^

^Vr

THE LIBRARY

OF

THE UNIVERSITY

OF CALIFORNIA

LOS ANGELES

GIFT

Dr. K. R. Beigelman

'•k.

».

oPTiCKs:

O R, A

TREATISE

O F T H E

Reflections, Refradiqns^

InfieBions and Colours

O F

LIGHT.

ne Fourth Edition, correSied,

By Sir ISAAC NEWTON, Knt.

L O N D 0 N:

Printed for William Innys at the Wefl-
End of St. Paul's, Mdccxxx.

©

837

■ ^. 'it

Advertifement L

ART of the en-
fui?ig Difeourfe a-
bout hight ivas
"Written at the De-
fire of fame Gen-
tlemen of the Royal -Society, in
the Tear 1^7^, and then fent to
their Seeretary, and read at their
Meetings, and the refiivas add-
ed about tivehe Tears after to
complete, the Theory ; except the
third Book, and the lafl Propo-
fit ion of the Second, vjhich "were
fince put together out of f car-
ter d Papers, To a\:oid be-
ing engaged in Difputes about

A z thefe

Advertifement.

thefe Matters, I haw hitherto de-
layed the printing, and jhould
flill ha've delayed it, had not the
Importunity of Friends prevailed
upon me. If any other Papers
nvrit on this SubjeB are got out
of my Hands they are imperfeB,
and ivere perhaps ^written before
I had tried all the Experiments
here fet do'von, and fully fatisfi-
ed my felf about theLaivs of Re*
fraBions and Compofttion of Co-
lours. I have here publijUd "vjhat
I think proper to eome abroad,
mping that it may not be tran-
Jlated into another hanguage
mthout my Confem.

The Crowns of Colours, ivhieh
fometimes appear about the Sun
and Moon, I ha'oe endea'voured
to gi've an Account of) but for

"want

Advertifement.

^o^ant of fufficient Obfer'vations
leave that Matter to be farther
examined. The Siibjeti of the
Third Book I have alfo left im-
perfeBy not having tried all the
Experiments "which I intended
ivhen Iivas about the fe Matters,
nor repeated fome ofthofe ivhich
I did try, until I had fatisfied
my felf about all their Circum-
fiances. To communicate vjhat
I have tried, and leave the refl
to others for farther Enquiry,
is all my Defign in publijhing
thefe Papers.

IndLettervjrittento Tlfr.Leib-
nitz in the Tear I (!) 7^, and pub-
lijhed by Dr, Wallis, / mention d
a Method by vohich I had found
fome general Theorems about
fquaring Curvilinear Figures,

or

Advertifement.

or comparing them mth the Co-
nic SeBions, or other the jimplefl
Figures mth v)hich they may be
compared. And fome Tears ago
I lent out a Manuscript contain-
ing fuch Theorems, and halving
fince met mth fome Things copi-
ed out of it, I have on this Occa-
fion made it public k, prefixing to
it ^//Introdudion, and Subjoin-
ing a Scholium concerning that
Method, And Ihavejoinedrnth
it another fmall TraB concern-
ing the Curvilinear Figures of
the Second Kind, "which ivas alfo
"written many Tears ago, and
made knov)n to fome Friends,
"who have folic it ed the making it
publicL

April r. T M

1704. X. -L^«

dvertifement 11.

this Second Edition
[hefeOpticks Iha've
oMtted the Mathema-
tical ^aBs publipd
at the End of the former Edi-
tion, as not belonging to the
SiibjeB. And at the End of
the Third Book I ha%w added
fome Queflions. And to fiev)
that I do not take Gratuity for
an ejfential Property of Bodies,
I have added one Queflion con-
cerning its Caufe, chiifing to
propofe it by "way of a Quefli-
on, becaufe I am not yet fatif-
fied about it for vjant of Expe-
riments.

^^- IN.

Advertisement to this
Fourth Edition.

HIS neuo Edition of
Sir Ifaac Newtonx
Opticks is carefully
printed frow> the Third
Edition, as it vjas correBed by
the Author s oivn Hand, and
left before his Death with the
Bookfeller, Since Sir Ifaac j*
Lediones Opticas, which he
public kly read in the Uni'verfity
of Cambridge in the Tears
l66^, 16^0, and 16'ji, are
lately printed, it has been thought
proper to make at the bottom of
the Pages fencer al Citations from
thence, where may be found the
Demonfirations, which the Au-
thor omitted in thefe Opticks. *

C I]

THE

FIRST BOOK

O F

OPTICKS.

PART I.

", Y Delign in this Book is not to ex-
plain the Properties of Light by Hy-
pothefes, but to propofe and prove
them by Reafon and Experiments :
In order to which I ihall premife the
following Definitions and Axioms.

B

DEFI-

B

O P T I C K S.
DEFINITIONS.

D E F I N. I.

T the Rays of Light I under/land its leafi
TartSy and thofe as well Siiccejive in the
fame Lines, as Contemporary in feveral Lines.
For it is manifeft that Light confifts of Parts,
both Succeflive and Contemporary j becaufe in
the fame place you may ftop that which comes
one moment, and let pafs that which comes pre-
fently after; and in the fame time you may
Hop it in any one place, and let it pafs in any
other. For that part of Light which is ftopp'd
cannot be the fame with fhat which is let pafs.
The leafl Light or part of Light, which may
be flopp'd alone without the reft of the Light,
or propagated alone, or do or fuffer any thing
alone, which the reft of the Light doth not or
fuifers not, I call a Ray of Light.

D E F I N. IL

Refrangibility of the Rays of Light, is their
T>ifpofition to be refraBed or turned out of their
Way in pafjing out of one tranfparent Body or
Medium into another. And a greater or lefs Re-
frangibility of Rays, is their Difpofition to be
turned more or lefs out of their Way in like^ In-
cidences on the fame Medium. Mathematicians
ufually confider the Rays of Light to be Lines
reaching from the luminous Body to the Body
illuminated, and the refradiion of thofe Rays to
be the bending or breaking of thofe lines in

their

BOOK! 3

their pafling out of one Medium into another.
And thus may Rays and Refradions be confi-
dered, if Light be propagated in an inftanr.
But by an Argument taken from the i^qua-
tions of the times of the Eclipfes of Jupiter i
BatelliteSy it feems that Light is propagated in
time, fpending in its pafTage from the Sun to us
about feven Minutes of time: And therefore I
have chofen to define Rays and Pvcfradions in
fuch general terms as may agree to Light in both
cafes.

D E F I N. in.

Reflexibility of Rays^ is fbeir Difpojitic?! to be
rejieSted or turned back into the fame Mediu?n jroni
any other Medium upon whoje Surface they fall.
And Rays are more or lefs refexible, which are
turned back more or lefs eafly. As if Light pafs
out of a Glafs into Air, and by being iiiclmed
more and more to the common Surface of the
Glafs and Air, begins at length to be totally re-
fledled by that Surface ; thofe io:::^ of Rays
which at like Incidences are refledted moft co-
pioully, or by inclining the Rays begin fooneil
to be totally refledted, are mofl reflexible.

D E F I N. IV.

I'he A?jgle of Licidence is that Angle, u-hick,
the Line defcribed by the incident Ray contains with
the Perpendicular to the refeSiing or refracting Sur--
face at the, Point of Incidence,

p2 DEFIN,

4 O P T I C K S.

D E F I N. V.

^ke Afigle of Reflexion or HefraBion^ is the

Angle which the line defcribed by the i'-eJleBed or re-

fraBed Ray coiitaineth with the Perpendicular to

the refleBing or refraSiifig Surface at the Point of

Incidence,

D E F I N. VL

'^he Sines of Incidence^ Reflexion^ and Refra-
Bion, are the Si?ies of the Angles of Incidence, Re-
fexion, and Refr/^Bio?!.

D E F I N. VII.

^hc Light ivhofe Rays are all alike Refran-
gible^ I call Simple, Homogeneal and Similar ;
and that whofe Rays are fome more Refrangible
than others, I call Compound, Heterogeneal and
Diffijnilar. The former Light I call Homoge-
neal, not becaufe I would affirm it fo in all re-
ipedts, but becaufe the Rays which agree in Re-
frangibility, agree at leaft in all thofe their other
Properties which I confider in the following
Difcourfe,

D E F I N. VIII.

\the Colours of Homogeneal Lights, I call Pri~
wary, Ilofjiogeneal and Simple j ajid thofe of He-
teroge??.eal Lights, Heterogeneal ajid Compound. For
thefe are always compounded of the colours of
Homogeneal Lights j as will appear in the fol-
lowing Difcourfe.

'O

AXIOMS.

B O O K I. 5

A X I 0 MS.

A X. I.

npHR Ajigks of RefexioJi and "Refracllon^ lit
in one and the fame Flane with the A?igle of In-
cidence.

A X. II.

'The Angle of Refexion is equal to the Angle of\
Incidence.

AX. III.

If the ref-aBed Ray be returned direclly back to
the Poifit of Incidence^ itJJ:all be rfraBed into the
Line before defcribed by the incident Ray.

A X. IV.

RefraBion out of the rarer Medium into the
denfer, is made towards the Perpendicular ; that
is, Jo that the A?igle of Refraclion be lefs than the
Angle of Incidence.

: A X. \.

The Siiie of Incidence is either accurately or
'very nearly in a green Ratio to the Sine of Re-
fraBion.

Whence if that Proportion be known in any
one Inclination of the incident Ray, 'tis known
in all the Inclinations, and thereby the Refra-
iftion in all cafes of Incidence on the fame refra-
<fting Body may be determined. Thus if the

B 3 R'efra-

6 O P T I C K S.

Refradion be made out of Air into Water, the
Sine of Incidence of the red Light is to the Sine
of its Refracftion as 4 to 3 . If out of Air into Glafs,
the Sines are as 17 to 11. In Light of other
Colours the Sines have other Proportions: but
the difference is fo little that it need feldom be
coniidered.

Suppofe therefore, that RS [ in Fig. i. ] repre-
fents the Surface of ftagnating Water, and that C
is the point of Incidence in which any Ray coming
in the Air from A in the Line A C is refledled or
refrad:ed, and I would know whither this Ray
fhall go after Reflexion or Refraction: I ereA
upon the Surface of the Water from the point
of Incidence the Perpendicular CP and produce
it downwards to Q^, and conclude by the firft
Axiom, that the Ray after Reflexion and Re-
fradiion, fliall be found fomewhere in the Plane
of the Angle of Incidence ACP produced. I let
fall therefore upon the Perpendicular C P jthe
Sine of Incidence A D j and if the refiedted
Ray be deflred, I produce AD to B fo that
D B be equal to A D, and draw C B. For this
Line C B fhall be the refiedted Ray j the Angle
of Reflexion B C P and its Sine B D being e-
qual to the Angle and Sine of Incidence, as they
ought to be by the fecond Axiom, But if the
refra(5led Ray be defired, I produce A D to H,
fo that D H may be to A D as the Sine of Re-
fradion 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 A C P with the Radius CA
defcribing a Circle ABE, I draw a parallel to the
Perpendicular CPQ^, the Line HE cutting tl^e

Circum-

B O O K I. 7

Circumference in E, and joining C E, this Line
CE fhall be the Line of the refradied Ray.,
For if E F be let fiiU perpendicularly on the
Line P Q^ this Line E F fliall be the Sine of Re-
fra<flion of the Ray C E, the Angle of Refradion
being E C Qj^ and this Sine E F is equal to D H,
and confequently in Proportion to the Sine of
Incidence AD as 3 to 4.

In like manner, if there be a Prifm of Glafs
(that is, a Glafs bounded with two Equal and
Parallel Triangular ends, and three plain and
well polifhed 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 Refradion of the Light in pafTing crofs this
Prifm be defired: Let ACB [inFig,2.] reprefent
a Plane cutting this Prifm tranfverlly to its three
Parallel lines or edges there where the Light
pafleth through it, and let D E be the Ray in-
cident upon the firft fide of the Prifm A C where
the Light goes into the Glafs ; and by putting
the Proportion of the Sine of Incidence to the
Sine of Refradion as 1 7 to 11 find E F the firft
refraded Ray. Then taking this Ray for the
Incident Ray upon the fecond fide of the Glafs
B C where the Light goes out, find the next
refraded Ray EG by putting the Proportion
of the Sine of Incidence to the Sine of Re-
fradion as II to 17. For if the Sine of Inci-
dence out of Air into Glafs be to the Sine of
Refradion as 17 to 11, the Sine of Incidence out
of Glafs into Air muil on the contrary be to the
Sine of Refradipn as 11 to 15^ by the third;
A?«tom»

S O P T I C K S.

Much after the fame manner, if A C B D [in
Fig. 2'] reprefent a Glafs fpherically convex on
both fides (ufually called aLem^ fuch as is a Burn-
ing-glafs, or Speftacle-glafs, or an Objedt-glafs of
a Telefcope) and it be required to know how
Light faUing upon it from any lucid point Q^
fhall be refra(5led, let Q^JVI reprefent a Ray
falling upon any point M of its firfl fpherical
Surface A C B, and by ered;ing a Perpendicular
to the Glafs at the point M, find the firll re-
fracted Ray M N by the Proportion of the
Sines 17 to 11. Let that Ray in going out of
the Glafs be incident upon N, and then find
the fecond refraded Ray N q by the Propor-
tion of the Sines 1 1 to 17. And after the fame
manner may the Refradion be found when the
Lens is convex on one fide and plane or con-
cave on the other, or concave on both fides.

A X. VI.

Homogeneal Rays which foiD from feveral Points
cf any Objecl^ and fall perpendicularly or almoji
perpendicularly on any refieSiing or refraBing Flane
or fpherical Surface^ Jhall afterwards diverge
from fo many other Points^ or be parallel to Jo
tnany other Lines, or converge to fo many other
Points^ either accurately or without any fetifble
'E,rror. And the fame thing will happen, if the
Rays be refcBed or refracted fucceffively 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 gi-
I'cn, that of the refleded or refraded ones may

be

B O O K I. 9

be found by finding the Refradtion of any two
Rays, as above j or niore readily thus.

Caf. I. Let ACB [in Fig. 4.] be a refleding or
refradling Plane, and Q^he Focus of the incident
Rays, and Q ^ C a Perpendicular to that Plane.
And if this Perpendicular be produced to q^
fo that ^ C be equal to Q^, the Point q fhall
be the Focus of the refledted Rays : Or if ^ C
be taken on the fame fide of the Plane with
Q^, and in proportion to Q^ as the Sine of
Incidence to the Sine of Refra6tion, the Point q
fliall be the Focus of the refracted Rays.

Caf 2. Let ACB [in Fig. 5.] be the refleding
Surface of any Sphere whofe Centre is E. Bi-
fed: any Radius thereof, ( fuppofe EC) in T,
and if in that Radius on the fame fide the Point
T you take the Points Q^nd ^, fo that T Q^
T E, and T q^ be continual Proportionals, and
the Point QJ)e the Focus of the incident Rays,
the Point q fliall be the Focus of the refiedted
ones.

Caf. 3. Let ACB [in Fig. 6.] be the refnidting
Surface of any Sphere whofe Centre is E. In
any Radius thereof E C produced both ways
take E T and C t equal to one another and fe-
verally in fuch Proportion to that Radius as
the lefi^er of the Sines of Incidence and P^e-
fradion hath to the difference of thofe Sines.
And then if in the fame Line you find any two
Points Q^nd ^, fo that T QJ^e to E T as E /^
to / q^ taking t q the contrary way from / which
T QJAeth from T, and if the Point QJ)e the
Focus of any incident Rays, the Point q fliall be
the Focus of the refracted ones>

2 And

lo O P T I C K S.

And by the fame means the Focus of the Rays
after two or more Reflexions or Refradions may
be found.

Caf.^. Let ACBD [in Fig. 7.] be any refrad-
ing Lens , fpherically Convex or Concave or
Plane on either fide, and let C D be its Axis
( that is, the Line which cuts both its Surfaces
perpendicularly, and paiTes through the Centres
of the Spheres,) and in this Axis produced let
F andybe the Foci of the refradled Rays found as
above, w^hen the incident Rays on both iides the
Lens are parallel to the fame Axis j and upon the
Diameter F f bifecCled in E, defcribe a Circle.
Suppofe now that any Point QJ>e the Focus of
any incident Rsys. Draw QJ^ cutting the faid
Circle in T and t^ and therein take t q m fuch
proportion to / E as /^ E or T E hath to T Q^
Let / ^ lie the contrary way from t which T Q
doth from T, and q fhall be the Focus of the,
rcfrafted Rays without any 'fenfible Error, pro-
vided the Point QJ)e not fo remote from the
Axis, nor the Lens fo broad as to make any of
the Rays fall too obliquely on the refracting
Surfaces. *

And by the like Operations may the reflecting
or refracHiing Surfaces be found when the two
Foci are given, and thereby a Lens be formed,
which Ihall make the Rays flow towards or
from what Place you pleafe. -f-

* In our Author's LeEliones Optica:, Part I. Seft. IV. Prop. 29,
30, there is an elegant Method of determining thefe Foci ; not only
in fpherical Surfaces, but likewife in any other curved Figure what-
ev«r : And in Prop. 32, 33, the fame thing is done tor any Ray ly-
ing out of the Axis.

f Ibid. Prop. ^4.

. Sq

B O O K I. It

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 fhall after Re-
flexion or Refra6lion flow from or towards the
Point q found by the foregoing Rules. And if
the incident Rays flow from or towards feveral
points Q^ the refleded or refradled Rays fliall
flow from or towards fo many other Points q
found by the fame Rules. Whether the refle<5t-
ed and refracted Rays flow from or towards the
Point q is eafily known by the fltuation of that
Point. For if that Point be on the fame flde
of the refleding 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 refradled from it ; and if the
incident Rays flow towards Q, the refleded
flow from q, and the refraded towards it. And
the contrary happens when q is on the other
fide of the Surface.

A X. VIL

Wherever the Rays which come from all the
Points of any Object meet again in Jo many
Poi?its after they have been made to converge by
RefeBion or RefraBion^ there they will make a Pi'
Bure of the ObjeB upon any white Body on which
they fall.

So if PR [in Fig. 3.] reprefent any Objed with-
out Doors, and A B be a Lens placed at a hole
in the Window-ihut of a dark Chamber, where-
by the Rays that come from any Point Q^of
I that

12 O P T I C K S.

that Qbje6t are made to converge and meet a-
gain in the Point q j and if a Sheet of white Pa-
per be held at q for the Light there to fall up-
on it, the Pidlure of that Objed; P R will ap-
pear upon the Paper in its proper jQiape and Co-
lours. For as the Light which comes from the
Point Q^goes to the Point q, fo the Light which
comes from other Points P and R of the Objed:,
will go to fo many other correfpondent Points
p and r ( as is manifell by the fixth Axiom j ) fo
that every Point of the Objed: fhall illuminate a
correfpondent Point of the Pidure, and there-
by make a Pidture like the Objed in Shape and
Colour, this only excepted, that the Pidture fhall
be inverted. And this is the Reafon of that vul-
gar Experiment of cafting the Species of Objeds
from abroad upon a Wall or Sheet of white Pa-
per in a dark Room.

In like manner, when a Man views any Objed:
P QR, [in Fig. 8.] the Light which comes from
the feveral Points of the Objed is fo refraded
by the tranfparent fkins and humours of the
Eye, (that is, by the outward coat E F G, called
the "Tunica Corfiea, and by the cryftalline hu-
mour A B which is beyond the Pupil ;;z ^ ) as to
converge and meet again in fo many Points in
the bottom of the Eye, and there to paint the
Pidure of the Objed upon that fkin (called the
Tunica Retina ) with which the bottom of the
Eye is covered. For Anatomifts, when they have
taken off from the bottom of the Eye that out-
ward and moft thick Coat called the Dura Ma-
ter^ can then fee through the thinner Coats,
the Pidures of Objeds , lively paint^ there-
on^

B O O K I. 13

on. And thefe Pidlures, propagated by Mo-
tion along the Fibres of the Optick Nerves in-
to the Brain, are the caufe of Vilion. For ac-
cordingly as thefe Pidtures are perfed: or im-
perfedl, the Objed: is feen perfectly or imperfed:-
ly. If the Eye be tinged with any colour (as in
the Difeafe of the yawidice) fo as to tinge the
Pidures in the bottom of the Eye with that
Colour, then all Objeds appear tinged with the
fame Colour. If the Humours of the Eye by
old Age decay, fo as by (hrinking to make the
Cornea and Coat of the Ci'yiialline Humour grow
flatter than before, the Light will not be re-
frad:ed enough, and for want of a fufficient Re-
fraction will not converge to the bottom of the
Eye but to fome place beyond it, and by con-
fequence paint in the bottom of the Eye a con-
fufed Pidlure, and according to the Indifl:in(ft-
nefs of this Pidture the Objed: will appear con-
fufed. This is the reafon of the decay of fight
in old Men, and fhews why their Sight is mend-
ed by Spedacles. For thofe Convex glalTes fup-
ply the defed of plumpnefs in the Eye, and by
increafing the Refradion make the Rays con-
verge fooner, fo as to convene diftindly at the
bottom of the Eye if the Glafs have a due de-
gree of convexity. And the contrary happens
in fhort-fighted Men whofe Eyes are too plump.
For the Refradion being now too great, the
Rays converge and convene in the Eyes before
they come at the bottom > and therefore the
Pidure made in the bottom and the Vifion
caufed thereby will not be diftind, unlefs the
Object be brought fo near the Eye as that the ,

place

14 o p T I c k: s.

place where the converging Rays convene may
be removed to the bottom, or that the plump-
nefs of the Eye be taken off and the Refrad:i-
ons diminifhed by a Concave-glafs of a due de-
gree of Concavity, or laflly that by Age the
Eye grow flatter till it come to a due Figure:
For fhort-fighted Men fee remote Objeds beft
in Old Age, and therefore they are accounted to
have the moft lafling Eyes.

A X. VIII.

An ObjeB fcen by Reflexion or "RefraSiion, ap'
pears in that place from whence the Rays after their
laji Reflexion or RefraBion diverge in falling on the
SpeBators Eye,

If the Object A [in Fig.^!\ be feen by Reflexion
of a Looking-glafs m n^ it fliall appear, not in its
proper place A, but behind the Glafs at a, from
whence any Rays AB, AC, AD, which flow from
one and the fame Point of the Objed, do after
their Reflexion made in the Points B, C, D, di-
verge in going from the Glafs to E, F, G,
where they are incident on the Spectator's Eyes.
For theJf^ Rays do make the fame Picture in the
bottom of the Eyes as if they had come from
the Objed: really placed at a without the Inter-
pofition of the Looking-glafs; and all Vifion is
made according to the place and fliape of that
Pidure.

In like manner the Obje6t D [in Fig. 2.] feen
through a Prifm, appears not in its proper place
D, but is thence tranflated to fome other place
d fituated in the laft refraded Ray F G drawn
backward from F to d. And

B O O K I. 15

And fo the'Objed: Q^[ in Fig. 10.] feentlirough
tlie Lens A B, appears at the place q from whence
the Rays diverge in paffing from the Lens to the
Eye. Now it is to be noted, that the Image of
the Objed; at q is fo much bigger or lelTer than
the Objed: it felf at Q^, as the diftance of the
Image at q from the Lens A B is bigger or lefs
than the diftance of the Objed: at C^rom the
fame Lens. And if the Objedl be feen through
two or more fuch Convex or Concave-glafl'es,
every Glafs fhall make a new Image, and the
Object fhall appear in the pkce of the big-
nefs of the laft Image. Which confideration un-
folds the Theory of Microfcopes and Telefcopcs.
For that Theory coniifts in almoll nothing elfe
than the defcribing fuch Glafles as fliall make the
laft Image of any Objedl as diHind and large and
luminous as it can conveniently be made.

I have now given in Axioms and their Ex-
plications the fum of what hath hitherto been
treated of in Opticks. For what hath been ge-
nerally agreed on I content my felf to allume
under the notion of Principles, in order to what
I have farther to write. And this may fuffice
for an Introdu6tion to Readers of quick Wit
and good Underftanding not yet verfed in Op-
ticks : Although thofe who are already acquaint-
ed with this Science, and have handled GlalTes,
will more readily apprehend what followeth.

PROPO"

O P T I C K S.

PROPOSITIONS.

P ROP.l T H E O R. I.

T IG HTS which differ in Colour, differ alfo in
Degrees of Refrangibility,

The Proof by Experiments.

Exper. I. I took a black oblong ftifF Paper
terminated by Parallel Sides, and with a Per-
pendicular right Line drawn crofs from one
Side to the other, diftinguifhed it into two e-
qual Parts. One of thefe parts I painted with
a red colour and the other with a blue. The
Paper was very black, and the Colours intenfe
and thickJy laid on, that the Phaenomenon
might be more confpicuous. This Paper I
view'd through a Prifm of folid Glafs, wllofe
two Sides through which the Light pafled to the
Eye were plane and well polifhed, and contained
an Angle of about fixty degrees ; which Angle
I call the refracting; Angle of the Prifm. And
whilft I view'd it, I held it and the Prifm before
a Window in fuch manner that the Sides of the
Paper were parallel to the Prifm, and both thofe
Sides and the Prifm were parallel to the Horizon,
and the crofs Line was*alfo 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 fame

Paper

B O O K I. J7

Paper by the Light refle6led from It to the Eye.
Beyond the Prifm was the Wall of the Chamber
under the Window covered over with black
Cloth, and the Cloth was involved in Darknefs
that no Light might be reflected from thence,
which in palTing by the Edges of the Paper to
the Eye, might mingle itfelf with the Light of
the Paper, and obfcure the Phaenomenon there-
of. Thefe things being thus ordered, I found
that if the refracting Angle of the Prifm be
turned upwards, fo that the Paper may feem to
be lifted upwards by the Refraction, its blue
half will be lifted higher by the Refradlon ; ban
its red half. But if the refrad:ing Angle of the
Prifm be turned downward, fo that the Paper
may feem to be carried lower by the Refra-
d:ion, its blue half will be carried fomethin^
lower thereby than its red half Wherefore in
both Cafes the Light which comes from the
blue half of the Paper tlirough the Prifm to
the Eye, does in like Circumitances fuffer a
greater Refradion than the Light which comes
from the red half, and by confequence is m.ore
refrangible.

Ilhijlration. In the eleventh Figure, M N
reprefents the Window, and D E the Paper
terminated with parallel Sides D J and H E,
and by the tranfverfe Line F G diftinguiilied
into two halfs, the one D G of an intenfely
blue Colour, the other F E of an intenfely
red. And ^ hC c a b reprefents the Prifm
whofe refrading Planes KB b a and KC c a
meet in the Edge of the refracting Angle *% a.
This Edge A a being upward, is paralldftoth to

C the

i8 O P T I C K S.

the Horizon, and to the Parallel-Edges of the
Paper D J and HE, and the tranfverfe Line FG
is perpendicular to the Plane of the Window.
And de reprefents the Image of the Paper {0,^x1
by Refraction upwards in fuch manner, that the
blue half DG is carried higher to dg than the
red half F E is to fe^ and therefore fuffers a
greater Refrad:ion. If the Edge of the refracting
Angle be turned downward, the Image of the
Paper vv^ill be refraded downward j fuppofe to
^ e, and the blue half will be refracted lower to
^ y, than the red half is to 9 g.

Exper, 2. About the aforeiaid Paper, whofe
two halfs were painted over with red and blue,
and which was ftifflike thin Pafteboard, I lapped
feveral times a llender Thred of very black Silk,
in fuch manner that the feveral parts of the
Thred might appear upon the Colours like fo
many black Lines drawn over them, or like
long and {lender dark Shadows caft upon them.
I might have drawn black Lines with a Pen,
but the Threds were fmaller and better defined.
This Paper thus coloured and lined I fet againft
a Wall perpendicularly to the Horizon, fo that
one of the Colours might ftand to the Right
Hand, and the other to the Left. Clofe before
the Paper, at the Confine of the Colours below,
I placed a Candle to illuminate the Paper ftrong-
ly : 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 diftance of fix Feet, and one or two
Inches from the Paper upon the Floor I ereCted
a Giafs Lens four Inches ajid a quarter broad,

which

B O O K I. x^

which might colled: the Rays coming from the
feveral Points of the Paper, and make them con-
verge towards fo many other Points at the fame
diftance of fix Feet, and one or two Inches on
the other fide of the Lens, and fo form the Image
of the coloured Paper upon a white Paper placed
there, after the fame manner that a Lens at a
Hole in a Window cafts the Images of Objedts
abroad upon a Sheet of white Paper in a dark
Room. The aforefiid white Paper, ere<5i:ed per-
pendicular to the Horizon, and to the Rays
which fell upon it from the Lens, I moved
fometimes towards the Lens, fometimes from
it, to find the Places where the Images of the
blue and red Parts of the coloured Paper appear-
ed mojft diftindt. Thofe Places I eafily knew by
the Images of the black Lines which I had made
by winding the Silk about the Paper. For the
Images of thofe fine and flender Lines (which
by reafon of their Blacknefs were like Shadows
on the Colours) were confufed and fcarce vifi-
ble, unlefs when the Colours on either fide of
each Line were terminated moft diftindlly. No-
ting therefore, as diligently as I could, the
Places where the Images of the red and blue
halfs of the coloured Paper appeared mofl di-
flindt, I found that where the red half of the
Paper appeared diftindt, the blue half appeared
confufed, fo that the black Lines drawn upon
it could fcarce be feen ; and on the contrary,
where the blue half appeared mofl diftindt, the
red half appeared confufed, fo that the black
Lines upon it were fcarce vifible. And between
the two Places where thefe Images appeared

C 3 diflindt

2® O P T I C K S.

diftind there was the diftance of an Inch atid a
half; the diftance of the white Paper from the
Lens, when the Image of the red. half of the co-
loured Paper appeared moft diftind, being greater
by an Inch and an half than the diftance of the
fame white Paper from the Lens, when the Image
of the blue half appeared moft diftind:. Irv
like Incidences therefore of the blue and red
upon the Lens, the blue was refradted more by
the Lens than the red, fo as to converge fooner by
an Inch and a half, and therefore is more refran-
gible.

Illiijlration. In the twelfth Figure, D E iig-
nifies the coloured Paper, D G 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 diftind, and h i the fame
Paper in that Place where the blue half appeared
diftind:. The Place h i was nearer to the Lens
M N than the Place H J by an Inch and an
half

^ Scholium. The fame Things fucceed, notwith-
ftanding that fome of the Circumftances be va-
ried y as in the firft Experiment when the Prifm
and Paper are any ways inclined to the Hori-
zon, and in both when coloured Lines are
drawn upon very black Paper. But in the De-
fcription of thefe Experiments, I have fet down
fuch Circumftances, by which either the Phae-
nomenon might be render'd more confpicuous,
or a Novice might more eafily try them, or by
which I did try them only. The fame Thing, I
have often done in the following Experiments :
Concerning all which, this one Admonition may

fuffice.

B O O K I. 2£

fuffice. Now from thefe Experiments It follows
nor, that all the Light of the blue is more refran-
gible than all the Light of the red : For both
Lights are mixed of Rays differently refrangible,
fo that in the red there are fome Rays not lefs re-
frangible than thofe of the blue, and in the blue
there are fome Rays not more refrangible than
thofe of the red : But thefe Rays, in proportion to
the whole Light, are but few, and ferve to dimi-
nifh the Event of the Experiment, but are not
able to deftroy it. For, if the red and blue Co-
lours were more dilute and weak, the diflance of
the Images would be lefs than an Inch and a half;
and if they were more intenfe and full, that di-
ftance would be greater, as will appear hereafter.
Thefe Experiments may fuffice for the Colours of
Natural Bodies. For in the Colours made by the
Refradtion of Prifms, this Propof tion will ap-
pear by the Experiments which are now to fol-
low in the next Fropolition.

PROP. 11. The OR. II.

lie Light of the Sim confifls of Rajs
differently Refrangible,

The Proof by Experiments.

Exper. 3. TN a very dark Chamber, at a round
jj Hole, about one third Part of an
Inch broaa, made in the Shut of a Window, I
placed a Glafs Prifm, whereby the Beam of tlie
Sun's Light, which came in at that Hole, might
be refraj^ed upwards toward the oppofite \Vail

C 3 of

22 O P T I C K S.

of the Chamber, and there form a colour'd I-
mage of the Sun. The Axis of the Prifm ( that
is, the Line paffing through the middle of the
Prifm. from one end of it to the other end pa-
rallel to the edge of the Refracting Angle ) was
in this and the following Experiments perpen-
dicular to the incident Rays. About this Axis
I turned the Prifm flowly, and faw the refradt-
ed Light on the Wall, or coloured Image of
the Sun, firfl to defcend, and then to afcend.
Between the Defcent and Afcent, when the I-
mage feemed Stationary, I ftopp'd the Prifm,
and fix'd it in that Pofture, that it fhould be
moved no more. For in that Pofture the Re-
fractions of the Light at the two Sides of the
refracting Angle, that is, at the Entrance of the
Rays into the Prifm, and at their going out of
it, were equal to one another*. So alfo in other
Experiments, as often as I would have the Re-'
fractions on both fides the Prifm to be equal to
one another, I noted the Place where the Image
of the Sun formed by the refraCted Light ftood
ftill between its two contrary Motions, in the
common Period of its Progrefs and Regrefs ; and
when the Image fell upon that Place, I made
faft the Prifm. And in this Pofture, as the moft
convenient, it is to be underftood that all the
Prifms are placed in the following Experiments,
unlefs where fome other Pofture is defcribed.
The Prifm therefore being placed in this Po-
fture, I let the refracted Light fall perpendicu-
larly upon a Sheet of white Paper at the oppo-
fite Wall of the Chamber, and obferved the Fi-

* See eur AuthorV Leftiones Optica, Parti. Se£i. i. § !©•
StU, II. § 29. and SeSl. III. frop. 25. gurc

B O O K I. Q3

gure and Dimenrions of the Solar Image form-
ed on the Paper by that Light. This Image
was Oblong and not Oval, but terminated with
two Rectilinear and Parallel Sides, and tv/o Se-
micircular Ends. On its Sides it was bounded
pretty diftindtly, but on its Ends very confuled-
ly and indiftindly, the Light there decaying
and vanifl:iing by degrees. The Breadch of this
Image anfwered to the Sun's Diam.eter, and was
about two Inches and the eighth Part of an
Inch, including the Penumbra. For the Image
was eighteen Feet and an half dlftant from the
Prifm, and at this diftance that Breadth, if di-
minifhed by the Diameter of the Hole in the
Window-fhut, that is by a quarter of an Inch,
fubtended an Angle at the Prifm of about half
a Degree, which is the Sun's apparent Diame-
ter. But the Length of rhe Image was about ten
Inches and a quarter, and the Length oi the Re-
d-ilinear Sides about eight Inches ; and the re-
fracting Angle of the Prifm, whereby fo great a
Length was made, was 64 degrees. With a lefs
Angle the Length of the Image was lefs, the
Breadth remaining the fame. If the Prifm was
turned about its Axis that way which made the
Rays emerge more obliquely out of the fecond
refracting Surface of the Prifm, the Image foon
became an Inch or two longer, or morej and
if the Prifm was turned about the contrary
way, fo as to make the Rays fall more obliquely
on the firft refraCting Surface, the Image fooa
became an Inch or two fhorter. And there-
fore in trying this Experiment, I was as curi-
Qus as I could be in placing the Prifm by xhe

C 4 abo\^*

24 O P T I C K S.

above-mention'd Rule exadtly in fuch a Poflure,
that the Refradions of the Rays at their Emer-
gence out of the Prifm might be equal to that
at their Incidence on it. This Prifm had fome
Veins running along within the Glafs from one
end to the other, which fcattered fome of the
Sun's Light irregularly, but had no fenfible Ef-
fect in increafing the Length of the coloured
Spedirum. For I tried the fame Experiment
with other Prifms with the fame Succefs. And
particularly with a Prifm which feemed free
from fuch Veins, and whofe refracting Angle
was 625 Degrees, I found the Length of the
Image 95 or 10 Inches at the diflance of i8|
Feet from the Prifm, the Breadth of the Hole
in the Window-fhut being J of an Inch, as be-
fore. And becaufe it is eaiy to commit aMi-
llake in placing the Prifm in its due Pofture, I
repeated the Experiment four or five Times,
and always found the Length of the Image that
which is fet down above. With another Prifm
of clearer Glafs and better Polifh, which feem-
ed free from Veins, and whofe refracting Angle
was 631 Degrees, the Length of this Image at
the fam^e diftance of i8i Feet was alfo about 10
Inches, or loi Beyond thefe Meafures for a-
bout a : or i of an Inch at either end of the
SpeCtrum the Light of the Clouds feemed to be a
little tinged with red and violet, but fo very
faintly, that I fufpeded that TinCture might ei-
ther v/holly, or in great Meafure arife from fome
Rays of the Spedtrum fcattered irregularly by
fome Inequalities in the Subftance and Polilli of
the Glafs, and therefore I did not include it in
I tliefe

B O O K I. 25

thefe Meafures. Now the different Magnitude
of the hole in the Window-fhut, and different
thicknefs of the Prifm where the Rays palled
through it, and different inclinations of the
Prifm to the Horizon, made no fenfible chan-
ges in the length of the Image. Neither did
the different matter of the Prifms make any:
for in a Veffel made of polifhed Plates of Glafs
cemented together in the fhape of a Prifm and
filled with Water, there is the like Succefs of
the Experiment according to the quantity of
the Refradlion. It is farther to be obferved,
that the Rays went on in right Lines from the
Prifm to the Image, and therefore at their very
going out of the Prifm had all that Inclina-
tion 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 re-
ceived, they could not poffibly be fo much incli-
ned to one another *. For let E G [ mFig. 1 3.] re-
prefent the Window-fhut, F the hole made there-
in through which a beam of the Sun's Light
was tranfmitted into the darkned Chamber, and
ABC a Triangular Imaginary Plane whereby the
Prifm is feigned to be cut tranfverfly through
the middle of the Light. Or if you pleafe, let
ABC reprefent the Prifm it felf, looking di-
redtly towards the Speftator's Eye with its nearer
end; And let X Y be the Sun, MN the Pa-
per upon which the Solar Image or Spectrum is
caff, and P T the Image it felf whofe fides to-
wards 1; and w are Redlilinear and Parallel, and
ends towards P and T Semicircular. YKHP

and

* See OMx Author's Lenionei Opticcy Part. I. Sect. i. §.5.

^6 d p T I c K a

and X L J T are two Rays, the firft of. which
comes from the lower part of the Sun to the
higher part of the Image, and is refraded in the
Prifm at K and H, and the latter comes from
the higher part of the Sun to the lower part of
the Image, and is refradted at L and J. Since
the Refradions on both fides the Prifm are e-
qual to one another, that is, the Refraction at
K equal to the Refradion at J, and the Refra-
dion at L equal to the Refradion at H, fo that
the Refradions of the incident Rays at K and L
taken together, are equal to the Refradions of
the emergent Rays at H and J taken together :
it follows by adding equal things to equal things,
that the Refradions at K and H taken together,
are equal to the Refradions at J and L taken
together, and therefore the two Rays being e-
qually refraded, have the fame Inclination to
one another after Refradion which they had
before ; that is, the Inclination of half a Degree
anfwering to the Sun's Diameter. For fo great
was the Inclination of the Rays to one another
before Refradion. So then, the length of the
Image P T would by the Rules of Vulgar Op-
ticks fubtend an Angle of half a Degree at the
Prifm , and by Confequence be equal to the
breadth 'y w -, and therefore the Image would
be round. Thus it would be were the two
Rays XL JT and YKHP, and all the reft which
form the Image P w T 'u, alike refrangible.
And therefore feeing 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 fuffer the greateft Re-
fradion,

BOOK I. a;

fradion, mufl be more refrarxgible than thofe
which go to the lower end T, unlefs the Inequa-
lity of Refradtion be cafual.

This Image or Spectrum P T was .coloured,
being red at its leaft refradled end T, and vio-
let at its moil refraded end P , and yellow
green and blue in the intermediate Spaces.
Which agrees with the firft Proportion, that
Lights which differ in Colour, do alio differ in
Refrangibility. The length of the Image in the
foregoing Experiments, I meafured from the
fainteft and outmoft red at one end, to the
fainteft and outmoft blue at the other end, ex-
cepting only a little Penumbra, whofe breadth
fcarce exceeded a (quarter of an Inch, as was
faid above.

Exper. 4. In the Sun's Beam which was pro-
pagated into the Room through the hole in the
Window-fhut , at the diffance of fome Feet
from the hole, I held the Prifm in fuch a Po-
llure, that its Axis might be perpendicular to
that Beam. Then I looked through the Prifm
upon the hole, and turning the Prifm to and
fro about its Axis, to rhake the Image of the
Hole afcend and defcend-, when between its
two contrary Motions it feemed Stationary, I
ftopp'd the Prifm, that the Refradions of both
fides of the refrading Angle might be equal to
each other, as in the former Experiment. In
this Situation of the Priim viewing through it
the faid Hole, I obferved the length of its re-
fraded Image to be many times greater than
its breadth, and that the moH: refraded part
■ thereof appeared violet, the lead refraded red,
2 the

28 O P T I C K S.

the middle parts blue, green and yellow in or-
der. The fame thing happen'd when I remo-
ved the Prifm out of the Sun's Light, and look-
ed through it upon the hole fliining by the
Light of the Clouds beyond it. And yet if the
Refradtion were done regularly according to
one certain Proportion of the Sines of Inci-
dence and Refradion as is vulgarly fuppofed,
the refraded Image ought to have appeared
round.

So then, by thefe two Experiments it appears,
that in equafi Incidences there is a confiderable
inequality of Refractions. But whence this in-
equality arifes, whether it be that fome of the
incident Rays are refradled more, and others lefs,
conftantly, or by chance, or that one and the
fame Ray is by Refrad;ion difturbed, fliatter'd,
dilated , and as it were fplit and fpread into ma-
ny diverging Rays, as Grimaldo fuppofes, does
not yet appear by thefe Experiments, but will
appear by thofe that follow.

Exper. 5. Confidering therefore, that if in
the third Experiment the Image of the Sun
jfhould be drawn out into an oblong Form, ei-
ther by a Dilatation of every Ray, or by any o-
ther cafual inequality of the Refradions, the
fame oblong Image would by a fecond Refra-
dion made fideways be drawn out as much in
breadth by the like Dilatation of the Rays, or o-
ther cafual inequality of the Refradions fide-
ways, I tried what would be the Effeds of fuch
a fecond Refradion. For this end I ordered
all things as in the third Experiment, and then
placed a fecond Prifm immediately after the

firfl

B O O K L 2p

I firfl: in a crofs Pofition to it, that it might again
refrad; the beam of the Sun*s Light which came
to it through the firfl: Prifm. In the firfl Prifm
this beam was refracted upwards, and in the
fecond fideways. And I found that by the Re-
fraction of the fecond Prifm, the breadth of the
Image was not increafed, but its fuperior part,
which in the firfl Prifm fuffered the greater Re-
fradlion, and appeared violet and blue, did again
in the fecond Prifm fuffer a greater Refradlion
than its inferior part, which appeared red and
yellow, and this without any Dilatation of the
Image in breadth.

Illiijiration. Let S [in Fig. 14. ] reprefent
the Sun, F the hole in the Window, ABC tlie
iirfl Prifm, D H the fecond Prifm, Y the round
Image of the Sun made by a diredl beam of
Light when the Prifms are taken away, P T
the oblong Image of the Sun made by that beam
pafling through the firfl Prifm alone, when the
fecond Prifm is taken away, and p t the Image
made by the crofs Refradions of both Prifms
together. Now if the Rays which tend to-
wards the feveral Points of the round Image Y
were dilated and fpread by the Refraction of
the firfl Prifm, fg that they fhould not any lon-
ger go in fmgle Lines to fingle Points, but that
every Ray being fplit, fliattered, and changed
from a Linear Ray to a Superficies of Rays di-
verging from the Point of Refraction, and ly-
ing in the Plane of the Angles of Incidence and
Refraction, they fhould go in thofe Planes to
fo many Lines reaching almofl from one end of
the Image P T to the other, and if that Image

fhould

50 ' OP T I C K S.

fhould thence become oblong: thofe Rays and
their feveral parts tending towards the feveral
Points of the Image P T ought to be again di-
lated and fpread fide ways by the tranfverfe
Refraftion of the fecond Prifm, fo as to com-
pofe a four fquare Image, fuch as is reprefented
at iH. For the better underftanding of which,
let the Image P T be diftinguiflied into five e-
qual parts P QK, KQRL, LRSM, MSVN,
N VT. And by the fame irregularity that the
orbicular Light Y is by the Refraction of the
firft Prifm dilated and drawn out into a long
Image P T, the Light P QK which takes up a
fpace of the fame length and breadth with the
Light Y ought to be by the Refraftion of the
fecond Prifm dilated and drawn out into the
long Image tt q k p, and the Light K QjR. L into
the long Image kqrl, and the Lights LRSM,
MSVN, N V T, into fo many other long I-
mages /r ^?;7, ?nsvny nvtl, and all thefe long
Images would compofe the four fquare Image
•TT?. Thus it ought to be were every Ray dila-
ted by Refraction, and fpread into a triangular
Superficies of Rays diverging from the Point
of Refradlion. For the fecond Refradion
would fpread the Rays one way as much as the
firft doth another, and fo dilate the Image in
breadth as much as the firft doth in length.
And the fame thing ought to happen , were
fome Rays cafually refradled more than others.
But the Event is other wife. The Image P T
was not made broader by the Refraction of the
fecond Prifm., but only became oblique, as 'tis
reprefented at / ^ , its upper end P being by

the

B O O K I. 31

the Refradion tranflatedto a greater diftance than
its lower end T. So then the Light which went
towards the upper end P of the Image, was ( at
equal Incidences ) more refraded in the fecond
Prifm, than the Light which tended towards the
lower end T, that is the blue and violet, than the
red and yellow j and therefore was more refran-
gible. The fame Light was by the Refradion of
the iirft Prifm tranflated farther from the place.
Y to which it tended before Refraction ; and
therefore fuffered as well in the firft Prifm as in
the fecond a greater Refradion than the reft of
the Light, and by confequence was more refran-
gible than the reft, even before its incidence on
the firft Prifm.

Sometimes I placed a third Prifm after the
fecond, and fometimes alfo a fourth after the
third, by all which the Image might be often
refraded fideways: but the Rays which were
more refradted than the reft in the firft Prifm
were alfo more refraded in all the reft, and that
without any Dilatation of the Image fideways :
and therefore thofe Rays for their conftancy of a
greater Refraction are defervedly reputed more
refrangible.

But that the meaning of this Experiment may
more clearly appear, it is to be confidercd that
the Rays which are equally refrangible do fall
upon a Circle anfwering to the Sun's Difque.
For this was proved in the third Experiment.
By a Circle I underftand not here a perfect geo-
metrical Circle, but any orbicular Figure whofe
length is equal to its breadth,' and which, as
to Senfe, may feem circular. Let therefore A G

[in

32 O P T I C K S.

[in Fig. 15.] reprefent the Circle which all the
niofl: refrangible Rays propagated from the
whole Difque of the Sun, would illuminate and
paint upon the oppofite Wall if they were a-
lonej E L the Circle which all the leafl refran-
gible Rays would in like manner illuminate and
paint if they were alone; B H, C J, DK, the
Circles which fo many intermediate forts of
Rays would fucceffively paint upon the Wall,
if they were fmgly propagated from the Sun
in fucceflive order, the reft being always inter-
cepted ; and conceive that there are other in*
termediate Circles without Number , which
innumerable other intermediate forts of Rays
would fucceffively paint upon the Wall if the
Sun fliould fucceffively emit every fort apart.
And feeing the Sun emits all thefe forts at once,
they muft all together illuminate and paint in-
numerable equal Circles, of all which, being
according to their degrees of Refrangibility
placed in order in a continual Series, that ob-
long Spedrum P T is compofed which I defcri-
bed in the third Experiment. Now if the
Sun's 'circular Image Y [in Fig. 14, 15.] which
is made by an unrefradled beam of Light was
by any Dilation of the fnigle Rays, or by any
other irregularity in the Refra<5lion of the iirft
Prifm, converted into the oblong Spedtrum,
P T : then ought every Circle AG, B H, C J,
^c. in that Spedtrum, by the crofs Refradion
of the fecond Prifm again dilating or other wife
fcattering the Rays as before, to be in like man-
ner drawn out and transformed into an oblong
Figure, and thereby the breadth of the Image

" FT

B O O K I. 3 3

PT would be now as much augmented as tlie
length of the Image Y was before by the Refra-
dionof the firftPrifmj and thus by the Refra-
ctions of both Prifms together would be formed
a four fquare Figure p ir t% as I defcribed a-
bove. Wherefore fmce the breadth of the Spe-
drum PT is not increafed by the Refradion
fideways, it is certain that the Rays are nqt fplit
or dilated, or otherways irregularly fcatter'd
by that Refradtion, but that every Circle is by
a regular and uniform Refradion tranflated
entire into another Place, as the Circle AG
by the greateft Refradion into the place a gy
the Circle B H by a lefs Refradioh into the
place b h, the Circle C J by a Refradion ftill
lefs into the place c i, and fo of the reft) by
which means a new Spedrum p t inclined to
the former P T is in like manner compofed of
Circles lying in a right Line ; and thefe Circles
muft be of the fame bignefs with the former,
becaufe the breadths of all the Spedrums Y,
P T and /> / at equal diftances from the Prifms
are equal.

I conlidered farther, tliat by the breadth of
the hole F through which the Light enters in-
to the dark Chamber , there is a Penumbra
made in the Circuit of the Spedrum Y, and
that Penumbra remains in the redilinear Sides
of the Spedrums P T and pt. I 'placed there-
fore at that hole a Lens or Objed-glafs of a Te-
lefcope w^hich might caft the Image of the Sun
diftindly on Y without any Penumbra at all,
and found that the Penumbra of the redilinear
Sides of the oblong Spedrums P T and / 1 was

D alfo

34 O P T I C K S.

alfu thereby taken away, fo that thofe Sides ap-
peared as diilindily defined as did the Circum-
ference of the firft Image Y. Thus it happens
if the Glafs of the Prifms be free from Veins,
and their Sides be accurately plane and well
polifhed without thofe numberlefs Waves or
Curies which ufually arife from Sand-holes a
little fmoothed in polilliing with Putty. If the
Glafs be only well polifhed and free from Veins,
and the Sides not accurately plane, but a little
Convex or Concave, as it frequently happens;
yet may the three Spedtrums Y, P T and p t
want Penumbras , but not in equal diftances
from the Prifms. Now from this want of Pe-
numbras, I knew more certainly that every one
of the Circles v/as refracted according to fome
inoft regular, uniform and conftant Law. For
if there were any irregularity in the Refra(5tion,
rhe right Lines A E and G L, which all the Cir-
cles in the Spe6lrum P T do touch, could not
by that Refraction be tranflated into the Lines
a e and ^ / as diflind: and fcraight as they were
before, but there would arife in thofe tranflated
Lines fome Penumbra or Crookednefs or Un-
dulation, or other fenfible Perturbation contrary
to what is found by Experience. Whatfoever
Penumbra or Perturbation fhould be made in the
Circles by the crofs Refraction of the fecond
Prifm, all that Penumbra or Perturbation would
be confpicuous in the right Lines ae and gl
which touch thofe Circles. And therefore fince
there is no fuch Penumbra or Perturbation in
thofe right Lines, there muft be none in the Cir^
cles. Since the difbance between thofe Tangents

■2 or

B O O K r. 35

or breadth of the Spedrum is not increafed
by the Refra<5tions, the Diameters of the Circles
are not increafed thereby. Since thofe Tangents
continue to be right Lines, every Circle wiiich
in the iirft Prifm is more or lefs refraded, is
exactly in the fame proportion more or lefs re-
fracted in the fecond. And feeing all thefe
things continue to fucceed after the lame man-
ner when the Rays are again in a third Prifm,
and again in a fourth refra6led fideways, it is
evident that the Rays of one and the fame Circle,
as to their degree of Refrangibility, continue al-
ways uniform and homogeneal to one another,
and that thole of feveral Circles do differ in de-
gree of Refrangibility, and that in fome certain
and conflant Proportion. Which is the thing I
was to prove.

There is yet another Clrcumflance or two of
this Experiment by which it becomes Hill more
plain and convincing. Let the fecond Prifm
DH [in Fig, i6.] be placed not immedi-
ately after the firlt , but at fome diftance
from it; fuppofe in the mid-way between it
and the Wall on which the oblong Spe<5truni
PT is caft, fo that the Light from the firft
Prifm may fall upon it in the form of an ob-
long Spedrum -r^ parallel to this fecond Prifm,
and be refraded tideways to form the oblong
Spedrum pt upon the Wall. And you- will
find as before, that this Spedirum /> / is inclined
to that Spedrum P T, which the firft Prifm
forms alone without the fecond; the blue ends
P and p being farther diftant from one another
than the red ones T and /, and by confequence

D 2 ' that

3^ O P T I C K S.

that the Rays which go to the blue end cr of
the Image <t 7, and which therefore fuffer the
greateft Refradion in the firft Prifm, are again
in the fecond Prifm more refradied than the
reft.

The fame thing I try'd alfo by letting the
Sun's Light into a dark Room through two lit-
tle round holes F and (p [in Fig. 17.] made in
the Window , and with two parallel Prifms
ABC and a/Sy placed at thofe holes ( one at
each ) refra6ting thofe two beams of Light to
the oppofite Wall of the Chamber, in fuch man-
ner that the tv/o colour'd Images P T and M N
which they there painted were joined end to end
and lay in one flraight Line, the red end T of
the one touching the blue end M of the other.
For if thefe two refracfted Beams were again.
by a third Prifm DH placed crofs to the two
firft , refraded fideways , and the Spedlrums
thereby tranilated to fome other part of the
Wall of the Chamber, fuppofe the Sped:rum
P T to pt and the Spedrum M N to m ;/, thefe
tranflated Spedrums p t and. m n would not lie
in one ftraight Line with their ends contiguous
as before, but be broken oif from one another
and become parallel, the blue end m of the I-
mage m n bein^ by a greater Refradion tran-
flated farther from its former place M T, than
the red end t of the other Image p t from the
fam.e place M T ; which puts the Propofition
pad Difpute. And this happens whether the
third Prifm D H be placed immediately after
the two firft, or at a great diftance from
them, fo that the Light refraded in the two

firfl

B O O K I. ' 37

iirft Prifms be either white and circular, or co-
loured and oblong when it falls on the third.

^xper. 6. In the middle of two. thin Boards
I made round holes a third part of an Inch in
diameter , and iri the Window-fliut a much
broader hole being made to let into my dark-
ned Chamber a large Beam of the Sun's Light;
I placed a Prifm behind the Shut in that beam
to refradl it towards the oppofite Wali, and
clofe behind the Prifm I fixed one of the Boards,
in fuch manner that the middle of the refradled
Light might pafs through the hole made in it,
and the reft be intercepted by the Board. Then
at the diftance of about twelve Feet from the
firft Board I fixed the other Board in fuch man-
ner, that the middle of the refraded Light which
canie through the hole in the firft Board, and
fell upon the oppofite Wall, might pafs through
the hole in this other Board , and the reft being
intercepted by the Board might paint upon it
the coloured Spectrum of the Sun. And clofe
behind this Board I fixed another Prifm to rc-
fra<ft the Light v/hich came through the hole.
Then I returned fpeedily to the firft Prifm, and
by turning it llowly to and fro about its Axis,
I caufed the Image which fell upon the fecond
Board to move up and down upon that Board,
that all its parts might fucceflively pafs through
the hole in that Board and fall upon the Prifm
behind it. And in. the mean time, I noted the
places on the oppofite Wall to which that Light
after its Refraftion in the fecond Prifm did pafs ;
and by the difference of the places I found that
the Light which being ir.olt refraded in the

JD 3 firft

38 O P T I C K S.

firfl Prifm did go to the blue end of the Image,
was again more refraded in the fecond Prifm
than the Light which went to the red end of
that Image, which proves as well the firfl Pro-
portion as the fecond. And this happened whe-
ther the Axis of the two Prifms were parallel, or
inclined to one another, and to the Horizon in
any given Angles.

TUnJlration. Let F \\xs.Fig. i8.] be the wide
hole in the Window-ihut, through which the
Sun fliines upon the firfl Prifrii ABC, and let
the refracted Light fall upon the middle of the
Board D E, and the middle part of that Light
upon the hole G made in the middle part of that
Board. Let this trajed:ed part of that Light
fall again upon the middle of the fecond Board
d e, and there paint fuch an oblong coloured I-
mage of the Sun as was defcribed in the third
Experiment. By turning the Prifm ABC flow-
iy 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 pafs fucceffively
through the hole g which is made in the mid-
dle of that Board. In the mean while another
Prifm abcisto be fixed next after that hole gy
to refrad: the trajed:ed Light a fecond time.
And thefe things being thus orderea, I marked
the places M and N of the oppofite Wall upon
which the refracted Light fell, and found that
whilft the two Boards and fecond Prifm re-
mained unmoved, thofe places by turning the
firfl: Prifm about its Axis were changed perpe-
tually. For when the lower part of the Light

which

B O O K I. 3p

which fell upon the fecond Board d e \vas call
through the hole g, it went to a lower place M
on the Wall, and when the higher part of that
Light was caft through the fame hole o-, it went
to a higher place N on the Wall, and wheii any
intermediate part of the Light was caft through
that hole, it went to fome place on the Wall be-
tween M and N. The unchanged Pofition of
the holes in the Boards, made the L^cidence
of the Rays upon the fecond Prifm to be the
fame in all cafes. And yet in that common In-
cidence fome of the Rays were more refra(5tcd,
and others lefs. , And thofe were more refraded
in this Prifm, which by a greater Refradion in
the firft Prifm were more turned out of the
way, and therefore for their Conftancy of being
more refradied are defervedly called more refran-
gible.

Exper. J. At two holes made near one ano-
ther in my Window- fliut I placed two Prifms,
one at each, which nii?;ht caft upon the oppo-
fite Wall (after the manner of the third Expe-
riment) two oblong coloured Luages of the
Sun. And at a little diftance from the Wall I
placed a long (lender Paper with ftraight and pa-
rallel edges, and ordered the Prifms and Pa-
per fo, that the red Colour of cneiCmage might
fall diredly upon one half of the Paper, and
the violet Colour of the other Image upon the
other half of the fame Paper ; fo that the Pa-
per appeared of two Colours, red and violet,
much after the manner of the painted Paper
in the firft and fecond Experiments. Then
with a black Cloth I covered the Wall behind

D 4 thQ

40 O P T I C K S.

the Paper, that no Light might be refledied from
it to difliirb the Experiment, and viewing the
Paper through a third Prifm held parallel to it,
I faw that half of it which was illuminated by
the violet Light to be divided from the other
half by a greater Refra(5lion, efpecially 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 feemed contiguous at one of
their Angles like the painted Paper in the firft
Experiment. Which alfo happened when the
Paper was too broad.

Sometimes inftead of the Paper I ufed a white
Thred, and this appeared through the Prifm
divided into two parallel Threds as is repre-
fented in the nineteenth Figure , where D G
denotes the Thred illuminated with violet Light
from D to E and with red Light from F to G,
and d e fg are the parts of the Thred feen by
Refradion. If one half of the Thred be con-
ftanrly illuminated v/ith red, and the other half
be ilkuninated with all the Colours fucceffively,
( which may be done by caufing one of the
Prifms to be turned about its Axis whilft the
other remains unmoved) this other half in view-
ing the Thred through the Prifm, will appear
in a continual right Line with the firfl half when
illuminated with red, and begin to be a little
divided from it when illuminated with Orange,
jind remove farther from it when illuminated
yvith yellow, and ftill farther when with green,
^nd farther when with blue, and go yet farther
pff when illuriiinated with Iiidigo, and fartheft

when

B O O K L 41

when with deep violet. Which plainly fhews,
that the Lights of feveral Colours are more and
more refrangible one than another, in this Order
of their Colours, red, orange, yellow, green,
blue, indigo, deep violet j and fo proves as well
the firft Proportion as the fecond.

I caufed alfo the coloured Spedrums P T
[ in Fig. ij. ] and M N made in a dark Cham-
ber by the Refradions of -two Prifms to lie in
a Right Line end to end, as was defcribed above
in the fifth Experiment, and viewing them
through a third Prifm held parallel to their
Length, they appeared no longer in a Right
Line, but became broken from one another, as
they are reprefented at ^ ^ and ;;/ ;/, the violet
end m of the Specftrum m n being by a greater
Refradion tranllated farther from its former
Place M T than the red end t of the other
Spedrum pt.

I farther caufed thofe two Spedtrums P T
[ in Fig. 20. ] and M N to become co-incident
in an inverted Order of their Colours, the red
end of each falling on the violet end of the o-
ther, as they are reprefented in the oblong Fi-
gure PTMN J and then viewing them through
a Prifm D H held parallel to their Length, they
appeared not co-incident, as when view'd with
the naked Eye, but in the form of two diftindt
Spedrums p t and m n croffing one another in
the middle after the manner of the Letter X.
"Which fliews that the red of the one Spedrum
and violet of the other, which were co-incident
at PN and MT, being parted from one another
by a greater Refradipn of the violet to p and m

thau

42 O P T I C K S.

than of the red to n and /, do differ in degrees of
Refrangibility.

I illuminated alfo a little Circular fiece of
white Paper all over with the Lights of both
Prifms intermixed, and when it was illumina-
ted with the red of one Speftrum, and deep
violet of the other, fo as by the Mixture of
thofe Colours to appear all over purple, I view-
ed the Paper, firft at a lefs diflance, and then
at a greater, through a third Prifmj and as I
went from the Paper, the refracted Image there-
of became more and more divided by the une-
qual Refraction of the two mixed Colours, and
at length parted into two diftind: Images, a red
one and a violet one, whereof the violet v/as
fartheft from the Paper, and therefore fuffered
the greateft Refraction. And when that Prifm
at the Window, which caft the violet on the Pa-
per was taken away, the violet Image difiip-
peared ; but when the other Prifm was taken
away the red vaniflied ; which fhews, that thefe
two Images were nothing elfe than the Lights
of the two Prifms, which had been intermixed
on the purple Paper, but were parted again by
their unequal Refradions made in the third
Prifm, through which the Paper was view'd.
This alfo was obfervable, that if one of the
Prifms at the Window, fuppgfe that which caft
the violet on the Paper, v/as turned about its
Axis to make all the Colours in this order,- vio-
let, indigo, blue, green, yellow, orange, red,
fall fucceffively on the Paper from that Prifm,
the violet Image changed Colour accordingly,
turning fucceffively to indigo, blue, green, yel-
low

B O O K ^. 45

low and red, and in changing Colbur came nearer
and nearer to the red Image made by the other
Prifm, until when it was alfo red both Images be-
came fully co-incident.

I placed alfo tv/o Paper Circles very near one
another, the one in the red Light of one Prifm,
and the other in the violet Light of the other.
The Circles were each of tliem an Inch in diame-
ter, and behind them the Wall was dark, that- the
Experiment might not be diflurbed by any Light
coming from thence. Thefe Circles thus illu*
minated, I viewed through a Prifm fo held, that
the Refradlion might be made towards the red
Circle, and as 1 went from them they came nearer
and nearer together, and at length became co-
incident } and afterwards when I went flill far-
ther off, they parted again in a contrary Order,
the violet by a greater Refradtion being carried
beyond the red.

Exper. 8. In Summer, when the Sun's Light
ufes to be ftrongefl, I placed a Prifm at the
Hole of the Window-fliut, as in the third Expe-
riment, yet fo that its Axis might be parallel to
the Axis of the. World, and at the oppofite
Wall in the Sun's refrad:ed Light, I placed an
open Book. Then going fix Feet and two Inches
from the Book, 1 placed there the above-
mentioned Lens, by which the Light reflected
from the Book might be made to converge and
meet again at the diftance of fix Feet and two
Inches behind the Lens, and there paint the
Species of the Book upon a Sheet of white Pa-
per much after the manner of the fecond Ex-
periment. The Book and Lens being made fall,

I no-

44 O P T I C K S.

I noted the Place where the Paper was, when
the Letters of the Book, illuminated by the
fuUeft red Light of the Solar Image falling upon
it, did cafl their Species on that Paper moft
diftinftly : And then I ftay'd till by the Motion
of the Sun, and confequent Motion of his Image
on the Book, all the Colours from that red to
the middle of the blue pafs'd over thofe Let-
ters J and when thofe Letters were illuminated
by that blue, I noted again the Place of the Pa-
per when they caft their Species moft diftincftly
upon it : And I found that this laft 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 fooner therefore
did the Light in the violet end of the Image
by a greater Refradion 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 thefe Colours be diluted and weak-
ned by the Mixture of any adventitious Light,
the diftance between the Places of the Paper
will not be fo great. This diftance in the fe-
cond Experiment, where the Colours of natural
Bodies were made ufe of, was but an Inch and
an half, by reafon of the Imperfection of thofe
Colours. Flere in the Colours of the Prifm,
which are manifeftly more full, intenfe, and
lively than thofe of natural Bodies, the diftance
is two Inches and three quarters. And were the
Colours ftill more full, I queftion not but that
the diftance would be confiderably greater. For
the coloured Light of the Prifm, by the inter-
fering of the Circles defcribed in the fecond

Figure

B O O K L 45

Figure of the fifth Experiment, and alfo by the
Light of the very bright Cloiick next the Sun's
Body intermixing with thefe Colours, and by
the Light fcattered by the Inequalities in the
Polifh of the Prifin, was fo very much com-
pounded, that the Species which thofe faint and
dark Colours, the indigo and violet, caft upon
the Paper were not diilind enough to be well ob-
ferved.

Exper. g. A Prifm, whofe two Angles at its
Bafe 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 Cham-
ber through a Hole in the Window-fhut, as in
the third Experiment. And turning the Prifin
flowly. about its Axis, until all the Light which
went through one of its Angles, and was refradl-
ed by it began to be refled:ed by its Bafe, at
which till then it went out of the Glafs, I cb-
ferved that thofe Rays which had fuifered the
greateft Pvcfradiion were fooner reflected than
the refi:. I. conceived therefore, that thofe Ravs
of the refledled Light, which were mofi: re-
frangible, did firfl of all by a total Reflexion
become more copious in that Light than the
refi:, and that afterwards the refi: alfo, by a total
Reflexion, became as copious as thefe. To try
this, I made the refledted Light pafs through
another Prifm, and being refracted by it to fall
afterwards upon a Sheet of white Paper placed
at fome difiance behind it, and there by that
Refradion to paint the ufual Colours of the
Prifm. And then caufing the firfi: Prifm to be
turned about its Axis as above, I obferved that

when

4<5 O P T I C K S.

when thofe Rays, which in this Prifm had fuf-
fered the greateft Refraction, and appeared of a
bkie and violet Colour began to be totally re-
flected, the blue and violet Light on the Paper,
which was moft refracted in the fecond Prifm,
received a fenlible Increafe above that of the
red and yellow, which was leafl refracted ; and
afterwards, when the reft of the Light which
was green, yellow, and red, began to be totally
reflected in the firft Prifm, the Light of thofe
Colours on the Paper received as great an In-
creafe as the violet and blue had done before.
Whence 'tis manifeft, that the Beam of Light
reflected by the Bafe of the Prifm, being aug-
mented firft by the more refrangible Rays, and
afterwards by the lefs refrangible ones, is com-
pounded of Rays diiferently refrangible. And
that all fuch reflected Light is of the fame Na-
ture with the Sun's Light before its Incidence
on the Bafe of the Prifm, no Man ever doubt-
ed y it being generally allowed, that Light by
fuch Reflexions fuffers no Alteration in its Modi-
fications and Properties. I do not here take No-
tice of any RefraCtions made in the fides of the
firft Prifm, becaufe the Light enters it perpendi-
cularly at the firft fide, and goes out perpendicu-
larly at the fecond fide, and therefore fuffers
none. So then, the Sun's incident Light being of
tlie fame Temper and Conftitution with his emer-
gent Light, and the laft being compounded of
Rays differently refrangible, the firft muft be in
like manner compounded.

lUuJtratmi. In the twenty-firft Figure, ABC
is the firft Prifm, B C its Bafe, B and C its

equal

B O O K I. 47

equal Angles at the Bafc, each of 4^ Degrees,
A its reftangular Vertex, F M a beam of the
€un's Light let into a dark Room through a
hole F one third part of an Inch broad, M its
Incidence on the Bafe of the Prifm, M G a lefs
refrafted Ray, M H a more refradted Ray, M N
the beam of Light refleded from the Bafe,
V X Y the fecond Prifm by which this beam in
paffing through it is refradled, N t the lefs re-
fraded Light of this beam, and N/> the more
refraded part thereof. When the firft Prifm
A B C is turned about its Axis according to the
order of the Letters ABC, the Rays MH e-
merge^more and more obliquely out of that
Prifm, and at length after their moft oblique
Emergence are refleded towards N, and going
on to p do increafe the Number of the Rays
N^. Afterwards by continuing the Motion of
the iirft Prifm, the Rays M G are alfo refleded
to N and increafe the number of the Rays N f.
And therefore the Light MN admits into its
Compofition, firft the more refrangible Rays,
and then the lefs refrangible Rays, and yet af-
ter this Compofition is of the fame Nature with
the Sun's immediate Light F M, the Reflexion
of the fpecular Bafe B C caufing no Alteration
therein.

Rxper. 10. Two Prifms, which were alike
in Shape, I tied fo together, that their Axis and
oppofite Sides being parallel, they compofed a
Parallelopiped. x^nd, the Sun finning into my
dark Chamber through a little hole in the Win-
dow-fliut , I placed that Parallelopiped in his
beam at fome diftancc from the hole, in fuch a

Pofi:urc\

O P T I C K S.

Pofture, that the Axes of the Prifms might be
perpendicular to the incident Rays , and that
thole • Rays being incident upon the firft Side
of one Prifm, might go on through the two
contiguous Sides of both Prifms, and emerge
out of the laft Side of the fecond Prifm. This
Side being parallel to the firft Side of the firfl
Prifm, caufed the emerging Light to be paral-
lel to the incident. Then, beyond thefe two
Prifms I placed a third, which might refrad;
that emergent Light , and by that Refradiion
caft the ufual Colours of the Prifm upon the
oppofite Wall, or upon a fheet of white Paper
held at a convenient Diftance behind the Prifm
for that refracCled Light to fall upon it. After
this I turned the Parallelopiped about its Axis,
and found that when the contiguous Sides of
the two Prifms became fo oblique to the inci-
dent Rays, that thofe Rays began all of them to
be refled:ed, thofe Rays which in the third
Prifm had fuffered the greateft Refraction, and
painted the Paper with violet and blue, were
firft of all by a total Reflexion taken out of the
tranfmitted Light , the reft remaining and on
the Paper painting their Colours of green, yel-
low, orange and red, as before ; and afterwards
by continuing the Motion of the two Prifms,
the reft of the Rays alfo by a total Reflexion
vanift^ed in order, according to their degrees
of Refrangibility. The Light therefore which
emerged out of the two Prifms is compound-
ed of Rays differently refrangible, feeing the
more refrangible Rays may be taken out of it,
while the lefs refrangible remain. But this

Light

B O O K I. 4p

Light being trajeded only through the parallel
Superficies of the two Prifms, if it fuffer'd any
change by the Refradlion of one Superficies it
lofl that Impreihon by the contrary Refraction
of the other Superficies, and fo being refbor'd to
its priftine Conftitution, became of the fame Na-
ture and Condition as at firfl before its Incidence
on thofe Prifms ; and therefore, before its Inci-
dence, was as much compounded of Rays diffe-
rently refrangible, as afterwaVds.

llliiftration. In the twenty fecond Figure
ABC and BCD are the two Prifms tied together
in the form of a Parallelopiped , their Sides
B C and C B being contiguous, and their Sides
A B and C D parallel. And H J K is the third
Prifm, by which the Sun's Light propagated
through the hole F into the dark Chamber, and
there pafiing through thofe fides of the Prifms
AB, BC, CBandCD, is refraded at O to
the white Paper P T, falling there partly upon
P by a greater Refra6ticn, partly upon T by a
lefs Refraction, and partly upon R and other in-
termediate places by intermediate Ref rations.
By turning the Parallelopiped A C B D about its
Axis, according to the order of tlie Letters A,
C, D, B, at length when the contiguous Planes
B C and C B become futhciently oblique to the
Rays F M, which are incident upon them at M,
there will vanifh totally out of the refraded
Light OPT, firfl of ail the mofl refraded Rays
OP, (the reft OR and O T remaining as be-
fore ) then the Rays O R and other intermedi-
ate ones, and laftly, the leaft refracted Rays OT-
For when the Plane BC becomes fufficiently

E oblique

50 O P T I C K S.

oblique to the Rays incident upon it , tliofe
Rays will begin to be totally refleded by it to-
wards N J and firft the moft refrangible Rays
will be totally refledted ( as was explained in
the preceding Experiment ) and by Confequence
muft firft difappear at P , and afterwards the
reft as they are in order totally refledted to N,
they niuft difappear in the fame order at R
and T. So then the Rays which at O fuf-
fer the greatefl Refraftion, may be taken out
of the Light M O whilft the reft of the Rays
remain in it , and therefore that Light M O
is compounded of Rays differently refrangi-
ble. And becaufe the Planes A B and C D
are parallel, and therefore by equal and con-
trary Refradlions deftroy one anothers Ef-
fects, the incident Light F M muft be of the
fame Kind and Nature with the emergent Light
M O, and therefore doth alfo confifl of Rays
differently refrangible. Thefe two Lights F M
and M O, before the moft refrangible Rays are
feparated out of the emergent Light M O, a-
gree in Colour, and in all other Properties lo
far as my Obfervation reaches , and therefore
are defervedly reputed of the fame Nature and
Conftitution, and by Confequence the one is
compounded as well as the other. But after
the moft refrangible Rays begin to be totally
refledted, and thereby feparated out of the e-
mergent Light M O, that Light changes its Co-
lour from white to a dilute and faint yellow,
a pretty good orange, a very full red fuccef-
fively, and then totally vanifties. For after the
moft refrangible Rays which paint the Paper at
2 P with

B O O K I. 51

P with a purple Colour^ are by a total P.efje^
xion taken out of the beam of Light M O, the
reft of the Colours which appear on the Paper
at R and T being mix'd in the Liglit M O
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 reft
which appear between R and T ( that is the yel-
low, orange, red and a little green) being mix-
ed in the beam MO compouiid there an orange;
and when all the Rays are by Reflexion taken
out of the beam M O, except: the leaft refran-
gible, which at T appear of a full red, their
Colour is the fame in that beam M O as after-
wards at T, the Refrafticn of the Prifm H J K
ferving only to feparate the differently refrangible
Rays, without making any Alteration in their
Colours, as ftiall be more fully proved hereafter.
All which confirms as well the firft Propofition
as the fecond.

Scholium. If this Experiment and the former
be conjoined and made one by applying a fourth
Prifm VX Y [in Fig. 22.] to refra(5t the refied:ed
beam M N towards //>, the Conclufion will be
clearer. For then the Light N/> v/hich in the
fourth Prifm is more refracted,- will become ful-
ler and ftronger when the Light O P, which in
the third Prifm H J K is more refracted, va-
nifties at P; and afterwards when the lefs re-
fracted Light O T vanifhes at T, the lefs re-
fraded Light N t will become increafed whilft
the more refracted Light at p receives no far-
ther increafe. And as the traje6ted beam M O
in vanifbing is always of fuch a Colour as ought

52 o p T I c K s:

to refult from the mixture of the Colours which
fall upon the Paper P T , fo is the refleded
beam M N always of fuch a Colour as ought to
refult from the mixture of the Colours which
fall upon the Paper p t. For when the mofl
refrangible Rays are by a total Reflexion taken
out of- the beam M O, and leave that beam of
an orange Colour, the Excefs of thofe Rays in
the refled:ed Light, does not only make the vio-
let, indigo and blue at p more full, but alfo
makes the beam M N change from the yellowidi
Colour of the Sun's Light, to a pale white in-
clining to blue, and afterward recover its yel-
lowifli Colour again, fo foon as all the reft of the
tranfmitted Light M O T is reflected.

Now feeing that in all this variety of Expe-
riments , whether the Trial be made in Light
refledled, and that either from natural Bodies,
as in the firft and fecond Experiment, or fpe-
cular, as in the ninth; or in Light refrad:ed,
and that either before the unequally refracted
Rays are by diverging fepa rated from one an-
other, and loling their whitenefs which they
have altogether, appear feverally of feveral Co-
lours, as in the fifth Experiment; or after they
are feparated from one another, and appear co-
lour'd as in the fixth, feventh, and eighth Ex-
periments; or in Light trajedted through paral-
lel Superficies, deftroying each others Eifedis,
as in the tenth Experiment ; there are always
found Rays, which at equal Incidences on the
fame Medium fufFer unequal Refractions, and
that without any fplitting or dilating of fmgle
Rays, or contingence in the inequality of the
3. Refra-

B O O K I. 53

Refradtions, as is proved in the fifth and fixth
Experiments. And feeing the Rays which dif-
fer in Refranglbility may be parted and forted
from one another, and that either by Refradion
as in the third Experiment, or by Reflexion as in
the tenth, and then the fcveral forts apart at
equal Incidences fuffer unequal Refradions, and
thofe' forts are more refracted than others after
Separation, which were more refraded before
it, as in the fixth and following Experiments,
and if the Sun's Light be trajeded through three
or more crofs Prifms fucceffively, thofe Rays
•which in the firft Prilm are refraded more than
others, are in all the following Prifms refraded
more than others in the fame Rate and Propor-
tion, as appears by the fifth Experiment j it's
manifeft that the Sun's Light is an heterogeneous
Mixture of Rays, fome of which are conftantly
more refrangible than others, as was propofed.

PROP, m. Theor. III.
'The Suns Light conftjls of PMys differing
in Reflexibility^ and thofe Puiys are more
reflexible than others 'which are more
refra?igible.

np H I 8 is manifeft by the ninth and tenth
*■- Experiments : For in the ninth Experi-
ment, by turning the Prifm about its Axis, un-
til the Rays within it which in going out into
the Air were refraded by its Bafe, became fo
oblique to that Bafe, as to begin to be totally

E 3 refiede4

54 O P T I C K S.

refleded thereby; thofe Rays became iirft of all
totally refledied, which before at equal Inciden-
ces with the reft had fuffered the greateft Refra-.
(Stion. And the fame thing "happens in the Refle-
xion made by the commDn Bafe of the two
Prifms in the tenth Experiment.

PROP. IV. Prob. L

7v fepa7^ate from one another the heteroge-
neous Rays of compound Light,

^"T^ H E heterogeneous Rays are in fome mea-
-*- fure feparated from one another by the
Refradion of the Prifm in the third Experi^
ment, and in the fifth Experiment, by taking a-r
way the Penumbra from the redilinear fides of
the coloured Image, that Separation in thofe ve-
ry rcdilinear lides or ftraight edges of the I-
mage becomes perfed. But in all places be-
tween thofe rectilinear edges, thofe innumera-
ble Circles there defcribed, which are feveral-
ly illuminated by homogeneal Rays, by interfe-
ring with one another, and being every where
commix'd , do render the Light fufficiently
compound. But if thefe Circles, whilft their
Centers keep their Diftances and Pofitions, could
be made lefs in Diameter, their interfering one
with another, and by Confequence the Mixture
of the heterogeneous Rays would be propor-
tionally diminiih'd. In the twenty third Figure
let AG, BH, CJ, DK, EL, FM be the Cir-
cles which fo many forts of Rays flowing frppi

the

B O O K I. 55

the fame dlfque of the Sun, do in the third Ex-
periment illuminate j of all • which and innu-
merable other intermediate ones lying in a con-
tinual Series between the two rectilinear and pa-
rallel edges of the Sun's oblong Image P T ,
that Image is compos'd, as was explained in
the fifth Experiment. And let ^^, bh^ ci^ d ky
e /, fm be fo many lefs Circles lying in a like
continual Series between two parallel right Lines
^y and g m with the fame diftances between their
Centers, and illuminated by the fame forts of
Rays, that is the Circle a g with the fmie fort
by which the correfponding Circle A G was il-
luminated, and the Circle b h with the furie fort
by which the correfponding Circle B H was illu-
minated, and the reft of the Circles ci, d k, el,
fm refped;ively, with the fame forts of Rays by
which the feveral correfponding Circles C J,
D K, EL, F M were illuminated. In the Fi-
gure P T compofed of the greater Circles, three
of thofe Circles A G, B H, C J, are fo ex-
panded into one another, that the three forts of
Rays by which thofe Circles are illuminated ,
together with other innumerable forts of inter-
mediate Rays, are mixed at Q^^ in the middle of
the Circle B H. And the like Mixture happens
throughout almofl the whole length of the Fi-
gure P T. But in the Figure p t compofed of
the lefs Circles, the three lefs Circles a g^ b hy c /,
which anfwer to thofe three greater, do not ex-
tend into one another j nor are there any v/liere
mingled fo much as any two of the three forts of
Rays by which thofe Circles are illuminated, and

E 4 whicls

5^

O P T I C K S.

which in the Figure P T are all of them inter-
mingled at B H.

Now he that fhall thus conlider It, will eafily
underfland that the Mixture is diminifhed in
the fame Proportion with the Diameters of the
Circles. If the Diameters of the Circles whilil .
their Centers remain the fame, be made three
times lefs than before, the Mixture will be alfo
three times lefs; if ten times lefs, the Mixture
will be ten times lefs, and fo of other Propor-
tions. That is, the Mixture of the Rays in the
greater Figure P T will be to their Mixture in
the lefs/>/, as the Latitude of the greater Fi-
gure is to the Latitude of the lefs. For the La-
titudes of thefe Figures are equal to the Dia-
meters of their Circles. And iience it eafily fol-
lows, that the Mixture of the Rays in the re-
'fra(fted Spedlrum pt is to the Mixture of the
Rays in the dired: and immediate Light of the
Sun, as the breadth of that Spedrum is to the
difference between the length and breadth of the
fame Specflrum.

So then, if we would diminifh the Mixture
of the Rays, we are to diminifli the Diameters
of the Circles. Now thefe would be diminifh-
ed if the Sun's Diameter to which they anfwer
could be made lefs than it is, or ( which comes
to the fame Purpofe) if without Doors, at a
great diflance from the Prifm towards the Sun,
fom.e opake Body were placed, with a round
iioje in the middle of it , to intercept ail the
Sun's Light , excepting fo much as coming
from the middle of his Body could pafs through

that

BOOK! 57

that Hole to the Prifm. For fo the Circles A G,
B H, and the reft, would not any longer anfwer
to the whole Difque of the Sun, but only to that
Part of it which could be feen from the Prifm
through that Hole, that it is to the apparent Mag-
nitude of that Hole view'd from the Prifm. But
that thefe Circles may anfwer more diftindtly to
that Hole, a Lens is to be placed by the Prifm to
cafl the Image of the Hole, (that is, every one
of the Circles AG, BH, &c.) . diflindly upon
the Paper at PT, after fuch a manner, as by a
Lens placed at a Windovy% the Species of Ob-
jects abroad are caft diftindtly upon a Paper
within the Room, and the red:ilinear Sides of
the oblong Solar Image in the fifth Experiment
became diilind: without any Penum.bra. If this
be done, it will not be neceflary to place that
Hole very far off, no not beyond the Win-
dow. And therefore inftead of that Hole, I
ufed the Hole in the Window-lluit, as fol-
lows.

Expcr. II. In the Sun's Light let into my
darken'd Chamber through a fmall round Hole
in my Window-fluit, at about ten or twelve
Feet from the Window, I placed a I^ens, by
which the Image of the Hole might be diilindly
call upon a Sheet of white Paper, placed at
the diftance of fix, eight, ten, or twelve Feet
from the Lens. For, according to the diffe*
rence of the Lenfes I ufed various diftances,
which I think not worth the while to defcribe.
Then immediately after the Lens I placed a
Prifm, by which the trajeded Light might be
refracted either upwards or fide-ways, and there-

' by

y8 O P T I C K S.

by the round Image, which the Lens alone did
caft upon the Paper might be drawn out into a
long one with Parallel Sides, as in the third Ex-
periment. This oblong Image I let fall upon
another Paper at about the fame diftance from
the Prifm as before, moving the Paper either
towards the Prifm or from it, until I found the
juil diftance where the Redilinear Sides of the
Image became moft diflind:. For in this Cafe,
theCircular Images of the Hole, which compofe
that Image after the fame manner, that the Cir-
cles ag^ bh^ ci^ &c. do the Figure ^/ [in Fig.21^
were terminated moft diftindly without any
Penumbra, and therefore' extended into one ano-
ther the leaft that they could, and by confequence
the Mixture of the heterogeneous Rays was now
the leaft of all. By this means I ufed to form
an oblong Image (fuch as is p t) [in Fig. 23,
and 24.] of Circular Images of the Hole, (fuch
as are agy bh, ciy &;c.) and by ufmg a greater
or^lefs Hole in the Window-fhut, I made the
Circular Images a g, b hy ciy Sec. of which it
was formed, to become greater or lefs at pleafure,
and thereby the Mixture of the Rays in the
Image p t to be as much, or as little as I de-
fired.

IlluJlratio7i. In the tu'enty-fourth Figure, F
reprefents the Circular Hole in the Window-
fhut, MN the Lens, whereby the Image or Spe-
cies of that Hole is caft diftindly upon a Paper
at J, ABC the Prifm, whereby the Rays are at
their emerging out of the Lens refrafted from.
J towards another Paper at p /, and the round
Image at J is turned into an oblong Image pt

falling

B O O K I. s-p

falling on that other Paper. This Image // con-
lifts of Circles placed one after another in a Recti-
linear Order, as was fufficiently cxplaii^^ed in the
fifth Experiment j and thefe Circles are equal to
the Circle J, and confequently anfwer in magni-
tude to the Hole F^ and therefore by diminifhing
that Hole they may be at pleafure diminiihed,
whilft their Centers remain in their Places. By
this means I made the Breadth of the Image p t
to be forty times, and fometimes fixty or feventy
times lefs than its Length. As for inflance, if
tlie Breadth of the Hole F be one tenth of an
Inch, and MF the diflance of the Lens from the
Hole be 12 Feet; and \i pV> or pM the diftance
of the Image pi from the Prifm or Lens be 10
Feet, and the refracting Angle of the Prifm be
62 Degrees, the Breadth of the Image pt will
be one twelfth of an Inch, and the Length about
iix Inches, and therefore the Length to the
Breadth as 72 to i, and by confequence the
Light of this Image 71 times lefs compound
than the Sun's dired: Light. And Light thus far
iimple and homogeneal, is fufficient for trying
all the Experiments in this Book about fimple
Light. For the Compofition of heterogeneal
Rays is in this Light fo little, that it is fcarce to
be difcovered and perceiv'd by Senfe, except per-
haps in the indigo and violet. For thefe being
dark Colours, do eafily fuffer a fenfible Allay
by that little fcattcring Light which ufes to be
refraded irregularly by the Inequalities of the
Prifm.

Yet inftead of the Circular Llole F, 'tis better
to fubftitute an oblong Hole iliaped like a long

Paral-

6o O P T I C K S.

Parallelogram with its Length parallel to the
Prifm ABC. For if this Hole be an Inch or
two long, • and but a tenth or twentieth Part of an
Inch broad, or narrower j the Light of the Image
ft will be as fimple as before, or fimpler, and
the Image will become much broader, and there-
fore more fit to have Experiinents try'd in its
Lisht than before.

Inftead of this Parallelogram Hole may be fub-
ftituted a triangular one of equal Sides, whofe
Bafe, for inftance, is about the tenth Part of an
Inch, and its Height an Inch or more. For by
this means, if the Axis of the Prifm be parallel to
the Perpendicular of the Triangle, the Image />^
[in Fig. 25.] will now be form'd of equicrural
Triangles ^o-j bh^ ci, dk^ el,f?ji, &c. and in-
numerable other intermediate ones anfwering to
the triangular Hole in Shape and Bignefs, and lying
one after another in a continual Series between
two Parallel Lines ^y^and gm. Thefe Triangles,
are a little intermingled at their Bafes, but not at
their Vertices ; and therefore the Light on the
brighter Side af of the Image, where the Bafes
of the Triangles are, is a little compounded, but
on the darker Side gm \% altogether uncom-
pounded, and in all Places between the Sides the
Compofition is proportional to the diftances of
the Places from that obfcurer Side gm. And ha-?
ving a Spedrum pt oi fuch a Compofition, we
m.ay try Experiments either in its fcronger and lefs
fimple Light near the Side af^ or in its weaker and
fimpler Light near the other Side gm, as. it fhall
feem mofl convenient.

But

B O O K L 6 1

But ill making Experiments of this kind, the
Chamber ought to be made as dark as can be,
left any Foreign Light mingle it felf with the
Light of the Spedrum p t^ and render it com-
pound J efpecially if we would try Experiments
in the more fmiple Light next the Side g m of
the Spectrum J which being fainter, will have
a lefs proportion to the Foreign Light ; and fo
• by the mixture of that Light be more troubled,
and made more compound. The Lens alfo
ought to be good, fuch as may ferve for opti-
cal Ufes, and the Prifm ought to have a large
Angle, fuppofe of 65 or 70 Degrees, and to be
well wrought, being made of Glafs free from
Bubbles and Veins, with its Sides not a little
convex or concave, as ufually happens, but truly
plane, and its Polifli elaborate, as in working
Optick-glalTes, and not fuch as is ufually wrought
with Putty, whereby the edges of the Sand-
holes being worn away, there are left all over
the Glafs a numberlefs Company of very little
convex polite Rifings like Waves. The edges
alfo of the Prifm and Lens, fo far as they may
make any irregular Refraftion, muft be covered
with 2l black Paper glewed on. ilad all the
Light of the Sun's-Beam let into the Chamber,
which is ufelefs and unprofitable to the Experi-
ment, ought to be intercepted v/ith black Pa-
per, or other bkck Obftacles. For otherwife
the ufelefs Light being refled:ed every way in
the Chamber, will mix with the oblong Spe-
ctrum, and help to difturb it. In trying thefe
Things, fo much diligence is not altogether ne-
celiary, but it will promote tlie Succefs of the

Expe-

6i O P T I C K S.

Experiments, and by a veiy fcrupulous Examiner
of Things deferves to be apply'd. It's difficult
to get Glafs Prifms lit for riiis Purpofe, and there-
fore I ufed fometimes prifmatick VelTels made
with pieces of broken Looking-glaffes, and filled
with Rain Water. And to increafe the Refradion,
I fometimes impregnated the Water ftrongly with
Saccharum Saturni,

PROP. V. Theor. IV.

Homogeneal Light is refraSied regularly
^without any D Hat atio7if putting or Jhatter^
ing of the Rays ^ a7id the co?if ufed Vijion of
ObjeBs feen through refraEiing Bodies by
heteroge7ieal Light arifes from the diffe-^
rent Refrangibility of fever al forts of Rays,

TH E firft Part of this Propofition has been
already fufficiently proved in the fifth Ex-
periment, and will farther appear by the Experi-
ments which follow.

Exper. 12. In the middle of a black Paper I
made a round Hole about a fifth or fixth Part of
an Inch in diameter. Upon this Paper I caufed
the Spedrum of homogeneal Light defcribed
in the former Propofition, fo to fall, that fome
part of the Light m.ight pafs through the Hole
of the Paper. This tranfmitted part of the
Light I refrafted with a Prifm placed behind
^he Paper, and letting this refracted Light fall
perpendicularly upon a white Paper two or
three Feet diftant from the Prifm, 1 found that

the

B O O K I. 63

the Spe6trum formed on the Paper by this Light
was not oblong, as when 'tis made ( in the third
Experiment) by refra-fling the Sun's compound
Light, but was (fo far as I could judge by my
Eye ) perfedily circular, the Length being no
greater than the Breadtl 1. Which fhev/s, 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 Lich in diameter,
and in the Sun's unrefra6ted heterogeneal white
Light I placed another Paper Circle of the fame
Bignefs. And going from the Papers to the di-
ftance of fomeFeet, I viewed both Circles through
a Prifm. The Circle illuminated by the Sun's he-
terogeneal Light appeared very oblong, as in the
fourth Experiment, the Length being many times
greater than the Breadth j but the other Circle,
illuminated with homogeneal Light, appeared cir-
(iular and diftindtly defined, as when 'tis view'd
with the naked Eye. Which proves the whole Pro-
pofition.

Exper. 14. In the homogeneal Light I placed
Flies, and fuch-like minute Objedls, and view-
ing them through a Prifm, I faw their Parts as
diftindlly defined, as if I had viewed them with
the naked Eye. The fame Objed:s placed in
the Sun's unrefradted hetero2;eneal Lig-ht, which
was white, I viewed alio through a Prifm, and
faw them rnoxl confufcdly defined, fo that I
could not diftinguiili their fmaller Parts from
one another. I placed alfo the Letters of a
fmall print, one while in the homogeneal Light,
and then in the heterogeneal, and viewing them

through

^4 O P T I C K S.

through a Prifm, they appeared in the latter Cafe
fo confufed and indiftin^t, that I could not read
them J but in the former they appeared fo diftindt,
that I could read readily, and thought I faw them
as diflind:, as when I view'd them with my naked
Eye. In both Cafes I view'd the fame Objeds,
through the fame Prifm at the fame diftance from
me, and in the fame Situation. There was no
difference, but in the Light by which the Objedts
were illuminated, and which in one Cafe was
iimple, and in the other compound ; and there-
fore, the diftindl Vifion in the former Cafe, and
confufed in the latter, could arife from nothing
elfe than from that difference of the Lights.
Which proves the whole Propofition.

And in thefe three Experiments it is farther
very remarkable, that the Colour of homogeneal
Light w^as never changed by the Refrad:ion.

PROP. VL Theor. V.

T'he Sine of Incidence of every Ray confi-
dered apart ^ is to its Sine of RefraEiion
i7i a given Ratio,

THAT every Ray confider'd apart. Is con-
ftant to it felf in fome degree of Refran-
gibility, is fufficiently manifeft out of what has
been faid. Thofe Rays, which in the firfh Re-
fra(5tion, are at equal Incidences moll refraded,
are alfo in the following Refradions at equal

Inci-

BOOK!. S^

Incidences moft refracted ; and fo of the leaft
refrangible, and the reft which have any mean
Degree of Refrangibility, as is manifeft by the
fifth, fixth, feventh, eighth, and ninth Expe-
riments. And thofe which the firft Tiilie at
like Incidences are equally refraded, are again
at like Incidences equally and uniformly retract-
ed, and that whether they be refraded before
they be feparated from one another, as in the
fifth Expernnent, or whether they be refradted
apart, as in the twelfth, thirteenth and four-
teenth Experiments. The Refraction therefore
of every Ray apart is regular, and what Rule that
Refradiion obferves we are now to (liew*.

The late Writers in Opticks teach, that the
Sines of Incidence are in a given Proportion
to the Sines of Refradion, as was explained in
the fifth Axiom ; and fome by Inllruments fit-
ted for meafuring of Refractions, or otherwife
experimentally examining this Proportion, do
acquaint us that they have found it accurate.
But whilft they, not underftanding the difife-
rent Refrangibility of feveral Rays, conceived
them all to be refraCted according to one and
the fame Proportion, 'tis to be prefumed that
they adapted their Meafures only to the middle
of the refracted Light ; fo that from their Mea-
fures we may conclude only that the R^iys
which have a mean Degree of Refrangibility,
that is, thofe which when feparated from the
reft appear green, are refraCted according to a
given Proportion ,of their Sines. And there-

* This is •venfulh treated of in our Author'/ Left. Optic Part \,
Seil.lL

F fore

6& O F T I C K S.

fore we are now to fhew, that the like given
Proportions obtain in all the reft. That it
fhould be fo is very reafonable, Nature being
ever conformable to her felf -, but an experimen-
tal Proof is defired. And fuch a Proof will be had,
if we can fliew that the Sines of Refradion of
Rays differently refrangible are one to another ia
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 Propor-
, tion to the equal Sines of Incidence, thofe other
Sines of Refradtion will alfo be in given Propor-
tions 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 Refradion are in a given Proportion tQ
one another.

Exper. 15. The Sun fhining into a dark Cham-
ber through a little round Hole in the Window-
fhut, let S [in Fig. 26.] reprefent his round
white Image painted on the oppofite Wall by
his dired: Light, P T his oblong coloured
Image made by refrading that Light with a
Prifm placed at the Window -, and p t, or
2p 2.t^ or 3/> 3 Z', his oblong colour'd Image
made by refrading again the fame Light fide-
ways with a fecond Prilm placed immediately
after the firft in a crofs Pontion to it, as was
explained in the fifth Experiment j that is to
fay, p t when the Refradion of the fecond
Prifm is fmall, zp 2 t when its Refracftion is
greater, and 3 /> 3 ^ when it is greateft. For

fuch

B O O K I. 6j

fuch will be the diverfity of the Pvefradions, if
the refrading Angle of the fecond Prifm be of
various Magnitudes 3 fuppofc of fifteen or twen-
ty Degrees to make the Image pt^ of thirty or
forty to make the Image 2p 2t^ and of fixty to
make the Image 3/> 3/. But for want of folid
Glafs Prifms with Angles of convenient Big-
neffes, there may be Veffels made of poliflied
Plates of Glafs cemented together in the form of
Prifms and filled with Water. Thefe things be-
ing thus ordered, I obferved that all the folar
Images or coloured Spectrums P T , />/ , 2p
2.ty 3/> 3^ did very nearly converge to the place
S on which the dired Light of the Sun fell
and painted his white round Image when the
Prifms were taken away. The Axis of the Spe-
ctrum PT, that is the Line drawn through the
middle of it parallel to its re(5tilinear Sides ,
did when produced pafs exadtly through the
middle of that white round Image S. And when
the RefracStion of the fecond Prifm \t^s equal
to the Refradion of the firfi:, the refrading An*
gles of them both being about 60 Degrees, the
Axis of the Spectrum 3/^3^ made by that Re-
fraction, did when produced pafs alfo throuo-h
the middle of' the fame white round Imao-e S.
But when the Refraction of the fecond Prifm
was lefs than that of the firft, the produced
Axes of the SpeClrums tp or 2t 2p made by
that Refraction did cut the produced A^xis of
the Spectrum TP in the points m and fi, a lit-
tle beyond the Center of that white round I-
mage S. Whence the proportion of the Line
3/ T to the Line 3/>P was a little greater than

F 2 the

6% O P T I C K S.

d^e Proportion of 2/T to 2/>P, and this Pro-
portion a little greater than that of iT to p P.
Now -^vhefi the Light of the Spedtrum P T falls
perpendicularly upon the Wall , thofe Lines
3 4fT, 3/»P, and2^T, 2/P, and ^T, /P, are
the Tangents of the Refra<5tions, and therefore
hy this Experiment the Proportions of the Tan--
gents of the Refradions are obtained , from
whence the Proportions of the Sines being de-
rived, they come out equal, fo far as by view-
ing the SpeftrumSj and ufing fome mathemati-
cal R^albiiing i could eftimate. For I did not
irtaJic an accurate Computation. So then the
Propolition holds true in every Ray apart, fo
hr as appears by Experiment. And that it is
accurately true, may be demonftrated upon this
Suppolition. 1'hat Bodies refi-a^ Light by a5fing
zipoti its Rays in Li?i€s perpmdicular to their Sur^
faces. But in order to this Demonftration, I muil
diftinguifh the Motion of every Ray into two
Motions, the one perpendicular to the refradiing
Surface, the other parallel to it, and concerning
the perpendicular Motion lay down the follow-
ing Propolition.

If any Motion or moving thing whatfoever he
incident with any Velocity on any broad and
thin fpace terminated on both fides by two paral-
lel Planes , and in its Paffage through that
fpace be urged perpendicularly towards the far-
ther Plane by any force which at given diftances
fi-om the Plane is of given Quantities ; the per-
pendicular velocity of that Motion or Thing,
at is emerging out of that fpace, fhall be always
equal to the fquare Root of the funi of the
3 . fquare

B O O K I. 69

fquare of the perpendicular velocit}^ of xki'iX
Motion or Thing at its Incidence on that fpace^
and of the fquare of the perpendicular velocity
wliich that Motion or Tiling would have at its
Emergence, if at its Incidence its perpendicular
velocity '^vas infinitely little.

And' the fame Propofition holds true of any
Motion or Thing perpendicul^ly retarded in its
paffage through that Ipace, if inilead of the iura
of the two Squares you take their ditference;.
The Demonflration Mathematicians v*ill eafily
find out, and therefore I iliall not trouble the
Reader with it.

Suppofe now that a Ray coming mod oblique-
ly in the LineMC [in Fig. i.] be refradted at
C by the Plane RS into the Line CN, and.jf
it be required to find the Line CE, into which
any other Ray AC fliall be refradjed ; let MC,
AD, be the Sines of Incidence of the two Rays,
and NG, EF, their Sines -of Refradion, and
let the equal Motions of the incident Rays be
reprcfented by the equal Lines MC and AC,
and the Motion M C being confidered as parai^
lei to the refracting Plane, let the other Motion
AC be diflinguiflied into two Motions AD
and DC, one of which AD is parallel, and tlie
other DC perpendicular to the refracfting Sur-
face. In like manner, let the Motions of the
emerging Rays be diftinguifh'd into two, whereof

the perpendicular ones are -^ CG and ^ CF.

And if the force of the refracting Plane begins
to a<ft upon the Rays either in that Plane or at
a Certain diftance from it on the one fide, and
ends ^t a certain diftance from it on the other

F 3 Side

^o OPTIC K s.

fide, and in all places between .thofe two limits
ad:« upoa the Rays in Lines perpendicular to
that refrading Plane, and the Actions upon the
Rays at equal diftances from the refrading Plane
be equal, and at unequal ones either equal or un-
equal according to any rate whatever j that Mo-
tion of the Ray which is parallel to the re-
frading Plane, will fuffer no Alteration by that
Fopce 5 and that Motion which is perpendicular
to it will be altered according to the rule of the
foregoing Proportion. If therefore for the per-
pendicular velocity of the emerging Ray C N

you write -^^ CG as above, then the perpendi-
cular velocity of any other emerging Ray CE
which was -^-^CF, will be equal to the fquarc

Root of CD^ -h f§^ CGq. And by fquaring

thefe Equals, and adding to them the Equals
AD^ and MC^ — CD^, and dividing the
Sums by the Equals CF^-f-EF^ and CG^-f-

NG^', you will have ~-^ equal to jf^- Whence

to, the Sine of Incidence, is to E F the Sine of
efradion, as MC to NG, that is, in a given
ratio. And this Demonftration being general,
without determining what Light is, or by what
kind of Force i: is refraded, or alTuming any
thing farther than that the refrading Body ada
upon the Rays in Lines perpendicular to its Sur-.
face J I take it to be a very convincing Argument
of the full truth of this Propoiition,

So then, if the ratio of the Sines of Inci-
dence and Refradion of any fort of Rays be

found

BOOK I. 7.1

' found in any one cafe, 'tis given in all cafes; and
this may be readily found by the Method in the
following Propofition.

PROP, VII. Theor. VI.
^he PerfeEiion of Telef copes is hnpeded by
the different Refrangibilitj of the Rays
of Light.

THE Imperfedtion of Telefcopes is vul-
garly attributed to the fpherical Figures of
the Glaffes, and therefore Mathematicians have
propounded to figure them by the conical Sedi-
ons. To fhew that they are miftaken, I have in-
ferted this Propofition ; the truth of which will
appear by the nieafure of the Refractions of the
feveral forts of Rays ; and thefe meafures I thus
determine.

In the third Experiment of this firft Part,
.where the refracting Angle of the Prifm was 62^
Degrees, the half of that Angle 31 deg. 15 min.
is the Angle of Incidence of the Rays at their go-
ing out of the Glafs into the Air * ; and the Sine of
this Angle is 5 188, the Radius being loooo. When
the Axis of this Ptifm was parallel to the Horizon,
and the Refraction of the Rays at their Incidence
6n this Prifm equal to that at their Emergence out
of it, I obferved v/ith a Quadrant the Angle which
the mean refrangible P ays, ( that is thofe which
went to the middle of the Sun's coloured Image )
made with the Horizon, and by this Angle and the
Sun's altitude obferved at the fame time, I found the

• Seesur AxiXhox's Left. Optic. Parti. Sed. II. §. 29.

F 4 Angle

7x O P T I C K S.

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 3 1 deg.
15 min. makes the Angle of Refracflion, which is
therefore 5 3 deg. 35 min. and its Sine 8047. Thefe
are the Sines of Incidence and Refradtion of the
m^an refrangible Rays, and their Proportion in
round Numbers is 20 to 3 1. This Glafs was of a
Colour inclining to green. The laft of the Prifms
mentioned in the third Experiment was of clear
white Glafs. Its refracting Angle 635 Degrees.
The Angle which the emergent Rays contained,
with the incident 45 deg. 50 min. The Sine of
half the firft Angle 5262. The Sine of half the
Sum of the Angles 8157. ^^^^ their Proportion in
round Numbers 2a to 3 1, as before.

From the Length of the Image, which was
about 95 or 10 Inches, fubdud its Breadth, which
was 2s Inches, and the Rerhainder 71 Inches
would be the Length of the Image were the Sun
but a Point, and therefore fubtends the Angle
which the moft and leafl refrangible Rays, when
incident on the Prifm in the fame Lines, do

.'contain with one another after their Emergence.
"Whence this x^^ngle is 2 deg. o'. f. For, the

^^if^ance between the Image and the Prifm
where this Angle is made, was iSj- Feet, and
at that diftance the Chord 7^ Inches fubtends
an Angle of 2 deg. o'. y". Now half this Angle
is the Angle which thefe emergent Rays con-

' taiH 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 fame emergent mean refrangible Rays,

were

B O OK I. 73

were they co-incident to them within the Clafs,
and fuffered no other Refraction than that at.their
Emergence. For, if two equal Refractions, the
one at the Incidence of the Rays on the Prifm,
the other at their Emergence, make half the
Angle 2 deg. o'. 7''. then one of thofe RefraCtions
will make about a quarter of that Angle, and this
quarter added to, and fubduded from the Angle
of Refraction of the mean refrangible Rays,
which was 53 deg. 35', gives the Angles of Re-
fraCtion of the moft and leaft refrangible Rays
54 deg. 5' 2", and 53 deg. 4' 58", whofe Sines
are 8099 and 7995, the common Angle of In-
cidence being 31 deg. 15', and its Sine 5188;
and thefe Sines in the leafl round Numbers are in
proportion to one another, as 78 and 'jj to 50.

Now, if you fubduCt the common Sine of In-
cidence 50 from the Sines of RefraCtion 'jy and
78, the Remainders 27 and 28 fliew, that in fmall
Refractions the RefraCtion of the leafl refrangi-
ble Rays is to the Refraction of the moft refran-
gible ones, as 27 to 28 very nearly, and that the
difference of the RefraCtions of the leafl refran-
gible and mofl refrangible Rays is about the
27kh Part of the whole RefraCtion of the mean
refrangible Rays.

Whence they that are skilled in Opticks.will
eafily underfland, *' that the Breadth of the leafl
circular Space, into which ObjeCt-glaffes of Te-
lefcopes can colleCt all forts of Parallel Rays, is
about the 27^th Part of half the Aperture of the
Glafs, or 55 th Part of the whole Aperture ; and

* This is demonfi rated in our AuihoiV Led. Optic. Part I. SeSI. IV.
Fyp. 57.

that

74 O P T I C K a

that the Focus of the moft refrangible Rays is
nearer to the Objeft-glafs than the Focus of the
leaft refrangible ones, by about the 275th Part of
the diflance between the Objed:-glafs and the
Focus of the mean refrangible ones.

And if Rays of all forts, flowing from any
one lucid Point in the Axis of any convex Lens,
be made by the Refra(3:ion of the Lens to con-
verge to Points not too remote from the Lens,
the Focus of the mofl: refrangible Rays fliall be
nearer to the Lens than the Focus of the leaft
refrangible ones, by a diflance which is to the
275th Part of the diftpnce of the Focus of the
mean refrangible Rays from the Lens, as the di-
ftance between thrt Focus and the lucid Point,
from whence the Rays flow, is to the diflance be-
tween that lucid Point and the Lens very nearly.

Now to examine whether the Difference be-
tween the Refra([lions, v^hich the mofl refrangi-
ble and the leaft refrangible Rays flowing from
the fame Point fuffer in the Objed-glafTes of Te-
lefcopes and fuch-like Glafles, be fo great as is
here defcribed, I contrived the following Experi-
ment. •

Exper. 16. The Lens which I ufed in the fe-
cond and eighth Experiments, being placed fix
Feet and an Inch diflant from any Obje6t, col-
leifled the Species of that Objed: by the mean
refrangible Rays at the diflance of fix Feet and
an Inch from the Lens on the other fide. And
therefore by the foregoing P-ule, it ought to col-
led the Species of that Objedl by the leafl re-
frangible Rays at the diftance of fix Feet and
31 Inches from the Lens, and by the mofl re-
• -' frangible

BOOK! 75

frangible ones at the diftance of five Feet and
iQi Inches from it: So that between the two
Places, where thefe lead and moft refrangible
Rays colledl the Species, there may be the di-
ftance of about 5^ Inches. For by that Rule,
as fix Feet and an Inch (the diftance of the Lens
from the lucid Obje6t) is to twelve Feet and
two Inches ( the diflance of the lucid Objedt
from the Focus of the mean refrangible Rays )
that is, as One is to Two; fo is the 27ith Part
of fix Feet and an Inch '(the diftance between
the Lens and the fame Focus) to the diftance
between the Focus of the moft refrangible Rays
and the Focus of the leaft refrangible ones,
which is therefore 5g Inches, that is very nearly
5^ Inches. Now to know whether this Meafure
was true, I repeated the fecond and eighth Ex-
pariment with coloured Light, which was lefs
compounded than that I there made life of:
For I now feparated the heterogeneous Rays
from one another by the Method I defcribed
in the eleventh Experiment, fo as to make a
coloured SpecStrum about twelve or fifte^sn Times
longer than broad. This Spectrum I caft on a
printed Book, and placing the above-mentioned
Lens at the diftance of lix Feet and an Inch
from this Spectrum to colleft the Species of
the illuminated Letters at the fame diftance on
the other lidey I found that the Species of the
Letters illuminated with blue were nearer to
the Lens than thole illuminated with deep
red by about three Inches, or three and a quar-
ter ; but the Species of the Letters illumi-
nated with indigo and violet appeared fo con-
I fufed

75 O P T I C K S.

fufed and indiftindt, that I could not read them :
Whereupon viewing the Prifm, I found it was
s^ full of Veins running from one end of the Glafs
to the other j fo that the Refradion could not
be regular. I took another Prifm therefore
which was free from Veins, and inftead of the
Letters I ufed two or three Parallel black Lines
a little broader than the Strokes of the Let-
ters, and calling the Colours upon thefe Lines
in fuch manner, that the Lines ran along the
Colours from one end of the Spedrum to the
other, I found that the Focus where the indigo,
or confine of this Colour and violet caft the
Species of the black Lines mofl diilindly, to
be about four Inches, or 4^ nearer to the Lens
than the Focus, where the deepefl red caft the
Species of th^ fame black Lines mofl diilind:-
ly. The violet was fo faint and dark, that I
could not difcern the Species of the Lines di-
ilindly by that Colour j and therefore confi-
dering that the Prifm was made of a dark co-
loured Glafs inclining to green, I took another
Prifm of clear white Glafs ; but the Spedrum
of Colours which this Prifm made had long
white Streams of faint Light (liooting out from
both ends of the Colours, which made me con-
clude that fomething w'as amifs j and viewing
the Prifm, I found two or three little Bubbles
ja the Glafs, which refraded the Light irregu-
lar! v. Wherefore I covered that Part of the Glafs
with black Paper, and letting the Light pafs
throucrh another Part of it which was free from
fuch Bubbles, the Spedrum of Colours became
free from thofe irregular Streams of Light, and,

was

B o o k: I. >7

was now fuch as I defircd. But ftill^I found
the violet fo dark and faint, that I could fcarce
fee the Species of the Lines by the violet, and*
not at all by the deepeft Part of it, which was
next the end of the Spc,(5lrum. I fufpeded there-
fore, that this faint and dark Colour might be
allayed by that fcattering Light which was re-
fraded, and refleded irregularly, partly by fome
very fmall Bubbles in the GlafTes, and partly
by the Inequalities of their Polifh ; which
Light, tho' it was but little, yet it being of a
white Colour, might fuffice to affed the Senfe
fo ftrongly as to difturb the Phaenomena of that
weak and dark Colour the violet, and there-
fore I tried, as in the 12th, 13th, and 14th Ex-
periments, whether the Light of this Colour
did not confifl of a fenfible Mixture of heteroge-
neous Rays, but found it did not. Nor did the
Refradlions caufe any other fenfible Colour than
violet to emerge ©ut of this Light, as they
would have done out of white Light, and by
confequence out of this violet Light had it been
fenlibly compounded with white Light. And
therefore I concluded, that the reafon why I
could not fee the Species of the Lines diftindly
by this Colour, was only the Darknefs of this
Colour, and Thinnefs of its Light, and its di-
ftance from the Axis of the Lens j I divided
therefore thofe Parallel black Lines into equal
Parts, by which I might readily know the di-
ftances of the Colours in the Speftrum from
one another, and noted the diftances of the
Lens from the Foci of fuch Colours, as c<ift the .
Species of the Lines dillindtly, and then confi-

dered

'7& O P T I C K S.

dered vvlaether the difference of thofe distances
bear fuch proportion to 5| Inches, the greatefl
Difference of the diftances, which the Foci of
the deepefl red and violet ought to have from
the Lens, as the diflance of the obferved Co-
lours from one another in the Speftrum bear to
the greatefl diflance of the deepeft red and
violet meafured in the Redilinear Sides of the
Spedrum, that is, to the Length of thofe Sides,
or Excefs of the Length of the Spedrum above
its Breadth. And my Obfervations were as fol-
lows.

When I obferved and compared the deepefl
fenfible red, and the Colour in the Confine of
green and blue, which at the Redilinear Sides
of the Spedirum was diftant from it half the
Length of thofe Sides, the Focus where the Con-
fine of green and blue cafl the Species of the
Lines diflindly on the Paper, was nearer to the
Lens than the Focus, where the red cafl thofe
Lines diflind:ly on it by about 25 or 2~ Liches.
For fometimes the Meafures were a Jittle greater,
fometimes a little lefs, but feldom varied from
one another above \ of an Inch. For it was very
difficult to define the Places of the Foci, with-
out fome little Errors. Now, if the Colours
diflant half the Length of the Image, ( mea-
fured at its Rectilinear Sides) give 25 or 2| Diffe-
rence of the diflances of their Foci from the
Lens, then the Colours dillant the whole Length
ought to give 5 or 55 Inches difference of thofe
diflances.

Bpt here it's to be noted, that I could not
fee the red to the full end of the Sped:rum,

biit

B O O K I. 7p

but only to the Center of the Semicircle which
bounded that end, or a little farther j and there-
fore I compared this red not with that Colour
which was exadlly in the middle of the Spedlrum,
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
Spedjum, but the Length of its Redilinear Sides,
fo compleating the femicircularEnds into Circles,
when either of the obferved Colours fell within
thofe Circles, I meafured the diftance of that
Colour from the femicircular End of the Spe-
drum, and fubdudting half this diftance from
the meafured diftance of the two Colours, I
took the Remainder for their corrected di-
ftance; and in thefe Obfcrvations fet down this
correfted diilance for the difference of the di-
flances of their Foci from the Lens. For, as
the Length of the Rectilinear Sides of the Spe-
<3:rum would be the whole Length of all the
Colours, were the Circles of which ( as we
Ihewed) that Spedrum confifts contraded and
reduced to Phyfical Points, fo in that Cafe this
correded diftance would be the real diftance of
the two obferved Colours.

When therefore I farther obferved tlie deepcft
fenfible red, and that blue whofe correded di- .
ftance from it was i_ Parts of the Length of
the Redilinear Sides of the Spedrum, the diffe-
rence of the diftances of their Foci from the
Lens was about 3^ Inches, and as 7 to 12, fo is
3? ^o S'v

When

8o O P T I C K S.

When I obferved the deepeft fenfible red, and
that indigo whofe corredied diftance was ~ or | of
the Length of the Rediilinear Sides of the Spe-
(ftrum, the difference of the diftances of theii^
Foei from the Lens, was about 3I Inches, and as
2 to 3, fois3|to 5I.

When I obferved the deepefl fenfible red, and
that deep indigo whofe corredted diftance from
one another was ^ or l of the Length of the
Rectilinear Sides of the Spectrum, the diffe-
rence of the diftances of their Foci from the
Lens was about 4 Inches -, and as 3 to 4, fo
is 4 to 5|.

When I obferved the deepeft feniible red,
and that Part of the violet next the indigo,
whofe corredled diftance from the red was {|
or I of the Length of the Red:ilinear Sides of the
Spedlrum, the difference of the diftances of their
Foci from the Lens was about 4- Inches, and
as 5 to 6, fo is 4i to 55. For fometimes, when
the Lens was advantageoufly placed, fo that its
Axis refpedted the blue, and all Things elfe
were well ordered, and the Sun ftione clear, and
1 held my Eye very near to the Paper on
which the Lens caft the Species of the Lines, I
could fee pretty diftind:ly the Species of thofe
Lines by that Part of the violet which was next
.the indigo J and fometimes I could fee them
by above half the violet. For in making thefe
Experiments I had obferved, that the Species
of thofe Colours only appear diftindt, which were
in or near the Axis of the Lens : So that if the
blue or indigo were in the Axis, I could fee
their Species diftindlyj and then the red ap-
peared

B O O K L 8i

peared much kfs diftin6t than before. Wherefore
I contrived to make theSped:riim of Colours flior-
ter than before, fo that both its Ends might be
nearer to the Axis of the Lens. And now its
Length was about 2t Inches, and Breadth a^
bout r 01* i of ^^^ Inch. Alfo inftead of the
black Lines on which the Spectrum was caft, I
made one black Line broader than thofe, that I
might fee its Species more eafily j and this Line I
divided by Ihort crofs Lines into equal Parts, for
meafuring the diflances of the obferved Colours.
And now I could fometimes fee the Species of
this Line with its Divifions almofl: as far as the
Center of the femicircular violet End of the
-Spedrunij and made thefe farther Obferva-^
tions.

When I obferved the deepeft fenfible red, and
that Part of the violet, whofe correfted diftance
from it was about ' Parts of the Re<ftilinear Sides
of the Spectrum, the Difference of the diftances
of the Foci of thofe Colours from the Lens^
was one time 4], another time 47, another time
4t Inches J and as 8 to 9, fo are 47, 4t> 4t, to
5?> 5t'^^ 5^ refpedively.

When I obferved the deepeft fenfible red,,
and deepeft fenfible violet, ( the correded di-
ftance of which Colours, when all Things were
ordered to the beft Advantage, and the Sun
(hone very clear, was about H or iy Parts of the
Length of the Rectilinear Sides of the colour-
ed Spedrum ) I found the Difference of the di-
ftances of their Feci from the Lens fometimes
4|- fometimes ^^y and for the moft part ^ In-

G . ehgsi

8i O P T I C K S.

ches or thereabouts ; and as ii to 12, or 15 to
16, fo is five Inches to 5* or 51. Inches.

And by this ProgreiTion of Experiments I fatif-
fied my felf, that had the Light at the very Ends
of the Spedrum been ftrong enough to make the
Species of the black Lines appear plainly on the
Paper, the Focus of the deepefh violet would
have been found nearer to the Lens, than the
Focus of the deepeft red, by about 5^ Inches
at leaft. And this is a farther Evidence, that
the Sines of Incidence and Refradion of the fe-
veral forts of Rays, hold the fame Proportion to
one another in the fmallefl Refractions w^hich they
do in the greateft.

My Progrefs in making this^ice and trouble-
fome Experiment I have fet down more at large,
that they that iliall try it after me niay be aware
of the Circumfpe(llion requifite to make it fuc-
ceed well. And if they cannot make it fuc-
ceed fo well as I did, they may notwithftand-
ing coUedl by the Proportion of the diftance of
the Colours of the Spedrum, to the Difference
of the diftances of their Foci from the Lens,
what would be the Succefs in the more diftant
Colours by a better trial. And yet, if they ufe
a broader Lens than I did, and fix it to a long
ftrait Staif, by means of which it may be rea-
dily and truly diredled to the Colour whofe Fo-
cus is defired, I queftion not but the Experi-
ment will fucceed 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 Spedlrum being remote
from the Axis, caft their Species lefs diflindtly

1 on

B O O K t 85

on the Paper than they would have done, had the
Axis been fucceffively diredled to them.

Now by what has been faid, it's certain that the
Rays which differ inRefrangibilitydo not converge
to the fame Focus j but if they flow from a lucid
Point, as far from the Lens on one fide as their
Foci are on the other, the Focus of the moft re-
frangible Rays fhall be nearer to the Lens than that
of the leafl refrangible, by above the fourteenth
Part of the whole diflance j and if they flow from
a lucid Point, fo very remote from the Lens, that
before their Incidence they may be accounted pa-
rallel, the Focus of the moft refrangible Rays fliall
be nearer to the Lens than the Focus of the kail
refrangible, by about the 27th or 2 8 th Part of their
whole diftance from it. And the Diameter of the
Circle in the middle Space between thofe two
Foci which they illuminate, when they fall there
on any Plane, perpendicular to the Axis (which
Circle is the leaft into which they can all be ga-
thered ) is* about the 55th Part of the Diameter
of the Aperture of the Glafs. So that 'tis a won-
der, that Telefcopes reprefent Objeds fo diftindt
as they do. But were all the Rays of Light
equally refrangible, the Error ariflng only from
the Sphericalnefs of the Figures of Glaffes would
be many hundred times lefs. For, if the Obje6t-
glafs of a Telefcope be Plano-convex, and the
Plane fide be turned towards the Objedlj and
the Diameter of the Sphere, whereof this Glafs
is a Segment, be called D, and the Semidiame-
ter of the Aperture of the Glafs be called S, and
the Sine of Incidence out of Glafs into Air, be
to the Sine of Refradtion as I to R j the Rays

G 2 which

84 O P T I C K S.

w hich come parallel to the Axis of the Glafs, fhall
in the Place where the Image of theObjed: is moft
diflindly made, be fcattered all over a little Circle,

whofe Diameter is — X very nearly, * as

Iq Dquad. ^ ^'

I gather by computing the Errors of the Rays by
the Method of infinite Series, and rejecting the
Terms, vi^hofe Quantities are inconfiderable. As
for inflance, if the Sine of Incidence I, be to the
Sine of Refradion R, as 20 to 3 1, and if D the
Diameter of the Sphere, to which the Convex-
fide of the Glafs is ground, be 100 Feet or 1200
Inches, and S the Semidiametcr of the Aperture be
two Inches, the Diameter of the little Circle,

(that IS ^ -) will be , (or

Iq ycD quad. 20 X 20 X 1 200 X i zoo

961 X

72000000 ) Parts of an Inch. But the Diameter of

the little Circle, through which thefe Rays are
fcattered by unequal Refrangibility, will be about
the 55 th Part of the Aperture of the Objed-glafs,
which here is four Inches. And therefore, the
Error arifing from the Spherical Figure of the
Glafs, is to the Error arifing from the different Re-
frangibility of the Rays, as to - . that is

*^ ■ •' ■' 72000000 rj*

as I to 5449 ; and therefore, being in comparifon
fo very little, deferves not to be confidered.

But you will fay, if the Errors caufed by the
different Refrangibility be fo very great, how
comes it to pafs, that Objeds appear through
Telefcopes fo diflind: as they do ? I anfwer, 'tis

* Hovj to do this, is pezvn in our AuthorV Left. Optic. Part I.
Se^. IV. Pnp.^x.

becaufe

B O O K I. 85

becaufe the erring Rays are not fcattered uni-
formly over all that Circular Space, but colleded
infinitely more denfely in tlie Center than in
any other Part of the Circle, and in the Way
from the Center to the Circumference, grow
continually rarer and rarer, fo as at the Circum-
ference to become infinitely rare 5 and by rea-
fon of their Rarity are not flrong enough to be
vifible, unlefs in the Center and very near it.
Let ADE [in Fig. 27.] reprefent one of thofe
Circles defcribed with the Center C, and Semi-
diameter AC, and let BFG be a finaller Circle
concentrick to the former, cutting with its Cir-
cumference the Diameter AC in B, and bife<fl
AC in N } and by my reckoning, the Denfity of
the Light in any Place B, will be to its Denfity
in N, as AB to BC; and the whole Light with-
in the Icffer Circle BFG, will be to the whole
Light within the greater A ED, as the Excefs
of the Square of A C above the Square of A B,
is to the Square of AC. As if B C be the fifth
Part of AC, the Light will be four times dcn-
fer in B than in N, and the whole Light within
the lefs Circle, will be to the whole Light with-
in the greater, as nine to twenty-five. Whence
it's evident, that the Light within the lefs Cir-
cle, mufl ftrike the Senfe much more ftrongly,
than that faint and dilated Light round about
between it and the Circumference of the grea-
ter.

But it's farther to be noted, that the mcft lu-
minous of the Prifmatick Colours are the yeU
low and orange. Thefe aifed: the Senfes more
ftrongly than all the reft together, and next to

G 3 thefc

S6 O P T I C K S.

thefe in flrength are the red and green. Th^
blue compared with thefe is a faint and dark
Colour, and the indigo and violet are fnuch
darker and fainter, fo that thefe compared with
the ftronger Colours are little to be regarded^
The Images of Ohjecfls are therefore to be pla-?
ced, not in the Focus of the mean refrangible
Rays, which are in the Confine of green and
blue, but in the Focus of thofe Rays which are
in the middle of the orange and yellow j therQ
where the Colour is moil: luminous and fulgent^
that is in the brighteft yellow, that yellow which
inclines more to orange than to green. And
by the Refraction of thefe Rays (whofe Sines of-
incidence and Refraction in Glafs are as 17 apd
1 1 ) the Refradion of Glafs and Cryflal for Op-
tical Ufes is to be meafured. Let us therefore
place the Image of the Objed; in the Focus of
thefe Rays, and all the yellow and orange will
fall within a Circle, wnofe Diameter is about
the 250th Part of the Diameter of the Aperture
of the Glafs. 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 thefe two Coloi;irs will
fall within the fame Circle, and two fifth Parts
will fall without it round about y and that which
falls without will be fpread through alinoil as
much more fpace as that which falls within,
and fo in the grofs be almoft three times rarer.
Of the other half of the red and green, (that is
of the deep dark red and willow green) about
pne quarter will fall within this Circle, and

three

B O O K I. 87

three quarters without, and that which falls
without will be fpread through about four o^
five times more fpace than that which falls with-
in ; and fo in the grofs be rarer, and if com
pared with the whole Light within it, will be
about 25 times rarer than all that taken in the
grofs J or rather more than 30 or 40 times ra-
rer, becaufe the deep red in the end of the
Spedtmm of Colours made by a Prifm is very-
thin and rare, and the willow green is fome-
thing rarer than the orange and yellow. The
Light of thefe Colours therefore being fo very
much rarer than that within the Circle, will
fcarce affe<5t the Senfe, efpecially fince the deep
red and willow green of this Light, are much
darker Colours than the reft. And for the fame
reafon the blue and violet being much darker
Colours than thefe, and much more rarified,
may be neglected. For the denfe and bright
Light of' the Circle, will obfcure the rare and
weak Light of thefe dark Colours round about
it, and render them almoft infenfible. The
fenfible Image of a lucid Point is therefore
fcarce broader than a Circle, whofe Diameter is
the 250th Part of the Diameter of the Aperture
of the Objedt-glafs of a good Telefcope, or not
much brorder, if you except a faint and dark mifty
Light round about it, which a Spectator wifr.
fcarce regard. And therefore in a Telefcope,
whofe Aperture is four Liches, and Length an
hundred Feet, it exceeds not 2" 45'", or 3". And
in a Telefcope whofe Aperture is two Inches,
and Length 20 or 30 Feet, it may be 5" or 6",
and fcarce above. And this anfwers well to

G 4 Expe-

88 O P T I C K S.

Experience : For fpme Aftronomers have found
the Diameters pf the fix'd Stars, in Telefcopes
of between 20 and 60 Feet in length, to be a-
bout 5" or 6", or at moft 8'' or 10" in diame-
ter. But if the Eye-Glafs be tinfted faintly
with the Smoak of a Lamp or Torch, to ob-
fcure the Light of the Star, the fainter Light
in the Circumference of the Star ceafes to be
vilib .-, and the Star (if the Glafs be fufficiently
foilta witli Smoak ) appears fomething more
like a mathematical Point. And for the fame
Reafon, the enormous Part of the Light in the
Circumference of every lucid Point ought to be
Icfs difcernible in fhorter Telefcopes than in lon-
ger, becaufe the^fhorter tranfmit lefs Light to the
Eye.

Now, that the fix'd Stars, by reafon of their
immenfe Diliance, appear like Points, unlefs fo
far as tl^eir Light is dilated by Refra6lion, may
appear from hence j that when the Moon pafTes
over them and eclipfes them, their Light vanifhes,
not gradually like that of the Planets, but all at
once J and in the end of the Eclipfe it returns
into Sight all at once, or certainly in lefs time
than the fecond of a Minute ; the Refradion of
the Moon's Atmofphere a little protrading th^
time in which the Light of the Star firfl vaniilies,
^nd afterwards returns into Sight.

NoWj if we fuppofe the fenfible Image of a lu-
cid Point, to be even 250 times narrower than
the Aperture of the Glafs 5 yet this Image would
be fciil much greater than if it were only from
th^ fpherical Figure of the' Glafs. For were
i^ not for the different Refrangibility of the

Raysj

B O O K I. 8p

Rays, its breadth in an loo Foot Tclefcope

whofe aperture is 4 Inches, would be but ^-^^^^—

parts of an Inch, as is manifeil by the foregoing
Computation. And therefore in this cafe the
greateft Errors arifing from the fpherical Figure
of the Glafs, would be to the greateft fenfible
Errors arihng from the different Refrangibihty

of the Rays as ^^^^ to ^ at moft, that is on-
ly as I to 1200. And this fufficiently (hews that
it is not the fpherical Figures of Glalfes, but the
different Refrangibihty of the Rays which hin-
ders the perfeftion of Telefcopes.

There is another Argument by w4iich it may
appear that the different Refrangibihty of Rays,
is the true caufe of the imperfed:ion of Tele-
fcopes. For the Errors of the Rays arifmg from
the fpherical Figures of Obje6t-glaffes, -Are as the
Cubes of the Apertures of the Objed: Glaffes ;
and thence to make Telefcopes of various
Lengths magnify with equal diftindlnefs , the
Apertures of the Objeft-glaffes, and the Charges
or magnifying Powers ought to be as the
Cubes of the fquare Roots of their lengths;
which doth not anfwer to Experience. But
the Errors of the Rays arifing from the different
Refrangibihty, are as the Apertures of the Ob-
jedt-glaffes ; and thence to make Telefcopes of
various lengths, magnify with equal dillin6tnefs,
their Apertures and Charges ought to be as the
fquare Roots of their lengths ; and this anfwers
to Experience, as is v/ell know^n. For Inffance,
^ Tclefcope of 64 Feet in length, with an Aper-

2 turQ

90 O P T I C K S.

ture of 2 1 Inches, magnifies about 120 times,
with as much diftinftnefs as one of a Foot in
length, with ^ of an Inch aperture, magnifies i^
times.

Now were it not for this different Refrangi-
bility of Rays, Telefcopes might be brought to
a greater perfeftion than we have yet defcrib'd,
by compofmg the Objedi-glafs of two Glaffes
with Water between them. Let A D F C [in Fig,
28.] reprefent the Objed:-glafs compofed of two
Glaffes ABED and BEFC, alike convex on th®
outfides AGD and CHF, and alike concave
on the infides BME, BNE, with Water in
the concavity BMEN. Let the Sine of Inci-
dence out of Glafs into Air be as I to R, and
out of Water into Air, as K to R, and by con-
fequence out of Glafs into Water, as I to K:
and let the Diameter of the Sphere to which the
convex fides AGD and CHF are ground be
D, and the Diameter of the Sphere to which
the concave fides BME and BNE, are ground
be to D, as the Cube Root of KK — KI to the
Cube Root of R K-— R I : and the Refractions
on the concave fides of the Glaffes, will very
much corred the Errors of the Refradions on
the convex fides, fo far as they arife from the
fphericalnefs of the Figure. And by this means
might Telefcopes be brought to fufiicient per-
fection, were it hot for the different Refrangi-
bility of feveral forts of Rays. But by reafon
of this different Refrangibility, I do not yet fee
any other means of improving Telefcopes by
Refractions alone, than that of increafing their
lengths, for which end the late Contrivance of

Hugenhis

B O O K I. pi

Jlugenius feems well accommodated. For very
long Tubes are cumberfome, and fcarce to be
readily managed, and by reafon of their length
are very apt to bend, and fhake by bending, fo
as to cauie a continual trembling in the Objects,
whereby it becomes difficult to fee them difl;in(fl-
ly: whereas by his Contrivance the Glaffes are
readily manageable, and the Objed-glafs being
fix'd upon a flrong upright Pole becomes more
fteady.

Seeing therefore the Improvement of Tele-
fcopes of given lengths by Refradions is defpe-
ratej I contrived heretofore a Perfpedive by-
Reflexion , ufmg inftead of an Objed-glafs a
concave Metal. The diameter of the Sphere
to which the Metal was ground concave was a-
bout 25 Englijh Inches, and by confequence
the length of the Inftrument about fix Inches
and a quarter. The Eye-glafs v/as Plano-con-
vex, and the diameter of the Sphere to which
the convex iide was ground was about t of an
Inch, or a little lefs, and by confequence it
niagniiied between 30 and 40 times. By ano-
ther way of meafuring 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 Eye-
glafs and the Eye, and perforated in the mid-
dle with a little round hole for the Rays to pafs
through to the Eye. For this Circle by being
placed here, ftopp'd much of the errroneous
Light, which otherwiie would have difturbed

the

p2 O P T I C K S.

the Vifion. By comparing it with a pretty good
Perfped;ive of four Feet in length, made with
a concave Eye-glafs, I could read at a greater
diftance with my own Inftrument than with the
Glafs. Yet Objedts appeared much darker in
it than in the Glafs, and that partly becaufe
more Light was loft by Reflexion in the Metal,
than by Refraction in the Glafs, and partly be-
caufe my Inftrument was overcharged. Had it.
magnified but 30 or 25 times, it would have
made the Obje(5t appear more brisk and pleafant,
Tv/o of thefe I made about 16 Years ago, and
have one of them flill by me, by which I can
prove the truth of v/hat I write. Yet it is not
fo 2:ood as at the firft. For the concave has been
divers times tarnifhed and cleared again, by rub-
bing it with very foft Leather. When I made
thefe an Artifl in London undertook to imitate it;
but ufing another way of polifhing them than I
did, he fell much fhort of what I had attained
to, as I afterwards underftood by difcourfmg.
the Under- work man he had employed. The
Polifh I ufed was in this manner. I had
two round Copper Plates, each fix Inches in
Diameter, the one convex, the other concave,'
ground very true to one another, On the con-
vex I ground the Objedt-Metal or Concave
which was to be polifli'd, 'till it had taken the
Figure of the Convex and was ready for a
Poliih. Then I pitched over the convex very'
thinly, by dropping melted Pitch upon it, and
warming it to keep the Pitch foft, whilft I
ground it with the. concave Copper wetted
to make it fpread eavenly all over the convex.
^ Thus

BOOK I. 95

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 1 could.
Then I took Putty which I had made very fine
by wafhing it from all its groiler Particles, and
laying a little of this upon tlie Pitch, I ground
it upon the Pitch with the concave Copper, till
it had done making a Noife ; and then upon the
Pitch I ground the Objed:-Metal with a brisk
motion, for about two or three Minutes of
time, leaning hard upon it. Then I put frefh.
Putty upon the Pitch, and ground it again till it
had done making a noife, and afterwards ground
the Objed:-Metal upon it as before. And this
Work I repeated till the Metal was poliflied,
grinding it the laft time with all my llrength
for a good while together , and frequently
breathing upon the Pitch, to keep it moift with-
out laying on any more frefli Putty. The Ob-
jedl-Metal was two Inches broad, and about one
third part of an Inch thick, to keep it from
bending. I had two of thefe Metals, and when
I had poliflied them both, I tried which was
beft, and ground the other again, to fee if I could
make it better than that which I kept. And
thus by many Trials I learn'd the way of po-
lifhing, till I made thofe two reflecting Perfpe-
dlives I fpake of above. For this Art of po-
lilhing will be better learn'd by repeated Pra-
ctice than by my Defcription. Before I ground
the Objedt-Metal on the Pitch, I always ground '
the Putty on it v/ith the concave Copper, till it
had done making a noife, becaufe if the Parti-
cles of the Putty were not by this means made

to

^4 O P T I C K S.

to flick faft in the Pitch, they would by rolling
up and down grate and fret the Objed-Metal and
fill it full of little holes.

But becaufc Metal is more difficult to polifll
than Glafs, and is afterwards very apt to be
fpoiled by tarnifhing, and reflects not fo much
Light as Glafs quick-filver'd over does : I would
propound to ufe inflead of the Metal, a Glafs
ground concave on the forefide, and as much
convex on the back-fide, and quick-filver'd o-
ver on the convex fide. The Glafs mufl be e-
very where of the fame thicknefs exactly. O-
therwife it will make Objedls look colour'd and
indiftind:. By fuch a Glafs I tried about five or
fix Years ago to make a reflecfling Telefcope of
four Feet in length to magnify about 150 times,
and I fatislied my felf that there wants nothing
but a good Artift to bring the Delign to perfe--
ftion. For the Glafs being wrought by one of
our London Artifls after fuch a manner as they
grind GlalTes for Telefcopes, though it feemed as
well wrought as the Objed:-glaires ufe to be, yet
when it was quick-filver'd, the Reflexion dif-
covered innumerable Inequalities all over the
Glafs. And by reafon of thefe Inequalities, Ob-
jedls appeared indiftindl in this Inflrument. For
the Errors of refledled Rays caufed by any Ine-
quality of the Glafs, are about fix times greater
than the Errors of refradled Rays caufed by
the like Inequalities. Yet by this Experiment
I fatisfied my felf that the Reflexion on the
concave fide of the Glafs, which I feared would
diflurb the Vifion, did no fenfible prejudice to
it, and by confequence that nothing is wanting

to

B O O K I. p5

to perfed thefe Telefcopes, but good Workmen
who can grind and polifh GlaiTes truly fpherical.
An Objedt-glafs of a fourteen Foot Telefcope,
made by an Artificer at Lo?ido)i, I once mended
confiderably, by grinding it on Pitch with Put-
ty, and leaning very eafily on it in the grinding,
left the Putty {hould fcratch it. Whether this
way may not do well enough for polifhing thefe
reflecting Glaffes, I have not yet tried. But he
that Ihall try either this or any other way of po-
liftiing which he may think better, may do well
to make his GlafTes ready for poliihing, by grind-
ing them without that Violence, wherewith our
Londofi Workmen prefs their Glafles in grinding.
For by fuch violent preiTure, Glafles are apt to
bend a little in the grinding, and fuch bendino^
will certainly fpoil their Figure. To recom-
mend therefore the confideration of thefe refled-
ing GlaiTes to fuch Artifts as are curious in fi-
guring GlafTes, I fliall defcribe this optical Inftru-
ment in the following Propofition.

PROP. VIII. Prob. II.
To pjorten Telefcopes.

LET ABDC [mFig.2g.] reprefent a Glafs
fpherically concave on the forefide AB, and
as much convex on the backfide CD, fo that
it be every where of an equal thicknefs. Let it
not be thicker on one fide than on the other,
left it make Objects appear colour'd and indi-

ftina,

^6 O P T I C K S.

flindl , and let it be very truly wrought and
quick-filver'd over on the backfide; and fet in
the Tube VXYZ which muft be very black
within. Let EFG reprefent a Prifm of Glafs
or Cryftal placed near the other end of the
Tube, in the middle of it, by means of a han-
dle of Brafs or Iron FGK, to the end of which
made flat it is cemented. Let this Prifm be
redangular at E, and let the other two Angles
at F and G be accurately equal to each other,
and by confequence equal to half right ones,
and let the plane fides FE and GE be fquare,
and by confequence the third fide F G a redlan-
gular Parallelogram , whofe length is to its
breadth in a fubduplicate proportion of two to
one. Let it be fo placea in the Tube , that
the Axis of the Speculum may pafs through the
middle of the fquare fide EF perpendicularly
and by confequence through the middle of the
fide FG at an Angle of 45 Degrees, and let the
fide E F be turned towards the Speculum, and
the diftance of this Prifm from the Speculum
be fuch 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 Prifm
at the fide EF, and be reflected by the fide
FG, and thence go out of it through the fide
GE, to the point T, which muft be the com-
mon Focus of the Speculum ABDC, and of a
Plano-convex Eye-glafs H, through which thofe
Rays muft pafs to the Eye. And let \ - Rays at
their coming out of the. Glafs pafs . irough
a fmall round hole, or aperture made in a lit*
tie plate of Lead, Brafs, or Silver, wherewith

the

B O O K I. 97

the Glafs is to be covered, which hole mufl be
no bigger than is neceflary for Light enovigh to
pafs through. For fo it will render the Objedt
diftindt, the Plate in which 'tis made intercept-
ing all the erroneous part of the Light which
comes from the verges of the Speculum AB.
Such an Inftrument well made, if it be fix Foot
long, (reckoning the length from the Speculum
to the Prifm, and thence to the Focus T ) will
bear an aperture of fix 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 Inftrument be
made longer or fhorter, the aperture muft be in
proportion as the Cube of the fquare-fquare Root
of the length, and the magnifying as the aper-
ture. But it's convenient that the Speculum be
an Inch or two broader than the aperture at the
leaft, and that the Glafs of the Speculum be
thick, that it bend not in the working. The
Prifm EFG muft be no bigger than is necelTary,
and its back lide FG muft not be quick-lilver'd
over. For without quickfilver it will refledl all
the Light incident on it from the Speculum.

In this Inftrument the Objedl will be invertc^,
but may be erected by making the fquare fides
FF and EG of the Prifm EFG not plane but
fpherically convex, that the Rays may crofs as
well before they come at it as afterwards between
it andj.rj-e Eye-glafs. If it be defired that the
Inft^^ iie.it bear a larger aperture, that may be
alfo Qone by compofmg the Speculum of two
GlalTes with Water between them.

H If

pg O P T I C K S.

If the Theory of making Telefcopes could at
length be fully brought into Pradtice, , yet there
would ' be certain Bounds beyond which Tele-
fcopes could not perform. For the Air through
which we look upon the Stars, is in a perpetual
Tremor J as may be ften by the tremulous Moti-
on of Shadows call: from high Towers,- and by-
the twinkling of the fix'd Stars. But thefe Stars
do not twinkle when viewed through Telefcopes
which have large apertures. For the Rays of
Light which pafs through divers parts of the
aperture, tremble each of them apart, and by
means of their various and fometimes contrary
Tremors, fall at one and the fame time upon dif-
ferent points in the bottom of the Eye, and their
trembling Motions are too quick and confufed to
be perceived feverally. And all thefe illuminated
Points conftitute one broad lucid Point, com-
pofed of thofe many trembling Points confufed-
ly and infenlibly mixed with one another by very
ihort and fwift Tremors, and thereby caufe the
Star to appear broader than it is, and without
any trembling of the whole. Long Telefcopes
may caufe Objeds to appear brighter and larger
than fliort ones can do, but they cannot be fo
formed as to take away that confuiion of the
Rays which arifes from the Tremors of the At-
mofphere. The only Remedy is a moft ferene
and quiet Air, fuch as may perhaps be found on
the tops of the higheft Mountains above the grof- .
ier Clouds.

THE

THE

FIRST BOOK

O F

OPTICKS.

PART II.

PROP, I. Theor. I.

T%e Phczno7nena of Colours hi refraEled or
refie&ed Light are not caufed by new
Modifications of the Light varioufly im-
frefsd^ according to the various Termi-
nations of the Light and Shadow.

Exper. I.

The Proof by Experiments.

O R if the Sun fhine into a
I very dark Chamber through
an obiong hole F, [in Fig. i.]
whofe breadth is tlie fixth or
eighth part of an Inch, or fomething lefs j and
his beam F H do afterwards pafs firft through a

H 2 very

i6o O P T i C K S.

very large Prifm ABC, diftant about 20 Feet
from the hole, and parallel to it, and then ( with
it3 white part) through an oblong hole H, whofe
breadth is about the fortieth or lixtieth part of
an Inch, and which is made in a black opake
Body GI, and placed at thediftanceof two or
three Feet from the Prifm, 'in a parallel Situa-
tion both to the Prifm and to the former hole,
and if this white Light thus tranfmitted through
the hole H, fall afterwards upon a white Paper
//, placed after that hole H, at thediftanceof
three or four Feet from it, and there paint thC;
ufual ' Colours of the Prifm, fuppofe red at /,
yellow at s, green at r, blue at ^, and violet
at p ', you may with an Iron Wire, or any fuch
like (lender opake Body, whofe breadth is a-
bout the tenth part of an Inch, by intercepting
the Rays at k, /, w, ;z or 0, take away any one
of the Colours at t, s, r, q or />, whilft the other
Colours remain upon the Paper as before j or
with an Obftacle fomething bigger you may
tak away any two, or three, or four Colours
together, the reft remaining: So that any one
of the Colours as well as violet may become
outmoft in the Confine of the Shadow towards
^, and any one of them as well as red may be-
come outmoft in the Confine of the Shadow to-
wards /, and any" one of them may alfo bor-
der upon the Shadow made within the Colours
by the Obftacle R intercepting fome interme-
diate part of the Light; and, laftly, any one of
them by being left alone, may border upon the
Shadow on either hand. All the Colours have
themfelves indifferently to any Confines of Sha-

I dow.

BOOK I. lor

dow, and therefore the differences, of thefe Co-
lours from one another, do not arife from the
different Confines of Shadow, whereby Light
is varioufly modified, as has hitherto been the
Opinion of Philofophcrs. In trying thefe things
*tis to be obferved, that by how much the holes
F and H are narrower, and the Intervals be-
tween them and the Prifm greater, and the
Chamber darker, by fo much the better doth the
Experiment fucceed ; provided the Light be
not fo far diminifhed, but that the Colours at
pt he fufficiently vifible. To procure a Prifm
of folid Glafs large enough for this Experiment
will be difficult, and therefore a prifmatick Vef-
fel muft be made of poliili'd Glafs Plates ce-
mented together, and filled with fait Water or
clear Oil.

Exper. 2. The Sun's Light let into a dark
Chamber through the round hole F, [in Fig. 2.]
half an Inch wide, paffed firft through the Prifm
ABC placed at the hole, and then through a
Lens PT fomething more than four Inches
broad^ and about eight Feet diflant from the
Prifm, and thence converged to O the Focus
of the Lens diftant from it about three Feet,
and there fell upon a white Paper D E. If that
Paper was perpendicular to that Light incident
upon it, as 'tis reprefented in the pollure DE,
all the Colours upon it at O appeared white.
But if the Paper being turned about an Axis
parallel to the Prifm, became very much incli-
ned to the Light, as 'tis reprefented in the Po-
fitions de-Andi ^i-, the fame Light in the one
cafe appeared yellow and red, in the other blue.

H 3 Here

102 O P T I C K S.

Here one and the fame part of the Light in one
and the fame place, according to the various In-
clinations of the Paper, appeared in one cafe
white, in another yellow or red, in a third blue,
whilft the Confine of Light and Shadow, and
the Refradions of the Prifm in all thefe cafes
remained the fame.

Expcr. 3. Such another Experiment may be
more eaiily tried as follows. Let a broad beam
of the Sun's Light coming into a dark Cham-
ber through a hole in the Window-fhut be re-
fracted by a large Prifm ABC, [in Fig. 3.]
whofe refradting Angle C is more than 60 De-
grees, and fo foon as it comes out of the Prifm,
let it fall upon the white Paper DE glewed up-
on a ilifF Plane; and this Light, when the Pa-
per is perpendicular to it, as 'tis reprefented in
DE, will appear perfed:ly white upon the Pa-
per; but when the Paper is very much inclin'd
to it in fuch a manner as to keep always paral-
lel to the Axis of the Prifm, the whitenefs 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 pofture J^, or into blue and violet, as in
the pofture ^ e. And if the Light before it fall
upon the Paper be twice refracted the fame
way by two parallel Prifms, thefe Colours will
become the more confpicuous. 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 co-
lour'd all over with one uniform Colour, the
Colour being always the fame in the middle of

the

B O O K I. 103

the Paper as at the edges, and this Colour chan-
ged according to the various Obliquity of the
reflefting Paper, without any change in the Re-
fradlions or Shadow, or in the Light which fell
upon the Paper. And therefore thefe Colours
are to be derived from fome other Caufe than the
new Modifications of Light by Refradions and
Shadows.

If it be aiked, what then is their Caufe ? I
anfwer, That the Paper in the poilure Jt', being
more oblique to the more refrangible Rays than
to the lefs refrangible ones, is more ilrongly illu-
minated by the latter than by the former, and
therefore the lefs refrangible Rays are predomi-
nant in the refledted Light. And where-ever
they are predominant in any Light, they tinge it
with red or yellow, as may in fome meafure ap-
pear by the firft Propofition of the firfl Part of
this Book, and will more fully appear hereafter.
And the contrary happens in the poflure cf the
Paper ^e, 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 Si-
tuation varioufly , without any refped to any
Confine or Shadow. If fuch a Bubble be co-
ver'd with a concave Glafs, to keep it from be-
ing agitated by any Wind or Motion of the Air,
the Colours will flowly and regularly change
their Situation , even whilll the Eye and the
Bubble, and all Bodies which emit any Light,
or caft any Shadow , remain unmoved. And
therefore their Colours arife from fome regular

H 4 Caufe

104 O P T I C K S.

Caufe which depends not on any Confine of Sha-
dow. What this Caufe is will be fliewed in the
next Book.

To thefe Experiments may be added the
tenth Experiment of the firft Part of this firft
Book, where the Sun's Light in a dark Room be-
ing trajeded through the parallel Superficies of
two Prifms tied together in the form of a Paralle-
lopipede, became totally of one uniform yellow
or red Colour, at its emerging out of the Prifms.
Here, in the production of thefe Colours, the
Confine of Shadow can have nothing to do.
For the Light changes from white to yellow,
orange and red fuccefiively, without any alte-
ration of the Confine of Shadow : And at both
edges of the emerging Light where the con-
trary Confines of Shadow ought to produce
different Effeds , the Colour is one and the
fame, 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 fame as at the edges, the
whole Light at its very firft Emergence being of
one uniform Colour, whether white, yellow,
orange or red, and going on thence perpetual-
ly without any change of Colour, fuch as the
Confine of Shadow is vulgarly fuppofed to wotk
in refradted Light after its Emergence. Nei-
ther can thefe Colours arife from any new Mo-
difications of the Light by Refradions, becaufe
they change fuecefiively frorri white to yellow,
orange and red, v^hile the Refradtions remain
the fame, and alfo becaufe the Refradions are
made contrary ways by parallel Superficies which

deftro'y

B O O K I. 105

deftroy one another's Effeds. They arife not
therefore from any Modifications of Light made
byRefradions and Shadows, but have foire or her
Caufe. What that Caufe is we (hewed abov-e in
this tenth Experiment, and need not here re-
peat it.

There is yet another material Circumftance of
this Experiment. For this emerging Light being
by a third Prifm HIK" [in Fig. 22. Part L] re-
fradled towards the Paper FT, and there painting
theufual Colours of the Frifm, red, yellow, green,
blue, violet : If thefe Colours arole from the Re-
fradions of that Frifm modifying the Light, they
would not be in the Light before its Incidence on
that Frifm. And yet in that Experiment we
found, that when by turning the two firft Prifms
about their common Axis all the Colours were
made to vanifh but the red; the Light which
makes that red being left alone, appeared of
the very fame red Colour before its Incidence
on the third Frifm. And in general we find
by other Experiments, that when the Rays
which differ in Refrangibility are feparated from
one another, and any one Sort of them is con-
fidered apart, the Colour of the Light which
they compofe cannot be changed by any Re-
fraction or Reflexion whatever, as it ought to
be were Colours nothing elfe than Modifica-
tions of Light caufed by Refractions, and Re-
flexions, and Shadows. This Unchangeablenefs
of Colour I am now to defcribe in the following
Propofition.

PROP,

io6 O P T I C K S.

PROP. IT. Theor. II.

u47/ homogeneal Light has its proper Colour
anfweriftg to its Degree of Refrangibi-
lity^ and that Colour cannot be changed
by Reflexions and RefraSiions,

IN the Experiments of the fourth Propofition
of the firfh Part of this firft Book, when I had
leparated the heterogeneous Rays from one ano-
ther, the Spedrum pt formed by the feparated
Rays, did in the Progrefs from its End^, on which
the moft refrangible Rays fell, unto its other
End /, on which the leaft 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
Succeffion perpetually varying. So that there ap-
peared as many Degrees oi Colours, as there were
forts of Rays differing in Refrangibility.

Exper.^. Now, that thefe Colours could not be
changed by Refradtion, I knew by refradiing with
aPrifm fometimes one very little Part of tbisLight,
fometimes another very little Part, as is defcribed
in the twelfth Experiment of the firft Part of this
Book. For by this Refradtion the Colour of the
Light was never changed in the leaft. If any
Part of the red Light was refracted, it remained
totally of the fame red Colour as before. No
orange, no yellow, no green or blue, no other
new Colour was produced by that Refradtion.
Neither did the Colour any ways change by
repeated Refradtions, but continued always the

fame

B O O K I. 107

fame red entirely as at firft. The like Con-
ftancy and Immutability I found alfo in the blue,
green, and other Colours. So alfo, if I looked
through a Prifm upon any Body illuminated with
any Part of this homogeneal Light, as in the four-
teenth Experiment of the firfl Part of this Book
is defcribed ; I could not perceive any new Co-
lour generated this way. All Bodies illumina-
ted with compound Light appear through Prifms
confufed, (as was faid above) and tinged with
various new Colours, but thofe illuminated with
homogeneal Light appeared through Prifms
neither lefs diflincfl, nor otherwife colour'd,
than when viewed with the naked Eyes. Their
Colours were not in the leaft changed by the
Refrad:ion of the interpofed Prifm. I fpeak
here of a fenfible Change of Colour : For the
Light which I here call homogeneal, being not
abfolutely homogeneal, there ought to arife
fome little Change of Colour from its Hetero-
geneity. But, if that Heterogeneity was fo lit-
tle as it might be made by the faid Experiments
of the fourth Propofition, that Change was not
fenfible, and therefore in Experiments, where
Senfe is Judge, ought to be accounted none
at all.

Exper. 6. And as thefe Colours were not
changeable by Refradions, fo neither were they
by Reflexions. For all white, grey, red, yel-
low, green, blue, violet Bodies, as Paper, Afhes,
red Lead, Orpiment, Lidico, Bife, Gold, Sil-
ver, Copper, Grafs, blue Flowers, Violets,
Bubbles of Water tinged with various Colours,
Peacock's Feathers, the Tindure of Lignum

NepbrU

io8 G P T I C K S.

Nephriticiwi^ and fuch-like, in red homogeneal
Light appeared totally red, in blue Light totally
blue, in green Light totally green, and fo of other
Colours. In the homogeneal Light of any Cc-
lour they all appeared totally of that fame Co-
lour, with this only Difference, that fome of them
reflected that Light more ftrongly, others more
faintly. I never yet found any Body, which by
reflecting homogeneal Light could fenfibly change
its Colour.

From all which it is manifeft, that if the Sun's
Light confifted of but one fort of Rays, there
wduld be but one Colour in the whole World,
nor would it be poflible to produce any new Co-
lour by Reflexions and Refradlions, and by confe-
quence that the Variety of Colours depends upon
the Compofition of Light.

DEFINITION.

TH E homogeneal Light and Rays which
appear red, or rather make Obje<fls apr
pear fo, I call Rubrifick or Red-making ; thofe
which make Objects appear yellow, green, blue,
and violet, I call Yellow-making, Green-making,
Blue-making, Violet-making, and fo of the reft.
And if at any time I fpeak of Light and Rays
as coloured or endued with Colours, I would
be underftood to fpeak not philofophically and
properly, but grolly, and accordingly to fuch
Conceptions as vulgar People in feeing all thefe
Experiments would be apt to frame. For the
Rays to fpeak properly are not coloured. In
them there is nothing elfe than a certain Power

and

B O O K I. lop

dndDifpofition to ftir up aSenfatlon of this or that
Colour. For as Sound in a Bell or mufical String,
or other founding Body, is nothing but a trem-
bling Motion, and in the Air nothing but that
Motion propagated from the Objed, and in the
Senforium 'tis a Senfe of that Motion under the
Form of Sound ; fo Colours in the Objedt are no-
thing but a Difpofition to refledl this or that fort
of Rays more copioufly than the reftj in the
Rays they are nothing but their Difpolitions to
propagate this or that Motion into the Senforium,
and in the Senforium they are Senfations of thofe
Motions under the Forms of Colours.

PROP, III. Prob. I.

To defifte the Refra77gibility of the fever al
forts of homogeneal Light anfwering to
the feveral Colours,

FOR determining this Problem I made the
following Experiment. *
Exper, 7. When I had caufed the Redtilinear
Sides AF, GM, [in /%4.] of the Spedrum of
Colours made by the Prifm to be dirtiniflly de-
fined,^ as in the fifth Experiment of the firft Part
of this Book is defcribed, rhere were found in it
all the homogeneal Colours in the fame Order
and Situation one among another as in the
Spe^rum of fimple Light, defcribed in the
fourth Proportion of that Part. For the Cir-
cles of which the Spedrum of compound Light
* 5^^ «Ar AuthorV Lea. Optic. Partll. Se^.U. /. 239.

PT

jio O P T I C K S.

P T is compofed, and which in the middle Parts
of the Spectrum interfere, and are intermix'd with
one another, are not intermix'd in their outmoft
Parts where they touch thofe Redilinear Sides
AF and GM. And therefore, in thofe Redi-
linear Sides when diftindly defined, there is no
n^w Colour generated by Refradlion. I obferved
alfo, that if any where between the two outmoft
Circles TMF and PGA a Right Line, as y^,
w^as crofs to the Spectrum, fo as both Ends to
fall perpendicularly upon its Rectilinear Sides,
there appeared one and the fame Colour, and de-
gree of Colour from one End of this Line to
the other. I delineated therefore in a Paper
the Perimeter of the Speft'rum FAP GMT,
and in trying the third Experiment of the firft
Part of this Book, I held the Paper fo that
the Spe([lrum might fall upon this delineated
Figure, and agree with it exactly, whilft an
Affiiiant, whofe Eyes for diftinguilhing Colours
were more critical than mine, did by Right
Lines cc{Bj ^^, g^, &c. drawn crofs the Spe-
ctrum, note the Confines of the Colours, that
is of the red M a /3 F, of the orange a ^ ^ /3,
of the yellow ye^^, of the green g ^9 ^, of the
blue »iix9, of the indico iXfjua, and of the vio-
let AGA^. And this Operation being divers
times repeated both in the fame, and in feveral
Papers, I found that the Obfervations agreed
well enough with one another, and that the
Redilinear Sides MG and FA were by the faid
crofs Lines divided after the manner of a Mufi-
cal Chord. Let GM be produced to X, that
MX may be equal to GM, and conceive
2 GX,

BOOK L III

GX, aX, iX, «X, gX, yX, aX, MX, to be

in proportion to one another, as the Numbers,
I, I, f, 1, f, f, i'tt, 4, and fo to reprefent the Chords
of the Key, and of a Tone, a third Minor, a
fourth, a fifth, a fixth Major, a feventh and an
eighth above that Key : And the Intervals M a,
ay, ye, in, »', 'A, and aG, will be tlie Spaces
which the feveral Colours ( red, orange, yel-
low, green, blue, indigo, violet ) take up.

.Now thefe Intervals or Spaces fubtending the
Differences of the Refradlions of the Rays go-
ing to the Limits of thofe Colours, that is, to
the Points M, a, y, g, y\, j, A, G, may without
any fenfible Error be accounted proportional
to the Difierences of the Sines of Refradion of
thofe Rays having one common Sine of Inci-
dence, and therefore fince the common Sine of
Incidence of the mofl and leaft refrangible Rays
out of Glafs into Air was ( by a Method defcri-
bed above) found in proportion to their Sines
of Refraction, as 50 to yy and 78, divide the
Difference between the Sines of Refradiion 77
and 78, as the Line GM is divided by thofe
Intervals, and you will have 77, 77?, yy^, 77-f,
77t> 77h 77iy 78, the Sines of Refradion of thofe
Rays out of Glafs into Air, their common Sine
of Incidence being 50. So then the Sines of
the Incidences of all the red-making Rays out
of Glafs into Air, were to the Sines of their Re-
fradions, not greater than 50 to yy, nor lefs
than 50 to yyiy but they varied from one ano-
ther according to all intermediate Proportions.
And the Sines of the Incidences of the green-
making

Ill O P T t C K S.

making Rays were to the Sines of their Refradli-.
ons in all Proportions from that of 50 to 'j'jl^
unto that of 50 to 'j'j^. And by the like Limits
above-mentioned were the Refrddlions of the
Rays belonging to the reft of the Colours .de-
fined, the Sines of the red-making Rays extend-
ing from 77 to 'j'j^^ thofe of the orange-making
from 771- to.77-f, thofe of the yellow-making
from j'j}^ to 77 j, thofe of the green-making
from 'j'jy^ to "jji^^ thofe of the blue-making from
77 i to 'J'j^i thofe of the indigo-making from
'i']^ to ji^L^ and thofe of the violet from 77I to

Thefe are the Laws of the Refradlons made
out of Glafs into Air, and thence by the third
Axiom of the iirfl Part of this Book, the Laws of
the Refractions made out of Air into Glafs are ea-
fily derived.

Exper. 8. I found moreover, that when Light
goes out of Air through feveral contiguous re-
fracting Mediums as through Water and Glafs,
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 con-
trary Refractions 'tis fo corrected, that it emer-
geth in Lines parallel to thofe in which it was
incident, continues ever after to be white. But
if the emergent Rays be inclined to the inci-
dent, the Wnitenefs of the emerging Light will
by degrees in paffing on from the Place of Emer-
gence, become tinged in its Edges with Co-
lours. This I try'd by refraCting Light with
Prifms of Glafs placed within a Prifmatick Vef-
iel of Water. Now thofe Colours argue a di-
verging

B O O K I. 113

▼erging and feparation of the heterogeneous Rays
from one another by means of their unequal Re-
fractions, as in what follows will more fully ap-
pear. And, on the contrary, the permanent
whitenefs argues, that in like Incidences of the
Rays there is no fuch feparation of the emerging
Rays, and by confequence no inequality of their
whole Refrad:ions. Whence I feem to gather
the two following Theorems.

1. The Exceffes of t-he Sines of Refracflion of
feveral forts of Rays above their common SiAe of
Incidence when the Refractions are made out of
divers denfer Mediums immediately into one and
the fame rarer Medium, fuppofe of Air, are to
one another in a given Proportion.

2. The Proportion of the Sine of Incidence
to the Sine of Refradtion of one and the fame
fort of Rays out of one Medium into another,
is compofed of the Proportion of the Sine of
Incidence to the Sine of Refradtion out of the
firft Medium into any third Medium, and of the
Proportion of the Sine of Incidence to the Sine
of Refradtion out of that third Medium into the
fecond Medium.

By the firft Theorem the Refradtlons of the
Rays of every fort made out of any Medium in-
to Air are known by having the Refradtion of
the Rays of any one fort. As for inftance, if
the Refradtions of the Rays of every fort out
of Rain-water into Air be defired, let the com-
mon Sine of Incidence out of Glafs into Air be
fubdudted from the Sines of Refradtion, and

I the

114 O P T I C K S.

the ExcelTes will be 27, 27^, 27 1, 27J, ^jl,
2j\, 275, 28. Suppofe now that the Sine of
Incidence of the leaft refrangible Rays be to
their Sine of Refraction out of Rain-water into
Air as 3 to 4, and fay as i the difference of thofe
Sines is to 3 the Sine of Incidence, fo is 27 the
leaft of the ExcefTes above-mentioned to a fourth
Number 8 1 j and 8 1 will be the common Sine of
Incidence out of Rain-water into Air, to which
Sine if you add all the abovementioned ExcefTes,
you will have the defired Sines of the Refrad:ions
108, io8f, 108-I, iq8', 108 ", 1085, io8|,
109.

By the latter Theorem the Refradlion out of
one Medium into another is gathered as often
£s you have the Refractions out of them both in-
to any third Medium. As if the Sine of Inci-
dence of any Ray out of Glafs into Air be to its
Sine of Refradion, as 20 to 3 i, and the Sine of
Incidence of the fame Ray out of Air into Wa-
ter, be to its Sine of Refraction as 4 to 3; the
Sine of Incidence of that Ray out of Glafs into
Water will be to its Sine of RefraCtion as 20 to 3 1
and 4 to 3 jointly, that is, as the FaCtum of '20
and 4 to the FaCtum of 3 1 and 3, or as 80 to 93.

And thefe Theorems being admitted into Op-
ticks, there would be fcope enough of hand-
ling that Science voluminoufly after a new man-
ner *j not only by teaching thofe things which
tend to the perfection of Vifion, but alfo-by
determining mathematically all kinds of Phae-
nomena of Colours which could be produced

* Js is done in our Author'i Left. Optic. Part I. SeSl. III. and
IV. and Par til. Se^. II.

by

BOOK I. rx5*

by Refradlions. For to do this^ there is nothing
elle requifite 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 almoft all the Phsenomena
defcribed in thefe Books, befide fome others lefs
neceffary to the Argument; and by the fuccelles
I met with in the Trials, I dare promife, that to
him who fhall argue truly, and then try all things
with good 'Glaffes and fufficient Circumfpeclion,
the cxpeded Event will not be wanting. But he
is firft to know what Colours will arife from any
others mix'd in any affigned Proportion.

PROP. IV. Theor. hi.
Colours may be produced by Compofttion
ix^hich Jljall belike to the Colours of homO"
■ geneal Light as to the Appear a7ice of Co-
lour^ hut not as to the hrmiut ability of
Colour and Co7iflitution of Light. Aftd
thofe Colours by how much they are more
co7npounded by fo much are they lefs full
and inte?ife^ a?id by too much Compofition
they may be diluted and weflke?id till they
ceafey and the Mixture beco77ies white or
grey, 'There may be alfo Colours produced
by Compoftio?tj which are not fully like
any of the Colours of homoge?2eal Light.

FOR a Mixture of homogeneal red and yel-
low compounds an Orauge, like in appea-
I 2 ranee

ii6 O P T I C K S.

ranee of Colour to that orange which in the
feries of unmixed prifmatick Colours lies between
them; but the Light of one orange is homogeneal
as to Refrangibility, and that of the other is he-
terogeneal, and the Colour of the one, if viewed
through a Prifm, remains unchanged, that of
the other is changed and refolved into its compo-
nent Colours red and yellow. And after the fame
manner other neighbouring homogeneal Colours
may compound new Colours , like the in-
termediate 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
Compofition. For the yellow and blue on either
hand, if they are equal in quantity they draw the
intermediate green equally towards themfelves in
Compofition, and fo keep it as it were in i^qui-
librio, 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 ftill a middle Colour.
To this mix'd green there may be farther added
fome red and violet, and yet the green will not
prefently ceafe, but only grow lefs full and vivid,
and by increalingthe red and violet, it will grow
more and more dilute, until by the prevalence of
the added Colours it be overcome and turned into
whitenefs, or fome other Colour. So if to the
Colour of any homogeneal Light, the Sun's white
Light compofed of all forts of Rays be added,
tliat Colour will not vanifh or change its Species,
but be diluted, and by adding more and more
white it will be dikited more and more perpetu-
ally. Laflly, If r^d and violet be mingled, there
1 will

B O O K I. 117

will be generated according to their various Pro-
portions various Purples, fuch as are not like in
appearance to the Colour of any homogeneal
Light, and of thefe Purples mix'd v^dth yellow
and blue may be made other nev^ Colours.

PROP. V. Theor. IV.
Whiumjs and all grey Colours hetwee?i
white and blacky may be compounded of
Colours^ and the whitenefs of the Suns
Light is compounded of all the primary
^Colours mix'd in a due Proportion,

The Proof by Experiments.
Exper. 9.np H E Sun fliining into a dark Cham-

-*- ber through a little round hole in
the Window-fliut , and his Light being there
refraded by a Prifm to cafl his coloured Image
PT [in Fig. 5.] upon the oppofite Wall : I held
a white Paper V to that Image in fuch manner
that it might be illuminated by the colon r'd
Light refle(5ted from thence, and yet not inter-
cept any part of that Light in its paflage from
the Prifm to the Spectrum. And I found that
when the Paper was held nearer to any Colour
than to the reft, it appeared of that Coiour to
which it approached neareft^ but when it was
equally or almoft equally diftant from all the
Colours, fo that it might be equally illumina-
ted by them all it appeared white. And in this
laft fituation of the Paper, if fome Colours were

I 3 inter-

ii8 O P T I C K S.

, intercepted, the Paper loft its white Colour, and
appeared of the Colour of the reft of the Light
which was not intercepted. So then the Pa-
per was illuminated with Lights of various Co-
lours, namely, red, yellow, green, blue and
violet, and every part of the Light retained its
'proper Colour, until it was incident on the Pa-
per, and became refleded thence to the Eycj
fo that If it had been- either alone ( the reft of
the Light being intercepted ) or if it had a-
bounded moft , and been predominant in the
Light refled:ed from the Paper, it would have
tinged the Paper with its own Colour j and yet
being mixed with the reft of the Colours in a
due pi:oporti6n, it made the Paper look white,
and therefore by a Compoiition with the reft
produced that Colour. The feveral parts of
the coloured Light refleded from the Spectrum,
whilft they are propagated from thence through
the Air, do perpetually retain their proper Co-
lours, becaufe wherever they fall upon the Eyes
of any Spedator, they m.ake the feveral parts of
the Spectrum to appear under their proper Co-
lours. They retain therefore their proper Co-
lours when they fall. upon the Paper V, and fo
\)y the confuficn and perfed: mixture of thofe'
Colours compound the whitenefs of the Light
refleded from thence.

Expcr. lo. Let that Spe6trum or folar Image
]^T [in Fig. 6,'\ f^ll now upon the Lens MN
above four Liches broad, and about fix Feet di-
ftarit fi'om the Prifm ABC and fo figured that
it may caufe the coloured Light which diverg-^
^ph from the Prifm to converge and meet again-

"i a*.

"B O O K I. iig

at its Focus G, about fix or eight Feet diflant
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 folar Image
(fuppofe 2X pt) will appear upon it intenfely
coloured after the manner above-explained, and
that by receding from the Lens thofe 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 perfed: mixture they
will wholly vanifh and be converted into white-
nefs, the whole Light appearing now upon the
Paper like a little white Circle. And after-
wards by receding farther from the Lens, the
Rays which before converged will now crofs
one another in the Focus G, and diverge from
thence, and thereby make the Colours to appear
again, but yet in a contrary order; fuppofe at
^i, where the red t is now above which before
was below, and the violet p is below which be-
fore was above.

Let us now flop the Paper at the Focus G,
where the Light appears totally white and cir-
cular, and let us confider its whitenefs. I fay,
that this is compofed of the converging Colours.
For if any of thofe Colours be intercepted at
the Lens, the whitenefs will ceafe and degene-
rate into that Colour which arifeth from the
compofition of the other Colours which are not
intercepted. And then if the intercepted Co-
lours be let pafs and fall upon that compound
Colour, they mix with it, and by their mixture

I 4. reilore

I20 O P T I C K S.

ilore the whitenefs. 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 pafs, they will fall upon this compounded
orange, and together with it decompound a
white. So alfo if the red and violet be inter-
cepted, the remaining yellow, green and blue,
will compound a green upon the Paper, and
then the red and violet being let pafs will fall up-
on this green, and together with it decompound
a white. And that in this Compoiition of white
the feveral Rays do not fuffer any Change in their
colorific Qualities by ading upon one another,
but are only mixed, and by a mixture of their
Colours produce white, may farther appear by
thefe Arguments.

If the Paper be placed beyond the Focus G,
fuppofe at h^i, and then the red Colour at the
Lens be alternately intercepted, and let pafs a-
gain, the violet Colour on the Paper will not fuf^
fer any Change thereby, as it ought to do if the
feverai forts of Rays adted upon one another in
the Focus G, where they crofs. Neither will
the red upon the Paper be changed by any alter-
nate flopping, and letting pafs the violet which
crolieih it.

And if the Paper be placed at the Focus G,
and the white round Image at G be viewed
through the Pnfm HIK, and by the Refradiion
of that Prifm be tranllated to the place ri', and
there sppear tinged with various Colours, name-
ly, the violet at v and red at r, and others be-
tween, and then the red Colours at the Lens

be

B O O K I. 121

be often ftopp'd and let pafs by turns, the red
at r will accordingly difappear, and return as of-
ten, but the violet at v will not thereby fuffer any
Change. And fo by flopping and letting pafs
alternately the blue at the Lens, the blue at v
will accordingly difappear and return, without
any Change made in the red at r. The red there-
fore depends on one fort ot Rays, and the blue
on another fort, which in the Focus G v/here
they are commix'd, do not acTt on one another.
And there is the fame Reafon of the other Co-
lours.*

I confidered farther, that when the moft re-
frangible Rays P/>, and the leaft refrangible
ones T t, are by converging inclined to one ano-
ther, the Paper, if held very oblique to thofe
Rays in the Focus G, might refled: one fort of
them more copioully than the other fort, and
by that Means the remedied Light would be
tinged in that Focus with the Colour of the pre-
dominant Rays, provided thofe Rays feverally
retained their Colours, or coloriiic Qualities in
the Compofition of White made by them, in tliat
Focus. But if they did not retain them in that
White, but became all of them feverally endued
there with a Difpof^tion to flrike the Senfe with
the Perception of White, then they could never
lofe their Whitenefs by fuch Reflexions. I in-
clined therefore the Paper to the Rays very oblique-
ly, as in the fecond Experiment of this fecondPart
of the firft Book, that the moft refrangible Rays
might be more copioufiy refieded than the refl,
and the Whitenefs at Length changed fucceffively
into blue, indigo, and violet. Then I inclined it

the

122 O P T I C K S.

the contrary Way, that the leaft refrangible Rays
might be more copious in the reflected Light than
the reft, and the Whitenefs turned fucceffively to
yellow, orange, and red.

Laftly, I made an Inftrument X Y in fafhion
of a Comb, whofe Teeth being in number fix-
teen, were about an Inch and an half broad, and
the Intervals of the Teeth about two Inches
wide. Then by interpofmg fucceffively the
Teeth of this Inftrument near the Lens, I inter-
cepted Part of the Colours by the interpofed
Tooth, whilft the reft of them went on through
the Interval of the Teeth to the Paper DE, and
there painted a round Solar Image. But the Pa-
per I had iirft placed fo, that the Image might
appear white as often as the Comb was taken
away j and then the Comb being as was faid in-
terpofed, that Whitenefs by reafon of the inter-
cepted Part of the Colours at the Lens did al-
ways change into the Colour compounded of
thofe Colours which were not intercepted, and
that Colour was by the Motion of the Comb
perpetually varied fo, that in the paffing of every
Tooth over the Lens all thefe Colours, red, yel-
low, green, blue, and purple, did alw^ays fuc-
ceed one another. I caufed therefore all the
Teeth to pafs fucceffively over the Lens, and
when the Motion w^as flow, there appeared a
perpetual Succeffion of the Colours upon the
Paper : But if I fo much accelerated the Mo-
tion, that the Colours by reafon of their quick
Succeffion could not be diftinguiffied from one
another, the Appearance of the fmgle Colours
ceafed. There was no redj no yellow, nq

green.

B O O K I. 123

green, no blue, nor purple to be feen any lon-
ger, but from a Confulion of rhem all there a-
rofe one uniform white Colour. Of the Light
which now by the Mixture of all the Colours ap-
peared 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 re-»
tains its proper Colour till it ftrike the Senfo-
rium. If the Impreffions follow one another
flowly, fo that they may be feverally perceived,
there is made a diftind: Senfation of all the Co-
lours one after another in a continual SucceA
fion. But if the Impreffions follow one ano-
ther fo quickly, that they cannot be feverally
perceived, there arifeth out of them all one
common Senfation, which is neither of this
Colour alone nor of that alone, but hath it felf
indifferently to 'em all, and this is a Senfation
of Whitenefs. By the Quicknefs of the Succei^
lions, the Impreffions of the feveral Colours are
confounded in the Senforium, and out of that
Confufion arifeth a mix'd Senfation. If a burn-
ing Coal be nimbly moved round in a Circle
with Gyrations continually repeated, the whole
Circle will appear like Fire ; the reafon of which
is, that the Senfation of the Coal in the feve-
ral Places of that Circle remains imprefs'd on
the Senforium, until the Coal return again to
the fame Place. And fo in a quick Confecu-
tion of the Colours the Impreffion of every Co-
lour remains in the Senforium, until a Revolu-
tion of all the Colours be compleated, and that
firit Colour return again. The Impreffions there-
fore of all the fucceffive Colours are at once in

the

124 O P T I C K S.

the Senforium, and jointly ftir up a Senfation of ,
them all ; and fo it is manifeft by this Experi-
inent, that the commix'd Impreffions of all the
Colours do ilir up and beget a Senfation of white,
that is, that Whitenefs is compounded of all the
Colours.

And if the Comb be now taken away, that all
the Colours may at once pafs from the Lens to
the Paper, and be there intermixed, and toge-
ther refleded thence to the Spectator's Eyes; their
Impreffions on the Senforium being now more
fubtilly and perfe(5lly commixed there, ought
much more to ftir up a Senfation of White-
nefs.

You may inftead of the Lens ufe two Prifms
HIK and LMN, which by refracting the co-
loured Light the contrary Way to that of the
^rft Refraction, may make the diverging Rays
converge and meet again in G, as you fee repre-,
fented in the feventh Figure. For where they
meet and mix, they will Qompofe a white Light,
as when a Lens is ufed.

Exper. 1 1. Let the Sun's coloured Image P T
[in Fig. 8.] fall upon the Wall of a dark Cham-
ber, as in the third Experiment of the firft Book,
and let the fame be viewed through a Prifm
aifCy held parallel to the Prifm ABC, by whofe
Refraction that Image was made, and let it now
appear lower than before, fuppofe in the Place
S over-againft the red Colour T. And if you
go near to the Liiage P T, the SpeCtrum S will
appear oblong and coloured like the Image P T $
but if you recede from it, the Colours of the
SpeCtrum S will be contracted more and more,

and

B O O K T. 125

and at length vanifli, that Sped:rum S becoming
perfedly round and white j and if you recede yet
farther, the Colours will emerge again, but in a
contrary Order. Now that Spedlrum S appears
white in that Cafe, when the Rays of feveral
forts which converge from the feveral' Parts of
the Image P T, to the Prifm abc, are fo re-
fradted unequally by it, that in their PalTage
from the Prifm to the Eye they may diverge
from one and the fame Point of the Spedirum
S, and fo fall afterwards upon one and the
fame Point in the bottom of the Eye, and there
be mingled.

And farther, if the Comb be here made ufe of,
by whofe Teeth the Colours at the Image PT
may be fucceffively intercepted ; the Spe(ftrum S,
when the Comb is moved llowly, will be perpe-
tually tinged with fucceiTive Colours: But when
by accelerating the Motion of the Comb, the
Succeffion of the Colours . is fo quick that they
cannot be feverally feen, that Spedrum S, by a
confufed and mix'd Senfation of them all, will
appear white.

Exper. 12. The Su.i ihining* through a large
Prifm ABC [in Fig, 9.] upon a Comb X Y,
placed immediately behind the Prifm, his Light
which pafTed through the Interftices of the
Teeth fell upon a white Paper D E. The
Breadths of the Teeth were equal to their In-
terftices, and feven Teeth together w^th their
Interftices took up an Inch in Breadth. Now,
when the Paper was about two or three Inches
diftant from the Comb, the Light which paf-
fed through its. feveral Interftices painted fo

many

126 O P T I C K S.

many Ranges of Colours, kl^ mn, op^ qr^ &c.
which were parallel to one another^ and conti-
guous, and without any Mixture of white. And
thefe Ranges of Colours, if the Comb was moved
continually up and down with a reciprocal Mo-
tion, afcended and defcended in the Paper, and
when the Motion of the Comb was fo quick, that
the Colours could not be diftinguiflied from
one another, the whole Paper by their Con-
fufion and Mixture in the Senforium appeared
white.

Let the Comb now reft, and let the Paper
be removed farther from the Prifm, and the fe-
veral Ranges of Colours will be dilated and
expanded into one another more and more, and
by mixing their Colours will dilute one ano-
ther, and at length, when the diftance of the
Paper from the Comb is about a Foot, or a
little more (fuppofe in the Place 2D 2E) they
will fo far dilute one another, as to become
white.

With any Obftacle, let all the Light be now
ftopp'd which paffes through any one Literval
of the Teeth, fo that the Range of Colours which
comes from thence may be taken away, and
you will fee the Light of the reft of the Ranges
to be expanded into the Place of the Range taken
away, and there to be coloured. Let the in-
tercepted Range pafs on as before, and its Co-
lours falling upon the Colours of the other
Ranges, and mixing with them, will reftore the
Whitenefs.

Let the Paper 2 D 2 E be now very much in-
clined to the RaySj fo that the moft refrangible

Rays

BOOK I. 127

Rays may be more copioufly refleded than the
reft, and the white Colour of the Paper through
the Excefs of thofe Rays will be changed into
blue and violet. Let the Paper be as much in-
clined the contrary way, that the leaft refran-
gible Rays may be now more copioufly refledl-
ed than the reft, and by their Excefs the White-
nefs will be changed into yellow and. red. The
feveral Rays therefore in that white Light do
retain their colorific Qualities, by which thofe
of any fort, whenever they become more co-
pious than the reft, do by their Excefs and Pre-
dominance caufe their proper Colour to ap-

And by the fame way of arguing, applied to the
third Experiment of this fecond Part of the firft
Book, it may be concluded, that the white Colour
of all refracted Light at its very firft Emergence,
where it appears as white as before its Incidence,
is compounded of various Colours.

Exper, 13. In the foregoing Experiment the
feveral Intervals of the Teeth of the Comb do
the Office of fo many Prifms, every Interval pro-
ducitig the Phcenomenon of one Prifm. Whence
inftead of thofe Intervals ufing feveral Prifms,
I try'd to compound Whitenefs by mixing their
Colours, and did it by ufing only three Prifms,
as alfo by ufing only two as follows. Let two
Prifms ABC and a be, [in Fig. 10.] whofe re-
frading Angles B and b are equal, be fo placed
parallel to one another, that the refrading An-
gle B of the one may touch the Angle c at the
Bafe of the other, and their Planes C B and
cbj at which the Rays emerge, may lie in Di-

redum.

128 O P T I C K S.

re(5luin. Then let the Light trajedied through
them fall upon the Paper M N, diiftant about 8
or 12 Inches from the Prifms. And the Co-
lours generated by the interior Limits B and c
of the two Prifms, will be mingled at P T, and
there compound white. For if either Prifm be
taken away, the Colours made by the other will
appear in that Place P T, and when the Prifmi
is reftored to its Place again, fo that its Co-
lours may there fall upon the Colours of the
other, the Mixture of them both will reftore the
White nefs.

This Experiment fucceeds alfo, as I have tried,
when the Angle b of the lower Prifm, is a lit-
tle greater than the Angle B of the upper, and
between the interior Angles B and f, there in-
tercedes fome Space B c, as is reprefented in
the Figure, and the refrading Planes B C and
b c, are neither in Directum, nor parallel to one
another. For there is nothing more requilite
to the Succefs of this Experiment, than that
the Rays of all forts may be uniformly mixed
upon the Paper in the Place P T. If the moft
refrangible Rays coming from the fuperior
Prifm take up all the Space from M to P, the
Rays of the fame fort which come from the in-
ferior Prifm ought to begin at P, and take up
all the reft of the Space from thence towards
N. If the leaft refrangible Rays coming from
the fuperior Prifm take up the Space M T, the
Rays of the fame kind which come from the
other Prifm ought to begin at T, and take up
the remaining Space TIN. If oric fort of the
Rays which have intermediate Degrees of Re-

frangibility,

B O O K I. 129

frangibillty, and come from the fuperlor Prifm
be extended through the Space M Q^ and ano-
ther fort of thofe Rays through the Space M JR.,
and a third fort of them through the Space M S,
the fame forts of Rays coming from the lower
Prifm, ought to illuminate the remaining Spaces
QN, R N, S N, refpedively. And the fame is
to be underftood of all the other forts of Rays.
For thus the Rays of every fort will be fcattered
uniformly and evenly through the whole Space
MN, and fo being every where mix'd in the fame
Proportion, they muft every where produce the
fame Colour. And therefore, fince by this Mix-
ture they produce white in the Exterior Spaces
MP and TN, they muft alfo produce white
in the Interior Space PT. This is the reafon
of the Compolition by which Whitenefs was pro-
duced in this Experiment, and by what other
way foever I made the like Compofition, the Re-
fult was Whitenefs.

Laftly, If with the Teeth of a Comb of a due
Size, the coloured Lights of the two Prifms
which fall upon the Space PT be alternately in-
tercepted, that Space P T, when the Motion of
the Comb is flow, will always appear coloured,
but by accelerating the Motion of the Comb fo
much that the fucceffive Colours cannot be
diftinguifhed from one another, it will appear
white.

Exper, 14. Hitherto I have produced White-
nefs by mixing the Colours of Prifms. If now
the Colours of natural Bodies are to be min-
gled, let Water a little thicken'd with Soap be
agitated to raife a Froth, and after that Froth

K has

130 O P T I C K S.

has ftood a little, there will appear to one that
{hall view it intently various Colours every where
in the Surfaces of the feveral Bubbles j but to
one that fliall go fo far off, that he cannot diftin-
guifh the Colours from one another, the whole
Froth will grow white with a perfedl White-
nefs.

Exper. 15. Laftly, In attempting to compound
a white, by mixing the coloured Powders which
Painters ufe, I conlider'd that all coloured Pow-
ders do fupprefs and flop in them a very confi-
derable Part of the Light by which they are illu-
minated. For they become coloured by refledl-
ing the Light of their own Colours more co-
pioufly, and that of all other Colours more fpa-
ringly, and yet they do not refied: the Light of
their own Colours fo copioufly as white Bodies
do. If red Lead, for inflance, and a white Pa-
per, be placed in the red Light of the colour'd
Spedtrum made in a dark Chamber by the Re-
fraction of a Prifm, as is defcribed in the third
Experiment of the firfl Part of this Book ; the Pa-
per will appear more lucid than the red Lead,
and therefore refledis the red-making Rays more
copioufly than red Lead doth. And if they be
held in the Light of any other Colour, the
Light reiledled by the Paper will exceed the
Light reflefted by the red Lead in a much
greater Proportion. And the like happens in
Powders of other Colours. And therefore by
mixing fuch Powders, we are not to exped; a
flrong and full White, fuch as is that of Pa-
per, but fome dusky obfcure one, fuch as might
arife from a Mixture of Light and Darknefs,

I or

BOOK I. 131

or from white and black, that is, a grey, pr
dun, or ruflet brown, fuch as are the Colours'
of a Man's Nail, of a Moufe, of Afhcs, of or-
dinary Stohes, of Mortar, of Dull: and Dirt in
High-ways, and the like. And fuch a dark white
I have often produced by mixing colour 'd Pow-
ders. For thus one Part of red Lead, and five
Parts of Viridc lEris, compofed a dun Colour
like that of a Moufe. For thefe two Colours
were feverally fo compounded of others, that
in both together were a Mixture of all Co-
lours; and there was lefs red Lead ufed than
Viride Mr is, becaufe of the Fulnefs of its Co-
lour. Again, one Part of red Lead, and four
Parts of blue Bife, compofed a dun Colour
verging a little to purple, and by adding to
this a certain Mixture of Orpiment and Viride
Mris in a due Proportion, the Mixture loft its
purple TinQure, and became perfed:ly dun.
But the Experiment fucceedcd belt without Mi-
nium thus. To Orpiment I added by little
and little a certain full bright purple, which
Painters ufe, until the Orpiment ceafed to be
yellow, and became of a pale red. Then I di-
luted that red by adding a little Vitide JEris,
and a little more blue Bife than Viride Mris, un-
til it became of fuch 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 Whitenefs to that of Afhes, or of Wood newly
cut, or of a Man's Skin. The Orpiment re-
fledled more Light, than did any other of the
Powders, and therefore conduced more to the
Whitenefs of the com.pounded Colour than thev.
. K 2 fo

132 O P T I C K S.

To affign the Proportions accurately may be diffi-
cult, by reafon of the different Goodnefs of Pow-
ders of the fame kind. Accordingly, as the Co-
lour of any Powder is more or lefs full and lumi-
nous, it ought to be ufed in a lefs or greater Pro-
portion.

Now, confidering that thefe grey and dun Co-
lours may be alfo produced by mixing Whites
and Blacks, and by confequence differ from
perfedt Whites, not in Species of Colours, but
only in degree of Luminoufnefs, it is manifefl that
there is nothing more requifite to make them
perfectly white than to increafe their Light fuffici-
ently ; and, on the contrary, if by increafmg
their Light they can be brought to perfedl White-
nefs, it will thence alfo follow, that they are of
the fame Species of Colour with the beft 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,
Biie. and Viride Mrh ) and rubbed it thickly
upon the Floor of my Chamber, where the Sun
{hone upon it through the opened Cafement ;
and by it, in the fhadow, I laid a Piece of white
Paper of the fame Bignefs. Then going from
them to the diflance of 12 or 18 Feet, fo that
I could not difcern the Unevennefs of the Sur-
face of the Powder, nor the little Shadows let
fall from the gritty Particles thereof j the Pow-
der appeared intenfely white, fo as to tranfcend
even the Paper it felf in Whitenefs, efpecially
if the Paper were a little fliaded from the Light
of the Clouds, and then the Paper compared
5 with

,A

B O O K I. 133

with the Powder appeared of fuch a grey Colour
as the Powder had done before. But by laying
the Paper where the Sun fliines through the
Glafs of the Window, or by fhutting the Win-
dow that the Sun might fhine through the Glafs
upon the Powder, and by fuch other fit Means of
iiicreafing or decreafnig the Lights wherewith the
Powder and Paper were illuminated, the Light
wherewith the Powder is illuminated may be*
made ilronger in fuch a due Proportion than
the Light wherewith the Paper is illuminated,
that they fhall both appear exadly alike in
Whitenefs. For when I was trying this, a Friend
coming to vifit me, I ftopp'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 beft, and wherein they dif-
fered ? And after he had at that diflance viewed
them well, he anfwer'd, that they were both good
Whites, and that he could not fay which was
beft, nor wherein their Colours differed. Now,
if you confider, that this White of the Powder
in the Sun-fliine was compounded of the Co-
lours which the component Powders ( Orpi-
ment. Purple, Bife, and Viride JEris ) have in
the fame Sun-fhine, you muft acknowledge by
this Experiment, as well as by the former, that
perfedt Whitenefs may be compounded of Co-
lours.

From what has been faid it is alfo evident,
that the Whitenefs of the Sun's Lisrht is com-
pounded of all the Colours wherewirh the feve-
ral forts of Rays whereof that Light confifts,
when by their feveral Refrangibilities they are

K 3 fepa-

134 O P T I C K S.

feparated from one another, do tinge Paper or any
other white Body whereon they fall. For thofe
Colours {hy Prop.ll. Part 2.) are unchangeable,
and whenever all thofe Rays w^ith thofe their Co-
lours are mix'd again, they reproduce the fame
white Light as before.

PROP. VI. Prob. II.

Lt a mixture of Primary Colour s-^ the
^luantity and S^uality of each bei7tg
given^ to know theColour of the Compound,

WITH the Center O [m Fig. 11.] and
Radius OD defcribe a Circle ADF, and
diltinguiih its Circumference into feven Parts
DE, EF, FG, GA, AB, B C, CD, propor-
tional to the feven Mufical Tones or Intervals
of the eight Sounds, «So/, /^, fa^ fol^ la^ mi, fa,
fol, contained in an eight, that is, proportional
to the Number ~, 75, ts, |, 15, is, \. Let the firfl
Part I>E reprefent a red Colour, the fecond E F
orange, the third F G yellow, the fourth C A
green, the fifth AB blue, the fixth BC indigo,
and the feventh C D violet. And conceive that
thefe are all the Colours of uncompounded Light
gradually pafiing into one another, as they do
when made by Prifms j the Circumference
DEFGABCD, reprefenting the whole Series
of Colours from one end of the Sun's colour'd
Image to the other, fo that from D to E be
all degrees of red, at E the m.ean Colour be-
tween red and orange, from E to F all de-
crees

B O O K I. 135

grees of orange, at F the mean between orange
and yellow, from F to G all degrees of yellow,
and fo on. Let p be the Center of Gravity
of the Arch D E, and q^ r, j, t, u^ Xy the Cen-
ters of Gravity of the Arches E F, F G, G A, -
A B, B C, and C D refpedively, and about
thofe Centers of Gravity let Circles proportio-
nal to the Number of Rays of each Colour in
the given Mixture be defcrib'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-ma-
king Rays in the Mixture, and fo of the reft.
Find the common Center of Gravity of all thofe
Circles p, q^ r, s, t, z/, x. Let that Center be
Z; and from the Center of the Circle ADF,
through Z to the Circumference, drawing the
Right Line O Y, the Place of the Point Y in the
Circumference Ihall ihew the Colour arifmg from
the Compofition of all the Colours in the given
Mixture, and the Line OZ fhall be propor-
tional to the Fulnefs or Intenfenefs of the
Cok)ur, that is, to its diftanCe from Vv^iitenefs.
As if Y fall in the middle between F and G,
the compounded Colour fliall be the beft yel-
low J if Y verge from the middle towards F
or G, the compound Colour fliall accordingly
be a yellow, verging towards orange or green.
If Z fall upon the Circumference, the Colour
fhall be intenfe and florid in the higheft Degree ;
if it fall in the mid- way between the Circum-
ference and Center, it fhall be but half fo
intenfe, that is, it fhall be fuch a Colour as
would be made by diluting the intenfeil yellow

K 4 with

136 O P T I C K S.

with an equal quantity of whitenefs ; and if it
fall upon the center O, the Colour fhall have loft
all its intenfenefs, 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
fhall not be any of the prifmatick Colours, but
a purple, inclining to red or violet, according-
ly as the point Z lieth on the fide of the line
DO towards E or towards C, and in general
the compounded violet is more bright and more
fiery than the uncompounded. Alfo if only two
of the primary Colours which in the circle are
pppofite to one another be rnixed in an equal
proportion, the point Z {hall fall upon the cen-
ter O, and yet the Colour compounded of thofe
two fhall not be perfectly white , but fome
faint anonymous Colour, For I could never
yet by mixing only two primary Colours pro-
duce a perfeft white. Whether it may be com-
pounded of a mixture of three taken at equal
diftances in the circumference I do not know,
but of four or five I do not much queftion but
it may. But thefe are Curiofities of little or no
moment to the underflanding the Phaenomena
of Nature. For in all whites produced by Na-
ture, there ufes to be a mixture of all forts of
Rays, and by confequence a compofition of all
Colours.

To give an inftance of this Rule; fuppofe a
Colour is compounded of rhefe homogeneal
Colours, of violet one part, of indigo one part,
of blue two parts, of gi^een three parts, of yel-
)pw five parts, of orange fix parts, and of red

ten

B O O K I. 137

ten parts. Proportional to thefe parts defcribe
the Circles x, v, /, s, r, q, p, refpedively, that is,
fo that if the Circle x be one, the Circle 1; may-
be one, the Circle f two, the Circle s three, and
the Circles r, q and/>, five, fix and ten. Then I
find Z the common center of gravity of thefe
Circles, and through Z drawing the Line OY,
the Point Y falls upon the circumference between
E and F, fomething nearer to E than to F, and
thence I conclude, that the Colour compounded
of thefe Ingredients will be an orange, verging a
little more to red than to yellow. Alfo I find
that OZ is a little lefs than one half of O Y, and
thence I conclude, that this orange hath a little
lefs than half the fulnefs or intenfenefs of an un-
compounded orange j that is to fay, that it is
fuch an orange as may be made by mixing an ho-
mogeneal orange with a good white in the pro-
portion 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 pra-
dtice, though not mathematically accurate ; and
the truth of it may be fufliciently proved to Senfe,
by flopping any of the Colours at the Lens in the
tenth Experiment of this Book. For the refi: of
the Colours which are not fi:opp'd, but pafs on to
the Focus of the Lens, will there compound
either accurately or very nearly fuch a Colour, as
by thi^ Rule ought to refult from their Mixture.

FRO P.

138 O P T I C K S.

PROP. VIL The OR. V.

/ill the Colours in the Univerfe which are
made by Lights and depend not on the
Power of Imagination^ are either the
Colours of homogeneal Lights^ or com-
founded of thefe-^ and that either accu-
rately or very nearly^ according to the,
Rule of the foregoing Problem,

FOR it has been proved (in Frop. i. Fart 2.)
that the changes of Colours made by Refra-
d:ions do not arife from any new Modifications of
the Rays imprefs'd by thofe Refradions, and by
the various Terminations of Light and Shadow,
as has been the conftant and general Opinion of
Philofophers. It has alfo been proved that the
feveral Colours of the homogeneal Rays do con-
ftantly anfwer to their degrees of Refrangibility,
[Prop. I. Part i. andPrc/^. 2. Part 2.) and that
their degrees of Refrangibility cannot be changed
by Refractions and Reflexions [Prop. 2. Part i.)
and by confequence that thofe their Colours
are likewife immutable. It has alfo been pro-
ved diredlly by refrafting and reflecting homo-
geneal Lights apart, that their Colours cannot be
changed, [Prop. 2. Part 2.) It has been proved
alfoj that when the feveral forts of Rays are mix-
ed, and in croflmg pafs through the fame'fpace,
they do not ad- on one another fo as to change
each others colorific qualities. [Exper. 10. Part 2.)
but by mixing their Adions in the Senforium be-
get

BOOK I. 139

get a Senfation differing from what either would
do apart, that is a Senfation of a mean Colour
between their proper Colours j and particularly
when by the concourfe and mixtures of all forts
of Rays, a white Colour is produced, the white
is a mixture of all the Colours which the Rays
would have apart, [Frop. 5. Part 2.) The Rays
in that mixture do not lofe or alter their feveral
colorific qualities, but by all their various kinds
of Adions mix'd in the Senforium, beget a Sen-
fation of a middling Colour between all their Co-
lours, which is whitenefs. For whitenefs is a
mean between all Colours, having it felf indiffe-
rently to them aU, fo 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 prefcnrly lofe its Colour, but a white Powder
mix'd with any Colour is prefently tinged with
that Colour, • and is equally capable of being
tinged with any Colour whatever. It has been
fhewed alfo, that as the Sun's Light is mix'd of
all forts of Rays, fo its whitenefs is a mixture of
the Colours of all forts of Rays -, thofe Rays ha-
ving from the beginning their feveral colorific
qualities as well as their feveral Refrangibilities,
and retaining them perpetually unchanged not-
withftanding any Refradtions or Reflexions they
may at any time fuffer, and that whenever any
fort of the Sun's Rays is by any means (as by
Reflexion in Exper. g. and 10. Part i. or by
Refradion as happens in all Refractions) fepara-
ted from the reft, they then manifell; their proper
Colours. Thefe things have been prov'd, and
the fujn of all this amounts to the Propofitioa

here

I40 O P T I C K S.

here to be proved. For if the Sun's Light is
mix'd of feveral forts of Rays, each of which
have originally their feveral Refrangibilities and
colorific Qualities, andnotwithftanding their Re-
.fraftions and Reflexions, and their various Sepa-
rations or Mixtures, keep thofe their original
Properties perpetually the fame without alterati-
on ; then all the Colours in the World muft be
fuch as conftantly ought to arife from the origi-
nal colorific qualities of the Rays whereof the
Li2;hts confift by which thofe Colours are feen.
And therefore if the reafon of any Colour what-
ever be required, we have nothing elfe to do than
to confider how the Rays in the Sun's Light have
by Reflexions or Refraftions, or other caufes, been
parted from one another, or mixed together j or
otherwfe to find out what forts of Rays are in the
Light by which that Colour is made, and in what
Proportion ; and then by the laft Problem to
learn the Colour which ought to arife by mixing
thofe Rays (or their Colours) in that proportion.
I fpeak here of Colours fo far as they arife from
Light. For they appear fometimes by other Cau-
fes, as when by the power of Phantafy wc fee Co-
lours in a Dream, or a Mad-man fees things be-
fore him which are not there; or when we fee
Fire by flriking the Eye, or fee Colours like the
Eye of a Peacock's Feather, by prefTing our Eyes
in either corner whilft we look the other way.
Wliere thefe and fuch like Caufes interpofe nor,
the Colour always anfwers to the fort or forts
of the Rays whereof the Light confifts, as I
have conftantly found in whatever Phasnomena of
Colours I have hitherto been able to examine.

I aiall

B O O K I. 141

I {hall in the following Proportions give inftan-
ces of this in the Phaenomena of chiefeft note.

PROP, VIII. Prob. III.

By the difcove7'ed Properties of Light to
explain the Colours made by Prijms.

LET ABC [in Fig. 12.] reprefent a Prifnl
refracting the Light of the Sun, which
comes into a dark Chamber through a hole F <j>
almofl as broad as the Prifm, and let M N re-
prefent a white Paper on which the refracted
Light is caft, and fuppofe the moil refrangible
or deepeft violet-making Rays fall upon the
Space Pttj the leaft refrangible or deepeft red-
making Rays upon the Space T7, the rniddle,
fort between the Indigo-making and blue-mu-
king Rays upon the Space Qv, the middle fort
of the green-making Rays upon the Space Rp,
the middle fort between the yellow-making and
orange-making Rays upon the Space S a-, and o-
ther intermediate forts upon intermediate Spa-
ces. For fo the Spaces upon which the feveral
forts adequately fall will by reafon of the diffe-
rent Refrangibility of thofe forts be one lower
than another. Now if the Paper MN be fo
near the Prifm that the Spaces PT and ^-j do
not interfere with one another, the diftance be-
tween them T it will be illuminated by all the
forts of Rays in that proportion to one another
which they have at their very firft coming out

of

142 O P T I C K S.

of the Prifm, and confequently be white. But
the Spaces P T and ttT on either hand, will not
be illuminated by them all, and therefore will
appear coloured. And particularly at P, where
the outmofl violet-making Rays fall alone, the
Colotir mufi: be the deepeft violet. At Q^here
the violet-making and indigo-making Rays are
mixed, it mufl: 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
muft (by the conftrudtion of the fecond Pro-
blem ) compound a middle Colour between in-
digo arid blue. At S where all the Rays are
mixed, except the red-making and orange-ma-
king, their Colours ought by the fame Rule to
compound a faint blue, verging more to green
than indigo. And in the progrefs 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 whitenefs. ^

So again, on the other fide of the white at r,
where the leaft refrangible or utmoft red-ma-
king Rays are alone, the Colour mull: be the
deepeft red. At a the mixture of red and o-
range will compound a red inclining to orange.
At ^ the mixture of red, orange, yellow, and
one half of the green muft compound a middle
Colour between orange and yellow. At ^ 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 progrefs

from

B O O K I. 143

from V to TT, where by a mixture of all forts of
Rays it will become white.

Thefe Colours ought to appear were the Sun*s
Light perfedly white: But becaufe it inclines to
yellow, the Excefs 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 fo the Colours In
order from P to r ought to be violet, indigo,
blue, very faint green, white, faint yellow, o-
range, red. Thus it is by the computation : And
they that pleafe to view the Colours made by a
Prifm will find it fo in Nature.

Thefe are the Colours on both fides the white
when the Paper is held between tlie Prifm and
the Point X where the Colours meet, and the
interjacent white vaniflies. For if the Paper be
held flill farther off from the Prifm, the mofl
refrangible and leaft refrangible Rays will be
wanting in the middle of the Light, and the refl .
of the Rays which are found there, will by mix-
ture produce a fuller green than before. Alfo
the.yellowand blue will now become lefs com-
pounded, alid by confequence more intenfe than
before. And this alfo agrees with experience.

And if one look through a Prifm upon a
white Objed: cncompafTed with blacknefs or
darknefs, the reafon of the Colours arifing on
the edges is much the fame, as will appear to
ons that fhall a little confider it. If a black Ob-
jed: be encompafTed with a white one, the Co-
lours which appear through the Prifm are to be
derived from the Light of the white one, fpread-
ing into the Regions of the black, and therefore

they

144 O P T I C K S.

they appear in a contrary order to that, when a
white Objeft is furrounded with black. And the
fame is to be underftood when an Obje6l is view-
ed, whofe parts are fome of them lefs luminous
than others. For in the borders of the more and lefs
luminous Parts, Colours ought always by the fame
Principles to arife from the Excefs of the Light
of the more luminous, and to be of the fame
kind as if the darker parts were black, but yet to
be more faint and dilute.

What is faid of Colours made by Prifms may
be eafily applied to Colours made by the GlalTes
of Telefcopes or Microfcopes, or by the Hu-
mours of the Eye. For if the Objedl-glafs of
a Telefcope be thicker on one fide than on the
other, or if one half of the Glafs, or one half
of the Pupil of the Eye be cover'd with any
opake fubftance j the Objedi-glafs, or that part of
it or of the Eye which is not cover'd, may be
confider'd as a Wedge with crooked Sides, and
* every Wedge of Glafa or other pellucid Subftance
has the effect of a Prifm in refradiing the Light
which paffes through it *.

How the Colours in the ninth and tenth Ex-
periments of the lirfl Part arife from the diffe-
rent Reflexibility of Light, is evident by whar
was there faid. But it is obfervable in the ninth
Experiment, that whilft the Sun's dired: Light
is yellow, the Excefs of the blue-making Rays
in the refleded beam of Light MN, fuffices
only to bring that yellow to a pale white incli-
ning to blue, and not to tinge it with a mani-

* See eur AuthorV Left. Optic. Part II. Se^. II. fa^. i6g, &(.

feftly

B Q O K I. 145

feftly blue Colour. To obtain therefore a better
blue, I ufed inftead of the yellow Light of the
Sun the white Light of the Clouds^ by varying a
little the Experiment, as follows.

Exper, 16. Let HFG [in Fig. 13.] repre-
fent a Prifm in the open Air, and S the Eye of
the Spedator, viewing the Clouds by their
Light coming into the Prifm at the Plane Side
FIGK, and refleded in it by its Bafe HEIG,
and thence going out through its Plane Side
H E F K to the Eye. And when the Prifm and
Eye are conveniently placed, fo that the Angles
of Incidence and Reflexion at the Bafe may be
about 40 Degrees, the Spe£latpr will fee a Bow
MN of a blue Colour, running from one End
of the Bafe to the other, with the Concave Side
towards him, and the Part of the Bafe IMNG
beyond this Bow will be brighter than the other
Part E M N H on the other Side of it. This blue
Colour M N being made by nothing elfe than by
Reflexion of a fpecular Superficies, feems fo odd
a Phaenomenon, and fo difficult to be explain-
ed by the vulgar Hypothefis of Philofophers,
that I could not but think it deferved to be taken
Notice of. Now for underftanding the Rea-
fgn of it, fuppofe the Plane. ABC to cut the
Plane Sides and Bafe of the Prifm perpendicu-r
larly. From the Eye to the Line B C, wherein
that Plane cuts the Bafe, draw the Lines S^
and S/', in the Angles S^^: 50 degr. i, and Stc
49 degr. Vt, and the Point p will he the Limit
beyond which none of the moft refrangible
Rays can pafs through the Bafe of the Prifm,
and be refraded, whofe Incidence is fuch thai;

L t'hey

14,6 OPTIC K S.

they may be refieded to the Eye ; and the Point
t will be the like Limit for the leaft refrangi-
ble. Rays, that is, beyond which none of them
can pafs through the Bafe, whoie Incidence is
fuch that by Reflexion they may come to the
Eye. . And the Point r taken in- the middle
Way betv/een p and ^, will be the like Limit
for the meanly . refrangible Rays. And there-
fore all the leaft refrangible Rays which fall
upon the Bafe beyond /, that is, between t and B,
and can come from thence to the Eye, will be
refledted thither : But on this fide t^ that is,
between t and f, many of thefe Rays will be
tranfmitted through the Bafe. And all the moft
refrangible Pvays which fall upon the Bafe be-
yond ^, that is, between p and B, and can by
Reflexion come from thence to the Eye, will be
refleded thither, but every where between p
and r, many of thefe Rays will get through the
Bafe, and be refraded j and the fame is to be
underftood of the meanly refrangible Rays on
either fide of the Point r. Whence it follows,
that the Bafe of the Prifm rriufl every where
between t and B, by a total Reflexion of all forts
of Rays to the Eye, look white and bright.
And every where between p and C, by reafon of
the Tranfmiflion of many Rays of every fort,
look more pale, obfcure, and dafk. But at r,
and in other Places between p and /, where all
the more refrangible Rays are refledied to the
Eye, and many of the lefs refrangible are. tranf-
.mitted, the Excefs of the moft refrangible in
the refleded Light will tinge that Light with
their Colour, which is violet and blue. Arid-

this

B O O K I. 147

this happens by taking the Line C/r/B any
.where between the Ends of the Prilm H G
and EI.

PROP, IX. prob. r\^.

By the difcGvered Pf'operties of Lighi to
explain the Colours of the Rain-bow,

THIS Bow never appears, but where it
n|ins in the Sun-fhine, and may be made
artiticially by fpouting up Water which may
break aloft, and fcatter into Drops, and fall down
like Rain. For the Sun fliining upon thefe
Drops certainly caufes the Bow to appe^f* to a
Spectator ftanding in a due Polition 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 un-
derllood by fome of the Antients, and of late
more fully difcover'd and explain'd by the fa-
mous Antoniiis de Dominis Archbilhop of ^pa-
lato, in his Book De Radiis Visits & Liicis, pub-
lifhed by his Friend Bartolus at Venice^ in the
Year 161 1,. and written above 20 Yeai's before.
For he teacher' there how the interior Bow is
made in round Drops of Raiii by two Refracti-
ons of the Sun's Light, and one Reflexion be-
tween them, and the exterior by two Refradti-
ons, and two forts of Reflexions between them
in each Drop of Vv^ater, and proves his Expli-
cations by Experiments made witba Phial full
lof Water, and with Globes of Glafs filled

L 2 with

148 O P T I C K S.

with Water, and placed in the Sun to make the
Colours of the two Bows appear in them. The
fame Explication Des-Cartes hath purfued in his-
Meteors, and mended that of the exterior Bow.
But whilft they underftood not the true Ori-
gin of Colours, it's neceffary to purfue it here
a little farther. For underftanding therefore how
the Bow is made, let a Drop of Rain, or any
other fpherical tranfparent Body be reprefented
by the Sphere BNFG, [in Fig. 14.] defcribed
with the Center C, and Semi-diameter C N.
And let AN be one of the Sun's R^s inci-
dent upon it at N, and thence refradled to F,
where let it either go out of the Sphere by Re-
fraction towards V, or be refle<5ted to G ; and
at G " let it either go out by Refradion to R, or
be refledled to H; and at H let it go out by
Refrad:ion 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 Per-
pendiculars CD and CE, and produce CD till
it fall upon the Circumference at L. Parallel to
the incident Ray AN draw the Diameter B Q^
and let the Sine .of Incidence out of Air into
Water be to the Sine of Refradion as I to R.
Now, if you fuppofe the Point of Incidence N
to move from the Point B, continually till it
come to L, the Arch Q F will firil increafe and
then decrcafe, and fo will the Angle A X R
which the Rays A N and G R contain ; and the
Arch QJ' and Angle AXR will be biggeft
when ND is to CN as -/H^RR to v/ 3 RR, in
which cafe NE will be to ND as 2 R to I. Alfo
the Angle AYS, which the Rays AN and HS

contain

B O O K I. 149

contain will firft decreafe, and then increafe and
grow leaft when ND is to CN as y'llZlRK to
^8RR, in which cafe NE will be to ND, as
3 Rtol. And fo the Angle which the next emer-
gent Ray ( that is, the emergent Ray after three
Reflexions) contains with tlie incident Ray AN
will come to its Limit when ND is to CN
as y/li— KR to / 15 RR, in which cafe NE will
be to N D as 4 R 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 N D is to
CN as /ii — KK to v/ 24 RR, in which cafe NE
will be to ND as 5 R to I i and fo on infinitely,
the Numbers 3,8, 15, 24, &c. being gather'd by
continual Addition of the Terms of the arithme-
tical Progreflion 3, 5, 7, 9, ^c. The Truth of all
this Mathematicians will ealily examine.* > .

Now it is to be obferved, that as when the Sun
comes to his Tropicks, Days increafe and decrcafe
but a very little for a great while together j fo when
by increaling the diflance CD, thefe Angles come
to their Limits, they vary their quantity but very
little for fome time together, and therefore a fir
greater Number of the Rays which fill upon all
the Points N in the Quadrant BL, {hall emcrg. in
theLimits of thefe Angles, than in any other Incli-
nations. And farther it is to be obferved, that the
Rays which differ in Refrangibility will have dif-
ferent Limits of their Angles of Emergence, and
by confequence according to their different De^
grees of Refrangibility emerge moft copioufly

_, * This is demonjirated in our Author'j Ledl. Optic Part I. Se^l. IV.
Prop. 35 and 36.

L 3 in

150 O P T I C K S.

in different Angles, and being feparated from one
another appear each in their proper Colours,
And v/hat thole Angles are may be eaiily ga-
ther'd from the foregoing Theorem by Com-
putation.

For in the leaft refrangible Rays the Sines I
and R (as was found above) are io8 and 8i,
and thence by Computation the greateft Angle
AXR will be found 42 Degrees and 2 Minutes,
and the kail Angle AYS, 50 Degrees and c^j
Minutes. And in the moll refrangible Rays the
Sines I and R are 109 and 81, and thence by
Computation the greateft Angle AXR wilh be
found 40 Degrees and 17 Minutes, and the leaft
Angle AYS 54 Degrees and 7 Minutes.

Suppofe now \^\'^x. O [ in Fig. 15. ] is the Spe-
6lator's Eve, 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 Mm. 50 Degr. c^-j Min. and 54 Degr. 7 Min.
refpe6tively, and thefe Angles turned about
their common Side O P, fhall with their other
Sides OE, OF; OG, OH, defcribe the Verges
of two Rain-bows AF BE and CHDG. Foi*
if E, F, G, H, be drops placed any where in
the conical Superficies defcribed by OE, OF,
OG, OH, and be illuminated by the Sun's Rays
SE, SF, SG, SH; the Angle SEO being e-
qual to the Angle POE, or 40 Degr. 17 Min.
ihall be the greateft Angle in which the moft
refrangible Rays can after one Pvetiexion be re-
fradled to the Eye, and therefore all the Drops
in the Line O E Inall fend the moft refrangible
Rays moft copioufly to the Eye, and thereby

ftrike

BOO KllC fi5a

i\nkt the ^fes with the deepeft violet Colour in
that Region. And in like manner the^^ngle SFO
being equal to the Angle POF, or 42 Degr.
2 Min. fhall be the greateft in which the Icall: re-
frangible Rays after one Reflexion can emerge
out of the Drops, and therefore thofe Rays
.fliall come moft copioufly to the Eye from the
Drops in the Line O F, and flrike the Senfes with
the deepeft red Colour in that Region. And by
■the fame Argument, the Rays which have inter-
mediate Degrees of Refrangibility fliall comeiinofl
copioufly from Drops between E and F, and'llirike
the Senies with the intermediate Colours, in the
Order which their Degrees of Refrangibility rc-
€|uiie, that is in the Progfefs 'from E toF, or
from the infide of the Bow to the outfide in this
order, violet, indigo, blue, green, ycllow,"^^ orange,
red. But the violet, by the mixtiue of the white
Light of the Clouds, will appear laint and in-
cline to purple.

- Again, the Angle SGO being equal to the
Angfe POG, or 5oGr. 51 Min. fhall be the Iciift
Angle in which the leaft refrangible Rays can
after two Reflexions emerge out of the Drops,
and therefore the leafl refrangible Rays lliall
come moffc copioufly to the Eye from the Drops
i-n the Line OG, and firike the StnfQ with the
deepeft red in that Region. And the Angle
SHO being equal to the Angle POH, or 54 Gr.-
7 Min. fliall be the leafl Angle, in which the moft
refrangible Rays after two Pvcfiexions can emerge
out of the Drops J and therefore thofe Rays
fhall come mofl copioufly to the Eye froni^
the Drops in the Line OFI, and ilrike the Senfes

L 4 with

152 O P T I C K S.

with the deepeft violet in that Region. And by the
fame Argument, the Drops in the Regions be-
tween G and H fliall ftrike the Senfe with the in-
termediate Colours in the Order which their
Degrees of Refrangibility require, that is, in the
Progrefs from G to H, or from the infide of the
Bow to the outiide in this order, red, orange, yel-
low, green, blue, indigo, violet. And fmce
thefe four Lines OE, OF, OG, OH, may be
■fituated any where in the above-mention'd co-
iiical Superficies ; what is faid of the Drops
and Colours in thefe Lines is to be underftood
of the Drops and Colours every where in thofe
Superficies.

Thus iliall there be made tv^o Bows of Co-
lours, an interior and ftronger, by one Reflexion
jn the Drops, and an exterior and fainter by
two J for the Light becomes fainter by every
Reflexion. And their Colours fhall lie in a con-
trary Order to one another, the red of both Bows
bordering upon the Space GF, which is be-
tween the Bows. The Breadth of the inte-
rior Bow EOF meafured crofs the Colours fhall
be I Degr. 45 Min. and the Breadth of the ex-
terior GOH fhall be 3 Degr. 10 Min. and the
diflance between them GOF fhall be 8 Gr. 15
Min. the greateft Semi-diameter of the inner-
mofl, that is, the Angle POF being 42 Gr. 2
Min. and the leafl Semi-diameter of the outer-
mofl POG, being 50 Gr. 57 Min. Thefe are
the Meafures 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 in^
creafed, and ^heir Diflance decreafed by half a

Degree,'

B O O K I. 153

Degreq, and (o the breadth of the interior Iris
will be 2 Degr. J5 Min. that of the exterior 3
Degr. 40 Min. their diftance 8 Degr. 25 Min.
the greateft Semi-diameter of the interior Bow
42 Degr. 17 Min. and the leail of the exterior
50 Degr. 42 Min. And fuch are the Dimenfions
of the Bows in the Heavens found to be very
nearly, when their Colours appear ftrong and
perfed:. For once, by fuch means as I then liad,
I .meafured the greateft 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, befides the outmoft faint red ob-
fcured by the brightnefs of the Clouds, for
which we may allow 3 or 4 Minutes more. , The
breadth of the blue was about 40 Minutes more
belides the violet, .which was fo much obfcu-
red by the brightnefs of the Clouds, that I could
not meafure its breadth. But fuppofing 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 t De-
grees, as above. The leail diftance between this
Iris and the exterior Iris was about 8 De2;rees and
30 Minutes. The exterior Iris was broader than
the interior, but fo faint, efpecially on the blue
fide, that I could not meafure its breadth di-
ftindlly. At another time when both Bows ap-
peared more diftind:, I meafured 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 fame Colours in the interior
as 3 to 2.

this

154 O P T I C K S.

This Explication of the Rain-bow is yet far-
ther confirmed by the known Experiment (made
by Antonius de Domini s and Des-Cartes ) of
hanging up any where in the Sun-iliine a Glafs
Globe filled with Water, and viewing it ih fuch
a poflure, 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 ( fuppofe at O ) {hall fee a full i:ed
Colour in that fide of the Globe oppofed to
the Sun as 'tis reprefented at F, and if that An-
^gle become lefs (fuppofe by depreflnig the Globe
to E) there will appear other Colours, yellow,
green and blue fucceflive in the fame fide of
the Globe. But if the- Angle be made about
50 Degrees (fuppofe by lifting up the Globe to
G) there will appear a red Colour in that Me
of the Globe towards the Sjun, and if the An-
gle be made greater (fuppofe by lifting up tlie
Globe to H) the red will turn fucceffively to
the other Colours, yellow, green and blue. The
fame thing I have tried, by letting a Globe reft,
and raifing or depreifing the Eye , or other-
wife moving it to make the Angle of ajufl mag*
nitude. ;u y-.

I have heard it reprefented, that if the Light
of a Candle be refraded by a Prifm to the Eye ;
when the blue Colour falls upon the Eye, the
Spe<5tator {hall fee red in the Prifm, and when
the red falls upon the Eye he fhall fee blue ;
and if this were certain , the Colours of . the
Globe and Rain-bow ought to appear in a. con-
nary order to what we find. But the Colours
^ of

BOOK I. 155

of the Candle being very faint, the miftake feems
to arife from the difficulty of difcerning what
Colours fall on the Eye. For, on the contrary,
I have fometimes had occafion to obferve in the
Sun's Light refraded by a Prifm, that the Spe-
ctator always fees that Colour in the Prifm which
falls upon his Eye. And the fame I have found
true alfo in Candle-light. For when the Prifm
is moved (lowly from the Line which is drawn
diredly from the Candle to the Eye, the red ap-
pears firft in the Prifm and then the blue, and
therefore each of them is feen when it falls upon
the Eye. For the red pafTes over the Eye firft,
and then the blue.

The Light which comes through drops of
Rain by two Refra6tions without any Reflexion,
ought to appear ftrongeft at the diftance of a-
bout. 26- Degrees from the Sun, and to decay
gradually both ways as the diftance from him in-
creafes and decreafes. And the fame is to be un-
derftood of Light tranfmitted through fphe-
"rical Hail-ftones. And if the Hail be a little
flatted , as it often is , the Light tranfmitted
may grow fo ftrong at a little lefs diftance than
that of 26 Degrees, as to form a Halo about
the Sun or Moon ; which Halo, as often as the
Hail-ftones are duly figured may be colour'd,
and then it muft be red within by the leaft re-
frangible Rays, and blue without by the moft
refrangible ones, efpecially if the Hail-ftones
have" opake Globules of Snow in their center
to intercept the Light within the Halo {asHu^
genius has obferv'd) and make the infide there-
of more diftind')y defined than it would other-
wife

156 O P T I C K S.

wife be. For fuch Hail-ftones, though fpheri-
cal, by terminating the Light by the Snow,
may make a Halo red within and colourlefs
without, and darker in the red than without,
as Halos ufed to be. For of thole Rays which
pafs clofe by the Snow the Rubriform will be
ieaft refracted, and fo come to the Eye in the di-
refteft Lines.

The Light which pafTes through a drop of
Rain after two Refra6:ions, and three or more
Reflexions, is fcarce ftrong enough to caufe a
fenfible Bow; but in thofe Cylinders of Ice by
which Hiigenius explains the Parhelia^ it may
perhaps be fenfible.

PROP. X. Prob. V.
By the difccvered Properties of Light to
explain the permanent Colours of Natu-
ral Bodies,

THESE Colours arife from hence , that
fome natural Bodies refled: fome forts of
Rays, others other forts more copioufly than the
reft. Minium refledts the Ieaft refrangible or
red-rfiaking Rays moft copioufly, and thence ap-
pears red. Violets refled: the moft refrangible
moft copioufly, and thence have their Colour,
and fo of other Bodies. Every Body refledls the
Rays of its own Colour more copioufly than the
reft, and from their excefs and predominance in
the refleded Light has its Colour.

Exper^

B O O K I. 157

Exper. ij. For if in the homogeneal Lights
obtained by the folution of the Problem pro-
pofed in the fourth Propolition of the firft Part
of this Book, you place Bodies of feveral Co-
lours, you will find, as I have done, that every
Body looks mofl fpiendid and luminous in the
Light of its own Colour. Cinnaber in the ho-
mogeneal red Light is mofl refplendent, in the
.green Light it is manifeftly lefs refplendent, and
in jhe blue Light ftill lefs. Lidigo in the vi-
olet blue Light is moll refplendent, and its fplen-
dor is gradually diminiih'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 com-
pound green, are more flrongly refle6ted than the
other Colours red and violet, and fo of the reft.
But to make thefe Experiments the more mani-
feft, fuch Bodies ought to be chofen as have the
fulleft and moft vivid Colours, and two of thofe
Bodies are to be compared together. Thus, for
inftance, if Cinnaber and ultra-nMxv'mt blue, or
fome other full blue be held together in the red
homogeneal Light, they will both appear red,
but the Cinnaber will appear of a ftrongly lumi-
nous and refplendent red , and the ultra-mz-
rine blue of a faint obfcure 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 ftrongly luminous and
refplendent blue, and the Cinnaber of a faint
and dark blue. Which puts it out of difpute,
that the Cinnaber reflecfts the red Light much
more copioufly than the ////n;-marine doth, and
2 the

158 O P T I C K S.

the ulfra-m^i'lne refleds the blue Light much
more copioully than theCinnaber doth. The fame
Experiment may be tried fuccefsfully with red
Lead and Indigo, or with any other two colour'd
Bodies, if due allowance be made for the diffe-
rent ftrength or wealoiefs of their Colour and
Light.

And as the reafon of the Colours of natural
Bodies is evident by thefe Experiments, fo it is.
farther confirmed and put pafl difpute by ,the
two firft Experiments of the firft Part, where-
by 'twas proved in fuch Bodies that the reflefed
Lights which differ in Colours do differ alfo in
degrees of Refrangibility.^ For thence it's cer-
tain, that fome Bodies reflect the more refran-
gible, others the lefs refrangible Rays more co-
piouily.

And that this is not only a true reafon of thefe
Colours, but even the only reafon, may appear
farther from this Confideration, that the Colour
of homogeneal Light cannot be changed by the
Reflexion of natural Bodies.

For if Bodies by Reflexion cannot in the leafl
change the Colour of any one fort of Rays, they
cannot appear colour'd by any other means than
by refle(^ting thofe which either are of their
own Colour, or which by mixture muft pro-
duce it.

But in trying Experiments of this kind care
muft be had that the Light be fufficiently ho-
mogeneal. For if Bodies be illuminated by the
ordinary prifmatick Colours, they will appear
neither of their own Day-light Colours, nor of
the Colour of the Light caft on them, but of

fome

BOOK!. 159

feme middle Colour between both, as I have
found by Experience. Thus red Lead (for in-
ftance ) illuminated with the ordinary prifma-
"tick 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 lefs compounded.
For becaufe red Lead appears red when illumi-
nated with white Light , wherein all forts of
Rays are equally mix'd, and in the green Light
all forts of Rays are not equally mix'd, the Lx-
cefs of the yellow-making , green-making and
blue-making Rays in the incident green Light,'
will caufe thofe Rays to abound fo niuch in the
refle<^ted Light, as to draw the Colour from red
towards their Colour. And becaufe the red Lead
refle(fts the red-making Rays moft copioufly in
proportion to their number, *and next after them
the orange-making and yellow-making Rays ;
thefe Rays in the refledted Light will be more in
proportion to the Light than they were in the in-
cident green Light, and thereby will draw the
refleded Light from green towards their Co-
lour. And therefore the red Lead will appear
neither red nor green, but of a Colour between
both.

In tranfparently colour'd Liquors 'tis obfer-
vable, that their Colour ufes to vary with their
thicknefs. Thus, for inftance, a red Liquor in
a conical Glafs 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 ftili
thicker becomes red, and where 'tis thickeft

V the

i6o O P T I C K S.

the red is.deepefl anddarkeft. For it is to be
conceiv'd that fuch a Liquor flops the indigo-
making and violet-making Rays moft eafily, the
blue-making Rays more difficultly, the green-'
making Rays ftill more difficultly, and the red-
making moft difficultly : And that if the thick-
nefs of the Liquor be only fo much as fuffices
to Hop a competent number of the violet-ma-
king and indigo-making Rays, without dimi-
nifliing much the number of the reft, the reft
muft (by Prop. 6. Part 2.) compound a pale
yellow. But if the Liquor be fo much thicker
as to ftop alfo a great number of the blue-ma-
king* Rays, and fo^ie of the ^reen-making, the
reft muft compound an orange j and where it is
fo thick as to ftop alfo a great number of the
green-making and a confiderable number of the
yellow-making, the I'eft muft begin to compound
a red, and this red muft grow deeper and darker
as the yellow-making and orange-making Rays
are more and more ftopp'd by increafmg the
thicknefs of the Liquor, fo that few Rays befides
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 Veftel, found in a clear Sun-
fhine Day, that when he was funk many Fa-
thoms deep into the Water, the upper part of
his Hand on which the Sun ftione dired:ly
through the Water and through a fmall Glafs
Window in the Vefiel appeared of a red Co-
lour, like that of a Damask Rofe, and the Wa-
ter below and the under part of his Hand
illuminated by Light refleded from the Water

below

BOOK I. i6i

below look'd green. For thence it may be ga-
ther'd, that the Sea- Water refleds back the violet
and bhie-making Rays moft eafily, ,and lets the •
red-making Rays pafs moft freely and copioufly to
ffreat Depths. For thereby the Sun's direct Light
at all great Depths, by reafcn of the predomi-
nating red-making Rays, muft appear red j and
the greater the Depth is, the fuller and in-
tenfer muft that red be. And at fuch Depths
as the violet-making Rays fcarce penetrate unto,
the blue-making, green-making, and yellow-
making Rays being refleded from below more
copioully than the red-making ones, muft com-
pound a green.

Now, if there be two Liquons of full Colours,
fiif)pofe a red and a blue, and both of them fo
thick as fuffices to tnake their Colours fufficiently
full; though either Liquor be fufficiently tranfpa-
tenz apart, yet will you not bfe able to fee through
Doth together. For, if only the red-making Rays
pafs through one Liquor, arid only the blue*
making through the other, no 'Rays can pafs
through both. This Mr. H^ok' tried cafuilly
^ith Glafs Wedges filled with red and blue Li-
quors, and was furprized at the unexpeded Event,
the reafon of it being then unknown ; which
makes me truft the more to his Experiment,
though I have not tried it my felf. But he
that would repeat it, muft take care the Li-
quors be of very good and full Colours.

Now, whilft Bodies become coloured by refled:-
ing or tranfmitting this or that fort of Rays more
eopiouily than the reft, it is to be conceived that
they ftop and ftrfle in themfelves the Rays

M > which

i62 O P T I C K S.

which they do not refledt or tranfmit. For, if
Gold be foliated and held between your Eye and
. the Light, the Light looks of a greenifh blue,
and therefore mafTy Gold lets into its Body the
blue-making Rays to be reflected to and fro
within it till they be ftopp'd and ftifled, whilft
it refle(5ls the yellow-making outwards, and
thereby looks yellow. And much after the fame
manner that Leaf Gold is yellow by refle<ited,
and blue by tranfmitted Light, and maify Gold
.is yellow in all Pofitions of the Eye -, there are
foqie Liqi:jors, as the Tincfture of Lignum
Nephriticumy and fome forts of Glafs which
tranfmit one fort of Light moft copioufly, and
refled another fort, and thereby look of feve-
4^al Colours, according to the Pofition of the
Eye to the Light. But, if thefe Liquors or
.Glafles were fo thick and mafTy that no Light
could get through them, I queftion not but they
fwould like all other opake Bodies appear or
ohe and the fame Colour in all Pofitions of the
Eye, though this I cannot yet affirm by Expe^
rience. For all colour'd Bodies, fo far as my
Obfervation reaches, may be feen through if
made fufficiently thin, and therefore are in fome
meafure tranfparent, and differ only in degrees
of Tranfparency from tinged tranfparent Li-
<juors; thefe Liquors, as well as thofe Bodies,
by a fufficient Thicknefs becoming opake. A
tranfparent Body which looks of any Colour by
tranfmitted Light, may alfo look of the fame
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

BOOK L .161

then the refleded Colour will be diminlfhed, and
perhaps ceafe, by making the Body very thick,
and pitching it on the backfide to diminifh the
Reflexion of its farther Surface, fo that the Light
refle(3;ed from the tinging Particles may predomi-
nate. In fuch Cafes, the Colour of the reflecfted
Light will be apt to vary from that of the Light
tranfmitted. But whence it is that tinged Bo-
dies and Liquors refledt fome fort of Rays, and
intromit or tranfmit other forts, fhall be faid in
the next Book. In this Propofition I content my
felf to have put it paft difpute, that Bodies have
fuch Properties, and thence appear colour'd.

PROP. XI. Prob. VI.

By mixing colour d Lights to compound a
beam of Light of the fa^ne Colour and
Nature with a beam of the Su?is direEi
Light y and therein to experience the
Truth of the foregoing Propoftions,

LET ABC abc [in Fif[. 16.] reprefent a
Prifm, by which the Sun's Light let into
a dark Chamber through the Hole F, may be
refradted towards the Lens MN, and paint upon
it at py q, r, j, and /, the ufual Colours vio-
let, blue, green, yellow, and red, and let the
diverging Rays by the Refrad:ion of this Leng
converge again towards X, and there, by the
mixture of all thofe their Colours, compound a
white according to what was fhewo above.

M 2 Then

i64 OPTIC K S.

Then let another Prifm DEG deg, parallel to
the former, be placed at X, to refrad: that white
Light upward* towards Y. Let the refracting,
Angles of the Prifms, and their diflances from
the Lens be equal, fo that the Rays which con-
verged from the Lens towards X, and without
Refradion, would there have crofled and di-
verged again, may by the Refradtion of the fe-
cond Prifm be reduced into Parallelifm and
diverge no more. For then thofe Rays will re-
compofe a beam of white Light XY. If the
refradting Angle of either Prifm be the bigger,
that Prifm muft be fo much the nearer to the
Lens. You will know when the Prifms and the
Lens are well fet together, by obferving if the
beam of Light X Y, which comes out of the fe-
cond Prifm be perfectly white to the very edges
of the Light, and at all diftances from the Prifm
continue perfectly and totally white like a beam
of the Sun's Light. For till this happens, the
Polition of the Prifms and Lens to one another
muft be correded ; and then if by the help ©f a
long beam of Wood, as is reprefehted in the
Figure, or by a Tube, or fbme other fuch In-
ftrument made for that Purpofe, they- be made
faft in that Situation, you may try all the fame
Experiments in this compounded beam of Light
X Y, which have been made in the Sun's dired:
Light. For this compounded beam of Light
has the fame appearance, and is endow'd with
all. the fame Properties with a diredt beam of the
Sun's Light, fo far as my Obfervation reaches.
And in trying Experiments in this beam you
may by flopping any of the Colours /, q^ r, />

and

B O O K I. 165

and /, at the Lens, fee how the Colours produce^
in the Experiments are no other than thofe which
the Rays had at the Lens before they entered the
Compofition of this Beam : And by confcqijence>
that they arife not from any new Modifications of
the Light by Refradtions and Reflexions, but from
the various Separations and Mixtures of the Rays
originally endow'd with theircolour-making Qua-
lities.

So, for inftance, having with a Lens 4, Liches
broad, and two Prifms on either hand 6i Feet
diftant from the Lens, made fuch a beam of
compounded Light ; to examine the reafon of
the Colours made by Prifms, I rcfraded this com-
pounded beam of Light XY with another Prifm.
HIK kh, and thereby call the ufual Prifma-
tick Colours PQRST upon the Paper LV
placed behind. And then by flopping any of
the Colours />, ^, r, j, /, at the Lens, I found
that the fame Colour would vanifh at the Pa-
per. So if the Purple p was ftopp'd at the
Lens, the Purple P upon the Paper would vanifh,
and the reft of the Colours would remain un-
alter'd, imlefs perhaps the blue, fo far as fome
purple latent in it at the Lens might be fepa-
rated from it by the following RefraSions. And
fo by intercepting the green upon the Lens, the
green R upon the Paper would vanifli, and fo
of the refl j which plainly fhews, that as the
white beam of Light XY was compounded of
feveral Lights varioufly colour'd at the Lens,
fo the Colours which afterwards emerge out of
it by new Refradlions are no other than thofe
of which its Whitenefs was compounded. The

M 3 Refradion

i66 O P T I C K S.

Refradion of the Prifm HIK /^^ generates the
Colours PQ^ST upon the Paper, not by chan-
ging the colorific Qualities of the Rays, but by
feparating the Rays which had the very fame colo-
rific Qualities before they enter'd the Compofition
of the refradied beam of white Light X Y. For
otherwife 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 reafon of the Co-
lours of natural Bodies, I placed fuch Bodies
in the Beam of Light XY, and found that they
all appeared there of thofe their own Colours
which they have in Day-light, and that thofe
Colours depend upon the Rays which had the
fame Colours at the Lens before they enter'd the
Compofition of that beam. Thus, for inflance,
Cinnaber illuminated by this beam appears of
the fame red Colour as in Day-light ; and if
at the Lens you intercept the green-making and
blue-making Rays, its rednefs will become more
full and lively : But if you there intercept the
red-making Rays, it will not any longer ap-
pear red, but become yellow or green, or of
lome other Colour, according to the forts of
Rays which you do not intercept. So Gold
in this Light XY appears of the fame 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 Ihews that its yellownefs arifes from
the Excefs of the intercepted Rays tinging that
Whitenefs with their Colour when they are let
pafs. So the Infuiion of Ugmm Nephriticum

(as

B O O K I. 167

(as I have alfo tried) when held in this beam of
Light XY, looks blue by the reflected Part of the
Light, and red by the tranfrrjitted Part of it, as
when 'tis view'd in Day-light j but if you intercepc
the blue at the Lens the Infufion will lofe its re-
fled:ed blue Colour, whilft its tranfmitted red re-
mains perfect, and by the lofs of fome blue-
making Rays, wherewith it was allay'd, becomes
more intenfe and full. And, on the contrary, if
the red and orange-making Rays be intercepted at
the Lens, the Infufion will lofe its tranfmitted red,
whilft its blue will remain and become more full
and perfedl. Which fhews, that the Infufion
does not tinge the Rays with blue and red, but
only tranfmit thofe mofl copioufiy which were
red-making before, and refledts thofe moft copi-
oufly which were blue-making before. And after
the fame manner may theReafons of other Phaeno-
mena be examined, by trying thorn in this artificial
beam of Light XY.

M 4 THE

THE

SECOND BOOK

OF

OPTICKS.

P A R T I.

Obfervations concerning the Reflexions y Re-
fraBionSy and Colours of thi^t tranfpa-
rent Bodies,

T has been obferved by others,
that tranfparent Subftances, as
Glafs, Water, Air, &V. when
made very thin by being blown
into Bubbles, or otherwife formed
into Plates, do exhibit various Co-
lours according to thcjr various thinnefs, altho' at

a greater

BOOK II. 169

a greater tlucknefs they appear very clear and
colour! efs. In the former Book I forbore to
treat of, thefe Colours, becaufe they feemed of a
more difficult Confideration, and were not necef-
fary for eftabliihing the Properties of Light there
difcourfed of. But becaufe they may conduce to
farther Difcpveries for compleating the Theory of
Light, efpecially as to the conftitution of the
parts of natural Bodies, on which their Colours
or Tranfparency depend j I have here fet down
an account of thern. To render this Difcourfe
fhort and didindt, I have fiifl defcribed the prin-
cipal of my Obfervations , and then confider'd
and made ufe of them. The Obfervations are
thefe.

Ohf. I., Comprefiing two Prifms hard toge-
ther that their fides (which by chance were a
very little convex) might fomewhere touch one
another : I found the place in which they touch-
ed to become abfolutely tranfparent, as if they
had there been one continued piece of Glafs,
For when the Light fell fo obliquely on the
Air, which in other places was between them,
as to be all refledcds ic feemed in that place of
contact to be wholly tranfmitted, infomuch that
when look'd upon, it appeared like a black or
dark fpot, by reafon that little or no fenfible
Light was refledled from thence, as from other
places ; and when looked through it feemed ( a^
it were) a hole in that- Air which was formed
into a thin Plate, by being comprefs'd between
the Glafles. And through this hole Objeds that
were beyond might be feen diftindly , which
could not at all be feen through other parts of

the

lyo O P T I C K S.

the GlafTes where -the Air was interjacent. Al-
though the GlafTes were a little convex, yet this
transparent fpot was of a confiderable breadth,
which breadth feemed principally to proceed
from the yielding inwards of the parts of the
GlafTes, by reafon of their mutual prefTure. For
by prefTing them very hard together it would be-
come much broader than otherwife.

Obf. 2. When the Plate of Air, by turning
the Prifms about their common Axis, became (o
little inclined to the incident Rays, that fome of
them began to be tranfmitted, there arofe in it
many flender Arcs of Colours which at firfl were
fhaped almofl like the Conchoid , as you fee
them delineated in the firfl Figure. And by con-
tinuing the Motion of the Prifms, thefe Arcs
increafed and bended more and more about the
faid tranfparent fpot, till they were compleated
into Circles or Rings incompafling it, and af-
terwards continually grew more and more con-
tradted.

Thefe Arcs at their firfl appearance were of
a violet and blue Colour, and between them
were white Arcs of Circles , which prefently
by continuing the Motion of the Prifms became
a little tinged m their inward Limbs with red
and yellow, and to their outward Limbs the
blue was adjacent. So that the order of thefe
Colours from the central dark fpot, was at that
time white, blue, violet j black, red, orange,
yellow, white, blue, violet, &c. But the yel-
low and red were much fainter than the blue and
violet. *

2 ' The

BOOK 11. 171

The Motion of the Prifms aBout their Axis
being continued, thefe Colours contracl^ed more
and more, Shrinking towards the whitenefs on
either fide of it, until they totally vaniihed into
it. And then the Circles in thofe parts appear'd
black and white, without any other Colours in~
termix'd. But by farther moving the Prifms
about, the Colours again emerged out of the
whitenefs, the violet and blue at its inward
Limb, and at its outward Limb the red and yel-
low. 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.

Obf. 3. When the Rings or fome parts of
them appeared only black and white, they were
very diftindl and well defined, and the blacknefs
feemed as intenfe as that of the central Spot.
Alfo in the Borders of the "Rings, where the
Colours began to emerge out of the white-
nefs, they were pretty diftind: , which made
them vifible to a very great multitude. I have
fometimes number'd above thirty Succeffions
(reckoning every black and white Ring for one
Succeflion) and feen more of them, which by
reafon of their fmalnefs I could not number.
But in other Pofitions of the Prifms, at which
the Rings appeared of many Colours, I could
not diftinguiih above eight or nine of them, and
the Exterior of thofe were very confufed and
dilute.

In thefe two Obfervations to fee the Rings di-
ilin<5t, and without any other Colour than bl^ck
and white, I found it neceflary to hold my Eye

at

172 O P T I C K S.

at a good diftance from them. For by ap-
proachijfjg nearer, although in the fame inclina-
tion of my Eye to the Plane of the Rings, there
emerged a bluifH Colour out of the white,
which by dilating it felf more and more into
the black, render'd the Circles lefs diflindt, and
left the white a little tinged with red and yel-
low. I found alfo by looking through a flit or
oblong hole, which was narrower than the pupil
of my Eye, and held clofe to it pjirallel to the
Piifms, I could fee the Circles much diftindter
and vifible to a far greater number than other-
wife.

Ohf.\> To obferve more nicely the order of
the Colours which arofe out of the white Cir-
cles as the Rays became lefs and lefs inclined
to the Plate of Airj I took two Objed-glafTes,
the one a Plano-convex for a fourteen Foot
Telefcope, and the other a large double Con-
vex for one of about fifty Footj and upon this,
laying the other with its plane fide downwards,
I prelfed them (lowly together,, to make the
Colours fucceffively emerge in the middle of the
Circles, and then fiowly lifted the upper Glafs
from the lower to make them fuccefTively vaniih
again in the fame place. The Colour, which
by preffing the GlalTes together, emerged laft in
the middle of the other Colours, would upon its
firft appearance look like a Circle of a Colour
almoft uniform from the circumference to the
center, and by compreffing the GlaiTes ftill more,
grow continually broader until a new Colour
emerged in its center, afid thereby it becanie a
Ring encompaihng ^hat new Colour. And by

2 com-

BOOK IL t73

domprefiing the Gkfles ftill more, the diameter
of this Ring would increafe, and the breadth of
its Orbit or Perimeter decreafe until another new
Colour emerged in the center of the laft: And
fo on until a third, a fourth, a fifth, and other
following new Colours fuccefiively emerged
there, and became Rings encompalfmg the inner-
moft Colour, the laft of which was the black
Spot. And, on the contrary, by lifting up the
upper Glafs from the lower, the diameter of the
Rings would decreafe, and the breadth of their
Orbit increafe, until their Colours reached fuc-
cefiively to the center ; and then they being of a
confiderable breadth, I could more eafily difcern
and diftinguifti their Species than before. And
by this means I obferv'd their Succeflion and
Quantity to be as foUoweth.

Next to the pellucid central Spot made by
the contadl of the Glaffes fucceeded blue, white,
yellow, and red. The blue was ib little in quan-
tity, that I could not difcern it in the Circles
made by the Prifms, nor could I well diftinguifti
any violet in it, but the yellow and red were
pretty copious, and feemed 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 encompaffmg thefe were
violet, blue, green, yellow, and red: and thefe
were all of them copious and vivid, excepting
the green, which was very little in quantity, and
feemed much more faint and dilute than the
other Colours. Of the other four, the vio-
let was the leaft in extent, and the blue lefs
than the yellow or red. The third Circuit or

^ Order

174. O P T I C K S.

Order was purple, blue, green, yellow, and
red ; in which the purple feemed more reddifh
than the violet in the former Circuit, and the
green was much more confpicuous , being as
brisk and copious as any of the other Colours,
except the yellow, but the red began to be a lit-
tle faded, inclining very much to purple. Af-
ter this fucceeded the fourth Circuit of green
and red. The green was very copious and live-
ly, inclining on the one lide to blue, and on
the othtr fide to yellow. But in this fourth
Circuit there was neither violet, blue, nor yel-
low, and the red was very imperfe6l and dir-
ty. Alfo the fucceeding Colours became more
and more imperfed: and dilute, till after three
or four revolutions they ended in perfedt
whitenefs. Their form, when the Glafles were
moft comprefs'd fo as to make the black Spot
appear in the center, is delineated in the fe-
Gond Figure ; where a, b, f, ^, e : /, ^, h, /,
k : /, w, w, 0, p: q, r : s, t : v, x : )\ z, de-
note the Colours reckon'd in order from the
center, black, blue, white, yellOw, red: vio-
let, blue, green, yellow, red: purple, blue,
green, yellow, red: green, red: greenifh blue,
red: greenifli blue, pale red: greenifli blue,
reddifh white.

Obf. 5. To determine the interval of the
Glalfes, or thicknefs of the interjacent Air, by
which each Colour was produced, I meafured
the Diameters of the firfl fix Rings at the moft
lucid part of their Orbits, and fquaring them, I
found their Squares to be in the arithmetical Pro-
greffion of the odd Numbers, i, 3, 5, 7, 9, 1 1.

And

BOOK II. 175

And fince one of thefe Glafles was plane, and
the other fpherical, their Intervals at thofe Rings
jnuft be in the fame Progreffion. I meafured alio
the Diameters of the dark or faint Rings between
the more lucid Colours, and found their Squares
to be in the arithmetical Progrelfion of the. even
Numbers, 2, 4, 6, 8, 10, 12. And it being very
nice and difficult to take thefe meafures exadly;
I repeated them divers times at divers parts of
ihe GlafTes, that by their Agreement I might be
confirmed in them. And the lame method I ufed
in determining fome others of the following Ob-
fervations.

Obf. 6. The Diameter of the fixth Ring at

the moil lucid part of its Orbit was -^ parts of

an Inch, and the Diameter of the ' Sphere on
which the double convex Objedt-glals was
ground was about 102 Feet, and hence I ga-
thered the thicknefs of the Air or Aereal Inter-
val of the Glaffes at that Ring. But fome time
after, fufpedting that in making this Obfervatioii
I had not determined the Diameter of the
Sphere with fufficient accuratenefs, and being
uncertain whether the Plano-convex Glafs was
truly plane, and not fomething concave or con-
vex on that fide which I accounted plane ; and
whether I had not preiTed the GlafiTes together,
as I often did, to make them touch j ( For by
preffing fuch GlalTes together their parts eafily
yield inwards, and the Rings thereby become
fenfibly broader than they would be, did the
GlalTes keep their Figures.) I repeated the
Experiment , and found the Diameter of the

fixth

176 O P T I C K S.

fixth Iticid Ring about -^ parts of an Inch. 1

repeated the Experiment alfo with fuch an Ob-
jed-glafs of another Tclefcope as I had at hand.
This was a double Convex ground on both
fides to one and the fame Sphere, and its Fo-
cus was diftant from it 83 f Inches. And thence,
if the Sines of Incidence and Refraction of the
bright yellow Light be affumed in proportion
as II to 17, the Diameter of the Sphere to
which the Glafs was figured will by computa-
tion be fougd 182 Inches. This Glafs I laid
upon a flat one, fo that the black Spot appear-
ed in the middle of the Rings of Colours with-
out any other PrelTure than that of the weight
of the Glafs. And now meafuring the Diame-
ter of the fifth dark Circle as accurately as I
could, I found it the fifth part of an Inch pre-
cifely. This Meafure was taken with the point$
of a pair of CompaiTes on the upper Surface
on the upper Glafs, and my Eye was about
eight or nine Inches diftance from the Qlafs,
almofl perpendicularly over it, 'and the Glafs
was r of an Inch thick, and thence it is eafy to
colled: that the true Diameter of the Ring be-
tween the Glaffes was greater than its meafur'd
Diameter above the Glaffes in the Proportiort
of 80 to y9, or thereabouts, and by confequence
equal to ^| parts of an Inch, and its true Semi-
diameter equal to tV parts. Now as the Dia-
meter of the Sphere (.182 Inches) is to the Se-
mi-diameter of this fifth dark Ring .(t* parts of
an Inch) fo is this Semi-diameter to the thick-
: nefs of the Air at this fifth dark Ring j which is

there-

BOOK II. ?t77

therefore -7^^— or — ^^ Parts of an Inch ; and
^ 567931 1774784 ^

the fifth Part thereof, viz. tke -r^ Part of an

•0739

Inch, is the Thicknefs of the Air at thefirft
of thefe dark Rings.

The fame Experiment I repeated with another
double convex Objed'-glafs ground on both fides
to one and the fame Sphere. Its Focus was di-
flarit from it i68j Inches, and therefore the Dia-
meter of that Sphere was iS'4 Inches. This
Glafs being laid upon the fijme plain, Glafs,
the Diameter of the fifth of the dark Rings,
when the black Spot in their Center appear'd
plainly without preffing the Glailes, was by the
meafure of the Compafles upon fhe upper Glafs

!ii Parts of an Inch, and by. confequence be-
tween theGlaffes it was ~^:.. For the upper Glafs

was ^ of an Inch thick, arid rhy Eye was diitant
from it 8 Inches. And a third proportional to
"half this from the Diameter ,,©jf the/Sphere is

,,-r- Parts of an Inch. Thi^ is therefore the
Thicknefs of the Air at this. Ring, and a fifth
Part thereof, viz. the ~— th Part of. an Incli is

the Thicknefs thereof at the firfl of the Rings, as
above.

I tried the fame Thing, by laying thefe Obje(5t-
glafies upon flat Pieces of a broken Looking-
glafs, and found the fame Meafures of the
Rings: Which makes me rely upon them till

N they

178 O P T I C K S.

.they can be determin'd more accurately byGlailes
ground to larger Spheres, though in fuch GlafTes
greater care muft be taken of a true Plane.

Thefe Dimenfions were taken, when my Eye
was placed almoft perpendicularly over the Glaf-
fes, being about an Inch, or an Inch and a quar-
ter, diilant from the incident Rays, and eight
Inches diftant from the Glafs j fo that the Rays
were inclined to the Glafs in an Angle of about
four Degrees. Whence by the following Obfer-
vation you will underftand, that had the Rays
been perpendicular to the GlafTes, the Thicknefs
of the Air at thefe Rings would have been lefs ia
the Proportion of the Radius to the Secant of four
Degrees, that is, of loooo to 10024. Let the
ThicknefTes found be therefore dimini{h'd in this

Proportion, and they will become —^ and --^ — ^.

or ( to ufe the nearefl round Number ) the

g~^th Part of an Inch. This is the Thicknefs of

the Air at the darkeft Part of the iirft dark Ring
made by perpendicular Rays; and half this Thick-
nefs multiplied by the ProgreiTion,' i, 3, 5, 7, g^
iiy^^c. gives the Thicknefles of the Air at the
moft luminous Parts of all the brighteft Rings, viz,

{^y T^o) T^oy r78^> ^^' ^heir arithme-
tical Means ^^, - g^~, ^j^^, &c. being its
ThicknefTes at the darkefl Parts of all the dark
ones.

Oi/.j.

BOOK IL

179

Obf. 7. The Rings were leaft, when my Eye
was placed perpendicularly over theGlafTes in the
Axis of the Rings : And when I view'd them
obliquely they became bigger, continually fwel-
ling as I removed my Eye farther from the Axis.
And partly by meafuring the Diameter of the
fame Circle at feveral Obliquities of my Eye,
partly by other Means, as alfo by making ufe of
the two Prifms for very great Obliquities, I found
its Diameter, and confequently the Thicknefs of
the Air at its Perimeter in all thofe Obliquities to
be very nearly in the Proportions exprefs'd in
this Table.

Angle of In-

Angle of Re-

Diameter

"Ihickricf

cidence on

f ration in-

of the

of the

the Air.

to the Air.

Ring.

Air. .

Deg. Min.

00 00

00 00

10

\^

06 26

10 00

IOtV

IOtV

12 45

20 00

lOf

IQi

18 49

30 00

lOA

Ilf

24 30

40 00

IIv

13

29 37

50 00

12k

i5i

33 58

60 00

14

20

35 47

65 00

i5i

23t

37 19

70 00

i6t

28^

3S 33

7S 00

'^I

37

39 27

'80 00

22f

52i

40 00
.. 40 II

85 GO

29

Hu

90 00

3<

\ 122',

N 2

In

i8o O P T I C K S.

* In the two firll Columns are exprefs'd the Obli-
quities of the incident and emergent Rays to the
Plate of the Air, that is, their Angles of Inci-
dence and Refraction. In the third Column the
Diameter of any colour'd Ring at thofe Obliqui-
ties is exprelTed in Parts, of which ten conffcitute
that Diameter when the Rays are perpendicular.
And in the fourth Column the Thicknefs of
the Air at the Circumference of that Ring is
exprelTed in Parts, of which alfo ten eonfti-
tute its Thicknefs when the Rays are perpen-
dicular.

And from thefe Meafures I feem to gather
this Rule: That the Thicknefs of the Air is pro-
portional to the Secant of an Angle, whofe Sine*
is a certain mean Proportional between the Sines.'
of Incidence and Refradlion. Arid that mean
. Proportional, fb far as by thefe Meaftires I caw
determine it, is the firft of an hundred and fix
arithmetical mean Proportionals between thofe»
Sines counted from the bigger Sine, that; is,
* from the Sine of Refradion when the Re-
fraction is made out of the Glafs into the^
Plate of Air, or from the Sine of Incidence when*
the Refraftion is made out oi the ■ Plate of Air
into the Glafs. ,

O^.' 8. The dark Spot in the middle of the
Rings increafed alfo by the Obliquation of the
Eye, although almofl infenfibly. But, if inftead
of the ObjeS-glafTes the Prifms were made ufe
of, its Increafe was more manifefl when viewed
fo, obliquely that no Colours appeared about
it. ' It was leafl when the Rays were incident
moll obliquely on the interjacent Air, and as

the

BOOK II. i8i

the obliquity decreafed it increafed more and
more until the colour'd Rings appear'd, and
then decreafed again, but not fo much as it in-
creafed before. And hence it is evident, that
the Tranfparency was not only at the abfolute
Contad of the GlalTes, but alfo^here they had
fome little Interval. I have fometimes obferved
the Diameter of that Spot to be between half
and two fifth parts of the Diameter of the ex-
terior Circumference of the red in the firft Cir-
cuit or Revolution of Colours when view'd al-
moft perpendicularly ; whereas when view'd ob-
liquely it hath wholly vanifli'd and become
opake and -white like the other parts of the
Glafs 3 whence it may be coUeded that the
Glaffes did then fcarcely, or not at all, touch
one another, and that their Interval at the pe-
rimeter of that Spot when view'd perpendicu-
larly was about a fifth or fixth part of their In-
terval at the circumference of the faid red.

O/y^rT'. 9.. By looking through the two conti-
guous Objed-glafies, I found that the interja-
cent Air exhibited Rings of Colours, as well
by tranfmitting Light as by refleding it. The
central Spot was now white, and from it the
order of the Colours were yellowifli red; black,
violet, blue, white, yellow, red; violet, blue,
green, yellow, red, &c. But thefe Colours
were very faint and dilute, unlefs when the
Light was trajecled very obliquely through the
Glaffes : For by that means they became pretty
vivid. Only the firft yellowifh red , like the
blue in the fourth Obfervation, was fo little and
faint as fcarcely to be difcern'd. Comparing

N 3 the

i82 O P T I C K S.

the colour'd Rings made by Reflexion, with
thefe made by tranfmilTion of the Light j I
found that white was oppofite to black, red to
blue, yellow to violet, and green to a Compound
of red and violet. That is, thafe parts of the
Glafs were black when looked through, which
when looked upon appeared white, and on the
contrary. And fo thofe which in one cafe exhi-
bited blue, did in the other cafe exhibit red.
And the like of the other Colours. The man-
ner you have reprefented in the third Figure,
where A B, CD, are the Surfaces of theGlaifes
contiguous at E, and the black Lines between
them are their Diftances in arithmetical Progref-.
iion, and the Colours written above are feen by
refiedied Light, and thofe below by Light tranf-
mitted.

Oof. 10. Wetting the Objed-glafTes a little

■ at their edges, the Water crept in flowly be-
tween them, and the Circles thereby became
lefs and the Colours more faint : Infomuch that
as the Water crept along, one half of them at
which it firft arrived would appear broken off
from the other half, and contracted into a lefs
Room. By meafuring them I found the Pro-
portions of their Diameters to the Diameters of
the like Circles made by Air to be about itvtu.
to eight, and confequently the Intervals of the
Glaffes at like Circles, caufed by thofe two Me-
diums Water and Air, are as about three to four.

• Perhaps it may be a general Rule, That if any
other Medium more or lefs denfe than Water
be comprefs'd between the Glaffes, their Inter-
vals at the Rings cavifed thereby will be to their

Intervals

BOOK II. 183

Intervals caufed by interjacent Air, as the Sines
are which meafure the Refrad;ion made out of
that Medium into Air.

Obf. II. When the Water was between the
Glafles, if I prefTed the upper Glafs varioully 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 prefently vanilh. Its appearance
was fuch as interjacent Air would have caufed,
and it exhibited the fame Colours. But it was
not Air, for where any Bubbles of Air were in
the Water they would not vanilli. The Refle-
xion- muft have rather been caufed by a fubtiler
Medium, which could recede through the Glaf-^
fes at the creeping in of the Water.

Obf. 12. Thefe Obfervations were made in
the open Air. But farther to examine the Effects
of colour'd Light falling on the Glaffes, I dar-
3cen'd the Room, and view'd them by Reflexion
of the Colours of a Prifm caft on a Sheet of
white Paper, my Eye being fo placed that I
could fee the colour'd Paper by Reflexion in the
Glalfes , as in a Looking-glals. And by this
means the Rings became diftind:er and vifible to
a far greater number than in the open Air. I
have fometimes feen more than twenty of them,
whereas in the open Air I could not difcern above
eight or nine.

Obf. 13. Appointing an A ffiftant to move the
Prifm to and fro about its Axis, that ail the
Colours might fucceffively fall on that part of
the Paper which I faw by Reflexion from that

N 4 part

j84 OPTIC K S.

part of "the GlafTes, where the Circles appear'd,
£o thax all. the Colours might be fucceffively re,
fiefted from the Circles to my Eye whilft I held
it immovable, I found, the Circles which the
red Light made to be manifeftly bigger than
thofe which were made by the blue and violet.
And it was very pleafant to fee them gradually
fwell or contrad: accordingly as the Colour of the
Light was changed. The Interval of the Glaf-
fes at any of the Rings when they were made by
|:he utmoft red Light, was to their Interval at the
fame Ring when made by the utmoft violet,
greater than as 3 to 2, and lefs than as 13 to 8.
By the moft of my Obfer vat ions it was as 14 to
9. And this Proportion feem'd very nearly the
fame in all Obliquities of my Eye ; unlefs whea
two Prifms were made ufe of inftead of the Ob^
jedi-glafTes. For then at a certain great obliquity
of my Eye, the Rings made by the feveral Co-
lours {eem'd equal, and at a greater obliquity
thofe made by the violet would be greater than
the fame Rings made by the red: the Refrad:ion
of the Prifm in this cafe caafing the moft refran^
gible Rays to fall more obliquely on that plate of
the Air than the leaft refrangible ones. Thus
the Experiment fucceeded in the colour'd Light,
which was fufhciently ftrong and copious to
jnake the Rings fenfible. And thence it may be
gather'd, that if the moft refrangible and leaft
refrangible Rays had been copious enough to
make the Rings fenfible without the mixture of
other Rays, the Proportion which here was 14 to
9 would have been a little greater, fuppofe 14?
or 14T to 9.

BOOK IT. 185

Obf. 14. Whilft the Prifm was turn'd about
its Axis with an uniform Motion, to make all
the feveral Colours fall fucceffively upon the
Objedi-glafles, and thereby to marke the Rings
contrad: and dilate : The Contradion or Dilata-
tion of each Ring thus made by the variation of
its Colour was fwifteft in the red, and floweft
in the violet, and in the intermediate Colours
it had intermediate degrees of Celerity. Com-
paring the quantity of Contrad:ion and Dilata-
tion made by all the degrees of each Colour, I
found that it was greatefl in the red j lefs in
the yellow, ftill lefs in the blue, and leaft in the
violet. And to make as juft an Eftimation as I
could of the Proportions of their Contrad:ions
or Dilatations, I obferv'd that the whole Con-
traction or Dilatation of the Diameter of any
Ring made by all the degrees of red, was to
that of the Diameter of the fame 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 greatefl Diame-
ter of the fame Ring made by the outmoft red,
and the leaft Diameter thereof made by the
outmoft violet : Contrary to what happens in
the Colours of the oblong Spedlrum made by
the Refraction of a Prifm, where the red is
moft contracted , the violet moft expanded ,
and in the midft of all the Colours is the Con-
fine of green and blue. And hence I feem to
collect that the thicknefies of the Air between
the GlaiTcs there, where the Ring is fucceffive-
ly

i86 O P T I C K S.

ly made by the limits of the five principal Co-
lours ( red, yellow, green, blue, violet ) in or-
der ( 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 fixth lengths of -aXhord which found the
Notes in a fixth Major, Jhl^ la, mi\ fa, Jol, la.
But it agrees fomething better with the Obferva-
tion to fay, that the thickneffes of the Air be-
tween the GlafTes there, where the Rings are
fuccefTively made by the limits of the feven Co-
lours, red, orange, yellow, green, blue, indi-
go, violet in order, are to one another as the
Cube Roots of the Squares of the eight lengths
^f a Chord, which found the Notes in an eighth,
Jhl, la, fa, Jbl, la, mi, fa, fol ; that is, as the
Cube Roots of -the Squares of the Nurinbers, i,

8 f J i i ^ I

§> 5> 4J 1; Si '^J 2*

Obf 15. Thefe Rings were not of various
Colours like thofe made in the open Air, but
appeared all over of that prifmatick Colour on-
ly witli which they were illuminated. And by
projediing the prifmatick Colours immediately
upon the GlalTes, I found that the Light which
fell on the dark Spaces which were between
the colour'd Rings was tranfmitted through the
GlalTes without any variation of Colour. For
on a white Paper placed behind, it would paint
Rings of the fame Colour with thofe which
were refleded, and of the bignefs of their im-
mediate Spaces. And from thence the origin

I of

BOOK II. 187

of thefe Rings Is manifefl; namely, that the Air
.between the Glaffes, according to its various
thicknefs, is difpofed in fome places to refledt,
and in others to tranfmit the Light of any one
Colour (as you may fee reprefented in the
fourth Figure ) and in the fame place to refled:
that of one Colour where it tranfmits that of
another. ,

Obf. 16. The Squares of the Diameters of
thefe Rings made by any prifmatick Colour were
in arithmetical Progrefilon, as in the fifth Ob-
fervation. And the Diameter of the fixth Cir-
cle, when made by the citrine yellow, and

viewed almofl perpendicularly, was about ^

parts of an Inch, or a little lefs, agreeable to the
fixth Obfervation.

The precedent Obfervations were made with
a rarer thin Mediuni; terminated by a denfer,
fuch as was Air or Water comprefs'd between
two GlalTes. In thofe that follow are fet down
the Appearances of a denfer Medium thin'd
within a rarer, fuch as are Plates of Mufcovy
Glafs, Bubbles of Water, and fome other thin
Subftances terminated on all fides with Air.

Obf. 17. If a Bubble be blown with Water
firft made tenacious by dilTolving a little Soap
in it, 'tis a common Obfervation, that after a
while it will appear tinged with a great variety of
Colours. To defend thefe Bubbles from being
agitated by the external Air (whereby their Co-
lours are irregularly moved one among ano-
ther, fo that no accurate Obfervation can be
made of themj as foon as I had blown any of

thorn

i88 OPTIC K S.

them I cover'd it with a clear Glafs, and by that
means its Colours emerged in a very regular
order, like fo many concentrick Rings encom-
paffing the top of the Bubble. And as the Bub-
ble grew thinner by the continual fubfiding of
the Water, thefe Rings dilated flowly and over-
fpread the whole Bubble, defcending in order to
the bottom of it, where they vanifn'd fuc-
celTively. In the mean while, after all the Co-
lours were emerged at the top, there grew in the
center of the Rings a fmall round black Spot,
like that in the firft Obfervation, which con-
tinually dilated it felf till it became fometimes
more than i or ^ of an Inch in breadth before
the Bubble broke. At firft I thought there had
been no Light refleded from the Water in that
place, but obferving it more curioufly, I faw
within it feveral fmaller round Spots, which
appeared much blacker €nd darker than the
reft, whereby I knew that there was fome Re-
flexion at the other places which were not fo
dark as thofe Spots. And by farther Tryal I
found that I could fee the Images of fome
things (as of a Candle or the Sun) very faintly
refled:ed, not only from the great black Spot,
but alfo from the little darker Spots which were
within it.

Belides the aforefaid colour'd Rings there
would often appear fmall Spots of Colours, af-
cending and defcending up and down the fides
of the Bubble, by reafon of fome Inequalities in
the fubfiding of the Water. And fometimes
fmall black Spots generated at the fides would
2 afcend

BOOK II. 189

afcend up to the larger black Spot at the top of
the Bubble, and unite with it.

ObJ. 18. Becaufe the Colours of thefe Bubbles
were more extended and lively than thofe of the
Air thinn'^d between two GlafTes, and fo more
eafy to be diiliinguilli'd, I Ihall here give you a
farther defcription of their order, as they were
obferv'd in viewing them by Reflexion of the
Skies when of a white Colour, whilft a black
fubftance was placed behind the Bubble. And
they were thele, 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 fir ft Succeffions of red and blue
were very dilute and dirty, efpecially the firft,
where the red feem'd in a manner to be white.
Among thefe there was fcarce any other Colour
fenfible befides red an^ blue, only the blues ( and
principally the fecond blue ) inclined a little to

green.

The fourth red was alfo dilute and dirtv, bur
not fo much as the former three ; after that fuc-
ceeded little or no yellow , but a copious
green, which at firft inclined a little to yellow,
and then became a pretty brisk and good wil-
low green, and afterwards changed to a bluiib
Colour; but there fucceeded neither blue noF
violet. •

The fifth red at firft inclined very much to
purple, and afterwards became more bright
and brisk, but yet not very pure. This was
fucceeded with a very bright and intenfe yel-
low» which was but little in quantity, and foon

chang'd

xgo O P T I C K S.

chang'4 to green: But that green was copious
and fomething more pure, deep and lively, than
the former green. After that follow'd an ex-
cellent blue of a bright Sky-colour, and then a
purple, which was lefs in quantity than the blue,
and much inclined to red.

The fixth red was at firft of a very fair and
lively fcarlet, and foon after of a brighter Co-
lour, being very pure and brisk, and the beft
of all the reds. Then after a lively orange fol-
low'd an intenfe bright and copious yellow,
which was alfo the beft of all the. yellows, and
this changed firft to a greenifti yellow, and then
to a greenifli bluej but the green between the
yellow and the blue, was very little and dilute,
feeming rather a greenifli white than a green.
The blue which fucceeded became very good,
and of a very fair bright Sky-colour, but yet
fomething inferior to the former blue 3 and the
violet was intenfe and deep with little or no
rednefs in it. And lefs in quantity than the
blue.

In the laft red appeared a tin6lure of fcarlet
next to violet, which foon changed to a bright-
er Colour, inclining to an orange j and the yel-
low which follow'd was at firft pretty good
and lively, but afterwards it grew more dilute,
until by degrees it ended in perfed: whitenefs.
And this whitenefs, if the Water was very te-
nacious and well-temper'd, would fiowly fpread
and dilate it felf over the greater part of the
Bubble; continually growing puler. at the top,
where at length it would crack in many places,
and thofe cracks, as they dilated, would appear

of

BOOK II. . rgt

of a pretty good, but yet obfcure and dark
Sky-colour; the white between the blue Spots
diminifliing, until it refembled the Threds of
an irregular Net-work, and foon after vanifh'd,
and left all the upper part of the Bubble of the
faid dark blue Colour. And this Colour, after
the aforefaid manner, dilated it felf downwards,
until fometimes it hath overfpread the whole
Bubble. In the mean while at the top, which
was of a darker blue than the bottom, and ap-
pear'd alfo full of many round blue Spots, fome-
thing darker than the reft, there woiild emerge
one or more very black Spots, and within thofe,
other Spots of an intenfer blacknefs, which I
mention'd in the former Obfervation ; and thefe
continually dilated themfelves until the Bubble
broke.

If the Water was not very tenacious, the black
Spots would break forth in the white, without
any fenfible intervention of the blue. And fome-
times they would break forth within the prece-
dent yellow, or red, or perhaps within the blue
of the fecond order, before the intermediate Co-
lours had time to difplay themfelves.

By this defcription you may perceive how great
an affinity thefe Colours have with thofe of Air
defcribed in the fourth Obfervation, although
fet down in a contrary order, by reafon that
they begin to appear when the Bubble is thick-
eft, and are moft conveniently reckon'd from
the loweft and thickeft part of the Bubble up-
wards.

Obf. 19. Viewing in feveral oblique Poiitions
of my Eye the Rings of Colours emerging on

the

192 O P T I C K S.

the top of the Bubble, I found that they were
fenfibly dilated by increafing the obliquity, but
yet not fo much by far as thofe made by thinn'd
Air in the feventh Obfervation. For there they
v/ere dilated fo much as, when view'd moft ob-
liquely, to arrive at a part of the Plate more than
twelve times thicker than that where they ap-
pear'd when viewed perpendicularly j whereas ii;i
this cafe the thicknefs of the Water, at which
they arrived when viewed moil obliquely, was to
that thicknefs which exhibited them by per-
pendicular Rays, fomething lefs than as 8 to 5'.
By the beft of my Obfervations it was between
15 and 15; to 10; an increafe about 24 times lefs
than in the other cafe.

Sometimes the Bubble would become of an
uniform thicknefs all over, except at the top of
it near the black Spot, as I knew, becaufe it
would exhibit the fame appearance of Colours
in all Portions of the Eye. And then the Co-
lours which were feen at its apparent circumfe-
rence by the obliquefl Rays, would be different
from thofe that were feen in other places, by
Rays lefs oblique to it. And divers Spedtators
might fee the fame part of it of differing Co-
lours, by viewing it at very differing Obliqui-
ties. Now obferving how much the Colours at
the fame places of the Bubble, or at divers pla*
ces of equal thicknefs, were varied by the fe-
veral Obliquities of the Rays; by the affiflance
of the 4th, 14th, 1 6th and i8th Obfervations,
as they are hereafter explain'd, I colled: the
thicknefs of the Water requifite to exhibit any
one and the fame Colour, at feveral Obliquities,

to

BOOK II.

193

to be very nearly in the Proportion expTeffed in

this Table.

Incidence on
the Water.

Rejra5lion into
the Water.

Thicknefs of
the Water.

Deg. Min.

Deg. Min.

00 00

00 00

10

15 00

II II

loi

30 00

22 I

10^

45 00
60 00

7S 00
90 00

32 2

40 30

• 46 25

48 35

I If
13

In the two firft Columns are exprefs'd the
Obliquities of the Rays to the Superficies of the
Water, that is, their Angles of Incidence and
Refradion. Where I fuppofe^ that the Sines
which meafure them are in round Numbers, as
3 to 4, though probably the DifTolution of Soap
in the Water, may a little alter its refradive
Virtue. In the third Colpmn, the Thicknefs of
the Bubble, at which any one Colour is exhibit-
ed in thofe feveral Obliquities, is exprefs'd in
Parts, of which ten conftitute its Thicknefs when
the Rays are perpendicular. And the Rule
found by the feventh Obfervation agrees well
with thefe Meafures, if duly apply'd -, namely,
that the Thicknefs of a Plate of Water requifite
to exhibit one and the fame Colour at feveral
Obliquities of the Eye, is proportional to the
Secant of an Angle, whofe Sine is the firft of an
hundred and fix arithmetical mean. Proportion

O. nals

194 OP TIC KS.

nals between the Sines of Incidence and Refradion ^
counted from the lelTer Sine, that is, from the
Sine of Refrad:ion when the Refradion is made
out of Air into Water, otherwife from the Sine
of Incidence.

I ,have fometimes obferv'd, that the Colours
whi<;h arife on polifh'd Steel by heating it, or on
Bell-metal, and fome other metalline Sub-
ftances, 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 thefe Co-
lours are not fo great and fenfible as of thofe
made by Water. For the Scoria, or vitrified Part
of the Metal, which mofl Metals when heated or
melted do continually protrude, and fend out
to their Surface, and which by covering the
Metals in form of a thin glafly Skin, caufes
thefe Colours, is much denfer than Water ; and
I find that the Change made by the Obliquation
x)f the Eye is leaft in Colours of the denfeft thin
Subilances.

Obf. 20. As in the ninth Obfervation, fo here,
the Bubble, by tranfmitted 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, feemed red at its apparent Circumference,
if the Clouds at the fame time, or immediately
after, were view'd through it, the Colour at its
Circumference would be blue-. And, on the

contrary.

BOOK IL 19$

.contrary, when by refleded Light it appeared
blue, it would appear red by tranfmitted Light.

Obf. 2 1. By wetting very thin Plates of Muf-
CGvy Glals, whole thmnels made the like Co-
lours appear, the Colours became more taint and
languid , efpecially by wetting the Plates on
that fide oppofite to the Eye: But I could not
perceive any variation of their Species. So then
the thicknefs of a Plate requiiite to produce
any Colour, depends only on the denlity of the
Plate, and not on that of the ambient Medium.
And hence, by the loth and i6th Obfervations,
may be known the thicknefs which Bubbles of
Water, or Plates of Mufco'-cy Glafs, or other
Subftances, have at any Colour produced by
them.

Obf, 22. A thin tranfparent Body, which is
denfer than its ambient Medium, exhibits more
brisk and vivid Colours than that which is fo
much rarer; as I have particularly obferved iii
the Air and Clafs. For blowing Glafs very thin
at a Lamp Furnace, thofe Plates encompalTed
with_ Air did exhibit Colours much more vivid
than thofe of Air made thin between two Glaf-
fes.

Obf. 23. Comparing the quantity of Light
refledted from the feveral Rings, I found that
it was mpft copious from the iiril or inniofi;,
and in the exterior Rings became gradually lef^
and lefs. Alfo the whitenefs of the iirft Ring
was flronger than that refleded from thofe
parts of the thin Medium or Plate which wxre
without the Rings j as I co aid manifeftly per-
ceive by viewing at a diftance the Rings made

C a by

196 O P T I C K S.

by the two Objed-glafTes ; or by comparing tw6
Bubbles of Water blown at diflant Times, in the
firft of which the Whitenefsappear'd, which fuc-
ceeded all the Colours, and in the other, the
Whitenefs which preceded them all.

Obf. 24. When the two Objeil-glafTes were
lay'd upon one an cither, fo as to make the Rings-
of the Colours appear, though with my naked Eye
I could not difcern aljove eiffht or nine of thofe

o

Rings, yet by viewing them through a Prifm I
have feen a far greater Multitude, infomuch that
I could number more than forty, befides many
others, that were fo very fmall and clofe together,
that I could not keep my Eye fteady on them fe-
verally fo as to number them, but by their
Extent I have fometimes eftimated them to be
more than an hundred. And I believe the Expe-
riment may be improved to the Difcovery of far
greater Numbers. For they feem to be really un-
limited, though vifible only fo far as they can be
feparated by the Refradion of the Prifm, as I (hall
hereafter explain.

But it was but one fide of thefe Rings, namely,
that towards which the Refraction was made,
which by that Refradion was render'd diftind:,
and the other fide became more confufed than
when view'd by the naked Eye, infomuch that
there I could not difcern above one or two,
and fometimes none of thofe Rings, of which
I could difcern eight or nine with my naked
Eye. And their Segments or Arcs, which on
the other fide appear'd fo numerous, for the
moft part exceeded not the third Part of a Cir-
cle. If the Refraction was very great, or the

Prifm

B O O K II. 197

Prilm very diftant from the Ohjed-glalTes, the
middle Part of thofe Arcs became alfo confu-
fed, fo as to difappear and conftitute an even
Whitenefs, whiUl on either fide their Ends, as
alfo the whole Arcs farthefl from the Center,
became diftinder than before, appearing in the
Form as you fee them defign'd in the hfth Fi-
gure.

The Arcs, where they feem'd diflindteft, were
only white and black fuccellively, without any
other Colours intermix'd. But in other Places
there appeared Colpurs, whofe Order was inverted
by the Kefradtion in fuch manner, that if I firft
held the Prifm very near the Objedt-glafles, and
then gradually removed it farther off towards my
Eye, the Colours of the 2d, 3d, 4th, and fol-
lowing Rings flirunk towards the white that
emerged between them, until they wholly va-
nifli'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 fometimes fo lay'd one Objed-glafs
upon the other, that to the naked Eye they
have all over feem'd uniformly white, without
the leaft Appearance of any of the colour'd
Rings ; and yet by viewing them through a
Prifm, great Multitudes of thofe Rings have
difcover'd themfelves. And in like manner
Plates of Miifcovy Glafs, and Bubbles of Glafs
blown at a Lamp-Furnace, which were not fo
tlijn as to exhibit any Colours to the naked Eye,
have through the Prifm exhibited a great Va^
riety of them ranged irregularly up and down in

O 3 the

198 O P T I C K S.

the Form of Waves. And fo Bubbles of Water,
before they began to exhibit their Colours to the
naked Eye of aBy-ftander, have appeared through
fl Prlfrn, girded about with many parallel and
horizontal Rings ^ to produce v^hich Effed:, it
was neceffary to hpld the Prifm parallel, or
very nearly parallel to the Horizon, and to
difpofe it {q th^t the Rays might be refraded
upwards.

T H»E

THE

SECOND BOOJ^

O F

OPTICKS

PART II.

Remarks tipo-n the foregoing Obfervatio?ts,

A V I N G given my Obfervations
of thefe Colours, before I make
life of them to unfold the Caufes
of the Colours of natural Bodies,
it is convenient that by the fim-
pleft of them,fuch asare the ad, 3d,
4th, 9th, I2thj 1 8th, 20th, and 24th, I firft ex-

O 4 plaiu

20O ; O P T I C K S.

plain the more compounded. And firft to fhew
now the Colours in the fourth and eighteenth
Obiervations are produced, let there be taken in
any Right Line from the Point Y, [in Ffg.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, 5, f^g, t, |, ^, |, |, i,
whereby the Lengths of aMulical Chord to found
all the Notes in an eighth are reprefented; that
is, in the Proportion of the Numbers 6300, 68 14,
71 14, 7631, 8255, 8855, 9243> loooo. And
at the Points A, B, C, D, E, F, G, H, let Perpen-
diculars A a, B /3, &c, be erefted, by whofe In-
tervals the Extent of the feveral Colours fet under-
neath againft them, is to be reprefented. Then
divide the Line A a in fuch Proportion as the
lumbers i, 2, 3, 5, 6, 7, 9, xo, 1 1, &c. fet at
the Points of Divifion denote. And through
thofe Divifions from Y draw Lines 1 1, 2 K, 3 L,
5 M, 6 N, 7 O, &c.

Now, if A 2 be fuppofed to reprefent the
Thicknefs of any thin tranfparent Body, at which
the outmoft Violet is moft copioully reflected
in the firft Ring, or Series of Colours, then by
the 13th Obfervation, HK will reprefent its
Thicknefs, at which the utmoft Red is moft co-
pioufly refleded in the fame Series. Alfo by
the 5th and i6th Obfervations, A 6 and HN
will denote the ThicknelTes at which thofe ex-
treme Colours are moft copioufly refledied in
the fecond Series, and A 10 and HQ^he Thick-
neffes at which they are moft copioufly refledl-
ed in the third Series, ■ and fo on. And the
Thicknefs at which any of the intermediate Co-
i lours

BOOK II. 20I

iours are reflefted moft copioufly, will, accor-
ding to the 14th Obfervation, be defined by the
diftance of the Line AH from the intermediate
parts of the Lines 2 K, 6N, 10 Q, &c. againft
which the Names of thofe Colours are written
below.

But farther, to define the Latitude of thefe
Colours in each Ring or Series, let A i defign
the leajft thicknels, and A 3 the greateft thi,ck-
nefs , at which the extreme violet in the firft
Series is reiledted, and let HI, and H L, de-
fign the like limits for the extreme red, and let
the intermediate Colours be limited by the in-
termediate parts of the Lines il, and 3L, a-
gainfi; which the Names of thofe Colours are
written, and fo on: But yet with this caution,
that the Reflexions be fuppofed flrongefl at the
intermediate Spaces, 2K, 6N, ioQ> ci?r. and
from thence to decreafe gradually towards thefe
limits, 1 1, 3L, 5M, 7O, &c. on either fide;
where you muft not conceive them to be pre-
cifely limited, but to decay indefinitely. And
whereas I have afiign'd the fame Latitude to e-
very Series, I did it, becaufe although the Co-
lours in the firfl Series feem to be a little broad-
er than die* reft, by reafon of a ftronger Re-
flexion tliere, yet that inequality is fo infenfi-
ble as fcarcely to be determin'd by Obferva-
tion.

Now according to this Defcription, concei-
ving that the Rays originally of feveral Colours
are by turns refleded at the Spaces 1 1 L 3, 5M
O7, 9P R 1 1, ^c. and tranfmitted at the Spaces
AHIi, 3LM5, 7 OP 9, &c, it is eafy to know

wliat

202 O P T I C K S.

what Colour muft in the open Air be exhi-
bited at any thickneis of a tranlparent thin Bo-
dy. For if a Ruler be -applied parallel to AH,
at that diftance from it by which the thicknefs
of the Body is reprefented, the alternate Spaces
il L3, 5M O7, &c. which it croiTeth will de-
note the reflected original Colours, of which
the Colour exhibited in the open Air is com-
pounded. Thus if the conftitutiop of the green
in the third Series of Colours be defired, apply
the Ruler as you fee at tt p cr 9, and by its paffing
through fome of the blue at tt and yellow at cr,
as' well as through the green at ^, you may con-
clude that the green exhibited at that thicknefs of
the Body is principally conflituted of original
green, but not without a mixture of fome blue
and yellow.

By this means you may know how the Co-
lours from the Center of the Rings outward
ought to fucceed in order as they were defcri-
bed in the 4th and i8th Obfervations. For if
you move the Ruler gradually from AH through
all diflances, having pafs'd over the firfl Space
which denotes little or no Reflexion to be made
by thinneft Subftances, it will firft arrive at i the
violet, and then very quickly at the blue and
green', which together with that violet com-
pound blue, and then at the yellow and red, by
whofe farther addition that blue is converted
into whitenefs, which whitenefs continues du-
ring the tranfit of the edge of the Ruler from
I to 3, and after that by the fucceffive dehci-
cnce of its component Colours, turns firfl to
co-mpound yellow, and then to red, and lafl of
9 all

BOOK IT. 203

■all the red ceafeth at L. Then begin the Co-
lours of the fecond Series, which fucceed in
order during the tranfit of the edge of the
Ruler from 5 to O, and are more lively than
before , becaufe more expanded and fevered.
-And for the fame reafon, inftead of the former
v^hite 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 fucceed in or-
der; firft, the violet, which a little interferes
with the red of the fecond order, and is there-
by inclined to a reddifli purple; then the blue
and green, which are lefs mix'd with other
Colours, and confequently more lively than be-
fore, efpecially the green: Then follows the
yellow, forne of which towards the green is di-
Itintt and good, but that part of it towards the
fucceeding red, as alfo that red is mix'd with
the violet and blue of the fourth Series, where-
by various degrees of red very much inclining
to purple are compounded. This violet and
blue, which fliould fucceed this red, being mix-
ed with , and hidden in it , there fucceeds a
green. And this at firft is much inclined to
blue, but foon becomes a good green, the on-
ly unmix'd and lively Colour in this fourth Se-
ries. For as, it verges towards the yellow, it
begins to interfere with the Colours of the fifth
Series , by whofe mixture the fucceeding yel-
low and red are very much diluted and made
dirty, efpecially the yellow, which being the
v/eaker Colour is fcarce able to iTiew it felf.

After

204 O P T I C K S.

After this the feveral Series interfere more and
more, and their Colours become more apd more
intermix'd, till after three or four more revo-
lutions ( in which the red and blue predominate
by turns) all forts of Colours are in all places
pretty equally blended, and compound an even
whitenefs.

And fmce by the 15th Obfervation the Rays
endued with one Colour are tranfmitted, where
thofe of another Colour are reflected, the reafon
of the Colours made by the tranfmitted Light in
the 9th and 20th Obfervations is from hence
evident.

If not only the Order and Species of thefe
Colours, but alfo the precife thicknefs of the
Plate, or thin Body at which they are exhibited,
be defired in parts of an Inch, that may be alfo
obtained by affiftance of the 6th or i6th Obfer-
vations. For according to thofe Obfervations
the thicknefs of the thinned Air, which be-
tween two GlalTes exhibited the moil luminous

fjarts of the firfl fix Rings were ^7^^ -^^

-4 — —1— — 1— —V- parts of an Inch,

178000 178000^ 178000^ 178000 -I

Suppofe the Light refle(5ted moll copioufly at
thefe thicknefles be the bright citrine yellow,
or confine of yellow and orange, and thefe thick-
nefles will be Fa, Fyu, Fr, F|, Fo, F7. And
this being known, it is eafy to determine what
thicknefs of Air is reprefented by G(p, or by any
other difl:ance of the Ruler from A H.

But farther, fince by the loth Obfervation the
thicknefs of Air was to the thicknefs of Water,

which

BOOK 11. 205

which between the fame GlaiTes exhibited the
fame Colour, as 4 to 3, and by the 21ft Obfer-
vation the Colours of thin Bodies are not varied
by varying the ambient Medium j the thick-
nefs of a Bubble of Water, exhibiting any Co-
lour, will be J of the thicknefs of Air produ-
cing the fame Colour. And fo according to
the fame loth and 21ft Obfervat ions, the thiok-
nefs of a Plate of Glafs, whofe Refradion of
the mean refrangible Ray, is meafured by the
proportion of the Sines 31 to 20, may be \° of
the thicknefs of Air producing the fame Co-
lours; and the lijce of other Mediums. I do
not affirm , that this proportion of 20 to 3 r,
holds in all the Rays ; for the Sines of other
forts of Rays have other Proportions. But the
differences of thofe Proportions are fo little
that I do not here confider them. On thefe
Grounds I have compofed the following Table,
wherein the thicknefs of Air, Water, and Glafs,
at which each Colour is mofl intenfe and fpeci-
fick, is exprelfed in parts of an Inch divided in-
to ten hundred thoufand equal parts.

• me

2o6

O P T I C K a

I'he thicknefs of colour d Plates and Particles of

-^

Their Colours of the
4kft Order, *\

^Very black

Black

Beginning of
Black

Blue

White
I Yellow

Orange
vRed

r Violet

V Indigo

A Blue

Of thcfecond Order, J Green
Alellow
y Orange
/ Bright red
L Scarlet

of the third Order,<

Purple

Indigo

Blue

Green

Yellow

Red

Bluifh red

Bluifli green
Green

Yellowiih green
Red

Ofihe fifth Order, {Gre^eniih blue

-rvr 1 r 1- « J TGreenifli blue
Of the fixth Order, \^q^

of the fevemh Or-rGreeniih blue
der, (.Ruddy white

of the fourth Order,*

^ Jir.

Water.

Ghfs.

1

J

J-'

1

T

^ [

I

}

2 a

+

Tr

2

Ij-

It

^1

I'r

lir

5t

3^ .

3f

7^

5f

41

8

6

5t

9

H

5t-

II*-

81-

7t

li^

^f

8tt

14

loi-

9

i5t

11^

^t

16}

I2|

lof

17^

1?

ii>

i8f

'3^

u^

i9f

i+i

12f

21

i5i

i3t^

22t'-

i6±

147

23?-

T-lVo

I5t',-

^51

18-,^,

16^

27^

20.1

i7t

^9.

^4

1%^

1L_

24

20}

34

ijf

22

5 54

2cr;

2Z^

3^

27

237-

Jf7_

2<5

4<?

34t

/-9i

52f

391-

34

5H

44

38

^5

48} 1

42

71

557
57|-

45t

77

49f

Now

BOOK IL 20 j

• Now if this Table be compared with the 6th
Scheme, you will there fee the conftitntion of
each Colour, as to its Ingredients, or the ori-
ginal Colours of which it is compounded, and
dience be enabled to judge of its Intenfenefs or
Imperfection ; which may fuffice in explication
of the 4th and i8th Obfervations, unlefs it be
farther delired to delineate the manner how
the Colours appear, when the two Objed;-glaf-
fes are laid upon one another. To do which,
let there be defcribed a large Arc of a Circle,
and a ftreight Line which may -touch that Arc,
and parallel to that Tangent feveral occult
Lines, at fuch diftances from it, as the Num-
bers fet againft the feveral Colours in the Ta-
ble denote. For the Arc, and its Tangent, will
reprefent the Superficies of the Glalles termi-
nating the interjacent Air; and the places where
the occult Lines cut the Arc will (how at what
diftances from the center, or Point of contadl,
each Colour is refiedled.

There are.alfo other Ufesof this Table: For
by its afiirtance the thicknefs of the Bubble in
the 19th Obfervation was determin'd by the Co-
lours which it exhibited. And fo the-bignefs of
the parts of natural Bodies may be conje-
diured by their Colours, as ihall be hereafter
fhewn. Alfo, if two "or more very thin Plates
be laid one upon another, fo as to compofe one
Plate equalling them all in thicknefs, the refult-
ing Colour may be hereby determin'd. For in-
flance, Mr. Hook obferved, as is mentioned in
his Micrograpkia^ that a faint yellow Plate of
Miijccoy Glafs laid upon a bli^e one, conftituted

a very

2o8 O P T I C K S.

a very deep purple. Tke yellow of the firfl Or-
der is a faint one, and the thicknefs of the Plate
exhibiting it, according to the Table is 42, to
which add 9, the thicknefs exhibiting blue of
the fecond Order, and the Sum will be 13I,
which is the thicknefs exhibiting the purple of
the thir4 Order.

To explain, in the next place, the circum-
ftances of the 2d and 3d Obfervations 5 that is,
how the Rings of the Colours may ( by turning
the Prifms about their common Axis the con-
trary way to that expreffed in thofe Obferva-
tions ) 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 muft be remember'd, that thofe Rings
of Colours are dilated by the obliquation of the
Rays to the Air which intercedes the GlalTes,
and that according to the Table in the 7th Ob-
fervation, their Dilatation or Increafe of their
Diameter is mofl manifeft and fpeedy when
they are obliquefl:. Now, the Rays of yellow
being more refra(5led by tne firft Superficies of
the faid Air than thofe of red, are thereby
made more oblique to the fecond Superficies,
at which they are refieded to produce the co-
lour'd Rings, and confequently the yellow Cir-
cle in each Ring will be more dilated than the
red ; and the Excefs of its Dilatation will be fo
much the greater, by how much the greater is
the obliquity of the Rays, until at laft it be-
come of equal extent with the red of the fame
Ring. And for the fame reafon the green, blue
and violet, will be alfo fo much dilated by the

ftill.

BOOK II. 209

iibill greater obliquity of their Rays, as to be-
come all very nearly of equal extent with the
red, that is, equally diltant from the center of
the Rings, And then all -the Colours of the
fame Ring mull be coincident, and by their
mixture exhibit a white Ring. And thefe white
Rings muft have black and dark Rings between
them, becaufe they do not fpread and interfvire
with one another, as before. And for that rea-
fon alfo they mufl become diftindler, and vifible
to far greater numbers. But yet the violet be-
ing obliqueft will be fomething more dilated,
in proportion to its extent, than the other Co-
lours, and fo 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 fenfibly
dilated than the red and yellow, and fo being
farther removed from the center of the Rines,
the Colours muft 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 in-
terior. And the violet, by reafon of the great-
eft obliquity of its Rays, being in proportion
moft of all expanded, will fooneft appear at
the exterior Limb of each white Ring, and be-
come more confpicuous than the reft. And the
feveral Series of Colours belonging to the feve-
ral Rings, will, by their unfolding and fpread-
ing, begin again to interfere, and thereby ren-
der the Rings lefs diftindt, and not vifible to fo
great numbers.

P If

2IO O P T I C K S.

If inflead of the Prifms the Objed-glafleS be
made ufe of, the Rings which they exhibit be-
come not white and diilindl by the obhquity of
the Eye, by reafon that the Rays in their paflage
through that Air which intercedes tne Glafles
are very nearly parallel to thofe Lines in which
they were lirft incident on the GlafTes, and con-
fequently the Rays endued with feveral Colours ^
are not inclined one more than another to that
Air, as it happens in the Prifms.

There is yet another circumftance of thefe
Experiments to be confider'd, and that is why
the black and white Rings which when view'd
at a diftance appear diftincft, fliould not only be-
come confufed by viewing them near at hand,
but alfo yield a violet Colour at both the edges
of every white Ring. And the reafon is, that
the Rays which enter the Eye at feveral parts
of the Pupil, have feveral Obliquities to the Glaf-
fes, and thofe which are mofl oblique, if confi-
der'd apart, would reprefent the Rings bigger
than thofe which are the leaft oblique. Whence
the breadth of the Perimeter of every white
Ring is expanded outwards by the obliquefl
Rays, and inwards by the leafi oblique. And
this Expanfion is fo much the greater by how
much the greater is the difference of the Obli-
quity ; that is, by how much the Pupil is wider^
or the Eye nearer to the Glafles. And the
breadth of the violet muft be mofb expanded,
becaufe the Rays apt to excite a Senfation of
that Colour arc mofl oblique to a fecond or
farther Superficies of the. thinn'd Air at which
they are rcfiedted, and have alfo the grearefl

varia-

BOOK II. 211

variation of Obliquity, which makes that Co-
lour fooneft emerge out of the edges of the
white. And as the breadth of every Ring is
thus augnaented, the dark Intervals niufl be di-
minifli'd, until the neighbouring Rings become
continuous, and are blended, the exteiior iiril,
and then thofe nearer the center j fo that they
can no longer be diftinguifh'd apart, but feem to
conflitute an even and uniform whitenefs.

Among all the Obfervations there is none ac-
companied with fo odd circumftances as the
twenty-fourth. Of thofe the principal are, that
in thin Plates, v/hich to the naked Eye feem of
an even and uniform tranfparent whitenefs,
without any terminations of Shadows, the Re-
fraction of a Prifm fhould make Rings of Co-
lours appear, whereas it ufually makes Objedts
appear colour'd only there where they are ter-
minated with Shadows, or have parts unequal-
ly luminous ; and that it fliould make thofe
Kings exceedingly diftindl and white, although
it ufually renders Objeds confufed and colour-
ed. The Caufe of thefe things you will under-
ftand by confidering, that all the Rings of Co-
lours are really in tiie Plate, when vie w'd with
the naked Eye, although by reafon of the great '
breadth of their Circumferences they fo much
interfere and are blended together, that they
feem to conflitute an uniform whitenefs. But
when the Rays oafs through the Prifm to the
Eye, the Orbits of the feveral Colours in every
Ring are refraded, fome more than others, ac-
cording to their degrees of Pvcfrangibility : By
which means the Colours on one fide of the

P 2 Ring

212 O P T I C K S.

Ring (that is in the circumference on one fide of
its center, ) become more unfolded and dilated,
and thofe on the othef fide more complicated and
contraded. And where by a due Refra(3:ion they
are fo much contradied, that the feveral Rings'
become narrower than to interfere with one ano-
ther, they muft appear diftind:, and alfo white,
if the conftituent Colours be fo much contrad:ed
as to be wholly coincident. But on the other
fide, where the Orbit of every Ring is made
broader by the farther unfolding of its Colours,
it muft interfere more with other Rings than be-
fore, and fo become lefs diftind;.

To explain this a little farther, fuppofe the
concentrick Circles A V, and B X, [in Fig. 7.]
reprefent the red and violet of any Order,-
which, together with the intermediate Colours,
conllitute any one of thefe Rings. Now thefe
being view'd through a Prifm, the violet Circle
B X, will, by a greater Refraction, be farther
tranllated from its place than the red A V^ and
fo approach nearer to it on that fide of the Cir-
cles, towards which the Refractions are made.
For inftance -, if the red be tranflated to a v,
the violet may be tranflated to I? x, fo as to ap-
proach nearer to it at x than before y and if the
red be farther tranllated to av, the violet may
be fo much farther tranflated to b x as to con-
vene with it at X ; and if the red be yet farther
tranflated to a T, the violet may be ftill fo much
farther tranflated to /? | as to pafs beyond it at
§, and convene with it at e and f. And this
being underllood not only of the red and vio-
let, but of all the other intermediate Colours,

and

BOOK II. 213

and alfo of every revolution of thofe Colours,
you will ealily perceive how thofe of the fame
revolution or order, by their nearnefs at x v
and T J, and their coincidence at x v, e and J\
ought to conftitute pretty diftindt Arcs of Cir-
cles, efpecially at x v, or at e and f; and that
they will appear feverally at x Vy and at x v ex-
hibit whitenefs by their coincidence, and again
appear feveral at T |, but yet in a contrary or-
der to that which they had before, and ftill re-
tain beyond e and f. But on the other fide,
at a I?, a b, or a l3, thefe Colours mufl: become
much more confufed by being dilated and fpread
fo as to interfere with thofe of other Orders.
And the fame confufion will happen at T | be-
tween e and f^ if the Refraction be very great,
or the Prifm very diftant from the Objcdt-glaf-
fes : In which cafe no parts of the Rings will
be feen, fave only two little Arcs at e and J\
whofe diftance from one another will be aug-
mented by removing the Prifm flill farther from
the Objed-glafTes : And thefe little Arcs mult
be diftindtefl and w^hiteft at their middle, and
at their ends, where they begin to grow con-
fufed, they mull be colour'd. And the Colours
at one end of every Arc mufl be in a contrary
order to thofe at the other end, by reafon that
they crofs in the intermediate white ; namely,
their ends, which verge towards T g, will be
red and yellow on that fide next the center,
and blue and violet on the other fide. But
their other ends which verge from. T J, will on
the contrary be blue and violet on that fide to-

P 2 ^ya^ds

214 O P T I C K S.

wards the center, and on the other fide red and
yellow.

Now as all thefe things follow from the pro-
perties of Light by a mathematical way of rea-
foning, fo the truth of them may be manifefted
by Experiments. For in a dark Room, by view-
ing thefe Rings through a Prifm, by reflexion
of the feveral prifmatick Colours, which an
affiftant caufes to. move to and fro upon a Wall
or Paper from whence they are reflected, whilft
the Spe6:ator's Eye, ihe Prifm, and the Objed:-
glaffes, (as in the 13th Obfervation,) are placed
Iteadyj the Polition of the Circles made fuc-
ceifively by the feveral Colours, will be found
fuch, in refped: of one another, as I have de-
scribed in the Figures a b x ^0^ or a b x v, or
a /S I T. And by the fame method the truth of
the Explications of other Obfervations may be
examined.

By what hath been faid, the like Phaenomena
of Water and thin Plates of Glafs may be un-
derftood. But in fmall fragments of thofe Plates
there is this farther obfervable, that where they
lie flat upon a Table, and are turned about their
centers whilfl they are view'd through a Prifm,
they will in fome poflures exhibit Waves of va-
rious Colours ; and fome of them exhibit thefe
Waves in one or two Pofitions only, but the
mofc of them do in all Pofitions exhibit them,
and make them for the mofl part appear al-
mioft all over the Plates. The reafon is, that
the Superficies of fuch Plates are not even, but
have many Cavities and Swellings, which, how
fhallow foever, do a little vary the thicknefs of

th^

BOOK II. 215

tlie Plate. For at the feveral fides of thofe Ca-
vities, for the Reafons newly defcribed, there
ought to be produced Waves in feveral po-
llures of the Prifm. Now though it be but
fome very fmall and narrower parts of the Glafs,
by which thefe Waves for the niofl part are cau-
fed, yet they may feem to extend themfelves
over the whole Glafs, becaufe from the narrow-
eft of thofe parts there are Colours of feveral
Orders, that is, of feveral Rings, confufedly re-
fleded, which by Refraction of the Prifm are
unfolded, feparated, and, according to their
degrees of Refraction, difperfed to feveral pla-
ces, fo as to conftitute fo many feveral Waves,
as there were divers orders of Colours promifcu-
oufly reflected from that part of the Glafs.

Thefe are the principal Phasnomena of thin
Plates or Bubbles, whofe Explications depend
on the properties of Light, which I have here-
tofore deliver'd. And thefe you fee do necef-
farily follow from them, and agree with them,
even to their very leaft circumftancesj and not
only fo, but do very much tend to their proof.
Thus, by the 24th Obfervation it appears, that
the Rays of feveral Colours, made as well by thin
Plates or Bubbles, as by Refradions of a Prifm,
haye feveral degrees of Refrangibility j where-
by thofe of each order, which at the reflexion
from the Plate or Bubble are intermix'd with
thofe of other orders, are feparated from them
by Refraction, and aflbciated together fo as to
become vifible by themfelves like Arcs of Cir-
cles. For if the Rays were all alike refrangi-
ble, 'tis impofiible that the whitenefs, which

P 4 to

2i6 O P T I C K S.

to the naked Senfe appears uniform, fhould by
Refraction have its parts tranfpofed and ranged
into thofe black and white Arcs.

It appears alfo that the unequal Refradlions
of difforin Rays proceed not from any contin-
gent irregularities ; fuch as are Veins, an uneven
Polifh, or fortuitous Polition of the Pores of
Glafs ; unequal and cafual Motions in the Air
or /Ether, the fpreading, breaking, or dividing
the fame Ray into many diverging parts ; or the
like. For, admitting any fuch irregularities,
it v^ould be impoiTible for Refractions to render
ihofe Rings fo very diflincft, and well defined,
as they do in the 24th Obfervation. It is ne^
cefTary therefore that every Ray have its proper
and conftant degree of Refrangibility connate
with it, according to which its refraction is ever
juflly ^nd regularly perform'd^ and that feveral
flays have feveral of thofe degrees.

And what is faid of their Refrangibility may
be alfo underflood of their Reflexibility, that is,
of their Difpofitions to be refle<^ed, fome at a
greater, and others at a lefs thicknefs of thin
Plates or Bubbles j namely, that thofe Difpofi-
tions are alfo connate with the Rays, and im-
mutable ; a^ may appear by the 13 th, 14th, and
J 5 th Obfervations, compared with the fourth and
eighteenth.

By the precedent Obfervations it appears al-
fo, that whitenefs is a diihmilar mixture of all
polours, and that Light is a mixture of Rays
endued with all thofe Colours. .For, confider-
ing the multitude of the Rings of Colours in
jhe ^d^ I2th5 and 24th Obfervations, itismani-
"■■^ ■ ; feft,

BOOK 11. 217

feft, that although in the 4th and i8th Obfer-
vations there appear no more than eight or
jiine of thofe Rings, yet there are really a far
greater number, which fo much interfere and
mingle with one another, as after thofe eight
or nine revolutions to dilute one another whol-
ly, and conllitute an even and fenfibly uniform
whitenefs. And confequently that whitenefs
muft be allow'd a mixture of all Colours, and
the Light which conveys it to the Eye muft
be a mixture of Rays endued with all thofe Co-
lours.

But farther J by the 24th Obfervation it ap-
pears, that there is a conftant relation between
Colours and Refrangibility ; the moft refrangi-
ble Rays being violet, the leaft refrangible red,
and thofe of intermediate Colours having pro-
portionably intermediate degrees of Refrangibi-
lity. And by the 13th, 14th, and J5th Obfer-
vations, compared with the 4th or i8th, there
appears to be tlie fame conftant relation be-
tween Colour and Reflexibility ; the violet be-
ing in like circumftances refleded at leaft thick-
nelfes of any thin Plate or Bubble, the red at
greateft thicknelTes, and the intermediate Co-
lours at intermediate thicknefles. Whence it
follows, that the colorifick Difpofitions of Rays
are alfo connate with them, and immutable^ and
by confequence, that all the Produdions and
Appearances of Colours in the World are de-
rived, not from any phyfical Change caufed in
Light by • Refradion or Reflexion, but only
Irom the various Mixtures or Separations of
|lays, by virtue of their different Refrangibility

or

-^

218

O P T I C K S.

or Reflexibility. And in this refped the Scicncd
of Colours becomes a Speculation as truly ma-
thematical as any other part of Opticks. I mean,
fo far as they depend on the Nature of Light,
and are not produced or alter'd by the Power
v of Imagination, or by ilriking or preffing the
Eye.

THE

THE

SECOND BOOK

O F

OPTICKS.

PART III.

Of the permanejit Colours of natural Bo-
dies^ and the Analogy between them and
the Colours of thiii tranfparent Plates*

AM now come to another part of
this Defign, which is to confider how
the PhiEnomena of thin tranfparent
Plates fland related to thofe of all o-
ther natural Bodies. Of thefe Bodies I have al-
ready told you that they appear of divers Co-
lours,

220 O P T I C K S.

lours, accordingly as they are difpofed to refled:
moft copiouily the Rays originally endued with
thofe Colours. But their Conflitutions, where-
by they refied: fome Rays more copiouily than
others, remain to be difcover'd ; and thefe I lliall
endeavour to manifeft in the following Propo-
iitions.

P R O p. I.

*ith'ofe Superficies of t ran/ parent Bodies refieEi the
greatejl quantity of Lights which have the great-
eft refraBing Power ^ that is, which i7itercede
Mediums that differ mofi in their refraBiije Den-
Jities. And in the Confines of equally refraBing
Mediums there is no Kefiexion.

TH E Analogy between Reflexion and Re-
fradion will appear by confidering, that
when Light paffeth obliquely out of one Medi-
um into another which refracts from the per-
pendicular, the greater is the difference of their
refradive Denfuy, the lefs Obliquity of Inci- •
dence is requifite to caufe a total Reflexion,
For as the Sines are which meafure the Refra-
(Ttion, fo is the Sine of Incidence at which the
total Reflexion begins, to the Radius of the
Circle ; and confequently that Angle of Inci- *
dence is leaft where there is the greateft difl^e-
rence of the Sines; Thus in the paffing of
Light out of Water into Air, where the Refra-
ction is meafured 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

BOOK II. ill

Iti pafling out of Glafs into Air, where the Re-
fradiion is meafured by the Ratio of the Sines
20 to 31, the total Reflexion begins when the
Angle of Incidence is 40 Degrees 10 Minutes;
and fo in paffing out of Cryftal, or more flrong-
ly refrading Mediums into Air, there is ftill a lefs
obliquity requifite to caufe a total reflexion.
Superficies therefore v/hich refrad; mofl: do
fooneft refled: all the Light which is incident
on them, and fo muft be allowed moft flrongly
reflexive.

But the truth of this Propofition will farther
appear by obferving, that in the Superficies in-
terceding two tranfparent Mediums, (fuch as are'
Air, Water, Oil, common Glafs, Cryftal, me-
talline Glafies, Ifland Glafl^es, white tranfparent
Arfenick, Diamonds, ^c.) the Reflexion is
ftronger or weaker accordingly, as the Super-
ficies hath a greater or lefs refrading Power.
For in the Confine of Air and Sal-gem 'tis
ftronger than in the Confine of Air and Water,
and ftill ftronger in the Confine of Air and .com-
mon Glafs or Cryftal, and ftronger in the Con-
fine of Air and a Diamond. If any of thefe,
and fuch like tranfparent Solids, be immerged
in Water, its Reflexion becomes much weak-
er than before j and ftill weaker if they be im-
merged in the more ftrongly refrading Liquors
of well rectified Oil of Vitriol or Spirit of Tur-
pentine. If Water be diftinguifli'd into two
parts by any imaginary Surface, the Reflexion
in the Confine of thofe two parts is none at all.
In the Confine of Water and Ice 'tis very little ;
in that of Water and Oil 'tis fomething greater;

la

222 O P T I C K S.

in that of Water and Sal-gem ftill greater ; and
in that of Water and Glafs, or Cryftal, or other
denfer Subftances ftill greater, accordingly as
thofe Mediums differ more or lefs in their re-
frading Powers. Hence in the Confine of com-
mon Glafs and Cryftal, there ought to be a
weak Reflexion, and a ftronger Reflexion in
the Confine of common and metalline Glafs;
though I have not yet tried this. But in the
Confine of two Glafies of equal denfity, there
is not any fenfible Reflexion ; as was fliewn in
the firft Obfervation. And tlie fame may be
underftood of the Superficies interceding two
Cryftals, or two Liquors, or any other Sub-
ftances in which no Refradion is caufed. So
then the reafon why uniform pellucid Mediums
(fuch as Water, Glafs, or Cryftal,) have no fen-
fible Reflexion but in their external Superficies,
where they are adjacent to other Mediums of
a diflferent denfity, is becaufe all their conti-
guous parts have one and the fame degree of
denfity.

Prop. II.

^he leajl parts of almojl all jtatiiral Bodies are
in fome meajure tranfparent : And the Opa-
city of thofe Bodies arifeth from the multi-
tude of "Reflexions caufed in their intertial
Parts,

'Tp HAT this is fo has been obferved by o-

-*• thers, and will eafily be granted by them

that have been converfant with Microfcopes.

And it may be alfo tried by applying any fub-

flancc

BOOK JL 223

ftance to a hole through which fome Light is
immitted into a dark Room. For how opake
foever that Subftance may feem in the opea
Air, it will by that means appear very manifeft-
ly tranfparent, if it be of a fufficient thiniiefs.
Only white metalline Bodies miift be excepted,
which by reafon of their exceffive denfity feem
to refled: almoft all the Light incident on their
firft Superficies j unlefs by folution in Menftru-
ums they be reduced into very fmall Particles,
and then they become tranfparent.

Prop. IIL

Between the parts of opake mid colour d Bodies
are many Spaces^ either empt)\ or repleniJUd
with Mediians of other DenfitieSy as Water
between the tingijig Corpufcles wherewith a-
ny Liquor is impregnated ^ Air between the
aqueous Globules that confiitute Clouds or Mijh\
and for the mofl part Spaces loid of both Air
and Water ^ but yet perhaps not wholly ^coid of
all Subjlance^ between the parts of hard Bo-
dies,

' I ^ H E truth of this Is evinced by the two
-^ precedent Propofitions : For by the fe-
cond Propofition there are many Reflexions
made by the internal parts of Bodies, which, by
the firll Propoiition, would not happen if the
parts of thole Bodies were continued without
any fuch Interftices between them ; becaufe Re-
flexions are caufed only in Superficies, which
intercede Mediums of a differing denfity, by
'Frop, I.

• ^ Buc

224 O P T I C K S.

But farther, that this difcontinuity of parts
is the principal Caufe of the opacity of Bodies,
will appear by confidering, that opake Subftan-
ces become tranfparent by filling their Pores
with any Subftance of equal or almoft equal den-
fity with their parts. Thus Paper dipped in
Water or Oil, the O cuius Mundi Stone fteep'd
in Water, Linnen Cloth oiled or varniih'd, and
many other Subilances foaked in fuch Liquors
as will intimately pervade their little Pores, be-
come by that means more tranfparent than other-
wife ; fo, on the contrary, the mofh tranfparent
Subftances may, by evacuating their Pores, or
feparating their parts, be render'd fufficiently o*
pake ; as Salts or wet Paper, or the Oculus Mun-
di Stone by being dried, Horn by being fcraped,
Glafs by being reduced to Powder, or otherwife
flawed; Turpentine by being ftirred about with
Water till they irdx imperfectly, and Water by
being form'd into many fmall Bubbles, either a-
lone in the form of Froth, or by fliaking it to-
gether with Oil of Turpentine, or Oil Olive, or
with fome other convenient Liquor, with which
it will not perfectly incorporate. And to the in-
creafe of the opacity of thefe Bodies, it condu-
ces fomething, tliat by the 23d Obfervation the
Reflexions of very thin tranfparent Subftances are
conliderably ftronger than thofe made by the
faipe Subftances of a greater thicknefs,

Prop*

BOOK IL 225

Prop. IV.

The Farts of Bodies and their Interftices mi/fl not
be lefs than of feme definite bignefs^ to render^
them opake and colour d.

■p.OR the opakeft Bodies, if their parts be
■*- fubtilly divided, (as Metals, by being diflbl-
ved in acid Menftruums, ^c^ become perfect-
ly tranfparent. And you may alfo remember,
that in the eighth Obfervation there 'was no
fenfible reflexion at the Superficies of the Ob-
ied-glaffes, where they were very near one an-
other, though they did not ablblutely touch.
And in the 1 7th Obfervation the • Reflexion of
the Water- bubble where it became thinriell was
almofl infenfible, fo as to caufe very black Spots
to appear on the top of the BubblCj by the want
of reflected Light.

On thefe grounds I perceive it is that Water,
Salt, Glafs, Stones, and fuch like Subftances,
are tranfparent. For, upon divers Confidera-
tions, they feem to be as full of Pores or Inter-
ftices between their parts as other Bodies are,
but yet their Parts and Interftices to be too
fmall to caufe Reflexions in their common Sur-
faces.

Q^ Prop.

226 O P T I C K S.

P R O p. V.

^he tranfparcnt farts of Bodies, according to their
Je-veral Jizes^ reJieEl Rays of one Colour^ and
traifmit thofe of another y on the fame grounds
that thin Plates or Bubbles do refeB or tranfmit
thofe Rays, Atid this, I take to be the ground of
all'their Colours.

*P O R if a thinn'd or plated Body, which
-■- being of an even thicknefs, appears all o-
ver of one uniform Colour, fliould be flit into
Threads, or broken into Fragments, of the fame
thicknefs with the Plate j I fee no reafon why
every Thread or Fragment fhould not keep its
Colour, and by confequence why a heap of thofe
Theads or Fragmmts fliould not conflitute a
Mafs or Powder of the fame Colour, which the
Plate exhibited before it was broken. And the
parts of all natural Bodies being like fo many
Fragments of a Plate, muft on the fame grounds
exhibit the fame Colours.

Now, that they do fo will appear by the affi-
nity of their Properties. * The finely colour'd
Feathers of fome Birds, and particularly thofe
of Peacocks Tails, do, in the very fame part of
the Feather, appear of feveral Colours in feveral
Pofitions of the Eye, after the very fame man-
ner that thin Plates were found to do in the
7th and 1 9th Obfervations, and therefore their
Colours arife from the thinnefs of the tranfpa-
rent parts of the Feathers; that is, from the
flendernefs of the very fine Hairs, or Capilla-
menta^ which grow put of the fides of the

groifer

BOOK II. 227

grofler lateral Branches or Fibres of thofe Fea-
thers. And to the fame purpofe it is, that the
"Webs of fome Spiders, by being fpun very fine,
have appeared colour'd, as fome have oblerv'd,
and that the colour'd Fibres of fome Silks, by
varying the Pofition of the Eye, do vary their
Colour. Alfo the Colours of Silks, Cloths,
and other Subftances, which Water or Oil can
intimately penetrate, become more faint and
obfcure by being immerged in thofe Liquors,
and recover their Vigor again by being dried ;
much after the manner declared of thin Bodies
in the loth and 21ft Obfervations. Leaf-Gold,
fome forts of painted Glafs, the Infufion of
Lignutn Nephritiaun, and fome other Subilan-'
ces, refledl one Colour, an(i tranfmit another;,
like thin Bodies in the 9th and 20th Obferva-
tions. And fome of thofe colour'd Powder5
which Painters ufe, may have their Colours a
little changed, by being very elaborately and
finely ground. Where I fee not what can be
juftly pretended for thofe changes, befides the
breaking of their parts into lefs parts by that
contrition, after the fame manner that the Co-
lour of a thin Plate is changed by varying its
thicknefs. For which reafon alfo it is that the
colour'd Flowers of Plants and Vegetables, by
being bruifed, ufually become more tranfparenz
than before, or at leafl in fome degree or o-
ther change their Colours. Nor is it much lefs
to my purpofe, that, by mixing divers Liq^uors,
very odd and remarkable Produd:ions and
Changes of Colours may be effected, of which
no caufe can be more obvious and rational than

Q^ that.

228 O P T I C K S.

tha:t the faiine Corpufcles of one Liquor da vari-
oufly ad upon or unite with the tinging Corpufcles
of another, fo as to make them fwell, or fhrink,
( whereby not only their bulk but their denfity
alfo may be changed,) or to divide them into
fmaller Corpufcles, (whereby a colour'd Liquor
may become tranfparent,) or to make many of
them affociate into one clufter, whereby two
tranfparent Liquors may compofe a colour'd one.
For we fee how apt thofe faiine Menftruums are
to penetrate and diffolve Subftances to which
they are applied, and fome of them to precipi-
tate what others diilblve. In like manner, if we
confider the various Phaenomena of the Atmo-
fphere, we may obferve, that when Vapours are
iirft raifed, they hinder not the tranfparcncy of
the Air, being divided into parts too fmall to
caufe any Reflexion in their Superficies. But
when in order to compofe drops of Rain they
begin to coalefce and conflitute Globules of all
intermediate lizes, thofe Globules, when they
become of a convenient fize to refle6t fome Co-
lours and tranfmic others, may conftitute Clouds
of various Colours according to their fizes. And
I fee not what can be rationally conceived in fo
tranfparent a Subftance as Water for the produ-
ction of thefe Colours, befides the various fizes
of its fluid and globular Parcels.

Prop,

BOOK 11. 229

Prop. VI.

^he parts of Bodies 011 ivhich their Colours depend ^
are denjer than the Medium which pervadet
their Interjiices,

np HIS will appear by confidering, that the
-■" Colour of a Body depends not only on
the Rays which are incident perpendicularly
on its parts, but on thofe alfo which arc inci-
dent at all other Angles. And that according
to the 7th Oblervation, a very little variation
of obliquity will change the refled:ed Colour,
where the thin Body or fmall Particle is rarer
than the ambient Medium, infomuch that fuch
a fmall Particle will at diverfly oblique Inci-
dences refledl all forts of Colours, in fo great a
variety that the Colour refuking from them all,
confufedly refled:ed from a heap of fuch Parti-
cles, muft rather be a white or grey than any
other Colour, or at beft it muft be but a very
imperfecft and dirty Colour. Whereas if the
thin Body or fmall Particle be much denfer than
the ambient Medium, the Colours, according to
the 19th Obfervation, are fo little changed by
the variation of obliquity, that the Rays which
are refled;ed leafl obliquely may predominate
over the feft, fo much as to caufe a heap of fuch
Particles to appear very intenfely of their Co-
lour.

It conduces alfo fomething to the confirma-
tion of this Propolition, that, according to the
22d Obfervation, the Colours exhibited by the
denfer thin Body within the rarer,' are more

0^3 ^ brisk

130 O P t I C K S.

brisk than thofe exhibited by the rarer within the
denfer.

I Prop. VII.

*the bignefs of the component parts of natural Bo-
dies may be conjellured by their Colours.

FO R fince the parts of thefe Bodies, by
Frop, 5. do mofl probably exhibit the
fame Colours with a Plate of equal thicknefs,
provided they have the fame refradiive denlity ;
and fince their parts feem for the mcft part to
have much the fame dehfity with Water or
Glafs, as by many circumftances is obvious to
colledt J to determine the fizes of thofe parts,
you need only have recourfe to the precedent
Tables, in which the thicknefs of Water or
Glafs exhibiting any Colour is exprefled. Thus
if it be defired to know the diameter of a Cor-
p.ufcle, which being of equal denlity with Glafs
ihall refled: green of the third Orders the Num-
ber 165 (hews it to be ^-^ parts of 'an Inch.
^ I 0000 A

The greatefl: difficulty is here to know of
what Order the Colour of any Body is. And
for this end we muft have recourfe to the 4th
and 1 8th Obfervations ; from whence may be
coUedted thefe particulars.

■Scarlets y and other reds^ oranges y and yel~
JowSy if they be pure and intenfe, are mofl pro-
bably of the fecond order. Thofe of fhe firfl
and third order alfo may be pretty goodj only
the yellow of the firfl order is faint, and the

_ orange

BOOK II. 231

orange and red of the third Order have a great
Mixture of violet and bkie.

There may be good Greens of the fourth Order,
but the pureft are of the third. And of this
Order the green of all Vegetables feenis to be,
partly by reafon of the Intenfenefs of their Co-
lours, and partly becaufe when they wither fome
of them turn to a greenifh yellow, and others
to a more perfed: yellow or orange, or perhaps
to red, paiTing firft through all the aforefaid in-
termediate Colours. Which Changes feem to
be effected by the exhaling of the Moifture
which may leave the tinging Corpufcles more
denfe, and fomething augmented by the Accre-
tion of the oily and earthy Part of that Moifture.
Now the green, without doubt, is of the fame
Order with thofe Colours into which it changeth,
becaufe the Changes are gradual, and thofe Co-
lours, though ufually not very full, yet ar&
often too full and lively to be of the fourth
Order.

Blues and Purples may be either of the fe-
cond or third Order, but the beft are of the
third. Thus the Colour of Violets feems to be
of that Order, becaufe their Syrup by acid Li-
quors turns red, and by urinous and alcaiizate
turns green. For fince it is of the Nature of
Acids to diffolve or attenuate, and of Alcalies
to precipitate or incrailate, if the Purple Co^
lour of the Syrup was of the fecond Order, an
acid Liquor by attenuating its tinging Cor-
pufcles would change it to a red of the in ft Or-
der, and an Alcali by incralTating them would
change it to a green of the fecond Order ;

Qjj. which

232 O P T I C K S.

which red and green j efpecially the green, feem
too imperfed: to be the Colours produced by
thefe Changes. But if the faid Purple be fup-
pofed of the third Order, its Change to red of the
fecond, and green of the third, may without any
Inconvenience be allow'd.

If there be found any Body of a deeper and lefs
reddifh Purple than that of the Violets, its Colour
moft probably is of the fecond Order. But yet
there being no Body commonly known whofe Co-
lour is conftantly more deep than theirs, I have
made ufe of their Name to denote the deepeft and
leaft reddilh Purples, fuch as manifeftly tranfccnd
their Colour in purity.

The blue of the firft Order, though very faint
and little, may poffibly be the Colour of fome
Subftances j and particularly the azure Colour
of the Skies feems to be of this Order. For all
Vapours when they begin to condenfe and coa-
lefce into fmall Parcels, become firft of that Big-
nefs, whereby fuch an Azure muft be reflected be-
fore they can conftitute Clouds of other Colours.
And fo this being the firft Colour which Vapours
begin to refled, it ought to be the Colour of the
fineft and moft tranfparent Skies, in which Va-
pours are not arrived to that Grofliiefs requifite to
refled: other Colours, as we find it is by Expe-
rience.

JVhitenefs, if moft intenfe and luminous, is
that of the firft Order, if lefs ftrong and lumi-
nous, a Mixture of the Colours of feveral Or-
ders. Of this laft kind is the Whitenefs of
Froth, Paper, Linnen, and moft white Sub-
ftances j of the former I reckon that of white

Metals

BOOK II. 233

Metals to be. For whilft the denfell of Metals,
Gold, if foliated, is tranfparent, and all Metals
become tranfparent if dilfolved in Menftriiums
or vitrified, the Opacity of white Metals ari-
feth not from their Denfity alone. They be-
ing lefs denfe than Gold would be more tranf-
parent than it, did not fome other Caufe con-
cur with their Denfity to make them opake.
And this Caufe I take to be fuch' a Bignefs of
their Particles as fits them to refledl the white of
the firft order. For, if they be of other Thick-
nefi!es they may refled: other Colours, as is ma-
nifeft by the Colours which appear upon hot
Steel in tempering it, and fometimes upon the
Surface of melted Metals in the Skin or Scoria
which arifes upon them in their cooling. And
as the white of the firfl order is the Itrongefl
which can be made by Plates of tranfparent
Subftances, fo it ought to be ftronger in the
denfer Subftances of Metals tlian in the rarer
of Air, Water, and Glafs. Nor do I fee but
that metallick Subftances of fuch a Thicknefs as
may fit them to reflect the white of the firft or-
der, may, byreafon of their great Denfity (ac-
cording to the Tenor of the firft of thefe Pro-
pofitions) refled: all the Light incident upon
them, andfo be as opake and fplendent as it's
poflible for any Body to be. Gold, or Copper
mix'd with lefs than half their Weight of Silver,
or Tin, or Regulus of Antimony, in fufion, or
amalgamed with a very little Mercury, become
white J which fhews both that the Particles of
white Metals have much more Superficies, and
fo are fmaller, than thofe of Gold and Copper,

and

234- O P T I C K S.

and alfo that they are fo opake as not to fuflef
the Particles of Gold or Copper to fhine through
them. Now it is fcarce to be doubted, but
that the Colours of Gold and Copper are of
the fecond or third order, and therefore the
Particles of white Metals cannot be much big-
ger than is requifite to make them reflect the
white of the firft order. The Volatility of Mer-
cury argues that they are not much bigger,
nor may they be much lefs, left they lofe their
Opacity, and become either tranfparent as they
do when attenuated by Vitrification, or by Solu-
tion in Menftruums, or black as they do when
ground fmaller, by rubbing Silver, or Tin, or
Lead, upon other Subftances to draw black
Lines. The firft and only Colour which white
Metals take by grinding their Particles fmaller,
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 firft order. But, if you would
hence gather the Bignefs of metallick Particles,
you muft allow for their Denfity. For were
Mercury tranfparent, its Denfity is fuch that
the Sine of Incidence upon it ( by my Compu-
tation) would be to the Sine of its Refraction,
as 7 1 to 20, or 7 to 2. And therefore'the Thick-
nefs of its Particles, that they may exhibit the
fame Colours with thofe of Bubbles of Water,
ought to be lefs than the Thicknefs of the
Skin of thofe Bubbles in the Proportion of 2
to 7. Whence it's pofiible, that the Particles
of Mercury m.ay be as little as* the Particles of

fome

BOOK II. 235

(ome tranfparent and volatile Fluids, and yet
refled the white of the firft order.

Laftly, for the produdtion of blacky the Cor-
pufcles mufl be lefs than any of thofe which ex-
hibit Colours. For at all greater fizes there is
too much Light reflected to conftitute this Co-
lour. But if they be fuppofed a little lefs than
is requifite to refled^ the white and very faint
blue of the firfl order, they will, according to
the 4th, 8th, i7thand iSthObfervations, refled:
fo very little Light as to appear intenily black,
and yet may perhaps varioully refrad it to and
fro within themfelves fo long, until it happen
to be ftifled and loft, by which means they will
appear black in all pofitions of the Eye without
any tranfparency. And from hence may be under-
flood why Fire, and the more fubtile diffolver Pu-
trefaction, by dividing the Particles of Subftan-
ces, turn them to black, why fmall quantities
of black Subftances impart their Colour very
freely and intenfly to other Subftances to which
they are applied ; the minute Particles of thefe,
by reafon of their very great number, eaftly o-
verfpreading the grofs Particles of others ; why
Glals ground very elaborately with Sand on a
Copper Plate, 'till it be well poliftVd, mukes
the Sand, together with what is worn off" from
the Glafs and Copper, become very black :
wiiy black Subftances do fooneft of all others
become hot in the Sun's Light and burn, (which
Effed: may proceed partly from the multitude
of Refradions in a little room, and partly from
the eafy Cominotion of fo very fmall Cor-
pufcies; ) and why blacks are ufually a little in-
clined

236 O P T I C K S.

clined to a bluifli Colour. For that they are Co
may be feen by illuminating white Paper by
Light refie.ded from black Subftances. For the
Paper will ufually appear of a bluifh white j and
the reafon is, that black borders on the obfcure
blue of the order defcribed in the i8th Obferva-
tion, and therefore refled:s more Rays of that Co-
lour than of any other.

In thcfe Defcriptions I have been the more
particular, becaufe it is not impoffible but that
Mifcrofcopes may at length be improved to the
difcovery of the Particles of Bodies on which
their Colours depend, if they are not already in
fome meafure arrived to that degree of per-
fedion. For if thofe Inftruments are or can be
fo far improved as with fufficient diflindtnefs
to reprefent Objedls five or fix hundred times
bigger than at a Foot diftance they appear to
our naked Eyes, I fliould hope that we might
be able to difcover fome of the greatefi; of thofe
Corpufcles. And by one that would magnify
three or four thoufand times perhaps they might
all be difcover'd, but thofe which produce
blacknefs. In the mean while I fee nothing ma-
terial in this Difcourfe that may rationally be
doubted of, excepting this Pofition : That tran-
fparent Corpufcles of the fame thicknefs and
denfity with a Plate, do exhibit the fame Co-
lour. And this I would have underftood not
without fome Latitude,, as well becaufe thofe
Corpufcles may be of irregular Figures, and
many Rays muft be obliquely incident on them,
and fo have a fliorter way through them than
the length of their DiameterSj as becaufe the

flraitnels

B O O K II. 237

ftraknefs of the Medium put in on all fides
within fuch Corpufcles may a little alter its Mo-
tions or other qualities on which the Reflexion
depends. But yet I cannot much fufped: the
laft , becaule I have obferved of fome fmall
Plates of Mufcovy Glafs which were of an even
thicknefs, that through a Microfcope they have
appeared of the fame Colour at their edges and
corners where the included Medium was ter-
minated, which they appeared of in other pla-
ces. However it will add much to our Satif^
fadion, if thofe Corpufcles can be difcover'd
with Microfcopes ; which if we fhall at length
attain to, I fear it will be the utmofl improve-
ment of this Senfe. For it feems impoflible to
fee the more fecret and noble Works of Nature
within the Corpufcles by reafon of their tranfpa-
rency.

Prop. VIII.

^he Cmife of Refcxion is not the impinging of
Light on thefolid or impervious parts of Bodies^
as is commonly believed.

np HIS will appear by the following Confi-
-°- derations. Firft, That in the paflage of
Light out of Glafs into Air there is a Reflexion
as ftrong as in its palTage out of Air into Glafs,
or rather a little ftronger, and by many degrees
ilronger than in its pallage out of Glafs into Wa-
ter. And it feems not probable that Air {hould
have more flrongly refleding parts than Waf^r
or Glafs. But if that ihould poflibly be fuppo-
fed, yet it will avail nothing j for the Reflexion

238 O P T I C K S. '

is as flrong or ftronger when the Air is drawn
away from the Glafs, ( fuppofe by the Air-Pump
invented by Otto Gueriet^ and improved and made
ufeful by Mr. Boyle) as when it is adjacent to it.
Secondly, If Light in its pafTage out of Glafs
into Air be inqident more obUquely than at an
Angle of 40 or 4 1 Degrees it is wholly refleded,
if lefs obliquely it is in great meafure tranfmit-
ted. Now it is not to be imagined that Light at
one degree of obliquity fhould meet with Pores
enough in the Air to tranfmit the greater part of
it, and at another degree of obliquity fliould
meet with nothing but parts to refled: it wholly,
efpecially coniidering that in its palTage out of
Air into Glafs, how oblique foever be its Inci-
dence, it finds Pores enough in the Glafs to tranf-
mit a great part of it. If any Man fuppofe that
it is not refledled by the Air, but by the outmofl
fuperficial parts of the Glafs, tliere is itill the
fame dithculty: Befides, that fuch a Suppofition
is unintelligible, and will alfo appear to be falfe
by applying Water behind fome part of the Glafs
inllead of Air. For fo in a convenient obliquity
of the Rays, fuppofe of 45 or 46 Degrees, at
which they are all refleded where the Air is adja-
cent to the Glafs, they Ihall be in great meafure
tranfmitted where the Water is adjacent to it;
which argues, that their Reflexion or Tranfmiffi-
on depends on the conilitution of the Air and
W^ater behind the Glafs, and not on the ftriking
of the Rays upon the parts of the Glafs. Third-
ly, If the Colours made by a Prifm placed at
the entrance of a Beam of Light into a darken'd
Room te lucceffively call: on a fecond Prifm

placed

BOOK II. 239

placed at a greater diftance from the former,
in luch manner that they are all alike incident
upon it, the fecond Prifm may be lo inclined to
the incident Rays, that thole which are of a
blue Colour fliall be all refleded by it, and yet
thofe of a red Colour pretty copioufly tranlmit-
ted. Now if the Reflexion be caufed by the
parts of Air or Glafs, I would ask, why at the
fame Obliquity of Incidence tiie blue fliould
wholly impinge on thofe parts, fo as to be all
reflected, and yet the red find Pores enough
to be in a great meafure tranfmitted. Fourth-
ly, Where two Glaffes touch one another, there
is no fejifible Reflexion, as was declared in the
iirft Obfervation; and yet I fee no feafon why
the Rays fhould not impinge on the parts of
Glafs, as much when contiguous to other Glafs
as when contiguous to Air. Fifthly, When
the top of a Water-Bubble (in the 17th Obfer-
vation, ) by the continual fubflding and exha-
ling of the Water grew very thin, there Vv^as
fuch a little and almofl infenfible quantity of
Light reflected from it, that it appeared in-
tenfly black; whereas round about that black
Spot, where the Water was thicker, -the Refle-
xion was fo ftrong as to make the Water feem
very white. Nor is it only at the leaft thick-
nefs of thin Plates or Bubbles, that there is no
manifeft Reflexion, but at many other thick-
neffes continually greater and greater. For in
the 15th Obfervation the Rays of the fame Co-
lour were by turns tranfmitted at one thicknefs,
and refledied at another thicknefs, for an in-
determinate number of Succeflions. And yet
I in

2/,o , O P T I C K S.

in the Superficies of the thinned Body, where
it is of any one thicknefs, there are as many
parts for the Rays to impinge on, as where it
is of any other thicknefs. Sixthly, If Reflexion
were caufed by the parts of reflecting Bodies,
it would be impoilible for thin Plates or Bub- .
bles, at one and the fame place, to refled; the
Rays of one Colour, and tranfmit thofe of ano-
ther, as they do according to the 13 th and 15 th
Obfervations. For it is not to be imagined
that at one place the Rays which, for infliance,
exhibit a blue Colour, fliould have the fortune
to dalh upon the parts, and thofe which exhi-
bit a red to hit upon the Pores of the Body 5
and tfien at another place, where the Body is
either -a little thicker, or a little thinner, that
on the contrary the blue fhould hit upon its
pores, and the red upon its parts. Laftly, Were
the Rays of Light refleded by impinging on
the folid parts of Bodies, their Reflexions from
polifh'd Bodies could not be fo regular as they
are. For in polifliing Glafs with Sand, Putty, or
Tripoly, it is not to be imagined that thofe
Subftances can, by grating and fretting the Glafs,
bring all its leafl: Particles to- an accurate Polifh;
fo that all their Surfaces fliall be truly plain or
truly fpherical, and look all the fame way, fo
as together to compofe one even Surface. The
fmaller the Particles of thofe Subftances are,
the fmalier will be the Scratches by which they
continually fret and wear away the Glafs until
it be polifli'd j but be they never fo fmall they
can wear away the Glafs no otherwife than by
grating and fcratching it, and breaking the
3 Protu-.

BOOK 11. 241

Protuberances; and therefore polifli it no o-
therwife than by bringing its roughnefs to a ve-
ry fine Grain, lb that the Scratches and Fret-
tings of the Surface become too fmall to be
vifible. And therefore if Light were refled:ed
by impinging upon the folid parts of the Giafs,
it would be fcatter'd as much by the moll po-
lilh'd Glafs as by the rougheft. So then it re-
anains a Problem, how Glafs poliili'd by fretting
Subftances can refled; Light lb regularly as it
does. And this Problem is fcarce otherwife to
be folved, than by faying, that the Reflexion of
a Ray is etfe(5ted, not by a lingle point of the
reflecting Body, but by Ibme power of the Bo-
dy which is evenly diffufed all over its Surface,
and by which it a6ls upon the Ray without im-
mediate Contad:. For that the parts of Bodies
do a(fl upon Light at a diftance Ihall be Ihewn
hereafter.

Now if Light be refled:ed, not by impinging
on the folid parts of Bodies, but by fome other
principle j it's probable that as many of its Rays
as impinge on the folid parts of Bodies are not
refleded but ftifled and loll in the Bodies. For
otherwife we mull allow two forts of Refle-
xions. Should all the Rays be refledled which, ,
impinge on the internal parts of clear Water or
Cryllal, thofe Subftances would rather have a
cloudy Colour than a clear Tranfparency. To
make Bodies look black, it's necefiary that ma-
ny Rays be llopp'd, retained, and loft in them ;
and it feems not probable that any Rays can be
llopp'd and ftifled in them which do not im-
pinge on their parts.

R And

a+2 O P T I C K S.

And heilce we may underftand that Bodies
are much more rare and porous^, than is com-
monly believed. Water is nineteen times light-
er, and by confequence nineteen times rarer
than Gold ; and Gold is fo rare as very readily
and vv^ithout the leafl oppofition to tranfmit the
magnetick Effluvia, and eafily to admit Quick-
filver into its Pores, and to let Water pafs
through it. For a concave Sphere of Gold fil-
led with Water, and folder'd up, has, upon pref-
fmg the Sphere with great force, let the Water
fqueeze through it, and ftand all over its out-
fide in multitudes of fmall Drops, like Dew,
without burfting or cracking the Body of the
Gold, as I have been inform'd by an Eye-wit-
nefs. From all which we may conclude, that
Gold has more Pores than folid parts, and by
confequence that Water has above forty times
more Pores than Parts. And he that fhall find
out an Hypothefls, by which Water may be fo
rare, and yet not be capable of compreffion by
force, may doubtlefs by the fapie Hypothefis
make Gold, and Water, and all other Bodies, as
much rarer as he pleafesj fo that Light may
find a ready pafTage through tranfparent Sub-
ftances.

The Magnet ads upon Iron through all denfe
Bodies not magnetick nor red hot,' without a-
ny diminution of its Virtue ; as for inftance,
through Gold, Silver, Lead, Glafs, Water.
The gravitating Power of the Sun is tranfmit-
ted through the vafl Bodies of the Planets with-
out any diminution, fo as to ad; upon all their
parts to their very centers with the fame Force

and

B O O K II. 243

and according to the fame Laws, as if the part
upon which it ads were not furrounded with
the Body of the Planet. .The Rays of Light,
whether they be very fmall Bodies . projeded,
or only Motion or Force propagated, are mo-
ved in right Lines ; and whenever a Ray of
Light is by any Obftacle turned out of its rcdi-
linear way, it will never return into the fame
redilinear way, unlefs perhaps by very great ac-
cident. And yet Light is tranfniittcd through
pellucid folid Bodies in right Lines to very .great
diftances. How Bodies can have a futikient
quantity of Pores for producing thefe EtfcAs is
very difficult to conceive, but perhaps not al-
together impolTible. For the Colours of Bodies
arife from the Magnitudes of the Particles winch
refled them, as was explained above. Now if
we conceive thefe Particles of Bodks to be fo
difpofcd amongll themfelves, that the Intervals
or empty Spaceb between them may be equal in
magnitude to them all j and that tne£e i^arii-
cles may be compufed of other Particles nmch
fmaller, which have as much empty Space be-
tween them as equals all the Magnitudes of
thefe fmaller Particles: And that in like man-
ner theie fmaller Particles are again compufed
of others much fmaller, all which together are
equal to all the Pores or empty Spaces between
them; and fo on perpetually till \ou come to
fond Particles, fuch 2.\ have no Pores or empty
Spaces within them : And if in any grofs Lody
there be, for inftance, three fuch degrees of
Particles, the leaft of which are folid ; this Bo-
dy will have feven times more Pores than folid

R 2 Parts.

244 O P T I C K S.

Parts. But if there be four fuch degrees of
Particles, the leaft of which are folid, the Bo-
dy will have fifteen times more Pores than folid
Parts. If there be five degrees, the Body will
have one and thirty times more Pores than folid
Parts. If fix degrees, the Body will have fixty
and three times more Pores than folid Farts. And
fo 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 refeB and refradf Light by o?ie and the
fame power, ^varioiijly exercijed in 'various- Cir-
cumjiances.

THIS appears by feveral Confiderations.
Firft, Becaufe when Light goes out of
Glafs into Air, as obliquely as it can pofiibly
do. If its Incidence be made ftill more oblique,
it becomes totally refledted. For the power of
the Glafs after it has refracfled the Light as ob-
liquely as is poflible, if the Incidence be ftill
made more oblique, becomes too firong to let
any of its Rays go through, and by confequence
caufes total Reflexions. Secondly , Becaufe
Light is alternately reflected and tranfmitted
by thin Plates of Glafs for many Succeflions,
accordingly as the thicknefs of the Plate increa-
fes in an arithmetical Progreflion. For here
the thicknefs of the Glafs determines whether
that Power by which Glafs ad:s upon Light
ihall caufe it to be rcfle(5ted, or fufier it to be

tranf-

BOOK 11.

245

tranfmitted. And, Thirdly, becaufe thofe Sur-
faces of tranfparent Bodies which have the great-
eft refradling power, refled the greateft quan-
tity of Light, as was fliewn in the fir'll Propofi-
tion.

Prop. X.

If Light be fwifter in Bodies 'than in Vacuo, in
the proportion of the Sines which 7ncafure the
RefraElion of the Bodies, the Forres of the
Bodies to refcB and refrafl Light, are very
nearly proportional to the denfities of the fame
Bodies ; excepting that unBuous a?id fulphureous
Bodies refraSt more than others of this fame den-

LE T AB reprefent the refrading plane Sur-
face of any Body, and IC a Ray incident
very obliquely upon the Body in C, fo that the

Angle ACI may be Infinitely little, and let CR
be the refracfled Ray. From a given Point B
perpendicular to the refradling Surface ered: B R
meeting with the refrading Ray C R in R, and
if C R reprefent the Motion of the refraded
Ray, and this Motion be diftinguifh'd into two
Motions CB and BR, whereof C B is paral-

R 3 lei

246 O P T I C K S.

lei to the refracting Plane, and BR perpendi-
cular, to it: CB fhall reprefent the Motion ^o.f
the incident Ray, and B R the Motion genera-
ted by the Reiradtion, 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 fides by two parallel Planes, be urged for-
ward in all parts of that Space by Forces tend-
ing direftly forwards towards the laft Plane, and
before its Incidence on the firil Plane, had no
Motion towards it, -or but an infinitely little
one J and if tlie Forces in all parts of that Space,
between the Planes, be at equal diftances from
the Planes equal to one another, but at feveral
diftances be bigger or lefs in any given Propor-
tion, the Motion generated by the Forces in
the whole pafiage of the Body or thing through
that Space fliall be in a fubduplicate Proportion
of the Forces, as Mathematicians will eafily
underftand. And therefore, if the Space of adti-
vity of the refrafting Superficies of the Body
be confider'd as fuch a Space, the Motion of
the Ray generated by the refracting Force of
the Body, during its pafiage through that Space,
that is, the Motion B R, muft be in fubdupli-
cate Proportion of that refracting Force. I fay
therefore, that the Square of the Line B R, and
by confequence the refracting Force of the Bo-
dy, is very nearly as the denfity of the fame Bo-
dy. For this will appear by the following Ta-
ble, wherein the Proportion of the Sines which
meafure the Refracftions of feveral Bodies, the
Square of B R, fuppofing C B an unite, the Den-

fities

BOOK II. 247

fities of the Bodies eftimated by their Specifick
Gravities, and their Refradtive Power in refpea
of their Denfities are fet down in feveral Co-
lumns.

The P report

ion 1 The Square

Theden-

The re-

of the %i

ncs of B R,

ffy and

fiaSliz'e

of Incidt

nee

to which

fpccifick

Pcicer

The refrafting Bo-

and Refra-

the refra-

gravi-

of the

dies.

ftion of yel-

Slingforce

ty of

Bod^ i n

lovj Light

of the Bo-

thi Bo-

refpeH

dy is pro-

dy.

of its

portionate

denfity .

APieudo-Top.-.zius,

being a natural,

pellucid, brittle,

23 to

H

I '699

4*27

3979

hairy Stone, of a

yellow Colour.

Air.

3201 to 3

200

o''ooo62 5

0'00I2

5208

Glafs of Antimony.

17 to.

9

2*568

5'28

4864

A Selenitis.

61 to

41

I '2 1 3

2*252

5386

Glafs vulgar.

31 to

20

I '4025

2'58

543^

Cryibl 0*" the Rock.

25 to

16

1^445

2*65

5450

Jfl.lnd Cryftal.

5 to

3

i'778

2*72

6536

Sal GemmDC.

17 to

II

i'388

2*143

6477

Alume.

35 to

24

1*1267

1*714

6570

Borax.

22 to

»5

I'lSii

1*714

67.6

Niter.

32 to

21

i'345

i'9

7079

Dantzick Vitriol.

303 to

200

1*295

1*715

755 »

Oil of Vitriol.

10 to

7

1*041

>'7

6124

Rain Water.

529 to

396

0*7845

i'

7845

Gum Arabick.

31 to

21

1*179

i'37S

8574

Spirit of Wine well
reftified.

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

Linfeed Oil.

40 to

27

1*1948

0*932

12819

SpiritofTurpcntipe.

25 to

17

1*1626

0*874

13222

Amber.

14 to

9

1*42

1*04

13654

A Diamond.

1 00 -to

41 l4'949

3*4

i4556__

The Refradibn of the Air in this Table is de-
termin'd by that of the Atmofphere obferved

R 4 by

248 O P T I C K S.

by Aftronomers. For, if Light pafs through many
refradling Subftances or Mediums gradually denfer
and denfer, and terminated with parallel Surfaces,
the Sum of all the Refradions will be equal to
the iingle Refraction which it would have fuirer'd
in paffing immediately out of the firft Medium
into the lafl. And this holds true, though the
Number of the refradling Subftances be increafed
to Infinity, and the Diftances from one another
as much decreafed, fo that the Light may be
refraded in every Point of its Paflage, and by
continual Refradions bent into a Curve-Line.
And therefore the whole Refradlion of Light
in paffing through the Atmofphere from the
higheft and rareft Part thereof down to the loweft
and denfeil Part, mufl be equal to the Re-
fradion which it would fuffer in paffing at
like Obliquity out of a Vacuum immediately
into Air oi equal Denfity with that in the loweft
Part of the Atmofphere.

Now, although a Pfeudo-Topaz, a Selenitis,
Rock Cryftal, Ifland Cryftal, Vulgar Glafs
(that is. Sand melted together) 'and Glafs of
Antimony, which are terreftrial ftony alcalizate
Concretes, and Air which probably arifes from
ftich Subftances by Fermentation, be Subftances
very differing from one another in Denfity, yet
by this Table, they have their refradive Powers
almoft in the fame Proportion to one another
as their Denfities are, excepting that the Re-
fradion of that ftrange Subftance, Ifland Cryftal
is a little bigger than the reft. And parti-
cularly Air, which is 3500 Times rarer than
the Pfeudo-Topaz, and 4.400 Times rarer than
a Glafs

BOOK IL 249

Glafs of Antimony; and 2000 Times rarer than
the Seleniti8, Glafs vulgar, or Cryflal of the
Rock, has notwithftanding its rarity the fame re-
fradive Power in refped: of its Denfity which
thofe very denfe Subftances have in refped of
theirs, excepting fo far as thofe differ from one
another.

Again, the Refraction of Camphire, Oil Olive,
Linfeed Oil, Spirit of Turpentine and Amber,
which are fat fulphureous unduous Bodies, and
a Diamond, which probably is an unduous Sub-
ftance coagulated, have their refradive Powers in
Proportion to one another as their Denlities with-
out any confiderable Variation. But the re-
fradive Powers of thefe undluous Subftances are
two or three Times greater in refpedt of their
Denfities than the refradive Powers of the former
5ubftances in refped of theirs.

Water has a refradive Power in a middle de-
gree between thofe two forts of Subflances,
and probably is of a middle nature. For out
of it grow all vegetable and animal Subftances,
which confift as well of fulphureous fat and in-
flamable Parts, as of earthy lean and alcalizate
ones.

Salts and Vitriols have refradive Powers in a
middle degree between thofe of earthy Subflances
and Water, and accordingly are compofed of
thofe two forts of Subflances. For by dill illation
and redification 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

250 O P T I C K S.

Spirit of Wine has a refradiv^e Power in a
middle degree between thofe of Water and oily
Subftances, and accordingly feems to be compo-
fed of both, united by Fern^.entation; the Water,
by means of fome faline Spirits with which 'tis
impregnated, dillolving the Oil, and volatizing
it by the Ad;ion. For Spirit of Wine is inflama-
blc by means of its oily Parts, and being diftilled
often from Salt of Tartar,, grow by every diftil-
lation more and more aqueous and phlegma-
tick. And Chymiils obferve, that Vegetables
(as Lavender, Rue, Marjoram, (^f. ) diftilled ^^r
fe^ before fermentation yield Oils without any
burning Spirits, but after fermentation yield ar-
dent Spirits without Oils : W^hich fliews, that
their Oil is by fermentation converted into Spi-
rit. They find alfo, that if Oils be poured in a
fmall quantity upon fermentating Vegetables,
they diftil over after fermentation in the form
of Spirits*

So then, by the foregoing Table, all Bodies
feem to have their retradive Powers propor-
tional to their Denfities, (or vei'y nearly;) ex-
cepting fo far as they partake more or lefs of
iulphureous oily Particles, and thereby have their
refradiive Power made greater or lefs. Whence
it feems rational to attribute the refrad-ive Power
of all Bodies chiefly, if not wholly, to the ful-
phureous Parts with which they abound. For
it's probable that all Bodies aJDOund more or lefs
with Sulphurs. And as Light congregated by a
Burning-glafs ads moft upon fulphureous Bo-
dies, to turn them into Fire and Flame ; fo,
fince all Adion is mutual. Sulphurs ought to a6t

moft

BOOK II. 251

moil upon Light. For that the action between
Light and Bodies is mutual, may appear from
this Confideration ; That the denfeil Bodies
which rtfrad: and reflect Light moft Wrongly,
grow hotteft in the Summer Sun, by the adtion
of the refradcd or refied:ed Light.

I have hitherto explain'd the power of Bo-
dies to reflect and refradt, and (liew'd, that thin
tranfparent Plates, Fibres, and Particles, do, ac-
cording to their feveral thickneifes and dcnli-
ties, refled: feveral forts of Ravs, and thereby
appear of feveral Colours; and by confecjuence
that nothing more is requifitc for producing all
the Colours of natural Bodies, than the feveral
fizes and denfities of their tranfparent Particles.
But whence it is that thefe Plates, Fibres, and
Particles, do, according to their feveral thick-
nelTes and denfities, refledt feveral forts of kays,
I have not yet explain'd. To give fome infight
into this matter, and make way for underftand-
ing the next part of this Book, I fhall conclude
this part with a few more Proportions. Thofe
which preceded refpeft the nature of Bodies,
thefe the nature of Light : For both mufl be
underftood, before the reafon of their Adlions
upon one another can be known. And becaufe
the laft Propofition depended upon the velocity
of Light, I will begin with a Propofition of that
kind.

Prop.

252 O P T I C K S.

Prop. XL

Light is propagated from luminous Bodies in
time, and Jpends about feven or eight Mi-
nutes of an Hour in paffing from the Sun to the
Earth,

'l ^ HIS was (obferved firfl by Roemer, and
-*- then by others, by means of the Eclipfes of
the Satellites of Jupiter. For thefe Eclipfes,
when the Earth is between the Sun and Jupiter,
happen about itvtn. or eight Minutes fooner
than they ought to do by the Tables, and when
the Earth is beyond the Sun they happen about
feven or eight Minutes later than they ought to
do; the reafon bemg, that the Light of the
Satellites has farther to go in the latter cafe
than* in the former by the Diameter of
the Earth's OrbiL Some inequalities of time
may arife from the Excentricities of the Orbs of
the Satellites ; but thofe cannot anfwer in all the
Satellites, and at all times to the Poiition and
Diftance of the Earth from the Sun. The mean
motions of Jupiter s Satellites is alfo fwifter in
his defcent from his Aphelium to his Perihelium,
than in his afcent in the other half of his Orb.
But this inequality ha^ no refpcd: to the pofition
of the Earth, and in the three interior Satellites
5s infenfible, as I find by computation from the
Theory of their Gravity.

Prop.

BOOK IL

Prop. XII.

253

Every Ray of Light in its pajfagc through any
refraBing Surface is put into a certain trajijicnt
Conjlitution or State ^ which in the progrefs
of the Ray returns, at equal Intervals^ and
difpofes the Ray at every return to be eafily
tranfmitted through ' the next refraSfitjg Sur-
face, and betiveen the returns to be eafdy refieSied
by it.

TH I S is manifeil by the 5th, 9th, 12th,
and 15th jObfervations. For by thofe Ob-
fervations it appears , that one and the fame
fort of Rays at equal Angles of Incidence on a-
ny thin tranfparent Plate, is alternately refledled
and tranfmitted for many Succeffions according-
ly as the thicknefs of the Plate increafes in
arithmetical Progreffion of the Numbers, o,

I, 2, 3, 4, 5, 6, 7, 8, ^c. fo that if the firft
Reflexion ( that which makes the firfl: or inner-
moft of the Rings of Colours there defcribed )
be made at the thicknefs i, the Rays fliall be
tranfmitted at the thicknelTes o, 2, 4, 6, 8, lo,

12, ^c. and thereby make the central Spot and
Rings of Light, which appear by tranfmillion,
and be refledied at the thicknefs i, 3, ^, 7, o,

I I, ^c. and thereby make the Rings which
appear by Reflexion. And- this alternate Re*-
flexion and TranfmilTion, as I gather by the 24th
Obfervation, continues for above an hundred
viciflitudes, and by the Obfervations in the next
part of this Book, for many thoufands, being
propagated from one Surface of a Glafs Plate to

the

254 O P T I C K S.

the other, though the thicknefs of the Plate be
a quarter of an Inch or above : So that this al-
ternation feems to be propagated from every
refrading Surface to all diflances w^ithout end or
limitation.

This alternate Reflexion and Refradtion de-
pends on both the Surfaces of every thin Plate,
becaufe it depends on their diflance. By tlie
21 ft Obfervation, if either Surface of a thin
Pjate of Miifcovy Glafs be wetted, the Colours
caufed by the alternate Reflexion and Refraction
grow faint, and therefore it depends on them
both.

It is therefore performed at the fecond Surface;
for if it were perform'd at the firft, before the
Rays arrive at the fecond, it would not depend
on the fecond.

It is alfo influenced by fome action or difpo-
fition, propagated from the firft to the fecond,
becaufe other wife at the fecond it v^ould not
depend on the firft. And this adion or difpo-
fition, in its propagation, intermits and returns
by equal Intervals, becaufe in all its progrefs it
inclines the Ray at one diftance from the- firft
Surface to be reflefted by the fecond, at ano-
ther to be tranfmitted by it, and that by equal
Intervals for innumerable viciflitudes. And be-
caufe the Ray is difpofed to Reflexion at the
diliances i, 3, 5, 7, 9, ^c. and to Tranfmiflion
at the diftances o, 2, 4, 6, 8, 10, Gfr. (for its
tranfmillion through the firft Surface, is at the
diftance o, and it is tranfmitted tiirough both
together, if their diftance be infinitely little or
much lefs than i ) the difpofition to be tranf-
I mit.e4

BOOK 11. 255

mitted at the diftances 2, 4, 6, 8, 10, &c. is to be
accounted a return of the lame difpofition which
the Ray firft had at the diftance o, that is at its
tranfmiffion through the firft refradling Surface.
All which is the thing I would prove.

What kind of adion or difpofition this is;
Whether it confifts in a. circulating or a vibra-
ting motion of -the Ray, or of the Medium, or
fomething elfe, I do not here enquire. Thofe
that are averfe from alTenting to any new Dif-
coveries, but fuch as they can- explain by an Hy-
pothecs, may for the prefent fuppofe, that as
Stones by falling upon Water put the Watef in-
to an undulating Motion, and all Bodies by
percufTion excite vibrations in the Air; fo the
Rays of Light, by impinging on any refracting
or reflecfting Surface , excite vibrations in the
refrafting or refiecfting Medium or Subftance,
and by exciting them agitate the folid parts of
the refrad:ing or reflecting Body, and by agita-
ting them caufe the Body to grow warm or
hot; that the vibrations thus excited are pro-
pagated in the refradting or reflecfting Medium
or Subftance, much after tlie manner that vibra-
tions are propagated in the Air for caufing
Sound, and move fafter than the Rays fo as to
overtake thenij and that when any Ray is in
that part of the vibration which confpires with
its Motion, it eafily breaks through a refrading
Surface, but when it is in the contrary part of
the vibration which impedes its Motion, it is
eafily reflected ; and, by confequence, that e-
very Ray is fucceftively difpofed to be eafily re-
flected, or eafliy tranfmitted, by every vibration

which

256 O P T I C K S.

which overtakes it. But whether this Hypothe-
lis be true or falfe I do not here conlider. I con-
tent my felf with the bare Difcovery, that the
Rays of Light are by fome caufe or other alter-
nately difpofed to be refled:ed or refraded for
many viciffitudes.

DEFINITION.

I'he returns of the difpofition of any Ray to be
refeBed I will call its Fits of eafy Reflexion,
and thofe of its difpoftion to be tranfmitted its
Fits of eafy Tranfmiffion, and the [pace it
pa[fes between every return and the next re-
tunty the Interval of its Fits.

Prop. XIII,

'The reafon why the Surfaces of all thick tranf-
farent Bodies refledi part of the Light inci^
dent on thein^ and refraSi the reji ^ isy that
fome Rays at their Incidence are in Fits of eafy
Reflexion^ a7id others in Fits of eafy Tranf-
mifjion.

np HIS may be gather'd from the 24th Ob-
-*- fervation, where the Light reflected by
thin Plates of Kv: and Glafs, which to the naked
Eye appear'd evenly white all over the Plate, did
through a Prifm appear waved with many Suc-
ceffions of Light and Darknefs made by alter-
nate Fits of eafy Reflexion and eafy Tranfmiffi-
on, the Prifm fevering and difl:inguifliing the
Waves of which the white refledled Light was
compofed, as was explain' d above.

And

BOOK II; 2^7

And hence Light is in Fits of cafy Reflexion
and eafy Tranfmiflion, before its Incidence on
tranfparent Bodies. And probably it is put in-
to fuch Fits at its firfl emilTion from luminous
Bodies, and continues in them during all its pro-
grefs. For thefe Fits are of a lafting naturcj as
will appear by the next part of this Book.

In this Proportion I fuppofe the tranfparent
Bodies to be thick j becaufc if the thicknefs of
the Body be much lefs than the Interval of the
Fits of eafy Reflexion and Tranfmitiion of the
Rays, the Body lofeth its refleclling power. For
if the Rays, which at their entering into the'
Body are put into Fits of eafy Tranfmiflion, ar-
tive at the farthefl Surface of the Body before
they be out of thofe Fits, they muil: be tranfmit-
ted. And this is the reafon why Bubbles' of
Water lofe their refledling power when they
grow very thin ; and why all opake Bodies, when
reduced into very fmall parts, become tranfpa^
rent.

Prop. XIV.

'Thofe Surfaces cf tranfparent Bodies^ which if the
Ray be in a Fit of 'Refratlicn do rfra6i it vicf:
fli-ongly^ if the Ray be in a Fit of Rcfiexion do
refeB it 7nofi eafdy.

FO R we fhewed above, in Frop. 8. that thai
caufe of Reflexion is not the impinging of
Light on the folid impervious parts of Bodies^
but fome other power by which thofe folid
parts ad; on Light at a diilance. We fhewed
alio in Frop, 9. that Bodies refled: and refrad:

S Lighc

258 O P T I C K S.

Light by one and the fame power, varloufly ex-
ercifed in various circumftances; and in Prop. i.
that the moft ftrongly refracting Surfaces refledt
the moft Light: All which compared together
evince and ratify both this and the laft Propo-
rtion.

Prop. XV.

In any one and the fame fort of Rays, emerging in
any Angle out of any refraSling Surface into one
and the fame Medium, the hitervalaf the fol-
lowing Fits of eafy Refexion and 'T^ranfmifjion
are either accurately or very nearly, as the ReB-
angle of the Secaiit of the Angle of RefraSlion,
and of the Secant of another Angle, whofe Sine
is the firfi of 106 arithmetical mean Rroporti-
onals, between the Sines of Incidence and Refra-
Bion, counted from the Si?2e of RefraBion.

T^ H I S is manifefl by the 7th and 19th Obfcr-
••■" vations.

Prop.

B O O K n. 259

Prop. XVI.

Lt fever al forts of Rays e-merging in equal Anglci.
out of any refradiing Surface into the fame Me^
dium^ the Litervals of the foiio'wing hits of eafy
'Reflexion and eafy T'ranfniJJion are either accu-
rately, or very nearly, as the Cube-Roots of the
Squares of the lengths of a Chord, which fownd
the Notes in an Eight, fol, la, fa, fol, la, mi,
fa, fol, ivith all their imter mediate degrees an-
fuoering to the Colours of thofe Rays, accordtfg to
the Analogy defcrihed in the feventh Experiment
of the fecond Part of theflrft Book.

np H I S is manifeft by the 13th and 14th Ob-
■*■ fervations.

Prop. XVII.

Jf Rays of any fort pafs perpendicularly ifito feve^
ral Mediums, the hitcrvcls of the Fits cf eafy
Reflexion and l^ranfmiflion in any one Medium,
are to thofe Intervals in any other, as the Sine of
Incidence to the Sine of RefraBion, wlmi the
Rays pafs out of the flrfl of thofe ti^o Mediums
into the fecond.

T^ H I S is manifeft by the loth Obferva-
-^ tion.

S 2 Prop,

26o O P T I C K S.

Prop. XVIII.

If the Rays nvhich paint the Colour in the Confine
of yellow and orange pafs perpejidicularly out of
any Medium into Air, the Intervals of their Fits

of eafy Reflexion are the th part of an Inch,

And of the fa?ne length are the Intervals of their
Fits of ' eafy I^ranfmifjion,

^ I ^ H I S is manifeft by the 6th Obfervation.
-*" From thefe Propofitions it is eafy to col-
led: the Intervals of the Fits of eafy Reflexion
and eafy Tranfmiffion of any fort of Rays refra-
ined in any Angle into any Medium j and thence
to know, whether the Rays fhall be reflected, or
tranfmitted at their fubfequent Incidence upon
any other pellucid Medium. Which thing, be-
ing ufeful for underflanding the next part of this
Book, was here to be fet down. And for the
fame reafon I add the two following Propofi-
tions.

Prop,

BOOK II. 261

Prop. XIX.

If any fort of Rays faUi7ig on the polite Surface
of any pellucid Medium be refeBed back^ the Fits
of eafy Refexion^ which they have at the point of
Refexion, fall fill continue to return j a?jd the
Returns fiall be at diftances from the point of
Refexicn in the arithmetical prcgrejfon of the
'Numbers 7.^ 4, 6, 8, 10, 12, &c. and between
thefe Fits the Rays pall be in Fits of eafy 7'rafif
mijjion.

"P O R fiRce the Fits of eafy Reflexion and
•*- Qafy TranfmilTion are of a returning na-
ture, there is no reafoa why thefe Fits, which
continued till the Ray arrived at the reflecting
Medium, and there inclined the Ray to Refle-
xion, ihould there ceafe. And if the Ray at the
point of Reflexion was in a Fit of eafy Reflexion,
the progreflion of the diftances of thefe Fits
from that point mufl: begin from o, and fo be of
the Numbers o, 2, 4, 6, 8, &c. And therefore
the progreffion of the dillances of the interme-
diate Fits of eafy Tranfmiflion, reckon'd from
the fame point, mufl be in the progreflion of
the odd Numbers i, 3, 5, 7, 9, ^c. contrary
to what happens when the Fits are propagated
from points of Refradion.

S3 Prop,

262 O P T I C K S.

Prop. XX.

^he Intervals of the Fits of eafy Reflexion and,
eafy T'ranfmifjion^ propagated from points of
KeHexion into afiy Medium^ are equal to the
Intervals of the like Fits^ which the fame Rays
would ba-vey if refraBed into the fame Medium
in Angles of Rejraciion equal to their Angles of
Reflexion,

'P O R when Light is refleded by the fecond
■"- Surface of thin Plates, it goes out after-
wards fieely at the firft Surface to make the
Rin^s of Colours which appear by Reflexion j
and, by the freedom of its egrefs, makes the
Colours of thefe Rings more vivid and ftrong
than thofe which appear on the other fide of
the Plates by the tranfmitted Light. The re-
fieded Rays are therefore in Fits of eafy Tranf-
miffion at their egrefs; v/hich would not always
happen, if the Intervals of the Fits within the
Plate after Reflexion were not equal, both in
kngth and number, to their Intervals before it.
And this confirms alfo the proportions fet down
in the former Propofition. For if the Rays
both in going in and out at the firfh Surface be
in Fits of eafy Tranfmiffion, and the Intervals
and Numbers of thofe Fits between the firft
and fecond Surface, before and after Reflexion,
be equal, the diftances of the Fits of eafy
Tranfmiflion from either Surface, muft be in
the fame prpgreffion after Reflexion as before ;
that is, from the firft Surface which tranfmit-
ted them, in the progreffion of the even Num-.

bers

B O O K IL 263

bers o, 2, 4, 6, 8, (^c. and from the fecond
which refledled them, in that of the odd Num-
bers I, 3, 5, 7, &c. But thefe two Propofi-
tions will become much more evident by the
Obfervations in the following part of this
Book.

S4

THE

THE

SECOND BOOK

O F

OPTICKS

PART IV.

Qbfervations concerning the Reflexions and
Colour^ of thick tranfparent polij^d
Platzs.

HERE Is no Glafs or Speculum how
well foever polifliedjbut, befides the
Light which it refradts or refledls re-,
gularlyj fcatters every way irregularly
a faint Light, by means of which the
polifh'd Surface, v/hen illuminated in a dark room

by

BOOK II. 265

by a beam of the Sun's Light, may be eafily feen
in all pofitions of the Eye. There are certain
Phaenomena of this fcatter'd Light, which when
I firft obferved them, feem'd very flrange and
furprizing to me. My Obfervations were as fol-
lows.

Obf. I. The Sun fhining into ray darkened
Chamber through a hole one third of an Inch
wide, riet the intromitted beam of Light fall
perpendicularly upon a Glafs Speculum ground
concave on one fide and convex on the other,
to a Sphere of five Feet and eleven Inches Ra-
dius, and Quick-filver'd over on the convex
fide. 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
diftance of about live Feet and eleven Inches
from the Speculum, in fuch manner, that the
beam ©f Light might pafs through a little hole
made in the middle of the Chart to the Specu-
lum, and thence be reflected back to the fime
hole: I obferved upon the Chart four or five
concentric Irifes or Rings of Colours, like Rain-
bows, encorapaffing the hole much after the
manner that thofe, which in the fourth and fol-
lowing Obfervations of the firft part of this third
Book appear'd between the Objedl-glaiTes, en-
compafled the black Spot, but yet larger and
fainter than thofe. Thefe Rings as they grew
larger and larger became diluter and fainter, fo
that the fifth was fcarce vifible. Yet fome-
times, when the Sun llione very clear, there
appear'd faint Lineaments of a fixth and fe-
vgnth. If the diftance of the Chart from the

S,pecu-»

266 O P T I C K S.

Speculum was much greater or much lefs than
that of fix Feet, the Rings became dilute and
vaniQi'd. And if the diftance of the Speculum
from the Window was much greater than that
of fix Feet, the refledied beam of Light would
be fo broad at the diftance of fix Feet . from the
Speculum where the Rings appear'd, as to ob-
fcure one or two of the innermoft Rings. And
therefore I ufually placed the Speculum at a-
bout fix Feet from the Window j fo that its
Focus might there fall in with the center of its
concavity at the Rings upon the Chart. And
this Pofiiure is always to be underfi:ood in the
following Obfervations where no other is ex-
prefs'd.

Obf. 2. The Colours of thefe Rain-bows fuc-
ceeded one another from the center outwards,
in the fame form and order with thofe which
were made in the ninth Obfervation of the firft
Part of this Book by Light not refledled, but
tranfmitted through the two Objedi-glafiTes. For,
firfi:, there was in their common center a white
round Spot of faint Light, fomething broader
than the refleded beam of Light, which beam
fometimes fell upon the middle of the Spot, and
fometimes by a little inclination of the Specu-
lum receded from the middle, and left the Spot
white to the center.

This white Spot was immediately encompaf-
fed with a dark grey or rufleti and that dark grey
with the Colours of the firfi: Iris; which Colours
on the infide next the dark grey were a little
violet and indigo, and next to that a blue, which
on the outfide grew pale, and then fucceeded a

little

BOOK 11. 267

little greenifh yellow, and after that a brighter
yellow, and then on the outward edge of the
Iris a red which on the outfide inclined to pur-
ple.

This Iris was immediately encompaffed with a
fecond, whofe Colours were in order from the in-
fide outwards, purple, blue, green, "yellow, light
red, a red mix'd with purple.

Then immediately foUow'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 feem'd of a bluifli
green within, and red without, but fo faintly
that it was difficult to difcern the Colours.

Obf. 3. Meafuring the Diameters of thefe
Rings upon the Chart as accurately as I could,
I found them alfo in the fame proportion to
one another with the Rings made by Light tranf-
mitted through the two Objed-glafies. For
the Diameters of the four iirfl of the brjf^ht
Rings meafured between the brightefl parts of
their Orbits, at the diftance of fix Feet from the
Speculum were 144, 2I, 2— 3^ Inches, whofe
Squares are in arithmetical progreffion of the
numbers i, 2, 3, 4. If the white circular Spot
in the middle be reckon'd amongfl the Rings,
and its central Light, where it fsems to be n:oil
luminous, be put equipollent to an infinitely
little Ring ; the Squares of the Diameters of the
Rings will be in the progrefiion o, i, 2, 3, 4,
&c. I meafured alfo the Diameters of the dark
Circles between thefe luminous ones, and found
their Squares in the progreflion of the num-
bers

268 O P T I C K S.^

bers T, It, 2^, 3^, '&c. the Diameters of the
firft four at the diftance of fix Feetsfrom the
Speculum, being i.?^, 2tV, 2t, 3tt Iiiches. If
the diftance of the Chart from the Speculum
was increafed or diminilhed, the Diameters of
the Circles were increafed or diminifhed pro-
portionally.

Obf. ^. By the analogy between thefe Rings
and thofe defcribed in the Obfervations of the
firft Part of this Book, I fufpedted that there
were many more of them which fpread into
one another, and by interfering mix'd their Co-
lours, and diluted one another fo that they could
not be feen apart. I viewed them therefore
through a Prifm, as I did thofe in the 24th Ob-
fervation of the firft Part of this Book. And
when the Prifm was fo placed as by refradling
the Light of their mix'd Colours to feparate
them, and diftinguilh the Rings from one ano-
ther, as it did thofe in that Obfervation, I could
then fee them diftind:er than before, and eafily
number eight or nine of them, and fometimes
twelve or thirteen. And had not their Light
been fo very faint, I queftion not but that I might
have feen many more.

Ohf. 5. Placing a Prifm at the Window to re-
fradl the intromitted beam of Light, and caft
the oblong Speftrum of Colours on the Specu-
lum : I covered the Speculum with a black Pa-
per which had in the middle of it a hole to let
any one of the Colours pafs through to the Spe-
culum, whilft the reft were intercepted by
the Paper. And now I found Rings of that Co-
lour only which fell upon the Speculum. If

the

BOOK II. 269

the Speculum was illuminated with red, the
Rings were totally red with dark Intervals, if
with blue they were totally blue, and fo of the
other Colours. And when they v/ere illumi-
nated wi'th any one Colour, the Squares of their
Diameters meafured between their moil lumi-
nous Parts, were in the arithmetical Progreilion
of the Numbers, o, i, 2, 3, 4, and the Squares
of the Diameters of their dark Intervals in the
Progreffion of the intermediate Numbers j, It,
2f, 33. But if the Colour was varied, they va-
ried their Magnitude. In the red they were lar-
geft, in the indigo and violet leaft, and in the
intermediate Colours yellow, green, and blue,
they were of feveral intermediate Bigneffes an-
fwering to the Colour, that is, greater in yel-
low than ia green, and greater in green than in
blue. And iicnce I knew, that when the Spe-
culum was illuminated with white Light, the
red and yellow on the outlide of the Rings were
produced by the hoA refrangible Rays, and the
blue and violet by the moir refrangible, and that
the Colours of each Ring fpread into the Co-
lours of the neighbouring Rings on either fide,
after the manner explain'd in the firft and fe-
cond Part of this Book, and by mixing diluted
one another fo tliat they could not be diflin-
guifli'd, unlefs near the Center where they were
leaft mix'd. For in this Obfervation I could
fee the Rings more diftindly, and to a greater
Number than before, being able in the yellow
Light to number eight or nine of them, be-
iides a faint ihadow of a tenth. To fatisfy my
felf how much th^ Colours of the feveral Rings

fpread

270 O P T I C K S.

fpread Into one another, I meafured the Dia-
meters of the fecond and third Rings, and found
them when made by the Confine of the red and
orange to? be to the fame 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. Alfo the Circles
made fuccefiively by the red, yellow, and green,
differ'd more from one another than thofe made
fuccefTively by the green, blue, and indigo. For
the Circle made by the violet was too dark to
be feen. To carry on the Computation, let us
therefore fuppofe that the Differences of the
Diameters of the Circles made by the outmoft
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 in-
digo and violet, and outmoft violet, are in pro-
portion as the Differences of the Lengths of a
Monochord which found the Tones in an Eight j
jbl, la^ fa, Jol, la, mi, fa, fol, , that is, as the
Numbers ir, tV, tV, t'-, tV, tV> ■^' ^"d if the
Diameter of the Circle made by the Confine of
red and orange be 9 A, and that of the Circle
made by the Confine of blue and indigo be 8 A
as above ; their difference 9 A — 8 A will be
to the difference of the Diameters of the Cir-
cles made by the outmoft red, and by the Con-
fine of red and orange, as tV -1- tt A- rV -^ tV ^o \,
that is as tV to \, or 8 to 3, and to the diffe-
rence of the Circles m.ade by the outmoft vio-
let, and by the Confine of blue and indigo, as

TT 4- TT -1- tV 4- vT to rr 4- iV, that is, as -iy to tV>

or

BOOK IL 271

or as 16 to 5. And therefore thefe differences
will be g A and /g A. Add the firft to 9 A and
fubdud the lafi: from 8 A, and you will have the
Diameters of the Circles made by the leafl and

moft refrangible Rays ''i. A and -^ A. Thefe di-
ameters are therefore to one another as 75 to
61^ or 50 to 41, and their Squares as 2500 to
168 1, 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
outmoft red and outm-oft violet, in the 13 th Ob-
fervation of the firft part of this Book.

Ol?f. 6. Placing my Eye where thefe Rings
appear'd plaineft, I faw the Speculum tinged all
over with Waves of Colours, (red, yellov/, green,
blue J ) like thofe which in the Obfervations of
the firft part of this Book appeared between
the Obje(3:-glaffes, and upon Bubbles of Water,
but much largei". And after the manner of thofe,
they were of various magnitudes in various Po-
litions of the Eye, fwellin-^ and ihrinking as I
moved my Eye this way and that way. They
were formed like Arcs of ccnccntrick Circles, as
thofe were 5 and v/hen my Eye was over againft
the center of the concavity of tho Speculum, (that
is, 5 Feet and 10 Inches diftant from the Specu-
lum,) their common center was in a right Line
with that center of concavity, and with the
hole in the Window. But m other poftures of
my Eye their center had other pofitions. They
appear'd by the Light of tlie Clouds propagated
to the Speculum through the hole in the Win-
dow J and when the Sun {hone through that

2 hole

272 O P T I C K S.

hole upon the Speculum, his Light upon it was
of the Colour of the Ring whereon it fell, but by
its fplendor obfcured the Rings made by the Light
of the Clouds, unlefs when the Speculum was
removed to' a great diftance from the Window,
fo that his Light upon it might be broad and faint.
By varying the polition 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 refleded
Light conflantly varied upon the Speculum, as it
did upon my Eye, the fame Colour always ap-
pearing to a By-ftander 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 thefe refledled Colours, propagated
thither from the Speculum in feveral Angles, and
that their produdion depended not upon the ter-
mination of Light and Shadow.

Obf. J. By the Analogy of all thefe Pheno-
mena with thofe of the like Rings of Colours
defcribed in the f rft part of this Book, it feem-
ed to me that thefe Colours were produced by
this thick Plate of Glafs, much after the manner
that thofe were produced by very thin Plates.
For, upon trial, I found that if the Quick-fil-
ver were rubb'd off from the backfide of the
Speculum, the Glafs alone would caufe the
fame Rings of Colours, but much more faint
than before j and therefore the Phaenomenon
depends not upon the Quick-lilver, unlefs fo far
as the Quick-hlver by increaiing the Reflexion
of the backfide of the Glafs increafes the Light
of the Rings of Colours. I found alfo that a
Speculum of Metal without Glafs made fome

Years

BOOK II. 273

Years fince for optical ufes, and very well
wrought, produced none of thofe Rings j and
thence I underfbood that thefe Rings arifc not
from one fpecular Surface alone, but d'epend
upon the two Surfaces of the Plate of Glafs
whereof the Speculum was made, and upon the
thicknefs of the Glafs between them. For
as in the 7th and 19th Obfervations of the firft
part of this Book a "thin Plate of Air, Water,
or Glafs of an even thicknefs appeared of one
Colour when the Rays were perpendicular to
it, of another v/hen they were a little oblique,
of another v/hen more oblique, of another when
ftill more oblique, and fo on y fo here, in the
lixth Obfervation, the Light which emerged
out of the Glafs in feveral Obliquities,- made tlie
Glafs appear of feveral Colours, and being pro-
pagated in thofe Obliquities to the Chart, tiierc
painted Rings of thofe Colours. And as the
reafon why a thin Plate appeared of feveral Co-
lours in feveral Obliquities of the Rays, v/as,
that the Rays of one and the fame fort are re-
fleded by the thin Plate at one obliquity and
tranfmitted at another, and thofe of other forts
tranfmitted where thefe are refleded, and re-
flected where thefe are tranfmitted : So the
reafon why .the thick Plate of Glafs whereof
the Speculum was made did appear of various
Colours in various Obliquities, and in thofe
Obliquities propagated thofe , Colours to the
Chart, was, that the Rays of one and the
fame fort did at one Obliquity emerge out
of the Glafs, at another did not emerge, but
were refleded back towards the Quick-filver

T . by

t74 O P T I C K S.

by the hither Surface of the Glafs, and according-
ly as the Obliquity became greater and greater,
emerged and were refiedted alternately for ma-
ny Succeffignsj and that in one and the fame
Obliquity the Rays of one fort were refled:ed,
and thofe of another tranfmitted. This is ma-
nifeft by the fifth Obfervation of this part of this
Book. For in that Obfervation, when the Spe-
culum was illuminated by any one of the prif-
matick Colours, that Light made many Rings
of the fame Colour upon the Chart with dark
Intervals, and therefore at its emergence out of
the Speculum was alternately tranfmitted and
not tranfmitted from the Speculum to the Chart
for many SuccefTions, according to the various
Obliquities of its Emergence. And when the
Colour caft on the Speculum by the Prifm was
varied, the Rings became of the Colour cafl on
it, and varied their bignefs with their Colour,
and therefore the Light was now alternately
tranfmitted and not tranfmitted from the Spe-
culum to the Chart at other Obliquitiss than
before. It feemed to me therefore that thefe
Rings were of one and the fame original with
thofe of thin Plates, but yet with this difference,
that thofe of thin Plates are made by the alter-
nate Reflexions and Tranfmiffions of the Rays
at the fecond Surface of the Plate, after one paf-
fage through itj but here the Rays go twice
through the Plate before they are alternately re-
ileded and tranfmitted. Firft, they go through
it from the firfi: Surface to the Quick-filver, and
then return through it from the Quick-filver
to the firil Surface, and there are either tranf-
mitted

BOOK II. 275

micted to the Chart or refledled back to the
Quick-filver, accordingly as they are in their
Fits of eafy Reflexion or Tranfmiffion when
they arrive at that Surface. For the Intervals
of the Fits of the Rays which fall perpendicu-
larly on the Speculum,, and are reiledled back
in the fame perpendicular Lines, by rcafon" of
the equality of tbefe Angles and Lines, are of
the fame length and number within the Glafs
after Reflexion as before, by the 19th Propofl-
tion of the third part of this Book. And there-
fore fince all the Rays that enter through the
iirll: Surface are in their Fits of eafy Tranfmif-
fion at their entrance, and as many of thefe as
are refledted by the fecond are in their Fits of
eafy Reflexion there, all thefe mufl: be again in
their Fits of eafy Tranfmiffion at their return
to the firil, and by confequence there go Out
of the Glafs to the Chart, and form upon it the
white Spot of Light in the center of the Rings.
For the reafon holds good in all forts of Rays,
and therefore all forts mufl go out promifcu-
oufly to that Spot, and by their mixture " caufe
it to be white. But the Intervals of the Fits of
thofe Rays which are reflected more obliquely
than they enter, mull: be greater after Reflexion
than before, by the 15th and 20th Propcfitlons.
And thence it may happen that the Rays at their
return to the firli Surface, may in certain Ob-
liquities be in Fits of eafy Reflexion, and return
back to the Qu]ck-f:!ver, and in other interme-
diate Obliquities be again in Fits of eafy Tranf-
miffion, and fo go out to the Chart, and paint
on it the Rings of Colours about the white Spot.

T 2 And

276 O P T I C K S.

And becaufe the Intervals of the Fits at equal
obliquities are greater and fewer in the lefs re-
franf^ible Rays, and lefs and more numerous in
rhe more refrangible, therefore the lefs refrangi-
ble at equal obliquities fhall make fewer Rings
than the more refrangible, and the Rings made
by thofe iliall be larger than the like number of
Rings made by thefej that is, the red Rings
fhali 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 Obfervation. And therefore the firll
Ring of all Colours encompaffing the white
Spot of Light lliall be red without any violet
within, and yellow, and green, and blue in the
middle, as it was found in the fecond Obferva-
tion ; and thefe Colours in the fecond Ring, and
thofe that follow, fliall be more expanded, till
they fpread into one another, and blend one an-
other by interfering.

Thefe feem to be the reafons of thefe Rings
in general j and this put me upoi;i obferving the
thicknefs of the Glals, and confidering whether
the dimenfions and proportions of the Rings may
be truly derived from it by computation.

Obf. 8. I meafured therefore the thicknefs of
this concavo-convex Plate of Glafs, and found it
every where \ of an Inch precifely. Now, by
the fixth Obfervation of the firft Part of this
Book, a thin Plate of Air tranfmits the brighteft
Light of the firft Ring, that is, the bright yel-
low, when its thicknefs is the g-^ th part of an

Inchi and by the tenth Obfervation of the fame

Part,

BOOK IT. 277

Parr, a thin Plate of Glafs trLinfmits the fame
Light of" the farrie Ring, when its diicknefs k
lefs in proportion of tb.e Sine of Refrad:ion to
the Sine of Incidence, that is, when its thick-

nefs is the ,-- 1 '";;;;;; th or - ' — th part of an Inch,
1^13000 137545 ^

fappofing the Sines are as 1 1 to 17. And it this
thickncfs be doubled, it tranfmits the fame bright
Light of thefecond Ring; if trippled, it tranf-
mits that "of tlie third, and fo on; the bright
yellow Light in all thefe cafes being in its Fits
of Tranfmiiiion. And therefore if its thickncfs
be multiplied 34386 times, fo as to become J of
an Inch, it tranfmits the fame bright Liglit of
the 34386th Ring. Suppofe this be the bright
yellow Light tranfmitted perpendicularly from
the refled-ing convex lide of the Glafs through
the concave fide to the white Spot in the cen-
ter of the Rings of Colours on the Chart: And
by a Rule in the 7th and igvh Obfervations in
the firft Part of this Book, and by the J5ch and
20th Propofitions of the third Part of this Book,
if the Rays be made oblique to the Glafs, the
thickncfs of the Glafs requilite to tranfmit the
fame bright Light of the fame Ring in any ob-
liquity, is to this fliickncfs of; of an Inch, as the-
Secant of a certain Angle to the Radius, the
Sine of which. Angle is the firfl of an hundred
and fiX arithmetical Means between the Sines
of Incidence and Rcfrartion, counted from the
Sine of Incidence when the Refrac^liion is made
out of any plated Body into any Medium en-
compafTmg it ; that isj in this cafe, out of Glafs
into Air. Now if the thicknefs of the Glafs be

T 3 increafed

278 O P T I C K S.

increafed by degrees, fo as to bear to its firft
thicknefs, (viz. that of a quarter of an Inch,)'
the Proportions which 34386 .(the number of
Fits of the perpendicular Rays in ^oing through
the Glafs tov/ards 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 Glafs towards the
firft, fecond, third, and fourth Rings of Co-
lours, ) and if the firfl thicknefs be divided in-
to 1 00000000 equal parts, the increafed thick-
nefies will be 1 00002908, 1 00005 8 1 6, 1 00008725,
and 100011633, and the Angles of which thefe
thicknelTes are Secants will be 26' 13", 37' 5",
45' 6", and 52' 26", the Radius being looooooooj
and die Sines of thefe Angjjes are 762, 1079,
1321, and 1525, and the proportional Sines of
Refradion 1 172, 1659, 203 1, and 2345, the Ra-
dius being 1 00000. For fmce the Sines of In-
cidence out of Glafs into Air are to the Sines
of Refraiftion as 11 to 17, and to the above-
mentioned Secants as 1 1 to the iirft of 106 arith-
metical Means betVv^een 11 and 17, that is, as;

1 1 to II —>, thofe Secants will be to the Sines
106'

of Refradion as 11 -j^ to 17, and by this Ana-
logy will give thefe Sines. So then, if the ob-
liquities of the Rays to the concave Surface of
the Glafs be fuch that the Sines of their Refra-
dion in paiTing out of the Glafs through that
Surface into the Air be 1172, 1659, 2031, 2345,
the bright Light of the 34386th Ring fhall e-
jnerge at the thickneffes of the Glafs, which are

2 to

BOOK II. 279

to 5 of aninch as 34386 to 34385,.34384, 34383,
34382, refpedively. And therefore, if the thick-
nefs in all thefe Cafes T3e 5 of an Inch (as it is in
the Glafs of which the Speculum was made)
the bright Light of the 34385th Ring fhall e-
merge where the Sine of Refracftion is 1 172,
and that of the 34384th, 34383th, and 34382th
Ring where the Sine is 1659, 2031, and 2345
refpedtively. And in thefc Angles of Refra-
ction the Light of thefe Rings fliall be propaga-
ted from the Speculum to the Chart, and there
paint Rings about the white central round Spot
of Light which we faid was the Light of thp
34386th Ring. And the Semidiameters of thefe
Rings fhall fubtend the Angles of Refraction
made at the Concave-Surface of the Speculum,
and by confequence their Diameters flrjll be to
the diftance of the Chart from the Speculum as
thofe Sines of Refraction doubled are to the
Radius, that is, as 1172, 1659, 2031, and 2345,
doubled are to 1 00000. And therefore, if the
diftance of the Chart from the Concave-Surface
of the Speculum be fix Feet ( as it was in the
third of thefe Obfervations ) the Diameters of
the Rings of this bright yellov/ Light upon the
Chart fhall be i'688, 2*389, 2*925, 3*375 Inches:
For thefe Diameters are to fix Feet, as the above-
mention'd Sines doubled are to the Radius.
Now, thefe Diameters of the bright yellow
Rings, thus found by Computation are the
very fame with thofe found in the third of thefe
Obfervations by meafuring them, viz. with
I IS, 2g, 2ii, and 3g Inches,, and therefore the
1 heory of deriving thefe Rings from the thick-

T 4 nsfs

28o O P T I C K S.

nefs of the Plate of Glafs"* of which the Specu-
.lurii was made, and from the Obliquity of the
emerging P.ays agrees with the Obfervation. In
this Computation 1 have equalled the Diameters
of the bright Rings made by Light of all Co-
lours, to the Diameters of the Rings made by
the bright yellow. For this yellow makes the
brighteft Part of the Rings of all Colours. If
you defire theDiameters of the Rings made by the
Light of any other unmix'd Colour, you may
find them readily by putting them to the Diame-
ters of the bright yellow ones in a fubduplicate
Proportion of the Intervals of the Fits of the
Rays of thofe Colours when equally inclined to
the refrading or reflecting Surflice which caufed
thofe Fits, that is, by putting the Diameters of
the Rings made by the Rays in the Extremities
and Limits of the feven Colours, red, orange,
yellow, green, blue, indigo, violet, proportio-
nal to the Cube-roots of the Numbers, i, |, ^, J,
|, 55 -^5 ly which exprefs the Lengths of a Mono-
chord founding the Notes in an Lighth: For
by this m.eans the Diameters of the Rings of
thefe Colours will be found pretty nearly in
the fame Proportion to one another, which
they ought to have by the fifth of thefe Obferva-
tions.

And thus I fatisfy'd my felf, that thefe Rings
were of the fame Kind and Original with thofe
of thin Plates, and by confequenxe that the Fits
or alternate Difpofitions of the Rays to be
refleded and tranfmirted are propagated to
great diftances from every refleding and re-
frading Surface. But yet to put the mat-
ter

BOO K II, 281

ter out of doubt, I added the following Obfer-
vation.

Obf. 9. If ^thefe Rings thus depend on the
thicknels of the Plate of Glafs, ' their Diameters
at equal diilances from feveral Speculums made
of iuch CDncavo-convex Plates of Glafs as are
ground on the fame Sphere, ought to be recipro-
cally in a fubduplicate Proportion of the thick-
neffes of the Plates of Glafs. And if this Pro-
portion be found true by experience it will amount
to a demonftratlon that thefe Rings (like thofe
formed in thin Plates) do depend on the thick-
nefs of the Glafs. I procured therefore ano-
ther concavo-convex Plate of Glafs ground on
both lides to the fame Sphere with the former
Plate. Its thicknefs was l^ Parts of an Inch ;
and the Diameters of the three hYi\. bright Rings
meafured between the brightell Parts of their
Orbits at the diftance of fix Feet from the
Glafs were 3. 4^-. 5J. Inches. Now, the thick-
nefs of the other Glafs being \ of an Inch v/as
to the thicknefs of this Glafs as ? to 4 that is
as 31 to 10, or 310000000 to icooooooo, and
the Roots of thefe Numbers are 1 7607 and loooo,
and in the Proportion of the iirlt of thefe Roots
to the fecond are the Diameters of the brip-ht
Rings made in this Obfervation by the tliinner
Glafs, 3. 4fi. 57, to the Diam.eters of the fime
Rings made in the tliird of thefe Obfervations"
by the thicker Glafs i-.^. 2!. 2^k, that is, the Dia-
meters of the Rings are reciprocally in a fubdu-
plicate Proportion of the thickneffcs of the Plates
of Glafs.

282 O P T I C K S.

So then in Plates of Glafs which are alike
concave on one fide, and alike convex on the
other fide, and alike quick-filver'd on the con-
vex fides, and differ in nothing but ' their thick-
nefs, the Diameters of the Rings are reciprocally
in a fubduplicate Proportion of the thickneffes of
the Plates. And this fhew^s fufticiently that the
Rings depend on both the Surfaces of the Glafs,
They depend on the convex Surface, becaufe they
lare more luminous when that Surface is quick-
filver'd over than when it is without Quick-filver.
They depend alfo upon the concave Surface, be-
caufe without that Surface a Speculum makes them
not. They depend on both Surfaces, and on the
difiiances between them, becaufe their bignefs is
varied by varying only that diftance. And this
dependance is of the fame kind with that which
the Colours of thin Plates have on the difi:ance
of the Surfaces of thofe Plates, becaufe the big-
nefs of the Rings, and their Proportion to one
another, and the variation of their bignefs arifing
from the variation of the thicknefs of the Glafs,
and the Orders of their Colours, is fuch as ought
to refult from th© Propofitions in the end of the
third Part of this Book, derived from the Phaeno-
mena of the Colours of thin Plates fet down in
the firfi: Part.

There are yet other Phenomena of thefe Rings
of Colours, but fuch as follow from the fame
Propofitions, and therefore confirm both the
Truth of thofe Propofitions, and the Analogy be^
tween thefe Rings and the Rings of Colours
made by very thin Plates. I fhali fubjoin fome
of them.

ObJ\

BOOK II. 283

Obf. 10. When the beam of the Sun's Light
was refleded back from the Speculum not di-
redly to the hole in the Window, but to a pLce
a little diftant 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 in-
cident Light, and the beam of the refleded
Light, and by confequence in the center of the
fpherical concavity of the Speculum, whenever
the Chart on which the Rings of Colours fell
was placed at that center. And as the beam of
refledfed Light by inclining the Speculum re-
ceded more and more from the beam of inci-
dent Light and from the common center of the
colour'd Rings between them, thofe Rings grew
bigger and bigger , and fo alfo did the white
round Spot, and new Rings of Colours emer-
ged fucceffively out of their common center,
and the white Spot became a white Ring en-
compaffing them 3 and the incident and reflected
beams of Light always fell upon the oppofite
parts of this white Ring, illuminating its Peri-
meter like two mock Suns in the oppofite parts
of an Iris. So then the Diameter of this Ring,
meafured from the middle of its Light on one
lide to the middle of its Light on the other fide,
was always equal to the diftance between the
middle of the incident beam of Light,'' and the
middle of the refleded beam meafured 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 confequence to their Angles
pf Refradion at their entrance into the Glafs,

but

284 O P T I C K S.

but yet their Angles of Reflexion were not in
the fame Planes with their Angles of Inci-
dence.

' Obf. 1 1. The Colours of the new Rings Were
in a contrary order to thofe of the former, and
arofe after this manner. • The white round Spot
of Light in the middle of the Rings continued
white to the center till the diftance of the inci-
dent and refleded beams at the Chart was about
8 parts of an Inch, and then it began to grow
dark in the middle. And when that diftance was a-
bout ItV of an Inch, the white Spot was become
a Ring encompaffing a dark round Spot which in
the middle inclined to violet and indigo. And
the luminous Rings encompafling it were grown
equal to thofe dark ones which in the four firft
Obfervations encompafled them, that is to fay,
the white Spot was grown a white Ring equal to
the firft of thofe dark Rings, and the firft of
thofe luminous Rings was now grown equal to
the fecond of thofe dark ones, and the fe-
cond of thofe luminous ones to the third of
thofe dark ones, and fo on. For the Diameters
of the luminous Rings were now itV, 2'V, 2j,
3 iV, S^c. Inches.

When the diftance between the incident and
reflected beams of Light became a little big-
ger, there emerged out of the middle of the
dark Spot after the indigo a blue, and then out
of that biue a pale green, and foon after a yel-
low and red. And when the Colour at the
center was brighteft, being between yellow and
red, the bright Rings were grown equal to thofe
Rings -which in the four firft Obfervations next

encom-

BOOK II. 285

encompaiTed them; that is to fay, the white
Spot in the middle of thofe Rings was now be-
come a white Ring equal to the iirft of thofe
bright Rings, and the firft of thofe bright ones
was now become equal to the fecond of thofe,
and fo on. For the Diameters of the white
Ring, and of the other luminous Rings encom-
paffing it, were now 1 44, 2|, 2|i, 3|., J^c. or
thereabouts.

When the diftance of the two beams of
Light at the Chart was a little more increafed,
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 brighteft being between yellow
and red, the former indigo, blue, green, yel-
low and, red, were become an Iris or Ring of
Colours equal to the firlt of thofe luminous
Rings which appeared in the four firfh Obfer-
vations, and the white Ring which was now
become the fecond of the luminous Rings was
grown equal to the fecond of thofe, and the
lirft of thofe which was now become the third
Ring was become equal to the third of thofe,
and fo on. For their Diameters were Itx, 2g,
2-rT, 3 1- Inches, the diftance of the two beams
of Light, and the Diameter of the v/hite Ring
being 2t Inches.

When thefe two beams became more diflant
there emerged out of the middle of the pur-
plifh red, firft 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 purplilh red) were become a Ring

equal

286 O P T. I C K S.

equal to the firft of the bright Rings mentioned
in the four firfl Obfervations, and the Rings
about this Ring were grown equal to the Rings
about that refpedtively j the diftance 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 be-
gan now to grow very dilute, and if the di-
ftance between the two Beams was increafed
half an Inch, or an Inch more, they vanifh'd
whilfl the white Ring, with one or two of the
Rings next it on either fide, continued ftill vi-
able. But if the diftance of the two beams of
Light was ftill more increafed, thefe alfo va- .
nifhed: For the Light which coming from fe-
veral parts of the hole in the Window fell up-
on the Speculum in feveral Angles of Incidence,
made Rings of feveral bigneffes, which diluted
and blotted out one another, as I knew by inter-
cepting fome part of that Light. For if I in-
tercepted that part which was neareft to the
Axis of the Speculum the Ring's would be lefs,
if the other part which was remoteft from it
they would be bigger.

Obf. 12. When the Colours of the Prifm
were caft fucceffively on the Speculum, that
Ring which in the two laft Obfervations was
white, was of the fame bignefs in all the Co-
lours, but the Rings without it were greater in
the green than in the blue, and ftill greater in
the yellow, and greateft in the red. And, on the
contrary, the Rings within that white Circle
were lefs in the green than in the blue, and ftill

lefs

BOOK II. 287

lefs in the yellow, and leaft in the red. For the
Angles of Reflexion of thofe Rays which made
this Ring, being equal to their Angles of Inci-
dence, the Fits of every reflected Ray within
the Glafs after Reflexion are equal in length
and number to the Fits of the fame Ray with-
in the Glafs before its Incidence on the refled:-
ing Surface. And therefore flnce all the Rays
of all forts at their entrance into the Glafs were
in a Fit of Tranfmiffion, they were alfo in a Fit
of Tranfmiflion at their returning to the fame
Surface after Reflexion j and by confequence
were tranfmitted, and went out to the white
Ring on the Chart. This is the reafon why
that Ring was of the fame bignefs in all the Co-
lours, and why in a mixture of all it appears
white. But in Rays which are reflefted in o-
ther Angles, the Intervals of the Fits of the
leaft refrangible being greateft, make the Rings
of their Colour in their progrefs from this white
Ring, either outwards or inwards, increafe or
decreafe by the greateft fteps ; fo that the Rings
of this Colour without are greateft, and within
leaft. And this is the reafon why in the laft
Obfervation, when the Speculum was illumina-
ted with white Light, the exterior Rings made
by all Colours appeared red without and blue
within, and the interior blue without ^nd red
within.

Thefe. are the Pha?nomena of thick convexo-
concave Plates of Glafs, which are every where
of the fame thicknefs. There are yet other
Phaenomena when thefe Plates are a little thick-
er on one fide than on the other, and others

when

288 O P T I C K S.

when the Plates are more or lefs concave than
convex, or plano-convex, or double-convex. For
in all thefe cafes the Plates make Rings of Co-
lours, but after various manners; all which, fo
far as I have yet obferved, follow from the Pro-
pofitions in the end of the third part of this
Book, and fo confpire to confirm the truth of
thofe Propofitions. But the Phaenomeiia are
too various, and the Calculations whereby they
follow from thofe Proportions too intricate to
be here profecuted. I content my felf with ha-
ving profecuted this kind of Phaenomena fo far
-as to difcover their Caufe, and by difcovering
it to ratify the Propofitions in the third Part of
this Book.

Obf. 13. As Light reflecSled by a Lens quick-
iilver'd on the backfide makes the Rings of Co-
lours above defcribed, fo it ought to make the
like Rings of Colours in pafling through a drop
of Water. At the firft Reflexion of the Rays
within the drop, fome Colours ought to be
tranfmitted, as in the cafe of aj^ens, and others
to be refie(^l:ed back to the Eye. For inftance,
if the Diameter of a fmall drop or globule of
"Water be about the 500th part of an Inch, fo
that a red-making Ray in paffing through the
middle of this globule has 250 Fits of eafy
Tranlhiifiion within the globule, and that all
the red-making Rays which are at a certain di-
ftance from this middle Ray round about it
have 249 Fits within the globule, and all the
like Rays at a certain farther diftance found a-
bout it have 248 Fits, and all thofe at a cer-
tain farther diftance 247 Fits, and fo on; thefe

concern-

BOOK II. 2S9

concentrick Cirdes of Rays after their tranf-
miiTion, falling on a white Paper, will make
concentrick Rings of red upon the Paper, fup-
pofing the Light .which pafles through one An-
gle globule, llrong enough to be fenlible. And,
in like manner, the Rays of other Colours will
make Rings of other Colours. Suppole now
that in a fair Day the Sun ihines through a thin
Cloud of fuch globules of Water or Hail, and
that the globules are all of the fame bignefs;
and the Sun feen through this Cloud fhall ap-
pear encompaffed with the like concentrick
Rings of Colours, and the Diameter of the firfl:
Ring of red fliall be 7 1. Degrees, that of the fe-
cond 10 i Degrees, that of the third 12 Degrees
33 Minutes. And accordingly as the Globules
of Water are bigger or lefs, the Rings lliall be
lefs or bigger. This is the Theory, and Expe-
rience anfwers it. For in 'jiuh; 1692, I faw by
reflexion in a Veflel of ftagnating Water three
Halos, Crowns, or Rings of Colours about the
Sun, like three little Rain-bows, concentrick
to his Body. The Colours of the firft or In-
nermoft Crown were blue next the Sun, red
without, and white in the middle between the
blue and red. Thofe of the fecond Crown
were purple and blue within, and pale red with-
out, and green in the middle. And thofe of
the third were pale blue within, and pale red
without; thefs Crowns enclofed one another
immediately , fo that their Colours proceeded
in this continual order from the Sun outward:
blue, white, red 3 purple, blue, green, pale

U yello;v

290 O P T I C K S.

yellow and red j pale blue, paid red. The Di-
ameter of the fecond Crown meafured from
the middle of the yellow and red on one fide
of the Sun, to the middle of the fame Colour
on the other fide was gr Degrees, or therea-
bouts. The Diameters of the firfl and third
1 had not time to meafure, but that of the firfl
feemed to be about five or fix Degrees, and
that of the third about twelve. The like
Crov/ns appear fometimes about the Moon;
for in the beginning of the Year 1664, Fel?r,
19th at Night, I faw two fuch Crowns about
her. The Diameter of the firfi: or innermoft
was about three Degrees, and that of the fe-
cond about five Degrees and an half Next a-
bout the Moon was a Circle of white, and next
about that the inner Crown, which was of a
bluifli green within next the white, and of a
yellow and red without, and next about thefe
Colours were blue and green on the infide of
the outward Crown, and red on the outfide of
it. At the fame time there appear'd a Halo a-
bout 22 Degrees 35' diftant from the center of
the Moon. It was elliptical, and its long Dia-
meter was perpendicular to the Horizon, verg-
ing belovv farthefk from the Moon. I am told
that the Moon has fometimes three or more
concentrick Crowns of Colours encompafiing
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 ap-
pear, and the Colours will be the more lively.
The Halo at the diilance of 22t Degrees from

the

BOOK

IL 291

By its beino; oval

the Moon is of another fort,
and remoter from the Moon beiow than above,
I conclude, that it v^cis made by Refradlion in
fome fort of Hail or Snow floating in the Air in
an horizontal pofture, the refra<5ting Angle being
about 58 or 60 Degrees.

U 2

THE

^

1

©^

m

i

1

>^

THE

THIRD BOOK

O F

OPTICKS

PART 1.

Ohfervations concerning the Inflexions of
the Rays of Lights and the Colours
made thereby.

RIMALDO has inform'd us, that
if a beam of the Sun's Light be let in-
to a dark Room through a very fmall
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 ilrait Lines,

and

BOOK III. 293

and 'that thefe Shadows have three parallel
Fringes, Bands or Ranks of colour'd Light ad-
jacent to them. Rut if the Hole be enlarged
the Fringes grow broad and run into one ano-
ther, fo that they cannot be diftinguifh'd. Thefe
broad Shadows 'and Fringes have been reckon'd
by fome to proceed from the ordinary refra6tion
of the Air, but without due examination of the
Matter. For the circumftances of the Phano-
nienon, fo far as I have obferved them, are as
follows.

Obf. I. I made in a piece of Lead a fmall
Hole with a Pin, whofe breadth was the 42d
part of an Inch. For 2 1 of thofe Pins laid to-
gether 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 fuch like flender Subftances placed in this
beam of Light, were confiderably broader than
they ought to be, if the Rays of Light pa fled
on by thefe Bodies in right Lines. And parti-
cularly a Hair of a Man's Head, whofe breadth
was but the 280th part of an Inch, being held in
this Light, at the diftance of about twelve Feet
from the Hole, did caft a Shadow which at the
diftance of four Inches from the Hair was the
fixtieth part of an Inch broad, that is, above "
four times broader than the Hair, ' and at the di-
ftance of two Feet from the Hair Vs^as about the
eight and twentieth part of an Inch broad, that
is, ten times broader than the Hair, and at the
diftance of ten Feet was the eighth part of an
Inch bsoad, that is 35 times broader,

U 3 Nor

294 O P T I C K S.

Nor is it material whether the Hair be en-
compaffed with Air, or with any other pellucid
Subllance. For I wetted a polifli'd Plate of
Glafs, and laid the Hair in the Water upon the
Glafs, and. then laying another polifli'd Plate of
Glafs upon it, fo that the Water* might fill up
the fpace between the GlafTes, I held them in
the aforefaid beam of Light, fo that the Light
might pafs through them perpendicularly, and
the Shadow of the Hair was at the fame di-
flances as big as before. The Shadows of
Scratches made in polifh'd Plates of Glafs were
alfo much broader than they ought to be, and
the Veins In polifh'd Plates of Glafs did alfo caft*
the like broad Shadows. And therefore the
great breadth of thefe Shadows proceeds from
feme other caufe than the" Refraction of the
Air.

Let the Circle X [in Fig. i.] reprefent the
middle of the Hair; ADG, BEH, CFI,
three Rays pafTmg by one fide of the Hair at
feveral diflances ; KNQ^LOR, MPS, three
other Rays paffmg by the other fide of the Hair
at the like diflancesj D, E, F, and N, O, P, the
places where the Rays are bent in their paf-
fage by the Hair j G, H, I, and Q^, S, the
places where the Rays fall on a Paper GQ^
I S the breadth of the Shadow of the Hair cafl
on the Paper, and TI, VS, two Rays paffing
to the Points 1 and S without bending when
the Hair is taken away. And it's manifefl that
all the Light between thefe two Rays TI and
VS is bent in paffmg by the Hair, and turned
alide from the Shadow I S, becaufe if any part

cf

BOOK III. 295

of this Light were not bent it would fall on the
Paper within the Shadow, and there illuminaie
the Paper, contrary to experience. And becaufe
when the Paper is at a great diftance from the
Hair, the Shadow is broad, and ■ therefore the
Rays TI and VS are *at a great diftance from
one another, it follows that the Hair ads unon
the Rays of Light at a good diltance in their paf-
fing by it. But the Action is frrongeft on the
Rays which pafs by at leaft^ diflances, and
grows weaker and weaker accordingly as the
Rays pafs by at diftances greater and greater, as
is reprefented in the Scheme : For thence it
comes to pafs, that the Shadow of the Hair is
much broader in proportion to the diflance of the
Paper from the Hair, when the Paper is nearer
the Hair, than when it is at a great diftance
from it.

0I?j:2. The Shadov/s of all Bodies (Metals,
Stones, Glafs, Wood, Horn, Ice, &c. ) in this
Light were border'd with three Parallel Fringes
or Bands of coloured Light, whereof that which
was contiguous to the Shadow was broadeft
and moft luminous, and that which was remo-
teft from it was narroweft, and fo faint, ^ as not
eafily to be vifible. It v/as difficult to diftinguiili
the Colours, unlefs when the Light fell very ob-
liquely/upon a fmooth Pap:-r, or fome other
fmooth white Body, fo as to make them appear
much broader than they would otherwife do.
And then the Colours were plainly vifible in
this Order: The tirft or innermoft Fringe wViS
violet and deep blue next the Shadow, and then
light blue, green, and yellow in the middle, ai :d

U 4 .r^^d

2o6 O P T I C K S.

red without. The fecond Fringe was almoft
contiguous to the firft, and the third to the fe-
cond, and both were blue within, and yellow and
red without, but their Colc^rs were very faint,
cfpecially thofe of the third. The Colours there-
fore 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 polifh'd Plates of Glafs were bor-
der'd with the like Fringes of colour'd Light.
And if Plates of Looking-glafs floop'd off near
the edges with a Diamond-cut, be held in the
fame beam of Light, the Light which paffes
through the parallel Planes of the Glafs will be
border'd with the like Fringes of Colours where
thofe Planes meet with the Diamond-cut, and
by this means there will fometimes appear four
or five Fringes of Colours. Let AB, CD [in
Vig. 2.] reprefent the parallel Planes of a Look-
ing-glafs, and B D the Plane of the Diamond-
cut, making at B a very obtufe Angle with the
Plane AB. And let all the Light between the
Rays ENI and FBM pafs diredly through the
parallel Planes of the Glafs, and fall upon the
Paper between I and M, and all the Light be-
tween the Rays GO and HD be refraded by
the oblique Plane of the Diamond-cut BD,
and fall upon the Paper between K and L;
and the Light which paffes diredly through the
parallel Planes of the Glafs, and falls upon the
Paper between I and M, will be border'd with
three or more Fringes at M.

So

BOOK III. 297

So by looking on the Syn through a Feather
or black Rifcband held clofe to the Eye, feveral
Rain-bows will appear j the Shadows which the
Fibres or Threds caft on the T'unica Retina^
being border'd wi^h' the like Fringes of Co-
lours.

^kf'Z' When the Hair was twelve Feet diftant
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 alfo when
the Shadow fell perpendicularly upon the fame
Scale placed nine Feet beyond it j I meafured the
breadth of the Shadow and Fringes as accu-
rately as I could, and found them in Parts of an
Inch as follows.

The

298

O P T I C K S.

At tloe I)iftance of

hcAf a
Foot

Nine
Feet

I
9

The breadth of tliC Shadow

1

The breadth between the Middles
of the brightefl Light of the in-
nermofl Fringes oh either fide
the Shadow . '^

h or ,\

I

^3i

1 d

T

I

~l~

r

?T

I
TT

The breadth between the Middles
of the brightefl Light of the
middlemoft Fringes on either
fide the Shadow

The breadth between the Middles
of the brighteft Light of the
outmofl Fringes on either fide
the Shadow

I I

The diflance between the Middles
of the brightefl Light of the firfl:
and fecond Fringes

The diflance between the Middles
of the" brightefl Light of the fe-
cond and third Fringes

I To

The breadth of the luminous Part
(green, white, yellow, and red)
of tiie firfl Fringe

1 70

The bread tlx oi tne darker bpact
between the firfl and fecond
Fringes

I
140

The breadcli of the luminous Pan
of the fecond Fringe

27^

The breadth ot the darker Space
between the fecond and third
Fringes

T4~

Tiiefe

BOOK III. 299

Thefe Meafures I took by letting the Shadow
of the Hair, at half a Foot diflance, fall fo ob-
liquely on the Scale, as to appear twelve times
broader than when it fell perpendicularly on it
atthe fame diftance, and fetting down in this
Table the twelfth part of the Meafures I then
took.

ObC. 4. When the Shadow and Fringes were
caft obliquely upon a fmooth white Body, and
that Body was removed farther and farther
from the Hair, the firft Fringe began to appear
and look brighter than the reft of the Light
at the diftance of lefs than a quarter of an Inch
from the Hair, and the dark Line or Shadow
between that and the fecond Fringe began to
appear at a lefs diftance from the Hair than that
of the third part of an Inch. The fecond Fringe
began to appear at a diftance from the Hair of
lefs than half an Inch, oand the Shadow between
that and the third Fringe at a diftance lefs than
ail Inch, and the third Fringe at a diftance lefs
than three Inches. At greater diftances they
became much more fenlible, but kept very
nearly the fame proportion of their breadths
and intervals which they had at their firft ap-
pearing. For the diftance between ♦ the middle
of the firft, and middle of the fecond Fringe,
was to the diftance between the middle of the
fecond and middle of the third Fringe, as three
to two, or ten to feven. And the laft of thefe
two diftances was equal to the breadth of the
bright Light or luniinous part of the firft Fringe.
And this breadth was to the breadth of the
bright Light of the fecond Fringe as feven to

four,

30O O P T I C K S.

four, and to the dark Interval of the firft and
fecond Fringe as three to two, and to the like
dark Interval between the fecond and third as
two to one. For the breadths of the Fringes
feem'd to be in the progreffion of the Numbers
I) v^i v^l, and their Intervals to be in the
fame progreffion with them j that is, the Frin-
ges and their kitervals together to be in the
continual progreffion of the Numbers i, /?, /f,
</!, v'i-, or thereabouts. And thefe Proportions
held the fame very nearly at all diftances from
the Hair ; the dark Intervals of the Fringes be-
ing as broad in proportion to the breadth of the
Fringes at their firil appearance as afterwards at
great dillances from the Hair, though not fo dark
and diftind:. •

Obf. 5. The Sun fhining into my darken'd
Chamber through a hole a quarter of an Inch
broad, I placed at the diilance of two or three
Feet from the Hole a Sheet of Pafteboard, which
was black'd all over on both fides, and in the
middle of it had a hole about^ three quarters
of an Inch fquare for the Light to pafs through.
And behind the hole I faften'd to the Palte-
board with Pitch the blade of a ffiarp Knife, to
intercept fome part of the Light which paffied
through the hole. The Planes of the Pafte-
board and blade of the Knife were parallel to
one another, and perpendicular to the Rays.
And when they w^re fo placed that none of
the Sun's Light fell on the Pafteboard, but all of
it pafied through the h.ole'to t*he Knife, and there
part of it fell upon the blade of the Knife, and
part of it paifed by its edge j I let this part of

the

BOOK III. 301 '

the Light which paiTed by, fall on a white Pa-
per two or three Feet beyond the Knife, and
there faw two ftreams of faint Light fhoot out
both ways from the beam of Light into the flia-
dow, like the Tails of Comets. But becaufe the
Sun's dired: Light by its brightnefs upon the
Paper obfcured thefe faint ftreams, fo that I
could fcarce fee them, I made a little hole in
the midft of the Paper for that Light to pafs
through and fall on a black Cloth behind it ;
and then I faw the two ftreams 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 ftrong for the fpace of about
a quarter of an Inch, or half an Lich, and in all
* its progrefs from that direct Light decreafed
gradually till it became infenfible. The whole
length of either of thefe ftreams meafured up-
on the Paper at the diftance of three Feet from
the Knife was about fix or eight Inches ; fo that
it fubtended an Angle at the edge of the Knife
of about 10 or 12, or at moft 14 Degrees. Yet
fometimes I thought I faw it ftioot three or four
Degrees farther, but with a Light fo very faint
that I could fcarce perceive it, and fufpe(5ted it
might ( in fome meafure at leaft ) arife from
fome other caufe than the two ftreams did. For
placing my Eye in that Light beyond the end
of that ftream which was behind the Knife, and
looking towards the Knife, I could fee a line of ^ •
Light upon its edge, and that not only when
my Eye was in the line cf the Streams, but al-
fo when it was without that line either towards

the

302 O P T I C K S.

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 innermofl Fringe, and narroweft
when my Eye was fartheft from the dired: Light,
and therefore feem'd to pafs between the Light
of that Fringe and the edge of the Knife, and
that which palTed nearefl the edge to be mofl .
bent, though not all of it.

Ohf. 6. I placed another Knife by this, fo
that their edges might be parallel, and look to-
wards one another, and that the beam of Light
might fall upon both the Knives, and fome part
of it pafs between their edges. And when the
diflance of their edges was about the 400th
part of an Inch, the ftream pjlrted in the mid- ^
die, and left a Shadow between the two parts.
This Shadow was fo black and dark that all the
Light which pafTed between the Knives feem'd
to be bent, and turn'd afide to the one. hand or
to the other. And as the Knives ftill approach'd
one another the Shadow grew broader, and the
ftreams ihorter at their inward ends which were
next the Shadow, until upon the contad; of the
Knives the whole Light vahilh'd, leaving its place
to the Shadow.

And hence I gather that the Light which is
leaft bent, and goes to the inward ends of the
ftreams, palTes by the edges of the Knives at
the greatefh diftance, and this diflance when
the Shadow begins to appear between the
ftreams, is about the Sooth part of an Inch. And
the Light which paffes by the edges of the
Knives at diftances ftill lefs and lefs, is more and

more

BOOK III. 303

more bent, and goes ta thofe parts of the
ftreams which are farther and farther from the
diredt Light; becaufe when the Knives approach
one another till they touch, thofe parts of the
ftreams vanifti laft v/hich are fartheil from the
dired Light.

Obf. 7. In the fifth Obfervation the Fringes
did not appear, but by reafon of the breadth of
the hole in the Window became fo broad as to run
into one another, and by joining, to rriake one
continued Light in the beginning of the ftreams.
But in the fixth, as the Knives approached one
another, a little before the Shadow appeared
between- the two ftreams, the Fringes began
to appear on the inner ends of the Streams on
either fide of the dired: Light ; three on one
fide made by the edge of one Knife, and three
on the other fide made by the edge of the o-
ther Knife. They Were diftindeft when the
Knives were placed at the greateft diftance from
the hole in the Window, and ftill became more
diftind: by making the hole lefs, infomuch that
I could fometimes fee a faint lineament of a
fourth Fringe beyond the three above men-
tion'd. ' And as the Knives continually ap-
proach'd one another, the Fringes grew di-
ftinder and larger, until they vanifh'd. The
outmoft Fringe vanifli'd firft, and the middle-
moft next, and the innermoft laft. And after
they were all vanifh'd', and the line of Light
which was in the middle between them was
grown very broad, enlarging it felf on both fides
into the ftreams of Light defcribed in the fifth"
Obfervation, the above-rnention'd Shadow be-

.1 ■ gan

304- O P T I C K S.

gan to appear in the middle of this line, and
divide it along the middle into two lines of
Li^ht, and increafed until the whole Light va-
nilh'd. This enlargement of the Fringes was
fo great that the Rays which go to the inner-
moft Fringe feem'd ' to be bent above twenty •
times more v/hen this Fringe was ready to va-
nifh, than when one of the Knives was taken
away.

And from this and the former Obfervation
compared, I gather, that the Light of the firffc
Fringe pafTed by the edge of the Knife at a di-
flance greater than the Sooth part of an Inch,
and the Light of the fecond Fringe paiTed by
the edge of the Knife at a greater diftance than
the Light of the firft Fringe did, and that of
the third at a greater diftance than that of the
fecond, and that of the ftreams of Light defcri-
bed in the fifth and fixth Obfervations pafTed by
the edsies of the Knives at lefs diftances than that
of any of the Fringes.

Obf. 8. I caufed the edges of two Knives
to be ground truly ftrait, and pricking their
points into a Board fo that their edges might
look towards one another, and meeting near
their, points contain a redtilinear Angle, I faften'd
their Handles together with Pitch to make this
Angle invariable. The diftance of the edges of
the Knives from one another at the diltance of
four Inches from the angular Point, where the
edges of the Knives met, was the eight;: part
of an Inch j 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

BOOK III. 305

of the Sun's Light, let into my darken'd Cham-
ber through a Hole the 420! Part of an Inch wide,
at the diftance of 10 or 15 Feet from the Hole,
and let the Light which pafled between their edges
fall very obliquely upon a fmooth white Ruler at
the diftance of half an Inch, or an Inch from
the Knives, and there faw the Fringes by the
two edges of the Knives run along the edges of
the Shadows of the Knives in Lines parallel to
thofe edges without growing fenfibly broader,
till they met in Angles equal to the Angle
contained by the edges of the Knives, ai d
where they met and joined they ended without
croffing one another. But if the Ruler was
held at a much greater diftance from the
Knives, the Fringes w^here they were firther
from the Place of their Meeting, were a little
narrower, and became fomething broader and
broader as they approach'd nearer and nearer to
one another, and after they met tiiey crofs'd
one another, and then became much broader
than before.

Whence I gather that the diftances at which
the Fringes pafs by the Knives are not increafed
nor alter'd by the approach of the Knives, but
the Angles in whicli the Rays are there bent
are much increafed by that approach ; and that
the Knife which is neareli any Ray determines
which way the Ray ftiall be bent, and the other
Knife increafes the bent.

Obf, 9. When the Rays fell very obliquely
upon the Ruler at the diftance of the third Part,
of an Inch from the Knives, the dark Line be-
tween the firft and fecond Fringe of the Sha-

X dow

3o6 O P T I C K S.

dow of one Knife, and the dark Line between
the firft and fecond Fringe of the Shadow of
the other Knife met with one another, at the
diftance of the fifth Part of an Inch from th«
end of the Light which pafTed between the
Knives at the concourfe of their edges. And
therefore the diftance of the edges of the Knives
at the meeting of thefe dark Lines was the i6oth
Part of an Inch. For as four Inches to the
eighth Part of an Inch, fo is any Length of the
edges of the Knives meafured from the point
of their concourfe to the diftance of the edges
of the Knives at the end of that Length, and fo
is the fifth Part of an Inch to the i6oth Fart.
So then the dark Lines above-mention'd meet
in the middle of the Light which pafTes be-
tween the Knives where they are diftant the
i6oth Part of an Inch, and the one half of that
Light pafles by the edge of one Knife at a di-
ftance 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 pafies by the edge of the other Knife,
at a diftance 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 diftance from the
Knives greater than the third Part of an Inch,
the dark Lines above-mention'd meet at a greater
diftance than the fifth Part of an Inch from
the end of the Light which pafTed between the
Knives at the concourfe of their edges ; and
therefore the Light which falls upon the Paper
where thofe dark Lines meet pafles between the .

Knives

BOOK III.

307

Knives where the edges are diftant above the
160th part of an Inch.

For at another time, when the two Knives
were diltant eigiit Feet and five Inches from the
little hole in the Window, made with a fmall
Pin as above, the Light which fell upon the Pa-
per where the aforefaid dark lines met, paffed
between the Knives, where the dillance between
their edges was as in the following Table, w^hen
the diftance of the Paper from the Knives was
alfo as follows.

Dijiaiices of the Paper
from the Knhes i}i
Inches.

Dijtances betixeen . the
edges of the Kfiizrs in
millefmal parts of an
Inch.

. 3i-

32.
96.

131-

o'oi2

0'020

•^ o'o34

■ o'o^7
o'oSi

o'oS/

And hence I gather, that the Light which
makes the Fringes upon the Paper is not the
fame Light at all diftances of the Paper from
the Knives, but when the Paper is held near
the Knives, the Fringes are made by Light
which pafTes by the edges of the Knives at a
lefs diftance, and is more bent than when the
Paper is held at a greater diftance from the
Knives.

X 2

Obf

3o8 OPTIC K S.

Obf. 10. When the Fringes of the Shadows
of the Knives fell perpendicularly upon a Paper
at a great diftance from the Knives, they'w^ere
in the form of Hyperbola's, and their Dimen-
fions were as follows. Let CA, CB [in Fig. 3.]
reprefent Lines drawn upon the Paper parallel
to the edges of the Knives, and between which
all the Light would fall, if it pafled between
the edges of the Knives without inflexion ; DE
a Right Line drawn through C making the An-
gles A CD, 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; eisy fkt^ and glv^ three hyper-
bolical Lines reprefenting the Terminus of the
Shadow of one of the Knives, the dark Line
between the firft and fecond Fringes of that
Shadow, and the dark Line between the fecond
and third Fringes of the fame Shadow ; xip, ykq,
and z/r, three other hyperbolical Lines repre-
fenting the Terminus of the Shadow of the other
Knife, the dark Line between the firfl and fecond
Fringes of that Shadow, and the dark line be-
tween the fecond and third Fringes of the fame
Shadow. And conceive that thefe three Hyper-
bola's are like and equal to the former three, and
crofs them in the points /', i, and /, and that the
Shadows of the Knives are terminated and diflin-
guifh'd from the lirft luminous Fringes by the
lines e i s and x ip, until the meeting and crof-
fmg of the Fringes, and then thofe lines crofs
the Fringes in the form of dark lines, termina-
ting the firft luminous Fringes within fide, and
diftinguifhing them from another Light which

begins

BOOK III. 309

begins to appear at /, and illuminates all the
triangular fpace /j^DEj. comprehended by thefe
dark lines, and the right line DE. Of thefe
Hyperbola's one Afymptote is the line DE, and
their other Afymptotes are parallel to the lines
C A and C B. Let r 'v reprefent a line drawn
any where upon the Paper parallel to the Afym-
ptote DE, and let this line crofs the right lines
AC in w, and B C in «, and the fix dark hy-
perbolical lines in />, ^, ^ 3 J, ^, i' ; and by mea-
suring the diftances /) J, gt, r'-j, and thence
collecting the lengths of the Ordinates n p, n q^
nr or m s^ m /, m v^ and doing this at feveral
diftances of the line r v from the Afymptote DD,
you may find as many points of thefe Hyperbo-
la's as you pleafe, and thereby know that thefe
curve lines are Hyperbola's differing little from
the conical Hyperbola. And by meafuring the
lines C /, C k, C /, you may find other points of
thefe Curves.

For inftance; when the Knives were diftant
from the hole in the Window ten Feet, and the
Paper from the Knives nine Feet, and the An-
gle contained by the edges of the Knives to
which the Angle ACBis equal, was fubtend-
ed by a Chord which was to the Radius as i
to 32, and the diftance of the line rv from the
Afymptote DE was half an Inch: I meafured
the lines pSy qt, rv, and found them 0*35,
o'65, o'98 Inches refped;ively ; and by adding
to their halfs the line r m n^ ( w^hich here was
the 128th part of an Inch, or 0*0078 Inches,) the
Sums «^, nq^nVy were o' 1828, ©'3328, 0*4978
Inches. I meafured alfo the diftances of the

X 3 brighteft

3IO O P T I C K S.

brightefl parts of the Fringes which run between
fq and st, qr and t 'U, and next beyond r and 'u>
and found them o'5, o'B, and iij Inches.

Obf. II. The Sun fhining into my darkened
Room through a fmall round hole made in a
Plate of Lead with a flender Pin, as above ; I
placed at the hole a Prifm to refrad the Light,
and form on the oppofite Wall the Spedtrum
of Colours, defcribed in the third Experiment
of the firft Book. And then I found that the
Shadows of all Bodies held in the colour'd
Light between the Prifm 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 fenfi-
ble blue or violet, and in tiie deep blue Light
they were totally blue without any fenfible red
or yellow ; and fo in the green Light they were
totally green, excepting a little yellow and blue,
which were mixed .in the green Light of the
Prifm. And comparing the Fringes made in
the feveral colour'd Lights, I found that thofe
made in the red Light were largeft, thofe
made in the violet were leail, and thofe made
-in the green Vv^ere of a middle bignefs. For
the Fringes with which the Siradow of a Man's
Hair were bordered, being meafured crofs the
Shadow at the diftance of fix Liches from the
Hair, the diflance between the middle and moil;
luminous part of the iirfl or innermoft Fringe
on one. fide of the Shadow, and that of the like
Fringe on the other iide of the Shadow, was in

the full red Lieht -~ of an Inch, and in the full

violet

BOOK III. 311

violet ?V. And the like diftance between the
middle and mofl luminous parts of the fecond
Fringes on either iide the Shadow was in the full
red Light »'=-, and in the violet tV of an Inch.
And thefe diftances of the Fringes held the fame
proportion at all diftances from the Hair without
any fenfible 'variation.

So then the Rays which made thefe Fringes
in the red Light paffed by the Hair at a greater
diftance than thofe did which made the like
Fringes in the violet j and therefore the Hair
in caufing thefe Fringes adied alike upon the
red Light or leaft refrangible Rays at a greater
diftance, and upon the violet or moft refrangi-
ble Rays at a lefs diftance, and by thofe adions
difpofed the red Li^ht into larger Fringes, and
the violet into fmaller, and the Lights of inter-
mediate Colours into Fringes of intermediate big-
neftes without changing the Colour of any fort
of Light.

When therefore the Hair in the firft and fe-
cond of thefe Obfervations was held in the
white beam of the Sun's Light, and caft a Sha-
dow which was border'd with three Fringes of
coloured Light, thofe Colours arofe not from
any new modifications imprefs'd upon the Rays
of Light by the Hair, but only from the vari-
ous inflexions whereby the feveral Sorts of Rays
were feparated from one another, which before
feparation, by the mixture of all their Colours,
compofed the white beam of the Sun's Light,
but whenever feparated compofe Lights of the
feveral Colours which they are originally difpo-
fed to exhibit. In this i ithObfervation, where

X 4 the

312 O P T I C K S.

!Dhe Colours are feparated before the Light paf-
fes by the Hair, the leaft refrangible Rays, which
when feparated from the reft make red, were
infleded at a greater diftance from the Hair, fo
as to make three red Fringes at a greater di-
ftance from the middle of the Shadow of the
Hair j and the moft refrangible Rays which
when feparated make violet, were inflected at
a lefs diftance from the Hair, fo as to make
three violet Fringes at a lefs diftance from the
middle of the Shadow of the Hair. And other
Rays of intermediate degrees of Refrangibility
were inflefted at intermediate diftances from
the Hair, fo as to make Fringes of intermediate
Colours at intermediate diftances from the mid-
dle of the Shadow of the Hair. And in the
fecond Obfervation, where all the Colours are
mix'd in the white Light which pafles by the
Hair, thefe Colours are feparated by the vari-
ous inflexions of the Rays, and the Fringes
which they make appear all together, and the
innermoft Fringes being contiguous make on^^
broad Fringe compofed of all the Colours in .
due order, the violet lying on the infide of the
Frmge next the Shadow, the red on the out-
fide fartheft from the Shadow, and the blue,
green, and yellow, in the middle. And, in like
manner, the middlemoft Fringes of all the Co-
lours lying in order, and being contiguous,
make another broad Fringe compofed of all the
Colours -J and the outm.oft Fringes of all the
Colours lying in order, and being contiguous,
make a third broad Fringe compofed of all the
Colours. Thefe are the three Fringes of co-

lour'd

BOOK III. 313

lour'd Light with which the Shadows of all Bo-
dies are border'd in the fecond Cbfervation.

When I made the foregoing Obfervations, I
defign'd to repeat moft of thcm.with more care
and exadnefs, and to mJike fome new ones for
determining the manner how the Rays of Light
are bent in their palTage by Bodies, for making
the Fringes of Colours with the dark lines be-
tween them. But I was then interrupted, and
cannot now think of taking thefe things into far-
ther Confideration. And fince 1 have not finifh'd
this part of my Defign, I fhall conclude with
propofing only fome Queries, in order to a far-
ther fearch to be made by odiers.

^ery i. Do not Bodies a<5t upon Light at
a diltance, and by their action bend irs Raysj and
is not this action ( cceteris paribus ) flrongeft at
the leaft diftance ?

^. 2. Do not the Rays which differ in Re-
frangibility differ alfo in Flexibity j and are they
not by their different Inflexions feparatcd from
one another, fo as after feparation to niake the
Colours in the three Fringes above defer ibed ?
And after what manner are they infle(5ted to make
thofe Fringes ?

^. 3 Are not the Rays of Light in pafling
by the edges and fides of Bodies, bent feveral
times backwards and forwards, with a motion
like that of an Eel ? And do not the three Frin-
ges of colour'd Light above-mention'd arife from
three fuch bendings ?

^. 4. Do not the Rays of Light which fall
upon Bodies, and are refleded or refraded, be-
gin

314 O P T I C K S.

gin to bend before they arrive at the Bodies ; and
are they not reflecfled, refrafted, and infledied,
by one and the fame Principle, ading varioufly
in various Circumftances ?

^. 5. Do not Bodies and Light ad mutually
upon one another ; that is to fay. Bodies upon
Light in emitting, receding, refrading and in-
fleding it, and Light upon Bodies for heating
them, and putting their parts into a vibrating
motion vs^herein heat confifts ?

^. 6. Do not black Bodies conceive heat
more eafily from Light than thofe of other Co-
lours do, by reafon that the Light falling on them
is not refleded outw^ards, but enters the Bodies,
and is often refleded and refraded within them,
until it be ftifled and loft ?

^. 7. Is not the ftrength and vigor of the
a^ion between Light and fulphureous Bodies ob-
ferved above, one reafon why fulphureous Bodies
take fire more,readily, and burn more vehement-
ly than other Bodies do ?

^. 8. Do not all fix'd Bodies, when heated
beyoiifl a certain degree, emit Light and fhine ;
and is not this Emiffion perform'd by the vi-
brating motions of their parts ? And do not all
Bodies which abound with terreflrial parts, and
efpecially with fulphureous ones, emit Light
as often as thofe parts are fufficiently agitated j
whether that agitation be made by Heat, or by
Fridicn, or Percuffion, or Putrefadion, or by
any vital Motion, or any other Caufe? As for
infliance ; Sea- Water in a raging Storm ; Quick-
filver agitated in ^jacuo ; the Back of a Cat, or
Neck of a Horfe, obliquely ftruck or rubbed in

a dark

BOOK III. 315

a dark place ; Wood, Flefh and Fifli while they
putrefy ; Vapours ariling from putrefy 'd Wa-
ters, ufually call'd Ignes Fatui ; Stacks of moifl
Hay or Corn growing hot by fermentation ;
Glcfw-worms and the Eyes of fome Animals by
vital Motions J the vulgar Phofphoriis agitated
by the attrition of any Body, or by the acid
Particles of the Air; Amber and fome Dia-
monds by ftriking, preffing or rubbing them;
Scrapings of Steel ftruck off with a Flint ; Iron
hammer'd very nimbly till it become fo hot as
to kindle Sulphur thrown upon it ; the Axle-
trees of Chariots taking fire by the rapid rota-
tion of the Wheels ; and fome Liquors mix'd
with one another whofe Particles come toge-
ther with an Impetus, as Oil of Vitriol diftilled
from its weight of Nitre, and then mix'd with
twice its weight of Oil of Annifeeds. So alfo a
Globe of Glafs about 8 or 10 Inches in diameter,
being put into a Frame where it may be fwiftly
turn'd round its Axis , will in turning fhine
where it rubs againft the palm of ones Hand
apply 'd to it: And if at the fame time a <^iece
of white Paper or white Cloth, or the end of
ones Finger be held at the diftance of about a
quarter of an Inch or half an Inch from that
part of the Glafs where it is mojft in motion,
the eled:rick Vapour which is excited by the
fri6lion of the Glafs againft the Hand, will by
dafhing againft the white Paper, .Cloth or Fin-
ger, be put into fuch an agitation as to emit
Light, and make the white Paper, Cloth or Fin-
ger, appear lucid like a Glow-worm ; and in
rufhing out of the Glafs will fometimes pufti

againft

3i6 * O P T I C K S.

againft the Finger fo as to be felt. And the fame
things have been found by rubbing a long and
large Cylinder of Glafs or Amber with a Paper
held in ones hand, and continuing the fridiion till
the Glafs grew warm.

^. 9. Is not Fire a Body heated fo hot as to
emit Light copioufly? For what elfe is a red hot
Iron than Fire? And what elfe is a burning Coal
than red hot Wood ?

§u. 10. Is not Flame a Vapour, Fume or Ex-
halation heated red hot, that is, fo hot as to
fhine ? For Bodies do not flame without emit-
ting a copious Fume, and this Fume burns in
the Flame. The Igms Fatuus is a Vapour fhi-
ning without heat, and is there not the fame
difference between this Vapour and Flame, as
between rotten Wood fhining without heat and.
burning Coals of Fire ? In diftilling hot Spirits,
if the Head of the Still be taken off, the Va-
pour which afcends 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 in-
renfe, fume copioufly, and if the heat be great
enough the Fumes will (liine and become Flame.
Metals in fuflon do not flame for want of a co-
pious Fume, except Spelter, which fumes co-
pioufly, and thereby flames. All flaming Bo-
dies, as Oil, Tallow, Wa"^, Wood, foffil Coals,
Pitch, Sulphur, by flaming waflie and vanifli in-
to burning Smoke, which Smoke, if the Flame
be pur out, is very thick and vifible, and fome-
times fmells ftrongly, but in the Flame lofes its

fmell

BOOK III. 317

fmell by burning, and according to the nature
of the Smoke the Flame is of feveral Colours,
as that of Sulphur blue, that of Copper open'd
with fublimate green, that of Tallow yellow,
that of Camphire white. Smoke paffing 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 Char-
coal and Sulphur eafily take fire, and fet fire to
the Nitre, and the Spirit of the Nitre being
thereby rarified into Vapour , ruflies out with
Explofion much after the manner that the Va-
pour of Water rufhes out of an ^olipile^ the
Sulphur alfo being volatile is converted into
Vapour, and augments the Explofion. And
the acid Vapour of the Sulphur (namely that
which diftils under a Bell into Oil of Sulphur,)
entring violently into the fix'd Body of the Ni-
tre, fets loofe the Spirit of the Nitre, and ex-
cites a great Fermentation, whereby the Heat
is farther augmented, and the fix'd Body of the
Nitre is alfo rarified into Fume, and the Explo-
fion is thereby made more vehement and quick.
For if Salt of Tartar be mix'd with Gun-pow-
der, and that Mixture be warm'd till it takes
fire, the Explofion will be more violent and
quick than that of Gun-powder alone; which^
cannot proceed from any other caufe than the
action of the Vapour of the Gun-powder upon
the Salt of Tartar, whereby that Salt is rarified.
The Explofion of Gun-powder arifes therefore
from the violent aftion whereby all the Mixture
being quickly and vehemently heated, is rarified

r and

3i8 O P T I C K S.

and converted into Fume and Vapour: which
Vapour, by the violence of that adiion , be-
coming fo hot as to fhine, appears in the form of
Flame.

^. 1 1. Do not great Bodies conferve their
heat the longeft, their parts heating one ano-
ther, and may not great denfe and fix'd Bo-
dies, when heated beyond a certain degree, e-
mit Light fo copioufly, as by the Emilfion and
Re-a6tion of its Light, and the Reflexions and
Refradions of its Rays within its Pores to grow
ilill hotter, till it comes to a certain period of
heat, fuch as is that of the Sun ? And are not
the Sun and fix'd Stars great Earths vehemently
hot, whofe heat is conferved by the greatnef^
of the Bodies, and the mutual Adiion and Re-
action between them, and the Light which they
emit, and whofe parts are kept from fuming a-
way, not only by their fixity, but alfo by the
vaft weight and denfity of the Atmofpheres in-
cumbent upon them ; and very ftrongly com-
preffing them, and condenfing the Vapours and
Exhalations which arife from them? For if
Water be made warm in any pellucid Veflel
emptied of Air, that Water in the Vacuum will
bubble and boil as vehemently as it would in
the open xAir in a Veffel fet upon the Fire till
it conceives a much greater heat. For the
weight of the incumbent Atmofphere keeps
down the Vapours, and hinders the Water from
boiling, until it grow much hotter than is re-
quifite to make it boil in vacuo. Alfo a mix-
ture of Tin and Lead being put upon a red hot
Iron in vacuo emits a Fume and Flame^ but the
3 fame

BOOK III. 319

fame Mixture in the open Air, by reafon of the
incumbent Atmofphere, does not fo much as e-
mit any Fume which can be perceived by Sight.
In like manner the great weight of the Atmo-
fphere which lies upon the Globe of the Sun
may hinder Bqdies there from riling up and
going away from the Sun in the form of Va-
pours and Fumes, unlefs by means of a far
greater heat than that which on the Surface of
our Earth would very eafily turn them into Va-
pours and Fumes. And the fime great weight
may condenfe thofe Vapours and Exhalations as
foon as they fliall at any time begin to afcend
from the Sun, and make them prefently fall
back again into him, and by that adion increafe
his Pleat much after the manner that in our
Earth the Air increafes the Heat of a culinary
Fire. And the fame weight may hinder the
Globe of the Sun from being diminifh'd, unlefs
by the Emiflion of Light, and a very fmall quan-
tity of Vapours and Exhalations.

%/. 12. Do not the Rays of Light in falling
upon the bottom of the Eye excite Vibrations
in the Tunica Retina? Which Vibrations, be-
ing propagated along the folid Fibres of the op-
tick Nerves into the Brain, caufe the Senfe of
feeing. For becaufe denfe Bodies conferve their
Heat a long time, and the denfeft Bodies con-
ferve their Heat the longeft, the Vibrations of
their parts are of a lalling nature, and there-
fore may be propagated along folid Fibres of
uniform denfe Matter to a great diftance, for
conveying into the Brain the impreffions made
upon all the Organs of Senfe. For that Motion

which

320 O P T I C K S.

which can continue long in one and the fame part
of a Body, can be propagated a long way from
one part to another, fuppofing the Body homo-
geneal, fo that the Motion may not be refleded,
reffaded, interrupted or diforder'd by any un-
evennefs of the Body.

^. 13. Do not feveral forts of Rays make
Vibrations of feveral |)ignefres, which according
to their bignelfes excite Senfations of feveral Co-
lours, much after the manner that the Vibrations
of the Air, according to their feveral bignelfes
excite Senfations of feveral Sounds ? And parti-
cularly do not the moft refrangible Rays excite
the fhorteft Vibrations for making a Senfation of
deep violet, the leafl refrangible the largeft for
making a Senfation of deep red, and the feveral
intermediate forts of Rays, Vibrations of feveral
intermediate bigneffes to make Senfations of the
feveral intermediate Colours ?

^. 14. May not the harmony and difcord of
Colours arife from the proportions of the Vibra-
tions propagated through the Fibres of the op-
tick Nerves into the Brain, as the harmony and
difcord of Sounds arife from the proportions of
the Vibrations of the Air? For fome Colours, if
they be view'd together, are agreeable to one
another, as thofe of Gold and Indigo, and others
difagree.

^i. 15. Are not the Species of Objedls feen
with both Eyes united where the optick Nerves
meet before they come into the Brain, the Fi-
bres on the right fide of both Nerves uniting
there, and after union going thence into the
Brain in the Nerve whicji is on the right fide of

thq

BOOK III. .21

the Head, and the Fibres on the left fide of
both Nerves uniting in the fame place, and af-
ter union going into the Brain in the Nerve
which is on the left fide of the Head, and thefe
tw^o Nerves meeting in the Brain in fuch a man-
ner that their Fibres make but one entire Spe-
cies or Pidure, half of which on the right fide
of the Senforium comes from the right fide of
both Eyes through the right fide of both op-
tick Nerves to the place where the Nerves meet,
end from thence on the right fide of the Head
into the Brain, and the other half on the left
fide of the Senforium comes in like manner from
the left fide of both Eyes. For the op tick
Nerves of fuch Animals as look the fame way
with both Eyes (as of Men, Dogs, Sheep, Oxen,
&c\) meet before they come into the Brain, but
the optick Nerves of fuch Animals as do not
look the fame way with both Eyes (as of Fifiics,
and of the Chameleon,) do not meet, if I am
rightly inform'd.

^. 1 6. When a Man in the dark prefTes either
corner of his Eye with his Finger, and turns his
Eye away from his Finger, he will fee a Circle
of Colours like thofe in the Feather of a Pea-
cock's Tail. If the Eye and the Finger remain
quiet thefe Colours vanifh in a fecond Minute of
Time, but if the Finger be moved with a qua-
vering Motion they appear again. Do not thefe
Colours arife from fuch Motions excited in the
bottom of the Eye by the PrelTure and Motion
of the Finger, as at other times are excited
there by Light for caufing Vifion ? And do not
the Motions once excited continue about a Se-

,y cond

322 O P T I C K S.

cond of Time before they ceafe ? And when a
Man by a ftroke upon his Eye fees a flafh of
Light, are not the Hke Motions excited in the
Retina by the ftroke ? And when a Coal of Fire
moved nimbly in the circumference of a Cir-
cle, makes the whole circumference appear like
a Circle of Fire ; is it not becaufe the Motions
excited in the bottom of the Eye by the Rays
of Light are of a lafting nature, and continue
till the Coal of Fire in going round returns to
its former place ? And confidering the lafting-
nefs of the Motions excited in the bottom of
the Eye by Light, are they not of a vibrating
nature ?

%/. 17. If a Stone be thrown into ftagnating
Water, the Waves excited thereby continue-
fome time to arife 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 diftances. And the Vi-
brations or Tremors excited in the Air by per-
cuffion, continue a little time to move from the
place of percufTion in concentrick Spheres to
great diftances. And in like manner, when a Ray
of Light falls upon the Surface of any pellucid
Body, and is there refra(fted or reflected, may not
Waves of Vibrations, or Tremors, be thereby
excited in the refracting or reflecfling Medium at
the point of Incidence, and continue to arife
there, and to be propagated from thence as long
as they continue to arife and be propagated, when
they are excited in the bottom of the Eye by the
Prellure or Motion of the Finger, or by the Light
which comes from the Coal of Fire in the Ex-
periments.

B o o ic in. 323

perimetits abovemention'd ? and are not thefa
Vibrations propagated from the point of Inci-
dence to great diltances ? And do they not over-
take the Rays of Light, and by overtaking them
fucceffively, do they not put them into the Fits
of eafy Reflex io.^. and eafy Tranfmiinon defcribed
above? For if the Rays endeavour to recede from
the denfeft part of the Vibration, they may be
ahernately accelerated and retarded by the Vi-
brations overtaking them.

%. 18. If in two large tall cylindrical Vef-*
fels of Glafs inverted, two little Thermometers
be fufpended fo as not to touch the Veffels, and
the Air be drawn out of one of thefe Veffels,
and thefe Veffels thus prepared be carried out
of a cold place into a warm one; the Thermo-
meter ift 'Vacuo will grov/ warm as much, and
almoft as foon as the Thermometer which is
not in vacuo. And when the Veffels are carri-
ed back into the cold place, the Thermometer
in vacuo will grow cold almofi: as foon as the
other Thermometer. Is not th^e Heat of the
warm Room convey'd through the Vacuum by
the Vibrations of a much fubriler Medium than
Air, which after the Air was drawn out remain-
ed in the Vacuum f And is not this Medium the
fame with that Medium by which Light is re-
fracted and refleded, and bv whofe Vibrations
Light communicates Heat to Bodies, and is
put into Fits of eafy Reflexion and eafy Tranf-
miffion ? And do not the Vibrations of this Me-*
dium in hot Bodies contribute to the intenfenefs
and duration of their Heat ? And do not hot
Bodies communicate their Heat to contiguous

y 3 cdld

324 O P T I C K S.

cold ones, by the Vibrations of this Medium
propagated from them into the cold ones ? And
is not this Medium exceedingly more rare and
fubtile than the Air, and exceedingly more ela-
ftick and adlive? And doth it not readily per-
vade all Bodies? And is it not ( by its elaftick
force) expanded through all the Heavens ? .

^. 19. Doth not the Refradtion of Light
proceed from the different denfity of this JEzhe-
real Medium in different places, the Light re-
ceding always from the denfer parts of the Me-
dium? And is not the denfity thereof greater
in free and open Spaces void of Air and other
groffer Bodies, than vi^ithin tjie Pores of Wa-
ter,' Glafs, Cryflal, Gems, and other compacfl
Bodies? For w^hen Light paffes through Glafs
or Cryflal, and falling very obliquely upon the
farther Surface thereof is totally refleded, the
total Reflexion ought to proceed rather from the
denfity and vigour of the Medium w^ithout and
beyond the Glafs, than from the rarity and w^eak-
nefs thereof

^. 20. Doth not this Ethereal Medium in
paffing out of Water, Glafs, Cryflal, and other
compad: and denfe Bodies into empty Spaces,
grov^ denfer and denfer by degrees, and by that
means refraft the Rays of Light nor in a point,
but by bending them gradually in curve Lines ?
And doth not the gradual condcnfation of this
Medium extend to fome diflance from the Bo-
dies, and thereby caufe the Inflexions of the
Rays of Light, which pafs by the edges of denfe
Bodies, at fome diflance from the Bodies ?

^.

BOOK III. 325

^. 21. Is not this Medium much rarer with-
in the denfe Bodies of the Sun, Stars, Planets
and Comets, than in the empty celeftial Spaces
between them ? And in pafling from them to
great diftances , doth it not grow denfer and
denfer perpetually, and thereby caufe the gra-
vity of thofe great Bodies towards one another,
and of their parts towards the Bodies; every
Body endeavouring to go from the denfer 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 hun-
dredth part of an Inch from Its Body, and ra-
rer there than at the fiftieth part of an Inch ftom
its Body, and rarer there than at the Orb of
Saturn, I fee no reafon why the Increafe of
denfity fhould flop any where, and not rather
be continued through all diftances from the Sun
to Saturn^ and beyond. And though this In-
creafe of denfity may at great diftances be ex-
ceeding flow, yet if the elaftick force of this
Medium be exceeding great, it may fufhce to
impel Bodies from the denfer parts of the Me-
dium towards the rarer , with all that power
which we call Gravity. And that the elaflick
force of this Medium is exceeding great, may
be gather'd from the fwiftnefs of its Vibrations.
Sounds move about 1 140 EnMh Feet in a fe-
cond Minute of Time, and in feven or eight
Minutes of Time they move about one hundred
Englijlo Miles. Light moves from t':e Sun to
us in about feven or eight Minutes f Time,
which diflance is about 70000000 Eng jh Miles,
fuppofing the horizontal Parallax of tiic Sun to

Y 3 be

3^6 O P T I C K S,

be about 12". And the Vibrations or Pulfes of
this Medium, that they may caufe the akernatc
Fits of eafy TraDfiriillion and eafy Reflexion, .
muft be fwlJtcr th; n Light, and by confequencc
above 700000 amL?. fwiirer.than Sounds. And
therefore the eUitick force of this Medium, in
proportion to its denfiiy, muft be above 70000Q
X 700000 (that is, above 490000000000) times
greater than the elaftick force of the Air is in
proportion to its deufity. For the Velocities of
the Puh'es of ehifticiv Mediums are in a fubdupU^
cate Ratio of the Hlailiciries and the Rarities of
the Mediums taken together.

As Attraction is ilronger in fmall Magnets
than in great ones in proportion to their Bulk,
and Gravity is greater in the Surfaces of fmall
Planets than in thofe of great ones in propor-
tion to their bulk, and fmall Bodies are agita-
ted much more by eledric attradion than great
ones J fo the fmallnefs of the Rays of Light
may contribute very much to the power of
the Agent by which they are refraded. And
fo if any one fhould fuppofe that Mther ( like
our Air) may contain Particles which endeavour
to recede from one another ( for J do not know
what this Mther is) and that its Particles are
exceedingly fmaller than thofe of Air, or even
than thofe of Light: The exceeding fmallnefs
of its Particles may contribute to the greatnefs
of the force by which thofe Particles may re-,
cede from one anqther, and thereby make that
Medium exceedingly more rare and elaftick
than Air, and by confequence exceedingly lefs
able to refift the motions of Projediles, and

exceed-

BOOK III. 327

exceedingly more able to prefs upon grofs Bodies,
by endeavouring to expand it lelf.

^/. 22. May not Planets and Comets, and all
grofs Bodies, perform their Motions more freely,
and with lefs refiftance in this ^Ethereal Medium
than in any Fluid, which fills all Space ade-
quately without leaving any Pores, and by confe-
quence is much denfer than Quick'-lilver or Gold?
And may not its refiftance be fo fmall, as to be
inconfiderable ? Forinftance; 1£ this Mther (for
fo I will call it ) fhould be - fuppofed 700000
times more elaftick than our Air, and above
700000 times more rare j its refiftance would
be above 600000000 times lefs than that of Wa-
ter. And fo fmall a refiftance would fcarce
make any fenfible alteration in the Motions of
the Planets in ten thoufand Years. If any one
would ask how a Medium can be fo rare, let
him tell me how the Air, in the upper parts of
the Atmofphere, Qin be above an hundred thou-
fand thoufand times rarer than Gold. Let him
alfo tell me, how an eledtrick Body can by Fri-
ction emit an Exhalation fo rare and fubtile, and
yet fo potent, as by its Emiflion to caufe no
fenftble Diminution of the weight of the de-
rrick Body, and to be expanded through a
Sphere, whofe Diameter is above two Feet, and
yet to be able to agitate and carry up Leaf Cop-
per, or Leaf Gold, at the diftance of above a
Foot from the eledrick Body? And how the
Effluvia of a Magnet can be fo rare and fubtile, as
to pafs through a Plate of Glafs without any Reii-
ftance or Diminution of their Force, and vet fo
potent as to turn a magnetick Needle beyond the
Glafs? y 4 ^,

328 0 P T I C K S.

^/. 23. Is not Vifion perform'd chiefly by the
Vibrations of this Medium, excited in, the bot-
tom of the Eye by the Rays of Light, and pro-
pagated through the folid, pellucid and uniform
Capillamenta of the optick Nerves into the place
of Senfaticn ? And is not Hearing perform'd by
the Vibrations either of this or fome other Medi-
um, excited in the auditory Nerves by the Tre-
mors of the Air, and propagated through the fo-
lid, pellucid and uniform Capillamenta of thofe
Nerves into the place of Senfatiofi ? And fo of
the other Senfes.

^. 24. Is not Animal Motion perform'd by
the Vibrations of this Medium, excited in the
Brain by the power of the Will, and propaga-
ted from thence through the folid, pellucid and
uniform Capillamenta of the Nerves into the
Mufcles, for contrad:ing and dilating them ? I
fuppofe that the Capillamenta of the Nerves are
each of them folid and uniform, that the vibra-
ting Motion of the iEthereal Medium may be
propagated along them from one e;id to the other
uniformly, and w^ithout interruption: For Ob-
ftrudions in the Nerves create Palfies. And that
they may be Sufficiently uniform , I fuppofe
them to be pellucid when view'd fmgly, tho' the
Reflexions in their cylindrical Surfaces may make
the whole Nerve ( compofed of many Capilla-
menta) appear opake and white. For opacity
.arifes from reflecting Surfaces, fuch as may di-
fturb and interrupt the Motions of this Medium.

^/. 25. Are there not other original Proper-
ties of the Rays of Light, befides thofe alrea-
dy defcribed ? An inftance of another original

Fro-

BOOK III. 329

Property we have in the Refradion of Illand
Cryftal , defcribed firft by Erajmm Bartholine^
and afterwards more exadly by Hugeniin^ in his
Book De la Lumiere, This Gryftal is a pel-
kicid fiffile Stone, clear as Water or Cryftal of
the Rock, and without Colour j enduring a red
Heat without lofing its tranfparency, and in a
very ftrong Heat calcining without Fufion.
Steep'd a Day or two in Water, it lofes its na-
tural Polifh. Being rubb'd on Cloth, it attracfls
pieces of Straws and other light things, like Am-
bar or Glafs; and with Aqua Jortis it makes an
Ebullition. It feems to be a fort of Talk, and
is found in form of an oblique Parallelopiped,
with lix parallelogram Sides and eight folid An-
gles. The obtule Angles of the Parallelograms
are each of them 10 1 Degrees, and 52 Minutes;
the acute ones 78 Degrees and 8 Minutes. Two
of the folid Angles oppofite to one another, as
C and E, are compalTed each of
them with three of thefe obtufe ^'* '/£"""
Angles, and each of the other
fix with one obtufe and two acute ones. It
cleaves eaiily in planes parallel to any of its
Sides, and not in any other Planes. It cleaves
with a glofly polite Surface not perfectly plane,
but with fome little unevennefs. It is eafily
fcratch'd, and by reafon of its foftnefs it takes a
Polifh very difficultly. It polifhes better upon
polifh'd Looking-glafs than upon Metal, and
perhaps better upon Pitch, Leather or Parch-
ment. Afterwards it muft be rubb'd with a lit-
tle Oil or white of an Egg, to fill up its Scratches;
whereby it will become very tranfparent and po-
lite.

330

O P T I C K S.

lite. But for feveral Experiments, it is not necef-
fary to polifh it. If a piece of this cryflalline
Stone be laid upon a Book, every Letter of the
Book feen through it will appear double, by
means of a double Refracflion. And if any beam
of Light falls either perpendicularly, or in any
oblique Angle upon any Surface of this Cryftal,
it becomes divided into two beams by means of,
the fame double Refraction. Which beams are of
the fame Colour with the incident beam of Light,
and feem equal to one another in the quantity of
their Light, or very nearly equal. One of thefe
Refra<flions is perform'd by the ufual Rule of Op-
ticks, the Sine of Incidence out of Air into this
Cryftal being to the Sine of Refradion, as five to
three. The other Refra(5tion, which may be cal-
led the unufual Refraction, is perform'd by the
following Rule.

5\

H ^

Let ADBC reprefent the refrading Surface

of
\

BOOK III. 331

of the Cryftal, C the biggeft folid Angle at that
Surface, GEHF the oppofite Surface, and CK
a perpendicular on that Surface. This perpen-
dicular makes with the edge of the Cryftal C F,
an Angle of 19 Degr. 3'. Join KF, and in it
take KL, fo that the Angle KCL be 6 Degr.
40'. and the Angle LCF 12 Degr. 23'. And if
ST reprefent any beam of Light incident at T
in any Angle upon the refracfting Surface AD B C,
let TV be the refradted beam determin'd by the
given Portion of the Sines 5 to 3, according to
the ufual Rule of Opticks. Draw V X parallel
and equal to KL. Draw it the fame way from
V in which L liethfromK; and joining TX,
this line T X fhall be the other refracted beam
carried from T to X, by the unufual Refra-
d;ion,

If therefore the incident beam S T be perpen-
dicular to the refra(5ling Surface, the two beams
TV and TX, into which it fhall become di-
vided, fliall be parallel to the lines CK and CL ;
one of thofe beams going through the Cryftal
perpendicularly, as it ought to do by the ufual
Laws of Opticks, and the other T X by an unu-
fual Refradion diverging from the perpendicular,
and making with it an Angle V T X of about 6 1
Degrees, as is found by Experience. And
hence, the Plane VTX, and fuch like Planes
which are parallel to the Plane C F K, may be
called the Planes of perpendicular Refradion.
And the Coaft towards which the lines KL and
VX are drawn, may be call'd the Coaft of unu-
fual Refraction.

In like manner Cryftal of the Hock has a
5 double

332 O P T I C K S.

double Refra(5tion : But the difference of tl^ two
Refradions is not fo great and manifefl as in
Ifland Cryftal.

When the beam S T incident on Ifland Cry-
ftal is divided into two beams T V and T X,
and thefe two beams arrive at the farther Surface
of the Giafs ; the beam T V, which was refra-
cted at the firfl Surface after the ufual manner,
Ihall be again refracted entirely after the ufual
manner at the fecond Surface ; and the beam T X,
which was refracted after the unufual manner in
the firft Surface, lliall be again refradlied entirely
after the unufual manner in the fecond Surface ;
fo that both thefe beams fliall emerge out of the
lecond Surface in lines parallel to the firft incident
beam S T.

And if two pieces of Ifland Cryftal be pla-
ced one after another, in fuch manner that all
the Surfaces of the latter be parallel to all the
correfponding Surfaces of the former: The
Rays which are refradted after the ufual man-
ner in the flrft Surface of the firft Cryftal, ftiall
be reflated after the ufual manner in all the
following Surliices j and the Rays which are re-
fraded alter the unufual manner in the firft Sur-
face, fhaii be relradted after the unufual manner
in all tlie following Surfaces. And the fame thing
happens, though the Surfaces of the Cryftals be
any ways inclined to one another, provided that
their Planes of perpendicular Refradlion be pa-
rallel to ope another.

And therefore there is an original difterencc

an the Rays of Light, by means of which fome

Rays are m this Experiment conftantly refra(S-

k.' ed

BOOK m. 333

cd after the ufual manner, and others conftant-
ly after the unufual manner : For if the diffe-
rence be not original, but arifes from new Mo-
difications imprefs'd on the Rays at their firft
Refrad:ion, it would be aker'd by new Modi-
fications in the three following Refractions;
whereas it fuffers no alteration, but is conftant,
and has the fame effed upon the Rays in all the
Refractions. The unufual Refraction is there-
fore 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 difcover'd.

^. 26. Have not the Rays of Light feveral
fides, endued with feveral original Properties ?
For if the Planes of perpendicular Refradtion
of the fecond Cryftal be at right Angles with
the Planes of perpendicular RefraCtion of the
firft Cryftal, the Rays which are refradted after
the ufual manner in paffing through the firft
Cryftal, will be all of them refradted after the
unufual manner in pafling through the fecond
Cryftal; and the Rays which are refradted af-
ter the unufual manner in paffing through the
firft Cryftal, will be all of them refradted after
the ufual manner in paffing through the fecond
Cryftal. And therefore there are not two forts
of Rays differing in their nature from one ano-
ther, one of which is conftantly and in all Po-
fitions refradted after the ufual manner, and the
other conftantly and in all Pofitions after the
unufual manner. The difference between the
two forts of Rays in the Experiment mention'd
in the 25th Queftion, was only in the Pofitions

I ©f

334 O P T I C K S.

of the Sides of the Rays to the Planes of pef<»
pendicular Refrad:ion. For one and the fame
Ray is here refraded fometimes after the ufual,
and fometimes after the unufual manner, ac-
cording to the Polition which its Sides have to
the Cryflals. If the Sides of the Ray are poii-
ted the fame way to both Cryflals, it is refra^
fted after the fame manner in them both : But
if that fide of the Ray which looks towards
the Coaft of the unufual Refradion of the iirft
Cryftal, be 90 Degrees from that fide of the
fame Ray which looks toward the Coaft of the
unufual Refradion of the fecond Cryltal, (which
may be effected by varying the Pofition of the
fecond Cryftal to the firft, and by confequence
to the Rays of Light, ) the Ray {hall be refraded
after feveral manners in the feveral Cryflals.
There is nothing more required to determine
whether the Rays of Light which fall upon the
fecond Cryflal fhall be refraded after the ufual
or after the unufual manner, but to turn about
this Cryflal, fo that the Coafl of this Cryflal's
unufual Refradion may be orf this or on that
fide of the Ray. And therefore every Ray may
be confider'd as having four Sides or Quarters,
two of which oppofite to one another incline
the Ray to be refradled after the unufual man-
ner, as often as either of them are turn'd to-
wards the Coafl of unufuil Refradion j and the
other two, whenever either of them are turn'd
towards the Coafl of unufual Refradion, do not
incline it to be otherwife refracted than after
the ufual manner. The two iirfl may there-
fore be call'd the Sides of unufual Refradion-

And

BOOK in. 335

And fince thefe DifpofitioRS were in the Rays
before their Incidence on the fecond, third, and
fourth Surfaces of the two Cryflals, and fuffer-
ed no alteration ( fo far as appears, ) by the Re-
fra(flion of the Rays in their paflilge through
thofe Surfaces, and the Rays v/ere refrad:ed by
the fame Laws in all the four Surfaces ; it ap-
pears that thofe Difpofitions were in the Rays
originally, and fufier'd no alteration by the firil
Refradion, and that by means of thofe Difpofi-
tions the Rays -were refradied at their Incidence
on the firft Surface of the firfh Cryilal, fome of
them after the ufual, and fome of them after the
unufual manner, accordingly as their Sides of
vinufual Refradion were then turn'd towards the
Coaft of the unufual Refradion of that Cryilal,
or lideways from it.

Every Ray of Light has therefore two oppo-
fite Sides, originally endued with a Property on
which the unufual Refradion depends, and the
other two oppofite Sides not endued with that
Property. And it remains to be enquired, whe-
ther there are not more Properties of Light by
which the Sides of the Rays differ, ani are di-
ftinguifh'd from one another.

In explaining the difference of the Sides of
the Rays above mention'd, I have fuppofed that
the Rays fall perpendicularly on the firfl Cry-
ftal. But if they falK obliquely on it, the Suc-
cefs is the fame. Thofe Rays which are refra-
ded after the ufual manner in the firfl Cryflal,
will be refraded after the unufual manner in the
fecond Cryflal, fuppoiing the Planes of perpen-
dicular

336 O P T I C K a

dicular Refradtion to be at right Angles with one
another, as above j and on the contrary.

If the Planes of the perpendicular Refraction
of the two Cryflals be neither parallel nor per-
pendicular to one another, but contain an acute
Angle : The two beams of Light which emerge
out of the firfl Cryftal, will be each of them di-
vided into two more at their Incidence on the fe-
cond Cryftal. For in this cafe the Rays in each
of the two beams will fome of them have their .
Sides of unufual Refradlion, and fome of them
their other Sides turn'd towards the Coaft of the
unufual Refradtion of the fecond Cryftal.

^/. 27. Are not all Hypothefes erroneous
which have hitherto been invented for explain-
ing the Phaenomena of Light, by new Modifica-
tions of the Rays ? For thofe Phaenomena de-
pend not upon new Modifications, a§ has been
fuppofed, but upon the original and unchange-
able Properties of the Rays.

^. 28. Are not all Hypothefes erroneous,
in which Light is fuppofed to confift in Pref-
lion or Motion, propagated through a fluid Me-
dium ? For in all thefe Hypothefes the Phaeno-
mena of Light have been hitherto explain'd by
fuppofing that they arife from new Modifica-
tions of the Rays j which is an erroneous Sup-
pofition.

If Light confifted only in PreiTion propaga-
ted without adhial Motion, it would not be a-
ble to agitate and heat the Bodies which refrad:
and refledl it. If it confifted in Motion propa-
gated to all diftances in an inftant, it would re-
quire an infinite force every moment, in every

fhining

BOOK IIL 337

fhinlng Particle, to generate that Motion. And
if it confiiled in Preflion or Motion, propaga-
ted either in an inftant or in time, it would bend
into the Shadow.' For Preffion or Motion
cannot be propagated in a Fluid in right Lines,
beyond an Obitacle which ftops part of the Mo-
tion, but will bend and fpread every way into
the quiefcent Medium which lies beyond the
Obftacle. Gravity tends downwards, but the
PrelTure of Water arifnig from Gravity tends
every way with equal Force, and is propagated
as readily, and with as much force lideways as
downwards, and through crooked paflages as
through ftaait ones. The Waves on the Surface
of ftagnating Water, paffing by the fides of a
broad Obftacle which Itops part of them, bend
afterwards and dilate themfelves gradually into
the quiet Water behind the Obftacle. The
Waves, Pulfes or Vibrations of the Air, where-
in Sounds confift, bend manifeftly, though not
fo much as the Waves of Water. For a Bell
or a Cannon may be heard beyond a Hill which
intercepts the fight of the founding Body, and
Sounds are propagated as readily through crook-
ed Pipes as through ftreight ones. But Light
is never known to follow crooked Paftages nor
to bend into the Shadow. For the fix'd Stars
by the Interpofition of any of the Planets ceafe
to be fien. And fo do the Parts of the Sun
by the Interpofition of the Moon, Mercury or
Venm. The Rays which pafs very near to the
edges of any Body, are bent a little by the adion
of the Body, as we ftiew'd above j but this
bending is not towards but from the Shaiow,

Z and

338 O P T I C K S.

and is perform'd only in the paffage of the Ray
by the Body, and at a very fmall diftance from
it* So foon as the Ray is pafl the Body, it goes
right on.

To explain the unufual Refra^ion of Ifland
Cryftal by PreiTion or Motion propagated, has
not hitherto been attempted ( to my knowledge)
except by Huygms^ who for that end fuppofed
two feveral vibrating Mediums within that Cry-
ftal. But when he tried the Refradions in two
fucceffive pieces of that Cryftal , and found
them fuch as is mention'd above; he confef-
fed himfelf at a lofs for explaining them. For
PrefTions or Motions, propagated from a Ihining
Body through an uniform Medium, muft be
on all fides alike j whereas by thofe Experi-
ments it appears, that the Rays of Light have
different Properties in their different Sides. He
fufpeded that the Pulfes of /Ether in pafling
through the firft Cryftal might receive certain
new Modifications, which might determine
them to be propagated in this or that Medium
within the fecond Cryftal, according to tht

Pofition of that Cryftal.
M^is tour dirt comment But what Modifications

ceU fe fait, je nay rlen ^l^^fg might be he COuld
trove jufqu id qui me fa- r. ^ i • i r

tisfaje. c. H. de la iumi- Hot lay, nor think of any
ere. c. 5. p. 91. thing fatisfadory in that

Point. And if he had
knov^n that the unufual Refradlion depends not
on new Modifications, but on the original and
unchangeable Difpofitionsof theRays, he would
have found it as difficult to explain how thofe
Pifpofitions which he fuppofed to be imprefs'd

_ on

BOOK IIL 339

on the Rays by the firft Cryftal, could be in
them before their Incidence on that Cryftal,
and in general, how all Rays emitted by £hi-
ning Bodies, can have thpfe Difpofitions in
them from the beginning. To me , at leafl:,
this feems inexplicable ,. if Light be nothing
elfe than Preffion or Motion propagated through
Mther,

And it is as difficult to explain by thefe Hy-
pothefes, how Rays can be alternately in Fits
of eafy Reflexion and eafy Tranfmiffion j unlefs
perhaps one might fuppofe that there are in all
Space two ^Ethereal vibrating Mediums, and
that the Vibrations of one of them conftitute
Light, and the Vibrations of the other are fwift-
er, and as often as they overtake the Vibrations
of the firft, put them into thofe Fits. But how
two Mthers can be diffufed through all Space,
one of which ads upon the other, and by con-
fequence is re-a<5led upon, without retarding,
fliattering, difperling and confounding one an-
others Motions, is inconceivable. And againft
filling the Heavens with fluid Mediums, unlefs
they be exceeding rare, a great Objedion arifes
from the regular and very lafting Motions of
the Planets and Comets in all manner of Courfes
through the Heavens. For thence it is mani-
feft, that the Heavens are void of all fenfible
Refiftance, and by confequence of all fenfible
Matter.

For the refifling Power of fluid Mediums a-
rifes partly from the Attrition of the Parts of
the Medium, and partly from the Vis inertia
of the Matter. That part of the Refiftance of

Z 2 afphe-

340 O P T I C K S.

a fpherical Body which arifes from the Attrition
of the Parts of the Medium is very nearly as the
Diameter, or, at the moft, as the FaSfum of the
Diameter, and the Velocity of the fpherical Bo-
dy together. And that part of the Reliflance
which arifes from the Vis inertia of the Matter,
is as the Square of that FaBiim. And by this
difference the two forts of Refiftance may be di-
flinguifh'd from one another in any Medium;
and thefe being diftinguifh'd, it will be found
that almoft all the Refiftance of Bodies of a com-
petent Magnitude moving-in Air, Water, Quick-
filver, and fuch like Fluids with a competent Ve-
locity, arifes from the Vis inertice of the Parts of
the Fluid.

Now that part of the refifting Power of any
Medium which arifes from the Tenacity, Fri-
ction or Attrition of the Parts of the Medium,
may be dimini(h'd by dividing the Matter into
fmaller Parts, and making the Parts more fmooth
and flippery: But that part of the Refiftance
which arifes from the Vis inerti(X, is proportio-
nal to the Denfity of the Mattel, and cannot be
diminifh'd by dividing the Matter into fmaller
Parts, nor by any other means than by decrea-
iing the Denlity of the Medium. And for thefe
Reafons the Denlity of fluid Mediums is very
nearly proportional to their Refiftance. Li-
quors which differ not much in Denfity, as Wa-
ter, Spirit of Wine, Spirit of Turpentine, hot
Oil, differ not much in Refiftance. Water is
thirteen or fourteen times lighter than Quick-
. iilver, and by confequence thirteen or fourteen
times rarer, and its Refiftance is lefs than that

of

BOOK III. 341

of Quick-filver in the fame Proportion, or there-
abouts, 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 confequence eight or nine
hundred times rarer, and accordingly its Refi-
ftance is lefs than that of Water -in the fame
Proportion, or thereabouts j as I have alfo found
by Experiments made with Pendulums. And in
thinner Air the Reiiftance is ftill lefs, and at
length, by ratifying the Air, becomes infenfi-
ble. For fmall Feathers falling in the open Air
meet with great Refiftance, but in a tall Glafs
well emptied of Air, they fall as fail as Lead or
Gold, as I have feen tried feveral times. Whence
the Refiftance feems ftill to decreafe in propor-
tion to the Denlity of the Fluid. For I do not
find by any Experiments, that Bodies moving
in Quick-filver, Water or Air, meet with any
oaher fenfible Refiftance than what arifes from
the Denfity and Tenacity of thofe fenfible Flu-
ids, as they would do if the Pores of thofe Flu-
ids, and all other Spaces, were filled with a
denfe and fubtile Fluid. Now if the Refiftance
in a Veffel well emptied of Air, was but an
hundred times lefs than in the open Air, it
would be about a million of times lefs than in
Quick- filver. But it feems to be much lefs in
fuch a Veffel, and. ftill much lefs in the Hea-
vens, at the height of three or four hundred
Miles from the Earth, or above. For Mr. Boyle
has fliew'd that Air may be rarified above ten
thoufand times in VefTels of Glafs j and the
Heavens are much emptier of Air than any Va-^

23. cuiim

342 O P T I C K S.

cuum we can make below. For fmce the Air
is comprefs'd by the Weight of the incumbent
Atmoiphere., and the Denfity of Air is propor-
tional to the Force compreffing it, it follows by
Computation, that at the lieight of about fe-
ven and a half Engliflj Miles from the Earth, the
Air is four times rra-er than at the Surface of the
Earth J and at the height of 15 Miles it is fix-
teen times rarer than that at the Surface of the
Earth J and at the height of 22^, 30, or 38 Miles,
it is refpedively 64, 256, or 1024 times rarer,
or thereabouts J and at the height of 76, 152,
228 Miles, it is about loooooo, 1 000000000000,
or loooGOOoooooooooooo times rarer j and fo
on.

Heat promotes Fluidity very much, by dimi-
nifliing the Tenacity of Bodies. It makes ma-
ny Bodies fluid which are not fluid in cold, and
increafes the Fluidity of tenacious Liquids, as
of Oil, Balfam, and Honey, and thereby de-
creafes their Refiftance. But it decreafes not
the Refiftance of Water confiderably, as it would
do if any confiderable part of the Refiftance of
Water arofe from the Attrition or Tenacity of
its Parts. And therefore the Refiftance of Wa-
ter arifes principally and almoft entirely from
the Vis inertice of its Matter j and by confe-
quence, if the Heavens were as denfe as War»
ter, they would not have much lefs Refiftance
than Water J if as denfe as Quick-filver, they
would not have much lefs Refiftance than Quicks
filver; if abfolutely denfe, or full of Matter
without any Vacimm^ let the Matter be never
fo fubtil and fluid, they would have a greater

Refiftance

BOOK m. 343

Refiftance than Qulck-filver. A folid Globe in
fuch a Medium would lofe above half its Mo-
tion in moving three times the length of its
Diameter, and a Globe not folid ( fuch as are
the Planets, ) would be retarded fooner. And
therefore to make way for the regular and lad-
ing Motions of the Planets and Comets,- it's ne-
ceffary to empty the Pleavens of all Matter, ex%
cept perhaps fome very thin Vapours, Steams,
or Effluvia, arifmg from the Atmofpheres of the
Earth, Planets, and Comets, and from fuch an
exceedingly rare ;^thereal Medium as we de-
fcribed above. A denfe Fluid can be of no ufe
foi- explaining the Phaenomena of Nature, the
Motions of the Planets and Comets being better
explain'd without it. It ferves only to difturb
and' retard the Motions of thofe great Bodies,
and make the Frame of Nature languifh : And
in the Pores of Bodies, it ferves only to ftop
the vibrating Motions of their Parts, wherein
their Heat and A<fl:ivity conlifts. And as it is
of no ufe, and hinders the Operations of Na-
ture, and makes her languifn, fo there is no e-
vidence for its Exiftence, and therefore it oueht
to be rejected. And if it be rejeded, the Hy-
pothefes that Light confiils in Preffion or Mo-
tion, propagated through fuch a Medium, are
rejeded with it.

And for rejeding fuch a Medium, we have
the Authority of thofe the oldeft and moll ce-
lebrated Philofophers -of Greece and Phcenkiay
who made a Vacuum^ and Atoms, and the Gra-
vity of Atoms, the firft Principles of their Phi-
lofophyj tacitly attributing Gravity to fo.Ec- o-

Z 4 thci

344- O P T I C K S.

ther Caufe than denfe Matter. Later Philofo-
phers baniili the Confi deration of fuch a Caufe
out of natural Philofophy, feigning Hypothefes
for explaining all things mechanically, and re-
ferring other Caufes to Metaphylicks : Whereas
the main Bufniefs of natural Philofophy is to
argue from Phcenomena without feigning Hy-
pothefes, and to deduce Caufes from Effects,
till we come to the very firft Caufe, which cer-
tainly is not mechanical ; and not only to un-
fold the Mechanifm of the World, but chiefly
to refolve thefe and fuch like Queftions. What
is there in places almofl empty of Matter, and
whence is it that the Sun and Planets gravitate
towards one another, without denfe Matter be-
tween them ? Whence is it that Nature doth
nothing in vain ; and whence arifes all that Or-
der and Beauty which we fee in the World ?
To what end are Comets, and whence is it that
Planets move all one and the fame 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 contri-
ved with fo much Art, and for what ends were
their feveral Parts ? Was the Eye contrived
without Skill in Opticks, and the Ear without
Knowledge of Sounds ? Plow do the Motions
of the Body follow from the Will, and whence
is the Inftindt in Animals ? Is not the Senfory of
Animals that place to which the fenfitive Sub-
itance is prefent, and into which the fenfible
Species of Things ap carried through jthe Nerves
and Brain, that there they may be perceived

BOOK III. 345

by their immediate prefence to that Scbftancc ?
And thefe things being rightly difpatch'd, does
it not appear from Plia^nomena that there is a
Being incorporeal, living, intelligent, omnipre-
fent, who in infinite Space, as it were in his Sen-
fory, fees the things themfelves intimately, and
throughly perceives them, and comprehends
them wholly by their immediate prefence to
himfelf : Of which things the Images only car-
ried through the Organs of Senfe into pur little
Senforiums, are there feen and beheld by that
which in us perceives and thinks. And though
every true Step made in this Philofophy brings us
not immediately to the Knowledge of the firll
Caufe, yet it brings us nearer to it, and on that
account is to be highly valued.

^. 29. Are not the Rays of Light very
fmall Bodies emitted from lliining Subllances ?
For fuch Bodies will pafs through uniform Me-
diums in right Lines without bending into the
Shadow, which is the Nature of the Rays of
Light. They will alfo be capable of feveral
Properties, and be able to conferve their Pro-
perties unchanged in paffing through feveral
Mediums, which is another Condition of thq
Rays of Light. Pellucid Subllauces a6t upon
the Rays of Light at a diftance in refracting-, re-
flecting, and inflecting them, and the Rays m.u-
tually agitate the Parts of thofe Subfl:ances at ^a
difl:arce for heating them i and this ACtion and
Re-aUion at a difl:ance very much refembles an
attractive Force between Bodies. If RefraCtion
be perform'd by Attraction of the Rays, the
Sines of Incidencs muft be to the Sines of Re-
fraCtion

346 O P T I C K S.

fraftion in a given Proportion, as we {hew'd in
our Principles of Philofophy : And this Rule is
true by Experience. The Rays of Light in
going out of Giafs into a Vacuum^ are bent to-
wards the Glafs ; and if they fall too obliquely
on the Vacuum^ they are bent backwards into
the Glafs, and totally reflected j and ^ this Refle-
xion cannot be afcribed to the Refiftance of an
abfolute Vacuum^ but muft be caufed by the
Power of the Glafs attracting the Rays at their
going out of it into the Vacuum^ and bringing
them back. For if the farther Surface of the
Glafs be moiflen'd with Water or clear Oil, or
liquid and clear Honey, the Rays which would
otherwife be refleded will go into the Water,
Oil, or Honey ; and therefore are not refle(5ted
before they arrive at the farther Surface of the
Glafs, and begin to go out of it. If they go out
of it into the Water, Oil, or Honey, they
go on, becaufe the Attraction of the Glafs is
almoft 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 Glals, the At-
traction of the Glafs either bends and refraCts
them, or brings them back and reflects them.-
And this is ftill more evident by laying together
two Prifms of Glafs, or two ObjeCt-glaSes of
very long Telefcopes, the one plane, the o-
ther a little convex, and fo compreffing them
that they do not fully touch, nor are too far a-
funder. For the Light which falls upon the
farther Surface of the firfl Glafs where the In-
terval between the Glaffes is not above the ten

hundred

BOOK III. 347

hundred thoufandrh Part of an Inch, will go
through that Surface, and through tbe Air or
Vacuum between the GlaiTes, and enter into the
fecondGlafs, as was explain'd in the firft, fourth,
and eighth Obfervations of the firft Part of the
fecond Book. But, if the fecond Glafs be taken
away, the Light which goes out of the fecond
Surface of the. firft Glafs into the Air or Va-
cuum^ will not go on forwards, but turns back
into the firft Glafs, and is reflecftcd ; and there-
fore it is drawn back by the Power of the firft
Glafs, there being nothing elfe to turn it back.
Nothing more is requifite for producing all the
variety of Colours, and degrees of Refrangibi-
lity, than that the Rays of Light be Bodies of
different Sizes, the leaft of which may take
violet the weakeft and darkeft of the Colours,
and be more cafily diverted by refrad:ing Sur-
faces from the right Courfe ; and the reft as
they are bigger and bigger, may make tlie
ftronger and more lucid Colours, blue, green,
yellow, and red, and be more and more diHi-
cultly diverted. Nothing more is requifite for
putting the Rays of Light into Fits of eafy Re-
flexion and eafy Tranfmiffion, than that they be
fmall Bocjies which by their attractive Powers,
or fome other Force, ftir up Vibrations in what
they ad; upon, which Vibrations being fwifter
than the Rays, overtake them fucceftively, and
agitate them fo as by turns to increafe and de-
creafe their Velocities, and thereby put them
into thofe Fits. And laftly, the unufual Refra-
(ftion of Ifland-Cryftal looks very much as if it
were perform'd by fome kind of attractive vir-
tue

348 O P T I C K S.

tue lodged in certain Sides both of the Rays,
and of the Particles of the Cryftal. For were
it not for* fome kind of Difpofition or Virtue
lodged in fome Sides of the Particles of the
Cryflal, and not in their other Sides, and which
inclines and bends the Rays towards the Coafl
of unufual Refraction, the Rays which fall per-
pendicularly on the Cryllal, would not be re-
fraded towards that Coafl rather than towards
any other Coaft, both at their Incidence and at
their Emergence, fo as to emerge perpendicu-
larly by a contrary Situation of the Coaft of
unufual Refradion at the fecond Surface ; the
Cryftal acting upon the Rays after they have
■pafs'd through it, and are emerging into the
Air; or, if you pieafe, into a V aciium' And
lince the Cryftal by this Difpofition or Virtue
does not ad: upon the Rays, unlefs when one
of their Sides of unufual Refradion looks to-
wards that Coaft, this argues a Virtue or Difpo-
fition in thofe Sides of the Rays, which an-
fwers to, and fympathizes with that Virtue or
Difpofition of the Cryftal, as the Poles of two
Magnets anfwer to one another. And as Mag-
netifm may be intended and remitted, and is
found only in the Magnet 2nd in Iron : So this
Virtue of refrading the perpendicular Rays is
greater in Ifland-Cryftal, lefs- in Cryftal of the
Rock, and is not yet found in other Bodies. I
do not fay that this Virtue is magnetical : It
feems to be of another kind. I only fay, that
wnatever it be, it's difficult to conceive how
the Rays of Light, unlefs they be Bodies, can
have a permanent Virtue in two of their Sides
I which

BOOK III. 349

which is not in their other Sides, and this without
any regard to their PoUtion to the Space or Me-
dium through which they pafs.

What I mean in this Queftion by a Vacuum^
and by the Attradions of the Rays of Light to-
wards Giafs or Cryftal, may be undcrftood ' by
what was faid in the i8th, 19th, and 20th Que-
ftions.

^eji. 30. Are not grofs Bodies and Light con-
vertible into one another, and may not Bodies re-
ceive much of their A(^l:ivity from the Particles
of Light which enter their Compofition? For all
fix'd Bodies being heated emit Light fo long as
they continue fufficiently hot, and Light mutually
flops in Bodies as often as its Rays ftrike upon
their Parts, as we fliew'd above. I know no
Body lefs apt to fliine than Water; and yet Wa-
ter by frequent Diftillations changes into fix'd
Earth, as Mr.Boy/e^ has try'd ; and then this Earth
being enabled to endure a fufficient Heat, {hines
by Heat like other Bodies.

The changing of Bodies into Light, and Light
into Bodies, is very conformable to the Courfe
of Nature, which feems delighted with Tranf-
mutations. Water, which is a very fluid taflelefs
Salt, fhe changes by Heat into Vapour, which is
a fort of Air, and by Cold into Ice, which is a
hard, pellucid, brittle, fufible Stone ; and this
Stone returns into Water by Heat, and Vapour
returns into Water by Cold. Earth by Heat be-
comes Fire, and by Cold returns into Earth.
Denfe Bodies by Fermentation rarify into feve-
ral forts of Air, and this Air by Fermentation,
and fometimes without it, returns into denfe

Bodies.

350 O P T I C K S.

Bodies. Mercury appears fometimes in the form
of a fluid Metal, fometimes in the form of a hard
brittle Metal, fometimes in the form of a corro-
live pellucid Salt call'd Sublimate, fometimes in
the form of a taftelefs, pellucid, volatile white
Earth, call'd Mercip^ius Dulcis j or in that of a
red opake volatile Earth, call'd Cinnaber j or in
that of a red or vv^hite Precipitate, or in that of
a fluid Salt ; and in Diftillation it turns into
Vapour, and being .agitated i?i VaciiOj it fhines
like Fire. And after all thefe Changes it re-
turns again into its firfl: form of Mercury.
Eggs grow from infenfible Magnitudes, and
change into Animals j Tadpoles into Frogs ;
and Worms into Flies. All Birds, Beaflis and
Fifhes, Infers, Trees, and other Vegetables,
with their feveral Parts, grow out of Water
and watry Tinctures and Salts, and by Putre-
fadtion return again into watry Subftances. And
Water ftanding a few Days in the open Air,
yields aTindurc, which (like that of Malt) by
ftanding longer yields a Sediment and a Spi-
rit, but before Putrefaction is fit Nourifhment
for Animals and Vegetables. And among fuch
various- and fl:range Tranfmutations, why may
not Nature change Bodies into Light, and Light
into Bodies ?

^leji. 3 1. Have not the fmall Particles of Bo-
dies certain Powers, Virtues, or Forces, by which
they adt at a diftance, not only upon the Rays
of Light for reflecting, refra(fling, and inflect-
ing them, but alio upon one another for pro-
ducing a great Part of the Phaenomena of Na-
ture ? For it's well known, that Bodies ad:

one

BOOK TIL 351

one upon anotlier by the Attradions of Gravity,
Magnetifm, and Eledtricity j and thefe Inftances
ihew the Tenor and Courfe of Nature, and make
it not improbable but that there may be more at-
tradlive Powers than thefe. For Nature is very
confonant and conformable to her felf How
thefe Attradtions may be perform'd, I do not here
confider. What I call Attraction may be per-
form'd by impulfe, or by fome other means un-
known to me. I ufe that Word here to fignify
only in general any Force by which Bodies tend
towards one another, whatfoever be the Caufe.
For we muft learn from the Phcenomena of
Nature what Bodies attradt one another, and
what are the Laws and Properties of the At-
traction, before we enquire the Caufe by which
the Attraction is perform'd. . The Attractions of
Gravity, Magnetifm, and EleCtricity, reach to
very fenfible diflances, and fo have been obferved
by vulgar Eyes, and there may be others which
reach to fo fmall diflances as hitherto efcape Ob-
fervation j and perhaps eleCtrical Attraction may
reach to fuch fmall diftances, even without being
excited by FriCtion.

For when Salt of Tartar runs per IDeliquium,
is not this done by an Attraction between the
Particles of the Salt of Tartar, and the Parti-
cles 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 Deliqimirn^
but for want of fuch an Attraction ? Or why
docs not -Salt of Tartar drav^^ more Water out
of the Air than in a certain Proportion to its
quantity, but for want of an attractive Force
2 after

^52 O P T I C K S.

after it is fatiated with Water ? And whence
is it but from this attractive Power that Water
which alone diftils with a gentle luke-warm
Heat, will not diftil from Salt of Tartar with-
out 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 fatiated draws no
more, and in Diftillation lets go the Water very
difficultly ? And when Water and Oil of Vi-
triol poured fucceffively into the fame Veffel
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 coa-
lefce with Violence, and by confequence rufli to-
wards one another with an accelerated Mo-
tion ? And when Aqua fortis, or Spirit of Vi-
triol poured upon Filings of Iron, dilTolves 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 rufh to-
wards the Parts of the Metal with violence,
and run forcibly into its Pores till they get be-
tween its outmoft Particles, and the main Mafs
of the Metal, and furrounding thofe Particles
loofen them from the main Mafs, and fet them
at liberty to float off into the Water ? And
when the acid Particles, which alone would
diftil with an eafy Heat, will not feparate from
the Particles of the Metal without a very vio-
lent

BOOK III. 353

lent Heat, does not this confirm the Attradtioa
between them ?

When Spirit of Vitriol poured upon com-
mon Salt or Salt-petre makes, an Ebulhtion with
the Salt, and unites wich it, and in Diftillatian '
the Spirit of the common Salt 'or Salt-petre
comes over much eafier than it would do be-
fore, and the acid part of the Spirit of Vitriol
ilays behind j does not this argue that the fi:<'d
Alcaly of the Salt attrads the acid Spirit ot the
Vitriol more ftrongly than its own Spirit, and
not being able to hold them both, lets go its
own? And when Oil of Vitriol is draw^n off
from its weight of Nitre j and from both the
Ingredients a compound Spirit of Nitre is diflil-
led, 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 Sub-
ftanCes, or Oil of Turpentine thicken'd with a
little Balfam of Sulphur, and the Liquors grow fo
very hot in mixing, as prefently to fend up a burn-
ing Flame ; does not this very great and fudden
Heat argue that the two Liquors mix with vio-
lence, and that their Parts in mixing run to-
wards one another with an accelerated Motion,
and cla(h with the greateft Force ? And is it
not for the fame reafon that well redlified Spi-
rit of Wine poured on the fame compound Spi-
rit fla{hes*f and that the Piilvis fuUninam, com-
pofed of Sulphur, Nitre, and Salt of Tartar,
goes off with a more fudden and violent Ex-
plofion than Gun-powder, the acid Spirits of
the Sulphur and Nitre ruihing towards one an-
other, and towards the Salt of Tartar, with fo

A a great

354- O P T I C K S.

great a violence, as by the (hock to turn the
whole at once into Vapour and Flame ? Where
the DilTolution is flow, it makes a flow Ebulli-
tion and a gentle Heat j and where it is quick-
er:, it makes a greater Ebullition with more
heat ; and where it is done at once, the Ebul-
lition is contraded into a fudden Blaft or vio-
lent Explofion, with a heat equal to that of
Fire and Flame. So when a Drachm of the a-
bove-mention'd compound Spirit of Nitre was
poured upon half a Drachm of Oil of Carraway
Seeds i?i vaciio^ the Mixture immediately made
a flafh like Gun-powder, and burll the ex-
haufted Receiver, which was a Glafs fix Inches
wide, and eight Inches deep. And even the
grofs Body of Sulphur powder'd, and with an
equal weight of Iron Filings and a little Water
made into Pafte, ads upon the Iron,* and in five
or fix hours grows too hot to be touch'd, and
emits a Flame, And by thefe Experiments com-
pared 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, mi-
neral Corufcations, Earthquakes, hot fuffoca-
ting Exhalations, Flurricanes, and Spouts; we
may learn, that fulphureous Steams abound in
the Bowels of the Earth and ferment with Mi-
nerals, and fomietim^es take fire with a fudden
Corufcatlon and Explofion; and if pent up in
fubterraneous Caverns, burfl the Caverns with a
great {baking of the Earth, as in fpringing of a
Mine. And then the Vapour generated by the
Explofion, expiring through the Fores of the

3 Earth,

BOOK III. 355

Earth, feels hot and fuffocateSj and iiiakes Tem-«
pefls and Hurricanes, and fometimes caufes the"
Land to Hide, or the Sea to boil, and carries
up the Water thereof in Drop3, which by their
weight fall down again in Spouts, ^xlfo fome
fulphureous Steams, at all times when the Earth
is dry, afcending into the Air, ferment there
with nitrous Acids^ and fometimes taking fire
caufe Lightning and Thunder, and fiery Me-
teors. For the Air abounds with acid Vapours
fit to promote Fermentations, as appears by the-
rufling of Iron and Copper in it, the kindling
of Fire by blowing, and the beating of the
Heart by means of Refpiration. Now the a-
bove-mention'd Motions are fo great and violent
as to fhew t]iat in Fermentations the Particles of
Bodies which almofi: reft, are put into new Mo-
tions by a very potent Principle, w^hich ad:s up-
on them only when they approach one another,
and caufes them to meet and clafh with 2;reat vi*
olence, and grow hot with the motion, and dafli
one another into pieces, and vapifli into Air, and
Vapour, and Flame.

When Salt of Tartar per deliqiiium^ being
poured into the Solution of any Metal, preci-
pitates the Metal, and makes it fail down to the
bottom of the Liquor in the form of Mud:
Does not this argue tliat the acid Particles are
attracted more ftrong-ly by the Salt of Tartar
than by the Metal, and by the ftronger Attra-
d:ion go from the Metal to the Salt of Tartar ?
And fo when a Solution of Iron in Anna forth
diffolves the Lapis Calciminarh^ and lets go the
Iron, or a Solution of Copper difiblves Iron im-

A a 2 merfed

356 O P T I C K S.

irierfed in it and lets go the Copper, or a So-
'4ution of Silver difTolves Copper and lets go the
Silver, or a Solution of Mercury in Aquafortis
being poured upon Iron, Copper, Tin, or Lead,
difTolves the Metal and lets go the Mercury ;
does not this argue that the acid Particles of
the Aqua fortis are attracted more ftrongly by
the Lapis Calamniaris than by Iron, and more
flrongly by Iron than by Copper, and more
ftrongly by Copper than by Silver j and more
ftrongly by Iron, Copper, Tin, and Lead, than
by Mercury ? And is it not for the fame reafon
that Iron requires more Aqua fortis to dilTolve
it than Copper, and Copper more than the other
Metals ; and that of all Metals, Iron is dilTolved
moft eafily, and is mofi: apt to ruft ; and next af-
ter Iron, Copper?

When Oil of Vitriol is mix'd w^ith a little
Water, or is run per deliquiuni^ and in Diftil-
lation the Water afcends difficultly, and brings
over v^rith it fome part of the Oil of Vitriol in
the form of Spirit of Vitriol, and this Spirit be-
ing poured upon Iron, Copper,' or Salt of Tar-
tar, unites with the Body and lets go the Wa-
ter 'j doth not this fliew that the acid Spirit is at- ■
traded by the Water, and more attracted by
the fix'd Body than by the Water, and there-
fore lets go the Water to clofe v^ith the fix'd
Body ? And is it not for the fame reafon that
the Water and acid Spirits which are mix'd to-
gether in Vinegar, Aqua fortis^ and Spirit of
Salt, cohere and rife together in Diftillation ;
but if the Mejiftruum be poured on Salt of Tar-
tar, or on Lead, or Iron, or any fix'd Body

which

BOOK III. 357

which it can diflblve, the Acid by a fironger At-
traction adheres to the Body, and lets go ths
Water ? And is it not alfo from a mutual At-
tracftion that the Spirits o£ Soot and Sea-Sak
unite and compofe the Panicles of Sal-armo-
niac, which are lefs volatile than before, be-
caufe grofler and frc€r from Water ; and that
the Particles of Sal-armoniac in Sublimation car-
ry up the Particles of Antimony, which will not
fublime alone ; and that the Particles of Mer-
cury uniting with the acid Particles of Spirit
of Salt compofe Mercury fublimate, and with
the Particles of Sulphur, compofe Cinnaber;
and that the Particles of Spirit of Wine and
Spirit of Urine well redlitied unite, and letting
go the Water which dillblved them, compofe a
confident Body; and that in fubliming Cinna-
ber from Salt of Tartar, or from quick Lime,
the Sulphur by a ftronger Attraftion of the Salt
or Lime lets go the Mercury, and flays with
the fix'd Body ; and that when Mercury fubli-
mate is fublimed from Antimony, or from Re-
gulus of Antimony, the Spirit of Salt lets go the
Mercury, and unites with the antimonial Me-
tal which attracts it more ftrongly, and ftays
with it till the Heat be great enough to make
them both afcend together, 'and then carries
up the Metal with it in the form of a very fu^
fible Salt, called Butter of Antimony, although
the Spirit of Salt alone be almoft as volatile as
Water, and the Antimony alone as fix'd as
Lead ?

When yi^ua fortis diffolves Silver and not
Gold, and Aqua regia diffolves Gold and not

A a 3 Silver,

35^

O P T I C K S.

Silver, may it not be faid that Aqua forth is
fubtil enough to penetrate Gold as well as Sil-
ver, but wants the attracflive Force to give it
Entrance j and that Aqua regia is fubtil enough
to penetrate Silver as v/ell as Gold, but wants
the attractive Force to give it Entrance ? For
Aqua rcgia is nothing elfe than Aqua fortis
mix'd v/ith fome Spirit of Salt, or with Sal-ar-
moniac J and even common Salt diiTolved in A-^
qua fcrtis^ en.ibies the Metijiruwrn to dilfolve
Gold, though the Salt be a grofs Body. When
therefore Spirit of Snlt precipitates Silver out
of Aqua fortis^ is it not done by attrading and
jnixing with the Aqua Jortisy and not attrad:-
jng, or perhaps repelling Silver? And when
Water precipitates Antimony out of the Subli-
mate of Antimony and Sal-armoniac, or out of
putter of Antimony, is it not done by its dif^
folving, mixing with, and weakening the Sal^
grmoniac or Spirit of Salt, and its not attract-
ing, or perhaps repelling the Antimony ? And
is it not for want of an attradive virtue be-
tween the Parts of Water and Oil, of Quick-^
lilver and Antimony, of Lead and Iron, that
thefe Subllances do not mixj .and by a weak
Attradion, that Quick-filver and Copper mix
difiicultly j and fi'om a flrong one, that Quick-
filver. and Tin, Antimony and Iron, Water and
Salts, mix readily? And in general, is it not
from the fame Principle that Heat congregates;
homogeneal Bodies, and feparates heterogeneal
ones?

When Arfenick with Soap gives a Regulus^

and with Mercury fublimate a volatile fufible

^ ■ Salt,

BOOK III. 359

Salt, like Butter of. Antimony, doth not this
lliew that Arfenick, which is a Subftance totally
volatile, is compounded of fix'd and volatile
Parts, ftrongly cohering by a mutual Attradion,
fo that the volatile will not afcend without car-
rying up the fixed ? And fo, when an equal
weight of Spirit of Wine and Oil of Vitriol
are digefted together, and in Diftillation yield
two fragrant and volatile Spirits which will not
mix with one another, and a fix'd black Earth
remains behind ; doth not this fliew that Oil of
Vitriol is compofed of volatile and fix'd Parts
ftrongly united by Attradion, fo as to afcend to-
gether in form of a volatile, acid, fluid Salt,
until the Spirit of Wine attrads and feparates
the volatile Parts from the fixed ? And there-
fore, fince Oil of Sulphur per Campcmam is of
the fame Nature with Oil of Vitriol, may it not
be inferred, that Sulphur is alfo a mixture of
volatile and fix'd Parts fo ftrongly cohering by
Attradion, as to afcend together in Sublima-
tion. By diflblving Flowers of Sulphur in Oil
of Turpentine, and diftilling the Solution, it is
found that Sulphur is compofed of an inflama-
ble thick Oil or fat Bitumen, an acid Salt, a
very fix'd Earth, and a little Metal. The three
firfl were found not much unequal to one
another, the fourth in fo fmall a quantity as
fcarce to be worth confidering. The acid Salt
difix)lved in Water, is the fame with Oil of Sul-
phur per Campanam, arid abounding .much in
the Bowels of the Earth, and particularly in
Markafites, unites it felf to the other Ingredi-
ents of the Markafite, which are. Bitumen, I-

A a 4 ron,

360 O P T I C K S.

ron. Copper, and Earth, acid with them corn-
pounds Alkim, Vitriol, and Sulphur. With the
Earth alone it compounds AUum ; with the Me-
tal alone, or Metal and Earth together, it com-
pounds Vitriol; and with the Bitumen and Earth
it compounds Sulphur. Whence it comes to
pafs that Markances abound v/ith thofe three Mi-
nerals. And is it not from the mutual Attradtior^
of the Ingredients that they ftick together for
ccmpoundins; thefe Minerals, and that the Bitu-
men carries up the other Ingredients of the Sul-
phur, which without it would not fublime ? And
the fame Queftion may be* put concerning all,
or almofc all the grofs Bodies in Nature. For
all the Parts of Animals and Vegetables are com-
pofed of Subftances volatile and fix'd, fluid and
folid, as appears by their Analyfis ; and fo
are Salts and Minerals, fo far as Chymifls have
been hitherto abl? to examine their Compofi-
tion.

When Mercury fublimate is re-fublimed with
frefh Mercury, and becomes Mercurius Dulcis^
which is a white taftelefs Earth fcarce dilTolva-
ble in Water, and Mercurius Dulcis re-fublimed
with Spirit of Salt returns into Mercury fubli-
mate ; and when Metals corrpded with a little
acid turn into ruft, which is an Earth taftelefs
and indiffolvable in Water, and this Earth im-
bibed with more acid becomes • a metallick
Salt ; and when fome Stones, as Spar of Lead,
diifolv^d in proper M^nfiruums become Salts ;
do not thef.:; tilings fhew that Salts are dry Earth
and watry Acid united by Attradion, and that
the Earth \\all not become a Salt without fq

muql^

BOOK III. 361

much acid as makes it diffolvable in Water ? Do
not the {harp and pungent Taftes of Acids
arife from the ftrong Attradtion whereby the
acid Particles rufli upon and agitate the Par-
ticles of the Tongue ? And when Metals are dif-
folved in acid MenJi?'immSy and the Acids in
conjunction with the Metal ad after a different
manner, fo that the Compound has a different
Tafte much milder than before, and fometimes
a fweet one j is it not becaufe the Acids ad-,
here to the metallick Particles, and thereby
lofe much of their Aftivity ? And if the Acid
be in too fmall a Proportion to make the Com-
pound diffolvable in Water, will it not by ad-
hering flrongly to the Metal become unadive and
lofe its Tafle, and the Compound be a taflelefs
Earth ? For fuch things as are not diffolvable by
the Moiflure of the Tongue, ad not upon the
Tafle.

As Gravity makes the Sea flow round the
deafer and weightier Parts of the Globe of the
Earth, fo the Attraction may make the watry
Acid flow round the denfer and compader Par-
ticles of Earth for compofing the Particles of
Salt. For otherwife the Acid would not do
the Ofhce of a Medium between the Earth and
common Water, for making Salts diffolvable in
the Water j nor would Salt of Tartar readily
draw off the Acid from diffolved Metals, nor
Metals the Acid from Mercury. Now, as in the
great Globe of the Earth and Sea, the denfefl
Bodies by their Gravity fink down in Water,
^nd always endeavour to go towards the Cen-
ter of the 'Globe; fo in Particles of Salt, the

denfefl

362 O P T I C K S.

denfcft Matter may always endeavour to approach
the Center of the Particle : So that a Particle of
Salt may be compared to a Chaos ; being denfe,
hard, diy, and earthy in the Center j and rare,
foft, moift, and watry -in the Circumference.
And hence it feems to be that Salts are of a
lafting Nature, bejng fcarce dellroy'd, unlefs by
drawing away their watry Parts by violence,
or by letting them foak into the Pores of the
central Earth by a gentle Heat in Putrefa-
ction, until the Earth be diflblved by the Wa-
ter, and feparated into fmaller Particles, which
by reafon of their Smallnefs make the rotten
Compound appear of a black Colour. Hence
ilfo It may be, that the Parts of Animals and
"Vegetables preferve their feveral Forms, and
affimilate their Nouriihment j the foft and moift
Nourifhment eafily changing its Texture by a
gentle Heat and Motion, till it becomes like the
denfe, hard, dry, and durable Earth in the Cen-
ter of each Particle. But when the Nourilh-
ment grows unfit to be allimilated, or the cen-
tral Earth grows too feeble to affimilate it, the
Motion ends in Confufion, Putrefacftion, and
Death.

If a very fmall quantity of any Salt or Vitriol
be dilfolved in a great quantity of Water, the.
particles of the Salt or Vitriol will not fmk to
the bottom, though they be heavier in Specie
than the Water, but will eveidy diffufe them-
felves into all the Water, fo as to make it as fa-
line 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 ex-
pand

BOOK III. 363

pand themfelves, and get as far afunder as the
quantity of Water in which they float, will al-
low ? And does not this Endeavour imply that
they have a repulfive Force by which they fly
from one another, or at leaft, that they attrad:
the Water more llrongly than they do one ano-
ther ? For as all things afcend in Water which
are lefs attraded than Water, by the gravitating
Power of the Earth j fo all the Particles of Salt
which float in Water, and are lefs attraded than
Water by any one Particle of Salt, muil recede
from that Particle, and give way to the more at-
traded V/ater.

When any faline Liquor is evaporated to aCu-
ticle and let cool, the Salt concretes in regular
Figures j which argues, that the Particles of the
Salt before they concreted, floated in the Liquor
^t equal difl:ances in rank and file, and by confe-
quence that they aded upon one another by fome
Power which at equal diilances is equal, at une-
qual diftances unequal. For by fuch a Power
they will range themfelves uniformly, and with-
out it they will float irregularly, and come to-
gether as irregularly. And fmce the Particles
of Ifland-Cryftal ad all the fame way upon
the Rays of Light for caufing the unufual Re-
fradion, may it not be fuppofed that in the For-
mation of this Cryfl:al, the Particles not only
ranged themfelves in rank and file for concreting
in regular Figures, but alfo by fome kind of po-
lar Virtue turned their homogeneal Sides the
fame way.

The Parts of all homogeneal hard Bodies
which fully touch one another, flick together

N'ery

364 OPTIC K S.

very ftrongly. And for explaining how this
may be, fome have invented hooked Atoms,
which is begging the Queftion^ and others tell
us that Bodies are glued together by reft, that
is, by an occult Quf.lity, or rather by nothing;
and others, that they flick together by confpi-
ring Motions, that is, by relative reft . amongft
themfelves. I had rather infer from their Co-
hefion, that their Particles attrad: one another by
fbme Force , which in immediate Contaft is ex-
ceeding ftrong, at fmall diftances performs the
chymical Operations above-mention'd , and
reaches not far from the Particles with any fenfi-
ble -Effea.

All Bodies fcem to be compofed of hard Par-
ticles : For otherwife Fluids would not congeal 5
as Water, Oils, Vinegar , and Spirit or Oil of
Vitriol do by freezing ; Mercury by Fumes of
Lead; Spirit of Nitre and Mercury, by diflbl-
ving the Mercury and evaporating the Flegm ;
Spirit of Wine and Spirit of Urine, by deflegm-
ing and mixing them; and Spirit of Urine and
Spirit of Salt, by fubliming them together to
make Sal-armoniac. Even the Rays of Light
feem to be hard Bodies ; for otherwife they
would not retain different Properties in their
different Sides, And therefore Hardnefs may
be reckon'd the Property of all uncompounded
Matter. At leaft, this feems to be as evident
as the univerfal Impenetrability of Matter. For
all Bodies, fo far as Experience reaches, are ei-
ther hard, or may be harden'd; and we have
no other Evidence of univerfal Impenetrability,
befides a large Experience without an experi-
mental

BOOK III. 365

mental Exception. Now if compound Bodies
are fo very hard as we find fome of them to
be, and yet are very porous, and confift of Parts
which are only laid together j the fimple Par-
ticles which are void of Pores, and were never
yet divided, muft be much harder. For fuch
hard Particles being heaped up together, can
fcarce touch one another in more than a few
Points, and therefore muft be feparable %by
much lefs Force than is requifite to break a fo~
lid Particle, whofe Parts touch in all the Space
between them, without any Pores or Interftices
to weaken their Cohelion. And how fuch ve-
ry hard Particles which are only laid together
and touch only .in a few Points, can flick toge-
ther, and that (b firmly as they do, without the
a{rifi;ance of fomething which caufes them to
be attracted or prefs'd towards one another, is
very difficult to conceive.

The fame thing I infer alfo from the cohe-
ring of two polifh'd Marbles in vacuo^ and from
tlie llanding of Quick-filver in the Barometer at
the height of 50, 60 or 70 Inches, or above,
when ever it is well-purged of Air and careful-
ly poured in, fo that its Parts be every where
contiguous both to one another and to the
Glais. The Atmofphere by its weight prefles
the Quick-filver into the Glafs, to the height of
29 or 30 Inches. And fome other Agent railes
it higher, not by preihng it into the Glafs, but
by making its Parts flick to the Glafs, and to
one another. For upon any difcontinuation of
Parts, made either by Bubbles or by fhaking the

Glafs,

366 O P T I C K S.

Glafs, the whole Mercury falls down to the
height of 29 or 30 Inches.

And of the fame kind with thefe Experi-
ments are thofe that follow. If two plane po-
lifh'd Plates of Glafs ( fuppofe two pieces of a
polifh'd Looking-glafs ) be laid together, fo that
their fides be parallel and at a very fmall di-
ftance from one another, and then their lower
edggs be dipped into Water, the Water will
rife up between them. And the lei's the di-
ftance of the Glaffes is, the greater will be the
height to which the Water will rife. If the
diftance be about the hundredth part of an Inch,
the Water will rife to the height of about an
Inch J and if the diilance be greater or lefs in
any Proportion, the height will be reciprocally
proportional to the diftance very nearly. For
the attractive Force of the Glaffes is the fame,
whether the diftance between them be greater
or lefsi and the weight of tlie Water drawn
up is the fame, if the height of it be recipro-
cally proportional to the diftance of the Glaffes.
And in like manner , Water afcends between
two Marbles polifti'd plane, when their poliftied
lides are parallel, and at a very little diftance
from one another. And if flender Pipes of
Glafs be dipped at one end into ftagnating Wa-
ter, the Water will rife up within the Pipe, and
the height to which it riles will be reciprocally
proportional to the Diameter of the Cavity of
the Pipe, and will equal the height to which it
rifes between two Planes of Glafs, if the Semir-
diameter of the Cavity of the Pipe be equal to
the diftance betv/een the Planes, or thereabouts.

And

BOOK IIL 367

An.d thefe Experiments fucceed after the fame
manner in 'vacuo as in the open Air, (as hath
been tried before the Royal Society, ) and there-
fore are not influenced by the Weight or Pref-
fiire of t!^e Atmofphere.

And if a large Pipe of Giafs be fiiied with
fifted Afhes well preffed together in the Glafs,
.and one end of the Pipe be dipped into ftagna-
ting Water, the Water will rife up flowly^ in
the Afhes, fo as in the fpace of a Week or Fort-
night to reach up within the Glafs, to the height
of 30 or 40 Inches above the ftagnating Water.
And the Water rifes up to this height by the
Action only of thofc Particles of the Aihes which
are upon the Surface of the elevated Water;
the Particles which are within the Water, at-
tra6ting or repelling it as much downwards as
upwards. And therefore the Action of the Par-
ticles is very ftrong. But the Particles of the
Alhes being not lb denfe and clofe together
as rhofe of Glafs, their Action is not fo flrong
as that of Glafs, which keeps Quick- fiiver fuf-
pended to the height of 60 or 70 Inches, and
therefore a6ls with a Force which would keep
Water fufpcnded to the height of above 60
Feet.

By the fame Principle, a Sponge fucks in
Water, and the Glands in the Bodies of Ani-
mals, according to their feveral Natures and
Difpofitions, fuck in various Juices from the
Blood. . ■ -

If two plane polifh'd Plates of Gafs three or
four Inches broad, and twenty or twenty five
long, be laid one of them parallel to the Ho-
rizon,

368 O P T I C K S.

1-izon, the other upon the firft, fo as at one of
their ends to touch one another, and contain an
Angle of about lo or 15 Minutes, and the fame
be firft moiften'd on their inward fides with a
Glean 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 Glafs at thei.
other end j fo foon as the upper Glafs is laid •
down upon the lower, fo as to touch it at one
end as above, and to touch the Drop at the other
end, making with the lower Glafs an Angle of
about 10 or 15 Minutes; the Drop will begin to
move towards the Concourfe of the GlalTes, and
will continue to move with an accelerated Mo-
tion, till it arrives at that Concourfe of the
Glailes. For the two Glaffes attradt the Drop,
and make it run that way towards which the At-^
tradlions . incline. And if when the Drop is in
motion you lift up that end of the Glaffes where
they meet, and towards which the Drop moves,
the Drop will afcend between the Glaffes, and
therefore is attracted. And as you lift up the
Glaffes more and more, the Drop will afcend
flower and flower, and at length reit, being then
carried downward by its Weight, as much as up-
wards by the Attraction. And by this means
you may know the Force by which the Drop is
attracted at all diftances from the Concourfe of
the Glaffes. ^

Now by fome Experiments of this kind,
(made by Mr. Hauksbee) it has been found that
the Attraction is almofl reciprocally in a dupli-
cate Proportion of the diflance of the middle
of the Drop from the Concourfe of the Glaffes,

viz.

BOOK III. 369

1/2;. reciprocally in a limple Propoition, by rea-
fon of the fpreading of the Drop, and its touch-
ing each Glafs in a larger Surface; and again re-
ciprocally in a fimple Proportion, by* reaibn of
the Attradions growing ftronger within the
fame quantity of attracting Surface. The At-
traction therefore within the fame quantity of
attrading Surface, is reciprocally as the diftance
between the Glaiies. And therefore where the
diftance is exceeding fmall, the Attraction muft
be exceeding great. By the Table in the fe-
cond Part of the fecond Book, wherein the
thicknefles of colour'd Plates of Water be-
tween two Glafles are fet down, the thicknefs
of the Plate where it appears very black, is
three eighths of the ten hundred thoufandth
part of an Inch. And where the Oil of O-
ranges between the Glafles is of this thicknefs,
the Attraction coUeCled by the foregoing Rule,
feems to be fo ftrong, as within a Circle of an
Inch in diam.eter, to fuffice to hold up a
Weight equal to that of a Cylinder of Water
of an Inch in diameter, and two or three Fur-
longs in length. And where it is of a lefs
thicknefs the Attraction mny be proportionally
greater, and continue to increafe, until the
thicknefs do not* exceed that of a iinglc Par-
ticle of the Oil. There are therefore Agents
in Nature able to make the Particles of Bo-
dies ftick together by very ftrong Attractions.
And it is the Bufinefs o£ experimental Philofophy
to find them out.

B b ^ . Now

370 O P T I C K S.

fjow the fmalleft Particles of Matter may co-
here by the ftrongeil Attra61:ions, and compofe
bigger Particles of weaker Virtue ; and many of
thele may* cohere and compofe bigger Particles
whofe Virtue is flill weaker, and fo on for divers
Succeffions, until the Progrellion end in the big-
geft Particles on which the Operations in Chymi-
Itry, and the Colours of natural Bodies depend,
and which by cohering compofe Bodies of a fen-
fible Magnitude. If the Body is compact, and
bends or yields inward to Preflion without any
Hiding of its Parts, it is hard and elaftick, re-
turning to 'its Figure with a Force riling from
the mutual AttracCtion of its Parts. If the
Parts flide upon one another, the Body is mal-
leable or foft. If they flip eafily, 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 flick to things, it is
humid ; and the Drops of every fluid affed a
round Figure by the mutual Attradiion of their
Parts, as the Globe of the Earth and Sea affedrs a
round Figure by the mutual Attraction of its Parts
by Gravity,

Since Metals difTolved in Acids attradt but a
fniall quantity of the Acid, their attradiive Force
can reach but to a fmall diftance from them.
And as in Algebra, where affirmative Quanti-
ties vanifli and ceafe, there negative ones be-
gin J fo in Mechanicks, where Attradion cea-
fes, there a repulfive Virtue ought to fucceed.
And that there is fuch a Virtue, feems to fol-
low from the Reflexions and Inticxions of the
I Rays

BOOK III. 371

Rays of Light. For the Rays are repelled by
Bodies in both thefe Cafes, without the imme-
diate Contad; of the reflecting or inflecting Bo-
dy. It feems alfo to follow from the Emillion
of Light ; the Ray fo foon as it is ihaken off
from a fhining Body by the vibrating Motion of
the Parts of the Body, and gets beyond the
reach of Attraction, being driven away with ex-
ceeding great Velocity. For that Force which
is fufficient to turn it back in Reflexion, may
be fufficient to emit it. It feems alfo to fol-
low from the Produdion of Air and Vapour.
The Particles when they are fjjaken off from
Bodies by Heat or Fermentation, fo foon as
they are beyond the reach of the Attradion of
the Body, receding from it, and alfo from one
another with great Strength, and keeping at a
diftance, fo as fometimcs to take up above a
Million of Times more fpace than they did be-
fore in the form of a denfe Body. WliicJi vafh
Contradion and Expanfion feems unintelligible,
by feigning the Particles of Air to be fpringy
and ramous, or rolled up like Hoops, or by
any other means than a repulfive Power. The
Particles of Fluids which do not cohere 100
ftrongly, and are of fuch a Smallncfs as renders
them mofl: fufceptibk of thofe Agitations which
keep Liquors \n a Fluor, are mofl: eafily fepa-
rated and rarifled into Vapour, and in the Lan-
guage of the Chymifl:s, they are volatile, rari-
fying with an eafy Heat, and condenfing with
Cold. But thofe which are groffer, and fo lefs
ibfceptible of Agitationj or cohere by a flironger
B b 2 Attradion,

372 O P T I C K S.

Attradlon, are not feparated without 'a fironger
Pleat, or perhaps not without Fermentation.
And thefe iaft are the Bodies which Chymifls
call fix'd, and being rarified by Fermentation,
become true permanent Air j thofe Particles re-
ceding from one another with the greateft
Force, and being moft difficultly brought toge-
ther, which upon Conrad: cohere moft ftrongly.
And becaufe the Particles of permanent Air are
grofter, and arife from denfer Subftances than
thofe of Vapours, thence it is that true Air is
more ponderous than Vapour, and that a moift
Atmofphere is lighter than a dry one, quantity
for quantity. From the fame repelling Power
it feems to be that Flies walk, upon the Wa-
ter -without wetting their Feet ; and that the
Obje<5t-giaiTes of long Telefcopes lie upon one
another without touching j and that dry Pow-
ders are difficultly made to touch one ano-
ther fo as to ftick together, unlefs by melting
them, or wetting them with Water, which by
exhaling may bring them together ; and that
two poliih'd Marbles, which by immediate Con-
tad ftick together, are difficultly brought fo
clofe together as to ftick.

And thus Nature will be very conformable
to herfelf and very fimple, performing all the
great Motions of the heavenly Bodies by the
Attradion of Gravity which intercedes thofe
Bodies, and almoft^U the fmall ones of their
Particles by fome other attractive and repelling
Powers which intercede the Particles. The
Vis inertias is a paffive Principle by which Bo-
dies

BOOK III. 373

dies perfift in their Motion or Reft, receive Mo-
tion in proportion to the Force kiiprefTing it,
and refift as much as they are itfifted. By
this Principle alone there never could Ivxvq been
any Motion in the World. Some other Principle
was neceffary for putting Bodies into Motion ;
and now they are in Motion, fome other Prin-
ciple is neceflary for conferving the Motion.
For from the various Compofition of two Mo-
tions, 'tis very certain that there is not always
the fame quantity of Motion in the World. For
if two Globes joined by a Ilendtr 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 j the Sum of
the Motions of the two Globes, as often as the
Globes are in the right Line defcribed 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
Liftance it appears that Motion may be got or
loft. But by reafon of the Tenacity of Fluids,
and Attrition of their Parts, and the Weakneli
of Elafticity in Solids, Motion is much more
apt to be loft than got, and is always -upon the
Decay. For Bodies which are either abfolutely
hard, or fo foft as to be void of Elafticity,
will not rebound from one another. Impene-
trability makes them only ftop. If two equal
Bodies meet diredly t^i 'vacuo, they will by the
Laws of Motion ftop where they meet, and
lofe all their Motion, and remain in reft, unlefs

B b 3 they

374 O P T I C K S.

they be elafcick, and receive new Motion froi^
their Spring. If they have lb much Elafticit]
aSifuffices to make them re- bound with a quar-
ter, or half, or three quarters of tlie Force with
which they come together, they will lofe three
quarters, or half, or a quarter of their Motion.
And this may be try'd, by letting two equal
Pendulums fall againft one another from equal
heights. If the Pendulums be of Lead or foft
Clay, they will lofe all or almoft all tlieir Mo-
tions: If of elaftick Bodies they will lofe all but
what they recover from their Elafticity. If it
be faid, that they can lofe no Motion but what .
they communicate to other Bodies, the confe-
quence l;, that i?t vacuo they can lofe no Mo-
tion, but when they meet they muft go on and
penetrate one another's Dimenlions. If three
equal round Veffels be filled, the one with Wa-
ter, the other with Oil, the third with molten
Pitch, and the Liquors be ftirred about alike
to give them a vortical Motion j the Pitch by
its Tenacity will lofe its Motion quickly, the
Oil being lefs tenacious will keep i^ longer, and
the Water being lefs tenacious will keep it long-
eft, but yet will lofe it in a fliort time. Whence
it is eafy to underftand, that if many contiguous
Vortices of molten Pitch were each of them as
large as thofe which fome fuppofe to revolve
about the Sun and fix'd Stars, yet thefe and all
their Parts would, by their Tenacity and Stiffnefs,
communicate their Motion to one another till
they all refted among themfelves. Vortices of
Oil or Water, or fome fluider Matter, might

continue

BOOK III. 375

continue longer in Motion ; but unlefs the Mat-
ter were void of all Tenacity and Attrition of
Parts, and Communication of Motion, (which
is not to be fuppofed,) the Motion v/ould con-
ftantly decay. Seeing therefore the variety of
Motion which we find in the World is ahvays
decreafing, there is a neceflity of confer ving
and recruiting it by adive Principles, fuch as
are the caufe of Gravity, by which Planets and
Comets keep their Motions in their Orbs, and
Bodies acquire great Motion in falling; ai>d the
caufe of Fermentation, by which the Heart and
Blood of Animals are kept in perpetual Motion
and Heat; the inward Parts of the Earth are
conftantly warm'd, and in fome places grow
very hot; Bodies burn and fhine. Mountain^
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,
befides what is owing to thefe ad:ive Principles.
And if it were not for thefe Principles, the Bo-
dies of the Earth, Planets, Comets, Sun, and
all things in them, would grow cold and freeze,
and become inadtive Mafles ; and all Putrefadi-
on, Generation, Vegetation and Life would ceafe,
and the Planets and Comets would not remain in
their Orbs.

All thefe things being confider'd, it feems pro-
bable to me, that God in the Beginning form'd
Matter in folid, mafly, hard, impenetrable, move-
able Particles, of fuch Sizes and Figures, and with
fuch other Properties, and in fuch Proportion

B b 4 to

376 OPTIC K S.

to Space, as moft conduced to the End £o\
which he form'd them j and that thefe primi-)
tive Particles being Solids, are incomparably
harder than any porous Bodies compounded of
them J even lb very hard, as never to v^^ear or
break in pieces ; no ordinary Pov^er being able
to divide what God himfelf made one in the jErft
Creation. While the Particles continue entire,
they may compofe Bodies of one and the fame
Nature and Texture in all Ages : But fhould
they wear away, or break in pieces, the Nature
of Things depending on them, would be chan-
ged. Water and Earth, compofed of old worn
Particles and Fragments of Particles, would not
be of the fame Nature and Texture now, with
Water and Earth compofed of entire Particles
in the Beginning. And therefore, that Nature
may be lafting, the Changes of corporeal Things
are to be placed only in the various Separations
and new Aflbciations and Motions of thefe per-
manent Particles j compound Bjodies being apt
to break, not in the midfi of fclid Particles, but
where thofe Particles are laid together, and only
touch in a few Points.

It feems to me farther, that thefe Particles
have not only a Vis i?ierticej accompanied with
fuch paffive Laws of Motion as naturally refult
from that Force, but alfo that they are moved
by certain adive Principles, fuch as is that of
Gravity, and that which caufes Fermentation,
and the Cohefion of Bodies. Thefe Principles
I confider, not as occult Qualities, fuppofed to
refult from the fpeciiick Forms of Things, but

as

BOOK in. 377

PS general Laws of Nature, by which the Things
themfelves are form'd; their Truth appearing
to us by Phenomena, though their Caufes be
not yet difcover'd. For theie are manifeil Qua-
lities, and their Caufes only are occult. iVud
the Arijloteiians gave the Name of occult Qua-
lities, not to manifeil Qualities, but to iuch
Qualities only as they fuppofed to lie hid im
Bodies, and to be the unknown Caufes of ma-
nifeft Effeds : Such as would be the Caufes of
Gravity, and of m.agnetick and eledrick At-
tradtions, and of Fermentations, if we fliould
fuppofe that thefe Forces or Adions arofc from
Qucilities unknov/n to us, and uncapable of be-
ing difcovered and made manifeil. Such oc-
cult Qualities put a Hop to the Improvement
of natural Philofophy, and therefore of. late
Years have been rcjedled. To tell us that e-r
very Species of Thii^gs is endow'd with an oc-
cult fpecifick Quality by which it ads and pro- v
duces manifefl Etfeds, is to tell us nothing: But
to derive two or three general Principles of Mo-
tion from Phaenomena, and afterwards to tell us
how the Properues and Adions of ail corporeal
Things follow from thofe manifeil Principles,
would be a very great ilep in Philofophy, though
the Caufes of thofe Principles were not yet dif-
cover'd : And therefore I fcruple not to propbfe
the Principles of Motion above-mention'd, they
being of very general Extent, and leave tl^ir*
Caufes to be found out.

Now by the help of thefe Principles, all ma-
terial Things feern to have been comoofed of

the

378 O P T I C'k S.

the hard and folid Particles above-mention'!
varioufly aiTociated in the iirfl Creation By th)
Counfel of an intelligent Agent. For it beeame)
him who created them to fet them in order.
And if he did fo, it's unphilofophical to feek
for any other Origin of the World, or to pre-
tend that it might arife out of a Chaos by the
mere Laws of Nature j though being once
form'd, it may continue by thofe Laws for ma-
ny Ages. For while Comets move in very ex-
centrick Orbs in all manner of Pofitions, blind
Fate could never make all the Planets move
one and the fame way in Orbs concentrick,
fome inconfiderable Irregularities excepted,
which may have rifen from the mutual Ad:ions
of Comets and Planets upon one another, and
which will be apt to increafe, till this Syflem
wants a Reformation. Such a wonderful Uni-
formity in the Planetary Syflem mufl be allow-
ed the Effect of Choice. And fo muft the
Uniformity in the Bodies of Animals, they ha-
ving generally a right and a left fide fhaped a-
like, and on either fide of theii: Bodies two
Legs behind, and either two • Arms, or two
Legs, or two Wings before upon their Shoul-
ders, and between their Shoulders a Neck run-
ning down into a Back-bone, and a Head up-
on it J and in the Head two Ears, two Eyes, a
Nofe, a Mouth, and a Tongue, alike fituated.
•Alfo the firfl Contrivance of thofe very artifi-
cial Parts of Animals, the Eyes, Ears, Brain,
Mufcles, Heart, Lungs, Midriff, Glands, La-
rynx, Hands, Wings, fwimming Bladders, na-
tural

BOOK III. 379

. nral Spedlacles, and other Organs of Senfe and
Motion J and the Inftin(!^ of Brutes and Infeds,
can be the effed of nothing elfe than the Wif-
dom and Skill of a powerful ever-living Agent,
who being in all Places, is more able by
his Will to niove the Bodies within his bound-
lefs uniform Senforium, and thereby to form
and reform the Parts of the Univerfe, than we
are by our Will to move the Parts of our own
Bodies. And yet we are not to confider the
World as the Body of God, or the feveral Parts
thereof, as tlie Parts of God. He is an uni-
form Being, void of Organs, Members or Parts,
and they are his Creatures fubordinate to him,
and fubiervient to his Will j 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 Senfe into the place of its Sen-
fation, where it perceives them by means of its
immediate Prefence, without the Intervention
of any third thing. The Organs of Scnic are
not for enabling the Soul to perceive the Spe-
cies of Things in its Senforium, but only for
conveying them thither j and God has no need
of fuch Organs, he being every where prefent
to the Things themfelves. And fince Space is
divifible in injimtum^ and Matter is not necef-
farily in all places, it may be, alfo allow'd that
God is able to create Particles of Matter of fe-
veral Sizes and Figures, and in feveral Propor-
. tions to Space, and perhaps of different Denli-
ties and Forces, and theieby to vary the Laws
of Nature, and make Worlds of feveral forts in

feveral

380 O P T I C K S.

feveral Parts of the Univerfe. At leafl, I fee i^j-
thiiig of Contradidiion in all this.

As in Mathematicks, fo in Natural Philofo-
phy, the Inveftigation of difficult Things by the\
Method of Analyfis, ought ever to precede the
Method of Compofition. This Analylis con-
fifts in making Experiments and Obfervations,
and in drawing general Concluiions from them
by Induction, and admitting of no Objections
againft the Conclufions, but fuch as are taken
from Experiments , or other certain Truths.
For Hypothefes are not to be regarded in ex-
perimental Philofophy. And although the ar-
guing from Experiments and Obfervations by
Induction be no Demonftration of general Con-
clufions ; yet it is the befl way of arguing which
the Nature of Things admits of, and may be
looked upon as fo much the flronger, by how
much the Induction is more general. And if
no Exception occur from Phaenomena, the Con-
clufion may be pronounced generally. But if
at any time afterwards any Exception fliall oc-
cur from Experiments, it may then begin to be
pronounced with fuch Exceptions as occur. By
this way of Analylis we may proceed from Com-
pounds to Ingredients, and from Motions to the
Forces producing them j and in general, from
Effeds to their Caufes , and from particular
Cauies to more general ones, till the Argument
end in the moll general. This is the Method
of Analyfis : And the Synthefis coniifls in af-
fuming the Caufes difcover'd, and eftablifh'd
as Principles, and by them explaining the Phae-

nomena

{ BOO K III. 381

noraena proceeding from them, and proving the
Explanations."

In the two firfl -Books of thefe Opticks, I
. proceeded by this Analyfis to difcover and prove
' the original Differences of the Rays of Light in
refped: of Refrangibility, Reflexibility, and Co-
lour, and their alternate Fits of eafy Reflexion
and eafy Tranfmiffion, and the Properties of
Bodies, both opake and pellucid, on which
their Reflexions and Colours depend. And
thefe Difcoveries being proved, may be alTumed
in the Method of Compofition for explaining
the Phzenomena arifmg from them: An In-
ftance of which Method I gave in the End of
the firft Book. In this third Book I have only
begun the Analyfis of what remains to be dif-
cover'd about Light and its Eflfcdts upon the
Frame of Nature, hinting feveral things about
it, and leaving the Hints to be examin'd and
improv'd by the farther Experiments and Ob-
fervations of fuch as are inquifitive. And if
natural Philofophy in all its Parts, by purfuing
this Method, Ihall at length be perfedied, the
Bounds of Moral Philofophy will be alfo enlar-
ged. For fo far as we can know by natural
Philofophy what is the firlt Caufe, what Power
he has over us, and what Benefits we receive
from him, fo 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
Worlhip of falfe Gods had not blinded the Hea*-
then, their moral Pmioibphy would have gone
farther than to the four Cardinal Virtues j and

infi:ead

382

O P T I C K S.

infteadof teaching the Tranfmigration of Souls,
and to worfhip the Sun and Moon, and dead
Heroes, they would have tajught us to worfhip
our true Author and Benefactor, as their Ance-
ftors did under the Government of Noah and his
Sons before they corrupted themfelves.

FINIS.

BOOKS printed for William Innys.

Is A A CI Newtoni, Equ. Aur. in Academia Cantabrigienfi Ma-
thefeos olim Profeflbris Lucafiani Leftiones opiicae. 4/0. 1729.

The fame in Englijh. %vo. 1728.

Univerfal Arithmctick. By Sir Ifaac Newton. The Second E-
dition. %vo. 1728.

Opticas : Sive de Reflexionibus, Refraflionibus, Inflexionibus &
Coloribus Lucis Libri ties, Authore Ifaaco Newton, Equite Au-
rato. Latine reddidit Samuel Clarke, S. T. P. Editio fecunda,
auftior. 8cff. 1719-

Philofophise Naturalis Principia Mathcmatica. Authore Ifaaco
Newton, Equ. Aur. Editio tertia, aufta ^ emendata. \to. 1726.

The Method of Fluxions both Direft and Inverfe : The former
being a Tranllation from the Marquis de V Hofpital, and the latter
fupplied by the Tranflator, E. Stone, F. R. S. Jn two Volumes.
%vo. 1730. _ /

Epiilola ad amicum de Cotelii Inventis Ciirvarum ratione, ^V.
\to. 1722.

An Analytick Treatife of Conic Sedlions. By E. Stone. \t9.

Mathematical Elements of Natural Phiiofophy confirm'd by Ex-
periments : Or an Introduftion to Sir Ij'aac Newton's Phiiofophy.
By1V.J.'sGravefandt,hL.D. In two Vols. 8:/^. The Third
Edition. 1726.

Phyfico-Theology : Or a Demonftration of the Being and Attri-
butes of God, from his Works of Creation ; with large Notes and
many curious Obfervations. By IV. Derham, Canon of WindjoTy
and F. R. S. The Seventh Edition. %vo. 1727.

Mr. Derhani's Allro-ThcoJogy : Or a Demonftration of the Be-
ing and Attributes of Gc I from a Survey of the Heavens; with
Cuts. The Fifth Edition. Sr-a. 1726.

Philofophical Letters between the la:e Learned Mr. Ray and fe-
veral of his Ingenipus Correfpendents, Natives and Foreigners. To
which are added thofe of fra^icis Wiiloughby, Efq; The whole
confining of many curious Difcoverics and Improvements in the
Hii^ory of Quadrupeds, Birds, Fifr.es, Infefts, Plants, Fofiils,
Fountains, idc. Publifhed by Mr. Dcrhatn. Zvo.

Mr. Ray\ Three Phyiico-Theologlcal Difcourfes, concerning
I. The primitive Chaos, and Creation of the World. II. The
general Deluge, its Caufes artd EfFedls. III. The DilTolution of
the World and future Conflagration, l^c. Illuftrated with Copper-
Plates. The fourth Edition, with Additions. %vo.

His Wifdom of God in the Works of the Creation. The

Ninth Edition. %vo. 1727.

Mr. Ronayne\ Treatile of Algebra. The Second Edition, with
Additions. Sec. 1727

Geometria Organica : Sive Defcriptio Linearum Curvarum uni-
verfilis. Auftore Colino Mac Laurin, Math. Col. Abred. Prof. &
R. S. S. 4/(?. 1720.

Aa

BOOKS printed for W. I n N y s. •

An Introduftion to Natural Philofophy : Or PhiJorophrcal Le-
£lures read in the Univerfity of Oxford, A. D. 1 700. To which
zre added, The DcmonHrations of Mr. Huyge?;is Theorems, con-
cerning Force and circular Motion. By yo/:?n Kei'/, M. D. Sav.
Prof, of Allronomy, and F. R. S. The Second Edition. Svff.

PhilofophicrJ Tranfaclinns, giving fome Account of the prefent
"Ehidertakings, Studies and Labours of the Ingenious, in many con-
fiderable Parts of the World. Vol. 36. Continued and publifh'd
by JV. Rr/ity, M. D. and Reg. Soc. Seer. 4/1?. 1730.

The Lives of the French, Italian and Gerjnaii Philofophers, late
Members of the Royal Academy of Sciences in Paris. Together
with Abftracls of the chqicefl Pieces communicated by them to that
Tlluftrious Society. To which is added, the Preface of the Ingeni-
ous Monfieur Fonicnelie, Sccretgry and Author of the Hiilory of
the faid x'\cademy, ^vo.

\Leonaidi Plukeneti'. M. D. Opera omnia Botanica in fex Tomoe
divifa,. viz. I. II. III. Phytographise. IV. Almageftum Botani-
<wm. V. Almagefti Botanici MantifTa. VI. Amaltheum Botani-
cum in quibus Stirpes illuftriores minus cognitae, exoticae, Rarioref-
due novjffime detcftae ad plures Chiliadas defcribuntur. Turn
ionibus Tabulis JEntis CCCCLIV. fumma cura depiftis Figu-
fintur.

I Methodus Incrementorum direfla & univerfa. Auftore Brook
Taylor, L. L. D. & Reg. Soc. Seer. 4/^. 171 7.
i The Pollhumous Works of Dr. Robert Hcoke; in which, I. The
j^refcnt Deficiency of natural Philofophy is difcourfed of, with
tiie Methods of rendring it more certain and beneficial. II. Of
the Nature, Motion and Effedls of Light, particularly that of the
Sun and Comets. III. An hypothetical Explication of Memory ;
how the Organs made ufe of by the Mind in its Operation may be
inechanically underftood. IV. An Hypothefis and Explication of
^e Cauie of Gravity, or Gravitation, Maignetifm, iffc. V. Dif-
courfes of Earthquakes, their Caufes and Effects, and Hiftories of
fcveral : To which are annex'd, Phyfical Explicntions of feveral
of the Fables in Oviifs Metamorphofis, very difisrent from other
Mythologick Interpreters. VI. Ledures for improving Navi-
gation and Aftronomy, with the Defcriptions of feveral new and
ufeful Inlh-uments-, illuftrated with Sculptures To thefe Dif-
courfes is prefix'd the Author's Life. By Richard IVttller, R. S.
Seer. Folio.

Synopfis Univerfa Medicina TraFltca : Sive doftiffimorum vi-
rorum de Morbis eorumque Caufis ac Rem.ediis judicia. Accefle-
runt nunc demum cafus nonnulli oppido rari. Authorc J. Allen, M.D.
Editio tertia;, prioribus, triente plus, auftior. In 2 Vol. 'ivo. 1729.

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