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# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
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du
1
ssls  l s

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NMV -A
cili. Marg. 193
Auter treulaneu a Bhemorkungeu vou lecniz Rcat.
15 L=
2
Bet  2. 68, 7 3, _. O.; 10c, L 
32,3, C ac. ; D. A66, ACb. Abd 1.7 se

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buntrerniteno

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Mf   s. f . fer f s f.. fet  u   t sessll
se nideae ouo
1. NIa

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sabula vigrutionis corporum 2bk. f. (3
b. 69
3
nmsica 92. Ng. lib. 2. p. 18. 31
H. Z 65) bb. 75d2
So2 A LeenoiZ Scc Fron  Hrutton

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d

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OR, A
IRH A IISF
OF THIF
AFFLFXIONS, RE FRLATIO.
TNEL EXIONS and COLOVRS
O
A L 5O
PIO TREATISES
OF TFL F.
PECTES and MIAGTETO
d F
L. O N DO N,
Printed FOr S a MI. SNFTH. and BENI W a
Vard.
MDCCIV.
Printers t0 the ROyaI
E. Paul
Ocietr, at the Princes Art

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D
A
3
u
u
0
a
024
Mi se

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ADYFRTISFM21
Art oftheensuins Discourse about Licht Was reritten
at the desire of some Crentlemen of the Royal Societ,
en the Tear 1675. and then sent to their Secretary, and
read at their Mectines, and the rest vas added about
Prvelve Tears after to complete the Pheory; except the
Third Bock, and the last. Proposition of the Second, rehich
rere since put tocether out of scattered Papers. Lo avoid
bens encared in Disputes about these Matters,  have
Bitherto delayed the Printine, and Mould stitt bave de
layed it, Bad not ihe importunity os Friends prevaile d uxon
me. If any other Papers rerit on this Subject are eot out
ef my FTands they are imperfect, and rvere perhaps rritten
before Yhad tried al the L’xperiments bere set dore,
and fully satissied my sels about the Lares of Refractions
and C omposition of. Colours. T have here Publisped rehat
Tthint proper to come abroad, vistine that it may not be
Pranstate d into another Laneuare vuithout my Consent.
TheCirorensof Colours, Wehich sometimes appear about
the Sun and Moon, T have endeavoured t0 rive an Ac
count of: but for rvant of sufficient Observations leave that
Matter tobe further examined. The Subject of the Third
Book  have also lest imperfect, not bavine tried all the
RXpe-

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Fixperiments rehich Y intended rhen P vas about these
Matters, nor repeated some of those rehich  did try, until
Thad satisfied my self about alltheir Circumstances. Yo
communicate rehat l have tried, and leave the rest 10
ocbers for further Pnquiry, is al my Desien in publistrine
these Papers.
In a Lerter reritten to Vr. Lcibnitz in the l ear 1676.
and publistred by Dr. W altis, Ymentioned a Method by
rehich TBad found some general Pheorems about squarine
Ciurvilinear Ficures, or comparine them roith the Conic
Sections, or other the simplest Firures roith rehich theymay
be compared. And some Tears aco Tlent out a Manuscript
containins such F Beorems, and havine since met roith some
Fhines copied ont of it. Phave on this Occasion made it
publick, presixine to it an Introduction and subjomnine a
Scholium concernine that Method. Und l have joined
oith et another smalt Pract concernine the Curvilinear
Fieures of the Second Rind, rehich ruas also reritten
many Tears aco, and made knoron to some Friends, rise
bave solicited ibe matine it publict.

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TNC F PLCDL LDOR
OF
e A R F 
Y Delion in this Book is noc to explain che Pro-
perries ot Lighe by Frpocheles, but to propose
and prove them by Realon and Experiments:
In order to which, PMall premise che tollowins Detini-
e  O1e
DE F LN. I.
DY the Rays of Lioht P understand ils least Parts, and those
as vellSuccessive in the same Lines as Contemporary in se
veral Lines. For ic is manifest chac Lighe consists ot parts
boch Succellire and Contemporary; because in che lame
place rou may Aop chat which comes one moment, and
lec pals chac ihich comes presently atcer; and in che lame
cime rou may Cop ic in any one place, and lec ic pals in
any ocher. For thac pare oF Lighe which is AopE cannOE
be che lame rich chac irhich is lec pals. The lcast Liphe
Or pare ot Lighe, Which may be sope alone wichout che
rest ot che Liphe, or propapaced alone, or do or luster any
chine
cions and Axioms.

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ching alone, whichche rest of che Lighe doch noc or suF
ers nOL, I caIl a Ray oE Liotc.
DE FIVI. II.
Refrangibility of. the Rays of Zight, is their Disposition to be
refracted or turned out of their Way in passinz out of one trans-
parent Body or Medium into another. And a greater or less Re-
frangibility of Rays, is their Disposition to be turned more or less
out of their Way in lihe Incidences on the same Medium. Mache-
maticians ulually consider che Rars ot Lighe eo be Lines
reachinu trom che luminons Body ro the body illumina-
ced, and che refraction ot chose Rays eo bc che bendino
or breakcine of chose Lines in cheir passing ont ol one Me-
dium inco anocher. And chus may Rays and Retractions
be considered, il Lighe be propagated in an instanc. BuE
by an Aroument cakcen trom che AEquations of che times
ot che Felipses oF FupiterS Satellites it Scems thac Liphe is
propasated in time, spending in ies pallase trom che sun
rous about seven pinures ot time: And cheretore I have
cholen to detine Rars and Retractions in such general
cerms as may agree to Lishe in boch cales.
DE FFN. HI.
Restexibility of Rays, is their Disposition to be turned back into
the same Medium from any other Nedium upon whose Surface they
fall. And Pays are more or les reflexible, which are returned
back more or less easity. A5 it LiphE palS ouE OF GlaIS inEO
Air, and by being inclined more and more to the com-
mon Surtace et che ClaIs and Rir, begins ax lenoch co be
cocally reflected by that Surtace; thole TOrts oF Rays Which
at like Incidences are reflected most copiousty, or by in-
clining che Rays begin Coonest ro be torally reflected, are
most refexible.
F

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DEFFN. IV.
The Angle of Incidences ls that Anele Which the Line described
by the mnula a cous mith the Perpendicular to the reste-
Eting or refractinq Surface at the Point of Incidence.
DF F IXI. V.
The An LGunh or Refraction, is the angle nhich the
Line described by the reflected or refracted Ray containeth with
the Perpendicular to the reftectine or refractine Surface at the
Doint of Incidence.
D E F IN. VI.
The Sines of Incidence, Reftexion, and Refraction, are che
Sines of the angles of Incidence, Restexion, and Refraction.
DE FINT. VII.
The Lighe mhose Rays are all alike Refransible, T call Sim-
ple, FTomozeneal and Similar; and that whose Rays are some
more Refransible than others, I call Compound, FLeterozeneal and
Dissimilar. The Former Lighe I call Hlomogeneal, noc
because I vould attrm it (o in all respects; buc because
the Rars which aorec in Retrangibiliey, aoree ac least in
all those their ocher Properties. Which I consider in che
Follomins Discourse.
DE FINT. VIII.
The Colours of FTomoreneal Liebts, L call Frinar), LLM
reneal aud Simple; and those of Fleterozeneal Lichts, Leterore
neal and Compound. For chele are alirars compounded ot
che colours of Homogeneal Lighes; a5 will appear in che
Tollomins Discourse.
XI.

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 X (O M S.
A Z. I.
ITL L. Angles o Incidence, Restexion, and Refraction, lye
u one  isse same Plane.
A X. H.
The Anele axton is equal to the Angle of Incidence.
A X. TII.
IF the refracted Ray be returned directly back to the Point
of. Incidence, it sall be refracted into the Line before descri-
bed by the incident Ray.
A X. IV.
Refraction out of the rarer Nedium into the denser, is made
comards the Perpendicular; that is, so that the Angle of Refra-
ction be less than the Angle of Incidence.
A X. V.
Fhe Sine of Incidence, is either accurately, or very nearly in a
siven Ratio to the Sine of. Refraction.
Whence it char Proportion be knoun in any one incli-
nation of the incidene Ray, eis known in aIl che Inclina-
tions, and chereby che Retraction in aIl cases ot Incidence
on che lame retractins Body may be decermined. Thus
it che Retraction be made out oF Rir inco Water, the Sine
ofincidence of the red Lighe is eo. che Sine oF its Retra-
ction 25 4 10 3. IF ou ot Air into Clals, che Sines are
25

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25 17 20 11. In Lighe ot orher Colours the sines have
ocher Proporrions: buc che difference is (o licele chat it
necd seldom De consdered.
Suppose theretore, that R S reprelents the surtace oF Fig. P.
Ragnaring Wacer, and C is che point ot Incidence in
irhich any Ray comins in che Air trom A in che Line
AC is reflected or retracted, and I vould know irhether
ehis Ray Phall g0 atter ReAerion or Retraction: I crect
uxon che surtace of che Water trom the point ot Inci-
dence the Perpendicular C P and produco ic donmards
t0, and conclude by che Airst Axiom, thac che Ray af-
cer Rellexion and Retraction, Phall be Found Comerhere in
che Plane ot che Angle of Incidence AC P produced.
lec Falt cheretore uxon che Perpendicular C P the sine ot
Incidence AD, and it che reftected Ray be delired, Ipro-
duce AD eo B (0 thac D B bC equal tO AD, and dram
CB. For chis Line C B Phall be the reffected Ray; the
Angle ot Rellexion B C P and ies Sine BD being equal
co che Angle and sine ot Incidence, as ther oughe to bc
by che second Axiom. Bur it che retracted Ray be de-
sired, Iproduce AD eoTI, (0 that D II may BC EO ALd
as the sine ot Retraction to che sine ot Incidence, thac is
25 3 c04; and abouc che Center C and in the Plane A C P
wich the Radius C A describing a Cirele AB F I draw
Parallel cothe Perpendicular C P C, the Linc HP cuctine
the circumterence in F, and jorning CP, chis L inc C F
Pail be che Line of che refracted Ray. For iFP, F BC lec
fall perpendicularty on the Linc P C, this Line P F Phalb
De che sine ot Retraction of che Ray CF, che Angle oF
Retraction being P C (; and chis sine F F is equal eo
DII, and consequencr in Proporrion ro the sine of inci
dence A D a5 310 A.

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In like manner, if there bc 2 Prism oF Glals (hat is a
Class bounded rich evo Pqual and Parallel Triangular
ends, and chrec plane and vell polithed Sides, which meet
in chrec Parallel Lines runnins trom che chrec Anoles ot
one end co the chree Angles ot che ocher end) and it che
Retraction oF che Lighe in pallins crols chis Prilm be desi-
red: TeE ACB represent a Plane curtinq chis Prilm eran
rersly co ies chree Parallel lines or edges there uhere the
Liphic passech chrough ic, and lec dF. bc che Ray inci-
dene upon che first side oF the Prilm A C Where the LixhE
gocs inco che Olals; And by purtins che Proportion ot
che sine ot Incidence eo che sinc ot Retraction a5 17 +0
12 End F F che first retracted Ray. Then calcinq chis Ray
For che Incident Ray upon the sccond side oF che Cla(S B C
irhere che Liohe goes ouE, find che next retracted RaY FC
br purtins che Proportion ot che sine ot Incidence to che
Sine oF Retraction a5 11 +0 17. For it che sinc ot Inci-
denCe OHE OF Rir into Glass bC co ehe sine ot Retraction
25 17 20 1I, che Sine oF Incidence out ot Gla(s intO Rir
must on the contrary be co che sine of Retraction a5 11
eo 17, by che chird Ariom.
Much after che Pame manner, iF A C B D reprelent a
Class spherically Conrex on boch sides Culually called a
Tens, such as is a Burming-glals, or Spectacle-slals, Or an
Object. olals ot a Telelcope) and ic be required to know
hoir Lighe Falling uxon ic trom aur lucid poine 2 Phal
be retracted, lec M reprelent a Ray Fallins uxon any
point MI oF ies first spherical Surtace ACB, and by crectino
a Perpendicular to the Clals at che poine MI, find ehe Airst
retracred Ray M N by che Proportion oL che Sines 17
EOII. Let chac Ray in goins out ot che Clals be inci-
dene uxon N, and chen find che second retracted R ay N g
by che Proportion oF che Sines 1I +0 17. And atter che
Tame
Fig. 2.

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same manner may che Retraction be Found when the
Lens is Conrex on one side and Plane or Concare on
che ocher, or Concare on boch Sides.
A X. VI.
Fhomogeneal Rays nhich Rom from severat Points of any Ob-
sect, and faii almost Perpendiculariy on any reftectine or refra-
etinz Plane or Spherical Surface, Pall aftermards diverge from
lo many ether Points, or be Parallel to so many other Lines, or
converge to se many other Points, either accurately or without any
sensible Frror. And the same thing will happen, if the Rays be
reflected or refracted successively by tuo or three or more Plane
or spherical Surfaces.
The Poine Erom Which Rays diverge or eo which chey
conrerge may be called cheir Focus. And the FocuS ot
che incident Raysbeing giren, thac ot che reflected or re-
Fracted ones may be tound by finding the Retraction ot
any trvo RaYS, as above; or more readily chus.
Cas. 1. Let ACB BC 2 retlectinq or retracting Plane, Fiz. 4.
and 2 che Focus oF che incident Rays, and C q C 2 per-
pendicular eo thac Plane. And il this perpendicular be
produced eo q (0 thac qC bc equal eo C, the point q
Thall be the Focus ot the refected Rays. Or it gC bc
cakcen on che Pame sde et che Plane wrich C and in PrO-
portion co C as che sine ot Incidence co the sine ot
Retraction, che point q Phall be the Focus ot che retrac
ted Rays.
Cas. 2. Tet A C B Be che rehecrins SurFaCC OF anY Fig. 5.
Sphere whole Center is F. Bileet any Radius thereot (sup-
Dosc F C) in Y, and if in chac Radius on the lame Side che
Poine Prou cake che Poines  and q. (0 that I O, TF,
aud Tg be continual Proportionals, and che point Q be
tlac

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he FOcus oF che incidene Rays, che poine q Pall bc chc
Focus oF che rellected ones.
Cas. 3. Let ACB bC the retractin Surtace ot any
Sphere nhose Center is F. In any Radius chereof L C
produced boch mars rake F. T and Ct Sererally in Cuch
Proportion co that Radius as the leller ot che sines ot
Incidence and Retraction hach co che difference et those
Sines. And chen il in che Came Line ron And any evo
Points  and g, (0 chac T ( bC EOF T aS F FEO t9.
cakcins t q the contrary may trom tirhich T C liech From
l, and it che Poine be the Focus ot any incidene RaYS,
the Point g Mall be che Focus ot che retracted ones.
And by che Came means che Focus of che Rars atrer
ervo or more Reherions or Retractions mar be Found.
Cas. 4. L et A C BD bc any retractins Lens, spheri-
cally Conrex or Concare or Plane on cicher side, and let
CD bC ies Aris (thac is the Line irhich curs boch ies Sur-
faces perpendicularir, and passes chrouoh che Centers ot
che Spheres,) and in this Aris lec F and fbc the Foci ot che
retracted Rays Found as abore, irhen che incident Rays
on boch Gidesthe Lens are Parallel cothe lame Aris; and
uxon the Diamerer F f bilecced in F, describe a Circle.
Suppole non chat anx Poine Q bc che Locus ot any inci-
dene RayS. Dra LP curting che laid Circle in P andt
and cherein cake t. g in such Proportion to + F aStF Or TF
hathco TO. Lec tg lye che contrary way trom tirhich
TO doih trom T, and g Thall. be the Focus of the retrac
ced Rays ithout aur sensible Error, provided che Poinr
Obc noc lo remore trom che Axis, norche Lens (o brond
25 eo makie any oF che Rars FaII too obliquely on che
retractino Surtaces.
And by che like Operations mar che reflecting or re-
traccins Surtaces be tound nhen cherro Foci are giren,
and
. 6

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C9
and chereby a Lens be Formed, which Pall make che Rays
Ao comards or trom irhac place rou please.
50 chen che meaninq of chis Ariom is, thac il RayS
Fall uxon any Plane or Spherical Surtace or Lens, and
betore cheir Incidence Ron From or tomards any Point,
cher Chall atrer ReRlexion or Retraction RoW trom Or tO-
ards che Point q Found by che Foregoins Rules. And it
ehe incidene Rays Aor From or comards sereral poines ,
the reslected or retracred Rays PBaII ROm From or tormards
Co many orner Poines g Found by che lame Rules. Whe
cher che refecced and refracted Rays Ron From or torrards
che Poine q is casily lnonn by che situarion oF that Point.
For it chac Poine be on che lame side oF the reAectin Or
retractinq surtace or Lens ich che Point , and che in-
cidenc Rars Aou From che Point , the reflected Aon to-
wards che Poinc q and ehe retracred trom ic; and it che
incident Rays Aor corards , che reftected Aon From qu
and che retracced corrards ic. And the contrary happens
wrhen q is on che ocher (ide ot that Surtace.
A X. VII.
Wherever che Rays wbich come from all che Doints of any Ob-
ject meet azain in so many Points afcer they have been made to
converze by Restexion or Refraction, there they nill mate a Dic-
ture of che Objeet upon any inbite Dody on Which they fall.
S0 it PR reprelent any Object withoue DOOrs, and AB Fis. 3.
be a Lens placed ac a hole in che Wincon- uE oF a dark
Chamber, Whereby che Rays that come trom any Point
Ot chac Objece are made co converse and mecc ag2in in
the Point q; and if a Sheet ot wrtrice Paper be held ac q
For the Lighe chere eo FaII upon ic: the Picture OF FhAE
Object PR Will appear upon che Paper in ies proper Strape
27C

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and Colours. For as che Lighe erhrich comes trom che
Point  gOcs to che Point q, (0 che Lighe which comes
From ocher Poines P and R oF che Object, will 00 10(0
manr ocher correspondene Poines p and r (a5 is manifest
by che sixch Axiom;) (o chat every Poine ot che Obiece
Phall illuminare a correspondent Point ot chePicture, and
chereby makce a Picture like che Object in Strape and Co-
lour, chis onty excepted char the Picture Phall be inverred.
And ehis is ehe reason of thac Vulgar Experiment oF cast-
ino che species ot Objeces From abroad upon a WaII Or
Street ot irhice Paper in a dark RoOm.
In like manner When a NTan riers any ObieCE P QR,
ehe Liohe irtrich comes From ehe sereral Poines ot Tne Ob-
ject is (o retracted by che cransparene skins and humours
Ot the Ere, (chac is by che outmard Coat EFC called che
Funica Cornea, and by che cerstalline humour AB irhich is
berond che Pupil mk) as to converse and meer again at
Comans Poines in che bortom of che Fye, and chere eo paine
the Picture oF che Object upon ehac skin (called the Tu-
niea Retina) wich irhich the boccom et the Ere is corered.
For Anatomists irhen cher have taken oH from the Bor-
tom of che Fre chac outmard and most chick Coac called
he Dura Mater, can chen see chrouoh ehe chinner COats
che Dictures oF Objects lively painced chereon. And chese
Pictures propasated by Mocion alons che Fibres of che Op.
rick Nerres into the Brain, are the cause ot VisiOn. FOr
accordinolr as chele Pictures are pertect or impertece, the
Obiect is scen pertectly or impertectlr. IF che Eye be tin-
red wich any colour (as in che Dileale oF the faundise) (0
25to tinge the Pictures in the bocrom of the Fye mith chat
Colour, then all Objects appear tinsed trich che lame Co-
LOur. IF che humours ot chc Pre by old Aoc decar, (0
25 b7 Chrinkins ro malie che Cornea and Coat oF the Cry-
stalline
Fuis. 8.

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stalline humour exow Haccer chan betore, the Lihe ill noc bc
retracced enorph, and For ranc of a sufficient Retraction
ill noc converge to the bocrom ot che Ere bur colome
place berond ic, and by consequence paint in the boccom
OfcheEre a contuled Picture, and accordinq to the indistinct-
nels oF ehis Picture che Object mill appear contused. This
isthe reason of che decar of sighe in old Men, and Phews
Why cheir sighe is mended by Spectacles. Forthole Con-
rex. glasses supply che detect oF plumpnels in che Frc, and
by encrealine che Retraction make theRays conrerse looner
(0 asto conrene distinctly ac che bocrom ofche Fre if the
Clals hare a due degree ot conrexier. And the contrarr
happens in Chorc-Siehred Nen Whose Pres are t00 plump.
For che Retraction beins non t00 great, che Rays conrerge
and conrene in che Fyes betore cher come ac thebortom;
and cheretore chePicture made in the borcom and che Vision
caused chereby will noc be distinct, untels che Object be
broughe lo near che Fre as thar cheplace irhere the con-
vergins Rays conrenc may be remoredtotheborom, or
thac ehe plumpness ot che Fve be taken of and che Retra-
ctions diminithed by a Concare-glals of a due degrec ot
Concarier, or la sly chat by AgC the Eye gron Aaccer eill ic
come co a due Figure: For Chore-(ighred Nen lec remore
Objects best in Old AgC, and cheretore chey are accounced
cohare che mostlacting LyCs.
A X. VIII.
An Object seen by Reflexion or Refraction, appears in that place
from ihence the Rays after their last Reflexion or Refraction di-
verge in fallins on the Spectators Fye.
IF che Object A be seen by Rehexion oF a L 0okins- F18. 9.
alS m n, iC Pall appear, noc in ies proper place A, buc
Behinc

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behind the Clals ac a trom Whence any RayS AB, AC,
AD, ihich Ro From one and che Came Poine ot che Ob-
ject, do atrer cheir Reflexion made in che Poines B, C, D.
diverse in goins trom the Ola(s EOF, F, C, irhere cher
are incident on the Spectators Fres. For chese Rays do
make che same Picture in the borrom of che Fyes a5 it
cher had come Erom the Obiece really placed ac a withove
chie incerpolicion oF che Looking-slals; and all Vision is
made accordins co che place and Chape oF chac Picture.
In like manner the Objece D seen chrough a Prilm ap-
Pears noc in ies proper place D, buc is chence translaced to
Tome octier place d’Scuared in the last retracted Ray FC
drawn backmard FrOm E CO d.
jr. 10. And Coche Object  Pcen chrough che Lens AB, appCarS
ac che place q trom whence the Rars diverse in pastine
Fromthe Lens to the Ere. Now it isto benored, charthe
Imase oF the Objecc ac g is lo much bigger or lesser than
the Obiect ic PelF ac 2, 25 che distance ot the Imase ac
gtrom che Lens AB is bigger or lels chan che distance ot
che Objece ac  From che lame Lens. And if che Obiect
De scen chrousti erro or more luch Convex or Concave-
olasses, everr Clals Call make a ne Imase, and the Ob-
ject Phall appear in che place and ot che bignels ot the last
Image. Which consideration untotds the Theory oFMi-
crolcopes and Telelcopes. For thac Theory consists in i-
most noching else chan the describing such Classes as PaII
make che last Image ot anr Object a5 distinct and large
and luminous as ic can conreniently be made.
Phare noi siren in Axioms and cheir Pxplications the
Curm of ihac hath hicherco been creaced ot in Opticks.
For irhat hach been generally agreed on l contene my
selE eo allume under chenocion ot Principles, in order to
Whac l hare Further co reice. Andchis may suttice For an
TnEro-
Fig. 2

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3
Ineroduction eo Readers oF quick Wir and g00d Under-
standins noc vec versed in Opticks: Althouoh thole who
are alread acquainced u s setene, anare
handled Classes, will more readily apprehend what Fol-
eesect.
PROP. I. ThCOr. I.
IOHITS which difter in Colour, difter allo in De-  ot
srees ot Retrangibiliey.
The Proos by Fxperiments.
Exper. 1. P cook a black oblone siff Paper terminated
b Parallel Sides, and with a Perpendicular riohe Line
draun crols trom onc Side co che other, distinguished ic
into erro equal Parts. One ot chele Parrs I painced wich
a red Colour and che other wich a bler. The Paper was
verr black, and che Colours incense and chickly laid on,
chac che Phaenomenon mighe be more conspicuous. This
Paper I riered chroueh a Prilm oF solid Olals, Whose tvo
Sides chrouoh which che Lighe passed co che Eye vere
plane and ell polisted, and concained an Angle oF abOuE
Sixer Dcorees: Wrhich Angle Icall the retractine Angle ot
che Prilm. And Whilst I viered ic, I held ic betore a
Windor in such manner chac the Sides of che Paper ivere
Parallel co chePrism, and boch chose Sides and che Prism
Parallet co che HTorizon, and the crols Line perpendicular
co ic; and thac che Lighe wrhich fell trom che Window
NIDOM
Garen
u

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C
upon che Paper made an Angle wich the Paper, cqual eo
chac Anole ertrich as made wich che lame Paper by che
Liohe resected trom it to the Erc. Berond che Prism was
che W aII oF che Chamber under che Window corered over
vich black Cloch, and che Cloch was involved in Ddark-
nels thac no Lighe miohe be reRected From chence, wtrich
in passins by che edges ot che Paper ro che Erc, mighe
minole ic selF wich che Lighe of che Paper and obscure che
Phaenomenon chereot. These chinos beino thus ordered,
Y Found chac it che retractine Anole ofche Prilm be curned
upmards, (0 thac chie Paper may seem co be litced upmards
by che Retraction, ies ble halt wrill be lifced hixher by
che Retraction chan ies red halt. Bur it che retractin
Anole ot the Prism be curned domnmard, (o thac the Pa-
per may seem co be carried lorver by che Retraction, its
blem halt rill be carried Pomething lover thereby chan
its red halF. Wheretore in boch cales the Liphe whicta
comes From che ble hale ot che Paxer chrouoh the Prism
cothe Ere, docs in like Circumstances lufter a greater Re-
Fraction chan ehe Liphe inhich comes trom che red halt,
and br consequence is more retransible.
plustration. In che Elerench Figure, M N reprelents che
Windo, and D F che Paper terminaced ich parallet sides
D) andHIF, and by checransrerse Line FO distinguithed
into erro halts, che one DC ot an incenselr bler Colour
ehe Other F FOF an incenselr red. AAd BA C Cab repre-
senes ehe Prilm whose retracting Planes ABB a and A C CA
meet in che edge ot che retractins Anele A a. This edoc
Aa beins uprard, is parallel boch to che Horiron and eo
che parallel edges oF che Paper D) and HL. And dere-
prelenes che lmage oF che Paper seen by Retraction up-
mards in such manner chac che blem halt DC is carried
trigher co de chanche red half F P. is to fe, and cheretore
Custers
F1g. 11

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sutters 2 greater Retraction. IF che edge of che retractine
Ansle be curned domnmard, che Image ot the P’aper vill
Be retracted domnmard suppose co dc, and che bler halt.
ill be retracted lover eo dr chan the red haIF is EO PE.
Exper. 2. Abouc che atorelaid Paper, whose erro halts
vere painced over rich red and bleu, and ihich iras siH
like chin Pastboard, I lapped sereral cimes a Pender chred
ot very black Silk, in such manner chac che several ParES
ot che chred mixhe appear upon che Colours like lo mans
black Liries dramn over chem, or like long and Pender
dark Stradons cast uxon chem. I mighe hare dramn black.
Lines wich a Pen, Buc che chreds vere smaller and bctter
detincd. This Paper chus coloured and lined I set againct
2 Wall perpendiculartr cocheHorizon, (ochat one oFchc
Colours mighe sand co che righe hand and che other to
the letr. Close betore che Paper at the contine of the Co-
lours belou I placed a Candle co illuminate the Paper
Arongly: For the Experimene as cried in che Nighe.
The Aame of che Candle reached up to the lorver edge ot
che Paper, or a very licele hipher. Then ac the distance ot
Six Feet and onc or ero Tnches trom che Paper upon che
Floor I crected a glass Lens tour lnches and a quarter
broad, which mighe collect che Rays cominq trom chc
sereral Points of the Paper, and make chem conrerge to-
Wards (o manr ocher Poines ac the lame distance Ot sIX
Fcet and one or erro Inches on che ocher side of che Lens,
and (0 form che Imaxe ot the coloured Paper upon a whice
Paper placed chere; afcer che same manner thaL 2 L enS aE
a hole in a Windor casts the Images of Objects abroad
uxon a Sticet of whice Paper in a dark Room. The atore-
Caid irhice Paper, crected perpendicular co che HOrizOn
and to the Rays itich Fell uxon ic from the Lens, Imored
Cometimes tomards che Lens, Pometimes From ic, to find

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chie places where che Images ot che blem and red parrs ot
ehe coloured Paper appeared most diltinct. Thole places
I casilr lneu by che lmages ot che black Lines which L
had made br windins che silk abouc che Paper. For the
Tmgoes of thole fine and Pender Lines Cirhich by reason ot
their blacknels iere like Stradtons on che CoIOUrS) Were
contused and scarce risible, unlels when che Colours on ci-
cher sde ot cach Line ivere terminared most distinctr.
Norino cheretore, 25 diligently a5 Ecould, che places irtere
the Tmares of the red and ble halts ot che coloured Pa-
per appeared most distinct, I Found chac irhere che red
halt oF che Paper appeared distinct, the bler halt appeared
contused, (0 that che black Lines drann uxon ic could
scarce be seen; and on che contrary where che bler halt
appeared most dictinct che red halt appeared contusea, 10
chac che black Lines uxon ic ivere scarce visible. And be-
cireen che evo places irtrere chese Images appeared dictinet
chere as che distance ot an Inch and a halt: the distance
Ot che wrhire Paper From che Lens, Wrhren che Image ot che
red halt os the coloured Paper appeared most dictinet, bc-
ing orcater by an Inch and an halt chan che distance ot che
lame whire Paper from che Lens irtien che Imagc ot che
blen hale appeared most distinct. In like Incidences there-
Fore ot the bler and red upon the Lens, the bleur Was re-
Fracted more by che Lens chan che red, (0 2S EO COnVerOC
Cooner by an lrch and an halt, and cheretore is more retran-
sible.
Eig. 12. Illustration. In che Pveltch Fieure, DP Signities the co-
loured Paper, DO the bler halt, FP che red halE, MIW
che Lens, HI) che ihice Paper in chac place wrhere the red
halE Wirh ies blacke Lines appeared dictinct, and hi che larme
Paper in chat place irhere theblew halt appeared distinct.
lhe place hi was nearer eo he Lens MN rhan che place
TIJ by an tuch and an halt.
Scholium.

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Scholium. The lame chinos succeed normichstandinq chac
Tome oF che Circumstances be raried: as in che trst Px-
periment wrhien che Prism and Paper are any nars inclined
co the Horizon, and in boch irtien coloured Lines arc
drann upon verr black Paper. Buc in che Delcription ot
chele Experimenes, Phare sec donn Cuch Circumstances
by irhich cither che Phaenomenon miohe be rendred more
conspicuous, or a Norice mighe more casily ery them, or
by irtrich I did ery chem ontr. The Came chins Ihare
otren done in the follomins Experiments: Concerning all
irhich chis one Admonition may luffice. Nou From chese
Fixverimenes ic Follons noc thac all che Lighe ot che blen
is more Retranoible chan all che Lighe ot che red; FOr
boch Lighes are mixed ot Rars differeney Retrangible,
Sothat in the red chere are Lome Rays noc lels Retrangible
than those ot che blen, and in che blen chere are lome
Rars noc more Retransible chan thole ot thered; BUE
chese Rays in Proportion co che Whole Lighe are buc ferr,
and serve co diministr che Frene of the Experimene, bue
are noc able co destror it. For il che red and blen Co-
lours ivere more dilure and weak, che distance ot cheIma-
ses mould be lels than an lnch and an halt; and it they
vere more intense and Full, that distance mould be greater,
25 will appear hereatter. Phele Experiments may suftice
For che Colours ot Dacural Bodies. For in the Colours
made by che Retraction ot Prisms this Propolicion will
appear by che Experiments which are no to tollon in che
nexe Provosition.

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P ROP. II. THCOT. TI.
The Lighe of the Sun consists of Pays differently Refrancible,
The PrOOF by ExpCTImeNES.
Exper. 3.  N a very dark Chamber ac a round hole aboue
B onc chird pare ot an Tnch broad made in che
SAnE oF a Nindom I placed a Class Prism, whereby che
beam ofthe suns Lighe irhich came in ac chac hole miohe
be retracted upvards corard che oppolice Wall oF che
Chamber, and there form a coloured Image ot the
Sum. Thc Axis oF che Prilm (thac is che Line passino
chrouoh the middle ot che Prilm trom one end ot ic tO
che ocher end Parallel to the edoc of che Retracting AnelC)
vas in chis and che Collowins Experimenes perpendicular
to the incidene Rars. AbouE ehis Axis I curned che PrisM
Plomly, and Par che refracted Liohe on the WaII Oc cO-
loured Image ot the sun Arst to descend and then eo a(
cend. Betreen che Descent and AIcent wrhen che Image
seemed Scationarr, IRopE che Prilm, and fixc ic in chat
Polture, chac ic Thould Be mored no more. For in thac
posture the Retractions of che Liohe ac the erro sides ot
che Retractins Angle, chac is ac che entrance of che Rays
into che Prism and ac cheir goins out oF it, vere equal eo
one anocher. S0 allo in ocher Lixperimenes as otcen a5 L
rould hare che Retractions on Boch sides ehe Prismm co be
equal to one anocher, Inored the place utere the Imase
ot the sun formed by che retracted Lighe Aood Aill bC-
LWreen IES cro contrarY Mocions, in the common Perioc
OF its proorels and corels; and nhen che Imaxe fell upon
thac place, Imade tast the Prilm. And in chis pocture, as
et

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the most conrenient, ie is eo be understood thac all che Prisms
are placed in che follorinu Experimenes, untels where lome
ocher polture is described. The Prilm cheretore beins pla-
ced in chis posture, I lec the retracted Liphe Fail perpendi-
cularty uxon a Steet oF irhice Paper ac the opposItE W aIL
ot the Chamber, and obserred che Figure and Dimensions
OF the Solar Imase Formed on the Paper by chac Lipht.
Phis Image wras Oblono and noc Oral, bue cerminared
rich vo Rectilincar and Parallel Sides, and cvo Sermi-
circular Ends. On ies Sides ic was bounded precer distinctr,
buc on ics Fnds very contuleds and indistincly, ehe Lighe
chere decaxins and vanistns by deorees. The breadch ot
this Imase anlivered co che Suns Diameter, and iras about
erro tnches and the cioheh pare oF an tnch, including che
Penumbra. For thelmage iras ciphreen Fcet and an halt
distane from che Prism, and ac chis distance chac breadch it
diministred by che Diameter oF che hole in che W indo-(BUE,
chac is by a quarcer oF an Inch, subcended an Angle ac che
Prilm oF about halt a Deorec, ertrich is che SuInS apPareHE
Diamecer. Buc che lensch ofthe Image was abouc ren Inches
and a quarrer, and che lenoch of che Rectilincar Sides about
eiohe Inches; And che retractine Anele ot che Prilm wrhere-
by (0 great a lenoch vas made, ias 64 deor. Wich a lels
Angle che lenech ot the Image was lels, che breacth re
mainins che Came. IF che Prilm as turned about its AZIS
thac War irhich made che Rays emerse more obliquolY Out
et ehe second retractinq Surtace ot the Prilm, che tinase loon
became an Inch or ermo longer, or more; and il che Prilim
as turned about the concrarr may, (0 as eo make che Ra75
fall more obliquely on the first retracting Surtace, chelmage
Coon became an Tuch or ero Phorrer. And cheretore in cry
ino chis Experimene I as as curious as I could be in pla-
cing che Prilm by che aborementioned Rule exactly in
TuC

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Such a posture chac che Retractions ofthe Rays at cheir emer-
sence out ot che Prilm miehe be equal co chac ac cheir inci-
dence on it. This Prilm had lome Veins runnino alone
richin che Class trom onc end co the ocher, which (cac-
cered lome oF che Suns Lighe irregulartr, buc had no sen
sible effect in encreasine che lenorh ot the coloured Spec-
CrUMI. For I eried che lame Experiment ich ocher Prilms
rich che same succels. And parcicularly wich a Prim
wrtrich seemed Erec From such Veins, aud ihose retractins
Angle ras 62 Dcorees, I Found che lenoch of che Image 93
or 10 Tuches ac che distance of 18= Feec trom che Prism
the breadch of che hole in che Windon- Phuc being = OF an
Tnch as betore. And because ic iS Ca(C EO COMMIE 2 mi-
Aakce in placing che Prilm in ies due polture, I repeated
the Experiment tour or tire cimes, and alvars Found che
lenoch ot the Image chac ihich is sec down abore. Wich
anocher Prism oF clearer Class and betrer Pollistr, which
scemed trec trom Veins and irhole retractins Angle was
63: Deorees, che lenoch ot this image ac che lame diltance
oF 18 = Feet as al(o aboue 10 Inches, Or 103. Berond
chele Mlealures for abour ? Or ? ot an Inch ac cicher end oF
the Spectrum the Lighe ot che Clouds scemed ro be a licele
tinged rich red and riolet, buc lo verr tainely chac I suspe-
eted thac rincture mishe cither whollr or in great mealure
arise trom Lome Rays ot the Spectrum scaccered irre-
oularly by some inequalicies in che substance and Polist
oF che OlaIs, and cheretore I did noc include ic in chele
Nealures. Nom the disterent Magnicude ot che hale in
cheWindo-Phur, and differene chicknels of che Prilm Wwhere
ehie Rars passed chrough ic, and different inclinations of che
Prim eo the FTorizon, made no sensible chanoes in che
lenoch ot che Image. Neicher did che differene macter ot
ehe

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che Prims makie any: For in a Vessel made of polistrec
Plates oF Class cemented cogether in the Chape ot a Prisir
and Alled wich Water, chere i5 che like SuCCeIS OFFMC FX-
periment according co che quanciey ot che Retraction. IE
is furcher co be obserred, chat che Rays vene on in riohe
Lines trom the Prism eo che Image, and cheretore ac cheir
very going out ot the Prilm had all chac Inclination eo
one anocher trom irhich che lenoch ot the Image pro-
ceeded, chat is the Inclination ot more than tro DCorces
and an haIt. And vec according to the Lars oF Opticks
vulsarty receired, they could noc possibly be lo muchi in-
clined to one anocher. For let FO reprelent cheWindon- Fir. 13
PhuE, F che hole made cherein chrouxh irtrich a beam of the
Suns Lighe as transmitted inco che darkned Chamber, and
ABC a Friangular Imaginary Plane whereby the Prism is
seioned to bc cur erantrerllr chrouph the midale ot che
Lighe. Or il rou please, let AB C represene che Prism ic
selF, looling directly cormards che Spectators Eye wich ies
nearer end: And lec X Y b0 the Sun, MI N thePaper upon
irtrich ehe solar Image or Spectrum is cast, and P Y thc
Image ic selF whose sides corrards V and W are Rectili-
near and Parallel, and ends corrards P and T Semicir.
cular. YKTIP and ZL F T are thetro Rays, the ErA
ot which comes from che lorver part ot the Sun co. che
higher part of che Image, and is retracted in the Prilm ae
K and II, and che latrer comes from the higher part ol
the sun eo che lorver part ot che Image, and is retracted
aEL and J. Since the Retractions on boch sides the Prilm
are cqual co one another, thac is che Retraction at R equal
co the Retraction at T, and che Retraction at L equal EO
che Retraction ac FI, (0 chac che Retractions ol the inci-
dene RaYS ac K and L taken together arc equal to che
Retractions oF che emergent RayS ac II and J caken toge-
chex.

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cher: ic Follons by addins equal chines eo equal chines.
chac the Retractions ac R and HI caken together, are equal
co che Retractions at J and L caken togecher, and there
Fore che ero Rays beins equally retracted have che lame
Inclination eo one anocher alcer Retraction wrhich cher had
betore, chac is che Inclination oF halF a Dcoree ansiverine
eO EHe SUMS DIAMCCCF. FOr (0 great vas the Inclinacion
oF che Rars co one anocher betore Retraction. S0 then,
the lensch ot chelmage P P rould br che Rules oF Vul-
sar Opticks subrend an Angle oF halE 2 Dcorce ac the
Prism, and by consequence be equal to che breadch vn:
and cheretore che Image rontd be round. Thus ic would
bC WerC thC EVO RayS ZL TT and YK FIP and aIl che
rest irtrich Form che Image P n TV, alike Retranoible.
And cheretore secinu by Experience ic is Found chac che
Image is noc round bue aboue tire cimes longer chan
broad, che Rars irhich goins eo che upper end P ot che
Image sufter che orearest Retraction, mustbe more Retran-
eible chan thole irhich g0 co che lorver end Y, untels che
inequalier ot Retraction be casurl.
This Image or Spectrum P Piras coloured, being red
dc ies least retracted end T, and violet ac ies most retracted
end P, and vellon orcen and bler in che incermediate
Spaces. Which aorees rich che first Propolition, thac Liohes
irtrich difter in Colour do also differ in Retrangibilier.
Phe lengch ot che Image in che Foregoins Experients L
mealured Crom che Faincest and ourmost red ac one end, e0
che faincest and ouemost ble ac the other end.
Exper. 4. In che suns beam intich ras propagared in-
coche Room chrouph che hole in che Windo- PhUE, aE
che distance ot some Fece From the hole, Iheld che Prilm
in such a polture chac ies Aris miche be perpendicular eo
chac beam. Then I looted chroush che Prilm upon che
hole.

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hole, and curmins che Prism co and Fro about its AXiS EO
makce chelmage of the hole alcend and descend, irhen be-
circen its truo contrarr Morions ic secmed Cationary, l
Rope the Prim chac che Retractions on Boch sides ot che
retractins Anele mighe be equal eo cach ocher as in che
Former Experimene. In this Sicuation of che Prism riew-
ins chrouoh ic che Caid hole, I observed the lenoth ot ies
retracted Image to be manr cimes orcater chan ies breadeh,
and chac the most retracted pare chereot appeared violet,
the least retracted red, the midale pares ble orcen and
vellon in order. The Came ching happened when I rc-
mored che Prilm out ot the suns Lighe, and looled
chrough ic upon che hole Chining by che Lighe of che
Clonds berond ic. And rec il che Retraction vere donc
regularlr accordins to one certain Proportion of the Sines
ot Incidence and Retraction as is vulsarly supposed, chc
retracted Image oughe eo hare appeared round.
S0 chen, by chese tro Experimenes ic appears thac in
equal Incidences chere is a considerable inequalier of RC-
Fractions: Buc Whence chis inequaliey arises, Wrhecher ic be
that Fome oF che incidene RayS are retracted more and
others lels, constanely or by chance, or thac one and che
Tame Ray is by Retraction disturbed, Pharcered, dilaced,
and as ic vere (plic and spread inco many dirergine Rays,
25 Grimaldo supposes, does noc rec appear by chele Lxperi-
menes, buc rill appear br chole chac Follon.
Exper. 5. Considerins cheretore, chac if in che chird PX-
perimene che lmaxe oF che Sun Phomld be dravn oue inco
an oblons torm, cither by a Dilatation oF erery RaY, Or
by any ocher calual inequalier of che Retractions, the lame
oblone Imase ould by 2 second Retraction made Side-
ays Be deamn ouc as much in breadch by che likee Dila-
cation of che Rays or ocher casual inequalier ot che Re-
tractions

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T2
Fractions Sidemays, I eried whac vould be che Ffects ot
Such a second Retraction. For chis end Pordered all chings
as in che chird Fxperimene, and chen placed a second Prilm
immediatel atcer che tirst in a cross Posirion eo ic, thac ic
mighe again retract che beam of the suns Liphe which
came eo ic chrough che tirst Prilm. In che first Prilm ehis
bcam as retracted uprards, and in che second Sidevars.
And I Found chac by che Retraction oF the second Prilm
chebreadch ot che Image mas noc increaled, buc ies supe-
rior pare which in che trst Prilm Cuffered che greater Re-
traction and appeared riolet and blen, did again in che
second Prilm Cutter a greacer Retraction chan ies inferior
parc, wrhich appeared red and vellon, and chis wichoue
any Dilacion ot che lmage in breadch.
Illustration. L et S represent che Sun, F the hole in the
Windor, ABC che first Prilm, DHI che second Prism, Y
the round Image ot che sun made by a direct beam ot
Liohe when che Prisus are catcen awar, P Y che oblone
Image oF che sun made by chac beam palsins chrouoh che
First Prism alone irhen the sccond Prilm is takcen avar, and
pe che lmage made by che crols Retractions oF boch
Prilms cogecher. Now it che Rays irtrich cend cowards
the sereral Poines oF che round Image Y ivere dilared and
spread by che Retraction oF che frst Prilm, (0 chac they
Thould noc any longer 80 in single Lines ro lingle Points,
but chat everr Ray beins splic, Chatrered, and changed
From a Linear Ray co a Superticies of Rays diveroino
From che Poinc of Retraction, and lying in che Plane ot
che Angles of Incidence and Retraction, cher Chould
90 in chole Planes to (0 mans Lines reachins almost
trom one end ot che Image PP eo che other, and it
thac Image Phould thence become oblons: thole Rays
and chei lereral pares cendins conards the sereral Points ot
the
14

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che Imase P T ouohe to be again dilated and spread Side-
rays by che cransverse Retraction oF the lecond Prilm, (9
25 co compole a toursquare Imasc, such as is reprelented
aC I. For che berrer understandinq of wrhich, lec the Image
PT be distinonilhed into AVC Cqual PATES POR, RORL,
LRSMI, NISVN, NVT. And by che lame irregularitr
chat che Orbicular Lighe Y is by che Retraction ot che Arst
Prilm dilared and drann out inco a lone Image P P, chc
che Lighe P OK which cakes up a space ot the lame lenoth
and breadch rich che Lighe Y oughe to be by che Retra-
ction et che second Prism dilaced and dranon oue into che
lone Image r g kP, and che LighEK O R L into the lonp
Image kgrI, and the LighES L RR SMI, NISV N, NV T
into (o manr ocher lons Images lr5 m, msVn, nV +I; and
all chese lons Images vould compose che Fourlquare Imasc
I. Thus ic oughe to be ivere crery Ray dilaced By RC-
traction, and spread into a criangular Superticies of RaYS
direroins from che Point of Retraction. For che lecond
Retraction vould spread che Rays one ay as much as the
trst dorh anocher, and (0 dilace che Image in breadth 25
much a5 che tirst doch in lenech. And che Came chins
oughe co happen, vere lome Rays calually retracted more
chan ochers. Buc the Fvene is ocherwise. TheImage P I
was noc made bronder by the Retraction ot che second
Prilm, buc ontr became oblique, 25 tis reprelenced ac pt,
itS uxper end P beins by che Retraction eranllared 10 2
oreater distance chan ies lover end T. S0 chen che Liohe
which ene cormards che upper end P oF che ImasC, Wa5
(aE equal Incidences) more retracted in che second Prilm
than che Lighe wrhich cended corrards che lover end I.
chac is che ble and rioler, chan the red and rellor; and
cheretore mas more Retrangible. Phe Came Liphe was by
the Retraction oF che first Prim cranllated Furcher trom the
Place

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place Y eo which ic cended betore Retraction; and there-
Fore suffered a5 well in che Airst Prilm as in che second à
oreater Retraction chan the rest of che Lighe, and by con-
lequence was more Retransible chan che rest, even betore
its incidence on the Arst Prilm.
Sometimes I placed a chird Prilm atcer the lecond, and
Cometimes also a Fourth atcer che chird, by ait irhich che
Imagc miohe bc otren retracted sidermars: buc che Rays
erhich ivere more retracted chan the rest in che Airst Prilm
ivere alsomore retracted in aIl the rest, and chac without
any Dilararion of the lmage sidemars: and cheretore thole
Rars For cheir constaner ot a greater Retraction are de-
serredy repured more Retrangible.
ie. 15. Buc chac che meanins of chis Experimene may more
cleartr appear, ic is to be considered chac che Rays wtrick
are cquallr Retransible do Fall upon a circle ansivering to
chesuns Disque. For this iras proved in che chird Experi-
ment. By a circle I understand noc here a pertect Ceo-
metrical Circle, buc any Orbicular Figure whose lenoth is
equal ro its breadeh, and wrhich, as to sense, mar scem
circular. Let cheretore AO reprelent the circle wrhich all
che most Retransible Rays propasaced trom che whole
Disque ot the sun, vould illuminace and paint uxon the
oppolice Wall it chey vere alone; LL che circle which aI)
the least Retranoible Rars ould in like manner illuminare
and paine it cher irere alone; BHI, CT, DR, che circles
wrhich (o manx intermediare Pores ot Rars rould succel-
hvely paint upon che Wall, it cher iere linglr propasaced
trom the sun in succeltire Order, che rest being alivars in-
tercepted; And conceire chac there are other intermediare
Circles rithout number irtrich innumerable ocher incer-
mediare Corrs ot Rays ould successirely paint uxon che
nall it che sun Chould succetsirely emic erery POrE aparE.
And

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And seeing the Sun emies all chese sOrES ac oncC, chey must
all cogccher illuminace and paine innumerable equal cir-
cles, oF allirhich, being according eo cheir degrees oF RC-
Fransibilier placed in order in a continual series, that ob-
lons Spectrum P P is compoled irhich I delcribed in the
chird Experimene. Nou it che suns circular Image Y
irtrich is made by an unrefracted beam ot Lighe was by
any dilatation ot che single Rays, or by anr ocher irregu-
larier in the Retraction ot the Arst Prilm, conrerted into
che Oblono Spectrum, P V: then oughe erery circle AO,
BII, C J, exc. in thac Spectrum, by che crols Retra-
ction ot che second Prilm again dilatins or ochermile
Scarrering che Rays as before, to be in like manner drawn
ouc and eranstormed into an Oblons Figure, and chereby
the breadch of the Image P P ould be no as much aug-
mented as the lenoth ot che Imase Y was betore by che Re-
Fraction ot the first Prism; and chus by che Retractions ot
boch Prisms cogether ould be formed a Foursquare Figure
pr +7 25. I described abore. Wheretore Cince the breaden ot
the Spectrum P T is noc increaled by che Retraction Side-
Ways, ic is cerrain chac che Rays are noc split or dilaced, Or
ochermars irregularty scacrered by chac Retraction, buE
thac erery circle is by a regular and unitorm Retraction
eranclate d entire into anocher place, as che circle AC by
the oreatest Retraction into che place ag, the circle BII by
a lels Retraction inco the place bh, the circle CF bY 2 RC-
Fraction sill less inco the place ci, and 50 oF che rett; by
Which means a nem Spectrum pt inclined co che FOrmer
D T is in likce manner compoled ot circles lyins in 2
riohe Linc; and these circles must be ot che same bignels
rich the Former becanse the breadths ot aII che Spe-
Arums Y, P T and pF ac equal distances trom the Prisns
are equal.
lCO1L

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I considered Furcher chac by che breadch ot the hole F
chrouoh wrhich che Lighe enters into the Darke Chamber,
there is a Penumbra made in che circuie ot che Spectrum
T, and chac Penumbra remains in the rectilinear Sides ot
the Spectrums P Pand pt. I placed cheretore ac char hole
2 Lens or Object. glals ot a l’elelcope itich miohe cast
che Image ot the sun distinetly on Y wichout any Penum-
bra ac aIl, and Found chac che Penumbra ot the Rectili-
near Sides oF the oblons Spectrums P T and pt vas allo
cherebr cakcen arar, (o chac chole Sides appcared as di-
Rinctir detired as did che Circumterence ot the trst Imaoe
Y. Thus ic happens it che Olass of the Prilms be free
trom veins, acd cheir Sides be accuratetr plane and vell
polished wichoue chole numberlels vares or curles irtrich
ulually arise trom Sand holes a licele smoothed in polist-
ino wich PuteY. IE ehe Class be ouly well polished and
Frec trom reins and che sides noc accurarely plane bue a
licele Conrex or Concare, 25 ic trequeney happens; rec
may chethrec Spectrums Y, P I and pt manc Penumbras,
buc noc in equal distances trom che Prisms. No From
this mane et Penumbras, Ikneu more certainty chac every
one ot the circles as retracted accordine co lome most
regular, uniform, and constane lar. For il chere ivere
any irregularier in cheRetraction, che riohe Lines AC and
OL irhrich all che circles in the spectrum P Y do touch.
could noc br chac Retraction be translaced into che Lines
ae and el as dictinet and sraiohe as they vere betore, buc
chere mould arise in chose cranslated Lines Lome Penubra
or croolcednels or undulation, or ocher sensible Percurba-
eion contrary ro whac is tound by Experience. Whaclo-
ever Penumbra or Percurbation Bould be made in che
circles by the cross Retraction ot the sccond Pris, aII
that Penumbra ox Perturbation rould De conspicuous in
che

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cherighe Lines a c and sl which couch chose circles. And
cheretore lince chere is no such Penumbra or Percurbation
in chose righe Lines there must be none in the circles.
Since che distance becwreen those Pangents or breadeh ot
che Spectrum is noc increased by che Retractions, the Dia-
meters ot che circles are nor increased chereby. Since thole
l’angenes continue eo be righe Lines, every circle irhich
in the Arst Prilm is more or less retracted, is exactly in
the Came Proportion more or lels retracted in the second.
And secing aII chele chines continue co succeed atrer the
lame manner wrhen che Rays arc axain in a third Prilm,
and apain in a Fourth retracted Sidemars, ic is cvident thac
the Rays oF one and the lame circle as co cheir degree ot
Retrangibiliey continue alirars Uniform and Flomogeneal
toone anocher, and char chole ot sereral circles do differ
in deoree oF Retransibilier, and chac in lome certain and
constane Proportion. Which is theching lWras eo prove.
Lhere is vet anocher Circumstance or cvo ot this PX- Fig. 16.
Periment br which ic becomes Aill more plain and con-
vincino. Lec che second Prism D FT be placed noc imme-
acely alter atcer che Arst, buc at Pome distance from it;
Suppole in che mid.-var betireen ic and the W’all on which
the oblons Spectrum PT is cast, (0 chac che Lighe From
the first Prism may Fall uxon ic in che form ot an oblono
Spectrum, 21 Parallel co chis second Prism, and be retracted
Sidewars co torm che oblons spectrum pt upon che WV alI.
And ron will find as betore, chac chis Spectrum pt is in-
clined cochat Spectrum P P, irhich che Frst Prilm FOrIMS
alone rithoue che second; the ble ends P and p being fur-
cher distane from one anocher chan ehe red ones T andt,
and by consequence chac che Rars wrhich 90 to che blen
end oF chelmage 27 ana irhich cheretore sufter che grearest
Retraction in che first Prilm, are again in che second Prilm
more retracted chan che rect.
The

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The Pame ching Pery d also by lecting che suns Lighe
into a darke Room chrough erro licele round holes Fando
made in che indon, and wich erro Parallel Pritns ABC
and aβ3 placed ac those holes (one at cach) retractine
chose erro beams of Lighe eo che oppolire WVaIl of che
Chamber, in such manner thar che cvo colourd Images
P T and mn irhrich cher chere painced vere jorned end co
end and lay in one sraighe Line, the red end Y oF chc
one couching che blew end m ot che other. For it chele
evo retracted beams ivere apa in by a chird Prism D II pla-
ced crost co the ero ArI, retracted Siderrars, and the Spe-
ctrums cherebr cranslaced to lome other pare ot the Wall
ot che Chaber, suppole the Spectrum PI +o pF and
the Spectrum MXIcomn, chese cranslaced Spectrums pt
andmn vould noc lie in one sraiohe Linc wich their ends
conciouous as betore, buc be broken oft from one anocher
and become Parallel, the bleur end ot che lmage mnbeing
by a orcacer Retraction cranslaced Carcher From its Former
place MT, chanche red endt of che ocher Imase pt trom
che tame place MIT itrich purs che Propolition past di-
spute. And chis happens rhether che chird Prism D HIBC
placed immediacely atcer che cwo First or ac 2 oreat distance
trom them, (0 chac che Lighe retracted in che ero Arst
Prisns De cicher irtrice and circular, or coloured and ob-
lono when ic Falls on che chird.
Fxper. 6. In che midele ot ero chin Boards L made
round holes a chird part ot an Inch in Diameter, and in
the Windon. Phuc a much broader hole, beino made to lec
inco my darkned Chamber a larse beam ot che Suns
Lighe; I placed a Prilm behind che Strut in chat DeaM EO
retract ic corards che oppolice Wall, and clole behind che
Prism I Exed one ot che Boards, in luch manner chac che
middle of che retracted Lighe mighe pals chrouoh che hole
made
Fig. 17.

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made in ic, and che rest be intercepced by che Board.
Then ac che distance ot aboue evelre Feccfrom the Arst
Board I Axed che orher Board, in such manner chac che
midale of che refracted Liphe Which came chrouoh che hole
in che first Board and fell upon che opposice WalI mighe
Pals chrouch che hole in ehis ocher Board, and che rest bC-
ins intercepted by che Board miphe paint upon ic theco-
loured Spectrum oF the Sun. And close behind this Board
I fixed anocher Prism eo refract che Lighe irtich came
chrouph che hole. Then P recurned spccdily eo che Rrst
Prilm, and br curming ic Rowtr to and tro aboue its AXis,
Icaused che Image irhich Fell upon che second Board eo
more up and donn uxon chac Board, chac all IES PaTES
mighe succeslirelr pals chrough che hole in thac Board and
Fali uxon che Prism behind ic. And in che mean time, L
noced che places on che oppolice Wall eo irhich that Lighe
aEcer ies Retraction in che second Prism did pals; and by
che difference ot che places I Found thac the Lighe irtrich
being most retracted in the first Prilm did 90 eo the blev
end ot chc Image, was 2gain more refracted in che second
Prilm chanthe Liohe wrtrich wene coche red end et chat
Image, Wrhich prores as well che Airst Proposition a5 the
second. And ehis happened whether the Axis of che emo
Prilms ivere parallel, or inclined ro one anocher and eo che
tlorizon in any siren Angles.
Illustration. L ec F be che ide hole in the Windo-PHUE, Fic. 18
chrouoh irhich che sun Phines upon che first Prilm ABC,
and lec the retracted Lighe Fal uxon the midale ot che
BOard DC, and che middle pare of thac Lighe upon che
hole O miade in che middle oF thac BOard. Lec this Era-
jected pare oF the Liohe fall again upon che middle of the
second Board de and chere paine such an oblons coloured
mage of the sun as as described in thethird ExperimenE.

## Folio 32 — 1677894601:0042
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By curnino che Prilm ABC. RoIy eo and Fro aboue its
Axis this Imase will be made ro more ux and donn che
Board de, and by chis means allits parts trom onc end to
the ocher mar be made eo pals successively chronoh the
hole s which is made in the middle of chac Board. In the
mean while anocher Prilm ab c iS to bc Axed nexe atrer
chac hole e to retract the crajected Lighe a second cime.
And chele chines beins chus ordered, l marked che places
UI and NV oF che oppolire Wall upon which the refracted
Lighe Fell, and Found chac whils the erro Boards and second
Prilm remained unmored, chole places by curmins the trst
Prilm abour ies Aris ivere changed perperuallr. For When
thc lorver pare of che Lighe which tell uxon che second
Board de Was cast chrouoh the hole e ic went to a lorver
place M on che WVaII, and when che hioher parE OF ChAE
Liphe vas cast chrough che lame hole g, ic vent ro a higher
Place NI on che W all, and when any incermediare pare ot
he Liohe Wras cast chrough chat hole ic venero lome place
on che W all becircen MI ard H. The unchanged Policion
OF che holes in che Boards, made the Incidence ot che Rays
lipon che second Prilm to be che lame in aIl cales. And
vec in chac common Incidence lome oF che Rays ere more
retracted and others lels. And chole ivere more retracted
in ehis Prilm erhich by a greater Retraction in the AirI
Prilm ere more turned out ot the maz, and cheretore For
cheir constaney ot beins more retracted are deserredly cal-
led more Retrangible.
Exper. 7. Ac cuo holes made near one anocher in my
Windo-Phuc I placed cro Prisims, one ar cach, irhich
mighe cast upon che oppolire Wall (atter the manner ot
the chird Experimene) tro oblons coloured Images ofche
Sun. And ac a licele distance trom che Wall I placed a
lons Pender Paper wich straiohe and Parallet edges, and
ordered

## Folio 33 — 1677894601:0043
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ordered the Prisms and Paper (0, chat che red Colour ot
onc Image mighe Fall directly upon one hale ot the Paper,
and che violet colour ot the ocher Image uxon the ocher
halt oF che Came Paper; (0 chat the Paper appeared oF cwo
Colours, red and violet, much afcer che manner of che
Painced Paper in che first and second Experimenes. Then
rich a black Cloch I corered the W all Behind the Paper,
chac no Lighe miphe be reflected From ic eo dicturb che
Experimene, and riemino che Paper chrouph a chird Prilm
held parallel co ic, I Pa chac halt ot ic nrhich mas illumi-
naced by che Violetliohe co bc dirided From che other
hale by a orcacer Retraction, especially wrhen l vene a g00d
ay oH Erom ehe PapeT. FOT When I viewed iC EOO RCaL
at hand, che ero hals of the Paper did nor appear fully
dirided Crom one anocher, but seemed contiguous ac one
oF cheir Anoles likce che painted Paper in che trst Expe-
riment. Which also happened irhen the PapeF WaS EOO
broad.
Somecimes instead ot che Paper J uled a whice Thred,
aud chis appeared chrouph che Prism divided inco enO P2-
rallel Threds as is reprelented in che ioch Pigure, Where Fiz. 19.
DC denores the Thred illuminaced wich violet Lighe
From D eo F and wich red Liohe From F c0C, and de f8
arc che pares of the Thred seen by Retraction. IF one halt
oE che Thred be constanely illuminaced wich red, and che
ocher hals be illuminaced rich all che Colours successirel,
Cirtrich may be done by caulins one of che Prisms co be
cured abouc ues Axis whilse che ocher remains unmoved)
ehis ocher hale in viemino che Thred chrouxh che Pribm.
ill appear in a continued righe Linc wich che Arst haIF
Wwhen illuminaced ich red, and begin co be a licele diri-
ded from ic when illuminated rich Orange, and remove
Furcher trom ic irhen illuminaced wirh Vello, and Ailt
Furcher

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-
turcher when wich Crcen, and Further when wich Blewr, and
50 yec turcher oH when illuminated rich Indigo, and tur-
chest wrhen rich decp Violet.. Which plainly Chews, chat
che Liohes oE several Colours are more and more Retran-
sible one than anocher, in chis order oE cheir Colours, RCd,
Orange, Tello, Crcen, Blewr, Indiso, decp Violec; and
(0 prores 25 ell che tirst Propolition as the second.
I caused allo che coloured SpectrumS P Y and MIW
made in a dark Chamber by che Retractions ot emo Prilms
to lre in a rixhe Line end eo end, 25 ras delcribed above
in che fitch Experimene, and rieming chem chrouoh a chird
Prilm held Parallet co cheir lenoth, cher appeared no longer
in a riphe Line, bur became broken trom one another, 25
ther are represented at pt and mn, the riolet end m of che
Spectrum mn being by a greater Retraction translated
Furcher From ies former place MI. Tchanthe red end t oF che.
Other Spectrum pt.
Fio. 20. Iturcher caused chole cuo Spectrums P T and IN tO
become co.incident in an inverted order ot cheir Colours,
che red end ot cach Falling on the violet end ot the ocher;
25 cher are reprelented in the oblons Figure P TMIN;
and ehen rieminq chem chronoh a Prilm D) HI held P’aral-
sel cocheir lenoh, chey appcared noc co- incident as when
viered wich che nakced Ere, buc in che form et evo di-
Rinet. Spectrums pF and mn crostns one anocher in che
middle atter the manner ot che lecter Z. Which CheWVS
chac the red ot che one spectrum and violet ot che orher,
erhich ivere co. incident ac P N and VIY, beins parted
trom one anocher by a greater Retraction oF the violet tO
p and m chan ot the red co n and t, do differ in degrees ot
Retrangibilier.
lilluminated also a licele circular piece of white P’aper
all over rich che Liglus ot boch Prilms incermixed, and
Whem
F1g. 17.

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wrhen ic was illuminated wich the red ot one spectrum and
decp violet oF che other, (0 as by the mixture of thole
Colours to appear all over purple, I riered che Paper,
first ac a less distance, and then ac a oreater, chrouon a
chird Prilm; and as I ene from che Paper, che retracted
lnage chereot became more and more dirided by che un-
equal Retraction of che euo mixed Colours, and ac lenoth
parted into ruo dictinet Images, a red onc and a riolet onc,
Whereot che violer as furthest from che Paper, and there-
fore Cuffered che prearest Retraction. And irhen thac Prilm
ac the Windon which cast the violet on the Paper WaS ta-
Len avay, che violet Image disappeared; but when the ocher
Prism ras calcen avar che red ranistred: wrhich Phews chac
thele evo Tmages ivere noching else chan che Lighes ot che
eiro Prilms rhich had been intermired on che purple Pa-
Per, buc ivere parted again by their unequal Refractions
made in the chird Prism chrouph wtrich che PapeF WaS
vierred. This also ras obserrable chac it one of the
Prisins at che Windor, suppose thac ihich cast che violet
On ChC PapeF, WaS Furned abOVE iEs AXis eo malce aII che
Colours in this order, Violet, Indigo, Blew, Orcen, Vel-
loir, Oranse, Red, Fall successirelr on the Paper from chat
Prilm, che violet lmase changed Colour accordinely, anc
in changins Colour came nearer co the red onc, uneil irhien
ic ras also red cher boch became tully coincident.
Iplaced allo erro paper circles very near one anocher,
che one in che red Liehe ot onc Prism, and che ocher in
the violet Liohe ot che ocher. The circles vere cach ot
ehem an Tuch in Diamecer, and behind chem che WV aII Was
dark chac the Fxperimene miphe noc be disturbed by any
Liohe coming trom chence. These circles chus illuminared,
lriemed chrouoh a Prism P0 held chac che Retraction miohe
bemade corrards che red circle, and as I wene from them
chey

## Folio 36 — 1677894601:0046
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they came nearer and nearer cogecher, and ac length be
came co-incident; and atcermards trhen Lvenc sil Furcter
Of, cher parced again in a contrary order, che violet b7 2
orcacer Retraction beins carried berond che red.
Exper. 8. In Sumer wtien che SunS LIGHE UTES CO
besrongest, Lplaced a Pritur ac ehic hole oF che Windon-
MHHE, 25 in che chird EXPCTIMCHE, vec (O chac ies AXis iohE
be Parallel eo the Axis oF che Nortd, and ac che opposite
Wall in the Suns refracted Liohe, I placed an open BOOL.
Phen coins six Fecc and erro Inches From cne BOOL, L
placed chere che aborementioned Lens, by vrhich che Liohe
rehlected From. the B00k miohe be made c0 converse and
incet 2gain ac che distance ot sIX Feer and erro Inches be-
hind che Lens, and chere paine che Species ot che BoOk
upon a Pheet ot rrhice Paper much afcer the manner of che
second Experiment. The Book and Lens beino made Falt.
Inoced che place vrhere the Paper rras, vrhen che LCrcerS
oF che Book, illuminaced by the Fullest red Lixhe of che
Solar Image Falline uxon ic, did cast cheir Species on chac
Paper most distinctly; And chen I stay d eill by che MIO-
cion of che sun and consequent Morion ot his Image on
the Bo0k, allche Colours From thac red eo che middle ot
che blem passd over chose Leccers; and wrtien those L ccrers
vere illuminared by chac bleu, I noced again the place ef
he Paper when cher cast cheir Species most distinctly upon
ic: And IFound chac this las place oF the PapeF WaS RCaTeF
co the Lens chan ies Former place by about erro Tnches and
an halt, or erro and chree quarters. So much looner chere-
Fore did che Lighe in che riolet end ot the lmage by 2 grea-
cer Retraction converge and meet, chan che Liphe in che
red end. BuE in eryino chis che Chamber wras as dark 25 I
could make ic. For it chese Colours be diluced and weak-
ned by chemixcure ot ans adrencicious Ligte, che distance
Neer

## Folio 37 — 1677894601:0047
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becrveen che places oF che P’aper willnor belo ereat. This
distance in the lecond Exporimone ivhere che Colours ot
nacural Bodies aere made use ot, ras buc an Inch and a
halt, by realon ot cheimperlection of chole Colours. Ilere
in ehe Colours ot che Prilm, which are manifestly more
Fuil, incense, and lively chan chose ot nacural Bodies, the
distance is erro Tnches and chrec quarters.. And ivere che
Colours Aill more FuII, I question noc bur chac che di-
Aance mould be considerably greater. For the coloured
Lighe oF che Prism, by che incerterins ot che Circles de-
Scribed in che rith Figure oF che sitch Experimene, aud al(0
by che Lighc oF che very briohe Clouds nexe the SunS
Body incermixins wich chele Colours, and by che Lighe
Scaccered by che inequalicies in che polith of che Prilm, Was
(0 veey much compounded, chac che Species irhich chole
faine and dark Colours, cheindigo and Violet, cast upon
che Paper vere noc distinet enouph co be well observed.
Exper. 9. A Prilm, Whole cro Angles ac ies Bale were
equal co one anocher and halE rishie ones, and che chird
a ristic onc, I placed in a bcam oF che Suns Lighe lec in-
co a darke Chamber chrouoh a hole in che W indo- (HUE
25 in che chird Experiment. And curning che Prilm AOWIY
abouc ies Axis uneil all che Liohe ihich vent chrouoh one
oF ies Aneles and as retracted by ic began to be reflected
by ies Bale, ac wrhich eill ehien ic vent out of che Clals,
P obserred chac chose Rars irhich had (uffered che greacest
Retraction vere looner reflected chan che rest. I conceired
cheretore chac thole Rays ot che refected Lighe, wrtich
vere most Retranoible, did First of all by a toral Reflexion
becore more copious in chat Lixhe chan che rest, and
chac atcermards che rest al(o, by 2 cocal ReAexion, be-
came as copious as chele. Po try chis, Imade che re-
Aected Lighe pals chrough anocher Prilm, and beins retra-
Ctec

## Folio 38 — 1677894601:0048
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cted by ic eo Fall attermards upon a Pheec ot white Paper
placed ac lome distance behind ic, and chere by chat RC-
Fraction eo paine the usual Colours of the Prism. And
then causine the Arst Prism eo be curned about ies Aris 2S
abore, loblerred char when chose Rays irtrich in chis Prism
had suftered the grearest Retraction and appeared ot a ble
and violet Colour began to be cotallr reflected, the blen
and violet Liohe on ehe Paper erhich as most retracted
in che second Prism receired a sensible increale above chac
oF the red and vellon, irtich was least retracted; and
afcermards wrhen che rest of che Lighe which as orcen.
vellor and red besan eo be cocallr reflected in he Arst
Prilm, che lighe of chose Colours on che Paper receired as
rrent an increale a5 the riolet and bler had done betore.
Whence eis manifest, chac che beam ot Liohe refected by
che Base oF che Prism, beins auomented Arst by che more
Retrangible Rars and afcermards by che less Retrangible
ones, is componnded ot Rars differeney Retrangible.
And chac aIl such refected Lighe is of che Came Nature
wich ehe suns Liohe, betore ies Incidence on che Bale ot
che Prilm, no Man erer doubced: ic beins generally al-
lored, thar Liphe by such Reflexions Cufters no Alceration
in ies Modifications and Propercies. I do noc here take
notice ot any Retractions made in the Sides of the Arst
Prilm, because che Lighe enters it perpendicularty ac the
Tirst Side, and goes ouc perpendicularty ac che second Side,
and cheretore suHers nonc. S0 then, che Suns incident
Liohe beins ot che lame cemper and consticution wich his
emersent Lighe, and che last beins compounded of Rays
differently Retrangible, che tirst must be in like manner
compounded.
Illustration. In the 2Ith Fignre, A B C is the First Prilm,
BC is Base, B and C its equal Angles ac che Bale, cach
O
5. 21.

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OF 45 degrees, A its RectangulaF V extex, FMI a beam oF.
the suns Lighe let into a darke Room chrouoh a hole 
one chird part of an tnch broad, M its Incidence on theBale
oF che Prilm, MI C a lels retracted Ray, MI HI a more retract-
ed RaY, HI N che beam of Lighe reflected trom the Bale,
V X Y che second Prism by irtrich chis beam in passins
chrouoh ic is retracted, NV+ che lels retracted Lighe oF this
beam, and Np the more retracted part chereot. When che
trst Prilm AB C is curned abouc ies Axis accordins co the
order ot the LetterS AB C, che RaYS M H emerge more
and more obliquelr our ot chat Prilm, and ac lenoch atter
cheir most oblique Emergence arc reflected comards I,
and goins on to p do increale che number of che RayS VI p.
Atcerrrards by continuine che mocion of che tirst Prilm, che
RaySMTC are alo reflected ro WI and increale che number ot
the RayS NF. And cheretore che Li∞HE MI N admits into
us Compolition, trst che more Retransible RayS, and chen
the less Retransible Rars, and vec atcer this Compolicion
15 oFche Pare Nacure rrich che sun simmediare LighE FMI,
che ReRlexion oF che specular Base B C caulins no AIter2-
tion cherein.
Exper. 10. Trro Prisins, which ivere alikce in Chape, 
cied so cogecher, thac their Axes and oppolue Sides beins
Parallel, cher compoled a Parallelopiped.. And, che Sun
Phining into my dark Chamber chrough a licele hole in che
Windon-PhUE, I placed. thac Parallelopiped in his beam ac
Come distance From chehole, in such a polture thac the AXeS
OF the Prilms mighe be perpendicular eo che incidene RayS,
and chac chole Rays being incident uxon che first Side ot
one Prilm, mist 00 on chrouch che ciro contiguous Sides
oF boch Prilms, and emerse out of the last Side oF the sc-
cond Pris. This Side beino Parallet co the Arst Side ot
che first Prilm, cauled che emergins Lighe to be Parallel
C

## Folio 40 — 1677894601:0050
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cocheincident. Then, berond these evo Prisns P placed
2 chird, uhich mighe retract chac emergene Liolc, and by
thac Retraction cast che ulual Colours oF ehe Prism upon
che oppotire Wall, or upon a Theec of Wvtrice P’aper held at
2 conreniene distance behind che Prilm For chac cefracted
Lighero Fall upon ic. ACrer this Pcurned the Paralleloxived
abone ies Aris, and Found chac irhen che contiouons Sides
oF the ervo Prilms became (0 oblique eo che incident R ays
thac chose Rays began all ot chemi ro be reflected, chole
Rars irhich in che chird Prim had suftered che creacest Re-
Fraction and painced che Paper wich riolet and bleur, rvere
tirst ot all br a cocal Rellexion calcen oue ot che cransmitred
Lighe, che rest remainins and on che P’aper paincine cheir
Colours of Oreen; Vellon, Orange, and Red as betore;
and afcermards by concinuing che morion otthe cmo Prisms,
the rest ot che Rays also br a cocal Rellexion ranisted in
order, accordino co cheir deorees ot Retrangibilier. The
Lighe cheretore irtrich emerged oue ot ehe cro Prisms is
compounded oE Rars differenely Retransible, secing che
more Retrangible Rars may be caken out of ic wrhile che
less Retransible remain. Buc chis Lighe being crajected
only chrouoh che Parallel Superficies ot che crro Prisins, it
ic suttered any change by che Retraction ot one Superficies
ic lost chat impression by the concrary Retraction of che
other Superficies, and (o being restored eo ies pristine con-
sticution became ot che lame nacure and condirion as ac Erst
betore ils Incidence on chose Prilms; and cheretore, betore
its Incidence, ias as much compounded of Rays differenelr
Retrangible as atcerrards.
Illustration. In che 22th Figure AB C and B CD are che
the cruo Prilms cied cogecher in che form ot a Parallelo-
piped, cheir Sides B C and CB beins contionous, and
cheir Sides AB and C D Parallel. And FIY K is the chird
Prilmm.
18. 22.

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Prism, by which thesuns Lighe propagated chrough che
hole F into che dark Chamber, and chere passine chrouoh
those Sides oF the Prims AB, BC, CB and CD, is retra-
ctedat Ocorhenhite Paper P P, Falline chere parrly upon
e by a creater Retraction, parely upon Y by a less Retra-
ction, and parely upon R and ocher intermediace places by
intermediare Refractions. By turnins che Parallelopiped
ACBD abouE ies Aris, accordins eo the order of the L er-
TerS A, C, D, B, at lenoch when che contiouous Planes BC
and CB become (ufficientlr oblique co che Rays IM,
irhrich are incidene upon them ac MI, there ill ranish co-
callu ont ot che retracted Liohe OP T, Arst oF all che most
retracted RaysOP, (the rest OR and O I remainins 25
before) chen che RarS OR and orher intermediate ones,
and lastlr, che least retracted RayS OT. For When che
Plane BC Decomes sufficientty oblique eo the Rays inci-
dent upon ic, chose Rays will bcoin eo be tocally reftect-
ed by ic comards N; and first che most Retrangible Rays
will be cocallr reflected (as mas explained in the precedins
experiment) and by consequence must first disappear ac P,
and afcermards che rest as cher are in order cocally rehect-
ed eo N, cher must disappear in che lame order ac R and
T. S0 chen che Rays irhich at O sufter che grearest RC-
Fraction, may be caken onc ot che Lighe MIO whilst the rest
ofthe Rays remain in ic, and cherefore that LighE MO is
Compounded of Rays difterently Retrangible. And be-
cause che Planes AB and CD are parallel, and cheretore
by equal and concrary Retractions destroy one anothers
Ffects, the incident LighE F NI must BC oF che same kind
and nacure wich the emergent Lighe MO, and cheretore
doch also consist ot Rays difterenely Retrangible. These
erro Liohes FMI and MO, betore che most retrangible RarS
are separated oue oF che emersent Lighe MIO agrec in C0-
TOur.

## Folio 42 — 1677894601:0052
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lour, and in all ocher propercies (o tar as my obserration
reaches, and cheretore are deservedly repuced ot che same
Nacure and Consticucion, and by conséquence che one is
compounded asmell as ehe orher. Buc afcex che most RC
Fransible Rays begin eo be torallr reflected, and chereby
Separared ouc ot che emersent LigheMO, chac Lighe changes
its Colour trom wrhice co a diluce and taint vellorr, a precty
sood oranse, 2 very tull red luccelirely and chen cotallr
ranithes. For atcer ehe mostRetransible Rays irhich paine
the Paper ac P rich a Purple Colour, are by a tocal re-
Aexion cakcen out oF che Beam oF lighe MIO, che rest of
the Colours itrich appear on che Paper at R and Y beino
mixed in che lighe MO compound chere a faine vello,
and atcer che blue and pare ot che ercen irhrich appear on
the Paper becreen P and R are cakcen awar, the rest irhich
appear beeireen R and Y (chac is che Vellor, Orange, Red
and a licele Crcen) being mixed in ehe Beam MIO com
Dound chere an Oranse; and irhien all che Rays are by re-
Aexiontaken out oF che Beam MIO, exceptche lealt Retran-
sible, irhich ac T appear ot a Tuil Red, their Colour is
thc lame in chac Beam MIO aS atcermards ac T, che RC-
traction ot che Prilm FIJK serring only co separace che
differenty Retrangible Rays, Wichouc makins any alceration
in cheir Colours, 25 Thall be more fully proved hereateer.
AIL ertrich contrrms 25 vell che first Propolition as che se-
cond.
Scholium. IFchis Fxperimene and che former be conjorned
Eig. 22. and made one, by axplyins a Fourch Priim VX Y EO re-
tract the refected Beam M N corards ip, che conclusion
will be clearer. For then the lighe Np irtich in che 4eh
Prim is more retracted, ill become tuller and Aronger
Wrhen che Lighe OP, itich in che chird Prilm IIYK is
more retracted, ranictres ac P; an d attermards inhen che lels
retracted

## Folio 43 — 1677894601:0053
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retracted Lighe OT ranishes ac T, the lels retracted Liphe
Ht ill become encreased whilst che more refracted Lighe
at p receires no further encreale. And as the erajected
Beam MIO in vanictins is alivars of such a Colour a5
oughe co retule From che mixture of che Colours ihich
fall uxon che Paper D T, Cois che retected BeaM NIDT al
prars ot such a Colour as ouphe eo retule trom the ix
ture oF che Colours itich Fall upon thC PaPeE pF. FOF
when che most retrangible Rays are by a eoral ReAexion
taken oue ot ehe Beam NTO. and leare thac Beam Ot aM
Oranse Colour, the excels oF chose Rars in the resected
Lighe, does noc only makce cheviolet, Indiso and Bluc at
Pmore FuII, buc aIso makces the Beam N N chansc FrOM
the velloith Colourorche sun sLighe, e0 a pale whice in-
clinins co blue, and altermard recorer ies rellowist Co-
lour asain, (0 TOon 25 aII the rest oF che cransmicced lighE
MIOTis reflected.
Nom sccing chac in all chis rarieer ot Experiments,
Whecher the crial be made in Liohe reflected, and ehat cithex
from natural Bodies, 25 in che Arst and second FxperimenE,
Or Specular, 25 in cheTTinch; or in Lighe retracted, and
chac cither betore the unequallr retracted Rays are by di-
verging separated trom one anocher, and losing cheir whire-
vels irhich cher hare alcogether, appear severally ot sere-
ral Colours, 25 in ehe Eteh Experimene; or atcer cher are
separated from one anocher, and appear Coloured as in che
Circh, Sevench, and ciptich Experiments; or in Lighc era-
jected chrough Parallet superticies, destrorins cach ochers
Fiffects as in che ioch Experimene; chere are alvars Found
RaYs, irhich ac equal Incidences on che lame Medium SuF-
fer unequal Retractions, and chac ichout aur spliceing or
dilatins oF sinsle Rays, or concingence in che inequalier
OF the Retractions, as is proved in the fitth and SIXTh LX
Periments;

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C44
perimenes; and sceing che Rays ihichdister in Retrangibi-
lier may be parted and Corced trom onc anocher, and chat
cither by Retraction as in the chird Experiment, or by Re-
Aexion as in che centh, and chen che several COrES aPARE aE
equal Incidences sufter unequal Retractions, and chole POrrS
are more retracted than ochers atcer separation, wrhich vere
more retracted betore ic, a5 in che sixch and Following Fx-
perimenes, andit che sunsLighe be trajected chrouoh chrec
ormore cross Prilins Successirelr, those Rars which in che
turst Prilm are retracted more chan ochers are in all chetol-
lomins Prilms, retracted more then ochers in che lame rate
and proporcion, a5 appears by che fitth Experiment; itS
manifest chac che Sun sLighe is an Hlecerogeneous mixture ot
RarS, Lome oF nhich are constanels more Retrangible then
Ochers, as was to be propoled.
ROP. TII. THCOT. TTI.
TheSuns Lieht consists of Pays differins in Reflexibility, and
those Pays are more Reflexible than others which are more Re-
frangible.
VFTIS is manifest by che ninch and centh Experi-
ents: For in che ninch Experiment, by curmine
the Prilm about ies Axis, uneil che Rays wichin ic irhich in
foins our into che Air ivere retracted by ies Bale, became
(0 oblique to thac Base, as eo begin to be torallr reffected
cherebr; chole Rays became Arst oF all corally reflected,
irtrich betore at equal Incidences rich the rest had suffered
the orearest Retraction. And che Came chins happens in
the Rellexion made byche commonBase of che cwo Prims
in cherench Experiment.
PR

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PROF. IV. PrOD. =
T0 separate from one another the Tleteroseneous Rays of
ta
Compound Light.
IFTF HleterogenconS Rays are in Pome meature sepa-
rated From one anorhier by the Retraction ot che
Prilm in che chird Fxperimene, and in the ffth Fxperiment
by calcing arar che Penumbra trom the Rectilinear Sides ot
the Coloured lmage, thac separation in those verr Reccili-
near Sides or Araighe edges ot the Image becomes pertect.
Buc in aIl places berween those rectilinear edges, thole in-
numerable Circles chere described, which are severally illu-
minated by Hlomogeneral Rays, by incerterins wich one
another, and beins ererr ihere commixt, do render che
Liohe Cufticiendy Compound. Buc il chele Circles, Whilst
their Cenrers keep their distances and posirions, could be
made less in Diamerer, cheir incertering one ith anocher
and by consequence che mixture of che FICcerOgeneOUS
RaYS Would be proportionally diministred. In che 23ch Fig. 23.
Figure lec AG, BFI, CT, DR, EL, FM bC the Circles
erhich (0 many fores of Rays Aorwing trom che lame Dilque
oF the Sun, do in che chird Experiment illuminate; oF aII
irtrich and innumerable octrer incermediare ones lyins in a
Continual Series beteen che erro Rectilinear and Parallel
edges ot che suns oblons Imase P P, chac Image is com-
poled as as explained in che fitch Experiment. And lec
a8, bh, ci, dk, et, fm be (0 many lels Circles lying in
a like continual series berireen erro Parallel righe Lines a f
and em with che same distances becireen cheir CenterS,
and illuminated by ehe same POrts oF RaYS, chat is che
Circle a 8 wrich the lame Pore by irhich che correspondine
Circle

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C46)
Circle RC was illuminated, and che Circle bh rith thesame
Porc by ihich che corresponding Circle BHIas illuminated,
and the rest of the Circles ci, dR el, fm respectirelr.
rich che Came Corrs oF Rays by irhich che several corre-
sponding Circles CT, DK, F L, FM ivere illuminated.
In cheFigure P P compoled ot che orcater Circles, chree
ot those Circles AG, BH, CJ, are (0 expanded into one
anocher, chac che chree (orts oF RayS by itrich chole Cir-
cles are illuminated, cogether wich ocher innumerable POreS
oF incermediare Rays, are mixed ac QR in che midale of
che CireleBFI. And che like mixture happens chrouoh-
out almost che ihole lenseh oF che Ligure PI. Buc in
che Figure pr compoled ot che lels Circles, che chrec lels
Circles ag, bh, ci, Which ansiver to chose chree greater, do
nOF extend into one anocher; nor are chere aur ntere
minsled (o much 25 any erro of che chree Pores oF RaYS
by irtich chose Circles are illuminated, and ihich in che
Figure P T are all oF chem incerminoled ac BFI.
No hochac Phall thus consider ic, ill casily understand
chac che mixture is diminithed in che Came Proportion
wich che Diameters oF che Circles. IF the Diamerers ot
che Circles whils cheir Cencers remain che lame, be made
chrec times lels chan betore, che mixcure will bc also chrec
cimes lels; il cen cimes lels, the mixture will be cen eimes
lels, and (o of ocher Proportions. Thacis, the mixture
OF che Rays in chegrearer Figure P I will be co cheir mix-
cure in che lels pt, 25 che Lacitude of the greater Figure is
co che Lacieude ot che lels. For che Lacicudes of these Fi-
oures are equal co che Diameters ot cheir Circles. And
hence ic easily follons, thac che mixture oF che Rays in che
retracted Spectrum pF is to che mixture ol che Rays in the
direet and immediare Liohe oF chesun, as che breadth oF
chac Spectrum is coche ditterence bermeen che lengeh and
breadch ot chelame Spectrum.
Sc

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So chen, it We would diministr che mixeure oF Che R ayS,
ve are eo diministr che Diamerers of ehe Circles. NOW
these rould be diminithed it the Suns Diameter co nhich
cher ansirer could be made lels than ic is, or (phich comes
co the lame purpose) il without Doors, at a greac distance
teom the Peilm corards the sun, some opakce body vere
Placed, ich a round hole in themidale oF iC, EO InFerCCDE
all che suns Liehit, exceptine (o much as coming from
che middle oF his Body Conld pals chrovoh chat nole eo
the PrIH. FOr (O che Circles AG, BH and che rest,
would noc aur longer antirer co the irhole Dilque ot che
Sun, buc onty to chac pare of ic irhich conld Be scen
From che Prism chrouoh chac hole, that is eo the appareHE
magnieude ot chac hole riemed trom che Prism. Buc chac
phele Circles may ansiver more distinctiy co chac hole a
Fens is eo be placed by che Prism co cast che Image of the
hole, (chac is, every ore oF the Circles AC, B FI, eC.) di-
Rinctly uxon che Paper at P P, atcer such a manner as by
a Lens placed ac a Windoir che Species of Objects abroad
are cast distinctly uxon a Paper wichin che Room, and the
Rectilincar Sides of che oblong solar Image in the fitth
Experimene became distinet withour any Penumbra. IF
ehis be done ic will noc be necessary eo place that hole
very Far of, no noc berond che Windo. And cherctore
instead ot chac hole, Lused che hole in che Window- CHVE
25 FOllOWS.
Exper. 11. In che Suns Lighe lec inco my dartened
Chamber chrouoh a (mall round hole in my Windou-
CHUE, aE abOUE 10 OF 12 Feet From the Window, I placed
a Lens, by irtrich che Image ot che hole mighe be di-
Ctinctly cast uxon a Theec ot irhite Paper, placed ac the
distance ot lix, ciohe, cen or evelre Feet trom che L ens.
for accordine co the difference of che Lenses l’used rarious
distances,

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distances, wrhich T chink noc worth che while eo describe.
Then immediacely atcer che Lens I placed a Prilm, by
irtich che trajected Lighe mighe be retracted cicher up-
wards or Cderrars, and chereby che round Imase which
the Lens alone did cast upon the Paper mighe be drarn
out inco a lono one wich Parallet sides, 25 in che chird
Experiment. This oblono Image I lec Fall uxon anocher
Paper ac aboue che Pame distance From che Priim 25 Be-
Fore, morins che Paper cicher comards ehe Prism or From
ic uneil I Found che just distance irhere che Rectilinear
Sides of che Imase became most dictinct. For in this case
the circular Images of chehole which compose thaclmage
atcer the lame manner thac the Circles aq, bh, ci, _c. d0
. D che Figure pF, vere cerminaced most distinetly withoue any
Penumbra, and cheretore excended inco one anorher che
least chac ther could, and by consequence the mixeure et
the Hecerogeneous Rars mas no che least oF aIl. By chis
jo. 22, neans Iused ro form an oblong Image (such as is pF) ot
ma LA. circular Images of chehole (such a5 are a g, bh, c1, _C.)
and by ulinz a orcater or less hole in the Windon-PBuE, I
made the circular Images ag, bh, c1, _c. Ot which ic was
Formed, to become orcarer or lels at plcasure, and chereby
the mixture oF che Rars in che Image pt eo bc as much
Or as licele as I desired.
Fig. 24. Illustration. In che 24th Figure, F reprelenes che circular
hole in he Windon-PhUE, NIN che Lens Whereby chc
Imase or Species oF thac hole is cast distinctly uxon a
PapeF aE J, AB C the Prilm whereby che Rays are ac cheir
emeroins ouc of the Lens retracted From J corvards ano-
cher Paper ac pt, and che round lmage ac F is curned into
an oblong Tmage pr Falline on chat ocher Paper. This
Imase pt consists ot Circles placed one alcer anocher in a
Rectilinear order, as was sufticieney explained in che fiteh
Experiment;

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Experimene; and chese Circles are equal eo che Circle L,
and conlequenely ansirer in Magnicude ro the holef; and
cheretore by diministrins chac hole chey max be ac plealure
diministred, uhilst cheir Centers remain in cheir places.
By chis means I made the breadth ot che Image pF eo bc
Forer cimes, and Cometimes sixtr or serener times lels than
ies lenoch. AsFor instance, it the breadth ot che hole F
be i oF an Tuch, and MIF che distance of che Lens From
the hole be 12 Fece; and it pB Or pMI che distance ot
the Image pt Fromthe Prilm or Lens bC 10 Feet, and che
retractins Anole ot the Prilm bc 62 dcorees, the breadch
Ofche Image pF wili be= ot an tuch and the lenoch abouE
SixInches, and cheretore che length eo the breadth 25 72
co1, and by consequence the Lighe of this Image 71 times
less componnd chan the Suns direct Lighr. And Lighe
chus Far simple and Fomogencal, is sutticient For erving
aIl che Experimenes in chis B00k about simple LiohE. FOr
che composirion of Hlecerogeneal Rays is in this Lighe (0
licele thac ic is scarce eo be dilcorered and perceired by
sense, excepe perhaps in the Indiso and Violet; For thele
beins dark Colours, do casilr sulter a senlible allar by chat
lictle scarrering Lighe which ules to be retracte d irreoularty
by che inequaliceis ofche Prilm.
Tet instead ot the circular hole F, eis berrer to sybsti-
cure an oblone hole Phaped like a lone Parallelogram
wich ies lenoch Parallel eo the Prism ABC. For it this
hole be an Tuch or ero lono, and buc a centh or erventieth
part ot an lnch broad or narrover: che Lighe oF chelmage
PF Wrill be 25 Simple as betore or simpler, and che Image
Will become much broader, and cheretore more Ac to have
Experiments cried in ies Liohe than betore.
Instead oF this Parallelopram hole may be substicured a
Friangular one ot equal Sides, whose Base For instance is
abOut

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about che centh part ot an Iuch, and ies heiphe an Inch Or
MOTC. For by this means, if che Axis of che Prism be
Parallel co che Perpendicular of che Triangle, thelmage
18. 23. pt will non be Formed oF Fquicrural Prianeles a5, bB, c1,
dk, et, fm, ecc. and innumerable ocher intermediare ones
anliverins co che Triansular hole in Chape and bignels, and
Lring one atcer anocher in a continual Scries Between EwO
Parallel Lines a f and 5 m. These Frianoles are a lietle
interminoled ac their Bases buc nor ac cheir Verrices, and
cheretore che Lighr on che brighrer sde af ot che Image
irtiere che Bales oFthe Friangles are is a licele compounded,
buc on che darker side z m is altogether uncompounded,
and in all places becireen che sides the Composition is
Proportional co che distances of the places trom thac ob-
scurer Cide s m. And harins a Spectrum pF oF such 2
Compolition, e mar ery Experiments cicher in its Aronger
and less simple Lighe near che side af, or in ies meaker
and simpler Lixhe near che ocher side lm, as ic Call scem
most conrenient.
Buc in makins Experimenes of chis kind che Chamber
oucht to be made as dark as can bc, least anr Forreion
Lighe mingle ic selt rich che Lighe oF che spectrum pt,
and render it compound; especially it re mould ery Lx
perimenes in the more simple Lighe nexe the side e m ot
che Spectrum; which beins fainter, will have a lels Pro-
portion co che Forreion Lishe, and (0 by che mixture ot
chac Lighe be more troubled and made more compound.
The Lens allo ouphe to bc g00d, such as may serre For
Optical Ules, and che Prism oughe to have a larre Angle,
suppose of 70 deorees, and to be well iroueht, beins
made ot Class tree trom Bubbles and Veins, wich ies sides
noc a licele Conrex or Concare as ulually happens bue
eruly Plane, and irs pollich elaborate, as in workins Oprick-
slacles.

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S+
Elasses, ane not such as is ulually vrouohe wich PTY,
Whereby che cdees oF che Sandholes beins worn awar,
there are lete all orer the Clals a numberlels companr ot
very licele Conrex police rilines likce Wares. The edges
allo ot che Prilm and Lens (0 tar a5 cher may maktce any
irregular Refraction, must be corered ith a black Paper
olemed on. And all che Liphe of the sunsbeam let into
the Chamber irtich is useless and inproticable ro thC FXs
perimene, ouohe cobe incercepced ich black Paper Or Ocher
black Obstacles. For ochermise che uselels Liphe beins
refected erery iay in che Chamber, ill mix wich che
oblons spectrum and help eo disturb ic. In erying chele
chines so much Diligence is noc altogether neceltary, but
ic ill promote che succels of che Experiments, and by 2
very scrupulous Examiner ot thines déserres to be applicd.
ses difficule eo set slals Prilms sic For ehis purpole, and
and cheretore lused Cometimes Prilmatick Vetsels made
wich pieces ot broken Looking. glasses, and filled wich rain
NaceT. And eo increase che Retraction, ICometimes im-
pregnaced che W acer Aronsly rich Saccharum Saturni.
PROP. V. THCOT. IV.
FTomozeneal Lieht is refracted recularte mithout any Dilatation
splittins or satterine of thé Rays, and the confused Vision
of Objects seen throuch Refractinz Bodies by Fheterogeneal
Lieht arises from che different Refrangibility of several sorts
of Ray5.
IHIE Ars ParE oF ehis Proposicion has been alreads
sufticieney prored in che fitch Experimene, and will
furcher appear by che Experimenes whichi tollon.
Lipeto a

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Fxper. 12. In the midale of a black Paper I made 2
round hole about a ftch or sixch parc ot an Tnch in Dia-
meter. Upon chis Paper I cauled che Spectrum ofHlomo-
geneal Lighe described in the Former Proposition, (010
fail, chac Come parc of che Lighe mishue pals chrouch che:
hole of che Paper. This transmitred parr of che Liohe l
retracted rith a Prilm placed behind che Paper, and ler-
cing chis retracted Lighe tall perpendicularly uxon a whice
P’aper erro or chrec Feet distant trom che Prism, I Found
chac che Spectrum Formed on che Paper by chis Liohe ras
noc oblone, a5 irhen eis made (in che chird Experiment)
By Retractins ehe suns compound Liphe, buc was ((0 Far
25 I could judsc by my Fyc) pertectlr circular, thelenoch
being no oreacer chan the breadch. Which Phens chac this
Lighe is retracted regularly ichout an Dilaration of the
Ray5.
Exper. 13. In che Hlomogeneal Liphe I placed a Circle
oF: ot an Tuch in Diamecer, and in che suns unretracted
Hlecerogencal Wrhice LigheI placed anocher Paper Circle ot
chelame bignels. Andgoinstromthe Paperstochedistance
oFlome Feet, Ivieved boch Circles chrouoh a Prism. The
Circle illuminate d by thesun sHleterogeneal Lighe appear-
ed rery oblone as in che fourch Experiment, che lenoch
being many cimes orcater chan che breadth: buc che ocher
Circle illuminated wich Hlomogeneal Lighe appeared Cir-
cular and distinctli defined as when eis vierred wich che
nakced Fyc. Which proves the whole Proposition.
Exper. 14. In che Homogeneal LigheI placed Flies and
Tuch like Minuce Objects, and vicwins chem chrough a
Prism, I Pa cheir Parrs as distinetly defined as it Phad
riemedchem rich che naked Ere. Phe lame Objects pla-
ced in che suns unretracted Flererogeneal Liphe ihich as
nhire l viered also chrouoh a Prism, and Pam them most
contuledly

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contusedly detined, (o chat Lcould noc distinguiltr cheir smat
ler Pares trom onc anocher. I placed also che L etters oF a
lmall Princ one while in che Hlomogencal Lighe and chen
in che Heterogencal, ana riemins chem chrouoh a Prilm,
cher appeared in the larrer case (0 contuled and indistinct
chac L could noc read chem; buc in che former they ap-
Peared (0 distinct chac l could read readily, and choughe
L.Cam chem as distinct a5 irhen I viered chem wich ny
naked Ere. In boch cases I ricred che lame Objects
chrouoh che lame Prism ac che lame distance trom me and
in che lame Sicuation. There ras no difference buc in the
Lighe by irhich che Objects iere illuminated, and ertich
in onc case mas simple and in che ocher Compound, and
cheretore che distinet Vision in che former case and contu-
sed in che lacter conld arise trom noching elle chan trom
chac difference ot che Lighes. Which prores che wrhole
Propolirion.
And in chele chree Experiments ic is Further verr remar-
hable, chac che Colour ot Homogeneal Lighe ras nerer
chansed by che Retraction.
DROP. VI. THCOT. V
The Sine of. Incidence of every Ray considered apart, is to ils Sine
of. Refraction in a siven Ratio.
ITI A Y every Ray considered apare is constant to
it Celt in Pome certain derree ot Retrangibilier, is
Cufticienely manifest out of wrhat has been Caid. Thole
Rays which in che Arst Retraction are ac equal Incidences
most retracted, arc also in che follomine Retractions at
equal Incidences most retracted; and (0 oF che least R e-
trangible, and che rest which hare auy mean degree ot
Retran-

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C54
Retranoibiliey, as is manifest by che sch, 6ch, 7ch, 8th,
and oth Experimenes. And chose which che Arst cime ac
like incidences arc equally retracted, arc 2rain at like In-
cidences equallr and uniformly retracted, and chac whe-
cher cher be retracted betore cher be separaced From one
anothier as in the sth Experiment, or Wwhecher ther be re-
Fracted apare, as in the 12ch, 13th and 1ath Experiments.
The Retraction cheretore oF every Ray apare is regular,
and wtrac Rule chac Retraction oblerres e are nOW
Eo TheW.
The lace Vricers in Opricks ceach, chac the Sines oF In-
cidence are in a oiven Proportion co che Sines ot Retra-
ction, 25 was explained in the sch Axiom; and lome by
Instrumenes Aicced For measurine Retractions, or ochermise
experimentally examinins chis Proportion, do acquaine us
ehat ther hare Found ic accurate. Buc Whils cher, nOc
understanding che different Retransibilier of several RayS,
conceired chem all ro bc retracted accordine to one and
che lame Proporrion, eis co be prelumed thac cher adapred
their Mealures only co the middle ot the retracted Lighe;
(o thac trom cheir Measures e may conclude only chac
che Rays irhich hare a mean deoree of Retrangibilier.
thac is chose irhich when separaced trom che rest appear
orcen, are retracted accordins to a siren Proportion ot
cheir Sines. And cheretore we are no co Phew rhac phe
like siren Proportions obtain in all che rest. Thac il
Thould be (o is very realonable, Nature being ever contor-
mable to her selF: buc an experimental Proot is delired.
And such a ProoF will be had it we can Phew thac che
Sines ot Retraction ot Rars differenely Retransible are
one to anocher in a giren Proportion irten cheir sines ot
Incidence are equal. For il the sines oF Retraction oF aII
che Raysare in giren Proportions tothe sine of Retraction

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s
oF 2 Ray Wrhich tias a mean degree of Retrangibiliey, and
chis sinc is in a giren Proporcion co the equal sines ot
Incidence, those ocher Sines of Retraction will also bc in
siven Proportions coche equal sines ot Incidence. Nou
When che sines of Incidence are equal, ic will appear by
the folloino Experimene that the Sines of Retraction are
in a giren Proportion to one another.
Exper. 15. The Sun Chinins into a dark Chamber
chroueh a licele round hole in che Windor-Buc, lec S re-Fis. 26.
present his round uhice image painced on the opposice
Nall by his direct Ligne, P This oblong coloured Imase
made by retractinq chac Lighe wich a Prilm placed ac che
Windon; and pF, Or 2p2t, or 3P 3t, hisoblone coloured
lmage made by retractins again che lame Lighe sidemays
ich a second Prism placed immediacely atcer che frst in
a crols Policion eo ic, as vas explained in che fitch Fxperi-
menE: thac is eo Par, pt When cheRefraction of the second
Prilm is (malI, 2p 2 F When ies Retraction is greater, and
3P 3t when ic is greatest. For such will be the diversiey
ot che Retractions it che retractins Angle oF che sccond
Prilm be oF various Magnicudes; suppOse OF FIIECCN OF
civener degrees ro makce the Image pi, oF chirey Or
forey comakce the Image 2p 2F, and ot sixer co mate
the lmage 3p 3t. Buc for anc ot solid Class Prilms wich
Angles ot conrenient bignesles, chere mar be Vessels
made ot polistred Places ot Class cemented cogether in the
Form of Prilms and filled wich Wacer. Thelechines beins
thus ordered, I obserred chac alt the Colar Images Or co-
loured Spectrums P P, pt, 2p 2t, 3P 3c did very nearty
converse co che place S on irhich che direct Lighe ot the
Sun Fell and painced his irhice round Image when che
Prisms vere calcen arvar. TheAxis of che Spectrum P I,
chac is the Line drann chrough che middle oF ic Parallel t0
HES

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ips R ectilincar Sides, did hen produced pals exactly chrouoh
the midale ot thac white round Image S. And when che
Refraction of the second Prilm ras equal eo the Retraction
oF chetirst, che retractins Angles ot chem boch being about
60 decrees, che Axis ot che spectrum 3P 3t made by chac
Retraction, did ihen produced pals allo chroueh che mid
ile of che lame irtrice round Image S. Buc When the RC
Fraction of che sccond Prilm as lels chan chac of the Arst,
che produced Axes oF the Spectrums FP Or 2+ 2p made
by chat Retraction did cur che produced Axis oF the SpC-
ctrum TP in che Poines m andn, a licele berond che Cen-
cer ot chac nhice round Image S. Whence the Proportion
OFche. Linc 3+T eo che Linc 3 p P was a licele orcarer chan
hePrOpOrtiOn OF 2FT +02 pP, and chis Proporcion a licele
oreater than chat OFFT eO pP. Now when che Lighe ot
che Spectrum P TFalls perpendicularty uxon the W all, chosc
Lines 3FT, 3PP, and 2F l, 2P P and+P, pP, are che l’an-
genes of che Retractions; and cheretore by chis Experiment
che Proportions of the langenrs of che Retractions are ob-
cained, trom Whence che Proportions ot chesinesbeins derir-
ed, cher come out equal, (0 taras br viering the spectrums
and ulins lome Machemacical realonins I could Estimate.
For I did noc make an Accurace C omputation. S0 then
che Propolition holds erue in every Ray apart, (0 Far 25 ap-
pearsby Experiment. And thac ic is accurately true may
be demonstraced uxon chis Suppolicion, That Bodies refract
Zicht by acting upon its Rays in Lines Perpendicular to their
Surfaces. Buc in order eo chis Demonstration, I muct di-
Cinguith che Mocion ot erery Ray into tuo Mocions, che
one Perpendicular to the retractins Surtace, the other Pa-
rallel coic, and concernins che Perpendicular Mocion lay
donn chetollorins Propolition.

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IF any Motion or moving ching wrhacloerer be incident
rich ans relocier on any broad and chin space termina-
ced on boch sides by erro Parallel Planes, and in its paltage
chroush chac space bc urged perpendiculartr corrards the
turcher Plane by any Force irhich at siren distances trom
che Plane is of given quancicies; the perpendicular Velo-
ciey ot chat Mocion or Thing, ac its emergins out of chac
Space, Ball bc alvars equal eo the Square ROOE oF chc
Summ oF che Square ot che perpendicular Velociey ot
ehac Norion Or Thins at ies Incidence on thac space;
and ot che Square ot che perpendicular Velociey irhich
chac Mocion or Thing vould hare ac ies Emergence, il
ac iis Incidence irs perpendicular Velocier as intinicely
licele.
And che same Proxosition holds Erre OF anv. NTOtiOn OF
Fhins perpendicularty recarded in ies pastage chrouoh chac
Space, it instead of the summ ot che ero Squares rou cake
cheir difference. The Demonstration Machemaricians will
calily find out, and cheretore I CalI noc trouble the Rea-
der wich ic.
Suppose nom chac a Ray comins most obliquely in che Fiz. 1.
Line MIC be retracted at C by che Plane RS inco che Line
CHI, and it ic be reguiredt co End che Line CF inco which
any ocher Ray AC ThaII be retracted; let MIC, AD, BC
the sines ot incidence of che tvo RaYS, and NTC, FF, cheir
Sines of Retraction, and lec the equat Morions of che In-
cident Rays be represented by chc equal Lines MI C and
AC, and che Morion MC being considered as parallel to
che retractins Plane, lec the ocher Mocion AC bC distin-
Suihed InEO EIVO NTOtiOnS AD and DC, one ot irhich
AD is parallel, and che orher DC perpendicular to the re
tractino surtace. In like manner, lec the Mocions oF che
emerins Rays be distinguistrd inco cro, Whereot the per-
pendicular

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N
perpendicular ones arC N CO and FF CF. And is che
Force of the retracting Plane begins to act uxon che RaYS
cicher in chac Plane or ac a certain distance from ic on the
one side, and ends at a certain distance from ic on the
ocher side, and in alI places becireen those erro Limits acts
upon che Rays in Lines perpendicular ro chat ratractine
Plane, and che Actions upon the Rars ac equal distances
From che retracting Plane be cqual, and ac unequal ones ei-
cher equal or unequal accordins to any rate Whaterer:
chac motion of che Ray irhich is Parallel to che retractine
Plane wrill sutter no alteration by chac force; and thatmo-
cion irhich is perpendicular eo ir rill be alcered accordino
eo che rule oF the Foregoins Proposition. IF cheretore FOF
che perpendicular Velocier of che emergins Rar CNY vou
MC
irrite p CC as abore, chen che perpendicular Velocier
AD
ot any ocher emereins Ray CF which was FF CF, will be
equal eo the (Guare ROOC OF CD9 -
NC. 9
NOq C69. And
by Cquarins chese equals, and adding eo them the Equals
ADgandNICg---CD9. and dividing che summs by che
Equals CFg F F Fg and CC9 ] NCG, You wil have
ADC
MICq
EFq equal EO NOg. Whence AD, the Sine ot Incidence,
is EO F. F the Sinc oF Retraction, as NC eO NO, thac is.
in 2 siren ratio. And ehis Demonstration being general.
richour decermining irhiat Lighic is, or by whac kind ot
Force ic is retracted, or alluming any ching Furcher chan
chac che retracting Body acts upon che Rays in Lines per-
pendicular to its Surtace; Pcake ic to be a very conrincine
Argumene of the tuIl Truch ofchis Propolicion.

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(59
50 chen, il che ratio oF che sines of Incidence and Re-
traction otany Pore of Rays be Found in any onc Cale, tis
siren in all Cales; and chis mar be readily found by che
Mechod in che Follorrine Propolition.
PROF. VII. THCO. VI.
The Perfection of Tele scopes is impeded by the different Refran-
sibilitys of the Rays of Light.
FTF imporfection oF Velelcopes is milgarty accri-
buced co che spherical Figures oF che Glastes, and
cheretore Machematicians hare propounded to Figure them
by che Conical Sections. Fo Chew chat chey are milta-
ken, Phare inserced this Propolition; the cruth of which
will appear by che meatures oFche Retractions oF che sere-
ral POres OF Rays; and chele meatures l thus determine.
in che chird experiment oFche Arst BOOk, Wrhere che re-
tractins Anole ot che Prism was 62 deorees, che halt ot
chac Angle 31 de8. 15 min. is che Angle ot Incidence ot
che Rays at cheir goins our ofche Clals inco the Air; and
the sine oF this Anole is 5188, che Radius being 10000.
When che Axis oF chis Prilm was parallel to che HIOrizOn,
and che Retraction oF che Rays ac their Incidence on chis
Prism equal to chac ac cheir Pmergence ouc of ic, l oblerred
wicha Guadran the Ansle which che mean retrangible Ray5
(thacis, cholewhich enero che midele otchesuns colour-
ed Imase) made wich cheHorizon and by chis Angle and
che suns alcicude obserred at che lame time, PFound che
Angle which che emersent Rays contained wich che incidenc
cobe 44 deg. and 10 min. and chehals of chis Angle ad-
ded co che Angle ol Incidence 31 des. 15 min. makces che
Angle

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Angle of Retraction, which is cheretore 53 deg. 35 min. and
itS Sine 8047. These are che sines ot Incidence and RC-
traction of che mean retransible Rays, and cheir proportion
in roundnum bersis 201031. This Classmas oF a colourir-
clininq to oreen. The last of che Prilims mentioned in the
chird Lxperimene as ot clear irhice Clals. Ies retractine
Angle 63: deorees. The Angle. which the CMeKGCNE R ayS
concained, ich che incident 15 deg. 50 min. The Sinc ot
halF che First Angle 5262. The Sine oF halt che Sume
OFthe Anoles 8157. And cheir proportion in round num-
bers 20 10 31 a5 betorc.
From che Lensch oE che Image, ihich as about 92 Or
10Tnches, Fubduet its Breadch; Which Was 2 Inches, and
the Remainder 73 Tnches vould beche lenethofche Image
ivere the sun buc a pome, and cheretore subcends the An-
ole irhich che most and least retransible Rays, when inci-
dent on che Prism in che lame Lincs, do contain with one
anocher atter cheir Emergence. Whence chis Anole is
2 deg. 0. 7. For che distance betreen che lmageand the
Prilm nhere chis Angle is made, Was 18 = Feet, and ac chiac
distance the Chord 7? Inches subtends an Angle ol 2 deg.
0. 7. NTow half chis Angle is che Angle wrtich chele e-
mergent Rays contain ich che emergene mean retrangible
RayS, and a quarter chereot, that is 30. 2. may bc ac-
counted che Angle which cher rould concain irhich ehc
Tame emergene mean retrangible Rays, ivere ther coninci-
dene eo ehem ichin che Class and (uftered no octer Re-
Fraction chen thac at their Emergence. For if erro equal
Refractions, the one ac the incidence of che R WVS on the
Prism, the ocher ac their Emergence, makce half the Angle
2 deg. 0. 7. then one ot thole Retractions ill make
aboue a quarter ot thac Angle, and this quarter added to
aA

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and subducted From the Anole oF Retraction oF the mean
retranoible RayS, Which was 53 deg. 35, gires the An-
oles ot Retraction of che most and least retrangible Rays
54 de8. 5 2, and 53 deg. 4 58, Whole Sincs are 8099
and 7995, the common Angle ot Incidence beins 31 de8.
15 and its Sine 5188; arid chese sines in che least round
numbers are in proportion to one another a5 78 and 7 7
10 50.
Noir il rou subduet che common sine ot Incidence 50
trom the Sines of Retraction 77 and 78, the remainders
27 and 28 Them chac in (mall Retractions che Retraction
OF che least retransible Rays isto the Retraction of the molt
retransible ones 25 271028 very nearly, and chat the dit-
ference ofthe Retractions of che least retrangible and most
retransible Rars is about the 27th pare oF che Whole Re-
Fraccion ot che mean retranoible Rars.
WVhence cher chac are stilled in Opricks will casils un-
derstand, chac che breadch ot che. least circular space into
irtrich Obiecc. Glasses ot Telelcopes can collect all Ports ot
Parallet RayS, is abouc the 27sch part oF half che aperture
ot che ClalS, Or 55ch parc oF che whole aperture; and
chac che Focus of the most retransible Rays is nearer to the
Objecc- Class chanthe Focus ot the least retransible ones, by
abouc che 27th part ot che distance berween. the Objecr.
Class and che Focus ofthe mean retrangible ones.
And is Rays oFall Pores, Roing from any one lucid point
in che Axis of any conrex Lens, be made by the Retraction
ot che Lens EO COnVerse to poins not too remore from the
Lens, che Focus ol the most retrangible Rays BaIl bC
nearer co che L ens chan the Focus ot che least retrangible.
ones, by a distance irtich is ro che 27sch pare oF che di-
Aance ot che Focus of the mean retrangible Rays From che
Lens as che distance becireen thac Focus and the lucid
POImE

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poine trom whence che Rays Ro is co che distance be-
erreen thac lucid poine and che Lens verr nearty.
Non co examine whecher che difference berrmeen theRe-
Fractions irhich che most retrangible and che least retran-
sible Rays Aoming trom che lame poine sufter in the Ob-
ject. Clasles oF Telelcopes and such like Clases, DC (O OPCAE
a5 is here described, I contrired che Folloins Experi-
ment.
Exper. 16. The Lens which I uled in che second and
eiehcha Tixpcrimenes, being placed Ex Feet and an Tuch dil-
eant Crom any Object, collected che Species ot chat Object
by che mean retransible Rays ac che distance Ot (IX Fece
and an Juch From che Lens on che other Cde. And CherC-
Foreby che Foregoing Rule ic oughero collect the Speciesot
chat Object by che lcast retransible Rays ac the distance ot
SIX Fcer and z 2 Inchestrom the Lens, and by che most re-
Frangible ones ac che distance of fire Fcet and 10: Inches
Erom ic: S0 chac becween the eno Places where these least
and most retransible Rays collect che species, there may
De che distance ot about 5: Inches. For by thac Rule, 25
Sx Feec and an Inch (che distance of che Lens Erom the
lucid Objece) is eo evelre Fece and ewo Tnches (che di-
Rance of che lucid Objece From che Focus of che mean re-
Frangible RaY5) chac is, as one is eo cro, (0 is the 273th
parc oF six Feec and an Inch (che distance becween che L ens
and che Came Focus) to the distance betmeen the Focus ot
che most retransible Rays and che Foeus ot che least re
transible ones, irtich is theretore s = Inches, thac is very
nearly s: Tnches. Non to Hnom irhecher ehis mealure
ras erue, P repeated che second and cioheh Experiment ot
chisBook wich coloured Lighe, irtrich nas less compound-
ed ehan chac I chere made ile OF: FOr L no separared che
HCTCTO.

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heterogeneous Rays trom one anocher by che Mechod I de-
scribed in the iich Experiment, (0 a5 co make a coloured
Spectrum abouc ervetre or sitccen cimes longer than broad.
This Spectrum I cast on 2 princed b0ok, and placing che
aborementioned L ens ac the distance ot sIX Fect and an
Inch trom chis Spectrum o collect che Species ot che illu-
minated Letrers ax the same distance on the ocher (ide, L
found chac the Species of the Lerrers illuminated with Blue
vere nearer eo the Lens chan chole illuminated wich decp
Red by abour chree Tnches or threc and a quarter: buc the
Species oF the Leccers illuminated wich Indiso and Violet
appeared so contused and indistinct, chac I could noc read
chem: Whercupon vieming che Prilm, I Found ic ras full
oF Veinsrunnine from one end ot che Clals to che ocher;
Cochac the Retraction conld nor be regular. Itook ano-
cher Prilem cheretore ertich as trec trom Veins, and in-
Cead oEthe Lecters Puscd erro or chrec Parallel black Lines
2 lierle broader chan che Aroakes of che Letters, and cast-
ins che Colours upon chele Lines in luch manner that the
Lines ran along che Colours from one end of che spectum
co the ocher, l Found chac che Focus wrhere che Indico, Or
contine ot ehis colour and Violet cast the species of che
Black Lines most distinctly, cobe aboue + Tnches or 1 near-
er to the Lensthan che Focus where the decpest R ed cast
the Species ot che lame black Lines most distinetr.
Phe violet mas (0 fainc and darke, chac I could nOc
discern che Species ot che Lines distincty by chac Co-
tour; and cheretore considerins thac the Prism was made
ot a dark coloured Class inclinins eo Creen, L rook anocher
Pism ot clear Wrhice Cla(s; bur ehe Spectrum ot Colours
irtrich ehis Prism made had lone nhice Screams ot Faint
Liohe Chooring out trom boch cnds of the Colours, hich
made me conclude char Comethins ras amils; and viem-
in8

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ins che Prism, I Found ervo or chrec licele Bubbles in che
Class which retracted che Lighe irregularty. Wheretore L
corered chat pare oF the Class wich black Paper, and let-
eins che Lighe pals chrough anocher part ot ic wrhich vas
Frec trom uch Bubles, che Spectrum ot Colours became
Frectrom chole irregular Screams ot Lighe, and ras non
(uch asI. desired. Buc Rill I Found the Violer (0 dark and
Faine, chac l could scarce sec the Species oF the Lines by the
Violet, and noc ac all by che decpest pare oF ic, irtrich was
nexe che end ot che Spectrum. I Suspected cheretore chac
this Faine and dark Colour miohe be allared by thac scar-
cerins Lighe irhich as retracted, and reflected irregularty
parely by some very (mail Bubbles in che Clastes and
parely by che inequalicies of cheir Polictr: Wtrich Lighe,
tho ic was bue licele, vec ic beinq ot 2 Whice ColOuT,
miphe sustice co affect che sense (0 sronoly as eo dicturb
the Phaenomena ofthat weak and darke Colour che Violet,
and cheretore I cried, a5 in the 12th, 13th, 1ath Experi-
menes, Whecher che Liohe ot chis Colour did nor consist ot
a sensible mixture oF hecerogeneous Rays, bur found ic did
nOc. Nor did che Retractions cause any other sensible
Colour chan Violet eo emerge out of chis Lighe, 25 chey
vould hare done our ot Whice Lighe, and by con-
lequence out of this Violet Lighe had ic been sensi-
bly compounded wich Whice Lighe. Andcheretore Icon-
cluded, chat the realon why lcould noc sec the Species ot
the Lines distinctly by this Colour, was only che darknels
oF ehis Colour and Thinnels oF ies Lighe, and ies dis
cance Fromthe Axis oF the Lens; I dirided cheretore chose
Parallet Black Lines inco equal Pares, by which P miohe
readily lnom che distances ot che Colours in che spectrum
trom one another, and nored che distances OF che L enS
trom the Foci of such. Colours as cast che Species ot che
Lines

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Lines distinctir, and chen considered whether che disse-
rence of chole distances bear such proporrion eo s: Tnches,
che orearest difference ot the distances which che Foci ot
che decpest Red and Violet ouphe to hare From the Lens,
25 che distance of che obserred Colours From one anorher
in the Spectrum Bear coche like distance ofthe deepest Red
and Violet measured in the rectilinear Cdes of che Spect
rum, chac is, co the lenorh of thole sides or excels ot che
lerisch oF che Specerum abore ies breadch. And my Ob-
Serrations ivere a5 FollOms.
Wlhen Lobserred and compare d the deepest sen sible R ed,
and che Colour in che contine of Crcen and Bluc, wtich
ac chac rectilincar sides ofthe Spectrum as distane From it
halt che lenoch ofchole sides, the Focus where the contine
oF Creen and Blue cast che Species of the Lines distinctly
On the PaPEF, WaS nearer to the Lens chen the Focus ihere
the Red cast chose Lines dictinctly on ic by about 2 = OF
23 Tnches. For Comerimes che Nealures vere a lirele grea
cer, Cometimes a licele less, buc seldom varied From one
another above : ot an Inch. For ic was verr difticule co
detine che Places of che Foci, wichoue Pome licele Frrors.
Noi il che Colours distane half che lenech oF che Image,
(measured at its rectilinear Sides) give 2= Or 23 difference
oF che distances oftheir Foci trom the Lens, thenthe Co
Jours distane che whole lenoch ought to gire 5 Or 5: Inches
difference ofthole distances.
Buc herc ies co be noced, that L could nor sec the Red
co the tuil End oF che spectrum, bue only eo che CCnFEF
oF che Semicircle wrhich bounded thac End, or 2 licele Far-
cher; and cheretore l compared chis Red noc wich chat Co-
Tour irhich was exactly in che midele ofthespectrum, or
contine oF Creen and Blue, buc rich chac which verged 2
licele more co che Blue chanro the Creen: And a5 l reck-
Onec

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oned the wtole leneth at che Colours noc o be chenhole
lorsch oEche Spectrum, buc ihe lensch ot its rectilinear
Tides, (0 complerins chesomicinlar Fnds inco Circles, ivhen
cicher of che obserred Colours Fell michinthole Circles, 
mealured che distance et cac Colour srom che Find of che
Spoctrum, and subductins halethe distance trom che mea-
sured distance ot che Colours, L cook che remainder FOr
cheir corrected distances; and un chese Obserrations sec
donn chis corrected diltance for che difference ot cheir di-
Aances From. che Lens. For asthe lenorh ofthe rectilincar
sides of che Spectrum nvould bethe whole lenochi oF all che
Colours, Wvere che Circles of ntich las ve Chemed) chat
Spectrum consilts contracted and roduced ro Physical
Poines, Co in chac Cale chis corrected distance rould be che
real distance ot che oblerred Colours.
Wten cheretore L Furcher obserredthe deepestsensible R ed,
and chac Blue irhose corrected distance trom ic i2s  ParES
oFche lensch oE ohe rectilinear sides of the Spectrum, the
difference oF che distances ot cheir Foci trom che L ens Wvas
abOuc 8 Inches, ana 25 7 10 12 (0. 153 1053
When I obserred che decpest sensible Red, and chat Indi-
∞o nhole corrected distance ras = Or = oF che lenoch of che
rectilincar Cides of che Spectrum, che ditterence ot the di
sances of cheir Foci From che L ens, mas abour z2 luches,
and 25 2 10 3. (0 15 3:- 10 55.
When P obserred che deepest sensible Red, and chac deep
Indigo nhole corrected distance trom one anocher was = Or
ot che lengch of the rectilincar sides ot the spectum, che
difference ot the distances of their Foci tromthe L ens Was
abouc 4 Inches; and 25 3 20 4 (O is A EO 5
Wtien I obserred che deepest sensible Red, and chat part
of che Violet next the Indiso hole corrected distance trom
he Red Was Ox s oF che lenech oEche rectilinear sides ot
che

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che Spectrum, che ditference ot the distances ot cheir Foci
From the Lens mas aboue 4: Inches; and 25 5 106, l0 is
4= C0 52. For Cometimes when the L ens Was adrantagi-
ousty placed, Co that ies Aris respected che Blue, and aII
thines else ere well ordered, and thesun Cone clear, and
Pheld my Eye very near co che Paper on irhrich che Pens
cast che Species of che Lines, Pcouid sec preter distinctly
che Species ofthose Lines by chac part oF che Violet wrhich
was next che indipo; and lometimes P could sec chem by
abore halt che Violet. For in makeine chele Experiments
Thad obserred, thac che species ot thole Colours ontr ap-
Peared distince which ivere in ox near the Aris oFthe L enS:
So chat if che Blue or Indigo vere in the Aris, T contd see
cheir Species distincelr; and chen che Red appearedmuch
tels distince chan Betore. WHeretore I contrived eo make
the Spectrum oF Colours Chorrer chan betore, (0 thac both.
ies Ends mighe be nearer eo the Axis oF che Lens. And
non ies lensch ras abouc 2; Tuches and breadch about = Or
SOF an Tnch. AIso instead oF che black Lines on irtrich che
Specrum vas cast, I made one black Line broader chan
chole, chat L miphe see its Species more casilr; and chis
Line I dirided by Chore cross Lines inco equal ParES, FOT
mealurinothe distances oF the observed Colours. And nOW
J could Pomerimes sec che species ob this. L ine with its diri-
Tons almost 25 Far 25 che Cencers of the Senicireular Violee
tind ot che Speccrum, and made chese furcher Obserrations.
When L obserred che deepest sensible Red, and chac part
ol the Violet whose corrected distance From ic mas aboue
Parts ot the rectilinear sides of the Spectrum che difference
OFche distances ol che Foci oF chole Colours From the L ens,
was one time 4 anocher time 4 anochercime 13, Inches,
FF.
anel 25 8 c0 9, (0 are 4 13 4 3 4 5, 10 5 5 5n 55 respectivetus
W

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When I obserred che deepest sensible Red, and deepest
sensible. Violet, (che corrected distance of which Colours
When all chines ivere orderedco che bekt adrancage, andchc
Sun Chone very clear, was about Or is parrs ot che length
oF che rectilinear sides oF che coloured Specerum,) IFound.
che difference oF che distances of their Foci trom che Lens.
Cometimes  Pometimes 5:, and tor che most parts Tuches
Or chereabouts: and 25 21. E0 12, Or 15 t0 26, (0 is fire.
Inches. 10 5: Or 5= Inches.
And by chis progression oF Experiments I Cacissied my
SelF, chac had che liphe acche very Ends of chespectrum been
Arons enouph ro makie che species ot che black Lines ap-
pear plainty on che Paper; the Focus ofthe deepest Vio-
Tet ould hare been Found nearer co che Lens, than the Fo-
cus oF the decpest Red, by abour s: Tnches ax least: And
ehis is a Furcher Fvidence, chac the Sines ot Incidence and
Retraction ot che several COrts ot RayS, hold che same pro-
portion. co one anoctrer in che smallest Retractions nhich
cher do in che orcacest.
Hy proorels in makine chis nice and tronblelome Fxpe-
riment l. have sec donnmore at large, thac cher chac PaII
ery ic atcer me may be avare of che Circumspection res
quisite eo make ic succced well. And il cher cannor make
it succced (o well as I did, cher mar nocwichstandino col-
lect by che Proportion ot the distance ofche Colours in che
Spectrum, co che difference of. the distances ot their Foci
From che Lens, wtrat mould be che succels in the more di-
Aant Colours by a becrer Trial. And vet il ther ule a
broader Lens chan I did; and Eix ic to a lone sreiohe Staf
by means ot which ic mar be readily and cruly directed co
che Colour whose Focus is delired, I question noc buc che
Experimene will succced beccer wich ehem chan ic did. wich
me. For I directed che Axis as nearls as I could 1o the
midole

## Folio 69 — 1677894601:0079
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000079.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
midale of che Colours, and chen the faint Fnds ot che
Spectrum being remoretrom the Axis, cast their Species lels
distinetlr on che Paper than cher vould have done had che
Axis been successirely directed to chem.
Now by nhac has been said ies certain, chac che RayS
which differ in retrangibilicy do nor converge to the lame
Focus, buc it cher Aon trom 2 lucid poinc, 25 Far From
the Lens on onc sde as their Foci are one the other, che
Focus of the most retranoible RayS PMaII BC nearer tO che
Liens chan chac oF che least retrangible, by abore the four-
ceenth pare oF che whole distance: and it cher Row trom a lu-
cid poine, (0 very remore trom che Lens thar betore cheir
Incidence cher may be accoinred Parallel, the Focus oFche
most retrangible Rars Phall be nearer coche Lens than che
Locus ofcheleastretransible, br about the 27th or28ch ParE
oF cheir irhole distance From ic. And che Diameter oF che
Circle in the midele space becreen thole trro Foei which
cher illuminate when cher fall chere on any Plane, perpen-
dicular eo che Axis Cirtrich Circle is the least into irtich
chey can all bc gachered) is about che 55ch parc oF theDia-
meter ot che aperture oF che Cla(s. So chac tis a wonder
chac Telescopes reprelent Objects (0 distinet asther do. BUE
ivere alt che Rays oF Lighe equally retransible, the Error
arilins ouly from che sphericalnels ot che Figures oF Clastes
vould be mans hundred times lels. For il che Object
Class of a Telelcope be Plano-convex, and che Plane (ide
be curned comards che Object, and che Diamerer ot the
Sphere Whereotchis Clals is a segment, be called D, and chc
Semidiameter oFthe aperture of the Clals bc called S, and
che sinc ot lncidence out of Clals into Rir, be co the sine et
Retraction a5 ItO R: che Rars which come Parallel co che
axis oF che Cla(S, Chall in che Place where che lmage of the
Object is mot distinctly made, be scarrered all orer a lictle
Circle.

## Folio 70 — 1677894601:0080
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000080.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
Circle Wvtrose Diameter i5 =  S cub.
D quad. Very nearly, 25 Y 92-
ther by compucins che Frrors oF che Rays by che method
oF infinice series, and rejecting che Perms irhose quanti
ciries are inconsiderable. As For inistance, it the sine ofln-
cidence I, bc to che Sinc oF Retraction R, 25 20 t0 31, and
it D che Diameter of che Sphere to which che Conrex side
oF che Cilass is ground, bc 100 Fcet or 1200 Inches, and
S che Semidiamerer ot che aperture be cuo Inches, che
R X S cub.
Diameter oF che licele Circle (chac is T= D quad ) will DC
X 8
20 X 1200X +200 (OF 2600000) Parts oF an Inch. BuE the
Diamerer ot che licele Circle chrouph which chese RayS are
scattered by unequal retrangibilier, will be abouc the 55ch
pare ot che aperture ot the Object. Clals which here is FOuF
Auches. And cheretore the Frror arisino From che spherical
Figure of che Cla(s, is to che Error arising trom che disse-
s
rene Retrangibilier oF che RayS, 25 360
e0 815I: and cheretore beins in Comparison lo very licele,
delerres noc eo De considered.
Buc rou will Car, il che Errors caused by che different re-
Franoibilier be (0 very oreac, hon comes ic to pals chat Ob.
jects appear chrough Pelescopes (o dictinet as eney do: l an-
siver, Eis because che errino Rays are nor scarcere d uniform.
Iy orer all chac circular space, but collected infinicely more
denselr in che Center chan in anr ocher part ot the Circle,
and in che may trom che Cencer ro che Circumterence oro
continually rarer and rarer, (o a5 ac the Circumterence t0
become intinitelr rare; and by realon ot cheir rariey are
noc srone enouch eo bevisible, unlels in the Center and re-
YY ReaT it. L ET ADF reprelene one ot chole Circles de-
Scribed ich ehe Center C and Semidiamecer AC, and let
BFO be 2 smaller Cirele concentrie eo che Former, curtine
ith
i

## Folio 71 — 1677894601:0081
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000081.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
uvich its Circumterence che Diameter AC in B, and BelCCE
AC in NI, and br my reckonino che dentey oF oe Liote
in ary place B will be eo ies dentier in NI, a5 AB EO BC;
andche wtrole Lighe wichin che locter Circle BFC, Will. be
co ehe nhole Listuc richin che grCateE AFD, as the Excels ot
the Square oF. AC abore che Square oF AB, is to che Square
oF AC. AS iF BC be the ftch parE OF AC, the Lighue will bC
tour cimes denser in Bchan in N, and chewhole Lighewich-
in chelels Circle, will be corhe whole Liphe ichin che grea-
Ter, a5 nine to eiveney fire. Whence ics erident chac the
Lighe richin che less Circle, mustsrikce che sense much more
Aronoly, chan chac Faine and dilaced lighe round about be-..
cween ic and che Circumterence ot the greater.
Buc its turcher eo be noced, chac che most luminous ot
che prilmatick Colours are che Velloir and Oranse. Thele
aftect che Senles more Arongly chanall cherest together, and
nexc co chese in Arenoch are che Red and Creen. TheBluc.
compared with chese is a Fainc and dark Colour, and the In-
diso and Violet are much darker and fainter, (o that chele
compared ith che Aronger Colours are licele to be regard.
cd. Thc Images of Objects are cheretore to be placed, noc
in the Locus ot che mean retrangible Rays irtrich are in chc
contine of Creen and Blue, bur in che Focus ot chole Rays
ertrich are in che midele of che Orange and Pelloir; chere:
nhere the Colour is most luminous and fulgent, chat 15 I
che brightest Vellow, chat Xello which inclines Ore tO
Orange chan eo Green. And by che Retraction ot chele
RaYS lnhole Sines ot Incidence and Retraction in Clals:
are 25 17 and 11.) the Retraction oF Clals and Crystal For
optical ules is to be mealured. Let us theretore place the
lmage ot che Object in the Focus ofthese Rays, and all the
Tellon and Oransc Will Fall wichin a Circle, Whole Dir
mecer is abouc che 250ch parc of che Diamecer ot chie aper.
TUTE

## Folio 72 — 1677894601:0082
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000082.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
cure oFche Clals. And it rou add che briohrer half oF che
Red, (thac half erhich is nexe cheOrange, and che briphteK
halF oF che Creen, (chat half irtich is nexe the YcllOW,) a-
Bont chree ftrh pares of che Lighe oF chese ewo Colours rill
Fail wrichin che lame Circle, and eiro fifch pares will Fall wich-
out ic round about; and thac which Falls ichone will be
spread chronoh almost as much more space as chac irtich
Falls wichin, and (0 in the orols be almost chree cimes ra-
FeT. OF che ocher halF ot che Red and Green, (chat is ot
the deep darke Red and Willor OrCen) abOUE OnC QUarECF
Will FaII wichin ehis Circle, and chree quarrers writhour, and
chat erhich Falls withour will be spread chronoh aboue Four
or sire times more space than thac irtich Fall within; and (0
in chc oross berarer, and it compared with che ihole Lighe
arichin ic, willbe abouc 25 cimes rarer chan all chac cakien in
cheorols; or rather more chan 30 Or 40 rimes rarer, bc-
cause the deep red in the end ot che Spectrum ot Colours
made by a Prism is very chin andrare, and che Willon Oreen
is Comethins rarer chan che Orange and Vellor. The Lighe
OFchese Colours cheretore bring (o verr much rarer chan thac
richin che Circle, will Ccarce affect che sense especially since
the deep Red and Willo. Orcen of chis Lighe, are much
darker Colours chen the rest. And For che lame realon the
Bluc and Violer beins much darker Colours chanchese, and
much more raritied, may be neglected. For che dense and
briohe Liohe ot the Circle, ill obscure che rare and weak
Liohe oFchele dark Colours round about ic, and render them
almost insensible. The sensible Imase of 2 lucid point is
cheretore scarce broader than a Circle Whose Diameter is
the 25oth part ofthe diameter ofthe aperture oF che Object
Olass of a 000d Telescope, or noc much bronder, il vou
excepe a fainc and darke mistr liglie round aboue ic, ihich
aSpectator will scarce regard. And cheretore in a Tele(copc
urhose

## Folio 73 — 1677894601:0083
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000083.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
nhole aperture is four tnches, and length an hundred Fcct,
IE excecds nOt 2 45, Or 3. And in a Velescope nhose
aperture is tro Tnches, and lenoch 20 or 30 Feet, it may
BC s’Or 6’and scarce abore. And chis Ansivers well EO
Experience: For Pome Asronomers have found che Dia-
Meters OF Fhe AXE STarS, in Telescopes oF BCtWWCCn EvenEy
and lixey Fcet in leneth, eo bc abour + Or 5 Or ac most
S in Diameter. But it che Fre-Clals be tincted Faincly
wich che lnoke oF a L amp or Torch, eo obscure the Lighe
OF che Scar, the Fainter Liohe in the circumterence oF the
Star ceales co be risible, and the Scar (it che Class be suffici-
enely Coiled mich Cinoke) appears lomechins more like aNI2-
themarical Poinc. And FOr the Came reaION, FHC CnOROUS
part oFche Lighe in che Circumterence ot every lucid Poine
oughe co be lels discernable in Phorter Pelelcopes than in
longer, becaule che Phorcer transnit lels Lighe co the Fyc.
Nou il e suppole che sensible Image oF a lucid pOint,
to be eren 250 times narrover than che aperture ot che
Clals: yet vere ic noc for the ditterent retrangibiliey ot che
Rays, ies breadch in an 100 Foor Pelescope whose aperture
is 4 Inches woula be buc , 6ô Parts oF an Tuch, 25 is ma-
nifest by che foregoins Computation. And cheretore in
chis Cale che greatest Errors arising from che (pherical Figure
ot che Clals, vould be to che greatest sensible Errors ari-
Cins trom che differene retrangibilier oF che RaYS a5 360̂0000
EO  at nost, thac is onty 25 1 +0 1826. And chis sutt-
cientr Phews chac ic is noc che spherical Pioures ot Classes
buc che differene retrangibilier of ihe Rays irhich hinders thc
perfection ot Pelelcopes.
There is anocher Rroument by irhich ic may appear chac
the different retranoibilier oF Rars, is the cruc Cause ot che
imverfection of Telescopes. For che Errors of che Rays
aritins trom che spherical Figures of Object-Clalles, are a5
che

## Folio 74 — 1677894601:0084
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000084.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
ehic Cubes ofche apertures ofthe Object. Glasses; and thence
eo makce Telescopes of rarious lenochs, magnity wich equal
28
distinctnels, the apertures ot che Object-Glalles, and the
Charges or magnitrine Porers, oushc to bcas the Cubes ot
ehic (quare RoOrS oF cheir lenochs; irhich dorh noc ansiver
EO Experience. Buc che errors of che Rays arising From
the different retrangibilicr, are 25 the apertures ot che Ob.
ject. Classes, and chence eo make Telescopes oF rarious
lenochs, magnify rich cqual distinctnels, their apertures and
charses ouphe ro be. 25 the (quare RoOrs oF their lengetis;
and chis ansivers to experience 25 is vell knoWn. For in-
Aance, a Pelelcope oF 64 Feet in lenoch, ich an aperture
OF 22 Tnches, magnities abour 120 cimes, with as much dis-
tinctnels as one oF a Foor in lengeh, with = of an Inch aper
cure, magnities 15 times.
Non ivere it noc for this differene retransibiliey oF RayS,
Pelescopes miphe be brouche to a greater Perfection than
re hare ret described, by composine che Object-Clals ot
erro Glasses rich Wacer Becreen cheM. L EE ADFC repre
sent che Object-Clals compoled ot rmo Classes ABFD and
and BEFC, alike conrex on the outsides AOD and CTIE,
and alike concare on che insides BMTE, BNE, wich Wacee
in the COnCariEY BMTENT. Lec che Sinc ot Incidence ou ef
ClaS inEO Air bC 2SIEO R and ONE OF W aCeT INEO RIr 1S R
EOR, and by consequence out ot Cla(s into WV ater 25 T +0
K: and let the Diameter oF che Sphere to which the conrex
Sides ACD and CFIF are ground be. D; and the Diameter
of the Sphere eo irhich che concare sides BMIF and BNF
are ground beto D, 25 the CuDC ROOE OF HK -HI eo che
CuDC ROOE OF RK = RI: and che ReFractions on the con-
care sides of the Classes, rill verr much correct the Prrors
of che Retractions on the conrex sides, (0 tar as they arise
trom che sphericalnels oF che Figure. And by chis means
mighe

## Folio 75 — 1677894601:0085
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000085.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
mighe Telescopes be broughe eo sufticient perfection, wereit
noc For chedifferent retransibilier of sererallors oF RayS. BUE
by realon oFchis different retransibilier, I do noc rec lec any
Ocher means of improvins Pelescopes by Retractions alonc
chan chac ot increasine cheir lenechs, For which end che late
contrirance oF FIurenius seems well accommodated. FOr
very lons Tubes are cumbersome, and scarce to be readily
managed, and by reason ot cheir Length arC VerY apE EO
bend, and Phake by bendins (o as to cause a continual
cremblins in che Objects, whereby ic becomes difticule t0
lec them distinctlr: Wrhereas by his contrirance che Clastes
are readily manascable, and che Object. Clals beins fxc uP-
On a srong upriehe Pole becomes more ceddr.
Sccins cheretore che improvement of lelescopes of siven
lenochs by Retractions is desperare; I contrired herecotore a
Perspectire by reflexion, uling instead of an Object Olals
2 concare Metal. The diameter of the Sphere eo which
the Mecaliras ground concare as about 25 Englichr Inches,
and by consequence che lenoch of che Instrumene abOue sIX
Inches and a gnarter. The Eye-Olals was plano- COnVeK,
and che Diamerer of the Sphere eo which the conrex side Was
oround as aboue : OF an Inch, or a licele less, and by con-
sequence ic magnihed between z0 and +o times. BY ano-
cher ray ot meaturins l Found chac ic magnitied aboue
25 cimes. The Concare Nletal bore an aperture ot an Inch
and a chird pare; buc che aperture ras limired noc by an
opakce Circle, corerins the Limb of the Necal round abouL,
but by an opalce circle placed becween the Fye- Clals and che
Fre, and pertorated in the micdle wich a licele round hole
For che Rars co pass chrough co the Fyc. For chis Circle
by being placed here, sope much ot che erroneous Lighe,
Wrhich ocherrise rould have disturbed che Vision. BY com-
Parins ic wich a pretey 800d Perspectire of Four Feer in
2 2
lenseh,

## Folio 76 — 1677894601:0086
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
lenocti, made rich a concare Fre-Olass, I conld read at a
preater distance with my omn Instrumene chan wich che
Cla(5. Vec Objects appeared much darker in ic chan in chc
Olass, and chac parely because more Lighe was los by re-
Rexion in che Mecal, chen by refraction in the Cla(s, and
parcly because my Instrumene ras overcharoed. FTad ic
magnitied buc 30or 25 times it mouldhare madeche Object
appear more briske and plealane. Tiro oF chelelmade abour
16Tcars 200, and trare one ot chem Aill by me by whick
P. Can prove che cruch of whac l wrice. Tec it is noc l0g00d
25 ac the Arst. For che concare has been divers rimes car-
nistred and cleared again, by rubbing ic wich rery Potc L ca-
cher. When I made chese, an Arrist in London underrook
eo imicace ic; buc ulins anocher war ot polistring chem
ehan I did, he FelI much PhOrE oF what I had actained tO,
25 I alcermards understood by discourtino the under- W Ork-
man he had implozed. The Polish luled as on chisman-
ner. Phad erro round Copper Places cach sx Tnches in
Diameter, the one conrex chie ocher concare, ground re-
ey crue to one anocher. On the conrex I oround che Ob-
ject. ecal or concare irhich iras eo be polistid, eill ic had
calcen the Fioure ot the conrex and was readr For a Polistr.
Fhen Ipicched over che conrex very chinly, by dropping
melced pitch uxon ic aud warmine ic eo kecp the pirch
TOF, Wrhilst I ground ic rich the concare Copper werred to
makie ic spread erenty all over the convex. Phusby work-
ins ic well I made ic as thin 25a Croac, and atcer the con-
rex ras cold Iground ic again 1o sire it as true a Figure 25
Icould. Then P cook Pucer wrhich L had made very fine
by walhins ic trom all ies groller Particles, and lavins a lic-
de oF chis upon the picch, I ground ic uxon che Pirch wich
che concare Copper till ic had done makins a noise; and
then upon che Pirch Peround che Object. Mecal with a brisk
Mocion

## Folio 77 — 1677894601:0087
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
Notion, for about ero or chree Minures ot rime, leanine
hard uxon II. Then I puc Frech Pucer uxon che Pich and
oround ic 2gain eill ic had done makcing a noise, and atter-
wards ground che Object Metal upon ic as betore. And
ehis Work I repeaced eill che Mecal vas polistred, grindine
it che last eime ich alI my Srengch For 2000d while coge-
cher, and trequener breaching upon che Picch to keep ic
moist rithour lazins on aur more Frestr Puter. The Ob-
sect. Metal iras evo Inches broad and aboue one third pare
oF an Tuch chick, eo kecp ic trom bending. I had ewo ot
chese Metals, and wten l had polithed chem boch I cried
irtich ras best, and oround che ocher axain to sec if P conla
makce ic beccer chan chac irtich IKepE. And chus by mans
Frials I learne che way of polistrins, till I made thole tvo
refectins Pespectires I spake oF abore. For this ArE ot
polictiins will be becter learne by repeated Practice chan by
my descripcion. Betore I ground che OBject Mecal on the
Picch, I alivars oround che Puter on ic rich che concave
Copper eill ic had done matins a noise, because it che Par-
ticles oF che Puter vere noc by this means made co sick
Fast in che Pitch, cher vould by rollins ux and donngrate
and tret the Object Necal and AII ic FuIl ot licele holes.
But because Necal is more difficule ro polith than Class
and is aftermards very ape to be spoiled by carnilhins, and
reflects nor (o much Lighe as Clals quick-silvered over does:
Twould proxound conse insteadot theMecal, a Cilals ground
concare on the Forelide, and as much conrex on the back-
Side, and quick- Silrered orer on the convex Side. The Clals
must be every irhere of che lame chicknels exactlr. Ocher-
rile ic ill make Objects look coloured and indistinct. By
Tuch a Cla(s P eried aboue five Or (IX Tears 290 to male
a refectins Pelescope offour Fect in lensch eo magnity a-
bour 150cimes, and IPatistied my selF chae chere WAnES nO-
chino

## Folio 78 — 1677894601:0088
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
thins buE 2 800d Artist co brins che desion to Pertection.
For the Clals being irroughe by one ot our London Arcicts
atter such 2 manner as cher grind Classes For Telelcopes,
tho ic scemed as Well rouche a5 che Object Glastes ule 10
be, vec when ic as quick- silrered, che reflerion dilcorered
innumerable Inequalities all orer che Clals. And by reason
ot chese Inequalicies, Objects appeared indictinet in chis In-
ATUeHE. FOr the Errors ot reflected Rays caused by any
Inequalier ofche Clals, are aboue lix times oreater than the
Frrors ot retracted Rays caused by the like Inequalicies. Yet
by chis Experimene I Pacisfied my selF thac the refterion on
the concare side of che OlaIs, Which I Feared ronld disturb
che rision, didno sensible prejudice ro ic, and by consequence
chac nochins is mantins to pertect chele Telelcopes, bue
oood Wortemen uho can grind and polith Glasses cruly sphe-
rical. An Object Clals ot a tourtcen Foor Telescope, made
BV one et our Pondon Artificers, I once mended considera
bIy, by crindins ic on Dicch wich Puter, and leanins ve-
ry casily on ic in che grinding, lest che Pucer Phould Scrarch
ic. Whecher chis rar mas nov do ell enouoh For polistr
ins chele reflecting Clalles, I have noc vet cried. Bue he
chat Phallery cicher this or any ocher rar of polictrinq wrhich
he mar chink becter, may do well eo make his Clasles rer
dy For polictrins by grinding chem wichour chac violence,
Whererich our London Workmen prels cheir Clasles in prind-
ing. For by such riolent presture, Cilasses are ape eo bend
2 licele in che grindins, and suchbending will cerrainly spoil
their Figure. Po recommend cherefore the consideration
oF these reflectins Glasles, to such Artists aS are CuriOUS IH
tixurins Classes, I Phall deseribe chis Oprical Instrument ip
che Collowins Propotuion.

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aL. DII. L+00. Ll.
To sorten Felescopes.
ET ABDC represent a Clals spherically coneare On Fiz. 29.
the Foreside AB, and as much conrex on the back-
Side CD, Po that ic be every irhere ot an equal chicknels. L eF
ic noc be chicker on one side than on the ocher, lest ic make
Objects appear coloured and indictinet, and let it be very
cruly irroushe and quick-silvered overon chebacksde; and
sec inche Tube VXVZ which must be very black rithin.
LeE FFC reprelent a Prism of Clals or Crystal placed near
the ocher end of the Tube, in che middle of ic, by means ot
2handle oF BraIS OF ITON FOK, to che end ot ehich made
Aac ic is cemented. Lec chis Prilm be rectangular aF F, and
lec che ocher erro Anoles at F and O be accurately equal EO
each ocher, and by consequence equalco halt righe ones, and
lec the plane Cides FF and OF be square, and by conse
quence the chird Side FO a rectansular parallelooram, whole
lenseh is eo its breach in a Tubduplicate proportion ot ervo
eo onc. Lec ic bc (0 placed in the Tube, thac che Axis oF
thespeculum may pals chrouoh che midale ot the square
lide F.F perpendiculartr, and by consequence chrouoh the
midele oFche side F C ac an Anele oF 45 deorces, and lec the
Side EF be curned tomards che speculum, and the distance
oFchisPrim Erom che Speculum be such chac che Raysofche
lighc PD RS, _cc. Wrhichare incidene upon the speculum in
Tines Parallel co che Aris chereof may encer che Prism ac
ehe Side FF, and be redlected by che side F G, and chence
50 oue ot ic chrouoh che side CF, to che poine Y itict
must be the common Focusof the Speculum ABDC, and ot
2 Plano- convex Pre- Ola(s FI, chrouch ihich chole RayS
must pals coche Frc. And lec che. Rays at cheir comins
DuF

## Folio 80 — 1677894601:0090
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out of che Cla(s pals chroush a (mall round hole, Or aper-
cure made in a licele Plate ol Lcad, Brals, or Silver, Where
rich the Cilass is to be corered, itrich hole must be no
bioger chan is necellarr for liohe enough co pass chrouoh.
Fior (0 it will render the Object distinct, the Plare in wrhich
cis made intercepting all che erroneous pare oF che Lighe
irhich comes From che Verges ot che speculum AB. Such
an Instrumene ell made if ic be 6 Foor long, (reckonine
che lenoch from che Speculum eo che Prilum, and FhenCC EO
Ehe FOcuS T) ill bear an aperture of 6Tnches ac che Spe-
culum, and magnity becreen ero and chrec hundred cimes.
Buc che hole II here limies che aperture wrich more advan-
eage, chen it che aperture iras placed ac the speculum. IF
che Instrument be inade longer or Phorter, the aperture must
bc in proporcion as the Cube of che square ROOE of ehe
lenoch, and che magnitrins as che apercure. Buc itS COn
veniene chac che speculum be an luch or erro broader chan
ehe apercure ac che least, and chac che Clals of the speculum
be chick, chac ic bend noc in the morkeing. The Prilm FFO
must be no bigger chan is necellarr, and its back sde FO
must noc be quick-silvered orer. For Without quick- silver
ie will refect all che Liohcincident on ic trom chespeculum.
In chis Instrument che Object rill be inverced, buc may
De crected by makcing che square Sides FF and FC oF the
PriIm FFC noc plane buc spherically convex, chac the RayS
may crols as Well betore ther come ac ic as attermards bc-
circen ic and che Fre- Olals. IF ic be delired chac the Instru-
ment bear a larger aperture, char may bc allo done by com
Polins che Speculum oF ciro Glastes wich Wacer Betreen
chem.
AI

## Folio  -  — 1677894601:0091
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16.
16. V.
is. 3.
Book L. Place L. Part L.
18. 2
TIB. 5.
F. 9T
28.7
RIED WILHELM LEIBNIZ BIBI
ACHSISCHE LA

## Folio  -  — 1677894601:0092
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S stt a sl t lt seltatt attat  t. a su.  as st  ot ( sat    . B tatl ablt ssiluti d sot otelt Hut s HBt   Au s (a se  . . s l MB)H H. M sBH ult snt . I. HI IB1IHBIGIII
NIEDERSACHSISEHELANDESBIBLIOTHEK
: Leion.
38
GOTTFRIED WILHELM LEIBNIZ BIBLIOTHIEK

## Folio  -  — 1677894601:0093
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 8.
B00k I. Plate HI. PaPFI.
. .            .......
... . . . .
1 usm..
f18. 9.
im
l1810.
mmf
I
I
. . . . . . . . . 2
C6. -.
WILHELM LEIBI
HE

## Folio  -  — 1677894601:0094
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 s. test a sl  t lta seltates ottat  sat Hu.  t set  Abt ( lu l ut  t b  stuss s  M  ut l l A s M Hu (  H   M uet  lu L  H H. I B.1II ).l1
HIEDERSACHSISCHE LANDESBIBLIOTHEK
r: Leibn. 1
36
DOTTFRIED WILHELM LEIBNIZ BIBLIOTHEK

## Folio  -  — 1677894601:0095
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a
.. .
e
N
d
... . . . . . . .
3
 . .... . . . . . . . 7
.
16.
B00k T. Plate HI. Par2 I.

## Folio  -  — 1677894601:0096
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VIEDERSACHSISCHE LANDESBIBLIOTHEK
car: LCitn. Maro. 1.
GOTTTNILD BBILIILCHILCIBNIZ BIBLIOTHEK

## Folio  -  — 1677894601:0097
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f18. 19.
FI8. 21.
1C
BOOK, L. Plate, WV. Part, l.

## Folio  -  — 1677894601:0098
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  B. (. ( a  es  sut. Hte seula M. M    . (.  . ((a  s H. fult H . HGae H (saus A. Mabu . Gu. B.La. Sl ulIHB. B Ht  Bu . S slu
NIEDERSACHSISCHE LANDESBIBLIOTHEK
Matur: Leitor. Mar9. 193
BC
SOTTTRILD BVILHILLMILEIBNIZ BIBLIOTHEK

## Folio  -  — 1677894601:0099
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Oidi
B. 24
F..
d
27
BOOR, I. Part L. Plate V.
25
e
1e 28.
3C
1
Ad H. I

## Folio  -  — 1677894601:0100
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.
I
II
1
tHILMH
1
1
III
11
11
l
IIIIIII
1 1
I1 siHI
MHIIHIII
I MH. B. HIBHIII
NIEDERSACHSISCHE LANDESBIBLIOTHEK
atur: Loitn. Maro. 193, (1
OTTFRIED WILHELM LEIBIIL BIDLIMIER

## Folio 81 — 1677894601:0101
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d
BI
TTT F
L BOOn
F
P A R T TI.
PROP. I. THFOR. I.
Jhe Phanomena o Colours in refracted or reflectea Lieht
are not caused hy nere modifications of the Lie ht various-
ly imprest, accorns to the various terminations of the
De Proes By Paperiments.
F Z P F R. T.
OR if the sun ine into a very dark Chamber Fie. I.
throuoh an oblons FTOle F, Whole breadth is the
lixth or eiohth part of an Inch, or Pomethins lels; and
his Beam LII do altermards pals Arst chroueh a very
larse Prism ABC, distant about 20 Feet trom thie
ITole,
Lisht and Shadore.

## Folio 82 — 1677894601:0102
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TTole, and paraslel toit, and then (with its wrhite part)
chrouoh an oblons HIOleHI, wrhose breadth is about
the fortieth or sixtieth part oF an Inch, and irhich 15
made in a black opake Body GL, and placed at the
distance ot tro or three Feet trom the Prilm, in a pa-
callel situation boch to the Prilm and to the former
TIole, and ifthis irhite Lioht thus transmitted throuoh
the Hole HI, Fall asterrards uxon a Wrhite Paper pt,
placed alter that HIole H, at the distance oF three or
tour Fcet trom it, and there paint the ulual Colours ot
the Prim, suppole red at t, vellor at S, Sreen at Y,
blue at q, and violet at p; rou may with an iron Wire,
Or any such like Plender opake Bodr, Wrhose breadth is
about thetenth part of an luch, by interceptins the rays
at H, l, M, n OrO, takce aray any one oF the C OlOurS
aEC, S, L, GOr P, WrhilA the other COlours remain ux-
on the Paper as betore; or rith an obstacle lomethine
bisger rou may talce avaz any tro, or three, Or FOUL C0.
Jours together, the rest remainins: So that any one ot
the Colours as well as violet may become outmost in
the contine ot the Pado torrards p, and any one ot
them a5 Wveil as red mar become outmost in the contine
OFthe Bacoi corrardst, and any onc of them mav al(0
border uxon the Madon made within the Colours Dy
the obsacle R interceptine Pome intermediate part ot
the Licht; and, lattls, anr onc ol them by. beine
lest alone mar border uxon the Madorr on cither hand.
AII the Colours hare themlelres indifferenty to any
contines ot Phado, and theretore the difterences otthele
ColoursFrom one another, do not arile from the ditse-
rent contines of. Tador, Whereby Liont is rariousy
modified as has hitherto been the Opinion oF Philolo
PhCIS.

## Folio 83 — 1677894601:0103
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phers. In eryins these chinss tis tobe obserred, that
by hom muchthe FToles L’and HI are narrorer, and the
interrals betireen them, and the Prilm oreater, and the
Chamber darter, by so much the becter doth the Fx
periment succced; provided the Light be not (0 Far
diministred, buc that the Colours at pt bc Cusficientr
risible. T0 procure a Prilm oF Colid Cilass larse enough
For this Fixperiment will De difficult, and therctore a
prilimatiek Vessel must be made ot politted Cilals. Plates
cemented together, and tulled wich Nater.
E Z P F R. TI.
The Suns Lishe let into a dark Chamber throush Fis. 2.
theround Holeti, halEan luch ide, passed Arst through
che Prilm ABC placed at the HTole, and then throush
a Lens PY Comethins more than tour Inches broad, and
about eishit Fcet distant trom the Prilm, and thence con-
versed to Othe Locus oF the Lens distant trom it about
chree Lcet, and there Feil upon a irhite Paper DF. IF
that Paper ras perpendicular to that Lishe incident up-
on it, a5 tis reprelented in the posture DL, alltheCo.
lours upon it at O appeared irhite. But il the Paper
beins turned about an Axis parallel to the Prilm, DC-
came very much inclined to the Light aS tis reprelen.
ted in the positions de and sc; the tame LishE in The
one case appeared vellor and red, in the other blue.
lere one and the lame part of the Lisht in one and the
lame place, accordins to the rarious inclinations of the
Caper, appeared in one case irhite, in another vellor
or redu in a chird blue, Whils che contine oC Ligtt and
Stractow,

## Folio 84 — 1677894601:0104
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84
Stracto, and the retractions oF the Prisim in aII these
cales remained the lame.
AZ PF R. TTI.
Such another Fxperiment may be more casily tricd
a5 Follos. Let a broad beam ofthe Suns Light comine
into a dark Chamber throuh a HTole in the WVindon
But De refracted by a larse Prim ABC, wrhole re
Tractins Ansle C. is more than 60 degrees, and (o loon
a5 it comes out of the Prilm let it tail uxon the irhite
PapeF DF. glered upon a sit plane, and this Lisht
Wrhien the Paper is perpendicular to it, 25 tis seprelen-
ted in DF, Will appear pertectis irhite upon the Paper,
but irhien the Paper is very much inclined to it in tuch
a manner a5 to keep alirars parallel to the Axis of the
Prism, the erhiteness ot the wrhole Lishe upon the
Paper ill accordins to the inclination ot the Paper
this ar, or that war, chanse cither into vellor and
red, a5 in the posture des or into blue and violet, a5
in thepolture oc. And if the Light betore it fail upon
the Paper be tvice refracted the Came ray by tmo pa-
rallet Prisms, these Colours rill become the more con-
Spicuous. FTere alI the middle parts oF the brond Beam
OFwrhite Light prhich fell upon the Paper, did rithout
any contine ot hadtor to moditr it, become coloured
aII over rith onc unitorm Colour, theColour beins al-
ays the tame in the middte ot the Paper as at the
cdges, and this Colour changed accordinq the rarious
obliquitr ot the retlectins Paper, without any chanse
in the retractions or Bado, or in the. Liont which
Fell uxon the Paper. And theretore these Colours are
Fig. 3.

## Folio 85 — 1677894601:0105
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65
to be derired Erom (ome other cause than the new mo-
difications ot Liohe by refractions and MadorS.
TF it be asked, Whac then is their cause d I anfivei,
That the Paper in the posture de, Deins more ob-
lique to the more retransible rars than to the lels re-
Fransible ones, is more Aronsly illuminated by the lat-
ter than by the former, and theretore the lels retran-
sible rays are predtominant in the refected Light. And
erhrererer they are predominant in any Light they tinge
it with red or zelloir, as may in lome mealure appear by
the Airst Proposition ot the Arst Book, and will more Fully
appear herealter. And the contrary happens in the
pocture oF the Paper oc, the more retransible rays De-
ins then predominane wrhich alrars tinse Light wich
blues and riolets.
E Z P F R. IV.
TheColours oF Bubbles With Wrhich Childien play
arc rarious, and change their situation variousr, with.
out aur sespect to aur contine ot Badow. IF such a
Bubble De corered rith a concare Gilass, to kecp it From
Deins agitated by any ind or motion ot the AIr, the
Colours rill Rorrly and regularty change their situa-
tion, eren hilsthe Fre, and the Bubble, and aIl B0.
dies vrhich emit any Light, or cast any Chadou, re-
mainunmored. And theretore their Colours arise From
Pome reoular cause ertrich depends not on any contine ot
Padtor. Whatthis cause is wrill be Merred in the MexF
BoOk.
T0

## Folio 86 — 1677894601:0106
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Pothese Fxperiments may be added the tenth FX-
periment oE che tirst B0ok, Wrhere the suns Light in a
dark Room beins trajected throush the parallel superti-
cies oftiro Prilmstied together in the form ot a Paral.
lelopide, became totally ot one unitorm vellor or red
COlOur, at its emergins out of the Prilms. Hlere, In
the production ot these Colours, the contine oF Madon
can have nothins t0 do. Forthe Lisht chanses FrOM
Wrhite tovellor, oranse and red successirely, rithout any
alteration oEthe contine of strador: And at both edges ot
theemergins Lisht irhere thecontrary contines oF Ma-
dorr ousht to produce ditterent efects, the Colour 15
one andche Came, Wrhether it be rrhute, sellorr, oranse
or red: And in the midale ot the emersins Light,
artrere there is no contine ot Mador at aIL, the COIOUE
i5 the very lame a5 at the edges, the Wtrole Lioht at its
very tirk emergence beins ot one unitorm Colour, irhe
cherwrhite, vellor, oranse or red, and goins on thence
perpetually richout ans chanse ot Colour, cuca a5 the
contine ot strador is vulsarty suppoled to worke in ie
Fracted Lisht alter us emergence. Ncither can thele
Colours arise trom any new moditications ot the Light
by retractions, becaule they chanse successirels trom
Wrhitetorellor, oranse and red, rrhile the retractions
remain the same, and allo becaule the retractions are
made contrary rays by parallel superticies wrhich de-
Aroy one anothers effects. Lhey arile not theretore
trom ans modifications oF Lishe made by retractions
and Chadors, but hare Lome other cause. What that
cause 15 ive ered abore in this tenth Lixperiment,
and need not here repeat II.
L. DetC

## Folio 87 — 1677894601:0107
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There is vet another material circumstance oF thIS
Fixperiment. For this emergins Light being by a third Fic. 22.
Prilm FIIK retracted torrardsthe Paper PP, and there Part 1.
Daintins the usual Colours of the Prism, red, vellou,
sreen, blue, violet: IF these Colours arose from the
retractions of thac Prilm moditvins the Light, they
ronld not be in the Light betore its incidence on that
Prilm. And vet in that Fixperiment re Found that
Wvtren brturnine the trro Arlt Prisins about their com
ion AXis aII the Colours vere made to vani but the
red; the Lisht rhich makes that red beins letr alone,
appeared ot the verr Pame red Colour betore its inci-
dence on the third Prism. And in general ve find by
other Fxperiments that when the rars erhich ditter in
retransibilitr are separated From one another, and auy
one Cort ot them is considered apart, the Colour ot the
Lisht irhich ther compose cannot De changed by any
retraction or reflexion whaterer, as it ougnt to beWere
Colours nochins else than modifications ot Light cauled
Oy retractions, and reflexions, and Padous. This un-
changeablenels ot Colour J am nou to describe in the
Follorrins Propolition.
PROP. TI. THFOR. TI.
Al homoreneat Feht has its proper Colour anfrverine to
its deoree of refransibility, and that Colour cannot be
chansed by reflexions and refractions.
In ThC ExperimentS OF thC Ath Proxolition oF the Firs
B0oK, Wrhen l had separated the heteroseneous rays
om one another, the Spectrum pt Formed by the sepa-
ratect

## Folio 88 — 1677894601:0108
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rated rars, did in the prooresstrom its end p, on rrhich
the most retransible rars Fels, unto its other end L, On
erhrich the least retransible rars tell, appear tinged wich
this Series of Colours, violet, indico, blue, sreen, vel
low, oranse, red, toscther ith all cheir intermediate
degrees in a continual succestion perpetually varyins:
S0 that there appeared as many desrees oF COlOurs, 25
there were Ports oF rays ditterins in retransibility.
AIZ P F R. V.
Now that these Colours could not De changed by re-
Fraction, Iknew by retractino rith a Prilm Lometimes
one very licele part oF this Lishe, Cometimes another
very little part, as is delcribed in the i2th fixperiment
OF the ArsE BOOK. For by this retraction the Colour ot
the Lisht ras nerer changed in che lealt. IF any part
OFthe red Lisht as retracted, it remained totally ot
the lame red Colour as betore. Ho oranse, no vel
lorr, no green, or blue, no other new C Olour Wras prO.
duced Oy that retraction. Neither did the Colour ans
rays chanse by repeated retractions, but continued al-
avars the lame red entirely as at Arst. The like con-
staner and immutabilier I tound allo in the blue, orcen,
and ottier COlours. S0 allo iFI looked throuoh a Prilm
uxon any body illuminated with ans part ofthis homo
oeneal Lient, a5 in the gth Fxperiment oF te first
Book is described; l could not perceire any nem C0
lour generated this ray. AII Bodies illuminated ith
compound Light appear throushi Prisins confused (as
WraS. laid abore) and tinsed rith rarious new C OIOUTS,
but those illuminated rith homogeneal Light appeared
throusI

## Folio 89 — 1677894601:0109
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89)
chrough Prisins neither less distinct, nor ottermise co-
loured, than wrhen riemed rith the nakced Ryes. Pheir
Colours ere not in the least changed by the retraction
et the interpoled Prism. I EpeaK here oE a senible
chanoe oF C OIOUE: Por the LishE which I here calt hO-
mogeneal, Deins not absolutelr homogeneal, there ouoht
to arise lome litele chanse ot Colour trom its heteroge-
neitr. But if that heterogeneitr wras (o little as it might
Demade, by the laid Experiments of the tourth PropO-
lition, that chanse ras not sensible, and theretore, in
fixperiments irhere sense is judse, ought to be accoun.
ted none aC aII.
E Z P E R. VI.
And as thele Colours ivere not chanseable by retra-
ctions, lo neither vere ther by resexions. For aII
irhite, srer, red. vellor, sreen, bluc, violet Bodies, 45
Paver, ACes, red L ead, Orpiment, Indico, Bisc, Grola,
Silver, Copper, Cirase, blue Florvers, Violets, Bubbles
ot Water tinged rith rarious Colours, Peacocks Fea-
thers, the tincture ot Fionum Nephriticum, and Tuch
like, in red homogeneal Light appeared totally red, in
blue Light totallr blue, in green Light totally orcen,
and (0OF other COlours. In the homogeneal Lightot
ot an Colour ther all appeared totally ot that lame
Colour, with this onlr ditterence, that some ot them
reflected that Lighe more Aronsly, others more Faintly.
lnever vet tound any Body irhich by reflectins homo-
veneal Lishe could sensibly chanse its C olOur.
FTOL

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(G
D
From ail Wrhich it is manitest, that if the Suns Light
consisted ot but one Port oF rays, there would be but
one Colour in the Wwhole Worid, nor mould it be pol-
Sible co produce anr ne Colour by rellexions and ie
Fractions, and by consequence that the rariety oF C0.
lours depends upon the compolition ot Lisht.
DF F TNTT TON.
Thehomoseneal lighc. aud rays wtricti appear redq
or rather make Objects appear (0, L call rubrific
or red makns; thole erhich make Objects appear
vello, oreen, blue and violet, I call vello-ma-
kins, sreen makins bluc- makrimg, violet-makine,
and (o oftherest. And itat any cime I speak ot
lioht and rars as coloured or endued rith C0-
lours, Iirould De understood to (peak not philo.
Cophically and properir, but grolly, and accor-
dins to luch conceptions as rulsar People in sec-
ins all these Experiments rould De apt to Frame.
Lor the rays to speak property are not coloured.
In them there is nothine elle than a certain porver
and dispolition to stir up a sentation ot this or that
ColOUT. For as Pound in a Bell or muticalStrins,
Ox other Coundins Bod, is nothins but a trem-
blino Mocion, and in the Air nothino but that
Motion propasated trom the Object, and in the
Senlorium tis a senle oF tliat Motion under the
torm ot lound; (o Colours in. the Obiect are no-
thins but a dispolition to reflect this or that COrF
ot rays more copioully than the rett; in the rayS
cher are nochins but their dispolitions to propa-
sate

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(OT)
sare this or that Motion into the Sentorium, and
in thesentorium ther are senlations of thole NO-
tions under EhC FOTIS OF C OIOUES.
PROP. TII. PROB. I.
o define the refransibility of the several sorts of homo-
seneal Lioht ansrverine to the several Colours.
For determinins this Problem Imade the follovins
tixperiment.
F Z P F R. VII.
When Thad caused the rectilinear line sides AF, GTNI, Fig. 4.
oFthe Spectrum et Colours made br the Priim co DC
distinetly detined, a5 in the Riech fixperiment oF the
Arst Book is described there vvere Found in it dII the
homoseneat Colours in the Came order and stvation
one amons another as in the Spectrum ot simple Lignt,
described in the FOUTEM FXPCTImeNE OF Fhat BOOK. FOF
the Circles of irhich the Spectium ot compound Lignt
eT is compoled, and irhich in the midale parts ot
the Spectrum intertere and are intermist with one ano-
ther, are not intermixt in their outmost parts where
they touch thole rectilinear sides AF and CTMI. And
theretore in thole rectilinear sides wrhen distinctiy deti-
ned, there is no new Colour generated by retraction. l
obserred allo, that it any where betureen the trvo out
most Circles PMF and PG A a right linc, 25 Y0, WaS
crols tothe Spectrum, (0 a5 at both ends to FaII per-
vendiculariy uxon its rectilincar lides, there appeared
Nt
OnC

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E
one and che Tame Colaur and degree ot Colour From one
end ofthis line cothe other. L delineated cheretore in
a Paper che perimeter oF the Spectrum I A P GMI L,
and in tryins ehethird Fxperiment oE the APA BOOL, 
held che Paper s0 that the Spectrum mighe FaII upOn
this delincated Figure, and agree with it exactly, wrhil
an Asistant irhose Lyes For diltinsuithins Colours vere
more critical thanmine, did by ristt lines aB, 78u cl, 86
deawn crols the Spectrum, noce the contines oF the CO-
lours chat is oF thC red MIa BF OF FHC OTANOE a XA B. O1
the vellorr rc58, ot thegreencnde, oF the blue n2nDq
of the indico inux, and oF the violet n CFAH. And
chis operation beirss divers times repeated both in the
Tame and in sereral PapeES, I Found that the OB
Terrations agreed elt enough writh one another, and
thatthe rectilinear sides MI Ci and F’A vere by the Caict
crols lines dirided after the manner oF a mutical Chord.
L et GMI bC produced to Z, that M Z may bc equat
toGM, and conceire (Z, n Z,  Z, nZ, ck, Y2, aZ,
M Z, tobe in proportion to one another, a5 the num
DerS 19 57 89. 9 5 33 103 23 and (0 to reprelent the
Chords oF the Ker, and oE a Pone, a third MinOr, 2
tourth, a fitth, a lixth Major, a serenth, and an eighttr.
abore that Key: And the interrals M =, a7, YC, en, n1,
n, and. n Ci, Will. be the spaces Wrhich the several C0-
lours (red, oranse, vellor, oreen, blue, indico, riolet)
Take UP.
Nor chese intervals or spaces subtendino the difte
rences ot the retractions oE the rars soins to the limits
OF those Colours, That 15, to. The PoinEs , ag. 7, C 12, 2, (5,
may without any sentible Frror be accounted propor
tional to the differences oFthe lines oFretraction ofthole
1475

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rars havins one common fine of incidence, and chere.
Fore since the common tine ot incidence ot the most and
least retransible rars out oF CilaIs into Air WaS, (By à
method deleribed abore) Found in proportion to their
sines oF retraction, a5 50 t077 and 78, divide the dif-
ference Detreen the fines ot refraction 77 and 78, 25 the
line CM is dirided by those interrals, rou will have
7
733 7723 7733 773, 78, the tines ol
retraction ot thole rars out ot Clals into Rir, their
common sine of incidence beins 50. S0 then the lines
OE the incidences oF all the red makins rays out ot
Cilals into Rir, vere to the lines oF their retractions,
not greater than 50 10 77, nor le(s than50 +0775, but
raried trom one anocher accordins to all interme-
diate PFOPOTtIONS. And the sines oF the incidences
ot the sicenmakins rays vere to. the sines ot
their retractions in all proportions From that ol 50
1077, Unto that of 50+0 77:. And by the like limits
abore mentioned ivere the retractions of. the ravs De.
longins tothe rest ot the Colours detined, the lines ot
the red-makcins rays extendino From 77 t0775, thole
ofthe oranse- makcins From 775t0 77, thoseofthe vel-
lor malcins From 77: 10773, thole ofthe green makins
Erom 77: t077= thole otthe blue makins From 77 = t0
75, those oF the indico-makins From 773 t0 775, anc
thole oFthe violet From 773 1078.
Phese are the Laws ot the refractions made out ot
Colals into Rir, and thence by the three AXioms ot the
tirst Boole the l’aws oF the retractions made out of Air
into Cilals are catily derived.
a X L L. HL.

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L 21
E Z P F R. VTII.
Y fourid moreorer that wrhen Light goes out ot Rii
chrouch several contiouous retractins Mediums a5
chrouoh Water and Glals, and thence soes out again
into Rir, irhether the retractins superticies be parallel
or inclined to one another, that Light as often a5bY
contrary retractionstis so corrected, that it emerseth
in lines parallel to those in irtich it ras incident,
continues ever alter to be Wrhite. But il the emer.
sent rars be inclined to the incident, the erhitenels ot
the emergins Lieht iil by degrees in passins on From
the place ofemergence, become tinged in its edges with
COlours. This lerred by retractins Light rith Prisins
oFGlals mithin a prismatick Vessel oF Water. Nou thole
Colours argue a diversins and separation of the hetero.
geneous rays From one another by means oF their un
equal retractions, as in ertrat follors will nore fulty
apPeaT. And, on the contrary, the permanent wrhite
nels argues, that in like incidences ot the rays there is
no such separation of the emersins rars, and by conse
quence noinequalier oftheir wrhole retractions. Whence
lscem to gether thetrro follorrins Theorems.
T. The Fxcesses oF the sines oF refraction oE sererat
Forts oF rars abore their common sinc ot incidence irhen
the retractions are made out ot divers denser mediums
immediatels into one and the lame rarer medium, are
to one another in a siven Proportion.

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195
2. The Proportion of the sine ot incidence to theline
et refraction ot onc and the lame fort ot rays out of onc
medium into another, is composed of the Proportion ol
che ine oE incidence to the sinc ot retraction out of the
tiest medium into aur third medium, and ot the Pro-
Portion oF the line ot incidence to the sine oF retraction
out oF thac third medium intothe lecond medium.
By the Ars Theorem the retractions of the rars ot
every Tort made out of anx medium into Air are knon
Oy havins che retraction oF the cars oF any one Cort. AS
tor instance, it the refractions ot the rays ot everr lort
out oF Rain-ater into Air be delired, let the common
Eine oF incidence out ot Citass into Air De subducted
From the fines ot refraction, and the Lxcesses will DC
7, 2753 2753 2753 272, 273, 279, 28. Suppole non
chatthe Ane ot incidence of the least retrangible rars be
eo their sine ot retraction out ot Rain water into AII 25
threc tO Four, and Car as I the difference ot thole sines
is toz the tine ot incidence, (0 is 27 the least of the
Lxcelles abore. mentioned to a Fourth number 8T; and
8+ Will De the common sion ot incidence out of Rain-
water into Air, tortrich line it vou add aIl theabore
mentioned Fixcesses vou rill have the dehired sines ot
the retractions 108, 10807. 1083, 108;, 108;, 1083,
2083, 109.
By thelatter Theorem theretraction out of onc me-
dium into another is sathered as otten as vou have
the retractions out of them both into any third medium.
AS. iF the line oF incidence of any ray out oF Cilals into
Air be to its tine ot retraction a5 20 t0 3r, and the sinc
ot incidence of the lame ray out of Air into Water, DC
te

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CC
EO itS sinc oF refraction aS FOUF tO three; the sine ol
incidence ot that rar ont ot GlaIS into WVater Will BCFO
its sinc ot refraction a5 20 t0 3r and 4 toz jorntly, that
15, 25 the Factum oF 20 and 4 to the F’actum oF ZL and
33 OF 4580 +093.
And these Theorems beins admitted into Opticks,
there rould be (copeenoush ot handlinq that Science
voluminoullr alter a neur manner; not ontr by teachins
thole chinss irhich tend tothe perfection ot vision, but
alloby determinins mathematicasIr all kinds oF Phaeno-
mena ot Colours wrhich could be produced by retra-
etions. For todo this, there is nothing else requisite
than to find out the separations ot heterOgeNCOUS FaYS,
and their various mixtures and proportions in everi
mixture. By chis way oE arsuins linvented almioit
allthe Phaenomena described in these BO0kS, Beside Tome
othiers lels necellary to the Aroument; and by the
successes I met rith in the tryals, I dare promile, that
tohim wtro Mail argue truly, and then try all chings
rith good Cilasses and sufficient circumspection, the
expectederent illnot bemantino. But he is Arst to
knom wrhat Colours ill arise from any others mixt in
any aftigned ProPOrtiOM.
PROP. IV. THEOR. TTI.
Colours may he produced hy composition rehich salt be lite
to the Colours of homooeneal Fieht as to the appearance
ofColour, but not as to the immutabilitus of Cotour and
constitution of Tieht. And those Colours hy horo mucto
they are more compounded by so much are they less fult
aud inteuse, and by too much composition they may be
dilutet

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diluted aud roeateened till they cease. There may be
also Colours produced hy composition, resbichare not fully
litre any of the Colours of homoseneal Lioht.
For a mixture of homoseneal red and vellon com
pounds an oranse, like in appearance oF Colour to that
oranse irhich in the series oF unmixed prilmatick C0
lours lies betreen them; but the Light oF one Oranse
is homogeneal a5 to retrangibilier, that of the other 15
heteroseneal, and the Colour ot the one, it vieved
chrough a Prilm, remains unchanged, that ofthe othei
15 chansed and relolved into its component COlOuIs red
and velloir. And alter che lame manner other neish.
bourins homoseneal Colours may compound new C0.
lours, likce the intermediate homoseneal Ones, a5 Yel-
Porr and oreen, the Colour betreen them both, and af-
termards, it blue be added, there ill be made a green
the midele Colour ofthe thrce wrhich enter the compo.
Sition. For the vello and blue on cither hand, if ther arc
equa linquancits chey dram theintermediate sreen equal-
Iy torrards themselres in composition, and lo kecp it a5
it ivere in equilibrio, thac it verse not more to thc
vellor on the one hand, than to the blue on the othei,
but by cheir mixt actions remain sill a middle Colour.
Lo this mixed green there may be further added
fome red and violet, and vet the orcen will not present
Ir cease but onty oroi less fuil and vivid, and by in-
creulne the red and riolet it willoror more and more
dilute, uneil by the preralence ot the added Colours it
De overcome and tuined into rrhitenels, or lome other
Colour. E0 il tothe Colour ot any homoseneal Lignt,
che Suns wrhite Lisht compoled of aIl Toris oF rayS BC
addcd.

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F
added, that Colour ill not vanist or change its spe-
cies but be diluted, and by addins more and more irhite
it rill be diluted more and more perpetuallr. Last.
IV. if red and riolet be mingled, there ill be generated
accordins to their rarious Proportions various Purples,
Tuch as are not like in appearance to the Colour ot ans
homosencal Light, and oF thele Purples mixt with vel-
lorr and blue may be made other new COlOUES.
eROP. V. THEOR. IV.
WBiteness and al erey Colours betreeen rebite and black,
may be compounded of Colours, and the rehiteness of the
Suns Fisht is compounded of au the primary Colours
mint in a due proportion.
The Proos by Fxperiments.
F X P F R. IZ.
The Sun Mining into a dark Chamber throuoh d
little round Hole in the Windom Cut, and his Lighe
beins there retracted by a Prilm to cast his coloured.
Imase PT uxon the OppOsite WVaII: I held a wrhite Pa-
per V to that Imase in such manner that it might be
illuminated br the coloured Lisht reflected From thence,
and vet not intercept any parc oF that Lighe in its pal
lase trom the Prilm tothe Spectrum. And I Found that
irtren the Paper was held nearer to anr Colour than t0
the rest, it appeared of that C olour to irhich it ap
proached nearest; but wrhen it ras equally or almolt
cquaIIy
F18. 5.

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(99
equally distant From aII the COlours, (0 that it mighe
Dc equallr illuminated by them aI it appeared irhite.
And in this last situation of the Paper, if some COlours
avere intercepted, the Paper lost its irhite Colour, and
appeared oF the Colour ot the rest ot the LiohE irhick
ras not intercepted. Sothenthe P’aper vras illuminated
rith Lighes ot rarious Colours, namely, red, vellonr,
sreen, blue and violet, and erery part ot the Light re
cained its prover Colour, until it ras incident on the
Paper, and became reflected thence to the FyC; (o that
if it had been cither alone (the rest ot che Light being
intercepted) or it it had abounded most and been prC-
dominant in the Light rehlected From the Paper, it vould
have tinged the Paper rith its onn Colour; and vet De-
ins mixed with the rest of the Colours in a due propor-
tion, it made the l’aper look white, and theretore by a
composition rith the rest produced that Colour. Jne
sereral parts ot the coloured Lixht refected from the
Spectrum, Wrhilsthey are propasated trom thence thro
the Air, do perpetually retain their proper COlOuIS,
becaule Wrhererer cher Fall uxon the Rres ot any Specta-
tor, ther make the leveral parts ot the Spectrum to
appear under their proper COlours. Pher retain there
Fore their proper Colours wrtien ther Fall upon the la-
per V, and (0 by the contution and pertect mixture ot
chose Colours compound the wrhitenels oE the Ligh
reftected from thence.
E Z P F. R. Z.
et thatSpectrum or lon mae l’a sun sn apoh Fic. 6
the Lens M N abore tour luches broad, and about siX
Fcet

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(10O
Fcet distant from the Prilm ABC, and (0 figured that
it may cause thecoloured Fishe irhich diveroeth From
ehe Prilm to converse and incet again at iES FOCUS C,
about siX Or eient feet distant From the Lens, and
chere to Call perpendicularty upon a irhrite Paper DF.
And iCyou more this Paper to and Fro, rou will per-
ceire that near the Lens, as at de, the wrtroie Colar limage
(suppose at pF) will appear uxon it intenstr coloured
alter the manner abore explained, and thatby recedin
From the Lens those Colours will perpetuallr come 10.
vards one another, and by mixine more and more di-
lute one another continuallr, until at leneth che l’aper
come to the Focus Ci, irhere by a pertect mixture they
Will irhollr ranistr and be converted into wrhitenels, che
Wrhole Lisht appearins nou uxon the P’aper likce a lictle
arhite Circle. And alterards by recedine Further From
the Lens, the rars Wrhich betore converoed will non
cross one anothier in the Focus C, and diverse From
thence, and therebr make the COlours Io appeai acaI,
but vet in a contrary order; suppose at oc, Wrhere the
red t is nou abore erhrich betore ras belou, and the
riolet p is belo erhich betore Wras above.
Let uS nOW ROp the Paper at thC FOcuS C artrere
the Lighe appears totallr wrhite and circular, and let us
consider its irhiteness. I Cay, that this is compoled ot
the conrersins Colours. For iE any ot thole Colours
De intercepted at the Lens, the mhitenels rill cease and
derenerate into that Colour irhich ariseth from the
compolition ot the other Colours irhrich are not inter-
cepted. And then it the intercepted Colours be let
pals and Fall uxon that compound Colour, ther mix
with it, and by their mixture rettore the irhitenels.

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CIC
SoiEthe riolet, blue and ereen De intercepted, the re-
mainins vellorr, oranse and red irill compound upon
the Paper an oranse, and then it the intercepted Co-
ours De let pals ther will Fail uxon this compounded
oranse, and together rith it decompound a Wrhite. 50
allo iF the red and riolet be intercepted, the remainine
vellorr, green and blue, rill compound a green uxon
thePaper, and then the red and riolet beins let pals
Wrill Falluxon thisereen, and together rith it decom-
pound a Wrhice. And ehat in this composition ot irtrite
che sereral rays do not lutter any chanse in their colori-
tic qualities by actins upon one another, but are ouly
mixed, and by a mixture ot their COlours produce
arhite, may Further appear by chese Arsuments.
IEthe Paper beplaced berond the Locus Cr, suppose
at oc and then the red Colour at the Lens be alternate.
ly intercepted, and let palsagain, the riolet Colour on
the Paper willnot Cutter ans chanse thereby, 25 it ought
to do it che sereral forts ot rars acted upon one another
in the Locus C, wrtiere they crols. Neither ill the
red upon che Paper be chansed by any alternate Aop.
Dins, and lettins, palsthe riolet irhich crosseth it.
And if che Paper Deplaced at the tocus Ci, and the
Wrhite round Imase ac Ci be riered throush the Prilm
AIIK, and by the retraction of that Prilm De transtated
tothe place rV, and there appear tinsed with rarious
Colours, namely, the violet at r and red at r, and
others betureen, and then the red Colour at the L ens De
otten HopE and let pass by curns, the red at r will ac-
cordinsly dilappear and return as otten, but the violet
at r Wrill not chereby luitter any chanse. And lo by
toppins and lettins pass alternately the blue aE the
LeHSus

## Folio 102 — 1677894601:0122
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Lens, theblue ac eWrill accordinsly disappear and re
turn, wichout ans change made in the red at P. ThC
red cheretore depends on one lort ot rays, and the blue
on ariother Fort, Wrhich in the Focus Ci ertrere they are
commixt do not aet on one another. And there is th.
Pame realon of the other Colours.
lconsidered Further, that wrhen the most retrangible
rays PP, and che least retransible ones IF, are by con
vergins inclined toone another, the Paper, it held very
oblique tothose rays in the Locus C, mioht reRect one
Tort ot them more copioustr than the other COrt, and D)
that means the refected Light rould be tinged in that
Focus rith the Colour ot the predominant FayS, prO
vided those rars sererally retained their C OlOurS OF CO
loritc qualities in the composition ot wrhice made by
them in that Focus. But il they did noc retain them
in that White, but became all ot them Ceverally endued
there ith a disposition to Prike the sense with the per-
ception oF wrhite, then ther could nerer lose their irhite
nels by such reflexions. Linclined theretore the l’aper
tothe rays very obliquelr, as in the second Experiment
ofthis Book, that the most retrangible rays might De
more copioully reflected than the rest, and the wrhite
Dels at lensth changed successirelr into blue, indico
and violet. Then linclined it the contrary wrar, tha
themost retransible rars mistit Demore copious in the
retlected Light than the rest, and the erhiteness turnec
Succellively to rellorr, oranse and red.
LaHIY, I made an Instrument ZY in fastrion ot
Comb, wrtose Teeth being in nuDer SIXECen Werc
about an Ineh and an half broad, and the interrals oF thC
Pceth about trro Inches ride. Phen by interpolus
Tue

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Tuccessirely the Teeth of this Instrument near the L enS,
l’intercepted part of the Colours by the interpoled
Looth, WrhilCt the rest otthem ent on throughthe in-
terral oF the Teeth tothe Paper DF, and there pain-
ted a round Colar Image. Bucthe Paper I had Arst Pla-
ced lo, thac the Image misht appear white a5 otten
a5the Comb as taken avay; and then the Comb bC-
ins as as Caid interpoled, that wrhiteness by realon ot
che intercepted part oF the COlours at the Lens did al-
rars chanse into the Colour compounded ot thole
Colours Wrhich irere not intercepted, and that Colour
ras by the motion ofthe Comb perpetually varied l0
that in the passins ot every Tooth over the Lens aII
thele Colours red, vellor, sreen, blue and purple, did
alrars succeed one another. I cauled theretore allthe
Leethto pass successirely over the Lens, and irhen the
motion ras Por, there appeared a perpetual succession
ot the Colours upon the P’aper: But it Llo much acce-
lerated the motion, thatthe Colours by reason of their
quick succession couid not be distinguithred From one
another, the appearance of the linsle Colours cealed..
Phere rras no red, no vello, no sreen, nO bluC, nOL
Durple to be scen ans longer, buc trom a contulion ot
ehem all there arose one unitorm white C olour. OF he
Light whrich nou by the mixture ot all the Colours ap-
peared white, there ras no part really irhite. One
part Was red, another vellor, a third green, a Fourth
blue, a tilth purple, and every part retains itS PrODeF
Colour till it srikre thesenlorium. IF the impreltions
tollo one another Rlolr, (o that cher mar De leve-
rally perceired, there is made a distinet lenlation oF aII.
the Colours one alter another in a continual succestion.
BUL

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10
But il the impressions follou onc anocher (o quickl
that ther cannot be severally perceired, there ariseth
out ot them ail one common sentation, Wrhich is net
ther oF this Colour alone nor ofthat alone, but hath it
selF indifferentlr to em aIl, and this is a sensation ob
arhiteness. By the quickness ot the succestions the im
prections ofthe sereral Colours are contounded in FhC
Senlorium, and ont ot that contntion arileth a mixt sen-
Cation. IF a burnino Coal benimbly moved round in a
Circle rith Crrations continually repeated, the irhole
Circle will appear liketire; the realon ot wrtrich is, that
the sensation oF the Coal in the several places oF that
Circle remains imprest on the sensorium, until the
Coat return again to the same place. And (0 in a
quick consecution of the Colours the imprection ot every
Colour remains in the Senlorium, until a rerolution ot
alt the Colours De compleated, and FhaL AEC COIOUE re-
turnagain. Theimpressions cheretoreot all the successire
Colours are at once in thesentorium, and joynelr sir up
a senlation of them alI; and lo it is manitest by this F X
periment, that the commixe impreltions oF aII the CO-
Jours do cir up and Deget a senlation ot irhite, thac 15,
that erhiteness is compounded ot aII the COlOurS.
And if the Comb De non taken arrar, chat all the
Colours mar at once pals from the Lens to the Papei
and be there intermixed, and tosether retlected thence
to the Spectators Lyes; their imprections on the Senlo.
rium beins nor more subtily and perfectlr commixed
chere, ought much more toltir up a senlation ofihite
NClS.
du

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(1OG
Tou may instead oE ehe Lens ule erro Prisins HIK
and L. MN, irhich by retractinq the coloured Lixnt
the contrary ray to that of the krst retraction, may
make the diverging rars converse and meet again in 
25you sec it represented in the leventh Fisure. For Fis. 7.
irtere they meet and mix they riil compole a white
Light as irhen a Lens is uled.
F X P F. R. ZI.
Let the Suns coloured Image P P Fall upon the WV alI F15. 8.
OEa dark Chamber, a5 in the third Lxperiment oF the
AxIFBOOK, and let the lame be riemed chrourh a Prism
abc, held parallel to ihe Prism ABC, by Whose retra-
ction that lmase ras made, and let it nou appear lorrer
than before, suppole in the place S over against the red
colour Y. And it rou go near tothe lmase PY, the
Spectrum S rill appear oblons and coloured like the
LinasC PT; but it rou recede trom it, the Colours ot
the Spectrum S will be contracted more and more, and
at lensth vanist, that Spectrum S becomine perfectly
round and irhite; and il vou recede vet Further, the
Colours rill emerse asain, but in a contrary order.
Nor that Spectrum S appears irhite in that case irten
the rays oE lereral Ports irhich conrerse From the leve-
ral parts oF the linage PY, to the Prilin abc, are (0
retracted unequally by it, that in their pallage From the
Prisin to the tiye ther may diverse trom one and the
same point of the Spectrum S, and (0 FaI afterrards
uxon one and the lame point in the bortom ofthe lse,
ind there beminsled.
d o

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(100
And Furthei, it the Comb be here made use oF, bY
Wrhose Tceththe Colours at theTmage PY may be suc
cessivels intercepted; the Spectrum S irten the Comb
is mored Romly ill be perpetually tinged rith luc.
celtire COlOurs: But wrtien by acceleratine, the motion
ofthe Comb, the succestion ot the Colours is (o quick
that ther cannot be sererally seen, that Spectrum S, by
a contuled and mixt senlation ot them all, rill appeai
Wvhite.
F. Z P F R. ZII.
The Sun Cinins chrough a larse Prism ABC. UPON
a Comb Z X, placed immediately behind thePrism, his
Lisht vrhich passed through the interstices of the P’eeth
Fell upon a White Paper DF. ThC BrCAdEHS OE tHC
Tecth rvere equat to their interstices, and seven Pecth
together with their interstices took up an Inch in
breadth. Nour irten the Paper Was about FWO Oi
threc Inches dictant from the Comb, the Lisht vrhich
passed throush its sereral interstices painted so many
ranges ot Colours kl, Mn, OD, gr, Oc. Wrhich Wecc
Parallel to one anocher and contiguous, and without anx
mixture otwrhite. And these ranges ot Colours, il the
Comb ras mored continually ux and dovn with a re-
ciprocal motion, alcended and descended in the Papei,.
and irhenthe motion oE the Comb ras (o quick, that
the COlours could not be distinsuishred trom one another,
theirhole Paper by their contution aud mixture in the
Senlorium appeared irtute.
F18. 9.
la

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p
10
Let the Comb no rest, and let the Paper be remo-
red further From the Prisim, and the several ranges ot
Lolours prill be dilated and expanded into one another
more and more, and by mixine their Colours rill di
lute one anocher, and at lensth, wrtien the distance
oF thc Paper Erom the Comb is about a HoOt, Or a
little more (suppose in the place 2D 2F) they rilt
lo Far dilute one anoctrer as to become white.
Nith any Obstacle let aII the Lishe De no AOpE
Wrhich passes throush aur onc incerral ot the Teeth, (0
that the range of Colours irhich comes From thence may
De taken arrar, and vou rrill sec the light ofthe rest ot
cheranges to De expanded into the place of the range
caken drar, and there to be coloured. L et the inter-
cepted ranse pass on as betore, and its Colours Fallins
upon the Colours of the other ranges, and mixins rith
them, will restore the irhitenes.
LCt. the Paper 2D 2 F. be non very much inclined to
che rays, (o that the mos retransible rays may be more
copioulr reflected thanthe rest, and thewhite Colour
otthe Paper throush the excess ot those rars rill DC
changed into blue and violet. Let the Paper DC a5
much inclined the contraer rar, that the least retran.
sible rars may be nom more copioustr reflected than
the rest, aud by their excels the irhitenels rill De
chansed into vellon and red. The sereral rars there-
tore in that irhite Light do retain their coloritic qua-
lities, by wrhich thole ot arir Cort, Wrhen- ever ther be-
come more copious than the rest, do by their excels
aud predominance cause their prover Colour to ap.
DeaF.
la

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(108
And by the Came ray oE arguins, applied to the third
tixperiment of this Book, it may be concludedu that
the irhite Colour ot all retracted Light at ies very tirs
emersence, irhere it appears as Wrhite as betore its inci.
dence, is compounded ot rarious C OlOUrS.
E. Z P F. R. ZIII.
In the foresoine Experiment the sereral interrals ol
the Teeth of the Comb dothe office oF (0 any PrIIInSq
everr interral producins the Phaenomenon oF one Prilm.
Whence instead of those interrals ulins several Prisms, l
ter dto compound irtiitenelsby mixins their C olours, and
did it by utins only chree Prilims, 25 al(0 by utins only
1c. 10. trro as Tollors. Pet trro Prilms ABC. and abC, wrhole
retractins Angles B and D are equal, DC (0 placed paralIel
toone another, that the refractinq Anole B oF the one
mar touch the Anele c at the bale oF the other, and
their planes C. B and cb, at Wrtrich the raYS emergC, inaV
Ire in directum. Lhen let the Light trajected throusl
ehem Fall upon the Paper M NV, dictant about 8 O1 12
lnches trom che Prilins. And the COlourS generated
br the interior limits B and c ot the tiro Prilms, rill
beminsled at PP, and there compound wrhite. Por il
cither Priln betaken awar, the Colours made by the
other rill appear in that place PP, and wrhen the Pritin
15 resored to its place aeain, (o that its Colours mav
there Fall uxon the Colours ol the ocher, the mixture
oF them both ill rectore the irhitenels.
L. HIId

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109
This Experiment succceds al(o, a5 Phare tryed, Wrhen
he Ansle b of thelover Prilm, is a lictle greater than
the Ansle B oE the apper, and betrreen the interior
Angles B and c, there intercedes lome (pace BC, 25 15
reprelented in the Pioure, and the retractino planes
BC. and DC, are neither in directum, nor parallet to
one another. For there is nothins more requisite t0
che success oF this Experiment, than that the rays oF aII
lorts mar be unitormly mixed upon the P’aper in the
place PT. IF the most retransible raus comins from
thesuperior Prim takce up all thespace trom. M toP, the
rars ot the Came Cort irhich come tiom the interior
Prilm ouoht to begin at P, and take up all the rest ofthe
SpaCOFrom thence torards N. TE the least retransible
rars comine trom the superior Prisin take up the (pacC
T, the rars of the sainc kind irtrich come from the
Other Prilim ought tobegin at P, and take ux theremain-
ins Space TN. TEone lort ot the rars rhich hare in-
termediate degrees ot retransibilitr, and come trom the
Cuperior Prilm De extended chroughthe (pace MIO, and
nother FOrt ot those rars throuoh. the (PACC MIR, aud
a thisd Cort of them through the space MS, the lame
Corts oE rays comins tromthe louer Prilm, ousht to il-
luminate the remainine spaces GN, RH, SN relpe
etivelr. Audthe Came is to be understood of aIl the
ottier Ports ofrars. Forthus therars ot every Port will
Belcattered unitormly and erentr throuch the itole
Epace AIHI, and (o beins everr irhere mixt in the lame
proportion, they must erery wrhere produce the lame
COlour. And theretore since by this mixture they pro-
duce irhice in the exterior spaces M P and lH, ther
must also produce irhite in thie interior space PI. Phis
la

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(11O
is the reason oE che compotition by irhich irhiteness
vas produced in this lixperiment, and by wrhat other
var foerer I made the like composition the relult was
Wrhitenels.
PasIY, IE rith the Teeth ot a Comb oF a due (2C,
che coloured Fighes oF the trvo Prilms irhich FaII uxon
the (pace PY De alternately intercepted, that spacc
T, irtien the motion ofthe Combis llon, Will alrays
appear coloured, but by acceleratins the motion ol
the Cob (o much, that che succestive Cotours can
not be distinguishred Erom one another, it will appeas
erhite.
F Z PF R. ZIV
Hlitherto I hare produced wrhiteness by mixino the
Colours oF Prilms. IFno the ColOurS OF natural BO
dies are tobe mineled, let Water a litele chickned rith
Soap be asitated to raise a troth, and alter that Fxoth
has Hood a little, there rill appear to onc that al
viem it intently rarious Colours everr irhere in thC
Turtaces ot the leveral BubBles; but tO One FMaL MAI
50 (0 Car oHfthat he cannot distinsuishr theC olours FrOM
one another, theirhole Froth ill gro irhite rith a
verfect irhitenelo.
E Z P F. R. ZV
Lastlr, in altemptins to compound a irtite br mixins
che coloured Porrders irhich Painters ule, I considered
chat aIl coloured Porrders do supprels arid Aop i
them a very considerable part oF the Lisht by irhich
thes

## Folio 111 — 1677894601:0131
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LPTI
chey are illuminated. Por ther become coloured By
reflectins the Lighe oFtheir omn Coloursmore copioull),
and chat oE all other Colours more sparinsly, and yet
ther do not refect the Light ot their omn Colours (0
copiouslr as Wrhite Bodies do. IF red Lcad, Tor instance,
and a Wrhice Paper, be placed in the red Lieht ot chc
coloured Spectrum made in a dark Chamber by the re-
Fraction oF a Prisin as is described in thethird Lperi-
ment oFthe Aest B0ok; the Paper will appear more lu-
cid than the red Lead, and theretore reflects the red-
makine raysmore copiousr than red L. cad doth. And
iFthey be held in the Light of anr other Colour, the
Lishe refected by the Paper will exceed the Light re-
Aected by. the red Lead in a much sreater proportion.
And the likce happens in Porrders ot other Colours.
And cheretore by. mixins such Porrders e are not to
expect a srons and fullirhite, such as is that of Papei,
but Come duster obleure one, luch as miont arise From a
mixture ofliont and darknels, or From irhite and black,
that 15, a srer, or dun, or russet bron, uch asare the
Colours ot a Mans Nail, OF a Nouse, oF ACeS, OF OF-
dinaxy Stones, OF NOrtar, OF Dust and Dirt in High
raro and the like. And such a darke irhite Lhave
osten produced by mixins coloured Porrders. L’or thus
one part ot red Lead, and tre parts ot Viride Lris, com
Posed à dun Colour like that of a Moule. Por thele
erro Colours vere sererallr (o compounded oE others,
that in both tosether vere a mixture oF aIl C OlOurs; and
there Wras lels red Lead uled than Viride Aris, becaule
oF the Fulnels oF its Colour. Again, one part ot red.
Lead, and tour parts otblue Bile, compoled a dun C0-
lour vergins a licile to purple, and by addins to this a
certa

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L
certain mixture oF Orpiment and Viridi ris in a due
proportion, the mixture lost its purple tincture, and be.
came perfectlr dun. But the Lxperiment succeeded Best
without Minium thus. Po Orpiment I added by little
and litele a certain FuII briohe purple, wrhich Painters
rise until the Orpiment ceased to Dc rellorr, and became
oF a pale red. Then I diluted that red by addine a
litele Viride Airis, and a litele more blue Bile than i
ridi Aeris, until it became ot such a grer or pale White,
a5 versed to no one oF the COlours more than to ano
cher. For thus it became of a Colour equal in wrhite
nelS EO thaE OF ACtes Or OF Wood nely CUL, Or OE a
MlansSKin. The Orpiment rehected more LighE Fhan
did aur other of che Porrders, and theretore conduced
more tothe irhitenels of the compounded Colour than
tier. L0 alsion the proportions accurateiz may De
difficult, by realon of the different, goodnels oF POW-
ders of the lame kind. Accordinsly a5 the COlour ol
any Porrderis more or less FuII and luminous, it ought
to be uled in a lels Or greater proportion.
Nor considerins that thele erer and dun Colours
may be alio produced by mixins ertites and blacks, aud
br consequence ditter trom pertect wrhites not in Species
ot Colours but ontr in deoree otluminousnels, it is ma
nifest that there is nothins more requisite to make
them perfectly irhite than to increase cheir Lioht sutr
ciently; and, on the contrary, il by increatins their
Lichether can bebrouehe to pertect irhiteness, it rill
chence allo follo, that they are ot the lame Species ot
Colour vrith the best irhices, and difser From them only
in thequantier of Light. And this I trred as FolIOIS.
ltook thethird of the abore mentioned orer mixtures
chac

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p
TI2
(that wrtrich iras compounded of Orpiment, Purple,
Bise and Viride LAris) and rubbed it thickly uxon the
Hoor ot my Chamber, irhere the Sun phone upon it
chroueh the opened Calement; and by it, in the Mra-
dorr, llaid a piece of Wrhite Paper ot the lame bignels.
Phen coino From them to the distance ot 12Or 18 Fcet,
Tothat I could not discern the unerenne(s ot the Curtace
oFthe Porrder, nor the little ados let Fail From the
sritey particles thereot; the Porrder appeared intensty
erhite, 10 asto transcend even the Paper it selE in wrhite
nels, especially if the Paper vere a litele haded From
The Light oF the Clouds, and then the Paper compared
rith che Porder appeared of such a grey Colour as the
Porrder had done betore. But by lavine the Paper
Wrhere the sun Mines throuoh the Class oFthe Windo,
or by Buctino the Windom that the Sun mishe ine
throuoh the Class upon thePorrder, and by such other
tit means of increasins or decrealins the Lights irtere
rith the Ponder and Paper ivere illuminated, the
Lieht wheremith the Poirder is illuminated may De
made Aronser in Tuch a due proportion than the Light
rheremich the Paper is illuminated, thac ther MaII Boch
appear exactly alike in vrhitenels. For irhen I Was
eryins this, a Friend comins to vilit me, I Aopt him
at the door, and betore I told him irtrat the Colouis
arere, or irhiat Trras doins; Lasket him, Which ot che
tro irhites irere thebest, and wherein they differed e
And alter he hrad at that distance riemed them vell, he
ansrered, That they vere both good erhites, and chat
he could not Car which vas best, nor wherein their Co-
lours differed. Nou il vou consider, that this erhite
OF the Porrder in the Sun. Mine rras compounded of the
COtOUrS

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(124
Colours irtich the component Porrders (Orpiment,
Purple, Bile, and Viride ris) hare in the Pame Sun
ine, vou must acknomledse by this Lxperiment, 25
vell asby theformer, that pertect wrhitenets may De
compounded ot C OlOurS.
From what has been Caid it is also crident, FHAL FHC
artriteness oF the SunsLight is compounded oF aII thc
Colours Whererith the severat Torts ot cars wrhereot
chat Lighe consists, Wrhen by their sereral retransibili
ties ther are separated From one another, do tinse P’apei
or any other irhite Body Whereonther Fall. For thole
Colours by Prop. 2. are unchanseable, and irheneree
aII thole raps rith those their ColOurS are mint agaIB
chey reproduce the lame wrhite Lislit as betore.
PROP. VI. PROB. TI.
In a mixture of primary Colours, the quantity and quality
of each beine siven, to tenores the Colour of the com-
pound.
s. II. Withthe Center O and Radius OD describe a Circie
ADF, and distinguittr its circumterence into leven parts
DE, E F, FC, CA, AB, BC, C. D, PropOrtiOnA) 10
ehe seren musical Pones or Interrals oEche ciohe Sounds,
Sol, la fau sol, la min fa sol, contained in an Fient,
that is, proporcional to the numDeIS 3, 163 203 5 10n 167
. L et the trI PAEE DF reprelent a red ColOUI, thC
second R Liorange, the third sC vellor, the Fourth
CTI orcen, the fiFch AB blue, the SXth BC indico,
and the seventh C. D violet. And conceire that thele
are all the Colours oF uncompounded. Lisht gradually
pasInS
18 1a  6b

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TTB
passins into one another, as they do irhen made by
PTISIS; ThC CITCUIFCTeNCO D F. LGFABC D, represen-
tins the wrhole series ot Colours From one end oF the
Suns coloured Image to the other, (0 that From D to f.
bc al degrees of red, at l. themean Colour betreen red
andorange, Erom F. 10 Lall desrees oF OransC, ac F the
inean betreen oranse and vello, From L t0 C aIl de-
srees oF vellorr, and (0 on. P et p bc the center ot
Srarity oFthe ArCh DH, and 9, E, Sq C, V, Z9 thC centers
ot grarits oF the Arches FL, FC GA, AB, BC.
and C. D respectirely, and about thole centers ot gra-
viey let Circles proportional to the number oF rays ot
each Colour in the siren mixture be described; that 15,
the circle p proportionalto the number oF the red. ma-
kins rars in the mixture, the Circle q proportional to
che number ot the orangemakcins rars in the mixture,
and (ooF therest. Find the common center of gravitr.
OF all those Circles P, G, 1, S, C, V, Z. L et that center
bCZ; and From the center ofthe Cirele ADF, throueh
Zto the circumterence, dramins the rishit line L,
the place ofthe point P in the circumterence MaII MCW:
the Colour aritins From the composition oF aII the CO-
lours in the siven mixture, and the line OZ Mall. DC
proportional to the tulnels or intensene(s of the COlour,
that i5, t0 its distance from irhiteness. A5 it YFaIL in
the midele Detireen F and C, the compounded Colour
MalI bethe best vello; il Prerse trom the midale to-
rards L’Or Cr, the compounded Colour Mall accordins
ly be a vellorr, versins torarde oranse or sreen. IIL
tallupon the circumterence the Colour Mall be intenle
and Rorid in thehighest degrec; it it Fall in the mid
vay betveen the circumterence and center, it Mall be
BUE

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C116
but halfCo intense, that is, it hall BC Fuch a Cotour 45
rould bemade by diluting the intensest vellon with an
equal quantitr ot wrhiteness; and it it Fai uxon the
center O, the Colour Mall tare los all its intensenels,
ond become a irhrite. Butit is to be noted, That iF the
point Z. FaIl in or near the line OD, the main insredients
beino the red and riolet, the Colour compounded MalL
not beany of the prilmatic Colours, but a purple, I1I.
clining to red or violet, accordinsly as thie point L
lieth on the side oF the line DO FoWAEdS F. Or Forrards C9
and in general thecompounded violet is more brisht and
more tiery thanthe uncompounded. AIIO it only tro
ot the primary Colours wrhich in the Circle arc oppolite
to one another De mixed in an equil proportion, the
DOint Z MaII FaII uxon the center O, and vet the C0.
lour compounded ot thole trro haIl not be pertectli
ehite, but Come faint anonymous Colour. For I could
never ret br mixins only trro primary Colours produce
a pertect irhite. Whether it mar De compounded ot a
mixture ot three taken at equal distances in the circum-
Ference Idonot KROW DUEOFTOUT Or Are I de not much
question but it mav. But these are curiosities oF litrle
or no moment to the understandins the Phaenomena ot
nature. For in aIl wrhites produced by nature, there
uses to be a mixture oF aII Ports ot rays, and by conse
quence a composition oF aII C olours.
lo sire an instance ofthis Rule; suppose a Colour is
compounded ot thele homogencal Colours, ot riolet
 part, ot indico I part, OF blue 2 Parts, OForeen Z partS,
Ot vellorr s parts, OF oranse 6 Parts, and ot red 10 parts.
Proportional to thele parts l delcribe the Circles X, V, l,
Sg F, G. P respectirely, that 15, (0 that if the Circle X

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T1
Dc r. trie Cirele r may be L, the Circle t2, theC irele.
62, and the Circles r, 9 and p, 5, 6 and 10. Then L
find Z the common center ot sraritr ot these Circles,
and throuoh Z drawins the line OP, the point Y FaIIS
uxon rhe circumterence betmeen F.and l, some thine
nearer to F. Than to F, and thence L conclude, that the
Colous compounded ot thele ingredients riil be an
oranse, vergins a little more to red than to vellor:
AICO I find that OZ is a little less than one halF ot
DT, and thence I conclude, that this oranse hath a
ditele less than halE the Fulness or intenlene(s oF an Un-
compounded oranse; that is to Cay, that it is such an
oranse as may be made by mixins an homogenea l oranse
vith a g0od irhite in the proportion of the line OZ 10
h. linc Z Y, this proportion beins not ofthe quantities
oFmixed oranse and irhrite porrders, but ot the quan-
tities ofthe lighis retlected from them.
Phis Rule l conceire accurate enoueh for practile,
choush not mathematicallr accurate; and the truth ot.
it may be sufticiently proved to sense, by Roppins any
et the COlours at the Lens in che centh Fxperiment ot
this BOOk. For the rest ot the Colours wrhich arc not
Atopped but pass on to the Focus oF the Lens, wii
there compound either accurately or very neartr such.
2Colour a5 by this Rule oueht to retult trom their
emixture.
PROFo

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PROP. VII. THEOR. V.
Al the Colours in the Oniverse rehich are made by Fiehbu
and depend not on the porver of imacination, are
either the Colours of homoseneat Pishts, or compoundec
of these and that either accurately or very nearly, ac
cordine to the Rule of the feresoine Problem.
For it has been proved (in Prop. I. Lib. 2.) That the
changes oF Colours made by retractions do not arilé
trom any new modifications of the rays imprest by thole
retractions, and by the various terminations ot light
and Mraco, as hasbeen the constant and general Opi
nion otPhilolophers. Ithas allo been proved that the
sereral Colours ot the homogeneal rays do constantl)
antiver to their degrees ofretransibilitr, (ProP. I. F ib. 1.
and CrOD. 2. F ib. 2.) and that cheir desrees ot retransI
bilies cannot be chansed by retractions and reflexions,
(PrOp. 2. Lib. 1.) and by consequence thât thole their
Colours are likerile immutable. It has allo been pro.
ved directis by retractins and reflectins homoseneat
Lishes apart, that their Colours cannot be chanced,
(PrOP. 2. Fib. 2.) IE has been proved al(o, that wrhen
the sereral Corts ot rars are mixed, and in croctins pals
throuoh the lame space, ther do not act on onc anothei
l0 a5 to chanse cach others coloritick qualities, (L. Xper.
10. Fib. 2.) Dut by mixins their actions in the senlo
rium beget a lenlation difterins trom irhat cither rouid
do apart, that is a senlation oF a mean C. Olour Betreen
racir proper Colours; and particularly erhen by che
concourse and mixtures oF all Corts ot cays, a wrhite
COlOus

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F
Colour is produced, the wrhice is a mixture of altthie
Colours erhich the rays rould have apart, (PFOP. 5.
FiB. 2.) The cays in chat mixture donot tose or alter
their Sereral colorikick qualities, but BY aIL their various
kinds ot actions mixt in the sensorium, beget a senta-
tion ot a middline Colour betreen aIl their Colours
ertrich is erhiteness. For erhiteness is a mean Detiveen
aII ColOurs, havins it selE indifferently to them all, 50
as rith equal Facility co be tinged rith any oE them.
A red Porrder mixed with a litele blue, or a blue rith
a litele red, doth not prelentlr lose its Colour, but a
Wrhrice Ponder mixed rrith ans Colour is prelently tin-
sed rith that Colour, and is equallr capable of beine
tinsed rith ans Colour irhat-ever. Ithas been Cherved.
alto; that as the sunsListt is mixed oFaII POrtS OFraYS,
Lo ies Wrhiteness is a mixture of the Colours oF aIL FORtS
Otrars; those rars having trom the besinnins their le
veral coloritic qualities as Well astheir leveral retrangi-
Disities, and retainins ehem perpetually unchans d not-
Wriehstandins any retractions or reflexions ther may at
any time sutter, and that irhen erer any Port oF the
Suns rars is by any means (as by rellexion in KXpeF. 9
and 10. Lib. T. Or by refraction as happens in aIl re:
tractions) separated Erom the relt,s they then manitest
their prover Colours. These things hare been proved,
anA the sum oE all this amounts to the Propolition here
Fo DCprored. For it the Suns Lighe is inixed ot le-
veral COrES OF rarS, Cach oF Wrhich have originally cheir.
Cereral retransibilicies and colorikick qualities, and not-
withcanding their refractions and reflections, and their
various separations or mixtures, kecp chole their ori-
sinal properties perpetualr the lame rithout altera-
tiOn

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TT20
rion; then aIl theColours in the Norld must De such as
constantly oughe to arile From the original coloritic qua
lities oF the rars whereot the Lishes consist br erhich
those Colours are seen. And theretore if the realon ot
any Colour Wrhat. erer De required, re hare nothins elle
to do then to consider hour the rars in the Suns Light
hare by rellexions or retractions, or other causesbeen par.
ted trom one another, or mixed togethei; or othermileto
find out irtrat Ports ot rars arc in the Light by irhich
that Cotour is made, and in rhat proportion; and
then by the lalt Problem to learn the Colour rhich
oughe to arise by mixins chole rars (Or their COIOurS)
in that proportion. I speak here oF C Olours (0 Far 45
they arise trom Liglt. For ther appear lometimes by
Other caules, a5 wrhen by the porrer ot phantasy ve
sec Colours in a Dream, or amad Man Pees Fhinos betore
him wrhich are not there; or erhenre sec Fire By Arikins
The Fye, or sec Colours like the fiye oF a Peacocks
Feather, by pressins our Rires in cither corner wrhilst
ve look the other war. Where thele and such lite
causes interpose not, the Colour alivars ansivers t0
the Cort or Ports of the rays whereot the Lioht con(iAS,
a5 Itrare constantr Found in Wrhat ever Phaenomena ol
Colours Thare hitherto been able to examin. LMaII in
thefollorrinq Propolitions sive instances ot this in the
Phaenomena ot chietes note.

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PROD. VITI. PROB. TTI.
By the discovered Properties of Zisht to explain the
Colours made by Prisms.
L et ABC represent a Prilin refractins the Light OF Fig. 12.
chesun, irhicti comes into a dark Chamber through a
HTole F e alnost as broad as the Prilm, and let MIN
reprelent a irtrite Paper on wrhich the retracted Light is
Cast, and suppose the most retransible or deepest violet
makins cays FaIl upon the space PX, the leas retran-
sible or decpest red- makins rays uxon the space VI.
the middle Port betreen the Indico-makins aud blue.
matcins rays upon thespace 2x, the middle Port oF che
Freenmakins rars upon the (paceRe, themidale (Ort
Detreen the vellorr-makins and orange-makrins rays
uxon the (paceSo and other intermediate COrtS upOn
intermediate spaces. For Pothe spaces upon which the
several COrts adeguatelr Fall Wrill br realon et the ditte-
rent retransibilier oF thole COrtS Be one lorver than ano-
ThET. No ifthe Paper MN De Ponear the Prilm thatthe
SpaCeS P T and r do not intertere ith one another, the
distance betrreen them T x ill De illuminated by aII
the lorts oFrars in that proportion to one another wrtrich
ther have at their very tirst comine out ot the Prilin,
and consequentlr be rvhite. But the spaces Pl and n
on cither hand, will not be illuminated by them aIl,
and theretore will appear coloured. And particularly
at P, Wrhere the outmost riolet makins rars Fallalone,
the Colour must be the decpest violet. At Cirhere thC
violet makins and indico makine rays are mixed, it
must

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must be a violet inclinins much to indico. At R erhere
che violet makins, indico makins, blue makins, and
one halE oF the sreen-makins rars are mixed, their Co.
Jours must (by the construction of the second Problem)
compound a middle Colour Detreen indico and blue.
AF S Where all the rays aie mized except the red-mi
kins and oranse makcins, their C Olours ousht by the lame
Ruleto compound à faint blue, vergins more to greeH
chan indie. And in the proorels trom S to T, this blue
willoror more and more taint and dilute, till at l,
artrere allthe Colours besin to be mixed, it end In
erhitenels.
Soasain, on the other side oFthe Wrhite at T, irhere
che least retransible or utmost red makins rays are alone
the Colour mustDe the deepest red. AF o the mixture
ot red und oranse rrill compound a red inclinins 13
orange. Ace the mixture oF red, oranse, vello, and
one half, oF the ereen must compound a middle C.Olous
betreen oranse and vellorr. AFx the mixture oF alt
Colours but violet and indico rill compound a Faint
velloir, versins more to green than to oranse. And
chis yellor ill grour more taint and dilute continuaIIs
in its progrels Trom x to n, Where by a mixture oF all
COrts oF rars it will become irhite.
Phese Colours ougheto appear rere the Suns Light
pertectly irhute: But because it inclines to vellor, theex-
cels oF the vellom makcins rays Whereby tis tinged rrich
thatCOlour, beins mixed with the taint blue betreen
Sand I, rill dra it to a Fdint sreen. And (0 the
Colours in order trom P to J oushe to be riolet, indico,
blue, very taint green, Wrhite, taint vellor, oranse, red.
Lhus it is by che computation: And ther chat pleale 10
rien

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C723.
rie the Colours made by a Prilm rill fiud ie (o in
TTature.
Pheleare the Colours on both sides the irhice wrhen
the Paper is held betmeen the Prisin, and the point X
ertrere the Colours meet, and the interjacent wrhite ra-
nistres. For iEthe Paper beheld sill FarFHeL OH ErOm FhC
Prim, the most retransible and least retransible rays
erils be rantino in the midale of the Lioht, and the rest
ottherars Wrhich are tound there, rill by mixture pio.
duce a fuller orcen than Before. AIO the rellon and
blue rill nou become less compounded, and by con-
lequence more intense than betore. And this allo
dFrees rith experience.
And it one look chrough a Prisin upon a Wrhite Objeet
encompassed ith blackness or darkness, the reaion ot
the Colours arisins on the edges is much the Lame, 25
Wrill appear to one that all a little consider it. IF 8
black Object be encompassed with a Wrhite one, the C0-
lours ihich appear chrough the Prisin are tobe derived
From the LightoF chewhite one, spreadins into the RC
sionsoFthe black, and theretore ther appear in a con-
trary order tothat, in irhich they appear irhen a erhite
Objeet is surrounded with black. And the Came is t0
De understood when an Object is viered, vrhole parts
arc lome ofthem less luminous than others. For in the
Borders oF the more and less luminous parts, Colours
oughe alivars by the Came Principles to arise from the
excels of the Lisht oEthe more luminous, and to be of
che Came kind as il the darker parts Were black, but y et
to be more taint and dilute.
L
What

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C124
WNhat is said oF Coloursmade by Prisins may be catily
applied to Colours made by the Crlasses ol Pelescopesi
or Microlcopes, or by the humours ofthe Ryc. Forit
the Object. Sla(s oF a Pelescope De thicker on one side
than on the ottier, or it one halE ot the Cla(S, Or One
halFot the Pupil ofthe Fye De corered rith any opake
substance: the Object-stals, or that part of it or oF the
Eyerrhichis not corered, may be considered a5 a Wedse
ith crooked sides, and erery Wedse oF Cilals, or other
vellucid substance, has the effect of a Prism in retractins
che Lishe irhich passes through it.
NTou the Colours in theoth and Toth Fxperiments
OE the hrst Part arise From the ditferent refexibilier ob
Lighe is crident by irhrat ras there laid. But it is obler-
vable in the oth Lixperiment, that Wrhils the suns di
rect Light is vellor, the excels of the bluc-makins
rays in the reflected Beam oF Light MN, suttices only
to brins that vellorr to a pale wrhite inclinins to blue,
and nocto tinse it with a manitestls blue Colour. F0
obtain theretore a better blue, Luled instead ot the yel
lon Light oFthe Sun the white Lisht ot the Clouds, by
rarvins a little the eexperiment a5 Follons.
EX PE R. XVF.
Let HFC represent a Prilm in the open Air, and 5
thefre ottheSpectator, riemins the Clouds by theis
Lighe comins into the Prilm at the plane side FICK
and retlected in it by us bale FlF. LC, and thence soin8
out through its plain sde IIHLR to the Fiye. And
Wrhen the Prilm and Fre are conveniently placedus lo
that che Ansles ot incidence and sellexion at the bale
may
6 15.

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l125
may be about 40 degrees, the Spectator will sec a BOW
MN oF a bluc Colour, runnins trom one end of the:
bale tothe other, with the concare side torrards him,
und the part oF the base IMNC berond this Bour vill.
Dc brishter chan the other paRE PNINET on the ocher
lide ot it. This blue Colour NIN beins made by no-
thins elle than by refexion of a specular luperticies,
Peems (o odd a Phaenomenon, and lounaccountable For
by the rulsar Hypothelis oF Philolophers, that L’could
not but think ic deserred to betaken notice of. Nou
For understanding the reason oF it, suppole the plane
ABC. to cut the plane sides and base ot the Prilin per-
Dendicularir. From the Lye tothe line BC, Wrherein that
Plane cutsthe base, drar the lines Sp and SF, in the
Ansles SpC 50 degr.  and Stc 49 degr. 20, and the
Doint p ill be che limit bexond ertrich nonc ofthe most.
retransible rars can passthroueh the base of thePrilm,
and be retracted, irtiose incidence is Cuch that ther may
Berehlected tothe Fire; and the point t will bethe like
limit For the least retransible rays, that is, berond
Wrhich none of them can pals throueh the base, irhole
incidence is uch that br refexion they may come tothe
LyC. And the pointr taken in the middle war betreen
Pand F, Wrill be the like limit for the meanly retransible
raYS. And theretore aII the retransible rars irhich FaII
uxon the base berond t, that is, betireen t and B, and.
cin come trom thence to the Lye Wiil De resected thi-
ther: Buc on this side F, that i5, betreen. F and C, many
Ot thele rars wil be transmitted throush the bale.
And all. the most refransible rays wrhich FalI upon the.
bale beyond ps that is, betireen p and B, and can by
reflexion come tromthence tothe lye, will De retlected.
Thither,

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(126
Thither, but erery irhere betreen t and c, many ol
thele rars riil set through the base and be retracted;
and the lame is to be understood ot the meanly reFFAN-
sible rars on cither side ofthe point r. Whence it Fol
lorrs, that the base oF the Prilm must everr irhere BC-
trcen t and B, by a total reflexion oF aII Corts OF rayS to
the Fye, look irhite and brioht. And every irhere
petrreen and C by realon ofthe trantinission ot many
cars oferery lort, look more pale, obscure and dark.
But at L, and in ottier places betireen pand E, Wrhere
all the more retransible rays are refected to the Fye,
and mans ot the lels retransible are transmitted, the
excels oFthe most retrangible in the reRected Lioht will
tinse that Lioht rith their Colour, wrhich is violet and
blue. And this hrappens by takins the line C. pPFB anV
irhere betreen the ends ot the Prilm II CF and F I.
PROP. TZ. PROB. IV.
By the discovered Properties of Fisht to explain ibe
Colours of the Rain- b020.
Phis Bor never oppears but irhere it Rains in the
Sun-hine, and may be made axtificially by spoutine up
Water irhich may break alost, and scacter into DrOpS,
and Fall dorn like Rain. For the Sun ining upon thele
Drops certainly caules the Bor to appear to a Specta
tor Handins in a due position to the Rain and Sun. And
dence it isno agreedupon, that this Bou ismade by
retraction of the suns Light in Drops oF Falling Rain.
This as understood by lome ot the Ancients, and ot
late more tully discorered and explained by the Famous
Antonius

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Antonius de Dominis Archibistop oF Spilato, in his Bo0k
De Radiis Visus  Fucis, publiched by his Friend Bar-
tolus at Venice, in the VCaE LBFT, and Wrritten above
tiventr Pears betore. For he teaches there horr the
interior Bou is made in round DropS oF Rain by tivo
retractions ot the suns Light, and one reflexion be-
treen them and the exterior by trro retractions and
trro lorts ot rellexions betureen them in cach DroP ot
Nater, and prores his Explications by sixperiments
made witha Phial Full oF Water, and with Cilobes oFGla(S
tilled with WVater, and placed in the sun tomakie the
COlOurS OF the tmo BOS appear in theim. ThC CamC
Explication Des-Cartes hach purtued in his MetCOES,
and mended that ot the exterior BOW. But Wrhils they
undersood not the true origin oF Colours, its necestary
to pursue it here a little Further. For understandins
theretore hor the Bor is made, let a DEOBOF Rain OE
any other spherical transparent Body be reprelented by
the Sphere BNF C, described withthe Center C, and Fis. 24.
Semi-diameter C. NI. And leF AN BC onC OF the SunS
rars incident upon it at N, and thence retracted to f,
erhere let it cither so out ofthe Sphere by retraction to-
vards V, or be resected to C; and at C let it either 50
out by retraction to R, or De reflected toHI; and at II
let it 50 out by retraction torrards S, cuttins the inci
dent ray in Z; produce ANY and R C, till ther meet IM
L, and UpON AZ and NF let FaII the perpendiculars
C. D and C. F and produce C. D till it Fall uxon the cir-
cuinterence at L. Parallel to the incident ray A N dca
the Diameter BO, and let the sine ot incidence out ot
Air into Water De to the sine ot refraction as I to
R. Noi it vou suppose the point ot incidence Nta
MOVE

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move trom the point B, continually eill ic come tOL,
the Arch OF will firs increase and then decrease, and
(0 will the AnelC AZR erhich the caYS AN and CTR
contain; and the Arch OF and AnOlC AX R will BC
Bisoes irhen ND iS EO CN aS V II RR EO VZ RR,
in erhich case NF ill bCtO ND a5 2R +oI. AIOthe
Anele A YS irhich the rayS A N and IIS contain rill
Trst decrease, and then increase and sior least irten
ND iS EO C N aS V TI-RR EOVB RR, in wrhich cale
NVF. Will bC EOND aS ZR tOL. And Cothe Anole irhich
the next emersent ray (that is, the emersent ray aftei
chree rellexions) contains with the incident pay AN
will come to its limit Wrhen NDis to C. N aS V II. RR t0
VISRR, in Wrhich case N F will bC EO ND a5 4 R t0 ,
and the Ansle irhich the ray next alter that emergent,
that is, the rar emersent alter tour rellexions, con
tains rith the incident vill come to its limit, wrtren
ND is tO C. N, AS VTTRR tOV 24 RR, in irtrich case
NF will BC tO ND aS SR toI; and (0 on intinitel,
thenumbers 3, 8, 15, 24, Dc. beins gathered by conti.
nualaddition ofthe terms oFthe arithmetical progression
3,5,7,9,5c. Thetruth oF all this Mathematicians will
Catly examinc.
Norr it is to be obserred, that as wrhen the Sun comes
tohis Propicks, dars increale and decreale but a very
little for a great Wrhiletogether; Po wrhen by increat.no
the distance C. D, these Anoles come to their limitsu
ther vary their quantiey but very little For Pome time
together, and theretore a tar greater number oFthe rayS
irtich Fall upon all the points N in the Ouadrant
BL, Mall emerse in the limits oF these AnSleS,
then in auy other inclinations. And Further it 1
te

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L129
tobe observed, thatthe rars irhich ditter in retransi.
bilies rilthare different limits oftheir Ansles oE emer-
sence, and by consequence accordins to their different
degrees oFretransibilitr emerse most copiously in dif-
terent Angles, and beins separated from one another
appeas each in their proper C Olours. And wrhat thole
Ansles are may be easils sathered trom the FOregOInO
Lheorem by computation.
For in the least retransible raysthe sines Land R (a5
ras found abore) are 108 and 8r, and thence by
computation the grentest Anole AZR ili be tound
42 desrees and 2 minutes, and the leal Ansle AYS,
50 degr. and 57 minutes. And in the most retransible
rays the sines I and R arc 109 and BT, and thence by
computation the greatest Ansle AZ R vill bC Found
Odeorees and 17 minutes, and the Least Ansle AYS
54 desrees and7 minutes.
Suppolenon that isthe Spectator SFre, and OP a line Fig. 15.
drarn parallel to the Suns rars, and let POF, POF,
eOC, POE, be Ansles oF 40 desr. 27 min. 42 degr.
2 mIn. 50degr. 57 min. and 54 desr. 7 min. relpectirels,
aud chese Ansles turned about their common side Ol,
Mail rith their otlier sides OF, OF; OCi, OHI de-
deleribe the veroes of tro Rain- bOWS AFBF and
CHIDC. For iF H, F, G, II, bc DropS placed any
arhere in the conical superticies described by OF, Ol,
OG, OTI, and be illuminated by the SunS raYS SF
SF, SG, SHI; the AnslC SFO beins equal to the
Ansle POF or 40 degr. 17 min. CalI DC che sreatest
Anele in wrhich themost retransible rays can atter Onc
cellexion De retracted to the fiy e, aud cheretore all che
Drops in che line O F. Mall send che most retransible
1+γ4

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T2
rayS most copioussy to the FyC, and chereby Arike FIC
sentes rrith the deepet riolet Colour in that region.
And in like manner the Anele SFO beins equal 1
the Ansle POF, Or 42 deg. 2 min. Malt be the greatel
in erhich the least retrangible rays atcer one reflexion
canemerse out of the Drops, and theretore thole rav
MaIl come most copioustr to the FyC From the DrOPS In
theline OF, and Arike the senses rith the decpest red
Colour in that region. And by the Tame argument,
the rars prhich hare intermediate degrees ot retrangibi
liey Mail come most copiousr From Drops Betreen
F. and F, and Arike the senses wich the intermediate
Colours in the order erhich their degrees ot retrangibi
lity require, that is, in che prosrels From P. LO F, Ot
Fromthe inside of the Bon tothe outlide in this ordei,
riolet, indico, blue, green, vellor, orange, red. Butthe
violet, by the mixture of thewhite Light oF theC louds,
Will appear faint and incline to purple.
Again, the Ansle SCO beins equal to Anole POC,
OF 50 gr. GY min. Phall De the least Anole in irtich che
least retrangible rays can alter trro reflexions emerge out
ofthe Drops, and theretore the least retrangible rays Mall
comemost copiously tothe Rye From the Drops in the
line OG, and srike the senle rith the deepest red ii
that resion. And the Angle SFTO beins equal t0 the
Ansle POFL Or 54 GT. 7 min. MaII DC the leaH AnglC in
ertrich the most retrangible rars a(ter ero reflections cam
emerse out oEthe DrOpS, and theretore thole rars Mal
come most copioussy tothe Fre From the Drovs in the
line OFI, and srike the senses rich the deepest riolet in
that resion. And by thelame areument, the DropSin
the regions betreen C and HI Mall Aritce the sense iriclo
+

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3I
the intermediate Colours in the order wrhich their de
Prees ot retransibilies require, that 15, in the progrels
trom CrtoFI, or From che inside of the Bor tothe out
side in this order, red, oranse, vello, creen, blue, in-
dico, riolet. And since thele Tour lines OF, OF, OC.
OFI, may be lituated any irhere in the aborementioned
conical superticies, ertrat is laid ot the Drops and C0.
lours in these lines is to be underHood ofthe Drops
aud Colours every erhere in thole superticies.
Lhus MaII there be made tro Bows oF C OIOUIS, aN
interior and Aronser, by one restexion in the DTOpS,
and an exterior and tainter by trro; tor the Lishe De-
comes Fainter by every ressexion. And their LOlOUTS
Mall ly in a contrarr order to onc anothei, the red ot
boch Bours borderins uxon thespace CF irhich is be-
tireen the Borrs. Phe breadth oF the interior Bo
L.OF mealured crols the Colours Mail bC 1 degr. 45 mIn.
and the breadth of the exterior (OFI MaII BC 2
decr. 10min. and the distance betreen them (O L
Mall bC8GF. 55 min. the sreatest Semi-diameter oF the
innermole, that 15, the AnslC POF beinS 42 gF. 2 MIM.
and the least Semi-diameter ot the outermost POCr, bC-
In8 G0EC. 57 min. Phele are the meatures oF the BOWS,
a5 thes ould be rere the sun but a point; tor by che
breadth ot his Body che breadth of che Borsrill be in
creased and cheir distance decrealed by halt a degree,
and (o thehreadth os the interior lris ill be 2 degr.
5 min. ehat ot the exterior 3 desr. 40 min. cheir di-
Htance Bdegr. 25 min. the sreatest Demi-diameter oF ThC
interior Bon 42 desr. 57 min. and the least oF the ex-
erior 50 degr. 42 min. And such are the dimensions
ethe Borrs in che earens found io berery nearts,
WvHEI

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olen their Colours appear RronS and perfect. FOF
once, br luch means a5 I then had, I ineasured thc
srcatest Semi-diameter otthe interior Tris about 12 de
crees, the breadth ot the red, vellor and sreen in that
lris 63 or 64 minutes, behdes the ontmos faint red ob
Ecured by Brightness oF the Clouds, For wtrich ire
may alloir 3 or q minutes more. The breadeh oF the
Dlue ras about 40 minutes ore besides the violet,
ertich ras Fo much obleured by the briohtnels oF thC
Clouds that I CouId nOE meature itS BrCadE. BUF
suppolins the breadth of the blue and violet together
to equal that ot the red, vello and sreen together, the
Wrhrole breadth ot this lris wisl be about 2 degrees a5
abore. The least distance betreen this Tris and the ex
terior Tris ras about 8 degrees and z0 minutes. The ex
terior Iris Was broader than the interior, buE (0 Faint,
especially on the blue ide, that L could not mealure its
breadtm distinctlr. At another time When BOTH BONS
appeared more distinct, I measured the breadth oF the
interior Tris 2 gr. 10, and the breadth of the red, vel
lorr and sreen in the exterior Iris, Wras to the breadt
otthe lame Colours in the interior 25 3 t02.
This Fixplication oE the Rain- BoW is vet Further con
tirmed by the kenovn Fxperiment (made by Antonius
de Dominis and Des-Cartes) ot tranging up any Where
in the Sun- hine a CiL IIS-Clobe filled rith Water, ane
riemins it in such a posture that the rays wrhich come
From the Globetothe tre may contain rith the Sun
cays an Angle oF cither 42 Or 50 degrees. For il the
Ansle De about 4.2 Or 43 degrces, the Spectator (suj
Dose at O) Mail sec a tuit red Colour in that side oF tH
Globe apposed to the Sun as tis represented at f
an

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it thac Angle become lels (luppoie by depressins the
Globe to F.) there ill appear other COlours, vellorr,
orcen and blue successively in the lame side ot theClobe.
Butifthe Ansle be made about 50 degrees (suppose by
liftins up theClobe to G)chere Wrill appear a red Colour
in that side of the Clobe torrards the Sun, and it the
Ansle De made sreater (suppole by littins up the Cilobe
toHI) the red rill turn successively tothe other Colours
Vellorr, sreen and blue. Phelame thins lhave tried by
lettins a Cilobe rest, and raitins or depressins the Lye,
Or otheririse movins it to make the Ansle ot a just
magnitude.
l have heard it represented, that it the Light oF a
Candle De retracted by a Prilin to the fiyc; Wrhen the
blue Colour Falls upon the Fire the Spectator MaI lec
red in the Prisin, and wrhen the red Falls upon the Fye
he MaIl see blue; and if this irere certain, the COlours
oF the Clobe and Rain borr ousht to appear in a CON-
trary order to wrhat re find. But the Colours OF the
Canele beins very Faint, the mistakce leems to arile trom
the difficuler oF discernins irtrat Colours FaII on the
Fre. FOr, on thecontrary, Phare Lometimes had Oc
cation to observe in the suns Light retracted by a Prilm,
that the Spectator alivars sees that Colour in the Prilm
ertrich Falls uxon his Fve. And the lame Phare Found
true allo in Canele Light. For Wvhen the Prilm is mo-
ved llo ly trom theline which is drawndireetly fromthe
Candle to the Fye, the red appears Arst in the Prism and
thentheblue, and theretore cach ot them is seen When
it falls uxon the fiye. For thered pastes overthelive
Rrs, and then the bluE.
L. L1C.

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3
The Light irtrich comes throush DropsoF Rain by
truo refractions mithout auy reflexion, ouglitto appeai
Aronoest at the distance ot about 26 degrees From the
Sun, and to decar sradually both mays as the distance
from him increales and decreales. And the Tame IS to
be underctood ot Lighe transmitted through spherical
Hail-Rones. And if the Hait bC a litele Hatted, a5 il
otten is, the Light transmitted mar sro lo Arons at
a litele lels distance than that oF 26 degrees, a5 to form
a Flalo about the Sun or Moon; Wrhich HTalo, as otten
25 the Hail.Rones are duly tioured may be coloured,
and then it must be red within br the least retrangible
cars, and blue without bythe most retransible anes, espe.
cially ilthe FTail- Rones hare opake GElobules oF Sno in
their center to intercept the Light ithin the ITalo (15
Flueenius has obserred) and makce the inside thereotmore
distinetir dehined than it vould otherrise be. For
Tuch Fail-sones, though spherical, by terminatins the
Light by the Sno, may make a tlalo red within and
colourlesswithout, and darker in the red than rith.
ont, a5 Tlalos use to bc. For ofthole rars erhich pals
close br the Snoir the rubritorm ill De least retractedu
and (o come tothe Rye in the directes lines.
Phe Lightrrhich passes chroush a Drop ofrain after
tvo retractions, and three or more resexions, is lcaree
Arons enouch to cause a Pensible Bour; but in thole Cy
linders ofTCe by ertrich Fucenius explains the Parhetiu
il may pechaps be sentibole.

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3d
PROP. Z. PROB. V.
By the discovered Properties of Lisht 10 explain ehe per-
manent Colours of naturat Bodies.
Phese Colours arise from hence, that lome natural
Bodies resleet lome Ports oFrars, others other lortsmore
copioustr thanthe rest. Minium refects th= least re-
transible or red. makins rays most copiousy, and thence
appears red. Violets refect the mostretrangible, most
copioussy, and thence hare their Colour, and lo oF other
Bodies. Lvery Bodr refects the rays oF its omn COlOur
more copioussr thanthe rest, and trom their excels and
predominance in the reflected Light has its C OlOUF.
E Z P F R.. ZV. IL..
For is the homoseneal Lights obtained by the Colu.
tion of the Problem proxosed in the ath Propolition ot
ehe Frst Book rou place Bodies oF sereral CotOurs, jou
Will find, 25 I hare done, that everr Body lookS nost
Eplendid and luminous in the Lighe of its omn COlour.
Cinnaber in the homogeneal red Light is most resplen-
dent, in the sreen Lisht it is manitestlr less resplen-
dent, and in the blue Light AiII lel5. Indico in the
violet blue Lighe is most resplendent, and its splendor
is gradualls diministred as it is remored thence by de
orces throuzh the green and vellon Lieht to the red.
By a Leck thegreen Light, and next that the blue and
vello Which compound oreen, are more Aronsly re-
Aected

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C
136
Aectedthan the other Coloursred and riolet, and (o ofthe
rest. But tomake these Fxperimentsthe more manifest,
luch Bodies ouoht to be chosen as trave the Fullest and
most virid Colours, and tro ot thole Bodies are to DC
compared together. Thus, tor instance, it Cinnaber
and ultra marine blue, or Pome other FuII blue be
held together in the homoseneal Lighe, ther rill both
appear red, but the Cinnaber ill appear oF a Aronsl)
luminous and resplendent red, and the ultra marine
blue oF a Faint oblcure and dark red; and it ther be
held togecher in the blue homogeneal Light they will
both appear blue, but the ultra maxine will appear o
a Aronsly luminous and resplendent bluc, and the
Cinmaber oF a Faine and dark blue. Which puts it out
ot dispute, that the Cinnaber restects the red Light
muchinore copiously than the ultra marine doth, and
the ultra marine retlects the blue Lioht much more co
piousr chan the Cinnaber doth. The lame Fxperiment
nar De tryed succestuily rith red Lead and Indico, ot
Writh any other trro coloured Bodies, iF due allorvance
be made for che ditferent Arensth or Wreaknels oF theis
Colour and LioHt.
And a5 therealon oF the Colours ot natural Bodies is
erident by chese Fxperimenes, lo it is Further contirmed
and put past dispute by the turo trst Lxperiments ofthe
tirs BO0k, Wrhereby trras proved in tuch Bodies that
the rellected Lighe Which ditter in Colours do dister also
in degrees ot retransibilier. For chence itS CerFaim,
that lome Bodies retleet the more retransible, othere
the lels retransible rassmore copiousty.

## Folio 137 — 1677894601:0157
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And that this is not only a true realon of thele C0-
COurS, but eren the only realon may appear further
trom this consideration, that the Colour ot homogeneal
Lisht cannot be chansed by the restexion oE natural
Bodies.
for it Bodies by refexion cannot in the least change
the C Olour oF any one sort ot rayS, ther cannot appear
coloured by any ocher means than by reflectins thole
ertrich cither arc of their omn Colour, or wrhich by
mixture nust produce it.
But in trying Experiments of this kind care must be
had that the Lighe De sufficieney homoseneal. For il
Bodies be illuminated by the ordinary prismatick CO-
lours, they ill appear neither ot their omn day. light
COlourS, nor oF the Colour oF the Light cast on them,
but oF lome midele Colour betreen both, 25 I hare
Found by Lxperience. Thus red Leud (For instance)
illuminated erith the ordinary prismatiek ereen iil
not appear cither red or green, but Oranse Or vellor,
Or Detreen vellorr and oreen accordinsly, as the oreen
Liont by irhich tis illuminated is more or less com-
Pounded. For because red Leud appears red wrhen il.
luminated rith wrhite Lighe, Wrherein aIl COrts OF rays
are equally mixed, and in the green Light aIl POrts of
raysare not equaliy mixed, the excels ot the vellon-
makcins, sreen makins and blue making rays in the
incident green Lighe, rill cause thole rays to abound
lo much in the refected Light as to draw the Colour
trom red torrards their Colour. And because the rec
Lead reflects the red makins rays most copiouss in
proportion to their number, and next alter them the
oranse makins and vellor. makins rayS; these rars in
thC

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the retlected Ligtt rill be more in proportion to the
Lishe than they irere in the incident sreen Light, and
thereby rill dear the reflected Light From green tO
ards cheir C olour. And theretore the red Lead rrill ap
Dear neither red nor green, butota Colour between Both.
In transparentlr coloured Liquors tis obserrable,
that their Colour uses to varr vrith cheir chickenels.
Thus, For instance, a red Liquor in a conical Glals
hreld betrreen the Lighe and the Lre, looks oF a palc
and dilute vellon at the boctom ertrere tis thin, and d
licele hieher erhere tis thicker orors oranse, and erhere
etio RiIl thicker becomes red, and irhere eis thickel
the red is decpest and darkest. For it is to bc conceirea
that such a Liquor Aops the indico makins and violet
makins rare nost casilr, the blue makcing cays moic
difhcultly, the green makins cars Aill more dificule),
and the red makins most difficulelr: And that if the
thickness oF the Liquor be onty (o much a5 Tussicest
Aop a competent number oE the violet makins and in
dico makcins rars, Writhout diminithinq much the num
ber ofthe rest, the rest must (By PFOp. 6. F ib. 2.) Com
pound a pale vello. But it the Liguor De lo muche
thieker asto Hop alo à sreat number ot theblue maliv
rays, and lone of the green makine, the rest must COI
pound an orange; and irhrere it is (0 thick a5 eo A0]
alo a sreat number ot the green makins and a consi
derable number oF the vellon makins, the rest mul
begin to compound a red, and this red must sror deepet
and darker as the vellor makins and oranse makine
cays are more and more Aope by increasins the thick
nels oF the Liguor, (0 that seur rays besdes the red
makins can set throush.

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OEchis kind is an Experiment lately related to me by
MIP. Flalley, erho, in dirins decp into the Sea, Found
in a clear Sun Phine day, that irtien he ras Cunk many
Lathoms deep into che Water, theupper part oF his
Hland in irtrich the Sun one directis through the
Nater looked oF a red Colour, and the under part ot
his Lland illuminated by Lisht reflected trom the Water
belor looked oreen. For thence it may be sathered,
that the Sea- rater reflects back the violet and blue
makcins rars most catilr, and lets thered makins rays
Palo most ticely and copioully to creat depths. FOr
chereby thesuns direct Lisht at all sreat depths, by
realon ot the predominatins red makins rays, mult
appeur red; and the greater the depth is, the Fuller
and intenter mustthat red be. And at such dexths a5
the violet makins rays scarce Denetrate unto, the blue-
makins, srcen makcins and vellormakins rayS beIM
reslected trom beloir more copiously chan thered makIM
Ones, must compound a sreen.
Nou it chere be tiro Liquors of Fui Colours, sup-
Pole a red and a bluc, and Both oE them (0 thick a5
lustices to make their COlours sufficiently FuIl; though
cither Liquor De Cutticienely transparent apart, Vet
vill vou not be able to see through both together. LOr
it ouly thered makins cays pals through one Liquor,
and onlr the blue makcins chroush the other, no rayS
can pass chroush both. This MP. Hoote tried calually
rith Glals redges filled rith red and blue Liguors,
and ras surprized at the unexpected erent, the realon
oFit beine then untnomn; irhich mates me trust the
more to his Lxperiment, thoush lhare not eryed it
My PeIE. But he that rould repeat it, must take care
the Liquors be ol very 800d and FuII COlOurS.

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NTorr Wrhils Bodies Decome coloured by reflecting oi
transmittins ehis or that fort ot rays more copiousY thai
the restu it is to be conceired that cher Aop and stisse i1
themselrestherars irhich ther do not rehect or tranlmit.
For if Giold be Foliated and held betreen vour Rye and
cheLisht, theLighe lools blue, and theretore massy Crola
lets into its Body the blue makins cays to be rellecte
to and Fro within it till they be sopt and stised, Wrhit
it relects the vellor-makinq outrrards, and therebs
J0oks vellon. And much alter the Pame manner that
LeaF-Sold is yeltor by reflected, and blue by cransinit.
ced Lisht, and massi Gold is vellor in aII positions o
the Fye; there are lome Liquors as the tincture o
Fionum Nephriticum, and Pome Ports oF Cilals which
eransmit ore Port of Lioht most copioussy, and retlect
another (ort, and thereby look ot Several C OlOurS, ac
cordinq tothe position oF the F ve tothe Light. But i
these Liguors or Glalles vere lo thick and massy that
no Lislit could set throuoh them, L quection not bu
that ther rould like alt other opake Bodies appear ol
one and the same Colour in all pohtions ot ehe fiser
though this lcannot yet attirm br experience. For al
coloured Bodies, (0 Far as my Observation reaches, may
be leen through it made sufticiently chin, and theretoie
are in lome mealure transparent, and ditter only in de
orees of transparency erom tinged transparent Liquors;
chese Liguors, a5 vell as chole Bodies, by a sufticient
chichnels becomins opake. A transparent Body irhicl
looks oF any Colour by transinitred Lient, may alla
look ot the lame Colour by rehlected Lighe, the L1gI
ot that Colour Deine reflected by the Further surtace o
ehe Body, Or by the Air berond it. And thenthe ie
Aected Colour irill be diministred, and perhaps ceale,
MakIBS

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T4I
makcins the Body very thick, and pitchins ic on che
Back. Side to diminim the reflexion of its further surtace,
lo that the Lighe reflected trom che tingins particles
may predominate. In luch cales, the Colour otthe re-
Aected Light rill De apt to vary From that of thelighe
cransmitted. But irhence it is that tinsed Bodies and
Liquors rellect lome Cort oFrays, and intromit or trant-
mit other lorts, Bail be Paid in the next B0Ok. In thIS
Propolition I content my (elEto hare put it past dispute,
that Bodies have such Proverties, aud TheNCE aDDCAI.
coloured.
PROP. ZT. PROB. VI.
By mixins coloured Fiehts to compound a Beam of Light
of the same Colour and LTature roith a Beam of the Suns
direct Lioht, and therein to experience the truth. of the
foresoine Propositions.
Let AB C abC represent a Prilm by irhich theSun SFi8. 16.
Liont let into a dark Chamber throush the HIole L, iMav.
De retracted torards the LenS MNI, and paint upon it
At P, 4, F, S andt, theulual Colours violet, blue, sreen.
vellorr and red, and let the diversine cays by there-
Fraction of this Lens conrerge again torards Z, and
there, by themixture oF all thole their COlours, compound
a Wrtrite accordins to what was hernabore. Then let
another Prilin DF. C,dC8, Parallet to the Former, DC
Placed at X, to retraet that White Lighe upmards to-
Wards Y. L et the retractinq Angles oF the Prilms,
and their diltances From the Lens De equal,u (o that thc.
cays irtrich converoed trom the Lens torards X, and.
rithont retraction, rould there hare crosled and. diver-
sed aeain, may by the retraction oEthe lecond Prilin be.
reduced.

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1
reduced into Paralleliim and diverse nO MOrC. FOr
chenthole rars rill recompole a Beam ot irhice Light
XV. IF the refractins Anele ot cither Prisin De the
bigoer, that Prilm must be lo much the nearer to the
LenS. Tou Wil knom irhen the Prisins and the L enS
are Well set together by oblerrins it the Beam ot Light
Z Pirhrich comes out of the second Prism De pertectiy
erhite tothe verr edges oF the Light, and at aII distan
ces trom the Prilm continue perfectlu and totallr mhite
like a Beam of the SunsLient. For till this happens,
the position of the Prisims and Lens to onc anothei nust
De corrected, and then if by the help ot a lons Beam ot
Nood, as is reprelented in the Figure, or by a Tube,
Or lome other tuch instrument made For that purpole,
ther be made Fast in that situation, you may tey aIl the
lame Lxperiments in this compounded Beam oF Light
XV, irtich in the Foresoins Lixperiments hrare been
imade in the Suns direet Lisht. Lior thus compounded
Beam oF L iohEhasthe Pamme appearance, and is endoved
rith aIl the same Properties rith a direet Beam OF the
SunsLiohe, PoFaras my Obserration reaches. And in
errins Experiments in this Beam you may by Roppins
any OEthC COlOUES P, 9, r, Sand L, at the lens, sec hon
the Colours produced in the Lixperiments are no ether
chan those rrhich ehe rars had at the P ens before thev
entered the compolition ot this Beam: And by conte.
quence chat they arise not From any neur moditications
OEthe Lighe by retractions and reflexions, but Fromthe
various leparations and mixtures ot the cays originally
endored rith their colour-makins qualities.
S0, For instance, havine with a Lens 4 Inches broad,
and to Prilms on cicher Hland 6 Feet distant From the
P. enS, made such a Beam ot compounded Light: to
eXaIIM

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examin the reason ol che Colours made by Prilins, L
retracted this compounded Beam oF LieHE Z Y ricli
another Prilim HITIKh, and thereby cast theulual pril
matick Colours PORS Puxon che P’aper I. V placed DC.
hind. And then by Pcoppins anz ot the COlOurs p, 4.
r, S, t, at the Lens, l Found that the tame Colour vould
vanistr at the Paper. 50 it the purple P ras Copped al
the Lens, the purple P uxon the Paper rould vanistr,
and the rest oF the Colours vould remain unaltered,
unless pertraps the blue, (0 tar as lome purple latene in
it at the Lens mioht De separated From it by the Fol-
Lowins retractions. And lo by interceptins the sreen
upon the Lens, the green R upon the P’aper vould va-
nistrus and (o oEthe rest; irhich plainly chews, that a5
the wrhite Beam oF Light Z Y was compounded ot se-
ve Lishts rariousr coloured at the P. ens, (0 thel0.
lours irhich afterrards emerse out of it by new retra-
ctions are no other than thole ot wrhich its Wrlitenels
ras compounded. The refraction oF the Prisim HIIK
kh generates the ColOUrS PORST upon the PaPeF,
noc by changins the coloritic qualities ot the rays, but
by separatins therays vrhich had the rerr Came coloritic
qualities betore ther entered the compolition ot the re-
tracted Beam Wrhite otLightZV. For otherwisethe rays
erhich ivere oF one Colour at the Lens misht be ot anon
ther upon the Paper, contrary to what ve find.
So again, to examin the reason of the COlOurS OF Ra-
cural Bodies, Iplaced such Bodies in the Beam oF LishE
XY, and Found that they ail appeared there oF thole
their omn Colours wrhich they have in Day.light, and
that those C Olours depend upon the rays wrhich had tha
lame COlours at cheLens betore ther entred the compo.
Etion

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sition oF thatBeam. Thus, For instance, Cinnaber illumi-
nated by this Beam appears of the lame red Colour as in
Daylight; and it at ihe Lens rou intercept the green-
makins and blue makins raps, its redness will become
more tuIl and livelr: But it rou there intercepe the red
makins cars, it rill noc anr longer appear red, but be-
come vellor or sreen, or ot Lome other COlOur, ACcOr
dins to the lorts ot cars Which vou do not intercept.
50 Giold in this LiohE Z Y appears oF the Came velton
Colour as in Dar-liehe, but by interceptins at the L ens a
duc quantier of the vellon-makine cays it rill appeai
Wrtrite like Silver (a5 l hare erved) ertich Mews that its
vellornessariles trom the excels ot the intercepted rays
ringing that whiteness rith their Colour Wrhen ther are
let pa(5. So the intution oF Fionum Nephriticum (a5 l
trare allotrred) wrhen held in enis Beam OF LioHEX Y,
looks blue by the reflected part ot the Lighe, and vellon
by chetransinitted part ot it, as when tisviemed in Day-
lioht, but if rou interceptthe blue at the. Lens the infir
tion irill lose its refected blue Colour, Wrhil its tran-
mitted red remains pertect and br the loss ofsome blue
mmakins cars whererith it was allared becomes more in-
tense and FuII. And, on thecontrary, if the red and orange
makins rays De intercepted at Pens, the infusion vii
lole ies transmitted red, whilR its blue vrill remain and
become more Full and perfect. Which Cers, that the in-
fution does not tinge the rarsrith blue and vellorr, but
ouly transinit those most copioully wrhich rvere red- ma-
king betore, and reflects thole molt copiouslr irhich vere
blue makino betore. And alter the lame manner may the
reaIons oF other Phaenomena be examined, by eryins
ehem in this artificial Beam oF LishtXL.
V

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18. 4.
siD
e
BOOK I. Parc I. Plate I.
5
6. 3.

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36
37
atur: Leiton. Mar9. 193, [+
38
39
ttnnronec diviitr
NNIEDEHSAENSISEIIL ENNDESBIDEHTHEK

## Folio  -  — 1677894601:0167
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...
... . . . .. . . . . .
2
S
B00kI. Part H. Plate I.
18. 6.
 . . . . .   . . . . .  . 2 .  . . .  . 2  . . . . . 2 . 2 1 ∞ . 2 2 . - 20. 9

## Folio  -  — 1677894601:0168
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2
tast. tH sel. tcttu. Sitat Ates. tstet tl.  AHal itsot ll  setil  sets  felto s ie ts. sl  . S e it  . H sulit fll. C sts.    u llIII.A. selat Ias
6
ur: Leibn. Mar9. 193,
38
OTTFRIED MLHLCMILEIBIAIL SIDEIDTHEK
NIEDEHSACPISISCMIL BIODLSOIDCIOTHEK

## Folio  -  — 1677894601:0169
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re
 Se
I2. 10
. 2L.
Nt
BookL. Paxt I. P late HI.
6.
e
e
range L
FRIED WILHELMLE

## Folio  -  — 1677894601:0170
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TOTTFRIED WILHELM LEIBNIZ BIBLIOTHEK
m
NIEDERSACHSHEME LAODESOIDLIOTHEK
6
atur: Leibn. Marg. 193
37
38
39

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6. 23.
1C. 26.
B00k I. ParF HI. PLaLCN.
24
.. --
25
FRIED WILHELM LEIBNIZ BIBI

## Folio  -  — 1677894601:0172
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 sl
1
ttit
t
11
u
 e
l dl l t 111
atit t  
 a
thCHsCEsbioMe
atur: Loitn. Mar9. 193, (172
TOTTFRIED WILHELM CLIONIL SIDEN TNEK

## Folio 1 — 1677894601:0173
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t.C
1
e
NVI
I
P A H
Observations concernine the Reflexions, Refractions, and
Colours of thin transparent Bodies.
I has been obserred by others that transparent
 Substances, as Gla(S, Water, AIr, 1c. Wrhen made
verr thin by beins blonn into Bubbles, or othermile
Formed into Plates, do extribit rarious COlOUES ACCOI-
dins to their rarious chinness, although at a greater
thieknels ther appear very clear and colourlels. In
the Former Book I Forbore to treat ot thele C Olours,
becaule they scemed ot a more difficult consideration,
and ivere not necessarr For ectablitins the Properties
ot Light there discoursed ol. But becaule they may
conduce to Further discoreries for completins the
Pheory ot Lighe, especially a5 to the constitution ot
The pares ot natural Bodies, on Wrhich their Colours or
lranspareney depend: I have here let donn an ac-
count oF them. T0 render this Discourse Chort and
distinct, Phave sirst described che principal ot my
A a
Obter-

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C
2
Obterrations, and then considered and made use ot
Them. The Obserrations are thele.
OB5.
Compressins Erro Prisins hard tosether CtaE Cheir
Sides (Wrhich by chance vere a very little conrez) mighe
Tormerhere touch oie another: L Found the place iI
ertrich ther touched to become ablolutely transparent,
asit ther had there been one continued piece ot CTla(S.
For erhen the Lioht Fell (o obliquelz on the Air, wrtict
in other places ras betreen them,asto be all reflected;
it seemed in that place ot contact to be wholly trans-
mitted, infomuch thatirhien looked uxon, it appearea
like a black or dark Spot, by reason that little Or no
sensible Lisht ras reflected trom thence, as From otter
places; and Wrhen looked through it seemed (as it Wrerc)
ahole in that Air irhich was formed into a thin Plate,
by beins compresed betureen the Cilasses. And throuon
this hole Objects thativere berond mioht De seen di-
Cinctlr, Wrhich could noc at aIl be seen through other
Parts oF the Cilalles irhere the Air as interjacent. AI-
though theCilasses ivere a little convex, vet this trans-
parent Spot was ota considerable breadtn, which breadth
eemed principally to procced trom the vielding inmards
ot the parts ot the Citalses, by reason ot their rutual
pressure. For by prellins them very hard together it
rould become much broader than othermile.
S.

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 II.
When the Plate oFAir, by curnine the Prisms about
their common AXis, became (0 litele inclined to the in-
cident Ray5, that lome of them besan to be transinit.
tedque there arole in it many Aender ATCS oF C olOUES
irhrich at fixst ere Chaped almost like the Conchoid,
as you sec them delineated in the tirst Figure. And Fis. 1.
Or continuins the motion of the Prisms, thele Arcs in-
Crealed and bended more and more about the laid trans-
parent Spot, till they rvere completed into Circles or
Ringsincompassins it, and afterrards continually sre
more and more contracted.
These ArCSat their Ars appearance rere ot a violet
and blue Colour, and betreen them erere white AECS
OF Circles, Wrhich presentr br continuinu the motion ot
the Prisims became a little tinged in their inmard Limbs
rith red and vellon, and to their outmard Limbs the
blue ras adjacent. So chat che order ot these COIOurS
From the central dark Spoc, mas ac that time irhite,
blue, violet; black; red orange, vellow, Wrhite, blue,
violet, Dc. But the vellorr and red vere much fainter
than the blue and violet.
Themotion ot the Prisims about theis Axis being con-
tinued, these Colours contracted more and more, Crink-
ins torrards the whitenels on cither side ot ic until ther
Totalr vanistred intoit. And then the Circles in thole
Parts appeared black and wrhite, rithout any other CO-
lours intermixed. But by Further movins the Prisims
about, the Colours again emersed out ofthe irhitenets,
the riolet and blue as its inmard Limb, and at its out
A a 2
vard

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C4
vard Limb the red and vellorr. So that now their order
Trom the central Spot ras rhite, vello, red; black;
violet, blue, irhite, yellorr, red, Oc. contrarr to wrhat
It Wwas Detore.
OBS. TTI.
When the Rings or lome parts ot them appeared only
black and Wrhite, cher vere very distinct and well de-
fined, and the backness seemed as intense as Fhat OE
the central Spot. Alo in the borders oF the RinGS,
erhere the COlours Degan toemerse out oF the irhite-
vels, ther ivere pretty distinct, wrhich made them vi-
Tible to a verr oreat Multitude. I have Cometimes
numbred abore thirtr Succestions (reckonine crery
black and wrhuite Rirs For one Succeltion) and seeu
more of them, Wtrich br realon ot their Cmalne(s I could
nOt nUM BET. But in other PONtiOnS OF thC PTITIMS, at
ertrich the Rings appeared otmans Colours, lcould not
distinguistr abore cistit or nine ot them, and the exte-
rior ot thole ivere verr contuled and dilute.
In these erro Obserrations to sec the Rines distinct,
and rithont anr other Colour than black and wrhite, l
tound it neceltarr to hold my tive at a g00d distance
Erom them. For by approachinsnearer, although in the
Tame inclination of my Fse to the plane ot the RingS
there emeroed à blueitt Colour out ot the wrtrite,
Which by dilatinq it Celt more and more into the black
rendred the Circles less distinet, and lett ce irhite a
litele tinged with red and vellorr. L Found also by
Lookins throush a Dit or oblone hole, utrich Was
parromer than the Puxil oFmy Lye, and held clole to

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5
it parallel to the Prisms, Lcould sec the Cireles much
distincter and risible to a tar greater number than
Otherwile.
OBS. IV.
Pooblerre more nicely br the order ot the Colours
Wvhich arose out ot the white Circles a5 the Rays DC-
came less and lels inclined to the plate ot Air; l took
tiro Object Glasses, the one a Plano-conrex For a Four-
teen-Foot Telescope, and the other a larse double con-
rex For onc ot about fter-Foot; and upon this, larins the
Other rith its its plane-side dornmards, I pressed them
llowlytogether, to make the Colours succeltirely emerse
in the midele ot the Circles, and ehen Romly listed
the upper Glass trom the lorver to make them succet-
Cively vanistr acain in the Came place. The ColouI,
irhich by pressins the Cilasles together emerged last in
the middle oF the other Colours, rould uxon its Arst
appearance look like a Cirele ot a Colour alinost uni-
torm trom the circumterence to the center, and by
comprellins the Clables siil more, gro continuallu
broader until a ner Colour emersed in its center, and
thereby it became a Rins encompallino that new C0-
lOur. And DV compressins the GElastes Rill more, the
Diameter ot this Rins vouid encrease, and the breadtm
oF its Orbit or Perimeter decrease until another nem
Colour emerged in the center ot the last: And IO OI
until a third, a Tourth, a fitth, and other Follorina
nem Colours successirely emersed there, and became
Rinos encompassino the innermost Colour, the last ot
rhich as the black Spot. And, on the contrarY, by
littins

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littins up the upper Cilass From the lorver, the diameter
OF the Rinss rould decreale, and the breadth ot their
Orbit encrease, untit their Colours reached succestirely
to the center; and then ther beins ot a considerable
breadth, Icould more calilr dilceen and distinguisr
their Species than betore. And by this means l ob.
serred their Succestion and Ouantity 10 be 25 F0l-
lorveth.
Next, tothe Dellucid central Spot made by the con-
tact ot the Glasses succceded blue, wrhite, vellorr, and
red, the blue ras (o licele in quantier that Icousd not
discern it in the circles made by the Prilms, nor could
I Well distinguittr ans violet in it, but therellor and
red ivere preter copious, and secmed about as much
in extent as the white, and tour or Are times more
than theblue. The next Circuit in order ot COlOurS
immediatelr encompassine thele ivere violet, blue,
srcen, vellor, aud red, and thele vere aIl oF them co-
pious and rivid, exceptins the green, Wrhich as very
litele in quantitr, and seemed much more taint and
dilure than the other Colours. OF the other tour, the
violet ras the least in extent, and the blue less than
the rellor or red. The third Circuit or Order Wras
purple, blue, sreen, vello, and red; in irtrich the
purple scemed more reddisr than the violet in the
tormer Circuit, and the green ras much more conspi-
cuous, beins as brisque and copious as any oF the ottier
Cotours, except the rellor; but the red began to bc
a litele Faded, inclinins very much to purple. AFter
this succeeded thie Fourth Circuit of green and red. Tne
oreen vas very copious and livelr, inclinins on the onc
side to blue, and on the other side to vello. But in
thic

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this Fourth Circuit there was neither riolet, blue, nor
vellorr, and the red vas verr impertect and dirtr.
AICO the Succcedins C olours became more and more iim-
perfect and dilute, tiII AFTCF THECC OE FOUF RevoluTiONS
cher ended in pertect irhitenels. Pheir Form, Wrhenthc
Glastes ere most compresed (0 a5 to make the black
Spot appear in the Center, is delineated in the Second
LIBUTC; Where a, b,C, d, e: f, 8, h, i, k: l, M, nn 0, P: 9, r: F15. 2.
5, t: V, X: y denote the Colours reckned in order trom
the center, Black, blue, irhite, vellorr, red: violet,
blue, srcen, relloir, red: purple, blue, sreen, vello,
red: green, red: sreenittr blue, red: greenittr blue,
Pale red: greenitt blue, reddittr erhite.
OBS. V.
To determine the interral oF che Glases, Or thick
nels oF the interjacent Air, by erhich cach Colour was
produced, I meatured the Diameters ot the APA AX
Rings at the most lucid part ot their Orbits, and squa-
rins them, I Found their Squares to be in the Arith-
metical Progression ot the odd NumBCES, L. 3. 5. 7. 9. TI.
AndAnce one et these GElasses ras Plain and the other
Spherical, their Interrals at thole Rings must be in the
Pame Progrestion. I measured also the Diameters ot
the dark or Faint Rings Becreen the more lucid Co-
lours, and Found their Squares eo be in the Arithme
tical Progression of the eren NUMBeES, 2. 4. 6, 8, 10, 12.
And it beinq very nice and difficule to take these mea-
Tures exactly; P repeated them at dirers times at dirers
Parts oF the Glasses, that by their AOrcement I mioHE
be contirmed in them. And the tame Method I used in
deter-

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determinins some others o the Follovins Obserra.
LIOIS.
OBS. V1
Phe Diameter oF the Exth Rins at the most lucid
Part oF its Orbit ras 5 parts ot an luch, and the Dia-
meter ot the Sphere on which the double conrex Ob.
ject.Clals mas sround ras about 102 Feet, and hence
lgathered the thickness of the Air or Aereal Interval
ot the Glasses at that Ring. But lome time alter, suI-
pectins that in makins this Obserration I had not de-
termined the Diameter of the Sphere writh sufficient ac-
curatenels, and beins uncertain rhether che Plano-
conrex Cilass iras truls plain, and not Comethins con-
care or conrex on that side irhich l’accounted plain;
and irhether Lhad not pressed the Gilasses together, 25
Potten did, to make them touch. (For by prestins luch
Classes together their parts catily vield inmards, and
the Rings thereby become sensibly broader than they
vouldbe, did the Cilasses kecp their Figures.) I re-
Peated the Lxperiment, and tound the Diameter ot
the lixtl lucid Rins about;es parts ot an Iuch. Iic-
Peated the Experiment allo rith such an Object- (ila(5
OF another Telelcope as Phad at hand. Pnis rras a double
conrex sround on both sides to onc and che lame
Sphere, and its Locus ras distant trom it 83: Tuches.
And thence, il the sines ot incidence and retraction ot
the bright vellorr Lisht be altumed in proportion 25
1I to 17, the Diamerer ot the Sphere to erhich the
Class as figured rill by computation be Found 182 In-
ches. This Cilass L laid upon a Aat one, (o that the
black

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10
block Sxocappeared inthe middle ot the RinoSOFC olOuES
without any other presture than that ot the reisht ot
the Cilass. And no mealurins the Diameter ot the
tifch dark Cirele as accurate lr as l could, I Found it the
titth part ot an Ineh preciselr. This measure vras taken
rith the points ot a pair of Compasses on the upper sUI-
tace on the uipper CitlaIs, and my Liye ras about cieht
Or nine Tnches distance trom the Cilals, almost perpen-
dicularly over ic, and the Class Was? oF an Inck thick,
and thence ic is caly to collect that the true Diameter
Ot the Rins betrcen the Glasses Was greater than its
mealured Diameter abore the Classes in the proportion
et 80 t079 or thercabouts, and br consequence equal
co  PartS oF an Inch, and its true Semi-diameter equal
10  PartS. Nor a5 the Diameter oF the Sphere (182 In-
ches) is to the Semi-diameter of this htch darke Rins
EDaLES OF an Inch) (0 is this Semi-diameter to the
thickness oF the Air at this Ateh dark Ring; irhich is
ThereFOrC;  OF inasa PaNtS oF an Inch, and the ftch
1c
parE ThCTCOF; viZ. ThC aBth part oF an Tuch, is che
thicknels oF the AIr at the RPK OF these dark RInOS.
The same Experiment lrepeated rith another dou-
ble conrex Object- glass ground on both sdes to one and
the Came Sphere. IES Focus was distant From it 168
Inches, and cheretore the Diameter ot chat Sphere Wras
184 Tnches. This Glass beine laid uxon the lame
plain Gla(S, the Diameter OF the AEEH oF the dark
Rinss, Wrhen the black Spot in their center appeared
plainty without pressins the Glasses, as by the mea-
lure ot the Compasses upon the upper Cila(s s parts
ot an Inch, and by consequence betireen the Gilasles it
23
Va5  FOr the upper CilaIS ass ot an lnch thick,
and

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L
and my Fre ras distant Erom it 8 Tnches. And a third
proportional to halt this From the Diameter of the
Sphiere 15 soeso Parts oF an Inch. This is theretore the
chicknels oF the Air atthis Ring, and a titth part there-
ot, viz. the sosioth parc ot an Inch is the thieknels there
OE at the Erst oF the Ringo as above.
Perred the lame thins by lavins these Object-C7lasco
upon Hat pieces of a broken Lookins-glats, and tound
the same meatures oF the Rings: Whuch MakeS ME
rely uxon them till ther can be determined more ac-
curatelr by Cilasses ground to larger Spheres, though
in Cuch Cilases greater care muit De taken OE a FruC
Plaim.
Phele Dimentions wrere taken irhen my Pye WaS
placed almost perpendicularly orer the GlaPes, beins
about an luch, or an lnch and a quarter, distant Erom
the incident rays, and cight luches distant Erom the
Cla(s; (0 that che rays ivere inclined tothe Cilals in an
Ansle ot about 4 degrees. Whence by the Tollorvins
Oblerration rou will understand, that had the rays
been pervendicular to the CElases, the thickneis otthe
Air at these Rings ould hare been less in the PropOr-
tion ot the Radius to the secant oF 4 degrees, that is ot
10000. P et the thicknesses tound be theretore dimi-
nistred in this proportion, and ther vill oecome ssogo and
s Or (to usc the nearest round number) thC sguo th
part ot an Inch. Thisis the thickness oF the Air at the
darkelt part ot che Arst dark Rins made by perpendi-
cular rayS, and hals this chieknels multiplied by the
progreltion, 1,3,597, 9, TI, c. Sires thethicknesles of the
Air at the most luminous parts oE aIl the brishtelt
LII8S, VIZ. 1oS e eces  SC. Theis arithmeticat
MeaNS

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B
CII
MCanS 1e 17oc 17000 C. Deins is thieknesses at the
duxkest parts oF aIl the dark Ones.
OBS. VII.
The Rings vere least wrhen my Fye iras placed per-
pendiculariy over the CElases in the AXis oF the RinoS:
And irtien l vierred them obliquely ther became big
Ger, continually (velling as P remored my fre Further
trom ehe AXis. And partly by meaturine the Diameter
oE the Came Circle at sererat obliquities ot my Eye,
Partly by other means, 25 also by makcins use oF thc
to Prisins For very sreat obliguities. IFoundits Dia-
meter, and consequenelr the thickness oF the Air at its
Perimeter in alI those obliquities to be rerynearly in the
proportions expressed in this Pablc.
Angle of Tn- I Anele of Re- 1 Diameter of (Thickness of
cidence on the fraction into the Rine.
Air.
the Air.
de5. min.
00 00 00 00
TC
06 26 10 00, 10;
12 45 20 00 10-
18 49 30 00 103
24 30 40 00 113
29
50 00 127
33 58 60 00 14
35 47 65 00
3
38
39
15.
19 70 00 163
335
75 00
27 80 00
19
227
40 00 85 00 29
40 1Y 90 00
ibe Air.
1
TO1
10
L
32
20

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In the erro Rest Columnsarc expressed the obliquities
ot the incident and emergent rays to the plate ot the
Air, that is, their ansles of incidence and retraction. In
the third Column the Diameter ot any coloured Rine
at thole obliquities is expresed in parts, ot irtrich ten
conscitute that Diameter irhen the rurs arc perpendicu-
lar. And in the Tourth Column the thickness ot the AIr
at the circumterence ot that Rins is expressed in parts
OE wrhich al(o ten constiture that thicknels irhren the rayS
are perpendicular.
And From these meatures I Ecem to sather this Rule:
That thethickness oF the Air is proportional tothe sc-
Cant OF an ansle, wrhole Sine is a certain mean prOPOT-
tional betreen the Sines ot incidence and retraction.
And that mean proportional, (0 tar a5 by thele meatures
lcan decermine iE, IS the tirst ot an hundred and six
arichmetical inean proportionals betreen thole Sines
counted fiom the sine ot retraction irtren the retra
ction is made out of the Cla(s into the plate oF RIT, Or
From the Sine ot incidence wrten the retraction is
made out ot the plate ot Air into the Cila(5.
OBS. VIII.
The dark Spot in the middle of the Rinos inerealed
also by the obliquation of the Lye, althoush almost in-
Censibly. But it instead ofthe Object-Cilaces the Prisms
evere made use otq its increase as more manifest irhen
viemed (0 obliquely that no Colours appeared about it.
Itras least irhen the rays rere incident most obliquely
on the interjacent Air, and as the obliguier decrealed
it increaled more and more until the coloured RingS ap-
Dearec,

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Pedred, and chen decreased asain, but not (o much a5
it increased betore. And hence it is evident, that the
transparenes was not onty at the ablolute contaet of the
Gtales, but also irhere they had some licele incerral.
hare Lometimes obserred the Diameter oF that Spot to
Debetreen halE and trro Atth parts ot the Diameter ot
the exterior circumterence ot the red in the Arst cir-
cuit or rerolution ot C olours Wrhen viemed almost per-
Dendicularlr; irhereas irhen viered obliquely it hath
Wrhrolly vanished and become opatce and irhite like the
Other parES OF the GEla(S; wrtrence ic mar be collected
that the CElasses did then Icarcely, or not at all, touch
one another, and that their interval at theperimeter
OF that Spot hen riemed perpendicularir iras about a
tilch or sixth part oE their interral at the circumterence
oF the Caid sed.
OBS. IZ.
By looking throueh the trro contiguous Object.
Glasses, IFound that the interjacent Air extribited Ringo
OE ColOuIS, a5 Weil by transmitting Lightas by rehect-
ins it. The central Spot mas non irtute, and trom it
the order oF the Colours vere vellowitti red; black;
violet, blue, irhite, vello, red; violet, blue, sicen,
vellorr, rec, 190. But chele Colours ivere very faint
and dilure untels irtren the Light was trajected rery
obliquely chroush the Glases: lor by that means they
became preter virid. Onty the Arst yellorvistr red, like
the blue in the Courth Oblerration, was so litele and
Taine as Ccarcely to be discerned. Comparins the co-
loured Rings made by relexion, rrith chele made by
trant-

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14 7
transmission of the Lioht; I Found that wrhite ras op-
Polite to black, red to blue, vellor to riolet, and green
to a compound ot red and violet. That is, thole parts
OEthe Clals evere black Wrhen looked throuoh, irhich
vrtien looked uxon appeared irhite, and on the con-
trarr. And Co those erhich in one case extribited blue,
did in the other case exhibit red. And the like ot the
Other COIOuES. The manner von have represented in
the chird Figure, ertrere AB, C. D, are the Turtaces ot
the Glases Contionous at F and the black lines be-
tireen them are their distances in arithmetical progres-
Tion, and the Colours wrritten abore arc seen by re-
Aected Lisht, and thole belou by Light transmitted.
DB5. Z.
Wetting the ObjectGlasses a little at their edges,
the rater crept in llowir betrreen them, and theCir-
cles therebr became lels and the Colours more faint:
Insomuch that as the Water crept alone one hale ot
them ac wrhich ic tirst arrived rould appear broken of
Trom che other halt, and contracted into a lels room.
By meaturins them I Found the proportions ot their
Diameters to the Diameters oF the like Circles made by
Air to be about seven to eight, and consequenelr the in-
tervals ot the Cilasses at like Circles, caused by thole
trro mediums Water and Rir, are as about threc toFour.
Perhaps it may be a general Rule, That it any other
medium more or lels dense than ater be compressed
betreen che Cilases, their interrals at the Rings caused
thereby will Bc to their interrals caused by interjacent
AII,
18. 3.

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15
Air, asthe Sies alC trhich meature the retraction made
out oF that medium into AIT.
OBS. XI.
Vhen the Water as betreen the Cilases, iF L PTCS
led the upper GlaIs variously at its edses to make the
Rines more nimbly from one place to another, a little
ertite Spot vould immediatelr tollo the center ot
chem, irtrich upon ercepins in oE the ambient Water
into that place vould presenely vanit. LES appearanCe
Wras Tuch as interiacent Air vould have caused, and it
extribited the Tame COlours. But it ras nat AII, FOr
irhrere any bubbles oFAir vere in themater they mould
not ranistr. The reffexion must have rather been caused
by a subtiler medium, irhich could recede throush. thc
Gilasses at the crcepins in ot the rater.
OB5. XII.
These Obserrations rrere made in the open AIr. BUF
Further to examin the effects ot coloured Lighe Fallins
on theGrlasses, Idarkened the Room, and viered them
by rellexion of the Colours ot a Prism cast on a Sheet
oF irhite Paper, my Pye beins (0 placed that l could.
sec the coloured Paper br reflexion in the. GilaBeS, 25.
in a Lookins- sla(s. And by this means the Rings BC-
came distineter and risible to a far greater number than
in the open Air. Ihave Pometimes seen more than
civenty ot them, whereas in the open Air L could HOC
disceen abore etCHE OF NINC.
d ad

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OBS. ZTII.
Appointins au assistant to more the Prism t0 and
Fro about IES AXIS, that aI the Colours might succes-
Sivelr FaII On Chat Part OF the Paper Wtrich I CaW bY
rellexion trom that part ot the Gilalles, irhere the Cir-
cles appeared, (0 that all the Colours might be succel-
sivelr reffected trom the Circles to my Lye Whilst Iheld
it immorable, I. Found the Circles wrhich the red Lioht
made to be maniteslr bioger than those which vere
made by the blue and violet. And it was verr plea-
Tant to sec them gradually sirell or contract accordins
25 the Colour of the Lighe as changed. The inter-
val oF the Glasses at any of the Rings Wrhen they vere
nade by the utmost red Lioht, was to their interral at
the Pame Ring wrhen made bythe utmost violet, greater
than 25 3 +0 2, and lels than a5 13 +08, by the most ot my
Oblerrations it Wras 25 14 t09. And this proportion
Ccemed reey neariy the lame in all obliquities ot my
tire; untels wrhen tro Prilmsiere made usc ot instead
ot the Object-GitaRes. FOr Then AE a certain orCaL
obliguier ot my Fire, the Rings made by the several
Colours seemed equal, and at a greater obliquity. thole
made by the violet rould De grcater than the same
Rings made by the red. Theretraction oF the Prism
in ehis case cautins the most retrangible rays +0 FaII
more obliguely on that plate of the Aix than the least
retransible ones. Thus the Fxperiment (uccceded in
the coloured Light, rhich ras Cufsiciently Atrons and
copious to make the Rings sensible. And chence it
may be sathered, that il the most retransible and least
retran-

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retransible rays had been copious enough to male the
Rinss sensible rithout the mixture oE other rays, the
proportion which here Was 14 to 9 ould hare been a
licile greater, Cuppole 14; Or 14; 109.
OBS. XIV.
WhilE ehe Prisim was turn d about its Axis wict an
uniform motion, to make aII the leverat COlours FaII
luccessirels uxon the Object. Cilastes, and therebr t0
make the Rines contraet and dilate: The contraction
or dilation ot cach Ring thus made by the variation ot
Is Colour ras Criftest in thered, and Nomest in the
violet, and in the intermediate Colours it had inter-
mediate degrees ot celeritr. Comparins the quantity
ot contraction and dilation made by all the degrees ot
each Colour, I Found that it Wras greatest in the red;
less in the rellor, siIl less in the blue, and least in the
violet. And to make as just an estimation asl could ot the
proportions oftheir contractions or dilations, lobserved
that the Wtole contraction or dilation of the Dinmeter
OF any Rins made by aII the degrees oF red, Wras to that
oF the Diameter oF the lame Rine made by aII the de-
siees oFriolet, as about Four to three, or Aire to Four, and
chat wrhen the Lisht ras of the midele Colour betireen
vellorr and sreen, the Diameter ot the Rins Wras very
nearly an arithmetical mean betreen the greatest Dia-
meter ot the Came Ring made by the outmost red, and
the lealt Diameter thereot made by the outmost violet:
Contrary to irhrat happens in the Colours of the oblone
Spectrum made by the retraction ot a Prism, Where the
red ismost contracted, the violet most expanded, and

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1
18
in the midst oF all the Colours is che contine OF BrCCH
and blue. And hence I Peem to collect that the thick-
nesses oF the Air betreen the Glases there, Wrhere the
Ring is successively made by the limits of the sire prin-
cipal Colours (red, vellorr, sreen, blue, violet) in order
(that is, by the extreme red, by the limit ot red and
velloir in the midale ot the oranse, by the limit ot
vellorr and sreen, by the limit of sreen and blue, by
the limit of blue and violet in the midale oF the in-
dico, and by the extreme violet) are to one auother
very nearly as the six lensths ot a Chord irhich Cound
the notes in a Sixth Major, sol, la mi, fa sol, la. BUF
it aorees Lomethins becter rith the Oblerration to CaY,
that the chicknesses oF the Rir betmeen the CTlaRes there,
Wrtere the Rings are successirely imade by the limies oF
theseren Colours, red, oranse, rello, sreen, bluc, in-
diso, violet in order, are to one another as the CuDe-
r0ots oF the Squares oF the cioht lensths ot a Chord,
irhich Cound the notes in an eistth, sol, la fu- sol, la-
mi fa sol; that 15, a5 the C uDC-TOOtS OF the SquareS
2 2 3
0
aC The NumberS, Ly 9 63 a3 33 33 103 2
OB S. XV.
Thele Rings ere not oF varions Colours like thole
made in the open AIT, but appeared aIL over oF that
prismatique Colour only rith ertrich they evere illu
minated. And by projectins the prismatique Colours
immediately upon theClases, I Found that the LighE
ertrich fell on the dark Spaces ertrich ivere becreen
the coloured Rings, as transmitted chrough the
Glasles rithout any rariation ot COlOUT. FOr On a
Wvhite

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P
191
irhite Paper placed behind, it rould paint Rings ot
chelame Colour rith those irhrich iere reflected, and
oF the bigness ot their immediate Spaces. And From
chence the orisin oF these Rinss is manifest; namet),
Lhat the Air betreen the Glabes, accordins to its V2-
rious thickness, is dispoled in lome places to retlectu
and in others to trantmit the Lishe ot any onc CO-
lour (a5 you may sec represented in the Fourth Figure) Fis. 4.
and in the Came place to retect that oF one COlOUF
arhere it transmits that ot another.
O BS. XVI.
The Squares oF the Diameters oF thele Rines made
by ans prismatique Colour vere in arithmetical PrO-
srection a5 in the titth Obserration. And the Diameter
oF the Sixth Circle, wrhen made by the citrine yellon,
and viemed almost perpendicularir, Wras about  PaFIS
ot an Tnch, or a litele less, agrecable to the sixth Ob.
Terration.
The precedent Obserrations ivere made with a raret
thin medium, terminated by a denser, such a5 was Air
Or Water compressed betreen tiro Clases. In those
thac tollor are set donn the appearances ot a denser
medium thin d rithin a rarer, such a5 are plates ot
Muscory slass, Bubbles ot Nater, and some ottier Thin
substances terminated on all. sides With AII.

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DBS. AYCL.
IF a Bubble be Blonn writh Nater Arst made tenacious
by dissolrins a licele Soap in il, tis a common Obser-
rarion, that alter a wrhile it will appear tinged with a
sreat rarietr ot Colours. To detend thele Bubbles
From beins axitated by the external Rir (erhereby their
Colours are irregularty mored onc amons another, (0
thatno accurate Oblervation can De iade ot theII) 25
Toon a5lhad blonn any ot them I covered it with a
clear Class, and by that means its Colours emerged in
a verr regulai order, like so manr concentrick Rings
incompastins the cop oE the Bubblc. And as the
Bubble grer thinner by ehe continual subsidins oF the
Water, these Rings dilated llorrly and over- spread thc
ertrole Bubble, descendins in order tothebottom ol it,
ertrere they vanistred successivelr. In the mean Wrhile,
alter all the Colours irere emerged at the top, there
ore in the Center of the Rines a CmaIl round black
Spoc, like that in the Ars Oblerration Which conti-
nuall dilated it SelE tilL IE DCCaME LOICtIIES MOTC FHan
ox 2 ot an Inch in breadth betore the Bubble BTOke:
AFArK Ichoughechere had been no LishereRected From
the Water in that place, but oblerving it more cu-
riouslr, I Car ithin it sereral Cinaller round SpOtS,
ertrich appeared much blacker and darker than the rect,
Wrherebr lHne that there iras lome reflexion at the
other places irhich ivere not (0 dark as those Spots.
And by Further eryal Itouud chatl could sec the lmases
ot lome thines (as oF a Candle or thc Sun) very faint-
Ey refsected, noc ontu trom the sreat black Spot, but
aHC

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p
21
also trom the lictle darker Spots irtrich vere rittr
IN It.
Behdes the atoresaid coloured Rinos there would
otten appear linall Spors of Colours, alcendins and de
cendins ux and donn the sides ofthe Bubble, by realon
ot lome inequalities in the subsidins of the Water.
And Cometimes Imall Black Spots generated at the sides
rould alcend ux to the larser black Spot at the top ot
cheBubble, and unite with it.
OBS. XVIII.
Because the Colours oF these Bubbles Were mOrC Cx
tended and lively than chole ot the Air thin d betreen
tiro Glasses, and lo more casy to to dittinguistied, L
Chall here sire vou a Further description oC their order,
a5 ther evere obserred in riemins them by reslexion ot
the Skies when oF a erhite Colour, wrhils a black Sub-
Ctance ras placed behind the Bubble. And they were.
these, recu blue; red, blue; red, Blue; Led, Srcen;
red, vellor, oreen, blue, purple; red, vellon, sreen,
blue, violet; red vellor, irtute, blue, black.
Thethree Arst Successions of red and blue ivere very
dilute and dirty, especially the first, irhere the red
Ceemed in a manner to be wrhite. Amons these there
was scarce any other Colour sensible belides red and
blue, only che blues (and principally the sccond blue)
inclined a litle to green.
Che Tourth red iras also dilute and dirty, but not
(0 much. astheformer three; alter that succeeded little
or no vellorr, but a copious green, wtrich at tirst incli-
ned a direle toyello, and chen became à preuy brisque
and

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(22
and good wiltom oreen, and attermards changed to a
bluit Colour; but there succceded neither blue nOr
violet.
The stch red at first inclined rery much to purple,
and alterards became more brighe and brisque, but
Vet nOF rery pure. This ras succeeded ith a very
brighit and intense vellor, wrhich iras bue lictle in
quantity, and soon chansed to sreen: But that srcen
ras copious and Pomethins more pure, deep and lively,
than the tormer oreen. Atter that followed an excel-
lent blue ot a brighe stey-colour, and then a purple,
Wrhrich iras less in quantier than the blue, and much
inclined to red.
ThC AXtH Red WaS at APK OF a very Fair and lively
Scarlet and Coon atter ot a brionter Colour, Deins
verr pure and brisque, and the best ot aii the
reds. Then alter a lively oranse Folloed an intense
bright and copious vellor, irtrich ras alo the best
oF all the yelloirs, and this chansed Arst to a sreenisi
vellour, and then to a greenittr blue; but tho grCen
betireen the vellor and the blue, us very licele and
dilute, scemins rather a sreenitm erhite than a green.
The bluc irtich succeeded became verr sood, and ot a
very tair bright stey- colour, but vet Pomethins inferior
to the former blue; and the violet ras intense and
deep rith little or no rednels in it. And less in quan-
tier than the blue.
In the last red appeared a tincture oF scartet next
to violet, irhich Coon chansed to a briohter C OlOur,
inclinins to an oranse; and the rellon irtrich tollored
ras at trst preter good and livelr, but altervards it
orem more dilute, until by degrées it ended in perfect
orhite.

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23
Wrhiteness. And this whitenels, it the Water ras very
tenacious and well. tempered, vould Aonly spread and
dilate it selF orer the oreater part ot the Bubble; con-
einually gromine paler at the cop, irhere at lensth it
rould crack in manr places, and those cracks, as ther
dilated, rould appear ot a prettr eood, but y et obseure
and dark sky-colour; the itite betreen the blue Spots
diministrins, until it resembled the threds ot an irre
sular Net-Work, and soon alter vanistred and lett aI
the upper parE OF the BubblC oF the Paid darte blue
ColOur. And this ColOur, atter the atorelaid manner,
dilated it selE dornivards, until sometimes it hath
Oversoread the Wrhole Bubble. In the mean wrhile at
the cop, Wrhich was ot a darkeer blue than the bottom,
and appeared alto tuil ot manz round blue Spots, lome-
ching darker than the rest, there ould emerse one
Or more very black Spots, and richin chole other SpOtS
OF an incenser blackness, wrhich I mentioned in the
Former Obserration; and these continually dilated
themlelres until the Bubble Broke.
TF EHC WVater WaS NOE verr cenacious the Black SpOtS
rouid break Forth in the irhite, without auy sentible
intervention ot the blue. And Lometimes ther mouild
break Forth rithin the precedent vellou, or red, Or
perhraps rithin the blue ot the second order, betore
the intermediate Colours had time to displar them-
Telves.
By this description vou may perceire hou great an
affinier these Colours hare rith those ot Air descri-
bed in the Fourth Obserration, although set donn in
a contrary order, by reason that ther begin to appear
artien the Butoble is thickest, and are most conre
niently

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24
niently reckoned trom the lorrest and thiekest part ot
the Bubble uprraids.
OB5. ZIZ.
Viewins in sereral oblique positions ot my five
the Rings ot Colours emergins; on thetopot the Bubble,
lFound that ther ivere sensibly dilated by increasins
che obliquier, but vet not (o much by tar a5 thole
made By thind Air in the seventh Observation. For
there they vere dilated (o much as, wrhen vieved
nost obliquelr, to arrire at a part of the plate more
than trelre times thicker than that irhrere they ap-
peared irtien riemed perpendiculariy; irhereas in this
case the thicknels oF the Water, at irhich chey arrived
irhien riered most obliquelr, Wras to that chicknels
arhich exhibited them by perpendicular raYs, Come-
chins leIs thanas 8 +0 5. By the best oEmy Oblervations
it Wras betreen 15 and 15: to 10, au increale about
24 times less than in the other case.
Sometimes the Bubble rouid become et an unitorm
thicknels all over, except at the top ot it neur the black
Spot, a5 I tner, because it rould exhribit the lame
appearance oF Colours in iIl Politions oEthe FyC. And
then the Colours irtrich ivere seen at iES appareNE CIE-
cumterence by the obliquest rars, vould De different
From thole that wrere seen in other places, by rays lels
oblique to it. And dirers Spectators might sec the
Tame part oF it oF difterins Colours, by vierins it at
very differine obliquities. Nou obserring hou much
the Colours at the lame places of the Bubble, or at di-
vers places ot equal thichnels, vere raried by the
severat

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B)
sereral obliquities ot the rays; by the asistance oF the
Ath, 24th, Ibth and 18th Obserrations, a5 they aic
hereaster explained, I collect the thickness of the Water
requisite to extibit any one and the lame Colour, at le-
veral obliquities, to De very nearly in Fhe PrOPOrtION
expresed in this Table.
Incidence on) Refraction in- (Thictness of
the Water. 10theWrater. The W ater.
des. min. des. min.
00 00 00 00
15 00
II
30 00 23
45 O0
22
60 00 40
75 00 46
90 001 48
2
C
10
In the trro Arst Columns are expressed the obliqui-
ties ot the rays to the luperticies oF the Water, that
15, their Ansles ot incidence and retraction. Where
lsuppole thac the Sines irhich mealure them are in
round numbers 25 3 t0 4, thoushi probably the disso.
lution oF Soap in ehe Water, may a lictle alter its
refractire Vertue. In the third Column the thicknels
oF the Bubble, at Wrhrich any one Colour is exhibited
in those sereral obliquities, is exprest in parts, of irhieta
ten conltiture that thickenels irhren che raYS are perpen-
diculat.
Thare Pometimes observed, thac the Colours wtrict
arise on polisted Sceel by heatins it, or on Bell. metal,
and some other metalline substances, when melted and
 C
pourect

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26
poured on the sround, where they may cool in the
open Air, hare, like the Colours oF Water-bubbICS,
been a litele charged by viewins them at divers ob-
liguities, and particularly that a deep blue, or violet,
irtren riered very obliquelr, hath been changed to a
decp red. But the chanses ot these C OIOUES are nOt (O
sreat and sensible as of thole made by Water. For the
Scoria or vitrihed part ot the Metal, Wrhich mort Me-
tals wrhien heated or melted do continuallu protiude,
and send ont to their Curtace, and irtrich by coverine
the Metals in torm ot a thin slastr skin, caules thele
Colours, is much denter than Water; and I And that
the chanse made by the obliquation of the Fycis lcast
in Colours ot the densest thin substances.
OBS. XX.
A5 in the ninth Obserration, Pohere, the Bubble, Dy
cransmitted Light, appeared ot a contrarr C olour to
that irhich it exhibited by rellexion. Thus Wrhen the
Bubble being looked on by the L ight ot the Clouds re-
Aected From it. seemed red at its apparent circumte-
rence, it the Clouds at the lame time, or immediatel
alter, vere viered through it, the Colour at its cir-
cumference mould De blue. And, on the contrary.
ertren by resected Lioht it appeared blue, it vouid ap-
Dear red by transmitred Lignt.
OBS. Z XI.
By wetting very thin plates oF Muscory-sta(S, Whote
Thinnels made ehe like COlOurs appear, the COlOUTS
DecaMC

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became more faint and languid; especially by wettins
ehre plates on that hide oppolite tothe Lve: But Lcoutd.
not perceire any variation ot their species. So then
the thickness ot a plate requisite to produce any C0
Tour, depends outr on the densier ot the plate, and
not on that of the ambient medium: And hence, by the
Toch and rbth Obserrations, mar be known thethick-
nels irhich BubbleS OFWater, or Plates oF Muscory.
BalS, Or Other substances, have at any C Olour Pio.
duced by them.
OBS. XXII.
A thin transparent Body, irhich is denser than its
ambient medium, exhribits more brisque and virid C0-
Tours than chat irtrich is so much rarer; 25 l have
particularly observed in the Aic and Gila(S. For blon-
ins Class very thin at a Lamp. Furnace, thole plates
incompassed rith Air did exhibit Colours much
more ririd than thole ot Air made thin betreen tro
Crlases.
OB5. ZXIII.
Comparins the quantier ot Light reflected From the
several Rings, I Found chac it ras most copious trom
the Arst or inmost, and in the exterior Rings De-
came sradually less and lels. AIIO the irhitenels ot
thC Arst Rins as Sronger than chat reftected from
thole pares oF the thinner medium irhich ivere with
out the RinES; as I could manifestly perceire by rien-
ins ac a dittance che Rings made by the tro bject
ti. C 2
ClaACS,

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28)
Glases; or by comparinq tuo Bubbles oF Water blonn
et distant times, in the Arst oF wrhrich che whitenels
appeared, wtich succeeded aHI the Colours, and in
ehe other, the rrhiteness irhich preceded them alL
OBS. ZZIV.
Wrtien the erro Object-Glasses rere lay d upon one
another, (0 a5 to make the Rinos OF the COIOUES aP-
Dear, though rith iny nakced Lyc I could not discern
abore 8 Or 9 ot thole Rings, vet by riemins them
throuoh a Prism I have seen a tar greater multitude,
infomuch that L could number more than forer Besides
many others, that ere (0 very (mall and clole toge-
ther, that I could not kecp my Lye Ceddy on them
Tererally (0 a5 to number them, but by their extent Thare
Fometimes eltimated tnem to De more than a hundied.
And Ibeliere the Lxperiment mar be improved tothe
discovery ot tar greater numbers. For they seem to
De really unlimited, thoush rilible onty (0 tar a5 they
can be separated by the refraction, as l Mall herealter
explaim.
But it ras but one sde et these Rinos, nametv, that
torards wrhich the retraction ras made, wrhich by that
retraction ras rendered distinet, and the other (ide be-
came more contuled than whren vierred by the naked
Fre, insomuch that there I could noc discern abore
one or tiro, and lometimes none ot thole Rings, ot
prtrich I could discern eight or nine rith my naked
Ere. And their Segments or AICS, Wrhich on the
other side appeared (o numerOUS, For the mott Part
excecded

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l29.
excceded not the third part ot a Circle. IF the RC
traction ras very great, or the Prilm very. distant trom
theObject-Classes, the midale part ot thole Ares BC-
came allo contused, (0 as to dilappear and constitute an
even Whitenels, Whils on cither side their ends, a5 al(o
the wrhole Ares Furthest From the center, became di-
cineter than before, appecrins in thetorm as. rou sce
ehem designed in the Atch Figure.
The ATCS, Wrhere ther secmed distinctest, vere only
erhite and black successivelr, without any other CO-
lours intermixed. But in other places there appeared
COlours, Whose order mas inverted by the retraction
in suchr manner, that it I Ars held the Prilm very near
the Object Cilasses, and then gradtuallr remored it
Turther otf torrards my Liye, the Colours of the 2d,
3d, Ath, and follorring Rings Chrunk torrards the irhite
that emeroed berreen them, until ther wholly va-
nimed into it at the midale ot the AICS, and after-
ards emersed again in a contrarr order. But at
the ends ot the Ares ther retained their order un-
changed.
I have Pometimes (0 lar d one Objcet. CTa(s upon
the other, that to the naked fire ther have all over
Feemed unitormly wrhite, without the least appearance
oF ans oF the coloured Rings; and vet by vierine
them through a Prisim, sreat multitudes ofthose Rings
hare dilcorered themselres. And in likce manner plates
oF Mulcorr-clas, and Bubbles ot Cilass blovn at a
Lamp. Furnace, irhich ivere not (othin as to exhibit
any Colours tothe naked Fiye, have throuoh the Prism
extribited a great variety ot them ranged irregui
laris ux and donn in the form oE iraves. And 10
Bubbles
18. 5

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(307
Bubbles OF Water, betore ther began eo extibie their
Colours to the naked Fye ot a By-Btander, have ap.
peared throush a Prism, sirded about rith mans pa
Fallel and horizontal Rings; to produce erhich effect,
ic ras necelsarr eo hold ehe Prilm parallel, or very
nearly parallel eo the Hloriron, and to dispose it (a
chat the rays mishr be retracted upiraeds.
L dit

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TTF
L L
P A R Y II.
Remartes upon the foresoins Observations.
Arins siren my Obserrations ot thele COlOurs,
a  vetore l make use ot them to untold theCaules
et the Colours ot natural Bodies, it is convenient that
by the simplest ot them, Cuch a5 arc the 2d, 3d, 4Fh,
oth, 12th, IBth, 20h, and 24Ch, I ArAt explain the
more expounded. And Ars to Peur hor the Colours
in the Fourth and eighteenth Oblerrations are produ.
ced, let there De taken in auy rishit line trom the point
L, the lensths YA, YB, LC, YD, TE, LF, YG, Fic. 5.
YH, in provortion to one another, a5 the CiuDe. rOOts
0 2 3 2 5 8
oF the Squares oF the numDeTS, 3 16,5, 3  c, 3 l, Wrhere.
by thelensths ota musical Chord to lound iIl the Notes
in an Fishth are represented; that is, in thC PFOPOT.
tion oE the numbers 6300, 6814, 7114, 7631, 8255,
8855, 9243, 10000. And at the points A, B, Cy D,
Eu F7

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2
Eu F, G, HI, let perpendiculars Aa, BB, 1c. De crected,
by wrhole intervals the extent ot the several Colours
Pet underneath against them, is to be represented. Phen
diride the line aa in such proportion as the numbers
1g 27 3,5, 6, 7, 9, 10, TT, Dc. Tet at the points ot divi-
sion denote. And through thole diritions From L
dear lines rI, 2I, 3Lg 5M, 6H, 7O, Oc.
Bo iF A2 bC luppoled to reprelent the thickness
oF ans thin transparent Body, at irhrich the outmost
violet is most copiousr reflected in the Airst Rins, oi
Series oF Colours, then by the 13th Observation LlR,
will represent ies thicknels, ac irtrich the utmost red
is most copiousy refected in the lame Series. AIIO
by the sthi and ibth Obserrations, A6 and HIN iii
denote the chicknecles at wrhich those extreme COlOuIS
are most copiousy rehected in the second Scries, and
A 2O and ITO the thichneses, at wrtich ther arc
most copioussy resected in the third Series, and lo on.
And the thicknels at wrhich aur ot the intermediate
Colours are reflected most copiousr, will, according to
the 1gth Obserration, De detined by the distance oF the
linc AHI From the intermediate parts oF the lines 2K,
6TT, 100, 1c. against irhich the names ot thole C0.
IOUES are Written belou.
But Further, to detine the latitude ofthese Colours in
each Rins Or Series, let A 1 design the leas chicknels,
and A 3 the greatest thicknels, at erhich the extreme
violet in the tirst Scries is resected, and Iet FTI. and
HIL delion the like limits For the extreme red, and
lec the intermediate Colours be limited by the inter-
medliate pares oF the lines II, and 3C against irtrich
the names of those COlours are rritten, and (0 on: BuI
vet

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L33
et rith this caution, that the reflections be suppoled
Hronsest at the intermediate Spaces, 2H, 6H, 10, dc.
nd trom thence ro decrease graduallr torards thele li-
mits, IL, 3L, 5M, 7O, Bc. on cither side; Wrhere
vou must not conceire them to be precisels limited,
but to decar indetinitelr. And Whereas lhare assigned
the same latitude to every Series, I did it, because 2)-
thouoh the Colours in the Arst Series lcem to be a little
broader than the rest, by reason ot a Aronser rellexion
chere, vet that incqualier is (o insentible a5 scarcely t0
Dc determined by Oblervation.
Noi accordins to this description, conceirine that
cherars originally oF several Colours are by turus re-
Aected at the Spaces TIL 3, GM O7, gPR FF, 1C.
andtransmitted at the Spaces AHII, 3L. M 5, 7OP9,
Oc. it is ea (y to know wrhrat Colour must in the open Air
De exhibited at any thickness oF a transparent thin body.
For it a Ruler DC applied parallel to AHI, at that di-
Rance From it by which thic thicknels of the body is
represented, the alternate SpaCeS F IL. Z, G MIO7, VC.
irhich it croseth ill denote the reflected orisinal CO-
lours, oF Wrhich the Colour exhibited in the open Air
is componnded. Thus it the constitution of the green
in the third Series oF Colours be delired, apply the
Ruter as rou sceat n ere, and by its passine through
Tome ot the blue at x and rellor ato, a5 well as through
the green at e, vou may conclude that the ereen extri-
bited at that thicknels oF the body is principally con-
cituced oC original srCen, BUE HOE WithOUE a MiXTIe
oE some bluc and yellor.
e

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By this means vou max Knor hou LHC COIOUrS FrOMI
the center oF the. Rings outrard oughe to succecd in
order as they ivere described in the Ath and L8th OB-
servations. For il rou inore the Ruler gradually From
AHI. Throuet all distances, having past over the Arst
space irtrich denotes little or no retlexion to be made
Dy thinnest substances, it rill Arst arrire at r the violet,
and then very quickly at the blue and srcen, rhict
together rith that riolet compound blue, and chen at
the velloir and red, by irtose turther addition that
blue is converted into wrhitenels, wrhich erhitenels con-
tinues during the transit of the edge ot the Ruler From
 +0 2. and after that br the successrre deheience ot
its Component Colours, turns tirst to compound rellon,
and then to red, and last oF aII the red ceasetM at Lo
Phen besin thie Colours ot the second Series, Wrhict
Tucceed in order durins the transit ot the edee of the
Ruler From 5 t00, and are more lively than betore,
because more expanded and severed. ANd FOr the
Pame reason, instead ot the Former wrhite chere inter-
cedes betireen the blue and vellorr a mixture of orange,
vellorr, oreen, blue and indico, all irhich together ought
to extribit a dilute and imperfect sreen. 50 theC0-
tours o thethird Series aI lucceed in order; Arst, the
violet, wrhich a litele interteres with the red ot the se
cond order, and is therebr inclined to a reddim purple;
chen the blue and ercen, irhich are lels mixed rrith
otter Colours, ard consequently inore livelr than be-
tore, especially the green: Phen Follorrs the vellon,
Tome of Wrhich tomards the oreen is distinct and good, but
that part of it torards the succcedins red, a5 allo that
red is mixed rith the violet and blue ot the tourth Se-
TICS

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ries, Wrhereby rarious degrées of red very mueh incli-
nins to purple are compounded. This riolet and blue,
Which Mould succced this red, beins mixed with, and
hidden in it, there lucceeds a sreen. And this at first
is much inclined to blue. but soon becomes à 500
sieen, the only unmixed and livels Colour in this
Tourth Series. For as it verges tomards the rellon, it
Desinsto intertere rith the Colours ot the Alth Series,
by vhose mixture the succcedins vellou and red are
vers much diluted and made dirtr, especialy the vel-
Tor, irhich beins thereaker Colour is scarce able to
ther it selE. ACter this the several Series intertere more
and more, and their Colours become more and more
intermixed, till alter three or tour more rerolutions
in erhich the red and blue predominate by turrs)
alI Corts ot Colours are in all places prerty equally ben-
ded, and compound an eren rsutenels.
And since by the rsth Obserration the rays indied
rith onc Colour are transmitted, irhere thole of ano-
ther Colour arc reflected, the reason of the Colours
made by thetransmicted Lishc in che ochand zoch OB.
lerrations is trom hence erident.
IE not only the order and species ot thele ColOuIs;
but alsothe precise thicknels ot the plate, or thin body
at irhich they are exhibited, be detired in parts of an
luch, that may be also obtained by alsistance of the bch
or 1bth Oblerrations. For accordins to thole Oblerva-
tions the thickness of the thinned Air, wtich betwween
trro Clasles exhibited the most luminous parts ot the
trs (IX RInGS WVETC iocun 17oeB iybéce ipo 1 i PaFIS OF
an luch. Suppole the Lient resected molt copioully
ac chese chichresses be chebrishr citrine yellour, or con-
tinc

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(367
tine ot vellon and orange, and these thicknesses will
DCGu Gv CE, C0, 67. And this beins KnoWn, it i5
easy to determine irtrat thickness of Air is represented
by C_ Or by any otter distance of the ruler trom
A II.
But Further, since by the roth Obserration the thick
ness oF Air iras to the thicknels oF Water, which DC
treen the Came CElasses exhribited the lame COlOur, 25
4t03, and by the 2ith Obserration the Colours ot
thin bodies are not varied by varrins the ambient me-
dium; the thickness ot a Bubble ot Water, extribiting
any Colour, will be3 oF the thicknels oF Air producins
thc Came Colour. And so according to the Tame Foch
and 2rth Obserrations the thickness oF a plate or
Olals, Wrhose refraction ot the mean retrangible ray, is
meatured by the proportion of the Sines 31 to 20,
may BC ~ oF the chickness oF Air producing the Came
ColOurS; and the like oF other mediums. I do not
attirm, that this proportion oF 20 +0 ZF, holds in aII
the cayS; For the Sines ot other Ports et rays hare other
Droportions. But the differences oF thole propOrtions
are (0. litele that I do not here consider them. On
chese Crounds I hare composed the tollowing Pable,
irherein the thickness oF AIT, Water, and GEla(S, aE
erhich each Colour is most intense and specitick, is ex
pressed in parts ot an Inch dirided into Ten hundred
chousand equat parts.
L BC

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D.
The tbs  coloured Plates and Particles os
OFelie toureh oder
OFEhC FttM Order;
Very Black
Black
Beginning ot
Blacl
BIuC
Wrhite
Tellon
Oranse
LRed
sViolee
Indico.
BIuC
OFCeM
OransC
Bright Red
eSCartet
Purple
Indico
Blue
eCreen
Tellon
Red
Bluistr R ed
Bluist Crcen
circen
Velloris Creet
CRed
S Crcenist BIue
Red
OEthe sixth Order, SCircenist Bluc
dRed
OEthe serenthorder, SCrcenisti Blue
134
35
30
03
.46
52
1582
6
Ruddy White (77
203
2)
O
342
398
48
572
cit
224
3
e
293
CtOW
Air. Water. CilasS.
2
a2c
2Ed
E
et
2
C2
123
12
26
23
253
DC
103
1.
203
2F
132
14a
52
2G2
Their Colours oF chc
Arst Order,
OF the Second Order, L Yellow
eF tho chird Order,
e4
12
0

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Non it this Pable be compared ith the bth Scheme,
vou rill there sec the constitution oF cach Coloui, a5
to its Ingredients, or the original Colours of which it
is compounded, ind chence be enabled to judge of its
intenteness or imperfection; irhich may suftice in ex-
plication ot the ath and rBth Obserrations, unless it
De Further dehred to delineate the manner hou the CO.
Jours appear, when the trro Object-Citasles are layd
uxon one another. Y0 do Which, let there be de
icribed a laroe AEC OF a Circle, and a Areighe Linc
ertrich inar touch that ArC, and parallet to that Tan-
sent severat occult Lines, at such distances From it, 25
the numbers set againstthe several Colours in the Table
denote. For the ArC, and its Tangent, will reprelent
the superticies ofthe Gilasses terminatins the interjacent
Air; aud the places irhere the occult Lines cut the
AEC Wvill BOW at what distances From the Center, Or
Point et contact, cach Colour is resected.
Phere arc allo other ules of this Pable: For by itS
altistance the thickness of the Bubble in the Tgth Ob.
serration as determined by the Colours irhich it ex-
Thribited. And (O the bignelS OF thC PATES OF natUTAL
Bodies may be conjectured by their Colours, as MaII DC
hereatter ern. AIIo, if tiro or more very thin plates
De lavd onc upon another, lo asto compole one plate
equallins them all in thicknels, the relultins Colour
may be herebr determined. For instance, MI. Hooke in
his Miscroeraphia obserres, that a Faint yellon plate ot
Muscory- sla(s lav dupon a blue one, constituted a very
deep purple. Therelloi ofthe ArH Order is a faint
one, and the thiekness of the plate exhribitins ic, ac
cordins to the Table is 43, to which add 9, the thick-
nels

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D
nels extribitins blue oF the second Order, and the sum
Will be 132, irhich is the thickness extibitins the
purple of the third Order.
To explain, in the next place, the Circumstances ot
the 2d and zd Obserrations; that is, ho theRings ot
the ColOurs may (by turming the Prisins about cheir
COmOn AXis the contrae mar to that expresed in
those Obterrations) De conrerted into wrhite and black
Rines, and aftermards into Rings oF Colours again, the
Colours oF each Ring lying non in an inverted order; it
must be remembred, that those Rinos oF Colours are di-
lated by the obliguation ot the cars to the Air whict
intercedes the Gilases, and that accordins to the Table
inthe ith Obserration, their dilatation or increase ot
their Diameter is most manifest and specdr wten they
are obliquest. No the rars oF velloir DeInG MOTE rC
Fracted by the first superticies oF the said Air than thole
oFred, are therebr made more oblique to the second su-
perticies, at irhrichi they are reflected to produce the co-
loured Rings, and consequenelr ehe relloir Circle in cach
Rinsrill Be more dilated than the red; and the excess oF
its dilatation will be somuch the greater, by hou much
thegreater is the obliguier of the rars, until at last it De-
comeotequal extent mith the red ot the same Ring. And
For the lame reason the oreen, blue and violet, will be also
(o much dilated by the Aill greater obliquier ot their
rayS, 45 to become aII verr nearly oF equal extent rittr
the red that is, equallr distant From ehe center of the
RingS. And then dIl the Colours of the lame Rino
must De coincident, and br their mixture extribit à
irtice Ring. And these wrhite Rings must hare black
arid dark Rines vetireeh etiem, because they do not
Epreact

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F
40
spread and intertere rith one another as betore. And
For that realon alfother muct become diltincter and vi-
sible to tar greater Numbers. But vet the riolet DeiMB
obliquest wrill be Comethins more dilated in provortion
to its extent thenthe other Colours, and lo very apt to
appear at the exterior verses ot cheirtute.
Alterwards, by a greater obliquity ot the rars, the
violet and blue become more sensibly dilated than the
red and rellorr, and (o beins turther remored from the
center oF the Rings, the Colours imust emerse out ot the
wrhrite in an order contrari to that irhrich cher had be-
Fore, the riolet and blue at the exterior limbs ot cach
Rins, and thered and yellor at the interior. Andtherio-
let, by realon of the sreatest obliquits ot its rays, beins
in proportion most ot all expanded, ill soonest appear
at the exterior limb of cach irtrite Ring, and become
more conspicuous than the rest. And the sereral Series
oE Colours belonsins to the sereral Rings, willu by
their untoldins and spreadins, besin asain to intertere,
and thereby render the Rings lels dictinet, and not visi-
ble to lo great numDerS.
IE instend oF the Prisins the Object-glases be made
ule ot, the Rings irhich they extribit become not wrhite
and distinet by the obliquits oF the Fse, by reason that
che rays in their pallase throush chat Air irhrich inter-
cedes the Crlases are very nearly parallel to thole Lines
in Which ther rere tirkincident on theCilabes, and con-
sequently the rars indued ith leveral COloursare not
nelined one more chan another to chat AIr, 25 it hap.
pens in the Prilms.
Lhereisyet another circumstance otthese Lxperiments
to be considered, and chac is irhiy the black aud erhite
Rin85

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L
Rinos irhich wrhen viered at a distance appear distinet,
hould noc only become contuled by riemins them near
ac hrand, but also vield a violet Colour at boch che
edges ot erery irhite Rins. And the realon is, thae che
cays irhich enter the Lye at sereral parts of thePupil,
trare several obliguities to the CilaBes, and thole wrhrich
are most oblique, it considered apart, rould represent
ehe Rinss bisger than thole irhichare the least oblique.
Nhence chebreadth. of the perimeter ot erery wrhite
Rins is expanded outrards by the obliquest FaYS,
and inmards by the least oblique. And this expantion
15 (0 much the greater by ho much the greater is thc
difference of the obliquier; that is, by hon much the
Puxil is rider, or the Fre nearer tothe Cilases. And
the breadth ot che violet must be molt expanded, De-
cause the rars apt to exeite à senlation ot that Coloui
are most oblique to a second, or turther superticies ot
che chin d Air at erhich ther are reftected, and have
also che greatest variation ot obliquier, erhich makes
thac Colour Coonest emerse out oF the edges ot the
irhite. And a5 thebreadth ot every Rins is thus aus-
mented, the dark interrals must be diministred, until
the. neistibourins Rinss become continuous, and arc
blendedu the exterior tirst, and then thole nearer the
Center, (0 that ther can no longer be dictinsuistid
apare, buc seem to constitute an even and unitorm
Wrhicenels.
Amons all the Obserrations there is none accompa-
nied rith (0 odd circumstances a5 the 24th. OFthole
the principal are, that in thin plates, irhich to the
nated Eye seem ot an even and unitorm transparent
Wrhite-

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C42)
erhiteness, rithout any terminations oF Madons, the
retraction oF a Priim Mould make Rings oF ColourS ap-
pear, Wrhereas it ulually makes Objects appear coloured
omly there irhiere they are terminated ith Madors, Or
hare parts unequally luminous; and that it Mould inake
those Rines excccdingly distinet and irtite, althoustr
it ulually renders Objects contuled and coloured. Thc
cause ot these things rou ill understand by considerins,
that aI the Rinos ot Colours are really in the plate,
irhien riemed rich the natced kiye, althoushi by realon
ot the great breadth ot their circumterences they 10
much incertere and are blended together, that ther leem
to constitute an even wrhiteness. But wrten the rays
Pals through the Prism to the Rye, the orbits of the
several Colours in crery Ring are retracted, Pome more
than others, accordins to their degrees of retrangibility:
By erhich means the Colours on one sde oF the Ring
(that is on onc side of its Center) become more untolded
and dilated, and those on the ottier hde more compli-
cated and contracted. And irhere by a due refraction
therare (o much contracted, that the serral Rings Be-
come narrorer than to intertere rith one another, they
must appear distinct, and also wrhite, il the constituent
Coloursbe so much contracted asto be Wwholly coincident.
But, on the other side, irhere the orbit ot every Rine
is made broader by the Further untoldinq oF its CO
lours, it must intertere more with ottier Rings than
betore, and (o become less dictinct.
T0 explain this a litele Further, suppose the concen-
triek Cireles AV, and BZ, reprelent thie red and riolet
oE ans order, irhich, cogecher irith the intermediate
COIOUTS,
Eis. 7.

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l43)
Colours, constitute any one of these Rings. Noir these
beins viemed throush a Prism, the riolet Circle BR,
Wwill by a greater retraction be turther transtated trom
ies place than the red AV, and (0 approach nearer t0
it on that side, torrards wrhich the retractions are made.
lior instance, il the red be eranstated to av, the violet
mas betranllated to bx, (0 asto approuch nearer to it
al x than betore, and it the red be Further transtated
to ar, the riolet may be (0 much Curther tranllated to
bX a5 to convene rith it at X, and if the red be vet
Further translated to ar, the violet mar be Aill (o much
Further tranlated to BE 25 to pals berond it at E, and
Convene mith it at e and f. And chis beins undertood
noc only of the red and violet, but oF all che other in-
termediate Colours, and allo ot every rerolution of
thole Colours, vou will casilr perceire hor thole of the
lame rerolution or order, by their nearnels at xv and
En and their coincidence aF XV, e and f, ousht to con-
Ritute preuy distinet Ares oF Circles, especials at XV,
Or ac e and f, and chat ther rill appear severally at
X 2, and at X r exhibit wrhiteness by their coincidence,
and again appear several at 25, but yet in a contrary
order to that irhich cher had betore, and Aill retain
beronde and f. But, on the ocher side, at ab, a b,
Or a B, these Colours must become much more contu-
sed by beins dilated and spread (0, a5 co intertere mith
thole oF other Orders. And the lame contusion will
hrappen at rE betreene andf, il the retraction be very
Sreat, or the Prim very dictant Fromthe Object. Crlalles:
In irhich ease no Parts oF the Rines ill be scen, Pave
onlys ero licele Aresiat e and f, whole distance trom onei
78 2
another,

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another will De augmented by remorins the Prisin
Ail Further From the Object. Cilasses: And these litele
Ares must be distinctest and irhitest at their middle, and
at their ends, wrtiere ther begin to grom contuled they
must De coloured. And the Colours at one end ot
erery Arc must be in a contrary order tothose at the
other end, by reason that ther crols in the interme.
diate rrhite; namely their ends, irhich verge torrards
XE, WWill De red and vellOu on TMat SIde ACXE FHCC en-
ter, and blue and riolet on the ottier side. But their
other ends wrhich verse Prom YE will on the contrary
De blue and riolet on that side torrards the C enter, and
on the ottier Eide red and vellorr.
Nor as all these things Follon From the Properties
OF Light by a mathematical ay ot reasonins, (0 the
truth ot them may be manifested by Fxperiments. For
in a darke room; by vierine these Rings throush a
Prism, by rellexion of the sereral prilmatique C Olours,
ertrich an assistant causes to more to and Fro upon à
Waii or Paper From Wrhence they are reftected, ivhils
the Spectators Fve the Prilin and the Object-GElactes
(a5 in the r3th Oblerration) are placed Reddr: the
position ot the Cireles made successirely by the severat
Colours, vill be found such, in respeet et one another,
25 I hare described in the Figures ab∞V OE aDZ V
Ox a BEY. And Dy the same nethod the Fruth ot
the Fixplications oF other Oplerrations may De exa-
mined.
By wtiat hath been Paid che like Phrenomina oF
Nater, and thin plates of Cilass may be understood.
But in (mall Fragments olttiole plates, there is this
Further

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C.45
surther obserrable, that where they lye Aat uxon a
Pableandare turned about their Centers Whilstthey are
viewed through a Prism, ther will in fome poltures
extribit rares oF rarious Colours, and Pome ot them ex-
hibitthele ares in onc or trro positions only, but the
inost oF them do in all positions extribit ehem, and inake
ehem For the molt part appear almost all over the plates.
Phe reason is, thât the Tuperticies oF luch plates are nOL
even, but have many carities and Cvellings, erhich hon
hallon soerer do a little rary the thickness of the
Plate. For at the sereral sides of thole carities, For
the reasons nemly described, there oughe to be produ-
ced irares in sereral poltures ofthe Prilm. Now thoustr
it De Dut Fome verr Tinall, and HAETOIeE PaTtS OF thC
Cla(S, by erhich chese mares For the most pALL arC CaU-
led, vet ther may seem to extend themsetres over the
Wrhole Citals, Decause From the narrowest ot thole parts
there are COlOurS OF severat Orders that is oF several
Rings, contusedly reslected, which by retraction of the
Prilm are untolded, separated, and accordins to their
degrees ot retraction, dispersed to sereral places, (0 25 10
constitute (o mans sereral erares, a5 there vere divers
orders ot. Colours promiscuousty reflected From that
Part oF the GElaIS.
These are the principal Phaenomena ot thin Plates
or Bubbles, irhole explications depend on the pro-
perties oF Light, Wrhich Phare heretotore delivered.
And these rou sec do necessarilr Follon tromthem, and
aoree with them, eren totheir very least circumstances;
and not only (0, but do very much tend to their proot.
EhuS, by che 24th Obserration, it appears, that tIC
FayS

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L
rars oF sereral Colours made a5 well by thin Plates or
Bubbles, 25 by. retractions ofa Prilm, have sereral de-
rces ot retransibilier, rherebr those ot cach order,
irhrich at their reflexion trom the Plate or Bubble arc
intermixed rith thole ot other orders, are separated
From them by retraction, and allociated together 1o a5 to
become visible by themselres like ArCS Ot CirclCS. FOT
il the rays vere aIl alike retransible, tis impossible that
the erhritenels, wrhich tothe naked sence appears uni-
Form, Thould by retraction hare its parts transposed and
ransed into thole black and wrhite AFCS.
IE appears allo that the unequal retractions ot dit.
form rays proceed not trom any continsent irregulari
ties; luch a5 are reins, an uneren polistu, or Fortuitous
polition ot the pores ot Cilals; unequul and calual mo.
tions in the Air or Ather; the spreadins, breakins, or
dividins the lame ras into mans diversins parts, Oi
thelike. For, admittins any Tuch irregularities, it rould
De impossible for retractions to render thole Rings (0
verr distinet, and vell detined, a5 ther do in the
24th Obserration. It is necellary theretore that eve.
ry ray have its proper and constant desree ot retran.
sibilir connate rith ic, accordins to wrhich its retraction
15 erer justly and regulariy pertormed, and that sere-
ralrays hare sereral ot thole degrees.
And irhat is Caid oF their retransibiliey may be ala
understood ot their reflexibilitr, thac is ot their dispo.
litions to De relected lome at a sreater, and others at a
less thickness, of thin. Plates oi Bubbles, namely, that
those dispositions are also connate with the rays, and
inmucable; 2s may appear by che 23th, 14ch, and
a5CH

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C4
sth Obserrations compared with the fourtti and
ciotth.
By the precedent Obserrations it appears also, thaF
Whiteness is a dissimilar mixture oF aIl Colours, and that
Light is a mixture oF rars indued rith all thole CO-
tOurS. For considerins the multitude oF the, RingS OF
ColOurS, in thc 2d, 12th and 24th Oblerrations, it is
manifest that althouoh in the ath and L8th ObCCeVA-
tions there appear no more than eiont or nine ot thole
RingS, Vet there are really a Far greater number, wrhich
lo muctr intertere aud mingle ith one anothiei, a5 alter
those eiont or nine revolutions to dilute one another
Wholly, and constitute an even and sensibly unitorm
Wrtitenels. And consequentr that irhitenels nust DC
alloved a mixture ot all Colours, and the Lishe whieh
Conrers it to the fiye must bea mixture oF rars indued
Writh aIl ThOTe COIOUES.
But Further, by the 24th Oblerration, IE apPCaIS,
that there is a constant relation between Cotours and
Retransibilier, the most retransible rars beins violet,
the least retransible red, and thole ot intermediate C0.
lourstravins proportionably intermediate degrees ot re-
Frangibilier. And by the 13th, 2gth and 1gth Ob(er-
vations, compared with the Athos IBth, There apPCaIS
to be the lame constant relation betrreen Colour and
Reslexibility, the riolet beino in like circumstances re-
Aected at least thicknesses ot any thin Plate or Bubble,
the red at sreatest thicknesses, and the intermediate
Colours at intermediate thickneRes. Whence it FOl-
lons, that the coloritique dispositions ot rars are al(0
connate riththem and immutable, and by consequence
that

## Folio 48 — 1677894601:0220
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C487
Ehat al the productions and appearances oF ColourS
in the World are derired not trom any phylical chanse
caused in Light by retraction or rellexion, but oniy
trom the rarious IXtureS Or leparations oF. PaYS, by
virtue ot their different Retransibilier or Rehexibiliey.
And in this respect the Science ot Colours becomes à
Speculation as truly mathematical as any other part ot
Optiques. I mean (0 Tar a5 ther depend on the nature
OE Lishe, and are not produced or altered by che pover
oCimagination, or by Ariteins or presins ThCLy es.

## Folio  -  — 1677894601:0221
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Fie: 2
FIS. 2.
EVX Vt Sr qponalluit efed C
BOOK, l.
Llate, l.
c defchik lmnopgrS +VXYZ
 d Sodt BdE DE
e
Ed
e6dB
ePC
FIg. 3.
2
E 3
5
3
d
a e5S
 e
de BdIABEB Ed Ed La
 S R  sepa
e
2B3sE
=
8
LD

## Folio  -  — 1677894601:0222
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. s  s sl . l ia. I  . I IIIIIIIIII..
s s s sa   s sscl s  s  IIIB. (HII(IIH) IIH.LIIl1IIIIIII
35
36
alur: Leibn. Mar9.
GOTIFRIED WILHELM LEIBNIZ BIDEIOTTRK
NIEDERSACHSISEHELLANIDESBIBLNTHEK
eeeeee

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B00k, II.. Plate, I.
18. 5.
6 3
lC. d.
f16. 7
d
E
E
 X (5 II
A 1 X 5 e
c
as f.b d. se  d

## Folio  -  — 1677894601:0224
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11
111I
IIII iA si s si tsoot
p
1111I
1111
E1
atur: L eibn. Mar9. 193, (3
OTTTNIED HILMICLMTLLIBIMIL BIDLIOTHEK
NIEDLNSALTTSISEMTL LNIODLSOIDBRTHEK

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=
 LLL
 am
d F
 e d
P A R Y ITI.
Of the permanent Colours of naturat Bodies, and the
Analory betreeen them and the Colours of thin trans-
parent Plates.
Am no come to another part of this Dehon, irhicte
15 to consider hon the Phaenomena of thin trantpa-
rent Plates Aand related to those oE aII other natural
Bodies. OF these Bodies Phare already told rou that
they appear oE divers Colours, accordinsly a5 ther are
dispoled to resseet most copiousr the rars originals
indued rith those Colours. But their Consticutions,
Whereby ther relleet some rars more copiousy than
others, remains to be discorered, and these L MaII en
dearour to manifest in the Follomins Propohtions.
eROt
TR

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PROP. +o
Those superficies oftransparent Bodies reflect the rreatest
quantity of Lisht, rehich have the oreatest refractino porver;
that is, rehich intercede mediums that differ most in their
refractive densities. And in the confines of equally re-
fractine mediums thereis no reflexion.
The Analosy betreen reflexion and retraction will
appear by considerins, that irhien Listit passeth ob-
liquelr out ot one medium into another irhich retracts
from the perpendicular, the greater is ditference ot
their retractire density, the lels obliquity is requisite
to cause a total retlexion. For a5 the Sines arc irtrich
measure the retraction, (0 is the sine ot incidence at
ertrich the total reflexion begins, to the radius of the
Cirele, and consequentlr that incidence is least irhere
there isthe oreatest ditterence et the Sines. Phus in the
palsins oF Light out oF Water into AIr, Where the
refraction is mealured by the Ratio oF the Sines 3 t0 4,
the total retlerion begins wrhen the Angle ot incidence
is about 48 degrees 35 minutes. In passins out oFCila(s
into Air, irhere che retraction is meatured by the Ratio
OF the Sines 20 t0 3r, the total rellexion begins erten
the Anele oF incidence is 40 deg. 10 min. and (0 in
passins out oF crystal, or more sronely refractinq me
diums into Air, there is Aill a less obliquity requisite
to cause a total reslexion. Superticies theretore irhich
retract most do (oonest refleet aII the Lioht which is in
cident on them, and (o must be allored most Atrongly
xet exIre.
BUC

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5
But the truth oF this Propostion ill Further appear
br observins, that in the superticies interceding trro
transparent mediums, such asare (Air, Water, Oyl, Com
ion-Gla(S, Crystal. MetallineClasses, IMand-Cilases,
irhute transparent Artnick, Diamonds, dc.) the re-
fexion is Aronger or meaker accordinslr, a5 the luper-
ticies hath a greater or lels retractins porrer. Lor in
the contine oF Air and Sal-gemm tis ltronger than in
thecontine of Air and Water, and Ciil stronser in the
contine oF Air and C ommon-CEla(SOF C PV StaL, and ArOnpeF
in the contine ot Air and a Diamond. IF anY ot thele, and
Tuch like transparent Solids, be immerged in Water, its
reflexion becomes much weaker than betore, and AilI
reakcer it ther be immereed in the more Aronglr re
Fractins Liquors oF ell. rectitied oyl ot Vitriol or Ipirie
ot Turpentine. TFWater be distinguisted into trro parts,
by ans imaginaer Curtace, the retexion in the contine
Ot thole tmo pares is none at aII. In the confine oF Wa-
ter and Ice tis verr litele, in thac of Water and Oyt tis
Tomethins grenter, in that of Water and Sal-gemm Aill
Sreater, and in that of Water and CtaIS, Or C Ersal, Or
ottrer denser substances Aill greater, accordinsly as thole
mediums disfer more or lels in their retractins pOIerS.
Flence in the contine ot Common-Citass and Crysal,
there ought tobe a reak rellexion, and a Aronser re
Aexion in the contine ot Common and Metallinc- Glals,
thoueh Phave not vet eried this. But, in the contine ot
tiro Cilasses oFequat densier, there is not any sensible re-
Aexion, a5 ras hewn in the frst Obserration. And
che lame may be understood ot the luperticies interce
dins tro Crystals, or trro Liquors, or any other Sub
stances in irtrich no retraction is cauled. S0 then the
AH 2
realon

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. 61
(52
reason Why unitorm pellueid mediums, (Tuch a5 Nater,
Gta(S, OE C xYAtaL) have no sensible cellexion but in
their external superficies, where ther are adjacent to
otter mediums of a ditterent density, is because ali
their contisuous parts have one and the lame degree
oF dentier.
P R O P. TI.
The least parts of almost al naturat Bodies are in some
measure transparent: And the opacity of those Bodies
ariseth from the multitude of reflexions caused in their in-
ternat Parts.
Thae this is C0 has been obterved by others, and
Wvilleaulr be sranted by them that have been convei-
Tant ith Miscroscopes. And it may be also tryed by
applyins any substance to a HIole throush irhich lome
Lishit is immitted into a dark room. For ho opake
foerer that substance may leem in the open Air, it viiI
by that means appear very manitestls transparent, it
it be oF a sufficient chinnels. Onlr irhite metalline B0-
dies must be excepted, irhich by realon ot their excel
sre densiey seem to reflect almost ai the Light incis
dent on their Arst Cuperticies, untess by Colution in
menstruums ther De reduced into very (mall particles,
and then they become transparent.
E R OP. IIE
Betreeen the parts of opate and coloured Bodies are
manu spaces, eitber emptus or replenisted roith mediums
of other densities; as Water betreeen the tingins corpuscles
roberevith any Liquor is impresnated, Air betreeen the
aqueous

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(B
aqueous globules that constiture Clouas or Mists; and for
the most part spaces void of both eir and W ater, but yet
perhaps not reholly void of au substance, betreeen the parts
of hard Bodies.
The truth oF this is erinced by the tuo precedent
Propostions: For by the second Propohtion there are
many reslexions made br the internal parts oF Bodies,
irtich, by the tirst Propolition, vould not happen it
che parts of thole Bodies vere continued without any
luch interstices betreen them, because reslexions arei
caused onty in superticies, irhich intercede mediums ot.
a differins density By PFOP. I.
But Further, that this discontinuitr ot parts is the
principal cause ofthe opacitr ot Bodies, riil appear by
considerins, that opake substances become transparent.
br Aillins their pores rith anx substance oF equal or al-
most equal densitr rith their parts. Thus Paper dip-
Ded in Water or Oyl, the Oculus mundi Stone Aecp d in
Water, Linnen- cloth oyled or varnithed, and mans other
substances Coaked in such Liguors as rill intimatelr
perrade their litele pores, become by that means more
transparent than othervile; (0, on the contrary, the
most transparent substances may by eracuatine their
Pores, or separatins their parts, be rendred lusticiently
Opake, a5 SalES Or WWet Paper, or the Oculus mundi Stone
by beins dried, Hlorn by beins scraped, Glals by beins
reduced to porrder, or otherrile Haved, lurpen-
tine by being sirred about rith Water till ther mix
impertectis, and Water by beins formed into many
Tmal Bubbles, cither alone in the Form ot FrotH, Or
by Makins it together with Oyl ot Turpentine, or
rich some other convenient Liquor, irich wrhich it will
BDE

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C54)
not perfectir incorporate. And to the increase ot the.
opacier oE thele Bodies it conduces Lomethins, that by
the 23ch Obserration the resexions ot very thin trant-
Parent substances are considerably sronger than thole
made by the lame substances ot a greater thickness.
P R O P. IV.
Phe parts of Bodies and their Interstices must not be
less than of some definite bioness, to render them opatee and
coloured.
For the opakest Bodies, it their parts be subtily
divided, (a5 Metals by beins dissolred in acid men-
Cruums, 1c.) become pertectly transparent. And vou
may illo remember, thac in the cishth Obserration
there iras no sensible reflexion at the superticies ot
the Object- Cilasses ertere ther vere very near one
anocher, though ther did not absolutelr touch. And
inthe 17th Obterration thereflexion oFtheWater-bubble
irhere it became thinnest as almost insensible, (0 25
eo cause verr blacke Spots to appear on the top ot the
Bubble by the rant ot refected Liglt.
On these gronnds I perceire it is that Water, Saltu
Cla(S, Stones, and such like substances, are transparent.
tor, uxon dirers considerations, ther leem eo be a5 FuII
ot pores or interstices becureen cheir pares as other BO.
dies rre, but yet their parts and interltices to Dc t00
5
1
ndl L Cause reflexions in their common Curtaces.
DROF.

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PROL. V.
The transparent parts of Bodies accordine 10 their se
verat sixes must reflect rays of one Colour, and transmit
those of another, on the same erounds that thin Plates or
Bubbles do reftect or transmit those rays. And ihis I tatee
to be the ground of au their Colours.
For it a thin d or plated Body, irhich beins OF an
eren ChiCkneIS, apPeAES AII OVET OF OnC UNIFOEIL CO-
lour. Bould be Hlit into chreds, or broken into tras.
inents, oF the Pame thickness with the plate; I sec no
realon wrhiy ererr thred or fragment Mould not kecp its
Colour, and by consequence wtr a heap ofthose chirede
Or Fragments Thould not constitute a mals or ponrder ot
the same Colour, wrhich the plate exhibited betore it
asbroken. And the parts ot aIl natural Bodies beine
like (O many FFaSMENIS OF a Plate, must on the lame
srounds exhribit the same COlOurS.
Nor that ther dos0, will appear by the aftinity oF
their properties. The tinely coloured teathers ot lome
Birds, and particularly thole ot Peacocks Pailo, do in
the very same part of the Feather appear oF several CO-
lours in sereral positions of the Fye, alter the very lame
manner that thin Plates rvere found to do in the 7th
and 1gch Obserrations, and theretore arise From the
thinnels oF che LTAN(PATeNE PaRES OF The Feathers; that
is, Fromthe Pendernels oF the verr tine Hairs, or C’apilla-
menta, Which gror out ot the sides of the grosser late.
eal DTaNCHCS OF ABTES OF thole FeatherS. And tothe
Came purpole it is, that the Webs oF lome Spiders by
beins

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o
beins ipun very fine hare appeared coloured as lome
hare obserred, and that the coloured Abres of some (IIks
by rarrins the polition of the Fve do vary their C0
IOur. AIIO the Colours oF AIHS, Cloths, and other sub.
stances, irtrich Water or Oyl can intimately penetrate,
become more faint and oblcure by beins immersed in
thole liquors, and recorer their visor again by beins
dried, much alter the manner declared of thin Bodies
in the Toth and 2rth Obserrations. LCaF- sold Fome
Forts ot painted Clals, the infusion ot Fionum Nephri-
ticum, and some other substances refeet one COlOur,
and transmit another, libe thin Bodies in theoth and
2oth Obserrations. And Pome ot thole coloured pour-
ders Which Painters ule, mar hrave their Colours a litcle
chansed, by beins very elaborately and tinelr ground.
Where I sec not what can be justly pretended tor thole
chanses, besides the breakins of their parts into less
parts by that contrition atter the lame manner chatthe
COlour ot a thin Plate is chansed by varrins its thick.
nels. For rrhichrealon al(o it is that thecoloured Rowers
oF Plants and Vesitables by being bruised ulually be-
come more transparent than betore, or at least in lome
degree or other chanse their COlOurS. NVOr IS it much
lels to my purpole, thatby mixins dirers liguors very
Odd and remarquable productions and changes of C0-
lours may be effected, ot irhich no cause can bemore
obrious and rational than that the Caline corpuscles ot
one liquor do rariousy aet upon or unite rith the
tingins corpuscles ot anocher, (0 a5 to make them svell,
Or Chrink (wrhereby not ouly their bulk but their den-
licy also may be changed) or to divide them into
Emaller corpuseles, (Whereby a coloured liquor may be-
COmmO

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COme Fran(DAPCHE) OE tO make mans ot tliem alociate
into one cluster, Wrhereby tuo transparent liguors may
compose a coloured onc. For re see hour ape thole
Taline menstruums are to penetrate and dissotre sub.
stances to wrhich ther are applied, and lome ot them
to precipitate what ottiers dissolre. In like manner, it
Wre consider the rarious Phaenomena of the Atmosphaere,
re may obserre, that wrhen Vapors are tirstrailed, ther
hinder not the transparener ot the Air, beins dirided
into parts t0o mail to caule an reflexion in their super-
ticies. But wrtren in order to compose drops ofrain they
begin to conlesce and constitute slobules ot aIl inter-
mediate Rres, thole globules irtien ther become ot a
convenient sive to reflect fome Colours and transmit
Others, mar constitute C louds ot various COlOurs aCcOr
ding to their (2CS. And I sec not irtrat can be ratio-
nullu conceired in (o transparent a substance as Water FOr
the production of these Colours, Desides the various
Eires oF its Auid and globuler Parcels.
PR OP. VI.
The parts of Bodies on rehich their Colours dépend
are denser than the medium, rehich pervades their in
terstices.
This rill appear by considerine, that the Colour ot
a Body depends not ontr on the rars wrhich are inci-
dent perpendicularty on its parts, but on thole allo
ertrich are incident at aIl other Angles. And that ac.
cordinq tothe 7th Obserration, a very litule variation
et obliguity will chanse the refected Colour irhere the
thin body or Imall particle is rarer than the ambient
medium,

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1
58
medium, insomuch that such a (maII particle will at di-
verir oblique incidences reflect aII Ports oF C OlOUIS, In
Cogreat a varietr that the Colour relultins from them
aI, contulealy reflected trom a heap ot such particles,
must rather be a wrhite or sres than anr other COlOuT,
Or at best it must be but a verr impertect and dirty C0-
IOur. Whereas it the thin body or Fmall particle be
much denter than the ambient medium, the Colours
accordins to the Tgth Oblerration are (o little changed
by the variation oF obliquitr, that the rars irtrich arc
refected least obliquelr may predominate over the rest
(0 much a5 to cause a heap ot luch particles ta appear
verr intensr of their COlOUr.
It conduces alio fomethinq to the contirmation ot this
Propohtion, that, accordins to the 22th Oblerration,
the Colours exhibited bythe denser thin bodr within
thecarer, are more brisque than thole exhribited by the
rares wrichin che denter.
PROP. VII.
The bioness of the component parts of naturat Bodies
may he conjectured by their Colours.
FOr lince the parts of these Bodies by PrOD. 5. d0
most probablr exhribit the lame Ciolours with a Plate ot
equalthichnels, provided they have the lame recractire
dentti; aud lince their parts leem For the most part 10
have much the lame densuy with Water or Cta(S, 45
by many circumstances is obrious to collect; to deter-
mine the sres oFthole parts you necd onsy hare recourle
to the precedent Lables, in Wrhich the thicknels otWa-
ter or Cilals exhibitins ans Colour is expressed. Thus
1

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59
il it De desred to knoir the Diameter ot a corpulele,
irhich beinq oF equat densiey with Glass Mall refleet
oreen oF the third order; the number 16: Teirs it to
 Parts oF an Inch.
The greates difficuley is here to lenoi oc ivtat order
the Colour oF any Body is. And For this end ire must
have recourse to the ath and 18th Obserrations, From
irtence may be collected these particulars.
Scarlets, and ottier reds, oranses and yellores it chey
De pure and intense are most probably ot the lecond or-
der. Those oF the Aust and third order allo mar bc
preter sood, onls the vellor of the tirst order is taint,
and the oranse and red of che thurd order have a great
mixture et violet and blue.
There maz be 800d greens oF the Foureh order, but
the purest are ot the third. And of this order the sreen
OF ail regitables seem to be, partly ey reason ot thein-
tenseness oF their Colours, and partls becaule when
they rither lome ot them turn to a greenistr vellon
and others to a more pertect vellor or orange, Or Pei-
hraps to red, passins tirst chroush aIl the atorelaid in-
termediate Colours. Which chanses leem to be effected
by the extralins of the moisture wrhich mas leave the
cingins corpulcles more dense, and lomethins ausmen-
cedby the accretion oF the oyiy and carthy part et
chatmoilture. Nor theoreen wrichout doubeis ot the
ame order rith those Colours into ihich it changettu,
because the changes are gradtual, and thole COlOUrS,
chouxh ulually not very Full, vet are otten t00 Tull and
lively to be ot the tourth order.
Blues

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(607
Blues and purples may be cither oF the second or third
order, but the best are of the third. Thus the COlOUF
oF riolets seems to be ot that order, because their Syrup
by acid Liquors turns red, and by urinous and alcali-
alC TUTNS greeM. For since it iS oF the nature oF ACIdS
to dissolve or attenuate, aud oF AIcalies to precipitate
or incrastate, if the purple Colour ot the Syrup iraS ot
the second order, an acid Liquor by actenuatinq its tino-
ins corpulcles vould chanse it to a red ot the Arst
order, and an AIcaly by incrassating them vould change
it to a preen ot the second order; Which red and oreen,
especially the oreen, seemtoo impertect to be the CO-
Jours produced by these changes. But il the laid purple
be supposed ot the third order, its change to red ot the
second, and sreen oE the third, may writhout any in-
convenience De alloved.
IF there De tound any Body ot a deeper and lels red-
dist purple than that ot the violets, its C olour most
probably is oF the second order. But vet their beino
no Body commonly known Wrhose Colour is constanttis
more decp thantheirs I hare made use oftheir name to
denote the deepest and least reddisti purples, luch a5
manifestly transcend cheir Colour in puritr.
The blue ot the first order, thouch verr faint and
little, may possiblr be the Colour oF. Tome substances;
and particulariy the arure COlour oF the Skys seems to
be oF this order. For alt rapours wrhen they beginto
condense and coalesce into linall parcels, become tirst ot
that bisnels wrhereby luch an Arure must be retlected
betore they can constitute C louds ot other Colours. And
(0 this being the hest Colour wrhich vapors begin to
refleet, it ought to bethe Cvlour oE thetinest and most
traML

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61
transparent Steys in Wrhich vapors are not arrivedto that
erolnels requisite to retteet other Colours, as we find it
15 bY experience.
WBiteness, it most intense and luminous, is that ofthe
trst order, it less Arons and luminous a mixture of the
Colours ot several orders. OF this last kind is the
ertriteness oF Froth, Paper, Linnen, and most wrhite sub-
Aances: OF the Former I reckon that ot wrhite metals to
bC. For Whilsthe densest oF metals, Gold, it foliated
i5 transparent, and ai metals become transparent it
dissolred in menstruums or vitrihied, the opacity ot
Wrhite metals arileth not from their densiey alone. Phey p. S2
being less dense than Gold rould De more transparent
Than it, did not lome other cause concur with their den-
Cier to makce them opatie. And this cause I take tobe
Tuch a bionels ot their particles as fes them to reflect
the wrhite oF the Ars order. For it they beot other
thicknesses ther may refect other COlOurs, a5 IS IaNI-
Fest by the Colours rhich appear upon hot Steel in tem-
pering it, and Cometimes upon the Curtace oF melted
metals in the Skin or Scoria wrhich arises uxon them in
their coolino. And a5 the white ot the tirst order is
the Arongest which can De made by Plates oftransparent
substances, so it ouoht to be Aronger in the denser sub.
Itances oF metals than in the rarer OF AIT, Water and
Gta(S. NVor do I see but that metallic substances ot luct
a thickness as mav Atthem to reReet the wtite ot the
Ars order, may, by reason of their great density (accOr-
dins to the tenour of the trst ofthele Propolitions) re-
Aect aIl the Lient incident uxon them, and (0 DC as
opake and splendent as its possible for any Body tobc.
iold, or C opper mixed rith lels than halttheir weignt
ot

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62
oFSilver, or Tin, or Resulus oF antimonr, in Fusion
or amalsamed rith a very little Nercurr become white;
artrich lheurs both that the particles ot wrhice metals
trave much more superticies, and (o are Linaller, than
those oF Gold and Copper, and also that ther are (0
opake as not to sutter the particles oFCiold or C opper to
Mine chrouoh them. Nour it is scarce to be doubted,
Bue that ehe Colours ot Grold and C opper are ot the le-
cond or third order, and theretoré the particles ot vrhite
metals cannot be much bigger than is requisite eo make
them resect the Wrhite of the Ars order. The volati-
lier oF Mercury argues that thez arc noc much bigger
nor may ther De much less, least cher lose their opacitr,
aud become cither transparent as ther do iten attenua-
ced by ritrification, or br Colution in menstruums, Or
black as thes do When sround (maller, by rubbins Sil-
ver Or Tin, Or L ead, uxon other Cubstances to drar Black
FInes. The Arst and onlr Colour which erhice metals
takce by grindins their particles smaller is black, aud
theretore their rrhite ought to De that vrhich borders
upon the black Spot in the center oF the RingS OF CO-
lOurs, That is, the wrhite ot the Arst order. But il rou
prould hence sather the bigress of metallic particles,
vou must altoir for their densitr. FOr ivere Mercury
transparent, ies density is such that the sine ot inci-
dence upon it (br my computation) vould be tothe
FiIne OF itS rCFTaCtION, 25 7F t0 20, OF 7 +0 3 And
theretore the thicknels ot ies particles, that ther mar
exhibit the Pame Colours rith those ot BabBleS OFNN 2-
ter, ouont to be lels than the thicknels oF the Skin OF
those Bubbles in the prOpOrtiOn OF 3 107. Whence
its Polsible that the particles oF Nercury may De as little

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25 the particles of some transparent and volatile Auids,
and yet retleet therrhite ol the Airst order.
Lastlr, For the production ot blacte, the corpuscles
mult be lels thon ans ot thole which exhribit ColOurS.
For at all oreater Rres there is t00 much Light reste-
ctedto constitute this Colour. But it they be suPPo-
sed a little lels than is requisite to reffect the white and
verr faint blue ot the Arst order, they willus accoraie
eo the Ath, 8th, 27th and rBth Oblervations, resseet
lo verr little 25 to appear intensr black, and vet may
Perhaps variouss retraet it to and tro rithin them-
letres (0 lons, until it happen to be Aisted and lott,
by erhich means thes rill appear black in ail positions
OE the fire rithont anr transparener. And Fromhence
mas be understood irtiy Fire, and the more subtile
distotrer Putretaction, by dividins the particles oF (ub-
itances, turnthem to black, irhy Imall quantities ot.
Black substances impart theis C olour verr Frecly and in-
tenssy co ocher substances to irhich ther are applied;
the minute particles ot these, by reason of their very
sreat number, easily orerspreadine the srols particles
OF others; Wrhy Cilass ground very claboratelr rith
Sand on a copper Plate, till it be vell polisted, maties
the Sand, tosether rith wrhatis worn oHtrom the Cilals
and Copper, become very black: Wrhy black substances
do (oonest of all others become hot in the suns Light
and burn, (erhrich etfeet may proceed partly trom the
nultitude ot refractions in a little room, and partly
trom the ealy commotion ot (0 verr (mall corpuIcles;)
and irhry blacks arc ulually a litele inclined to a bluilte
COlOUT. For that ther are (o may be seen by illumina-
Cins irhite Paper by Lishe reltected trom black (ub.
HanCCS.

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L64
AanCes. For the Paper will ulually appear ot a bluisti
wrtrite; and the reason is, that black borders on the
obicure blue oF the Ars order described in the 18th
Oblerration, and theretore reflects more rays ot that
Colour than ot any other.
In chese Descriptions I hare been the more particu-
lar, because it is not impossible but that MilcrolcoDeS
mar at lenoth be improved to the discovery ot the
particles of Bodies on rrhich their Colours depend, it
cherare not alreadr in lome meature arrived to thatde-
oree ot pertection. For iEthose Instruments are OF Can
be (0 tar improred as ith sufficient distinctnels to re-
prelent Objects tire or six hundred times bigger than
at a Foot distance ther appear to oui naked Fves, I
Chould hope that re mistit be able to discorer lome ot
the greatest ot thole corpuseles. And by onc that rould
magnier threc or tour thouland times perhaps ther
mioht aI be discorered, but those irhich produce Black-
nels. In the mean wrhile I sec nothins material in this
Discourse that mar rationallr be doubted ot excepting
this POTtIOn. That tranparent corpuscles et the lame
thichness and densicy with a Plate, do extribit the lame
CoIOUr. And this I vould have understood not With-
out lome latitude, 25 vell because those corpuscles may
be of irresular Figures, and many rays must be oblique-
ly incident on them, and lohare a Mhorter ray throush
them than the length ot their Diameters, 25 becaule the
Araitnels ot the medium pent in on aIl sides writhin Tuch
corpulcles mar a lictle alter its motions or otner qua-
lities on irtich the rettexion depends. But vet Ican-
not much suspeet the last, becaule I have observed ot
Come InaII Plates oF Mulcory-Cila(s irhich irere oF an
erem

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(65)
eren chickness, that through a Miscroscope ther have
appeared ot the Came Colour at their edges and cor-
ners wtere the included medium mas terminated, irhich
chey appeared oF in other places. Floverer it rill add
nuehto our Patisfaction, if those corpulcles conld be dis-
corered rith Miscroscopes; erhich it we Mail at lenoth
actain tO, I Fear it will Dc the utmost improrement ot
this sense. For it scems impostible to sec the more le-
eret and noble works of nature mithin the corpuleles
by realon of cheir transpareney.
P R O P, VITI.
The cause of Reflexion is not the impinoino of L ight on
the solid or impervious parts of Bodies, as is commonly be-
lieved.
This will appear by the follorine Considerations.
First, That in the passase of Lieht out ot Crlals into
Air there is a rellexion as Arons as in its pastase out ot
Air into Cla(S, Or rather a little Aronger, and by many
degrees sronger than in its passase out of Glass into
Water. And it seems not probable that Air Mould have
more refectino parts than Nater or Cla(S. But if that
Tould possibly De supposed, vet it will arail nothins;
For the reflexion is as srons or Aronger Wrtren the AIT1S
dramnaras trom the Cilals, (suppole in the Air Dump
invented by MIT. Boyle) 25 irhien it is adjacent to il.
Secondir, IFLighe in its paltase out of Crlass into Air
De incident more obliquelr than at an Ansle ot 40 Or
4Y degrees it is rhrolly retlected, it lels obliquely IE 15
in great meature trantimitted. Nom it is not to beima
Bined that Lishe at one desree ot obliquity Monta meet
H
WIF

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66
with pores enough in the Rir to transmit the greater
part ot it, and at anottier degree ot obliguitr Mould
neet rith nothine but paris to reslect it irholy, espe
ciallr contiderins that in its paltage out oF Air into
Gtals, hoir oblique Poerer De its incidence, it finds
pores enoush in the Glass to transmit the greatest part
OFit. TFanis Nan suppose that it is noc tesected by the
AIT, Dut bY the outmost superticiat parES OF the ClaIS,
there is Cill the same difficuler: Belides, that such3
Supposition is unintelligible, and rilt allo appear to be
False by applvins Water behind lome part ot theCilals
instead oF AIr. For (o in a convenient obliquitr of the
rars suppole oF 45 or 46 degrees, at wrhich thez are ail
rellected irtiere the Air is adjacent to the Gtals, they
MalI De In sreat measure transinitted Where the Water
15 adjacent to it; irhich argues, that their reftexion
et transmision depends on the constitution ot the Air
ahd Water Behind the Glass, and not on the srikins
Off the rays upOn the parts oF the CEla(S. Thirdly, IF
the Colours made by a Prilm placed at the entrance ot
a beam oF Light into a darkened room be successirely
cast on a second Prism placed at a greater distance From
tne Former, in such manner chat ther are all alike inci-
dent uxon it, the second Prism may be so inclined t0
the incident rars, that those erhich are oE a bluie Colour
MaltDe all rehlected by it, and vet thole oF a red COlour
pretty copiously transinitted. Norr is the reflexion De
caused br the DARES OF Air OE Gla(S, I Would ask, WhY
ac the same obliquitr ot incidence thie blue Mould wrhol-
I impinse on those parts (0 25 to be uIl retlected, and
vet the red tind pores enoush to be in great meature
transinitted. Fourthlr, Wrhere trro Gilalses touch one
another,

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another, there is no sensible reflexion as ras declared
in the tirst Obserration; and vet I sce no realon why
the rass Mould noc impinse on the parts oF CrtaIS a5
much irhen contisuous to other Crlals a5 Wrhen con-
tiguous to Air. Fisthly, When the top ot a Water-
bubble (in the 17th Obserration) by the continual (ub-
lidins and exhralins of the Water orem very thin, there
ras such a lictle and almost insensible quantitr ot Light
retlected trom it, that it appeared intenls black; Wrhere-
as round about that black Spot, Wrhere the Water Was
thicker, the reflexion iras lo Arons a5 to make the
Nater Icem very wrhite. Nor is it ouly at the lcast
chickness of thin Plates or Bubbles, that there iS, nO
manisest reflexion, but at mans other thickneses con-
tinualls greater and greater. For in the 15th Obler-
ration the rays oE the lame Colour vere by turns trans-
mitted at one thieknels, and reflected at another thick-
nels, For an indeterminate number ot luccesions. And
vet in the superticies ot the thinned Bod), Wrhere IE 15
oF any one thickness, there are a5 ManY PaFIS FOF FhC
rayS Eo impinse on, 25 irhere it is oF any other thick-
nels. Sixthly, IF reflexion ivere caused by the parts ot
retlectins Bodies, it rould be impossible for thin Plates
Or Bubbles at the lame place to refleet the rays ot one
Colour and transinit thole of another, a5 ther do accor-
dins to the 13th and Esth OblerVatIONS. FOT it 1S
not to be imasined that at one place the rays whieh
For instance exhibit a blue Colour, ould hare thefor-
tune to dastr upon the parts, and thole irhich extibit
a red to hit upon the pores oF the Body; and then at
another place, irhere the Body is cither a litelethicker,
Or a little thinner, that on the contrary the blue Mould
E K 2
tri

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68
hit upon itS POres, and the red upon IES parES. LasIY,
vere the rays ot Lighit reflected br impingins on the
Colid parts ot Bodies, their reflexions from polisted B0-
dies could not be (0 regular a5 ther arc. FOr in PO-
littrins Class with Sand, Putr or Pripoly, it is not to
De imasined that those substances can by sratins and
Trettins the Cla(s brins aI its least particles to an ac-
curate polist; (o that alI their Curtaces Mail BC truly
plain or truly Spherical, and look aIl ttre same way, lo
a5 toscther to compose one even surtace. The Pinallex
the particles of thole substances arc, the Imaller rii
Dethe Scratches by irhich ther continually tret and rear
array theCilass until it be politted, but be ther nerer
(0 linall they can rear array the Glass no othermile
than by gratins and seratchins it, and breakcins the
proturberances, and theretore polistr it no otherwile
than by bringins its rouchinessto a very tine GTrain, (0
that the scratches and Frettings of the surtace become
t00 (mall to be risible. And theretore il Lisht iere
reflected by impinsins upon the Colid parts of theGilals,
it rould De scattered as much by the most polished
Glas as by the roughest. So then it remains à PrO-
blem, hou Gilass polistred by frettins substances can re-
Rect Light so regularly as it docs. And this Problem
i5 scarce otherrrile to De Tolred than by Paving; that
the reflexion ot a ray is effected, not by a snsle point ot
the reflectins Bodr, but by fome porver ot the Body
irtrich is erenty diffused all over its Curtace, and by
erhich it aets upon the rar rithout immediare contact.
For thatthe parts of Bodies do act upon Light at a di-
Aance Phail be Mewn hereatter.
Now

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(60
Nou il Lighe De reRected not by impingins On tC
Tolid parts ot Bodies, but ty some other principle; its
Probable that as manr ot its rays as impinse on the
lolid parts oF Bodies are not reflected but stiffed and
lost in the Bodies. For othervise Wre must alloW LWO
lorts oF reflexions. Shrould all the rars De reffected wrhicp
impinse on the internal parts of clear Water or Crystal,
those substances vouid rather hare a cloudy Colour
than a clear transparener. To make Bodies look black,
iIS necestary that many rars be Aopt, retained and Iost
in them, and it seems not probable that any rays can
be Aopt and stisled in them irhich do not impinse On
Their partS.
And hence e mar understand that Bodies are much
more rare and porous than is commonty beliered. Wa-
ter is r9 times lighter, and by consequence 19 times
rarer than Gold, and Giold is (o rare as verr readilv
and rithout the least oppolition to transnit the mag-
netick FMuria, and casily to admit Ouick. silver into
its pores, and to let Water passthrough it. For a con-
care Sphere oF Gold Alled rith Water, and Podered up,
has uxon pressine the Sphere with sreat Force, let the
Nater squeeze throuon it, and Aand aIl over its out-
Side in multitudes oE (mall Drops, like dew, without
burstins Or crackins the Body ot the Grold as I have
been informed by an Fre witness. From all irhich re
may conclude, that Cold has more pores than solid
Parts, and by consequence that Water has abore Forty-
times more pores than parts. And hethat aII find out
an Llypothelis, by irhich Water may belo rare, and yet
noc be capable ot compression by Force; may doubrlels
by che lame Hypothesis make Gold and Water, and aH
Other

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P
7
other Bodies as much rarer as he pleales, Pothat Lieht
may find a seuds pallase chroush transparene lub.
Ctances.
PROP. 1Z.
Bodies reflect and refract Fisht hy one and the same
porver variousty exercised in various circumstances.
This appears by lererat Considerations. First, BC.
cause irtien Lisht soes out oF Citals into AIr, a5 ob.
liquetr a5 it can postibly do, il its incidence be made
AiIl more oblique, it becomes totally reflected. For
theporver of the Cilals atter it has retracted the Lighe
as obliquely a5 is possible if the incidence be sill made
more oblique, becomes to0 Arons to let any oF its rayS
50 chroush, and by consequence causes total rellexions.
Sccondly, Becaule Light is alternately reflected and
transmitted by chin Plates oF Cilass for many successions
accordinslr, a5 the thichnels of the Plate increases
in an arithmetical Progression. Forhere the thicknels
ol the Clals determines irhether that porrer by which
Class acts upon Lisht Mall cause it to be reRected, Or
Cusser it tobe transmitted. And, Thirdly, because those
Turtaces of transparent Bodies artich hare the sreates
retractins pover, relect the sreatest quantiey ot Lislitus
aS Was Cered in the hrst Proposition.
P R OP. Z.
L Laest de Pase io s bian in Vacud i lisC
propertion of the Sines rehich measure the refraction of the
Bodies, the forces of the Bodies to reflect and refract Lisht,
ar

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Bodtes, exceptine that V
E
ous a
fractmore thanotbers of this same densty
 sulphat cous oddies re-
are verus.
eartu proportionat to ihe densities of the same
L et AB represent the retractins plane TuxFaCC OF any
Gody, and Lea sus ccense ters nglels uxon the
Body in C, 50 that che Anele AC I may be intinitely
licele, and let C. R bethe retracted ray. From a given
point B perpendicular to the retractins surtace crect
BR mectinq with the retracted rar C R in R, and it
C. R revresent the motion of the retracted rar, and this
motion be distinguisted into trro motions C. B and BR,
Wrhereot C B is a parallet to the retracting plane, and
BR perpendicular to it: C. B Mall reprelent the motion
OF the incident rar, and BR the motion generated by
the retraction, a5 Opticians have ot late explained.
Nou il any body or thins in morins throueh any
pace oF a siving breadth terminated on both sides by
tiro parallet plains, be urged formard in all parts ot
that space by forces tendins directly Formards torrards
the last plain, and betore its incidence on the Ars
plane, had no motion Forards it, or but an infinicly
litele one; and it the Forces in aII parts ofthat space,
betireen the planes be at equal distances trom the planes
equal to one another, but at several dictances bebisger
Or lels in any siven proxortion, the motion generated
Oy the forces in therhole passage oE the body or chins
chrous

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C721
throush that space Mall be in a subduplicate proportion
ot the Forces, a5 Mathematicians rill casily understand.
And cheretore if the space ot actirity ot the retractins
superticies oE the Body bc considered a5 Tuch a space,
the motion ofthe ray generated by the retractins Force
ot the Body, during its paltase chroush that space
that is the motion BR must bc in a subduplicate
proportion ofthat retracting force: I Cay theretore that
thie square oF the Line BR, and by consequence the
refractins Force of the Body is verr nearly as the den-
sey ofthe Came Bodr. For this will axpear by the Fol.
lorrins Pable, Wrherein the proportion ot thesinesirhich
meature the retraxions of several Bodies, the square
OF BR suppotins C. B an unite, the densities of thc
Bodies ettimated by their specitick gravities, and theie
retractire porrer in respeet ol cheir densities are set
domn in sereral Columns.
The

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The retractine Bodies.
A Pscudo- Topazius, bc-
ClaIs oF Antimony
A Sclenitis
ClaIs vulsar
CryAal OFThe ROCK
TMland Cryetal
Sal Gemma
Alume
Borax
Nicer
Dantzick Virriol
OyIoF Vieriol
Rain Water
Cumm Arabic
Camphire
OytOlive
Lintleed Oyi
Spirit oF Purpentine
AMDaI
A Diamond
of theSines of BR, tomhich and speci. ctivepovere
refraction of force oftBeBo-of theB
vellon Lieht. dy is provor- dy.
onrbo
2310 24) x699
385F+03850000052
17 10 9 2568
6F10 AT X2T3
3T10 20) 1 4025
2510 16 1445
5 10
2778
1710 1T x388
3510 24 22267
2210 15 LFSTF
32+0 2T) 1345
30310 200) 1295
Spiritof ine mell recti.
Hied
3
The Proportion (Phe Sguare os he densit, The refra
ins a natural, Dellucid,
brittle, haier Stone, ot
a vellor Colour
Air
1OtO 7 1042
529+0 39607845
3210 21) X279
10010 7308765
310 2 L25
2210 15 XISFF
4010 27 1948
2510 27 X1626
24t0 9 1’42
10010 4T4949
10
8574
TOT21
12551
12607
72819
23222
13654
14550
Phe retraction of the Air in this Table is determined
Oy that oF the Atmosphere obserred by AMrOnOmeES.
tior if Light pals through many retractins Cubltances Or
mediums oradually denser and denser, and terminated
rith
in respect
es its denu
incidence and the refractine fic eravity of the Body
800r
226
1
272
0800
0990
O923
093-
0874
204
4
416
4864
356
4.
337
O

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(74
rith parallel Curtaces, the Cumm oF all the retractions
Wris be cqual to the linole refraction wrhich it would
have suttered in pastins immediatelr out ot the ArA
medium intothe last. Andthis holdstrue, thouch the
number ot the retractino substances be increaled to infi-
nity, and the distances trom one another as much de-
creased, (o that the Lighe may be retracted in crery
point of its passage, and by continual retractions bent
intoa curre Linc. And theretore the whole refraction
ofLight. in passins through the Atmosphere From the
hichest and rarest part thereot donnto the lovest and
densest part, must be equat tothe retraction wrhich it
vould lutter in passins at likre obliquier out oF a Va-
cuum immediatels into Air of equal density with that
in the lorrest part ot the Atmosphere.
No, by this Table, the refractions oF a Pscudo-T0-
Dazu a Selenitis, Rock CryCal, IMand CrrStal, Vulgar
CtaIS (that is, Sand melted together) and Cila(s of
Antimonr, irhich are terrestrial Hony alcalizate con-
cretes, and Air irhich probably arilestrom uch substances
Dy Fermentation, thoush these De substances very differins
From one another in densier, ret ther have their vetra-
etire porvers almost in the lame proportion to one ano-
theras their densitiesare, exceptins thatthe retractionot
that strange substance Illand- Crystal iS a litele bigger
thanthe rest. And particularir RII, irhich is 3400times
rarer thanthe Pleudo- Popaz, and 4200 times rater than
Ctass of Antimonr, has notrithstanding its raritr the
Came retractire porrer in respect ot its densier irhich
thole urorery dense substances hare in respect oF theirs,
exceptins (0 tar a5 thole trro ditter From one another.
228iIH9

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Asain, the refraction oF Camphire, Oyl. Olive, L int-
lecd OyI. Spirit ot Turpentine and Amber, wrhich aee
tat sulphureous unctuous Bodies, and a Diamond, Which
probabls is an unetuous substance congulated, have their
retractire porrers in proportion toone another as their
densties without anr considerable rariation. But the
retractire porer ot chese unctuous substances is tvo
Or three times greater in respect ot their densities than
the retractire porrers of theformer substances in respect
OF theirs.
Wacer has a retractire porver in a middle desree De-
Ereen chose tro Torts ot lubstances, and probablr is ot
a midale nature. Lor out of it gro all regetable and
animal substances, erhich consist as rell ot sulphureous
fat and inslamable parts, a5 oF carthy lean and alcali
2aLC OHCS.
Sals and Vitriols hare refractire porvers in a middle
decree betrrcen those ot curthy substances and Water,
and accordinsls are composed ot thole tiro lorts of sub.
Cances. For by distillation and rectification ot their
Spirits a great part of them soes into Water, and a sreat
Part remains behind in theform of a diy fixt carth ca
Pable ot vitrification.
Spirit oF Wine has a retractire porver in a midale
derree betrreen thole oF Water and oyly substances, and
accordinsly seems to De compoled ot both, united by
Fermentation; the Water, by means of lome Caline SpI-
rits rith irtich ris impregnated, dissolvins theOyt
and volatizins it by the action. For Spirit OF Winc 1S
inslamable by means oF its oylr parts, and beins dictil-
led olten From SaltoF Partar, srons by every dictilla-
tion more and more aqueous and Aesmatick. And
.1
Chymists

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Chymists obserre, that Vesitables (25 Lavender, Rue,
Marioram, 1c.) distilled per se, betore termentation
vield OyIS Without any burnins Spirits, but acter fer-
mentation rield ardene Spirits ithout Oyls: Which
Ches, thattheir OyI is by fermentation converted into
Spirit. Ther And alco, that it OyIs be poured in smalt
quantier upon termentatins Vesetables, ther distil over
alter fermentation in the Form ot Spirits.
Sothen, by the Foregoins Table, all Bodies Peem to
have their retractire porreis proportional to theu
densities, (or very nearly;) excepting (otar a5 ther
Partake more or less ot Culphurous oyiy particles, and
therebr hare their retractire porver made sreater or
lels. Whence it seems rational to attribute the retra-
ctire porrer oFall Bodies chieAtr, it not wholly, to the
Culphurous parts rith irhich ther abound. For itS
probable thât ail Bodies abound more or less with Sul.
Phurs. And as Lisht consresated by a Burnins:sla(s
acts most uxon Culphurous Bodies, to turn them in-
to tire and Aame; (0, since all action is mutual, Sul-
phurs oushit to act most uxon Light. For that the
action betreen Light and Bodies is mutual, nay appCaF
Trom this Consideration, That the densest Bodies irtrich
retract and reflect Lisht molt stronsly grour hottest in
the Summer-Sun, by the action of the retracted or re-
Aected Lighe.
I hare hitherto explained the porrer ot Bodies to re
Dect and retract, and Thewed, that thin transparent
plates, tibres and particles do, according totheir tereral
thicknesles and densities, retleet sereral lorts ot raYS,
and thereby appear ot leveral COlours, and by conte-
quence chat nochins more is requisite For producins ald
thC

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the Colours oF natural Bodies than the several sizes anc
densities oF their transparent particles. But Wwhence it
15 that thele plates, fibres and particles do, accordins
to their sereral thicknesses and densities, ressect severul
lorts oFraYS, Jhare not yet explained. Lo sire lome
intioht into this matter, and make may for understan-
dins the next Part oF this Bo0k, I Mall conclude this
Part with a ter more Propositions. Those irhich pre-
ceded respeet the nature of Bodies, thele the nature ot
Lishe: For both must be understood betore the reason
ot their actions upon one another can be KnOWM. And
Decaule the last Propolition depended upon the velo-
citu oF Light, L will besin rith a Proposition of that
Kind.
PR OP. ZI.
Lieht is propacated from luminous Bodies in time, and
spends about seven or eioht minutes of an hour in passine
From the Sun to the P artb.
Thiswas oblerred tirst by Romer, and then by others,
by means of the Eclipses ot the Satellites ot Fupiter.
tior these Fclipses, Wrhen the Farth is betreen theSun
and fupiter, happen about seven or eisht minutes fooner
chanther ousht to do bythe Pables, and Wrhen thekarth.
is berond the Sun ther happen about seren or eightmI-
nutes later than they ousheto do; the realonbeins, TMaL
the Light of thesatellites has Farther to g0 in the latter
case than in the Former by the Diameter of the LarthS
Orbit. Some inequalities ot time mar arile trom the
excentricities oF the Orbs ofthe Satellites; but thole
CanNOE anliver in alI che Satellites, and aC all FIMeS
10

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C
cothe polition and distance oF the Farth From the SuM.
The mean motions ot Fupiters Satellites is allo tritter
in his descent From his Aphelium to his Perihelium,
than in his accent in the ocher halt oFhis Orb: But this
inequalitr has no respect to the position of the Farth,
and in the three interior Satellites is insensible, as I And
by computation trom the Theory oCtheir sravier.
ERO P. XII.
Lvery ray of Lieht in ils passare throush any refra-
ctine surface i5 put into a certam transient constitution
or state, rehich in the prooress of the ray returns at
equat intervals, and disposes the ray at every return
1o be casily transmitted throuoh the next refractine sur-
face, and betreeen the returns to be easily reflected by
it:
This is manifest by the gth, oth, 12th and PGtM OB.
Terrations. For Dy thole Oblerrations it appears, that
one and the Pame Port ot rars at equal Angles ot inci-
dence on ary thin transparent plate, is alternatelr reAe-
Ated and transimitted For manz succections accordinely.
a5 the chickness oF the plate increases in arithmetical
prosreltion oF the numDers O, 1, 2, 3, 49 5, 6,7, 8,dc.
To that if the Arst resexion (that vrhich makes the AeA
or innermost ot the Rings oF Colours there described)
Demade atthe thickness L, the cars Pall be transmitted at
the thickneses 0, 27 4, 6, 8, 10, 12, 8c. and thereby
make the central Spot and Rings oF Light, irhich ap-
pear by transmission, and be reflected at the thicknels
2375, 7, 9, TI, 15c. and thereby make the Rings irhich
appCaI

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appear by rellexion. And this alternate reflexion and
transmistion, as Lgather by the 24th Obserration, con-
tinues For abore an hundred vicissitudes, and by the
the Oblerrations in the next part of this Book, Formany
thoulands, beins propasated trom onc Turtace ot a Glals-
plate to the other, Though the thicknels ot the plate
De a quarter ot an Inch or above: 50 that this alter-
nation seems tobe propasated trom every retractins
lurtace to aM distances without end or limitation.
Phis alternate reflexion and retraction depends on
both the Curtaces ot every thin plate, becaule it de
Dends on their dittance. By the 2rth Observation, It
cither Curtace oF a thin plate of Muscory-CilaIS DC vet-
ted, the Colours caused by the alternate retlexion
and refraction grorr faint, and theretore it depends on
them Both.
Itis theretore performed at the second Turtace, FOr
iF it avere performed at the ArHt, betore the rays ar
rire ac the second, it vould noc depend on the le-
cond.
IE is allo insluenced by some action or dispoltion,
propasated trom the tirst to the second, becaule other-
rise at the second it mould not depend on the tirst. And
this action or dispolition, in its propasation, intermits
and returns by equal interrals, because in aIl its pro-
sress it inclines the ray at one distance From the ArI
lurtace to De reslected by the second, at anottier to De
transmitted by it, and that by equal interrals for innu-
merable ricissitudes. And because the ray is dispoled
to reflexion at the distances 1, 3, 5, 7, 9, bc. and t0
transinission at the distanceS O, 2, 4, 6, 8, 10, dc, (For
us transmission chroush che trst surtace, is at the di
RANCC

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BC
Rance 0, and it is transmitted throuoh both tose-
ther, il their distance be intinitely licele or much lels
than L) the disposition to be transmitted at the distances
274, 6, 8, 10, Oc. 15to De accounted à recurn of the
Came disposition which the rar Arst had at the distance o,
that is at its transmission chroush the trst retractins (ur-
Face. AII erhich is the thins lould prove.
Whatkind et action or dilpontion tnis is Whether
it consist in a circulatins or a vibratins motion of the
rar, or of the medium, or Comethins else: I do not
here enquire. Thole that are averse trom assentins to
auy nerr discoreries, but such as ther can explain by an
lypothelis, may for theprelent suppole, that as Stones
by fallins upon Water put the Water into an undula-
tins motion, and all Bodies by percustion excite ribra-
tions in the AI; (0 the rays oF Lishit, by impinsins on
auy retractins or reflectins surtace, excite ribrations in
the retractins or reflectins medium or substance, and
by excitins them agitate the solid parts of the retractine
Or reflectins Body, and by agitatins them cause theBody
to siorr arm or hoc; that the vibrations thus excited
use propasated in the retractins or reflectins medium
or substance, much after the manner that ribrations are
propagated in the Air tor causins Cound, and more
taster than the rays (0 as to overtake them; and that
irtien any ray 15 in that part ofthe ribration wrhich con-
ipires rith its motion, it casils breakes through a re-
tractins Curtace, but irhen it is in the contraer part ot
che vibration erhich impedes its motion, it is casily
refsected; and, by consequence, that every rar is suc-
celsirely disposed to be ealily reflected, or casily tranl-
mitted, by every ribration which overtakes it. But
Wrhether

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81
Wrhether this Hypothels be true or FaIsC I do not here
consider. L content my selF writh the bare dilcorers,
That therars of Light are by lome cause or other alter-
hatels disposed to be ressected or retracted for many vi-
cissitudes.
DFFTNTTTON.
The returns of the disposition of any ray to be reflected
Preiu cau its Fits ot ealy rellexion, and those of
its disposition to be transmitted its Fits oF easy trans-
mittion, and the space it passes betreeen every re-
turn and the next return, the Interral oF its
FItS.
P R O P. ZTII.
The reason reby the surfaces of au thicte transparent
Bodies reflect part of ibe Fioht incident on them, and
refract the rest, is, that some rays at their incidence are
in Fits of easy reflexion, and others in Fits of easy trans-
mission.
Phis may be sathered trom the 24th Observation
Wrhere theLight reflected by thin plates oF Air and Crlals,
irtrich to thenaked Fre appeared erenlr irhite all over
theplate, did chrough a Prilm appear rared rith mans
successions oF Lisht and Darkenels made by alternate Ats
ot ealy rellexion and easy trantmission, the Prim
severins and distinguistring the rares ot irhich the
White reflected Light ras compoled, as as explained
abore.
st mm
And

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82
And hence Light is in fies ot easy resterion and casy
transimistion, betore its incidence on transparent Bodies.
And probably it is put into such AES at its Rrst emisiOn
From luminous Bodies, and continues in them durins
aII its progress. Por these trs are of a lastins Nature,
25 Will appear by the next part oF this BoOk.
In this Proposition I suppole the transparent Bodies
tobe thick, because if the thicknels ot the Body BC
muich less than che interval et the AIS OF eat rellexion
and transmission of the rays, the Body lolethits rerectino
porver. For it che rays, irhich at their enterins into
the Body are put into fts of ealy transmistion, arrive at
the turthest surtace ot the Body betore they be out oF
those Ats they must De transmitted. And this is the
reason whr Bubbles oF Water lose their reflectinqe porver
Wrhen ther oror very thin, and why all opake B0.
dies irtien reduced into very (mall parts become trans-
Parent.
P ROP. XIV.
Those surfaces of transparent Bodies, Which if the ray
be in a fit of refraction do refract it most stronoly, if the
ray be in a fit of reflexion do reflect it most easily.
For re Bhemed abore in Prop. 8. that the cause ot
reflexion is not the impingins ot Light on the solid
imperrious parts ot Bodies, but lome other porrer by
intrich those solid parts aet on Lighe at a distance. We
Chered also in Prop. 9. that Bodies retlect and retract
Lighe by one and the lame porver rariously exercised in
various circumstances, and in ProD. L. that the mot
Aronsly retractins surtaces refeet the most Light: AII
urtrict

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3
irtrich compared together crince and ratity both this
and the lact Propolition.
P RO P. XV.
In any one and the same sort of rays emersins in ans
Anele out of any refractine surface into one and the same
medium, the interval of the folloreins fits of easy reflexion
and transmission are either accurately or very nearly, as
the Rectanele of the secant of the Anole of refraction, and
et the secant of another anole, rehose sine is the first of
L0b arithmetical mean proportionals, betreeen the sines
of incidence and refraction counted from the sine of re-
fraction.
This is manifest by the 7th Obserration.
P RO P. XVI
In several forts ofrays emeroine in equal neles out
ef any refractins surface into the same medium, the inter-
vals of the follorvine fits of easy reflexion and easy trans
mission are either accurately, or very nearlys, as the Cube-
roots of the Squares of the lenoths of a Chord, rehich sound
the notes in an Pisht, Col, la, Fa, Col, la, min Fa, Coly reit h
al their intermediate derrees ansaverins to the Colours os
those rays, accordins to the Analogy described in the se
venth Fxperiment of the second B0ok.
Chis is manifest by the 13th and r4th Obserrations.
MII 2
 dac

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(84
PR O P. ZVII.
TFrays of any one sort pass perpendicularius into severat
mediums, the intervals of the fits of easy reflexion and
transmission in any one medium, is to those intervals in
any other as the sine of incidence to the sine of refraction,
rehen the rays pass out of the first of those truo mediums
into the second.
This is manifest by the roth Obserration.
eROP. XVIII.
TF the rays rehich paint the Colour in the confine of
vellore and oranse pass perpendicularlys out of any medium
into dir, the intervals of tbeir fits of easys reftexion are
the sth part of an Tuch. And of the same leneth are
the intervals of their fits of easy transmission.
This is manifest by the bth Obserration.
From these Propolitions it is eal to collect the in-
tervals ot the AIS et easy rellexion and casy transinis-
ton ot any sort ot rays retracted in any Anole into
any medium, and thence to kno, Wrhether the rays
Mail De reflected or transmitted at their sublequent
incidence uxon any other pellucid medium. Which
thins beinq usetul for understanding, the next part ot
this Book iras here tobe set dorn. And For the lame
realon L add the trro Collorrins Propolitions.
eLLet.

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P R OP. ZIX.
I any sort of rays fallins on the polite surface of any
pellucid medium be refected bacte, the fits of easus re-
fexion rehich they have at the point of reflexion, palt
stiu continue to return, and the returns sal be at di-
stances from the point of reflexion in the arithmetical
prooression of the numbers 2, 4, 6, 8, 10, 22, _C. and be-
treeen these fits the rays sai be in fits of easy trans-
mission.
FOT CinCe thC AES OF casy rellexion and easy tran-
mission are ot a returnins nature, there is no reason
rtr chele Ats, irhich continued till the cay arrired at
the reflectins medium, and there inclined the ray to
reflexion, Bould there cease. And it the cay at the
point ot reflexion ras in a ft ot casy resexion, the
progression oF the distances ot thele tuts trom that point
must besin From o, and (0 DC OF the numDerS O, 2,4,
6, 8, c. And theretore the prooression ot the di-
sances of the intermediate AIS oF casY tran(missIOn ZCC
koned From the lame point, must be in the progrestion
oF the odd numbers 1, 3, 5,7, 9, Dc. Contrary towrtrat
happens wrhen the Ats are propasated trom points et
retraction.
PROP. XZ.
The intervals of the fits of easy reflexion and easis
transmission, propasated from points of reflexion into any
medium, are equal to the intervals of the litee fits rehict
the same rays vould have, if refracteu into the same
medium

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C86
medium in Anoles of refraction equat to their Inoles of
reftexion.
For wrten Licht is reflected by the second lurtace ot
thinplates, it soes out afterrards Freely at the Arst sur-
tace to makre the Rings oF Colours wrhich appear by
rellexion, and by the frcedom ofits egrels, mâkes the
Colours oF these Rings more ririd and Crons thanthole
irhich appear on. the other sde oF the Plates by the
transmitted Light. Pherefected rassare theretore in
Ats oF casy transmission at their egress; irtrich would
not alirars happen, it the intervals ot the Aes within
the plate alter rettexion irere not equal both in lensth
andnumber totheir intervals beforeit. And this contrrms
allo theproportions let donn in the former Proposition.
Foritthe rars both in soins in and out at thetrst Curtace
be in fits of eals transmittion, and the interrals and num-
bers ot those tts betrreen the Arst and second Curtace,
betore and alter reflexion, bc equal; the distances ot
the Tts oF easy transmistion trom cither Curtace, must be
in the lame proorection alter rellerion as betore; that
15, trom the tirst Curtace wrhich transmitted them, in
theprogreltion ot the eren numbers O, 27 4, 6, 8, 1c.
and from the second ihich retlected them, in that ot
the odd numbers 2, 3, 5, 7, Sc. Buctheletro Pro-
positions rill become much more erident by theobser
vations in the follomins part of this BoOk.
IHF

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 LL La
e
e
 oa
dI
E A R T IV.
Observations concernins the Reflexions and Colours of
thicte transparent polisted Plates.
PrETere is no Glass or Speculum ho well Poerer
polictred, but, besides the Light erhich it retracts
or rellects regularir, scatters every ray irresularty à
Faint Liphe, Dy means ot irtrich the polithed surtace,
wrhren illuminated in a dark Room by a beam ot the
Suns Lighe, may be casily seen in aIl positions oF the
tire. There are certain Phaenomena ot this scattered
Lighe, irhich erhen IArs obserred them, secmed very
Arange and surprisine to me. Uy Obserrations vere
25 FoIIOWS.
B5.

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OB. S. L.
The Sun inins into my darkened Chamber chrouon
a TIOlC: Ot an Tuch vide, I let the intromitted beam
oF Light Fall perpendicularir uxon a Citals Speculum
oround concare on one lide and convex on the other,
toa Sphere ot Are Feet and eleren Tnches Radius, and
quicke- silrered orer on the conrex lide. And holdine
a Wrtrite opakce Chart, or a Juire of Paper at the Center
ot the Spheres toirhichthe Speculum ras ground, that
isqe at the distance ot about tive Feet and eleren Inches
from the Speculum, in such manner, that the beam ot
Lieht might pass throuch a little FTole made in the
middle oF the Chart to the Speculum, and thence be
reflected back to the lame HIole: I observed uxon the
Chart foux or fire concentric Trises or Rings oF Colours,
like Rain-Bows, encompassine the HIole much atter the
manner that those, irhich in the Fourth and tollowins
Obserrations ofthe tirst part of thisthird Book appeared
Detireen theObject. Cilalles, encompased the black SpOt,
buc vet larser and fainter than those. Thele Rings a5
ther srer larser and larser became diluter and Faintei,
10 that the tifth iras scarce vitible. Vet lometimes,
irhien the Sun Mhone very clear, there appeared faint
Lincaments ot a sixth and seventh. IF the distance ot
theChart trom the Speculum as much greater or muctu
lels than that oF six Fcet, the Rinss became dilute and
vanismed. And il the distance ot the Speculum From
the Windon as much sreater than that oF six Feet,
the rertected beam or Light rould De lo brond at the
distance oF six Feet trom the Speculum erhere the Rings
appeared,

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(89
appeared aS Lo obseure one Ox twO OPthe innermost
RingS. And theretore L uluallr placed the Speculum
at abOUE SIX Feet From the Windoi; (O thaE IES FOCUS
miohethere fall inrith the center oF its concariey at the
Rinss upon the Chart. And this posture is alirays to
be understood in the follorrins Oblerrations irhere no
Other is exprest.
OBS. C+.
The Colours of these Rain-bours Cucceeded one ano-
ther From the center outrards, in the same form and
order rith those irhich rere made in the ninth Obler-
vation oF the Arst Part oF this BoOK by Lighit not re-
Rected, but transmitted through the trro Object- CilaReS.
FOr, First, there as in their common center a white
round Spot of faint Light, Pomething broader than the
resected beam ot Lioht; wrhich beam Cometimes fel
uxon the middle of the Spot, and Cometimes by a little
inclination of the speculum receded From the midale,
and lest the Spot prhite to the center.
This ehite Spot mas immediately encompassed mith
a dark orey or russet, and that dartness ith the Co-
Jours oF the Frst Tris, Wrhich rere on the inside next
the darknels a litele riolet and indico, and next to that
a blue, irtich on the outhde srer pale, and then sUC-
cecded a little greenistr vellorr, and alter that a briehter
vellorr, and then on the outrard edse of the lris a red
Wrhich on the outside inclined to purple.
This Tris wras immediately encompassed rith a se
cond, irhole Colours vere in order trom the inside
VI
Ont

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L90
outwards, purple, blue, ercen, sellon, lisht red, a red
mixed rrich purple.
Then immediately folloed the Colours of the chird
Tris, irtich arere in order outrrards a green inclimIns
to purple, a 800d ereen, and a red more brishE chaM
that ot the Former Iris.
Lhe tourth and fitth Tris secmed ot a bluistr green
Within, and red without, but (o tamtly that it ras dit
ficult to discern the C Olouis.
OBS. TTI.
Meaturins the Diameters oF these Rings upOn thC
Charc as accurately a5 l could, I tound them al(o In
the lame proportion to one anocher ith the RInSS
made by Lasht transmitted chroush the tuo Object-
ClaBes. For the Diameters of the tour trst ot the
brishe Rinss mealured betireen the brixhtest parts ot
cheir orbits, at thedittance ot six Feet trom che specu-
lum Were 11
163
N 2123 38 Luches, Whole squares are In
arichmetical prosrestion ot the numbers 1, 2, 3, 4. IE
che wtite circular Spot in the midale be reckoned
amonest the RinsS, and its central Lastt, irhere it
Teems to be most luminous, be put equipollent to an
intiutely little Rins; the squares olthe Diameters ofthe
Rings wilt be in the progrestion O, 1, 2, 3, 4, dc. I
mealured also the Diameters ot the dark Circles be-
circen chele luminous ones, and tound theis iquares
in the progrection oE the numbers;, 15, 23, 3:, c.
the Diameters oF the trst Pour at the distance ot six Fcet
trom the Speculum, beinS 16, 216, 23, 370 Inches. IE
che distance ot the Chart trom the Speculum iras in-
crealed

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Oc
crealed or diministred, the Diameters oF the Cireles rere
increased or diministied proportionally.
OB5.
IV.
Bothe analoor Betwreen these Rinos and those de
Seribed in theObservations oF the ArstPart OF this BOOk,
lEuspected that there rere manr more of them erhich
Epread into one another, and by intertering mixed their
Colours, and diluted one another (o that ther cousd
not be seen apart. Pviemed them theretore throuoh,
Prism, 25 I did those in the 24th Obserration oF the
Arst PaxE OF this BOOK. And Wrhen the Prism Was (O
placed as by refractinq the Lighe oF their mixed C0-
lours to separate them, and distinguistr the Rings trom
onc another, as it did those in that Obserration, I could
then sec them distincter than betore, and casily num-
per ejoht or nine ot them, and Cometimes trrelve pr
thirteen. And had noc their Lixhe been (0 very faint,
Iquection not but that I mighe have scen many more.
BS
Plucino a Prism at the Windom to retract the intro-
mitted beam ot Lioht, and cast the oblone Spectrum
OF ColourS on the Speculum: I corered the Speculum
Wvich a black Paper irhich had in the midale ofit a HIole
to let ans one ot the Colours pals throuoh to the Spe
culum, Wrhils the rest ivere intercepted by the Papei.
And nou I Found Rinos of that Colour only irtrich Fel
upon the Speculum. IF the Speculum iras illuminated
vich red the Rinss ivere totally red rith dark inter-
Nn 2
Val5,

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vals, it with blue they rere totally blue, and (0 ofthe
Other COlours. And wrhien they irere illuminated with
any one Colour, the Squares ot their Diameters mea-
Fured betreen their most luminous parts, vere in the
arithmetical prosrettion of the numbers 0, 1, 2, 3, 4, anc
the Squares of the Diameters of their dark intervals in
the progrestion ot the intermediate numbers ;, 15 237 3:3
But if the Colour as raried they raried their magni-
tude. In the red ther vere largest, in the indico and
violet least, and in the intermediate Colours vellon,
oreen and blue; ther ivere ofleveral intermediate bis-
nesles anlirerins to the Colour, that 15, greater in vel-
lor than in sreen, and greater in green than in blue.
And hence Lhnem that irhen the Speculum iras illumi-
naced rith wrhite Lishe, the red and rellor on the out
Tide ot the Rinos iere produced br the least retransible
rays, and the blue and violet by the most retransible,
and that che Colours ot each Rins spread into the. C0-
Jours of the neisibourins Rines on cither side, atter
the manner explained in the trst and second Part ot this
Book, and by mixins diluted one another (o that they
coutd not be distinguistred, unless near the center Wrhere
theravere least mixed. For inthis Obserration I could
sec the Rines more distinctiy, and to a greater number
thanbetore, beins able in the vellor Lighe to number
eishtor nine ot them, belides a taint Chador ot a tenth.
Lolatissy iny selt hor muchthe Colours oF the several
Rings Spread into one another, I meatured the Diame-
ters ot the second and third Rines, and Found them
wrhen made br the contine ot the red and orange to be
the Pame Diameters irtien made by the contine ot blue
erd indico, asg t0 B, ot chercabouts. F.OF iC Wus harc.

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to determine this proportion accuratelr. AIIO theC ir-
cles inade successirety by the red, vellorr and green,
differed more from one another than those made succel-
lively by cheoreen, blue and indico. For the Circle
made by the violet ras t00 dark to bC seen. Po Carry
on the computation, Let us theretore suppole that thC
differences oF the Diameters of the Circles made by the
ontmost red, the contine of red and oranse, the contine
OF oranse and vellor, the contine of vellon and green,
the contine oF green and blue, the contine ot bluc and
indico, the contine ot indico and violet, and outmost vio-
let, are in proportion as the differences of the lenoths
oF a Monochord irhich Cound the tones in an Fignt;
sol, Jan fa sol, la mi fa sol, that 15, 25 the numDerS 5
Iby 20 127 39 27 18. And iFthe Diameter ot the Circle made
by the contine of red and oranse bc g A, and that ot
the Circle made by the contine ot blue and indico be
8 A a5 abore, their diterence 9 A - - - - 8 A wiil DC t0
the ditterence of the Diameters ot the Circles made Dy
the outmostred, and br the contine ot red and orange,
25 25 F 22 F 22 + 27 t05, That 15 25 2, 103 Or 8 +0 Z, and 10
che difference ot the Circles made by the outmost violet,
aud by the contine ot blue and indico, 25 18 + 12 F 12 + 2
10 27 + 10, that 15, 45 27 10 31, Or 45 16t05. And there.
Fore thele differences ill be s A and 20 A. Add the
Fixs +09 A and subduet the last From 8 A, and vou
Wvis hare the Diameters ot the Circles made by the
least and most retranoible raYS s A and EZ A. These
Diameters are theretore to onc another 25 75 t06I=Or
50+0 AT, aud their Squares a5 2500 t0 1681, that 15,
45 3 t0 2 very neartr. Which proportion ditfers not
much trom che proportion ol che Diameters ot che
Circles

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94
Cireles made by the outmost red and outmos violet in
the r2th Obserration oF the Arst part oF this Bo0k.
OBS. VI.
Placins my Fye rrhere thele Rings appeared plainest,
ICarr the Speculum tinsed all over rith rares ot CO-
lours (red, vellor, sreen, blue;) like those irtrich in
theObserrations of the Arst Part ot this Book appeared
betireen the Object-Cilases and upon Bubbles oF Natei.
but much larger. And atter the manner ot thole, they
vere of rarious magnitudes in various politions of the
Eire, Cirelling and Crinkins a5 I mored my tire this
War and thatmar. Ther ivere Formed like AreS OF
concentrick Circles as those irere, and irhen my fiye
ras ovrer agains the center of the concaritr ot the Spe-
culum (that 15, 8 Fcet and 10 Tuches distance trom the
Speculum) their common center ras in a right Line
rith that center ot concarier, and with the Hiole in the
Windor. But in other poltures ot my fivetheir center
had other positions. They appeared by theLight oF
the Clouds propasated to the Speculum throush the
TTole in the Windor, and irhen the sun Bone throuoh
that ITole uxon the Speculum, his Light upon it Wras
ot the Colour of the Ring wrhereon it Fell, but by its
Splendor obscured the Rings made by the Light ot the
Clouds, unless rhen the Speculum ras remored to a
sreat distance trom the Windor, Cothathis Lisht uxon
ut mishit be broad and Faint. By varyins theposition ot
my Lese, and morins it nearer to Or Farther from the
direct beam ofthesuns Lisht, the Colour of the Suns
sefected Liehe constantly raried upon the Speculum,

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L9G
as it did uxon my Fye, the Came Colour alvays aP.
Pearins to a By. Rander upon my Leyc irhich to me ap-
Peared upon the speculum. And thence PHner that
the RingsoFColours upon the Chart irere made brthese
reflected COlours provasated thither from the Specu-
lum in sereral Angles, and that their production de-
pended noc upon the termination of Lisht and Shad-
dor.
OB5. VII.
By the AnalosY oF alI these Phaenomena With thole oE
the like Rinss oF Colours described in the trst Part oF
this Book, it scemed to me that these C OlOurS were
produced by this thick plate of Clals, much alter the
manner thac thole vere produced by very chin
plates. For, upon trral, I Found that it the Ouick-
lilrer vere rubbed off trom the back- side ot the Specu
lum, the Class alone ould, cause the Tame RiInsS Ot
Colours, buc much more faint thanbetore; and there.
tore the Phaenomenon depends not upon the Cuick-
Elver, untels Cotar as the Duiek-silver by the increa(in
the reflexion oFthe back. side oF the Cilals increales the
Light oF che Rings oF Colours. Ltound also that a SPC.
culum ot metal rithont Cilals made lome rears lince
for opticalules, and very ell irousht, produced none
OF thole Rings; and thence L understood that thele
Rinss arise not trom one specular surtace alone, but
dependupon thetro surtaces ofthe plate ot Cilass Wrhere,
oFthe Speculum ras made, and upon che chicknels ot
che Cilais betireen them. For a5 in the7th and T9th
Oblerrations oE che tirst Part oE this B0ok a chin plate

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LdC
OF RIr, Nater, Or Gla(S OF an even thickeness appearect
oF one Colour when the rars rrere perpendicular to it
ot another wrhen ther ivere a little oblique, ot another
artien more oblique, ot another when sill more oblique,
and (o on; Pohere, in the sixth Obserration, the Lioht
ertrich emersed out ot the Glass in sereral obliquities,
made the Cilals appear oF sererat COlours, and beins
propasated in those obliquities tothe Chart, there pain-
ted Rinos ot thole Colours. And as the reason wrty a
thin plate appeared of several Colours in sereral obli-
quities oF the rars, ras, that the rays otone and the lame
Tort are reflected by the thin plate at one obliquity and
trantmitted at another, and thole of other POrtS trans-
mitced erhere these arc reflected, and refected irhere
thele are transimitted: S0 the reason why the thick
plate oF Cilals irhereot the Speculum ras made did ap-
Pear ot rarious Colours in rarious obliquities, and in
those obliquities propasated those Colours tothe Chart.
ras, that the cars oF one and the Came lort did at one
obliquitr emerse out oF the Cila(s, at another did not
emerse but irere refected back torrards the Ouick- siI-
ver by che hither surface of the Clals, and accordinsly
a5 the obliquitr became greater and greater emerged
and rere retlected alternately FOr many suCCesIOnS, and
that in one and the lame obliguity the rays oF one TOrt
avere reflected, and those ot another transmitted. This
is manitest by the Rest Obserration oF this BOOK: FOF
in that Obserration, irhen the Speculum iras illumi-
nated by any one of the prisinatick Colours, that Light
made many Rines oFthe lame Colour uxon the Chart
ith dark interrals, and theretore at its emergence out
oE the Speculum as alternately transmitted, and not
trans.

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tranmitted From the Speculum to the ChaxE FOr many
luccessions, accordins to the rarious obliguities of its
emergence. And irhen the Colour cast on the Specu-
lum br the Priim ras varied, the Rings became ot
theColour cast on it, and raried their bigness vrith their
Lolour, and theretore the Lighe ras now alternatelv
transmitted and not transmitted from the Speculum to
the Lensat octier obliguities than betore. It scemed to
me theretore that these Rings vere oF one aud the lame
orisinal rith those of thin plates, but yet rith this
difference that those ot thin plates are made by the al-
cernate reflexions and transimistions ot the rars at thC
Second surface ot the plate alter one passase throuoh it:
But here the rays go trrice throuoh the plate betore
ther are alternately reflected and transmitted; Ars,
ther so throuoh it From the Ars Curtace to the Onick-
Eilver, and then return throueh it From the Ouick- silver
to the Arst Purtace, aud there are cither transmitted to
the ChaTE Or refected back to the Ouick-Silver, ac
cordinslr a5 ther are in their AtS oF ealie retlexion or
transnission when ther arrire at that surtace. For the
interrals oF the Res oF the rars irhich FaII perpendicu-
larly on the Speculum, and are reflected back in the
same perpendicular Lines, by reason ot the equality ot
chese Angles and Linesare of the same lensth and num-
ber within the Glals atter refexion as betore by the
T9th Proposition oF the third Part oF this B0OK. And
theretore lince aII the rays that enter throush the Ars
Turtace arc in their AES ot car transmision at their en-
trance, and as many ot these as are reffected by the le
cond are in their AEs oF casy reRlexion there, aII these
nust beagain in their fits or ealy transmission at their
TCTUTI

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returm to the trst, and by consequence there so out ot
the Citals co che Chart, and form apon it the white
Spot of Lishit in the center ot theRingo. For the rea-
son holds 800d in all Torts oF rays, and theretore al
Corts must 80 out promiscuoussy to that Spot, und by
cheur mixture caule it to be irhite. Buc the intervals
ot the Ats oF thole rars wrhich are rellected more ob-
liquely thanther enter, must be greater alter recexion
than betore by the 15th and 20th Prop. And thence
it may happen that the rars at their return to the first
Curtace, may in certain obliquities De in Ats ot caly re-
Aexion, and return back to the Ouick- silver, and in
other intermediate obliquities beasain in Ars oE ealy
transmission, and (0 50 out to the Chart, and paint on
it the Rinss oF C Olours about the white Spot. And
becaule the interrals of the tts at equal obliguities are
sreater and ferver in the less retransible rays, and lels
and more numerous in the more retransible, theretore
the lels retransible at equa l obliquities all make terver
Rings than the more retransible, and the Rings made
by thole Mall be larger than the like number of Rings
madeby theso; that is, the red Rinss MaII be larger
than the rellor, the vellor than che green, the green
than the blue, and the blue than the riolet, a5 they
ivere really tound to be in thesth Obserration. And
theretore the tirst Rins oF all Colours incompassine the
Wrhite Spot oF Lishit Ball De red rithout and violet
within, and vellor, and srcen, and blue in the midale,
25 it ras found in the lecond Oblerration; aud thele
Colours in the lecond Rins, and thole that Follo Chal
De more expanded till ther spread into one anothei
and blend one another by interterine
Lhesc.

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(99
These Peem tO bC THC ReAIONS OF these RingS in gC
neral, and this put me upon obserrine the thicknels oF
the Glass, and considerins wrhether the dimentions and
proportions ot the Rines may be truly derived From il
by computation.
OBS. VIIB
I mealured theretore the thicknels oF this concaro-
conrex plate oF Gla(s, and found it every- Wwhere i oF an
Inch precisetr. Noi, by the bch Obserration oF the
first Part OC this BOOK, a thin plate OF Air tran(mitS the
briohtest LisHEOF the ArA Rine, chat is the brighe vel.
lo, Wrhen its chickness is the epo tM Paxt OF an TnCH,
and by the roth Obserration ot the lame part, a thin
plate oFClalo transmits the lame Lighe oF the same Rins
iohen its thickness is less in proportion oF the sine ot
retraction to the sine of incidence, that is, When its
chicknels iS che tM OF in tM Part OF an LncH, suP-
Potins the sines are aS TY tO F7. And if this chicknels
De doubled it transmits the lame bright LighE oF the
Second Ring, it cripled it transinies that ot the chird,
and (0 on, the briohe vellon Light in all thele cales be-
ino in itS ftS oFtransmission. And theretore if its thick-
ness be multiplied 34386 times (0 as tobecome: oF an
Inch ic transmits che lame brighe LioHt oFthe 34386FH
Ring. Suppose this be the bright vellon Lighe trans-
mitted perpendicularty from the reflectins conrex sde
OF the Gilais through the concare side tothe Wrhite Spot
in the center oF the RingS OFColOurS On theChaRE: And
by a rule inthe seventh Obserration in the ArH PaPF OF
he srA BOOK, and by the 25th and 20th PropOsitiOnS
0

## Folio 100 — 1677894601:0276
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10O
OEthe third Part of this B00k, it the rays be made ob.
lique to the Clals, the chicknels oF the Glals requia
site to transmit the lame bright Light oEthe lame Rine
in any obliguitu is to this thicknels oF: oF an Inelu, 45
the lecant oF an Ansle wrhose line is the tirst oF an hun-
dred and Ex arichmetical means betrreen the sines ot
incidence and refraction, counted trom the fine et inci.
dence wrhen the retraction is made out ofanr plated B0-
dy into any medium incompalsins IE, That 15, In tls Cale,
OUE OF GEIA(S InEO AIT. NoW if the thickness oFthe GElaIS
De increaled by degrees, (0 as to bear to its tirit thicknels.
viz. That OE a quarter oF an Lnch) the PropOTtIOnS
wrtrich 34386 (the number oF fts of the perpendicular
FayS in Soins throush the Cilals torards thewhite SpOt
in the center oE The RInGS,) hath 10 34385, 34384,
34383 and 34382 (thenumbers oF thetits otthe oblique
cays in soins throueh the Glass torards the tirst, le
cond, third and Fourth Rinos oF C olours,) and it the
ErHt thickness be dirided into 100000000 equal Parts.
the increaled thicknesses Wrill DC 100002908, 100005816,
200008725 and 100011633, and the Angles oF wrhuch thele
chickneses are secants willbe 26 13, 375, 45 6 and
2 26 theRadius beins 100000000; and the sines ot
these Ansles are 762, 1079, 132F and 1525, and the
proportional tines oFretraction 1172, 1659, 2031 anc
2345, the Radius Deins 100000. Lor since the bnes
ot incidence out oF CilaIs into AII are to the neS
Ot retraction 25 Ir t0 17, and to theabore-mentioned
secants. a5 TI to the Ars OF 10b arithmetica) means
betreen TY and 17, that 15 45 LL FO 1I 166 thole se
cants vill De to the sines ot retraction a5 11586 10. 17
and by chis Analogy ill sire chele sines. S0 chen

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CTOT
it the obliquities of the rays to the concare Turtace ot
the Citass De luch thac cho sines oE their retraction I
passins out oE the Cilass throuph chac Curtace into the
AIr BC 2172, 7659, 2031, 2345, chebrishe Light ot
the 3438bch Rins Mall emerse at thechicknesses oF the
Ctals irtrich are to = ot an lnch 45 34386 10 34385,
34384, 34383, 34382, respectirely. And theretore it
the chicknels in allFhele cales be=OF an lnch (a5 it 1S in.
the Cilalo oFirtich the Speculum was made) thebrishe
LiohtoF che 34385th Rins Mall emerse irhere the line
OFretractionis 1172, and that oF the 34384Fl, 384383t
and 34382Fh Rins wrhere the (inc 15 1659, 203.1, a1d.
2345 respectirey. And in thele Angles oF retraction
che LishoF chele Rines MaIl be propasated trom the
Speculumto the Chart, and there paint Rinss about the.
Wrhite central round Spot oF Lighe wrhrich re laid wras
the LighE oF the 34386ch Rins. And the Semidiame
ters oF theleRinss Mall lubtend the Ansles ot retraction
made at the concare Curtace ot the Speculum, and by
consequence their Diameters MaM De to the distance ot
the Chart trom the Speculum as thole sines ofretraction
doubled are to the Radius chat 15 45 1172, 1659, 2031,
and 2345, doubled are t0 100000. And theretore it.
the distance of the Chart trom the concare surtace ot
the Speculum DC sIX Feet (a5 it ras in the third ofthele
Obserrations) the Diameters oF the Rings of this bright
vellon Lishe uxon the Chart MaII bC 1688, 2389,
2925, 3375 Inches: For thele Diameters are to6 Feet
as theaborementioned lines doubled are to the Radius.
Nor chese Diameters of thebrighe vello RingS, thus
tound by computation are the very lame with thole
tound in che chird otthele Oblerrations by mealurins
cMCM.

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C10
them (viz. Writh 113, 23, 22 and 33 Tnches, and there.
Fore the Theory ot deriring these Rines From thethick-
ness oFthe plate oF Glals of ertrich the Speculum Was
made, and from the obliguier of the emersins cars agrees
rith the Obserration. In this computation I have
equalled the Diameters ot the briont Rinos made by
Lieht ot aIl Colours, to the Diameters ot the Rinos
made by the brighe vellor. For this vellor makes the
briohtest part oF the Rines oF aII ColOuES. IF rou deBre
the Diameters oF the Rings made by the Light oF any
other unmixed Colour, rou may find them readily by
puttins them to the Diameters of the bright vellonr ones
in a subduplicate proportion ot the interrals of the Ats
otthe rays oF those Colours wrten equally inclined to
the retractins or reflectine surtace ertrich caused thole
Fts, that is, by putting the Diameters oF the Rings made
by the rays in the extremities and limits of the seren
Colours, red orange, vellor, green, blue, indico, violet
proportional the Cube-roots oF the numbers, 1, 8, 3,3
353 163 2 Wrhich express the lenotho oF a Monochard
Toundins the notes in an Fioht: For by chis means the
Diameter ot the Rinos ot these Colours will be Found
preter neaxty in the same proportion to one another.
Wrhichther oughe to have by the Aitth oF thele Obser-
rations.
And EuS I Catistied my selF that these RingS vere OF
the same kind and original rith thole ot thin plates,
and by consequence that the tts or alternate disposi
tions oF the rays to be reflected and transmitted axe PTO
Pasated to great distances trom every reflectins and re-
Fractins Curtace. But vet to put the matter out of doube
l added the follorinu Obserration.

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ut a
IEthele Rines thusdepend on thethickness oF the plate
oFCilaIs their Diametere at equal distances trom several
Speculums made ot tuch concaro conrex plates oF Cilals
as are ground on tlie lame Sphere, oushit to be recipro-
cally in a lubduplicate proportion of the thieknestes ot
the plates of CtaIS. And if this proportion befound
true by experience it ill amount to a demonstration
that thele Rings (like thole Formed in thin plates) do
depend on thethicknels oF the Cila(s. I procured there
tore another concaro conrex plate OE Cilals groundt On
both Sides to the lame Sphere rith the former plate:
les thickness iras 3. Parts ot an Inch; and the Diameters
oF the three Arst brishe Rinss mealured betreen the
brightest parts of their orbits at the distance ot 6 Feet
From the Cla(S ivere 3. 45. 55. Inches. Now thethick-
vess of the other Cilass beins : oF an Inch Wras to thick-
nels oF this CElaIS 45 = t0 3.3 that 15 45 3T t0 1O, Or
370000000 t0 100000000 and the roots ot chele numbers
arc 17607 and 10000, e in the proportion ofthe Arst.
oF these ioots to the second are the Diameters ot the
brishe Rings made in this Obserration by the thinner
GIa(S, 3. 45. 55to the Diameters oF the lame Ringsmade
in the third oCthele Obserrations by the thicker Clals
16. 25 212 That is, the Diameters ot the Rings are reci
procally in a subduplicate proportion of thicknesles oE
the plates oF CilalS.
S0 then in plates ot GElaIS which are alike concave On.
one side, and alike convex on the other side, and alike
quick.silrered on the convex sides, and differ in nothine
buE
E

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104
butcheir chickness, the Diameters oF the RinOS arC re-
ciprocallr in a lubduplicate proportion oFthe thickneses
oF the plates. And this Phers sufficiently that the Rinss
depend on Both the Turtaces ot the GElaIS. Thev de
pend on the conrex surtace because ther are more lu-
minous when that Furtace is quick-silvered over than
ertren it is without Ouick-silver. Ther depend aI(0
uvon the concare TuTFaCe, because Writhout that lurtace
a Speculum makes them not. Ther depend on Both
surtaces and on the distances betmeen them, because
their bioness is raried by varving only that distance.
And this dependance is of the same Kind with that
artrich the Colours et thin plates hare on the distance
OF the TUIEFaCeS OF those plates, because the bione(s
OF the Rings and their proportion to one another.
and the variation ot their bigness ariling fromthe raxiz
tion oF the thickness oF the Cla(S, and the orders ot
their ColOurS, is such as ought to retult From the PLopo-
Stions in the end oF the chird Part ot this Book, derired
From the the Phaenomena of the Colours of thin plates
set donn in the ArA Part.
There are yet otter Phaenomena oF these RingS OF
COlOurS DuE Fuch as Follo From the same Propostions.
and theretore contirm Both the truth ot thole PropOsi
tions, and the Analoey betireen these Rings and tne
Rinos oF Colours made by very thin plates. I MaII
Fubjoyn some oF them.

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F
BD. L2.
When the beam oF the SunsLisht was resected back
trom the Speculum not directir to the Hole in theWin-
dorr, but to a place a little dictant trom it, the common
CentEF OFthat SpOL, and oF aII the Rings oF C OlOurS FeII
in the middle rar betreen the beam ot the incident
Lishe, and the beam of the reRtected Lighe, and by
consequence in the center of the spherical concarity ot
ehe Speculum, Wrhenerer the Chart on wrhich the RinOS
OF Colours Fell ras placed at that center. And as the
beam oE rellected Light by inclinins the Speculum re-
Ceded more and more trom the beam ot incident Lisht
and trom the common center ot the coloured Rines be-
tircen them, thole Rines greir bigger and bigger, and
10 also did the irhite round Spot, and ner RingsOFCO-
lours emerged successirelr out ot their common center,
and the rhite Spot became a Wrhite Rins encompalIns
them; and the incident and reflected beams ot Light
alirars Feil upon the opposite parts otthis Rins, illumi-
natins its perimeter like tro moek Suns in the oppolite
Darts oF an Tris. S0 then the Diameter oF this RII8,
meatured From the midale ot its Lioht on one side to
the midele oF its Lixlit on the other side, ras alvays
equal to the distance betreen the midale ot the incident
beam ot Light, and the midale of the reftected beam
measured at the Chart on irhich the Rinos appeared:
And the rays wrhich Formed this Ring vere rellected by
che Speculum in Angles equal to their Angles oF InCI
dence, and by conlequence to their Angles oF retraction
de cheir entrance into the Clals, but y et their Ansles ot
reHexion

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106
retlexion rere not in the lame planes with their Angles
et incidence.
OBS. ZT.
ThC ColOuES OF the nem RingS tere in a COntrAEY
order to thole et the Former, and arole alter thio man-
ner. Therrhite round Spoc ot Lighe in the middle ot
the Rinos continued rrhite tothe center till the distance
ot the incident and reflected beams at the chart WaS
about 3 parts ot an Inch, and then IE bDETAN EO SPOW
dark in the midele. And when that distance wras about
17OF an Tuch, the Wrhite Spot ras become a Rins en
compastins a dark round Spot irhich in the middle IM.
clined to riolet and indico. And the luminous Rinos
incompassino it ivere srown equal to thole dark ones
ertrich in the four first Obserrations encompased them,
that is to Car, therhite Spot as srovn à White Rinc
equal to the tirst of thole dark Rings, and the ArA ot
those luminous Rings asnor grovin equal to the le
cond ot those dark ones, and the second ot those lumi-
nOuS OneS LO Fhe Fhird OF those dark ones, and (O OR.
For the Diameters oF the luminous Rings vere no lio,
163 233 320, VC. TMches.
Whenthe distance betrreen the incident and reftected
beams oF Light became a little Bigger, there emerged
out of the midale ot the dark Spot atter the indico a
blue, and then out ot that blue à pale green, and (OOn
aster a rellor and red. And irtien the Colour at the
center was brightest, beins betreen rellon and red,
thebright Rings vere sronn equal tothose Rings Wrhich
in the tour tirst Oblerrations next encompassed themm;
that

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IIC
that is to Cay, the irhite Spot in the middle oFthose
Rings iras no become à irhite Rins equal to the Arst
OE those brisht Rings, and the tirst of those bright ones
vas no become equal to the second os thole, and lo
On. For the Diameters of the white Rings, and of thc
Other luminous Rines incompaltins it, Were no Tis,
20, 212, 38, 1c. Or thereabouts.
When thedistance of the trro beams ot Light at the
Chart as à little more increaled, there emerged out
oE the midele in order after the red, a purple, a blue,
asreen, a vellorr, and a red inclinins much to purple,
and ertien the Colour ras hrishtest being betrreen vel-
lorr and red, the Former indico, blue, oreen, vellou and
redq rese become an lris or Rins ot Colours equal
tothe tirst oF thole luminous Rines wrhich appeared in
the Four Arst Obserrations, and the white Rins erhrich
ras non become the second ot the luminous RingS WraS
srown equal to the second ot those, and the ArA ot
those wrhich was non become the third Rins ras be-
come the third ot those, and (0 on. For their Diame
Ters Were 1i6, 25, 212, 38 Tnches, the distance of the
crvo beams ot Light, and the Diameter ot the wrhite
Rins beins 23 luches.
When thele trro beams became more distant there
emersed out oF the midele oF the purplistr red, tirst a
darker round Spot, and then out ot the midale of that
Spot a brishter. And nor theformer Colours (purple,
blue, Ercen, vello, and purplit red) rere become 2
Rins equal to the tirst of the briehe Rings mentioned in
che Four tirst Obserrations, and the Rins about thIS
Ring ivere sronn equal to the Rinos about that re-
rectively; che distance betreen the trro beams ol
L. 18t

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C108)
TigHt and che Diameter oF the irhite Rins (Wrtick
ras no become the third Rins) beins about z In-
CheS.
The Colours of the Rings in the middle Be~an nOu
to oro very dilute, and it the distance betreen thc
erro beams vas increaled halt an Tuch, or an Inch inOre,
ther vanisted erhilst the erhite Rins, rith onc or tvo
oF the Rings next it on cither side, continued sill vi-
Sible. But il the distance of the tro beams oF Lioht
aras siIl more increased these also ranistred: For the
Lioht Which comins From Ceveral parts ot the TTole in
the Windo Fell upon the Speculum in sereral Angles oF
incidence nade Rings oF sereral bignesses, irhich diluted
and blotted out one another, a5 l knew by interceptino
Pome part of that Lioht. For it l intercepted that part
erhich ras nearest to the AXis ot the Speculum the
Rings rould bc lels, it the other part erhich as re
motest From it ther rould be bisger.
OB5. XII.
When the C Olours oF the Prisin vere cast successirely
on theSpeculum, thac Rins irhich in the trro lastOB.
Terrations was white, as ot the tame bionels in aIl the
COlours. Dut the Rinos without it ivere oreater in the
oreen than in the blue, and Aill srcater in the vellon,
and sreatest in the red. And, on the contrarr, the
Rings wichin that irtite Circle ivere less in the orcen
than in the blue, and siil lels in the vellorr, and least
in the red. For the Aneles oF resexion OF those raYS
irtrich made this Rins Deins equal to their Angles ot
incidence, the ftsol every retlected ras within the Cila(s
after

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l109
alter reflexion are equal in lensth and number to the
fits ofthe Came cay rithin che Cilals Detore its incidence
on the retlectine surtace; and theretore lince aIl therayS
OF aII Ports at their entrance into the Cilals vere in a tut
ottransmistion, ther ivere allo in a tit of transmission at
theis returnins to the lame Curtace alter refexion; and
by consequence vere transmitted and vent out to the
Wrtrite Rins on theChart. Thisisthe realon why chat
Rins ras ol the Came bionels in aIl the Colours, aud
irhy in a mixture oE all ic appears wrhite. But in FaYS
irtrich are retlected in other Angles, the interrals ot che
ts of the least retransible beins createst, make the
Rinos oftheir Colour in their proerels from this irhite
Ring, either outards or inmards, increase or decrease
by the greatest Ceps; (0 that the RingsOF this C olour
rithout are greatest, and rithin least. And thisisthe
reason wrhr in the last Obserration, When the Specu-
lum ras illuminated writh white Lisht, che exterior
Rings made by alI Colours appeared red without aud
blue richin, and the interior blue without and red
Writhim.
Thele are the Phaenomena oF thick CONVeXO COnCaVC
plates oF Gila(s, vrhich are every wrhrere oFthe lamE
thicknels. There are vet other Phaenomena Wrhen thele
plates are a little thieker on one side than on the
other, and others irhen the plates are more or lels con-
care than ConVex, Or plano Conrex, or double- COnvex.
For in all these cases the plates make Rings OFC OIOUTS,
but alter various manners; all trich, 10 tar a5 lhave
yet obserred, tollon from the Propolitions in the end
oFthe chird part of this Book, and (0 conspire to con
tem the truth oE. those Propolicions. But che Phaeno
MEMa

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IITO
mena are t0o various, and the Calculations Whereby
ther follor From thole Provolitions too intricate t0 bC
here prolecuted. Icontent my selF rith havins prose-
cutedthis kind of Phaenomena 10 Far asto discovei their
cause, and by discorerins it to ratits the Propolitions
in the chird Part of this BoOk.
OBS. ZTTI.
A5 T ioHE retlected by a Lens quick-Cilvered on the
back-Fide makes the Rinos oF COlOurS above de
Ecribed, (0 it ought to make the like Rinos oF Colours
in pallins throust a drop oF Water. AC the sIrA LC
Rexion of the rars within the drop, Lome Colouis ouxtt
to be transmitted, 25 in the case ot a LenS, and Others
to be refected Back to the Fve. For instance, it the
Diameter oF d Cnalldcop or slobule ot WVater De about
the footh part oF an Tuch, (0 that a red makins cay in
passins through the midale ot this globule haS 290 fts
oFealy transmission ithin the globule, and that aIl the
red-makcins rars irhich are at a certain distance From
this midele rar round about it have 249 fits richin the
globule, and ail the like rays at a certain turther di-
Rtance round about it have 248 AEs, and aIl thole at a
certain Further distance 24. 7 Ats, and (0 on: Thele Con-
centrick Circles ot rars atter their transmistion, fallins
on a irhite Paper, rill make concentrick rinos of red
upen the Paper, supposins the Lighe irtrich pasles
throueh one linsle globule Arons enouph to be sensible.
And, in like manner, the rars ot othier Colours rill
make Rines oF other Colours. Suppole non that in a
Edir dar the Sun hines throuoh a ehin Cloud ot luch
slobules

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CTTI
globules oF Water or Hail, and that che globules are aII
OEthe Came bignels, and the Sun seen throuoh this Cloud
hall appear incompassed with the like concentrick Rings
OF ColOurs, and the Diameter ot the Arst Ring oF red
hallbe 7: degrees, that of the second 10: degrees, that
oFthe third 12 degrees 33 minutes. And accordingly
a5 the globules of Water are bigger or lels, the Rings
Mail be less or bigger. This is the Theory, and expe-
rience ansivers it. For in Fune 1692. l law by rellexion
in a Vessel oF stagnatins Water three HTalos CFOWNS OL
Rinos oF Colours about the Sun, like chree litele Rain-
bors, concentrick to his Body. The Colours of the
Ars or innermost C POwn ivere blue next the Sun, red
vichont and irhite in the middle betveen the blue
and red. Those ofthe second Cronn erere purple and
blue rithin, and pale red withont, and sicen in the
midale. And thole ot the third ivere pale blue with.
in, and pale red without; thele Cromns inclosed onc
another immediatelr, (o that their Colours procceded
in this continual order From the Sun ontrard: blue,
erhite, red; purple, blue, ereen, pale vello and red;
Pale blue, pale red. Phe Diameter ofthe lecond Cronn
measured trom the midale ofthe vellorr and red on one
Fide ot the Sun- to the middle et the lame ColOur on
the other side ras 9: degrees, or thereabouts. The Dia-
meters oF the krst and third I had not time to meature,
but that OF the Aes Seemed to De about AVC, OI SIX de-
orees, and thar of the third about trvelve. The like
Cxowns appear Cometimes about the Moon; tor in the
beginnine oF the rear 1664, Febr. Igth at nishe, l CaW
tuo luch Crowns abont per. The Diameter ot ehe Res
or innermolt ras about three degrees, and that ot the
second.

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(FI2
second abont sire degrees and an halt. Next about the
Moon as a Circle of White, and next about chat the
inner Crownerhrich ras of a bluistr oreen within nexethe
irtrite, and of a vellor and red without, and next about
these Colours vere blue and oreen on the inside of the
outrard CPorrn, and red on the outhde ot it. AL thC
Tame time there appeared a Tlalo about 22 degrces 35
distant from the center of the MOOn. It Wras Flliptical,
and its lone Diameter as perpendicular to thefloriron
vergins belon Farthest From the Moon. Jam told that
the Moon has Lometimes threc or more concentrick
Crorrns ofColours incompalsine one another next about
her Body. The more equal the globules oF Water Or
Ice are to one another, the mOre CFOWNS OF COlOUIS
Will appear, and the Colours rill be the more livelr.
The Halo at the distance ot 223 degrees From the Moon
is oF another COTF. By its beins oval and remoter trom
the Moon belon than abore, l conclude, that it Was
made by retraction in Pome Port of Hlail or Snow Aoatins
in the Air in an horizontal Potture, the retracting Angle
beins about 58 or 60 desiees.
F II F

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113
TTI L
CLeLana
d
Observations concernino the Inflexions of the rays of Lisht,
and the Colours made thereby.
IRimaldo has intormed us, that it a beam oF the
r SunS Light De let into a dark Room through a
very (malI Fole, the Madonrs oE chings in ehis LisHt
Will be larger than ther ousheto be it the raYS Went
on by the Bodies in Areioht Lines, and that these Ma-
dorrshave three parallel Fringes, bands or rankes oF co-
loured Lisht adjacent to them. But it the Hole be
enlarsed the trinses oro broad and run into one ano-
ther, lo that they cannot be distinguistred. Phele broad
hados and Trinses hrave been reckoned by Cometo pro-
ceed trom theordinary retraction of the Air, but rith.
out due examination ot the matter. Lor the cireum-
Carces oF the Phaenomenon, 10 tur 25 Lhare obserred
them, arc 25 FolIOWS.
d

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Bd. l.
I made in a piece of L ead a (maH Hole with a Pin,
arhole bresdth iras the +2th part oE an Inch. FOF 21
oE those Pins laid cosether took up the breadtm oF halt
an Tuch. Through this Hole I let into iny darkened
Chamber a beam ot the Suns. Lisht, and Found that the
Mados offTairs, Phred, Pins, Stras, and Cuch like Plen-
der Tubstances placed inthisbeam ofLisht, ere consider-
ably broader than ther ouolttobe, il the rarsot Liohe
passed on by thele Bodies in right Lines. And particu-
larls a Tlair ot a Mans Hlead, Wrhole breadth iras but
the28oth part ot an Inch, beins held in this Liolit, ae
the distance oF about telre Feet Erom theHtole, did
cast a Phadorr irtrich at the distance oF Four Tuches Fiom
the Flair was the sixtieth part ot an Tuch brond, thatis,
abore tour times bronder than theHlair, and at the di-
Cance oFtrro Feet From the Flair ras about the eiglt
and trventieth part ot an Inch brond, thatis, tentimes
broader than ihe Hair, and at the distance OFten FCCE
rasthe ciohth part of an lnch broad, that is 35 times
broader.
Nor is it material whether the llair be incompassed
rith Air, or rith any ottier pellucid substance. For I
retted a polistred plate ot Glals, and laid the Fair in
the Water upon the Cilals, and then lazins another po-
listred plate oF Cilals upon it, (0 that the Water mioht
AIl ux the space betreen the Cilases, I held them in
the atorelaid beam oF LishE, (0 that the LighemighE
Pass throush them perpendiculartr, and the adom
oFthe Llair ras at the lame distances as big as betore.
ThC

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1TB
Phe Bradorrs et scratches made in polisted plates ol
Glaso vere also much broader than they ousht to be,
and the Veins in polistred plates of Ctass did also cast the
like broad Badorrs. And theretore the great breadtt
oF thele Cadons procceds from Pome other cause than
the retraction oF tne AIT.
Vet the Circle Z represent the midale ofthe TTair; Fig. 1.
ADG, BETI, C FI, thrce cars passins by one side ot
the Fair at sereral distances; RNC, LOR, MPS,
chree ocher rays passins by the other side ot the Hlair at
che like distances; D, F, F and N, O, P, the places
irhere the cays are bent in their passase by thellai;
C, TI, Jand C, R, S, the places irhere the cars FaII on
a Paper CQ; ISthe breadth ofthe Madow ot theltair
cast on the Paper, and TI, VS, trro rays passins to the
Doints Iand S rithout bending irten the Fair is taken
airaY. And its manifest that aII the Light betireen
these tvO rayS AI and VS is bent in passins by the
Flair, and turned aside From the Padom 1S, because it
any part of this Liont vere noc bene it would Fall on
the Paper within the Mado, and chere illuminate the
Paper contrary to experience. And because irhen the
Caper is at a oreat distance trom the FTair, the Madon
is broad, and cheretore the rars II and VS are at a
dreat diltance trom one another, it Follos that the
tlair aets upon the rays oF Light at a g0od distance in
cheir passins br it. But the action is Arongest on the
rars rrhich pals by at least distances, and erors weaker
and weaker accordingly as the rars pass by at distances
sreater and greater, as is reprelented in the Scheme:
For thence it comes to pals, that the Macdow of the
lair is much broader in proportion eo the distance ot
th

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C116
the Paper Fromthe Flaii, When the Paper is nearer the
Flair chan when it is at a great distance trom it.
OBS. TI.
The Chadorre ot aIl Bodies (Metals, Stones, Gla(E,
Nood, HIorn, Ice, 1c.) in this Light ivere bordered
ith chree parallet Fringes or bands ot coloured Light,
erhereot that wrtrich ras contiouous to the thado Was
broadest and most luminous, and that ertrich was re-
motest From it was narrorest, and lotaint, a5 not calily
to be visible. It was difficult to distinguist the C olours
unless irhen the Light Fellvery obliguelr upon a (mooth
Paper, Or Come other linooth rrhite Body, 10a5to make
ehem appear much broader than ther vrould otherrile
do. And then the Colours ivere plainly ritible in this
order: The Arst or innermost Frinse rvas violet and decp
blue next the padorr, and then light blue, oreen and
vellorr in the midale, and red rrithout. The second
tringe rras alinost contiquous to the Arst, and the thiid
tothe second, and both rrere blue vrithin and vellovo
aud red vrithout, but their Colouis rrere very taint
especiallr those oF the third. The Colours theretore
procceded in this order From the Madorr, violet, indico
pale blue, sieen, vellorr, red; blue, vellorr, red; pale
blue, pale vellour and red. The thadorrs made by
Fcratches and bubbles in polistred plates ot Class rrere
Bordered rrith the like trinses ot coloured Lioht. And
ifplates ofLookins. glals 0op d offnear the edges vrith
a Diamond cut, be held in thelame beam ot Light, thc
Cisht irtich passes throuch the parallel planes ot the
Cilals will be De bordered rith the like tringes ot Co-
lOurS

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177
lours wrtere those Planes meet rith the Diamond cut,
and by this means there wriil Pometimes appear FOuT OK
tire Fringes oF COlours. Let AB, C. D reprelenc the Fis. 2.
Parallel planes oF a Lookins-sla(s, and BD the planc
ot the Diamond cut, makcins at B a very obtuse Angle
withthe plane AB. And let aII the Lighe Detireen che
TayS F N I and FBMI pals directly chroush the parallet
Planes oF the CEla(S, and FaII upon the Paper betireen l
and M, and aII the Lishe betreen the raYS CO and
HID De refracted by the oblique plane of the Diamond
cut B D, and FaII upon the Paper betreen I and L; and
the Lixhe irhich passes directlr chrouch the parallet
planes ofthe Cla(S, and FaIIS upon the Paper Betreen
land MI, Wil De bordered rith three or more fringes
AE NI.
OBS. TTI.
When the FPair as trvelve Feet distant Fromthe
tTole, and its Bhado Feil obliquelr upon a Rat vrhice
Ccale, ot Inches and parts ot an Inch placed halE a FOOL
berond it, and also irhen the Chadon Feil perpendicu-
laxiy uxon thesame scale placed nine Feet berond it;
I mealured the breadth of the Madon and tringes a5
accurately a5 lcould, and tound them in parts oF an
lnch a5 tollors.
dud

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(118)
At Ehe distance of
Phe breadth oF the Stado
Phe breadth betreen the midales ot
brishtest Fishe oEthe innermost trin
On cither side the Chadorr
Phe breadth betrreen the middles ot
brightest Lioht oF the middlemost Frin.
ses on cither side the Madon
Lhe breadth betreen the middles ot 1
brightest Light ot the outmost fringes
on cither side the Bado
The distance betreen the middles ot the
brightest Light oF the krst and lecond
FrInseS
The distance betreen the middles oF the
brishrest Lioht ot the second and third
Txinges
Phebreadth of the luminous part (grec
wrhite, vellor and red) ot che tAt
trinse
The breadth oF che darker space BetWCeK
the first and second Fxinses.
Lhe breadth ot the luminous part oF t
lecond tringe
Phebreadth ot the darker space Detee
the second and third trinses.
hals a nine
F0ot.
Feet.

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ET19
Phele meatures Y took by lettine the Chactor oF thC
FTair at halE a Foot distance FaII lo obliquelz on the
leale as to appear tvelre times broader than rrhen it
tell perpendicularir on it at the lame distance, and set-
cins dorn in this Table the tweltch part ot the mea-
Tures Ithentook.
OBS. TV
When the Badorr and Fringesrrere cast obliguely
upon a (mooth rrhice Body, and that Body iras remo-
ved further and surther From the Hlair, the Arst Frinse
Fegan to appear and look briehter than the rest ot the
Liont at the distance ot lels than a quarter oF an Inch
from the Iair, and the dark line or Madour Betveen
that and the lecond fringe besan to appear at a lels di-
tance fromthe HTair than that oF the third part OF an
Inch. The second trinse besan to appear at a distance
From the Fair of lels than halean Inch, and the Madow
betrreen that and the third Frinse at a distance lels than
an Inch, and the third Fringe at a distance less than three
Inches. At orcater distances ther became much inore
sensible, but kept very nearly the Came proportion ot
their breadctis and interrals erhich ther had at their Arst
appearins. For the distance betreen the midale ofthe
first and midale oF the second fringe, iras to the distance
hetureen the middle ot the second and midale oF the
third Frinse, a5 three to tWro, or ten to seven. And.
the lalt ot these trro distances rras equal to the breadth
OF the brighe Lighe or luminous part of the tirst Cringe.
And this breadchrras to the breadth oFthe bright Ligtt
oF the lecond tringe as seven to Four, and to the dark
interval

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CTT2
interral of the Erst and second Fringe as three to tro,
and to the like dark interval betreen the second and
third a5 two to onc. For the breadths oF the fringes
Ceemed to be in the progression of the numBerS L, V 3
 and their interrals to be in the lame progression
vrith them; that i5, the fringes and cheir interrals to-
gether to be in the continual progrestion ot the numbers
a, VE Or thereabouts. And thele pro-
portions held the Pame verr neartu at ait distances trom
ehc Hair; the dark Interrals ot the fringes beins a5
broad in proportion to the fringes at their tirst appea-
rance a5 alterwards at great distances trom the llair,
chouoh not (o dark and distinct.
OBS. V
The Sun ining into my darkened Chamber throustr
a TTole a quarter ot an Inch broad; I placed at the di-
Aance oF trro or threc Fcet From the Hole a Steet ot
Past. Board vrhichrras black d all over on both sdes,
aud in the middle ot it had a FTole about three quarters
oF an Inch square For the Light to pals throush. And
Behind the FIole I Fastened to the Past- Board vrith Pitch
the blade oF a Carp Rnite, to intercept lome part ot
theLishe vrhich passed throush the Hole. The planes
OF the Past. Board and blade of the Rnite rvere parallet
eo one another, and perpendicular to the rayS. And
vrhenther rrere lo placed that none ot the Suns Lighe
Fell on the Past-Board, but all oF it passed through the
Holetothe Ruite, and there part oF it fell upon the
blade ot the Rnite, and part ot it Pased by its cdgC:
let this pare ot the Lishr vrhich Passed by, FaIL On a
votte

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Wvhite Paper tro or three Fcet beyond theRnite, and
chere Car tro Areams ot taint Lisht Mhoot out both
rays tromthebeam oF Lishe into theMado like the
tails oFCOmets. But because the Suns direct Lightby
IIS brioheness upon the Paper obscured these taint
ltreams, (0 That L couid scarce sec them, Imade a litele
Hole in the midst oF the Paper For that Light to pals
chrouoh and FaII on a black cloth behind it; and then
law the tiro sreams plainly. They ivere likce one
another, and pretts nearty equal in lensth and breadth,
and quantier ot LioHt. Their Light at that end next
thesunsdirect Light as preter Arons For the (pace ol
about a quarter ot an luch, or halt an lnch, and in aII
uts prosrels trom that direct Lishit decrealed gradualIy
till it became insensible. Phewrhole lensth ot cither ot
These Rreams meatured uxon the Paper at the distance
ot threc Feet Trom the Rnite ras about sx or eisht
luches; (o that it Cubtended an Angle at the edge ot
theRnite oF abOut 10 OF 12, Or at molt 14 deGFCCS.
Vet Cometimes I thought I Ca it hoot three Or Four
degrees Further, but rith a Light so very taint thac I
could scarce perceive it, and luspected it misht (in
Tome measure at least) arile trom lome other cause than
the trro sreams did. For placins my lese in that Lighe
berond the end ot that Aream ertrich ras behind the
Knite, and lookins tormards the lnite, L could lec a
line oF Lisht uxon its edge, and that not only irhen
my Lye ras in the line of the creams, but allo irhen
IE eras Writhout that line cither tormards the point ofthe
Knise, or torrards thehandle. This line oF Lisht ap.
Deared contiguous to the edge ot the lnite, and Wras
harrover chan the Lisht oF che innermost tringe, and
narroreA

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narromest wrhien my Fre Was furthest fromthe direct
Lient, and theretore secmed to pals berween the Light
ot that fringe and the edge of the Rnite, and that
irhich passed nearest the edge to be most bent, though
not all oF it.
OBS. VI.
Y placed another Rnise by ehis (0 that Their cdges
mishit be paraIlel and lo0k torrards one another, and
thatthe beam oF Lignt might Fall upon boch the Rnives.
and some part oF it palo betrreen their edges. And
irten the distance oF their edoes as aboutthe 4OOth
DaEt OF an Tuch the Aream parted in the midale, and
Iett a ThadO DCTWCCM FHE ENO PATES. This Bacon
as (0 black and dark thdt alt the Lioht which parsed
betreen the Rnires scemed to be bent, and turned alide
tothe one hand or tothe other. And as the Knires AiI
approached one another the hado orew broader, and
the Areams Borter at their inmard ends wrhich vere
next the Cador, uneil upon the contact of the Knives
the irhole Lighe vanistied learins its place to the
Mracto.
And hence I gather thac the Lisht wrhich is least
bent, and soes to the imrard ends ot the Areams, pas-
ses bY the cdoes oF the Rnires at the greatest distance,
and this distance wrhen the Phador begins tO appCaF DC.
treen the Rreams is about the eight- hundredth DaFE OF
an Tnch. And the Light wrhich passes by che edees oF
the Rnires at distances AiII lelS and lels is more and
more bent, and soesto those parts OF the streams Wrhich
are further and turther trom the direct Lighe, because
avtrei

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I
Wrhen the Rnires approach one another cHII they touch,
those parts oF the streams ranistr last Wrhich are Furthest
tromthe direct Light.
OBS. VTI.
In che Atch Obserration the Fringes did not appear,
out by reaon of the breadth of the Hole inthe Win-
dour became (o broad as to run into one another, and
or jornins make one continued Light in the beginnine
OF the ArCAMIS. But in the EXth, a5 the Rnires ap-
Proached one another, a little betore the Chadon ap.
Veared betreen the trro Areams, thetringes began to
appear on the inner ends ot the Areams on either lide
oF the direct Liohe, threc on one side made by theedse
oF one Rnite, and three on the other side made by the
edse ot the other Knite. Lher ere distinctest irhen
the Rnires ivere placed at the greatest distance from the
LTole inthe Windou, and AiIl became more distinct by
makins the Hole lels, insomuch that P could Pometimes
sec a faint lineament ot a Fourth frinse berond thethree
abore mentioned. And as the Rnires continually ap.
proached one another, the tringes srerr distincter and
larger until ther vanistred. The outmost tringe va-
nithred trst, and the midalemole next, and the inner
most lact. And alter they vere all vanittred, and the
linc oF Lieht irtrich as in the midale betireen them
rassromn vers brond, entarsins it selt on both sides
intothe Areams oF Light described in the Ritth ObseF
vation, the aborementioned ado Besan to appear
in the midele ot this line, and diride it alons themidale
into trro lines ot Lighe, and increaled until the wrhole
RF
Liglt

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CT24
Fiohe ranisted. This inlargement oF che Fringes WaS
(0 great that the rays irhich 5o to the innermost Frinse
Seemed to De bent abore trventy times more irten this
Frinse ras reads toranittu, than wrtien onc ot the Knires
ras takenarrar.
And Fromthis and the Former Oblerration compared,
Tsather, that the Fight oF thetirst trinse passed by the
edoe ofthe Rnite at a distance greater than the eioht.
hundredth part oF an luch, and the Lishe of the second
Fringe Passed by the edee of the Rnite at a greater di-
Cance than the Lioht ot the Arest tringe did, and that
ofthe third at a greater distance than that ot the se-
cond, and that oF the sreams of Light described in
the titth and sixth Observations passed by the edges
oF the Rnires at lels distances than that ot any oF thC
Trinses.
OB5. VIII
lcaused the edges ot trro Knives to be pround truty
Areishe, and prickins their points into a board (0 that
their edoes misht look torrards one another, and meet-
ino near their points contain a rectilinear Anole, I Fas.
ned their handles tosether rith Pitch to make this
Ansle invariable. Ihe distance oF the edges of the
Knires From one another at the distance DE tour Inches
From the angular point, erhere the edges of the Knires
met, as theeigheh part ot an luch, and theretore the
Ansle contained by the edges ras about 1 degr. 54.
Lhe Knires thus Aixed together I placed in a beam of
thesuns Light, let into my darkened Chamber throuotr
a FIole the 42th part oF an lnch wide, at the distance
O

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125
oF ten or stteen Feet trom the HTole, and let che Listit
irhich passed betreen cheir edees Fall very obliquely
uxon a (nooth white Ruler at the distance ot halF au
Inch, or an Inch From the Rnires, and there law the
tringes made by the tiro edses of the Rnires run alone
the edoes of the Mados oF the Knires in lines parallel
to thole edges without gromins sensibly bronder, till
chey met in Ansles equaltothe Ansle contained by the
edges ofthe UEnires, and irhere ther met and jorned
ther ended wichout crossins one another. Buc it the
Ruler was held at a much sreater distance from the
Paper, thetringes became Lomethins bronder and broader
as ther approached one another, and alter ther net
thes eroned one another, and then became much broader
than betore.
Whence I sather that the distances ac irtrich tho
Tringes pass by the Rnires are not increaled nor altered
by the approuch ofthe Rnires, but the Angles in irtricti
the raysare there bent are much increaled by that ap
proach; and that the Knite erhich is nearest any cay
determines irhich was the ras MaIl De bent, and the
Other Rnite increales the bent.
adi LLL
When the rays fell very obliquels upon the RuIeT aC
thedittance of the third part of an lnch trom the Knires;
the dark line betureen the fust and second Fringe oF thC
Thadoir oF one Unite, and the dark line betireen the
tirst and second tringe ot the Madow of the other Rnite
met rith onc another, at the distance oE the Atth part
OE an Inch trom the end oE the Lishe wrhich passed be-
treei

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treen the Kuires at the concourle oE their edoes. And.
theretore the distance ot the edoes OF the Rnives at the
incetins, ot these dark lines rras the ibOth part oF an
Tnch. FOr as Four Inches to the eighth part oF an Inch,
(0 is aur lensth of the edges ot the Rnires inealured
From the point ot their concourse tothe distance ot the
edoes of the Rnires at the end ot that lenoth, and (0 is
thC AFEh parE eF an Inch to the TBOth paFL. S0 thenthe
dark lines abore mentioned meet in the midale ot the
Lisht erhich passes becreen the Knires wrhere they are
distant the 1both part ot an Tuch, and the one halE oF
that Lioht passes by the edse oF one Rnite at a distance
noc creater than the 320th part ot an Iuch, and fallins
upon the Paper makes the tringes ot the Mhadom of that
Rnise, aud the otter halt passes by the edse ot the
Other Knife, at a distance not sreater than the 320th
Dart of an luch, and Falling upon the Paper makres the
Fringes oF the Bado ot the other Inite. But if the
Paper De held at a distance From the Knires greater than
the third part ot an Inch, the dark lines abore men-
tioned meet at a preater distance than the AEth pAFE OF
an Inch From the end of the Lighe erhrich passed be-
trreen theKnires at the concourse ot their edoes; and
theretore the Light irhrich Falls upon the P’aper irhere
thole dark lines meet pasles betreen the Knires
irtiere their edges are distant abore the 1b0th part ot
au IMCM.
FOr at another time wrhen the trro Knires vvere di-
Aant eioht Feet and tire Tuches From Fhe litele Eole in
the Windo, made with a Cinall. P’in as abore the l iont
arhrich Fell uxon the Paper irhere the atoresaid dark
lines met. Passed betreen the Kuires, irhere the di-
Cance

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Rance Betireen their edges iras as in the follorvine
Pable, irtren the distance oEthe Paper tromthe Knires
WaS alus IBLIOWS.
Dist
ces of the Paper (Dist
the
che
nives
ances betveen th
the Rnir
et parts os
dees
ille
b.
001
O020.
O034.
008).
0081.
008
And hence Tgather that the Light erhich makes the
Fringes upon the Paper is not the lame Lisht ac aIl di-
Sances of the Paper From theRnires, but irhenthe la-
per is held near the Rnires, the tringes are made by
Light wrhich passes by the edges ot the Knires at a lels
distance, and is more bent than wrhen the P’aper is held
at a greater distance from the Rnires.
OB5. Z.
When the Fringes ot the Madors of the Knires fell
Derpendicularly upon a Paper at a great distance from
the Rnires, ther ivere in the form of Iyperbolas, and
their dimentions vere as Follorrs. L et C. A, C B repre
sent lines dramn upon the Paper parallel to the edges ot
the Rnires, and betrreen wrhich aIl the Light vould
Fall, is it passed betreen the edges oF the knires rith
out intlexion; DF. a righe line drann chroush C. makino
THC

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the Aneles AC.D, BC F equal to one anotter, and
terminatins allthe Lisht whith FaIlS upon the Paper From
the pointrrhere the edoes of the Rniresincet; eis, FKL,
and sIr, three lyperbolical lines representinq the ter-
minus oFthe Pador ot one ot the Rnires, the dark linc
betreen the tirst and second tringes oFthat Madour, and
the dark line betreen the second and third Fringes ot
the lame Mador; Zip, Vkg and 2lr, thrce other IIY.
perbolical lines reprelentinq the terminus of the Padon
OF thc other Knite, the dark line betveen the Ars and
second Fringes ot that Cador, and the dark line be-
treen the second and third Fringes ot the lame Padon.
And conceire that these three AIyperbolas are like and
equal to the Forimer threc, and crossthem in the points
ig k and l, and that the Phadtors oFthe Rniresare termi-
nated and distinguistred From the Airst luminous fringes
by the lines cis and xip, until the inectins and crol-
lins ofthe fringes, and then those lines crols thefringes
in theform oF dark lines, terminatins the Airst luminous
Frinses within side, and distinguistuns them from ano-
ther Lisht wrhich begins to appear at i, and illuminates
allthe triangular space ipD Ls comprehended by thelc
dark lines, and the risht line DH. OF thele Hy.
Perbolas one ACmptoteis the line DF, and their other
AEymptotes are paralel to the lines C. A and C. B. T et
er reprelent a line dramn ans erhere upon the l’aper
Parallel tothe ACymptote DF, and let this line crols
therisht lines AC. in m and BC. in n, and the sIX dark
lrperbolical lines in P, G Y; S, t V; and by meaturins
the distances pc, qt, PV, and thence collectinq the
the lenoctis oF the ordinates nP, HG, HF OF MS, ME,
mr and doins chis at sereral distances ot the line PV,
FrOm

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l12G
trom the Asymptote DF. vou mas find as mans points
OFthese Hyperbolas as rou pleale, and thereby kno
chat these curre lines are (Iy perbolas ditterins little From
the conical Hyperbola. And by meaturins the lines
1, C. k, C.L, rou may find other points ot thele
CUTVeS.
fior instance, When the Rnires vere dictant From the
tTole in theWindon ten Feet, and the Paper From the
Anires 9 Fcet, and the Ansle contained by the edges ot
the Enires to irhich the Angle AC. B is equal, Was sub.
tendes br. a chord wrhich Was to the Radius a5 I t0 32
aud the distance of the line er From the ACyimptote DF
vas hralt an luch: l incatured che LIneS PS, GC, EV,
and Found them o35, 065, 098 lnches respectivels,
and by addins to their halts the linc; mn (Which here
Wras the 128th part oF an Inch, or 00078 Inches) the
lUmIS HP, nG, AF, Were 01828, 03328,04978 In-
ches. I mealured also the distances ot the brightest
Paxts oFthe Fringes irhich run betireen p9 aud st, 9L
and EV, and next beyond r and v, and found chem 05,
08, and l17InCheS.
dB5.
Lhe Sun Cimins into my darkenea RoO CATOlBA a
lnall round HIole made in a plate ot L ead rith a llender
ein as abore; L placed at the Hole a Prilm to retraet
che Listt, and Form on the oppolite WaII theSpectrum
oF Colours, described in the third Lxperiment of the
Axst BOOk. And then I Found thatthe Madors oF aII
Bodies held in the coloured Lighe betveen the Prism
and che Nall, Were bordered wich (rinses Of che Colour

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OF that P ighE in Wrhich ther were held. Inthe Full red
Tieht thes irere totally red rithout any sensible bluc
or violet, and in the deep blue Lieht they ivere totally
blue ithout any sensible red or vellor; and lo in the
oreen Light ther vere totally sreen, exceptins a little
Vello and. bluc, which iere mixed in the green Light
ofthe Prilm. And comparino the fringes made in the
Lereral coloured Lights, I Found that thole made in the
red Light irere larsest, those made in the riolet vere
least, and etiose made in the oreen vere ot a midale
bionels. For the Frinses with wrhich the Madtorv OE a
Mans Hair rere bordered, beins measured crols the
Chadou at the distance oF six Tnches From theHtair; the
distance betreen the midale and most luminous part ot
the First Or innermost frinse on one side ot the Mado,
aud that of the likre fringe on the other side ot the Ma-
dorr, ras in the FuIl red Lishe;: oF an Tncl, and in
the FuII violet . And the like distance betireen the
midele and inost luminous parts of the second fringes on
either side theador rras in the FuII red Lieht :, and
in the violet= ot an Inch. And these distances ot the
Fringes held the lame proportion at aI distances Fror
the Llair writhout ans lentible variation.
So then the cars wtrich made chele tringes in the red
Liont passed by thetlair at a greater distance chan thole
did which made the like fringes in tho violet; and there-
Fore the FTair in caulins these fringes acted alike upon
the red Lighe or least retrangible rays at a greater di
stance, and upon the violet or most retransible rays at
a lels distance, and by those actions dispoled the rec.
Lighe into larger tringes, and the violet into smaller.
and the Lishus oE intermediate Colours into tringes ot
intei-

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131
intermediate bignesses without chansins the Colour ot
ot any lort ot Light.
When theretore the FPair in the Arst and second ot
thele Oblerrations as held in che irhite beam of the
Suns Light, and cast a Mado irhich iras bordered rith
chree Fringes of coloured Light, thole Colours arole not
trom any newr moditications imprest upon the rayS et
Light by theFlair, but only trom the rarious infections
Whereby the sereral (orts oF rays rere separated From
One another, irhich betore separation by the mixture
OE all their Colours, compoled che irhite beam ot the
Cuns Light, but wrhenerer separated compose Lights
OFthe sereral Colours trhich ther arc originally dilpo.
sed to exhribit. In this 13th Oblerration, irhere the
Colours are separated betore the Lisht passes by the
Hlair, the least retransible cars, irtrich irtien separa-
ted trom therest makce red, vere inflected at a sreater
dictance Fromthe Tlair, (0 a5 to make chree red tringes
at a creater distance From the middle of the Thado ot
thellair; and the most retransible rays wrtrich irhen
Separated make violet, ivere inflected at a lels distance
tromthellair, (0 a5 to make three violet Fringes at a
lels distance from the middle ot the ador ot the Flair.
And other rays ot intermediate degrees ot retransibi-
lier ivere inflected at intermediate dittances trom the
Flair, (0 a5to make frinses ot intermediate COlours at
intermediate distances from the midale of the sracton
oF the Flair. And in the second Obserration, Wrhere
all the Colours are mixed in the white Lisht irhich
Passes by the Flair, these Colours are separated by the
various intlexions of the rays, and the frinses Wrhich
chey make appear all tosecher, and the innermok
35
Frinses

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tringes beins contiguous make one broad fringe compo.
Ted oF all the Colours in due order, the violet lvins
on the insde of the fringe next the Padon, the red on
the onthide Furthest From the Bhado, and the blue,
oreen and vellor, in the midale. And, in Like inan-
ner, the middlemost Fringes oF all the Cclours lying in
Order, and beins contisuons, make another broad tringe
compoled ot aIl the Colours; and the outmost Frinces
OF aII the COlours lyins in order, and beins contiouous,
make a third brond Frinse compoled oF all the C OlOUES.
These are the three fringes ot coloured Lioht wittr
ertrich the Chactorrs ot all Bodies are bordered in the sc-
cond Oblerration.
WVtien Imade the Foregoins Obserrations, l detioned
to repeat nost oF them rith imore care and exactnels,
and tomake lome ner ones for determinins the man-
ner ho the rars of Lightare bent in their pastage by
Bodies For makins the Fringes oF Colours with the
dark lines betreen them. Buc Lwas theu interrup-
tedque and cannot no think ot takcins chele chines into
further consideration. And since l hare not tinistred
ehis part of my Delien, I MaII conclude, with prOPO
tins only some Oueries in order to a turther learch to
De made Dy Others.
Duery 2. Do not Bodies aec upon Light at a distance,
and by their action bend its rays, and is not this action
(cateris paribus) Aronsest at the least distance
du. 2. Donot the rays vrhich differ in retransibilitr
difter also in Rexibilitr, and are ther not bytheie dit-
terent inflexions separated From one anothei, (0 25
atter separation to make the Colours in thethree Fringes
abore

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133.
abore described: And alter irhat manner are they in-
Rected to makre those Fringes:
Du. 3. Are not the rays oF Lisht in passine by the
edges and sides oF Bodies, bent sereral times backrarde
and formards, rith a motion like that oF an Fel d And
donot the three Fringes ot coloured Listit above-men-
tioned arise From three Cuch bendings:
u. 4. Do not the rars oF Ligt irhich FaIl upon B0-
dies, and are reflected or retracted, begin to bend De-
tore ther arrire at the Bodies; and are ther not re-
Dected, refracted and infected by onc and the Pame
Principle, actins rarioully in rarious circumstances?
Du. 5. Do not Bodies and Light aet mutually upon
one another, that is to lay, Bodies upon Light in emit-
tins, refectine, retractins and inflectins it, and Light
upon Bodies For heatins them, and purtins their Parts
into a vibratins motion wherein heat contitts.
du. 6. Donot black Bodies conceire heat more easily
From Liont than those oF other Colours do, by realon
that the Lixht Fallins on them is not refected outrards;
but enters the Bodies, and is otten reflected and re-
Tracted mithin them, until it be stised and los:
Du. 7. Is not the Arenoth and vigor ot the action
betreen Light and (ulphureous Bodies obserred abore,
one realon irty Culphureous Bodies take Are more
readils, and burn more rehemently, then other B0.
dies dor.
Du. 8.. Do not aII fixt Bodies When heated beyond à
certain degree, emit Light and hine, and is not thIS
emittion pertormed by che vibratins motions ol their
Paxts:
10

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34
Du. 9. IS not Are a Body heated (0 hot a5 to emie
Liont copiousr For whrat else is a red hot Tron than
srC. And ertrat etse is a burnine Coal than red not
Wood :
Du. 10. IS not Rame a vapour, tume or extralation
Beated red hot, that. is, (o hot as tolhine: For Bodies
do not Hame rithout emittins a copious tume, and chis
Fume burns in the Rame. The Tonis l’atuus iS a rapOuE
inins without heat, and is there noc the lame diffe.
rence Detreen this vapour and Rame, a5 betreen pot-
ten Wood Minino Without heat and burnino Coals Ot
Fre. In distillins hor Spirits, il the head ot the siIl Be
taken of, the rapour irhich alcends out ot the Still il
take tire at the tame of a Candle, and turn into Rame,
and the Rame ill run alone the rapour trom theCandle
EOthe SFilI. Some Bodies heated br motion or termen-
tation, it the heat prou intense fume copiousy, and if
theheat be preat enough the tumes iil ine and De.
come Aame. Mletals in fution do Boc Hame For vant et
a copious fume, except Spelter wrhich tiimes copiousy,
and therebr Rames. AII Aamino Bodies, a5 Oyl, Tal.
lorr, Wax, Wood, FoNiI CoaIS, Pitch, Sulphur, by
Aaming raste and vanisti into burnins lmoke, irhich
Tinoke, it the Pame be put out, is very thick and visible,
and Pometimes linells Aronoly, but in the Aame loles
its Tinell by burnins, and accordins tothe nature of the
linoke the Aame is oF severat Colouis, 25 that ot SuI.
phur blue, that oF C opper opened rith Sublimate
sreen, thatof Pallon rellorr. Sinoke passine throven
Hame cannot but orom red hot, and red hot linoke can
hare no other appearance than that oF Hame.
I. l1

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du. II. Donot preat Bodies conterre their heat the
longest, their parts heatins one another, and may not
sreat dense and fx d Bodies, irtien heated berond à
certain degree, emit Light Pocopiousr, as by the emis-
hon and reaction ofits Light, and the resexions and re-
Fractions oF its rars rithin its pores to gro sill hot.
ter. till it comes to a certain period ot heat, fuch a5 15
THAE OEFhe SUIN : And arC nOt the SuM and AX d SFAES
sreat Farths rehementiy hot, whole heat is conserred
Oy the greatness of the Bodies, and the mutual action
and reaction betreen them, aud the Lioht wrhich they
emit, and irhole partsare kept trom tumins array, not
only by their fixier, but allo by the rast reistit and
densier of the Atmospheres incumbent upon them, and
very sronsly compressins them, and condentins the va-
pours and exhralations irhich arise From them:
Du. 22. Donot therars oF Lighe in falling uxon the
bottom oF the Fre excite ribrations in the lunica re
tina: Which ribrations, Deins propasated alone the
Colid fibres of the optick Nerres into the Brain, CaulC
the sense of secins. For becaule dente Bodies conserre
their heat a lons time, and the densest Bodies conterre
their heat the longest, the ribrations oF their paPtS arC
oF a lastins nature, and theretore may be propasatect
alons solid tibres ot unitorm dense matter to a great di-
Stance, For convering into the Brain the imprestions
inacte uxon aIl the Orsans of sense. For that motion
erhich con continue lons in one and che lame part of a
Bodi, can De propasated a lons ray ErOm One ParFtO
another, supposine the Body homogeneal, (0 that the
motion may not be retlected, retracted, interrupted oE
disordered by any unerennels oFthe Body
Ibo

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C
136
Du: T3. Donet several lort oF. rays make vibrations
oE sereral bignesses, trhich accordins to their bignestes
excite senlations ot several Colours, much atter the
manner that the ribrations ofthe Air, accordins to their
sereral bieneses excite sensations ot several Counds:
And particularly do not the most retrangible rays Cx
cire the Mortest vibrations For makins a senlation ot
decp violet, the least refransible the larsest for makine
a lentation of decp red, and the sereral intermediate
Torts ofrars, vibrations of several intermediate bigner-
ses to make senlations of the sereral intermediate C0-
lOUrS.
Du. 14. Iar noc the harmons and dilcord ot C0-
lours arise trom the proportions ot the ribrations propa-
sated through the sbres. oF the optick Nerres into the
Brain, a5 the harmonr and discord ot Pounds ariles trom
the proportions of the vibrations ot the Air? For lome
Colours areasrecable, as those of Crold and Indico, and
Others dilasree.
u. I5. ArenottheSpecies oF Objeets seen rrith both
tiyes united irhere the optick Nerres meet Fetore
they come into theBrain, the tibres on the rishie side
otboth Nerres unitins there, and alter uniOn gOIne
thence into the Brain in the Nerre wrhich is on the
righe side oFthe Flead, and the tibres on the lett side
ot both Perres unitins in the lame place, and atter
union soins into theBrain in the Nerre Which is on
the lete side oF the Head, and these trro Nerres meet-
ino in the Bram in such a manner that their tibres
male but onc entire Species or licture, halt ot irtict
on the. rishe side ot the Senlorium comes From the
right side oF boch Eyes throush che righe side ot
Doth

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(I
Doth optick Nerres to the place erhere the Nerves
meet, aud From thence on the rioht side ot the Fread
intothe Brain, and the other halt on the lest side of the
Sentorium comes in like manner From the lete Ade et
both Fyes. For the optick Nerres oFluch Animals a5
look the same ray with both tires (a5 oF Men, D095,
Stcep, OXen, IOC.) meet betore ther come into the
Bran, but the optick Nerres ot such Animals a5 d0
not lool the lame rar with both Fres (25 oF Fithes and
OF the Chameleon) do not meet, il I am righely in-
Formed.
Du. 16. WVhen a Man in the dark presses either cOr-
nex of his Fre rith his Finger, and turns his Fye array
From his Finger, he will sec a Circle ot Colours like
those in the Feather ot a Peacocks Tail: Do not thele
Colours arise From Cuch motions excited in the bottom
OF the Fve by the precture of thefinger, 25 at other
times are excited there by Lighe For cautins Vition: And
ertien a Man by a stroke upon his Five sces a Flat of
Light, are not the like Motions excited in the Retina
by thestroke:

## Folio  -  — 1677894601:0314
# No recognised text on this page (recognized).

## Folio  -  — 1677894601:0315
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T...
 mommuiimumen
S.
IB: 3
... -
BOOKM. Plate L.
TFRIED WILHELM LEIBNIZ BIBLIC
DERSACF

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p
lts  s   efss
eee
NIEDERSACHSBEME CNHODLSONDLIOTHEK
atur: Lcibn. Marg. 
3
Con CeBL BIBEITTIR

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-
F. IY LMIF R A TIO:
RLAHARUM
IF RTTI ORDIHIS.

## Folio  -  — 1677894601:0318
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Mitsii
 e s sH

## Folio 139 — 1677894601:0319
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E NT UM E R A TIO
trRuM
TF RTII ORDTHIS.
Tnex Geometricae secundum numerum dimen-
Linearum Ora
sionum aequationis qua relatio inter Ordinatas dines.
E ABICisas detinitur, rel (quod perinde est) secun-
dum numerum punctorum in quibus a linea recta
secari portunt, optime distinguuntur in Ordines.
Oua ratione linea primi Ordinis erit Recta Cola, cae
Secundi Cire quadratici ordinis erunt sectiones Conicae
e Circus. _ ex tertii hre cubici Ordinis Parabola
Cubica, Parabola Neiliana, Cillois veterum _ reli-
quae quas hic enumerare lulcepimus. Curra autem
primi generis, (siguidem recta inter C urras non eAt
numeranda) eadem est cum Linea secundi Ordinis,
_ Curra secundi generis eadem cum Linea Ordinis
tCTEII. Ft Linea Ordinis intinitesimi ea est quam
recta in punctis intinitis lecare potest, qualis est Spi-
ralIS, Cyclois, Ouadratrix e linea omnis quae per
cadii vel rotae rerolutiones intinitas generatur.
1
1
dectionum

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C14C
Sectionum Conicarum proprietates praecipuae +
sionem Conica. Ceometris paltim traduntur. Fit consimiles Tunt pro.
rum competunt Pletates Currarum secundi generis ∞ reliquarum, ut
Ex LequenEI PTOPPIETatUM PPAeCIPuaTUM enueIa-.
tione constabit.
Nam si rectae plures parallelae _ ad conicam se
cundi generis olonem uErinq; terminatae ducantur, recta duas Ca-
dinatae, Diame- Lam Bisecans bilecabit alias omnes, ideog; dicitur Dia-
meter tiourae _t rodeae bilectae dicuntur Ordinatim ap
plicatae ad Diametrum, e concurtus omnium Dia-
metrorum est Centrum hourae, _ interlectio C urvae dt
diametri V’ertex nomimatur, e diameter illa Axis
eAt cui ordinatim applicatae insictunt ad angulos ic-
ctos. Ft ad cundem modum in Curris secundi se-
BerIS, A rectae duae quaeris parallelae ducantur Occur-
rentes Currae in tribus punctis: recta quae ita secat
tras parallelas ut lumma duarum partium ex uno se
cantis latere ad curram terminatarum aequetur parti
Tertiae ex altero latere ad curram terminatae, codem
modo lecabit omnes alias his parallelas curraeq; in
tribus punctis occurrentes rectas, hoc est, ita ut lum-
a partium duarum ex uno ipIIs latere semper
cequetur parti tertia ex altero latere. LlaSItaq; FreS
partes quae hinc inde aequantur, Ordinatim appli-
catas et rectam lecantem cui ordinatim applicantur
Diametrum _ interlectionem diametri 8 cuerre V er-
ticem e concurtum duarum diametrorum Centrum
nominare licet. Diameter aucem ad Ordinatas re-
etanoula simodo aliqua lit, etiam Axis dici potest,
ex ubi omnes diametri in eodem puncto concurrunt
iAud erit Centrum generale.
lyper
Proprietates Se-
curr
superiorut
senorum.
Curvarum se-
tri Vertices, Cent
ra AXC

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C24I
Hyperbola primi generis duas Asymptotos, ca P2
Cundi tres, ea tertis quatuor ex non plures habere DO. earum propricta
test, e sic in reliquis. Et quemadmodum partestes.
lineae cujulris rectae inter Fyperbolam Conicam ∞
duas ejus AEymptotos lunt hinc inde aequales: sic in
Ayperbolis secundi generis l ducatur recta quaeris
lecans tam Curvam quam tres ejus ACymptotos in
Tribus punctis, Tumma duarum partium iltius recta
quae a duobus quibutris ACymptotis in eandem pla-
sam ad duo puncta Currae extenduntur aequalis erit
Parti tertiae quae a tertia ACymptoto in plasam con-
crariam ad tertium Curvae punctum extenditur.
Fit quemadmodum in Conicis sectionibus non Pa-
rabolicis quadratum Ordinatim applicatae, hoc et, eran versa.
rectansulum Ordinatarum quae ad contrarias par-
tes Diametri ducuntur, est ad rectangulum partium
Diametri quae ad Vertices Fllipseos vel Llyperbola
terminantur, ut data quaedam linea quae dicitur Latus
rectum, ad partem diametri quae inter Vertices jacet
_ dicitur Latus transver sum: sic in Curris non P’ara-
bolicis secundi generis Parallelepipedum (ub tribus
Ordinatim applicatis est ad Parallelepipedum (ub par-
tibus Diametri ad Ordinatas etres Verticesfigurae ab.
Ccistis, in ratione quadam data: in qua ratione ( (u-
mantur tres rectae ad tres partes diametri inter ver-
tices fsurae litas singula ad lingulas, tunc illae tres
rectae dici postunt Latera recta trgurae, _ illae partes
Diametri inter Vertices Latera transversa. L.F sicut
in Parabola Conica quae ad unam ex eandem diame
trum unicum tantum habet Verticem, rectangutum
CubOrdinatis aequatur rectangulo sub parte Diametri
quae ad Ordinatas et Verticem abscinditur de recta
quadam
Asymptoti C
Latera recta e.

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I142
quadam data quae Latus rectum dicitur, sic in Curris
decundi generis quae non nili duos habent Vertices ad
eandem Diametrum, Parallelepipedum sub Ordinatis
tribus aequatur Parallelepipedo lub duabus partibus
Diametri ad Ordinatas ex Vertices illos duos abscissis,
_ recta quadam data quae proinde Latus rectum
dici potest.
Deniq; sicut in Conicis sectionibus ubi duxe paral
num sub Paralle. elae ad Curram utrinq; terminatae secantur a dua-
jarum sermentis. bus parallelis ad Curvam utrinq; terminatis, prima
a tertia e secunda a quarta, rectanculum partium
primae est ad rectangulum partium tertiae ut rectan-
sulum partium secundae ad rectangulum partium
quartae: Sic ubi quatuor tales rectae occurrunt Curra
secundi generis singulae in tribus punctis, parallele.
pipedum partium primae rectae erit ad parallelepide.
dum partium tertiae, ut parallelepipedum partium
secundae ad parallelepipedum partium quartie.
Currarum secundi _ superiorum generum aeque
bolica e Parabo. C9; primi crura omnia in infinitum progredientia
licac eorum pla Del Fyperbolici (unt generis vel Parabolici. Crus FIy
perbolicum voco quod ad ACymptoton aliquam in in-
tinitum appropinquat, Parabolicum quod Asymptoto
destituitur. Haec crura ex tansentibus optime dig
nOICUntuT. Nam E punctum contactus in infinitum
abeat tangens cruris Lrperbolici cum AIymPEOtO
coincidet d tangens cruris Parabolici in infinitum
recedet, eranescet e nullibi reverietur. Invenitur
iditur ACymptotos cruris cujulris quaerendo tangen-
tem cruris illius ad punctum intinite dictans. Plaga
autem cruris intiniti inrenitur quaerendo positionem
rectae cujutris quae tansenti parallela est ubi pun-
etum
Rario contento-
Crura Eper-

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L
ctum contactus in intinitum abit. Nam haec rectu
in eandem plasam cum crure infinito dirisitur.
Lineae omnes Ordinis primi, tertui, quinti, sep.
cimi ex imparis cujusq; duo habent ad minimum varum omnoim
crura in intinitum vertus plasas oppolitas PrOSre seneris secundi ad
dientia. Et lineae omnes tertii Ordinis duo habent equationum casus
quatuor. Casus
ejulmodi crura in plasas oppoltas prosredientia in primus.
quas nulla alia earum crura insinita (Praeterguam
in Parabola Carteliana) tendunt. Si crura illa
sint Hyperbolici generis, st GAS eorum AIrmp-
totos e huic parallela agatur recta quaeris C. BC
ad Curvam utrinque (E tieri Potest) terminata
eademq; bilecetur in puncto Z, et locus puncti il. Fis. Lo
lius X erit FIrperbola Conica (puta X 8) cujus
una AIymptotOS eA AS. Sit ejus altera ACymp-
Eotos AB, X aequatio qua relatio inter Ordinatam
BC. e AbsCissam AB detinitur, S AB dicatuE Z 8
BC. y, Temper induet hanc formam XV yY L Cy = 2X
FbXX  CX. ] d. Ubi termini C, a, b, C, d, delig-
nant quantitates datas cum signis luis ) et afte-
ctas, quarum quaelibet deesse postunt modo ex carum
defectu figura in sectionem conicam non vertatur.
Potest autem FIyberbola illa Conica cum alrmpto-
tis suis coincidere, id est punctum X in recta AB
locari: e tunc terminus.  Cy decst.
Ath recta illa C. BC non potestutrinq; ad C urvam
terminari led Currae in unico tantum puncto occur-
rit: dee quamris positione datam rectam A B alrmp-
Eoto AS occurrentem in A, ut Xc aliam quamvis BC.
ymptoto illi parallelam Curraeque Occurrentem II
puncto C e aequatio qua relatio inter Ordinatam
BC
VIII.
Reductio Cur-
l.X.
Casus secunduia.

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144.
BC e ABIcissam AB detinitur, Temmper induet hanc
FOTIAM XY = aX-) DXZ F CX-F d.
Ouod si crura illa opposita Parabolici sint generis
recta C. B C ad Curram utrinque, E Heri potest, ter-
minata in plagam crurum ducatur a bilecetur in B,
et locus puncti B erit linea recta. Sit ista AB, ter
minata ad datum quodris punctum A, e sequatio
qua relatio inter Ordinatam BC. X AbIcisam AB
detinitur, semper induet hanc Formam, Yy = aX
FDXX + CX ] d.
At vero E recta ilta C. B C in unico tantum puncto
occurrat C urrae, ideoq; ad Curram utrinq; terminari
non postit: sit punctum illud C, X incidat recta illa
ad punctum B in rectam quamris aliam positione
datam X ad datum quodris punctum A terminatam
AB: X aequatio qua relatio inter Ordinatam BC. 8
ABICilam AC detinitur semper induet hanc Forma,
Y = 4X3. ] bZX- ] CX Y d.
Finumerando curras horum casuum, IIyperbolam
vocabimus inscriptam quae tota jacet in Alimptoton
angulo ad instar Arperbolae conicae, circumscriptam
quae Alymptotos secat X partes abscictas in Cinu (uo
amplectitur, ambieenam quae uno crure infinito in-
scribitur ex altero circumscribitur, convereentem
cujus crura concaritate lua seinvicem respiciunt de
in plasam eandem diriguntur, divergentem cujus crura
convexitate sua seinvicem recipiunt a in plagas con-
trarias dirisuntur, cruribus contrariis praeditam cujus
crura in partes contrarias convexa unt _ in plasas
contrarias infinita, Conchoidalem quae rertice concaro
_ cruribus divergentibus ad alymptoton applicatur,
ansuineam quae Aexibus contrariis alymproton secat
e
Casus terciu.
Casus quartus.
Nominaformu
pum.

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I145
e utrinq; in crura contraria producitur, cruciformem
quae conjugatam decustat, nodatam quae sciplam de-
cultat in orbem redeundo, cuspidatam cujus partes
duae in angulo contactus concurrunt ex ibi terminan-
tur, punctatam quae conjusatam habet Oralem infi-
nite parram id est punctum, e puram quae per im-
Pollibilitatem duarum radicum Orali, Nodo, C. uI-
Dide de Puncto conjusato priratur. Fodem sentu
Parabolam quoq; conversentem, diversentem, cruri-
bus contrariis praeditam, cruciformem, nodatam, cus.
paatam, punctatam e puram nominabimus.
Iu calu primo si terminus a x aftirmativus est Fi-
sura erit LEyperbola triplex cum (ex cruribus IIY- redundante
perbolicis quae juxta tres Alymptotos quarum nullae ejus cribus A.
lunt parallelae in infinitum prosrediuntur, binae juxta
unamquamq; in Plasas contrarias. Et hae ACymp-
toti s Terminus bXX non deest se mutuo secabunt
in tribus punctis triansulum (Dds) inter se con-
civentes, lin terminus b x x deest conversent omnes
ad idem punctum. In priori catu cape AD =
20, et Ad = A0 = 28, ac junse Dd, Do, X erunt
AD, Dd, Datres AIymptoti. In posteriori duc
ordinatam quamvis BC, et in ea utrinq; producta
cape hinc inde BF s BF sibi mutuo aequales e
in ea ratione ad A B quam habet ,d ad a, junSC9;
AF, AF, X CTUNE AB, AF, AF tres AIympoti.
Hanc autem Fyperbolam rocaus sedundantem
quia numero crurum Fyperbolicorum Sectiones C0-
nicaS superat.
In Lyverbola omni redundante ( neq; terminUS
improcs.
y delit neq; sit bb- 4 ac aequale + a C a Cur ra nUII- perbolae diametra
am habebit diametrum, sin eorum alteTUEEUM aC- C suu crururo
1
Cidat
XIII.
De Fyberbola
XIV.
De hujus TIy
infinttorum.

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EXL
cidat curra habebit unicam diametrum, _ ErCS si
utrumque. Diameter autem semper transit per in-
terlectionem duarum Alymptoton et bilecat rectas
omnes quae ad ACymptotos illas utrinq; terminantur
ee parallelae TunE  ATYmPEOTOtertia. KRq; abSCiRa
AB diameter Fisura quoties terminus er decst.
Diametrum vero absolute dictam hic ex in seguen-
tibus in vulsari signiticatu uturpo, nempe pra ab-
Scista quae passim habet ordinatas binas aequales ac
idem punctum hinc inde insistentes.
Si FIyperbola redundans nullam habet diametrum
vem redundantes fLTaNtUF AE quationis hujuS a X2 ] B X3 f CXX ] dX
quae diametro de= =0 radiceS quatUOE seu valores iptIUS X. Pde
habent Asymoto- Lunto AP, A ~, A X, A P. Frisantur ordinatae
10s crianeulum L L, 202,  PC, ex hae tansent C urram in punctis
totidem P, 2, tu e tangendo dabunt limites Cur-
rae per quos species ejus innotescet.
NTam A FadICeS OINeS AP, A D, AT, AD sunt
reales, ejusdem sieni X inaequales, Curra constat ex
tribus Fyperbolis, (inscripea circumseripta ec am-
bigena) cum Ovali. LExperbolarum una jacet ver-
TUS D, altera versus d tertia vertiis o, e Oralis
semper jacet intra triansulam Dd , atq; etiam in-
ter medios limites rXr, in quibus utiq; tansitur
ab ordinatis n X Wr. FF haec eA Species prima.
Si c radicibus duae maximae A n A p, vel duae mi-
nimae AP, A ~ aequantur inter se, _ ejusdem funt
Tioni cum alteris duobus, Oralis et Hyperbola cir-
cumleripta libi inxicem sunsuntur cocuntibus carum
punctis contactus) et t vel l_ r, _ crura IIyper-
bolae sese decussando in Oralem continuantur, txu-
ram nodatam efficientia. Quae species est secunda.
Fyperbolae no-
stituuntur es tres
capientes
i8.

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(247
Si e radicibus eres maxiae AP, AX, A v, Vel treS Fis. 5, 6.
MInIIa A X, A ~, AP aequentur inter le, Nodus in
cuspidem acutissimum ConvertCtur. Nam crura duo
Elyperbola circumseriptxe ibi in angulo contactus
concurrent et non ultra producentur. Et haec est
pecies tertia.
Si e radlicibus duae media A~ X Ar aequentur in- Fic. 7.
cer se, puncta contactus = X7 coincidunt, e propte-
rea Oralis interjecta in punctum eranuit, e constat
tigura ex tribus Hyperbolis, inscripta, circumseripta
_ amibigena cum puncto conjusato. Ouae est species
quarta.
Si duae ex radicibus sunt impossibiles _ reliquae Fic. 7, 8, 13, 14
duae inaequales _ ejusdem ligni (nam signa contraria
habere nequeunt,) purae habebuntur Lyperbolae tres
Eine Orali vel Nodo vel cuspide vel puncto conju-
sato, _ hae perbolae vel ad latera trianguli ab
Asympeotis comprehenti rel ad ansulos ejus jacebunt
et perinde speciem vel quintam vel sextam consti-
cuent.
Si e radicibus duae Tunt aequales _ aIFera du Fis. 9, 1O, 15, 16.
vel impossibiles lunt vel reales cum signis quae a (is
nis aequalium radicum diverta sunt, fisura crucifor-
mis trabebitur, nempe duae ex Fyperbolis seinvicem
decussabunt idq; vel ad verticem trianguli ab A-
simptotis comprehenti, vel ad ejus balem. Oua
duae species unt septima e Octava.
Si deniq; radices omnes sunt impossibiles vel s Fis. 11, 12.
omnes sunt reales de inaeguales e earum duae Tunt
aftirmatirae et alterae duae nesatirae, tunc duae habe-
duntur Lperbolae ad angulos oppositos duarum
Uu 2
ATymP

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(.148
AGmptoton cum FIyperbola ansuinea circa ACymp
toton tertiam. Quae lpeciescnona.
Fit hi sunt omnes radicum casus possibiles. Nam
li duae radices sunt aequales inter le, e aliae duae lunt
etiam inter se equales, Figura cradet Sectio Conica
cum linea recta.
Si HIyperbola redundans habet unicam tantum
decim redundan- Siametrum sit ejus Diameter AbIcica AB, X aequa-
rescumunicaran CiOnis hujus a X3 ] bXX ) CX  d = O quaerE ETCS Ed-
dices Ceu valores X.
Si radices illa lunt omnes reales e ejusdem heni,
Figura constabit ex Ovali intra triangulum Dd s ja-
cente ex tribus Iyperbolis adt angulos ejus, nempe
circum seripta ad angulum D X inseriptis duabus act
ansulos d X o. Et haec est species decima.
Si radices duae majores lunt aequales a tertia ejur-
dem signi, crura IIyperbolae jacentis rerlus D sele
decultabunt in Forma NVodi propter contactum Ova-
lis. Duae Species est undecima.
Si tres radices lunt aequales, TIyperbola ilta sit
cuspidata sine Ovali. Ouae Species est duodecima.
Si radices duxe minores Cunt aequales e tertia ejus-
dem tgni, Oralis in punctum eranuit. Ouae species
est decima tertia. In speciebus quatuor novissimis
Ayperbola quae jacet verlus D Alymptotos in sinu
uo amplectitur, reliqua duae in linu AIYmPtOLOM
Jacent.
Si duae exradicibus sunt impolsibileshabebunturtres
EErperbola purae linc Orali decustatione vel cuspide.
fit hujus casus species Tunt quatuor, nempe decima
quarta si Fyperbola circumleripta jacet vertus D a
decima
yperbolae duo-
tum Diametro.
Fic. 20.
ut

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Secima quinta si FTyperbola inscripta jacet rextusD,
decima lexta E HTyperbola circumscripta jacet (UD
bali do trianguli Dds, X decima septima si HIy per-
bola inseripta jacet sub eadem batI.
Si duae radices sunt aequales e certia signi diversi Fis. 24.
F18. 23.
Fieura erit cruciformis. Nempe duae extribus Hy-
perbolis seinricem decussabunt idq; vel ad verticem
triansuli ab A(ymptotis comprehensi vel ad ejus ba-
Tem. Ouae duae species sunt decima octara X decima
HOna.
Si duae radices unt inaequales ex ejusdem sioni e
tertia est signi diversi, dux habebuntur LEyperbola
in oppolitis angulis duarum atrimptoton cum Con-
choidali intermedia. Conchoidalis autem vel jace- Fic. 27.
(18. 26.
bit ad ealdem partes alrmptoti lua cum triangulo
ab asimptotis constituto, vel ad partes contrarias;
_ hi duo calus constituunt speciem rigelimam et vi-
gelimam primam.
Frperbola redundans quae habet tres diaetros
constat ex tribus IIrperbolis in sinubus alympEoton redundantes cun
acentibus, idq; vel ad angulos trianguli ab alrmpto. cribus Diametris.
15. 28.
tis comprehensi vel ad ejus latera. Catus prior dat Fig. 29.
Speciem rigelimam secundtam, dt polterior lpeciem vi-
gelImam tertiam.
Si tres alimptori in puncto communi se mutuo
decustant, vertuntur species quinta d sexta in viee vem aundantes
limam quartam, septima X octara in vigelimam cum asymptorii
tribus ad commu-
quintam, e nona in vigelimam sextam ubi Ansuinea ne punctum con-
non transit per concurtum asrmptoton, _ in risel. vergentibus.
mam septimam ubi transit per concursum illum, quo Fis. 30.
Fig. 31.
calu termini b ac d desunt, d concurtus aly mpto- F1 5. 32.
ton est centrum figurae ab omnibus ejus partibus Fis. 33.
Oppoltis
XVII.
Typerbolae duae
XVIIL
Fsyperbolae no-

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l15O
oppolitis aequaliter dictans. Ft hae quatuor species
Diametrum non hrabent.
Vertuntur etiam species decima quarta ac decima
sexta in vigelimam octaram, decima quinta ac de
cima septima in risetimam nonam, decima octava
ex decima nona in tricelimam, et rigelima cum rise.
Cima prima in tricesimam primam. Et ae species
unicam habent diametru.
Ac deniq: species vigelima secunda e vigelims
certia vertuntur in speciem tricelimam secundam cu
jus tres lunt Diametri per concurtum alrmptoton
transeuntes. Duae omnesi convertiones Facillime in-
celliguntur Faciendo ut triansulum ab alymptotis
comprehentum diminuatur donec in Punetum era.
nelcat.
Si in primo aequationum casu terminuS aX nC
defectivae diame- aCIruS est, Figura erit IIyberbola defectira unicam
rum non haben- habens alymptoton ec duo tantum crura Llyperbo.
lica juxta asimptoton illam in plasas Contrarias In-
tinite progredientia. Ft alrmptotos illa est Ordi-
nata prima ec principalis ACF. Si termInUS CY nON
deec troura nullam habebit Diametium, si deest ha-
bebic unicam. In priori casu species sC enume
rantUI.
Si aequationis hujus a x = bX F CXX ] dX ] Z CC,
TadiCeS OIHeS A X, A P, AP, A ∞, Cunt reales e in-
aequales, Figura erit Ayperbola ansuinea alimpto-
con dexu contrario amplexa, cum Ovali conjusata.
Ouae species est tricesima tertia.
Si radices duae mediae AP e Ap aequentur inter
le, Oralis et Anguinea junguntur lele decustantes
in Torma Nodi. Duae est species cricelima quaita.
Fis. 38
syperbola sex
Fid. 4C

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Si tres radices sunt aequales, NNOduS vertCtE in Fis. 41.
cuspidem acutissimum in vertice anguineae. Fit haec
est species tricesima quinta.
Si c tribus radicibus ejusdem signi duae maximae Fis. 43.
AP B A _ Tibi mutuo aequantur, Oralis in punctum
eranuit. Ouae Species est tricesima sexta.
Si radices duae quaeris imaginariae Cunt, Pola na-
nebit Anguinea pura linc Ovali, decussatione, cus
Pide vel puncto conjugato. Si Anguinea illa nOn Fis. 42.
transit per punctum A species est tricelima septima,
Cin transit per punctum illud A (id quod contingit Fis. 43.
ubi termini b ac d detunt,) punctum illud A erit
centrum fisurae rectas omnes per iptum ductas de
ad Curram utrinq; terminatas bilecans. Et haeC
est species tricesima octava.
In altero casu ubi terminus ey deest d propterea
Rioura Diametrum habet, E aequationis hujus aX
=bXX ] CX F d radices omnes AY, A F, A T, Punt ametrum haben-
reales, inaequales e ejuldem signi, figura erit HIyper-
bola Conchoidalis cum Ovali ad convexitatem. Oux
est speciestricelima nona.
es
Fis. 45.
Si duae radices sunt inaequales _ ejuldem signi e Fis. 44.
tertia est Ceni contrarii, Ovalis jacebit ad concari-
tatem Conchoidalis. Fstq; Species quadrasetima.
Si radices duae minores AT, AL, Tunt aequales Fis. 46.
_ tertia Ar est ejusdem signi, Oralis e Conchoi-
dalis junsentur sese decullando in modum NVodi.
Duae species est quadrasetima prima.
Si tres radices unt aequales, Nodus mutabitur in Fis. 47.
Cuspidem et tsura erit Cissois Veterum. Et haec est
species quadragesima secunda.
XX.
ser dolae sep.

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152
Si radices duxe majores sunt aequales, e tertia est
ejuldem tigni, Conchoidalis habebit punctum conju-
satum ad conrexitatem luam, estq; species quadra-
gelima tertia.
Si radices duae sunt aequales Xt tertia est tioni cont
trarii Conchoidalis habebit punctum conjusatum
ad concaritatem luam, eAq; species quadraselima
Quarta.
Si radices duxe sunt impossibiles habebitur COn-
choidalis pura line Orali, Nodo, Cuspide ret
puncto conjusato. Ouae lpecies est quadraselima
quinta.
SiguandO in primO RGUATIOMLII CALU TermInUS a X3
rem Parabolicae Clees e terminus bZ X non deest, Figura erit II)-
Diametrum non Perbola Parabolica duo habens crura Lly perbolica ad
Unam Alymptoton SAC X duo Parabolica in pla-
sam unam e eandem conversentia. Si terminus
ex non decst figura nullam habebit diametrum, Cin
dees habebit unicam. In priori casu species sunt
Mae.
Si tres radices AP, A w AX aequationis hujus
bX3 ] CZ -] dX ] : ce =0 unt inaequales X ejuldem
sioni, figura constabit ex Ovali X aliis duabus C urvis
quae partim FTrperbolicae lunt a partim Parabolicae.
Nempe crura Parabolica continuo ductu junguntur
cruribus IEyperbolicis sibi proximis. Fit haec est
species quadregelima lexta.
Si radices duae minores unt aequales de tertia est
ejusdem Pioni, Oralis dc una Currarum illarum
yperbolo. Parabolicarum junguntur X se decustant
in tormam NVodi. Oux species est quadrasesi.ni
Sepeima.
Fig. 49
i
48
15. 48, 45
i
Tsyperbola sep-
habentes.

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153
Si tres radices sunt aequales, Nodus ille in CuL- fis. 52.
Pidem vertitur. FCq; Species quadraselima octava.
Si radices duae majores unt aequales d tertia est Fis. 53.
ejuldem signi, Oralis in punctum conjusatum eva-
muit. Juae species eAt quadraselima nona.
Si duxe radices lunt impossibiles, manebunt purae Fis. 53, 54
illae duae currae EIyperboloparabolicae sine Oraliu
decullatione, cuspide vel puncto conjusato, et spe
Ciem quinquaselimam constituent.
Si radices duae sunt aequales dt tertia eAt (igni COn. L18. 53.
trarii, Currae illae hyperbolo parabolica junguntur
sele decussando in morem crucis. L.Cq; Species quin-
quaselima prima.
Si radices duae unt inaequales et ejuldem signi et Fis. 50.
certia est ligni contrarii, ligura eradet AIxperbola
anouinea circa AIYmptoton ACI, cum Parabola con-
Sugata. Ft haec est species quinquagelima secunda.
In altero casu ubi terminus er deest e figura
Diametrum habet, si duae radices aequationis hujus ruor Parabot
bXZ Y CX ] d =0 Tunt impossibiles, duae habentur Diametrum ha-
bentes.
figurae hrperbolo-parabolicae a Diametro AB hinc ris. 57.
inde aequaliter distantes. Ouae species est quinqua.
selima tertia.
Si aequationis illius radices duae lunt impossibiles, ris. 58.
Fisurae hyperbolo parabolicae junguntur sele de-
cultantes in morem crucis, ex speciem quinquaseli-
nam quartam constituunt.
Si radices illae sunt inaequales X ejusdem signi, Ha- Eis. 50.
Detur Irperbola Conchoidalis cum Parabola ex
eodem latere ACymptoti. Fcq; species quinquage
ma quinta.
XXII.
Syperbolae qua

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fig. 60.
154
Si radices illae Tunt signi contrarii habetUE C On-
choidalis cum Parabola ad alteras partes ACYmptoti.
Duae species est quinquasetima sexta.
(Siquando in primo aequationum casu terminus
verbolismi tsyper Uterq; a X _ b X X deest, figura erit FIrperbolismus
sectionis alicujus Conicae. IIyperbolilinum Agurae
voco cujus Ordinata prodit applicando contentum (ub
Ordinata Rrura illius e recta data ad ABCcictam com-
munem. ITac ratione linea recta vertitur in hyper.
bolam Conicam, ex sectio omnis Conica vertitur in
aliquam tisurarum quas hic Fyperbolilmos sectio-
num Conicarum voco. Nam aequatio ad Aguras
de quibus asimus, nempe Xy y ] Cy = Cx F d, seu
=
et V cc + 4dX Y 4 CXX generatur appli-
cando contentum sub Ordinata sectionis Conicae
CtV ec F 4 dX F + CX X _ recta data m ad currarum
Abscissam communem X. Unde liquet quod figura
genita LEyperbolismus erit Iperbola, Fllipleos vet
Parabolae perinde ut terminus c Z aftirmatirus est
vel nesatirus vel nullus.
Typerbolimus Hlyperbolae tres habet alumptotos
quarum una est Ordinata prima ex principalis Ad,
alterae duae sunt parallelae ABICillae AB _ ab eadem
hinc inde aequaliter distant. In Ordinata principali
Ad cape Ad, A5 hinc inde aequales quantitati VC
et per puncta d ac s’agc d8, 8y Alymptotos AB.
Ccistae A B parallelas.
Ubi terminus ey non deest tigura nullam ha-
bet diametrum. In hoc casu E aequationis hujus
CXX ] dX ] CC =0 radices duae AP, Ap sunt reales
XX
Ouatuor TYy
bola

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T1G5)
e inaequales (nam aequales esse nequeunt nili Agura Fis. Si.
sit Conica sectio) figura constabit ex tribus Hlyper-
bolis libi oppolitis quarum una jacet inter alymp-
totos parallelas et alterae duae jacent extra. ft haec
est species quinquasetima septima.
Si radices illae duae lunt impossibiles, habentur IIy-
Derbola duae oppolitae extra asymptotos parallelas et
Anguinea hyperbolica intra caldem. Hlaec figura
duarum est specierum. Nam centrum non habet Fis. 62:
ubi terminus d non deest; sed si terminus ille dec( 18. 63.
punctum A est ejus centrum. Prior species est quin-
quagesima octara, polterior quinquagelima nona.
Duod E terminus ey deest, tigura constabit Cx Fis. 64
tribus hrperbolis oppolitis quarum una jacet inter
aermptotos parallelas _ alterae duae jacent extra ut
in specie quinquaselima quarta, et praeterea diame-
trum habet quae est abscista AB. Ft haec est species
Texagesima.
TIrperbolismus Fllipseos per hanc aequationem de-
XNIV.
tinitur Xy y Y CY = CX ) d, e unicam habet aCymP Mps
toton quae est Ordinata principalis Ad. Si terMInUS Fis. 65.
eynon deect, tixura eAt Fyperbola anguinea sine dia-
metro atq;e etiam sinc centro li terminus d non deest.
Duae species est sexagelima prima.
At Ei terminus d deest, tixura habet centrum sine Fis. 66.
diametro e centrum ejus est punctum A. Species
vero est lexaselima secunda.
tt si terminus ey decst _ terminus d non decst, Fis. 67.
Fisura est Conchoidalis ad atymptoton AC, habetq;
diametrum sine centro, e diameter ejus est AbIciAa
AB. Duae species cst lexagelima tertia.
X
Ll)det.

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(156
FIyperbolismus Parabolae per hanc aegrrationem
lismi Parabola. dCFMIEUT Z Y Y-F CY = d; ex duas habet alymptotos,
AbIcictam AB _ Ordinatam primam E principalem
AC. IEyperbolae vero in hrac Agura Tunt duae, non
in alimptoton angulis oppolitis led in ansulis qui
lunt deinceps jacentes, idq; ad utrumq; latus ab.
scislae AB, _ vel sine diametro Ei terminus cy ha-
betur, vel cum diametro si terminus ille deest. Ouae
duae species tunt sexagesima quarta e Cexagelima
quinta.
In secundo aequationum casu habebatur aequatio
XY = 283] DZX ] CX ] d. Et Agura in hoc ca(U
hrabet quatuor crura intinita quorum duo Cunt hy-
perbolica circa alimptoton AC in contrarias partes
tendentia et duo Parabolica conversentia e cum
prioribus Speciem Pridentis Fere efformantia. FAq;
haec Figura Parabola ilta per quam Cartelius aequa-
tiones lex dimentionum construxit. Ihaec est igitur
species sexagelima sexta.
In tertio casu aequatio erat Y V = aX F DZX F CX
du e Parabolum desienat cujus crura divereunt
ab invicem X in contrarias partes infinite proore-
diuntur. AbIciCa AB est ejus diameter e species ejus
Cunt quinq; sequentes.
Si aequationis a x- f DX2 F CZ ] d = 0 radices om-
nes AT, AI, AF sunt reales _ inaequales, tigura est
Parabola divergens campanitormis cum Ovali ad
verticem. Ft species est lexagelima septima.
Si radices duae lunt aequales, Parabola prodit vel
nodata contingendo Oralem, vel punctata ob Oralem
infinite parram. Ouae duae species lunt sexagetima
octara et sexagetima nond.
XV
Duo Fsyperbo-
Fis. 6E
Fig. 69
Tridens.
EXVII
Parabolae quin-
que divergentes.
Fig. 70, 71.
S

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TB
Si tres radices Cunt aequales Parabola erit cuspi- Fis. 75.
aata in vertice. Ft hae est Parabola Neiliana quae
vulgo Temicubica dicitur.
Si radices duae unt impossibiles, habetur Parabola Fig. 73, 74.
pura campanitormis speciem septuagesimam primam
constituens.
In quarto casu aequato crat y = aX ) bXX ] CX AXVIII.
d, e haec aequatio Parabolam illam WV allisianam Parabola cubica
delignat quae crura habet contraria e cubica di-
Ci lolet. Fc sic species ommino sune leptuaginta
duce.
Fis. 71.
Si in planum infinitum a puncto lucido illumina-
tum umbrae tigurarum projiciantur, umbrae lectio. rum per Omoiu
num Conicurum semper erunt sectiones Conica, ea
Curvarum secundi generis semper erunt C urrae se
cundi seneris, exe currarum tertu seneris lemper
erunt Currae tertii generis, et sic deinceps in IntimI-
tum. Ft quemadmodum Circulus umbram proj
ciendo generat sectiones omnes conicas, sc Parabola
quinq; diversentes umbris luis generant e exhri-
bent alias omnes secundi generis curras, a sc
Currae quaedam simpliciores aliorum generum inve-
niri possunt quae alias omnes eorundem generum
curras umbris fuis a puncto lucido in planum Pro-
sectis Formabunt.
Diximus Curvas secundi generis a linea recta in
punctis tribus secari posse. Florum duo nonnun. eta duplict
quam coincidunt. UE cum recta per Ovalem intr-
nite parram transit vel per concurlum duarum par-
tium Currae se mutuo secantium vel in culpidem
cocuntium ducitur. Et siquando rectae omnes in
plagam
XXIX.
Genesis Curva
XXZ.
Curvarum pun

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L158.
plasam cruris alicujus infiniti tendentes Curram
in unico tantum puncto lecant (ut fit in ordinatis
Parabolae Cartelianae et Parabolae cubicae, nec non in
rectis AbIcisae Iyperbolismorum LIyberbolae _ Para-
bolae parallelis) concipiendum est quod rectae illae
per alia duo Curva puncta ad infinitam distan.
tiam lita (ut ita dicam) transeunt. Hlujusmodi
intersectiones duas coincidentes Eire ad finitam
Cint distantiam Cire ad infinitam, vocabiimus pun-
ctum duplex. Currae autem quae habent pun-
ctum duplex describi postunt per sequentia Theo-
remata.
T. Si anguli duo magnitudine dati PAD, PBD circa
scriptione orga- Polo5 Positione datos A, B rotentur, _ eorum crura
AP, BP concursu suo P percurrant lineam rectam;
crura duo reliqua AD, BD concursu suo D descri-
bent sectionem Conicam per polos A, B transeun.
tem: praeterquam ubi linea illa recta transit per po-
lorum alterutrum A vel B, vel anguli BAD, ABD
Timul cranescunt, quibus in casibus punctum D de-
Feribet lineam rectam.
2. Si Crura prima AP, BP concurTU CUO P
percurrant sectionem Conicam per polum alter-
utrum A transeuntem, crura duo reliqua AD, BD
concursu suo D describent Curram secundi gene
ris per polum alterum B transeuntem _ pun-
ctum duplex habentem in polo primo A per quem
sectio Conica transit: praeterquam ubi anguli
BAD, ABD cmul eranescunE, quo casu pun-
ctum
XXX
Theoremata de
Curvarum de-
nica

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C159)
ctum D describet aliam sectionem Conicam per po-
lum A transeuntem.
3. At E sectio Conica quam punctum P perCUE-
rit transeat per neutrum polorum A, B, punctum
Ddescribet curram secundi vel tertui generis pun-
ctum duplex habentem. Et punctum illud duplex
in concursu crurum describentium, AD, BD in-
venietur ubi anouli BAP, ABP Amul cranelcunt.
Curra autem descripta secundi erit generis (I an-
suli BAD, ABD timul cranelcunt, alias erit ter-
tii generis ex alia duo habebit puncta duplicia in
polis A _ B.
Jam sectio Conica determinatur ex datis ejus
punetis quinq: ∞ per eadem sic delcribi potest. nicarum desch
Ventur ejus puncta quinq; A, B, C, D, F. Jun- tio per data quin-
santur eorum tria quaeris A, B, C. _ trianguli ABC que puncta.
potentur anguli duo quiris C. AB, C. B A circa Ver-
tices TUOS A _ B, _ ubi CruTUM AC BC intersectio
C. Successire applicatur ad puncta duo reliqua D, l
incidat interlectio crurum reliquorum AB _ BA
in puncta P e O. Rsatur _ infinite producatur
recta PO, _ anculi mobiles ita rotentur ut intei-
sectio crurum AB, BA percurrat rectam PO, X
crurum reliquorum intersectio C describet propol
tam sectionem Conicam per Pheorema primum.
Curvae omnes secundi generis punctum duplex cundigeneris past
habentes determinantur ex datis carum punctisctum duplex ha
bentium deserie
septem, quorum unum est punctum illud duplex, rio per data sep-
X tem puttm
XXXII.
dectionum Co.
ZXXIII.
Curvarum se

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C
et per eadem puncta sic delcribi porsunt. Dentur
Carrae describendae puncta quaelibet septem A, B, C
D, Eu F, C quorum A est punctum dupsex. Jun-
eantur punctum A X alia duo quaeris c punctis puta
B _ C.; ee trianguli ABC rOtetur tum angulus
C. AB circa verticem Cuum A, tum angulorum reli-
quorum alteruter ABC circa verticem luum B. Fit
UDI CrUTUIM AC, BC. concurtus C. succelsire appli-
catur ad puncta quatuor reliqua D, F F, G incidat
concurtus crurum reliquorum AB e B A in puncta
QuatLOr P, Q, R, S. Per puncta illa quatuor e
quintum A describatur sectio Conica, X anculi prae-
tati C. AB, C. BA ita OteNEUL UE CrUTUM AB, B A
concursus percurrat sectionem illam Conicam, E
concurtus reliquorum crurum AC, BC. describet
Curram propolitam per Pheorema lecundum.
Si vice puncti C datur positione recta BC. quae
Curvam delcribendam tansit in B, lineae AD, AP
coincident, et vice anguli D A P hrabebitur linea recta
circa polum A rotanda.
Si punctum duplex A infinite distat debebit Recta
ad plasam puncti illius perpetuo dirisi e motu pa-
callelo terri interea dum angulus ABC circa polum
B POtatur.
Delcribi etiam postunt hae currae paulo aliter per
Pheorema tertium, sed descriptionem simpliciorem
poluisse sufticit.
Eadem methodo Curras tertii, quarti de superio
rum generum describere licet, non omnes quidem
Sed quotquot ratione aliqua commoda per inotum
localem deseribi posune. Nam curram aliquam
secundi

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(16T)
secundi vel superioris generis punctum duplex non
habentm commode describere Problema est inter
diffciliora numerandum.
Curvarum utus in Creometria est ut per earum
intersectiones Problemata Colvantur. PropOnatuE quatichum per a
aequatio construenda dimentionum norem XPF ) - B X7 scriptionem Cur-
t CX  dx5-] Cxt  F X3 ] 9XX ] hX  K =0. UBi varum.
M
b, C, d, Dc. Signiticant quantitates qualris datas
lignis Tuis L X - aftectas. ANumatur aequatio ad
Parabolam cubicam X = Y, ec aequatio prior, scri
Dendo Y prO X, Cradet v F BXYY F CYY + dXXY
CX V -)  in V -F FX3 - ]. 9XX ) HX ] K =0, aequatio ad
Curram aliam secundi generis. Ubi in vel Fdcese
Potest vel pro lubitu astumi. Et per harum Curra-
eum descriptiones e intersectiones dabuntur radices
aequationis construendae. Parabolam cubicam semet
deleribere sufficit.
Si aequatio construenda per defectum duorum ter-
minorum ultimorum lx X H reducatur ad septem
dimentiones, Curra altera delendo m, habebit pun-
ctum duplex in principio abscistae, et inde facile de-
Tcribi Potest ut TUPEa.
Si aequatio construenda per detectum termino-
rum trium ultimorum sZX ] RX K reducatur ad
sex dimentiones, Curra altera delendo feradet
sectio Conica.
Fit si per detectum sex ultimorum terminorum
equatio construenda reducatur ad tres dimentiones,
incidetur in constructionem Wallisianam per l’ara-
bolam cubicam et lincam rectaM.
C. On-
XXXIV.
Constructio a-

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Construi etiam postunt aequationes per HIyperbo-
lilmum Parabolae cum diametro. Ut h construenda
sit haec aequatio dimentionum novem termino penul-
timO CaTENS, d F CXX Y dX3. ] ex  FX 5X-] hX
=M
) kXS F IX =0; allumatur aequatio ad Ayperbolil-
mum illum ZXY = 1 _ Scribendo y PrO =, aequatio
construenda vertetur inhanc ay F CVY F dX yy ) CY
FFxY Y mXXγ. - 8. ] hX -] kXX ] IX3 =O, qua CUT-
vam secundi generis delignat cujus delcriptione
Problema Tolretur. Ft quantitatum m ac s alter-
utra hic deesse potest, vel pro lubitu assumi.
Per Parabolam cubicam d Curras tertii generis
construuntur etiam aequationes omnes dimentionum
non plusguam duodecim, et per eandem Parabolam
e curras quarti generis construuntur omnes dimen-
tonum non plusquam quindecim, Ft BC deinceps in
intinitum. Ft curvae illa tertii quarti d luperiorum
generum describi semper postunt inveniendo eorum
puncta per Creometriam planam. UE si construenda
AE aequatio ~ X ) a X 10-= BX-] CX ] dX ] Cx6] FX5
8X2 ] hx3 f ixX F kX Y 1=0, e descripta
hrabeatur Parabola Cubica; sc aequatio ad Pa-
rabolam illam cubicam X = y, a scribendo y
PTO X aequatio construenda vertetur in hanc
74-7 aX 53 =) CXXYY F FXXY - IXX =O, quae e
=dx
BX +KX
aequatio ad Curram tertii generis cujus descriptione
Problema solvetur. Deleribi autem potest haec Curra
inreniendo ejus puncta per Creometriam planam, prop
terea quod indeterminata quantitas x non nili ad
duas dimentiones ascendit.

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urvarum Lal. 1
ex

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l
Mh sll
HI
I
NIEDERSACHSISCHE LANDESBIBLIOTHEK
:Loibn. Mar9. 1
GOTTFRIED WILHELM LEIBNIZ BIBENTHEK

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urvarum Tab. I.

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1111)
l A.II (III
L A. L. Ait. AB tHC. A . Sat .  t.. Lf s.sa t H . fata.  t . sa   s. l. H. uld sit set    fita. L)I I. L. Ait. (B Aet A. HC H. IBILA BA. HILII IAIIHIIIII
e
NIEDERSACHSISCHE LANDESBIBLIOTHEK
:Leiton. Mar9. 19
SOTTFRIED WILHEEMELIONIL BIDENTHEK

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urvarum Tab. III.

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sl s slis
stant attat tititi
Mn sI
11
silist 
ttsitat stits ilii
Mpl
cibn. Mar9. 19.
GOTTFRIED WILHELM LEIBNIZ BIBLIOTHEK
NIEDERSACHSISCHE CAHDLSBIBLIOTHEK

## Folio  -  — 1677894601:0349
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e at clc. 2t.

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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 5 lines, status machine
 s fs f rere s erf u. er fH. t Mses f ss. Se suss  su sete s sal HLIIBI. sub. s  st. .I LHIIIIII. solu IBI IIII HIB.LI.IAI.BHBI IIIIIIIB
ur: Loiton. Marg. 13
39
GOTTTHLD NNEIILLLTCLIOTM BIDEIBTHEK
NIEDERSACHSISCHE LANDESBIDENTHEK

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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
cirvarum eu..
DWILHELMLEIBN

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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 6 lines, status machine
s si
11111l1111t 1t1tt 111 1t11111 t 11t 1tut 1t 1 s
8
dE
OTTERIED WILHELM LEIBNIZ BIBLRTHEK
enteideiIE

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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
urvarum lab. V

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11
: Loibn. Mar9.
SOTTTRILD DNCMLLETLLIBHIL BIBEITHEK
VIEDERSACNSISEMIL ENNODLSONDLRTHEK

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 m   atem 
D F,
Duadratura Currarum.

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II
si
 tt     i set   tt.    a tis

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165
 LLct
Uantitates Mathematicas non ut ex partibus
quam minimis constantes, sed ut motu conti-
nuo descriptas hic considero. Lineae deleri-
buntur ac describendo generantur non per appoli- sid motu partes
tionem partium sed per motum continuum puncto.
rum, Cuperticies per motum linearum, solida per
motum luperticierum, ansuli per rotationem late-
rum, tempora per Auxum continuum, et siC In Cae-
teris. Ila Ceneles in rerum natura locum vere ha-
bent X in motu corporum quotidie cernuntur. Ft
ad hunc modum Veteres ducendo rectas mobiles in
lonsitudinem rectarum immobilium genelin docue
runc rectangulorum.
Considerando isitur quod quantitates aequalibus
temporibus crescentes e crescendo senitae, provelo-
citate majori vel minori qua crelcunt AC GCNEFANEUE,
cradunt majores vel minores; mechodum quaerebam
deter.
apponuntur

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(266
determinandi quantitates ex relocitalibus motuum
vel incrementorum quibus generantur; et ha5 mo-
tuum vel incrementorum velocitates nominando Flu
aiones _ quantitates senitas nominando Fluentes, in
cidi paulatim Annis 16658 1666 in Mechodum Flu
datem I
Lluxiones unt quam proxime ut lluentium auo
menta aequalibus temporis particulis quam minimis
genita, X ut accurate loquar, sunt in prima ratione
ausmentorum nalcentium; exponi autem postunt per
lineas qualcunq; quae lunt iplis proportionales. Ut
E aFCaABC, ABDC Ordinatis BC, BD Cuper
baE A B unitormi cum motu progredientibus descri-
bantur, harum arearum Auxiones erunt inter se ut
Ordinatae describentes BC. _ BD, X per Ordinatas
illas exponi possunt, propterea quod Ordinatae illa
sunt ut arearum augmenta nascentia. Progre-
diatur Ordinata BC de loco Fuo BC in locum
quemvis novum b. C. Compleatur parallelogram-
mum BC ED, ac ducatur recta VPII quae Cur-
vam tansat in C ipAlq; DC e B A productis OCCUT-
rat in T _ V: e Abscistae AB Ordinatae BC, 8
P InCa CAEVa AC. C auomenta modo senita erunt
BB, FCeE CC; _ in horum augmentorum na(cen-
tium ratione prima Tunt latera trianguli C. F. I, id eoq;
Auxiones iplarum AB, BC Q A C lune ue trianouli
illius C. F I latera C. F, F. T _ CT EE per CadeIM
latera exponi poltunt, vel quod perinde es per la
tera trianguti contimitis VBC.
Todem recidit E Fumantur Duxiones in ultima
ratione partium erarieicentium. ASaLIE ECCIA C C
et producatur eadem ad H. Redeat OrdinatA DC
Ergo ad ministi
partes recurrit

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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
in locum Cuum priorem BC, e cocuntibus punctis
C X cu recta C. K coincidet cum tansente C HI, ec
triangulum eranclcens C. Fc in ultima sua forma
eradet simile triangulo C. F. T, _ ejus latera cranel-
centia C F, F C _ C c erunt ultimo inter sc ut funt
trianguli alterius C. F Y latera C. F, FI XC, T, &
propterea in hac ratione lunt Auxiones linearum AB,
BC. X AC. Si puncta C. _ c parro quoris inter-
vallo ab invicem distant recta C. R parro interrallo a
tansente C TIdistabit. UE recta CK cum tansente
C Flcoincidat d rationes ultimae lincarum C F H C X
Cc inveniantur, debent puncta C. Xt c coire _ OIm-
pino coincidere. Friores quam minimi in rebus
mathematicis non sunt contemmendi.
Simili argumento s circulus centro B radio BC
descriptus in longitudinem ABIcissae AB ad angulos
rectos unitormi cum motu ducatur, Auxio solidi se-
niti ABC erit ut circulus ille generans, e Auxio su-
perticiei ejus erit ut perimeter Circuli illius ee
Auxio lineae currae AC. conjunctim. Nam quo tem
vore Tolidum ABC. generatur ducendo circulum
illum in lonsitudinem AbIcisae AB, eodem super-
ticies ejus generatur ducendo perimetrum circuli il-
lius in longitudinem CUrVae AC.
Recta P Bcirca polum datum P revolvens secet aliam Fig. 2.
positione datam rectam AB: quaeritur proportio suxio-
num rectarum illarum AB  PB. Progrediatur
recta PB de loco uo PB in locum novum PB. In
PB CapiatUE P C iPEP B aequalis, e ad AB ducatur
PD c, ut angulus b PD aequalis sC ansulo DBC;
X ob similitudinem triangulorum bBC, bPD erit
rusmentum Bb ad ausmentum C. b ut Pb ad Db.
Redeat

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L168)
Redeat jam Pb in locum Cuum priorem PB vE aU
imenta illa eranescant, d eranelcentium ratio ulti-
ina, id est ratio ultima PB ad DB, ea eric quae est
PB ad D B, existente angulo PDB recto, _ prOP.
terea in hac ratione est Buxio ipsius AB adt Auxionem
iptius PB.
Recta PB circa datum Polum P revolvens secet
alias duas positione datas rectas ABd AF in B 
F: quaeritur proportio puxionum rectarum illarum
AB D AF. Frosrediatur recta revolvens PB de
lOco Tuo P B in IOCUI ROVAIM P B reCtAS AB, A L in
punctis D _c secantem, e rectae AF parallela BC
ducatur ipsi Pb occurrens in C, _c erit BB ad BC. ut
AD ad AC, _ BC. ad F. C ut P B ad P F, e conjunctis
rationibus BB ad F C ut ABEPB ad ACKPF.
Redeat jam linea PB in locum Cuum priorem PB, 8
ausmentum eranelcens BB erit ad ausmentum era-
nelcens F. C Ut ABKCP B ad AFNcP L, ideoq; in
hrac ratione est Duxio rectae AB ad Auxionem rectae
AF.
Hinc E recta rerolrens P B lineas quatris CurraS
Policione datas secet in punctis B a li, e rectae jam
inobiles AB, AF C urvas illas tansant in Sectionum
punctis B _ F: erit Auxio Currae quam recta, AB
tansit ad tuxionem Cuerae quam recta AV tangit.
UE ABSCPB ad AE: CPF. Id quod etiam creniet
Et recta PB Curram aliquam potitione datam perpe.
tuo tansat in puncto mobilil.
Fluat quantitas x uniformiter  invenienda sit puxio
quantitatis X. Duo tempore quantitas Z Auendo
eradit X F0, quantitas X eradet X. ] on, id est
per methodum serierum infinitarum, L-) nOXR.,

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C169
n. n∞0XM2] 9c. Ft aurmenta O X nOXN. I ] nn. nOOXn. 2
-1c. Cunt ad invicem ut I _ nX n. 1 ] nn. n07 n. 2 ] - 19C.
Fvanescant jam auomenta illa, X eorum eatio
ultima erit I ad nxn: ideoq; Auxio quantitatis
Z est ad Auxionem quantitatis X ut c ad 1X
Similibus argumentis per methodum rationum
primarum at ultimarum collisi postunt Auxiones li-
nearum seu rectarum seu currarum in casibus qui-
buscunque, ut de duxiones superticierum, angulo
rum e aliarum quantitatum. In finitis autem quan.
titatibus Analysin sic inctituere, de tinitarum nascen-
tium vel eranelcentium rationes primas vel ultimas
inrestisare, consonum est Creometriae Veterum: et
volui octendere quod in Methodo Eluxionum non
Opus st houras intinite parvas in Creometriam intro-
ducere. Peragi tamen potest Analysis in figuris qui-
buscunq; Peu finitis seu intinite parris quae figuris
eranescentibus finsuntur similes, ut et in tiguris quae
pro intinite parvis haberi Colent, modo caute pro-
sed aequelante procedindum est sive sefinite parvis sive fluxo
CedtaS. nibus utare
Fix Fluxionibus invenire Fluentes Problema dif-
ficilius est, _ solutionis primus sradus aequipollet
Duadraturae Currarum; de qua sequentia olim
(crip(I.

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2A
C
d. 
D F
a I
U
Ouadratura CCUrrarum
llantitates indeterminatAS UE MOtU Perpetud
crelcentes vel decrescentes, id est ut Auen-
tes vel detluentes in lequentibus considero, detignoq;
LITerIS Zy Y, X, V, e carum Auxiones seu celeritates
crescendi noto iildem literis punctatis 2, Y, X, V.
Sunt ex harum puxionum Auxiones seu mutationes
masis aut minus celeres quas iplarum Z Y, X V
Auxiones secundas nominare licet _ Sc dignare
en Y, X, V, e harum Auxiones primas seu iparUM
Zy Y, Z9 V AUXIOneS TETEIAS AC Z9 γ, Z, V, X quartaS HC
27 Y, X V. Et quemadmodum 2, Y, X, V TunE AU-
xiones quantitatum Z, Y, X, V, X hae Cunt Auxiones
quantitatum 2, 8, X, V e hae lunt Auxiones quantita
EU PrIMATUI Z, Y, Z, V: lic he quantitates contude-
rari postunt ut Auxiones aliarum quas sic designabo,
praestat non punctis sed numeris, uti afficientibus notamm differentialita
quaemihi est d. ita enim exponentes ediam frachi irrationales, indefiniti
differentialitatis adhiberi possunt, quod punctis indicari nequit.

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TF7T
2, Y, Z, V, ee hae ut Auxiones aliarum Z9 Y, X, V, &
11 1 u
1
hae uE Auxiones aliarUI Z, Y, Z, V. Dehionant igitur
29 29 292, 29 2929 2. Dc. Teriem quancitatum quarum
quaelibet posterior eAt Duxio praecedentis et quaelibet
prior est Auens quantitas Auxionem habens suble-
quentem. Similis eA Series Va2 22, V a2 22,
22. 22, V22 22, V22. 22, V22. 22, Ut de
series
22 7 22 22 - 22 22.  22 22 23 22 ] 22
22  22
2 2. a Z. 2 2 a 2. a
E omnia melius praestantur praefigendo literam d
uo differentialitatis es poneuto attaectam
C notandum est quod quantitas quaelibet
prior in his seriebus est ut area hourae curviliniae
cujus ordinatim applicata rectangula est quantitas
posterior _ abscilta cst Z: Uti V aZ ZL aFCA CUrVA
cujus ordinata est V a2- 22 _ ab(ciAa Z. Ouo au
tem spectant haec omnia patebit in Propolitionibus
Quae lEGNUNEUT.
PROF.

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PROP. I. PROB. I.
Data aequatione quotcunqu fluentes quantitates indol
vente, invenire sluxiones.
Solutio.
Mulciplicetur omnis aequationis terminus per in-
dicem dignitatis quantitatis cujulq:e Auentis quam
involvit, ex in lingulis multiplicationibus mutetur
dignitatis latus in Auxionem Cuam, e 288rC9a-
tum factorum omnium sub propriis cenis exit
aequatio nOVa.
Explicatio.
Sunto a B, C, d 2c. quantitates determinatae _
immutabiles, e proponatur aequatio quaeris quan
citates Auentes 2, Y, Z Oc. involrens, uti X = Zy Y
 aa2 b =0. Multiplicentur termini primo per
indices dignitatum x, e in singulis multiplication-
Dus pro dignitatis latere, seu x unius dimentionis,
Scribatur Z, _ Cumma Lactorum erit z X X- Xy y. Idem
trat in y a prodibit- XVY. Idem Aat in 2 X prO-
dibit a a2. Ponatur cumma Factorum aequalis ni
hilo, _ habebitur aequatio 3XX -- Xy y - 2Xy y
F222 =0. Dico quod hac aequatione detinitur se-
latio Auxionum.

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Demonstratio.
Nam sit 0 quantitas admodum parva s lunto
O2, OY, OZ, quantitatum 29 Y, X momenta 1d est in-
crementa momentanea (ynchrona. FF s Gjuantita-
tes Auentes jam lunt 2, V e Z, hae neit momentum
temporis incrementis Tuis 92, oy, ox auctae, eradent
2- O2, Y-  OY, X- j Ox, quae in aequatione pria pro
2, Y e X seriptae dant aequationem X3 - ) 3XXOX
= 3XOOXX ] 03x3- XYY - OXYY 2XOYY - 2X0OYY
XOOYY XOYY  aaZ- 2a07. b3 =0. SubducatUE
aequatio prior, _ rehiduum dirilum per o erit ZXX2
) 3XXOF -] X30O =XYY =2XYY -2XOyY -ZOYY -XOOYY
=ad2 =0. Minuatur quantitas o in insinitum, d neg-
lectis terminis eranelcentibus restabit 3rX? Xyy
2XγY + aa2. =0. D. F. D.
Explicatio plemor.
Ad eundem modum si aequatio eset X3 X7)
Faa V aX YY b3 = 0, PrOdUCCTCTUT 3X2X. Xyy
2XVV - dar aX YY = 0. UBi R AuxiOneMV aX- Vy
tollere relis, Pore V aX yy = 2, e Cxit aX YY = 2

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e (per hanc Propohtionem) aX =yY = 2 L2 PCV
2X 273
Z
27 HOC es aX 2y
= Y aX- 9y. Ft
inde 3X2X. Xyy- 2X7)
ax YY
a X 22aYY
Vax yy
=0
lit per operationem repetitam persitur ad Auxio
nes secundas, tertias e leguentes. Sit aequatio
273- 24  24 =0, e hiet per operationem primam
233 , 32772-422 =0, per Secundam 273 ]- 62772
32772--62727- 42.23-122223 =0, Per TCTEIAIM
2.33 -, 92732 f92772-7 282], y-7. 32772]- 182.7y7
1623- 42. 23- 362222 2422 =0
Ubi vero se pergitur ad Auxiones secundas, Ter-
Eias _ sequentes, convenit quantitatem aliquam ut
unitormiter Auentem considerare, et pro ejus Auxione
prima unitatem lcribere, pro secunda vero e se-
guentibus nihril. Sit aequatio 273 - 2+ ] a4 = 0, ut
supra; X Huat Z unitormiter, litq; ejus Auxio unitas,
et tiet per operationem primam y3 - 327y7 423 =0,
per Secundam 6yy2 ]. 3277 2  627 2y - +272 = 0.
Per tertiam 9yy2 f 18y2Y. = 32yy  f. 1827yy + 6273
2 4i = O.
Tn

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C+
6
In hujus autem generis aequationibus concipien-
dum est quod duxiones in lingulis terminis sint ejul-
dem ordinis, id est vel omnes primi ordinis Y, 2.
vel omnes secundi Y, y2, y2 2, vel omnes tertii
Y, VV, Y29 γ3, V 29 γ2 23 _C. Et ubi res aliter se
habet complendus est ordo per lubintellectas Auxio
nes quantitatis unitormiter Auentis. Sic aequatio
norissima complendo ordinem tertium ft 92yy
28Z72y-]-32.7y2- -187γYY ]. 6277-24223 =0.
PROP. II. PROB. II.
Invenire Curvas quae quadrari possunt.
Sit ABC. fgura invenienda, BC. Oedinatim ap. F15. 4.
plicata rectangula, de AB abscissa. ProduCatuE
C B ad F ut sE BF = 2, d compleatur paxallelo-
GFAMIUM ABF. D: _ aPEArUM ABC, ABFD
Auxiones erunt ut BC. X BF. APumatur igitur
aequatio quaeris qua relatio arearum detiniatur, e
inde dabitur relatio ordinatarum BC ec BF per
Prov. I.. G. F. L.
Ftujus rei exempla habentur in LloBon
duabus sequentibus.
 ACOP.

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F
PROP. III. YHE OR. I.
Si prO abSCICa A B CE aFCa A F, PCU ABKF PFOA
milcue scribatur Z, ∞ (i pFO C -  frn + 872n -) - h23n.  XC.
seribatur R: EE autem aTCA CUEVa 2BR erit.
ordinatim applicata BC =
D
en + D
+ 0
C + an Ec. + 2anB + 3an hE. 3n + _C. IR Z. B. 2 R a. 1
Demonstratio.
Nam sI sIt 2BRN = V, erit Per PFOP. 1, D7ZRA
=AZRR~ =V. PrO Ra in primo aequationis ter-
mino e 2 in secundo seribe RR~1 _ 27 e fet
D2R  a2.R in 23 + R., =V. Frat autem R = c  - F2n
523n-] - H23n _c. _ inde per PFOD. T. fit R =
Fx7- 2n87722 ) entr223r  ) Xc. Quibus substitu
tis e scripta BF. seu L prO 2y Aet
et
( (2, 8c B t23n f RC. In 2D R ~1 = v = BC.
2. F. D.
PROP.

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PROP. IV. THEOR. II.
Si CurrA abSCICTa AB SEZ, _E A pTO C L, FZn Y ∞ZIn
-eC. Scribatur R, ∞ pro K. ]. I2n ] Mx2n. ] _c. Ccri-
BatuES; SE autem area CUEVA 2R. S: erit Or-
dinatim applicata BC. =
Det ) n Fk 2.
FB
un Cl2.
2anSk22n. X . . . . . F . . . . . -
8
--2g
)en
1- 211
0
un
I 2n
-2uB
10
In 2. 1R L1G42
um Bmzins
= Zun
Demonstratur ad modum Propolitionis superioris.
PROP. V. TIEOR. III.
Si Curvae abscisa AB SIE Z, XC prO C F (7N- ]. 5227
F RZ3n ] XC. SCribatUE R: St autem ordinatim ap
plicata 2 R~ in a Y b7n + C22n ] d23n ] QC. X P0-
natUE D =F. F F a = 5. 5- 2 = F. C  a = V, QC. erit arCa
BR iN
2 +b sFA iC FB tEA
F -F 2, C
28 -. AB
x. - 2,C
221.
id =3FC. = BB vHA
Y  = 3,C
in ) _C. UIBI A, B, C, D, _C.
A d a
denotant

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C
E
denotant totas coefficientes datas terminorum sinsu-
lorum in serie cum signis (uis- ). _ nempe A primi
termini coefticientem nd B secundi coefficientem
b SFA
P -F 2, C
nC =, EB - t8A
C. tertii coetticientem
Sic deinceps.
F +
ee
Demonstratio.
Sunto suxta Propolitionem tertiam,
Currarum Ordinatae
221S AL2 31
19,A2318C.
DInFB = 21 181
an
..+
2in 6B23n ecC. 
. +D F3u, CD231_C. 3
_ carundem arca.
A 2 R
B2Dtn R2.
C. 78 I 2n R2
D= F3n R 2
Et E Cumma ordinatarum ponatur aequalis ordi-
natae a- ]- b71 -- C72n-) d23n- f XC. in 2d. R~ Tumma
arearUM ZR in A -) B7n ] - C 22n 1- D 3n -)- sEC. aequa-
lis erit area Currae cujus ista est ordinata. Aguen
tur isitur Ordinatarum termini correlpondentes, et
dtn FB
Aet a = DeA, b = +  CA  CB, C = + 2218 an
f. 6] 2n, CC. _C. _ inde se = A.
C= (B ]22nq SA -- D t rt an FB
D- ] 21C
BF an TA = B.
B. F 1,C
=C. Et sC deinceps in infi-
nitum
F
FmeBc
0

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l179
nIEUI. POnC jaM e =F. F Fa = 5. 5  a = F _C. X
In aFCA ZRAX A--B,1-(-C 221 ]. D23n XC. Ecribe ip
Torum A, B, C, _C. valores inventos e prodibit
leries propohta. J. L. D.
tit notandum est quod Ordinata omnis duobus
modis in seriem resolvitur. Nam indexn vel afr-
matirus est potest vel negatirus. Proponatur Ordi-
3K lZ2
nata 22 st2 123) m24. laec vel sic scribi Potest
7. 2X ZL I~2XK 122  M23, vel SIC ZX - 1-  3H∞ 2
XI -12 -,K2 3 =2. In Casu priore eAt a = ZH. D = 0.
C - - - 1. C = - k. F = -0. 8 - -l. H = -M. a -
2 v-
1. C - - -. V =- 0. In
posteriore es a = - - l. b =- 0. C = 3k. C--m. F---1.
3- -0. h --1. 2 -- -  1 - - - 1. 8 - 1 - - 1. D - - 2. F - - 2
1
t =- -r. V =- -. Pentandus est calus uter
que. Fit si serierum alterutra ob terminos tandem
deticientes abrumpitur ac terminatur, habebitur area
Currae in terminis finitis. Sic in exempli hujus
priore casu scribendo in serie valores iplorum a, b,
Cus C, Fg8, hu a, B, F, 5, tu V, termini omnes post pri-
mum cranelcunt in intinitum e area C urrae procit
2
=12 Im3. FF haec area ob signum nesatirum
adiacet abscissae ultra ordinatam productae. Nam
area omnis aftirmatira adjacet tam abscissae quam
ordinatae, nesatira vero cadit ad contrarias par-
tes ordinatae ex adjacet abscistae productae, manente
Scilicet Piono Ordinatae. Hloc modo series alter-
utra e nonnunquam utraque semper terminaEUE
ex tinita evadit h Curra geometrice quadrari po-
test. AC si Curra talem quadraturam non admit-
cit, series utraqe continuabitur in intinitum, a ea-
A a a:
TUM

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P180
enm altera converset _ aream dabie approximando,
praeterquam ubi s (propter aream intinitam) vel
nihil est vel numerus integer ex negatirus, vel ubi=
aequalis est unitati. Si ZminOr eM unItate, CONVeF
set series in qua index naftirmatirus est: tin Z unita
te major est converoet series altera. In uno casu
area adjacet abscissae ad usq;e ordinatam ductae, in
altero adjacet abscissae ultra ordinatam producia.
Nota insuper quod s Ordinata contentum eA (ub
Factore rationali  e Factore surdo irreducibili R
_ Factoris Curdi latus R non diridit Factorem ratio-
nalem (; Crit a - T = - = _ RV =R. Sin FactOrIS SUT-
di latus R dividit factorem rationalem semel, crit
a  1 = = X -) - Y _ RA+ =R = 1.: si dividit bis, Cxit
a - 1 = -  - - 2 8C R ~. 1 =-R + 12: E teF, CFIt a--T = X - 39
_ R~ 1 = -Rr 13. X SC deinceps.
Si Ordinata est Fractio rationalis irreducibilis ce
Denominatore ex duobus vel pluribus terminis com
Posito: relolvendus est denominator in divilores
Luos omnes primos. Et C dirisor st aliquis cui
nullus alius est aequalis, Curra quadrari nequit:
Sin duo vel plures sint dirilores aequales, rejicien
dus est corum unus, ∞ s adtuc alii duo vel plures
sint sibi mutuo aequales _ prioribus inaequales, ic
sciendus est etiam eorum unus, et sic in aliis omni-
Dus aequalibus s adhuc plures lint: deinde divilor
qui retinquitur vel contentum lub diriloribus omni-
bus qui relinquuntur, si plures Cunt, ponendum est
DTO R, E ejus quadrati reciprocum R = pFO RV, PPa
terquam ubi contentum illud est quadratum vel cu
bus vel quadeato quadratum, eEc. Quo ca lu Cjus latus
POHCI.

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F18T7
ponendum est pro R X Potestatis index 2 vel 3 vel 4
negatire sumptus pron. Xt Ordinata ad denomina.
TOrem R. vel R. vel R. vel REC. reducenda.
25 ]24 - 523- 22 ]82- 43 GuOniam MaeC
UER Ordinata (IE -25. + 24 - 823
Fractio irreducibilis est e denominatoris dirilores
Tunt pares, nemPC Z- I, 2 L, 2 1 _ 7.  , 2,
2.. F2, rejicio magnitudinis utriulque dirilorem
unum e reliquorum 2-- 1, 2 1, 2-) 2 conten
tum 23=32  2 DONO prO R _ ejus quadrati re-
CiprOCUM P PeU R -2 PrO R.=. Dein Ordina
tam ad denominatorem R TCu R- reduco, 8 Ft
6.
37
81
Id CA 23X8 - 92 - . 23X 2 = 32.
73 = 37 - - 2) quad.
Ft inde eA a = 8. b -- -9. c = = 0. d - - 1, XC
. 5 = O. H = 1. 2 2 = - 2. a = -- F-
B
C = 2. F = -
n = 1. B - 1 = 3. 0 = 4 = F. 5 = 3. t = 2. V = T. FF H15
222 terminis om-
nibus in tota serie post primum cranescentibus.
Si denig; Ordinata est Fractio irreducibilis ee ejus
denominator contentum est sub factore rationali 
e factore surdo irreducibili R, inveniendi sunt la-
Teris R dirilores omnes primi, ex rejiciendus est. di-
vicor unus maenitudinis cujulque e per dirilores
qui restant, siqui sint, multiplicandus est factor
racionalis 2: _ E Factum aequale est lateri R vel
lateris illius potectati alicui cujus index eA numerus
integer, eAto index ille m, e erit a -1 = - r - I, 8
34 - 4+ X- ] 99. XX- 99X3, 6974
R  =R r. m. UF Si Ordinata 
24 - L X cub. 93- ] 495 -. qXX - x
quoniam

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F182
quoniam factoris surdi latusR Pcu 93. ] - g9X -=gXX X3
diritores habet g F X, 9 ] X, 9 X qui duarum (unt
magnitudinum, rejicio dirisorem unum magnitudi
nis utriulq; ex per divisorem q F X qui relinquitur
multiplico factorem rationalem g9 XX. Ft quo-
niam Factum 93 7 99X-- 9XX 23 aequale est la-
teri R, POnOm = - L. X inde, Cum x AL 5 FF n- 1 = -2
Ordinatam isItur reduco ad denominatorem R. 4
d ft Z. X 39 + 29X1892X1893X3- 799X -69
X93.  gqX. 9XX X) 3. Unde est a = 39. b = 29_c.
C = 93. F= G9eC. 0 -- 1 = O. 0 = 1 = n
arCd
t=
- C =- T
V = 0. Ft his in serie scriptis prodit
399X. (- 3X3
scub. 23. ] aax axr-- ∞33 Terminis omnibus in lerie tota
post tertium eranelcentibus.
PROP. VI. THE.OR. IV.
Si Currae abscista AB Sit 2, X scribantuE R pro
C f(7n - 872n - . h7 3n-] _C. _ S pro K  ] l7n f m2 2n
Fn23n XC. Et autem ordinatim applicata z R ~2 Su.2
In a  D7n:] Cx2n) dr3n eC. et s terminorum, C, t,
B, h, eC. e Hc, l, m, n. ec. rectansuta sint.
Ck FK gK HK _C.
et
FI
SL HI _C.
em im om lmac.
en En sn hn _C.
ol

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(183
Fc Ei rectangulorum illorum coefficientes nUIE
rales ant respectire
0 = c.
F. ] 2 = 5. 5- 2 = E. C) n = V. _C.
F- v. = 5. 5. p = L. F.) B = V. V- ∞ = W. _C.
6-  = F., F. fv = v. v   = W. i   = X. _c.
C- s _ = V. V - ~ = W. W -  P = Z. X - p = Y. XC.
area Currae erit haec
DRASU
a
nb
TCK FFE, CK
c 7 1, 8k
Ek ( c - (2, EL L = v EN
oet  - 2  L-) - L, CM = v’en
F + 3, Ck
Ubi A denotat termini primi coefficientem datam
a cum SignO suO-P vel --, B coefsicientem datam
Ct
secundi, C. coetticientem datam tertii, et sic deinceps.
Terminorum veco, a, b, C, _C. K, l, m, XC. unuS
vel plures deesse polsunt. Demonstratur Propoltio
ad modum praecedentis, et quae ibi notantur hic ob-
tinent. Persit autem series talium Propositionum in
intinitum, a Proorestio seriei manifecta est.
n
trCB-
em
L 236
C
PROP.

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180
PROP. VII. THEOR. V.
Si pro C L FZn ( 87 2n  _C. TCribatUT R ut TUPEa, X
in Currae alicujus Ordinata 20Ln0 R. Lr maneant
quantitates datae o, n 2, C, F, S, EC. _x PFO0 dC x TCTI-
bantur successire numeri quicunq; inteori: et I
detur area unius ex C urris quae per Ordinatas in-
numeras sic prodeuntes detignantur s Ordinatae lunt
duorum nominum in vinculo radicis, vel s dentur
area duarum ex Curvis si Ordinatae Cunt trium nO-
minum in vinculo radicis, vel areae trium ex C urris
E Ordinatae Cunt quatuor nominum in vinculo radi-
Cis, e lic deinceps in intinitum: dico quod dabun-
TUE arCa Curvarum omnium. Pro nominibus hic
habeo terminos omnes in vinculo radicis tam de-
ficientes quam plenos quorum indices dignitatum
Tunt in prooressione arithmetica. Sic ordinata
Va+ aX3 , Xt Ob terminos duos inter 24e - a73
deticientes pro quinquinomio haberi debet. AF
Vat) xa binomium est Xc Va+ ] X1  trinonium.
cum progressio jam per majores differentias proce
dat. Proposiio vero sic demonstratur.
C AS.
Sunto Curalum cuaum Ordinatae prP.  R  1 8
7Ini RVI, X areae pA et gB, existente R quanti-
tate trium nominum c.fru- gren. Ft cum per
Prop.

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C1857
PrOD. TIT. SIE ZR area currae cujus Ocdinata est
 An  2XnE
priores de area e Ordinata posteriori, ex manebit
p = an
by2n in Z2 R~ Ordinata nora C UEVa, X
2an C
DR = pA -- 9B ejusdem area. PONC dC = P 8
oF. f anf =G de Ordinata eradet (3, 82 2n in Z. 1R~. 1, 8
area ZR DCA oFB in(B. Diride utranG; per
08- ang, X aream prodeuntem dic C, _ astumpta
utcung: I, erit EC area Currae cujus Ordinata est
p7dI E R~ 2. Fit qua ratione ex areis pA d 9B
ATCAM FC. Ordinatae p2P F2rI R~ congruentem inve-
nimus, licebit ex areis gB _ rC. aream quartam
puta ED ordinatae S2 L3=R. congruentem invenire,
_ sic deinceps in intinitum. Et par est ratio pro-
srestionis ab areis B Xx A in partem contrariam
Pergentis. Si terminorum 8, 9. ]-an, ec 0- ] - 2an aliquis de-
ficit e Ceriem abrumpie, altumatur area pa in prin-
cipioprogrestionis unius ex area qB in principio al-
terius, _ ex his duabus areis dabuntur areae omnes
in progrestione utraque. Ft contra, ex aliis duabus
areis altumptis ft recrestus per analyEn adt areas A
e B, adeo ut ex duabus datis caeterae omnes den-
FT. 9. F. O. HTic est casus Currarum ubi ipsius=
indexsauxetur vel diminuitur perpetua additione vel
subductione quantitatisn. Calus alter est C urra
rum ubi index augetur vel diminuitur unitatibus.
noo

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T186
C A5. II.
Ordinatae p7 IR. X 92 t RN, quibuS ATCX PA
ex qB jam respondeant, si in R. seu c f. F2n ] 97 2n du-
cantur ac deinde ad R vicissim applicentur, era-
dunt DC.) pF2n . P873n X ZB 1R ~ 1 eC gC2n - - gF2 2n
9973n X 2D. 2R~V. Et per PrOD. III. CA aZBR1
in 2EZ: (Eay 487 27
area Currae cujus Ordinata CA BaC)
in 2 2R~L, _ b2BInR. area CurVae cujuS Ordinata
est Ebezu TBBFZEn +0b873 in 2B =R ~. Ft harum qua-
an
-1 221
tuor arearum summa est pA. ) gB. F. a2 R  ] BZDI nR2
Ex lumma relpondentium ordinatarum
dC 
ADC
tan alE
p e
Pt
10
Lo BF
an
ipE
tgc +aC
b923n In 2. 1 R2-2
ean
+95
Si terminus primus tertius e quartus ponantur se-
orlum aequales nihilo, per primum tet dac ) Pe =0
(eu -B2 = D, Per Quartum =ob = nb - 2 ab = 9, _ Per
tertium (eliminando P ex 9)  =b. Unde secundus
A
nnats- tandse
adeoq; summa quatuor Ordinatarum est
amats aandse, d tr.RVI ex summa totidem respondentium
arearu eA a 2DR f 2057  FnR-D2A
2d 1 21 + 42a a8B.
Diri

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du
CTE
Dividtantur hae Tummae per. Anati gunae
ee A Ouotum
posterius dicatur D, erit D area currae cujus ordi-
nata est Ouotum prius  Tr Ra.r. Fit eadem ratione
ponendo omnes Ordinatae terminos praeter primum
aequales nihilo potest area C uerae inveniri cujus Or-
dinata est 28 =Rr. I. Dicatur area icta C, X qua ra-
tione ex areis A e B inventae lunt arexe C aC D, ex
his areis C. ac D inveniri postunt aliae duae F X L
Ordinatis zP =R~ Z ∞ 2 Fr .Rr2 congruentes, _ sic de-
inceps in intimitum. Et per analysin contrariam
regredi licet ab areis F _ F ad areas C, aCD, _
inde ad areas A ex B, aliasq; quae in progrestione se-
quuntur. Igitur A index  perpetua unitatum ad-
ditione vel lubductione augeatur vel minuatur, et
ex areis quae Ordinatis sic prodeuntibus respondent
duae simplicissimae habentur; dantur alia omnes in
intinitum. C. F. O.
C AS. TII.
FF per caTUS holCe duos conjunctos, A tam in
des o perpetua additione rel subductione iptIUSn
quam index n perpetua additione vel subductione
unitatis, utcunq; auseatur vel minuatur, dabuntur
areae singulis prodeuntibus Ordinatis respondentes.
2. F. C
L

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C AS. IV.
Et simili aurmento si ordinata constat ex qua-
cuor nominibus in vinculo radicali e dantur treS
arearum, vel si constat ex quinqe nominibus e
dantur quatuor arcarum, et sic deinceps: dabun-
tUI arex omnes quae addendo vel subducendo nume-
rumn indici d vel unitatem indici n generari poltunt.
Et par est ratio Currarum ubi ordinatae ex binomiis
conslantur, et area una carum quae non sunt geome-
trice quadrabiles datur. . F. O.
eROP. VIII. TH F. OR. VI.
Si prOC  Frn -]- 972n -) XxC. eE K f 17n- ] 1n2 2n. ]-XC.
icribantur R X S ut supra, ec in Currae alicujus Or-
dinata 2 Ino RVF Sul maneant quantitates datae 0,
n ng H C, Cg 39 tu lu M _C. _ prO~, r, _ v, Teri-
bantur successire numeri quicunq; intesei: e s
dentur arex duarum ex curris quae per ordinatas
Sc prodeuntes desionantur E quantitates R _S funt
binomia, vel Ei dentur areae trium ex curris R R
e S conjunetim ex quinq; nominibus constant, vel
areae quatuor ex curris E R SS conjunctim ex (ex
nominibus constant, e sc deinceps in intinitum:
dico quod dabuntur areae curvarum omnium.
Demonstratur ad modum Propolitionis luperioris.
Lll2.

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269
PROV. IX. THTEOR. VII.
Aquantur Currarum areae inter se quarum Or-
dinatae lunt reciproce ut Auxiones Ablcictarum.
Nam contenta sub Ordinatis _ Auxionibus AB.
scictarum erunt aequalia, et Auxiones arearum funt
ut haec contenta.
COROL. I.
Si assumatur relatio quaeris inter ABScissas dua-
rum Currarum, X inde Per PFOD. I. Quaeratur
relatio Ruxionum ABSCisarum, _ ponantur Ordi-
natae reciproce proportionales Auxionibus, inveniri
POTUInE INMUMETA C. UEVA QuarUM area sBI MUEUa
aequales erunt.
COROL. II.
Sic enim Curra omnis cujus haec est Ordinata
2 in C-] F2n -f 3,22n -] - _C. P astumendo quantitatem
quamris pro, ex ponendon =s X 2 = X, migrat in
aliam ibi aequalem cujus ordinata est ? , v8-n in
C F Fx f 3X2 f. 8C. (a.

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190
COROL. III.
FE Curra omnis cujus Ordinata est L in
2 - - b73 -, C22n -- _CC. X C- F- F2n  97=n XC. , aumen-
do quantitatem quamvis pro X ponendo n =5 X
25 = x miorat in aliam sibi equalem cujus ordinata
est.
_ nin a f BX L ex F_C. XC F FX - 9X 2 F _C p
COROT. IV.
Ft Curra omnis cujus Ordinata est nb in
a - - b21 7 C221  _C. X C ] Frn  872n ] RC.
XK  12n  I2En Y aC. u allumendo quantitatem
quamris pror_ ponendo n =5 ex 2 = X, migeat in
aliam sibi aequalem cujus ordinata est 2 X   in a F bX
FCx2 p AC. XC FFX - FSX2 f. _C pXKC- F IX Y MX  (_ C. s
COROL. V.
Et Curra omnis cujus Ordinata est  in
e-f. (21 - 8221- ec.  ponendo Z = x misrat in
XOFEXC L. FXN
BX 2 f _C.  id est XOI L TMA X F- F exHa A duO LUNE
nomina in vinculo radicis vel ∞0F, T n X 8 f fXn - CX 2)
Si tria Cunt nomina; e sic deinceps.
lO.

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lG
COROL. VI.
fit Curra omnis cujus Ordinata est  in
C -   F7n - - 37 2n - - XC. p X K - , - l7n ] 1Z2n- - _C. see
ponendo = =x miorat in aliam sibi aequalem cu-
jus ordinata est =op, Z C - p FX n - gX 2n -] XC.)
XH f IXn.  mX 2n. f Rc. J id est = 0t 1 + m. f m X F. + Cx 
XI.JKX R bina sunt nomina in rinculis radicum,
vel =DF 1  Ena. tme X 5 F Fxn - Cx Eyp~ X 1. ]- Lxju R tria
sunt nomina in rinculo radicis prioris ac duo in
vinculo posterioris: _ sc in aliis. Ft nota quod
areae duae aequales in novissimis hisce duobus CO-
rollariis jacent ad contrarias partes ordinatarum.
Si area in alterutra curra adjacet absciltae, area
huic aequalis in altera curra adjacet ablcistae pro-
ducta.
COROF. VII.
Si relatio inter Currae alicujus Ordinatam y e
Absciltam 2 detiniatur per aequationem quamvis
fectam hujus Formae, ya inC ] fyuzc (97 2n 728 7 Hy 3n , 38
 XC. = 2 In K ] Ion 25 - F my 21 = 25 + eC. huc
figura altumendo 5 = =  X = 2 2 X n = n -5
ast I Bs) IIOTaL
in aliam sibi aequalem cujus Abscisa X, Cx data
Ordinata

## Folio 192 — 1677894601:0384
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(192
Ordinata V, determinatur per aequationem non
aftectam; Vea Z C F Fon f e pen f tvon F SC P X K F lvu
FIVE + _C. ( =X.
COROL. VIII.
Si relatio inter Currae alicujus Ordinatam Y _
AbIcillam 2 detinitur per aequationem quamvis
attectam hujus Formae, ya in C - Fyn7.  8)2n 228 + dic.
ee in k- ]. 1yn2s f my 21228.  8C. F 27 in P. (9y12s
 xy En = 2S. F _ C. haec figura altumendo 5 -, X = s 2
p
act ). B1
n - 5 X v = act  71
s migrat in aliam sibi aequalem
cujus Abscicta X ex data Ordinata r determinatur
per aequationem minus affectam ve in c F. frn. ] - ov2n
F XC. = sx in k - IVn.  - V2n.  RC. - 5X in
P+ qua F ex 2a -. _C.
COROL. IX.
Curra omnis cujus Ordinata est r in
C21 : 2, 82 ] _C. X C - ]. F7n  972n XC. p. 2-
a. f B)e2. f (2. 1 a f 9r. tn f XC.(, si fiLD = on 
aTTumantUE X = C7 ]. F2. tn f 87. t2n  XC. , 0=
X d= = migrat in aliam sibi aequalem cujus ordi-
nata eAtXd X a f bXs. F nota quod ordinata prior
LT

## Folio 193 — 1677894601:0385
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C793
in hoc Corollario cradit simplicior ponendo n = I,
vel ponendo r = 1 8 efficiendo ut radix dignitatis
extrahi possit cujus index esta vel etiam ponendo
a = = I _ a = 1 = + =  =  UF aliOS CatUS Praete.
TCRM.
COROL. Z.
PrO Cx F2Vta , 87r 1 2n ). RC. vere querot
L en 52 + 2n- 1 ). _C. K 7 12n -)- 122n ) - _C. X nl u
1- v
= 2n1222 1- ] _C. Pcribantur R, F, Se S respectire, _
Curra omnis cujus ordinata eAt rdr f. e RS In R~ Su
X a5.  BRI, E fit  va = v = 8, = = 0,   = d
_ R Se = X migrat in aliam sibi aequalem cujus or-
dinata est X X a f. bX . Ft nota quod Ordinata
prior eradit simplicior, ponendo unitates PTOT, V,
_ a vel un ex Faciendo ut radix dignitatis extrahi
Poit cusus index est , vel ponendo = =1 vel
e =O.
PR OP. Z. PROB. TII.
Invenire figuras simplicissimas cum quibus Curra
quaeris seometrice compari potest, cujus ordinatim
applicata y per aequationem non affectam ex data ab
Ccista 2 determinatur.
l.le
C S.

## Folio 194 — 1677894601:0386
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ae.
LI9L
C A 5.
Sit Ordinata 222, e area erit par, ut ex PCOP. V.
vonendob = 0 = c = d = F = 8 = h X c = r, Facile col-
ligitur.
C A8. YI.
SIE Ordinata a2d.  X C f. Fru.  82 2 1. 1  8C. _ (
curra cum figuris rectilineis geometrice comparati
potest, quadrabitur per ProP. V. ponendo b =0 =c
=d. Sin minus convertetur in aliam curram sibi
aequalem cujus Ordinata est = L X C. F FX F SXRC p
per COrOl. 2. Prop. IX. Deinde C de dignitatum
indicibus n ec a - L peF PrOP. VII. rejiciantur uni-
tates donec dignitates illae tiant quam minima, de
renietur ad figuras simplicitsimas quae hac ratione
collisi poltunt. Dein harum unaquaeq: per C OrOl. 5.
Prop. IX. dat aliam quae nonnunquam simplicior
est. Ft ex his per Prop. III. X C OrOl. 9X 10.
Prop. IR. inter le collatis, figurae adhuc simpliciores
quandoq; prodeunt. Deniq: ex figuris simplicis-
timis actumpris facto regresta computabitur arca
quaelita.
Ad

## Folio 195 — 1677894601:0387
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C AS. TII.
Sit Ordinata 28 X a f. D2 f CZ 2n f. XC.
Z C-  - Frn-f. 572n - XC. , _ haec sigUTA S quadrari
potest, quadrabitur per Prop. V. Sin minus, di-
Rinouenda est ordinata in partes .= X a X C - F2n
. 872n -  XC. )2 1, 7d.r ∞ b7n X C-) (2n + 9221 - _C. s2. 1
XC. X per Cd l. 2. inveniendae sunt tisurae simpli-
cissimae cum quibus tisurae partibus illis respon-
dentes comparari postunt. Nam areae figurarum
partibus illis respondentium sub Cignis fuis F X
conjunetae component aream totam quaelitam.
C A S. IV.
Sit Ordinata 28.1 Z a F BZ1 F cZ2n - _EC. X
C f. F22  822n -]- XC. r. 2 X K -] L2  1X En -] CCC. (11.
X E Curra quadrari porest, quadrabitur per Prop. VI.
Sin minus, convertetur in simpliciorem per C orol. 4
Prov. IX. ac deinde comparabitur cum Aguris (Im-
plicissimis per Prop. VIII. & Corol. 6, 98 10.
Prop. IX. ut ft in C. a (u 2 e 3.
C A5. V
St Oramtata ex varie partibus constat, pailes
sinculae pro ordinatis currarum tocidem habendae
lunt, et currae illae quotquot quadrari possunt, isilla
C CC. 2
tim
195

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L196
tim quadranda sunt, carumq; ordinate de ordinata
tota demendae. Dein Curra quam ordinatae pars
relidua desienat scortim (ut in Calu 2, 3 X 4,)
cum tisuris simplicissimis comparanda est cum qui-
bus comparari potest. Et Cumma arearum omnium
Pio area Currae proposita habenda cAt.
COROT. I.
FTinc etiam Curra omnis cujus Ordinata eA Pa-
dix quadratica affecta aequationis lux, cum Aguris
simplicissimis seu reccilineis scu currilineis com-
Pari potest. Nam radix illa ex duabus partibus
semper constat quae seortim spectatae non lunt aequa-
num radices affectae. Proponatur aequatio aayy
 227y = 207 - 273y -7, e extracta radix erit
a3
a3 - . 2. 2
aa - F 22
22 cujus pars rationalis
aV a F 2423-
22- f 22 eE Pars irrationalis
ad F 22 Tunt
ordinatae currarum quae per hanc Propolitionem
vel quadrari poltunt vel cum tiguris simplicissimis
comparari cum quibus collationem seometricam. dd
muttunt.
ilc 1d. 110
quatris altectam detinitur quae per C Orol. 7. Lrop.
L. in aequationem ao dccla Cal, res qua
dratur
Ft curra omnis cujus Ordinata per aequationem

## Folio 197 — 1677894601:0389
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P
eratur per hanc Propolitionem si quadrari potest vel
comparatur cum figuris simplicissimis cum quibus
compari potest. Ft hac ratione Curra omnis quadra
tur cujus aequatio est trium terminorum. Nam aequa-
tio illa s affecta sic transmutatur in non affectam per
Corol.7. Prop. IL. ac deinde per C Orol. 2 _ 5. Prop.
TX. in Simplichimam migrando, dat vel quadratu.
ram tigurae E quadrari potest, vel curram simplicis
HMAI QUACII COIPATATUT.
COROL. ITI.
Et Curva omnis cujus Ordinata per aequationem
quamvis affectam detinitur quae per COrol. 8. PrOP.
IX. in aequationem quadraticam aftectam migrat;
vel quadratur per hanc Propolitionem e hujus CO-
xol. I. E quadrari potest, vel comparatur cum tisu.
ris simplicissimis cum quibus collationem geometri-
cam admittit.
SCFTOLL
Ubi quadrandae Cunt fgurae; ad Regulas tasce
generales semper recurrere nimis molectum esset:
praestat Figuras quae simpliciores Cunt a magis ului
esse postunt semel quadrare e quadraturas in Pa-
bulam reterre, deinde Pabulam consulere quoties
ejusmodi Curram aliquam quadrare oportet. Iu-
jus autem generis tunt Tabulae duae sequentes, in
quibus 2 denotat Abscistam, Y Ordinatam rectan.
Sulam

## Folio 198 — 1677894601:0390
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(7987
sulam _t Aream C urrae quadrandae, e d, c, F, 3,
5. h,n unt quantitates datae cum signis luis.  e-.
TABVF 
Curvarum simpliciorum quae quadrari possunt.
Currarum FOrMa. Curarum area.
Forma prima.
dxu t = Y.
Forma secunda.
d2
ec 20121 I EC2 = Y.
FOrma tertia.
7n-
den
NEC  neten = t, Vel ret. ) tr
1. d2.  VC f F2n = y. Ene R = F, existente R = VC L FZ
2. d2 VC. F2n = Y.
3. d23n VC FF2n = y
AC L SF2n
2GnfF dR = t.
16CC- 24C(2r ( 30(122n
roGnt3 dR3 = t.
4. d2n NC + F2 = y. =06C3 + 144 eclen 180el(r2n (210(3734
FOrA quarEa.
sC. F2n
d2. 21
VC FEEn
345n(+
AR =1.
st R = C
=Ac- (. 2F2H
bulc dR =C.
d2n

## Folio 199 — 1677894601:0391
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d
dCLH EZ21
IGn(3
L= 2
DC3 ad EIhda
205nE4
T ABVL A
Curvarum simpliciorum quae cum Fllipsi eo
Clyperbola compari possunt.
Sit jam aCD vel PGD vel CDS Sectio
Conica cujus area ad Ouadraturam C VEVa pFO- F1S. 5,6,7,8.
positae requiritur, scq; ejus centrum A, AXIS K2,
Vertex aq Semiaxis conjugatus AP, datum Abscisa
principium A vel a vel a ABICiNa AB vel a B vel
aB =Z, Ordinata rectangula BD = V, _ AICa
ABDP vel aBDC vel a BDC =s existente a (E OF-
dinata ad punctu a. TUInSantE RD, AD, aD. Du
Catur PanGCNS DP OccurrenS ABSCisa AB in Y,
e compleatur parallelogrammum ABDO. Ft
Eiquando ad quadraturam Currae propositae requi
runtur areae duarum sectionem Conicarum, dica-
tur posterioris Abscilta E Ordinata Y, _ Area 0
Sit autem difterentia duarum quantitatum ubi in
certum est utrum posterior de priori an prior de Po-
Aeriori subduci debeat.
L. NIVA

## Folio 200 — 1677894601:0392
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est
E
200
u
E
v 1010 1010
en
F
010, 110 rese
n
ds
s+
F

## Folio 201 — 1677894601:0393
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201
3
eod
 
 
e
(
E
e
11
2 111
E
su
e 1
ep
2)e
uia
.Ei
eta e si
vi
EI
e
X
X1 ~
L
si
 p
I e
ta BIX
-. =
in 1,F
2p
11
1-
 1S m se
2)F II = MI
 C
F V1N
x
e
pu
l 12 s
∞)- F 0sa = 0(52
a
ed
d
ri +
F
al

## Folio 202 — 1677894601:0394
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ce
∞I
512
njoi nlo
1
a 7  7
e
e
ad H
+
202
11
ae
s
2  3
1
s
sea
3
d
L

## Folio 203 — 1677894601:0395
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ttu
203.
0d
 e
2 110
 des
si
∞1 - 2)
∞1= ∞1
 so t
ed 
6 10 10
VIN  
PE
a ( 
Bd
ee
1 d 2

## Folio 204 — 1677894601:0396
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204)
+
 2 Z
12
2
sits
5
V
= n D a
51
s
0d
n
E
01d
ses
e si
1
C
1d - 1 0D l 0
5 E 
3 0o e 1 e ∞
0V. 1 to  a0  
t
i
a

## Folio 205 — 1677894601:0397
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In Tabulis hisce, series Curvarum cujusq; Formae
utrinq; in intinitum continuari potest. Scilicet
in Pabula prima, in numeratoribus arearum FOr
mae tertiae e quarcae, numeri coefficientes initialium
TerminOrUM (2, - 4, 16, - 96, 868, XC.) Generan
tur multiplicando numerOS 2,- 4, - 6, -- 10, Xc.
in se continuo, _ suiblequentium terminorum coet
ficientes ex initialibus derirantur multiplicando
iplos gradatim, in Forma quidem tertia, Per - 3)
63.
53
33 = 6 eC. IA Guarta VeTO PeF - 5 4
53 10 exC. Ft Denominatorum coefficientes
3T5, 105, ec. Prodeunt multiplicando numeros
93,5, 7, 9, ec. in le continuo.
In secunda rero Tabula, series Currarum Formx
primae, secundae, quintae, sextae, nonae e decimae opC
Colius dirisionis, d formae reliquae ope Propolitio.
nis tertiae X quartae, utrinq; producuntur in in-
finitum.
Ouinetiam hae series mutando signum numeri,
variari solent. Sic enim, c. 8. C urva = VC ] F2n = y,
eracit 2n
eR OP. IZ. THTEOR. VIII.
Sit ADTC. Curra quaeris Abscillam habCHS Fig. 9
AB = Z _ Ordinatam BD=-Y, _ SIt AF RC. C UrVa
alia cujus Ordinata BF aequalis est prioris arcae
A B. C.

## Folio 206 — 1677894601:0398
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F206
ADB ad unitatem applicatae, _EAFL C. Curra
tertia cujus Ordinata B F aequalis est secundae areae
AF B ad unitatem applicatae, _ AGMC. Curra
quarta cujus Ordinata BC aequalis est tertise areae
AFB ad unitatem applicatae, _E AHINC. Curra
quinta cujus Ordinata BEI aequalis est quartae aiex
ACB ad unitatem applicatae, e sC deincepS in
infinitumm. EF TUNtO A, B, C D, F XEC. AECR C UF-
varum Ordinatas habentium Y, 27, 2Y, 237, 233.
X Abicillam communem Z.
Detur ABICisa quaeris AC - L, Stq; BC - 1 7
=X, XC TUNEO P, C, R, S, T areae Currarum Ordi.
natas habentium X, XY, XXY, Xy, X2y ex AbIcillam
COIMLUINEI Z.
Terminenter autem hae areae omnes ad Absciltam
totam datam AC, nec non ad Ordinatam politione
datam a infinite productam C. I: X erit arearum
Cub initio politarum prima ADIC.- =A =- P, secunda
AEKC -TA B O. PErtA AFL. C =EA- 21B+C = -B
Duarta AGMTC. = E,A - 34B 13tC- D - .5. Ouinta
AFINC, =- 14 A- 4C3B. f GHC- ALD + F.

## Folio 207 — 1677894601:0399
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COROL.
Unde si Currae quarum Ordinata Tunt Y, 27.
2Y, 2Y, _C. vel V, XY, XY, Xy, _c. quadcari
possunt, quadrabuntUr CtIaM C UIEVA ADIC, AFKC.
AEL C ACTMC, _C. X habebuntur Ordinatae BF,
BE, BC, BEI areis Currarum proportionales.
SGTOLAOM.
Ouantitatum Auentium Auxiones esse primas,
secundas, tertias, quartas, alialq; diximus supra.
Pixe Huxiones sunt ut termini serierum intinita-
tum conversentium. Uch in sit quantitas AuenS X
Auendo eradtat Z- ] op, deinde resolvatur in seriem
3OO2 n2 + 13 - 3un + 21 937Y
= XC. terminus primus hujus seriei 2n erit quan-
titas illa Auens, secundus nozr erit ejus incremen-
cum primum seu differentia prima cui nascenti pro.
portionalis est ejus Auxio prima, tertius mn oZ
erit ejus incrementum secundum leu ditferentia se
cundta cur nascenti proportionalis eA ejus Auxio
et
secunda, GuarEUS I = 3u + ∞37r3 exit ejuS incremen.
tum tertium seu differentia tertia cui nalcenti
Ausio tertia proportionalis ett, ee sic deinceps in
infinetu.
LX POIIC

## Folio 208 — 1677894601:0400
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(20E
Fxponi autem poslunt hae Auxiones per C urrarum
Ordinatas BD, BF BF, BC, BHI, Sc. UI S
Ordinata BF (=  +DB
)Et quantitas Auens, erit
ejus Auxio prima ut ordinata BD. Si BF (= AF B.
Eit quantitas Auens, erit ejus Auxio prima ut Or-
dinata BF X Auxio secunda ut Ordinata BD. Si
BII (=
) sic quantitas Auens, erunt ejus Auxio
C
nes, prima, secunda, tertia _ quarta, ut Ordinatae
BC, BF, BF, BD respectire.
Et hinc in aequationibus quae quantitates tantum
duas incognitas involrunt, quarum una est quan-
titas uniformiter Auens et altera est Auxio quaelibet
quantitatis alterius Auentis, inveniri potest Auens
illa altera per quadEatUTAI CUErATUII. FXPONatUE
enim Auxio ejus per Ordinatam BD, X Si haeC SIE
duxio pria, quaeratUE area ADB =- BF X I, B
AuXiO leCuNdA, QUaeTATUE aECA AE B = =BFX L, (
Duxio tertia, GuaTatUE AECA A FB = = BGX I, XC.
e area inventa erit exponens Auentis quaesLX.
Sed et in aequationibus quae Auentem _ ejus
Duxionem primam sine altera Auence, vel duas
ejusdem Auentis duxiones, primam ec secundam,
vel secundam e tertiam, vel tertiam e quartam,
XC. line alterutra Auente involrunt: inreniri pol-
Tunt Aventes per quadraturam Currarum. Sit
aequatio dar = aV -  WV, existente v = BF,
v = BD, = = = AB ec 2 = = T, _ aequatio illa COm
plendo dimentiones Auxionum, eradet aav == aV2
2d2
~YZ, SCu or F or =2. Jam Auat r’ unitormiter de
1

## Folio 209 — 1677894601:0401
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2075
EsE ejus AUXIO V =L X erit ar Jvr 2, Xt quadrando
aa
Curram cujus Ordinata Cl ar jro d AbIcicta V, ha-
BebituE AuCNS Z. Adhac sit aequatio aar- aV f vv
existente v =BF, v = BF, v = BD _ 2 AB e
per relationem inter r X r seu BD _ BF invenie-
tur relatio inter AB e B F. ut in exemplo superiore.
Deinde per hanc relationem invenietur relatio in
ter AB X BF quadrando C UEVaM A F. B.
Aquationes quae tres incognitas quantitates invol-
runt aliquando reduci postunt ad aequationes quae
duas tantum involrunt, et in his casibus Auentes
invenientur ex Auxionibus ut supra. Sit aequatio
2 bXm =CXyuY- dyEuyy. Ponatur vuy =Y _ erit
a DXMCXV  drr. Hlac aequatio quadrando CUr-
vam cujus ABIcisa est X _ Ordinata v dat aream
V, _ aequatio altera pny =r regrediendo ad Auentes
dat yrt =v. Unde habetur AuenS Y.
Ouinetiam in aequationibus quae tres incognitas
involvunt et ad aequationes quae duas tantum in-
volrunt reduci non postunt, Auentes quandoq;
prodeunt per quadraturam Currarum. Sit aequatio
axm. f b xys = F CXFLyS. L SCXCy yo Fy yE existente
X = T. FF parS POsteTIOEF CXF L yS. LSCXEY y S-Fy vC
regrediendo ad Auentes, At CXry - -- ye quae
proinde est ut area Currae cujus Ablcissa eA Z e
Ordinata ax) hxyse, e inde datur AuCnS Y.
FCC
st

## Folio 210 — 1677894601:0402
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c
Sit aequatio X X a xm F BXyse-
dy Yr.1. FiF AUCHS
Ve1 tn
cujus, Auxio est. X X a x  F DX CrIE UE area C UIEVX
cujus Abscissa est x ec Ordinata e a Xn  bxul.
ltem Auens cujus Auxio est es sri erit ut area CurVae
Ve) tyn
cujus ABScisa est y e Ordinata errr id est
VC FEyn
(per Casum r. Formae quartae Pab. L.) uE asCa
t VC syn. POnC erGO  V C F tyn aequaLEM ArCd
Currae cujus AbIcisa est Z _ Ordinata a X m- (. B Xy
et trabebitur AuenS Y.
F.t nota quod Auens omnis quae ex Auxione prima
collisitur augeri potest vel minui quantitate quaris
non Auente. Ouae ex Auxione secunda colligitur
auseri potest vel minui quantitate quaris cujus
duxio secunda nulla est. Ouae ex Auxione tertia
collisitur auseri potest vel minui quantitate quavis
cujus Auxio terria nulla CAt. FF sic deincers in in.
tinitum.
Poltquam vero Auentes ex Auxionibus collectas
Tunt. E de veritate Conclutionis dubitatur, Auxio-
nes duentium inventarum vicissim colligendae sunt
e cum Puxionibus sub initio propolitis comparandae.
Tam  prodeunt aequales Conclusio recte le ta-
Det

## Folio 211 — 1677894601:0403
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C2TF7
Bet: Fin minus, corrisendae sunt Auentes SIC, ut
earum Auxiones Auxionibus Tub initio propostis
aeguenEur. Nam X Fluens pro lubitu astumi po-
rest e allumptio corrisi ponendo Auxionem AU-
entis asumptae aequalem Auxioni propolitae, ee ter
inos homolosos inter le comparando.
FE LIS PECiPUS Vid ad Ma)OLd UetuC

## Folio  -  — 1677894601:0404
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
E R R AY A.
BOOK I. Of Opticks.
DACC L. P. 3. l. 20. Properra Wobich, 1b. P. 5. l.5. and that C, P. 6. l. 9. DE, P. 21. l. 23.
are udu  in the MarE in puF FIZ. 24 C5 15, p. 30. l.7. MN, L.9. MI, P.
A4. L. 25. 45 was proposed, P. 52. l. T7. a paber Circle. D. 57. l. Ult. emergine, P. 60. l. 25.
contain with the, P. 64. l. r8. und 14tB, D. 65. l. 23. atthe, P. 66. l. 3. Semicircular, P. 67.
l. 25. Center, l. 3F. 43 Inches, P. 68. l.8. 2016, l.9. Or 55, P. 7T. l. T. bisect, P. 72. l. 13.
falls, L. 20. beins. PaxEIL. P. 86. L. 5. Delopipede, P. 89. l. 9. made by, P. 93. L. 18, 10773.
L. 28, 29, by the third axiom of the first Part of this B00l, the LaS, P. 105. l.5. sec repre-
sented, P. 244. l. 243 3, 267 20357 203 2635. P. 218, 119. FOr Lib. 1. Lib. 2. Write
ParFE. ParF Z. P. F22. L.9. indico, P. 130. l. 19. 10 the AnelC, P. 132. l. 6. By +he brieht-
ness, P. 135. L. 14. For if in the, l. 16. first Part you, D. 136. l. 26. first Part, l. 27. Tichts,
D. 137. L. 20. Green, accordinely as, P. 238. l. 21. Prop. 6. Part. 2. P. 139. l.5. On Wwhich,
P. 242. l. 17. XY which have been, P. 243. l.7. purple, l. 26. Severat Lis hr5, l. 24. of white.
BOOK. II.
P. G. L. G. Nicety the, P. 7. l.9. 7, 2 denote, l. 28. them divers, P. 20. l. 24, 2000101024,
D. 22. L. FL. Oliquities, F. P. 27. L.4. T4319, P. 25. l.FF. EOF, P. 3F. l. 12. More com-
pounded, D. 55. l. 3. sizes refect, l. 24. and rberefore their Colours arise, D. 65. l. 5. corpus-
cles can D. 7T. L. 17. Siven breadth, P. 84. l. 4. are rothose, D. 96. l. 24. Observarion of
ehis Part ofthis B0OR, P. 103. l. 17. Was to the thiceness, P. 205. l. 29. Of this abite RInS,
P. 207. I. 20. become equat 10 tbe third of those.
Fnumeratio Linearum.
D. 243. L. 20. datas sienis suis, P. 244. l. 27. respiciunt, P. 246. L. 5. sunt Asymproto, P.
54. l. T3. Cx ) d dat Ordinatam y =, l. I4. quae generarur.
Ouadratur a Curvarum.
P. 268. 1. 24 recta AB, P. 176. L. UIE.  2, FZM, P. 183. l. 13.l, b,6, C86. C, (.8, 5C. K, ty M,
eSc. P. 185. 1. 4. in Z8.1, P. 188. l. 24. 7B = 16, P. 190. l. 19, vet ∞D- Y 2 F 212.
P. 192. L. 18, 870 F 2y. P. 193. l. 22. aS0 F BR 7, c0.

## Folio  -  — 1677894601:0405
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Pag 2It.
Duacr. Tab. L.
2 2
RIED WILHELM LEIBN

## Folio  -  — 1677894601:0406
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. 4 od.
FBiI I
B Eodiila
 ll l  l  1111 t 1l l1 1 11  l 1 1 1 1 1 1 11111 11 t 11111 11 11 1 11111111111
d
dele
SOTTFRIED WILHELM LEIBNIZ BIBLIOTHEK
NIEDERSACHSISCHE BANDESBIBLIOTHEK
Leibn. Mar9.

## Folio  -  — 1677894601:0407
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s sls s s  s tel Ht  s  s llt s s sl. s  sut s o s a s salu
acnosente cuoo st
: Lcibn. Mar9. 19.

## Folio  -  — 1677894601:0408
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e
111II II

## Folio  -  — 1677894601:0409
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  e fe sn  st ffaH. fu .  Ple s . H. L B Sl (b (1 IB. 1
eitn. Nar9. 19

## Folio  -  — 1677894601:0410
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t    oti
voceunten

## Folio  -  — 1677894601:0411
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mnuam
etd n
GWLB Hannover 35
Spit

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.
de
111II