f -vw

I % >':.

1^ t

'?.1^^'^l"

^ '^3isLjJ

tm

THE LIBRARY

OF

THE UNIVERSITY

OF CALIFORNIA

LOS ANGELES

GIFT

Dr. K. N, Beigelman

.

' 'm ■■

DPTICKSi

O R, A

TREATISE

OF THE

REFLEXIONS, REFRACTIONS, INFLEXIONS and COLOURS

O F

L I G U T

ALSO

Two TREATISES

OF THE

SPECIES and MAGNITUDE

O E

I I

Curvilinear Figures

L 0 N D 0 A% Printed for Sam,. Smith, and Ben J. Walpo^ic©^

Printers to the Royal Society , at tliG PrJMi:''s Arms in St. FauPs Church-yard. MDCCIV*

-.f^: •■

>/

=-m

U

,1

p-^ftt-. <■"'*!? '- ^

^ AC 8

ADVERTISEMENT. ^'^],^^

PArt of the enfuing Difcourfe ahout Light was written at the dejire of J ome Gentlemen of the Royal Society,

in the Tear 1675. ^^^ ^^^^ fi^^ ^^ ^^^^^^ Secretary^ and read at their Meetings^ and the reft was added about Twelve Tears after to complete the Theory ; except the Third Book, and the laft Propo/ition of the Second, which werejince put together out offcattered Papers. To avoid heing engaged in Difputes about thefe Matters, I have hitherto delayed the Printing, and Jhould ftill huve de- layed it, had not the importunity of Friends prevailed upon me. If any other Papers writ on this Subject are got out <f my Hands they are imperfecl,and were perhaps written before I had tried all the Experiments her^ fet dovjn, and fully fatisfied my felf about the Laws of Refractions and Compojition of Colours. I have here Publifhed what I think proper to come abroad, wifhing that it may not be Tranftated into another Language without my Confent.

The Crowns of Colours, which fometimes appear about the Sun and Moon, I have endeavoured to give an Ac- count of; but for want offufficient Obfer vat ions leave that Matter to be further examined. The Subject of the Third Book I have alfo left imperfect, not having trieS all the

Expe-

Kxperhnents zvJucb I intended ivhen I vjas about thefe Matters, nor repeated fome of thoje ixjhich I did try, until Ihadjatisfied niyfeJf about all their Circumjlances. To communicate what I have tried, and leave the reft to others for further Enquiry, is all my Deji^a in publijhing thefe Papers.

In a Letter written to Mr.Leibnitz in the Tear 1 6'j6. and publ/fJoed by Dr. Wallis, I mentioned a Method by which I had found fome general Theorems about Jquaring Curvilinear Figures, or comparing them with the Conic Scilions, or other the Jim pie ft figures with which they may he compared. And fome Tears ago I lent out a Manufcript i-ontainingfuch Theorems, and having fince met with fome Things copied out of it, I have on this Occafton made it publick, prefixing to it an Introduclion and fubyjyning a Scholium concerning that Method. And I have pined with it another fmall Tract concerning the Curvilinear Figures of the Second Kind, which was alfo written ntany Tears ago, and made known to fome Friends, who bavejolktted the making it publick.

I. N.

The FIRST BOOK

O F

O P T I C K S

PART I.

MY D^fign in this Book is not to explain the Pro- perties of Light by Hypothefes, but to propofc and prove them by Reafon and Experiments ; In order to which , I (hall premife the following Defini- tions and Axioms.

DEFINITIONS,

D E F I N. L

Br the ^ys of Light I nnderftand its leajl Tarts , and thofe 06 wellSucceJJiVe in the fame Lines as Contemporary in Je' Veral Lines. For it is manifeft that Light confifts of parts both Succeflive and Contemporary 5 becaufe in the fame place you may flop that which comes one moment, and let pafs that which comes prefently afterj and in the fame time you may ftop it in any one place, and let it pafs in any other. For that part of Light which is ftopt cannot be the fame with that which is let pafs. The leaft Light or part of Light , which may be ftopt alone without the left of the Light, or propagated alone, or do or fuffer any

A thing

[2]

thing alone, which the reft of the Light doth not or fuf- ers not, I call a Ray of Light.

D E F I N. 11.

^efrangibil'tty of the ^ys of Lights ts their Difpofition to h refraHed or turned out of their Way in paffing out of one trmf' parent 'Body or 'Medium into another. And a greater er lefs (?^e- frangihility of^ys^ is their Difpofition to he turned more or lefs out of their Way in like Incidences on the fame Medium. Mathe- maticians ufually confider the Rays of Light to be Lines reaching from the luminous Body to the body illumina- ted, and the refradlion of thofe Rays to be the bending or breaking of thofe Lines in their paffing out of one Me- dium into another. And thus may Rays and Refi:ad:ions be confidered, if Light be propagated in an inftant. But by an Argument taken from the y£quations of the times of the Eclipfes of Jupiter'' s Satellites it feems that Light is propagated in time, fpending in its paflage from the Sun to us about Seven Minutes ol time : And therefore I have chofen to define Rays and Refractions in fuch general terms as may agree to Light in both cafes.

D E F I N. III.

^fexihility of ^ys, is their Difpofition to be turned hac{_ into the fame Medium from any other Medium upon whofe Surface they fall. Aid ^ys are more or lef^ reflexible , which are returned back^ more or lefs eafily. As if Light pafs out of Glafs into Air , and by being inclined more and more to the com- mon Surface of the Glafs and Air, begins at length to be totally reflected by that Surface 5 thofe forts of Rays which at like Incidences are reflected moft copiouily , or by in- chning the Rays begin fooneft to be totally reflected, are- moft reflexible. D E-

[ ? }

D E F I N. IV.

>

The Angle of Incidence^ is that Angle which the Line defcribed by the incident ^^y contains with the Perpendicular to the refle" fiing or refraSiing Surface at the Toint of Incidence.

D E F I N. V.

The Angle of ^flexion or ^fraBion, «■ the Angle which the Line defcribed by the rejleSled or refraBed ^y containeth with the perpendicular to the refleBing or refraBing Surface at the ^oint of Incidence.

D E F I N. VI.

The Sines of Incidence, Reflexion, and ^fraBion, are the Sines of the Angles of Incidence^ Reflexion, and ^efraBion.

D E F I N. VII.

The Light whofe ^ys are all alike ^J^efrangible, I call Sinu pie , Homogeneal and Similar j and that whofe ^ys are fome more ^frangible than others , I call Com^otmdj Heteroo-eneal and 'DiJJimilar. The former Light I call Homogeneal , not becaulc I would affirm it fo in all refpecfls ; but becaufe the Rays which agree in Refrangibility, agree at leaft ia all thofe their other Properties. Which I confider in the following Diicourfe.

D E F I N. VIII.

The Colours of Homogeneal Lights , / call Primary, Homo- geneal and Simple j and thofe of Heterogeneal Lights, Heteroge' neal and Compound. For thefe are always compounded of the colours of Homogeneal Lights 3 as will appear in the following Difcourfe. A 2 AX I-

C4] AXIOMS.

A X. I.

THE Angles of Incidence^ ^flexmi, and ^frafiion, lye ill one and the fatne Tlofie.

A X. II.

The Angle of ^flexion is equal to the Angle of Incidence.

A X. III.

If the refraSied ^y he returned direBly back, fo the Pointy of Incidence , it JJ^all he refrafied into the Line before defcri- bed by the incident (I(ay.

A X. IV.

^fraflion out of the rarer Medium into the denfer , is made towards the Perpendicular 3 that is, fo that the Angle of ^fra- Bion be leJJ than the Angle of Incidence.

AX. V.

The Sine of Incidence, is either accurately or "Very nearly in a giyen <B^tio to the Sine of ^fraElion.

Whence if that Proportion be known in any one Incli» nation of the incident Ray, 'tis known in all the Inclina- tions, and thereby the Refradion in all cafes of Incidence on the fame refracting Body may be determined. Thus if the Refradion be made out of Air into Water, the Sine of Incidence of the red Light is to the Sine of its Refra- ction as 4, to ^0. If out of Air into Glafs, the Sines are

as

C 5 ]

as 17 to 1 1. In Light of other Colours the Sines have ©ther Proportions : but the difference is fo little that if need feldom be considered.

Suppofe therefore, that R S reprefents the Surface of Fix- ftagnating Water , and C is the point of Incidence in which any Ray coming in the Air from A in the Line A C is reflected or refraded, and I would know whether this Ray fhall go after Reflexion or Refradlion : I ere(5l upon the Surface of the Water from the point of Inci- dence the Perpendicular C P and produce it downwards- to Q., and conclude by the firfl: Axiom, that the Ray af- ter Reflexion and Refrad:ion, fhall be found fomewhere in the Plane of the Angle of Incidence A C P produced. I let fall therefore upon the Perpendicular C P the Sine of Incidence A D, and if the reflected Ray be defired , I pro- duce A D to B fo that D B be equal to A D, and draw C B. For this Line C B fhall be the refleded Ray; the Angle of Reflexion B C P and its Sine B D being equal to the Angle and Sine of Incidence, as they ought to be by the fecond Axiom. But if the refradled Ray be de- fired, I produce AD toH, fo that D H may be to A Di as the Sine of Refra<5tion to the Sine of Incidence, that is as 3 to 4 ; and about the Center C and in the Plane A C P' with the Radius C A defcribing a Circle A B E I draw Parallel to the Perpendicular C P Q, the Line H E cutting' the circumference in E, and joyning C E, this Line CE (hall be the Line of the refradied Ray. For if E F be let fall perpendicularly on the Line P Q_ , this Line E F fhall be the Sine of Refradion of the Ray C E, the Angle of Refradion being E C Q; and this Sine E F is equal to DH, and confequently in Proportion to the Sine oflnci--- dence AD as 3 to 4.

C6]

• In like manner, if there be a Prifm of Glafs (that is a Glafs bounded with two Equal and Parallel Triangular ends, and three plane and well polifhed Sides, which meet in three Parallel Lines running from the three Angles of one end to the three Angles of the other end) and if the Refraction of the Light in paffing crofs this Prifm be dtCi' fi<r. 2. red : Let ACB reprefent a Plane cutting this Prifm tranf- verfly to its three Parallel lines or edges there where the Light paffeth through it, and let J E be the R.iy inci- dent upon the firft fide of the Prifm A C where the Light goes into the Glafs 3 And by putting the Proportion of the Sine of Incidence to the Sine of Refracftion as 17 to 1 1 find E F the firft refraded Ray. Then taking this Ray for the Incident Ray upon the fecond fide of the Glafs B C where the Light goes out, find the next refradted Ray F G by putting the Proportion of the Sine of Incidence to the Sine of Refrad:ion as 1 1 to 17. For if the Sine of Inci- dence out of Air into Glafs be to the Sine of Refraction as 17 to 1 1, the Sine of Incidence out of Glafs into Air muft on the contrary be to the Sine of RefraClion as i i to 17, by the third Axiom. fig-. 7 . Much afi:er the fame manner , if A C B D reprefent a Glafs fpherically Convex on both fides (ufually called a Lens, fuch as is a Burning- glafs, or Spectaclc-glafs, or an Objedt-glafs of a Telefcope) and it be required to know how Light falling upon it from any lucid point Q_ fliall be refracted, let Q.M reprefent a Ray falling upon any point M of its firft fpherical Surface ACB, and by ered:ing a Perpendicular to the Glafs at the point M, find the firft refracted Ray M N by the Proportion of the Sines 1 7 to 1 1 . Let that Ray in going out of the Glafs be inci- dent upon N, and then find the fecond refracted Ray N q by the Proportion of the Sines 1 1 to 1 7. And after the

fame

C7]

fame manner may the Refradlion be found when the Lens is Convex on one fide and Plane or Concave on the other, or Concave on both Sides.

AX. VI.

Homogened ^ys which flow from feVeral 'Points of any Oh' jeSl, and fall almoft ferpendicularly on any refiefiing or refra^ ilrng Tlane or Spherical Surface , Jhall afterwards diverge from fo many other Joints ^ or he ^Parallel to fo ynany other Lines, or conserve to fo ynany other 'Points, either accurately or without any fenfihle Error. And the fame thing will happen, if the ^ys he refleSied or rcfraSled fucceJJiVely hy two or three or 7?iore 'Playie or Jpherical Surfaces.

The Point from which Rays diverge or to which they converge may be called their Focus. And the Focus of the incident Rays being given, that of the refledted or re- fraded ones may be found by finding the Refradion of any two Rays, as above 5 or more readily thus.

Caf 1. Let ACB be a reflecting or refracting Plane, Fig. 4. and Q. the Focus of the incident Rays, and Q.^ C a per- pendicular to that Plane. And if this perpendicular be produced to q, fo that ^ C be equal to Q.C, the point q fhall be the Focus of the reflected Rays. Or if ^ C be taken on the fame fide of the Plane with Q_C and in Pro- portion to Q.C as the Sine of Incidence to the Sine of Refradiion, the point q fhall be the Focus of the refrac- ted Rays.

Caf. 2. Let A C B be the reflecting Surface of any Fig. 5. Sphere whofe Center is E. Bifect any Radius thereof (fup- pofe E C) in T, and if in that Radius on the fame fide the point T you take the Points Q. and q, fo that T Q., T E, and Tq be continual Proportionals, and the point Q.be

the

[8]

the Focus of the incident Rays , the point q (hall be the Focus of the refled:ecl ones.

Fig. 6. Caf. I . Let A C B be the refracting Surface of any Sphere whofe Center is E. In any Radius thereof E C 'produced both ways take E T and C t feverally in fuch Proportion to that Radius as the leflcr of the Sines of Incidence and Refradlion hath to the difference of thofe Sines. And then if in the fame Line you find any two Points Q. and q , fo that T Q. be to E T as E f to f ^, taking t q the contrary way from t which T Q. Heth from T, and if the Point Qbe the Focus of any incident Rays, the Point q fhall be the Focus of the refra(5led ones.

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

^jFtg. 7 . Caf. 4. Let A C B D be any refradling Lens , fpheri- cally Convex or Concave or Plane on either fide , and let C D be its Axis (that is the Line which cuts both its Sur- faces perpendicularly, and pafles through the Centers of the Spheres,) and in this Axis let F and /be the Foci of the refracted Rays found as above , when the incident Rays on both fides the Lens are Parallel to the fame Axis 3 and upon the Diameter F/ bifected in E, defcribe a Circle. Suppofe novj that any Point Q. be the Focus of any inci- dent Ray So Draw Q,E cutting the faid Circle in T and f, and therein take t q inilich Proportion to f E as f E or TE hath to T Q. Let t q lye the contrary way from t which T Q. doth from T, and q fhall be the Focus of the refrac- ted Rays without any fenfible Error , provided the Point Q_ be not fo remote from the Axis, nor the Lens fo broad as to make any of the Rays fall too obliquely on the refracting Surfaces.

And by the like Operations may the reflecting or re- fracting Surfaces be found when the two Foci are given,

and

[ 9 ]

and thereby a Lens be formed, which (liall make the Rayt flow towards or from what place you pleafe.

So then the meaning of this Axiom is , that if Ray$ fall upon any Plane or Spherical Surface or Lens, and before their Incidence flow from or towards any Point Q. , they (hall after Reflexion or Refraction flow from or to- wards the Point q found by the foregoing Rules. And if the incident Rays flow from or towards feveral points Q., the reflected or refracted Rays fball flow from or towards To many other Points q found by the fame Rules. Whe- ther the reflected and refracted Rays flow from or towards the Point q is eafily known by the fituation of that Point. For if that Point be on the fame fide of the reflecting or refracting Surface or Lens with the Point Q, and the in- cident Rays flow from the Point Q, the refle(5ted flow to- wards the Point q and the refracted from it 5 and if the incident Rays flow towards Q, the reflected flow from ^, and the refracted towards it. And the contrary happens when q is on the other fide of that Surface.

A X. VII.

Wherever the ^ys which come from all the Joints of any Ob' jeFi yneet again in fo many joints after they haVe been ?nade to converge by Reflexion or ^efraflion^ there they tvill make a Tic' ture of the Object upon any white 'Body on which they fall.

So if PR reprefent any Object without Doors, and ABFig. be a Lens placed at a hole in the Window-fhut of a dark Chamber, whereby the Rays that come from any Point Q_ of that Object are made to converge and meet again in the Point q 5 and if a Sheet of white Paper be held at q for the Light there to fall upon it : the Picture of that Object PR will appear upon the Paper in its proper Shape

B and

[lo]

and Colours. For as the Light which comes from the Point Q_ goes to the Point q, [o the Light which comes from orhcr Points P and R of the Object, will go to fo many other correfpondent Points fi and r (as is manifeft by the fixth Axiom 3) fo chat every Point of the Objecr fhall illuminate a correfpondent Point of the Picture, and thereby make a Picture like the Object in Shape and Co- lour, this only excepted that the Picture fhall be inverted. And this is the reafon of that Vule,ar Experiment of call- ing the Species of Objects from abroad upon a Wall 01 Sheet of white Paper in a dark Room. 8. In like manner when a Man viev.s any Object P Q.R, the Light which comes from the fevcral Points ol the Ob- ject is fo refracted by the tranlparenc skins and humours of the Eye, (that is by the outward coat EFG called the Tunica Comen, and by the cryftalline humour AB which is beyond the Pupil m k^) as to converge and meet again at fo many Points in the bottom of the Eye, and there to paint the Picture of the Object upon that skin (called the T«- nica ^tina) with which the bottom of the Eye is covered. For Anatomifts when they have taken off from the bot- tom of the Eye that outward and moft thick Coat called the Dura Matey, can then fee through the thinner Coats the Pictures of Objects lively painted thereon. And thefe Pictures propagated by Motion along the Fibres of the Op- tick Nerves into the Brain, are the caufe of Vifion. For accordingly as thefe Pictures are perfect or imperfect, the Object is feen perfectly or imperfectly. If the Eye be tin- ged with any colour Cas in the Difeafe of the Jaundi/e) fo as to tinge the Pictures m the bottom of the Eye with that Colour, then all Objects appear tinged with the fame Co- lour. If the humours of the Eye by old Age decay, fo 45 by llirinking to make the Coni£a and Coat of the Cry'

, Jlalline

["]

flalUne humour grow flatter than before, the Light will not be refracted enough , and for want of a fufficient Refradion will not converge to the bottom of the Eye but to fome place beyond it , and by confequence paint in the bottom of the Eye aconfufedPi(5ture,and according to the indiftindt- nefs of this Piifture the Objedt will appear confufed. This is the reafon of the decay of Sight in old Men, and fliews why their Sight is mended by Spedacles. Forthofe Con- vex-glafles fupply the defedl of plumpnefs in the Eye, and by encreafing the Refraction make theRays converge fooner fo as to convene diftincftly at the bottom of the Eye if the Glafs have a due degree of convexity. And the contrary happens in fhort-fighted Men whofe Eyes are too plump. For the Refra<5tion being now too great, the Rays converge and convene in the Eyes before they come at the bottom 5 and therefore thePiClure made in the bottom and the Vifion caufed thereby will not be diftind, unlefs the Objed be brought fo near the Eye as that the place where the con- verging Rays convene may be removed to the bottom, or that the plumpnefs of the Eye be taken off and the Refra- diions diminifhed by a Concave-glafs of a due degree of Concavity, or laftly that by Age the Eye grow flatter till it come to a due Figure : For fhort-fighccd Men fee remote Objeds beft in Old Age, and therefore they are accounted to have the moft laftmg Eyes.

A X. VIII.

An Ohjefi feen by Reflexion or ^fraSlion^ appears in that place from iphence the ^ys after their lajl ^flexion or l^frafiion di' yer^e in falling on the SpeHators Eye.

If the Objed A be feen by Reflexion of a Looking- Fig. ^\ glafs m ?i, it fliall appear, not in it's proper place A, but

B 2 behind

I-

[12]

behind the Glafs at 4, from whence any Rays AB, AC, A D, which flow from one and the fame Point of the Ob* jed, do after their Reflexion made in the Points B, C, D, diverge in going from the Glafs to E, F, G, where they are incident on the Spectator's Eyes, For thefe Rays do make the fame Picture in the bottom of the Eyes as if they had come from the Object really placed at a, without the interpofition of the Looking-glafs j and all Vifion is made according to the place and fhape of that Picture.

F/C-, 2. In like manner the Object D feen through a Prifm ap- pears not in its proper place D, but is thence tranflated to ibme other place d fituated in the lafl refracted Ray F G drawn backward from F to d.

Til. I o. And fo the Object Q. feen through the Lens A B, appean at the place q from whence the Rays diverge in pafling from the Lens to the Eye. Now it is to be noted, that the Image of the Object at q is fo much bigger or leffer than the Object it felf at Q., as the diftance of the Image at q from the Lens AB is bigger or lefs than the diftance of the Object at Q. from the fame Lens. And if the Object be feen through two or more fuch Convex or Concave- glaffes, every Glafs (hall make a new Image, and the Ob- jed fhall appear in the place and of the bignefs of the laft Image. Which confideration unfolds the Theory of Mi- erofcopes and Telefcopes. For that Theory confiils in al- moft nothing elfe than the defcribing fuch Glafles as fliall make the laft Image of any Obje(5t as diftindl and large and luminous as it can conveniently be made.

I have now given in Axioms and their Explications the fumm of what hath hitherto been treated of in Opticks. For what hath been generally agreed on I content my felf to afliime under the notion of Principles, in order to what I have further to write. And this may fuffice for an:

Intro-

[13]

Introdudion to Readers of quick Wit and good Under- ftanding not yet verfed in Opticks : Although thofe who are already acquainted with this Science , and have handled Glafles, will more readily apprehend what fol^ loweth.

PROPOSITIONS.

L

(p^I^OT. I. Theor. I.

I G H T S which differ in Colour, differ alfo in De- grees of Refrangibility.

The Proof hy E>cperiments.

Exper. I . I took a black oblong ftiff Paper terminated by Parallel Sides, and with a Perpendicular right Line drawn crofs from one Side to the other , diftinguifhed it into two equal Parts. One of thefe Parts 1 painted with a red Colour and the other with a blew. The Paper was very black, and the Colours intenfe and thickly laid on, that the Phacnomenon might be more confpicuous. This Paper I viewed through a Prifm of folid Glafs, whofe two Sides through which the Light paffed to the Eye were plane and well polifhed, and contained an Angle of about Sixty Degrees : which Angle I call the refrad:ing Angle of the Prifm. And whilft I viewed it, I held it before a Window in fuch manner that the Sides of the Paper were parallel to the Prifm, and both thofe Sides and the Prifm parallel to the Horizon, and the crofs Line perpendicular to it ; and. that the Light which fell from the Window

UpOft

117. I 1

[Hi

upon Vhe Piper made an Angle with the Paper, equal to that Angle which was made with the fame Paper by the .Light refieiled from it to the Eye. Beyond the Prifm was the Wall of the Chamber under the Window covered over with black Cloth, and the Cloth was involved in Dark- nefs that no Light might be refleded from thence, which in pafling by the edges of the Paper to the Eye , might mingle it felf with the Light of the Paper and obfcure the Phacnomenon thereof Thefe things being thus ordered, I found that if the refrading Angle of the Prifm be turned upwards, fo that the Paper may feem to be lifted upwards by the Refradion , its blew half will be lifted higher by the Refradion than its red half But if the refracting Angle of the Prifm be turned downward, fo that the Pa- per may feem to be carried lower by the Refradlion, its blew half will be carried fomething lower thereby than its red half Wherefore in both cafes the Light v/hich comes from the blew half of the Paper through the Prifm to the Eye, does in like Circumftances fuffcr a greater Re- fra(5lion than the Light which comes from the red half, and by confequence is more refrangible.

lUuftratiGn. In the Eleventh Figure, M "N reprefents the Window,and D E the Paper terminated with parallel Sides D J and H E, and by the tranfverfe Line F G diftinguilTied into two halfs, the one D G of an intenfely blew Colour, the other F Eof an intenfely red. And '^KCcab repre- fents the Prifm whofe refrading Planes h^b a and hQca meet in the edge of the refrading Angle A a. This edge A^ being upward, is parallel both to the Horizon and to the parallel edges of the Paper D J and H E. And de re- prefents the Image of the Paper feen by Refraction up- wards in fuch manner that the blew half D G is carried higher to d^ than the red half F E is to /e, and therefore"

fuffers

[15]

fufFers a greater Rcfradion. If the edge of the refracting Angle be turned downward, the Image of the Paper will be refraded downward fuppofe to ^i, and the blew half will be refraded lower to -^ 7 than the red half is to ?>s.

Exper. 2. About the afotefaid Paper, whofe two halfs were painted' over with red and blew, and which was ftiff like thin Pailboard, I lapped feierai times a llender thred of very black Silk, in fuch manner that the feveral parts of the thred might appear upon the Colours like fo many black Lines drawn over them , or like long and llender dark Shadows caft upon them. I might have drawn black Lines with a Pen, but the threds were fmaller and better defined. This Paper thus coloured and lined i let againft a Wall perpendicularly to the Horizon, fo that one of the Colours might ftand to the right hand and the other to the left. Clofe before the Paper at the confine of the Co- lours below I placed a Candle to illuminate the Paper ftrongly : For the Experiment was tried in the Night. The flame of the Candle reached up to the lower edge of the Paper, or a very little higher. Then at the diftance of Six Feet and one or two Inches from the Paper upon the Floor I eredled a glafs Lens four Inches and a quarter broad, which might colled the Rays coming from the feveral Points of the Paper, and make them converge to- wards fo many other Points at the fame diftance of fix Feet and one or two Inches on the other fide of the Lens, and fo form the Image of the coloured Paper upon a white Paper placed there 3 after the fame manner that a Lens at a hole in a Window cafts the Images of Objeds abroad upon a Sheet of white Paper in a dark Room. The afore- faid white Paper, erecled perpendicular to the Horizon and to the Rays Vv'hich fell upon it firom the Lens, I moved fometimes towards the Lens, fometimes from it, to find

the

[i6]

•tlie places where the Images of the blew and red parts of the coloured Paper appeared moft diftind. Thofe places 1 eafily knew by the Images of the black Lines which I had made by winding the Silk about the Paper. For the Images of thofe fine and flender Lines (which by reafon of their blacknefs were like Shadows on the Colours) were confijfed and fcarce vifible, unlefs when the Colours on ei- ther fide of each Line were terminated moft diftindily. Noting therefore, as diligently as I could, the places where the Images of the red and blew halfs of the coloured Pa- per appeared moft diftincft , I found that where the red half of the Paper appeared diftin(5t, the blew half appeared confufed, fo that the black Lines drawn upon it could fcarce be feen 5 and on the contrary where the blew half appeared moft diftinct the red half appeared confufed, fo that the black Lines upon it were fcarce vifible. And be- tween the two places where thefc Images appeared diftind: there was the diftance of an Inch and a hail : the diftance of the white Paper from the Lens, when the Image of the red half of the coloured Paper appeared moft diftind:, be- ing greater by an Inch and an half than the diftance of the fame white Paper from the Lens when the Image of the blew half appeared moft diftintft. In like Incidences there- fore of the blew and red upon the Lens, the blew was re- fradted more by the Lens than the red, fo as to converge fooner by an Inch and an half, and therefore is more refran- gible. Pi?. 12. Illuftration. In the Twelfth Figure, DE fignifies the co- loured Paper, D G the blew half, F E the red half, M N the Lens, H J the white Paper in that place where the red half wirh its black Lines appeared diftintfl, and hi the fame Paper in that place where the blew half appeared diftind:. The place hi was nearer to the Lens M N than the place H J by an Inch and an half. Scholtum.

[17]

Scholium. The fame things fucceed notvvithflanding that fome of the Circumftances be varied : as in the firft Ex- periment when the Pnfm and Paper are any uays inclined to the Horizon , and in both when coloured Lines are drawn upon very black Paper. But in the Defcription of thefe Experiments , I have fet down fuch Circumftances by which either the Phaenomenon might be rendred more confpicuous, or a Novice might more eafily try them, or by which I did try them only. The fame thing I have often done in the following Experiments : Concerning all which this one Admonition may fuffice. Now from thefe Experiments it follows not that all the Light of the blew is more Refrangible than all the Light of the red 3 For both Lights are mixed of Rays differently Refrangible, So that in the red there are fome Rays not lefs Refrangible than thofe of the blew , and in the blew there are iome Rays not more Refrangible than thofe of the red j But thefe Rays in Proportion to the whole Light are but feWj and ferve to diminifli the Event of the Experiment , but are not able to deftroy it. For if the red and blew Co- lours were more dilute and weak, the diftance of the Ima- ges would be lefs than an Inch and an half 5 and if they were more intenfe and full, that diftance would be greater, as will appear hereafter. Thefe Experiments may fuffice for the Colours of Natural Bodies. For in the Colours made by the Refraction of Prifms this Propofition will appear by the Experiments which are now to follow in the next Propofition.

TfJlOT.

[i8] PROP. II. Theor. II.

The Light of the Sun confifis of ^ys differently ^frangible.

The Proof by Experiments.

Exper. 3. TN a very dark Chamber at a round hole about j[ one third part of an Inch broad made in the Shut of a Window I placed a Glafs Prifm, whereby the beam of the Sun's Light which came in at that hole might be refrad:ed upwards toward the oppofite Wall of the Chamber , and there form a coloured Image of the Sun. The Axis of the Prifm (that is the Line paifing through the middle of the Prifm from one end of it to the other end Parallel to the edge of the Refrading Angle) was in this and the following Experiments perpendicular to the incident Rays. About this Axis I turned the Prifm flowly , and faw the refra(5l:ed Light on the Wall or co- loured Image of the Sun firft to defcend and then to af- cend. Between the Defcent and Afcent when the Image feemed Stationary , I ftopt the Prifm, and fixt it in that Pofture, that it fliould be moved no more. For in that poflure the Refractions of the Light at the two fides of the Refra<5ting Angle, that is at the entrance of the Rays into the Prifm and at their going out of it, were equal to one another. So alfo in other Experiments as often as I would have the Refractions on both fides the Prifm to be equal to one another, I noted the place where the Image of the Sun formed by the refrad:ed Light flood ftill be- tween its two contrary Motions, in the common Period of its progrefs and egrefs 5 and when the Image fell upon that plaeCj I made faft the Prifin. And in this pofture, as

the

[19]

the mod convenient,ic is to be underftood that all the Prifms are placed in the following Experiments, unlefs where feme other pofture is defcribed. The Prifm therefore being pla- ced in this pofture, I let the refra<5ted Light fall perpendi- cularly upon a Sheet of white Paper at the oppofite Wall of the Chamber, and obferved the Figure and Dimenfions of the Solar Image formed on the Paper by that Light. This Image was Oblong and not Oval, but terminated with two Rectilinear and Parallel Sides , and two Semi- circular Ends. On its Sides it was bounded pretty diftindly, but on its Ends very confufedly and indiftindlly, the Light there decaying and vanifhing by degrees. The breadth of this Image anfwered to the Sun's Diameter, and was about two Inches and the eighth part of an Inch , including the Penumbra. For the Image was eighteen Feet and an half diftant from the Prifm, and at this diftance that breadth if diminiflied by the Diameter of the hole in the Window-fliut, that is by a quarter of an Inch, fubtended an Angle at the Prifm of about half a Degree, which is the Sun's apparent Diameter. But the length of the Image was about ten Inches and a quarter, and the length of the Redilinear Sides about eight Inches 5 And the refracting Angle of the Prifm where- by fo great a length v/as made, was 64 degr. With a lefs Angle the length of the Image was lefs , the breadth re- maining the fame* If the Prifm was turned about its Axis that way which made the Rays emerge more obliquely out of the fecond refraCtino; Surface of the Prifm, the Imase foon became an Inch or two longer, or more; and if the Prifm was turned about the contrary way, fo as to mal^e the Rays fall more obliquely on the firft refracting Surface, the Image foon became an Inch or two fhorter. And therefore in try- ing this Experiment, I was as curious as I could be in pla- cing the Prifm by the above-mentioned Rule exaCtly in

C 2 fuch

[20]

fuch a pofture that the Refradions of the Rays at their emer-' gence out of the Prifm might be equal to that at their inci" dence on it. This Prifm had fome Veins running along within the Glafs from one end to the other , which feat- tercd fome of the Sun's Light irregularly, but had no fen- hble effed; in encreafing the length of the coloured Spec- trum. For I tried the fame Experiment with other Prifms with the fame Succefs. And particularly with a Prifm which feemed free from fuch Veins, and whofe refracting Angle was 6i\ Degrees, I found the length of the Image 9^

or 10 Inches at the diftance of 18- Feet from the Prifm, the breadth of the hole in the Window-fhut being i of an

4

Inch as before. And becaufe it is eafie to commit a mi- flake in placing the Prifm in its due pofture, I repeated the Experiment four or five times, and always found the length of the Image that which is fet down above. With another Prifm of clearer Glafs and better PoUifh, which feemed free from Veins and whofe refracting Angle was 63 ' Degrees, the length of this Image at the fame diftance of I 8 ^ Feet was alfo about 1 o Inches, or 10^. Beyond

thefe Meafures for about ' or - of an Inch at either end of

4 3

the Spe6trum the Light of the Clouds feemed to be a little tinged with red and violet, but fo very faintly that I fufpe- d:ed that tinCture might either wholly or in great meafure arife from fome Rays of the SpeCtrum fcattered irre- gularly by fome inequalities in the Subftance and Polifh of the Glafs , and therefore I did not include it in thefe Meafures. Now the different Magnitude of the hole in theWindow-fliut, and different thicknefs of the Prifm where the Rays paffed through it, and different inclinations of the Prifm to the Horizon, made no fenfible changes in the kngtK of the Image. Neither did the different matter of ^

the

[21]

the Prifms make any : for in a Veflel made of poliflied- Plates of Glafs cemented together in the (hape of a Prifm and filled with Water, there is the like Succefs of the Ex- periment according to the quantity of the Refradiion. It is fijrther to be obferved, that the Rays went on in right Lines from the Prifm to the Image, and therefore at their very going out of the Prifm had all that Inclination to one another from which the length of the Image pro- ceeded, that is the Inclination of more than two Degrees and an half And yet according to the Laws of Opticks vulgarly received, they could not poifibly be fo much in- clined to one another. For let EG reprefent the Window- fm-. i ?, (hut, F the hole made therein through which a beam of the Sun's Light was tranfmitted into the darkned Chamber, and ABC a Triangular Imaginary Plane whereby the Prifm is feigned to be cut tranfverfly through the middle of the Light. Or if you pleafe, let A B C reprefent the Prifm it felf, looking diretflly towards the Spectator's Eye with its nearer end : And let X Y be the Sun, MN the Paper upon which the Solar Image or Spectrum is caft, and P T the Image it felf whofe fides towards V and W are ReClili- near and Parallel, and ends towards P and T Semicir* cular. Y K H P and X L J T are the two Rays, the firft of which comes from the lower part of the Sun to the higher part of the Image, and is refracted in the Prifm at K and H, and the latter comes from the higher part of the Sun to the lower part of the Image, and is refraded at L and J. Since the Refrad:ions on both fides the Prifm are equal to one another, that is the Refradion at K equal to the Refradion at J, and the Refradion at L equal ta the Refradion at H, fo that the Refradions of the inci- dent Rays at K and L taken together are equal to the Refradions of the emergent Rays at H and J taken toge- ther ;.

[22]

ther : it follows by adding equal things to equal things, that the Refradions at K and H taken together, are equal to the Refrad:ions at J and L taken together , and there- fore the two Rays being equally refracted have the fame Inclination to one another after Refrad;ion which they had before, that is the Inclination of half a Degree anfwering to the Sun's Diameter. For fo great was the Inclination of the Rays to one another before Refradion. So then, the length of the Image P T would by the Rules of Vul- gar Opticks fubtend an Angle of half a Degree at the Prifm, and by confequence be equal to the breadth > v> ; and therefore the Image would be round. Thus it would be were the two Rays X L J T and Y K H P and all the reft which form the Image P jp T >, alike Refrangible. And therefore feeing by Experience it is found that the image is not round but about five times longer than broad, the Rays which going to the upper end P of the Image fuffer the greateft Refraction, muft be more Refran- gible than thofe which go to the lower end T , unlefs the inequality of Refrad:ion be cafual.

This Image or Sped:rum P T was coloured, being red at its leaft refracfted end T, and violet at its moft refi:a<5ted end P, and yellow green and blew in the intermediate ipaces. Which agrees with the firft Propofition, that Lights which differ in Colour do alfo differ in Refrangibiiity. The length of the Image in the foregoing Experiments I meafured from the faintefl and outmoft red at one end, to the faintefl and outmofl blew at the other end.

Exper. 4. In the Sun's beam which was propagated in- to the Room through the hole in the Window-fhut, at the diftance of fome Feet from the hole, I held the Prifm in fuch a poflure that its Axis might be perpendicular to that beam. Then I looked through the Prifm upon the ,

hole,

[23] ■

hole, and turning the Prifm to and fro about its Axis to make the Image of the hole afcend and defcend, when be- tween its two contrary Motions it feemed ftationary, I ftopt the Prifm that the Refradlions on both fides of the refradling Angle might be equal to each other as in the former Experiment. In this Situation of the Prifm view- ing through it the faid hole, I obferved the length of its refracted Image to be many times greater than its breadth, and that the moft refracted part thereof appeared violet, the leaft refradted red, the middle parts blew green and yellow in order. The fame thing happened when I re- moved the Prifm out of the Sun s Light , and looked through it upon the hole fhining by the Light of the Clouds beyond it. And yet if the Refradlion were done regularly according to one certain Proportion of the Sines of Incidence and Refracftion as is vulgarly fuppofed, the refracted Image ought to have appeared rouna.

So then, by thefe two Experiments it appears that in equal Incidences there is a confiderable inequality of Re* fradiions : But whence this inequality arifes, whether it be that fome of the incident Rays are refrad:ed more and others lefs, conftantly or by chance, or that one and the fame Ray is by Refra6tion difturbed, fhattered, dilated, and as it were fplit and fpread into many diverging Rays, as GrimaUo fuppofes, does not yet appear by thefe Experi- ments, but will appear by thofe that follow.

Exper. 5 . Confidering therefore, that if in the third Ex- periment the Image of the Sun fhould be drawn out into an oblong form, either by a Dilatation of every Ray, or by any other cafual inequality of the Refradions, the fame oblong Image would by a fecond Refradion made Side- ways be drawn out as much in breadth by the like Dila- tation of the Rays or other cafual inequality of the Rc-

frad:ions

[24]

iradions Sideways, I tried what would be the EfFctfls of

fiich a fecond Refra6lion. For this end I ordered all thinas

as in the third Experiment, and then placed a fecond Prifm

immediately after the firft in a crofs Pofition to it, that it

might again refra(5l the beam of the Sun s Light which

came to it through the firfl: Prifm. In the firft Prifm this

beam was refracted upwards, and in the fecond Sideways.

And I found that by the Refradlion of the fecond Prifm

the breadth of the Image was not increafed, but its fupe-

rior part which in the firft Prifm fuftered the greater Re-

fi-aition and appeared violet and blew, did again in the

fecond Prifm fuffer a greater Refradlion than its inferior

part, which appeared red and yellow , and this without

any Dilation of the Image in breadth.

fig. 1 4. lUuJlration. Let S reprefent the Sun, F the hole in the

Window, A B C the firft Prifm, D H the fecond Prifm, Y

the round Image of the Sun made by a direcft beam of

Lit^ht when the Prifms are taken away, P T the oblong

Image of the Sun made by that beam paffing through the

£ift Prifm alone when the fecond Prifm is taken away, and

pt the Image made by the crofs Refractions of both

Prifms together. Now if the Rays which tend towards

the feveral Points of the round Image Y were dilated and

fpread by the Refradion of the firft Prifm, fo that they

ITiould not any longer go in fingle Lines to fingle Points,

but that every Ray being fplit, fhattered, and changed

from a Linear Ray to a Superficies of Rays diverging

from the Point of Refraction, and lying in the Plane of

the Angles of Incidence and Refraction, they fliould

go in thofe Planes to fo many Lines reaching almoft

from one end of the Image P T to the other, and if

that Image fhould thence become oblong : thofe Rays

and their feveral parts tending towards the feveral Points qf

the

[25] the Image P T ought to be again dilated and fpread Side- ways by the tranfverfe Refraction of the fecond Prifm , fo as to compofe a fourfquare Image, fuch as is reprefented at t7. For the better underftanding of which, let the hiiage FT be diftinguifhed into five equal Parts PQ.K, KQ^RL, L R S M, M S V N, N V T. And by the fame irregularity that the Orbicular Light Y is by the Refradion of the firft Prifm dilated and drawn out into a long Image P T, the the Light P Q.K which takes up a fpace of the fame length and breadth with the Light Y ought to be by the Refra- (Stion of the fecond Prifm dilated and drawn out into the long Image -rq 4^ ^rid the Light K Q_R L into the long Image kqrl, and the Lights LRSM, MSVN,NVT into fo many other long Images I r s 7n, m s y n, nv tl -^ and all thefe long Images would compofe the fourfquare Image ■^1. Thus it ought to be were every Ray dilated by Re- fra<flion, and fpread into a triangular Superficies of Rays diverging from the Point of Refra6tion. For the fecond Refradiion would fpread the Rays one way as much as the firfl doth another , and fo dilate the Image in breadth as much as the firft doth in length. And the fame thing ought to happen, were fome Rays cafually refra6led more than others. But the Event is otherwife. The Image P T was not made broader by the Refraction of the fecond Prifm, but only became obHque, as 'tis reprefented ztpt, its upper end P being by the RefraAion tranflated to a greater diftance than its lower end T. So then the Light which went towards the upper end P of the Image, was (at equal Incidences) more refraded in the fecond Prifm than the Light which tended towards the lower end T, that is the blew and violet, than the red and yellow j and therefore was more Refrangible. The fame Light was by the Refradion of the firft Prifm tranflated further from the

D place

[26]

place Y to which it tended before RcFradion 3 and there- ' fore fuffered as well in the firft Prifm as in the fecond a greater Refraction than the reft of the Light, and by con- lequence was more Refrangible than the reft, even before its incidence on the firft Prifm.

Sometimes I placed a third Prifm after the fecond, and fometimes alfo a fourth after the third , by all which the Image might be often refraded fideways : but the Rays which were more refradcd than the reft in the firft Prifm were alfo more refradted in all the reft, and that without any Dilatation of the Image fideways : and therefore thofe Rays for their conftancy of a greater Refra(5tion are de- fervedly reputed more Refrangible. Mig. 15. But that the meaning of this Experiment may more clearly appear, it is to be confidered that the Rays which are equally Refrangible do fall upon a circle anfwering to the Sun's Difque. For this was proved in the third Experi- ment. By a circle I underftand not here a perfect Geo- metrical Circle, but any Orbicular Figure whofe length is equal to its breadth, and which, as to fenfe, may feem circular. Let therefore A G reprefent the circle which all the moft Refrangible Rays propagated from the whole Difque of the Sun, would illuminate and paint upon the oppofite Wall if they were alone ; E L the circle which all the leaft Refrangible Rays would in like manner illuminate and paint if they were alone ; B H, C J, D K, the circles which fo many intermediate forts of Rays would fuccef- fively paint upon the Wall, if they were fingly propagated from the Sun in fucceflive Order, the reft being always in- tercepted J And conceive that there are other intermediate Circles without number which innumerable other inter- mediate forts of Rays would fucceflively paint upon the Wall if the Sun fliould fucceflively emit every fort apart.

And

[27]

And feeing the Sun emits all thefe forts at once, they muft ail together illuminate and paint innumerable equal cir- cles, of all which, being according to their degrees of Re- frangibility placed in order in a continual fcries, that ob- long Spedtrum P T is compofed which I defcribed in the third Experiment. Now if the Sun's circular Image Y which is made by an unrefrad:ed beam of Light was by any dilatation of the fingle Rays, or by any other irregu- larity in the Refraction of the firll Prifm, converted into the Oblong Spectrum, P T : then ought every circle A G, B H, C J, <^c. in that Spectrum, by the crofs Refra- ction of the fecond Prifm again dilating or otherwife fcattering the Rays as before, to be in like manner drawn out and transformed into an Oblong Figure, and thereby the breadth of the Image P T would be now as much aug- mented as the length of the Image Y was before by the Re- fraction of the firft Prifm 3 and thus by the Refradions of both Prifms together would be formed a fourfquare Figure p"^ tl as I defcribed above. Wherefore fince the breadth of the Spedtrum P T is not increafed by the Refraction fide- ways, it is certain that the Rays are not fplit or dilated, or otherways irregularly fcattered by that Refracftion, but that every circle is by a regular and uniform Refraction tranOated entire into another place, as the circle A G by the greateft RefraCtion into the place ag^ the circle B H by a lefs Refraction into the place bh^ the circle C J by a Re- fraction ftill lefs into the place c/, and fo of the refl^ by which means a new SpeCtrum p t inclined to the former P T is in like manner compofed of circles lying in a right Line 5 and thefe circles muft be of the fame bignefs with the former, becaufe the breadths of all the Spe- Ctrums. Y, P T and pt at equal diflances from the Prifms' arc equal.

D 2 I con-

[28]

I confidered further that by the breadth of the hole F through which the Light enters into the Dark Chamber, there is a Penumbra made in the circuit of the Spedlrum Y, and that Penumbra remains in the rectilinear Sides of the Spedirums P T and pt. I placed therefore at that hole a Lens or Objecl-glafs of a Telefcope which might caft the Image of the Sun diftindly on Y without any Penum- bra at all, and found that the Penumbra of the Rectili- near Sides of the oblong Spedrums P T and pt was alfo thereby taken away, fo that thofe Sides appeared as di- ftinCtly defined as did the Circumference of the firft Image Y. Thus it happens if the Glafs of the Prifms be free from veins, atd their Sides be accurately plane and well polidied without thofe numberlefs waves or curies which, ufually arife from Sand-holes a little fmoothed in polifli- ing with Putty. If the Glafs be only well polifbed and. free from veins and the Sides not accurately plane but a little Convex or Concave, as it frequently happens 5 yet may the three Spe6trums Y, P T and pt want Penumbras, but not in equal diflances from the Prifms. Now from this want of Penumbras, I knew more certainly that every one of the circles was refra(5ted according to fome moft regular, uniform, and conftant law. For if there were any irregularity in theRefradtion, the right Lines A E and G L which all the circles in the Spe(5trum P T do touch, could not by that Refraction be tranflated into the Lines a e and g I as diftinCt and ftraight as they were before, but there would arife in thofe tranflated Lines fome Penumbra or crookednefs or undulation, or other fenfible Perturba- tion contrary to what is found by Experience. Whatfo- cver Penumbra or Perturbation fliould be made in the circles by the crofs Refradion of the fecond Prifm , all that Penumbra or Perturbation would be confpicuous in

the

[29] the right Lines a e and g I which touch thofc circles. And therefore fince there is no fuch Penumbra or Perturbation in thofe right Lines there mufl be none in the circles. Since the diftance between thofc Tangents or breadth of the Spedrum is not increafed by the Refrad:ions, the Dia- meters of the circles are not increafed thereby. Since thofc Tangents continue to be right Lines , every circle which in the firfl; Prifm is more or lefs refrad:ed , is exadlly in- the fame Proportion more or lefs refra(5led in the fecond. And leeing all thefe things continue to fucceed after the fame manner when the Rays are again in a third Prifm,' and again in a fourth refracted Sideways, it is evident that the Rays of one and the fame circle as to their degree ob Refrangibility continue always Uniform and Homogeneal- to one another, and that thofe of feveral circles do differ in degree of Refrangibility, and that in fome certain and- conftant Proportion. Which is the thing I was to prove.

There is yet another Circumftance or two of this Ex-F/^. i6, perimem by which it becomes flill more plain and con- vincing. Let the fecond Prifm D H be placed not imme- ately after after the firft, but at fome diftance from it 5 Suppofe in the mid-way between it and the Wall on which the oblong Spedlrum P T is caft, fo that the Light from thefirfl: Prifm may fall upon it in the form of an oblong Spcdrum, t7 Parallel to this fecond Prifm,and be refraded - Sideways to form the oblong Spedrum j? t upon the Wall. And you will find as before, that this Spedrum ^ f is in- clined to that Spedtrum P T, which the hrft Prifm forms- alone without the fecond ; the blew ends P and p beina fur- ther diftant from one another than the red ones T and t, and by confequence that the Rays which ctq to the blew end '^ of the Image ■^l and which therefore fuffer the greateftr Refradion in the firft Prifm, are again in the fecond Prifm more refraded than the reft. The

C 30 ]

F/g-. 1 7. The fame thing I try'd alTo by letting the Sun's Light into a dark Room through two little round holes F and p made in the Window, and with two Parallel Prifms ABC and A^y placed at thofe holes ( one at each ) refrad:ing thofe two beams of Light to the oppofite Wall of the Chamber, in fuch manner chat the two colour'd Images P T and m n which they there painted were joyned end to end and lay in one ftraight Line, the red end T of the one couching the blew end m of the other. For if thefe two refrad:ed beams were again by a third Prifm D H pla- ced croft to the two firft, refratied Sideways, and the Spe- <5trums thereby tranflated to lomc other part of the Wall of the Chamber , fuppofe the Sp-^flrum P T to pt and the Spe(5trum M N to m ?i, thefe iranflated Spe(5trums /> t and m n would not lie in one ftraight Line with their ends contiguous as before, but be broken off from one another and become Parallel, the blew end of the Image m n being by a greater Refradion tranflated farther from its former place M T, than the red end t of the other Image p t from the fame place MT which puts the Propofition paft di- ipute. And this happens whether the third Prifm D H be placed immediately after the two firft or at a great diftance from them , fo that the Light refra(fled in the two firft Prifms be either white and circular, or coloured and ob- long when it falls on the third.

Exper. 6. In the middle of two thin Boards I made round holes a third part of an Inch in Diameter, and in the Window-fhut a much broader hole, being made to let into my darkned Chamber a large beam of the Sun's Light 5 I placed a Prifm behind the Shut in that beam to relrad it towards the oppofite Wail, and clofe behind the Prifm I fixed one of the Boards, in fuch manner that the middle of the refrad:ed Light might pafs through the hole

made

[31]

made in it, and the reft be intercepted by the Board. Then at the diftance of about twelve Feet from the firft Board I fixed the other Board, in fuch manner that the middle of the refra<5ted Light which came through the hole in the firft Board and fell upon the oppofite Wall might pafs through the hole in this other Board, and the reft be- ing intercepted by the Board might paint upon it the co- loured Spectrum of the Sun. And clofe behind this Board I fixed another Prifm to refrad: the Light which came through the hole. Then I returned fpeedily to the firft Prifm, and by turning it flowly to and fi-o about its Axis, I caufed the Image which fell upon the fecond Board to move up and down upon that Board, that all its parts might fucccflively pafs through the hole in that Board and fall upon the Prifm behind it. And in the mean time, I noted the places on the oppofite Wall to which that Light after its Refraction in the fecond Prifm did pafs 5 and by the difference of the places I found that the Light which being moft refra(5led in the firft Prifm did go to the blew end of the Image, was again more refracted in the fecond Prifm than the Light which went to the red end of that Image, which proves as well the firft Propofition as the fecond. And this happened whether the Axis of the two Prifms were parallel, or inclined to one another and to the H®rizon in any given Angles.

Illuftration. Let r be the wide hole in the Window-fliut, p^v i g, through which the Sun fhines upon the firft Prifm ABC, and let the refraded Light fall upon the middle of the Board D E, and the middle part of that Light upon the hole G made in the middle of that Board. Let this tra- jeded part of the Light fall again upon the middle of the fecond Board d e and there paint fuch an oblong coloured Image of the Sun as was defcribed in the third Experiment.

By

C32]

'By turning the Prifm ABC flowly to and fro about it^ Axis this Image will be made to move up and down the Board d e, and by this means all its parts from one end to the other may be made to pafs fucceflively through the hole g which is made in the middle of that Board. In the mean while another Prifm a b c is to be fixed next after that hole^ to refracft the traje(5ted Light a fecond time. And thefe things being thus ordered, I marked the places M and N of the oppofice Wall upon which the refradled Light fell,and found that whilft the two Boards and fecond Prifm remained unmoved, thofe places by turning the firft Prifm about its Axis were changed perpetually. For when the lower part of the Light which fell upon the fecond Board d e was call through the hole ^ it went to a lower place M on the Wall , and when the higher part of that Light was caft through the fame hole^, it went to a higher place N on the Wall,- and wken any intermediate part of the Light was caft through that hole it went to fome place on the Wall between M and N. The unchanged Pontion of the holes in the Boards, made the Incidence of the Rays upon the fecond Prifm to be the fame in all cafes. And yet in that common Incidence fome of the Rays were more refracted and others lefs. And thofe were more refra(5ted in this Prifm which by a greater Refraction in the firft Prifm were more turned out of the way, and therefore for their conftancy of being more refi:a6ted are defervedly cal- led more Refrangible.

Exper. 7. At two holes made near one another in my Window-fliut I placed two Prifms , one at each, which might caft upon the oppofite Wall ( after the manner of the third Experiment ) two oblong coloured Images of the Sun. And at a little diftance from the Wall I placed a long flender Paper with ftraight and parallel edges, and

ordered

C33l

ordered the Prifms and Paper fo, that the red Colour of one Image might fall diredily upon one half of the Paper, and the violet colour of the other Image upon the other half of the fame Paper j fo that the Paper appeared of two Colours , red and violet , much after the manner of the painted Paper in the firft and fecond Experiments. Then with a black Cloth I covered the Wall behind the Paper, that no Light might be refleded from it to difturb the Experiment, and viewing the Paper through a third Prifm held parallel to it, I faw that half of it which was illumi- nated by the Violet-light to be divided from the other half by a greater Refradiion, elpecially when I went a good way off from the Paper. For when I viewed it too near at hand, the two halfs of the Paper did not appear fully divided from one another , but feemed contiguous at one of their Angles like the painted Paper in the firft Expe- riment. Which alfo happened when the Paper was too broad.

Sometimes inftead of the Paper I ufed a white Thred, and this appeared through the Prifm divided into two Pa- rallel Threds as is reprefented in the 19th Figure, where Fig^. ip. D G denotes the Thred illuminated with violet Light from D to E and with red Light from F to G, and d e fg are the parts of the Thred feen by Refradion. If one half of the Thred be conftantly illuminated with red, and the other half be illuminated with all the Colours fuccefiively, (which may be done by caufing one of the Prifms to be turned about its Axis whilft the other remains unmoved) this other half in viewing the Thred through the Prifm, will appear in a continued right Line with the firft half when illuminated with red , and begin to be a little divi- ded from it when illuminated with Orange, and remove further from it when illuminated with Yellow, and ftill

E further

[3+]

further when with Green, and further when with Blew, and go yet further off when illuminated with Indigo, and fur- theft when with deep Violet. Which plainly fhews, that the Lights of feveral Colours are more and more Refran- gible one than another, in this order of their Colours, Red, Orange, Yellow, Green, Blew, Indigo, deep Violet 3 and fo proves as M^ell the firft Propofition as the fecond. pifT. 17. I caufed alfo the coloured Spe6trums PT and M N made in a dark Chamber by the Refra6tions of two Prifms to lye in a right Line end to end, as was defcribed above in the fifth Experiment, and viewing them through a third Prifm held Parallel to their length, they appeared no longer in a right Line, but became broken from one another, as they are reprefented 3.t p t and tn », the violet end m of the Spectrum ?« n being by a greater Refradiion tranflated further from its former place M T than the red end t of the other Spedrum p t. Fi<r. 20. I further caufed thofe two Spedlrums P T and MN to- become co-incident in an inverted order of their Colours, the red end of each falling on the violet end of the other, as they are reprefented in the oblong Figure P T M N 5 and then viewing them through a Prifm D H held Paral- lel to their length, they appeared not co-incident as when viewed with the naked Eye , but in the form of two di- ftincfl Spe6trums p t and m n eroding one another in the middle after the manner of the letter X. Which fliews that the red of the one Spe(5trum and violet of the other, which were co-incident at P N and M T , being parted from one another by a greater Refraction of the violet to p and m than of the red to 71 and f, do differ in degrees of Refrangibility.

I illuminated alfo a little circular piece of white Paper all over witk the Lights of both Prilms intermixed, and

when

[35]

when it was illuminated with the red of one Spe(5lrum and deep violet of the other , fo as by the mixture of thoic Colours to appear all over purple , I viewed the Paper, firfi; at a lefs diflance , and then at a greater , through a third Prifm 5 and as I went from the Paper, the refra(5ted Image thereof became more and more divided by the un- equal Refra6tion of the two mixed Colours, and at length parted into two diftind: Images, a red one and a violet one, whereof the violet was furtheft from the Paper, and there- fore fufFered the greatefl: Refracflion. And when that Prifm at the Window which caft the violet on the Paper was ta- ken away,the violet Image difippeared j but when the other Prifm was taken away the red vaniflied : which fiiews that thefe two Images were nothing elfe than the Lights of the two Prifms which had been intermixed on the purple Pa- per, but were parted again by their unequal Refracflions made in the third Prifm through which the Paper was viewed. This alfo was oblervable that if one of the Prifms at the Window, fuppofe that which caft the violet on the Paper, was turned about its Axis to make all the Colours in this order, Violet, Indigo, Blew, Green, Yel- low, Orange, Red, fall fucceffively on the Paper from that Prifm, the violet Image changed Colour accordingly, and in changing Colour came nearer to the red one, until when it was alfo red they both became fully co-incident.

I placed alfo two paper circles very near one another, the one in the red Light of one Prifm, and the other in the violet Light of the other. The circles were each of them an Inch in Diameter, and behind them the Wall was dark that the Experiment might not be difturbed by any Light coming from thence. Thefe circles thus illuminated, I viewed through a Prifm fo held that the Refraction might be made towards the red circle , and as I went from them

-E 2 they

they came nearer and nearer together, and at length be- came co-incident 3 and afterwards when I went ftill further off, they parted again in a contrary order, the violet by a greater Refrad:ion being carried beyond the red.

Exper. 8. In Summer when the Sun's Light ufes to be ftrongeft, I placed a Prifm at the hole of the Window- fhut, as in the third Experiment, yet fo that its Axis might be Parallel to the Axis of the World, and at the oppofite Wall in the Sun s refracted Light, I placed an open Book. Then going Six Feet and two Inches from the Book, I placed there the abovementioned Lens,by which the Light refle*5led from the Book might be made to converge and meet again at the diftance of fix Feet and two Inches be- hind the Lens , and there paint the Species of the Book upon a flieet of white Paper much after the manner of the fecond Experiment. The Book and Lens being made fall, I noted the place where the Paper was, when the Letters of the Book, illuminated by the fullefl red Light of the Solar Image falling upon it, did caft their Species on that- Paper moft diftindly 5 And then I ftay'd till by the Mo- tion of the Sun and confecjuent Motion of his Image on the Book, all the Colours from that red to the middle of the blew pafs'd over thofe Letters 3 and when thofe Letters were illuminated by that blew, I noted again the place of the Paper when they caft their Species moft diftindily upon it : And I found that this laft place of the Paper was nearer to the Lens than its former place by about two Inches and an half, or two and three quarters. So much fooner there- fore did the Light in the violet end of the Image by a grea- ter Refradlion converge and meet , than the Light in the red end. But in trying this the Chamber was as dark as I could make it. For if thefe Colours be diluted and weak- ned by the mixture of any adventitious Light, the diftance

between

[37]

between the places of the Paper will not be fo great. This diftance in the fecond Experiment where the Colours of natural Bodies were made ufe of, was but an Inch and a half, by reafon of the imperfe(5tion of thofe Colours. Here in the Colours of the Prifm , which are manifeftly more full, intenfe, and lively than thofe of natural Bodies, the diftance is two Inches and three quarters. And were the Colours ftill more full , I queftion not but that the di- ftance would be confiderably greater. For the coloured Light of the Prifm, by the interfering of the Circles de- fcribed in the 1 1 th Figure of the fifth Experiment, and alfo by the Light of the very bright Clouds next the Sun's Body intermixing with thefe Colours, and by the Light fcattered by the inequalities in the polifh of the Prifm, was fo very much compounded, that the Species which thofe faint and dark Colours, the Indigo and Violet, caft upon the Paper were not diftin6t enough to be well obferved.

Expcr. 9. A Prifm, whofe two Angles at its Bafe were equal to one another and half right ones, and the third a right one, I placed in a beam of the Sun's Light let in- to a dark Chamber through a hole in the Window-fhut as in the third Experiment. And turning the Prifm flowly about its Axis until all the Light which went through one of its Angles and was refracted by it began to be refle<5led by its Bafe , at which till then it went out of the Glafs, I obferved that thofe Rays which had fuffered the greateil Refraction were fooner reflected than the reft. I conceived therefore that thofe Rays of the reflected Light, which were moft Refrangible, did firft of all by a total Reflexion become more copious in that L'ght than the reft , and that afterwards the reft alfo, by a total Reflexion, be- came as copious as thefe. To try this , I made the re- fleded Light pafs through another Prifm, and being refra-

aed

[38]

ded by it to fall afterwards upon a fbeet of white Paper placed at fome diftance behind it, and there by that Re- ira<5lion to paint the ufual Colours of the Prifm. And then caufing the firft Prifm to be turned about its Axis as above, I obferved that when thofeRays which in this Prifm had fuffered the greateft Refrad:ion and appeared of a blew and violet Colour began to be totally refleded , the blew and violet Light on the Paper which was mofl refra6ted in the fecond Prifm received a fenfible increafe above that ■of the red and yellow, which was leaft refracSted 5 and afterwards when the reft of the Light which was green, yellow and red began to be totally reflected in the firft Prifm, the hght ofthofe Colours on the Paper received as great an increafe as the violet and blew had done before. Whence 'tis manifeft, that the beam of Light refledied by the Bafe of the Prifm, being augmented firft by the more Refrangible Rays and afterwards by the lefs Refrangible ones, is compounded of Rays differently Refrangible. And that all fuch refledled Light is of the fame Nature with the Sun's Light, before its Incidence on the Bafe of the Prifm, no Man ever doubted : it being generally al- lowed, that Light by fuch Reflexions fuffers no Alteration in its Modifications and Properties. I do not here take notice of any Refrad:ions made in the Sides of the firft Prifm, becaufe the Light enters it perpendicularly at the firft Side, and goes out perpendicularly at the fecond Side, and therefore fuffers none. So then, the Sun's incident Light being of the fame temper and conftitution with his emergent Light, and the laft being compounded of Rays differently Refrangible , the firft muft be in like manner compounded. Fig. 1 1 . Illujlration. In the 2 1 th Figure, A B C is the firft Prifm, B C its Bafe, B and C its equal Angles at the Bafe, each

of

[39]

of 45 degrees, A its Re6langular Vertex, F M a beam of the Sun's Light let into a dark Room through a hole F one third part of an Inch broad, M its Incidence on theBafe of the Prifm,M G a lefs refraded Ray, M H a more refradt- ed Ray, M N the beam of Light refle(5led from the Bafe , V X Y the fecond Prifm by which this beam in paffing through it is refrad:ed, N t the lefs refracted Light of this beam, and N p the more refraded part thereof When the firft Prifm A B C is turned about its Axis according to the order of the Letters ABC, the Rays M H emerge more and more obliquely out of that Prifm, and at length after their mofl: oblique Emergence are refled:ed towards N, and going on to p do increafe the number of the Rays N p. Afterwards by continuing the motion of the firft Prifm, the Rays MG are alfo refled:ed to N and increale the number of the Rays N t. And therefore the Light M N admits into its Compoficion, firft the more Refrangible Rays, and then, the lefs Refrangible Rays, and yet after this Compofition is of the f\me Nature with the Sun's immediate Light F M, the Reflexion of the fpecular Bafe B C caufing no Altera- tion therein.

Exper. 1 o. Two Prifms, which were alike in fhape, I tied fo together, that their Axes and oppofite Sides being Parallel, they compofed a Parallelopiped. And, the Sun fhining into my dark Chamber through a little hole in the Window-fhut, I placed that Parallelopiped in his beam at fome diftance from the hole, in fuch a pofture that the Axes of the Prifms might be perpendicular to the incident Rays, and that thofe Rays being incident upon the firft Side of one Prifm, might go on through the two contiguous Sides of both Prifms, and emerge out of the laft Side of the fe- eond Prifm. This Side being Parallel to the firft Side of the firft Prifm , caufed the emerging Light to be Parallel

to

[4°]

CO the Incident. Then, beyond thefe two Prifms I placed a third, which might refrad: that emergent Light, and by that Refrad:ion caft the ufual Colours of the Prifm upon the oppofite Wall, or upon a fheet of white Paper held at a convenient diftance behind the Prifm for that refraded Light to fall upon it. After this I turned the Parallelopiped about its Axis, and found that when the contiguous Sides of the two Priims became fo oblique to the incident Rays that thofe Rays began all of them to be refled:ed , thofe Rays which in the third Prifm had fuflfered the greateft Re- fraction and painted the Paper with violet and blew, were firft of all by a total Reflexion taken out of the tranfmitted Licrht, the reft remaining and on the Paper painting their Colours of Green, Yellow, Orange, and Red as before 5 . and afterwards by continuing the motion of the two Prifms, the reft of the Rays alfo by a total Reflexion vanifhed in . order, according to their degrees of Refrangibility. The Li^ht therefore which emerged out of the two Prifms is compounded of Rays differently Refrangible , feeing the more Refrangible Rays may be taken out of it while the lefs Refrangible remain. But this Light being trajeded only through the Parallel Superficies of the two Prifms, if it fuffered any change by the Refraction of one Superficies it loft that impreflion by the contrary Refrad;ion of the other Superficies, and fo being reftored to its priftine con- ftitution became of the fame nature and condition as at firft before its Incidence on thofe Prifms 3 and therefore, before its Incidence, was as much compounded of Rays differently Refrangible as afterwards. Fig. 11. lllufiration. In the iith Figure ABC and B C D are the the two Prifms tied together in the form of a Parallelo- piped, their Sides BC and CB being contiguous, and their Sides A B and C D Parallel. And H J K is the third

Prifm,

[41]

Prifm, by which the Sun's Light propagated through the hole F into the dark Chamber, and there pafling through thofe fides of the Prifms AB, BC, CB and CD, is refra- (fted at O to the white Paper PT, falling there partly upon P by a greater Refradiion, partly upon T by a lefs Refra- d:ion, and partly upon R and other intermediate places by intermediate Refractions. By turning the Parallelopiped ACBD about its Axis, according to the order of the Let- ters A,C,D,B, at length when the contiguous Planes BC and CB become fufficiently oblique to the Rays F M, which are incident upon them at M, there will vaniCh to- tally out of the refradled Light OPT, firft of all the moll refraded Rays OP, (the reft OR and OT remaining as before) then the Rays O R and other intermediate ones, and laftly, the leaft refraded Rays O T. For when the Plane B C becomes fufficiently oblique to the Rays inci- dent upon it, thofe Rays will begin to be totally refled;- ed by it towards N 3 and firft the moft Refrangible Rays will be totally reflected (as was explained in the preceding experiment) and by confequence muft firft difappear at P, and afterwards the reft as they are in order totally refled:- ed to N, they muft difappear in the fame order at R and T. So then the Rays which at O fuffer the greateft Re- fraction, may be taken out of the Light MO whilft the reft of the Rays remain in it, and therefore that Light MO is Compounded of Rays differently Refrangible. And be- caufe the Planes A B and C D are parallel, and therefore by equal and contrary Refractions deftroy one anothers Effects, the incident Light F M muft be of the fame kind and nature with the emergent Light M O, and therefore doth alfo confift of Rays difl^erently Refrangible. Thefe two Lights FM and MO, before the moft relrangible Rays are feparated out of the emergent Light MO agree inCo-

F lour,

lour, and in all other properties fo far as uny obfervadion- reaches, and therefore are defervedly reputed of the fanrve Nature and Conftitution, and by confequence rhe one is compounded as well as the other. But after the moft Re- frangible Rays begin to be totally refleifled, and thereby feparated out of the emergentLightMO,that Light changes its Colour from white to a dilute and faint yellow, a pretty good orange, a very full red fucceflively and then totally vaniflies. For after the moft Refrangible Rays which paint the Paper at P with a Purple Colour, are by a total re- flexion taken out of the Beam of light M O, the reft of the Colours which appear on the Paper at R and T being mixed in the light M O compound there a faint yellow, and after the blue and part of the green which appear on the Paper between P and R are taken away, the reft which appear between R and T (that is the Yellow, Orange, Red and a little Green) being mixed in the Beam M O com- pound there an Orange 3 and when all the Rays are by re- flexion taken out of the Beam MO, except the leaft Refran- gible, which at T appear of a full Red, their Colour is the fame in that Beam M O as afterwards at T, the Re- fraction of the Prifm HJK ferving only to feparate the differently Refrangible Rays, without making any alteration in their Colours, as fliall be more fully proved hereafter. All which confirms as well the firft Propofition as the fe- c&ftd.

Scholium. If this Experiment and the former be conjoyned J*/^. 22. and made one, by applying a fourth Prifm VXY to re- fract the refled:ed Beam M N towards tp^ the conclufion will be clearer. For then the light N/> which in rhe 4th Prifm is more refradled, will become fuller and ftronger when the Light O P, which in the third Prifm H J K is more refracted, vaniflies at P j and afterwards when th« lefs

refracted

[43]

refracted Light O T vaniflies at T,the lefs refraded Light Nf will become encreafed whilft the more refradled Light at p receives no further encreafe. And as the traje6ted Beam M O in vanifhing is always of fuch a Colour as ought to refult from the mixture of the Colours which fall upon the Paper PT, fo is the refledied Beam MN al- ways of fuch a Colour as ought to refult from the mix- ture of the Colours which fall upon the Paper p t. For when the mofl refrangible Rays are by a total Reflexion taken out of the Beam M O, and leave that Beam of an Orange Colour, the excefs of thofe Rays in the refle6te<i Light, does not only make the Violet, Indigo and Blue at p more full, but alfo makes the Beam M N change from the yellowiili Colour of the Sun's Light, to a pale white in- clining to blue, and afterward recover its yellowifli Co- lour again, fo foon as all the reft of the tranfmitted light MOT is reflefted.

Now feeing that in all this variety of Experiments, whether the trial be made inLight reflected, and that either from natural Bodies, as in the firft and fecond Experiment, or Specular, as in the Ninth 5 or in Light refrad:ed, and that either before the unequally refradled Rays are by di- verging feparated from one another, and lofing their white- nefs which they have altogether, appear feverally of feve- ral Colours, as in the fifth Experiment j or after they are feparated from one another, and appear Coloured as in the fixth, feventh, and eighth Experiments 3 or in Light tra- jeded through Parallel fuperficies, deftroying each others Effeds as in the 1 oth Experiment 5 there are always found Rays, which at equal Incidences on the fame Medium fuf- fer unequal Refrad:ions, and that without any fplitting or dilating of fingle Rays, or contingence in the inequality of the Refradions, as is proved in the fifth and fixth Ex-

F 2 periments;

[44]

periments^ and feeing the Rays which differ in Refrangibi- iiry may be parted and forced from one another, and that cither by Refradion as in the third Experiment, or by Re- flexion as in the tenth, and then the feveral forts apart at equal Incidences fuffer unequal Refradtions, and thole forts are more refracted than others after feparation, which were more refracfled before it, as in the fixth and following Ex- periments, and if the Sun's Light be trajed:ed through three or more crofs Prifms fucceflively, thofe Rays which in the firfl Prifm are refraded more than others are in all the fol- lowing Prifms, refradied more then others in the fame rate and proportion, as appears by the fifth Experiment 3 it's manifeft that the Sun's Light is an Heterogeneous mixture of Rays, fome of which are conftantly more Refrangible then others, as was to be propofed.

PROP. III. Theor. III.

The Su?is Light conjifls of (^ys dijfenng in ^flexibility., and thofe ^ys are more ^flexible thati others which are more (?(f- frangible.

THIS is manifeft by the ninth and tenth Experi- ments : For in the ninth Experiment, by turning the Prifm about its Axis, until the Rays within it which in going out into the Air were refracted by its Bafe, became 10 oblique to that Bafe, as to begin to be totally refle<5ted thereby 3 thofe Rays became firft of all totally refle<5ted, which before at equal Incidences with the reft had fuffered the greateft Refra(5tion. And the fame thing happens in the Reflexion made by the common Bafe of the two Prifms in the tenth Experiment.

[45 J

PROP. IV. Prob. I.

To /eparate from one another the Heterogeneous ^ys of

Compound Light.

THE Heterogeneous Rays are in fomt meafure fepa- rated from one another by the Refra6tion of the Prifm in the third Experiment, and in the fifth Experiment by taking away the Penumbra from the RediHnear fides of the Coloured Image, that feparation in thofe very Rectili- near fides or ftraight edges of the Image becomes perfect. But in all places between thofe rectilinear edges, thofe in^- numerable Circles there defcribed, which are feverally illu- minated by Homogeneral Rays, by interfering with one another, and being every where commixt, do render the Light fuilficiently Compound. But if thefe Circles, whilft their Centers keep their diftances and pofitions, could be made lefs in Diameter, their interfering one with another and by confequence the mixture of the Heterogeneous Rays would be proportionally diminiflied. In the 2 3thF^. 23. Figure let AG, B H, C J, D K, EL, F M be the Circles which fo many forts of Rays flowing from the fameDifque of the Sun, do in the third Experiment illuminate 5 of all which and innumerable other intermediate ones lying in a continual Series between the two Re(5tilinear and Parallel edges of the Sun's oblong Image P T, that Image is com- pofed as was explained in the fifth Experiment. And lee 4^, bh, cij dl{^ el J fm be fo many lefs Circles lying in a like continual Series between two Parallel right Lines af and g m with the fame diftances between their Centers, and illuminated by the fame forts of Rays, that is the Circle ag with the fame fore by which the correfponding

Circle

Circle AG was illuminated, and the Circle hh with the fame fort by which the correfpondingCircle BHwas illuminated, and the reft of the Circles c *', dk, elj fm refpedively, with the fame fores of Rays by which the feveral corre- fponding Circles C J, D K, EL, FM were illuminated. In the Figure P T compofed of the greater Circles, three of thofe Circles AG, B H, CJ, are fo expanded into one another, that the three forts of Rays by which thofe Cir- cles are illuminated, together with other innumerable forts of intermediate Rays, are mixed at Q.R in the middle of the Circle B H. And the like mixture happens through- out almoft the whole length of the Figure P T. But in the Figure p t compofed of the lefs Circles, the three lefs Circles ag^ b h, c /, which anfwer to thofe three greater, do not extend into one another 5 nor are there any Vv^here mingled fo much as any two of the three forts of Rays by which thofe Circles are illuminated, and which in the Figure P T are all of them intermingled at B H.

Now he that fliall thus confider it, will eafily underftand that the mixture is diminifhed in the fame Proportion with the Diameters of the Circles. If the Diameters of the Circles whilft their Centers remain the fame, be made three times lefs than before, the mixture will be alfo three times lefs 5 if ten times lefs, the mixture will be ten times lefs, and fo of other Proportions. That is, the mixture of the Rays in the greater Figure P T will be to their mix- ture in the lefs p t, as the Latitude of the greater Figure is to the Latitude of the lefs. For the Latitudes of thefe Fi- gures are equal to the Diameters of their Circles. And hence it eafily follows, that the mixture of the Rays in the refracted Spectrum pt is to the mixture of the Rays in the dire<5t and immediate Light of the Sun, as the breadth of that Spedirum is to the difference between the length and breadth of the fame Spe^^rum. So

C47l

Se^ then, if we woul<J diminifli eli^ m'ixtmte of the Rays, we af€ to d'immifb the Diamerers &§ the Cireres. Now thefe wouW be diminiflied if the Sun^s Diameter to which they anfwer could be made lefs than it is, or (which comes to the fame puipofe) if without Dgofs, at a great diftance from the Prifm towards the Sun, fome opake body were placed, with a round hole in the middle of it, to intercept all the Sun's Light, excepting fo much as coming from the middle of his Body could pafs through that hole to the Prifm. For fo the Circles A G, B H and the reft, would not any longer anfwer to the whole Difque of the Sun , but only to that part of it which could be feen from the Prifm through that hole, that is to the apparent magnitude of that hole viewed from the Prifm. But that thefe Circles may anfwer more diftin<5lly to that hole a Lens is to be placed by the Prifm to caft the Image of the hole, (that is, every one of the Circles A G, B H, <6"c.) di- ftindly upon the Paper at P T, after fuch a manner as by a Lens placed at a Window the Species of Objedls abroad are caft diftindly upon a Paper within the Room, and the Rectilinear Sides of the oblong folar Image in the fifth Experiment became diftind: without any Penumbra. If this be done it will not be neceflary to place that hole very far off, no not beyond the Window. And therefore inftead of that hole, I ufed the hole in the Window-fliut as follows.

Exper. 1 1 . In the Sun's Light let into my darkned Chamber through a fmall round hole in my Window- fliut, at about i o or 1 1 Feet from the Window, I placed a Lens , by which the Image of the hole might be di- ftinClly caft upon a fheet of white Paper, placed at the diftance of fix, eight, ten or twelve Feet from the Lens. For according to the difference of the Lenfes I ufed various

diftances,

[48]

diftances , which I think not worth the while to defcribe. Then immediately after the Lens I placed a Prifm, by which the trajeded Light might be refracted either up- wards or Tideways, and thereby the round Image which the Lens alone did caft upon the Paper might be drawn out into a long one with Parallel Sides , as in the third Experiment. This oblong Image I let fall upon another Paper at about the fame diftance from the Prifm as be- fore, moving the Paper either towards the Prifm or from it, until I found the juft diftance where the Rectilinear Sides of the Image became moft diftin(5l. For in this cafe the circular Images of the hole which compofe that Image after the fame manner that the Circles d^, bh, ci, &c. do

Pig, 25. the Figure p f , were terminated moft diftin<5tly without any Penumbra, and therefore extended into one another the leaft that they could, and by confequence the mixture of the Heterogeneous Rays was now the leaft of all. By this

fin 1 ^ , means I ufed to form an oblong Image (fuch as is p t) of afid 24. circular Images of the hole (fuch as are a^, bh, ci^ &c. ) and by ufing a greater or lefs hole in the Window-fhut, I made the circular Images ag, b A, c /, &c. of which it was formed, to become greater or lefs at pleafure, and thereby the mixture of the Rays in the Image pt to be as much or as little as I defired.

Fk. 24. Illujlrat'wn. In the 24th Figure, F reprefents the circular hole in the Window-ftiut, M N the Lens whereby the Image or Species of that hole is caft diftin6tly upon a Paper at J, ABC the Prifm whereby the Rays are at their emerging out of the Lens refracted from J towards ano- ther Paper at p t, and the round Image at J is turned into an oblong Image p t falling on that other Paper. This Image p t confifts of Circles placed one after another in a Redilinear order, as was fufficiently explained in the fifth

Experiment 3

[49]

Experiment • and thefe Circles are equal to th£ Circle I, and confequently anfwer in Magnitude to the hole F ; and therefore by diminifhing that hole they may be at pleafure diminifhed , whirft their Centers remain in their places. By this means I made the breadth of the Image pt to be forty times, and fometimes lixty or feventy times lefs than its length. As for inftance, if the breadth of the hole F be - of an Inch, and MF the diftance of the Lens from the hole be i 2 Feet 3 and if /? B or pM the diftance of the Image pt from the Prifm or Lens be 10 Feet, and the refrading Angle of the Prifm be 6i degrees, the breadth of the Image p t will be ~ of an Inch and the length about fix Inches, and therefore the length to the breadth as 71 to 1, and by confequence the Light of this Image 71 times lefs compound than the Sun's direA Light. And Light thus far Simple and Homogeneal, is fufficient for trying all the Experiments in this Book about fimple Light. For the compofition of Heterogeneal Rays is in this Light fo little that it is fcarce to be difcovered and perceived by fenfe, except perhaps in the Indigo and Violet j for thefe being dark Colours, do eafily funer a fenfible allay by that little fcattering Light which ufes to be refradled irregularly by the inequaliteis of the Prifm.

Yet inftead of the circular hole F, 'tis better to fubfti- tute an oblong hole fliaped like a long Parallelogram with its length Parallel to the Prifm ABC. For if this hole be an Inch or two long, and but a tenth or twentieth part of an Inch broad or narrower : the Light of the Image p t will be as Simple as before or fimpler, and the Image will become much broader, and therefore more fit to have Experiments tried in its Light than before.

Inftead of this Parallelogram-hole may be fubftitnted a Triangular one of equal Sides, whofe Bafe for inftance is

G about

C50]

about the tenth part of an Inch, and its height an Inch of more. For by this means , if the Axis of the Prifm be Parallel to the Perpendicular of the Triangle , the Image Fig. 1'^. pt will now be formed of Ec^uicrural Triangles ag, hhj ci, ^k.-) ^h f'^^y ^^- ^^^ innumerable other intermediate ones anfwering to the Triangular hole in fhape and bignefs,and lying one after another in a continual Series between two Parallel Lines af z.nAgm. Thefe Triangles are a Httle intermingled at their Bafes but not at their Vertices, and therefore the Light on the brighter fide af of the Image where the Bafes of the Triangles are is a little compounded, but on the darker fide^?w is altogether uncompounded, and in all places between the fides the Compofition is Proportional to the diftances of the places from that ob- fcurer fide^ m. And having a Spedlrum p t o^ fuch a Compofition, we may try Experiments either in its ftronger and lefs fimple Light near the fide af, or in its weaker and fimpler Light near the other fide / w, as it (hall feem moft convenient.

But in making Experiments of this kind the Chamber ought to be made as dark as can be, leaft any forreign Light mingle it felf with the Light of the Spedrum p t, and render it compound 5 efpecially if we would try Ex- periments in the more fimple Light next the fide g ??i of the Spectrum 5 which being fainter, will have a lefs Pro- portion to the forreign Light, and fo by the mixture of that Light be more troubled and made more compound. The Lens alfo ought to be good, fuch as may ferve for Optical Mksy and the Prifm ought to have a large Angle, fuppofe of 7© degrees, and to be well wrought, being made of Glafs free from Bubbles and Veins, with its fides not a little Convex or Concave as ufually happens but truly Plane,and its pollifli elaborate, as in working Optick-

glafles

C5I]

glafles , and not fuch as is ufiially wrought with Putty, whereby the edges of the Sand-holes being worn away, there are left all over the Glafs a numberlefs company of very little Convex polite rifings like Waves. The edges alfo of the Prifm and Lens fo far as they may make any irregular Refraction, muft be covered with a black Paper glewed on. And all the Light of the Sun's beam let into the Chamber which is ufelefs and unprofitable to the Ex- periment, ought to be intercepted with black Paper or other black Obftacles. For otherwife the ufelefs Light being refled;ed every way in the Chamber , will mix with the oblong Spectrum and help to difturb it. In trying thefe things fo much Diligence is not altogether neceflary, but it will promote the fuccefs of the Experiments, and by a very fcrupulous Examiner of things deferves to be applied. It's difficult to get glafs Prifms fit for this purpofe, and and therefore I ufed fometimes Prifmatick Veffels made with pieces of broken Looking- glaffes, and filled with rain Water. And to increafe the Refradlion, I fometimes im- pregnated the Water ftrongly with Saccharum Saturni.

PROP. v. Theor. IV.

Homogeneal Light is re/rafted regularly ivithout any Dilatation

f putting or Jhattering of the ^ys , and the confufed Vijlon

of Objefis feen through ^fraHing 'Bodies by Hetcrogeneal

Light arifes from the different ^efrangibility of JeVeral forts

of llays.

TH E firfl: Part of this Propofition has been already fufficiently proved in the fifth Experiment, and will further appear by the Experiments which follow.

G 2 Exper. \ i .

[52]

Exper. 12. In the middle of a black Paper I made i round hole about a fifch or fixth part of an Inch in Dia- meter. Upon this Paper I caufcd the Spedrum of Homo- geneal Light defcribed in the former Propofition , fo to fall, that lome part of the Light might pafs through the hole of the Paper. This tranfmicted part of the Light I refracted with a Prifm placed behind the Paper, and let- ting this refracfled Light fall perpendicularly upon a white Paper two or three Feet diftant from the Prifm, I foand that the Sped:rum formed on the Paper by this Light was not oblong, as when 'tis made (in the third Experiment) by Refracting the Sun's compound Light, but was (fo far as I could judge by my Eye) perfed:ly circular, the length being no greater than the breadth. Which fhews that this Light is refraCled regularly without any Dilatation of the Rays.

Exper. 1 ^ . In the Homogeneal Light I placed a Circle of-' of an Inch in Diameter, and in the Sun's unrefrad:cd Heterogeneal white Light I placed another Paper Circle of the fame bignefs. And going from the Papers to the diflance of fomeFeet, I viewed both Circles through a Prifm. The Circle illuminated by the Sun's Heterogeneal Light appear- ed very oblong as in the fourth Experiment , the length being many times greater than the breadth : but the other Circle illuminated with Homogeneal Light appeared Cir- cular and difl;ind:ly defined as when 'tis viewed with the naked Eye. Which proves the whole Propofition.

Exper. 1 4. In the Homogeneal Light I placed Flies and fuch like Minute Objeds, and viewing them through a Prifm , I faw their Parts as diftindly defined as if I had ■viewed them with the naked Eye. The fame Objeds pla- ced in the Sun's unrefradied Heterogeneal Light which was white I viewed alfo through a Prifm, and faw them moft

confufedly

C53]

confufedly defined, fo thatlcould not diftinguifii their fmal* * [er Parts from one another. I placed alfo the Letters of a fmall Print one while in the Homogeneal Light and then in the Heterogeneal, and viewing them through a Prifm, they appeared in the latter cafe fo confufed and indiftinfib that I could not read them 5 but in the former they ap- peared fo diftind: that I could read readily, and thought I [aw them as diftinit as when I viewed them with my naked Eye. In both cafes I viewed the fame Objed:s through the fame Prifm at the fame diftance from me and in the fame Situation. There was no difference but in the Light by which the Objects were illuminated , and which in one cafe was Simple and in the other Compound, and therefore the diftind Vifion in the former cafe and confu- fed in the latter could arife from nothing elfe than from that difference of the Lights. Which proves the whole Propoficion.

And in thefe three Experiments it is further very remar- kable, that the Colour of Homogeneal Light was never changed by the Refrad;ion»

PROP. VI. Theor. V.

TT^e Sine of Incidence of e^ery ^ay confldered apart ^ is to its Sine of ^efraHion in a p)} en ^tio.

THAT every Ray confidered apart is conftant to it felf in fome certain degree of Refrangibility, is fufficiently manifeft out of what has been faid. Thofe Rays which in the firft Refradion are at equal Incidences moft refraded, are alfo in the following Refradions at equal Incidences moft refraded j and fo of the leaft Re- frangible, and the reft which have any mean degree of

Refran-

[54]

Refrangibilicy, as is manifefl by the 5tk, 6th, 7th, 8th, and 9th Experiments. And thofe which the firfl: time at • like Incidences are equally refracted, are again at like In- cidences equally and uniformly refracted, and that whe- ther they be refradled before they be feparated from one another as in the 5 th Experiment, or whether they be re- fracted apart, as in the i 2 th, i ^rh and 14th Experiments. The Refraftion therefore of every Ray apart is regular, and what Rule that Refradion obferves we are now to fliew.

Th« late Writers in Opticks teach, that the Sines of In- cidence are in a given Proportion to the Sines of Refra- d:ion, as was explained in the 5th Axiom 5 and fome by Inftruments fitted for meafuring Refradions, or otherwife experimentally examining this Proportion, do acquaint us that they have found it accurate. But whilft they, not underftanding the different Refrangibility of feveral Rays, conceived them all to be refra6ted according to one and the fame Proportion, 'tis to be prefumed that they adapted their Meafures only to the middle of the refracted Light 3 fo that from their Meafures we may conclude only that the Rays which have a mean degree of Refrangibilicy , that is thofe which when feparated from the reft appear green, are refracted according to a given Proportion of their Sines. And therefore we are now to fhew that the like given Proportions obtain in all the reft. That it fhould be fo is very reafonable, Nature being ever confor- mable to her felf : but an experimental Proof is defired. And fuch a Proof will be had if we can fliew that the Sines of Refraction of Rays differently Refrangible are one to another in a given Proportion when their Sines of Incidence are equal. For if the Sines of Refraction of all the Rays are in given Proportions to the Sine of Refraction

of

L55]

of a Ray which has a mean degree of Refrangibility, and this Sine is in a given Proportion to the equal Sines of Incidence, thofe other Sines of Refraction will alfo be in given Proportions to the equal Sines of Incidence. Now when the Sines of Incidence are equal , it will appear by the following Experiment that the Sines of Refraction are in a given Proportion to one another.

Exper. 1 5 . The Sun fliining into a dark Chamber through a little round hole in the Window- fhut, let S re-Pi^- ^<^» prefent his round white Image painted on the oppofite Wall by his dire6t Light, P T his oblong coloured Image made by refracting that Light with a Prifm placed at the Windowj and pt, or ip it^ or ^p 3 f, hisoblong coloured Image made by refraCting again the fame Light fideways with a fecond Prifm placed immediately after the firft in a crofs Pofition to it, as was explained in the fifth Experi- ment : that is to fay, pt when the RefraCtion of the fecond Prifm is fraall, ip it when its RefraCtion is greater, and ^p T,t when it is greateft. For fuch will be the diverfity of the Refractions if the refraCting Angle of the fecond Prifm be of various Magnitudes 5 fuppofe oF fifteen or twenty degrees to make the Image p ?, of thirty or forty to make the Image ip 1 1^ and of fixty to make the Image 3 /' 3 f . But for want of folid Glafs Prifms with Angles of convenient bignefles, there may be Veflels made of polifhed Plates of Glafs cemented together in the form of Prifms. and filled with Water. Thefc things being thus ordered, I obferved that all the folar Images or co- loured SpeCtrums V T, pt, ip it, 3;? 3 f did very nearly converge to the place S on which the direCt Light of the Sun fell and painted his white round Image when the Prifms were taken away. The Axis of the SpeCtrum PT, that is the Line drawn through the middle of it Parallel to

its

its Redilinear Sides, did when produced pafs exadly through the middle of that white round Image S. And when the Refraction of the fecond Prifm was equal to the Refradlion of the firfl, the refra6ling Angles of them both being about 60 degrees, the Axis of the Spectrum ^/^ ^ f made by that Refradion, did when produced pafs alfo through the mid- dle of the fame white round Image S. But when the Re- fraction of the fecond Prifm was lefs than that of the firft, the produced Axes of the Spedrums tp or it ip made by that Refra<ftion did cut the produced Axis of the Spe- ctrum TP in the Points w and «, a little beyond the Cen- ter of that white round Image S. Whence the Proportion of the Line ^ f T to the Line 3/? P was a little greater than the Proportion of 2 tT to i^P, and this Proportion a little greater than that of tT top]?. Now when the Light of the Spectrum P T falls perpendicularly upon the Wall, thofe Lines ^fT, ^p^, and it T, i/^P and t'T,/?P,are the Tan- gents of the Refractions 5 and therefore by this Experiment the Proportions of the Tangents of the RefraCtions are ob- tained, from whence the Proportions of the Sines being deriv- ed, they come out equal, fo far as by viewing the SpeCtrums and ufing fome Mathematical reafoning I could Eftimate. For I did not make an Accurate Computation. So then the Propofition holds true in every Ray apart, fo far as ap- pears by Experiment. And that it is accurately true may be demonftrated upon this Suppofition, Tl^at 'Bodies refraEl Light by ciEling upon its ^ys in Lines Perpendicular to their Surfaces. But in order to this Demonftration, I muft di- ftinguifh the Motion of every Ray into two Motions, the one Perpendicular to the refraCting Surface, the other Pa- rallel to it, and concerning the Perpendicular Motion lay down the following Propolltion.

If

C57]

If any Motion or moving thing whatfoever be incident with any velocity on any broad and thin Space termina- ted on both fides by two Parallel Planes, and in its paflage through that fpace be urged perpendicularly towards the further Plane by any force which at given diflances from the Plane is of given quantities 3 the perpendicular Velo- city of that Motion or Thing, at its emerging out of that fpace, fhall be always equal to the Square Root of the Summ of the Square of the perpendicular Velocity of that Motion or Thing at its Incidence on that fpace ; and of the Square of the perpendicular Velocity which tKat Motion or Thing would have at its Emergence, if at its Incidence its perpendicular Velocity was infinitely little.

And the fame Propofition holds true of any Motion or Thing perpendicularly retarded in its paflage through that fpace, if inftead of the Summ of the two Squares you take their difference. The Demonftration Mathematicians will eafily find out, and therefore I fhall not trouble the Rea- der with it.

Suppofe now that a Ray coming moll: obliquely in thepiv i. Line MC be refrad:ed at C by the Plane RS into the Line CN, and if it be required to find the Line CE into which any other Ray AC fliall be refrac1:ed 3 let MC, AD, be the Sines of incidence of the two Rays, and NG, EF, their Sines of Refradtion, and let the equal Motions of the In- cident Rays be reprefented by the equal Lines M C and AC, and the Motion MC being confidered as parallel to the refrading Plane, let the other Motion AC be diftin- guifhed into two Motions AD and DC, one of which AD is parallel, and the other DC perpendicular to the re- fracting Surface. In like manner, let the Motions of the emering Rays be diftinguifh'd into two, whereof the per-

H pendicular

C5BI

perpendicular ones are j^ CG and ^p CF. And if the

force of the refrading Plane begins to ad upon the Rays either in that Plane or at a certain diftance from it on the one fide, and ends at a certain diftance from it on the other fide, and in all places between thofe two Limits ads upon the Rays in Lines perpendicular to that rafi-ading Plane, and the Adions upon the Rays at equal diftances from the refrading Plane be equal, and at unequal ones ei- ther equal or unequal according to any rate whatever 5 that motion of the Ray which is Parallel to the refrading Plane will fuffer no alteration by that force ; and that mo- tion which is perpendicular to it will be altered according to the rule of the foregoing Propofition. If therefore for the perpendicular Velocity of the emerging Ray CN you

write ^ CG as above, then the perpendicular Velocity of any other emerging Ray CE which was ^ CF, will be

equal to the fquare Root of CD^ + -^^ CGq. And

by fquaring thefe equals, and adding to them the Equals AD^ and MC^ — CD^, and dividing the Summs by the Equals CVq -\- EVq and CG^ -|- NG^, you will have

Ypl equal to ^^. Whence AD, the Sine of Incidence,

is to EF the Sine of Refradion, as MC to NG, that is, in a given ratio. And this Demonftration being general, without determining what Light is, or by what kind of force it is refraded, or afluming any thing further than that the refrading Body ads upon the Rays in Lines per- pendicular to its Surface y I take it to be a very convincing Argument of the full Truth of this Propofition, ,

So

[59]

So tlien, if the ratio of the Sines of Incidence and Re- fra<5tion of any fort of Rays be found in any one Cafe, 'tis given in all Cafes 5 and this may be readily found by the Method in the following Propoficion.

PROP. VII. Theor. VI.

Tlje TerfeBion of Tele/copes is impeded hy the dijferent ^frati- gibility of the ^ys of Light.

TH E imperfedion of Telefcopes is vulgarly attri- buted to the fpherical Figures of the Glaffes, and therefore Mathematicians have propounded to Figure them by the Conical Sedions. To fliew that they are mifta- ken, I have inferted this Propofitionj the truth of which will appear by the meafures of the Refraftions of the feve- ral forts of Rays 5 and thefe meafures I thus determine.

In the third experiment of the firft Book, where the re- frad:ing Angle of the Prifm was 6i\ degrees, the half of that Angle 3 1 deg. 1 5 min. is the Angle of Incidence of the Rays at their going out of the Glafs into the Air 3 and the Sine of this Angle is 5188, the Radius being loooo. When the Axis of this Prifm was parallel to the Horizon, and the Refradion of the Rays at their Incidence on this Prifm equal to that at their Emergence out of it, I obferved with a Quadrant the Angle which the mean refrangible Rays (that is, thofe which wentto the middle oftheSun s colour- ed Image ) made with the Horizon and by this Angle and the Sun's altitude obferved at the fame time, I found the Angle which the emergent Rays contained with the incident to be 44 deg. and 40 min. and the half of this Angle ad- ded to the An^le of Incidence 3 i deg. 1 5 min. makes the

H 2 Angle

[do]

Angle of Refradion, which is therefore 5^ dcg. ^^ min. and its Sine 8047. Thefe are the Sines of Incidence and Re- fTa6tion of the mean refrangible Rays, and their proportion in round numbers is 10 ta^ 1. This Glafswas of a colour in- clining to green. The laft of the Prifms mentioned in the third Experiment was of clear white Glafs. Its refrad:ing Angle 63^ degrees. The Angle which the emergent Rays contained, with the incident 45 deg. 50 min. The Sine of half the firfl: Angle 5262. The Sine of half the Summ of the Angles 8157. And their proportion in round num- bers 20 to 31 as before.

From the Length of the Image, which was about 9I or

1 o Inches, fubdu6t its Breadth, which was 2 ^ Inches, and the Remainder 7' Inches would be the length of the Image were the Sun but a point, and therefore fubtends the An- ale which the moft and leaft refrangible Rays, when inci- dent on the Prifm in the fame Lines, do contain with one another after their Emergence. Whence this Angle is

2 dcCT. 0/ 7." For the diftance between the Image and the Prifm where this Angle is made, was 1 8 ~ Feet, and at that diftance the Chord 7^ Inches fubtends an Angle of 2 deg. o.' 7." Now half this Angle is the Angle which thefe e- meraent Rays contain with the emergent mean refrangible Rays, and a quarter thereof, that is 30. 2," may be ac- counted the Angle which they would contain which the fame emergent mean refrangible Rays, were they co-inci- dent to them within the Glafs and fuffered no other Re- fraction then that at their Emergence. For if two equal Refracflions, the one at the incidence of the Rays on the Prifm, the other at their Emergence, make half the Angle 1 deg. 0.' 7. then one of thofe Refradiions will make about a quarter of that Angle, and this quarter added to

and

[6I]

and fubduded from the Angle of Refradion of the mean refrangible Rays, which was 5 ^ deg. ^5', gives the An- gles of Refra(5t:ion of the moft and leaft refrangible Rays 54 deg. 5' 2", and 53 deg. 4' 58", whofe Sines are 8099 and 7995, the common Angle of Incidence being 3 1 deg. 15' and its Sine 5188- and thefe Sines in the leaft round numbers are in proportion to one another as 78 and 77 to 50.

Now if you fubdu(5l the common Sine of Incidence 50 from the Sines of Refra6lion 77 and 78, the remainders 17 and 28 (hew^ that in fmall Refractions the Refrad:ion of the leaft refrangible Rays is to the Rcfra6tion of the moft refrangible ones as 27 to 28 very nearly, and that the dif- ference of the Refractions of the leaft refrangible and moft refrangible Rays is about the 27^th part of the whole Re- fraction of the mean refrangible Rays.

Whence they that are skilled in Opticks will eafily un- derftand, that the breadth of the leaft circular fpace into which Object' Glafles of Telefcopes can collect all forts of Parallel Rays, is about the 27^th part of half the aperture of the Glafs, or 55 th part of the whole aperture 3 and that the Focus of the moft refrangible Rays is nearer to the Object-Glafs than the Focus of the leaft refrangible ones, by about the 27-^th part of the diftance between the Object- Glafs and the Focus of the mean refrangible ones.

And if Rays of all forts,flowing from any one lucid point in the Axis of any convex Lens, be made by the Refraction of the Lens to converge to points not too remote from the Lens , the Focus of the moft refrangible Rays fhall be nearer to the Lens than the Focus of the leaft refrangible ones, by a diftance which is to the 27^th part of the di- ftance of the Focus of the mean refrangible Rays from the Lens as the diftance between that Focus and the lucid

point

poiac from whence che Rays flow is to the diftance be- tween that lucid point and the Lens very nearly.

Now to examine whether the difference between the Re- fractions which the mofl: refrangible and the leaft refran- gible Rays flowing from the fame point fufl^er in the Ob- je(5t-GlaiTes ofTelefcopes and fuch like GlalTes, be fo great . as is here defcribed, I contrived the following Experi- ; ment.

Exper. 1 6. The Lens which I ufed in the fecond and -•eighth Experiments, being placed fix Feet and an Inch dif- 'tant from any Obje(ri;, colle(5led the Species of that Objed: 'by the mean refrangible Rays at the diflance of fix Feet and an Inch from the Lens on the other fide. And there- Tore by the foregoing Rule it ought to colle(fl: the Species of that Object by the leafl refrangible Rays at the diflance of 'fix Feet and 3 - Inches from the Lens, and by the mofl re- frangible ones at the diflance of five Feet and lo^ Inches from it : So that between the tvi o Places where thefe leafl and mofl refrangible Rays colle6t the Species, there may be the diflance of about 5-j Inches. For by that Rule, as >fix Feet and an Inch ( the diflance of the Lens from the lucid Object ) is to twelve Feet and two Inches ( the di- ■ftance of the lucid Object from the Focus of the mean re- frangible Rays) that is, as one is to two, fo is the 27 ^th part of fix Feet and an Inch (the diflance between the Lens and the fame Focus ) to the diflance between the Focus of 'the mofl refrangible Rays and the Focus of the leafl re- frangible ones, which is therefore 5 - Inches, that is very -nearly 5 '- Inches. Now to know whether this meafure was true, I repeated the fecond and eighth Experiment of "this Book with coloured Light, which was lefs compound- ..ed than that I there made ufe of : For I now feparated the

hetero-

h eterogeneous Rays from one another by the Method I de- fcribed in the i ith Experiment, fo as to make a coloured Spedrum about twelve or fifteen times longer than broad. This Spedlrum I caft on a printed book, and placing the above-mentioned Lens at the diftance of fix Feet and an Inch from this Spectrum to colled: the Species of the illu- minated Letters at the fame difiiance on the other fide, I found that the Species of the Letters illuminated with Blue were nearer to the Lens than thofe illuminated with deep Red by about three Inches or three and a quarter : but the Species of the Letters illuminated with Indigo and Violet appeared fo confufed and indiftind, that I could not read them : Whereupon viewing the Prifm, I found it was full of Veins running from one end of the Glafs to the other j fo that the Refradion could not be regular. I took ano- ther Prifm therefore which was free from Veins, and in- ftead of the Letters I ufed two or three Parallel black Lines a little broader than the ftroakes of the Letters, and caft- ing the Colours upon thefe Lines in fuch manner that the Lines ran along the Colours from one end of the Spedium to the other, I found that the Focus where the Indigo, or confine of this colour and Violet call the Species of the black Lines moft difi:!nd:ly,tobe about 4 Inches or 4^ near- er to the Lens than the Focus where the deepeft Red cafi; the Species of the fame black Lines mofl: diftindly. The violet was fo faint and dark, that I could not difcern the Species of the Lines diftinctly by that Co- lour J and therefore confidering that the Prifm was made of a dark coloured Glafs inclining to Green, I took another Pifm of clear white Glafs • but the Spedrum of Colours which this Prifm made had long white Streams of faint Light fliooting out from both ends of the Colours, which made me conclude that fomefhing was amifs j and view- ing

[64]

ing the Prifm, I found two or three little Bubbles in the Glafs which refracted the Light irregularly. Wherefore I covered that part of the Glafs with black Paper, and let- ting the Light pafs through another part of it which was free from fuch Bubles, the Sped:rum of Colours became free from thofe irregular Streams of Light, and was now fuch as I defired. But ilill I found the Violet fo dark and faint, that I could fcarce fee the Species of the Lines by the Violet, and not at all by the deepeft part of it, which was next the end of the Spectrum. I fulpedled therefore that this faint and dark Colour might be allayed by that fcat- tering Light which was refracted, and reflected irregularly partly by fome very fmall Bubbles in the Glafles and partly by the inequalities of their Polifli: which Light, tho' it was but little, yet it being of a White Colour, might fuffice to affect the Senfe fo ftrongly as to difturb the Pha^nomena of that weak and dark Colour the Violet, and therefore I tried, as in the 12th, i^th, 14th Experi- ments, whether the Light of this Colour did not confift of a fenfible mixture of heterogeneous Rays, but found it did not. Nor did the Refractions caufe any other fenfible Colour than Violet to emerge out of this Light, as they would have done out of White Light, and by con- fequence out of this Violet Light had it been fenfi- bly compounded with White Light. And therefore Icon- eluded, that the reafon why I could not fee the Species of the Lines diflindtly by this Colour, was only the darknefs of this Colour and Thinnels of its Light, and its dif- tance from the Axis of the Lens 3 I divided therefore thofe Parallel Black Lines into equal Parts, by which I might readily know the diflances of the Colours in the Spedirum from one another, and noted the diftances of the Lens from the Foci of fuch Colours as cafl the Species of the

Lines

Lines diftindly, and then confidered whether the diffe- rence of thofe diftances bear fuch proportion to 5 '^Inches, the greateft difference of the diftances which the Foci of the deepeft Red and Violet ought to have from the Lens, as the diftance of the obferved Colours from one another in the Spedrum bear to the like diftance of the deepeft Red and Violet meafured in the redlilinear fides of the Spect- rum, that is, to the length of thofe fides or excefs of the length of the Spectrum above its breadth. And my Ob- fervations were as follows.

When I obferved and compared the deepeft fenfibleRed, and the Colour in the confine of Green and Blue, which at that rectilinear fides of the Spe(ftrum was diftant from it half the length of thofe fides, the Focus where the confine of Green and Blue caft the Species of the Lines diftin(5tly on the Paper, was nearer to the Lens then the Focus where the Red caft thofe Lines di(5tin6tly on it by about i^ or 2 .' Inches. For fometimes the Meafures were a little grea- ter, fomctimes a little lefs, but feldom varied from one another above j of an Inch. For it was very difficult to define the Places of the Foci, without fome little Errors. Now if the Colours diftant half the length of the Image, ( meafured at its rectilinear fides ) give 2^; or 2 - difference of the diftances of their Foci from the Lens, then the Co- lours diftant the whole length ought to give 5 or 5I Inches difference of thofe diftances.

But here it's to be noted, that I could not fee the Red to the full End of the SpeCtrum, but only to the Center of the Semicircle which bounded that End, or a little far- ther 3 and therefore I compared this Red not with that Co- lour which was exactly in the middle of the SpeCtrum, or confine of Green and Blue, but with that which veracd a little more to the Blue than to the Green : And as I reck-

I oned

[66]

oried the whole length of the Colours not tob^ the whole length of the Spe(artim, but the leflgth of its reftiHnear fides, fo completing theSemicirlar Ends into Circles, when (iither of the obferved Colours fell within thofe Circles, I meafured the diftance of that Colour from the End of the Spedrum, and fubdu(fiing half the diftance from the mea- fured diftance of the Colours, I took the remainder for their cbrre(5ted diftance 3 and in thefe Obfervations fet down this correded diftance for the difference of their di- ftances from the Lens. For as the length of the redilinear fides of the Spectrum would be the whole length of all the ^Colours, were the Circles of which ( as we fhewed) that Spedrum confifts contra(5led and reduced to Phyfical Points, fo in that Cafe this correded diftance would be the real diftance of the obferved Colours.

When therefore I further obferved the deepeftfenfible Red, and that Blue whofe corre<5led diftance from it was ^ parts of the length of the redilinear fides of the Spectrum, the difference of the diftances of their Foci from the Lens was about ^- hiches, and as 7 to i 2 fo is 3 -J to 5 i.

When I obferved the deepeft fenfible Red, and that Indi- go whofe corrected diftance was ^ or J of the length of the rectilinear fides of the Spe6trum, the difference of the di- ftances of their Foci from the Lens, was about 3 '* Inches, and as 2 to 3 fo is 3 J-to '){.

When I obferved the deepeft fenfible Red, and that deep Indigo whofe corrected diftance from one another was ^ or ■' of the length of the redilinear fides of the Spedum, the difference of the diftances of their Foci from the Lens was about 4 Inches 3 and as 3 to 4 fo is 4 to 5 J.

When I obferved the deepeft fenfible Red, and that part of the Violet next the Indigo whofe correded diftance from the Red was {^ or j of the length of the redilinear fides of

the.

the Spedtrum, the difference of the diftances <)f their Foci from the Lens was about 4^ Inches j and as 5 to ($, fo is 4- to 5-. For fometimes when the Lens was advantagi- oufly placed, fo that its Axis relpeded the Blue, and all things elfe were well ordered, and the Sun fhone clear, and I held my Eye very near to the Paper on which the Lens caft the Species of the Lines, I could fee pretty diftinctly the Species of thofe Lines by that part of the Violet which was next the Indigo ; and fometimes I could fee them by above half the Violet. For in making thefe Experiments I had obferved, that the Species of thofe Colours only ap- peared dijftinct which were in or near the Axis of the Lens : So that if the Blue or Indigo were in the Axis, I could fe,e their Species diilinctly ; and then the Red appeared much lefs diftinct than before. Wherefore I contrived to majce the Spectrum of Colours fliorter than before, fo that both its Ends might be nearer to the Axis of the Lens. And now its length was about 2^ Inches and breadth about -or I of an Inch. Alfo inftead of the black Lines on which the Spectrum was caft, I made one black Line broader than thofe, that I might fee its Species more eafily ; and this Line I divided by fhort crofs Lines into equal Parts, for tneafuring the diftances of the obfervedColours. And now I could fometimes fee the Species of this Line v/ith its divi- iions almoft as far as the Centers of the Semicircular Violet End of the Spectrum, and made thefe further Qbfervations. When I oblerved the decpeft fenfible Red, and that part of the Violet whofe corrected diftance from it was about j Parts of the rectilinear fides of the Spe6lrum the difference •of the diftances of the Foci of thofe Colours from the Lens, was one time 4-*, another time 4^, anothertimc 4^, Inches, andasS to 9, foare4j, 4-;, 4I, to 5', ^^^5^^ refpedively.

I 2 When

[68]

When I obferved tlie deepeft fenfible Red, and deepefi: fenfible Violet, (the corrected dlftance of which Colours- when all things were ordered to the bed advantage, and the Sun fhone very clear, was about ^ or ^ parts of the length of the rectilinear fides of the coloured Spectrum, ) I found the difference of the diftances of their Foci from the Lens fometimes 4.' fometimes 5-, and for the mofl part 5 Inches or thereabouts : and as 11 to i 2 or 15 to i6, fo is five Inches to 5 ■; or 5 i Inches.

And by this progreflion of Experiments I fitisfied my felf, that had the light at the very Ends of the Spectrum been ftrong enough to make the Species of the black Lines ap- pear plainly on the Paper, the Focus of the deepeft Vic- let would have been found nearer to the Lens, than the Fo- cus of the deepeft Red, by about y- Inches at leaft. And this is a further Evidence, that the Sines of Incidence and Refra6tion of the feveral forts of Rays, hold the fame pro- portion to one another in the fmalleft Refracftions which they do in the greateft.

My progrefs in making this nice and troublefome Expe- riment I have fet down more at large, that they that fliall try it after me may be aware of the Circumfpedtion re- quifite to make it fucceed well. And if they cannot make It fucceed fo well as I did, they may notwithftanding col- led: by the Proportion of the diftance of the Colours in the Spedrum, to the difference of the diftances of their Foci from the Lens, what would be the fuccefs in the more di- ftant Colours by a better Trial. And yet if they ufe a broader Lens than I did, and fix it to a long ftreight Staff by means of which it may be readily and truly direded to the Colour whofe Focus is defired, I queftion not but the Experiment will fucceed better with them than it did with me,. For I direded the Axis as nearly as I could to the

middle-:

middle of the Colours, and then the faint Ends of the Spedrum being remote from the Axis, caft their Species lefs diftindly on the Paper than they would have done had the Axis been fucce/fively dire(5i:ed to them.

Now by what has been faid its certain, that the Rays which differ in refrangibility do not converge to the fame Focus, but if they flow from a lucid point, as far from the Lens on one fide as their Foci are one the other, the Focus of the moft refrangible Rays fliall be nearer to the Lens than that of che leafl refrangible, by above the four- teenth part of the whole diftance: and if they flow from a lu- cid point, fo very remote from the Lens that before their Incidence they may be accounted Parallel, the Focus of the mofl: refrangible Rays fliall be nearer to the Lens than the Focus of the leafl: refrangible, by about the 27th onSth part of their whole difliance from it. And the Diameter of the Circle in the middle fpace between thofe two Foci which they illuminate when they fall there on any Plane, perpen- dicular to the Axis (which Circle is the leafl; into which they can all be gathered) is about the 55th part of the Dia- meter of the aperture of the Glafs. So that 'tis a wonder that Telefcopes reprefent Objeds fo difl:in<5i: as they do. But were all the Rays of Light equally refrangible, the Error arifing only from the fphericalnefs of the Figures of Glafles would be many hundred times lefs. For if the Objed:- Glafsofa Telefcope be Plano-convex, and the Plane fide be turned towards the Objed, and the Diameter of the Sphere whereof this Glafs is a fegment,be called D, and the Semidiameter of the aperture of the Glafs be called S, and the Sine of Incidence out of Glafs into Air, be to the Sine of Refradlion as I to R : the Rays which come Parallel to the Axis of the Glafs, fliall in the Place where the Image of the Objed is mofl: diftindtly made, be fcattered all over a little

Circle

[70]

Circle whofe Diameter is ^ '^ Dfi^d. ^^^f ^^^^^Yj ^^ ^ ga- ther by computing the Errors of the Rays by the method of infinite Series, and rejeding the Terms whofe cjuanti- tities are inconfiderable. As for inftance, if the Sine of In- cidence I, be to the Sine of Refradion R, as 20 to ; i, and if D the Diameter of the Sphere to which the Convex fide of the Glafs is ground, be 100 Feet or 1200 Inches, and S the Semidiameter of the aperture be two Inches, the

Diameter of the little Circle ( that is fi^^j^ ) will be

— ^^— ( or ,z-^l„^^ ) parts of an Inch. But the

20 X 1200 x 1200 *■ 5600000 •' r

Diameter of the little Circle through which thefe Rays are Scattered by unequal refrangibility, will be about the 55 th part of the aperture of the Objed:-Glafs which here is four Inches. And therefore the Error arifing from the fpherical Figure of the Glafs, is to the Error arifing from the diffe- rent Refrangibility of the Rays, as ^^^^ to ^ that is as i to 8151 : and therefore being in Comparifon fo very little, deferves not to be confidered.

But you will fay, if the Errors caufed by the different re- frangibility be fo very great, how comes it to pafs that Ob- jed;s appear through Telefcopcs fo diilinfl as they do ? I an- fwer, 'tis becaufe the erring Rays are not fcattered uniform- ly over all that circular fpace, but collected infinitely more denfely in the Center than in any other part of the Circle, and in the way from the Center to the Circumference grow continually rarer and rarer, fo as at the Circumference to become infinitely rare 3 and by reafon of their rarity are p. not ftrong enough to bevifible, unlefs in the Center and ve-

^' ry near it. Let ADE reprefent one of thofe Circles de- fcribed with the Center C and Semidiameter AC, and let BFG be afmaller Circle concentric to the former, cutting

with

[71]

with its Circumference the Diameter AC in B, and befecc AC in N, and by my reckoning the denfity of the Light in anyplace B will be to its denfity inN, as AB to BC, and the whole Light within the leffer Circle BFG, will be to the whole Light within the greater AED, as the Excefs of the Square of AC above the Square of AB, is to the Square of AC. As if BC be the fifth part of AC, the Light will be four times denfer in Bthan in N, and the whole Light with- in the lefs Circle,will be to the whole Light within the grea- ter, as nine to twenty five. Whence it's evident that the Light within the lefs Circle, muflflrike the fenfe much more ftrongly, than that faint and dilated light round about be- tween it and the Circumference of the greater.

But its further to be noted, that the mofl luminous of the prifmatick Colours are the Yellow and Orange. Thefe ailed: the Senfes more ftrongly than all the refl together, and next to thefe in ftrength are the Red and Green. The Blue compared with thefe is a fiinc and dark Colour, and the In«f digo and Violet are much darker and fainter, fo that thefe compared with the ftronger Colours are little to be regard- ed. The Images of Objedis are therefore to be placed, not in the Focus of the mean refrangible Rays which are in the confine of Green and Blue, but in the Focus of thofe Rays which are in the middle of the Orange and Yellow 3 there where the Colour is moft luminous and fulgent, that is in the brighteft Yellow, that Yellow which inclines more to Orange than to Green. And by the Refradion of thefe Rays ( whofe Sines of Incidence and Refradion in Glafs are as 1 7 and 11) the Refradion of Glafs and Cryftal for optical ufes is to be meafured. Let us therefore place the Image of the Objed in the Focus of thefe Rays, and all the Yellow and Orange will fall within a Circle, whofe Dia- ineter is about the 250th part of the Diameter of the aper- ture

[72]

ture of the Glafs. And if you add the brighter half of the Red, ( that half which is next the Orange, and the brighter half of the Green, (that half which is next the Yellow,) a- bout three fifth parts of the Ijght of thefe two Colours will fall within the fame Circle,and two fifth parts will fall with- out it round about ; and that which falls without will be Ipread through almoft as much more fpace as that which falls within, and fo in the grofs be almoft three times ra- rer. Of the other half of the Red and Green, ( that is of the deep dark Red and Willow Green ) about one quarter will fall within this Circle, and three quarters without, and that which falls without will be fpread through about four or five times more fpace than that which fall within; and fo in the grofs be rarer, and if compared with the whole Light within it, willbe about 25 times rarer than all that taken in the grofs ; or rather more than 30 or 40 times rarer, be- caufe the deep red in the end of the Spedrum of Colours made by a Prifm is very thin and rare, and the Willow Green is fomething rarer than the Orange and Yellow. The Ltght of thefe Colours therefore bring fo very much rarer than that within the Circle, will fcarce afFed: the Senfe efpecially fince the deep Red and Willow Green of this Light, are much darker Colours then the reft. And for the lame reafon the Blue and Violet being much darker Colours than thefe, and much more rarified, may be neglected. For tlie denfe and bright Light of the Circle, will obfcure the rare and weak Light of thefe dark Colours round about it, and render them almoft infenfible. The fenfible Image of a lucid point is therefore fcarce broader than a Circle whofe Diameter is the 250th part of the diameter of the aperture of the Object Glafs of a good Telefcope, or not much broader, if you except a faint and dark mifty light round about it, which a Spectator will fcarce regard. And therefore in a Telefcope

whofe

[7?] . ,

vvhofe aperture is four Inches, and length an hundred Feet/ it exceeds not 2 '45', or 5". And in a Telefcope whofc aperture is two Inches, and length 20 or 30 Feet, it may be 5 "or 6" and fcarce above. And this Anfwers well to Experience : For fome Aftronomers have found the Dia- meters of the fixt Stars, in Telefcopes of between twenty and fixty Feet in length, to be about 4' or 5" or at moft 6" in Diameter. But if the Eye-Glafs be tinded faintly with the fmoke of a Lamp or Torch, to obfcure the Light of the Star, the fainter Light in the circumference of the Star ceafes to be vifible, and the Star (if the Giafs be fuffici- ently foiled with fmoke) appears fomething more like a Ma- thematical Point. And for the fame reafon, the enormous part of the Light in the Circumference of every lucid Point ought to be lefs difcernable in fhorter Telefcopes than in longer, becaufe the fhorter tranfmit lefs Light to the Eye.

Now if we fuppofe the fenlible Image of a lucid point, to be even 250 times narrower than the aperture of the Glafs: yet were it not for the different refrangibility of the Rays, its breadth in an 1 00 Foot Telefcope whofe aperture is 4 Inches would be but ^-^^^^ parts of an Inch, as is ma- nifeft by the foregoing Computation. And therefore in this Cafe the greateft Errors arifing from the fpherical Figure of the Glafs, would be to the greateft fenfible Errors ari- fing from the different refrangibility of the Rays as -53^ to ^-^ at moft, that is only as i to 1826. And this fuffi- ciently fliews that it is not the fpherical Figures of Glaffes but the different refrangibility of the Rays which hinders the perfection of Telefcopes.

There is another Argument by which it may appear that the different refrangibility of Rays, is the true Caufe of the imperfedion of Telefcopes. For the Errors of the Rays arihng from the fpherical Figures of Objed-Glafles, are as

K the

[ 74 3

tlic Cubes of the apeitures of the Objed^Glaflesjand thence to make Telefcopes of various lengths, magnify with equal cUftindnefs, the apertures of the Objed-GlafTes, and the C)harges or magnifying Powers, ought to be as the Cubes of the fcjuare Pvoots of their lengths 5 which doth not anfwer 10 Experience. But the errors of the Rays arifing from the d liferent refrangibility, are as the apertures of the Ob- jetft-Glafies, and thence to make Telefcopes of various leno^ths, magnify' with equal diftin(5lnefs, their apertures and charges ought to be as the fquare Roots of their lengths -,. and this aniwers to experience as is well known. For in- ftance, a Telefcope of 64 Feet in length, with an aperture of 1- Inches, magnifies about i 20 times, with as much dif- tind:nefs as one of a Foot in length, with j of an Jnch aper* ture, magnifies i 5 times.

Now were it not for this different refrangibility of Rays, Telefcopes might be brought to a greater Perfedion than we have yet defcribed, by compoffng the Objed-Glafs of two Glafles with Water between them. Let ADFC repre^ f^. 2 8.|-ent the Objed-Glafs compofed of two Glaffes ABED and and BEFC, alike convex on the outfides AGD and CHF, and alike concave on the infides BME, BNE, with Water in the concavity BMEN. Let the Sine of Incidence out of Glafs into Air be as I to R and out of Water into Air as K to R, and by confequence out of Glafs into Water, as I to K : and let the Diameter of the Sphere to which the convex fides AGD and CHF are ground be D, and the Diameter, of the Sphere to which the concave fides BME and BNE are ground be to D, as the Cube Root of KK— KI to the Cube Root of RK— RI: and the Refra^ions on the con- cave fides of the Glafles, will very much corrcd: the Errors of the Refractions on the convex fides, fo far as they arife from the fphericainefs of the Figure. And by this means

might

[75]

might Telefcopes be brought to fufficient perfe6bion, wercit not' for the diflferentrefrangibility of feveralforsof Rays. But by reafon of this different refrangibility, I do not yet fee any other means of improving Telefcopes by Refradlions alone than that of increafing their lengths, for which end the late contrivance of Hugenius feems well accommodated. For very long Tubes are cumberfome, and fcarce to be readily managed, and by reafon of their length are very apt to bend, and fhake by bending fo as to caufe a continual trembling in the Objects, whereby it becomes difficult to fee them diftindly : whereas by his contrivance the Glaffes are readily manageable, and the Objedl-Glafs being fixt up- on a ftrong upright Pole becomes more fteddy.

Seeing therefore the improvement of Telefcopes of given lengths by Refractions is defperate 3 I contrived heretofore a Perfpedlive by reflexion, ufing inftead of an Objed: Glafs a concave Metal. The diameter of the Sphere to which the Metal was ground concave was about 2 5 Englifli Inches, and by confe^uence the length of the Inftrument about (i3t Inches and a quarter. The Eye-Glafs was plano-convex, and the Diameterof the Sphere to which the convex fide was ground was about i of an Inch, or a little lefs, and by con- fequence it magnified between ^ o and 40 times. By ano- ther way of meafuring I found that it magnified about ^ 5 times. The Concave Metal bore an aperture of an Inch and a third part j but the aperture was limited not by an opake Circle, covering the Limb of the Metal round about, but by an opake circle placed between the Eye-Glafs and the Eye, and perforated in the middle with a little round hole for the Rays to pafs through to the Eye. For this Circle by being placed here, ftopr much of the erroneous Light, which otherwife would have difturbed the Vifion. By com- paring it with a pretty good Perfpedive of four Feet in

K 2 length,

length, made with a concave Eye-Glafs, I could read at x greater diftance with my own Inftrument than with the Glafs. Yet Objedts appeared much darker in it than in the Glafs, and that partly becaufe more Light was loft by re- flexion in the Metal, then by refrailion in the Glafs, and. partly becaufe my Inftrument was overcharged. Had it magnified but ^oor 25 times it would have made the Object appear more brisk and pleafant. Two of thefelmade about: 16 Years ago, and have one of them ftill by me by which "li can prove the truth of what I write. Yet it is not fo good as at thefirft> For the concave has been divers times tar- niflied and cleared again, by rubbing it with very foft Lea^- ther. When I made thefe, an Artift in London undertook; to imitate it 5 but ufing another way of polifliing them than I did, he fell much fhort of what I had attained to,. as I afterwards underftood by difcourfing the under- Work- man he had imployed. The Polifli I ufed was on this man- ner. I had two round Copper Plates each fix Inches in: Diameter, the one convex the other concave, ground ve- ry true to one another. On the convex I ground the Ob- jedl-Metal or concave which was to be polifh'd, till it had. taken the Figure of the convex and was ready for a Polifh. Then I pitched over the convex very thinly, by dropping melted pitch upon it and warming it to keep the pitch foft, whilft I ground it with the concave Copper wetted to make it fpread evenly all over the convex. Thus by work- ing it well I made it as thin as a Groat, and after the con- vex was cold I ground it again to give it as true a Figure as I could. Then I took Putty which I had made very fine by wafliing it from all its grofler Particles, and laying a lit- tle of this upon the pitch, I ground it upon the Pitch with the concave Copper till it had done making a noife j and then upon the Pitch I ground the Objed;-Mecal with a brisk

Motion

[77]

Motion, for about two or three Minutes of time, leaning hard upon it. Then I put frefh Putty upon the Pitch and ground it again till it had done making a noife, and after- wards ground the Obje<ft Metal upon it as before. And this Work I repeated till the Metal was polifhed, grinding it the lad time with all my flrength for a good while toge- the/, and frequently breathing upon the Pitch to keep ir moift without laying on any more frefh Putty. The Ob- ject-Metal was two Inches broad and about one third part of an Inch thick, to keep it from bending. I had two of thefe Metals, and when I had polifhed them both I tried which was beft, and ground the other again to fee if I could make it better than that which I kept. And thus by many Trials I learnt the way of poliiliing, till I made thofe two refledling Peipe6lives I fpake of above. For this Art of polifliing will be better learnt by repeated Practice than by my defcription. Before I ground the Objcvft Metal on the Pitch, r always ground the Putty on it with the concave Copper till it had done making a noife, becaufe if the Par- ticles of the Putty were not by this means made to flick fafl in the Pitch, they would by rolling up and down grate and fret the Objed Metal and fill it full of little holes.

But becaufe Metal is more difficult to polifh than Glafs and is afterwards very apt to be fpoiled by tarnifliing, and refle(5ts not fo much Light as Glafs quick-filvered over does: I would propound touleinfleadof theMetal, a Glafs ground concave on the forefide, and as much convex on the back- fide, and quick-filvered over on the convex fide. The Glafs mufl be every where of the fame thicknefs exactly. Other- wife it will make Objedls look coloured and indiflind. By fuch a Glafs I tried about five or fix Years ago to make a refliediing Telefcope of four Feet in length to magnify a- bout 1 50 times, and I fatisfied my felf that there wants no- thing

C78]

thincT but a good Artift to bring the defign to Perfe(flion. For the Glafs being wrought by one of our London Artifts after fuch a manner as they grind Glafles for Telefcopes, tho it feemed as well wrought as the Objed: Glafles ufe to be, yet when it was quick-nlvered, the reflexion difcovered innumerable Inequalities all over the Glafs, And by reafon of thefe Inequalities, Objeds appeared indifliindl in this In- flrument. For the Errors of refletfted Rays caufed by any Inequality of the Glafs, are about fix times greater than the Errors of refraded Rays caufed by the like Inequalities. Yet by this Experiment I fatisfied my felf that the reflexion on the concave fide of the Glafs, which I feared would difturb the vifion,didno fenfible prejudice to it, and by confequencc that nothing is wanting to perfed thefe Telefcopes, but good Workmen who can grind and polifti Glafles truly fphe- rical. An Objedi-Glafs of a fourteen Foot Telefcope, made by one of our London Artificers, I once mended confidera- bly, by grinding it on Pitch with Putty, and leaning ve- ry eafily on it in the grinding, lefl: the Putty fliould fcratch it. Whether this way may not do well enough for poliflv- ing thefe reflecting Glafles, I have not yet tried. But he that fhall try either this or any other way of polifhing which he may think better, may do well to make his Glafles rea- dy for polifliing by grinding them without that violence, wherewith our London Workmen prefs their Glafles in grind- ing. For by fuch violent preflure, Glafles are apt to bend a little in the grinding, and fuch bending will certainly fpoil rheir Figure. To recommend therefore the confideration of thefe refleding Glafles, to fuch Artiflis as are curious in figuring Glafles, I fhall defcnbe this Optical Infl:rument in the following Propofition.

PROP.

T

l79l PROP. VII. Prob. II.

To Jhorlen Tetef copes. ET ABDC reprefcnt a Glafs fphcrically concave on p;^ ^^^

_j the forefide AB, and as much convex on the back- fide CD, fo that it be every where of an equal thicknefs. Let k not be thicker on one fide than on the other, left it make Objei5ts appear coloured and indiftincH:, and let it be very truly wrought and quick-filveredoveron the backfide 3 and fet in the Tube VXYZ which mull be very black within. Let EFG reprefent a Prifm of Glafs or Cryllal placed near the other end of the Tube, in th^ middle of it, by means of a handle of Brafs or Iron FGK, to the end of which made flat it is cemented. Let this Prifm be rectangular at E, an-d let the other two Angles at F and G be accurately equal to each other, and by confeciuence equal to half right ones, and let the plane fides FE and GE be fquare, and by confe- queiuce the third fideFG a rectangular parallelogram, whofe lenCTch is to its breath in a fubduplicate proportion of two to one. Let it be fo placed in the Tube, that the Axis of the Speculum may pats through the middle of the fquare fide EF perpendicularly, and by confequence throuoh the middle of the fide F G at an Angle of 45 degrees, and let the fide EF be turned towards the Speculum, and the diftance ofthis Prifm from the Speculum be fuch that the Rays of the light PQ., RS, 8lc, which are incident upon theSpecuhim in Lines Parallel to the Axis thereof, may enter the Prifm at the fide EF, and be refleiCled by the fide F G, and thence go out of it through the fide GE, to the point T which muft be the common Focus of the Speculum ABDC, and of a Plano-convex Eye- Glafs H, through which thole Rays muft pafs to the Eye. And let the R.ays at their cominjr

out

[8o]

out of the Glafs pafs through a fmall round hole, or aper- ture made in a little Plate of Lead, Rrafs, or Silver, where- with the Glafs is to be covered, which hole muft be no bigger than is necelfary for light enough to pafs through. For fo it will render the Obje6t diftind, the Plate in which 'tis made intercepting all the erroneous part of the Light v\ hich comes from the Verges of the Speculum AB. Such an Inftrument well made if it be 6 Foot long, ( reckoning the length from the Speculum to the Prifm, and thence to the Focus T) will bear an aperture of 6 Inches at the Spe- culum, and magnify between two and three hundred times. But the hole H here lim.its the aperture with more advan- tage, then if the aperture was placed at the Speculum. If the Inftrument be made longer or fhorter, the aperture muft be in proportion as the Cube of the fquare Root of the length, and the magnifying as the aperture. But its con- venient that the Speculum be an Inch or two broader than the aperture at the leaft, and that the Glafs of the Speculum be thick, that it bend not in the working. The Prifm EFG muft be no bigger than is neceffary, and its back fide FG muft not be guick-filvered over. For without quick-filver it will refle6t all the Light incident on it from the Speculum. In this Inftrument the Objed: will be inverted, but may be ereded by making the fquare fides EF and EG of the Prifm EFG not plane but fpherically convex, that the Rays may crofs as well before they come at it as afterwards be- tween it and the Eye-Glafs. If it be defired that the Inftru- ment bear a larger aperture, that may be alfo done by com- pofing the Speculum of two Glafles with Water between them.

THE

L

"T

[80]

out of the Glafs pafs through a fmall round hole, or aper- ture made in a little Plate oi Lead, Brafs, or Silver, where- with the Glafs is to be covered, which hole muft be no bigger than is neceflary for light enough to pafs through. For fo it will render the Objec5t diftiniTr, the Plate in which 'tis made intercepting all the erroneous part of the Light which comes from the Verges of the Speculum AB. Such an Inftrument well made if it be 6 Foot long, ( reckoning the length from the Speculum to the Prifm, and thence to the Focus T) will bear an aperture of 6 Inches at the Spe- culum, and magnify between two and three hundred times. But the hole H here limits the aperture with more advan- tage, then if the aperture was placed at the Speculum. If the Inftrument be made longer or fhorter, the aperture muft be in proportion as the Cube of the fquare Root of the lencrth, and the magnifying as the aperture. But its con- venient that the Speculum be an Inch or two broader than the aperture at the leaft, and that the Glais of the Speculum be thick, that it bend not in the working. The Prifm EFG muft be no bigger than is neceflary, and its back fide FG muft not be quick-filvered over. For without quick-filver it will reflect all the Light incident on it from the Speculum. In this Inftrument the Object will be inverted, but may be ere(5led by making the fquare fides EF and EG of the Prifm EFG not plane but fpherically convex, that the Rays may crofs as well before they come at it as afterwards be- tween it and the Eye-Glafs. If it be defired that the Inftru- ment bear a larger aperture, that may be alfo done by com- pofing the Speculum of two Glafles with Water between -diem.

THE

_-- ^ A. ^t;_

^•'1 ot apti.

: mud be piii tlirouoi

ottlidiolit

i, (rail

ind thence to ' 1 1

■flit the Spi

'Mt idvan-'

JipffiDremul! : Roo' ot tli; :. Bu; Its coo- '

0 badet itiii i'tiicSpeculi nJtPnfaEFG

1 hick fide FG

itkSpKuluni

__; ^AjA

Bookl.Pklrl.Ri

Fi&3.

\

%

Fig. 6.

T E

t q

^^g-7.

	1	■^- m
i;^.^^	»l
	'	m

Fie: 8.

BookI.PlateJr.RrtI.

F'^S-9-

..<f-f-

Si

o

i

'/yieii-:^^

	r	■^
m	m
	n	la
*	r
i	i

INSERT

FOLD-OUT

OR MAP

HERE!

•

Bookl.Plate in. Parti

M^^

T

# M

F

'^

BoOK,l.Plate,IV. Pa,

•

o

■¥■0

m

INSERT

FOLD-OUT

OR MAP

HERE!

G H I K I. M

a- ^ c il c y

p a.::::::n:z:::Jj:zzjrz:::n::::::x) t e A I k I m

2t

ST

Fig. 26.

t T-
2yP iP T
	A

■,T7?1

/^/t? 19-

\

DEF

\

J...

6\^

n

^■f

r

T H E

4

FIRST BOOK

O F

O P T I C K S.

PART II.

PROP. I. THEOR. I.

T'he 'ph^enomena of Colours in refraSed or rejleBed Light are not caujed b>j new modifications of the Light variouf' ly imfref^ according to the variom terminations of the Light and Shadoisj.

The Proof hy Experiments.

EX PER. I.

FOR if the Sua fhine into a very dark Chamber _pio-. i, through an oblong Hole F, whofe breadth is the iixth or eighth part of an Inch, or fomething lets ; and his Beam FH do afterwards pafs hrft through a very large Prifm ABC, diftant about 20 Feet from the

L Hole,

Hole, and parallel to it, and then (with its white part) through an oblong Hole H, whole breadth is about the fortieth or lixtieth part of an Inch, and which is made in a black opake Body G I, and placed at the diftance of two or three Feet from the Prifm, in a pa- rallel fituation both to the Prifm and to the former Hole, and if this w^hite Light thus tranfmitted through the Hole H, fall afterwards upon a white Paper pt,. placed after that Hole H, at the diftance of three or four Feet from it, and there paint the ufual Colours of the Prifm, fuppofe red at t, yellow at s, green at r, blue at q, and violet at p ; you may with an iron Wire, or any fuch like flender opake Body, whole breadth is about the tenth part of an Inch, by intercepting the rays at k, 1, m, noro, take away any one of the Colours at t, s, r, q or p, whilft the other Colours remain up- on the Paper as before ; or with an obftacle fomething bigger you may take away any two, or three, or four Co- lours together, the reft remaining: So that anyone of the Colours as well as violet may become outmoft in the confine of the fhadow towards p, and any one of them as well as red may become outmoft in the confine of the ftiadow towards t, and any one of them may alfo border upon the ftiadow made within the Colours by the obftacle R intercepting fome intermedia^te part of the Light ; and, laftly, any one of them_ by-* being left alone may border upon the ftiadow on either hand. All the Colours have themfelves indifferently to any confines of ftiadow, and therefore the differences of thefe Colours from one another, do not arife from the diffe- rent confines of ftiadow, whereby Light is varioufty modified as has hitherto been the Opinion of Philofo-

phers.

[83]

pliers. In trying thefe things 'tis to be obferved, that by how much the Holes F and H are narrower, and the intervals between them, and the Prifm greater, and the Chamber darker, by lb much the better doth the Ex- periment iucceed ; provided the Light be not fo far diminifhed, but that the Colours at pt be fufficiently vilible. To procure a Pritm of folid Glafs large enough for this Experiment will be difficult, and therefore a prifmatick VelTel muft be made of polifhed Glafs-plates cemented together, and hlled with Water.

EX PER. 11.

The Sun's Light let Into -a dark Chamber through Fig'. 2. the round Hole F, half an Inch wide, pafled firft through tlie Prifm ABC placed at the Hole, and then through a Lens PT fomething more than four Liches broad, and about eight Feet diftant from the Prifm,and thence con- verged to O the Focus of the Lens diftant from it about three Feet, and there fell upon a white Paper D E. If that Paper was perpendicular to that Light incident up- on it, as 'tis repreiented in the pofture D E, all the Co- lours upon it at O appeared white. But if the Paper being turned about an Axis parallel to the Prifm, be- came very much inclined to the Light as 'tis reprefen- ted in the politions de and o\ j the fame Light in the one cafe appeared yellow and red, in the other blue. Here one and the fame part of the Light in one and the fame place, according to the various inclinations of the Paper, appeared in one cafe white, in another yellow or red, in a third blue, w^hilft the confine of Light and

L 2 Shadow,

[84-]

Shadow, and the refradions of the Prifm in all thefe cafes remained, the fame.

EXPER. III.

Fisr. ^. Such another Experiment may be more ealily tried as follows. Let a broad beam of the Sun's Light coming into a dark Chamber through a Hole in the Window fhut be refraded by a large Prifm ABC, whofe re- frading Angle C is more than 60 degrees, and fo foon as it comes out of the Prifm let it fail upon the white Paper D E glewed upon a ftiif plane, and this Lighty when the Paper is perpendicular to it, as 'tis reprelen- ted in DE, will appear perfectly white upon the Paper,, but when the Paper is very much inclined to it in liach a manner as to keep always parallel to the Axis of the Prifm, the whitenefs of the whole Light upon the Paper will according to the inclination of the Paper this way, or that way, change either into yellow and red, as in the pofture de^ or into blue and violet, as in the pofture ^s. And if the Light before it fall upon the Paper be twice refraded the fame way by two pa- rallel Prilms, thefe Colours will become the more con- Ipicuous. Here all the middle parts of the broad beam of white Light which fell upon the Paper, did without any confine of Ihadow to modify it, become, coloured all over with, one uniform Colour, the Colour being al- ways the fame in the middle of the Paper as at the edges, and this Colour changed according the various obliquity of the rerie6fing Paper, without any change in the refradions or fhadow, or in the Light which fell upon the Paper. And therefore tlicfe Colours are

to.

X85]

to be derived from fome other caufe than the new mo- difications of Light by refradions and fhadows.

If it be asked, What then is their caufe ? I anfwer, That the Paper in the pofture de ^ being more ob- lique to the more refrangible rays than to the lefs re- frangible ones, is more ftrongly illuminated by the lat- ter than by the former, and therefore the lefs refran- gible rays are predominant in the reflected Light. And wherever they are predominant in any Light they tinge it with red or yellow, as may in fome meafure appear by the firft Propofition of the firft Book,and will more fully appear hereafter. And the contrary happens in the poll:ure of the Paper e%, the more refrangible rays be- ing then predominant which always tinge Light with blues and violets.

EX PER. IV.

The Colours of Bubbles with which Children play are various, and change their lituation varioufly, with- out any refped to any confine of fhadow. If fuch a Bubble be covered with a concave Glafs, to keep it from being agitated by any wind or motion of the Air, the Colours will ilowly and regularly change their fitua- tion, even whilft the Eye, and the Bubble, and all Bo- dies which emit any i^ight, or caft any fhadow, re- main unmoved. And therefore their Colours arife from fome regular caufe which depends not on any confine of fliadow. What this caufe is will be fhewed in the next Book..

To

[8(5]

To tlicfe Experiments may be added the tenth Ex- periment of the firft Book, where the Sun's Light in a dark Room being trajeded through the parallel luperfi- cies of two Prifms tied together in the form of a Paral- lelopide, became totally of one uniform yellow or red Colour, at its emerging out of the Prifms. Here, in the production of thefe Colours, the confine of fhadow can have nothing to do. For the Light changes from white to yellow,orange and red fucceffively,withoutany alteration of the confine of (hadow: And at both edges of the emerging Light where the contrary confines of Hia- dow ought to produce different etfeds, the Colour is one and the fame, whether it be white, yellow, orange or red : And in the middle of the emerging Light, where there is no confine of ihadow at all, the Colour is the very fame as at the edges, the whole Light at its very firft emergence being of one uniform Colour, whe- ther white, yellow, orange or red, and going on thence perpetually without any change of Colour, fuch as the confine of fhadow is vulgarly fuppofed to work in re- fracted Light after its emergence. Neither can thefe Colours arife from any new modifications of the Light, by refradtions, becaufe they change lucceffively from white to yellow, orange and red, while the refradions remain the fame, and alio becaufe the refractions are made contrary ways by parallel fuperficies which de- ftroy one anothers efteCts. They arife not therefore from any modifications of Light made by refra61:ions jind fhadows, but have fome other caufe. What that caufe is we ihewed above in this tenth Experiment, and need not here repeat it.

There

[87]

There is yet another material circumftance of this Experiment. For this emerging Light being by a third Fig. 2 a. Prifm HI K refradled towards the Paper PT, and there Tart i. painting the ufual Colours of the Prifm, red, yellow, green, blue, violet : If thefe Colours arofe from the refractions of that Prifm modifying the Light, they wonld not be in the Light before its incidence on that Prifm. And yet in that Experiment v/e found that when by turning the two firft Prifms about their com- mon Axis all the Colours were made to vanilli but the red 3 the Light which makes that red being left alone, appeared of the very fame red Colour before its inci- dence on the third Prifm. And in general we find by other Experiments that when the rays which diifer in refrangibility are feparated from one another, and any one fort of them is confidered apart, the Colour of the Light which they compofe cannot be changed by any refradion or reflexion whatever, as it ought to be were Colours nothing elfe than modifications of Light caufed by refradions, and reflexions, and lliadows. This un- changeablenefs of Colour I am now to defcribe in the following Propofition.

PROP. II. THE OR. I L

u^ll homogeneal L'-ght has its frofer Colour anjisi>ertng to its degree of refrangdiltty^ and that Colour cannot be changed by rejlexions and refraHions,

In the Experiments of the 4th Propofition of the firft Book, when I had feparated the Jieterogeneous rays from one another, the Spectrum p t formed by the fepa- rated

[88]

rated rays, did in the progrefs from its end p, on which the moft refrangible rays fell, unto its other end t, on which the leaft refrangible rays fell, appear tinged with this Series of Colours, violet, indico, blue, green, yel- low, orange, red, together with all their intermediate degrees in a continual fucceflion perpetually varying : So that there appeared as many degrees of Colours, as there were forts of rajs differing in refrangibility.

EX PER. V.

Now that thefe Colours could not be changed by re- fraction, I knew by refradting with a Prifm fometimes one very little part of this Light, fometimes another very little part, as is defcribed in the 1 2th Experiment of the firft Book. For by this refraftion the Colour of the Light was never changed in the leaft. If any part of the red Light was refracted, it remained totally of the fame red Colour as before. No orange, no yel- low, no green, or blue, no other new Colour was pro- duced by that refradiion. Neither did the Colour any ways change by repeated refradions, but continued al- ways the fame red entirely as at firft. The like con- ftancy and im.mutability 1 found alio in the blue, green, and other Colours. So alfo if 1 looked through a Prifm upon any body illuminated with any part of this homo- geneal Light, as in the 1 4-th Experiment of the firft Book is defcribed ; I could not perceive any new Co- lour generated this way. All Bodies illuminated with compound Light appear through Prifms confufed ( as was faid above) and tinged with various new Colours, but thofe illuminated with homogeneal Light appeared

throug^h

[89]

through Prlfms neither kf^ diftinft, nor otherwife co- loured, than when viewed with the naked Eyes. Their Colours were not in the leaft changed by the refra£tion of the inter]^ofed Prilm. 1 Ipeak here of a fenfible change of Colour : For the Light which 1 liere call ho~ mogeneal, being not abfolutely homogeneal, there ought to arife fome little change of Colour from its heteroge- neity. But if that heterogeneity was fo little as it might be made, by the laid Experiments of the fourth Propo' fition, that change w^as not fenhble, and therefore, in Experiments where fenfe is judge, ought to be accoun- ted none at all.

EXPER. VI.

And as thcfe Colours were not changeable by refra- ftions. To neither were they by reflexions. For all white, grey, red, yellow, green, blue, violet Bodies, as Paper, Afhes, red Lead, Orpiment, Indico, Bife, Gold, Silver^ Copper, Grafs, blue Flowers, Violets, Bubbles of Water tinged with various Colours, Peacock's Fea- thers, the tincture of Lignum Nefhriticum^ and fuch like, In red homogeneal Light appeared totally red, in blue Light totally blue, in green Light totally green, and fo of other Colours. In the homogeneal Light of of any Colour they all appeared totally of that fame Colour, with this only ditierence, that fome of them refleded that Light more ftrongly, others more faintly. I never yet found any Body which by reflecting homo- geneal Light could fenfibly change its Colour.

M From

[90]

From all which it is manifeft, that if the Sun's Light confiftcd of but one fort of rays, there would be but one Colour in the whole World, nor would it be pof- fible to produce any new Colour by reBexions and re- fraftions, and by confequence that the variety of Co- lours depends upon the compoiition of Light.

'DEFINIT ION.

The homogeneal light and rays which appear red, or rather make Obje6ts appear ib, 1 call rubrific or red'makng ; thofe which make Objects appear yellow, green, blue and violet, 1 call yellow-ma- king, green-making^ blue-making, violet-making, and ib of the reft. And if at any time I fpeak of light and rays as coloured or endued with Co- lours, *I would be underftood to fpeak not philo- fophically and properly, but grolly , and accor- ding to fuch conceptions as vulgar People in fee- ing all thefe Experiments would be apt to frame. For the rays to fpeak properly are not coloured. In them there is nothing elfe than a certain power and difpofition to ftir up a lenfation of this or that Colour. For as found in a Bell or mufical String, or other founding Body, is nothing but a trem- bling Motion, and in the Air nothing but that Motion propagated from the Objedt, and- in the Senforium *tis a fenfe of that Motion under the form of found ; fo Colours in the Objed are no- thing but a difpoiition to refled: this or that fort of rays more copiouUy than the reft ; in the rays they are nothing but their difpofitions to propa- gate

[pt]

gate this or that Motion into the Senforium, and in the Senforium they are lenlations of thofe Mo- tions under the forms of Colours.

PROP. III. PROB. I.

To define the refravgibtltt'j of the jeveral forts of homo^ oeneal Lt<yht anfwermg to the feveral Colou'i

it J.

For determining this Problem 1 made the following Experiment.

EXPER. VII.

When I had caufed the rectilinear line (ides A F, G M, JFtg. 4. of the Speftrum of Colours made by the Prifm to be diftindlly denned, as in the fifth Experiment of the firft Book is defcribed, there were found in it all the homogeneal Colours in the fame order and fituation one among another as in the Spectrum of fimple Light, defcribed in the fourth Experiment of that Book. For the Circles of which the Sped:rum of compound Light PT is compofed, and which in the middle parts of the Sped: rum interfere and are intermixt with one ano- ther, are not intermixt in their outmoft parts where they touch thofe redilinear fides AF and GM. And therefore in thofe redilinear fides when diftinftly defi- ned, there is no new Colour generated by refraftion. I obferved alfo, that if any where between the two out- mofi: Circles TMF and PC A a right line, as 7^, was crofs to the Spectrum, fo as at both ends to fall per- pendicularly upon its reftilinear fides, there appeared

M 2 one

1^ 92 ]

one and the ratne Colour and degree ot Colour from one- end of this line to the other. I delineated therefore in a Paper the perimeter of the Spectrum FA PGMT, and in trying the third Experiment of the hrft Book, I held the Paper lb that the Spedtrum might fall upon this delineated Figure, and agree with it exactly, whilft an Affiftant whofe Eyes for dilKnguiiliing Colours were more critical than mine, did by right lines ^3) -c^, (^^crc drawn crofs the Spedtrum, note the confines of the Co- lours that is of the red M*/3F of the orange ayc/>/i^ of the yellow y s ^^, of the green '- 1 s ^ , of the blue n » x 9 , of the indico tXM>i5 and of the violet xGAm. And this operation being divers times repeated both in the lame and in leveral Papers , I found that the Ob- fervations agreed well enough with one another, and that the redtiiinear fides M G and FA were by the faid crofs lines divided after the manner of a mufical Chord. Let GM be produced to X, that MX may be equal toGM, and conceive GX, xX, 'X, ^'X,,^X, yX, «Xy MX, to be in proportion to one another, as the num- bers I, 9-, 6, 4^ p 1' ?6' i' and lb to rcprelent the. Chords of the Key, and of a Tone, a third Minor, a fourth, a fifth, a fixth Major, a feventh, and an eighth above that Key : And the intervals M -^ , " 7 , 7 - , ^ « , 1 ', '^, and xG, will be the fpaces which the fe vera I Co- lours ( rcd^ orange, yellow, green, blue, indico, violet ) take up.

Now thefe inter\als or fpaces fubtending the diffe- rences of the refractions of the rays going to the limits. of thofe Colours, that is^ to the points M, a, 7, =, 15,/, x, G, may without any fenfiblc Etror be. accounted propor- tional to the differences of the fines of reiradtion of thofe

rays

rays having one common fine of incidence, and there- fore fince the common fine of incidence of the moft and lea ft refrangible rays out of Glafs into Air was, (by a method defcribed above ) found in proportion to their fines of refradion, as 50 to 77 and 78, divide the dif- ference between the fines of refraction 77 and 78, as the line G M is divided by thofc intervals, you will have

77. 77«-> 77'-' 77v 77i^ 77l' 77'.,, 7^, the fines of refradion of thole rays out of Glafs into Air ,. their common fine of incidence being 50. So then the fines of the incidences of all the red-making rays out of Glafs into Air, were to the fines of their refraftions, not greater than 50 to 77, nor lefs than 50 to 77«-, but varied from one another according to all interme- diate Proportions. And the fines of the incidences of the green-making rays were to the fines of their refractions in all proportions from that of 50 to 77^, unto that of 50 to 77-;. And by the like. limits above-mentioned were the refradions of the rays be-: longing to the reft of the Colours defined, the fines of the red- making rays extending from 77 to 778-, thofe of the orangcrmaking from 775 to 77^ j thofe of the yel- low-making from 77^ to 77 1, thofe of the green-making from 777 to 7 7x J thofe of the blue-making from 77^ to 775, thofe of the indico-making from 77-j to 77,;, and • thofe of the violet from 77^ to 78.

Thefe are the Laws of the refrad ions made out of Glafs into Air, and thence by the three Axioms of tlie hrft Book the Laws of the refractions made out of Air. into Glafs areeafily derived.:

EXPER.

[94]

EX PER. VIII.

I found moreover that when Light goes out of Air through feveral contiguous refrafting Mediums as through Water and Glafs, and thence goes out again into Air, whether the refracting fupcrficies be parallel or inclined to one another, that Light as often as by contrary refractions 'tis fo corrected, that it emergeth in hues parallel to thofe in which it was incident, continues ever after to be white. But if the emer- gent rays be inclined to the incident, the whitenefs of the emerging Light will by degrees in palling on from the place of emergence, become tinged in its edges with Colours. This I tryed by refrading Light with Prifms of Glafs within a prifmatick Veffel of Water. Now thofe Colours argue a diverging and feparatioii of the hetero- geneous rays from one another by means of their un- equal refradions, as in what follows will more fully appear. And, on the contrary, the permanent white- nets argues, that in like incidences of the rays there is no fuch leparation of the emerging rays, and by confe- quence no inequality of their whole refradions. Whence 1 ieem to gether the two following Theorems.

I. The Exceffes of the fines of refraction of feveral forts of rays above their common fine of incidence when the refractions are made out of divers denfer mediums immediately into one and the fame rarer medium, are to one another in a given Proportion.

a. The

[P5]

a. The Proportion of the line of incidence to the fine of refraction of one and the fame fort of rays out of one medium into another, is compofed of the Proportion of the line of incidence to the line of refradion out of the firfl: medium into any third medium, and of the Pro- portion of the line of incidence to the line of refradion out of that third medium into the fecond medium.

By the firft Theorem the refractions of the rays of every fort made out of any medium into Air are known by having the refraClion of the rays of any one fort. As for inllance, if the refractions of the rays of every fort out of Rain-v/ater into Air be delired, let the common fine of incidence out of Glafs into Air be fubduded from the lines of refraCtion, and the Excefl'es will be ay, i-j\y if-, 27^ > 27-;, I-]], 279-, 28. Suppofenow that the fine of incidence of the leaft refrangible rays be to their fine of refraCtion out of Rain-water into Air as three to four, and fay as i the ditference of thofe fines is to 5 the fine of incidence, fo is 27 the leaft of the Excelies above-mentioned to a fourth number 8 1 ; and 81 will be the common fign of incidence out of Rain- water into Air, to which line if you add all the above- mentioned Excefles you will have the defired fines of the refractions 108, loSs, 1087, 1087 ^ io8i, loSf, 1089, 109.

By the latter Theorem the refraCtion out of one me- dium into another is gathered as often as you have the refractions out of them both into any third medium. As if the fine of incidence of any ray out of Glafs into Air be to its fine of refraCtion as ao to ^ i, and the fine of incidence of the fame ray out of Air into Water, be

to

to its fine of refraftion as four to three ; the fine of incidence of that ray out of Glafs into Water will be to its fine of refraction as lo to ^ i and 4 to^ joyntly, that is, as tjie Fadum of ao and 4. to the Factum of 3 1 and 3, or as 80 to 93.

And thele Theorems being admitted into Opticks, there would be fcope enough of handling that Science voluminoufly after a new manner ; not only by teaching thofe things which tend to the perfettion of vilion, but alfo by determining mathematically all kinds of Phaeno- mena of Colours which could be produced by refra- dtions. For to do this, there is nothing elfe requifite than to find out the reparations of heterogeneous rays, and their various mixtures and proportions in every mixture. By this way of arguing 1 invented almoft all the Phsenomena defcribed in thefe Books, befide fome others lefs neceflary to the Argument ; and by the fucceffes I met with in the tryals, I dare promife, that to him who iTiall argue truly, and then try all things with good Glafles and fufficient circumfpection, the expeded event will not be wanting. But he is firft to know what Colours will arife from any others mixt iu any affigned Proportion,

PROP. IV. THEOR. IIL

Colours mm he produced iy compofition which /ball ht like to the Colours of homogeneal Ljo^ht as to the affenrame of Colour^ but not as to the immuta/nlity of Colour and conjlttution of Light. j4nd thofe Colours ^y ho-w much they are more compounded b'j jo much are they UJs fuU ■ and inteufe^ and by too much comfo/ition they may be

diluted

[97]

diluted attd 'weakened till they ceaje. i here nia\' be alfo Colours froduced b'j comfofitioyi^ 'which are not jitlh like an'j oj the Colours of hsmogeneod Light.

For a mixture of homogeneal red and yellow com- pounds an orange, like in appearance of Colour to that orange which in the feries of unmixed prifmatick Co- lours lies between them; but the Light of one orange is homogeneal as to refrangibility, that of the other is heterogeneal, and the Colour of the one , if viewed through a Prifm, remains unchanged, that of the other is changed and refolved into its component Colours red and yellow. And after the fame manner other neigh- bouring homogeneal Colours may compound new Co- lours, like the intermediate homogeneal ones, as yel- low and green, the Colour between them both, and af- terwards, if blue be added, there w^ll be made a green the middle Colour of the three which enter the com.po- lition. For the yellow and blue on either hand,if they are equal in quantity they draw the intermediate green equal- ly towards themfelves in compofition, and fo keep it as it were in equillbrio, that it verge not more to the yellow on the one hand, than to the blue on the other, but by their mixt ad:ions remain ftili a middle Colour. To this mixed green there may be further added fome red and violet, and yet the green will not prefent- ly ceafe but only grow lefs full and vivid, and by in- creaiing the red and violet it will grow more and more dilute, until by the prevalence of the added Colours it be overcome and turned into whitenefs, or fome other Colour. So if to the Colour of any homogeneal Light, the Sun's white Light compofed of all lorts of. rays be

N added,

added, tltat Colour will not vanifh or change its fpe- cies but be diluted, and by adding more and more white it will be diluted more and more perpetually. Laft- ly, if red and violet be mingled, there will be generated according to their various Proportions various Purples, fuch as are not like in appearance to the Colour ot any homogeneal Light, and of theie Purples mixt with yel- low and blue may be made other new Colours.

PROP. V. THEOR. IV.

Whitenefs and all gre>j Colours Set'ween 'white and Mach^ ma'j be. compounded o\ Colours^ and the isuhitenefs of the Suns Light is compounded of all the f?imar>^ Colow's mixt in a due pofortion.

The Proof hy Experiments.

EX PER. IX.

jr^tr. e. The Sun fhining into a dark Chamber through a little round Hole in the Window fhut, and his Light being there refraded by a Prifm to call his coloured Image P T upon the oppohte Wall : I held a white Pa- per V to that Image in fuch m^anner that it might be illuminated by the coloured Light retiected from thence, and yet not intercept any part of that Light in its paf- fage from the Prifm to the Spedrum. And I found that when the Paper was held nearer to any Colour than to the reft, it appeared of that Colour to which it ap- proached nearcft 3 but when it was equally or almoft

equally

199}

equally diftant from all the Colours, Co that it might be equally illuiriinated by them all it appeared white. And in this laft lituation of the Paper, if fome Colours were intercepted, the Paper loll its white Colour, and appeared of the Colour of the reft of the Light which was not intercepted. So then the Paper was illuminated with Lights of various Colours, namely, red, yellow, green, blue and violet, and every part of the Light re- tained its proper Colour, until it was incident on the Paper, and became retiefted thence to the Eye ; fo that if it had been either alone (the reft of the Light being intercepted) or if it had abounded moft and been pre- dominant in the Light retleded from thePaper,it would have tinged the Paper w^ith its own Colour ; and yet be- ing mixed wdth the reft of the Colours in a due propor- tion, it made the Paper look white, and therefore by a compofition with the reft produced that Colour. The feveral parts of the coloured Light reflected from the Spedf rum, whilft they are propagated from thence thro' the Air, do perpetually retain their proper Colours, becaufe wherever they fall upon the Eyes of any Specta- tor, they make the feveral parts of the Spedrum to appear under their proper Colours. They retain there- lore their proper Colours when they fall upon the Pa- per V, and lb by the confufion and perfed mixture of thole Colours compound the whitenefs of the Light reflected from thence.

EX PER. X.

Let that Spedrum or folar Lnage P T fall now upon Ftg. 6. the Lens M N above four Inches broad, and about fix

N 2 Feet

[ loo]

Feet diftant from the Piifm ABC, and fo figured that it may caufe the coloured Light which divergeth from the Prifm to converge and meet again at its Focus G, about fix or eight Feet diftant from the Lens, and tliere to fall perpendicularly upon a white Paper DE. And if you move this Paper to and fro, you will per- ceive that near the Lens, as at de^ the whole folar Image (fuppofe at pt) will appear upon it intenfly coloured after the manner above-explained, and that by receding^ from the Lens thofe Colours will perpetually come to- wards one another, and by mixing more and more di- lute one another continually, until at length the Paper come to the Focus G, where by a perfed mixture they will wholly vanifli and be converted into whitenefs, the whole Light appearing now upon the Paper like a little white Circle. And afterwards by receding further from the Lens, the rays which before converged will now crofs one another in the Focus G, and diverge from thence, and thereby make the Colours to appear again, but yet in a contrary order ; fuppofe at c^£ , where the red t is now above which before was below, and the violet p is below which before v^-as above.

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

So.

\

C lOI ]

So if the violet, blue and green be intercepted, the re- maining yellow, orange and red will compound upon the Paper an orange, and then if the intercepted Co- lours be let pafs they will fall upon this compounded orange, and together with it decompound a white. So alio if the red and violet be intercepted, the remaining yellow, green and blue, will compound a green upon the Paper, and then the red and violet being let pafs will fall upon this green, and together with it decom- pound a white. And that in this compoiition of white the feveral rays do not fufFer any change in their colori- fic qualities by ading upon one another, but are only mixed, and by a mixture of their Colours produce white, may further appear by thefe Arguments.

If the Paper be placed beyond the Focus G, fuppofe at o'f , and then the red Colour at the Lens be alternate- ly intercepted, and let pafs again, the violet Colour on the Paper will not futfer any change thereby, as it ought to do if the feveral forts of raysaded upon one another in the Focus G, where they crofs. Neither will the red upon the Paper be changed by any alternate flop- ping, and letting pafs the violet which crolTeth it.

And if the Paper be placed at the Focus G, and the white round Image at G be viewed through the Prifm HIK, and by the refradion of that Prifm be tranflated to the place rv, and there appear tinged with various Colours, namely, the violet at v and red au r , and others between, and then the red Colour at the Lens be often ftopt and let pafs by turns, the red at r will ac- cordingly difappear and return as often, but the violet; at V will not thereby fuifer any change. And lb by flopping and letting pafs alternately the blue at the

Lens.

[ 102 ]

Lens, the blue at r will accordingly dilappear and re- turn, withoutany change made in the red at r. The red therefore depends on one ibrt of rays, and the blue on another fort, which in the Focus G where they are commixt do not aft on one another. And there is the lame realbn of the other Colours.

I conlidered further, that when the moft refrangible rays Pp, and the leaft refrangible ones Tt, are by con- verging inclined to one another, the Paper, if held very oblique to thofe rays in the Focus G, might relieft one Ibrt of them more copioufly than the other Ibrt, and by that means the refledted Light would be tinged in that Focus with the Colour of the predominant rays, pro- vided thofe rays feverally retained their Colours or co- lorific qualities in the compolition of white made by them in that Focus. But if they did not retain them in that white, but became all of them feverally endued there with a difpofition to ftrike the fenfe with the per- ception of white, then they could never lofe their white- neis by fuch reflexions. I inclined therefore the Paper to the rays very obliquely, as in the fecond Experiment of this Book, that the moft refrangible rays might be more copioufly reflected than the reft, and the white- ^ nets at length changed lucceflively into blue, indico^ and violet. Then 1 inclined it the contrary way, that the moft refrangible rays might be more copious in the refleded Light than the reft, and the whitenefs turned fucceflively to yeUow, orange and red.

Laftly, I made an Inftrument XY in fafhion of a Comb, whofe Teeth being in num.ber lixteen were about an Inch and an half broad, and the intervals of the Teeth about two Inches wide. Then by interpoflng

fuc-

[103]

fucceffively the Teeth of this Inftrumcnt near the Lerrs^ I intercepted part of the Colours by the interpofcd Tooth, whilft the reft of them went on through the in- terval of the Teeth to the Paper D E, and there pain- ted a round folar Image. But the Paper I had firft pla- ced fo, that the Image might appear white as often as the Comb was taken away ; and then the Comb be- ing as was laid interpofed, that whitenefs by reafon of the intercepted part of the Colours at the Lens did al- ways change into the Colour compounded of thofe Colours which were not intercepted, and that Colour was by the motion of the Comb perpetually varied fo, that in the palling of every Tooth over the Lens all thefe Colours red, yellow, green, blue and purple, did always fucceed one another. I caufed therefore all the Teeth to pais fucceffively over the Lens, and when the motion was flow, there appeared a perpetual fucceffion of the Colours upon the Paper : But if I fo much acce- lerated the motion, that the Colours by reafon of their quick fucceffion could not be diftinguilhed from one another, the appearance of the iingle Colours ceafed. There was no red, no yellow, no green, no blue, nor purple to be feen any longer, but from a confulion of them all there arofe one uniform white Colour. Of tj^e Light which now by the mixture of all the Colours ap- peared white, there was no part really white. One part was red, another yellow, a third green, a fourth blue, a fifth purple, and every part retains its proper Colour till it ftrike the Senforium. If the impreffions follow one another llowly, fo that they may be ieve- raliy perceived, there is made a diftind: fenfation of all the Colours one after another in a continual fucceffion.

But

[104]

But If the impreflions follow one another lb quickly that they cannot be feverally perceived, there arifeth out of them all one common fenlation, which is nei- ther of this Colour alone nor of tliat alone, but hath it lelf indifferently to 'em all, and this is a lenfation of whitenefs. By the quicknefs of the fucceffions the im- preffions of the feveral Colours are confounded in the Senforium, and out of that confution arileth a mixt icn- fation. If a burning Coal be nimbly moved round in a Circle with Gyrations continually repeated, the whole Circle will appear like hre ; the reafon of wiiich is, that the fenfation of the Coal in the feveral places of that Circle remains impreft on the Senforium, until the Coal return again to the fame place. And lb in a quick confecution of the Colours the impreffion of every Colour remains in the Senforium, until a revolution of all the Colours be compleated, and that firft Colour re- turn again. The impreffions therefore of all the fucceffive Colours are at once in theSenlbrium,and joyntly ftir up a fenfation of them all ; and lb it is manifeft by this Ex- periment, that the commixt impreffions of all the Co- lours do hir up and beget a feniation of white, that is, that whitenefs is compounded of all the Colours. j

And if the Comb be now taken away, that all the Colours may at once pals from the Lens to the Paper, and be there intermixed, and together relie<5ted thence to the Speftators Eyes ; their impreffions on the Senfo- rium bemg now more fubtily and perfedly commixed there, ought much more to iHr up a fenfation of white- •iiefs.

You

C 105 ]

You may inftead of the Lens ufe two Fril'ms HI K andLMN, which by refractmg the coloured Light the contrary way to that of the firft refraction, may make the diverging rays converge and meet again in G, as you fee it reprefented in tlie feventh Figure. For Ftg. 7. where they meet and mix they will compote a white Light as when a Lens is uied.

EX PER. XL

Let tl\e Sun's coloured Image PT fall upon the Wall Fig- 8. of a dark Chamber, as in the third Experiment of the lirftBook, and let the fame be viewed through a Prifm a be, held parallel to the Prifm ABC, by whofe refra- dion that Image was made, and let it now appear lower than before, fuppofe in the place S over againll the red colour T. And if you go near to the Image PT, the Speftrum S will appear oblong and coloured like the image PT; but if you recede from it, the Colours of the Spedrum S will be contracted more and more, and at length vanilli, that SpeCtrum S becoming perfectly \ round and v/hite ; and if you recede yet further, the ^Colours will emerge again, but in a contrary order. Now that Speftrum S appears white in that cafe when the rays of feveral forts which converge from the feve* ral parts of the Image PT, to the Prifm a be, are fo refracted unequally by it, that in their paffage from the Prifm to the Eye they may diverge from one and the iame point of the Spectrum S, and fo fall afterwards upon one and the fame point in the bottom of the Eye, mid there be min2,led.

O And

[lod]

And further, if the Comb be here made ufe of, by whofe Teeth the Colours at the Image PT may be luc- ceffively intercepted ; the Spedrum S when the Comb is moved flowly will be perpetually tinged with iiic- ceflive Colours : But when by accelerating the motion of the Comb, the fucceffion of the Colours is fo quick that they cannot be feverally feen, that Spectrum S, by a confufed and mixt lenlation of them all, will appear white.

EXPER. XII.

Jpio: 9. The Sun fhining through a large Prifm ABC upon a Comb X Y, placed immediately behind the Prifm, his Light which paffed through the interlaces of the Teeth fell upon a white Paper DE. The breadths of the Teeth were equal to their interftices, and feven Teeth together with their interftices took up an Inch in breadth. Now w^hen the Paper was about two or three Inches diftant from the Comb, the Light which paffed through its feveral interftices painted ib many ranges of Colours kl, mn, op, qr, ^r. which were parallel to one another and contiguous, and without anyi mixture of white. And thefe ranges of Colours, if the Comb was moved continually up and down with a re- ciprocal motion, afcended and defcended in the Paper,^ and when the motion of the Comb was fo quick, that the Colours could not be diftinguifhed from one another, the whole Paper by their confulion and mixture in the Senforium appeared white.

Let

[ 107 ]

Let the Comb now reft, and let the Paper be remo- ved further from the Prifm, and the feveral ranges of Colours will be dilated and expanded into one another more and more, and by mixing their Colours will di- lute one another, and at length, when the diftance of the Paper from the Comb is about a Foot , or a little more ( fuppofe in the place i D 2 E ) they will lb far dilute one another as to become white.

With any Obftacle let all the Light be now ftopt which paffes through any one interval of the Teeth, ib that the range of Colours which comes from thence may be taken away, and you will fee the Light of the reft of the ranges to be expanded into the place of the range taken away, and there to be coloured. Let the inter- cepted range pafs on as before, and its Colours falling upon the Colours of the other ranges, and mixing with them, will reftore the whitenefs.

Let the Paper 2D 2 E be now very much inclined to the rays, fo that the moft refrangible rays may be more copioufly reflefted than the reft, and the white Colour of the Paper through the excefs of thofe rays will be •v changed into blue and violet. Let the Paper be as \nuch inclined the contrary way, that the leaft refran- gible rays may be now more copioufly refleded than the reft, and by their excefs the whitenefs will be changed into yellow and red. The feveral rays there- fore in that white Light do retain their colorific qua- lities, by which thole of any fort, when-ever they be- come more copious than the reft, do by their excefs and predominance cauie their proper Colour to ap- pear.

O 5 And

[io8]

And by the fame way of arguing, applied to the third Experiment of this Book, it may be concluded, that the white Colour of all refracted Light at its very firll: emergence, where it appears as white as before its inci- dence^ is compounded of various Colours.

EX PER. XIII.

In the foregoing Experiment the feveral intervals of the Teeth of the Comb do the office of fo many Prifms, every interval producing the Phaenomenon of one Prifm. Whence inftead of thofe intervals ufing feveral Prifm?, I try'd to compound whitenefs by mixing their Colours,and did it by ufing only three Prifms, as alfo by ufing only Fig' lo- two as follows. Let two Prifms ABC and a b c, whole refrading Angles B and b are equal,be fo placed parallel to one another, that the refrafting Angle B of the one may touch the Angle c at the bale of the other, and their planes CB and cb, at which the rays emerge, may lye in directum. Then let the Light traje^ed through them fall upon the Paper M N, dillant about 8 or i 2 / Inches from the Prifms. And the Colours generatedr by the interior limits B and. c of the two Prifms, wil( be mingled at PT, and there compound white. For if either Prifm be taken away, the Colours made by the other will appear in that place PT, and when the Prifm is reftoredto its place again, fo that its Colours may there tall upon the Colours of the other, the mixture of them both will reftore the whitenels.

This

This Experiment fucceeds alio, as I have tryed, when the Angle b of the lower Prilm, is a little greater than the Angle B of the upper , and between the interior Angles B and c, there intercedes ibme fp:ice B c, as is teprelented in the Figure, and the retracing planes BC and be, are neither in directum, nor parallel to one another. For there is nothing raore requifite to the fucceis of this Experiment, than that the rays of all forts may be uniformly mixed upon the Paper in the place PT. If the moft refrangible rays coming from the fuperiorPriim take up all theipace from M to P, the rays of the fame fort which come from the inferior Prifm ought to begin at P, and take up all the reft of the fpacefrom thence towards N. If the leaft refrangible rays coming from the fuperior Prifm take up the ipace MT, the rays of the lame kind which come from the other Prifm ought to begin atT, and take up the remaiir- ing fpace T N. If one Ibrt of the rays which have in- termediate degrees of refrangibility,, and come from the fuperior Prifm be extended through the ipace MQ-, and another ibrt of thofe rays through the fpace MR, and a third fort of them through the ipace MS, the fame forts of rays coming from the lower Prifm, ought to ilr iluminate the remaining ipaces Q.N, RN, SN refpe- dively. And the lame is to be underllood of all the other ibrts of rays. For thus the rays of every fort wdll be fcattered uniformly and evenly through the whole fpace MN, and lb being every wiiere mixt in the fame proportion, they muft every where produce the lame Colour. And therefore lince by this mixture.they pro- duce white in the exterior Ipaces M P and TN, they muft alfo produce white in the interior ipace P T. This

is.

[no]

IS the reafon of the compofition by which whitcncfs was produced in this Experiment, and by what other way Ibever 1 made the like compofition the refult was whitcnefs.

Laftly, If with the Teeth of a Comb of a due (ize, the coloured Lights of