THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES GIFT Dr. M. N. Beigelinan \' ^ L / \ OPTICKS: O R, A TREATISE O F T H E Refledions , Refractions , Inflexions and Colours O F LIGHT. The Second Rditton^ with Addit'tons. By Sir Isaac Newton, Knt. LONDON: Printed for W. and J. Innys, Printers to the Royal Society, at the Prince' s-Jrms in St. PauVs Church- Yard. 1718. Advertisement L ART of the enfiiing Dif- coiirje about Light was written at the De/ire of fome Gentlemen oftheKoyal So- ciety, in the Tear i6is, ^^d then fent to their Secretary, and read at their Meetings, and the rejl was added about twelveTears af- ter to complete the Theory ; except the Third Book, and the laft Oh fervatton in the laft Part of the Second, which were finceput to- gether out of fcatterd Papers. To amid being engaged in Difputes A 2 about Advertifement. dhont thefe Matters, I have hi- therto delayed the printing, and Jhotildftillhave delay edit, had not the Importunity of Friends pre- vailed upon ?ne. If any other Pa- pers writ on this SiibjeB are got out of my Hands they are imper- fect, and were perhaps written before I had tried all the Expe- rhnents here fet down, and f idly fatisfied my f elf alout the Laws of Refractions and Compo/ition of Colours. I have here pullijljd ivhat I think proper to come A- broad, xviJJnng that it may not he trav fated into another Language Without my Confent. The Crowns of Colours, which fometimes appear about the Sun and Moon, I have endeavoured to give an Account of-, but for want Advertifement. want of fi/fficient Olfervatiom leave that Matter to he farther examined. The Siihjecl of the Third Book I have alfo left im- perfect, not havifig tried all the Experiments which I intended when I was Soui^thcfe Matters, nor repeated fonie of thofe which I did try , until I had fatisfied my felf ahoiit all their Circum- fiances. To communicate what I have tried, and leave the reft to others for farther Enquiry , is all ?ny De/ign in puUijlnng thefe Papers. In a Letter written to ]\ Ir. Lei b- liitz /;; the Tear 1676, and pnh- lified hy Dr Wallis, I inentiond a Method l?y which I had found fome general Theorems about fquaring Curvilinear figures , or Advertifemcnt. or comparing them with the Co- nic SeBions, or other the jimplefl Figures with which they may he compared. And fome Tears ago I lent out a Manufcrtpt contain-' ing fiich Theorems, and having fince met with ^ome Things cop- ed out of it, I have on this Occa- fion made it piblick, prefixi.g to it an Introdutlion, andfubjoin- tng a Scholium concerning that Method, And I have joined with it another f mall Tract concerning the Curvilinear Figures of the Second Kind, which was alfo written many Tears ago, and made known to fome Friends , who have folicited the inaking it pulTick. April I. T ]\I 1704. - ^' ^^' Advertisement IL A^ tins Second Edition of thefe Opticks I have o- mitted the Mathematical TraBs puMiJhed at the End of the former Edition , as not be- longing to the SnhjeEt. And at the End of the Third Book I have added fome ^/ejtions. And to JJjew that I do not take Gra- vity for an ejfential Property of Bodies, I have added one ^le- Jiion concerning its Caufe, chti- fing to propoje it hy way of a :^ie/iion, fecanfe I am not yet fatisfied alout it for want of J^xperiments. I N. July 16. 1717. ^ jg IK « JK -K «»•« -K «•!• IS IK -K «*■«?«)«•«•« -S -K jK * w'' X \ . ■ • • •■ CORRIGENDA. PAGE 3. line 17. read turned back., p. 7.. 1. ult. forF'^g. 5. r. Mucb. p. 4c. l.io. r.de znd fg. p. 5-7. I'i.r.-wliole. p.9f. l.zj. r.PT{pP.VUl. p.m. ].Z^. Intervab, andyou. p. i li. 1. Zf. r/jat »f ^»j*r- p.IJJ.l.li. r. rt»(^ the breadth. p. 157. 1. 24.. Y.redhomogeneal Light, p. I^o. J. $Z. X.the VeJJel appeared of a red Colour like. p. i(Sy. 1. 4. r. they entered, p. 19(3. 1,22. r. ff'"" «/ thePnfin, on. p.204. 1. 27. r. ru'W *« Fx, F ,iffimilar. The former Light I call Homoge- neal, not becaufe I would affirm it fo in all re- fpefts ; but becaufe the Rays which agree in Re- frangibility, agree at leafl in all thofe their other Properties which I confider in the following Difcourfe. DEFIN. VIII. The Colours of Homogeneal Lights, I call Tri- mary, Homogeneal and Simple-, and thofe of Heterogeneal Lights, Heterogeneal and Com- ponnd. For thefe are always compounded of the colours of Homogeneal Lights ; as will ap- pear in the following Difcourfe- AXIOMS. [5] AXIO MS. AX. I. THE Angles of Reflexion, and Refra^iion^ lie in one and the fame Tlane ijuitb the jingle of Incidence. AX. n. The Angle of Reflexion is equal to the Angle of Incidence. AX. in. If the Re framed Ray be returnea direBly back to the ^oint of Incidence.^ it floall be re- fratfed into the Line before defcribedby the in- cident Ray, AX. IV. RefraBion out of the rarer Medium intothe denfer, is made toijvards the "Perpendicular, that is, fo that the Angle of Re f ration be lefs than the Angle of Incidence. AX. V. The Sine of Incidence is either accurately or very nearly in a given Ratio to the Sine of Re'- fraction. Whence if that Proportion be known in any one Inclination of the incident Ray, 'tis known in all the Inclinations, and thereby the Refra- ^lon in all cafes of Incidence on the fame refra^ ding Body may be determined. Thus if the B 3 Refra- Rj2fra(^tion be made out of Air into Water, the Sine 'of Incidence of the red Light is to the Sine pfitsRefradionas 4to 3. If out of Air into Glafs, the Sines are as 17 to 11. In Light of other Colours the Sines have other Proportions : but the difference is fo little that it need feldom be confidered. Snppofe therefore, that R S [mFig.i.^ repre- fents the Surfaceof ftagnating Water, and that C is, the point of Incidence in which any Ray coming in the Air from A in the Line AC is retiedted or reffraded, and I would know whither this Ray fliall go after Reflexion or Refradion : I ereA Vipon the Surface of the Water from the point of Incidence the Perpendicular CP and produce it downwards to Q, and conclude by the firft Axiom., that the Ray after Reflexion and Re- fraction, ihall be found fomewhere in the Plane of the Angle of Incidence A CP produced. I let fall therefore upon the Perpendicular CP the Sine of Incidence AD; and if the refleded Ray be defired, I produce AD to B fo that DB be equal to AD, and draw CB. For this Line C B iliall be the reflefted Ray ; the Angle pf Reflexion BCP and its Sine BD being e- qual to the Angle and Sine of Incidence, as they ought to fcje by the fecond Axiom. But if the refi'a6led Ray be defired, I produce AD to H, fo that DH may be to AD as the Sine of Re- iraftion to the Sine of Incidence, that is (if the Light be red) as 3 to 4 ; and about the Center C and in the Plane ACP with the Radius C A defcribing a Circle ABE I draw Parallel to the Perpendicular C P Q, the Line H E cutting the Cireum- [7] Circumference inE, and joyningCE, this Line CE ihall be the Line of the refraded Ray. For if EF be let fall perpendicularly on the Line PQ, this Line EF ihall be the Sine of Re- fradion of the Ray C E, the Angle of Refradion being E C Q ; and this Sine E F is equal to D H, and confequently in Proportion to the Sine of Incidence A D as 3 to 4. In like manner, if there be a Prifm of Glafs (that is a Glafs bounded with two Equal and Parallel Triangular ends, and three plain and w^ell poliilied 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 theRefraftion of the Light in palling crofs this Prifm be defired : Let AC B [in Fig. i.] reprefent a Plane cutting this Prifm tranfverlly to its three Parallel lines or edges there where the Light paffeth through it, and let DE be the Ray inci- dent upon the firit fide of the Prifm A C where the Light goes into the Glafs ; and by putting the Proportion of the Sine of Incidence to the Sine of Refradion as 17 to 11 find EF the firll refrafted Ray. Then taking this Ray for the Incident Ray upon the fecond fide of the Glafs BC where the Light goes out, tind the next refraded R^y F G by putting the Proportion of the Sine of Incidence to the Sine of Re- fradion as 11 to 17. For if the Sine of Inci- dence out of Air into Glafs be to the Sine of Refradion as 17 to 11, the Sine of Incidence out of Glafs into Air muft on the contrary be to the Sine of Refradion as 11 to 17, by the third Axiom. B 4 P^g'^^ [8] Much after the fame manner, if ACBD [in Fig. 3.] reprefent a Glafs fpherically Convex on both fides (ufually called a Lens^ fuch as is a Birrn- ing-glafs, or Spedacle-giafs, or an Objeft-glafs of a Telefcope) and it be required to know how Light falling upon it from any lucid point Q iliall be relra(^ted, let QM reprefent a Ray falling upon any point M of its firft fpherical Surface A C B, and by ereft ing a Perpendicular to the Glafs at the point M, find the firft re- fra6fed Ray MN by the Proportion of the Sines 17 to 11. Let that Ray in going out. of the Glafs be incident upon N, and then find the fecond refraded Ray N q by the Proporti- on of the Sines 11 to 17, And after the fame inanner may the Refraction be found when the Lens is Convex on one fide and Plane or Con- cave on the other, or Concave on both fides. A X. VI Hofnogeneal Rays jeds from abroad upon a Wall or Sheet of white Paper in a dark Room. In Uke manner, when a Man views any Objed PQR, [ini^i^,8.] the Light which comes from the feveral Points of the Objed is fo refracted by the tranfparent skins and humours of the Eye, (that is by the outward coat EFG called the Tunica Cornea^ and by the cryftalline hu- mour A?j 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 Pidurc of the Objeft upon that skin (called the Tunica Retina) with which the bottom of the Eye is covered, For Anatomilts when they have taken off from the bottom of the Eye thatout- w^ard and moll thick' Coat called the 2)//r^ Ma- ter^ can then fee through the thinner Coats, the Pictures of Objeds lively painted there- on. And thefe Pidures propagated by Mo- tion along the Fibres of the Optick Nerves in- to the Brain, arc the caufe of Vifion. For ac- cordingly as thefe Pidures are perfed or im^ perfed, the Objed is feen perfedly or imperfecl- [13] ly. If the Eye be tinged with any colour (as in the Difeafe of the JaundifeJ fo as to tinge the Pidlures in the bottom of the Eye with that Colour, then all Objects appear tinged with the fame Colour. If the humours of the Eye by old Age decay, fo as by flirinking to make the Cornea and Coat of the Cryftalline htimoitr grow flatter than before, the Light will not be re- fraded enough, and fornvant of a fuiiicient Re- fradion will not converge to the bottom of the Eye but to fome place beyond it, and by con- fequencc paint in the bottom of the Eye a con- fuled Pidure, and according to the indiitind- nefs of this Pidure the Objed will appear con- fufcd. This is the reafon of the decay of fight in old Men, and fhews why their Sight is mend- ed by Spedacles. For thole Convex-glalFes fup- ply the defed of plumpnefs in the Eye, and by encreafmg the Refradion make the Rays con- verge fooner fo as to convene diilindly at the bottom of the Eye if the Glafs have a due de- gree of convexity. And the contrary happens in fliort-fighted Men whofe Eyes are too plump. For the Refradion being now too great, the Rays converge and convene in the Eyes before they come at the bottom ; and therefore the Pidure made in the bottom and the Vifion caufed thereby will not be diflind, unlefs the Objed be brought fo near the Eye as that the place where the converging Rays convene may be removed to the bottom, or that the plump- nefs of the Eye be taken off and the Refradi- on s diminifhed by a Concave-glafs of a due de- gree of Concavity, or laftly that by Age the I Eye [14] Eye gro'<^' flatter till it come to a due Figure : For iliort-fighted Men fee remote Objeds befl in Old Age, and therefore they are accounted to have the moft laiting Eyes. A X. VIII. An Obje5f feen by Reflexion or RefraBton^ nf fears in that flace from whence the Rays af- ter their laft Reflexion or RefraSiion diverge in falling on the SfeBator^s Eye. If the Objeft A [in Fig, 9.] be feen by Reflexion of a Looking-glafs m n, it fhall appear, not in its proper place A, but behind the Glafs at a, from whence anyRays AB, AC, AD, which flow from one and the fame Point of the Objed, do after their Reflexion made in the Points B, C, D, di- verge in going from the Glafs to E, F, G, where they are incident on the Speftator'sEyes. For thefe Rays do make the fame Pi6lure in the bottom of the Eyes as if they had come from the Objeft really placed at a without the inter- pofition of the Looking-glafs ; and all Villon is made according to the place and fliape of that Pidure. In like manner the Objeft D [in Fig. 2.] feen through a Prifm, appears not in its proper place D, but is thence tranflated to fome other place d fituated in the lait refraded Ray F G drawn backward from F to ^. And fo the Objeft Q [in Fig. 10.] feen through the Lens AB, appears at the place q from whence the Rays diverge in pafliingfrom the Lens to the Eye. Now it is to be noted> that the Image of the [»5] the Objeft at q is fo much bigger or lefler than the Objed: it felf at Q, as the diftance of the Image at q from the Lens AB is bigger or lefs than the dillance of the Objed at Q from the fame Lens. And if the Objed be feen through two or more fuch Convex or Concave-glilies, every Glafs Ihall make a new Image, and the Objed fliall appear in the place and of the big- nefs of the lail Image. Which confideration un- folds the Theory of Microfcopes and Telefcopes. For that Theory confilh in almoft nothing elfe than the defcribing fuch GlafTes as fliall make the laft Image of any Objeft as diilinft and large and luminous as it can conveniently be made. I have now given in Axioms and their Ex- plications the fumm of what hath hitherto been treated of in Opticks. P'or what hath been ge- nerally agreed on I content my felf to alTume under the notion of Principles, in order to what I have farther to write. And this may fuffice for an Introdudion to Readers of quick Wit and good Underflanding not yet verled in Op- ticks : Although thofe who are already acquain- ted with this Science, and have handled GlaiTes, will more readily apprehend what folio weth. TROTO^ [•«] L PROPOSITIONS. TROT.l The OR. I. IG HTS which differ in Colour^ differ alfi in T>egrees of Refrangihility, The Proof by Experiments. Exfer. I. I took a black oblong fliff Paper terminated by Parallel Sides, and with a Per- pendicular right Line drawn crofs from one Side to the other, dillinguiflied it into two e- quai Parts. One of thefe parts I 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 Phaenomenon might be more confpicuous. This Paper I view'd through a Prifm of folid Glafs, whofe two Sides through which the Light palTed to the Eye were plane and well polifhed , and contained an Angle of about fixty degrees : which Angle I call the refrafting Angle of the Prifm. And whiKlI viewed it, I held it and the Prifm before a Window infuch manner that the Sides of the Paper were parallel to the Prifm, and both thofe Sides and the Prifm were parallel to the Horizon, and the crofs Line was alfo parallel to it ; and that the Light which fell from the Window upon the Paper made an Angle with the Paper, equal to that Angle which was made with the fame Papef [17] Paper by the Light refle6ted from it to the Eye. Beyond thePriim was the Wall of the Chamber* under the Window covered over with black Cloth, and the Cloth was involved in Darknei's that no Light might be refleded from thence, which in palling by the edges of the Paper to the Eye, might mingle it felf with the Light of the Paper, and obfcure the Phaenomenon there- of Thefe things being thus ordered, I found that if the- refradiing Angle of the Prifm be turned upwards, fo that the Paper may feem to be lifted upwards by the Refraction, its blue half will be lifted higher by. the Refraclion than its red half But if the refrading Angle of the Prifm be turned downward, fo that the Paper may feem to be carried lower by the Re. ra- tion, its blue half, will be carried fomething lower thereby -than it^s red half W herefore in both cafe? the Light which comes from the blue half of the Paper through the Prii'm to the Eye, does in like Circumltances futier a greater Refradion than the Light which comes from the red half, and by confcquence is more refrangible. Illtijtration. In the eleventh Figure, MN reprefents^ the Window, and DE the Paper terminate,d with parallel Sides DJ and HE, and by the tranfverfe Line FG dilbnguifhed into ;two halfs, .fhe one D G of an intenfely blue Colour, the other FE of an intenfely red. And B A C^ ^^ reprefents the Prifm whofe refrafting Planes A B ^ ^ and A C ^ ^ rneet in the edge of the refrading Angle A a. This edge A.a being upward, is parallel both to C thof I .8] the Horizon and to the parallel edges of the Paper DJ and HE, and the tranfverfe Line FG is perpendicular to the Plane of the Window. And de reprefents the Image of the Paper feen by Refradion upwards in fuch manner that the blue half D G is carried higher to dg than the red half FE is to/^, and therefore fuffers a greater Refradion. If the edge of the refraft- ing Angle be turned downward, the Image of the Paper will be refrafted downward, fuppofe to <5^€, and the blue half will be refraded lower to ly than the red half is to /^ at equal diilances from the Prifms are equal. I confidered farther, that by the breadth of the hole F through \^'hich the Light enters in- to the dark Chamber, there is a Penumbra made in the circuit of the SpeCtrum Y, and that Penumbra remains in the reCtilinear Sides of the SpeCtrums P T and pt. I placed there- fore at that hole a Lens or ObjcCt-glafs of aTe- lefcope which might calt the Image of the Sun diftinctly on Y without any Penumbra at all, and found that the Penumbra of the reCtilinear Sides of the oblong SpeCtrums PT and/^ was D alfd [34] ^Ifo thereby taken away, . fo that thofc Sides ap- peared as difdnftly defined as did the Chxum- ferenee of the firlMmage Y. Thus it happens if the Glais of the Prilrns be .free from. Veins, and their Sides be accurately plane and well pohllied without thole numberiels Waves or Curies which ufually ariic from Sand-holes a little fmoothed in polifliing with Putty. If the Glafs be only well polillied and free from Veins and the Sides not accurately plane but a Httle Convex or Concave, as it frequently happens ; yet may the three Speflrums V, PT and / t want Penumbras, but not in e^ual diitances from the Prifms. Now from this want of Pen- umbras, I knew more certainly that every one of the Circles was refradled according to fome moft regular, uniform, and conilant law. For if there were any irregularity in the Refraftion, the right Lines A E and G L which all the Cir- cles in the Spedrum PT do touch, could not by that Refraftion be tranllated into the Lines ae and ^/ as diftinft and ftraight as they were before, but there would arife in thofe tranllated Lines fome Penumbra or Crookednefs or Un- dulation, or other fenfible Perturbation con- trary tG what is found by Experience. What- foever Penumbra or Perturbation Ihould be made in the Circles by the crofs Refraction of the fecond Prifm, all that Penumbra or Pertur- bation would be confpicuous in the right Lines a e and g I which touch thofe Circles. And therefore fmce there is no fuch Penumbra or Perturbation in thofe right Lines there mult be none in the Circles. Since the diitance between thofe [35] thofe Tangents or breadth of the Spedlrum is not increafed by the Refractions, the Diameters of the Circles arc not increafed thereby. Since thofe Tangents continue to be right Lines, e- very Circle which in the firfl Priini is more or lefs refraded, is exadly in the fame propor- tion more or lefs refracted in the fecond. And feeing all thefe things continue to fucceed af- ter the fame manner when the Rays are again in a third Prifm, and again in a fourth refra- ded fideways, it is evident that the Rays of one and the fame Circle, as to their degree of Re- frangibility continue always uniform and ho^ mogencal to one another, and that thofe of fcveral Circles do ditier in degree of Refran- gibility, and that in Ibme certain and conltant proportion. W hich is the thing I was to prove. There is yet another Circumllance or two of this Experiment by which it becomes flill more plaii aid convincing. Let the fecond Prifm DH [in Fi^. 16.'] be placed not im- mediately after the firit, but at fome diftance from it 5 fuppofe in the mid- way between it and the Wall on which the oblong Spectrum PTis caft, lb that the Light from the firll Prifm may fall upon it in the form of an oblong Speftrum tt] parallel to this fecond Prifm, and be refraded fideways to form the oblong Speftrum p t upon the Wall. And you will find as before, that this Speftmm/ ^Js. inclined to that Spectrum P T, which the firit Prifm forms alone without the fecond ; the blue ends P and p being farther diltant from one another than the red ones T and t^ and by confequence D 2, that [ 3^ 1 that the Rays which go to the blue eftd tt of the Imager? and which therefore futfer the greateil Refra^ion in the firftPrifm, are again in the fecond Prifm more refraded than the reft. The fame thing I try'd alfo by letting the Sun's Light into a dark Room through two lit- tle round holes F and (p [in Fig. 17.] made in the Window , and with two parallel Prifms ABC and ctf^y placed at thofe holes (one at each) refracting thole two beams of Light to the oppofite Wall of the Chamber, in fuch man- ner that the two colour'd Images PT and MN which they there painted were joined end to end and lay in one ftraight Line, the red end T of the one touching the blue end M of the o- ther. For if thefe two refraded Beams were again by a third Prifm D H placed crofs to the two firft, refrafted fideways, and the Spedrums thereby tranflated to fome other part of the Wall of the Chamber, fuppofe the Spedrum PT to/^ and the Spedrum MN to »?;?, thefe tranflated Spedrums/^ 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 blue end m of the L mage m n being by a greater Refradion tran- flated farther from its former place M T, than the red end t of the other Image / 1 from the fame place MT; which puts the Propoiition paft difpute. And this happens whether the third Prifm DH be placed immediately after the two firft, or at a great diftance fro^n them, fo that the Light refraded in the two fiiit [37] firil Prifms be either white and circular, or co- loured and oblong when it falls on the third. Expcr. 6. In the middle of two thin Boards I made round holes a third part of an Inch in diameter, and in the Window-lliur a-' much broader hole being made to let into my dark- ned Chamber a large beam of the Sun's Light ; I placed a Prifm behind the Shut in that beam to refradt it towards the oppoiite Wall, and clofe behind the Prifm I fixed one of the Boards, in fuch manner that the middle of the refrafted Light might pafs through the hole made in it, and the relt be intercepted by the Board. Then at the diftance of about twelve Feet from the tirll; Board I fixed the other Board in fuch man- ner that the middle of the refra6led Light which came through the hole in the hrll Board and fell upon the oppofiteW'all might pafs through the hole in this other Board, and the rell being intercepted by the Board might paint upon it the coloured Spedrum of the Sun. And ciofe behind this Board I fixed another Prifm to re- fract the Light which came through the hole. Then I returned fpeedily to the firlt Prifm, and by turning it flowly to and fro about its Axis, I caufed the Image which fell upon the fecond Board to move up and down upon that Board, that ail its parts might fucceifively 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 ; aftd by the difference of the places I found that the Light which being mofl refraded in the D 3 tirft [ 38 ]i firflPrifm didgo to the blue 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 tirlt Pro- portion as the fecond. And this happened whether the Axis of the two Prilms were pa- rallel, or inclined to one another and to the Horizon in any given Angles. llluftratton. Let F [inF/^. i8.] be the wide hole in the Window-fliut, through which the Sun fhines upon the firft Prifm ABC, and let the refrafted Light fall upon the middle of the Board DE, and the middle part of that Light upon the hole G made in the middle of that Board. Let this trajeded part of the Light fall again upon the middle of the fecond Board de and there paint fuch an oblong coloured I- mage of the Sun as was defcribed in the third Experiment. By turning the Prifrn ABC flow- ly to and fro about its 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 w^hich is made in the mid- dle of that Board. In the mean while another Prifm aifcis to be fixed next after that hole g to refraft the trajefted Light a fecond time. And thefe things being thus ordered, I marked the places M and N of the oppofite Wall upon which the refradted Light fell, and found that whilit the two Boards and fecond Prifm re- mained unmoved, thofe places by turning the firil Prifm about its Axis were changed perpe- tually. For when the lower part of the Light which [39] which fell upon the fecond Board d e was caft through the hole g it went to a lower place M on the Wailj and when the higher part of that Light was cad through the fame hole g; it went to a higher place N on the Wall, and when ^- ny intermediate part of the Light was catt through that hole it went to fome place' on thb Wall between M andN. ■ The unchanged Po- fition of the Holes in the Boards, made the In- <:idence of the Rays upon-tlie fecond Prifm to be the fame in all caies. And yet in that corat- mon hicidence fome of the Rays were more re- fraded and others lefs.. And thole were more refrat^ed in this Prifm wiiich by a greater Re- fradion in the firll Prifm were more turned out of the way, and therefore for their con- ftancy of being more retracted are- defervedly called more refrangible. Expcr. 7. At two holes made near one ano- ther in my Window-flnit I placed two Prifms, one at each, A^^hich might cait upon the 'opp.o- fiteWall (after the manner of the thirdExpe- criment) two oblong cdlour-ed Images' "oF the "Sun. And at a little diitance from the Wall I placed a long llender Paper with llraight and parallel edges, and ordered the Prifms and Pa- per fo, that the red Colour of one Image niight '•fall diredly upon one half of the Paper, and "he violet Colour of the other Image upon the o- ther half of the fame Paper ; lo that the Pa- per appeared of two Colours', red and violet, much after the manner of the painted Paper in the firil and fecond Experiments. Tnen With a black Cloth I covered the Wall behind D 4 the [4o] the Paper, that no Light might be refle(fi:ed from it to diflurb the Experiment , and viewr ing the Paper through a third Prifm held- pa- rallel to it, I faw that half of it which was il- luminated by the violet Light to be divided from the other half by a greater Refradiori, Cr fpecially when I went a good way gff 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 conti^ guous at one of their Angles Hke the painted Paper in the firlt Experiment, Which alfo happened when the Paper was too broad. Sometimes inflead of the Paper I ufed a white Thred, and this appeared through the Prifm divided into two parallel Threds as is reprer fented in the nineteenth Figure, where DG denotes the Thred illuminated with violet Light from D to E and with red Light from F to G, and de fg are the parts of the Thred fcen by Rcfradion. If one half of the Thred be con- ftantly illuminated with red, and the other half be illuminated with all the Colours fuccefTively, ( which may be done by caufing pne of the Prifms to be turned about its Axis whilll the other remains unmoved) this other half in view- ing the Thred through the Prifm, will appear in a continued right Line with the firil half when illuminated with red, and begin to be a little divided from it when illuminated with orange, and remove farther from it when illuminated with yellow, and Hill farther when with green, and farther when with blue, and go yet farther pff when illuminated with indigo, and fartheft W^hcn [4i] when with deep violet. Which plainly iliewsV that the Lights of feveral Colours are more ani more refrangibkjong than (ai)pther, in this or- der of theii^ Colours, red, ordfvge5,yellouVgj;pen,- blue, indigo, deep violet ; ai)4;fo proves; ^^Wj^il' the tirllPropolition as the;fecy>ud^ ..: ..::,,. ij^:^ I G.aufed aUp tl}Q colouj-ed,. Spcclrur^s :: Pol/ [in Fig. 17.'} and MN ma4^ in,a-dark Cham- ber by the Rpfradions of two j^riirhiSfto lye in a right Line end to end, as wasdefcril>e4-abpve in- the fifth. Experiment, iind viewing: them thrpugh a thir^.Prifm held parallel to theic ls^>gthj they appeared no longer in a right Line, })ut became broken from one another, as they ^re; reprefentcjd af.//^ aijd //;.;/, the violet Qndpt pf the Spe6lrum m n being by a greater Refra- jftion tranllated farther from its former place M T than the red end t of the otfier Spcii^trum pi' ./rJ7^'J - -, I farther caufcd thofe two'Spedrums PT £in Ftg. 20.] and MN to become co-incident in an inverted order of their Colours, the red end of each falling on the violet end of the o- ther, as they are reprefented in the oblong Fi- gure P T M N ; and then viewing them through a Prifm DH held parallel to their length, they appeared not co-incident as when viewed with the naked Eye, but in the form of two dillinc^l Spedrums / t and m ;/ croffing one another in the middle after the manner of the letter X. Which iliews that the red of the one Spedrum and violet of the other, which were co-incident at P N and M T, being parted from one another by a greater Refi'adion of thq violet to/ and m than f 42 ] thai! of the red' to;;/'and^,-(ioi differ in degrees of Refrangibility. •-'-- .■'>-; • - -1 i illuminated alfo a little circular piece? of white Paper all over With the Lights of both Prifms intermixed r^nd when it was illumina- ted with the red' of one Spe(?Lrum and ddep violet of the other, fo as by the mixture^of thofe Colours to appear all over purple, I view-l- ed the Paper, firil at a lefs diltoce,- and-theh at a greater, through a third Vviihi ; ^and-^as I went from the Paper, the refraijled Image t-here- of became more anel-more divided by the uMi qual Refraction of: the two Mxe"d> Colours, afld at length parted into two diftincl'Ithages, ii tdA one and a violet one, whereof the violet" Was farthefl from the Paper, arid therefore,; fufFered the greateflRefradion. And when that Prifm at the Window wliich caft the violet on theP^- per was taken away, the violet Image difap- peared; but when the other Prifm was taken away the red vaniflied : which lliews that thefe two Images were nothing elfe than the Lights df the two Prifms which had been intermixed on the purple Paper, but were parted again by their unequal Refradions made in the third Prifm through which the Paper was viewed. This alfo was obfervable , that if one of the Prifms at theWindbw, fuppofe that which caft the violet on the Paper, was turned about its Axis to make all the Colours in this order, vio- let, indigo, blue, green, yellow, orange, red, fall fucceffively on the Paper from that Prifm , the violet Image changed Colour accordingly; turning fucceffively to indigo, blue, green, yel- low [43] low and red, and in changing Colour came' nearer and nearer to the red Image made by the other Prilm, until when it was alibred both Images became fullv co-incident. I placed alio two Paper Circles very near 6ne another, the one in the red Liglit of onePriiirtj and the other in the violet Light of the othcr^. The Circles were each of them an Inch in dia- meter, and behind them the Wall was dark that the Experiment might not be dillurbed by any Light coming from thence. Thefe Circles thus illuminated, I viewed through a Prifm fo heM that the Refradlion might be made towards the red Circle, and as I went from them they camt nearer and nearer together , and' at- length be- came co-incident; and afterwards when I went Hill farther ofti they parted again in a cojitrary order, the violet by a greater Refradion being carried beyong the red. -i>i-« Exper. 8. In Summer when the Sun's Light ufes to be ftrongell, I placed a Prifm at the hole of the Wind ow-lhut, as in the third Expe- riment, yet lb 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 fix Feet and two In- ches from the Book, I placed there the above- mentioned Lens, by which the Light reflefted from the Book might be made to converge and meet again at the diftance of fix Feet and two Inches behind the Lens, and there paint the Species of the Book upon a Iheet of white Pa- per much after the manner of the fecond Ex- periment. The Book and Lens being made fall, I no- [44] I noted the place where the Paper was, when thie Letters of the Book ,, illuminated by the fullell red Light of the folar hnage falling up- on it, did call their Species on that Paper molt diftindly : And then I ftay'd til] by the Motion of the Sun and confequent Motion of his Image on the Book, all the Colours from that red to the middle of the blue pafs'd over thofe Let- ters ; and when thofe Letters were illuminated by that blue, I noted again the place of the Pa- per, when they call their Species moll dillindly upon it : And I found that this lalt place of the i?aper was nearer to the Lens than its former place by about two Inches and an half, or two and three quarters. So much fooner therefore did the Light in the violet end of the Image by a greater Refradion converge and meet, than the Light in the red end. But in trying this the Chamber was as dark as I could make it. For if thefe Colours, be diluted and weak- tied by the mixture of any adventitious Light, the diftance between the places of the Paper will not be fo great. This diltance in the fe- cond Experiment where the Colours of natural Bodies were made ufe of, was but an Inch and an half, by reafon of the imperfedion of thofe Colours. Here in the Colours of the Prifm , which are manifeftly more full, intenfe, and live- ly than thofe of natural Bodies, the dillance is two Inches and three quarters. And were the Colours flill more full, I queftion not but that the dillance would be confiderably greater. For the coloured Light of the Prifm, by the inter- fering of the Circles defcribed in the fecond Figure 45 ] Figure of the fifth Experiment, and alfobythe Light of the ^'ery 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 com- pounded, that the Species which thofe faint and dark Colours, the indigo and violet, cait upon the Paper were not diltinCt enough to be well obferved. Exper. 9. A Prifm, whofe two Angles at its Bale were equal to one another and half, right ones, and the third 2 right one, I placed in a beam of the Sun's Light let into a dark Cham- ber through a hole in the W'indow-ihut as in the third Experiment. And turning the Prifm flovvly about its Axis until all the Light which went through one of its Angles and was refra- fted by it began to be reflected by its Bafe, at which till then it v\x>nt out of the Glafs, I ob- ferved that thofe Rays which had fuffered the greatell Refraction were fooner rcflecfted than the reft. I conceived therefore that thofe Rays of the reflecfcd Light, which were molt re- frangible ^ did tirlt of all by a total Reflexion become more copious in that Light than the reft, and that afterwards the reft alio, by a to- tal Reflexion, became as copious as thefe. To try this, I made the reflected Light pais through another Prifm, and being refracted by it to fall afterwards upon a ilieet of white Paper placed at fome diltance behind it , and there by that* Refradion to paint the ufual Colours of the Prifm. And then caufmg the firlt Prifm to be turned about its Axis as above, I obferved that ' wiien [40 when thofe Rays which in thisPrifm had fuf^ fered the greatellRefradionand appeared of at a blue and violet Colour began to be totally re-* flecled, the blue and violet Light on the Papei? which was moll refrafted in the fecond Prifm received a fenfible increafe above that of the red and yellow, which was lead refrafted ; and afterwards when the rell of the Light which was green, yellow and red began to be totally refleded in the firfl Prifm, the Light of thofe Colours on the Paper received as great an in- creafe as the violet and blue had done before. Whence 'tis manifefl, that the beam of Light refleded by the Bafe of the Prifm, being aug- mented hrll bv the more refrangible Rays and afterwards by the lefs refrangible ones, is com- pounded of Rays diflerently refrangible. And that all fuch refleded Light is of the fame na- ture with the Sun's Light before its Incidence on the Bale of the Prifm, no Man ever doubt- ed : it being generally allowed , that Light by fuch Reflexions fullers no alteration in its Mo- difications and Properties. I do not here take notice of any Refradions made in the fides of the firll Prifm, becaufe the Light enters it per- pendicularly at the firit fide, and goes out per- pendicularly at the fecond fide, and therefore iufFers none. So then, the Sun's incident Light being of the fame Temper and Conflitution with his emergent Light, and the latf being compounded of Rays differently refrangible, the firlt muft be in Uke manner compounded. lllnjtrat'ion. In the twenty firll Figure, ABC is the firfl Prifm, BC its Bafe, B and C its equal [47] equal Angles' at . the , Bafe, each . of 45- Degrees, A its rettanguliir Vertex, F M a beam of the Sun's Light let into a dark Room through a hole F one third part of an hich broad, M its Incidence on the Bale of the Prifm, M G a lefs refraded Ray, M H a more rejraded Ray, MN the beam of Light reflected ; from the Bafe, VX Y the fecond Prifm by which this beam in palling through it is refracted, N^ the lels re- fraded Light of this beam, and N/ the more refra(^l:ed part thereof VV hen the firll Prifm ABC is turned about its Axis according to the order of the Letters ABC, the Rays MH e- mcrge more and more obUquely out of that Prifm , and at length after their mofi: oblique Emergence are reileded towards N, and going on to / do increafe the number of the Rays N/. Afterwards bv continuing the Morion of the firfc Priim, the Rays M G are aUb refleded to N and increaic the number of tiie Rays Nt. And therefore the Light M N admits into its Compofition , firll the more refrangible Rays, and then the lefs refrangible Ravs, and yet af- ter this Compoiition is of the iame nature with the Sun's immediarte Light F M, the PvcHexion of the fpecular Bafe B C caufmg no alteration therein. Efcper. 10. Two Prifms, which were alike in fliape, I tied lo together, that then* Axes and oppoiite bides being parallel, they compofed a Parallelopiped. And, the Sun ihining into my dark Chamber through a little hole in the Win- dow-ftiut, I placed that Parallelopiped in his beam at ibme dillance from the hole, in fuch a - poiture [ 48 ] poflure that the Axes of the Prifnis might Be perpendicular to the incident Rays, and that thole Rays being incident upon the lirlt Side of one Prifm , might go oh through the two contiguous Sides of both Prifms , and emerge out of the laft Side of the fecond Prifm. This Side being parallel to the firfl Side of the firfl Prifm, caufed the emerging Light to be paral- lel to the incident. Then, beyond thefe two Prifms I placed a third, which might refraft that emergent Light , and by that Refradlion call the ulual Colours of the Prifm upon the oppofite Wall, or upon a Iheet of white Papel^ held at a convenient dillance behind the Prifm- for that refrafted Light to fall upon it. After this I turned the Parallelopiped about its Axis, and found that when the contiguous Sides of the two Prifms became fo oblique to the inci- dent Rays that thofe Rays began all of therh to be reflected, thofe Rays which in the third Prifm had fuffered the greatefl Refradion and painted the Paper with violet and blue, were iirft of all by a total Reflexion taken out of the tranfmitted Light, the rell remaining and on the Paper painting their Colours of green, yel- lowy orange, and red as before ; and afterwards by continuing the Motion of the two Prifms, the reft of the Rays alfo by a total Reflexion vanifhed in order, according to their degrees of Refrangibility. The Light therefore which emerged out of the tw^o Prifms is compound- ed of Rays diflerently refrangible, feeing the more refrangible Rays may be taken out of it while the lefs refrangible remain. But this Light [49] Light being trajefted only through the parallel SuperHcies of the two Prifms, if it fuftcr'd any change by the Refradion of one Superficies it loll: that imprcllion by the contrary Refradion of the other Superhcies, and lb being rcllored to its prifline Conllitution became of the lame nature and condition as at firil: before its hici- dence on thofe Prifms ; and therefore, before its Incidence, was as much compounded of Rays differently refrangible, as afterwards. IlliLJiration. In the twenty fecond Figure ABC and BCD are the two Prifms tied toge- ther in the form of a Parallelopiped, their Sides B C and C B being contiguous, and their Sides AB and CD parallel. And HJK is the third Prifm, by which the Sun's Light propagated through the hole F mto the dark Chamber, and there paffing through thofe iidcs of the Prifms AB, BC, CB and CD, is refraded at O tc> the white P^^perPT, falling there partly upon P by a greater Refradion, partly upon T by t lefs Refradion, and partly upon Rand other in- termediate places by intermediate Refradions. By turning the Parallelopiped AC B D about its Axis, according to the order of the Letters Aj C, D, B, at length when the contiguous Planes B C iind C B become fufficiently oblique to' the RaysFM, which are incident upon them atM,- there will vaniih totally out of the refraded Light OPT, tirftofiill the moll refraded Rays OP, (the reft OR and OT remaining as be- fore) then the Rays O R and other intermedi- ate ones, and laftly, theleaft refraded RaysOT- For wh€Fi the Plane B C becomes futhcienrly E oblique - [ 50 ] oblique to the Rays incident upon it , tliole Rays will begin' to be totally refiecled by it to- wards N; and firll the moll refrangible Rays wiTi be totally reflc(^kd (as was explained in the preceding Experiment) and by confcquencc mult lirfl dilappear at P, and afterwards the reil as they are in order totally, rctieded to N, they mull dilappear in the i'ame order at R and T. So then the Rays which at O fuf- fer the greateft Refrac4ion, may be taken out of the Light M O whillt the reil of the Rays remain in it, and therefore that Light MO is. compounded of Rays diflerently refrangi- ble. And becaufe the Planes A Pj and CD are paiialiel, and therefore by equal and con- trary Refradions dcUroy one anothers Ef- fQtis, the incident Light FM mutl be of the fame kind and nature with the emergent Light MO, and therefore doth alfo conlid of Rays differently refrangible. Thefe two Lights F M and jM O, before the moil refrangible Rays arc feparated out of the emergent Light MO, a- gree in colour , and in all other properties fo far as my oblervation reaches, and therefore are defervcdly reputed of the famx nature and confutution, and by confequence the one is compounded as well as the other. But after the moil refrangible Rays begin to be totally rcileded, and thereby feparated out of the e- mergent Light MO, that Light changes its co- lour from white to a dilute and faint yellow, a pretty good orange , a very full red iuccef- iivcly and then totally vanifhes. For after the moft refrangible Rays which paint the Paper at " ■ P with [?l] P with a purple Colour, arc by a total Refle- xion taken out of the beam of Light M O, the refl; of the Colours which appear on the Paper at R and T being mixed in the Light MO compound there a faint yellow , and after the blue and part of the green which appear on the Paper between P and R are taken away, therelfc which appear between R and T (that is the yel- low, orange, red and a little green) being mix- ed in the beam MO compound there an orange ; and when all the Rays are by Reilexion takert out of the beam MO, except the leait refran- gible, which at T appear of a full red, their Colour is the farrie in that beam M O as after- wards at 1\ the Refradion of the Prifm H J K ferving only to feparate the differently refran- gible Rays, without making any alteration iri their Colours, as ihall be more fully proved hereafter. All which confirms as well the tiril Proportion as the fecond. Scljolinm. If this Experiment and the former be conjoined and made one by applying a fourth Prifm VX Y [in Fig. xx.] torefradthe refleft-^ ed beam MN towards r/, the conciufion will be clearer. For then the Light N/ which in the fourth Prifm is more refracted, will become fuller and flronger when the Light O P, which in the third Prifm HJ K is more refracled, va- nilhes at P ; and afterwards wiien the lefs re- fracted Light OT vanifiies at T, the lefs re- fracted Light N t will become ericreafed whiKl the more refraded Light at p receives no far- ther encreafe; And as the trajeded beam MO in vanifhing is always of fuch a Colour as oiight E 2; te^ t52l to refult from the mixture of the Colours which fall upon the Paper PT, fo is the reflc(^kd beam M N always of fuch a Colour as ought to refult from the mixture of the Colours which fall upon the Paper p t. For when the moil refrangible Rays are by a total Reflexion taken out ot the beam M O, and leave that beam of an orange Colour, the Excels of thole Rays in the refie(^kd Light, does not only make the violet, indigo and blue at / more full, but alfo makes the beam MN change from the yellow- ilh Colour of the Sun's Light, to a pale white inclining to blue, and afterward recover its yellovvifli Colour again, fo foon as all the reft of the tranimitted Light MOT is refleded. Now feeing that in all this variety of Expe- riments, whether the Trial be made in Light refleded, and that either from natural Bodies, as in the firll and fecond Experiment, or fpe- cular, as in the ninth ; or in Light refrained, and that either before the unequally refradcd Rays are by diverging feparated frome one an- other, and lofmg their whitenefs which they have altogether, appear feverally of feveral Co-^ lours, as in the tifth Experiment ; or after they are leparaied from one another, and appear co- lour'd as in the iixth, fcventh, and eighth Ex- periments ; or in Light trajeded through paral- lel buperticics, deltroying each others Etfec^ls, as in the tenth Experiment; there are always found Ravs, which at equal Incidences on the fame Alcdium luiier unequal Reflations, and that without any iplitting or dilating of fingle Raysj or contingence in the inequality of the Reira- [53] Refraflions, as is proved in the fifth and fixth Experiments*. And feeing the Rays which dif- fer in Refrangibility may be parted and farted from one another, and that either -by Refra- dion as in the third Experiment, or by Re- flexion as in the tenth , and then the fevcral forts apart at equal Incidences fu'der unequal Refractions, and thofe forts are more refra^rted than others after fcparation, which were more refraded before it, as in the fixth and follow- ing Experiments, and if the Sun's Light be tra- jected through three or more crofs Prifms fuc- cellively, thole Rays which in the tirdPrifm are refrafled more than others, are in all the following Prifms refracted more than others in the fame rate and proportion, as appears by the fifth Experiment ; it's manifcil that the Sun's Light is an heterogeneous mixture of Rays, fome of which are conltantly more re- frangible than others, as was propoled. TROT, in. The OR. III. The Suns Light conjifts of Rays differing in Re- flexibility^ and thofe Rays are more refiexible than others which are more refrangible. THIS is manifeft by the ninth and tentl^ Experiments : For in the ninth Experi- ment, by turning the Prifm about its Axis, un- til the Rays within it which in going out into, the Air were refrafled by. its Bafe, became fo oblique to that Bafe, as to begin to be totally E a refledeci [54] reflefled thereby ; thofe Rays became -firfl of all totally reflected, wnich before at equal In- cidences with the reft had fuftered the greatell Refradlion. And the fame thing happens in the Reflexion made by the common Bafe of the two Prifms in the tenth Experiment. TROT. IV. Prob. I. To feparate from one another the heterogeneous Rays of compound Light. Tf^H E heterogeneous Rays are in fome mea- \^ fure feparated from one another by the Refraftion of the Prifm in the third Experi- ment, and in the fifth Expcrinient by taking a- v/ay the Penumbra from the redilinear fides of the coloured Image, that feparation in thofe ve- ry redilinear lides- or ftraight -edges of the Ir mage becomes perfec^l. But in all places be- tween thofe rectilinear edges, thofe innumera- ble Circles there defcribed, which are fcveral- ly illuminated by homogeneal Rays, by interfe- ring vvith one another, and being every where comimix'd, do render the Light fufhciently compound. But if thefe Circles , whilli: their centers keep their diftances and pofitions, could be made kfs in diameter, their interfering one "with another and by confequence the mixture of the heterogeneous Rays would be propor- tionally diminifiied. In the tv/enty third Figure let AG, BH, CJ,.DK, EL, FM be the Cir- cles which iQ many forts of Rays flowing from the [ 55 ] the fame difqiic of the Sun, do in the third Experiment illuminate ; of all which and in- numerable other intermediate ones lying in a continual Scries between the two rectilinear and parallel edges of the Sun's oblong Image P T, that Image is compofed as was explained in the fifth Experiment. And let ag^ S/j, ci, dk^ el, fm be fo many lefs Circles lying in a like continual Series between two parallel right Lines af'\wd\.gm with the fame diilances be- tween their centers, and illuminated by the iame forts of Rays, that is the Circle ag with the fame fort by which the corrcfponding Cir- cle AG was illuminated, .and the Circle bb with the fame fort by which the corrcfponding Circle BEI w^as illuminated, and the rell: of the Circles f /*, dk, el, fni refpeCtivcly, with the fame forts of Rays by which the fever al corrc- fponding Circles Cj,"DK, EL, FM were il- luminated. In the Figure P T compofed of the greater Chxles, three of thofe Circles AG, BH, C J, are fo expanded into one another, that the three forts of Rays by which thofe Circles are illuminated , together with other innumerable forts of intermediate Rays, are mixed at QR in the middle of the Circle B H. And the like mixture happens throughout almod the whole length of the Figure P T. But in the Figure pt compofed of the lefs Circles, the three lefs Circles ag, b h, c i, which anfwer to thofe three greater, do not extend into one another; nor are there any where mingled fo m.uch as any two of the three forts of Rays by which thofe E 4 Circles [50 Circles are illuminated , and which in the Fi- gure PT are all of them intermingled at B H. Now he that fhall thus confider it, will eafily underltand that the mixture is diminiilicd 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 ; if ten times lefs, the mixture will be ten times lefs, and fo of other propor- tions. That is, the mixture of the Rays in the greater Figure PT will be to their mixture iri the lefs / ^, as the Latitude of the greater Fi- gure is to the Latitude of the lefs. For the Latitudes of thefe Figures are equal to the Di- ameters of their Circles. And lience it caiily follows, that the mixture of the Rays in the re- frafted Speftrum / r is to the mixture of the Rays in the direft and immediate Ligtit of the Sun, as the breadth of that Speclrum is to the diflerence between the length and breadth of the fame Spectrum. So then , if we would diminifh the mixture of the Rays , we are to diminiih the Diameters of the Circles. Now thefe would be diminifli- ed if the Sun's Diameter to which they anfwer could be made lefs than it is, or (which comes to the fame purpofe ) if without doors , at a great diilance from the Prifm towards the Sun, lome 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 pals through that [ 57 ] t\nt hole to the Prifm. For fo the Circles AG, BH and the reU, would not any longer anl'wcr to the whofe Dilque of the Sun, but only to that part of it which could be Jeen from the Prilm through that hole , that is to the appa- rent magnitude of that hole viewed from the Prifm. But that thefe Circles may anfwer more diftindly to that hole, a Lens is to be placed by the Prifm to call the Image of the hole, (that is, everyone of the Circles AG, BPI, &c.) di- Itindly upon the Paper at PT, after fuch a manner as by a Lens placed at a W indow the Species of Objeds abroad arc cail diitinCtly up- on a Paper within the Room, and the redili- near Sides of the oblong folar Image in the fifth Experiment became dillind without any Pen- umbra. If this be done it will not be nccefia- ry to place that hole very far off, no not beyond the \V indow. And therefore initead of that hole, I ufed the hole in the Window-ihut as follows. Exper, II. In the Sun's Light let into my darkned Chamber through a fmall round hole in my Window- fhut, at about ten or twelve Feet from the Window, I placed a Lens, by which the Image of the hole might be dillinft- ly call upon a Sheet of white Paper, placed at the diflance of fix, eight, ten or twelve Feet from the Lens. For according to the diffe- rence of the Lenfes I ufed various diilances, which I think not worth the v^hile to defcribe. Then immediately after the Lens I placed a Prifm, by which the trajec'led Light might be refraded either upwards or Tideways, and there- by [58] by the round Image which the Lens alone did cafl upon tlie Paper might be drawn out into a long one with parallel Sides, as in the third Ex- periment. This oblong Image I let fall upon another Paper at about the (iam.e didance from the Priim as before, moving the Paper either' towards the Prifm or from it, until I found the juil diflance where the reciilinear Sides of the image became moil diflind. For in this cafe the circular Images of the hole which compofe that Image after the fame manner that the Cir- cles ^?^, bh^ r/', &c. do the Figure/^ \mFig. a-3.] were terminated moil diitinftly without any Penumbra, and therefore extended into one another the lead that they could, and by confcquence the mixture of the heterogeneous Rays was now the Icail of all. By this means I uled to form an oblong Image (luch as is/^) [iniv^. 23, and 24.] of circular Images of the hole (fuch as are ag^ bh^ ci^ &:c.) and by u- iing a greater or lefs hole in the Window-ihut, I made the circular Images ag^ bh^ c i, &c. of which it was formed, to become greater or lefs at pleafure, and thereby the mixture of the Rays in the Iniage / ^ to be as much or as lit- tle as I defired. Illnftrat'wn. In the twenty fourth Figure, F reprcicnts the circular hole in the W indow- iliut, MN the Lens whereby the Image or Spe- cies of that hole, is call diitindly upon a Paper at J, ABC the Prifm whereby the Rays are at their emerging out of the Lens refraded from J towards another Paper at / ^, and the round Image at J is turned into an oblong Image / 1 falling S9 ] Ming on that other Paper. This Image/ /'con- flits of Circles placed one after another in a rc- ,6tilincar order, as was fuiiicienily explained in the fifth Experiment; and thefe Circles are e- qual to the Circle J, and conlcquently anfwer in magnitude to the hole F ;. and therefore by diminiihing that hole they may be at pleafure diminiihed, whilil their Centers remain in their places. By this means I m.ade the breadth of the Image / r to be forty times, and fometimes fixty or feventy times lefs than its length; As for inflance, if the breadth of the hole F be one tenth of an Inch, and MF the diilance of the Lens f -om the hole be ii Feet? and if/B or / Mthe di- ilance of the Image / t from the Prifm or Lens be lo Feet, and the refra6i:ing Angle of the Prifm be 61 Degrees, the breadth of the L mage / / will be one twelfth of an Inch and the length about fix Inches, and therefore the length to the breadth as 71 to i, and by confe- quence the Light of this Image 71 times lefs compound than the Sun's diredri: Light. And Light thus fir fimple and homogeneal, is fulH- cicnt for trying all the Experiments in this Book •about iimple Light. For the compofition of -heterogeneal Rays is in this Light fo little that it is fcarce to be difcovered and perceived by Senfe, except perhaps in the indigo and. vio- let. For thele being dark Colours, do eafily .fuffer a fenfible allay by that little fcattering Light which ufes to be reft-acf ed irregularly by the inequalities of the Priiin. Yet inflead of the circular hole F, 'tis better to fubftitute an oblong hole ihaped like a- lontr ParaU I^o] Parallelogram with its length parallel to the Priim 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 /i^ will beas fin^ple as before, or fimpler, and the Image will become much broader, and therefore more fit to have Experiments tried in its Light than before. Inilcad of this parallelogram hole may be fub- llituted a triangular one of equal Sides, whofe Bale for inllance is about the tenth part of an Inch, and its height an Inch or more. For by this means, if the Axis of the Prhm be parallel to the Perpendicular of the Triangle, the Image ft [in Fig. zf.] will now be formed of equi- crural Triangles ag^ bh^ cl, dk^ el^ fm, ike, and innumerable other intermediate ones an- fwering to the triangular hole in fliape and big- nefs, and lying one after another in a continual Series between two parallel Lines Rays, [89] Rays, its breadth in an loo Foot Telefcope whofe aperture is 4 Inches would be but A^^ - ■T -~ 720CC000 parts of an Inch, as is manifefl by the foregoing computation. And therefore in this cafe the greatell Errors ariiing from the fpherical Figure of the Glafs, would be to the greatell fenlible Errors arifmg from the different Refrangibility of the Rays as -— ^ to -^ at mod, that is on- ly as I to ixoo. And this ful^cicntlyfliews that it i:, not the fpherical figures of Glallls but the diucrent Refrangibility of the Rays which hin- ders 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 imperfection of Tele- fcopes. For the Errors of the Rays arifing from the fpherical Figures of Objeft-glalTes, are as the Cubes of the Apertures of the Objed- glafies ; and thence to make Telefcopes of va- rious lengths 5 magnify with equal diilinftnefs, the Apertures of the Objed-glafTes, and the Charges or magnifying Powers, ought to be as the Cubes of the fquare Roots of their lengths ; which doth not anfwer to experience. But the Errors of the Rays arifing from the different Refrangibility, are as the Apertures of the Ob- jed-glaffes, and thence to make Telefcopes of various lengths, magnify with equal diiHnchiefs, their Apertures and Charges ought to be as the fquare Roots of their lengths ; and this anfwers to experience, as is well known. For inttance, a Telefcope of 64 Feet in length, with an Aper- ■' ture I^o] ture of 1-} Inches, magnifies about iio times, with as much diltindnefs as one of a Foot in length, with -} of an Inch aperture, magnifies 15 times. Now were it not for this different Refrangi- bility of Rays, Telefcopes might be brought to a greater perfection than we have yet defcrib'd, by compofmg the Objed-Glafs of two GlalTes with Water between them. Let ADFC [in F/g. 28.] reprefenttheObjeft-glafscompofedoftwo Glaffes ABED and BEFC, alike convex on the outlidcs AGD and CHF, and aUke concave on the infides BME, BNE, with Water in the concavity BMEN. Let the Sine of Inci- dence out of Glafs into Air be as I to R, and out of Water into iVir as K to R, and by con- fequence out of Glafs into Water, as I to K : and let the diameter of the Sphere to which th» 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 K K — K I to the Cube Root of RK — RI: and the Refradions^ on the concave fides of the Glafles , will very much corre<^t the Errors of the Refraftions on the convex fides , fo far as they arife from the fphericalnefs of the Figure. And by this means might Telefcopes be brought to fufficient per- fedion, were it not for the different Refrangi- bility of feveral forts of Rays. But by reafon of this different Refrangibility, I do not yet fee any other means of improving Telefcopes by Refradions alone than that of increafing their lengths, for which end the late Contrivance of [91] Hngenius feems well accommodated. For ve- ry long Tubes arc cumberlbme, and fcarcc to be readily managed , and by reafon of their length are very apt to bend, and ihake by bend- ing lb as to caule a continual trembling in the Objects, whereby it becomes difficult to fee tiiem diilindly: whereas by his contrivance the Glalles are readily manageable, and the Object- glafs being fix'd upon a llrong upright Pole be- comes more Heady. Seeing therefore the Improvement of Tele- fcopes of given lengths by Refractions is defpe- rate ; I contrived heretofore a Perfpe(^tive by Reflexion , ufmg inflead of an Objed-glafs a concave Metal. The diameter of the Sphere to which the Metal was ground concave was a- bout if Engliih Inches, and by conlcquence the length of the Inlhument about iix Inches and a quarter. The Eye-glal's was Plano-con- vex, and the diameter of the Sphere to which the convex fide was ground was about 4 of an Inch , or a little lefs , and by confequence it magnified between 30 and 40 times. By ano- ther way of meafuring I found that it magnified about 35" times. The concave Metal bore an Aperture of an Inch and a third part ; but the Aperture was limited not by an opake Circle, covering the Limb of the Metal round about, but by an opake Circle placed between the Eye- glafs and the Eye, and perforated in the mid- dle with a little round hole for the Rays to pafs through to the Eye. For this Circle by being placed here, Itopp'd much of the erroneous Light 5 which otherwife would have dilbjrbed the [92] the Vifion. By comparing it with a pretty good PerfpecHve of four Feet in length, made with a concave Eye-glafs, I could read at a greater diftance with my own Infh-ument than with the Glafs. Y6t Objeds appeared much darker in it than in the Glafs, and that partly becaufe more Light was loil by Reflexion in the Metal, than by Refraction in the Glafs, and partly be- caufe my Inilrument was overcharged. Had it magnified but ^o or 25- times it would have made the Objeft appear more brisk and plea- fant. Two of thel'e I made about 16 Years a- go, and have one of them ilill by me by which I can prove the truth of what I write. Yet it is not fo good as at the firll. For the concave has been divers times tarniihcd and cleared a- gain,by rubbing it with very foft Leather. W hen I made thefe, an Artift in London undertook to imitate it ; but ufmg another way of polifliing them than I did , he fell much fliort of what I had attained to, as I afterwards underllood by difcourfmg the under Workman he had em- ployed. The Poliih I ufed was in this man- ner. I had two round Copper Plates each fix Inches in diameter, the one convex the o- ther concave, ground very true to one another. On the convex I ground the Objeft-Metal or Concave which was to be poliili'd, till it had taken the Figure of the Convex and was ready for a PoHlh. Then I pitched over the convex very thinly, by dropping melted Pitch upon it and warming it to keep the Pitch foft, whilft I ground it with the concave Copper wetted to make it fpread eavenly all over the convex. Thus Thus by working it well I made it as thin as a Groat, and after the convex was cold I ground it again to give it as true a Figure as 1 could. Then I took Putty which I had made very fine by ^^"afl^ing it from all its groiler Particles, and laying a little of this upon the Pitch, I ground it upon the Pitch with the concave Copper till it had done making a noife ; and then upon the Pitch I ground the Object-Metal with a brisk motion , for about two or three Minutes of time, leaning hard upon it. Then I put frelli Putty upon tjie Pitch and ground it again till it had done making a noiic,and aUerwarci;^ ground the Objed-Metal upon it as before. And this Work I repeated till the Metal was poliihed, grinding it the lall time with all my Ibength for a good while together, and frequently breathing upon the Pitch to keep ic moilt with- out laying on any more freih Putty. The Ob- jed-?vletal v> as 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 polillied them both I tried which was bell, and ground the other again to fee if I could make it better than that which I kept. And thus by many Trials I learn'd the way of po- lifhing, till I made thofe two receding Peripe- dives I {pake of above. For this Art of po- Hilling will be better learn d by repeated Pra- ctice than by myDefcription. Before I ground the Object-McLal on the Pitch, 1 always ground the Putty on it with the concave Copper till it had done making a noife , becaufe ii the Parti- cles of the Putty were not by this means made to [n] to flick faft in the Pitch, they would by rolling up and down grate and fret the Objed-Metal and fill it full of little holes. But becaufe Metal is more difficult to poliili than Glafs, and is afterwards very apt to be fpoilcd b}' tarnilhing, and refleds not fo much Light as Glafs quick-filver'd over does : I would propound to ufe inltead of the Metal, a Glafs ground concave on the forefide, and as much convex on the back-fide, and quick-filver'd o- ver on the convex iide. The Glafs muft be e- very where of the fame thicknefs exadly. O- therwife it will make Objects look colour'd and indillinft. By fuch a Glals I tried about five or fix Years ago to make a receding Telcfcope of four Feet in length to magnify about 15-0 times, and I fatisfied my felf that there wants nothing but a good Artill to bring the Defign to perfe- dion. For the GMs being wrought by one of our London Artills after fuch a manner as they grind Glafles for Telefcopes, tho' it feemed as well wrought as the Objeclil-glaires ufe to be, yet when it was quick-filver'd, the Reflexion dif- covered innumerable Inequalities all over the Glafs. And by reafon of thefe hiequaUties, Ob- jeds appeared indiilinCt in this hiilrument. For the Errors of retteded Rays caufed by any In- equality of the Glafs, are about fix times great- er than the Errors of refrafted Rays cauicd by the Hke 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, did no fenfible prejudice to it, and by conlequence that nothing is wanting to [95] to peifecl thcfe Tclefcopes, but good Work- men who can grind and polifli GlalFes truly fphericaL An Object-glafs of a fourteen Foot Telcfcopej made by an Artificer at London^ I once mended coniiderably, by grinding it on Pitch with Putty, and leaning very eafily on it in the grinding, ielt the Putty ihould fcratch it. Whether this way may not do well enough for pohihing thefe relieving Glaires, I have not yet tried. But he that fhall try either this or any other way of polilhing which he may think bet- ter, may do well to make his Glalles ready for polilhing by grinding them without that vio- lence, wherewith our London Workmen prcfs their Glalles in grinding. For by I'uch violent preflure, Glalles arc apt to bend a little in the grinding, and inch bending will certainly fpoii their Figure. To recommend therefore the confidcration of thefe reiiccting Glalles, to fuch Artills as are curious in figuring Glailes, I iliall delcribe this optical Inltrument in the follow- ing Propolition. T ROT. vn. Prob. n. To fl.wrten Telefto^es, LET ABDC {inF'ig. 29.] reprefent a Glafs fpherically concave on the forefide AB, ana as much convex on the backfide CD, fo that it be every where of an equal thicknefs. Let it notjae thicker on One fide than on the other, left it make Objeds appear colour'd and ^ indi- [9^ indiflindl, and let it be very truly wrought and quick-filver'd over on the backlide ; and f^:t in the Tube V X Y Z which mult be very black within. Let EFG reprctent a Prifm of Glals or Cryrtal placed near the other end of the Tube, in the middle of it, by means of a han- dle of Brafs or Iron FGK, to the end of which made flat it is cemented. Let this Prifm be rectangular atE, and let the other two Angles at F and G be accurately equal to each otner, . and by confequence equal to half right ones, and let the plane fides F E and G E be fquare, and by confequence the third fide F G a rectan- gular Parallelogram, whofe length is to its breadth m a fubdupUcate proportion of two to one. Let it be fo placed in the Tube, that the A^^is of the Speculum may pals through the middle of the fquare fide EF perpendicularly, and by confequence through the middle of the fide F G at an Angle of 45- Degrees, and let the fide E F be turned towards the Speculum., and the diftance of this Prifm from the Speculum be fuch that the Rays of the Light PQ, RS, ^c. •which are incident upon the Speculum in Lines parallel to the Axis thereof, may enter thePrilm at the fide EF, and be reflected by the fide FG, and thence go out of it through the fide GE, to the point T which mutt be the com- mon Focus of the Speculum ABDC, and of a Plano-convex Eye-glafs H, through which thofe Rays mult pafs to the Eye. And let the Rays at their coming out of the Glals pafs through a fmall round hole, or aperture made in a lit- tle plate of Lead, Brafs, or Silver, wherewith the [^7] the Glafs is to be covered, which hole mud be no bigger than is necellary for Light enough to pals through. For ib it will render the Ob- ject dillin(^i:, the Plate in which 'tis made inter- cepting all the erroneous part of the Light which comes from the verges of the Speculum A B. Such an Inltrument well made , if it be fix Foot long, (reckoning the length from the Speculum to the Priim, and thence to the I'o^ cus T) will bear an aperture of fix Inches at the Speculum, and magnify between two and three hundred times. But the hole H here limits the aperture with more advantage, than if the aperture was placed at the Speculum. If the Inlh-ument be made longer or Ihorter, the aper- ture mult be in proportion as the Cube of the fquare-iquare Root of the length, and the mag- nifying as the aperture. But it's convenient that the Speculum be an Inch or two broader than the aperture at the leall, and that the Glafs of the bpeculum be thick, that it bend not in the working. ThePrilm EFG muft be no bigger than is necellary, and its back fide F G mult not be quick-Tilver'd over. For without quick- filver it will relied all the Light incident on it from the Speculum. In this Inlb'ument the Objed: will be invert- ed , but may be ereded by making the fquare fides E F and EG of the Prifm EFG not plane but fpherically convex, that the Rays may crofs as well before they come at it as afterwards between it and the Eye-glafs. If it be defired that the Inllrument bear a larger aperture, that H may 1 58 1 may be alfo done by compofingvthe" Speciilum of two Glailes with Water between them. If the Theory of making Telefcopes could at length be fully brought into praftice, yet there would be certain Bounds beyond which Tele- fcopes could not perform. For the Air through which; w„e look upon the Stars, is in a perpe- tual Tremor ; as may be feen by the tremulous Motion of Shadows caft from high Towers, and by the twinkling of the fix'd Stars. But thefe Stars do not t\\ inkle when viewed through Telefcopes which have large apertures. For the Rays of Light which pafs through divers parts of the aperture, tremble each of them a- part, and by means of their various and fome- times contrary Tremors , fall at one and the fame time upon different points in the bottom of the Eye, and their trembling Motions are too quick and confufed to be perceived feverally. And all thefe illuminated Points conflitute one broad lucid Point , compofed of thofe many trembhng Points confufedly and infenfibly mix- ed with one another by*very fliort and fwift Tremors, and thereby caufe the Star to appear broader than it is, and without any trembling of the whole. Long Telefcopes may caufe Ob- jeds to appear brighter and larger than fhort ones can do , but they cannot be fo formed as to take away that confufion of the Rays which arifes from the Tremors of the Atmofphere.- The only remedy is a mod ferene and quiet Air, fuch as may perhaps be found on the tops of the higheft Mountains above the groffer Clouds. THE ^, Bookl.Ri-tlBatcI. kl.Paitl.BateJL -^ Book I.Rrtl.Plafe m. J^tg 16 w BoollPaitI.Hatel\' ;e a o ^ THE FIRST BOOK OPTICKS. PART II. TROT, I. Theor. I. The ThanoTiiena of Colours in refraBed or re^ fleBed Light are not can fed by new Modijl- cations of the Light varioujly imPrefs'dy ac^ cording to the -various Terminations of the Light and Shadozv, The Proof by Experiments. Exper. iv^^^fjOR if ±e Sun fhine into a very dark Chamber through an oblong hole F, VmFig. i.] whale breadth is the fixth or eighth part of an Inch, or fomething lefs ; and his beam F H do afterwards pafs Ml through a H X very [ loo ] vei7 large Prifm ABC, diftant about xo Feet from the hole, and parallel to it, and then (with its white part) through an oblong hole H, whofe breadth is about the fortieth or fixtieth part of an Inch, and which is made in a black opake Body G I, and placed at the diflance of two or three Feet from the Prifm, in a parallel Situa- tion both to the Prifm and to the former hole, and if this w^hite Light thus trafmitted through the hole H, fall afterwards upon a white Paper / r, placed after that hole H, at the dilfance of three. or four Feet from it, and there paint the ufual Colours of the Prifm, fuppofe red at t^ yellow at j, green at r, blue at ^, and violet at/; you may with an Iron Wire, or any fuch like flender opake Body, whofe breadth is a- bout the tenth part of an Inch, by intercepting the Rays at k^ /, w, 7tox o, takeaway any one of the Colours at ty /, r, q or/, whilll: the other Colours remain upon the Paper as before ; or with an Obftacle fomething bigger you may take away any two, or three, or four Colours together, the reil remaining : So that any one of the Colours as well as violet may become outmpft in the Confine of the Shadow towards /, and any one of them as well as red may be- come outmofl in the Confine of the Shadow towards t, and any one of them may alfo bor- der upon the Shadow made within the Colours by the Obilacle R intercepting fome interme- diate part of the Light ; and, laftly, any one of them by being left alone may border upon the Shadow on either hand. All the Colours have themfeives indifferently to any Confines of Sha- dow, [ loi ] dow, and therefore the differences of thefe Co- lours from one another, do not arife from the different Confines of Shadow, whereby Light is variouily moditied , as has hitherto been the Opinion of Philofophers. In trying thefe things 'tis to be obferved, that by how much the holes F and H are narrower, and the Intervals be- tween them, and the Prifm greater, and the Chamber darker, by fo much the better doth the Experiment fucceed ; provided the Light be not fo far diminiflied, but that the Colours 2Lt ptbe fufficiently vifible. To procure a Prifm of folid Glafs large enough for this Experiment will be difficult, and therefore a prifmatick Veircl mull be made of polifli'd Glafs Plates ce- mented together, and filled with fait Water or clear Oil. Exper. z. The Sun's Light let into a dark Chamber through the round hole F, [in Fig.^^ half an Inch wide, paifed firll through the Prifm ABC placed at the hole, and then through a Lens P T fomcthing more than four Inches broad , and about eight Feet dillant from the Prifm , and thence .converged to O the Focus of the Lens diltant from it about three Feet, and there fell upon a white Paper DE. If that Paper was perpendicular to that Light incident upon it, as 'tis reprefcnted in the polture DE, all the Colours upon it at O appeared white. But if the Paper being turned about an Axis parallel to the Prifm, became very much incli- ned to the Light as 'tis reprefented in the Po- fitions de and h\ the fame Light in the one cafe appeared yellow and red, in the other blue. H 3 Here [ 102 ] Here one and the fame part of the Light in one and the fame place, according to the va- rious Inchnations of the Paper, appeared in one cafe white, in another yellow or red, in a third blue, whilit the Confine of Light and Shadow, and the Refractions of the Priim in all thefe ca- fes remained the fame. Exper. 3. Such another Experiment maybe more eafily tried as follows. Let a broad beam of the Sun's Light coming into a dark Cham- ber through a hole in the Window-fliut be re- fracted by a large Prifm ABC, [in Fig. 3.] whofe refrading Angle C is more than 60 De- grees, and io foon as it comes out of the Prifm let it fall upon the white Paper DE glewed up- on a ftiii' Plane ; and this Light, when the Pa- per is perpendicular to it, as 'tis reprefented in DE, will appear perfedly white upon the Pa- per, but when the Paper is very much inclin'd to it in fuch a manner as to keep always paral- lel to the Axis of the Prifm, the whitenefs of the whole Light upon the Paper will according to the inclination of the Paper this way or that way, change either into yellow and red, as in the polture de^ or into blue and violet, as in the poilure ^g. And if the Light before it fall upon the Paper be twice refraded the fame way by two parallel Prifms, thefe Colours will become the more confpicuous. Here all the middle parts of the broad beam of white Light which fell upon the Paper, did without any Confine of Shadow to modify it , become co- lour'd all over with one uniform Colour , the Colour being always the fame in the middle of the [ 103 the Paper as at the edges, and this Colour chan- ged according to the various ObUquity of the reiicding Paper, without any change in the Re- fractions or Shadow, or in the Light which fell upon the Paper. And therefore theie Colours are to be derived from fome other Caufe than the new Modifications of Light by Refraftions and Shadows. If it be asked. What then is their Caufe ? I anfwer, That the Paper in the pofture de, be- ing more oblique to the more refrangible Rays than to the leis refrangible ones, is more flrong- ly illuminated by the latter than by the former, and tliereforc the lefs refrangible Rays are pre- dominant in the refleded Light. And where- ever they are predominant in any Light they tinge it with red or yellow, as may in fome mea- fure appear by the Hrlt Propolition of the tirft Book, and will more fully appear hereafter. And the contrary happens in the pofture of the Paper h^ the more refrangible Rays being then predominant which always tinge Light with blues and violets. Ex per. 4. The Colours of Bubbles with which Children play are various, and change their Si- tuation varioufly, without any refped to any Confine of Shadow. If fuch a Bubble be co- ver'd with a concave Glafs, to keep it from be- ing agitated by any Wind or Motion of the Air, the Colours will llowly and regularly change their Situation, even whilit the Eye, and the Bubble, and all Bodies which emit any Light, or call any Shadow, remain unmoved. And therefore their Colours arife from fome regular H 4 caufe [ I04 ] Caufe which depends not on any Confine of Shadow. What this Caufe is will be fliewed in the next Book. To thefe Experiments may be added the tenth Experiment of the firit Book, where the Sun's Light in a dark Room being traje61ed through the parallel Superhcies of two Prifms tied together in the form of a Parallelopipede, became totally of one uniform yellow or red Colour, at its emerging out of the Prifms. Here, in the production of thefe Colours, the Confine of Shadow can have nothing to da. For the Light changes from white to yellow, orange and red fucceirively, without any alte- ration of the Conhne of Shadow : And at both edges of the emerging Light where the con- trary Confines of Shadow ought to produce different Efteds, the Colour is one and the fame, whether it be white, yellow, orange or red: And in the middle of the emerging Light, where there is no Confine of Shadow at all, the Colour is the very fame as at the edges, the whole Light at its very firlt Emergence being of one uniform Colour, whether white, yellow, orange or red, and going on thence perpetual- ly without any change of Colour, fuch as the Confine of Shadow is vulgarly fuppofed to work in refraded Light after its Emergence. Nei- ther can thefe Colours arife from any new Mo- difications of the Light by Refractions, becaufe they change fucceflively from white to yellow, orange and red , while the Refradions remain the fame, and alfo becaufe the Refradions are made contrary ways by parallel Superficies which deitroy [105] deflroy one anothers Effccls. They arife not therefore from any Moditications of Light made by Refractions and Shadows, but have fome o- ther cauic. What that Caufe is we ihewed a- bove in this tenth Experiment, and need not here repeat it. There is- yet another material circumllance of this Experiment. For this emerging Light being by a third Prifm HIK [in Fig. 21. Tart i.] refracted towards the Paper FT, and there paint- ing the ufual Colours of the Prifm, red, yellow, green, blue, violet: If thele Colours arofe from the Refradions of that Prifm modifying the Light, they would not be in the Light before its Incidence on that Prifm. And yet in that Experiment we found that when by turning the two tiril: Prifms about their common Axis all the Colours were made to vaniih but the red; the Light which makes that red being left alone, appeared of the very fame red Co- lour before its Incidence on the thii-d Prifm. And in general we find by other Experiments ' that when the Rays which ditl^er in Refrangibi- lity are feparared from one another, and any one fort of them is confidered apart, the Co- lour of the Light which they compofe cannot be changed by any Refraction or Reflexion vv'hatever, as it ought to be were Colours no- thing elfe than Modifications of Light caufed by Refractions, and Reflexions, and Shadows. This unchangeablenefs of Colour I am now to defcribe in the following Propofition. "PROT. [ 10^ ] :.; TROT. II. The OR. IL j^ll'ho'mogeneai Light has its proper Colour an- fwertJig to its '\D'egrce of Refrangtbility^ and ■ that Colour cannot be changed by Reflexions and Refractions. IN the Experiments of the fourth Propofition of the hrft Book, when Ihad feparated the heterogeneous Rays from one another, theSpe- ^um / 1 formed by the feparated Ra^^s, did in the progrefs from its end / , on which the moll refrangible Rays fell, unto its other end ^, on which the leall refrangible Rays fell, appear tinged with this feries of Colours, violet, indi- go, blue, green, yellow, orange, red, together with all their intermediate degrees in a conti- nual Succeilion perpetually varying. So that there appeared as many degrees of Colour^,, as there were forts of Rays differing in Refrangi- bility. Exper. f. Now that thefe Colours could not be changed byRefracHon, I knew by refrading with a Prifm fomerimes one very little part of this Light, fometimes another very little part, as is defcribed in the twelfth Experiment of the firft Book. For by this Refraction the Co- lour of the Light was never changed m the leali. If any part of the red Light was refra(^ted, it remained totally of the fame red Colour as be- fore. No orange, no yellow, no green or blue, no other new Colour was produced by that Refradion. Neither did the Colour any ways change by repeated Refradions, but continued always [ I07 ] dways the fame red entirely as at firft. The like conltancy and immutability I found alfo in the blue, green, and other Colours. So alio it' I looked through a Prii'm upon any Body illu^ minated with any part ol' this homogeneal Light, as in the fourteenth Experiment of the firil Book is defcribed ; I could not perceive any new Co- lour generated this way. All Bodies illumina- ted with compound Light appear through Prilms confuied (as was laid above) and tinged w4th various new Colours, but thole illuminated with homogeneal Light appeared through Prilms neither lefs diilincl, nor otherwife colour'd , than when viewed with the naked Eyes. Their Colours were not in the lealt changed by the Refraction of the intcrpofed Prii'm. I fpeak here of a feniiblG change of Colour: Eor the Light which I here call homogeneal, being not ablolutely homogeneal , there ought to arife lb me little change of Colour from its hetero- geneity. But if that heterogeneity was fo lit- tle as it might be ma'de by the faid Experiments of the fourth Propofition, that change was not fenliblc, and therefore in E.xperiments, where Senle is Judge, ought to be accounted none at all. Exper. 6. And as thefe Colours were not changeable byRefradions, fo neither were they by Reflexions. For all white, grey, red, yel- low, green, blue, violet Bodies, as Paper, Alhes, red Lead, Orpiment, Indico, Bife, Gold, Sil- ver, Copper, Grafs, blue Flowers, Violets, Bubbles of Water tinged with various Colours^ Peacock's Feathers, the Tincture of Lignum Nepbri- [io8] Nepkriticttm^ and fuch like, in red homogeneal Light appeared totally red, in blue Light to- tally blue, in green Light totally green, and lb of other Colours. In the homogeneal Light of any Colour they all appeared totally of that fame Colour, with this only ditference, that fome of them refleded that Light more Itrong- ly, others more faintly. I never yet found any Body which by reflefting homogeneal Light could fenfibly change its Colour. From all which it is manifeft, that if the Sun's Light confifted of but one fort of Rays, there would be but one Colour in the whole World, nor would it be polTible to produce any new Colour by Reflexions and Refraftions, and by confequence that the variety of Colours de- pends upon the compofition of Light. 7>EF1NITI0K TH E homogeneal Light and Rays which appear red , or rather make Objeds ap- pear fo, I call Rubriiic or Red-making ; thofe which make Objeds appear yellow, green, blue and violet, I call Yellow-making, Green-ma- king, Blue-making, Violet-making, and fo of the reft. And if at any time I fpeak of Light and Rays as coloured or endued with Colours, I would be underftood to fpeak not philofo- phically and properly, but groffly, and accor- dingly to fuch Conceptions as vulgar People in feeing all thefe Experiments would be apt to frame. For the Rays to fpeak properly are not coloured. In them there is nothing elfe than a certain [ 109 ] certain power and dilpoiition to flir up a Sen- fation of this or that Colour. For as Sound in a Bell or mufical String, or other founding Bo- dy, is nothing but a trembling Motion, and in the Air nothing but that Motion propagated from the Objed:, and in the Senforium 'tis a Senfe of that Motion under the form of Sound ; fo Colours in the Objed are nothing but a Dif- polition to refled this or that fort of Rays more copioully than the. reft; in the Rays they are nothing but their Difpofitions to propagate this or that Motion into the Senforium, and in the Senforium they are Senfations of thofe Motions under the forms of Colours. TROT. m. Prob. I. To define the Refrangibility of the feveral forts of homogeneal Light avfjuering to the feve- ral Colours. FO R determining this Problem I made the following Experiment. Exper. 7. When I had caufed the rectili- near fides AF, GM, [in Fig. 4.] of the Spe- 6lrum of Colours made by the Prifm to be di- ftindly defined , as in the fifth Experiment of the firil Part is defcribed, there were found in it all the homogeneal Colours in the fame or- der and fituation one among another as in the Spedrum of fimple Light, defcribed in the fourth Propofition of tliat Part. For the Cir- cles of which the Spedrum of compound Light PT [i.o] PT is compofed, and which in the middle parts of the Spedrum interfere and are intermix'd with one another, are not intermix'd in their outmolt parts where they touch thofe redili- near fides A F and G M. And therefore in thofe redilinear fides when diflindly defined, there is no new Colour generated by Refra- ction. I obferved alfo, that if any where be- tween the two outmoft Circles T M F and PGA a right Line, as y'^\ was crofs to the Spe61rum, fo as at both ends to fall perpendi- cularly upon its redilinear iides, there appear- ed one and the fame Colour and degree of Co- lour from one end of this Line to the other. I delineated therefore in a Paper the perimeter of the Spedrum FA P GMT, and in trying the third Experiment of the firft Book, I held the Paper fo that the Speflrum might fall upon this delineated Figure, and agree with it exact- ly, whilflanAtFiltant whofeEyes for diftinguifh- ing Colours were more critical than mine, did by right Lifies *,/3, y^, e^, ^c. drawn crofs the Speftrum , note the Confines of the Colours, that is of the red M ^ /3 F, of the orange oLy^Bf of the yellow yi(^, of the green g-/? ^ 5 of the blue yjt)c&, of the indico iAi^k, and of the vio- let A G A jLt. And this Operation being divers tinies repeated both in the fame and in feveral Papers , I found that the Obfervations agreed well enough with one another, and that the rectilinear fides MG and FA were by the faid crofs Lines divided after the manner of a mu- fical Chord. Let GM be produced to X, that MX may be equal to GMj and conceive GX [ III ] GX, aX, iX, ^X, eX, yX, uX, MX, to be in proportion to one another, as the numbers, i» 4j h 4> h'U-^y-^y and lb to reprefent th^ Chords of the Key, and of a Tone, a third Mi- no]-, a fourth, a fifth, a lixth Major, a feventh and an eighth above that Key : And the Inter- vals Met, oLy,yey f>j, >? t, 7f7i'> 78, the Sines of Refradion of thof^ Rays out of Glafs into Air, their common Sine of Incidence being 5-0. So then the Sines of the Incidences of all the red-making Rays out of Glafs into Air, were to the Sines of their Re- fi'adions , not greater than 5-0 to 77, nor lefs than 5*0 to 7j-^y but they varied from one ano^ ther according to all intermediate proportions. And the Sines of the Incidences of the green- making [H2] making Rays were to the Sines of their Refra^ dions in all proportions from that of fo to 777, unto that of 50 to -j-j'^. And by the like lin:iits iibovementioned were the Refradions of the Rays belonging to the reft of the Colours de- lined, the Sines of the red-making Rays extend- ing from yy to yj^^ thofe of the orange-making from yy^ to yy\,, thofe of the yellow-making from yy^i to yy^^ thofe of the green-making from yy~ to yy^^ thofe of the blue-making from yiy^ to 777, thofe of the indigo-making from .77- to yy^^ and thofe of the violet from yy-^ to 78. Thefe are the Laws of the Refradions made out of Glafs into Air, and thencp by the third Axiom of the firlt part of this Book, the Laws of the Refractions made out of Air into Glafs are eafily derived. Exper. 8. I found moreover that when Light goes out of Air through feveral contiguous re- frading Mediums as through Water and Glafs, and thence goes out again into Air , whether the refrading Superficies be parallel or inclin'd to one another, that Light as often as by con- trary Refractions 'tis lb correded, that emer- geth in Lines parallel to thofe in which it was incident, continues ever after to be white. But if the emergent Rays be inclined to the inci- dent, the whitenefs of the emerging Light will by degi'ees in paffing on from the place ofE- mergence, become tinged in its edges with Colours. This I tryed by refrading Light with Prifms of Glafs placed within a prifmatickV^f- fel of Water. No W: thofe Colours argue a di- verging [ "3 ] Verging and f^aration of the heterogeneous Rays from one another by m^ans of their une-^ qual Refraftions, as in what follows will more fully appear. And, on the contrary, the per- manent whiteneis argues, that in like hiciden- ces of the Rays there is no fuch feparation of the emerging Kays, and by confequence no in- equaUty of their whole Refradions. Whence I feem to gather the two following Theorems. I. The ExcefTes of the Sines of Refradioii of feveral forts of Rays above their common Sine of Incidence when the Refraftions are made out of divers denfer Mediums immedi- ately into one and the fame rarer Medium, fup- pofe of Air, are to one another in a given Pro- portion. X. The Proportion of the Sine of Incidence to the Sine of Refradion of one and the fame fort of Rays out of one Medium into another^ is compofed of the Proportion of the Sine of Incidence to the Sine of Refradion out of the firft Medium into any third Medium, and of the Proportion of the Sine of Incidence to the Sine of Refradion out of that third Medium into the fecond Medium. By the firlt Theorem the Refractions of the Rays of every fort made out of any Medium in- to Air are known by having the Refradion of the Rays of any one fort. As for in (la nee, if the Refractions of the Rays of every fort out of Rain-water into Air be defired, let the com- mon Sine of Incidence out of Glafs into Air be I ^ fub« fubdudkd from the Sines of Refradion, and the Excefles will be 27 > ^74, 2,74, 274, 274, 27-f, 27^, 28. Suppofe now that the Sine of Incidence of the leaft refrangible Rays be to their Sine of Refradion out of Rain-water in- to Air as 5 to 4, and fay as i the difference of thofe Sines is to 3 the Sine of Incidence, fo is 27 the leaft of the ExcelTes above-mentioned to a fourth number 81 ; and 81 will be the common Sine of Incidence out of Rain-water into Air, to which Sine if you add all the a- bovcmentioned ExcelTes you will have the de- fired Sines of the Refractions 108, io84> 1084, 1084, 1084-5 loS-i, 108:7, 109. By the latter Theorem the Refradion out of one Medium into another is gathered as often as you have the RefraClions out of them both into any third Medium. As if the Sine of In- cidence of any Ray out of Glafs into Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence of the fame Ray out of Air into Water, be to its Sine of Rerradion as 4 to 3 ; the Sine of Incidence of that Ray out of Glafs into Water will be to its Sine of Refradion as 20 to 31 and 4 to 3 jointly, that is, as the Fa- dum of 20 and 4 to the Fadlum of 3 1 and 3 > or as 80 to 93. And thefe Theorems beir^g admitted into Op- ticks, there would be icope enough of hand- ling that Science voluminoully after a new man- ner ; not only by teaching thofe things which tend to the perfeClion of Vifion , but alfo by determining mathematically all kinds of Phae- nomena of Colours which could be produced , s by ["5] by Refia6tions. For to do this, there is nO" thing elle requifite than to find out the Separa- tions of heterogeneous Rays, arkd their various Mixtures and Proportions in ever}^ IVlixture. By this way of arguing I invented ahnoft all the Phaenomena defcribed in thefe Books, befide fome others lefs necelfary to the Argument; and by the fuccefTes I met with in the Trials, I dare promife, that to him who ihall argue tru- ly, and then try all things with good Glafles and fufBcient Circumfpedion, the expefted E- vent will not be wanting. But he is iirft to know what Colours will ariie from any others mix'd in any afligned Proportion. TROT. IV. Theor. m. Colours may be produced by Compojitton which /hall be like to the Colours of homogeneal Light as to the Appearance of Colour^ but not as to the Immutability of Colour and Conjiitution of Light, And thofe Colours by ho'w much they are ?nore compoMidedby fo much are they lefs full and intenfcy and by too much Compo- fition they may be diluted a7id weaken' d till they ceafey and the Mixture becomes white or grey. There may be alfo Colours produced by Compo/itiony which are not fully like any of the Colours of homogeneal Light, FOR a Mixture of homogeneal red and yel- low compounds an orange, like in appea- rance of Colour to that orange which in the I 2. feries [ "O feries of unmixed prifmatick Colours lies be- tween them ; but the Light of one orange is homogeneal as to Refrangibility , that of the oth^r is heterogeneal, and the Colour of the one, if viewed through a Prifm , remains un- changed, that of the other is changed and re- folved into its component Colours red and yel- low. And after the fame manner other neigh- bouring homogeneal Colours may compound new Colours, like the intermediate homoge- neal ones, as yellow and green, the Colour be- tween them both, and afterwards, if blue be ad- ded, tlicre will be made a green the midde Co- lour of the three which enter the Compofition. For the yellow and blue on either hand, if they are equal in quantity they draw the intermedi- ate green equally towards themfelves in Com- pofition, and fo keep it as it were in T^quilibrio, that it verge not more to the yellow on the one hand, than to the blue on the other, but by their mix'd Anions remain Itill a middle Colour. To this mix'd green there may be farther ad- ded fome red and violet, and yet the green will not prefently ceafe but only grow lefs full and vivid, and by increafmg the red and vio- let it will grow more and more dilute, until by the prevalence of the added Colours it be over- come and turned into whitenefs, or fome other Colour. So if to the Colour of any homoge- neal Light, the Sun's white Light compofed of all forts of Rays be added, that Colour will not vaniili or change its Species but be diluted , and by adding more and more white it will be diluted more and more perpetually. Laiftly, if ', - - - ^^^ red and violet be mingled, lere will be gene- rated according to their various Proportions various Purples, fuch as are not like in appear- ance to the Colour of any homogeneal Light, and of thefe Purples mix'd with yellow and blue may be made other new Colours. TROT. V. Theor. IV. Whitenefs and all grey Colours bet'vjecn "juhite and blacky may be compounded of Colour s^ and the whitenefs of the Suns Light is compound- ed of all the primary Colours mix'd in a due Trofortion. The Proof by Experiments. Exper. 9. T~^HE Sun ihining into a dark 1 Chamber through a little round hole in the VV^indow-fhut, and his Light being there refraded by a Prifm to call his coloured Image PT [in Fig. 5;.] upon the oppofite Wall: I held a white Paper \^ to that Image in fuch man- ner that it might be illuminated by the coloured Light refleded from thence, and yet not inter- cept any part of that Light in its paflage from the Prifm to the Spe£lrum. And I found that when the Paper was held nearer to any Colour thaa to the rell, it appeared of that Colour to which it approached nearefi: ; but when it was equally or almoil equally diflant from all the Colours , fo that it might be equally illumina- ted by them all it appeared white. And in this kit fituation of the Paper, if fome Colours were I 3 intcr-^ k [n8] intercepted, the Paper loft its white Colour, and appeared of the Colour of the reft of the Light which was not intercepted. So then the Pa- per was illuminated with Lights of various Co- lours, namely, red, yellovv, green, blue and violet, and every part of the Light retained its proper Colour, until it was incident on the Pa- per, and became reflefted thence to the Eye; fo that if it had been either alone (the reft of the Light being intercepted ) or if it had a- boundcd moft and been predominant in the Light reflected from the Paper, it would have tinged the Paper with its own Colour ; and yet being mixed with the reft of the Colours in a due proportion, it made the Paper look white, and therefore by a Compofttion with the reft produced that Colour. The fevcral parts of the coloured Light reflefted from the Spectrum, whilft they are propagated from thence through the Air, do perpetually retain their proper Co- lours, becaufe wherever they fall upon the Eyes of any Spedator, they make the feveral parts of the Spedrum to appear under their proper Co- lours. Tliey retain therefore their proper Co- lours when they fall upon the Paper V, and fo by the confufion and perfedt mixture of thofe Colours compound the whitenefs of the Light lefleded from thence. Exper. lo. Let that Spe(^rum or folar Image PT [in F'tg. 6.] fall now upon the Lens MN above four Inches broad, and about fix Feet di- ftant from the Prifm ABC, and fo fi glared that it may caufe the coloured Light which diverg- fx\\ frOiB th^ Prifm to converge and meet again 4t at its Focus G, about fix or eight Feet diflant from the Lens, and there to fall perpendicular- ly upon a white Paper D E. And if you move this Paper to and fro , you will perceive that near the Lens, as at de^ the whole folar Image (fuppofe 2X. ft) will appear upon it intenfely coloured after the manner above-expkiincd, and that by receding from the Lens thole Colours will perpetually come towards one another, and by mixing more and more dilute one another continually, until at length the Paper come to the Focus G, where by a pcrfed mixture they will wholly vanifli and be converted into white- nefs, the whole Light appearing now upon the Paper like a httle white Circle. And after- wards by receding futher 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 ap- pear again , but yet in a contrary order ; fup- pofe at hj where the red t is now above which before was below , and the violet / is below which before was above. Let us now flop the Paper at the Focus G where the Light appears totally white and cir- cular, and let us confidcr its \\hitcnefs. I fay, that this is compofed of the converging Colours. For if any of thofe Colours be intercepted at the Lens, the whitencfs will ccafe and degene- rate into that Colour which avifeth from the compofition of the other Colours \^ich are not intercepted. And then if the intercepted Co- lours be let pafs and fall upon that compound Colour, they mix with it, and by their mixture I 4 reitore [ 120 ] reflore the wKitenefs. So if the violet, blue and green be intercepted , the remaining yel- low, orange and red will compound upon the Paper an orange, and then if the intercepted Colours be let pafs they will fall upon. this com- pounded orange, and together with it decom- pound a white. So alfo if the red and violet be intercepted, the remaining yellow, green and blue, will compound a green upon the Pa- per, and then the red and violet being let pafs will fall upon this green , and together with it decompound a white. And that in this Com- pofition of white the feveral Rays do not fuffer any Change in their colorific qualities by ading upon one another, but are only mixed, and by a mixture of their Colours produce white, may farther appear by thefe Arguments. If the Paper be placed beyond the Focus G, fuppofe at £, and then the red Colour at the Lens be alternately intercepted, and let pafs a- gain, the violet Colour on the Paper will not fuffer any Change thereb)^ as it ought to do if the feveral forts of Rays aisled upon one ano- ther in the Focus G, where they crofs. Nei- ther wjjl the red upon the Paper be changed by any alternate flopping, and letting pafs the violet which crolleth 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 Refraclion of thatPriftn be tranflated to the place rvy and there' appear tinged with various Colours, name- ly, the violet at v and red at r, and others be- tween , and then the red Colour at the Lens be [ 121 ] be often ftopp'd and let pafs by turns, the red at r will accordingly diflippear and return as often, but the violet at v will not thereby fuf- fer any change. And fo by Hopping and letting pafs alternately the blue at the Lens, the blue at y will accordingly difappear and return, with- out any change made in the red at r. The red therefore depends on one fort of Rays, and the blue on another fort, which in the Focus G where they are commix'd do not a^l on one another. And the^e is the fame reafon of the other Colours. I confidered farther, that when the mod re- frangible Rays P/, and the leaft refrangible ones Tt, are by converging inclined to one a- nother, the Paper, if held very oblique to thofe Rays in the Focus G, might reflec^t one fort of them more copioully than the other fort, and by that means the reflected Light would be tinged in that Focus with the Colour of the pre-^ dominant Rays, provided thofe Rays feveraliy' retained their Colours or colorific Qualities in the Compofition 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 Itrike the Senfe with the perception of white, then they could never lofe their whitenefs by fuch Reflexions. I in- clined therefore the Paper to the Rays very ob- liquely, as in the fecond Experiment of this Book, that the mofl refrangible Rays might be more copioufly refleded than the rell, and the whitenefs at length changed fucceflively into blue, indigo and violet. Then I inclined it the [ 122 ] the contrary way, that the leafl refrangible Rays might be more copious in the retle&d Light than the reil., and the whitenefs turned fuc- cellively to yellow, orange and red. Laflly, I made an Inftrument X Y in fafhion of a Comb, whofe Teeth being in number fix- teen were about an Inch and an half broad, and the Intervals of the Teeth about two Inches wide. Then by interpofmg fucceflivety the Teeth of this Inftrument near the Lens, I in- tercepted part of the Colours by the interpofed Tooth, whilft the reft of them went on through the interval of the Teeth to the Paper D E, and there ipainted a round folar Image. But the Paper I had firft placed fo, that the Image might appear white as often as the Comb was taken away ; and then the Comb being as was faid in- terpofed, that whitenefs by realbn of the inter- cepted part of the Colours at the Lens did al- ways change into the Colour compounded of thofe Colours which were not intercepted, and that Colour was by the motion of the Comb perpetually varied fo, that in the palling of every Tooth over the Lens all thefe Colours , red , yellow, green, blue and purple, did always fuc- ceed one another. I caufed therefore all the Teeth to pais fucceffively over the Lens, and when the Motion was flow , there appeared a perpetual fucceftion of the Colours upon the Paper : But if I fo much accelerated the Mo- tion, that the Colours by reafon of their quick fucceiTion could not be diitinguiflied from one another , the appearance of the fmgle Colours ceafed. There was no red, no yellow, no green. [ 123 ] green, no blue, nor purple to be feen any lon- ger, but from a confufion of them all there a- rofe one uniform white Colour. Of the Light which now by the mixture of all the Colours ap- peared white, there w^as no part really white. One part was red, another yellow, a third green, a fourth blue, a fifth purple, and every part re- tains its proper Colour till it llrike the Senfori- um. If the Impreflions follow one another flowl}', fo that they may be fev^erally perceived, there is made a diilint^i: Senfation of all the Co- lours one after another in a continual fuccef- fion. But if the Impreflions follow one ano- ther fo quickly that they cannot be feverally perceived, there arifcth out of them all one common Senfation, which is neither of this Colour alone nor of that alone, but hath it felf indifferently to 'em all , and this is a Senfation of whitenefs. By the quickneis of the Succef- iions the Imprellions of the feveral Colours are confounded in the Senforium, and out of that confufion arifcth a mix'd Senfation. If a burn- ing Coal be nimbly moved round in a Circle with Gyrations continually repeated, the whole Circle will appear like Fire ; the reafon of w hich is, that the Senfation of the Coal in the feveral places of that Circle remains imprefs'd on the Senforium , until the Coal return again to the fame place. And fo in a quick confecu- tion of the Colours the ImprelTion of every Co- lour remains in the Senforium, until a revolu- tion of all the Colours be compleated, and that fir il Colour return again. The Impreflions there- fore of all the fucceiRve Colours are at once in the [ 124] the Senforium , and jointly iHr up a Senfation. , of them all ; and fo it is manifeit by this Expe- riment , that the commix'd Imprellions of all the Colours do llir up and beget a Senlation of white, that is, that whitenefs is compounded of all the Colours. And if the Comb be now taken away, that all the Colours may at once pafs from the Lens to the Paper, and be there intermixed, and to- gether retlecled thence to the Spedators Eyes ; their Impreflions on the Senforium being now more fubtilly and perfectly commixed there, ought much more to ftir up a Senfation of whitenefs. You may inflead of the Lens ufe two Prifms HIK and LMN, which by refrading the co- loured Light the contrary way to that of the iirll Refradion, may make the diverging Rays converge and meet again in G, as you fee re- prefcnted in the fcventh Figure. For where tiiey meet and mix they will compole a white Light, as when a Lens is ufed. Exper. II. Let the Sun's coloured hnage PT [in F//[. 8.] fill upon the Vv'all o. a dark Cham- ber, as in the third Experiment of the firlt Book, and let the fanje be vicu^ed through a Priim abc^ held parallel to the Prifni A B C, by whofe Refraclion that hn;^ge was made, and let it now appear lower than before, fuppofe in the place Sever againfl the red Colour T. And if you go near to the Image P T, the Spedrum S will appear oblong and coloured like thehiiagePT; Ixit if you recede from it, the Colours of the Spedrum S will be contradcd more and more, and I 125 ] and at length vanifh, that Spedrum S becoming perfedly round and white ; and if you recede yet farther, the Colours will emerge again, bur in a contrary order. Now that Spectrum S ap- pears white in that cafe when the Rays of le- vcral forts which converge from the fevcrai pans of the Image PT, to the Prifm al^c, are lb refra(^ted unequally by it, that in their paf- fage from the Prifm to the Eye they may di- verge from one and the fame point of the Spe- ctrum S, and fo fall afterwards upon one and the fame point in the bottom of the Eye, and there be mingled. And farther, if the Comb be here made ufe of, by whofe Teeth the Colours at the Image PT may be fuccellively intercepted; the Spe- the fame forts of Rays coming from the lower Prifm, ought to illuminate the remaining fpaces QN, RN, SN, refpedively. And the fame is to be undei'ltood of all the other forts of Rays. For thus the Rays of every fort will be fcattered liniformly and eavenly thro' the whole fpace MN, and fo being every where mix'd in the fame proportion, they mud every where produce the fame Colour. And therefore fmce by this mixture they produce white in the ex- terior fpaces MP and TN, they mull alfo pro- duce wiiite in the interior fpace PT. This is the reafon of the compoiition by which white- nefs was produced in this Experiment, and by what other way foever I made the like compo- fition the refult was whitenefs. Laitly, If with the Teeth of a Comb of a due fize, the coloured Lights of the two Prifms which M upon the fpace PT be alternately intercepted, that fpace PT, when the motion of the Comb is How, will always appear co- loured , but by accelerating the motion of the Comb fo much, that the fuccellive Colours cJmnot be diilinguilhed from one another, ic will appear white. Exper. 14. Hitherto I have produced Vv^hite- nefs by mixing the Colours of Prii'ms. If now the Colours of natural Bodies are to be min- gled , let Water a little thicken'd with Soap be agitated to raife a Froth, and after that Froth K has [i3o] has flood a little, there will appear to one that fhall view it intently various Colours every where in the Surfaces of the feveral Bubbles ; but to one that iliall go fo far off that he cannot di- llinguifli the Colours Irom one another , the vvhole Froth will grow white with a perfed whitenefs. ExPer. 15-. Lailly, in attempting to com- pound a white by mixing the coloured Powders which Painters ufe, I confider'd that all co- lour'd Powders do fupprefs and flop in them a very confidcrable part of the Light by which they are illuminated. For they become colour'd by refleding the Light of their own Colours more copioufly, and that of all other Colours more fparingly, and yet they do not refleft the Light of their own Colours fo copioufly as white Bodies do. If red Lead , for initance , and a white Paper, be placed in the red Light of the colour'd Spcdrum made in a dark Cham- ber by the P^efradion of a Prifm, as is defcri- bed in the third Experiment of the firfl Book ; the Paper will appear more lucid than the red Lead , and therefore refleds the red-making Rays more copioufly than red Lead doth. And if they be held in the Light of any other Co- lour, the Light refleded by the Paper will ex- ceed the Light refleded by the red Lead in a much greater proportion. And the like hap- pens in Powders of other Colours. And there- fore by mixing fuch Powders we are not to ex- ped a flrong and full white, fuch as is that of Paper, but fome dusky obfcure one, fuch as might arife from a mixture of light and dark- ^ nefs. [nl] il&fs, or from white and black, that is, a grey^ or dun, or ruiTet brown, fuch as are the Co- lours of a Man's Nail, of a Moufe, of Alhes, of ordinary Stones, of Mortar, of Dull and Dirt in High- ways, and the like. And fuch a dark white I have often produced by mixing colour'd Powders. For thus one part of red Lead, and five parts of Viride jEris, compo- fed a dun Colour Hke that of a Moufe. For thefe two Colours were feverally fo compound- ed of others, that in both together were a mix- ture of all Colours ; and there was lefs red Lead ufed than Viride ^^ris , becaufe of the fulnefs of its Colour. Again, one part of red Lead^ and four parts of blue Bife , compofed a dun Colour verging'a little to purple, and by ad- ding to this a certain mixture of Orpiment and Viride jEris in a due proportion, the mixture lolt its purple tindure , and became perfedly dun. Ikit the Experiment fucceeded belt with- out Minium thus. To Orpiment I added by little and little a certain full bright purple ji which Painters ufe until the Orpiment ceafed to be yellow, and became of a pale red. Then I diluted that red by adding a httle Viride M^ risy and a little more blue Bife than Viride M^ rus^ until it became of fuch a grey or pale vi^^hite^ as verged to no one of the Colours more than to another. For thus it became of a Colour e- qual in whifenefs to thatof A(hes or of Wood newly cut, or of a Man's Skin. The Orpiment reflec^ted more Light than did any other of thd Powders, and therefore conduced rnore td th^ whitenefs of the compounded Colour than they. I 132 ] To alTign the Proportions accurately may be difficult, by reafon of the different goodnefs of Powders oF the fame kind. Accordingly as the Colour of any Powder is more or lefs full and luminous, it ought to be ufed in a Icls or great- er proportion. Now confidering that thefe grey and dun Co- lours may be alfo produced by mixing whites and blacks, and by confequence ditier from perfed whites not in fpecies of Colours but on- ly in degree of Luminoufnefs , it is manifefl that there is nothing more requifite to make them perfedly white than to increafe their Light fufficicntly; and, oh the contrary, ifbyincrea- {mg their Light they can be brought to perfcft vvhitenefs, it will thence alfo follow, that they are of the famiC fpecies of Colour with the bell whites, and differ from them only in the quan- tity of Light. And this I tried as follows. I took the third of the abovemention'd grey Mixtures (that which was compounded of Orpiment, Pur- ple, Bifc, and Vtride ^ru) and rubbed it thick- ly upon the Floor of my Chamber, where the Sun llione upon it through the opened Cafe- ment ; and by it, in the ihadow, I laid a piece of white Paper of the fame bignels. Then going from them to the diflanceof iz or 18 Feet, lo that I could not difcern the uneavennefs of the Surface of the Powder, nor the little Shadows let fall from the gritty Particles thereof; the Powder appeared intenfely white, fo as to tran- fcend even the Paper it felf in whitenefs , efpe- cially if the Paper were a httle fliaded from the Light of the Clouds, and then the Paper com- pared [ '33 ] pared with the Powder appeared of fuch a grey Colour as the Powder had done before. But by laying the Paper where the Sun iliines thro* the Glafs of the Window, or by lliutting the Window that the Sun might Ihine through the Glais upon the Powder, and by fuch other fit means of increafmg or decreafmg the Lights wherewith the Powder and Paper were illumi- nated, the Light wherewith the Powder is illu- minated may be made itronger in fuch a due proportion than the Light whereuith the Paper is illuminated, that they fhall both appear ex- adlly alike in whitenefs. For when I was try- ing this, a Friend coming to vifit me, I llopp'd him at the Door, and before I told him what the Colours were, or what I was doing ; I ask- ed him. Which of the two Whites were the beft, and wherein they differed ? And after he had at that diflance viewed them well, he an- fwer'd. That they were both good Whites, and that he could not fay which was bell, nor wherein their Colours differed. Now if you confider, that this white of the Powder in the Sun-fhine was compounded of the Colours which the component Powders (Orpimcnt, Purple, Bife , and Vir'tde Mr is) have in the fame Sun-fliine, you muft acknowledge by this Experiment, as well as by the former, that per- feft whitenefs may be compounded of Colours. From what has been faid it is alfo evident, that the whitenefs of the Sun's Light is com-^' pounded of all the Colours Avhcrewith the fe- veral forts of Rays whereof that Light confifls, when by their feveral Ref-ai^.gibiUtiestliey are K 5 fepa- [i34] feparated from one another, do tinge Paper or any other white Body whereon they fall. For thofe Colours by Trcp. i. are unchangeable , and whenever all thofe Rays with thofe their Colours are mix'd again , they reproduce the fame white Light as before. . TROT. VI. Prob. II. In a mixture of primary Colours, the quantity and quality of each being given, to know the Colour of the Compound, WITH the Center O [in Fig. ii.] and Ra- dius OD defcribe a Circle ADF, and ditlinguiili its circumference into feven parts DE, EF, FG, GA, AB, BC, CD, propor- tional to the feven mufical Tones or Intervals of the eight Sounds, Sol, la, fa, fol, la, mi, fa^ fol, contained in an eight, that is, proportional to the number 7, t'^.-, t^, t> iv> tW ^. Let the firit part DE reprefent a red Colour, the fe- cond EF orange, the third FG yellow, the fourth C A green, the fifth AB blue, thefixth B C indigo, and the feventh C D violet. And conceive that thefe are all the Colours of un^ compounded Light gradually pafTmg into one another, as they do when made by Prifms ; the circumference DEFGABCD, reprefenting the whofe feries of Colours from one end of the Sun's colour 'd Image to the other , fo that from P to E be all degrees of red, at E the Xn^m CqIqi}}: between red and grange, from E toF [ 135] to F all degrees of orange, at F the mean be- tween orange and yellow, from F to G all de- grees of yellow, and fo on. Let f be the cen- ter of gravity of the Arch DE, and ^, r, j, r, «, A-, the centers of gravity of the Arches E F, FG, GA, AB, BC and C D refpertively, and about thofe centers of gravity let Circles pro- portional to the number of Rays of each Co- lour in the given Mixture be defcrib'd ; that is, the Circle / proportional to the number of the red-making Rays in the Mixture , the Circle q proportional to the number of the orange-ma- king Rays in the Mixture, and io of the reft. Find the common center of gravit)' of all rhofe Circles />, ^, r, j-, /, ?/, x. Let tbat center be Z; and from the center of the Circle AD F, through Z to the circumference, drawing the right Line O Y, the place of the Point Y in the circumference fhall iliew the Colour arifing from the compofition of all the Colours in the given Mixture, and the Line O Z Ihall be pro- portional to the fulnefs or intenfcncfs of the Colour, that is, to its diilance from vvhitenefs. As if Y fall in the middle between F and G, the compounded Colour Ihall be the beft yel- low; ^{ Y verge from the middle towards F or G, the compound Colour Ihall accordingly be a yellow, verging towards orange or green. If Z fall upon the circumference the Colour fhall be intenfe and florid in the higheii: degree ; if it fall in the mid way between the circum- ference and center, it fliall be but half fo intenfe, that is, it fhall be fuch a Colour as would be made by diluting; the intenfeft yellow K 4 with vvith an equal quantity of whitenefs; and if it fall upon the -center O, the Colour fliall have lofl all its intenfenefs, and become a white. But it is to be noted, That if the point Z fall in or near the line O D , the main ingredients being the red and violet, the Colour compounded fliall not be any of the prifmatick Colours, but a purple, inclining to red or violet, according- ly as the point Z lieth on the fide of the line D O towards E or towards C , and in general the compounded violet is more bright and more fiery than the uncompounded. Alfo if only two of the primary Colours which in the circle are oppofitc to one another be mixed in an equal proportion, the point Z fliall fall upon the cen- ter O, and yet the Colour compounded of thofe two fliall not be perfectly white, but fome faint anonymous Colour. For I could never yet by mixing only two primary Colours pro- duce a perfe(^t white. Whether it may be com- pounded of a mixture of three taken at equal dillances in the circumference I do not know, but of four or five I do not much queltion but it may. But thefe are Curiofities of little or no moment to the underftanding the Phaenomena of Nature. For in all whites produced by Na- ture, there ufes to be a mixture of alf forts of Rays, and by corrfequence a compofition of all Colours. To give an inflance of this Rule ; fuppofe a Colour is compounded of thefe homogencal Colours, of violet one part, of indigo one part, of blue two parts, of green three parts, of yel- low five parts, of orange fix parts, and of red ten [i37] ten parts. Proportional to thefe parts defcribe the Circles x, v, r, j", r, c/, p, refpedivelv, that is, lb that if the Circle x be one, the Circle ^' may be one, the Circle t two, the Circle s three, and the Circles r, ^ and /, five, fix and ten. Then I tind Z the common center of gravity of theie Circles, and through Z drawing the Line O Y, the Point Y falls upon the circumference between E and F, Ibme thing nearer to E than to F, and thence I conclude , that the Colpur compoundto of thefe Ingredients will be an o- range, ver'};ing a little more ro red than to yel- low. Alfo T tmd that O Z is a little lefs than one half of O Y, and thence I conclude, that this orange iiath a little lefs than half the ful- ncfs or intenft nefs of an uncompounded o- range ; that is to iay, that it is fuch an orange as may be made by mixmg an homogeneal o- range with a good while in the proportion of the Line O Z to the Line Z Y, this Proportion being not of the quantities of mixed orange and white Powders, but of the quantities of the Lights reflected from them. This Rule I conceive accurate enough for pradice, though not mathematically accurate ; and the truth of it may be fufficiently proved to Senfe , by Hopping any of the Colours at the Lens in the tenth Experiment of this Book. For the relt of the Colours which are riot llopp'd, but pafs on to the Focus of the Lens, will there compound either accurately or very nearly fuch a Colour as by this Rule ought to refult from their Mixture, "PROT. [i38] TROT. Vn. Theor. V. jill the Colours in the ^niverfe which are made by Lights and depend not on the Tower of 1- maginattony are either the Colours of homoge- neal Light Sy or compounded of thefe^ and that •either accurately or very nearly^ according to the Rule of the foregoing Troblem. FOR it has been proved (mTrop.i. Tart.z.) that the changes of Colours made by Re- fractions do not ariie from any new Moditica* tions of the Rays imprefs'd by thofe Refractions, and by the various Terminations of Light and Shadow, as has been the conflant and general Opinion of Philofophers. It has alfobeen pro- ved that the feveral Colours of the homogeneal Rays do conlbntly anfwer to their degrees of Refrangibility, (Trop.i. Tart i. and Trof.i. Tart 1.) and. that their degrees of Refrangibi- lity cannot be changed by Refractions and Re* flexions, (Trop.t. Tart, \.) and by confequence that thofe their Colours are likewife immuta- ble. It has alfo been proved diredtly by refra- cting and reflecting homogeneal Lights apart , that their Colours cannot be changed, (Trop. i, Tart.-L.) It has been proved alfo, that when the feveral forts of Rays are mixed, and in crof- fmg pafs through the fame fpace, they do not aCt on one another fo as to change each others colorific qualities. (Exper. lo. Tart.i.) but by mixing their ACtions in the Senforium beget a Senfation differing from what either would do apart, that is a Senfation of a mean Colour be- tween [ 139 ] tween their proper Colours; and particularly when by the concourle and mixtures of all forts of Rays, a white Colour is produced, the white is a mixture of all the Colours which the Rays would have apart , (Trop. $. Tart x.J The Rays in that mixture do not lofe or alter their feveral colorific qualities ,' but by all their various kinds of Adions mix'd in the Senfori- um , beget a Senfation of a middling Colour between all their Colours, which is whitenefs. For whitenefs is a mean between all Colours , having it felf indifferently to them all,'fo as with equal facility to be tinged with any of them. A red Powder mixed with a little blue, or a blue with a little red , doth not prefently lofe its Colour, but a white Powder mix'd with any Colour is prefently tinged with that Colour, and is equally capable of being tinged with any Colour whatever. It has been fliewed alfo, that as the Sun's Light is mix'd of all forts of Rays , fo its whitenefs is a mixture of the Colours of all forts of Rays ; thofe Rays having from the beginning their feveral colorific qua- lities as well as their feveral Refrangibilities, and retaining them perpetually tftichanged not- withllanding any Refractions or Reflexions they may at any time fuffer, and that whenever any fort of the Sun's Rays is by any means (as by Reflexion in Exper. 9 and 10. Tart i. or by Refraction as happens in all Refraftions ) fepa- rated from the reft , they then manifef t their proper Colours. Thefe things have been prov'd, ftnd the fum of all this amounts to the Propofi- tion here to be proved, For if the Sun's Light is [ ho] is mix'd of feveral forts of Rays, each of which ' have originally their feveral Refrangibilities and colorific Qualities , and notwithlbnding their Refradions and Reflexions , and their various Separations or Mixtures, keep thofe their ori- ginal Properties perpetually the fame without alteration; then all the Colours in the World mull be fuch as conftantly ought to arife from the original colorific qualities of the Rays where- . of the Lights confilt by which thofe Colours are feen. And therefore if the reafon of any Colour whatever be required, we have nothing elfe to do than to conlider how the Rays in the. Sun's Light have by Reflexions or Refraftions, or other caufes been parted from one another, or mixed together ; or otherwife to find out what forts of Rays are in the Light by which that Colour is made , and in what proportion ; and then by the lall Problem to learn the Co- lour which, ought to arife by mixing thofe Rays (or their Colours) in that proportion. I fpeak here of Colours lb far as thev arife fromLio;ht. For they appear fometimes by other Caufes, as when by the power of Phantafy we fee Colours in a dream, or a mad Man fees things before him which are not there ; or when we fee Fire by llriking the Eye, or fee Colours hke theE^^e of a Peacock's Feather, by prefiing our Eyes in either corner whillt we look the other way. Where thefe and fuch like Caufes interpofe not, the Colour aU'ays anfwers to the fort or forts of the Rays whereof the Light confifls , as I have conlfantly found in whatever Phaenomena of Colours I have hitherto been able to exa- . mine. [hi] mine. I fhall in the following Propofitions give inlhnces of this in the Phaenomena of chiefell note. TROT.VIU. Prob. m. . By the dtfcovered Properties of Light to ex" plain the Colours made by T^rtjms. LET ABC \\riFig. IX.] reprcfcnt a Prifm refra6]:ing the Light of the Sun, which comes into a dark Chamber through a hole F

the middle fort between the indigo-making and blue-ma- king Rays upon the Space Q;^, the middle fort of the green-making Rays upon the Space R^, the middle fo^t between the yellow-making and- orange-makingRays upon the Space So-, ando- ther intermediate forts upon intermediate Spa- ces. For fo the Spaces upon which the feveral forts adequately fall will by rcafon of the dif- ferent Retrangibility of thole forts be one lower than another. Now if the Paper M N be fo near the Prifm that the Spaces P T and ;r 7 do not interfere with one another, the diltance be- tween them Ttt will be illuminated by all the forts of Rays in that proportion to one another which they have at their very firfl coming out of [ H2 ] of the Prifm, and confequently be white. But the Spaces P T and 77-7 on either hand, will not be illuminated by them all, and therefore will appear coloured. And particularly at P, where the outmolt violet-making Rays fall alone, phe Colour mud be the deepelt violet. At Q where the violet-making and indigo-making Rays are mixed , it mult be a violet inclining much to indigo. At R where the violet-making, indi- go-making, blue-making, and one half of the green-making Rays are mixed, their Colours mult (by the conltru6tion of the fecond Pro- blem) com.pound a middle Colour between in- digo and blue. At S where all the Rays are mixed except the red-making and orange-ma- king, their Colours ought by the fame Rule to compound a faint blue, verging more to greeii than indigo. And in the progrefs from S toT, this blue \^'ill grow more and more faint and dilute, till at T, where all the Colours begin to be mixed, it ends in whitenefs. So again, on the other fide of the white at r, where the leaft refrangible or utmoft red-ma- king Rays are alone, the Colour mull be the deepelt red. At 0- the mixture of red and o- range will compound a red inclining to orange. At ^ the mixture of red, orange, yellow, and one half of the green mult compound a middle Colour between orange and yellow. At % the mixture of all Colours but violet and indigo will compound a faint yellow, verging more to green than to orange. And this yellow will grow more faint and dilute continually in its progrefs from [ 143 J from ;^ to TT, where by a mixture of all foiifs of Rays it will become white. Thefe Colours ought to appear were the Sun's Light perfeftly white : But becaufe it inclines to yellow, the Excefs of the yellow-making Rays whereby 'tis tinged with that Colour, be- ing mixed with the faint blue between S and T, will draw it to a faint green. And fo the Co- lours in order from P to r ought to be violet, indigo, blue, very faint gfeen, white, faint yel- low, orange, red. Thus it is by the computa- tion : And they that pleafe to view the Colours made by a Prifm will find it fo in Nature. Thefe are the Colours on both fides the white when the Paper is held between the Prifm, and the Point X where the Colours meet, and the interjacent white vaniihes. For if the Paper be held iHll farther off from the Prifm, the moil: refrangible and lead refrangible Rays will be wanting in the middle of the Light, and the reft of the Rays which are found there, will by mixture produce a fuller green than before. Al- fo the yellow and blue will now become lefs compounded, and by confcquence more intenfe than before. And this alfo agrees with expe- rience. And if one look through a Prifm upon a white Objed encompafled with blacknefs or darknefs, the reafon of the Colours arifmg^n the edges is much the fame, as will appear to one that Ihall a little confider it. If a black Ob- u jeft be encompailed wdth a white one, the Co- lours which appear through the Prifm are to be derived from the Light of the white one, fpread- ing [ 144 ] ingiffito the Regions of the black, and there- fore they appear in a contrary order to that^ when a white Objed is furrounded with black. And the fame is to be underllood when anOb- jed is viewed , whofe parts are Ibme of them lefs luminous than others. For in the borders of the more and lefs luminous parts , Colours ought always by the fame Principles to arife from the F,xcefs of the Light of the more lu- minous , and to be of the fame kind as if the darker parts were black , but yet to be more faint and dilute. What is faid of Colours made byPrifms may be ealily af)plied to (Colours made by theGlafles of Telefcopes or Microfcopes, or by the Hu- mours of the Eye. For if the Objed-glafs of a Telefcope be thicker on one fide than on the other, or if one half of the Glafs, or one half of the Pupil of the Eye be cover'd .with any opake fubltance:. the Objcd-glafs, or that part of it or of the F.ye which is not cover'd , may be confider'd as a Wedge with crooked Sides, and every Wedge of Glafs or other pellucid Subilance has the efictt of a Prifm in refrading the Light which pailcs through it. How the Colours in the ninth and tenth Ex- periments of the iirlt Part arife from the diffe- rent Reflexibility of Light, is evident by what was there laid. But it is obfervable in the ninth Experiment, that whilit the Sun's dired Light is yellow, the Excefs of the blue-making Rays in the retleded beam of Light MN, fuffices only to bring that yellow to a pale white incli- ning to blue , and not to tinge it with a mani- - feilly [ H5 ] feftly blue Colour. To obtain therefore a bet- ter blue, I ufcd inltead of the yellow Light of the Sun the white Light of the Clouds, by va- rying a little the Experiment, as follows. Ex^er.i6. LetHFG [ini^/V. 13.] repre- fent a Prifm in the open Air, ancf S the Eye of the Spcdator, viewing the Clouds by their Light coming into the Prifm at the plane lide FTGK, and reflected in it by its bale HEIG, and thence going out through its plane fide H E E K to the Eye. And wlien the Priim and Eye are conveniently placed, lb that the Angles of Incidence and Reflexion at the Bafe may be about 40 Degrees, the Spedator will fee a BoW M N of a blue Colour, running from one end of the Bafe to the other, with the concave fide towards him, and the part of the Bafe IMJ^G beyond this J^ow will be brighter than the other part EMNH on the other tide of it. This blue Co- lour MN being made by nothing elfe than by re- flexion of a fpecular Superficies, feems fo odd it Phainomenon, and fo difficult to be explain- ed by the vulgar Hypothecs of Philofophers^ that I could not but think it deferved to be ta- ken notice of. Now for undeiilanding the rea- fon of it , ilippofe the Plane ABC to cut the" plane Sides and Bafe of the Prifm perpendicu^ larly. From the Eye to the Line B C, where-^ in that Plane cuts the Bafe, draw the Lines S/ and S t^ in the Angles S/ c 50 dcgr. ^, and S ^ ^ 49 degr. ~, and the Point/ will be the UmiC beyond which none of the mod refrangible! Rays can pafs through the Bafe of the Prifm^ And be refracted, whofe Incidence is fuch that L they [ H^ they may be refle6led to the Eye; and the Point t will be the like limit for the leaft re- frangible Rays, that is, beyond which none of them can pafs through the Bale , whofe Inci- dence is fuch that by Reflexion they may come to the Eye. ' And the Point r taken in the mid- dle way between / and t^ will be the like limit for the meanly refrangible Rays. And there- fore all the leaft refrangible Rays which fall up- on the Bafe beyond ^, that is, between t and B, and can come from thence to the Eye will be refleded thither : But on this fide t , that is, between t and f , many of thefe Rays will be tranfmitted through the Bafe. And all the moil refrangible Rays which fall upon the Bafe be- yond /, that is, between p and B , and can by reflexion come from thence to the Eye, will be reflefted thither, but every where between/ and r, many of thefe Rays will get through the Bale and be refraded; and the fame is to be underitood of the meanly refrangible Rays on either fide of the Point r. Whence it follows, that the Bafe of the Prifm muft every where between t and B, by a total reflexion of all forts of Rays to the Eye, look white and bright. And every where between / and C , by reafon of the tranfmiflion of many Rays of every fort, look more pale, obfcure and dark. But at r, and in other places between / and ^, where all the more refrangible Rays are reflcded to the Eye, and many of the lefs refrangible are tranf- mitted , the Excefs of the moil refrangible in the refleded Light will tinge that Light with their Colour, which is violet and blue. And this [ H7 ] this happens by taking the Line C prfE any where between the ends of the Prifm H (i and E I. TROT. IX. Prob. IV. By the difcovered Properties of Lhht to explain the Colours of the Rain-bow. THIS Bow never appears but where ic rains in the Sun-fliine, and may be made artificially by fpouting up Water which may break aloft , and fcatter into drops , and fall down like Rain. For the Sun fliining upf)nthefe drops certainly caufes the Bow to appear to a Spedator Handing in a due pofition to the Raiil and Sun. And hence it is now agreed upon, that this Bow is made by rcfradion of the Sun's Light in drops of falling Rain. This was un- derflood by fome of the Ancients, and of late more fully difcover'd and explain'd by the fa- mous Antonius de TDominis Archbilhop of Spa^ lato^ in his Book T)e Radiis Visits ^ Luc is, pub- lillied by his Friend Bartolm at Venice, in the Year 1611, and written above 20 Years before^ For he teaches there how the interior Bow is made in round drops of Rain by two Refra- ctions of the Sun's Light, and one Reflexion between them, and the exterior by two Refra- ftions and two forts of Reflexions between them in each drop of Water, and proves his Explications by Experiments made with a Phial full of Water, and with Globes of Glafs filled L X with [ 148 ] with Water, and placed in the Sun to make the Colours of the two Bows appear in them. The fame Explication T)es-Cartes hath purfued in his Meteors , and mended that of the exterior Bow. But whiUl they underllood not the true origin of Colour's , it's ncceilary to purfue ic here a little farther. For underilanding there- fore how the Bou is made, let a drop of Rain or any other Ipherical tranfparent Body be repre- fented by the Sphere B N F G, [in Fi^. 14.] de- fcribed with the center C, and femi-diameter CN. And let AN be one of the Sun's Rays incident upon it atN, and thence refra61ed to F, where let it either go out of the Sphere by Refraftion towards \, or be refleded to G ; and at G let it either go out by Refraction to R, or be refleded to H ; and at H let it go out by Refra6lion towards S, cutting the incident Ray in Y ; produce A N and R G, till they meet in X, and upon A X and N F let fail the perpen- diculars CD and CE, and produce CD till it fall upon the circumference at L. Parallel to the incident Ray AN draw the diameter BQ, and let the Sine of Incidence out of Air into Water be to the Sine of Refraftion as I to R. Now if you fuppofe the Point of Incidence N to move from the Point B , continually till it comx to L, the Arch Q F will firll increafe and then decreafe, and fo will the Angle AXR which the Rays A N and G R contain ; and the Arch QF and Angle AXR will be biggeft when ND is to CN as v'hTIrr to v^ 3 RR, in which cafe N E will be to N D as 2 R to I. Al- fo the Angle AYS which the Rays AN and HS contain H9 ] contain will firfl decrcafe , and then increafc and grow lead when ND is to C N as -/nT-'RR to v/ 8 RR, in which cafe NE will be to ND as 3 R to I. And fo the Angle which the next emergent Ray (that is, the emergent Ray after three Reflexions) contains with the incident Ray AN will come to its limit when ND is to CN as v/iTTrr to v/ 15- RR, in which cafe NE will be to ND as 4 R to I. And the Angle which the Ray next after that emergent , that is, the Ray emergent after fom' Reflexions, contains with the incident will come to its limit, vvherf ND is to CN as i/ii-rr to ^ 24 RR, in which cafe NE will be to ND as fR to I; and fo on infinitely, the numbers 3, 8, 15-, 24, ^c. being gather'd by continual addition of the terms of the arithmetical ProgrelTion 3, 5, 7, 9, &c. The truth of all this Mathematicians will eafily ex- amine. Now it is to be obferved, that as when the Sun comes to his Tropicks, Days incrcafe and decreafe but a very little for a great while to- gether ; fo when by increaiing the diftance CD, thefe Angles come to their limits, they vary their quantity but very little for fome time to- gether, and therefore a far greater number of the Rays which fall upon all the Points N in the Quadrant BL, iliall emerge in the Hmits of thefe Angles, than in any other hiclinations. And farther it is to be obferved, that the Rays wiiich differ in Refrangibility will have difie- rent limits of their Angles of Emergence, and by confequence according to their different de- grees of Refrangibility emerge moft copioufly L 3 in [ i5o] in different Angles , and being feparated from one another appear each in their proper Co- lours. And what thofe Angles are may be ea- fily gather 'd from the foregoing Theorem by computation. For in the lead refrangible Rays the Sines I and R (as was found above) are io8 and 8i, and thence by computation the greatefl Angle A X R will be found 41 Degrees and x Minutes, and the leaft Angle AYS, 5-0 Degrees and 5*7 Minutes. And in the mofl refrangible Rays the €ines I and R are 109 and 81 , and thence by computation the greatefl Angle A X R will be found 40 Degrees and 17 Minutes, and the leaft Angle AYS 5-4 Degrees and 7 Minutes. Suppofe now that O [in Fig. i^.] is the Spe- ctator's Eye, and OP a Line drawn parallel to the Sun's Rays, and let POE, POF, POG, P O H, be Angles of 40 Degr. 1 7 Min, 41 Degr. a Min. 5-0 Degr. 5-7 Min. and 5-4 Degr. 7 Min. refpedlively , and thefe Angles turned about their common Side O P, fliall with their other Sides OE, OF; OG, OH, defcribe the Verges of two Rain-bows AF B E and C H D G. For if E, F, G, H , be drops placed any where in the conical Superficies defcribed by OE, OF, O G, OH, and be illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being e- qual to the Angle POE or 40 Degr. 17 Min, fliall be the greateft Angle in which the moft refrangible Rays can after one Reflexion be re- fraded to the Eye, and therefore all the drops in the Line O E fhall fend the mofl refrangible Rays mofl popioufly to the Eye? md thereby itrike [ 151 ] flrike the Senfes with the deepeft violet Colour in that Region. And in like manner the Angle SFO being equal to the Angle POF, or 41 Degr. 1 Min- fhall be the greatefl in which the leall refrangible Rays after one Reflexion can emerge out of the drops, and therefore thofe Rays fhall come mod copioufly to the Eye from the drops in the Line OF, and flrike the Senfes with the deeped red Colour in that Region. And by the fame Argument , the Rays which have intermediate degrees of Refrangibility fliall come moll copioufly from drops between E and F, and ilrike the Senfes with the intermediate Colours in the order which their degress of RefrangibiUty require, that is in the progrefs from E to F, or from the infide of the Bow to the outfide in this order, violet, indigo, blue, green, yellow, orange, red. But the violet, by the mixture of the white Light of the Clouds, will appear faint and incline to purple. Again , the Angle S G O being equal to the Angle POG, or 50 Gr. 5-1 Min. iliall be the lead Angle in which the leall refrangible Rays can after two Reflexions emerge out of the drops, and therefore the lead refrangible Rays fliall come mod copioufly to the Eye from the drops in the Line O G, and drike the Senfc with the deeped red in that Region. And the Angle SHO being equal to the Angle POH or 54 Gr. 7 Min. fliall be the lead Angle in which the mod refrangible Rays after two Reflexions can e- merge out of the drops, and therefore thofe Rays Ihall come mod copioufly to the Eye from the drops in the Line OH, and drike the Senies L 4 with [ 152 ] with the deeped violet in that Region. And by the fame Argument, the drops in the Re- gions between G and H fhall Itrike the Senfe with the intermediate Colours in the order which their degrees of Refrangibility require, that is, in the progrefs from G to H, or from the infide of the Bow to the outlide in this or- der, red, orange, yellow, green, blue, indigo, violet. And fmce thefe four Lines O E, O F, OG, OH, may be fituated any where in the abovemention'd conical Superficies, what is faid of the Drops and Colours in thefe Lines is to be underflood of the Drops and Colours every whepe in thofe Superficies. Thus iliall there be made two Bows of Co^ lours, an interior and flronger, by one Reflexion' in the drops, and an exterior and fainter by two ; for the Light becomes fainter by every Reflexion. And their Colours lliall lie in a con^ trary order to one another , the red of both Bows bordering upon the Space GF which is between the Bows. The breadth of the inte^ rior Bow EOF meafured crofs the Colours fhall be iDegr. 45Min. and the breadth of the exterior G O H iliall be 3 Degr. loMin. and the diflance between them GOF iliall be 8Gr. 15 Min. the greateil Semi-diameter of the inner^ moft, that is, the Angle P O F being 41 Gr. x Min. an'd the leaft Semi-diameter of the outer- moftPOG, being foGr. 57 Min. Thefe are the Meafures of the Bows , as they would be were the Sun but a point ; for by the breadth of his Body the breath of the Bows will be in- cregfed md their diitance decreafed by half a Degree^ [153] Degree, and fo the breadth of the interior Iris will be X Degr. ly Min. that of the exterior 3 Degr. 40 Min. tlieir diltance 8 Degr. z^ Min. the greatefl Semi-diameter of the interior Bow 4x Degr. 17 Min. and the lead of the exterior 50 Degr. 41 Min. And fuch are the Dimenfions of the Bows in the Heavens found to be very nearly, .when their Colours appear Itronj^ and perfed. For once, by fuch means as I then had, I meafured the greatefl Semi-diameter of the interior Iris about 42 Degrees, the breadth of the red, yellow and green in that Iris 63 or 64 Minutes , befides the outmolt faint red ob- fcured by the brightnefs of the Clouds , for which we may allow 3 or 4 Minutes more. The breadth of the blue was about 40 Minutes more befides the violet, which was fo much obfcu- red by the brightnefs of the Clouds, that I could not meafure its breadth. But fuppofing the breadth of the blue and violet together to equal that of the red, yellow and green together, the whole breadth oF this h-is will be about z-\ De- grees, as above. The lead diltance between this Iris and the exterior Iris was about 8 De- grees and 30 Minutes. The exterior his was broader than the interior, but fo faint, efpeci- ally on the blue iide, that I could not meafure its breadth diilindly. At another time when both Bows appeared more diiUnft , I meafured the breadth of the interior Iris 2 Gr. 10', and the breadth of the red, yellow and green in the exterior Iris, was to the breadth of the fame Colours in the interior as 3 to 2, Tills [ 154] , This Explication of the Rain-bow is yet far- ther confirmed by the known Experiment (made by Antomus de T>om'tnvs and 'T)es-Cartes ) of hanging up any where in the Sun-fliine a Glafs Globe tilled with Water, and viewing it in fuch a poflure that the Rays which come from the Globe to the Eye may contain with the Sun's Rays an Angle of either 41 or 50 Degrees. For if the Angle be about 4x or 43 Degrees , the Spedator (fuppofe at O) fhall fee a full red Colour in that fide of the Globe oppofed to the Sun as 'tis reprefented at F, and if that An- gle become lefs (fuppofe by deprefling the Globe to E) there will appear other Colours, yellow, green and blue fuccellively in the fame fide of the Globe. But if the Angle be made about 50 Degrees (fuppofe by lifting up the Globe to G) there will appear a red Colour in that fide of the Globe towards the Sun, and if the An- gle be made greater (luppofe by lifting up the Globe to H) the red will turn fuccellively to the other Colours, yellow, green and blue. The fame thing I have tried by letting a Globe reft, and railing or deprelfing the Eye, or o- therwife moving it to make the Angle of a jull: magnitude. I have heard it reprefented, that if the Light of a Candle be refracted by a Prifm to the Eye ; when the blue Colour falls upon the Eye the Spectator fliall fee red in the Prifm , and when the red falls upon the Eye he lliall fee blue ; and if this were certain , the Colours of the Globe and Rain-bow ought to appear in a con- trary order to what' we tind. But the Colours of of the Candle being very faint, the miflake feems to arife from the difficulty of diicernmg what Colours fall on the Eye. tor, on the con- trary, I have fometimes had occafion to ob- ferve in the Sun's Light refra^led by a Prifm, that the Sped:ator always fees that Colour in the Prifm which falls upon his Eye. And the f\me I have found true alfo in Candle-light. For when the Prifm is moved flowly from the Line which is drawn direc^tly from the Candle to the Eye, the red appears firll in the Prifm and then the blue , and therefore each of them is feen when it falls upon the Eye. For the red paf- fes over the Eye firft, and then the blue. The Light which comes through drops of Rain by two Refradions without any Reflexion, ought to appear Ibongelt at the diilance of a- bout ^6 Degrees from the Sun , and to decay gradually both ways as the diilance from him increafes and decreafes. And the fame is to be undcritood of Light tranfmitted through fpherical Hail-llones. And if the Hail be a lit- tle flatted, as it often is, the Light tranfmitted may grow fo Ih'ong at a little lefs diilance than that of 26 Degrees, as to form a Halo about the Sun or Moon ; which Halo, as often as the Hail-ftones are duly figured may be colour'd, and then it mud be red within by the lead re- frangible Rays, and blue without by the moll refrangible ones , efpecially if the Hail-ftones have opake Globules of Snow in their center to intercept the Light within the Halo (as H/f- genius has obferv'd) and make the infide there^ of more diftindly defined than it would other- wife wife be. For fuch Hail-ftones, though fphe- rical, by terminating the Light by the Snow , may make a Halo red within and colourleis without, and darker in the red than without^ as Halos ufe to be. For of thofe Rays which pafs clofe by the Snow the Riibriform will be leafl refrafted, and lb come to the Eye in the direflell Lines. The Light which pafTes through a drop of Rain after two Refractions, and three or more Reflexions, is fcarce llrong enough to caule a fenfible Bow ; but in thofe Cylinders of Ice by Vfliicli Hiigejiius explains the Tarbelia, it may perhaps be fenfible. TROT. X. Prob. V. By the difcovered Tropertics of Light to ex- flam the permanent Colours of Natural Bo- dies. THESE Colours arife from hence, that fome natural Bodies reflect fome forts of Rays, others other forts more copioufly than the red Minium refleds the leall refrangible or red-making Rays moll copioufly, and thence appears red. Violets reflect the moll refrangi- ble, moft copioufly, and thence have their Co- lour, and fo of other Bodies. Every Body re- ilefts the Rays of its own Colour more copi- oufly than the rell, and from their excefs and predominance in the refleded Light has its Colour. Exper, [ 157 ] Exper. 17. For if in the homogeneal Lights obtained by the Iblution of the Problem pro- pofed in the fourth Propofition of the firil Part you place Bodies of feveral Colours , you will find, as I have done, that> every Body looks moil fplendid and luminous in the Light of its own Colour. Cinnaber in the homogeneal red Light is molt refplendent , in the green Light it is manifelUy lei's refplendent, and in the blue Light Hill lefs. Indigo in the violet blue Light is moll refplendent, and its fplendor is gradu- ally diminilh'd as it is removed thence by de- grees through the green and yellow Light to the red. By a Leek the green Light, and next that the blue and yellow which compound green, are more Ibongly receded than the other Co- lours red and violet, and fo of the reft. But to make thefe Experiments the more manifcil:, fuch Bodies ought to be chofen as have the fulleil: and molt vivid Colours, and two of thofe Bodies are to be compared together. Thus, for in- ftance, if Cinnaber and ////^r^z-marine blue, or fome other full blue be held together in the homogeneal Light, they will both appear red, but the Cinnaber will appear of a flrongly lu- minous and refplendent red, and the nltra-m^- rine blue of a faint obfcure and dark red ; and if they be held together in the blue homogeneal Light they will both appear blue, but iWq ultra- marine will appear of a llrongly luminous and refplendent blue , and the Cinnaber of. a faint and dark blue. Which puts it out of difpute^ that the Cinnaber refleds the red Light much more copioufly than the ////^r^ marine doth, and the [158] the ultra-rmxmt refleds the blue Light much more copiouily than the Cinnaber doth. The fame Experiment may be tried fuccefsfully with red Lead and Indigo, or with any other two colour'd Bodies, if due allowance be made for the different ftrength or weaknefs of their Co- lour and Light. And as the rcafon of the Colours of natural Bodies is evident by thefe Experiments, fo it is farther confirmed and put palt difpute by the two firft Experiments of the firft Part, where- by 'twas proved in fuch Bodies that the refled- ed Lights which differ in Colours do differ alfo in degrees of RefrangibiUty. For thence it's certain, that fome Bodies refled the more re- frangible, others the lefs refrangible Rays more copioufly. And that this is not only a true reafon of thefe Colours, but even the only reafon may ap- pear farther from this confideration , that the Colour of homogeneal Light cannot be chan- ged by the Reflexion of natural Bodies. For if Bodies by Reflexion cannot in the lead change the Colour of any one fort of Rays, they cannot appear colour'd by any other means than by refleding thofe which either are of their own Colour, or which by mixture mud pro- duce it. But in trying Experiments of this kind care muft be had that the Light be fufliciently ho- mogeneal. For if Bodies be illuminated by the ordinary prifmatick Colours , they will appear neither of their own Day-light Colours, nor of the Colour of the Light caft on them , but of fome [ 159 ] fome middle Colour between both , as I have found by Experience. Thus red Lead (for in- ftance) illuminated with the ordinary prifma- tick green will not appear either red or green, but orange or yellow , or between yellow and green, accordingly as the green Light by which 'tis illuminated is more or lefs compounded. For becaufe red Lead appears red when illu- minated with white Light, wherein all forts of Rays are equally niix'd, and in the green Light all forts of Kays are not equally mix'd, the Ex- cefs of the yellow-making, green-making and blue-making Rays in the incident green Light, will caufe thofe Rays to abound fo much in the refledled Light as to draw the Colour from red towards their Colour. And becaufe the red Lead refleds the red-making Rays mofl copioufly in proportion to their number, and next after them the orange-making and yellow- making Rays ; thefe Rays in the reflected Light will be more in proportion to the Light than they were in the incident green Light, and there- by will draw the refleded Light from green to- wards their Colour. And therefore the red Lead will appear neither red nor green, but of a Colour between both. In tranfparently colour'd Liquors 'tis obfer- vable, that their Colour ufes to vary with their thicknefs. Thus, for inltance, a red Liquor in a conical Glafs held between the Light and the Eye , looks of a pale and dilute yellow at the bottom where 'tis thin, and a little higher where 'tis thicker grows orange , and where 'tis Itill thicker becomes red , and w^here 'tis thickell the [ 1^0 ] the red is deepeit and darkell. For it is to be conceiv'd that fiich a Liquor flops the indigo- making and violet-making Rays molt eafily, the blue-making Rays more difficultly, the green- making Rays itill more difficultly, and the red- making moll difficultly : And that if the thick- nefs of the Liquor be only lb much as fuffices to Hop a competent number of the violet-ma- king and indigo-making Rays , without dimi-^ milling much the number of the relt, the reft mult {by Tr op. 6. Tart z.) compound a pale yellow. But if the Liquor be fo much thicker as to itop alfo a great number of the blue-ma^ king Rays, and Ibme of the green-making, the relt mull compound an orange ; and where it is fo thick as to Hop alio a great number of the green-making and a conliderable number of the yellow-making, the relt mult begin to com- pound a red, and this red mult grow deeper and darker as the yellow-making and orange- making Rays are more and more Itopp'd by in- creafmg the thicknefs of the Liquor, fo that few Rays befides the red-making can get through. Of this kind is an Experiment lately related to me by Mr. Halley^ who, in diving deep into the Sea in a diving VelTel, found in a clear Sun- lliineDay, that when he was funk many Fathoms deep into the Water, the upper part of his Hand on which the Sun Ihone directly through the Water and through a fmall Glafs Window in the VelTel, like that of a Damask Rofe, and the Water below and the under part of his Hand illuminated by Light reflefted from the Water below below look'd green. For thence it may be ga« thcr'd, that the Sea Water refledls back the violet and blue-making Rays molt eafily, and lets the red-making Rays pafs moll freely and copioufly to great depths. For thereby the Sun's dired Light at all great depths, by reafon of the predominating red-making Rays, muft ap- pear red ; and the greater the depth is, the ful- ler and inteni'er mull that red be. And at fuch depths as the violet-making Rays fcarce pene- trate unto, the blue-making, green-making and yellow- making Rays being relieved from be- low more copioufly than the red-making ones, muft compound a green. Now if there be two Liquors of full Colours, fuppofe a red and a blue, and both of them lb thick as fulKces to make their Colours fuffici- ently full ; though either Liquor be fufficient- ly tranfparent ^part, yet will you not be able to fee through both together. For if only the red-making Rays pafs through one Liquor, and only the blue-making through the other, no Rays can pafs through both. This Mr. Hook tried cafually with Glafs Wedges filled with red and blue Liquors, and was furprized at the unex- peded event , the reafon of it being then un- known ; which makes me trull the more to his Experiment, though I have not tried it my felf But he that would repeat it, mull take care the Liquors be of very good and full Colours. Now whilft Bodies become coloured by refle(^- ing or tranfmitting this or that fort of Rays more copioufly than the reft, it is to be conceived that they flop and flifle in themfelves the Rays M which [ 1^2] which they do not refled or tranfmit. For if Gold be foliated and held between your Eye and the Light, the Light looks of a greenilh blue, and therefore malTy Gold lets into its Body the blue-making Rays to be reflefted to and fro within it till they be itopp'd and flifled , whilft it reflefts the yellow-making outwards, and thereby looks yellow. And much after the fame manner that Leaf Gold is yellow by re- fle6ied, and blue by tranfmitted Light, and maf- fy Gold is yellow in all Pofitions of the Eye ; there are fome Liquors, as the Tindure of L'tgnum Nephritkum^ and fome forts of Glafs which tranlmit one fort of Light molt copiouf- ly, and refleft another fort, and thereby look bf feveral Colours, according to the pofition of the Eye to the Light. But if thefe Liquors or GlalFes were fo thick and maffy that no Light could get through them, I quellion not but they would like all other opake Bodies appear of one and the fame Colour in all Pofitions of the Eye, though this I cannot yet affirm by ex- perience. For all coloured Bodies, fo far as my Obfervation reaches , may be feen through if made fufficiently thin, and therefore are in fome meafure tranfparent, and differ only in degrees of Tranfparency from tinged tranfparent Li- quors ; thefe Liquors, as well as thofe Bodies, by a fufficient thicknefs becoming opake. A tranfparent Body which looks of any Colour by tranfmitted Light , may alfo look of the fame Colour by reflefted Light , the Light of that Colour being refleded by the farther Surface of the Body, or by the Air beyond it. And then then the reflected Colour will be diminiflieds, and perhaps ce-:\(G, by making the Body very thick, and pitching it on the backfide to dimi- nifli the Reflexion of its farther Surface, fo that the Light refieded from the tinging Particles may predominate. In fuch cafes, the Colour of the retlefted Light will be apt to vary from that of the Light tranfmitted. But whence it is that tinged Bodies and Liquors refled fome foit of Rays , and intromit or tranfmit other forts, fhall be faid in the next Book. In this Propofition I content my felf to have put it paft dil'pute, that Bodies have fuch Properties^ and thence appear coloured. "PR OT. XL Pros. VI. By mixhig coloured Lights to compound a beam of Light of the fame Colour and Nature with a beam of the Sun's dire& Lights and thereiit to experience the Truth of the foregoing 'Fro-^ ^ofitions. LET. ABC ^^f {\ViFig.r6.'] reprefent a Prifm by which the Sun's Light let into a dark Chamber through the Hole F, may be refracted towards the Lens MN, and paint up- on it at/, ^, ;, J and ?, the uiual Colours vio- let, blue, green, yellow and red, and let the diverging Rays by theReiracfion of this Lens converge again towards X^ and there, by the mixture of all thoic their Colours, compound a white according to what was ilievvn above. M % Thefi Then let another Prifm D E G deg^ parallel to the former, be placed at X, to refradl that white Light upwards towards Y. Let the re- fra^ling Angles of the Prifms, and their diltances from the Lens be equal, fo that the Rays which converged from the Lens towards X, and with- out Refradion, would there have crofled and diverged again , may by the Refraftion of the fecond Prifm be reduced into Parallelifm and diverge no more. For then thofe Rays will re- compofe a beam of white Light X Y . If the refrading Angle of either Prifm be the bigger, that Prifm muil be fo much the nearer to the Lens. You will know when the Prifms and the Lens are well fet together, by obferving if the beam of Light XY which comes out of the fe- cond Prifm be perfedly white to the very edges of the Light, and at all diltances from the Prifm continue perfectly and totally white Hke a beam of the Sun's Light. For till this happens , the pofition of the Prifms and Lens to one another mufl be correded, and then if by the help of a long beam of Wood, as is reprefented in the Figure, or by a Tube, or fome other fuch In- ftrument made for that purpofe, they be made fafl in that fituation , you may try all the fame Experiments in this compounded beam of Light X Y, which have been made in the Sun's dired Light, For this compounded beam of Light has the fame appearance, and is endowed with all the fame Properties with a dired beam of the Sun's Light, fo far as my Obfervation reaches. And in trying Experiments in this beam you may by flopping any of the Colours /, ^, r^ s and [ 1^5 ] and t^ at the Lens, fee how the Colours pro- duced in the Experiments are no other than thofe which the Rays had at the Lens before they enter the compofition of this Beam : And by confequence that they arife not from any new modifications of the Light by Refradions and Reflexions , but from the various Separations and Mixtures of the Rays originally endow'd with their colour-making qualities. So, for inllance, having with a Lens 4-^ Inches broad, and two Prifms on either hand 6^ Feet diftant from the Lens, made fuch a beam of compounded Light : to examin the reafon of the Colours made by Prifms, I refracted this compounded beam of Light X Y with another Prifm HIK ^Z;, and thereby caft the ufual prif- matick Colours PQRSTupon the Paper LV placed behind. And then by flopping any of the Colours/,^, r, j, ^, at the Lens, I found that the fame Colour would vanifli at the Pa- per. So if the purple / was flopp'd at the Lens , the purple P upon the Paper would va- nifli, and the reft of the Colours would remain unalter'd, unlefs perhaps the blue, fo far as fome purple latent in it at the Lens might be feparated from it by the following Refradlions. And fo by intercepting the green upon the Lens, the green R upon the Paper would vanifh, and fo of the reft ; which plainly fhews, that as the white beam of Light X Y was compounded of feveral Lights varioufly colour'd at the Lens, fo the Colours which afterwards emerge out of it by new Refraftions are no other than thofe of which its whitenefs was compounded. The M 3 Refra- I 166] Refradiofi of thePrifm HIK >^^ generates the Colours PQRST upon the Paper, not by changing the colorific qualities of the Rays, but by feparating the Rays which had the very fame colorific qualities before they enter'd the Com- pofition of the refradied beam of white Light X Y. For otherwife the Rays which were of one Colour at the Lens might be of another upon the Paper, contrary to what we find. So again , to examin the reafon of the Cor lours of natural Bodies, I placed fuch Bodies in the Beam of Light X Y, and found that they all appeared there of thole their own Colours which they have in Day-light , and that thofe Colours depend upon the Rays which had the fame Colours at the Lens before they enter'd the Compofition of that beam. Thus, for in- stance , Cinnaber illuminated by this beam ap- pears of the fame red Colour as in Day-light 5 and if at the Lens you intercept the green-ma- king and blue-making Rays, its rednefs will be- come more full and lively : But if you there in- tercept the red-making Rays, it will not any longer appear red, but become yellow or green, . or of fome other Colour, according to the forts of Rays which you do not intercept. So Gold in this Light X Y appears of the fame yellow Colour as in Day-light, but by intercepting at the Lens a due quantity of the yellow-making Rays it will appear white hke Silver (as I have tried ) which fhews that its yellownefs arifes from the Excefs of the intercepted Rays tinging that whitenefs with their Colour when they are let pafs. So the infufion of L'tgnum Nephritic cum Book! PaitirnatEl # X ^8'- 5 V-W / • BookLPaitir.HatcI Fio- _^. „ .^ :- ^ ^' F ^»*F^ 1 !. "I iT^^^ • o FOLDOUT BLANK Bookl Fiitl . Plate HI o Book I Pail U/Hatc^ L X ^•y^ i cum ( as I have alfo tried ) when held in this beam of Light X Y, looks blue by the reflec^t- ed part of the Lights ^nd. red by thie. traxifmit- tjed part ^f%, as when 'tis view'd in Day-light, l|ut if you inte!Pcept the blue at the Lens the infufion will lofe its reflected blue Colour, whilil its tranfmitted red remains perfed and by the lofs of fome blue-making Rays wherewith it Was allay 'd becomes more intenfe and full. And, on the contrary, if the red and orange-making Rays be intercepted at the Lens, the Infufion will lofe its tranfmitted red, whillt its blue will re- main and become more full and perfed. Which lliews, that the Infufion does not tinge the Rays with blue and red, but only tranfmit thofe molt copioufly which were red-making before, and refleds thofe molt copioufly which were blue-making before. And after the fame man- ner may the Reafons of other Phaenomena be examined, by trying them in this artificial beam of Light XY. M4 THE li6S] THE SECO'ND BOOK OPTIC KS. PART I. Obfervations concerning the ReJIexions, Refra- Bionsy and Colours of thin transparent Bo- dies. |T has been obferved by others, that trani parent Subflances, as Glafs, War ter, Air, ^c. when made very thin by being blown into Bubbles, or otherwile formed into Plates, do exhibit various Colours according to their various thinnefs, although at a greater [ ^^9 ] a greater thicknefs they appear very clear and colourlefs. In the former Book I forbore to treat of thefe Colours, becaufe they feemed of a more difficult Confideration , and were not neceiTary for eftabUfliing the Properties of Light there difcourfed of But becaule they may con- duce to farther Difcoveries for completing the Theory of Light, efpecially as to the conltitu- tion of the parts of natural Bodies, on which their Colours or Tranfparency depend ; I have here fct down an account of them. To render this Difcourfe fliort and diffind, I have firlt de- fcribed the principal of my Obiervations , and then confider'd and made ufe of them. The Obfervations are thefe. Obf. I. Compreiling two Prifms hard toge- ther that their fides ( which by chance were a very little convex) might fomewhere touch one another : I found the place in which they touch- ed to become abfolutely tranfparent, as if they had there been one continued piece of Glals. For when the Light fell fo obliquely on the Air, which in other places was between them, as to be all reflefted ; it feemed in that place of contad to be wholly tranfmitted, infomuch that when look'd upon, it appeared Uke a black or dark fpot, by reafon that httle or no fenfible Light was refleded from thence, as from other places ; and when looked through it feemed (as it were ) a hole in that Air which was formed into a thin Plate, by being comprefs'd between the GlaiTes. And through this hole Objeds that were beyond might be feen diflinftly, which could not at all be feen through other parts of the [ I70 ] the GlafTes where the Air was interjacent. Al- though the Glalles were a little convex, yet this tranlparent fpot was of a conliderable breadth, which breadth fecmed principally to proceed from the yielding inwards of the parts of the GlaiTes, by reafon of their mutual preffure. For by preihng them very hard together it would become much broader than otherwife. Obf. X. W hen the Plate of Air, by turning the Prifms about their common Axis , became fo little inclined to the incident Rays, that fome of them l~)egan to be tranfmitted , there arofe in it many llender Arcs of Colours which at firlt were fhaped almoft like the Conchoid , as you fee them delineated in the firft Figure. And by continuing the Motion of the Prifms, thefe Arcs increafed and bended more and more a- bout the faid tranfparent fpot, till they were completed into Circles or Rings incompaffing it, and afterwards contiaually grew more and more contraded. Thefe Arcs at their firlt appearance were of ' a violet and blue Colour , and between them were white Arcs of Circles, which prefently by continuing the Motion of the Prifms became a Uttle tinged in their inward Limbs with red and yellow, and to their outward Limbs the blue was adjacent. So that the order of thefe Colours from the central dark fpot, was at that time white, blue, violet; black, red, orange, yellow, white, blue, violet, ^c. But the yel- low and red were much fainter than the blue and violet. The [I7i] The Motion of the Prifms about their Axis yoeing continued, thefe Colours contracted more [and more, fhrinking towards the whitenefs on either fide of it, until they totally vanillied in- to it. And then the Circles in thofe parts ap- peared black and white, without any other Co- lours intermix'd. But by farther moving the Prifms about, the Colours again emerged out of the whitenefs, the violet and blue at its inward Limb, and at its outward Limb the red and yellow. So that now their order from the cen- tral Spot was white, yellow, red; black; vio- let, blue, white, yellow, red, ^c. contrary to what it was before. Oiff. 3. When the Rings or fome parts of them appeared only black and white, they were very diftind and well defined , and the back- nefs feemcd as intenfe as that of the central Spot. Alfo in the Borders of the Rings, where the Colours began to emerge out of the white- nefs, they were pretty diilindl, which made thei3 vifible to a very great multitude. I have fome times number 'd above thirty Succeflions (reckoning every black and white Ring for one Succeffion) and feen more of them, which by reafon of their fmalnefs I could not number. But in other Pofitions of the Prifms , at which the Rings appeared of many Colours , I could not diltinguilh above eight or nine of them, and the Exterior of thofe were very confufed and dilute. In thefe two Obfervations to fee the Rings di- ftind:, and without any other Colour than black and white, 1 found it neceifary to hold my Eye at [ 172 ] at a good diftance from them. For by ap- proaching nearer, although in the fame inclina- tion of my Eye to the Plane of the Rings, there emerged a blueifli Colour out of the white, which by dilating it felf more and more into the black, render'd the Circles lefs diltind:, and left the white a little tinged with red and yel- low. I found alfo by looking through a ilit or oblong hole, which was narrower than the Pu- pil of my Eye, and held clofe to it parallel to the Prifms , I could fee the Circles much di- {l:in<^t:er and vifible to a far greater number than otherwife. Obf. 4. To obferve more nicely the order of the Colours which arofe out of the white Circles as the Rays became lefs and lefs incli- ned to the Plate of Air; I took two Objeft- glaffes, the one a Plano-convex for a fourteen Foot Telefcope , and the other a large double Convex for one of about fifty Foot ; and upon this, laying the other with its plane fide down- wards, I preiTed them flowly together, to make the Colours fucceffively emerge in the middle of the Circles, and then flowly lifted the upper Glafs from the lower to make them fucceffive- ly vanilh again in the fame place. The Colour, W'hich by prelling the GlafTes together emerged iaftinthe middle of the other Colours, would upon its firll appearance look like a Circle of a Colour almoft uniform from the circumference to the center, and bycompreffingtheGlaifes ftill more, grow continually broader until a new Co- lour emerged in its center, and thereby it became a Ring encompalling that new Colour. And by com- I 173 ] comprefTing the Glaflcs Hill more, the diameter of this Ring would increafe, and the breadth of its Orbit or Perimeter decreafe until another new Colour emerged in the center of the lalt: And fo on until a third , a fourth , a fifth , and other following new Colours fucccllivcly emer- ged there, and became Rings encompaffing the innermolt Colour, the lalt of which was the black Spot. And, on the contrary? by hfting up the upper Glafs from the lower, the diame- ter of theRings would decreafe, and the breadth of their Orbit increafe, until their Colours reach- ed fuccefTively to the center ; and then they being of a confiderable breadth, I could more eafily difcern and diilinguifli their Species than before. And by this means I obferv'd their Suc- cefTion and Quantity to be as followeth. Nexf to the pellucid central Spot made by the contacT: of theGlafles fucceeded blue, white, yello\\', and red. The blue was fo little in quan- tity that I could not dilcern it in the Circles made by the Prifms, nor could I well dilHnguilh any violet in it, but the yellow and red were pretty copious, and fcemed about as much in extent as the white, and four or five times more than the blue. The next Circuit in order of Colours immediately encompafling thefe were violet, blue, green, yellow, and red : and thefe were all of them copious and vivid, excepting the green. Which was very little in quantity, and feemed much more faint and dilute than the other Colours. Of the other four, the vio- let was the leaft in extent, and the blue lefs than the yellow or red. The third Circuit or Order Order was purple , blue, green, yellow, and red ; in which the purple feemed more reddifli than the violet in the former Circuit , and the green was much more confpicuous, being as brisk and copious as any of the other Colours, except the yellow ; but the red began to be a little faded, incHning very much to purple. Af- ter this fucceeded the fourth Circuit of green and red. The green was very copious and live- ly, inclining on the one fide to blue, and on the other fide to yellow. But in this fourth Circuit there was neither violet, blue, nor yel- low, and the red was very imperfed and dir- ty. Alfo the fucceeding Colours became more and more imperfed: and dilute, till after three or four revolutions they ended in perfedl whitenefs. Their form, wheri the GlafTes were mofl comprefs'd fo as to make the black Spot appear in the center, is deUneated in the le- cond Figure ; " where a^ b^ , f, 4 ^ •* /» gt h h k : /, m^ n^ o, f : q^ r : j, t : ^', x : y, z de- note the Colours reckon'd in order from the center, black, blue, white, yellow, red: vio- let , blue , green , yellow , red : purple , blue , green, yellow, red : green, red : greeniih blue, red : greenifh blue, pale red : greenifli blue, reddifti white. Obf. 5*. To determine the interval of the Glafles, or thicknefs of the interjacent Air, by which each Colour was produced, I meafured the Diameters of the firft lix Rings at the moit lucid part of their Orbits, and fquaring them, I found their Squares to be in the arithmetical Progreffion of the odd Numbers, i, 3, $, 7, 9, 11. And [ 175 1 And fince one of thefe Glalles was plane, and the other fphcrical, their Intervals at thole Rings muit be in the fame Progrefiion. I meafured alfo riie Diameters of the dark or faint Rings between the more lucid Colours, and found their Squares to be in the arithmetical Progref- fiQn of the even Numbers, 2, 4, 6, 8, 10, 12. And it being very nice and difficult to take theie meafures exadly ; I repeated them divers times at divers parts of the Glaifes, that by their Agreement I might be coniirmed in them. And the fame method I ufed in determming fome others of the following Obfervations. Obf. 6. The Diameter of the fixth Ring at the moft lucid part of its Orbit was -^ parts of an Inch , and the Diameter of the Sphere on which the double convex Objeclri: - glals was ground was about lox Feet, and hence I ga- thered the thicknefs of the Air or Aereal Inter- val of the Glailes at that Ring. But lome time after, fufpeding that in making this Obfervation I had not determined the Diameter of the Sphere with lufKcient accurateneib, and being uncertain whether the Plano-convex Clafs was truly plane, and not fomething concave or con- vex on that fide which I accounted plan-j; and whether I had not preiled the Glailes together, as I often did , to make them touch ; (For by prefling fuch Glailes together their parts eafily yield inwards, and the Rings thereby become fenlibly broader than they would be , did the Glafles keep their Figures.) I repeated the Experiment, and found the Diameter of the fixth fixth lucid Ring about ^~ parts of an Inch. I repeated the Experiment alfo with fuch an Ob- jeft-glafs of another Telefcope as I had at hand. This was a double Convex ground on both fides to one and the fame Sphere , and its Fo- cus was dillant from it 83' Inches. And thence, if the Sines of Incidence and Refradion of the bright yellow Light be afllimed in proportion as II to 17, the Diameter of the Sphere to which the Glafs was figured will by computa- tion be found i8i Inches. This Glafs I laid upon a flat one, fo that the black Spot appear- ed in the middle of the Rings of Colours with- out any other Prelfure than that of the weight of the Glafs. And now meafuring the Diame- ter of the fifth dark Circle as accurately as I could, I found it the fifth part of an Inch pre- cifely. This Meafure was taken with the points of a pair of Compafl'es on the upper Surface on the upper Glafs, and my Eye was about eight or nine Inches diftance from the Glafs, almofl perpendicularly over it , and the' Glafs was 4 of an Inch thick, and thence it is eafy to colleft that the true Diameter of the Ring be- tween the GlafTes was greater than its meafur'd Diameter above the GlafTes in the Proportion of 80 to 79, or thereabouts, and by confequence equal to i4 part of an Inch, and its true Semi- diameter equal to ^^- parts. Now as the Dia- meter of the Sphere (i8i Inches) is to the Se- mi-diameter of this fifth dark Ring (-yy parts of an Inch) fo is this Semi-diameter to the thick- nefs of the Air at this fifth dark Ring ; which is there- [ 177 ] therefore -~^ or ~— ~- parts of an Inch ; and 5-67931 17/47^4 * the fifth part thereof, viz. the ^^ part of an Inch, is the thicknefs of the Air at the firit of thefe dark Rings. The fame Experiment I repeated with ano- ther double convex Objeft-glals ground on both fides to one and the fame Sphere. Its Focus was diflant from it i684 Inches, and therefore the Diameter of that Sphere was 184 Inches* This Glafs being laid upon the fame plain Glals, the Diameter of the fitth of the dark Rings, when the black Spot in their center appear 'd plainly without preiling the GlalTes, was by the meafure of the Compailes upon the upper Glafs 600 P^^^^ ^^ ^"^ Inch, and by confequence be- 1222 tween the GlafTes it was g^. For the upper Glafs was 4 of an Inch thick, and my Eye was diltant from it 8 Inches. And a third propor- tional to half this from the Diameter of the Sphere is ^^ parts of an Inch. This is there- fore the thicknefs of the Air at this Ring, and a fifth part thereof, viz, the gj-:-th part of an Inch is the thicknefs thereof at the tirft of thQ Rings, as above. I tried the fame thing by laying thefe Ob- jed-glalfes upon flat pieces of a broken Look- ing-glafs, and found the fame Meafures of the Rings : Which makes me rely upon them till N they [ 178 ] they can be determin'd more accurately by Glaffes ground to larger Spheres, though in fuch GlalFes greater care mull be taken of a true Plane. Thefe Dimenfions were taken when my Eye was placed almoft perpendicularly over the Glalles, being about an Inch, or an Inch and. a quarter , diflant from the incident Rays , and eight Inches diflant from the Glafs ; fo that the Rays were inclined to the Glais in an Angle of about four Degrees. • Whence by the following Obfervation you will underftand, that had the Rays been perpendicular to the GlafTes, the thicknefs of the Air at thefe Rinffs would have been lefs in the proportion of the Radius to the Secant of four Degrees, that is of loooo to 10024. Let the thicknelTes found be therefore diminiih'd in this Proportion, and they will be- come en — and ^r~r » or ( to ufe the ncarefl 88952 S9063.' ^ -^ round number ) the 3-^th part of an Inch,! This is the thicknefs of the Air at the darkeft " part of the firlt dark Ring made by perpendi- cular Rays, and half this thicknefs multiplied by the Progrellion, i, 3, 5, 7, 9, 11, ^c. gives the thicknefles of the Air at the moil luminous parts of all the brightefl Rings, viz. ;zg^> i"78k> f^' '-^^ ^'' ^^^'^ arithmetical Means — h— -, ^n ■, ■■ r.' , ^c. being its 178000' 17800G' 178000' o thicknefles iit the darkeft parts of all the dark ones. s ' Obf, [ 175 ] Ohf 7. The Rings were leafl when my Eye was placed perpendicularly over the Glalles iii the Axis of the Rings: And when I view'd them obliquely they became bigger, continual- ly fwelling as I removed my Eye farther from the Axis. And partly by meafuring the Diame- ter of the fame Circle at feveral Obliquities of my Eye, partly by other means, as alfo by ma- king ufe of the two Prifms for very great'Obli- quities, I found its Diameter, and confequent- ly the thicknefs of the Air at its Perimeter in all thole Obliquities to be very nearly in the Proportions exprefs'd in this Table. Angle of In- Angle of Re- T)iameterThicknefs | cidence on fraction in- of the of the the Air. to the Air. Ring. Air. Deg. Min. 00 GO 00 03 10 10 06 26 10 oo 10.V IOtV IX 45- 20 OQ 10-^ IC| 18 49 30 oo io.| 114 24 30 40 00 114 13 29 37 5*0 00 124 15-4 33 5B 60 00 H 20 35- 47 6$ 00 15-7 2'3^ 37 19 70 00 i6| 28^ 38 33 75 00 ^n 37 39 27 80 03 22^ 5-2--? 40 CO 85- 00 2-9 84.V 40 II 90 00 35" 1224 N 2/ In [i8o] In the two firlt Columns are exprefs'd the Obliquities of the incident and emergent Rays to the Plate of the Air^ that is, their Angles of Incidence and Refradion. In the third Column the Diameter of any coloured Ring at thofe Ob- liquities is expreiled in parts, of which ten con- Ititute that Diameter when the Rays are per- pendicular. And in the fourth Column the thicknefs of the Air at the circumference of that Ring is expreiled in parts of which alfo ten conltitute its thicknefs when the Rays are perpendicular. And from thefe Mcafures I feem to gather this Rule : That the thicknefs of the Air is proportional to the fecant of an Angle, whofe Sine is a certain mean Proportional between the Sines of Incidence and Refraction. And that mean Proportional, fo far as by thefe Meafures I can determine it, is the fird' of an hundred and fix arithmetical mean Proportionals be- tween thofe Sines counted from the bigger Sine, that is, from the Sine of Refraction when the Refradion is made out of the Glafs into the Plate of Air, or from the Sine of Incidence when the Refraction is made out of the Plate of Air into the Glafs. Obj: 8. The dark Spot in the middle of the Rings increafed alfo by the Obliquation of the Eye, although almoll infenfibly. But if inflead of the Objed-glafles the Prifms were made ufe of, its Increafe was more manifeit when view- ed fo obliquely that no Colours appear'd about it. It u as leafl when the Rays were incident molt obliquely on the^ interjacent Air, and as I the [ isi ] the obliquity dccreafed it increafcd more and more until the coloured Rings appear'd, and then decreafed again, but not fo much as it in- creafed before. And hence it is evident, that the Tranfparency was not only at the abfolute Contact of the Glaifes, but alio where they had fome little Interval. I have fometimes oblcrved the Diameter of that Spot to be between half and two tifth parts of the Diameter of the ex- terior Circumference of the red in the iiril Cir- cuit or Revolution of Colours when view'd al- moit perpendicularly; whereas when viev/'d obliquely it hath wholly vaniili'd and become opake and white like the other parts of the Glafs; whence it may be colledred that the Glaifes did then fcarcely, or not at all, touch one another, and that their Interval at the pe- rimeter of that Spot when view'd perpendicu- larly was about a fifth or fixth part of their In- terval at the circumference of the faid red. Obf. 9. By looking through the two conti- guous Objeft-glaHes, I found that the interja- cent Air exhibited Rings of Colours, as well by tranfmitting Light as by reflefting it. The central Spot was now white, and from it the order of the Colours were yellovvifli red ; black, violet, blue, white, yellow, red ; violet, blue, green , yellow , red , ^c. But thefe Colours were very faint and dilute, unlefs when the Light was trajecfled very obhquely through the Glaifes : For by that means they became pretty vivid. Only the firft yellowiili red, like the blue in the fourth Obfervation, was fo little and faint as fcarcely to be difcern'd. Comparing N 3 the [l82] the coloured Rings made by Reflexion, with thefe made by tranfmiffion of the Light ; I found that white was oppofite to black, red to blue, yellow to violet, and green to a Compound of red and violet. That is, thofe parts of the Glafs were black when looked through, which when looked upon appear'd white, and on the contrary. And fo thofe which in one cafe ex- hibited blue, did in the other cafe exhibit red. And the hke of the other Colours. The man- ner you have reprefented in the third Figure, where A B, CD, are the Surfaces of the Glaf- fes contiguous at E, and the black Lines be- tween them are their Diftances in arithmetical Progreflion, and the Colours written above are feen by reflefted Light, and thofe below by Light tranfmitted. Obf. lo. VVetting the Objeft-glafles a little at their edges, the Water crept in flowly be- tween them, and the Circles thereby became lefs and the Colours more faint : hifomuch that as the Water crept along one half of them at which it fn*ft arrived would appear broken off from the other half, and contra61cd into a lefs Room. By meafuring them I found the Pro- portions of their Diameters to the Diameters qf the like Circles made by Air to be about fevcn to eight, and confequently the hitervals of the Glafles at like Circles, caufed by thofe two Me- diums Water and Air, are as about three to four, perhaps it may be a general Rule, That if any other Medium more or lefs denfe than Water be comprefs'd between the Glaifes, their Inter- vals ^t the Rings caufed thereby will be to their Intervals [.1 83] fortervals caufed by interjacent Air, as theSiue:? are which meafure the Refradion made out of that Medium into Air. O^/! n. When the Water was between the Glafles, if I prefTcd the upper Glafsvariou fly at its edges to make the Rings move nimbly from one place to another, a httle white Spot would immediately follow the center of them , which upon creeping in of the ambient Water into that place would prcfently vanifli. Its appearance was fuch as interjacent Air would have caufed, and it exhibited the fame Colours. But- if was not Air, for where any Bubbles cfAii* were in the Water they would not vanin.. The Refle- xion mufl: have rather been caufed by a fubtiler Medium, which could recede through the Glafles at the creeping in of the Water. 01^/^ 12. Thefe Obfervations were made in the open Air. But farther co examine the Ef- feds of colour'd Light Mling on the Glafl!es, I darken'd the Room, and view'd them by Re- flexion of the Colours of a PrifiT! cafl on a Sheet of white Paper, my Eye being fo placed that I could fee the colour'd Paper by Reflexion in the Glafles, as in a Looking-glafs. And by this means the Rings became diflincter and vifible to a hi' greater number than in the open Air. I have fometimes feen more than twenty of them, whereas in the open Air I could not dif- cern above eight or nine. Oi/f! 1 3. Appointing an AfTiflant to move the Prifm to and fro about its Axis, that all the Colours might fucceflively fall on that part of the Paper which I faw by Reflexion from thai N 4 " part I m 1 part of the Glaffes, where the Circles appear'd, fo that all the Colours rrlight be fuccefiively re- flefted from the Circles to my Eye whilft I held it immovable, I found' the "Circles which the red Li^^ht made to be manifeflly bigger than thole which were made by the blue and violet. And it was very pleafant to fee them gradually fwell oi' conrrad accordingly as the Colour of the Light was changed. . The Interval of the Glaf- fes at any of the Rings when they were made by the utmoft red Light, was to their Interval at the fame Ring when made by the utmoll: violet, greater than as 3 to 2, and lefs than as 13 to 8. By the molt of my Obfervations it was as 14 to 9. And this Proportion feem'd very, nearly the fame in all Obliquities of my Eye ; unlefs when two Prifms were made ufe of in- flead of the Objeft-glaiTes. For then at a cer- tain great obliquity of my Eye, the Rings made by the feveral Colours feem'd equal, and at -a greater obHquity thofe made by the violet would be greater than the fame Rings made by the red : the Refra6lion of the Prifm in this cafe cauling the moft refrangible Rays to fall more obliquely on that plate of the Air than the leall refrangible ones. Thus the Experiment fuc- ceeded in the colour'd Light , which was fuf- ficiently Ib'ong and copious to make the Rings fenfible. And thence it may be gather'd, that if the moft refrangible and leaft refrangible Rays had been copious enough to make the Rings fenfible without the mixture of other Rays, the Proportion which here was 14 to 9 would have been a little greater, fuppofe 144 or 144 to 9. [i85] Ohf. 14. Whilft the Prilm was turn'd about its Axis with an uniform Motion, to make all the feveral Colours fi\ll luccefiivcly upon the ObjcCl-glalles, and thereby to make the Rings contract and dilate : The Contraction or Dila- tation of each Ring thus made by the variation of its Colour was fwiftelt in the red, aiKl ilow- efl in the violet, and in the intermediate Colours" it had intermediate degrees of Celerity. Com- paring the quantity of Contraction and j)ilata- tion made by all the degrees of each Colour, I found that it 'was greateil in the red ; lefs in the yellow, Hill lefs in the blue, and leait in the violet. And to make as jull an Eltimation as I could of the Proportions of their Contradions or Dilatations , I obferv'd that the' whole Con- traction or Dilatation of the Diameter of anv Ring made by all the degrees of red , was to that of the Diameter of the fame Ring made by all the degrees of violet, as about four to three, or five to four, and that when the Light was of the middle Colour between yellow and green, the Diameter of the Ring was very nearly an arithmetical Mean between the greatelt Diame- ter of the fame Ring made by the outmoll: red, and the lead Diameter thereof made by the outmoll violet : Contrary to what happens in the Colours of the oblong Speclrum made by the Refradion of a Prifm, where the red is mod contraded, the violet moit expanded-, aind in the midit of all the Colours is the Con- fine of green and blue. And hence I feem to colle(^l that the thicknelTes of the Air between the Glailes there, where the Ring is fucce/Tive- [ 18^ ] ly made by the limits of the five principal Co- lours (red, yellow, green, blue, violet) in or- der (that is, by the extreme red, by- the hmit of red and yellow in the middle of the orange, by the limit of yellow and green, by the limit of green and blue, by the Hmit of blue and violet in the middle of the indigo, and by the extreme violet) are to one another very nearly as the fix lengths of a Chord which found the Notes in a /ixth Major, fol^ la^, m'l^ fa^ fol^ la. But it agrees fomething better with the Obfer- vation to fay , that the thicknelfes of the Air between theGlafles thercj where the Rings aret fucceilively made by the limits of the feven Co- lours, red, orange, yellow^ ^"eep? blue, indi- go , violet in order, are to one another as the Cube Roots of the Squares of the eighjt lengths of a Chord, which found the Notes in an eighth, fol^ Idy fay foly lay ffiiy fuy fil \ that is, as the Cube Roots of the Squares q{ ^he Numbers, I3 * S ? ^ J _9_ • ObJ. 15. Thefc Rings "were not of various Colours hke thofe made in the open Air, but appeared all over of that prifmatick Colour on- ly v/ith, which they were illuminated. And by projecting the priimatick Colours immediately upon the Glalles, I found that the Light which fell on the dark Spaces which were between the coloured Rings, was tranfmitted through the GlalTes without any variation of Colour. For on a white Paper placed behind, it would paint Rings of the fame Colour with thofe which vi^ere refleded, and of the bignefs of their im^ mediate Spaces. And from thence the origin of t ^S7] of thefe Rings is manifeft ; namely , that the Air between the Glafles, according to its vari- ous thicknefs, is dilpofed in fome places to re- fled, and in others to tranfmit the Light of a- ny one Colour ( as you may fee reprefented in the fourth Figure) ;ind in the lame place to re- fleft that of one Colour where jt tranfmits that of another. Obf. id. The Squares of the Diameters of thefe Rings made by any prifmatick Colour were in arithmetical Progi-cllion, as in the fifth Ob- fervation. And the Diameter of the fixth Cir- cle, when made by the citrine yellow, and viewed almolt perpendicularly, was about — parts of an Inch , or a little lefs , agreeable to the fixth Obfervation. The precedent Obfervations were made with a rarer thin Medium , terminated by a denfer, fuch as was Air or Water comprcfs'd between two Glafles. In thofe that follow are fet down the Appearances of a denfer Medium thin'd within a rarer , fuch as are Plates of Mufcovy G\'\k^ Bubbles of Water, and fome other thin Subftances terminated on all fides with Air. Obf, 17. If a Bubble be blown with Water firil made tenacious by dilTolving a little Soap in it, 'tis a common Obfervation, that after a while it will appear tinged vi'ith a great variety of Colours. To defend thefe Bubbles from be- ing agitated by the external Air (whereby their Colours are irregularly moved one among ano- ther, fo that no accurate Obfervation can be made of them,) as foon as I had blown any of them ti88] them I cover'd it with a clear Glafs, and by that means its Colours emerged in a very regular order, like fo many concentrick Rings encom- paffing the top of the Bubble. And as the Bub- ble grew thinner by the continual fubliding of the Water, thefe Rings dilated flowly and over- fpread the whole Bubble, defcending in order to the bottom of it, where they vaniili'd fuc- ceflively. In the mean while, after all the Co- lours were emerged at the top, there grew in the center of the Rings a fmall round black Spot, hke that in the firft Observation , which continually dilated it felf till it became fome- times more than 4 or i of an Inch in breadth before the Bubble broke. At firlt I thought there had been no Light reflefted froni the Wa- ter in that place , but obferving it more curi- oufly, I faw within it feveral fm-aller round Spots, which appeared much blacker and dark- er than the reft , whereby I knew that there was fome Reflexion at the other places which were not fo .dark as thofe Spots. And by far- ther Tryal I found that I could fee the Images of fome things (as of a Candle or the Sun) ve- ry faintly retledted, not only from the great black Spot, but alfo from the little darker Spots which Vere within it. Befides the aforefaid colour'd Rings there would often appear fmall Spots of Colours, af- cending and defcending up and down the fides of the Bubble, by reafon of fome Inequalities in the fubfiding of the Water. And fometimes fmall black Spots generated at the fides would afcend [ i89 ] alcend up to the larger black Spot at the top of the Bubble, and unite with it. Obf. 1 8. Becaufe the Colours of thefe Bub- bles were more extended and Hvely than thofe of the Air thinn d between two Glalles, and fo more eafy to be ditlinguiih'd , I fliall here give you a farther defcription of their order, as they w'ere obferv'd in viewing them by Reflexion of the Skies when of a white Colour , whilil a black fubltance was placed behind the Bubble. And they were thefe, red, blue; red, blue.; red, blue; red, green; red, yellow, green, blue, purple ; red, yellow, green, blue, violet ; red, yellow, white, blue, black. The three firil Succefllons of red and blue were very dilute and dirty, efpecially the firft, where the red feem'd in a manner to be white. Among thefe there w^as fcarce any other Colour fenfible befides red and blue, only the blues (and principally the fecond blue) inclined a Ht- tle to green. The fourth red was alfo dilute and dirty, but not fo much as the foiTner three; after that fucceeded little or no yellow, but a copious green, w^hich at firft inclined a little to yellow, and then became a pretty brisk and good wil- low green, and, afterwards changed to a bluifli Colour ; but there fucceeded neither blue nor \dolet. The fifth red at lirft inclined very much to purple, and afterwards became more bright ^nd brisk, but yet not very pure. This was fucceeded with a very bright and intenfe yel- low, which was but little in quantity, and foon chang'd t ^90] chdng'd to green : But that green was copious and Ibmething more pure, deep and lively, than the former green. After that follow'd an ex- cellent blue of a bright Sky-colour, and then a purple, which was lefs in quantity than the blue, and much inclined to red. The fixth red was at firfl of a very fair and lively Scarlet, and foon after of a brighter Co- lour, being very pure and brisk , and the beft of all the reds. Then after a lively orange fol- low'd an intenfe bright and copious yellow, which was alfo the bell of all the yellows , and this changed firfl to a greenifli yellow, and then to a greenifli blue ; but the green between the yellow and the blue, was very little and dilute, feeming rather a greenifli white than a green*. The blue which fucceeded became very good, and of a very fair bright Sky-colour , but yet fomething inferior to the former blue; aud the violet was intenfe and deep with little or no rednefs in it. And lefs in quantity than the blue. In the lafl red appeared a tindlure of fcarlet next to violet, which foon changed to a bright- er Colour, inclining to an orange ; and the yel- low which follow'd was at firfl pretty good and lively, but afterwards it grew more dilute, until by degrees it ended in perfed: whitenefs. And this whitenefs, if the Water was very te- nacious and well temper'd, would flovi^ly fpread and dilate it felf over the greater part of the Bubble ; continually growing paler at the top, v/here at length it would crack in many places, and thole cracks, as they dilated, would appear of [ ^91 ] of a pretty good, but yet obfcure and dark Sky-colour ; the white between the blue Spots diminifhmg, until it refembled the Threds of an irregular Net-v»^orky and foon after vani(h'd and left all the upper part of the Bubble of the faid dark blue Colour. And this Colour, after the aforefaid manner, dilated it felf downwards^ until fometimes it hath overfpread the whole Bubble. In the mean while at the top, which was of a darker blue than the bottom, and ap- pear'd alio full of many round blue Spots, fome- thing darker than the refl, there would emerge one or more very black Spots, and within thofe, other Spots of an intenier blacknefs , which I mention'd in the former Obferv^ation ; and thefe continually dilated themlelves until the Bubble broke. If the Water was not very tenacious the black Spots would break forth in the white, without any fenfible intervention of the blue. And fometimes they would break forth within the precedent yellow, or red, or perhaps within the blue of the fecond order, before the inter- mediate Colours had time to difplay themfelves. By this defcription you may perceive how great an affinity thefe Colours have with thofe of Air defcribed in the fourth Obfervation, al- though fet down in a contrary order, by reafoa that they begin to appear when the Bubble is thickeft, and are mofl conveniently reckon'd from the loweft and thickeft part of the Bub- ble upwards. O/ff 19. Viewing in feveral oblique Pofitions of my Eye the Rings of Colours emerging on the I ^92 ] ■ the top of the Bubble, I found that they were fenfibly dilated by increafmg the obliquity, but yet not fo much by far as thofe made by thinn'd Air in the feventh Obfervation. For there they were dilated fo much as, when view'd molt ob- liquely , to arrive at a part of the Plate more than twelve times thicker than that where they appear'd when viewed perpendicularly ; where- as in this cafe the thicknefs of the Water, at which they arrived when viewed mod oblique- ly, was to that thicknefs which exhibited them by perpendicular Rays , fomcthing lefs than as 8 to 5. By the belt of my Obfervations it was between 15" and ifv to 10; an increafe about 24 times lefs than in the other cafe. Sometimes the Bubble would become of an uniform thicknefs all over, except at the top of it near the black Spot , as I knew , becaufe it would exhibit the fame appearance of Colours in all Pofitions of the Eye. And then the Co- lours which were fecn at its apparent circumfe- rence by the obliqued Rays, would be different from thofe that were feen in other places, by Rays lefs oblique to it. And divers Spectators might fee the fame part of it of differing Co- lours, by viewing it at very differing Obliqui- ties. Now obferving how much the Colours at the fame places of the Bubble, or at divers pla- ces of equal thicknefs, were varied by the fe- veral Obliquities of the Rays ; by the afliftance of the 4th, 14th, 1 6th and 1 8th Obfervations, as they are hereafter explain'd , I colleCt the thicknefs of the Water requifite to exhibit any one and th'e fame Colour, at feveral Obliquities^ to [ 193 ] to be very nearly in the Proportion exprefTed in this Table. Incidence on the JVater. ReJra6iion in- to the JVater. Thicknefs of the Water. Deg. Min. OO OO Deg. Min. 00 00 10 15- 00 II II 107 30 00 22 I IOt 45- 00 60 00 15 00 90 00 32 2 40 30 46 25- 48 35- Hi 13 1^4 In the two firft Columns are exprefs'd the Obliquities of the Rays to the Superficies of the Water, that is, their Angles of Incidence and Refraftion. Where I fuppofe that the Sines which meafure them are in round Numbers, as 3 to 4, though probably the dilTolution of Soap in the Water, may a Uttle alter Jts refradive Virtue. In the third Column the thicknefs of the Bubble, at which any one Colour is exhibit- ed in thofe feveral Obliquities, is exprefs'd in parts, of which ten conllitute its thicknefs when the Rays are perpendicular. And the Rule found by the feventh Obfervation agrees well with thefe Meafures , if duly apply'd ; namely, that the thicknefs of a Plate of Water requiiite to exhibit one and the fame Colour at feveral Obliquities of the Eye, is proportional to the fecant of an Angle whole Sine is the firft of an hundred and fix arithmetical mean Proportio- O jials [ i?4 ] iials between the Sines of Incidence and Refra- ction counted from the lelfer Sine, that is, from the Sine of Refradion when the Refradion is made out of Air into Water, otherwife from the Sine of Incidence. I have fometimes obferv'd, that the Colours which arife on polifli'd Steel by heating it, or on Bell-metal, and fome other metalline Sub- llances, when melted and pour'd on the ground, where they may cool in the open Air, have, like the Colours of Water-bubbles, been a little changed by viewing tliem at divers Obliquities, and particularly that a deep blue,, or violet, when view'd very obliquel)^ hath been changed to a deep red. But the Changes of thefe Co- lours are not i'o great and fenlible as of thofe made by W ater. For the Scoria or vitritit d part of the jVIetal, which moil Metals when heated or jnelted do continually protrude, and fend out to their Surface, and which by covering the Metals in form of a thin glally Skin, caufes thefe Colours, is much denfer than W ater ; and I find that the Change made by the Obliquation of tix Eye is lead in Colours of the denlcll: thin Sublknces. Oi^f xo. As in the ninth Obfervation, fo here, the Bubble, by tranfmitted Light, appear'd of a contrary Colour to that which it exhibited by Reflexion, Thus when the Bubble being look'd on by the Light of the Clouds refleded from ir, feemed red at its apparent circumference, if the Clouds at the fame time, or immediately after, were view'd through it, the Colour at its circumference would be blue. And, on the contrary, [195] contrary, when by reflected Light it appeared blue, it would appear red by trani'mitted Light. Ob/.zi. By wetting very thin Plates of Muf- covy Glafs , whofe thinnefs made the like Co- lours appear, the Colours became more faint and languid, efpecially by wetting the Plates on that fide oppofite to the Eye : But I could not perceive any variation of their Species. So then the thicknefs of a Plate requifite to produce any Colour, depends only on the denfity of the Plate, and not on that or the ambient Medium. And hence, by the loth and i6thObfervations, may be known the thicknefs which Bubbles of Water, or Plates of Mufcovy Glafs, or other Subltances, have at any Colour produced by them. Ohf,%%. A thin tranfparent Body, w^hich is denfer than its ambient Medium, exhibits more brisk and vivid Colours than that which is fo much rarer ; as I have particularly obferved in the Air and Glafs. For blowing Glafs very thin at a Lamp Furnace , thofe Plates encompafled with Air did exhibit Colours much more vivid than thofe of Air made thin between two Glaf- Ohf. 23. Comparing the quantity of Light refleded from the feveral Rings , I found that it was molt copious from the tirll or inmoil^ and in the exterior Rings became gradually lefs and lefs. Alfo the whitenefs of the firit King was flronger than that redccfed from thofe parts of the thin Medium or Plate which were without the Rings ; as I could manifeilly per- •ceive by viewing at a diftance the Rings made O" X ^ bv [ ^9^ 1 b}^ the two Obje^l-glafTes ; or by comparing two Bubbles of Water blown at dillant times, in the firft of which the whitenefs appear 'd, which fucceeded all the Colours, and in the other, the whitenefs which preceded them all. Oi^J^ 24. When the two Objeft-glafTcs were lay'd upon one another, fo as to make the Rings of the Colours appear, though with my naked Eye I could not difcern above eight or nine of thofe Rings, yet by viewing them through a Prifm I have feen a far greater multitude, info- much that I could number more than forty, be- lides many others, that were fo very fmall and clofe together , that I could not keep my Eye Heady on them feverally fo as to number them, but by their Extent I have fometimes eftimated them to be more than an hundred. And I be- lieve the Experiment may be improved to the difcovery of far greater Numbers. For they feem to be really unlimited, though vifible on- ly fo far as they can be feparated by the Refra- aion, as I Ihall hereafter explain. But it was but one fide of thefe Rings, name- ly, that towards which the Refraction was made, which by that Refraction was render'd diftinft, and the other fide became more confufed than when view'd by the naked Eye, infomuch that there I could not difcern above one or two, and fometimes none of thofe Rings , of which I could difcern eight or nine with, my naked Eye. And their Segments or Arcs, which on the other fide appear'd fo numerous, for the mofl part exceeded not the third part of a Cir- cle. If the Refra6lion was verv great, or the Prifm I 197 ] Prifm very diftant from the Objeft-glafTes , the middle part of thofe Arcs became alio confu- fed , fo as to difappear and conltitute an even whitenefs, whilft on either fide their ends, as alfo the whole Arcs fartheft from the center, became diilin6ter than before, appearing in the form as you fee them defign'd in the tifth Fi- gure. The Arcs, where they feem'd diftin6leil, were only white and black fuccefTively, without any other Colours intermix'd. But in other places there appeared Colours, whofe order was in- veried by the Refradion in luch manner, that if I hrlt held the Prilm very near the Objedl:- glafTes, and then gradually removed it farther off towards myl'^ye, the Colours of the id, 3d, 4th , and following Rings llirunk towards the white that emerged between them , until they wholly vanifh'd into it at the middle of the Arcs, and afterwards emerged again in a con- trary order. But at the ends of the Arcs they retain'd their order unchanged. I have fometimes fo lay'd one Objc6t-glafs upon the other, that to the naked Eye they have all over feem'd uniformly white, without the leaft appearance of any of the colour'd Rings; and yet by viewing them through a Prifm, great multitudes of thofe Rings have difcover'd themfelves. And in like manner Plates of Mufcovy Glafs, and Bubbles of Glafs blown at a Lamp Furnace, which w^ere not fo thin as to exhibit any Colours to the naked Eye, have through the Prifm exhibited a great varie- ty of them ranged irregularly up and down in O 3 th^ ^- 1 158 ] the form of Waves. And fo Bubbles of Wa- ter, before they began to exhibit their Colours to the naked Eye of a By-ftander, have appear- ed through a Prifm , girded about with many parallel and horizontal Rings ; to produce which Effeci , it was neceilary to hold the Prifm pa- rallel , or very nearly parallel to the Horizon, and to difpofe it fo that the Rays might be re- fraded upwards. THE [ ^99 ] THE SECOND BOOK OPTIC KS. PART II. Remarks u^on the foregoing Obfervations. VV I N G given my Obfervations of thefe Colours, before I make ufe of them to unfold the Caufes of the Colours of na- tural Bodies, it is convenient that by the fimpleil of them, fuch as are the id, 3d', 4th, 9th, nth, 1 8th, loth, and 24th, Ifirflex- O 4 plain [ 200 ] ^ plain the more compounded. And firfi: to fliew how the Colours in the fourth and eighteenth Obfervations are produced, let there be taken in any right Line from the Point Y, [in Fig. 6.] the lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to one another, as the Cube Roots of the Squares of the Numbers, 4, t^, t> T? 75 4, V, I , whereby the lengths of a mufical Chord to found all the Notes in an eighth are reprefented ; that is, in the proportion of the Numbers 6300, 6814, 71 14, 7631, 815-5', 885-5', 9243, loooo. And at the Points A, B, C, D, E, F, G, H, let perpendiculars A ct, B /3, &c. be crcdcd , by whofe Intervals the Extent of the fcveral Colours fet underneath againft them, is to be reprefented. Then 'divide the Line A c* in fuch proportion as the Numbers i, 2, 3, 5-, 6, y, ^, 10, II, ^c. fet at the Points of Divifion denote. And through thofe Divifions from Y draw Lines il, xK, 3 L, 5M, 6N, 7O, ^c. Now if A 2 be fuppoled to reprefent the thicknefs of any thin tranfparentBody, at which the outmoft violet is molt copioufly reflected in the firll Ring, or Series of Colours, then by the 13th Obfcrvation, HKwill reprefent its thicknefs, at which the utmoft red is molt co- pioufly refledled in the fame Series. 'Alfo by the 5-th and 1 6th Obfervations, A 6 and HN will denote the thickneifes at which thofe ex- treme Colours are moil copioufly refledcd in the fecond Series, and A 10 and HQ the thick- nelFes, at which they are molt copioufly reliev- ed in the third Series, and fo on. And the thicknefs at which any of the intermediate Co- lours [ 20I ] lours are refleded mod copioufly, will, accor- ding to the 14th Obfervation, be defined by the diitance of the Line AH from the intermediate parts of the Lines xK, 6N, loQ, ^c, againfl which the Names of thofe Colours are written below. But farther, to define the Latitude of thefe Colours in each Ring or Series, let A i defign the lealt thicknefs, and A3 the greatell thick- nefs , at which the extreme violet in the firfl Series is refleded, and let HI, and HL, de- fign the like limits for the extreme red, and let the intermediate Colours be limited by the in- termediate parts of the Lines 1 1, and 3 L, a- gainfi: which tlie Names of thofe Colours are written, and fo on : But yet with this caution, that the Reflexions be fuppofed firongeit at the intermediate Spaces, 2K, 6 N, loQ, &c. and from thence to decreafe gradually towards thefe limits, 1 1, 3 L, 5- M, 7 O, ^c. on either fide ; where you mufi: not conceive them to be pre- cifely limited, but to decay indefinitely. And whereas I have afiign d the fame Latitude to e- very Series, I Aid it, becaufe although the Co- lours in the firlt Scries feem to be a little broad- er than the rell, by reafon of a fironger Re- flexion there, yet that inequality is fo infenfi- ble as fcarcely to be determin'd by Obferva- tion. Now according to this Defcription, concei- ving that the Rays originally of feveral Colours are by turns retleded at the Spaces il L 3, 5-1X1 O 7, y P R 1 1, ^c. and tranfmitted at the Spaces AHIi, 3L M5, 7OP9, &c. itiscafytoknow what [ 202 ] what Colour muft in the open Air be exhi- bited at any thicknefs of a tranfparent thin Bo- dy. For if a Ruler be applied parallel to AH, at that di (lance from it by which the thicknefs of the Body is reprefented the alternate Spaces 1 1 L 3, 5-M O 7, &c. which it crdifeth will de- note the refleded original Colours, of which the Colour exhibited in the open Air is com- pounded. Thus if the coniiitution of the green in the third Series of Colours be defircd, apply the Ruler as you fee at Tr^o-cp, and by its paf- fmg through Ibme of the blue at tt and yellow at