lines KL and
+VX are drawn, may be call'd the Coast of unusual Refraction.
+
+In like manner Crystal of the Rock has a double Refraction: But the
+difference of the two Refractions is not so great and manifest as in
+Island Crystal.
+
+When the beam ST incident on Island Crystal is divided into two beams TV
+and TX, and these two beams arrive at the farther Surface of the Glass;
+the beam TV, which was refracted at the first Surface after the usual
+manner, shall be again refracted entirely after the usual manner at the
+second Surface; and the beam TX, which was refracted after the unusual
+manner in the first Surface, shall be again refracted entirely after the
+unusual manner in the second Surface; so that both these beams shall
+emerge out of the second Surface in lines parallel to the first incident
+beam ST.
+
+And if two pieces of Island Crystal be placed one after another, in such
+manner that all the Surfaces of the latter be parallel to all the
+corresponding Surfaces of the former: The Rays which are refracted after
+the usual manner in the first Surface of the first Crystal, shall be
+refracted after the usual manner in all the following Surfaces; and the
+Rays which are refracted after the unusual manner in the first Surface,
+shall be refracted after the unusual manner in all the following
+Surfaces. And the same thing happens, though the Surfaces of the
+Crystals be any ways inclined to one another, provided that their Planes
+of perpendicular Refraction be parallel to one another.
+
+And therefore there is an original difference in the Rays of Light, by
+means of which some Rays are in this Experiment constantly refracted
+after the usual manner, and others constantly after the unusual manner:
+For if the difference be not original, but arises from new Modifications
+impress'd on the Rays at their first Refraction, it would be alter'd by
+new Modifications in the three following Refractions; whereas it suffers
+no alteration, but is constant, and has the same effect upon the Rays in
+all the Refractions. The unusual Refraction is therefore perform'd by an
+original property of the Rays. And it remains to be enquired, whether
+the Rays have not more original Properties than are yet discover'd.
+
+_Qu._ 26. Have not the Rays of Light several sides, endued with several
+original Properties? For if the Planes of perpendicular Refraction of
+the second Crystal be at right Angles with the Planes of perpendicular
+Refraction of the first Crystal, the Rays which are refracted after the
+usual manner in passing through the first Crystal, will be all of them
+refracted after the unusual manner in passing through the second
+Crystal; and the Rays which are refracted after the unusual manner in
+passing through the first Crystal, will be all of them refracted after
+the usual manner in passing through the second Crystal. And therefore
+there are not two sorts of Rays differing in their nature from one
+another, one of which is constantly and in all Positions refracted after
+the usual manner, and the other constantly and in all Positions after
+the unusual manner. The difference between the two sorts of Rays in the
+Experiment mention'd in the 25th Question, was only in the Positions of
+the Sides of the Rays to the Planes of perpendicular Refraction. For one
+and the same Ray is here refracted sometimes after the usual, and
+sometimes after the unusual manner, according to the Position which its
+Sides have to the Crystals. If the Sides of the Ray are posited the same
+way to both Crystals, it is refracted after the same manner in them
+both: But if that side of the Ray which looks towards the Coast of the
+unusual Refraction of the first Crystal, be 90 Degrees from that side of
+the same Ray which looks toward the Coast of the unusual Refraction of
+the second Crystal, (which may be effected by varying the Position of
+the second Crystal to the first, and by consequence to the Rays of
+Light,) the Ray shall be refracted after several manners in the several
+Crystals. There is nothing more required to determine whether the Rays
+of Light which fall upon the second Crystal shall be refracted after
+the usual or after the unusual manner, but to turn about this Crystal,
+so that the Coast of this Crystal's unusual Refraction may be on this or
+on that side of the Ray. And therefore every Ray may be consider'd as
+having four Sides or Quarters, two of which opposite to one another
+incline the Ray to be refracted after the unusual manner, as often as
+either of them are turn'd towards the Coast of unusual Refraction; and
+the other two, whenever either of them are turn'd towards the Coast of
+unusual Refraction, do not incline it to be otherwise refracted than
+after the usual manner. The two first may therefore be call'd the Sides
+of unusual Refraction. And since these Dispositions were in the Rays
+before their Incidence on the second, third, and fourth Surfaces of the
+two Crystals, and suffered no alteration (so far as appears,) by the
+Refraction of the Rays in their passage through those Surfaces, and the
+Rays were refracted by the same Laws in all the four Surfaces; it
+appears that those Dispositions were in the Rays originally, and
+suffer'd no alteration by the first Refraction, and that by means of
+those Dispositions the Rays were refracted at their Incidence on the
+first Surface of the first Crystal, some of them after the usual, and
+some of them after the unusual manner, accordingly as their Sides of
+unusual Refraction were then turn'd towards the Coast of the unusual
+Refraction of that Crystal, or sideways from it.
+
+Every Ray of Light has therefore two opposite Sides, originally endued
+with a Property on which the unusual Refraction depends, and the other
+two opposite Sides not endued with that Property. And it remains to be
+enquired, whether there are not more Properties of Light by which the
+Sides of the Rays differ, and are distinguished from one another.
+
+In explaining the difference of the Sides of the Rays above mention'd, I
+have supposed that the Rays fall perpendicularly on the first Crystal.
+But if they fall obliquely on it, the Success is the same. Those Rays
+which are refracted after the usual manner in the first Crystal, will be
+refracted after the unusual manner in the second Crystal, supposing the
+Planes of perpendicular Refraction to be at right Angles with one
+another, as above; and on the contrary.
+
+If the Planes of the perpendicular Refraction of the two Crystals be
+neither parallel nor perpendicular to one another, but contain an acute
+Angle: The two beams of Light which emerge out of the first Crystal,
+will be each of them divided into two more at their Incidence on the
+second Crystal. For in this case the Rays in each of the two beams will
+some of them have their Sides of unusual Refraction, and some of them
+their other Sides turn'd towards the Coast of the unusual Refraction of
+the second Crystal.
+
+_Qu._ 27. Are not all Hypotheses erroneous which have hitherto been
+invented for explaining the Phænomena of Light, by new Modifications of
+the Rays? For those Phænomena depend not upon new Modifications, as has
+been supposed, but upon the original and unchangeable Properties of the
+Rays.
+
+_Qu._ 28. Are not all Hypotheses erroneous, in which Light is supposed
+to consist in Pression or Motion, propagated through a fluid Medium? For
+in all these Hypotheses the Phænomena of Light have been hitherto
+explain'd by supposing that they arise from new Modifications of the
+Rays; which is an erroneous Supposition.
+
+If Light consisted only in Pression propagated without actual Motion, it
+would not be able to agitate and heat the Bodies which refract and
+reflect it. If it consisted in Motion propagated to all distances in an
+instant, it would require an infinite force every moment, in every
+shining Particle, to generate that Motion. And if it consisted in
+Pression or Motion, propagated either in an instant or in time, it would
+bend into the Shadow. For Pression or Motion cannot be propagated in a
+Fluid in right Lines, beyond an Obstacle which stops part of the Motion,
+but will bend and spread every way into the quiescent Medium which lies
+beyond the Obstacle. Gravity tends downwards, but the Pressure of Water
+arising from Gravity tends every way with equal Force, and is propagated
+as readily, and with as much force sideways as downwards, and through
+crooked passages as through strait ones. The Waves on the Surface of
+stagnating Water, passing by the sides of a broad Obstacle which stops
+part of them, bend afterwards and dilate themselves gradually into the
+quiet Water behind the Obstacle. The Waves, Pulses or Vibrations of the
+Air, wherein Sounds consist, bend manifestly, though not so much as the
+Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which
+intercepts the sight of the sounding Body, and Sounds are propagated as
+readily through crooked Pipes as through streight ones. But Light is
+never known to follow crooked Passages nor to bend into the Shadow. For
+the fix'd Stars by the Interposition of any of the Planets cease to be
+seen. And so do the Parts of the Sun by the Interposition of the Moon,
+_Mercury_ or _Venus_. The Rays which pass very near to the edges of any
+Body, are bent a little by the action of the Body, as we shew'd above;
+but this bending is not towards but from the Shadow, and is perform'd
+only in the passage of the Ray by the Body, and at a very small distance
+from it. So soon as the Ray is past the Body, it goes right on.
+
+[Sidenote: _Mais pour dire comment cela se fait, je n'ay rien trove
+jusqu' ici qui me satisfasse._ C. H. de la lumiere, c. 5, p. 91.]
+
+To explain the unusual Refraction of Island Crystal by Pression or
+Motion propagated, has not hitherto been attempted (to my knowledge)
+except by _Huygens_, who for that end supposed two several vibrating
+Mediums within that Crystal. But when he tried the Refractions in two
+successive pieces of that Crystal, and found them such as is mention'd
+above; he confessed himself at a loss for explaining them. For Pressions
+or Motions, propagated from a shining Body through an uniform Medium,
+must be on all sides alike; whereas by those Experiments it appears,
+that the Rays of Light have different Properties in their different
+Sides. He suspected that the Pulses of _Æther_ in passing through the
+first Crystal might receive certain new Modifications, which might
+determine them to be propagated in this or that Medium within the
+second Crystal, according to the Position of that Crystal. But what
+Modifications those might be he could not say, nor think of any thing
+satisfactory in that Point. And if he had known that the unusual
+Refraction depends not on new Modifications, but on the original and
+unchangeable Dispositions of the Rays, he would have found it as
+difficult to explain how those Dispositions which he supposed to be
+impress'd on the Rays by the first Crystal, could be in them before
+their Incidence on that Crystal, and in general, how all Rays emitted by
+shining Bodies, can have those Dispositions in them from the beginning.
+To me, at least, this seems inexplicable, if Light be nothing else than
+Pression or Motion propagated through _Æther_.
+
+And it is as difficult to explain by these Hypotheses, how Rays can be
+alternately in Fits of easy Reflexion and easy Transmission; unless
+perhaps one might suppose that there are in all Space two Æthereal
+vibrating Mediums, and that the Vibrations of one of them constitute
+Light, and the Vibrations of the other are swifter, and as often as they
+overtake the Vibrations of the first, put them into those Fits. But how
+two _Æthers_ can be diffused through all Space, one of which acts upon
+the other, and by consequence is re-acted upon, without retarding,
+shattering, dispersing and confounding one anothers Motions, is
+inconceivable. And against filling the Heavens with fluid Mediums,
+unless they be exceeding rare, a great Objection arises from the regular
+and very lasting Motions of the Planets and Comets in all manner of
+Courses through the Heavens. For thence it is manifest, that the Heavens
+are void of all sensible Resistance, and by consequence of all sensible
+Matter.
+
+For the resisting Power of fluid Mediums arises partly from the
+Attrition of the Parts of the Medium, and partly from the _Vis inertiæ_
+of the Matter. That part of the Resistance of a spherical Body which
+arises from the Attrition of the Parts of the Medium is very nearly as
+the Diameter, or, at the most, as the _Factum_ of the Diameter, and the
+Velocity of the spherical Body together. And that part of the Resistance
+which arises from the _Vis inertiæ_ of the Matter, is as the Square of
+that _Factum_. And by this difference the two sorts of Resistance may be
+distinguish'd from one another in any Medium; and these being
+distinguish'd, it will be found that almost all the Resistance of Bodies
+of a competent Magnitude moving in Air, Water, Quick-silver, and such
+like Fluids with a competent Velocity, arises from the _Vis inertiæ_ of
+the Parts of the Fluid.
+
+Now that part of the resisting Power of any Medium which arises from the
+Tenacity, Friction or Attrition of the Parts of the Medium, may be
+diminish'd by dividing the Matter into smaller Parts, and making the
+Parts more smooth and slippery: But that part of the Resistance which
+arises from the _Vis inertiæ_, is proportional to the Density of the
+Matter, and cannot be diminish'd by dividing the Matter into smaller
+Parts, nor by any other means than by decreasing the Density of the
+Medium. And for these Reasons the Density of fluid Mediums is very
+nearly proportional to their Resistance. Liquors which differ not much
+in Density, as Water, Spirit of Wine, Spirit of Turpentine, hot Oil,
+differ not much in Resistance. Water is thirteen or fourteen times
+lighter than Quick-silver and by consequence thirteen or fourteen times
+rarer, and its Resistance is less than that of Quick-silver in the same
+Proportion, or thereabouts, as I have found by Experiments made with
+Pendulums. The open Air in which we breathe is eight or nine hundred
+times lighter than Water, and by consequence eight or nine hundred times
+rarer, and accordingly its Resistance is less than that of Water in the
+same Proportion, or thereabouts; as I have also found by Experiments
+made with Pendulums. And in thinner Air the Resistance is still less,
+and at length, by ratifying the Air, becomes insensible. For small
+Feathers falling in the open Air meet with great Resistance, but in a
+tall Glass well emptied of Air, they fall as fast as Lead or Gold, as I
+have seen tried several times. Whence the Resistance seems still to
+decrease in proportion to the Density of the Fluid. For I do not find by
+any Experiments, that Bodies moving in Quick-silver, Water or Air, meet
+with any other sensible Resistance than what arises from the Density and
+Tenacity of those sensible Fluids, as they would do if the Pores of
+those Fluids, and all other Spaces, were filled with a dense and
+subtile Fluid. Now if the Resistance in a Vessel well emptied of Air,
+was but an hundred times less than in the open Air, it would be about a
+million of times less than in Quick-silver. But it seems to be much less
+in such a Vessel, and still much less in the Heavens, at the height of
+three or four hundred Miles from the Earth, or above. For Mr. _Boyle_
+has shew'd that Air may be rarified above ten thousand times in Vessels
+of Glass; and the Heavens are much emptier of Air than any _Vacuum_ we
+can make below. For since the Air is compress'd by the Weight of the
+incumbent Atmosphere, and the Density of Air is proportional to the
+Force compressing it, it follows by Computation, that at the height of
+about seven and a half _English_ Miles from the Earth, the Air is four
+times rarer than at the Surface of the Earth; and at the height of 15
+Miles it is sixteen times rarer than that at the Surface of the Earth;
+and at the height of 22-1/2, 30, or 38 Miles, it is respectively 64,
+256, or 1024 times rarer, or thereabouts; and at the height of 76, 152,
+228 Miles, it is about 1000000, 1000000000000, or 1000000000000000000
+times rarer; and so on.
+
+Heat promotes Fluidity very much by diminishing the Tenacity of Bodies.
+It makes many Bodies fluid which are not fluid in cold, and increases
+the Fluidity of tenacious Liquids, as of Oil, Balsam, and Honey, and
+thereby decreases their Resistance. But it decreases not the Resistance
+of Water considerably, as it would do if any considerable part of the
+Resistance of Water arose from the Attrition or Tenacity of its Parts.
+And therefore the Resistance of Water arises principally and almost
+entirely from the _Vis inertiæ_ of its Matter; and by consequence, if
+the Heavens were as dense as Water, they would not have much less
+Resistance than Water; if as dense as Quick-silver, they would not have
+much less Resistance than Quick-silver; if absolutely dense, or full of
+Matter without any _Vacuum_, let the Matter be never so subtil and
+fluid, they would have a greater Resistance than Quick-silver. A solid
+Globe in such a Medium would lose above half its Motion in moving three
+times the length of its Diameter, and a Globe not solid (such as are the
+Planets,) would be retarded sooner. And therefore to make way for the
+regular and lasting Motions of the Planets and Comets, it's necessary to
+empty the Heavens of all Matter, except perhaps some very thin Vapours,
+Steams, or Effluvia, arising from the Atmospheres of the Earth, Planets,
+and Comets, and from such an exceedingly rare Æthereal Medium as we
+described above. A dense Fluid can be of no use for explaining the
+Phænomena of Nature, the Motions of the Planets and Comets being better
+explain'd without it. It serves only to disturb and retard the Motions
+of those great Bodies, and make the Frame of Nature languish: And in the
+Pores of Bodies, it serves only to stop the vibrating Motions of their
+Parts, wherein their Heat and Activity consists. And as it is of no use,
+and hinders the Operations of Nature, and makes her languish, so there
+is no evidence for its Existence, and therefore it ought to be rejected.
+And if it be rejected, the Hypotheses that Light consists in Pression
+or Motion, propagated through such a Medium, are rejected with it.
+
+And for rejecting such a Medium, we have the Authority of those the
+oldest and most celebrated Philosophers of _Greece_ and _Phoenicia_,
+who made a _Vacuum_, and Atoms, and the Gravity of Atoms, the first
+Principles of their Philosophy; tacitly attributing Gravity to some
+other Cause than dense Matter. Later Philosophers banish the
+Consideration of such a Cause out of natural Philosophy, feigning
+Hypotheses for explaining all things mechanically, and referring other
+Causes to Metaphysicks: Whereas the main Business of natural Philosophy
+is to argue from Phænomena without feigning Hypotheses, and to deduce
+Causes from Effects, till we come to the very first Cause, which
+certainly is not mechanical; and not only to unfold the Mechanism of the
+World, but chiefly to resolve these and such like Questions. What is
+there in places almost empty of Matter, and whence is it that the Sun
+and Planets gravitate towards one another, without dense Matter between
+them? Whence is it that Nature doth nothing in vain; and whence arises
+all that Order and Beauty which we see in the World? To what end are
+Comets, and whence is it that Planets move all one and the same way in
+Orbs concentrick, while Comets move all manner of ways in Orbs very
+excentrick; and what hinders the fix'd Stars from falling upon one
+another? How came the Bodies of Animals to be contrived with so much
+Art, and for what ends were their several Parts? Was the Eye contrived
+without Skill in Opticks, and the Ear without Knowledge of Sounds? How
+do the Motions of the Body follow from the Will, and whence is the
+Instinct in Animals? Is not the Sensory of Animals that place to which
+the sensitive Substance is present, and into which the sensible Species
+of Things are carried through the Nerves and Brain, that there they may
+be perceived by their immediate presence to that Substance? And these
+things being rightly dispatch'd, does it not appear from Phænomena that
+there is a Being incorporeal, living, intelligent, omnipresent, who in
+infinite Space, as it were in his Sensory, sees the things themselves
+intimately, and throughly perceives them, and comprehends them wholly by
+their immediate presence to himself: Of which things the Images only
+carried through the Organs of Sense into our little Sensoriums, are
+there seen and beheld by that which in us perceives and thinks. And
+though every true Step made in this Philosophy brings us not immediately
+to the Knowledge of the first Cause, yet it brings us nearer to it, and
+on that account is to be highly valued.
+
+_Qu._ 29. Are not the Rays of Light very small Bodies emitted from
+shining Substances? For such Bodies will pass through uniform Mediums in
+right Lines without bending into the Shadow, which is the Nature of the
+Rays of Light. They will also be capable of several Properties, and be
+able to conserve their Properties unchanged in passing through several
+Mediums, which is another Condition of the Rays of Light. Pellucid
+Substances act upon the Rays of Light at a distance in refracting,
+reflecting, and inflecting them, and the Rays mutually agitate the Parts
+of those Substances at a distance for heating them; and this Action and
+Re-action at a distance very much resembles an attractive Force between
+Bodies. If Refraction be perform'd by Attraction of the Rays, the Sines
+of Incidence must be to the Sines of Refraction in a given Proportion,
+as we shew'd in our Principles of Philosophy: And this Rule is true by
+Experience. The Rays of Light in going out of Glass into a _Vacuum_, are
+bent towards the Glass; and if they fall too obliquely on the _Vacuum_,
+they are bent backwards into the Glass, and totally reflected; and this
+Reflexion cannot be ascribed to the Resistance of an absolute _Vacuum_,
+but must be caused by the Power of the Glass attracting the Rays at
+their going out of it into the _Vacuum_, and bringing them back. For if
+the farther Surface of the Glass be moisten'd with Water or clear Oil,
+or liquid and clear Honey, the Rays which would otherwise be reflected
+will go into the Water, Oil, or Honey; and therefore are not reflected
+before they arrive at the farther Surface of the Glass, and begin to go
+out of it. If they go out of it into the Water, Oil, or Honey, they go
+on, because the Attraction of the Glass is almost balanced and rendered
+ineffectual by the contrary Attraction of the Liquor. But if they go out
+of it into a _Vacuum_ which has no Attraction to balance that of the
+Glass, the Attraction of the Glass either bends and refracts them, or
+brings them back and reflects them. And this is still more evident by
+laying together two Prisms of Glass, or two Object-glasses of very long
+Telescopes, the one plane, the other a little convex, and so compressing
+them that they do not fully touch, nor are too far asunder. For the
+Light which falls upon the farther Surface of the first Glass where the
+Interval between the Glasses is not above the ten hundred thousandth
+Part of an Inch, will go through that Surface, and through the Air or
+_Vacuum_ between the Glasses, and enter into the second Glass, as was
+explain'd in the first, fourth, and eighth Observations of the first
+Part of the second Book. But, if the second Glass be taken away, the
+Light which goes out of the second Surface of the first Glass into the
+Air or _Vacuum_, will not go on forwards, but turns back into the first
+Glass, and is reflected; and therefore it is drawn back by the Power of
+the first Glass, there being nothing else to turn it back. Nothing more
+is requisite for producing all the variety of Colours, and degrees of
+Refrangibility, than that the Rays of Light be Bodies of different
+Sizes, the least of which may take violet the weakest and darkest of the
+Colours, and be more easily diverted by refracting Surfaces from the
+right Course; and the rest as they are bigger and bigger, may make the
+stronger and more lucid Colours, blue, green, yellow, and red, and be
+more and more difficultly diverted. Nothing more is requisite for
+putting the Rays of Light into Fits of easy Reflexion and easy
+Transmission, than that they be small Bodies which by their attractive
+Powers, or some other Force, stir up Vibrations in what they act upon,
+which Vibrations being swifter than the Rays, overtake them
+successively, and agitate them so as by turns to increase and decrease
+their Velocities, and thereby put them into those Fits. And lastly, the
+unusual Refraction of Island-Crystal looks very much as if it were
+perform'd by some kind of attractive virtue lodged in certain Sides both
+of the Rays, and of the Particles of the Crystal. For were it not for
+some kind of Disposition or Virtue lodged in some Sides of the Particles
+of the Crystal, and not in their other Sides, and which inclines and
+bends the Rays towards the Coast of unusual Refraction, the Rays which
+fall perpendicularly on the Crystal, would not be refracted towards that
+Coast rather than towards any other Coast, both at their Incidence and
+at their Emergence, so as to emerge perpendicularly by a contrary
+Situation of the Coast of unusual Refraction at the second Surface; the
+Crystal acting upon the Rays after they have pass'd through it, and are
+emerging into the Air; or, if you please, into a _Vacuum_. And since the
+Crystal by this Disposition or Virtue does not act upon the Rays, unless
+when one of their Sides of unusual Refraction looks towards that Coast,
+this argues a Virtue or Disposition in those Sides of the Rays, which
+answers to, and sympathizes with that Virtue or Disposition of the
+Crystal, as the Poles of two Magnets answer to one another. And as
+Magnetism may be intended and remitted, and is found only in the Magnet
+and in Iron: So this Virtue of refracting the perpendicular Rays is
+greater in Island-Crystal, less in Crystal of the Rock, and is not yet
+found in other Bodies. I do not say that this Virtue is magnetical: It
+seems to be of another kind. I only say, that whatever it be, it's
+difficult to conceive how the Rays of Light, unless they be Bodies, can
+have a permanent Virtue in two of their Sides which is not in their
+other Sides, and this without any regard to their Position to the Space
+or Medium through which they pass.
+
+What I mean in this Question by a _Vacuum_, and by the Attractions of
+the Rays of Light towards Glass or Crystal, may be understood by what
+was said in the 18th, 19th, and 20th Questions.
+
+_Quest._ 30. Are not gross Bodies and Light convertible into one
+another, and may not Bodies receive much of their Activity from the
+Particles of Light which enter their Composition? For all fix'd Bodies
+being heated emit Light so long as they continue sufficiently hot, and
+Light mutually stops in Bodies as often as its Rays strike upon their
+Parts, as we shew'd above. I know no Body less apt to shine than Water;
+and yet Water by frequent Distillations changes into fix'd Earth, as Mr.
+_Boyle_ has try'd; and then this Earth being enabled to endure a
+sufficient Heat, shines by Heat like other Bodies.
+
+The changing of Bodies into Light, and Light into Bodies, is very
+conformable to the Course of Nature, which seems delighted with
+Transmutations. Water, which is a very fluid tasteless Salt, she changes
+by Heat into Vapour, which is a sort of Air, and by Cold into Ice, which
+is a hard, pellucid, brittle, fusible Stone; and this Stone returns into
+Water by Heat, and Vapour returns into Water by Cold. Earth by Heat
+becomes Fire, and by Cold returns into Earth. Dense Bodies by
+Fermentation rarify into several sorts of Air, and this Air by
+Fermentation, and sometimes without it, returns into dense Bodies.
+Mercury appears sometimes in the form of a fluid Metal, sometimes in the
+form of a hard brittle Metal, sometimes in the form of a corrosive
+pellucid Salt call'd Sublimate, sometimes in the form of a tasteless,
+pellucid, volatile white Earth, call'd _Mercurius Dulcis_; or in that of
+a red opake volatile Earth, call'd Cinnaber; or in that of a red or
+white Precipitate, or in that of a fluid Salt; and in Distillation it
+turns into Vapour, and being agitated _in Vacuo_, it shines like Fire.
+And after all these Changes it returns again into its first form of
+Mercury. Eggs grow from insensible Magnitudes, and change into Animals;
+Tadpoles into Frogs; and Worms into Flies. All Birds, Beasts and Fishes,
+Insects, Trees, and other Vegetables, with their several Parts, grow out
+of Water and watry Tinctures and Salts, and by Putrefaction return again
+into watry Substances. And Water standing a few Days in the open Air,
+yields a Tincture, which (like that of Malt) by standing longer yields a
+Sediment and a Spirit, but before Putrefaction is fit Nourishment for
+Animals and Vegetables. And among such various and strange
+Transmutations, why may not Nature change Bodies into Light, and Light
+into Bodies?
+
+_Quest._ 31. Have not the small Particles of Bodies certain Powers,
+Virtues, or Forces, by which they act at a distance, not only upon the
+Rays of Light for reflecting, refracting, and inflecting them, but also
+upon one another for producing a great Part of the Phænomena of Nature?
+For it's well known, that Bodies act one upon another by the Attractions
+of Gravity, Magnetism, and Electricity; and these Instances shew the
+Tenor and Course of Nature, and make it not improbable but that there
+may be more attractive Powers than these. For Nature is very consonant
+and conformable to her self. How these Attractions may be perform'd, I
+do not here consider. What I call Attraction may be perform'd by
+impulse, or by some other means unknown to me. I use that Word here to
+signify only in general any Force by which Bodies tend towards one
+another, whatsoever be the Cause. For we must learn from the Phænomena
+of Nature what Bodies attract one another, and what are the Laws and
+Properties of the Attraction, before we enquire the Cause by which the
+Attraction is perform'd. The Attractions of Gravity, Magnetism, and
+Electricity, reach to very sensible distances, and so have been observed
+by vulgar Eyes, and there may be others which reach to so small
+distances as hitherto escape Observation; and perhaps electrical
+Attraction may reach to such small distances, even without being excited
+by Friction.
+
+For when Salt of Tartar runs _per Deliquium_, is not this done by an
+Attraction between the Particles of the Salt of Tartar, and the
+Particles of the Water which float in the Air in the form of Vapours?
+And why does not common Salt, or Salt-petre, or Vitriol, run _per
+Deliquium_, but for want of such an Attraction? Or why does not Salt of
+Tartar draw more Water out of the Air than in a certain Proportion to
+its quantity, but for want of an attractive Force after it is satiated
+with Water? And whence is it but from this attractive Power that Water
+which alone distils with a gentle luke-warm Heat, will not distil from
+Salt of Tartar without a great Heat? And is it not from the like
+attractive Power between the Particles of Oil of Vitriol and the
+Particles of Water, that Oil of Vitriol draws to it a good quantity of
+Water out of the Air, and after it is satiated draws no more, and in
+Distillation lets go the Water very difficultly? And when Water and Oil
+of Vitriol poured successively into the same Vessel grow very hot in the
+mixing, does not this Heat argue a great Motion in the Parts of the
+Liquors? And does not this Motion argue, that the Parts of the two
+Liquors in mixing coalesce with Violence, and by consequence rush
+towards one another with an accelerated Motion? And when _Aqua fortis_,
+or Spirit of Vitriol poured upon Filings of Iron dissolves the Filings
+with a great Heat and Ebullition, is not this Heat and Ebullition
+effected by a violent Motion of the Parts, and does not that Motion
+argue that the acid Parts of the Liquor rush towards the Parts of the
+Metal with violence, and run forcibly into its Pores till they get
+between its outmost Particles, and the main Mass of the Metal, and
+surrounding those Particles loosen them from the main Mass, and set them
+at liberty to float off into the Water? And when the acid Particles,
+which alone would distil with an easy Heat, will not separate from the
+Particles of the Metal without a very violent Heat, does not this
+confirm the Attraction between them?
+
+When Spirit of Vitriol poured upon common Salt or Salt-petre makes an
+Ebullition with the Salt, and unites with it, and in Distillation the
+Spirit of the common Salt or Salt-petre comes over much easier than it
+would do before, and the acid part of the Spirit of Vitriol stays
+behind; does not this argue that the fix'd Alcaly of the Salt attracts
+the acid Spirit of the Vitriol more strongly than its own Spirit, and
+not being able to hold them both, lets go its own? And when Oil of
+Vitriol is drawn off from its weight of Nitre, and from both the
+Ingredients a compound Spirit of Nitre is distilled, and two parts of
+this Spirit are poured on one part of Oil of Cloves or Carraway Seeds,
+or of any ponderous Oil of vegetable or animal Substances, or Oil of
+Turpentine thicken'd with a little Balsam of Sulphur, and the Liquors
+grow so very hot in mixing, as presently to send up a burning Flame;
+does not this very great and sudden Heat argue that the two Liquors mix
+with violence, and that their Parts in mixing run towards one another
+with an accelerated Motion, and clash with the greatest Force? And is it
+not for the same reason that well rectified Spirit of Wine poured on the
+same compound Spirit flashes; and that the _Pulvis fulminans_, composed
+of Sulphur, Nitre, and Salt of Tartar, goes off with a more sudden and
+violent Explosion than Gun-powder, the acid Spirits of the Sulphur and
+Nitre rushing towards one another, and towards the Salt of Tartar, with
+so great a violence, as by the shock to turn the whole at once into
+Vapour and Flame? Where the Dissolution is slow, it makes a slow
+Ebullition and a gentle Heat; and where it is quicker, it makes a
+greater Ebullition with more heat; and where it is done at once, the
+Ebullition is contracted into a sudden Blast or violent Explosion, with
+a heat equal to that of Fire and Flame. So when a Drachm of the
+above-mention'd compound Spirit of Nitre was poured upon half a Drachm
+of Oil of Carraway Seeds _in vacuo_, the Mixture immediately made a
+flash like Gun-powder, and burst the exhausted Receiver, which was a
+Glass six Inches wide, and eight Inches deep. And even the gross Body of
+Sulphur powder'd, and with an equal weight of Iron Filings and a little
+Water made into Paste, acts upon the Iron, and in five or six hours
+grows too hot to be touch'd, and emits a Flame. And by these Experiments
+compared with the great quantity of Sulphur with which the Earth
+abounds, and the warmth of the interior Parts of the Earth, and hot
+Springs, and burning Mountains, and with Damps, mineral Coruscations,
+Earthquakes, hot suffocating Exhalations, Hurricanes, and Spouts; we may
+learn that sulphureous Steams abound in the Bowels of the Earth and
+ferment with Minerals, and sometimes take fire with a sudden Coruscation
+and Explosion; and if pent up in subterraneous Caverns, burst the
+Caverns with a great shaking of the Earth, as in springing of a Mine.
+And then the Vapour generated by the Explosion, expiring through the
+Pores of the Earth, feels hot and suffocates, and makes Tempests and
+Hurricanes, and sometimes causes the Land to slide, or the Sea to boil,
+and carries up the Water thereof in Drops, which by their weight fall
+down again in Spouts. Also some sulphureous Steams, at all times when
+the Earth is dry, ascending into the Air, ferment there with nitrous
+Acids, and sometimes taking fire cause Lightning and Thunder, and fiery
+Meteors. For the Air abounds with acid Vapours fit to promote
+Fermentations, as appears by the rusting of Iron and Copper in it, the
+kindling of Fire by blowing, and the beating of the Heart by means of
+Respiration. Now the above-mention'd Motions are so great and violent as
+to shew that in Fermentations the Particles of Bodies which almost rest,
+are put into new Motions by a very potent Principle, which acts upon
+them only when they approach one another, and causes them to meet and
+clash with great violence, and grow hot with the motion, and dash one
+another into pieces, and vanish into Air, and Vapour, and Flame.
+
+When Salt of Tartar _per deliquium_, being poured into the Solution of
+any Metal, precipitates the Metal and makes it fall down to the bottom
+of the Liquor in the form of Mud: Does not this argue that the acid
+Particles are attracted more strongly by the Salt of Tartar than by the
+Metal, and by the stronger Attraction go from the Metal to the Salt of
+Tartar? And so when a Solution of Iron in _Aqua fortis_ dissolves the
+_Lapis Calaminaris_, and lets go the Iron, or a Solution of Copper
+dissolves Iron immersed in it and lets go the Copper, or a Solution of
+Silver dissolves Copper and lets go the Silver, or a Solution of Mercury
+in _Aqua fortis_ being poured upon Iron, Copper, Tin, or Lead, dissolves
+the Metal and lets go the Mercury; does not this argue that the acid
+Particles of the _Aqua fortis_ are attracted more strongly by the _Lapis
+Calaminaris_ than by Iron, and more strongly by Iron than by Copper, and
+more strongly by Copper than by Silver, and more strongly by Iron,
+Copper, Tin, and Lead, than by Mercury? And is it not for the same
+reason that Iron requires more _Aqua fortis_ to dissolve it than Copper,
+and Copper more than the other Metals; and that of all Metals, Iron is
+dissolved most easily, and is most apt to rust; and next after Iron,
+Copper?
+
+When Oil of Vitriol is mix'd with a little Water, or is run _per
+deliquium_, and in Distillation the Water ascends difficultly, and
+brings over with it some part of the Oil of Vitriol in the form of
+Spirit of Vitriol, and this Spirit being poured upon Iron, Copper, or
+Salt of Tartar, unites with the Body and lets go the Water; doth not
+this shew that the acid Spirit is attracted by the Water, and more
+attracted by the fix'd Body than by the Water, and therefore lets go the
+Water to close with the fix'd Body? And is it not for the same reason
+that the Water and acid Spirits which are mix'd together in Vinegar,
+_Aqua fortis_, and Spirit of Salt, cohere and rise together in
+Distillation; but if the _Menstruum_ be poured on Salt of Tartar, or on
+Lead, or Iron, or any fix'd Body which it can dissolve, the Acid by a
+stronger Attraction adheres to the Body, and lets go the Water? And is
+it not also from a mutual Attraction that the Spirits of Soot and
+Sea-Salt unite and compose the Particles of Sal-armoniac, which are less
+volatile than before, because grosser and freer from Water; and that the
+Particles of Sal-armoniac in Sublimation carry up the Particles of
+Antimony, which will not sublime alone; and that the Particles of
+Mercury uniting with the acid Particles of Spirit of Salt compose
+Mercury sublimate, and with the Particles of Sulphur, compose Cinnaber;
+and that the Particles of Spirit of Wine and Spirit of Urine well
+rectified unite, and letting go the Water which dissolved them, compose
+a consistent Body; and that in subliming Cinnaber from Salt of Tartar,
+or from quick Lime, the Sulphur by a stronger Attraction of the Salt or
+Lime lets go the Mercury, and stays with the fix'd Body; and that when
+Mercury sublimate is sublimed from Antimony, or from Regulus of
+Antimony, the Spirit of Salt lets go the Mercury, and unites with the
+antimonial metal which attracts it more strongly, and stays with it till
+the Heat be great enough to make them both ascend together, and then
+carries up the Metal with it in the form of a very fusible Salt, called
+Butter of Antimony, although the Spirit of Salt alone be almost as
+volatile as Water, and the Antimony alone as fix'd as Lead?
+
+When _Aqua fortis_ dissolves Silver and not Gold, and _Aqua regia_
+dissolves Gold and not Silver, may it not be said that _Aqua fortis_ is
+subtil enough to penetrate Gold as well as Silver, but wants the
+attractive Force to give it Entrance; and that _Aqua regia_ is subtil
+enough to penetrate Silver as well as Gold, but wants the attractive
+Force to give it Entrance? For _Aqua regia_ is nothing else than _Aqua
+fortis_ mix'd with some Spirit of Salt, or with Sal-armoniac; and even
+common Salt dissolved in _Aqua fortis_, enables the _Menstruum_ to
+dissolve Gold, though the Salt be a gross Body. When therefore Spirit of
+Salt precipitates Silver out of _Aqua fortis_, is it not done by
+attracting and mixing with the _Aqua fortis_, and not attracting, or
+perhaps repelling Silver? And when Water precipitates Antimony out of
+the Sublimate of Antimony and Sal-armoniac, or out of Butter of
+Antimony, is it not done by its dissolving, mixing with, and weakening
+the Sal-armoniac or Spirit of Salt, and its not attracting, or perhaps
+repelling the Antimony? And is it not for want of an attractive virtue
+between the Parts of Water and Oil, of Quick-silver and Antimony, of
+Lead and Iron, that these Substances do not mix; and by a weak
+Attraction, that Quick-silver and Copper mix difficultly; and from a
+strong one, that Quick-silver and Tin, Antimony and Iron, Water and
+Salts, mix readily? And in general, is it not from the same Principle
+that Heat congregates homogeneal Bodies, and separates heterogeneal
+ones?
+
+When Arsenick with Soap gives a Regulus, and with Mercury sublimate a
+volatile fusible Salt, like Butter of Antimony, doth not this shew that
+Arsenick, which is a Substance totally volatile, is compounded of fix'd
+and volatile Parts, strongly cohering by a mutual Attraction, so that
+the volatile will not ascend without carrying up the fixed? And so, when
+an equal weight of Spirit of Wine and Oil of Vitriol are digested
+together, and in Distillation yield two fragrant and volatile Spirits
+which will not mix with one another, and a fix'd black Earth remains
+behind; doth not this shew that Oil of Vitriol is composed of volatile
+and fix'd Parts strongly united by Attraction, so as to ascend together
+in form of a volatile, acid, fluid Salt, until the Spirit of Wine
+attracts and separates the volatile Parts from the fixed? And therefore,
+since Oil of Sulphur _per Campanam_ is of the same Nature with Oil of
+Vitriol, may it not be inferred, that Sulphur is also a mixture of
+volatile and fix'd Parts so strongly cohering by Attraction, as to
+ascend together in Sublimation. By dissolving Flowers of Sulphur in Oil
+of Turpentine, and distilling the Solution, it is found that Sulphur is
+composed of an inflamable thick Oil or fat Bitumen, an acid Salt, a very
+fix'd Earth, and a little Metal. The three first were found not much
+unequal to one another, the fourth in so small a quantity as scarce to
+be worth considering. The acid Salt dissolved in Water, is the same with
+Oil of Sulphur _per Campanam_, and abounding much in the Bowels of the
+Earth, and particularly in Markasites, unites it self to the other
+Ingredients of the Markasite, which are, Bitumen, Iron, Copper, and
+Earth, and with them compounds Allum, Vitriol, and Sulphur. With the
+Earth alone it compounds Allum; with the Metal alone, or Metal and
+Earth together, it compounds Vitriol; and with the Bitumen and Earth it
+compounds Sulphur. Whence it comes to pass that Markasites abound with
+those three Minerals. And is it not from the mutual Attraction of the
+Ingredients that they stick together for compounding these Minerals, and
+that the Bitumen carries up the other Ingredients of the Sulphur, which
+without it would not sublime? And the same Question may be put
+concerning all, or almost all the gross Bodies in Nature. For all the
+Parts of Animals and Vegetables are composed of Substances volatile and
+fix'd, fluid and solid, as appears by their Analysis; and so are Salts
+and Minerals, so far as Chymists have been hitherto able to examine
+their Composition.
+
+When Mercury sublimate is re-sublimed with fresh Mercury, and becomes
+_Mercurius Dulcis_, which is a white tasteless Earth scarce dissolvable
+in Water, and _Mercurius Dulcis_ re-sublimed with Spirit of Salt returns
+into Mercury sublimate; and when Metals corroded with a little acid turn
+into rust, which is an Earth tasteless and indissolvable in Water, and
+this Earth imbibed with more acid becomes a metallick Salt; and when
+some Stones, as Spar of Lead, dissolved in proper _Menstruums_ become
+Salts; do not these things shew that Salts are dry Earth and watry Acid
+united by Attraction, and that the Earth will not become a Salt without
+so much acid as makes it dissolvable in Water? Do not the sharp and
+pungent Tastes of Acids arise from the strong Attraction whereby the
+acid Particles rush upon and agitate the Particles of the Tongue? And
+when Metals are dissolved in acid _Menstruums_, and the Acids in
+conjunction with the Metal act after a different manner, so that the
+Compound has a different Taste much milder than before, and sometimes a
+sweet one; is it not because the Acids adhere to the metallick
+Particles, and thereby lose much of their Activity? And if the Acid be
+in too small a Proportion to make the Compound dissolvable in Water,
+will it not by adhering strongly to the Metal become unactive and lose
+its Taste, and the Compound be a tasteless Earth? For such things as are
+not dissolvable by the Moisture of the Tongue, act not upon the Taste.
+
+As Gravity makes the Sea flow round the denser and weightier Parts of
+the Globe of the Earth, so the Attraction may make the watry Acid flow
+round the denser and compacter Particles of Earth for composing the
+Particles of Salt. For otherwise the Acid would not do the Office of a
+Medium between the Earth and common Water, for making Salts dissolvable
+in the Water; nor would Salt of Tartar readily draw off the Acid from
+dissolved Metals, nor Metals the Acid from Mercury. Now, as in the great
+Globe of the Earth and Sea, the densest Bodies by their Gravity sink
+down in Water, and always endeavour to go towards the Center of the
+Globe; so in Particles of Salt, the densest Matter may always endeavour
+to approach the Center of the Particle: So that a Particle of Salt may
+be compared to a Chaos; being dense, hard, dry, and earthy in the
+Center; and rare, soft, moist, and watry in the Circumference. And
+hence it seems to be that Salts are of a lasting Nature, being scarce
+destroy'd, unless by drawing away their watry Parts by violence, or by
+letting them soak into the Pores of the central Earth by a gentle Heat
+in Putrefaction, until the Earth be dissolved by the Water, and
+separated into smaller Particles, which by reason of their Smallness
+make the rotten Compound appear of a black Colour. Hence also it may be,
+that the Parts of Animals and Vegetables preserve their several Forms,
+and assimilate their Nourishment; the soft and moist Nourishment easily
+changing its Texture by a gentle Heat and Motion, till it becomes like
+the dense, hard, dry, and durable Earth in the Center of each Particle.
+But when the Nourishment grows unfit to be assimilated, or the central
+Earth grows too feeble to assimilate it, the Motion ends in Confusion,
+Putrefaction, and Death.
+
+If a very small quantity of any Salt or Vitriol be dissolved in a great
+quantity of Water, the Particles of the Salt or Vitriol will not sink to
+the bottom, though they be heavier in Specie than the Water, but will
+evenly diffuse themselves into all the Water, so as to make it as saline
+at the top as at the bottom. And does not this imply that the Parts of
+the Salt or Vitriol recede from one another, and endeavour to expand
+themselves, and get as far asunder as the quantity of Water in which
+they float, will allow? And does not this Endeavour imply that they have
+a repulsive Force by which they fly from one another, or at least, that
+they attract the Water more strongly than they do one another? For as
+all things ascend in Water which are less attracted than Water, by the
+gravitating Power of the Earth; so all the Particles of Salt which float
+in Water, and are less attracted than Water by any one Particle of Salt,
+must recede from that Particle, and give way to the more attracted
+Water.
+
+When any saline Liquor is evaporated to a Cuticle and let cool, the Salt
+concretes in regular Figures; which argues, that the Particles of the
+Salt before they concreted, floated in the Liquor at equal distances in
+rank and file, and by consequence that they acted upon one another by
+some Power which at equal distances is equal, at unequal distances
+unequal. For by such a Power they will range themselves uniformly, and
+without it they will float irregularly, and come together as
+irregularly. And since the Particles of Island-Crystal act all the same
+way upon the Rays of Light for causing the unusual Refraction, may it
+not be supposed that in the Formation of this Crystal, the Particles not
+only ranged themselves in rank and file for concreting in regular
+Figures, but also by some kind of polar Virtue turned their homogeneal
+Sides the same way.
+
+The Parts of all homogeneal hard Bodies which fully touch one another,
+stick together very strongly. And for explaining how this may be, some
+have invented hooked Atoms, which is begging the Question; and others
+tell us that Bodies are glued together by rest, that is, by an occult
+Quality, or rather by nothing; and others, that they stick together by
+conspiring Motions, that is, by relative rest amongst themselves. I had
+rather infer from their Cohesion, that their Particles attract one
+another by some Force, which in immediate Contact is exceeding strong,
+at small distances performs the chymical Operations above-mention'd, and
+reaches not far from the Particles with any sensible Effect.
+
+All Bodies seem to be composed of hard Particles: For otherwise Fluids
+would not congeal; as Water, Oils, Vinegar, and Spirit or Oil of Vitriol
+do by freezing; Mercury by Fumes of Lead; Spirit of Nitre and Mercury,
+by dissolving the Mercury and evaporating the Flegm; Spirit of Wine and
+Spirit of Urine, by deflegming and mixing them; and Spirit of Urine and
+Spirit of Salt, by subliming them together to make Sal-armoniac. Even
+the Rays of Light seem to be hard Bodies; for otherwise they would not
+retain different Properties in their different Sides. And therefore
+Hardness may be reckon'd the Property of all uncompounded Matter. At
+least, this seems to be as evident as the universal Impenetrability of
+Matter. For all Bodies, so far as Experience reaches, are either hard,
+or may be harden'd; and we have no other Evidence of universal
+Impenetrability, besides a large Experience without an experimental
+Exception. Now if compound Bodies are so very hard as we find some of
+them to be, and yet are very porous, and consist of Parts which are only
+laid together; the simple Particles which are void of Pores, and were
+never yet divided, must be much harder. For such hard Particles being
+heaped up together, can scarce touch one another in more than a few
+Points, and therefore must be separable by much less Force than is
+requisite to break a solid Particle, whose Parts touch in all the Space
+between them, without any Pores or Interstices to weaken their Cohesion.
+And how such very hard Particles which are only laid together and touch
+only in a few Points, can stick together, and that so firmly as they do,
+without the assistance of something which causes them to be attracted or
+press'd towards one another, is very difficult to conceive.
+
+The same thing I infer also from the cohering of two polish'd Marbles
+_in vacuo_, and from the standing of Quick-silver in the Barometer at
+the height of 50, 60 or 70 Inches, or above, when ever it is well-purged
+of Air and carefully poured in, so that its Parts be every where
+contiguous both to one another and to the Glass. The Atmosphere by its
+weight presses the Quick-silver into the Glass, to the height of 29 or
+30 Inches. And some other Agent raises it higher, not by pressing it
+into the Glass, but by making its Parts stick to the Glass, and to one
+another. For upon any discontinuation of Parts, made either by Bubbles
+or by shaking the Glass, the whole Mercury falls down to the height of
+29 or 30 Inches.
+
+And of the same kind with these Experiments are those that follow. If
+two plane polish'd Plates of Glass (suppose two pieces of a polish'd
+Looking-glass) be laid together, so that their sides be parallel and at
+a very small distance from one another, and then their lower edges be
+dipped into Water, the Water will rise up between them. And the less
+the distance of the Glasses is, the greater will be the height to which
+the Water will rise. If the distance be about the hundredth part of an
+Inch, the Water will rise to the height of about an Inch; and if the
+distance be greater or less in any Proportion, the height will be
+reciprocally proportional to the distance very nearly. For the
+attractive Force of the Glasses is the same, whether the distance
+between them be greater or less; and the weight of the Water drawn up is
+the same, if the height of it be reciprocally proportional to the
+distance of the Glasses. And in like manner, Water ascends between two
+Marbles polish'd plane, when their polish'd sides are parallel, and at a
+very little distance from one another, And if slender Pipes of Glass be
+dipped at one end into stagnating Water, the Water will rise up within
+the Pipe, and the height to which it rises will be reciprocally
+proportional to the Diameter of the Cavity of the Pipe, and will equal
+the height to which it rises between two Planes of Glass, if the
+Semi-diameter of the Cavity of the Pipe be equal to the distance between
+the Planes, or thereabouts. And these Experiments succeed after the same
+manner _in vacuo_ as in the open Air, (as hath been tried before the
+Royal Society,) and therefore are not influenced by the Weight or
+Pressure of the Atmosphere.
+
+And if a large Pipe of Glass be filled with sifted Ashes well pressed
+together in the Glass, and one end of the Pipe be dipped into stagnating
+Water, the Water will rise up slowly in the Ashes, so as in the space
+of a Week or Fortnight to reach up within the Glass, to the height of 30
+or 40 Inches above the stagnating Water. And the Water rises up to this
+height by the Action only of those Particles of the Ashes which are upon
+the Surface of the elevated Water; the Particles which are within the
+Water, attracting or repelling it as much downwards as upwards. And
+therefore the Action of the Particles is very strong. But the Particles
+of the Ashes being not so dense and close together as those of Glass,
+their Action is not so strong as that of Glass, which keeps Quick-silver
+suspended to the height of 60 or 70 Inches, and therefore acts with a
+Force which would keep Water suspended to the height of above 60 Feet.
+
+By the same Principle, a Sponge sucks in Water, and the Glands in the
+Bodies of Animals, according to their several Natures and Dispositions,
+suck in various Juices from the Blood.
+
+If two plane polish'd Plates of Glass three or four Inches broad, and
+twenty or twenty five long, be laid one of them parallel to the Horizon,
+the other upon the first, so as at one of their ends to touch one
+another, and contain an Angle of about 10 or 15 Minutes, and the same be
+first moisten'd on their inward sides with a clean Cloth dipp'd into Oil
+of Oranges or Spirit of Turpentine, and a Drop or two of the Oil or
+Spirit be let fall upon the lower Glass at the other; so soon as the
+upper Glass is laid down upon the lower, so as to touch it at one end as
+above, and to touch the Drop at the other end, making with the lower
+Glass an Angle of about 10 or 15 Minutes; the Drop will begin to move
+towards the Concourse of the Glasses, and will continue to move with an
+accelerated Motion, till it arrives at that Concourse of the Glasses.
+For the two Glasses attract the Drop, and make it run that way towards
+which the Attractions incline. And if when the Drop is in motion you
+lift up that end of the Glasses where they meet, and towards which the
+Drop moves, the Drop will ascend between the Glasses, and therefore is
+attracted. And as you lift up the Glasses more and more, the Drop will
+ascend slower and slower, and at length rest, being then carried
+downward by its Weight, as much as upwards by the Attraction. And by
+this means you may know the Force by which the Drop is attracted at all
+distances from the Concourse of the Glasses.
+
+Now by some Experiments of this kind, (made by Mr. _Hauksbee_) it has
+been found that the Attraction is almost reciprocally in a duplicate
+Proportion of the distance of the middle of the Drop from the Concourse
+of the Glasses, _viz._ reciprocally in a simple Proportion, by reason of
+the spreading of the Drop, and its touching each Glass in a larger
+Surface; and again reciprocally in a simple Proportion, by reason of the
+Attractions growing stronger within the same quantity of attracting
+Surface. The Attraction therefore within the same quantity of attracting
+Surface, is reciprocally as the distance between the Glasses. And
+therefore where the distance is exceeding small, the Attraction must be
+exceeding great. By the Table in the second Part of the second Book,
+wherein the thicknesses of colour'd Plates of Water between two Glasses
+are set down, the thickness of the Plate where it appears very black, is
+three eighths of the ten hundred thousandth part of an Inch. And where
+the Oil of Oranges between the Glasses is of this thickness, the
+Attraction collected by the foregoing Rule, seems to be so strong, as
+within a Circle of an Inch in diameter, to suffice to hold up a Weight
+equal to that of a Cylinder of Water of an Inch in diameter, and two or
+three Furlongs in length. And where it is of a less thickness the
+Attraction may be proportionally greater, and continue to increase,
+until the thickness do not exceed that of a single Particle of the Oil.
+There are therefore Agents in Nature able to make the Particles of
+Bodies stick together by very strong Attractions. And it is the Business
+of experimental Philosophy to find them out.
+
+Now the smallest Particles of Matter may cohere by the strongest
+Attractions, and compose bigger Particles of weaker Virtue; and many of
+these may cohere and compose bigger Particles whose Virtue is still
+weaker, and so on for divers Successions, until the Progression end in
+the biggest Particles on which the Operations in Chymistry, and the
+Colours of natural Bodies depend, and which by cohering compose Bodies
+of a sensible Magnitude. If the Body is compact, and bends or yields
+inward to Pression without any sliding of its Parts, it is hard and
+elastick, returning to its Figure with a Force rising from the mutual
+Attraction of its Parts. If the Parts slide upon one another, the Body
+is malleable or soft. If they slip easily, and are of a fit Size to be
+agitated by Heat, and the Heat is big enough to keep them in Agitation,
+the Body is fluid; and if it be apt to stick to things, it is humid; and
+the Drops of every fluid affect a round Figure by the mutual Attraction
+of their Parts, as the Globe of the Earth and Sea affects a round Figure
+by the mutual Attraction of its Parts by Gravity.
+
+Since Metals dissolved in Acids attract but a small quantity of the
+Acid, their attractive Force can reach but to a small distance from
+them. And as in Algebra, where affirmative Quantities vanish and cease,
+there negative ones begin; so in Mechanicks, where Attraction ceases,
+there a repulsive Virtue ought to succeed. And that there is such a
+Virtue, seems to follow from the Reflexions and Inflexions of the Rays
+of Light. For the Rays are repelled by Bodies in both these Cases,
+without the immediate Contact of the reflecting or inflecting Body. It
+seems also to follow from the Emission of Light; the Ray so soon as it
+is shaken off from a shining Body by the vibrating Motion of the Parts
+of the Body, and gets beyond the reach of Attraction, being driven away
+with exceeding great Velocity. For that Force which is sufficient to
+turn it back in Reflexion, may be sufficient to emit it. It seems also
+to follow from the Production of Air and Vapour. The Particles when they
+are shaken off from Bodies by Heat or Fermentation, so soon as they are
+beyond the reach of the Attraction of the Body, receding from it, and
+also from one another with great Strength, and keeping at a distance,
+so as sometimes to take up above a Million of Times more space than they
+did before in the form of a dense Body. Which vast Contraction and
+Expansion seems unintelligible, by feigning the Particles of Air to be
+springy and ramous, or rolled up like Hoops, or by any other means than
+a repulsive Power. The Particles of Fluids which do not cohere too
+strongly, and are of such a Smallness as renders them most susceptible
+of those Agitations which keep Liquors in a Fluor, are most easily
+separated and rarified into Vapour, and in the Language of the Chymists,
+they are volatile, rarifying with an easy Heat, and condensing with
+Cold. But those which are grosser, and so less susceptible of Agitation,
+or cohere by a stronger Attraction, are not separated without a stronger
+Heat, or perhaps not without Fermentation. And these last are the Bodies
+which Chymists call fix'd, and being rarified by Fermentation, become
+true permanent Air; those Particles receding from one another with the
+greatest Force, and being most difficultly brought together, which upon
+Contact cohere most strongly. And because the Particles of permanent Air
+are grosser, and arise from denser Substances than those of Vapours,
+thence it is that true Air is more ponderous than Vapour, and that a
+moist Atmosphere is lighter than a dry one, quantity for quantity. From
+the same repelling Power it seems to be that Flies walk upon the Water
+without wetting their Feet; and that the Object-glasses of long
+Telescopes lie upon one another without touching; and that dry Powders
+are difficultly made to touch one another so as to stick together,
+unless by melting them, or wetting them with Water, which by exhaling
+may bring them together; and that two polish'd Marbles, which by
+immediate Contact stick together, are difficultly brought so close
+together as to stick.
+
+And thus Nature will be very conformable to her self and very simple,
+performing all the great Motions of the heavenly Bodies by the
+Attraction of Gravity which intercedes those Bodies, and almost all the
+small ones of their Particles by some other attractive and repelling
+Powers which intercede the Particles. The _Vis inertiæ_ is a passive
+Principle by which Bodies persist in their Motion or Rest, receive
+Motion in proportion to the Force impressing it, and resist as much as
+they are resisted. By this Principle alone there never could have been
+any Motion in the World. Some other Principle was necessary for putting
+Bodies into Motion; and now they are in Motion, some other Principle is
+necessary for conserving the Motion. For from the various Composition of
+two Motions, 'tis very certain that there is not always the same
+quantity of Motion in the World. For if two Globes joined by a slender
+Rod, revolve about their common Center of Gravity with an uniform
+Motion, while that Center moves on uniformly in a right Line drawn in
+the Plane of their circular Motion; the Sum of the Motions of the two
+Globes, as often as the Globes are in the right Line described by their
+common Center of Gravity, will be bigger than the Sum of their Motions,
+when they are in a Line perpendicular to that right Line. By this
+Instance it appears that Motion may be got or lost. But by reason of the
+Tenacity of Fluids, and Attrition of their Parts, and the Weakness of
+Elasticity in Solids, Motion is much more apt to be lost than got, and
+is always upon the Decay. For Bodies which are either absolutely hard,
+or so soft as to be void of Elasticity, will not rebound from one
+another. Impenetrability makes them only stop. If two equal Bodies meet
+directly _in vacuo_, they will by the Laws of Motion stop where they
+meet, and lose all their Motion, and remain in rest, unless they be
+elastick, and receive new Motion from their Spring. If they have so much
+Elasticity as suffices to make them re-bound with a quarter, or half, or
+three quarters of the Force with which they come together, they will
+lose three quarters, or half, or a quarter of their Motion. And this may
+be try'd, by letting two equal Pendulums fall against one another from
+equal heights. If the Pendulums be of Lead or soft Clay, they will lose
+all or almost all their Motions: If of elastick Bodies they will lose
+all but what they recover from their Elasticity. If it be said, that
+they can lose no Motion but what they communicate to other Bodies, the
+consequence is, that _in vacuo_ they can lose no Motion, but when they
+meet they must go on and penetrate one another's Dimensions. If three
+equal round Vessels be filled, the one with Water, the other with Oil,
+the third with molten Pitch, and the Liquors be stirred about alike to
+give them a vortical Motion; the Pitch by its Tenacity will lose its
+Motion quickly, the Oil being less tenacious will keep it longer, and
+the Water being less tenacious will keep it longest, but yet will lose
+it in a short time. Whence it is easy to understand, that if many
+contiguous Vortices of molten Pitch were each of them as large as those
+which some suppose to revolve about the Sun and fix'd Stars, yet these
+and all their Parts would, by their Tenacity and Stiffness, communicate
+their Motion to one another till they all rested among themselves.
+Vortices of Oil or Water, or some fluider Matter, might continue longer
+in Motion; but unless the Matter were void of all Tenacity and Attrition
+of Parts, and Communication of Motion, (which is not to be supposed,)
+the Motion would constantly decay. Seeing therefore the variety of
+Motion which we find in the World is always decreasing, there is a
+necessity of conserving and recruiting it by active Principles, such as
+are the cause of Gravity, by which Planets and Comets keep their Motions
+in their Orbs, and Bodies acquire great Motion in falling; and the cause
+of Fermentation, by which the Heart and Blood of Animals are kept in
+perpetual Motion and Heat; the inward Parts of the Earth are constantly
+warm'd, and in some places grow very hot; Bodies burn and shine,
+Mountains take fire, the Caverns of the Earth are blown up, and the Sun
+continues violently hot and lucid, and warms all things by his Light.
+For we meet with very little Motion in the World, besides what is owing
+to these active Principles. And if it were not for these Principles, the
+Bodies of the Earth, Planets, Comets, Sun, and all things in them,
+would grow cold and freeze, and become inactive Masses; and all
+Putrefaction, Generation, Vegetation and Life would cease, and the
+Planets and Comets would not remain in their Orbs.
+
+All these things being consider'd, it seems probable to me, that God in
+the Beginning form'd Matter in solid, massy, hard, impenetrable,
+moveable Particles, of such Sizes and Figures, and with such other
+Properties, and in such Proportion to Space, as most conduced to the End
+for which he form'd them; and that these primitive Particles being
+Solids, are incomparably harder than any porous Bodies compounded of
+them; even so very hard, as never to wear or break in pieces; no
+ordinary Power being able to divide what God himself made one in the
+first Creation. While the Particles continue entire, they may compose
+Bodies of one and the same Nature and Texture in all Ages: But should
+they wear away, or break in pieces, the Nature of Things depending on
+them, would be changed. Water and Earth, composed of old worn Particles
+and Fragments of Particles, would not be of the same Nature and Texture
+now, with Water and Earth composed of entire Particles in the Beginning.
+And therefore, that Nature may be lasting, the Changes of corporeal
+Things are to be placed only in the various Separations and new
+Associations and Motions of these permanent Particles; compound Bodies
+being apt to break, not in the midst of solid Particles, but where those
+Particles are laid together, and only touch in a few Points.
+
+It seems to me farther, that these Particles have not only a _Vis
+inertiæ_, accompanied with such passive Laws of Motion as naturally
+result from that Force, but also that they are moved by certain active
+Principles, such as is that of Gravity, and that which causes
+Fermentation, and the Cohesion of Bodies. These Principles I consider,
+not as occult Qualities, supposed to result from the specifick Forms of
+Things, but as general Laws of Nature, by which the Things themselves
+are form'd; their Truth appearing to us by Phænomena, though their
+Causes be not yet discover'd. For these are manifest Qualities, and
+their Causes only are occult. And the _Aristotelians_ gave the Name of
+occult Qualities, not to manifest Qualities, but to such Qualities only
+as they supposed to lie hid in Bodies, and to be the unknown Causes of
+manifest Effects: Such as would be the Causes of Gravity, and of
+magnetick and electrick Attractions, and of Fermentations, if we should
+suppose that these Forces or Actions arose from Qualities unknown to us,
+and uncapable of being discovered and made manifest. Such occult
+Qualities put a stop to the Improvement of natural Philosophy, and
+therefore of late Years have been rejected. To tell us that every
+Species of Things is endow'd with an occult specifick Quality by which
+it acts and produces manifest Effects, is to tell us nothing: But to
+derive two or three general Principles of Motion from Phænomena, and
+afterwards to tell us how the Properties and Actions of all corporeal
+Things follow from those manifest Principles, would be a very great step
+in Philosophy, though the Causes of those Principles were not yet
+discover'd: And therefore I scruple not to propose the Principles of
+Motion above-mention'd, they being of very general Extent, and leave
+their Causes to be found out.
+
+Now by the help of these Principles, all material Things seem to have
+been composed of the hard and solid Particles above-mention'd, variously
+associated in the first Creation by the Counsel of an intelligent Agent.
+For it became him who created them to set them in order. And if he did
+so, it's unphilosophical to seek for any other Origin of the World, or
+to pretend that it might arise out of a Chaos by the mere Laws of
+Nature; though being once form'd, it may continue by those Laws for many
+Ages. For while Comets move in very excentrick Orbs in all manner of
+Positions, blind Fate could never make all the Planets move one and the
+same way in Orbs concentrick, some inconsiderable Irregularities
+excepted, which may have risen from the mutual Actions of Comets and
+Planets upon one another, and which will be apt to increase, till this
+System wants a Reformation. Such a wonderful Uniformity in the Planetary
+System must be allowed the Effect of Choice. And so must the Uniformity
+in the Bodies of Animals, they having generally a right and a left side
+shaped alike, and on either side of their Bodies two Legs behind, and
+either two Arms, or two Legs, or two Wings before upon their Shoulders,
+and between their Shoulders a Neck running down into a Back-bone, and a
+Head upon it; and in the Head two Ears, two Eyes, a Nose, a Mouth, and
+a Tongue, alike situated. Also the first Contrivance of those very
+artificial Parts of Animals, the Eyes, Ears, Brain, Muscles, Heart,
+Lungs, Midriff, Glands, Larynx, Hands, Wings, swimming Bladders, natural
+Spectacles, and other Organs of Sense and Motion; and the Instinct of
+Brutes and Insects, can be the effect of nothing else than the Wisdom
+and Skill of a powerful ever-living Agent, who being in all Places, is
+more able by his Will to move the Bodies within his boundless uniform
+Sensorium, and thereby to form and reform the Parts of the Universe,
+than we are by our Will to move the Parts of our own Bodies. And yet we
+are not to consider the World as the Body of God, or the several Parts
+thereof, as the Parts of God. He is an uniform Being, void of Organs,
+Members or Parts, and they are his Creatures subordinate to him, and
+subservient to his Will; and he is no more the Soul of them, than the
+Soul of Man is the Soul of the Species of Things carried through the
+Organs of Sense into the place of its Sensation, where it perceives them
+by means of its immediate Presence, without the Intervention of any
+third thing. The Organs of Sense are not for enabling the Soul to
+perceive the Species of Things in its Sensorium, but only for conveying
+them thither; and God has no need of such Organs, he being every where
+present to the Things themselves. And since Space is divisible _in
+infinitum_, and Matter is not necessarily in all places, it may be also
+allow'd that God is able to create Particles of Matter of several Sizes
+and Figures, and in several Proportions to Space, and perhaps of
+different Densities and Forces, and thereby to vary the Laws of Nature,
+and make Worlds of several sorts in several Parts of the Universe. At
+least, I see nothing of Contradiction in all this.
+
+As in Mathematicks, so in Natural Philosophy, the Investigation of
+difficult Things by the Method of Analysis, ought ever to precede the
+Method of Composition. This Analysis consists in making Experiments and
+Observations, and in drawing general Conclusions from them by Induction,
+and admitting of no Objections against the Conclusions, but such as are
+taken from Experiments, or other certain Truths. For Hypotheses are not
+to be regarded in experimental Philosophy. And although the arguing from
+Experiments and Observations by Induction be no Demonstration of general
+Conclusions; yet it is the best way of arguing which the Nature of
+Things admits of, and may be looked upon as so much the stronger, by how
+much the Induction is more general. And if no Exception occur from
+Phænomena, the Conclusion may be pronounced generally. But if at any
+time afterwards any Exception shall occur from Experiments, it may then
+begin to be pronounced with such Exceptions as occur. By this way of
+Analysis we may proceed from Compounds to Ingredients, and from Motions
+to the Forces producing them; and in general, from Effects to their
+Causes, and from particular Causes to more general ones, till the
+Argument end in the most general. This is the Method of Analysis: And
+the Synthesis consists in assuming the Causes discover'd, and
+establish'd as Principles, and by them explaining the Phænomena
+proceeding from them, and proving the Explanations.
+
+In the two first Books of these Opticks, I proceeded by this Analysis to
+discover and prove the original Differences of the Rays of Light in
+respect of Refrangibility, Reflexibility, and Colour, and their
+alternate Fits of easy Reflexion and easy Transmission, and the
+Properties of Bodies, both opake and pellucid, on which their Reflexions
+and Colours depend. And these Discoveries being proved, may be assumed
+in the Method of Composition for explaining the Phænomena arising from
+them: An Instance of which Method I gave in the End of the first Book.
+In this third Book I have only begun the Analysis of what remains to be
+discover'd about Light and its Effects upon the Frame of Nature, hinting
+several things about it, and leaving the Hints to be examin'd and
+improv'd by the farther Experiments and Observations of such as are
+inquisitive. And if natural Philosophy in all its Parts, by pursuing
+this Method, shall at length be perfected, the Bounds of Moral
+Philosophy will be also enlarged. For so far as we can know by natural
+Philosophy what is the first Cause, what Power he has over us, and what
+Benefits we receive from him, so far our Duty towards him, as well as
+that towards one another, will appear to us by the Light of Nature. And
+no doubt, if the Worship of false Gods had not blinded the Heathen,
+their moral Philosophy would have gone farther than to the four
+Cardinal Virtues; and instead of teaching the Transmigration of Souls,
+and to worship the Sun and Moon, and dead Heroes, they would have taught
+us to worship our true Author and Benefactor, as their Ancestors did
+under the Government of _Noah_ and his Sons before they corrupted
+themselves.
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