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Title: Opticks - or, a Treatise of the Reflections, Refractions, Inflections, - and Colours of Light
Author: Newton, Isaac, Sir, 1642-1727
Language: English
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Copyright Status: Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook. See comments about copyright issues at end of book.

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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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