^ '^3isLjJ tm THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES GIFT Dr. K. N, Beigelman . ' 'm ■■ DPTICKSi O R, A TREATISE OF THE REFLEXIONS, REFRACTIONS, INFLEXIONS and COLOURS O F L I G U T ALSO Two TREATISES OF THE SPECIES and MAGNITUDE O E I I Curvilinear Figures L N D A% Printed for Sam,. Smith, and Ben J. Walpo^ic©^ Printers to the Royal Society , at tliG PrJMi:''s Arms in St. FauPs Church-yard. MDCCIV* -.f^: •■ >/ =-m U ,1 p-^ftt-. <■"'*!? '- ^ ^ AC 8 ADVERTISEMENT. ^'^],^^ PArt of the enfuing Difcourfe ahout Light was written at the dejire of J ome Gentlemen of the Royal Society, in the Tear 1675. ^^^ ^^^^ fi^^ ^^ ^^^^^^ Secretary^ and read at their Meetings^ and the reft was added about Twelve Tears after to complete the Theory ; except the Third Book, and the laft Propo/ition of the Second, which werejince put together out offcattered Papers. To avoid heing engaged in Difputes about thefe Matters, I have hitherto delayed the Printing, and Jhould ftill huve de- layed it, had not the importunity of Friends prevailed upon me. If any other Papers writ on this Subject are got out The Angle of Incidence^ is that Angle which the Line defcribed by the incident ^^y contains with the Perpendicular to the refle" fiing or refraSiing Surface at the Toint of Incidence. D E F I N. V. The Angle of ^flexion or ^fraBion, «■ the Angle which the Line defcribed by the rejleSled or refraBed ^y containeth with the perpendicular to the refleBing or refraBing Surface at the ^oint of Incidence. D E F I N. VI. The Sines of Incidence, Reflexion, and ^fraBion, are the Sines of the Angles of Incidence^ Reflexion, and ^efraBion. D E F I N. VII. The Light whofe ^ys are all alike ^J^efrangible, I call Sinu pie , Homogeneal and Similar j and that whofe ^ys are fome more ^frangible than others , I call Com^otmdj Heteroo-eneal and 'DiJJimilar. The former Light I call Homogeneal , not becaulc I would affirm it fo in all refpecfls ; but becaufe the Rays which agree in Refrangibility, agree at leaft ia all thofe their other Properties. Which I confider in the following Diicourfe. D E F I N. VIII. The Colours of Homogeneal Lights , / call Primary, Homo- geneal and Simple j and thofe of Heterogeneal Lights, Heteroge' neal and Compound. For thefe are always compounded of the colours of Homogeneal Lights 3 as will appear in the following Difcourfe. A 2 AX I- C4] AXIOMS. A X. I. THE Angles of Incidence^ ^flexmi, and ^frafiion, lye ill one and the fatne Tlofie. A X. II. The Angle of ^flexion is equal to the Angle of Incidence. A X. III. If the refraSied ^y he returned direBly back, fo the Pointy of Incidence , it JJ^all he refrafied into the Line before defcri- bed by the incident (I(ay. A X. IV. ^fraflion out of the rarer Medium into the denfer , is made towards the Perpendicular 3 that is, fo that the Angle of ^fra- Bion be leJJ than the Angle of Incidence. AX. V. The Sine of Incidence, is either accurately or "Very nearly in a giyen cperiments. Exper. I . I took a black oblong ftiff Paper terminated by Parallel Sides, and with a Perpendicular right Line drawn crofs from one Side to the other , diftinguifhed it into two equal Parts. One of thefe Parts 1 painted with a red Colour and the other with a blew. The Paper was very black, and the Colours intenfe and thickly laid on, that the Phacnomenon might be more confpicuous. This Paper I viewed through a Prifm of folid Glafs, whofe two Sides through which the Light paffed to the Eye were plane and well polifhed, and contained an Angle of about Sixty Degrees : which Angle I call the refrad:ing Angle of the Prifm. And whilft I viewed it, I held it before a Window in fuch manner that the Sides of the Paper were parallel to the Prifm, and both thofe Sides and the Prifm parallel to the Horizon, and the crofs Line perpendicular to it ; and. that the Light which fell from the Window UpOft 117. I 1 [Hi upon Vhe Piper made an Angle with the Paper, equal to that Angle which was made with the fame Paper by the .Light refieiled from it to the Eye. Beyond the Prifm was the Wall of the Chamber under the Window covered over with black Cloth, and the Cloth was involved in Dark- nefs that no Light might be refleded from thence, which in pafling by the edges of the Paper to the Eye , might mingle it felf with the Light of the Paper and obfcure the Phacnomenon thereof Thefe things being thus ordered, I found that if the refrading Angle of the Prifm be turned upwards, fo that the Paper may feem to be lifted upwards by the Refradion , its blew half will be lifted higher by the Refradion than its red half But if the refracting Angle of the Prifm be turned downward, fo that the Pa- per may feem to be carried lower by the Refradlion, its blew half will be carried fomething lower thereby than its red half Wherefore in both cafes the Light v/hich comes from the blew half of the Paper through the Prifm to the Eye, does in like Circumftances fuffcr a greater Re- fra(5lion than the Light which comes from the red half, and by confequence is more refrangible. lUuftratiGn. In the Eleventh Figure, M "N reprefents the Window,and D E the Paper terminated with parallel Sides D J and H E, and by the tranfverfe Line F G diftinguilTied into two halfs, the one D G of an intenfely blew Colour, the other F Eof an intenfely red. And '^KCcab repre- fents the Prifm whofe refrading Planes h^b a and hQca meet in the edge of the refrading Angle A a. This edge A^ being upward, is parallel both to the Horizon and to the parallel edges of the Paper D J and H E. And de re- prefents the Image of the Paper feen by Refraction up- wards in fuch manner that the blew half D G is carried higher to d^ than the red half F E is to /e, and therefore" fuffers [15] fufFers a greater Rcfradion. If the edge of the refracting Angle be turned downward, the Image of the Paper will be refraded downward fuppofe to ^i, and the blew half will be refraded lower to -^ 7 than the red half is to ?>s. Exper. 2. About the afotefaid Paper, whofe two halfs were painted' over with red and blew, and which was ftiff like thin Pailboard, I lapped feierai times a llender thred of very black Silk, in fuch manner that the feveral parts of the thred might appear upon the Colours like fo many black Lines drawn over them , or like long and llender dark Shadows caft upon them. I might have drawn black Lines with a Pen, but the threds were fmaller and better defined. This Paper thus coloured and lined i let againft a Wall perpendicularly to the Horizon, fo that one of the Colours might ftand to the right hand and the other to the left. Clofe before the Paper at the confine of the Co- lours below I placed a Candle to illuminate the Paper ftrongly : For the Experiment was tried in the Night. The flame of the Candle reached up to the lower edge of the Paper, or a very little higher. Then at the diftance of Six Feet and one or two Inches from the Paper upon the Floor I eredled a glafs Lens four Inches and a quarter broad, which might colled the Rays coming from the feveral Points of the Paper, and make them converge to- wards fo many other Points at the fame diftance of fix Feet and one or two Inches on the other fide of the Lens, and fo form the Image of the coloured Paper upon a white Paper placed there 3 after the fame manner that a Lens at a hole in a Window cafts the Images of Objeds abroad upon a Sheet of white Paper in a dark Room. The afore- faid white Paper, erecled perpendicular to the Horizon and to the Rays Vv'hich fell upon it firom the Lens, I moved fometimes towards the Lens, fometimes from it, to find the [i6] •tlie places where the Images of the blew and red parts of the coloured Paper appeared moft diftind. Thofe places 1 eafily knew by the Images of the black Lines which I had made by winding the Silk about the Paper. For the Images of thofe fine and flender Lines (which by reafon of their blacknefs were like Shadows on the Colours) were confijfed and fcarce vifible, unlefs when the Colours on ei- ther fide of each Line were terminated moft diftindily. Noting therefore, as diligently as I could, the places where the Images of the red and blew halfs of the coloured Pa- per appeared moft diftincft , I found that where the red half of the Paper appeared diftin(5t, the blew half appeared confufed, fo that the black Lines drawn upon it could fcarce be feen 5 and on the contrary where the blew half appeared moft diftinct the red half appeared confufed, fo that the black Lines upon it were fcarce vifible. And be- tween the two places where thefc Images appeared diftind: there was the diftance of an Inch and a hail : the diftance of the white Paper from the Lens, when the Image of the red half of the coloured Paper appeared moft diftind:, be- ing greater by an Inch and an half than the diftance of the fame white Paper from the Lens when the Image of the blew half appeared moft diftintft. In like Incidences there- fore of the blew and red upon the Lens, the blew was re- fradted more by the Lens than the red, fo as to converge fooner by an Inch and an half, and therefore is more refran- gible. Pi?. 12. Illuftration. In the Twelfth Figure, DE fignifies the co- loured Paper, D G the blew half, F E the red half, M N the Lens, H J the white Paper in that place where the red half wirh its black Lines appeared diftintfl, and hi the fame Paper in that place where the blew half appeared diftind:. The place hi was nearer to the Lens M N than the place H J by an Inch and an half. Scholtum. [17] Scholium. The fame things fucceed notvvithflanding that fome of the Circumftances be varied : as in the firft Ex- periment when the Pnfm and Paper are any uays inclined to the Horizon , and in both when coloured Lines are drawn upon very black Paper. But in the Defcription of thefe Experiments , I have fet down fuch Circumftances by which either the Phaenomenon might be rendred more confpicuous, or a Novice might more eafily try them, or by which I did try them only. The fame thing I have often done in the following Experiments : Concerning all which this one Admonition may fuffice. Now from thefe Experiments it follows not that all the Light of the blew is more Refrangible than all the Light of the red 3 For both Lights are mixed of Rays differently Refrangible, So that in the red there are fome Rays not lefs Refrangible than thofe of the blew , and in the blew there are iome Rays not more Refrangible than thofe of the red j But thefe Rays in Proportion to the whole Light are but feWj and ferve to diminifli the Event of the Experiment , but are not able to deftroy it. For if the red and blew Co- lours were more dilute and weak, the diftance of the Ima- ges would be lefs than an Inch and an half 5 and if they were more intenfe and full, that diftance would be greater, as will appear hereafter. Thefe Experiments may fuffice for the Colours of Natural Bodies. For in the Colours made by the Refraction of Prifms this Propofition will appear by the Experiments which are now to follow in the next Propofition. TfJlOT. [i8] PROP. II. Theor. II. The Light of the Sun confifis of ^ys differently ^frangible. The Proof by Experiments. Exper. 3. TN a very dark Chamber at a round hole about j[ one third part of an Inch broad made in the Shut of a Window I placed a Glafs Prifm, whereby the beam of the Sun's Light which came in at that hole might be refrad:ed upwards toward the oppofite Wall of the Chamber , and there form a coloured Image of the Sun. The Axis of the Prifm (that is the Line paifing through the middle of the Prifm from one end of it to the other end Parallel to the edge of the Refrading Angle) was in this and the following Experiments perpendicular to the incident Rays. About this Axis I turned the Prifm flowly , and faw the refra(5l:ed Light on the Wall or co- loured Image of the Sun firft to defcend and then to af- cend. Between the Defcent and Afcent when the Image feemed Stationary , I ftopt the Prifm, and fixt it in that Pofture, that it fliould be moved no more. For in that poflure the Refractions of the Light at the two fides of the Refra<5ting Angle, that is at the entrance of the Rays into the Prifm and at their going out of it, were equal to one another. So alfo in other Experiments as often as I would have the Refractions on both fides the Prifm to be equal to one another, I noted the place where the Image of the Sun formed by the refrad:ed Light flood ftill be- tween its two contrary Motions, in the common Period of its progrefs and egrefs 5 and when the Image fell upon that plaeCj I made faft the Prifin. And in this pofture, as the [19] the mod convenient,ic is to be underftood that all the Prifms are placed in the following Experiments, unlefs where feme other pofture is defcribed. The Prifm therefore being pla- ced in this pofture, I let the refra<5ted Light fall perpendi- cularly upon a Sheet of white Paper at the oppofite Wall of the Chamber, and obferved the Figure and Dimenfions of the Solar Image formed on the Paper by that Light. This Image was Oblong and not Oval, but terminated with two Rectilinear and Parallel Sides , and two Semi- circular Ends. On its Sides it was bounded pretty diftindly, but on its Ends very confufedly and indiftindlly, the Light there decaying and vanifhing by degrees. The breadth of this Image anfwered to the Sun's Diameter, and was about two Inches and the eighth part of an Inch , including the Penumbra. For the Image was eighteen Feet and an half diftant from the Prifm, and at this diftance that breadth if diminiflied by the Diameter of the hole in the Window-fliut, that is by a quarter of an Inch, fubtended an Angle at the Prifm of about half a Degree, which is the Sun's apparent Diameter. But the length of the Image was about ten Inches and a quarter, and the length of the Redilinear Sides about eight Inches 5 And the refracting Angle of the Prifm where- by fo great a length v/as made, was 64 degr. With a lefs Angle the length of the Image was lefs , the breadth re- maining the fame* If the Prifm was turned about its Axis that way which made the Rays emerge more obliquely out of the fecond refraCtino; Surface of the Prifm, the Imase foon became an Inch or two longer, or more; and if the Prifm was turned about the contrary way, fo as to mal^e the Rays fall more obliquely on the firft refracting Surface, the Image foon became an Inch or two fhorter. And therefore in try- ing this Experiment, I was as curious as I could be in pla- cing the Prifm by the above-mentioned Rule exaCtly in C 2 fuch [20] fuch a pofture that the Refradions of the Rays at their emer-' gence out of the Prifm might be equal to that at their inci" dence on it. This Prifm had fome Veins running along within the Glafs from one end to the other , which feat- tercd fome of the Sun's Light irregularly, but had no fen- hble effed; in encreafing the length of the coloured Spec- trum. For I tried the fame Experiment with other Prifms with the fame Succefs. And particularly with a Prifm which feemed free from fuch Veins, and whofe refracting Angle was 6i\ Degrees, I found the length of the Image 9^ or 10 Inches at the diftance of 18- Feet from the Prifm, the breadth of the hole in the Window-fhut being i of an 4 Inch as before. And becaufe it is eafie to commit a mi- flake in placing the Prifm in its due pofture, I repeated the Experiment four or five times, and always found the length of the Image that which is fet down above. With another Prifm of clearer Glafs and better PoUifh, which feemed free from Veins and whofe refracting Angle was 63 ' Degrees, the length of this Image at the fame diftance of I 8 ^ Feet was alfo about 1 o Inches, or 10^. Beyond thefe Meafures for about ' or - of an Inch at either end of 4 3 the Spe6trum the Light of the Clouds feemed to be a little tinged with red and violet, but fo very faintly that I fufpe- d:ed that tinCture might either wholly or in great meafure arife from fome Rays of the SpeCtrum fcattered irre- gularly by fome inequalities in the Subftance and Polifh of the Glafs , and therefore I did not include it in thefe Meafures. Now the different Magnitude of the hole in theWindow-fliut, and different thicknefs of the Prifm where the Rays paffed through it, and different inclinations of the Prifm to the Horizon, made no fenfible changes in the kngtK of the Image. Neither did the different matter of ^ the [21] the Prifms make any : for in a Veflel made of poliflied- Plates of Glafs cemented together in the (hape of a Prifm and filled with Water, there is the like Succefs of the Ex- periment according to the quantity of the Refradiion. It is fijrther to be obferved, that the Rays went on in right Lines from the Prifm to the Image, and therefore at their very going out of the Prifm had all that Inclination to one another from which the length of the Image pro- ceeded, that is the Inclination of more than two Degrees and an half And yet according to the Laws of Opticks vulgarly received, they could not poifibly be fo much in- clined to one another. For let EG reprefent the Window- fm-. i ?, (hut, F the hole made therein through which a beam of the Sun's Light was tranfmitted into the darkned Chamber, and ABC a Triangular Imaginary Plane whereby the Prifm is feigned to be cut tranfverfly through the middle of the Light. Or if you pleafe, let A B C reprefent the Prifm it felf, looking diretflly towards the Spectator's Eye with its nearer end : And let X Y be the Sun, MN the Paper upon which the Solar Image or Spectrum is caft, and P T the Image it felf whofe fides towards V and W are ReClili- near and Parallel, and ends towards P and T Semicir* cular. Y K H P and X L J T are the two Rays, the firft of which comes from the lower part of the Sun to the higher part of the Image, and is refracted in the Prifm at K and H, and the latter comes from the higher part of the Sun to the lower part of the Image, and is refraded at L and J. Since the Refrad:ions on both fides the Prifm are equal to one another, that is the Refradion at K equal to the Refradion at J, and the Refradion at L equal ta the Refradion at H, fo that the Refradions of the inci- dent Rays at K and L taken together are equal to the Refradions of the emergent Rays at H and J taken toge- ther ;. [22] ther : it follows by adding equal things to equal things, that the Refradions at K and H taken together, are equal to the Refrad:ions at J and L taken together , and there- fore the two Rays being equally refracted have the fame Inclination to one another after Refrad;ion which they had before, that is the Inclination of half a Degree anfwering to the Sun's Diameter. For fo great was the Inclination of the Rays to one another before Refradion. So then, the length of the Image P T would by the Rules of Vul- gar Opticks fubtend an Angle of half a Degree at the Prifm, and by confequence be equal to the breadth > v> ; and therefore the Image would be round. Thus it would be were the two Rays X L J T and Y K H P and all the reft which form the Image P jp T >, alike Refrangible. And therefore feeing by Experience it is found that the image is not round but about five times longer than broad, the Rays which going to the upper end P of the Image fuffer the greateft Refraction, muft be more Refran- gible than thofe which go to the lower end T , unlefs the inequality of Refrad:ion be cafual. This Image or Sped:rum P T was coloured, being red at its leaft refracfted end T, and violet at its moft refi:a<5ted end P, and yellow green and blew in the intermediate ipaces. Which agrees with the firft Propofition, that Lights which differ in Colour do alfo differ in Refrangibiiity. The length of the Image in the foregoing Experiments I meafured from the faintefl and outmoft red at one end, to the faintefl and outmofl blew at the other end. Exper. 4. In the Sun's beam which was propagated in- to the Room through the hole in the Window-fhut, at the diftance of fome Feet from the hole, I held the Prifm in fuch a poflure that its Axis might be perpendicular to that beam. Then I looked through the Prifm upon the , hole, [23] ■ hole, and turning the Prifm to and fro about its Axis to make the Image of the hole afcend and defcend, when be- tween its two contrary Motions it feemed ftationary, I ftopt the Prifm that the Refradlions on both fides of the refradling Angle might be equal to each other as in the former Experiment. In this Situation of the Prifm view- ing through it the faid hole, I obferved the length of its refracted Image to be many times greater than its breadth, and that the moft refracted part thereof appeared violet, the leaft refradted red, the middle parts blew green and yellow in order. The fame thing happened when I re- moved the Prifm out of the Sun s Light , and looked through it upon the hole fhining by the Light of the Clouds beyond it. And yet if the Refradlion were done regularly according to one certain Proportion of the Sines of Incidence and Refracftion as is vulgarly fuppofed, the refracted Image ought to have appeared rouna. So then, by thefe two Experiments it appears that in equal Incidences there is a confiderable inequality of Re* fradiions : But whence this inequality arifes, whether it be that fome of the incident Rays are refrad:ed more and others lefs, conftantly or by chance, or that one and the fame Ray is by Refra6tion difturbed, fhattered, dilated, and as it were fplit and fpread into many diverging Rays, as GrimaUo fuppofes, does not yet appear by thefe Experi- ments, but will appear by thofe that follow. Exper. 5 . Confidering therefore, that if in the third Ex- periment the Image of the Sun fhould be drawn out into an oblong form, either by a Dilatation of every Ray, or by any other cafual inequality of the Refradions, the fame oblong Image would by a fecond Refradion made Side- ways be drawn out as much in breadth by the like Dila- tation of the Rays or other cafual inequality of the Rc- frad:ions [24] iradions Sideways, I tried what would be the EfFctfls of fiich a fecond Refra6lion. For this end I ordered all thinas as in the third Experiment, and then placed a fecond Prifm immediately after the firft in a crofs Pofition to it, that it might again refra(5l the beam of the Sun s Light which came to it through the firfl: Prifm. In the firft Prifm this beam was refracted upwards, and in the fecond Sideways. And I found that by the Refradlion of the fecond Prifm the breadth of the Image was not increafed, but its fupe- rior part which in the firft Prifm fuftered the greater Re- fi-aition and appeared violet and blew, did again in the fecond Prifm fuffer a greater Refradlion than its inferior part, which appeared red and yellow , and this without any Dilation of the Image in breadth. fig. 1 4. lUuJlration. Let S reprefent the Sun, F the hole in the Window, A B C the firft Prifm, D H the fecond Prifm, Y the round Image of the Sun made by a direcft beam of Lit^ht when the Prifms are taken away, P T the oblong Image of the Sun made by that beam paffing through the £ift Prifm alone when the fecond Prifm is taken away, and pt the Image made by the crofs Refractions of both Prifms together. Now if the Rays which tend towards the feveral Points of the round Image Y were dilated and fpread by the Refradion of the firft Prifm, fo that they ITiould not any longer go in fingle Lines to fingle Points, but that every Ray being fplit, fhattered, and changed from a Linear Ray to a Superficies of Rays diverging from the Point of Refraction, and lying in the Plane of the Angles of Incidence and Refraction, they fliould go in thofe Planes to fo many Lines reaching almoft from one end of the Image P T to the other, and if that Image fhould thence become oblong : thofe Rays and their feveral parts tending towards the feveral Points qf the [25] the Image P T ought to be again dilated and fpread Side- ways by the tranfverfe Refraction of the fecond Prifm , fo as to compofe a fourfquare Image, fuch as is reprefented at t7. For the better underftanding of which, let the hiiage FT be diftinguifhed into five equal Parts PQ.K, KQ^RL, L R S M, M S V N, N V T. And by the fame irregularity that the Orbicular Light Y is by the Refradion of the firft Prifm dilated and drawn out into a long Image P T, the the Light P Q.K which takes up a fpace of the fame length and breadth with the Light Y ought to be by the Refra- (Stion of the fecond Prifm dilated and drawn out into the long Image -rq 4^ ^rid the Light K Q_R L into the long Image kqrl, and the Lights LRSM, MSVN,NVT into fo many other long Images I r s 7n, m s y n, nv tl -^ and all thefe long Images would compofe the fourfquare Image ■^1. Thus it ought to be were every Ray dilated by Re- fra t and m n would not lie in one ftraight Line with their ends contiguous as before, but be broken off from one another and become Parallel, the blew end of the Image m n being by a greater Refradion tranflated farther from its former place M T, than the red end t of the other Image p t from the fame place MT which puts the Propofition paft di- ipute. And this happens whether the third Prifm D H be placed immediately after the two firft or at a great diftance from them , fo that the Light refra(fled in the two firft Prifms be either white and circular, or coloured and ob- long when it falls on the third. Exper. 6. In the middle of two thin Boards I made round holes a third part of an Inch in Diameter, and in the Window-fhut a much broader hole, being made to let into my darkned Chamber a large beam of the Sun's Light 5 I placed a Prifm behind the Shut in that beam to relrad it towards the oppofite Wail, and clofe behind the Prifm I fixed one of the Boards, in fuch manner that the middle of the refrad:ed Light might pafs through the hole made [31] made in it, and the reft be intercepted by the Board. Then at the diftance of about twelve Feet from the firft Board I fixed the other Board, in fuch manner that the middle of the refra<5ted Light which came through the hole in the firft Board and fell upon the oppofite Wall might pafs through the hole in this other Board, and the reft be- ing intercepted by the Board might paint upon it the co- loured Spectrum of the Sun. And clofe behind this Board I fixed another Prifm to refrad: the Light which came through the hole. Then I returned fpeedily to the firft Prifm, and by turning it flowly to and fi-o about its Axis, I caufed the Image which fell upon the fecond Board to move up and down upon that Board, that all its parts might fucccflively pafs through the hole in that Board and fall upon the Prifm behind it. And in the mean time, I noted the places on the oppofite Wall to which that Light after its Refraction in the fecond Prifm did pafs 5 and by the difference of the places I found that the Light which being moft refra(5led in the firft Prifm did go to the blew end of the Image, was again more refracted in the fecond Prifm than the Light which went to the red end of that Image, which proves as well the firft Propofition as the fecond. And this happened whether the Axis of the two Prifms were parallel, or inclined to one another and to the H®rizon in any given Angles. Illuftration. Let r be the wide hole in the Window-fliut, p^v i g, through which the Sun fhines upon the firft Prifm ABC, and let the refraded Light fall upon the middle of the Board D E, and the middle part of that Light upon the hole G made in the middle of that Board. Let this tra- jeded part of the Light fall again upon the middle of the fecond Board d e and there paint fuch an oblong coloured Image of the Sun as was defcribed in the third Experiment. By C32] 'By turning the Prifm ABC flowly to and fro about it^ Axis this Image will be made to move up and down the Board d e, and by this means all its parts from one end to the other may be made to pafs fucceflively through the hole g which is made in the middle of that Board. In the mean while another Prifm a b c is to be fixed next after that hole^ to refracft the traje(5ted Light a fecond time. And thefe things being thus ordered, I marked the places M and N of the oppofice Wall upon which the refradled Light fell,and found that whilft the two Boards and fecond Prifm remained unmoved, thofe places by turning the firft Prifm about its Axis were changed perpetually. For when the lower part of the Light which fell upon the fecond Board d e was call through the hole ^ it went to a lower place M on the Wall , and when the higher part of that Light was caft through the fame hole^, it went to a higher place N on the Wall,- and wken any intermediate part of the Light was caft through that hole it went to fome place on the Wall between M and N. The unchanged Pontion of the holes in the Boards, made the Incidence of the Rays upon the fecond Prifm to be the fame in all cafes. And yet in that common Incidence fome of the Rays were more refracted and others lefs. And thofe were more refra(5ted in this Prifm which by a greater Refraction in the firft Prifm were more turned out of the way, and therefore for their conftancy of being more refi:a6ted are defervedly cal- led more Refrangible. Exper. 7. At two holes made near one another in my Window-fliut I placed two Prifms , one at each, which might caft upon the oppofite Wall ( after the manner of the third Experiment ) two oblong coloured Images of the Sun. And at a little diftance from the Wall I placed a long flender Paper with ftraight and parallel edges, and ordered C33l ordered the Prifms and Paper fo, that the red Colour of one Image might fall diredily upon one half of the Paper, and the violet colour of the other Image upon the other half of the fame Paper j fo that the Paper appeared of two Colours , red and violet , much after the manner of the painted Paper in the firft and fecond Experiments. Then with a black Cloth I covered the Wall behind the Paper, that no Light might be refleded from it to difturb the Experiment, and viewing the Paper through a third Prifm held parallel to it, I faw that half of it which was illumi- nated by the Violet-light to be divided from the other half by a greater Refradiion, elpecially when I went a good way off from the Paper. For when I viewed it too near at hand, the two halfs of the Paper did not appear fully divided from one another , but feemed contiguous at one of their Angles like the painted Paper in the firft Expe- riment. Which alfo happened when the Paper was too broad. Sometimes inftead of the Paper I ufed a white Thred, and this appeared through the Prifm divided into two Pa- rallel Threds as is reprefented in the 19th Figure, where Fig^. ip. D G denotes the Thred illuminated with violet Light from D to E and with red Light from F to G, and d e fg are the parts of the Thred feen by Refradion. If one half of the Thred be conftantly illuminated with red, and the other half be illuminated with all the Colours fuccefiively, (which may be done by caufing one of the Prifms to be turned about its Axis whilft the other remains unmoved) this other half in viewing the Thred through the Prifm, will appear in a continued right Line with the firft half when illuminated with red , and begin to be a little divi- ded from it when illuminated with Orange, and remove further from it when illuminated with Yellow, and ftill E further [3+] further when with Green, and further when with Blew, and go yet further off when illuminated with Indigo, and fur- theft when with deep Violet. Which plainly fhews, that the Lights of feveral Colours are more and more Refran- gible one than another, in this order of their Colours, Red, Orange, Yellow, Green, Blew, Indigo, deep Violet 3 and fo proves as M^ell the firft Propofition as the fecond. pifT. 17. I caufed alfo the coloured Spe6trums PT and M N made in a dark Chamber by the Refra6tions of two Prifms to lye in a right Line end to end, as was defcribed above in the fifth Experiment, and viewing them through a third Prifm held Parallel to their length, they appeared no longer in a right Line, but became broken from one another, as they are reprefented 3.t p t and tn », the violet end m of the Spectrum ?« n being by a greater Refradiion tranflated further from its former place M T than the red end t of the other Spedrum p t. Fi which in rhe 4th Prifm is more refradled, will become fuller and ftronger when the Light O P, which in the third Prifm H J K is more refracted, vaniflies at P j and afterwards when th« lefs refracted [43] refracted Light O T vaniflies at T,the lefs refraded Light Nf will become encreafed whilft the more refradled Light at p receives no further encreafe. And as the traje6ted Beam M O in vanifhing is always of fuch a Colour as ought to refult from the mixture of the Colours which fall upon the Paper PT, fo is the refledied Beam MN al- ways of fuch a Colour as ought to refult from the mix- ture of the Colours which fall upon the Paper p t. For when the mofl refrangible Rays are by a total Reflexion taken out of the Beam M O, and leave that Beam of an Orange Colour, the excefs of thofe Rays in the refle6tefix Feet and an Inch ( the diflance of the Lens from the lucid Object ) is to twelve Feet and two Inches ( the di- ■ftance of the lucid Object from the Focus of the mean re- frangible Rays) that is, as one is to two, fo is the 27 ^th part of fix Feet and an Inch (the diflance between the Lens and the fame Focus ) to the diflance between the Focus of 'the mofl refrangible Rays and the Focus of the leafl re- frangible ones, which is therefore 5 - Inches, that is very -nearly 5 '- Inches. Now to know whether this meafure was true, I repeated the fecond and eighth Experiment of "this Book with coloured Light, which was lefs compound- ..ed than that I there made ufe of : For I now feparated the hetero- h eterogeneous Rays from one another by the Method I de- fcribed in the i ith Experiment, fo as to make a coloured Spedrum about twelve or fifteen times longer than broad. This Spedlrum I caft on a printed book, and placing the above-mentioned Lens at the diftance of fix Feet and an Inch from this Spectrum to colled: the Species of the illu- minated Letters at the fame difiiance on the other fide, I found that the Species of the Letters illuminated with Blue were nearer to the Lens than thofe illuminated with deep Red by about three Inches or three and a quarter : but the Species of the Letters illuminated with Indigo and Violet appeared fo confufed and indiftind, that I could not read them : Whereupon viewing the Prifm, I found it was full of Veins running from one end of the Glafs to the other j fo that the Refradion could not be regular. I took ano- ther Prifm therefore which was free from Veins, and in- ftead of the Letters I ufed two or three Parallel black Lines a little broader than the ftroakes of the Letters, and caft- ing the Colours upon thefe Lines in fuch manner that the Lines ran along the Colours from one end of the Spedium to the other, I found that the Focus where the Indigo, or confine of this colour and Violet call the Species of the black Lines moft difi:!nd:ly,tobe about 4 Inches or 4^ near- er to the Lens than the Focus where the deepeft Red cafi; the Species of the fame black Lines mofl: diftindly. The violet was fo faint and dark, that I could not difcern the Species of the Lines diftinctly by that Co- lour J and therefore confidering that the Prifm was made of a dark coloured Glafs inclining to Green, I took another Pifm of clear white Glafs • but the Spedrum of Colours which this Prifm made had long white Streams of faint Light fliooting out from both ends of the Colours, which made me conclude that fomefhing was amifs j and view- ing [64] ing the Prifm, I found two or three little Bubbles in the Glafs which refracted the Light irregularly. Wherefore I covered that part of the Glafs with black Paper, and let- ting the Light pafs through another part of it which was free from fuch Bubles, the Sped:rum of Colours became free from thofe irregular Streams of Light, and was now fuch as I defired. But ilill I found the Violet fo dark and faint, that I could fcarce fee the Species of the Lines by the Violet, and not at all by the deepeft part of it, which was next the end of the Spectrum. I fulpedled therefore that this faint and dark Colour might be allayed by that fcat- tering Light which was refracted, and reflected irregularly partly by fome very fmall Bubbles in the Glafles and partly by the inequalities of their Polifli: which Light, tho' it was but little, yet it being of a White Colour, might fuffice to affect the Senfe fo ftrongly as to difturb the Pha^nomena of that weak and dark Colour the Violet, and therefore I tried, as in the 12th, i^th, 14th Experi- ments, whether the Light of this Colour did not confift of a fenfible mixture of heterogeneous Rays, but found it did not. Nor did the Refractions caufe any other fenfible Colour than Violet to emerge out of this Light, as they would have done out of White Light, and by con- fequence out of this Violet Light had it been fenfi- bly compounded with White Light. And therefore Icon- eluded, that the reafon why I could not fee the Species of the Lines diflindtly by this Colour, was only the darknefs of this Colour and Thinnels of its Light, and its dif- tance from the Axis of the Lens 3 I divided therefore thofe Parallel Black Lines into equal Parts, by which I might readily know the diflances of the Colours in the Spedirum from one another, and noted the diftances of the Lens from the Foci of fuch Colours as cafl the Species of the Lines Lines diftindly, and then confidered whether the diffe- rence of thofe diftances bear fuch proportion to 5 '^Inches, the greateft difference of the diftances which the Foci of the deepeft Red and Violet ought to have from the Lens, as the diftance of the obferved Colours from one another in the Spedrum bear to the like diftance of the deepeft Red and Violet meafured in the redlilinear fides of the Spect- rum, that is, to the length of thofe fides or excefs of the length of the Spectrum above its breadth. And my Ob- fervations were as follows. When I obferved and compared the deepeft fenfibleRed, and the Colour in the confine of Green and Blue, which at that rectilinear fides of the Spe(ftrum was diftant from it half the length of thofe fides, the Focus where the confine of Green and Blue caft the Species of the Lines diftin(5tly on the Paper, was nearer to the Lens then the Focus where the Red caft thofe Lines di(5tin6tly on it by about i^ or 2 .' Inches. For fometimes the Meafures were a little grea- ter, fomctimes a little lefs, but feldom varied from one another above j of an Inch. For it was very difficult to define the Places of the Foci, without fome little Errors. Now if the Colours diftant half the length of the Image, ( meafured at its rectilinear fides ) give 2^; or 2 - difference of the diftances of their Foci from the Lens, then the Co- lours diftant the whole length ought to give 5 or 5I Inches difference of thofe diftances. But here it's to be noted, that I could not fee the Red to the full End of the SpeCtrum, but only to the Center of the Semicircle which bounded that End, or a little far- ther 3 and therefore I compared this Red not with that Co- lour which was exactly in the middle of the SpeCtrum, or confine of Green and Blue, but with that which veracd a little more to the Blue than to the Green : And as I reck- I oned [66] oried the whole length of the Colours not tob^ the whole length of the Spe(artim, but the leflgth of its reftiHnear fides, fo completing theSemicirlar Ends into Circles, when (iither of the obferved Colours fell within thofe Circles, I meafured the diftance of that Colour from the End of the Spedrum, and fubdu(fiing half the diftance from the mea- fured diftance of the Colours, I took the remainder for their cbrre(5ted diftance 3 and in thefe Obfervations fet down this correded diftance for the difference of their di- ftances from the Lens. For as the length of the redilinear fides of the Spectrum would be the whole length of all the ^Colours, were the Circles of which ( as we fhewed) that Spedrum confifts contra(5led and reduced to Phyfical Points, fo in that Cafe this correded diftance would be the real diftance of the obferved Colours. When therefore I further obferved the deepeftfenfible Red, and that Blue whofe corre<5led diftance from it was ^ parts of the length of the redilinear fides of the Spectrum, the difference of the diftances of their Foci from the Lens was about ^- hiches, and as 7 to i 2 fo is 3 -J to 5 i. When I obferved the deepeft fenfible Red, and that Indi- go whofe corrected diftance was ^ or J of the length of the rectilinear fides of the Spe6trum, the difference of the di- ftances of their Foci from the Lens, was about 3 '* Inches, and as 2 to 3 fo is 3 J-to '){. When I obferved the deepeft fenfible Red, and that deep Indigo whofe corrected diftance from one another was ^ or ■' of the length of the redilinear fides of the Spedum, the difference of the diftances of their Foci from the Lens was about 4 Inches 3 and as 3 to 4 fo is 4 to 5 J. When I obferved the deepeft fenfible Red, and that part of the Violet next the Indigo whofe correded diftance from the Red was {^ or j of the length of the redilinear fides of the. the Spedtrum, the difference of the diftances <)f their Foci from the Lens was about 4^ Inches j and as 5 to ($, fo is 4- to 5-. For fometimes when the Lens was advantagi- oufly placed, fo that its Axis relpeded the Blue, and all things elfe were well ordered, and the Sun fhone clear, and I held my Eye very near to the Paper on which the Lens caft the Species of the Lines, I could fee pretty diftinctly the Species of thofe Lines by that part of the Violet which was next the Indigo ; and fometimes I could fee them by above half the Violet. For in making thefe Experiments I had obferved, that the Species of thofe Colours only ap- peared dijftinct which were in or near the Axis of the Lens : So that if the Blue or Indigo were in the Axis, I could fe,e their Species diilinctly ; and then the Red appeared much lefs diftinct than before. Wherefore I contrived to majce the Spectrum of Colours fliorter than before, fo that both its Ends might be nearer to the Axis of the Lens. And now its length was about 2^ Inches and breadth about -or I of an Inch. Alfo inftead of the black Lines on which the Spectrum was caft, I made one black Line broader than thofe, that I might fee its Species more eafily ; and this Line I divided by fhort crofs Lines into equal Parts, for tneafuring the diftances of the obfervedColours. And now I could fometimes fee the Species of this Line v/ith its divi- iions almoft as far as the Centers of the Semicircular Violet End of the Spectrum, and made thefe further Qbfervations. When I oblerved the decpeft fenfible Red, and that part of the Violet whofe corrected diftance from it was about j Parts of the rectilinear fides of the Spe6lrum the difference •of the diftances of the Foci of thofe Colours from the Lens, was one time 4-*, another time 4^, anothertimc 4^, Inches, andasS to 9, foare4j, 4-;, 4I, to 5', ^^^5^^ refpedively. I 2 When [68] When I obferved tlie deepeft fenfible Red, and deepefi: fenfible Violet, (the corrected dlftance of which Colours- when all things were ordered to the bed advantage, and the Sun fhone very clear, was about ^ or ^ parts of the length of the rectilinear fides of the coloured Spectrum, ) I found the difference of the diftances of their Foci from the Lens fometimes 4.' fometimes 5-, and for the mofl part 5 Inches or thereabouts : and as 11 to i 2 or 15 to i6, fo is five Inches to 5 ■; or 5 i Inches. And by this progreflion of Experiments I fitisfied my felf, that had the light at the very Ends of the Spectrum been ftrong enough to make the Species of the black Lines ap- pear plainly on the Paper, the Focus of the deepeft Vic- let would have been found nearer to the Lens, than the Fo- cus of the deepeft Red, by about y- Inches at leaft. And this is a further Evidence, that the Sines of Incidence and Refra6tion of the feveral forts of Rays, hold the fame pro- portion to one another in the fmalleft Refracftions which they do in the greateft. My progrefs in making this nice and troublefome Expe- riment I have fet down more at large, that they that fliall try it after me may be aware of the Circumfpedtion re- quifite to make it fucceed well. And if they cannot make It fucceed fo well as I did, they may notwithftanding col- led: by the Proportion of the diftance of the Colours in the Spedrum, to the difference of the diftances of their Foci from the Lens, what would be the fuccefs in the more di- ftant Colours by a better Trial. And yet if they ufe a broader Lens than I did, and fix it to a long ftreight Staff by means of which it may be readily and truly direded to the Colour whofe Focus is defired, I queftion not but the Experiment will fucceed better with them than it did with me,. For I direded the Axis as nearly as I could to the middle-: middle of the Colours, and then the faint Ends of the Spedrum being remote from the Axis, caft their Species lefs diftindly on the Paper than they would have done had the Axis been fucce/fively dire(5i:ed to them. Now by what has been faid its certain, that the Rays which differ in refrangibility do not converge to the fame Focus, but if they flow from a lucid point, as far from the Lens on one fide as their Foci are one the other, the Focus of the moft refrangible Rays fliall be nearer to the Lens than that of che leafl refrangible, by above the four- teenth part of the whole diftance: and if they flow from a lu- cid point, fo very remote from the Lens that before their Incidence they may be accounted Parallel, the Focus of the mofl: refrangible Rays fliall be nearer to the Lens than the Focus of the leafl: refrangible, by about the 27th onSth part of their whole difliance from it. And the Diameter of the Circle in the middle fpace between thofe two Foci which they illuminate when they fall there on any Plane, perpen- dicular to the Axis (which Circle is the leafl; into which they can all be gathered) is about the 55th part of the Dia- meter of the aperture of the Glafs. So that 'tis a wonder that Telefcopes reprefent Objeds fo difl:in<5i: as they do. But were all the Rays of Light equally refrangible, the Error arifing only from the fphericalnefs of the Figures of Glafles would be many hundred times lefs. For if the Objed:- Glafsofa Telefcope be Plano-convex, and the Plane fide be turned towards the Objed, and the Diameter of the Sphere whereof this Glafs is a fegment,be called D, and the Semidiameter of the aperture of the Glafs be called S, and the Sine of Incidence out of Glafs into Air, be to the Sine of Refradlion as I to R : the Rays which come Parallel to the Axis of the Glafs, fliall in the Place where the Image of the Objed is mofl: diftindtly made, be fcattered all over a little Circle [70] Circle whofe Diameter is ^ '^ Dfi^d. ^^^f ^^^^^Yj ^^ ^ ga- ther by computing the Errors of the Rays by the method of infinite Series, and rejeding the Terms whofe cjuanti- tities are inconfiderable. As for inftance, if the Sine of In- cidence I, be to the Sine of Refradion R, as 20 to ; i, and if D the Diameter of the Sphere to which the Convex fide of the Glafs is ground, be 100 Feet or 1200 Inches, and S the Semidiameter of the aperture be two Inches, the Diameter of the little Circle ( that is fi^^j^ ) will be — ^^— ( or ,z-^l„^^ ) parts of an Inch. But the 20 X 1200 x 1200 *■ 5600000 •' r Diameter of the little Circle through which thefe Rays are Scattered by unequal refrangibility, will be about the 55 th part of the aperture of the Objed:-Glafs which here is four Inches. And therefore the Error arifing from the fpherical Figure of the Glafs, is to the Error arifing from the diffe- rent Refrangibility of the Rays, as ^^^^ to ^ that is as i to 8151 : and therefore being in Comparifon fo very little, deferves not to be confidered. But you will fay, if the Errors caufed by the different re- frangibility be fo very great, how comes it to pafs that Ob- jed;s appear through Telefcopcs fo diilinfl as they do ? I an- fwer, 'tis becaufe the erring Rays are not fcattered uniform- ly over all that circular fpace, but collected infinitely more denfely in the Center than in any other part of the Circle, and in the way from the Center to the Circumference grow continually rarer and rarer, fo as at the Circumference to become infinitely rare 3 and by reafon of their rarity are p. not ftrong enough to bevifible, unlefs in the Center and ve- ^' ry near it. Let ADE reprefent one of thofe Circles de- fcribed with the Center C and Semidiameter AC, and let BFG be afmaller Circle concentric to the former, cutting with [71] with its Circumference the Diameter AC in B, and befecc AC in N, and by my reckoning the denfity of the Light in anyplace B will be to its denfity inN, as AB to BC, and the whole Light within the leffer Circle BFG, will be to the whole Light within the greater AED, as the Excefs of the Square of AC above the Square of AB, is to the Square of AC. As if BC be the fifth part of AC, the Light will be four times denfer in Bthan in N, and the whole Light with- in the lefs Circle,will be to the whole Light within the grea- ter, as nine to twenty five. Whence it's evident that the Light within the lefs Circle, muflflrike the fenfe much more ftrongly, than that faint and dilated light round about be- tween it and the Circumference of the greater. But its further to be noted, that the mofl luminous of the prifmatick Colours are the Yellow and Orange. Thefe ailed: the Senfes more ftrongly than all the refl together, and next to thefe in ftrength are the Red and Green. The Blue compared with thefe is a fiinc and dark Colour, and the In«f digo and Violet are much darker and fainter, fo that thefe compared with the ftronger Colours are little to be regard- ed. The Images of Objedis are therefore to be placed, not in the Focus of the mean refrangible Rays which are in the confine of Green and Blue, but in the Focus of thofe Rays which are in the middle of the Orange and Yellow 3 there where the Colour is moft luminous and fulgent, that is in the brighteft Yellow, that Yellow which inclines more to Orange than to Green. And by the Refradion of thefe Rays ( whofe Sines of Incidence and Refradion in Glafs are as 1 7 and 11) the Refradion of Glafs and Cryftal for optical ufes is to be meafured. Let us therefore place the Image of the Objed in the Focus of thefe Rays, and all the Yellow and Orange will fall within a Circle, whofe Dia- ineter is about the 250th part of the Diameter of the aper- ture [72] ture of the Glafs. And if you add the brighter half of the Red, ( that half which is next the Orange, and the brighter half of the Green, (that half which is next the Yellow,) a- bout three fifth parts of the Ijght of thefe two Colours will fall within the fame Circle,and two fifth parts will fall with- out it round about ; and that which falls without will be Ipread through almoft as much more fpace as that which falls within, and fo in the grofs be almoft three times ra- rer. Of the other half of the Red and Green, ( that is of the deep dark Red and Willow Green ) about one quarter will fall within this Circle, and three quarters without, and that which falls without will be fpread through about four or five times more fpace than that which fall within; and fo in the grofs be rarer, and if compared with the whole Light within it, willbe about 25 times rarer than all that taken in the grofs ; or rather more than 30 or 40 times rarer, be- caufe the deep red in the end of the Spedrum of Colours made by a Prifm is very thin and rare, and the Willow Green is fomething rarer than the Orange and Yellow. The Ltght of thefe Colours therefore bring fo very much rarer than that within the Circle, will fcarce afFed: the Senfe efpecially fince the deep Red and Willow Green of this Light, are much darker Colours then the reft. And for the lame reafon the Blue and Violet being much darker Colours than thefe, and much more rarified, may be neglected. For tlie denfe and bright Light of the Circle, will obfcure the rare and weak Light of thefe dark Colours round about it, and render them almoft infenfible. The fenfible Image of a lucid point is therefore fcarce broader than a Circle whofe Diameter is the 250th part of the diameter of the aperture of the Object Glafs of a good Telefcope, or not much broader, if you except a faint and dark mifty light round about it, which a Spectator will fcarce regard. And therefore in a Telefcope whofe [7?] . , vvhofe aperture is four Inches, and length an hundred Feet/ it exceeds not 2 '45', or 5". And in a Telefcope whofc aperture is two Inches, and length 20 or 30 Feet, it may be 5 "or 6" and fcarce above. And this Anfwers well to Experience : For fome Aftronomers have found the Dia- meters of the fixt Stars, in Telefcopes of between twenty and fixty Feet in length, to be about 4' or 5" or at moft 6" in Diameter. But if the Eye-Glafs be tinded faintly with the fmoke of a Lamp or Torch, to obfcure the Light of the Star, the fainter Light in the circumference of the Star ceafes to be vifible, and the Star (if the Giafs be fuffici- ently foiled with fmoke) appears fomething more like a Ma- thematical Point. And for the fame reafon, the enormous part of the Light in the Circumference of every lucid Point ought to be lefs difcernable in fhorter Telefcopes than in longer, becaufe the fhorter tranfmit lefs Light to the Eye. Now if we fuppofe the fenlible Image of a lucid point, to be even 250 times narrower than the aperture of the Glafs: yet were it not for the different refrangibility of the Rays, its breadth in an 1 00 Foot Telefcope whofe aperture is 4 Inches would be but ^-^^^^ parts of an Inch, as is ma- nifeft by the foregoing Computation. And therefore in this Cafe the greateft Errors arifing from the fpherical Figure of the Glafs, would be to the greateft fenfible Errors ari- fing from the different refrangibility of the Rays as -53^ to ^-^ at moft, that is only as i to 1826. And this fuffi- ciently fliews that it is not the fpherical Figures of Glaffes but the different refrangibility of the Rays which hinders the perfection of Telefcopes. There is another Argument by which it may appear that the different refrangibility of Rays, is the true Caufe of the imperfedion of Telefcopes. For the Errors of the Rays arihng from the fpherical Figures of Objed-Glafles, are as K the [ 74 3 tlic Cubes of the apeitures of the Objed^Glaflesjand thence to make Telefcopes of various lengths, magnify with equal cUftindnefs, the apertures of the Objed-GlafTes, and the C)harges or magnifying Powers, ought to be as the Cubes of the fcjuare Pvoots of their lengths 5 which doth not anfwer 10 Experience. But the errors of the Rays arifing from the d liferent refrangibility, are as the apertures of the Ob- jetft-Glafies, and thence to make Telefcopes of various leno^ths, magnify' with equal diftin(5lnefs, their apertures and charges ought to be as the fquare Roots of their lengths -,. and this aniwers to experience as is well known. For in- ftance, a Telefcope of 64 Feet in length, with an aperture of 1- Inches, magnifies about i 20 times, with as much dif- tind:nefs as one of a Foot in length, with j of an Jnch aper* ture, magnifies i 5 times. Now were it not for this different refrangibility of Rays, Telefcopes might be brought to a greater Perfedion than we have yet defcribed, by compoffng the Objed-Glafs of two Glafles with Water between them. Let ADFC repre^ f^. 2 8.|-ent the Objed-Glafs compofed of two Glaffes ABED and and BEFC, alike convex on the outfides AGD and CHF, and alike concave on the infides BME, BNE, with Water in the concavity BMEN. Let the Sine of Incidence out of Glafs into Air be as I to R and out of Water into Air as K to R, and by confequence out of Glafs into Water, as I to K : and let the Diameter of the Sphere to which the convex fides AGD and CHF are ground be D, and the Diameter, of the Sphere to which the concave fides BME and BNE are ground be to D, as the Cube Root of KK— KI to the Cube Root of RK— RI: and the Refra^ions on the con- cave fides of the Glafles, will very much corrcd: the Errors of the Refractions on the convex fides, fo far as they arife from the fphericainefs of the Figure. And by this means might [75] might Telefcopes be brought to fufficient perfe6bion, wercit not' for the diflferentrefrangibility of feveralforsof Rays. But by reafon of this different refrangibility, I do not yet fee any other means of improving Telefcopes by Refradlions alone than that of increafing their lengths, for which end the late contrivance of Hugenius feems well accommodated. For very long Tubes are cumberfome, and fcarce to be readily managed, and by reafon of their length are very apt to bend, and fhake by bending fo as to caufe a continual trembling in the Objects, whereby it becomes difficult to fee them diftindly : whereas by his contrivance the Glaffes are readily manageable, and the Objedl-Glafs being fixt up- on a ftrong upright Pole becomes more fteddy. Seeing therefore the improvement of Telefcopes of given lengths by Refractions is defperate 3 I contrived heretofore a Perfpedlive by reflexion, ufing inftead of an Objed: Glafs a concave Metal. The diameter of the Sphere to which the Metal was ground concave was about 2 5 Englifli Inches, and by confe^uence the length of the Inftrument about (i3t Inches and a quarter. The Eye-Glafs was plano-convex, and the Diameterof the Sphere to which the convex fide was ground was about i of an Inch, or a little lefs, and by con- fequence it magnified between ^ o and 40 times. By ano- ther way of meafuring I found that it magnified about ^ 5 times. The Concave Metal bore an aperture of an Inch and a third part j but the aperture was limited not by an opake Circle, covering the Limb of the Metal round about, but by an opake circle placed between the Eye-Glafs and the Eye, and perforated in the middle with a little round hole for the Rays to pafs through to the Eye. For this Circle by being placed here, ftopr much of the erroneous Light, which otherwife would have difturbed the Vifion. By com- paring it with a pretty good Perfpedive of four Feet in K 2 length, length, made with a concave Eye-Glafs, I could read at x greater diftance with my own Inftrument than with the Glafs. Yet Objedts appeared much darker in it than in the Glafs, and that partly becaufe more Light was loft by re- flexion in the Metal, then by refrailion in the Glafs, and. partly becaufe my Inftrument was overcharged. Had it magnified but ^oor 25 times it would have made the Object appear more brisk and pleafant. Two of thefelmade about: 16 Years ago, and have one of them ftill by me by which "li can prove the truth of what I write. Yet it is not fo good as at thefirft> For the concave has been divers times tar- niflied and cleared again, by rubbing it with very foft Lea^- ther. When I made thefe, an Artift in London undertook; to imitate it 5 but ufing another way of polifliing them than I did, he fell much fhort of what I had attained to,. as I afterwards underftood by difcourfing the under- Work- man he had imployed. The Polifli I ufed was on this man- ner. I had two round Copper Plates each fix Inches in: Diameter, the one convex the other concave, ground ve- ry true to one another. On the convex I ground the Ob- jedl-Metal or concave which was to be polifh'd, till it had. taken the Figure of the convex and was ready for a Polifh. Then I pitched over the convex very thinly, by dropping melted pitch upon it and warming it to keep the pitch foft, whilft I ground it with the concave Copper wetted to make it fpread evenly all over the convex. Thus by work- ing it well I made it as thin as a Groat, and after the con- vex was cold I ground it again to give it as true a Figure as I could. Then I took Putty which I had made very fine by wafliing it from all its grofler Particles, and laying a lit- tle of this upon the pitch, I ground it upon the Pitch with the concave Copper till it had done making a noife j and then upon the Pitch I ground the Objed;-Mecal with a brisk Motion [77] Motion, for about two or three Minutes of time, leaning hard upon it. Then I put frefh Putty upon the Pitch and ground it again till it had done making a noife, and after- wards ground the Objej new modifications of the Light variouf' ly imfref^ according to the variom terminations of the Light and Shadoisj. The Proof hy Experiments. EX PER. I. FOR if the Sua fhine into a very dark Chamber _pio-. i, through an oblong Hole F, whofe breadth is the iixth or eighth part of an Inch, or fomething lets ; and his Beam FH do afterwards pafs hrft through a very large Prifm ABC, diftant about 20 Feet from the L Hole, Hole, and parallel to it, and then (with its white part) through an oblong Hole H, whole breadth is about the fortieth or lixtieth part of an Inch, and which is made in a black opake Body G I, and placed at the diftance of two or three Feet from the Prifm, in a pa- rallel fituation both to the Prifm and to the former Hole, and if this w^hite Light thus tranfmitted through the Hole H, fall afterwards upon a white Paper pt,. placed after that Hole H, at the diftance of three or four Feet from it, and there paint the ufual Colours of the Prifm, fuppofe red at t, yellow at s, green at r, blue at q, and violet at p ; you may with an iron Wire, or any fuch like flender opake Body, whole breadth is about the tenth part of an Inch, by intercepting the rays at k, 1, m, noro, take away any one of the Colours at t, s, r, q or p, whilft the other Colours remain up- on the Paper as before ; or with an obftacle fomething bigger you may take away any two, or three, or four Co- lours together, the reft remaining: So that anyone of the Colours as well as violet may become outmoft in the confine of the fhadow towards p, and any one of them as well as red may become outmoft in the confine of the ftiadow towards t, and any one of them may alfo border upon the ftiadow made within the Colours by the obftacle R intercepting fome intermedia^te part of the Light ; and, laftly, any one of them_ by-* being left alone may border upon the ftiadow on either hand. All the Colours have themfelves indifferently to any confines of ftiadow, and therefore the differences of thefe Colours from one another, do not arife from the diffe- rent confines of ftiadow, whereby Light is varioufty modified as has hitherto been the Opinion of Philofo- phers. [83] pliers. In trying thefe things 'tis to be obferved, that by how much the Holes F and H are narrower, and the intervals between them, and the Prifm greater, and the Chamber darker, by lb much the better doth the Ex- periment iucceed ; provided the Light be not fo far diminifhed, but that the Colours at pt be fufficiently vilible. To procure a Pritm of folid Glafs large enough for this Experiment will be difficult, and therefore a prifmatick VelTel muft be made of polifhed Glafs-plates cemented together, and hlled with Water. EX PER. 11. The Sun's Light let Into -a dark Chamber through Fig'. 2. the round Hole F, half an Inch wide, pafled firft through tlie Prifm ABC placed at the Hole, and then through a Lens PT fomething more than four Liches broad, and about eight Feet diftant from the Prifm,and thence con- verged to O the Focus of the Lens diftant from it about three Feet, and there fell upon a white Paper D E. If that Paper was perpendicular to that Light incident up- on it, as 'tis repreiented in the pofture D E, all the Co- lours upon it at O appeared white. But if the Paper being turned about an Axis parallel to the Prifm, be- came very much inclined to the Light as 'tis reprefen- ted in the politions de and o\ j the fame Light in the one cafe appeared yellow and red, in the other blue. Here one and the fame part of the Light in one and the fame place, according to the various inclinations of the Paper, appeared in one cafe white, in another yellow or red, in a third blue, w^hilft the confine of Light and L 2 Shadow, [84-] Shadow, and the refradions of the Prifm in all thefe cafes remained, the fame. EXPER. III. Fisr. ^. Such another Experiment may be more ealily tried as follows. Let a broad beam of the Sun's Light coming into a dark Chamber through a Hole in the Window fhut be refraded by a large Prifm ABC, whofe re- frading Angle C is more than 60 degrees, and fo foon as it comes out of the Prifm let it fail upon the white Paper D E glewed upon a ftiif plane, and this Lighty when the Paper is perpendicular to it, as 'tis reprelen- ted in DE, will appear perfectly white upon the Paper,, but when the Paper is very much inclined to it in liach a manner as to keep always parallel to the Axis of the Prifm, the whitenefs of the whole Light upon the Paper will according to the inclination of the Paper this way, or that way, change either into yellow and red, as in the pofture de^ or into blue and violet, as in the pofture ^s. And if the Light before it fall upon the Paper be twice refraded the fame way by two pa- rallel Prilms, thefe Colours will become the more con- Ipicuous. Here all the middle parts of the broad beam of white Light which fell upon the Paper, did without any confine of Ihadow to modify it, become, coloured all over with, one uniform Colour, the Colour being al- ways the fame in the middle of the Paper as at the edges, and this Colour changed according the various obliquity of the rerie6fing Paper, without any change in the refradions or fhadow, or in the Light which fell upon the Paper. And therefore tlicfe Colours are to. X85] to be derived from fome other caufe than the new mo- difications of Light by refradions and fhadows. If it be asked, What then is their caufe ? I anfwer, That the Paper in the pofture de ^ being more ob- lique to the more refrangible rays than to the lefs re- frangible ones, is more ftrongly illuminated by the lat- ter than by the former, and therefore the lefs refran- gible rays are predominant in the reflected Light. And wherever they are predominant in any Light they tinge it with red or yellow, as may in fome meafure appear by the firft Propofition of the firft Book,and will more fully appear hereafter. And the contrary happens in the poll:ure of the Paper e%, the more refrangible rays be- ing then predominant which always tinge Light with blues and violets. EX PER. IV. The Colours of Bubbles with which Children play are various, and change their lituation varioufly, with- out any refped to any confine of fhadow. If fuch a Bubble be covered with a concave Glafs, to keep it from being agitated by any wind or motion of the Air, the Colours will ilowly and regularly change their fitua- tion, even whilft the Eye, and the Bubble, and all Bo- dies which emit any i^ight, or caft any fhadow, re- main unmoved. And therefore their Colours arife from fome regular caufe which depends not on any confine of fliadow. What this caufe is will be fhewed in the next Book.. To [8(5] To tlicfe Experiments may be added the tenth Ex- periment of the firft Book, where the Sun's Light in a dark Room being trajeded through the parallel luperfi- cies of two Prifms tied together in the form of a Paral- lelopide, became totally of one uniform yellow or red Colour, at its emerging out of the Prifms. Here, in the production of thefe Colours, the confine of fhadow can have nothing to do. For the Light changes from white to yellow,orange and red fucceffively,withoutany alteration of the confine of (hadow: And at both edges of the emerging Light where the contrary confines of Hia- dow ought to produce different etfeds, the Colour is one and the fame, whether it be white, yellow, orange or red : And in the middle of the emerging Light, where there is no confine of ihadow at all, the Colour is the very fame as at the edges, the whole Light at its very firft emergence being of one uniform Colour, whe- ther white, yellow, orange or red, and going on thence perpetually without any change of Colour, fuch as the confine of fhadow is vulgarly fuppofed to work in re- fracted Light after its emergence. Neither can thefe Colours arife from any new modifications of the Light, by refradtions, becaufe they change lucceffively from white to yellow, orange and red, while the refradions remain the fame, and alio becaufe the refractions are made contrary ways by parallel fuperficies which de- ftroy one anothers efteCts. They arife not therefore from any modifications of Light made by refra61:ions jind fhadows, but have fome other caufe. What that caufe is we ihewed above in this tenth Experiment, and need not here repeat it. There [87] There is yet another material circumftance of this Experiment. For this emerging Light being by a third Fig. 2 a. Prifm HI K refradled towards the Paper PT, and there Tart i. painting the ufual Colours of the Prifm, red, yellow, green, blue, violet : If thefe Colours arofe from the refractions of that Prifm modifying the Light, they wonld not be in the Light before its incidence on that Prifm. And yet in that Experiment v/e found that when by turning the two firft Prifms about their com- mon Axis all the Colours were made to vanilli but the red 3 the Light which makes that red being left alone, appeared of the very fame red Colour before its inci- dence on the third Prifm. And in general we find by other Experiments that when the rays which diifer in refrangibility are feparated from one another, and any one fort of them is confidered apart, the Colour of the Light which they compofe cannot be changed by any refradion or reflexion whatever, as it ought to be were Colours nothing elfe than modifications of Light caufed by refradions, and reflexions, and lliadows. This un- changeablenefs of Colour I am now to defcribe in the following Propofition. PROP. II. THE OR. I L u^ll homogeneal L'-ght has its frofer Colour anjisi>ertng to its degree of refrangdiltty^ and that Colour cannot be changed by rejlexions and refraHions, In the Experiments of the 4th Propofition of the firft Book, when I had feparated the Jieterogeneous rays from one another, the Spectrum p t formed by the fepa- rated [88] rated rays, did in the progrefs from its end p, on which the moft refrangible rays fell, unto its other end t, on which the leaft refrangible rays fell, appear tinged with this Series of Colours, violet, indico, blue, green, yel- low, orange, red, together with all their intermediate degrees in a continual fucceflion perpetually varying : So that there appeared as many degrees of Colours, as there were forts of rajs differing in refrangibility. EX PER. V. Now that thefe Colours could not be changed by re- fraction, I knew by refradting with a Prifm fometimes one very little part of this Light, fometimes another very little part, as is defcribed in the 1 2th Experiment of the firft Book. For by this refraftion the Colour of the Light was never changed in the leaft. If any part of the red Light was refracted, it remained totally of the fame red Colour as before. No orange, no yel- low, no green, or blue, no other new Colour was pro- duced by that refradiion. Neither did the Colour any ways change by repeated refradions, but continued al- ways the fame red entirely as at firft. The like con- ftancy and im.mutability 1 found alio in the blue, green, and other Colours. So alfo if 1 looked through a Prifm upon any body illuminated with any part of this homo- geneal Light, as in the 1 4-th Experiment of the firft Book is defcribed ; I could not perceive any new Co- lour generated this way. All Bodies illuminated with compound Light appear through Prifms confufed ( as was faid above) and tinged with various new Colours, but thofe illuminated with homogeneal Light appeared throug^h [89] through Prlfms neither kf^ diftinft, nor otherwife co- loured, than when viewed with the naked Eyes. Their Colours were not in the leaft changed by the refra£tion of the inter]^ofed Prilm. 1 Ipeak here of a fenfible change of Colour : For the Light which 1 liere call ho~ mogeneal, being not abfolutely homogeneal, there ought to arife fome little change of Colour from its heteroge- neity. But if that heterogeneity was fo little as it might be made, by the laid Experiments of the fourth Propo' fition, that change w^as not fenhble, and therefore, in Experiments where fenfe is judge, ought to be accoun- ted none at all. EXPER. VI. And as thcfe Colours were not changeable by refra- ftions. To neither were they by reflexions. For all white, grey, red, yellow, green, blue, violet Bodies, as Paper, Afhes, red Lead, Orpiment, Indico, Bife, Gold, Silver^ Copper, Grafs, blue Flowers, Violets, Bubbles of Water tinged with various Colours, Peacock's Fea- thers, the tincture of Lignum Nefhriticum^ and fuch like, In red homogeneal Light appeared totally red, in blue Light totally blue, in green Light totally green, and fo of other Colours. In the homogeneal Light of of any Colour they all appeared totally of that fame Colour, with this only ditierence, that fome of them refleded that Light more ftrongly, others more faintly. I never yet found any Body which by reflecting homo- geneal Light could fenfibly change its Colour. M From [90] From all which it is manifeft, that if the Sun's Light confiftcd of but one fort of rays, there would be but one Colour in the whole World, nor would it be pof- fible to produce any new Colour by reBexions and re- fraftions, and by confequence that the variety of Co- lours depends upon the compoiition of Light. 'DEFINIT ION. The homogeneal light and rays which appear red, or rather make Obje6ts appear ib, 1 call rubrific or red'makng ; thofe which make Objects appear yellow, green, blue and violet, 1 call yellow-ma- king, green-making^ blue-making, violet-making, and ib of the reft. And if at any time I fpeak of light and rays as coloured or endued with Co- lours, *I would be underftood to fpeak not philo- fophically and properly, but grolly , and accor- ding to fuch conceptions as vulgar People in fee- ing all thefe Experiments would be apt to frame. For the rays to fpeak properly are not coloured. In them there is nothing elfe than a certain power and difpofition to ftir up a lenfation of this or that Colour. For as found in a Bell or mufical String, or other founding Body, is nothing but a trem- bling Motion, and in the Air nothing but that Motion propagated from the Objedt, and- in the Senforium *tis a fenfe of that Motion under the form of found ; fo Colours in the Objed are no- thing but a difpoiition to refled: this or that fort of rays more copiouUy than the reft ; in the rays they are nothing but their difpofitions to propa- gate [pt] gate this or that Motion into the Senforium, and in the Senforium they are lenlations of thofe Mo- tions under the forms of Colours. PROP. III. PROB. I. To define the refravgibtltt'j of the jeveral forts of homo^ oeneal Lt/i^ of the yellow y s ^^, of the green '- 1 s ^ , of the blue n » x 9 , of the indico tXM>i5 and of the violet xGAm. And this operation being divers times repeated both in the lame and in leveral Papers , I found that the Ob- fervations agreed well enough with one another, and that the redtiiinear fides M G and FA were by the faid crofs lines divided after the manner of a mufical Chord. Let GM be produced to X, that MX may be equal toGM, and conceive GX, xX, 'X, ^'X,,^X, yX, «Xy MX, to be in proportion to one another, as the num- bers I, 9-, 6, 4^ p 1' ?6' i' and lb to rcprelent the. Chords of the Key, and of a Tone, a third Minor, a fourth, a fifth, a fixth Major, a feventh, and an eighth above that Key : And the intervals M -^ , " 7 , 7 - , ^ « , 1 ', '^, and xG, will be the fpaces which the fe vera I Co- lours ( rcd^ orange, yellow, green, blue, indico, violet ) take up. Now thefe inter\als or fpaces fubtending the diffe- rences of the refractions of the rays going to the limits. of thofe Colours, that is^ to the points M, a, 7, =, 15,/, x, G, may without any fenfiblc Etror be. accounted propor- tional to the differences of the fines of reiradtion of thofe rays rays having one common fine of incidence, and there- fore fince the common fine of incidence of the moft and lea ft refrangible rays out of Glafs into Air was, (by a method defcribed above ) found in proportion to their fines of refradion, as 50 to 77 and 78, divide the dif- ference between the fines of refraction 77 and 78, as the line G M is divided by thofc intervals, you will have 77. 77«-> 77'-' 77v 77i^ 77l' 77'.,, 7^, the fines of refradion of thole rays out of Glafs into Air ,. their common fine of incidence being 50. So then the fines of the incidences of all the red-making rays out of Glafs into Air, were to the fines of their refraftions, not greater than 50 to 77, nor lefs than 50 to 77«-, but varied from one another according to all interme- diate Proportions. And the fines of the incidences of the green-making rays were to the fines of their refractions in all proportions from that of 50 to 77^, unto that of 50 to 77-;. And by the like. limits above-mentioned were the refradions of the rays be-: longing to the reft of the Colours defined, the fines of the red- making rays extending from 77 to 778-, thofe of the orangcrmaking from 775 to 77^ j thofe of the yel- low-making from 77^ to 77 1, thofe of the green-making from 777 to 7 7x J thofe of the blue-making from 77^ to 775, thofe of the indico-making from 77-j to 77,;, and • thofe of the violet from 77^ to 78. Thefe are the Laws of the refrad ions made out of Glafs into Air, and thence by the three Axioms of tlie hrft Book the Laws of the refractions made out of Air. into Glafs areeafily derived.: EXPER. [94] EX PER. VIII. I found moreover that when Light goes out of Air through feveral contiguous refrafting Mediums as through Water and Glafs, and thence goes out again into Air, whether the refracting fupcrficies be parallel or inclined to one another, that Light as often as by contrary refractions 'tis fo corrected, that it emergeth in hues parallel to thofe in which it was incident, continues ever after to be white. But if the emer- gent rays be inclined to the incident, the whitenefs of the emerging Light will by degrees in palling on from the place of emergence, become tinged in its edges with Colours. This I tryed by refrading Light with Prifms of Glafs within a prifmatick Veffel of Water. Now thofe Colours argue a diverging and feparatioii of the hetero- geneous rays from one another by means of their un- equal refradions, as in what follows will more fully appear. And, on the contrary, the permanent white- nets argues, that in like incidences of the rays there is no fuch leparation of the emerging rays, and by confe- quence no inequality of their whole refradions. Whence 1 ieem to gether the two following Theorems. I. The Exceffes of the fines of refraction of feveral forts of rays above their common fine of incidence when the refractions are made out of divers denfer mediums immediately into one and the fame rarer medium, are to one another in a given Proportion. a. The [P5] a. The Proportion of the line of incidence to the fine of refraction of one and the fame fort of rays out of one medium into another, is compofed of the Proportion of the line of incidence to the line of refradion out of the firfl: medium into any third medium, and of the Pro- portion of the line of incidence to the line of refradion out of that third medium into the fecond medium. By the firft Theorem the refractions of the rays of every fort made out of any medium into Air are known by having the refraClion of the rays of any one fort. As for inllance, if the refractions of the rays of every fort out of Rain-v/ater into Air be delired, let the common fine of incidence out of Glafs into Air be fubduded from the lines of refraCtion, and the Excefl'es will be ay, i-j\y if-, 27^ > 27-;, I-]], 279-, 28. Suppofenow that the fine of incidence of the leaft refrangible rays be to their fine of refraCtion out of Rain-water into Air as three to four, and fay as i the ditference of thofe fines is to 5 the fine of incidence, fo is 27 the leaft of the Excelies above-mentioned to a fourth number 8 1 ; and 81 will be the common fign of incidence out of Rain- water into Air, to which line if you add all the above- mentioned Excefles you will have the defired fines of the refractions 108, loSs, 1087, 1087 ^ io8i, loSf, 1089, 109. By the latter Theorem the refraCtion out of one me- dium into another is gathered as often as you have the refractions out of them both into any third medium. As if the fine of incidence of any ray out of Glafs into Air be to its fine of refraCtion as ao to ^ i, and the fine of incidence of the fame ray out of Air into Water, be to to its fine of refraftion as four to three ; the fine of incidence of that ray out of Glafs into Water will be to its fine of refraction as lo to ^ i and 4 to^ joyntly, that is, as tjie Fadum of ao and 4. to the Factum of 3 1 and 3, or as 80 to 93. And thele Theorems being admitted into Opticks, there would be fcope enough of handling that Science voluminoufly after a new manner ; not only by teaching thofe things which tend to the perfettion of vilion, but alfo by determining mathematically all kinds of Phaeno- mena of Colours which could be produced by refra- dtions. For to do this, there is nothing elfe requifite than to find out the reparations of heterogeneous rays, and their various mixtures and proportions in every mixture. By this way of arguing 1 invented almoft all the Phsenomena defcribed in thefe Books, befide fome others lefs neceflary to the Argument ; and by the fucceffes I met with in the tryals, I dare promife, that to him who iTiall argue truly, and then try all things with good Glafles and fufficient circumfpection, the expeded event will not be wanting. But he is firft to know what Colours will arife from any others mixt iu any affigned Proportion, PROP. IV. THEOR. IIL Colours mm he produced iy compofition which /ball ht like to the Colours of homogeneal Ljo^ht as to the affenrame of Colour^ but not as to the immuta/nlity of Colour and conjlttution of Light. j4nd thofe Colours ^y ho-w much they are more compounded b'j jo much are they UJs fuU ■ and inteufe^ and by too much comfo/ition they may be diluted [97] diluted attd 'weakened till they ceaje. i here nia\' be alfo Colours froduced b'j comfofitioyi^ 'which are not jitlh like an'j oj the Colours of hsmogeneod Light. For a mixture of homogeneal red and yellow com- pounds an orange, like in appearance of Colour to that orange which in the feries of unmixed prifmatick Co- lours lies between them; but the Light of one orange is homogeneal as to refrangibility, that of the other is heterogeneal, and the Colour of the one , if viewed through a Prifm, remains unchanged, that of the other is changed and refolved into its component Colours red and yellow. And after the fame manner other neigh- bouring homogeneal Colours may compound new Co- lours, like the intermediate homogeneal ones, as yel- low and green, the Colour between them both, and af- terwards, if blue be added, there w^ll be made a green the middle Colour of the three which enter the com.po- lition. For the yellow and blue on either hand,if they are equal in quantity they draw the intermediate green equal- ly towards themfelves in compofition, and fo keep it as it were in equillbrio, that it verge not more to the yellow on the one hand, than to the blue on the other, but by their mixt ad:ions remain ftili a middle Colour. To this mixed green there may be further added fome red and violet, and yet the green will not prefent- ly ceafe but only grow lefs full and vivid, and by in- creaiing the red and violet it will grow more and more dilute, until by the prevalence of the added Colours it be overcome and turned into whitenefs, or fome other Colour. So if to the Colour of any homogeneal Light, the Sun's white Light compofed of all lorts of. rays be N added, added, tltat Colour will not vanifh or change its fpe- cies but be diluted, and by adding more and more white it will be diluted more and more perpetually. Laft- ly, if red and violet be mingled, there will be generated according to their various Proportions various Purples, fuch as are not like in appearance to the Colour ot any homogeneal Light, and of theie Purples mixt with yel- low and blue may be made other new Colours. PROP. V. THEOR. IV. Whitenefs and all gre>j Colours Set'ween 'white and Mach^ ma'j be. compounded o\ Colours^ and the isuhitenefs of the Suns Light is compounded of all the f?imar>^ Colow's mixt in a due pofortion. The Proof hy Experiments. EX PER. IX. jr^tr. e. The Sun fhining into a dark Chamber through a little round Hole in the Window fhut, and his Light being there refraded by a Prifm to call his coloured Image P T upon the oppohte Wall : I held a white Pa- per V to that Image in fuch m^anner that it might be illuminated by the coloured Light retiected from thence, and yet not intercept any part of that Light in its paf- fage from the Prifm to the Spedrum. And I found that when the Paper was held nearer to any Colour than to the reft, it appeared of that Colour to which it ap- proached nearcft 3 but when it was equally or almoft equally 199} equally diftant from all the Colours, Co that it might be equally illuiriinated by them all it appeared white. And in this laft lituation of the Paper, if fome Colours were intercepted, the Paper loll its white Colour, and appeared of the Colour of the reft of the Light which was not intercepted. So then the Paper was illuminated with Lights of various Colours, namely, red, yellow, green, blue and violet, and every part of the Light re- tained its proper Colour, until it was incident on the Paper, and became retiefted thence to the Eye ; fo that if it had been either alone (the reft of the Light being intercepted) or if it had abounded moft and been pre- dominant in the Light retleded from thePaper,it would have tinged the Paper w^ith its own Colour ; and yet be- ing mixed wdth the reft of the Colours in a due propor- tion, it made the Paper look white, and therefore by a compofition with the reft produced that Colour. The feveral parts of the coloured Light reflected from the Spedf rum, whilft they are propagated from thence thro' the Air, do perpetually retain their proper Colours, becaufe wherever they fall upon the Eyes of any Specta- tor, they make the feveral parts of the Spedrum to appear under their proper Colours. They retain there- lore their proper Colours when they fall upon the Pa- per V, and lb by the confufion and perfed mixture of thole Colours compound the whitenefs of the Light reflected from thence. EX PER. X. Let that Spedrum or folar Lnage P T fall now upon Ftg. 6. the Lens M N above four Inches broad, and about fix N 2 Feet [ loo] Feet diftant from the Piifm ABC, and fo figured that it may caufe the coloured Light which divergeth from the Prifm to converge and meet again at its Focus G, about fix or eight Feet diftant from the Lens, and tliere to fall perpendicularly upon a white Paper DE. And if you move this Paper to and fro, you will per- ceive that near the Lens, as at de^ the whole folar Image (fuppofe at pt) will appear upon it intenfly coloured after the manner above-explained, and that by receding^ from the Lens thofe Colours will perpetually come to- wards one another, and by mixing more and more di- lute one another continually, until at length the Paper come to the Focus G, where by a perfed mixture they will wholly vanifli and be converted into whitenefs, the whole Light appearing now upon the Paper like a little white Circle. And afterwards by receding further from the Lens, the rays which before converged will now crofs one another in the Focus G, and diverge from thence, and thereby make the Colours to appear again, but yet in a contrary order ; fuppofe at c^£ , where the red t is now above which before was below, and the violet p is below which before v^-as above. Let us now ftop the Paper at the Focus G where the Light appears totally white and circular, and let us Gonfider its whitenefs. I fay, that this is compofed of the converging Colours. For if any of thofe Colours be intercepted at the Lens, the whitenefs will ceafe and degenerate into that Colour which arifeth from the compofition of the other Colours which are not inter- cepted. And then if the intercepted Colours be let pafs and fall upon that compound Colour, they mix with it, and by their mixture rcttore the whitenefs. So. \ C lOI ] So if the violet, blue and green be intercepted, the re- maining yellow, orange and red will compound upon the Paper an orange, and then if the intercepted Co- lours be let pafs they will fall upon this compounded orange, and together with it decompound a white. So alio if the red and violet be intercepted, the remaining yellow, green and blue, will compound a green upon the Paper, and then the red and violet being let pafs will fall upon this green, and together with it decom- pound a white. And that in this compoiition of white the feveral rays do not fufFer any change in their colori- fic qualities by ading upon one another, but are only mixed, and by a mixture of their Colours produce white, may further appear by thefe Arguments. If the Paper be placed beyond the Focus G, fuppofe at o'f , and then the red Colour at the Lens be alternate- ly intercepted, and let pafs again, the violet Colour on the Paper will not futfer any change thereby, as it ought to do if the feveral forts of raysaded upon one another in the Focus G, where they crofs. Neither will the red upon the Paper be changed by any alternate flop- ping, and letting pafs the violet which crolTeth it. And if the Paper be placed at the Focus G, and the white round Image at G be viewed through the Prifm HIK, and by the refradion of that Prifm be tranflated to the place rv, and there appear tinged with various Colours, namely, the violet at v and red au r , and others between, and then the red Colour at the Lens be often ftopt and let pafs by turns, the red at r will ac- cordingly difappear and return as often, but the violet; at V will not thereby fuifer any change. And lb by flopping and letting pafs alternately the blue at the Lens. [ 102 ] Lens, the blue at r will accordingly dilappear and re- turn, withoutany change made in the red at r. The red therefore depends on one ibrt of rays, and the blue on another fort, which in the Focus G where they are commixt do not aft on one another. And there is the lame realbn of the other Colours. I conlidered further, that when the moft refrangible rays Pp, and the leaft refrangible ones Tt, are by con- verging inclined to one another, the Paper, if held very oblique to thofe rays in the Focus G, might relieft one Ibrt of them more copioufly than the other Ibrt, and by that means the refledted Light would be tinged in that Focus with the Colour of the predominant rays, pro- vided thofe rays feverally retained their Colours or co- lorific qualities in the compolition of white made by them in that Focus. But if they did not retain them in that white, but became all of them feverally endued there with a difpofition to ftrike the fenfe with the per- ception of white, then they could never lofe their white- neis by fuch reflexions. I inclined therefore the Paper to the rays very obliquely, as in the fecond Experiment of this Book, that the moft refrangible rays might be more copioufly reflected than the reft, and the white- ^ nets at length changed lucceflively into blue, indico^ and violet. Then 1 inclined it the contrary way, that the moft refrangible rays might be more copious in the refleded Light than the reft, and the whitenefs turned fucceflively to yeUow, orange and red. Laftly, I made an Inftrument XY in fafhion of a Comb, whofe Teeth being in num.ber lixteen were about an Inch and an half broad, and the intervals of the Teeth about two Inches wide. Then by interpoflng fuc- [103] fucceffively the Teeth of this Inftrumcnt near the Lerrs^ I intercepted part of the Colours by the interpofcd Tooth, whilft the reft of them went on through the in- terval of the Teeth to the Paper D E, and there pain- ted a round folar Image. But the Paper I had firft pla- ced fo, that the Image might appear white as often as the Comb was taken away ; and then the Comb be- ing as was laid interpofed, that whitenefs by reafon of the intercepted part of the Colours at the Lens did al- ways change into the Colour compounded of thofe Colours which were not intercepted, and that Colour was by the motion of the Comb perpetually varied fo, that in the palling of every Tooth over the Lens all thefe Colours red, yellow, green, blue and purple, did always fucceed one another. I caufed therefore all the Teeth to pais fucceffively over the Lens, and when the motion was flow, there appeared a perpetual fucceffion of the Colours upon the Paper : But if I fo much acce- lerated the motion, that the Colours by reafon of their quick fucceffion could not be diftinguilhed from one another, the appearance of the iingle Colours ceafed. There was no red, no yellow, no green, no blue, nor purple to be feen any longer, but from a confulion of them all there arofe one uniform white Colour. Of tj^e Light which now by the mixture of all the Colours ap- peared white, there was no part really white. One part was red, another yellow, a third green, a fourth blue, a fifth purple, and every part retains its proper Colour till it ftrike the Senforium. If the impreffions follow one another llowly, fo that they may be ieve- raliy perceived, there is made a diftind: fenfation of all the Colours one after another in a continual fucceffion. But [104] But If the impreflions follow one another lb quickly that they cannot be feverally perceived, there arifeth out of them all one common fenlation, which is nei- ther of this Colour alone nor of tliat alone, but hath it lelf indifferently to 'em all, and this is a lenfation of whitenefs. By the quicknefs of the fucceffions the im- preffions of the feveral Colours are confounded in the Senforium, and out of that confution arileth a mixt icn- fation. If a burning Coal be nimbly moved round in a Circle with Gyrations continually repeated, the whole Circle will appear like hre ; the reafon of wiiich is, that the fenfation of the Coal in the feveral places of that Circle remains impreft on the Senforium, until the Coal return again to the fame place. And lb in a quick confecution of the Colours the impreffion of every Colour remains in the Senforium, until a revolution of all the Colours be compleated, and that firft Colour re- turn again. The impreffions therefore of all the fucceffive Colours are at once in theSenlbrium,and joyntly ftir up a fenfation of them all ; and lb it is manifeft by this Ex- periment, that the commixt impreffions of all the Co- lours do hir up and beget a feniation of white, that is, that whitenefs is compounded of all the Colours. j And if the Comb be now taken away, that all the Colours may at once pals from the Lens to the Paper, and be there intermixed, and together relie<5ted thence to the Speftators Eyes ; their impreffions on the Senfo- rium bemg now more fubtily and perfedly commixed there, ought much more to iHr up a fenfation of white- •iiefs. You C 105 ] You may inftead of the Lens ufe two Fril'ms HI K andLMN, which by refractmg the coloured Light the contrary way to that of the firft refraction, may make the diverging rays converge and meet again in G, as you fee it reprefented in tlie feventh Figure. For Ftg. 7. where they meet and mix they will compote a white Light as when a Lens is uied. EX PER. XL Let tl\e Sun's coloured Image PT fall upon the Wall Fig- 8. of a dark Chamber, as in the third Experiment of the lirftBook, and let the fame be viewed through a Prifm a be, held parallel to the Prifm ABC, by whofe refra- dion that Image was made, and let it now appear lower than before, fuppofe in the place S over againll the red colour T. And if you go near to the Image PT, the Speftrum S will appear oblong and coloured like the image PT; but if you recede from it, the Colours of the Spedrum S will be contracted more and more, and at length vanilli, that SpeCtrum S becoming perfectly \ round and v/hite ; and if you recede yet further, the ^Colours will emerge again, but in a contrary order. Now that Speftrum S appears white in that cafe when the rays of feveral forts which converge from the feve* ral parts of the Image PT, to the Prifm a be, are fo refracted unequally by it, that in their paffage from the Prifm to the Eye they may diverge from one and the iame point of the Spectrum S, and fo fall afterwards upon one and the fame point in the bottom of the Eye, mid there be min2,led. O And [lod] And further, if the Comb be here made ufe of, by whofe Teeth the Colours at the Image PT may be luc- ceffively intercepted ; the Spedrum S when the Comb is moved flowly will be perpetually tinged with iiic- ceflive Colours : But when by accelerating the motion of the Comb, the fucceffion of the Colours is fo quick that they cannot be feverally feen, that Spectrum S, by a confufed and mixt lenlation of them all, will appear white. EXPER. XII. Jpio: 9. The Sun fhining through a large Prifm ABC upon a Comb X Y, placed immediately behind the Prifm, his Light which paffed through the interlaces of the Teeth fell upon a white Paper DE. The breadths of the Teeth were equal to their interftices, and feven Teeth together with their interftices took up an Inch in breadth. Now w^hen the Paper was about two or three Inches diftant from the Comb, the Light which paffed through its feveral interftices painted ib many ranges of Colours kl, mn, op, qr, ^r. which were parallel to one another and contiguous, and without anyi mixture of white. And thefe ranges of Colours, if the Comb was moved continually up and down with a re- ciprocal motion, afcended and defcended in the Paper,^ and when the motion of the Comb was fo quick, that the Colours could not be diftinguifhed from one another, the whole Paper by their confulion and mixture in the Senforium appeared white. Let [ 107 ] Let the Comb now reft, and let the Paper be remo- ved further from the Prifm, and the feveral ranges of Colours will be dilated and expanded into one another more and more, and by mixing their Colours will di- lute one another, and at length, when the diftance of the Paper from the Comb is about a Foot , or a little more ( fuppofe in the place i D 2 E ) they will lb far dilute one another as to become white. With any Obftacle let all the Light be now ftopt which paffes through any one interval of the Teeth, ib that the range of Colours which comes from thence may be taken away, and you will fee the Light of the reft of the ranges to be expanded into the place of the range taken away, and there to be coloured. Let the inter- cepted range pafs on as before, and its Colours falling upon the Colours of the other ranges, and mixing with them, will reftore the whitenefs. Let the Paper 2D 2 E be now very much inclined to the rays, fo that the moft refrangible rays may be more copioufly reflefted than the reft, and the white Colour of the Paper through the excefs of thofe rays will be •v changed into blue and violet. Let the Paper be as \nuch inclined the contrary way, that the leaft refran- gible rays may be now more copioufly refleded than the reft, and by their excefs the whitenefs will be changed into yellow and red. The feveral rays there- fore in that white Light do retain their colorific qua- lities, by which thole of any fort, when-ever they be- come more copious than the reft, do by their excefs and predominance cauie their proper Colour to ap- pear. O 5 And [io8] And by the fame way of arguing, applied to the third Experiment of this Book, it may be concluded, that the white Colour of all refracted Light at its very firll: emergence, where it appears as white as before its inci- dence^ is compounded of various Colours. EX PER. XIII. In the foregoing Experiment the feveral intervals of the Teeth of the Comb do the office of fo many Prifms, every interval producing the Phaenomenon of one Prifm. Whence inftead of thofe intervals ufing feveral Prifm?, I try'd to compound whitenefs by mixing their Colours,and did it by ufing only three Prifms, as alfo by ufing only Fig' lo- two as follows. Let two Prifms ABC and a b c, whole refrading Angles B and b are equal,be fo placed parallel to one another, that the refrafting Angle B of the one may touch the Angle c at the bale of the other, and their planes CB and cb, at which the rays emerge, may lye in directum. Then let the Light traje^ed through them fall upon the Paper M N, dillant about 8 or i 2 / Inches from the Prifms. And the Colours generatedr by the interior limits B and. c of the two Prifms, wil( be mingled at PT, and there compound white. For if either Prifm be taken away, the Colours made by the other will appear in that place PT, and when the Prifm is reftoredto its place again, fo that its Colours may there tall upon the Colours of the other, the mixture of them both will reftore the whitenels. This This Experiment fucceeds alio, as I have tryed, when the Angle b of the lower Prilm, is a little greater than the Angle B of the upper , and between the interior Angles B and c, there intercedes ibme fp:ice B c, as is teprelented in the Figure, and the retracing planes BC and be, are neither in directum, nor parallel to one another. For there is nothing raore requifite to the fucceis of this Experiment, than that the rays of all forts may be uniformly mixed upon the Paper in the place PT. If the moft refrangible rays coming from the fuperiorPriim take up all theipace from M to P, the rays of the fame fort which come from the inferior Prifm ought to begin at P, and take up all the reft of the fpacefrom thence towards N. If the leaft refrangible rays coming from the fuperior Prifm take up the ipace MT, the rays of the lame kind which come from the other Prifm ought to begin atT, and take up the remaiir- ing fpace T N. If one Ibrt of the rays which have in- termediate degrees of refrangibility,, and come from the fuperior Prifm be extended through the ipace MQ-, and another ibrt of thofe rays through the fpace MR, and a third fort of them through the ipace MS, the fame forts of rays coming from the lower Prifm, ought to ilr iluminate the remaining ipaces Q.N, RN, SN refpe- dively. And the lame is to be underllood of all the other ibrts of rays. For thus the rays of every fort wdll be fcattered uniformly and evenly through the whole fpace MN, and lb being every wiiere mixt in the fame proportion, they muft every where produce the lame Colour. And therefore lince by this mixture.they pro- duce white in the exterior Ipaces M P and TN, they muft alfo produce white in the interior ipace P T. This is. [no] IS the reafon of the compofition by which whitcncfs was produced in this Experiment, and by what other way Ibever 1 made the like compofition the refult was whitcnefs. Laftly, If with the Teeth of a Comb of a due (ize, the coloured Lights of the two Prifms which fall upon the fpace PT be alternately intercepted, that fpace PT, when the motion of the Comb is flow, will always appear coloured, but by accelerating the motion of the Comb fo much, that the fucceffive Colours can- not be diftinguiflied from one another, it will appear white. EXPER. XIV. Hitherto I have produced whitenefs by mixing the Colours of Prifms. If now the Colours of natural Bo- dies are to be mingled, let Water a little thickned with Soap be agitated to raife a froth, and after that froth has Hood a little, there will appear to one that fliall view it intently various Colours every where in the furfaces of the feveral Bubbles ; but to one that fhall go fo far off that he cannot diftinguifh the Colours from one another, the whole froth will grow white with a' perfed whitenefs. EXPER. XV. Laftly, in attempting to compound a white by mixing the coloured Powders which Painters ufe, 1 confidered that all coloured Powders do fupprefs and ftop in them a very coniiderable part of the Light by which they [Ill] they are illuminated. For they become coloured by reflecting the Light of their own Colours more copioufly, and that of all other Colours morefparingly, and yet they do not reflect the Light of their own Colours lb copioufly as white Bodies do. If red Lead, for inftance, and a white Paper, be placed in the red Light of the coloured Spectrum made in a dark Chamber by the re- fradion of a Prifm, as is defcribed in the third Eperi- mentofthe firft Book 3 the Paper will appear more lu- cid than the red Lead, and therefore refieds the red^- making rays more copioufly than red Lead doth. And if they be held in the Light of any other Colour, the Light reflected by the Paper will exceed the Light re- fie&ed by the red Lead in a much greater proportion. And the like happens in Powders of other Colours. And therefore by mixing fuch Powders we are not to expert a fl:rong and fuU white, fuch as is that of Paper, but fome dusky obfcure one, fuch as might arife from a mixture of light and darknefs, or from white and black, that is, a grey, or dun, or ruffet brown, fuch as are the Colours of a Man's Nail, ofaMoufe, of Aflies, of or- \dinary Stones, of Mortar, of Duft and Dirt in High- \ways, and the like. And fuch a dark white I have often produced by mixing coloured Powders. For thus one part of red Lead,and Ave parts of Viride jEris^com- pofed a dun Colour like that of a Moufe. For thele tv\Ao Colours were feverally fo compounded of others, that in both together were a mixture of all Colours ; and there was lefs red Lead ufed than Vtride y^rw, becaufe of the fulneis of its Colour. Again, one part of red Lead, and four parts of blue Bife, compofed a dun Co- lour verging a little to purple, and by adding to this a certain [112] certain mixture of Orpiment and Vtnd't j!Eris in a due proportion, the mixture loft its purple tincture, and be- came perfedly dun. But the Experiment lucceeded beft without Minium thus. To Orpiment I added by little and little a certain full bright purple, which Painters ufe until the Orpiment ceafed to be yellow, and became ofa pale red. Then I diluted that red by adding a little Viride ^>m, and a little more blue Bile than J/^i- riiU jEris^ until it became of fuch a grey or pale white, as verged to no one of the Colours more than to ano- ther. For thus it became of a Colour equal in white- neis to that of Afhes or of Wood newly cut, or of a Man's Skin. The Orpiment refteded more Light than did any other of the Powders, and therefore conduced more to the whitenefs of the compounded Colour than they. To affign the proportions accurately may be difficult, by reaibn of the different goodneis of Pow- ders of the lame kind. Accordingly as the Colour of any Powder is more or lets full and luminous, it ought to be ufed in a lefs or greater proportion. Now confidering that thele grey and dun Colours may be alfo produced by mixing whites and blacks, and by conlequence differ from perfeft whites not in Species/ of Colours but only in degree of luminouiheis, it is ma- . nifeft that there is nothing more requiiite to miake them perfectly white than to increafe their Light fuffi- ciently ; and, on the contrary, if by increahng their Light they can be brought to perfect whitenefs, it will thence alio follow, that they are of the lame Species of Colour with the beft whites, and dift'er from them only in the quantity of Light. And this 1 tryed as follows. I took the third of the above-mentioned grey mixtures (that [113] (^that which was compounded of Oipiment, Purple, Bife and Viride Alerts) and rubbed it thickly upon the lioor of my Chamber, where the Sun Ihone upon it through the opened Caiement ; and by it, in the fha- dow, 1 laid a piece of white Paper of the fame bignefs. Then going from them to the dillance of 1 1 or 1 8 Feet, fo that I could not difcern the unevennefs of the furface of the Powder, nor the little fnadows let fall from the gritty particles thereof ; the Powder appeared intenfly white, fo as to tranfcend even the Paper it felf in white- nefs, efpecially if the Paper were a little iTiaded from the Light of the Clouds, and then the Paper compared with the Powder appeared of fuch a grey Colour as the Powder had done before. But by laying the Paper where the Sun fhines through the Glafs of the Window, or by Ihutting the Window that the Sun might fhine through the Glafs upon the Powder, and by fuch other £t means of increafing or decrealing the Lights where- with the Powder and Paper were illuminated , the Light wherewith the Powder is illuminated may be made ftronger in fuch a due proportion than the Light ^ wherewith the Paper is illuminated, that they fhall both appear exadly alike in whitenefs. For wdien I was trying this, a Friend coming to viht me, I ftopt him at the door, and before 1 told him what the Colours were, or what I was doing ; I askt him. Which of the two whites were the beft, and wherein they differed ? And after he had at that diftance viewed them, well, he anfwered, That they were both good wdiites, and that he could not fay which was beft, nor wherein their Co- lours differed. Now if you confider, that this white of the Powder in the Sun-fhine was compounded of the P Colours [11+] Colours which the component Powders ( Oipiment, Purple, Bile, and Viride jEris) have in the fame Sun- fhine, you muft acknowledge by this Experiment, as well as by the former, that perfect whitenefs may be compounded of Colours. From what has been faid it is alfo evident, that the whitenefs of the Sun's Light is compounded of all the Colours wherewith the feveral forts of rays whereof that Light coniifts, when by their feveral refrangibili- ties they are feparated from one another, do tinge Paper or any other white Body whereon they fall. For thole Colours by Prop. i. are unchangeable, and whenever all thofe rays with thole their Colours^ are mixt again^ they reproduce the fame white Light as before. PROP. VI PROS. IL Jn a mixture of ffimary Colours^ the quantity and quality of each being given ^ to.knovj the Colour of the com-- founds JFig.i I . With the Center O and Radius O D dcfcribe a Circle ADF, and diftinguifli its circumference into feven parts/ D E, E F, F G, G A, A B, B C, CD, proportional to' the feven muikal Tones or Intervals of the eight Sounds, *SW, la^ ftty jol^ la^ miy fa^ jol^ contained in an Eight, that is, proportional to the numbers ; , 7,, -f^, J-, 7,, -f^, ;. Let the hrft part D E reprefcnt a. red Colour, the lecond E F orange, the third F G- yellow^ the fourth GH green, the fifth AB blue, the lixth BC indico, and the feventh CD violet. And conceive that thefe are all the Colours of uncompoundcd Light gradually palling C "5 ] pafling into one another, as they do when made by Prilms ; the circumference DK FGABCD, repreien- ting the whole leries of Colours from one end of the Sun's coloured Image to the other, fo that from D to E be all degrees of red, at E the mean Colour between red and orange, from E to F all degrees of orange, at F the mean between orange and yellow, from F to G all de^ grees of yellow, and lb on. Let p be the center of gravity of the Arch DE, and q, r, s, t, v, x, the centers of gravity of the Arches EF, EG, G A, A B, BC and C D refpeftively, and about thole centers of gra- vity let Circles proportional to the number of rays of each Colour in the given mixture be defcribed; that is, the circle p proportional to the number of the red-ma- king rays in the mixture, the Circle q proportional to the number of the orange-making rays in the mixture, and fo of the reft. Find the common center of gravity of all thole Circles p, q, r, s, t, v, x. Let that center be Z ; and fromi the center of the Circle A D F, through Z to the circumference, drawing the right line O Y, the place of the point Y in the circumference fliall Ihew ■\the Colour ariling from the compofttion of all the Co- lours in the given mixture, and the line OZ fhall be proportional to the fulnefs or intenfenefs of the Colour, that is, to its diftancc from whitenefs. As if Y fall in the middle between F and G, the compounded Colour iliall be the beft yellow ; if Y verge from the middle to- wards F or G, the compounded Colour fhall according- ly be a yellow, verging towards orange or green. IfZ fall upon the circumference the Colour fliall be intenfe .and florid in the higheft degree ; if it fall in the mid- 'way between the circumference and center, it fliall be P 0. but but halffo intenfe, that is, it Ihall be fiich a Colour as would be made by diluting the intenleft yellow with an equal quantity of whitenefs ; and if it fall upon the center O, the Colour fliall have loft all its intcnfenels, 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 (hall not be any of the prifmatic Colours, but a purple, in- dining to red or violet, accordingly as the point Z lieth on the fide of the line DO towards E or towards C, and in general the compounded violet is more bright and more fiery than the uncompounded. Alfo if only two of the primary Colours which in the Circle areoppofite to one another be mixed in an equal proportion, the point Z fhall fall upon the center O, and yet the Co- lour compounded of thofe two Ihall not be perfedly white, but fome flint anonymous Colour. For I could never yet by mixing only two primary Colours produce aperfed white. Whether it may be compounded of a mixture of three taken at equal diftances in the circum- ference I do not know, but of four or five I do not much queftion but it may. But thefe are curiofities of little or no moment to the underftanding the Phaenomena otV nature. For in all whites produced by nature, there ufes to be a mixture of all forts of rays, and by confe^ quence a compofition of all Colours. To give an inftance of this Rule ; fuppofe a Colour is compounded of thefe homogeneal Colours, of violet 1 part, of indico i part, of blue i parts, of green 3 parts,, of yellow 5 parts, of orange 6 parts, and of red i o parts. Proportional to thefe parts I defcribe the Circles x, v, t, s, r, q, p refpe^tively, that is, fo that if the Circle x be [117] ^ be I, the Circle v may be i, the Circle t 2, the Circle s ^, and the Circles r, qandp, 5, 6 and 10. Then I find Z the common center of gravity of thefe Circles, and through Z drawing the line O Y, the point Y falls upon the circumference between E and F, fome thing nearer to E than to F, and thence I conclude, that the Colour compounded of thefe ingredients will be an orange, verging a little more to red than to yellow. Alfo 1 find that O Z is a little lefs than one half of OY, and thence I conclude, that this orange hath a little lefs than half the fulnefs or intenfenefs of an un- compounded orange ; that is to lay, that it is fuch an orange as may be made by mixing an homogeneal orange with a good w^hite 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 quan- tities of the lis;hts relieved from them. This Rule I conceive accurate enough for prailire, though not mathematically acairate ; and the truth of it may be fufficiently proved to fenfe, by flopping any of the Colours at the Lens in the tenth Experiment of this Book. For the reft of the Colours which are not \ftopped, 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. PROPJ Cu8j PROP. VII. THEOR. V. \^ll the Colours in the Univerje isjhich are made Sy Lj'^ht^ and defend 7iot on the fo^'joer of trnagmation^ are either the Colours of homogeneal Lights^ or comfoanded of thefe and that either accw ately or very nearly^ ac^ lordmg to the Kjule of the foregoing 'Problem, For it has been proved ( in Prop.i. Li^.'i.) that the changes of Colours made by retradions do not arife from any. new modifications of the rays impreft by thofe refractions, and by the various terminations of light and (hadow, as has been the conftant and general opi- nion of Philofophers. It has alfo been proved that the feveral Colours of the homogeneal rays do conftantly anfwer to their degrees of refrangibility, (Prop, i . Li^.i. andProp.a. L^'/^.^.j and that their degrees of refrangi- bility cannot be changed by refractions and retiexions, {Vvop.2. Li^.^') and by confequence that thofe their Colours are likewife immutable. It has alfo been pro- ved diredlly by refracting and reflecting homogeneal Lights apart, that their Colours cannot be changed,/ ( Prop.i. LiLi.) It has been proved alio, that when' the feveral forts of rays are mixed, and in crofling pafs through the lame Ijpace, they do not aCt on one another ;ib as to change each others colorifick qualities, (Exper. do. L.iLi.) but by mixing their aCtions in the Senfo- rium beget a fenfation differing from what either would do apart, that is a fenfation of a mean Colour between -^hcir proper Colours ; and particularly when by the Jioncourfe and mixtures .«f all forts of rays, a white Colour [119] Colour Is produced, tlie white is a mixture of all tlie Colours which the rays would have apart, ( Prop. 5. Lik 1. ) The rays in that mixture do not lofe or alter their feveral coloritick qualities, but by all their various kinds of aftions mixt in the Senforium, beget a fenfa- tion of a middling Colour between all their Colours which is whitenefs. For whitenefs is a mean between all Colours, having it felf indifterently to them all, fo as with equal facility to be tinged vv'ith 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 mixed with any Colour is prefently tin- ged with that Colour, and is equally capable of beincr tinged with any Colour what-ever. It has been fhewed alfo, that as the Sun's Light is mixed 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 fe- veral coloriiic qualities as well as their feveral refrangi- bilities, and retaining them perpetually unchang'd not- withft:mding any refradlions or reliexions they, may at any time lliffer, and that when-ever any fort of the \ Sun's rays is by any. means (as by reflexion in Exper. 9 vend 10. LiL i. or by refraction as happens in all re-^ fractions) feparated. from the reft, they then manifeft their proper Colours. Thefe things have been proved, ajid thefumof all this amounts to the Propolition here to be proved. For if the Sun's Light is mixed of le- veral forts of rays, each of which have originally their feveral refrangibilities and colorifick quilities, and not- withftanding their refractions and retiedtions, and their various feparations or mixtures^ keep thofe their ori- ginal properties perpetually the. lame without, altera- tion ; [I20] tlon ; then all the Colours in the World mull: be fuch as conllaiitly ought to arile from the original colorific qua- lities of the rays whereof the Lights conlift by which thole Colours are feen. And therefore if thereafon of kny Colour what-ever be required, we have nothing elie to do then to conlider how the rays in the Sun's Light have by reflexions or refractions, or other caufes been par- ted from one another ,or mixed together; or otherwile to find out wliat forts of rays are in the Light by which that Colour is made, and in what proportion ; and then by the laft Problem to learn the Colour which ought to arife by mixing thofe rays (or their Colours) in that proportion. I fpeak here of Colours fo far as they arife from Light. For they appear fometimes by other 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 3 or when we fee Fire by ftriking the Eye, or fee Colours like the Eye of a Peacock's Feather, by preffing our Eyes in either comes whilft we look the other way. Where thefe and fuch like caufes interpofe not, the Colour always anfwers to the fort or forts of the rays whereof the Light coniifts,^ as I have conftantly found in what-ever Phsenomena ot Colours 1 have hitherto been able to examin. I fhall in the following Propofitions give inftances of this in the Phenomena of chiefeft note. PROP. PROP. VIII. PROB. III. B-j the difcove7'ed Trover ties of Light to explain the Colours made hj Trijms, ^ Let ABC rcprefent a Prilm refrading the Light ofpj„-, i2, the Sun, which comes into a dark Chamber through a Hole F ? almoft as broad as the Prifm, and let M N rcprefent a white Paper on which the refraded Light is cart, and fuppofe the moft refrangible •t)r deepeft violet making rays fall upon the fpace Ptt, the leaft refran- gible or deepeft red-making rays upon the fpace T^, the middle fort between the Indico-making aud blue- making rays upon the fpace Q;^. , the middle fort of the green-making rays upon the fpace R e , the middle fort between the yellow-making and orange-making rays upon the fpace ScT 7 and other intermediate forts upon intermediate fpaces. For fo the fpaces upon which the feveral forts adequately fall will by reafon of the diife- rent rcfrangibility of thofe forts be one lower than ano- \ther. Now if the Paper MN be fo near the Prifm that the 'fpaces P T and ttT do not interfere with one another, the diftance between them T TT will be illuminated by all the forts of rays in that proportion to one another which they have at their very firft coming out of the Prilin, and confequently be white. But the fpaces PT and ^ on either hand, will not be illuminated by them all, and therefore will appear coloured. And particularly at P, where the outmoft violet-making rays fall alone, the Colour muft be the deepeft violet. At Q where the violet-making and indico-making rays are mixed , it (1 muft [122] miift be a violet inclining much to indico. At R where the violet'making , indico-making , blue'making, and one half of the green-making rays are mixed, their Co- lours muft ( by the conftrudtion of the fecond Problem) compound a middle Colour between indico and blue. At S where all the rays are mixed except the red-ma- king and orange-making,their Colours ought by the lame Rule to compound a faint blue, verging more to green than indie. And in the progrefs from S to T, tliis blue will grow more and more faint and dilute, till at T, where all the Colours begin to be mixed , it end in whitenefs. .^---So again, on the other fide of the w^hite at T, where the leaft refrangible or utmoft red-making i-ays are alone the Colour mult be the deepert red. At a the mixture of red and orange will compound a red inclining to orange. At e the mixture of red, orange, yellow, and one half of the green mull compound a middle Colour between orange and yellow. At x the mixture of all Colours but violet and indico will compound a faint yellow, verging more to green than to orange. And this yellow will grow more faint and dilute continually/' in its progrels from -^ to tt, where by a mixture of al^' forts of rays it will become white. Theie Colours ought to appear were the Sun's Light perfedly white: But becaufe it inclines to yellow,theex- cefs of the yellow-making rays whereby 'tis tinged with that Colour, being mixed with the faint blue between S and T, will draw it to a fa-int green. And fo the Colours in order from P to T ought to be violet, indico, blue, very faint green, white, faint yellow, orange, red. Thus it is by the computation : And they that pleale to view [123] /lew the Colours made by a Prifin will find it fo In NJature. Theie are the Colours on both fides the white when he Paper is held between the Prifm, and the point X vhere the Colours meet, and the interjacent white va- liflies. For if the Paper be held ftill farther off from the Mfm, the moft refrangible and leaft refrangible rays vill be wanting in the middle of the Light, and the reft )f the rays which are found there, will by mixture pro- luce a fuller green than before. Alfo the yellow and )lue will now become lefs compounded, and by con- equence more intenfe than before. And this alfo [grees with experience. And if one look through a Prifm upon a white Objed 'ncompafled with blacknefs or darknefs, the reafon of he Colours arifing on the edges is much the fame, as vill appear to one that ihall a little confider it. If a )lackObjed be encompaffed with a white one, the Co- ours which appear through the Prifm are to be derived rem the Light of the white one, fpreading into the Re- ;ionsof the black, and therefore they appear in a con- ,rary order to that, in which they appear when a white )bjed: is furrounded with black. And the fame is to le underftood when an Objed is viewed, whofe parts re fome of them lefs luminous than others. For in the borders of the more and lefs luminous parts, Colours mght always by the lame Principles to arife from the xcefs of the Light of the more luminous, and to be of he fame kind as if the darker parts were black, but yet be more faint and dilute. Q ^ What i [124] What is faid of Colours made by Prlfms may be eafil applied to Colours made by the Glafles of Telefeop or Microfcopes, or by the humours of the Eye. For i the Objecl'glafs of a Telefcope be thicker on one fid than on the other, or if one half of the Glafs, or on half of the Pupil of the Eye be covered with any opak fubftance : the Objed-glafs, or that part of it or of th Eye which is not covered, may be conlidered as a Wedg with crooked lides, and every Wedge of Glafs, orothe pellucid fubftaQce, has the effed of a Prifm in refradin; the Light which pafles through it. How the Colours in the 9th and loth Experiment of the firft Part arife from the different reflexibility Light,is evident by what was there faid. But it is obfer vable in the 9th Experiment, that whilft the Sun's di red Light is yellow, the excefs of the blue-makin| rays in the refleded Beam of Light M N, fuffices onb to bring that yellow to a pale white inclining to blue and not to tinge it with a manifeftly blue Colour. T( obtain therefore a better blue, 1 ufed in Head of the yel low Light of the Sun the white Light of the Clouds, bj. varying a little the Experiment as follows. EXPER. XVL F^""". 1 5. Let H F G reprefent a Prifm in the open Air, and [ the Eye of the Spedator, viewing the Clouds by thei Light coming into the Prifm at the plane tide FIGK and reiieded in it by its bafe H E I G, and thence goin^ out through its plain fide H E F K to the Eye. Am when the Prifm and Eye are conveniently placed, f( that the Angles of incidence and reflexion at the baft may be about 40 degrees, the Speftator 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 IMNG beyond this Bow will be brighter than the other part E M N H on the other iide ol^ it. This blue Colour MN being made by no- thing elfe than by reflexion of a fpecular fuperticies, leeins fo odd a Phaenomcnon, and fo unaccountable for by the vulgar Hypothelis of Fhilofophers, that I could- not but think it deferved to be taken notice of. Now for underftanding the realbn of it, fuppole the plane ABC to cut the plane fides and bafe of the Prifm per- pendicularly. From the Eye to the line BC, wherein that plane cuts the bafe, draw the lines Sp and S t, in the Angles Spc 50 degr. ;» andStc49 degr.-[s, and the point / will be the limit beyond which none of the mofb refrangible rays can pais through the bafe of the Prifm, and be refracted, whole incidence is fuch that they may be rctieded to the Eye ; and the point t will be the like limit for the leaft refrangible rays, that is, beyond which none of them can pafs through the bafe, whofe incidence is fuch that by reflexion they may come to the Eye. And the point r taken in the middle way between p and t, will be the like limit for the meanly refrangible' rays. And therefore all the refrangible rays which fall upon the bafe beyond t, that is, between t and B, and can comiC from thence to the Eye will be refleded thi- ther : But on this fide t, that is, between t and c, many . of thefe rays will be tranfmitted through the bafe. And all the moft refrangible rays which fall upon the bafe beyond p, that is , between p and B, and can by reflexion come from thence to the Eye, will be reflected • thithcr<» - thither, but every where between t and c, many of thefe rays will get through the bafe and be refraded ; and the faine is to be underftood of the meanly refran- gible rays on either fide of the point r. Whence it fol- lows, that the bale of the Prifm muft: every where be- tween t and B, by a total reflexion of all forts of rays to the Eye, look white and bright. And every where between p and C, by realbn of the tranfmiffion of many rays of every fort, look more pale, obfcure and dark. But at r, and in other places between p and t, where all the more refrangible raj's are refleifled to the Eye, and many of the lefs refrangible are tranfmitted, the excefs of the moft refrangible in the reflected Light, will tinge that Light with their Colour, which is violet and blue. And this happens by taking the line Cp r t B any where between the ends of the Prifm H G and E L PROP. IX. PROB. IV. jBy the difcovered Tro^erties of Light to explain the Colours oj the Rjitn'h'vi>. This Bow never appears but where it Rains in the Sun-(hine, 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 upon thefe Drops certainly caufes the Bow to appear to a Spefta^ tor itanding in a due pofition to the Rain and Sun. And hence it is now agreed upon, that this Bow is made by refradfion of the Sun's Light in Drops of tailing Rain. This was underfi:ood by fome of the Ancients, and of late more fully difcovered and explained by the Famous y^ntonius C 127 ] uiintomm de'Dominis Archbifhop of 6')'i/^if(?, in his Book ^e Radtk Vt[m if7 Lucis^ publiflied by his Friend Bar* tolm at Venice^ in the Year 1 6 1 1 , and written above twenty Years before. For he teaches there how the interior Bow is made in round Drops of Rain by two refradions of the Sun's Light, and one reflexion be- tween them, and the exterior by two refradions and two forts of reflexions between them in each Drop of Water, and proves his Explications by Experiments made with a Phial full ofWater,and with Globes ofGlafs filled with Water, and placed in the Sun to make the Colours of the two Bows appear in them. The fame Explication 'Des-Cartes hath purfued in his Meteors^ and mended that of the exterior Bow. But whilft they underfliood not the true origin of Colours, it's neceffary to purfue it here a little further. For underfl:anding therefore how the Bow is made, let a Drop of Rain or any other fpherical tranfparent Body be reprefented by the Sphere BN FG, defcribed with the Center C, and Fig. 14 > Semi-diameter CN. And let AN be one of the Sun's rays incident upon it at N, and thence refraded to F, where let it either go out of the Sphere by refradion to- wards V, or be reflected to G ; and at G let it either go out by refraction to R, or be reflected to H ; and at H let it go out by refraction towards S, cutting the inci- dent ray in Y ; produce A N and R G, till they meet in. X, and upon A X and N F let fall the perpendiculars CD and CE, and produce CD till it fall upon the cir- cumference at L. Parallel to the incident ray A N draw the Diameter B Q, and let the fine of incidence out of Air into Water be to the line of refradion as I to R. Now if you fuppofe the point of incidence N to move move from the point B, continually till it come to L, t4ie Arch QF will firft increale and then decreafe, and lb will the Angle AXR which the rays AN and GR contain; and the Arch QF and Angle AXR w^ill be biggell when ND is to CN as //hIrr to /^^ RR^ in which cafe N E will be to N D as a R to I. Alfo the Angle AYS which the rays A N and HS contain will firll decreafe, and then increafe and grow leaft when ND is to CNas //fTRR to//8 RR, in which 4:afe N E will be to N D as 5 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 // ii-rr to /^ 1 5 R R, in which cafe N E will be to N D as 4 R to I, and the Angle which the ray next after that emergent, that is, the ray emergent after four reflexions, con- tains with the incident will come to its limit, when N D is to C N/ as / ii-rr to //14 R R , in which cafe N E will be to N D as 5 R to 1 ; and fo on infinitely, the numbers 5, 8, 1 5, 24, ]5>c-. being gathered by conti- nualaddition of the terms of the arithmetical progreflion 5,5,7, 9,isV. The truth of all this Mathematicians will eaflly examine. Now it is to be obferved, that as when the Sun comes to his Tropicks, days increafe and decreafe but a very little for a great while together ; fo when by increaf ng the difl:ance C D, thefe Angles come to their limits, they vary their quantity but very little for fome time together, and therefore a far greater number of the rays which tall upon all the points N in the Quadrant BL, fhall emerge in the limits of thefe Angles, ^then in any other inclinations. And further it is to [129] to be obierved, that the rays which differ in refrangl- biHty will have different limits of their Angles of emer- gence, and by confequence according to their different degrees of refrangibility emerge moll copioufly in dif- ferent Angles, and being feparated from one another appear each in their proper Colours. And what thofe Angles are may be eafily gathered from the foregoing Theorem by computation. For in the leaft refrangible rays the fines I and R (as was found above) are 108 and 81, and thence by computation the greateft Angle AXR will be found 42 degrees and 0. minutes, and the leaft Angle AYS, 50 degr. and 57 minutes. And in the moft refrangible rays the fines I andR are 109 and 81, and thence by computation the greateft Angle AXR will be found 40 degrees and 1 7 minutes, and the leafi: Angle AYS 54. degrees and 7 minutes. Suppofe now that O is the Spectator's Eye, and OP a line fig. 1 5 , drawn parallel to the Sun's rays, and let PO E, POP, POG, POH, be Angles of 40 degr. i7min. 41 degr. 2 min. 50 degr. 57 min. and 54 degr. 7 min. refpedively, and thefe Angles turned about their common fide O P, Ihall with their other fides OE, OF; OG, OH de- defcribe the verges of two Rain-bows AFBE and CHDG. For if E, F, G, H, be Drops placed aiw where in the conical fuperficies defcribed by O E, O F, OG, OH, and be illuminated by the Sun's rays SE, SF, SG, SH; the Angle SEO being equal to the Angle POE or 40 degr. 17 min. fhall be the greateft Angle in which the moft refrangible rays can after one reflexion be refraded to the Eye, and therefore all the Drops in the line O E fhall fend the moft refrangible R I'j^ys [130] rays moft copiouny to the Eye, and thereby ftiike the fenles with the dcepeft violet Colour in that region. And in like manner the Angle SFO being equal to: the Angle P OF, or 4:2 deg. 2 min. fhall be the greateft in which the lead refrangible rays after one reflexion can emerge out of the Drops, and therefore thofe rays (hall come moft copioufly to the Eye from the Drops in the line O F, and ftrike the fenles with the deepeft red Colour in that region. And by the fame argument, the rays which have intermediate degrees of xefrmigibi- lity fhall come moft copioufly from Drops between E and F, and ftrike the fenles with the intermediate Colours in the order which their degrees of refrangibi- Uty require , that is, in the progrefs from E to F, or from the inflde of the Bow to the outiide in this order, violet, indico,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 Angle P O G,, or 50 gr. 51 min. fhall be the leaft Angle in which the l,eaft refrangible rays can after two reflexions emerge out of the Drops,and therefore the leaft refrangible rays fliall come moft copioufly to the Eye from the Drops in the line O G, and ftrike the fenfe with the deepeft red in that region. And the Angle S HO being equal to the Angle P OH or 54. gr. 7 min. fliali be the leaft Angle in which the moft refrangible rays after two reflediohs can emerge out of the Drops, and therefore thofe rays fhall come moft copioufly to the Eye from the Drops in the line O H, and ftrike the fenles with the deepeft violet in that region. And by the fame argument, the Drops in the regions between G and H fhall ftrike the fenfe with the CI30 the intermediate Colours in the order which tlicir de- grees of refrangibility require^ that is, in the progrefs from G to H, or from the iniide of the Bow to the out- lide in this order, red, orange, yellow, green, blue, in- dico, violet. And fince thefe four lines O E, O F, O G. O H, may be iituated any where in the above-mentioned conical fuperficies, what is faid of the Drops and Co- lours in thefe lines is to be underftood of the Drops and Colours every where in thofe fuperficies. Thus fliall there be made two Bows of Colours, an interior and ftronger, by one reflexion in the Drops, and an exterior and fainter by two ; for the Light be- comes fi3 inter by every reflexion. And their Colours {hall ly in a contrary order to one another, the red of both Bows bordering upon the fpace G F which is be- tween the Bows. The breadth of the interior Bow EOF meafured crofs the Colours fnall be i degr. 45 min. -ind the breadth of the exterior GOH ihall be -9 degr. lomin. and the difxance between them GOF ihall be 8 gr. 5 5 min. the greatefl: Semi-diameter of the innermoft, that is, the Angle POF being 4a gr. 2 min. gnd the leaft Semi-diameter of the outermoil P O G, be- ing 50 gr. 57 min. Thefe are the meafures of the Bows, ; as they would be w^re the Sun but a point ; for by the breadth of his Body the breadth of the Bows will be in- creafed and their diftance decreafed by half a deg,ree, and io the breadth of the interior Iris wall be 1 degr. 15 min. that of the exterior 9 degr. 40 min. their di- :iJance 8 degr. 25 min. the greateft Semi-diameter of the interior Bow 42 degr. 17 min. and the leaft of the ex- .terior 50 d^gr. 4a mJn. And fuch are the dimeniions r.iof the Bows in the Heavens found to be very nearly, ■ R 2 when [t3'2] when tht'ii" Colours appear ftrong and pcift'ct. For once, by fuch means as I then had, I nieafured the greateft Semi-diameter of the interior Iris about 4.2 de- grees, the breadth of the red, yellow and green in that Iris 63 or 64. minutes, befides theoutnToft faint red ob- fcured by brightncfs of the Clouds, for which we may allow 3 or 4 minutes more. The breadth of the blue was about 4.0 minutes more be (ides the violet, which was fo much obfcured by the brightnefs of the Clouds, that 1 could not meaiure its breadth. But fuppofing the breadth of the blue and violet together to equal that of the red, yellow and green together, the whole breadth of this Iris will be about 1^ degrees as above. The leaft diftance between this Iris and the ex- terior Iris was about 8 degrees and 50 minutes. The ex- terior Iris was broader than the interior, but fo faint, efpecially on the blue tide, that I could not meaiure its breadth diftindly. At another time when both Bows appeared more diftinft, I meafured the breadtli of the interior Iris 2 gr. ic, and the breadth of the red, yel- low and green in the exterior Iris, was to the breadth of the fame Colours in the interior as 5 to a. This Explication of the Rain-bow is yet further con- firmed by the known Experiment ( made by Antonim de Dominis and T)es -Cartes) of hanging up any where in the Sun-fhine a Gl ifs-Globe filled with Water, and viewing it in fuch a pofture that the rays which come from the Globe to the Eye may contain with the Sun's rays an Angle of either 4a or 50 degrees. For if the Angle be about 4.1 or 4.3 degrees, the Spectator ( fup- pofe at O) (hall fee a full red Colour in that fide of the Globe oppofed to the Sun as 'tis reprefented at F, and if [133.3 if that Angle become lets ( luppofe by depreffing tlie Globe to E) there will appear other Coloms, yellow, green and blue fucceffively in the lame (ide of the Globe. But if the Angle be made about 50 degrees (luppole 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 Angle be made greater (fuppofe by lifting up the Globe to H) the red will turn fucceffively to the other Colours yellow, green and blue. The lame thing I have tried by letting a Globe reft, and raihng or depreffing the Eye, or otherwife moving it to make the Angle of a juft magnitude. 1 have heard it reprefented, that if the Light of a Candle be refraded by a Prifm to the Eye ; when the blue Colour falls upon the Eye the Spedator fhall lee red in the Prifm, and when the red fliUs upon the Eye he fhall fee blue ; and if this were certain, the Colours of the Globe and Rain-bow ought to appear in a con- trary order to what we find. But the Colours of the Candle being very faint, the miftake feems to arife from the difficulty of difcerning what Colours fall on the Eye. For, on the contrary, I have fometimes had oc- calion to obferve in the Sun's Light refraded by a Prifm, that the Spe(ftator always fees that Colour in the Prifm which falls upon his Eye. And the fame I have found true alfo in Candle-Light. For when the Prifm is mo- ved (lowly from the line which is drawn directly from the Candle to the Eye,the red appears firft in the Prifiii and then the blue, and therefore each of them is feen when it falls upon the Eye. For the red paffes over the Eye firft, and then the blue. The 1 134-1 The Light wiiich comes through Drops of Ruin hy two refractions without any reflexion, ought to appear Ihongeft at tlie diftancc of about a 6 degrees from the Sun, and to decay gradually both ways as the dilbnce from him increales and dccreafes. And the fame is to be underftood of Light tranfmitted through fpherical Hail-ftoncii. And if the Hail be a little hatted, as it often is, the Light tranfmitted may grow fo ftrong at a little lefs diftance than that of 16 degrees, as to form a Halo about the Sun or Moon ; which Halo, as often as the Hail-ftones are duly figured may be coloured, and then it muft be red within by the lead refrangible rays,and blue without by the moft refrangible ones,efpe- xially if the Hail-flones have opake Globules of Snow in their center to intercept the Light within the Halo ( as Hugenim has obferved) and make the inlide thereof more -diftindly defined than it would otherwife be. For luch Hail-flones, though fpherical, by terminating the Light by the Snow, may make a Halo red within and colourlefs without, and darker in the red than with= out, as Halos ufe to be. For of thofe rays which pafs elofe by the Snow the rubriform will be leaft refradtedj and fo come to the Eye in the dire6teft lines. The Light which paiTes through a Drop of rain after two refractions, and three or more reflexions, is fcarce ftrong enough to caule a fenfible Bow ', but in thofe Cy- linders of Ice by w^hich Hugemm explains ih^ Tiifheha^ it may perhaps be fenfibk- PROP. P R O p. X. P R O B. V. Bj the dtfcovered properties of Light to explain the fer^ manent Colours of natural Bodies. Thefe Colours arlfe from hence, that fome natural Bodies refled fome forts of rays, others other forts more copiouQy than the reft. Minium reflects the leaft re- fi'angible or red-making rays raoft copioufly, and thence appears red. Violets reflect the moft refrangible, moft copioufly, and thence have their Colour, and fo of other Bodies. Every Body reflects the rays of its own Colour more copioufly than the reft, and from their excefs and predominance in the reflected Light has its Colour. EX PER. xvir. For if the homogeneal Lights obtained by the folu* tion of the Problem propofed in the 4.th Propolition of the firft Book you place Bodies of feveral Colours, you will find, as I have done, that every Body looks moft fplendid and. luminous in the Light of its own Colour, Cinnaber in the homogeneal red Light is moft refplcn- dent, in the green Light it is manifeftly lefs refpleiv dent, and in the blue Light ftill lefs. Indico in the violet blue Light is moft refplendent, and its fplendoK is gradually diminiflied 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 ftrongly re- fleaed. [13^] fleeted than the other Colours red and violet,and fo of the reft. But to make thcfe Experiments the more manifeft, luch Bodies ought to be choten as have the fulleft and moft vivid Colours, and twoof thole Bodies are to be compared together. Thus, tor inftance, if Cinnaber and ultra 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 ftrongly luminous and refplendent red, and the ultra marine blue of a faint obfcure and dark red ; and if they be held together in the blue homogeneal Light they will both appear blue, but the ultra marine will appear of a ftrongly luminous and relplendent blue, and the Cinnaber of a faint and dark blue. Which puts it out of difpute , that the Cinnaber reflects the red Light much more copiouily than the ultra marine doth, and the 2iltra marine retlefts the blue Light much more co- pioufly than the Cinnaber doth. The fame Experiment may be tryed fucccsfully with red Lead and Indico, or v,dth any other two coloured Bodies, if due allowance be made for the different ftrength or weaknefs of their Colour and Light. And as the reafon of the Colours of natural Bodies is evident by thefe Experimenrs, fo it is further confirmed and put paft difpute by the two firft Experiments of the firft Book, whereby 'twas proved in fuch Bodies that the reileded Light which differ in Colours do differ alfo hi degrees of refrangibility. For thence it's certain, that fome Bodies retie*^ the more refrangible, others the lefs refrangible rays more copioufly. And [137] And that this is not only a true reafon of thefe Co- lours, but even the only realbn may appear further from this conlideration, that the Colour of homogeneal Light cannot be changed by the reflexion of natural Bodies. For if Bodies by reflexion cannot in the leaft change the Colour of any one fort of rays, they cannot appear coloured by any other means than by refleding thofe which either are of their own Colour, or which by mixture muft produce it. But in trying Experiments of this kind care mufl: be had that the Light be fufficiently homogeneal. For if Bodies be illuminated by the ordinary prifmatick Co- lours, they will appear neither of their ow^n day-light Colours, nor of the Colour of the Light cafl: on them, but of fome middle Colour between both, as I have found by Experience. Thus red Lead ( for inftance ) illuminated with the ordinary prifmatick 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 com- pounded. For becaufe red Lead appears red when il- luminated with white Light, wherein all forts of rays are equally mixed, and in the green Light allforts of rays are not equally mixed, the excefs of the yellow- making, green-making and blue-making rays in the • incident green Light, will caufe thofe rays to abound fo m.uch in the reflected Light as to draw the Colour from red towards their Colour. And becaufe the red Lead reflects the red-making rays moft copioufly in proportion to their number, and next after them the orange-making and yellow-making rays ; thefe rays in S the A the refleded Light will be more in proportion to tlie Light than they were in the incident green Light, and thereby will draw the refleded Light from green to- wards their Colour. And therefore the red Lead will ap- pear neither red nor green,butofaColour between both. In tranfparently coloured Liquors 'tis oblcrvable, that their Colour ufes to vary with their thicknefs. Thus, for inftance, a red Liquor in a donical Glafs held between the Light and the Eye, looks of a pale and dilute yellow at the bottom wiiere 'tis thin, and a little higher where 'tis thicker grows orange,and where 'tis ftill thicker becomes red, and where 'tis thickeft the red is deepeft and darkeft . For it is to be conceived that fuch a Liquor ft ops the indico-making and violet- making rays moft ealily, the blue- making rays more difficultly, the green-making rays ftill more difficultly, and the red-making moft difficultly : And that if the thicknefs of the Liquor be only fo much as fuffices to ftop a competent number of the violet-making and in- dico-making rays, without diminilhing much the num- ber of the reft, the reft muft (by Prop. 6. Ltl^. 'i. j com- pound a pale yellow^ But if the Liquor be fo much thicker as to ftop alfo a great number of the blue-making rays, and fome of the green-making, the reft muft com- pound an orange ; and w^here it is fo thick as to ftop alfo a great number of the green-making and a confi- derable number of the yellow-making, the reft muft begin to compound a red, and this red muft grow deeper and darker as the yellow making and orange-making rays are more and more ftopt by increaftng the thick- nefs of the Liquor, lb that few rays beiides the red- making can get through^ Of [ 1 39 ] Of this kind is an Experiment liitely related to me by Mr. HaUe>j^ who, in diving deep into the Sea, found in a clear Sun-fhine day, that when he was lunk many Fathoms deep into the Water, the upper part of his Hand in which the Sun Ihone dire6tly through the Water looked of a red Colour, and the under part of his Hand illuminated by Light retieded from the Water below looked green. For thence it may be gathered, that the Sea .water refleds back the violet and blue- making rays moll: eaiily, and lets the red-making rays pals moft freely and copioully to great depths. For thereby the Sun's dired Light at all great depths, by reafon of the predominating red-making rays, mult appear red ; and the greater the depth is, the fuller and intenfer muft that red be. And at fuch depths as the violet-making rays fcarce penetrate unto, the blue- making, green-making and yellow-making rays being relieved from below more copioully than the red-making ones, mull compound a green. Now if there be two Liquors of full Colours, fup- pofe a red and a blue, and both of them fo thick as fuffices to make their Colours fufficiently full ; though either Liquor be fufficiently tranfparent apart, yet will you not be able to fee through both together. For if only the red-making rays pals 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 unexpected event, the reafon of it being then unknown 3 which makes me truft the more to his Experiment, though 1 have not tryed it my felf. But he that would repeat it, muft take care tiie Liquors be of very good and full Colours. S 2 Now [140] Now whilfl: Bodies become coloured by reliedling or tranfmitting this or that fort of rays more copiouOy than the reft, it is to be conceived that they ftop and ftifle in themfelves the rays which they do not retiector tranfmit. For if Gold be foliated and held between your Eye and the Light, the Light looks blue, and therefore maffy Gold lets into its Body the blue.making rays to be retleded to and fro within it till they be ftopt and ftifled, whilft it retlecls the yellow-nwking outwards, and thereby looks yellow. And much aftei' the fame manner that Leaf-gold is yellow by reflected, and blue by tranfmit- ted Light, and mafly Gold is yellow in all portions of the Eye ; there are fome Liquors as the tindure of Lignum iSfefhrit'icum^ and fome forts ot Glafs which tranfmit one fort of Light moft copioufly, and reileft another fort, and thereby look of feveral Colours, ac- cording to the polition of the Eye to the Light. But if thefe Liquors or Glaffes were ^io thick and maffy that no Light could get through them, 1 queftion not but that they would like all other opake Bodies appear of one and the fame Colour in all pofitions of the Eye, though this 1 cannot yet affirm by experience. For all coloured Bodies, fo tar as my Obfervation reaches, may be leen through if made fufficiently thin,., and therefore are in fome meaiure tranfparent, and differ only in de- grees of tranfparency from tinged tranfparent Liquors •_ thefe Liquors, as well as thole Bodies, by a fufficient thicknefs becoming opake. A tranfparent Body which looks of any Colour by tranfmJtted Light, may alio look of the fame Colour by reflefted Light, the Light of that Colour bein^ rerleded bv the furtlier furtace of the Body, or by the Air beyond it. And then the re- tleded Colour will be diminilhe'Uand perhaps ceale, by jnaking [ 141 ] making the Body very thick, and pitching it on the hick-fide to diminifli the reflexion of its further furface, fo that the Light reiiefted from the tinging particles .may predominate. In fuch cafes, the Colour of the re- fiedled Light will be apt to vary from that of the Light tranfmitted. But whence it is that tinged Bodies and Liquors refled: fome fort of rays, and intromit or trans- mit other forts, ihall be laid in the next Book. In this Propofition 1 content my felf to have put it paft difpute,, that Bodies have fuch Properties, and thence appear coloured. PROP. XL PROB. VL B'i mixing coloured Lights to corn-pound a Bcarri of Ltg/jp of the jame Colour and Mature isoith a Beam of the Suns- direSi JL'rght^ and therein to experience the truth of the. foregoing Tro-^o fit tons. Let A B Cab c reprefent a Prifm by which the Sun's Fig- i^» Light let into a dark Chamber through the Hole F, may be refraded towards the Lens M N, and paint upon it at p, q, r, s and t, the ufual Colours violet, blue, green^ yellow and red, and let the diverging rays by the re- iradion of this Lens converge again towards X, and thcrc,by the mixture of all thofe their Colours,compound a white according to what was fhewn above. Then let another Prifm DEGdeg, parallel to the former, be placed at X, to refrad that white Light upwards to-^ wards Y. Let the refrading Angles of the Prifms^ and their dillances from the Lens be equal, fo that the rays which converged from the Lens towards X, and". without refradion, would there have croffed and diver- ged again, may by the refraction of the fecondPriim be. reduced. reduced into Parallelifm and divcrsie no more. For then thole rays will recompofe a Beam of white Light XY. If the refrafting Angle of cither Prilm be the bigger, that Prifm mull be lb much the nearer to the Lens. You will know when the Prifms and the Lens are well let together by obferving if the Beam of Light XY which comes out of the fecond Prifm be perfedly white to the very edges of the Light, and at all diftan- cesfrom the Prifm continue perfectly and totally white like a Beam of the Sun's Light. For till this happens, the polition of the Prifms and Lens to one another mull be corrcdted, 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 inftrument made for that purpofe, they be made faft in that lituation, you may try all the lame Experiments m this compounded Beam of Light' XY, which in the foregoing Experiments have been made in the Sun's direct Light. For this compounded Beam of Light has the lame appearance, and is endowed with all the fame Properties with a diredt Beam of the Sun's Light, lb far as my Obfervation reaches. And in trying Experiments in this Beam you may by ftopping any of the Colours p, q, r, s and t, at the Lens, fee how the Colours produced in the Experijnents are no other than thofe which the rays had at the Lens before they entered the compoiition of this Beam : And by confe- cjuence that they arife not from any new modifications of the Light by refractions and reflexions, but from the various feparations and mixtures of the rays originally endowed with their colour-making qualities. So, for inrtance, 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 [ H3 ] txamin the reaibn of the Colours made by Prifms, I refraded this compounded Beam of Light XY with another Prifm H I K k h, and thereby caft the ufual pi if- matick Colours PQRST upon the iPaper LV placed be- hind. And then by Hopping any of the Colours p, q,.. r, s, t, at the Lens, 1 found that the fame Colour would vanifli at the Paper. So if the purple P was flopped at the Lens, the purple P upon the Paper would vanifh, and the reft of the Colours would remain unaltered, unlets perhaps the blue, fo far as fome purple latent ni it at the Lens might be feparated from it by the fol- lowing refractions. And lb by intercepting the green upon the Lens, the green R upon the Paper would va- nifh, and fo of the reft ; which plainly (hews, that as the white Beam of Light X Y was compounded of fe- ve Lights varioufly coloured at the Lens, lb the Co- lours which afterwards emerge out of it by new refra- ftions are no other than thofe of which its whitenefs was compounded. The refraction of the Prifm H I K kh 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 entered the compofition of the re- fraded Beam white of Light X Y. For otherwife the rays which were of one Colour at the Lens might be of ano- ther upon the Paper, contrary to what we find. So again, to examin the reafon of the Colours of na- tural Bodies, I placed fuch Bodies in the Beam of Light XY, and found that they all appeared there of thofe their own Colours which they have in Day-light, and that thofe Colours depend upon the rays which had the fame Colours at the Lens before they entred the compo- lition lition of that Beam. Thus, for inftance,Cinnaber illumi- nated by this Beam appears of the fame red Colour a-- in Day-light , and if at the Lens you intercept the green- making and blue-making rays, its rednefs will become more full and lively : But if you there intercept the red- making rays, it will not any longer appear red, but be- come yellow or green, or of Ibme other Colour, accor- ding to the forts of rays which you do not intercept. So Gokl in ti\is Light XY appears of the lame yellow Colour as in Day-light, but by intercepting at the Lens a due quantity of the yellow-m^aking rays it will appear white like Silver (as 1 have tryed) which fhews that its yellownels ariles from the excefs of the intercepted rays tinging that whitenels with their Colour when they are let pafs. ^ot\\Q m(\x(\on oi LigniimNefhrittcum (as I have alio tryed ) when held in this Beam of Light X Y, looks blue by the refieded part of the Light, and yellow by the tranfmitted part of it, as when 'tis viewed in Day- light, but if you intercept the blue at the Lens the infu- fion will lofe its reflected blue Colour, whilit its tranf- mitted red remains perfed: and by the lofs of ibme blue- making rays wherewith it was allayed becomes morein- tenfe and full. And, on the contrary, if the red and orange- making rays be intercepted at Lens, the infufion will loie its tranfmitted red, whilfl its blue will remain and become more full and perfect. Which fhews, that the in- ' fuiion does not tinge the rays with blue and yellow, but only tranlmit thofe moft copiouily which were red-ma- king before, and reflefts thole moll copioufly which were blue-making before. And after the lame manner may the peafons of other Phaenomena be examined, by trying them in this artificial Beam of Light X Y. THE / Book I. Part I. Plate 1. Book I. Part n. Plate E. X Book! Part H. Plate m. F£^.l^ Bookl. I'aitl.i'iatp CO THE ''"^ SECOND BOOK O F O P T I C K S. PART I. O^fervations concerning the Reflexions^ Refradiions^ and Colours of thin tranjfarent Bodies, IT has been obferved by others that tranfparent Subftances, as Glafs, Water, Air, he. when made very thin by being blown into Bubbles, or otherwife formed into Plates, do exhibit various Colours accor- ding to their various thinnefs, although at a greater thicknefs they appear very clear and colourleis. In the former Book I forbore to treat of thefe Colours, becaufe they feemed of a more difficult coniideration, and were not neceffary for eftablilhing the Properties of Light there difcourfed of. But becaufe they may conduce to further difcoveries for completing the Theory of Light, efpecially as to the conftitution of the parts of natural Bodies, on which their Colours or Tranfparency depend ; I have here let down an ac- count of them. To render this Difcourfe Ihort and diftind, I have lirft defcribed the piincipal of my A a Obfer= [2] Obfervations, and then confidered and made ufe of them. The Oblervations are thele. O B S. I. Compreffing two Prifms hard together that their Sides (which by chance were a very httle convex)might fomewhere touch one another : 1 found the place in which they touched to become abibUitely traniparent, as if they had there been one continued piece of Glafs. For when the Light fell fo obliquely on the Air, which in other places was between them,as to be all relieved ; it feemed in that place of contad: to be wholly tranf- mitted, infomuch that when looked upon, it appeared like a black or dark Spot, by reafon that little or no fenfible Light was reflected 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 compreffed between the Glaffes. And through this hole Objects that were beyond might be Ci^tn di- ftindly, which could not at all be feen through other parts of the Glafles where the Air was interjacent. Al- though the Glafles were a little convex, yet this tranf- parentSpot was of a coniiderable breadth,which breadth, feemed principally to proceed from the yielding inwards of the parts of the GlalTes, by reafon of their mutual preffure. For by preffing them very hard together it would become much broader than otherwife. OBS. [3] O B S. II. When the Plate of Au', by turnuig thePiifms about their common Axis, became lb little inclined to the in- cident Rays, that Ibme of them began to be tranfmit- ted, there arofe in it many flender Arcs of Colours which at firft were ihaped almoft like the Conchoid, as you fee them delineated in the firft Figure. Andi^^ig- ^ by continuing the motion of the Prifms, thefe Arcs in- creafed and bended more and more about the faid tranf- parent Spot, till tliey were completed into Circles or Rings incompaffing it, and afterwards continually grew more and more contracted. Thefe Arcs at their firft appearance were of a violet and blue Colour, and between them were white Arcs of Circles, which prefently by continuing the motion of the Prifms became a little tinged 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 Spot, was at that time white, blue, violet j black ; red, orange, yellow, white, blue, violet, 't^c. But the yellow and red were much fainter than the blue and violet. The motion of the Prifms about their Axis being con- tinued, thefe Colours contracted more and more,ilirink- ing towards the whitenefs on either fide of it, until they totally vanifhed into it. And then the Circles in thofe parts appeared black and white, without any other Co- lours intermixed. But by further moving the Prifms about, the Colours again emerged out of the whitenefs, the violet and blue as its inward Limb, and at its out- A a 2 ward [4] ward Limb the red and yellow. So that now their order from the central Spot was white, yellow, red ; black ; violet, blue, white, yellow, red, oc. contrary to what it was before. O B S. III. When the Rings or fome parts of them appeared only black and white, they were very diftind: and well de- fined, and the backnefs fcemed as intenfe as that of the central Spot. Alio in the borders of the Rings, where the Colours began to emerge out of the white- nefs, they were pretty diftintt, which made them vi- fible to a very great Multitude. I have fometimes numbred above thirty Sncceffions ( 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 diftinguifh above eight or nine of them, and the exte^ rior of thofe were very confuted and dilute. In thefe two Obfervations to fee the Rin^s diftinft. and without an-y oth^r Colour than black and white,! found it neceflary to hold my Eye at a good diftance from them. For by approaching nearer, although in the fame inclination of my Eye to the plane of the Rings, there emerged a blueifh Colour out of the white, which by dilating it felf more and more into the black rendred the Circles lefs diftintl:, and left the white a little tinged with red and yellow. I found alio • by looking through a flit or oblong hole , which was narrower than the Pupil of my Eye, and held clofe t€^ it. [5] it parallel to the Prifms, 1 could fee the Circles much dilHnder and vifible to a far greater number than Gtherwife, O B S. IV. To obferve more nicely by the order of the Colours which arofe out of the white Circles as the Rays be- came iefs and Icfs inclined to the plate of Air; 1 took two Objed GlafTes, the one a Plano-convex for a four- teen-foot Telefcope, and the other a large double con- vex for one of about fifty-foot; and upon this,laying the other with its its plane-fide downwards, I prefled them llowly togethcr^to make the Colours fucceflively emerge in the middle of the Circles,, and then flowly lifted the upper Glafs from the lower to make them fuccef- fively vanifli again in the fame place. The Colour,, which by preffing the Glaffes together emerged lafi: in the middle of the other Colours, would upon it& firft appearance look like a Circle of a Colour almoft uni- form from the circumference to the center , and by compreffing the Glaffes ftill moi"e, grow continually broader until a new Colour emerged in its center, and thereby it became a Ring encompafling that new Co- lour. And by comprefling the Glafles ftill more, the Diameter of this Ring would encreafe, and the breadth of its Orbit or Perimeter decreafe until another new Colour emerged in the center of the laft : And fo on iintil a third, a fourth, a fifth, and other following new Colours fucceilively emerged there^ and became Rings encompaffing the innermoft Colour, the laft of which was the black Spot. And, on the contrary, by lifting lifting up the upper Glals trom the lower, the diameter of the Rings would decreafe, and the breadth of their Orbit encreafe, until their Colours reached fucceflively to the center ; and then they being of a conliderable breadth, I could more ealily difcern and dirtinguifli their Species tlian before. And by this means 1 ob- ferved their Succeffion and Quantity to be as fol- loweth. .^ . Next, to the pellucid central Spot made by the con- tad of the GlafTcs lucceeded blue, white, yellow, and red, the blue was fo little in quantity that I could not difcern it in the circles made by the Prifms, nor could I well diftinguifli any violet in it, but the yellow and red were pretty copious, and ieemed 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 encompaffing thefe were violet, blue, green, yellow, and red, and thefe were all of them co- pious and vivid, excepting the green, which was very little in quantity, and Ieemed much more faint and dilute than the other Colours. Of the other four, the violet was the leaft in extent , and the blue lefs than the yellow or red. The third Circuit or Order was purple, blue, green, yellow, and red ; in which the purple ieemed more reddifh than the violet in the former Circuit, and the green was much more confpi- cuous, being as brifque and copious as any of the other Colours, except the yellow ; but the red began to be a little faded, inclining very much to purple. After this fucceeded the fourth Circuit of green and red. The green was very copious and lively, inclining on the one lide to blue, and on the other fide to yellow. But in this [7J . this fourth Circuit there was neither violet, blue, nor yellow, and the red was very imperfecl: and dirty. Alfo the fucceeding Colours became more and more im- perfed and dilute, till after three or four Revolutions tiiey ended in perfect whitenefs. Their Form, when the GliiHes weremoft comprcfTed fo as to make the black Spot appear in the Center, is delineated in the Second Figure ', where «, <^, r, ^, e ; f, g^ /j, z, h. : /, w, w, o, ^ ; q^ r : Fig. 2. J-, t : Vyx:y denote the Colours reck'ned in order from _ the center, black, blue, white, yellow, red : violet, blue, green, yellow, red : purple, blue, green, yellow, red : green, red : greenilli blue, red : greeniih blue, pale red : greeniili blue, reddiih white. O B S. V. To determine the interval of the GlafTes, or thick- nefs of the interjacent Air, by which each Colour was produced, I meafured the Diameters of the firft fix Rings at the moft lucid part of their Orbits, and fqua- ring them, I found their Squares to be in the Arith- metical Progreffion of the odd Numbers, i . 5. 5. 7. 9. 1 1 . And fince one of thefe Glaffes was Plain, and the other Spherical, their Intervals at thofe Rings muft be in the fame Progreffion. I meafured alfo the Diameters of the dark or faint Rings between the more lucid Co- lours, and found their Squares to be in the Arithme- tical Progreffion of the even Numbers, a. 4.. 6. 8. 10. la* And it being very nice and difficult to take thefe mea- fures exadly ; 1 repeated them at divers times at divers partsof the Glaffes, that by their Agreement I might be confirmed in them. And the fame Method I ufed in deter- determining fome others of t^e following Obferva- tions. O B S. VI. The Diameter of the fixth Ring at the moft lucid part of its Orbit was £, parts of an Inch, and the Dia- meter of the Sphere on which the double convex Ob- jedli-Glafs was ground was about loa Feet, and hence I gathered the thicknefs of the Air or Aereal Interval of the Glaffes at that Ring. But fome time after, fuf- peding that in making this Obfervation I had not de- termined the Diameter of the Sphere with fufficient ac- curatenefs, and being uncertain whether the Plano- convex Glafs was truly plain, and not fomething con- cave or convex on that lide which I accounted plain ; and whether 1 had not prefled the Glaffes together, as I often did, to make them touch (for by preffmg fuch Glaffes together their parts eafily yield inwards, and the Rings thereby become feniibly broader , than they would be, did the Glaffes keep their Figures) I re- peated the Experiment, and tound the Diameter of the iixth lucid Ring about 7;^ parts of an Inch. I re- peated the Experiment alfo with fuch an Objed-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 Focus was diftant from it 8^j Inches. And thence, if the Sines of incidence and refra6tion of the bright yellow Light be affumed in proportion as II to 17, the Diameter of the Sphere to which the Glafs was figured will by computation be found 1 82 In- dies. This Glafs 1 laid upon a flat one, fo that the black [9] black Spot appeared in the middle of the Rings of Colours without any other prelTure than that of the weight of the Glafs. And now meafuring the Diameter of the fifth dark Circle as accurately as I could, I found it the fifth part of an Inch precifely. This meafure was taken with the points of a pair of Compaffes on the upper fur- face on the upper Glafs, and my Eye was about eight or nine Inches diftance from the Glafs, almofi: perpen- dicularly over it, and the Glafs was '^ of an Inch thick, and thence it is eafy to coUeft that the true Diameter of the Ring between the Glaflcs was greater than its mcafured Diameter above the Glaffes in the proportion of 80 to 79 or thereabouts, and by confequence equal to ^ parts of an Inch, and its true Semi-diameter equal to ^ parts. Now as the Diameter of the Sphere ( 1 82 In- ches) is to the Semi-diameter of this fifth dark Ring ( ~ parts of an Inch ) fo is this Semi-diameter to the thicknefs of the Air at this fifth dark Ring ; which is therefore ^7^, or ,^^ parts of an Inch, and the fifth part thereof; viz. the -^ly^^^ P^'irt of an Inch, is the thicknefs of the Air at the firfi of thefe dark Rings. The fame Experiment I repeated with another dou- ble convex Objed-glafs ground on both fides to one and the fame Sphere. Its Focus was diftant from it 168^ Inches, and therefore the Diameter of that Sphere was 184. Inches. This Glafs being laid upon the fame plain Glafs, the Diameter of the fifth of the dark Rings, when the black Spot in their center appeared plainly without prefling the Glaffes, was by the mea- fure of the Compaffes upon the upper Glafs ^ parts of an Inch, and by confequence between the Glaffes it was g-^y. For the upper Glafs was I of an Inch thick, Bb and [lo] and iny Eye was diftant from it 8 Inches. And a third proportional to half this from the Diameter of the Sphere is ^^^ parts of an Inch. This is therefore the thicknefs of the Air at this Ring, and a fifth part there- of, viz. the issT-^th part of an Inch is the thicknefs there- of at the firft of the Rings as above. I tryed the fame thing by laying thefe Object-GlafTcs upon flat pieces of a broken Looking-glafs, and found the fame mcafures of the Rings : Which makes me rely upon them till they can be determined more ac- curately by Glaffes ground to larger Spheres, though in fuch GlalTes greater care muft be taken of a true plain. Thefe Dimenlions were taken when my Eye was placed almofl: perpendicularly over t]ie Glailes, being , about an Inch, or an Inch and a quarter, dillant from the incident rays, and eight Inches diftant from the Glafs ; fo that the rays were inclined to the Glafs in an Angle of about 4. degrees. Whence by the following Obfervation you will underftand, that had the rays been perpendicular to the Glaffes, the thicknefs of the Air at thefe Rings would have been lefs in the propor- tion of the Radius to the fecant of 4. degrees, that is of 1 0000. Let the thickneffes found be therefore dimi- nilhed in this proportion, and they will become 5^ and i^, or ( to ufe the neareft round number ) the g^th part of an Inch. This is the thicknefs of the Air at the darkeft part of the firft dark Ring made by perpendi- cular rays, and half this thicknefs multiplied by the progreffion,i,^,5,7,9, i i,i5)'ing on the Glafles, I darkened the Room, and viewed them by reflexion of the Colours of a Prifm call on a Sheet of white Paper, my Eye being fo placed that I could fee the coloured Paper by reflexion in the Glafles, as in a Looking-glafs. And by this means the Rings be- came diftind:er and viflble to a far greater number than in the open Air. I have fometimes feen more than twenty of them, whereas in the open Air I could not difcern above eight or nine. oBs:. [Id] O B S. XIII. Appointing an affillant to move the Prifm to and fro about its Axis, that all the Colours might fuccef- fiveiy fall on that part of the Paper which I faw by reflexion from that part of the GlafTes, where the Cir- cles appeared, fo that all the Colours might be fuccef- fively refle61:ed from the Circles to my Eye whilft I held it immovable, I found the Circles which the red Light made to be manifeftly bigger than thole which were made by the blue and violet. And it was very plea- lant to fee them gradually fwell or contrad: according as the Colour of the Light was changed. The inter- val of the Glaffes at any of the Rings when they wTre made by the utmoft red Light, was to their interval at the lame Ring when made bythe utmoft violet, greater than as ^ to 2, and lefs than as 1 5 to 8,by the moft of my Obfervations it was as 14. to 9. And this proportion feemed very nearly the fame in all obliquities of my Eye ; unlefs when two Prifms were made ufe of inftead of the Objed-Glaffes. For then at a certain great obliquity of my Eye, the Rings made by the feveral Colours feemed equal, and at a greater obliquity thole made by the violet would be greater than the fame Rings made by the red. The refraction of the Prifm in this cafe caufing the moft refrangible rays to fall more obliquely on that plate of the Air than the leaft refrangible ones. Thus the Experiment fucceeded in the coloured Light, which was fufBciently ftrong and copious to make the Rings fenfible. And thence it may be gathered, that if the moft refrangible and leaft refran- Ci7] refrangibk rays had been copious enough to make the Rings lenfible without the mixture of other rays, the proportion which here was 14. to 9 would have been a little greater, fuppofe 14. J or 14 Uo 9. O B S. XIV. Whilft the Prifni was turn'd about its Axis with an uniform motion, to make all the feveral Colours fall fucceffively upon the Object -Glaffes, and thereby to make the Rings contract and dilate : The contrad:ion or dilation of each Ring thus made by the variation of its Colour was fwifteft in the red, and floweft in the violet, and in the intermediate Colours it had inter- mediate degrees of celerity. Comparing the quantity of contraction and dilation made by all the degrees of each Colour, I found that it was greateft in the red ; lefs in the yellow, iHU lefs in the blue, and leaft in the J violet. And to make as juft an eftimation as 1 could of the 'proportions of their contractions or dilations, 1 obferved that the whole contradion or dilation of the Diameter of any Ring made by all the degrees of red, was to that of the Diameter of the fame Ring made by all the de- grees 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 greateft Dia- meter of the fame Ring made by the outmoft red, and the leaft Diameter thereof made by the outmoft violet : Contrary to what happens in the Colours of the oblong Spedrum made by the refradion of a Prifm, where the red is moft contracted J the violet moft expanded, and D d in # Ci8] in the'midft of all tlie Colours is the confine of green and blue. And hence 1 fecm to colled that the thick- nefles of the Air between tlie Glaffes there, where the Ring is fucceffively made by the limits of the five prin- cipal Colours (red, yellow, green, blue, violet) in order ( that is, by the extreme red, by the limit of red and yellow in the middle of the orange, by the limit of yellow and green, by the limit of green and blue, by the limit of blue and violet in the middle of the in- digo, and by the extreme violet ) are to one another very nearly as the fix lengths of a Chord which found the notes in a fixth Major, /r. Now if A 2 be iuppofed to reprefent the thicknefs of any thin traniparent Body , at which the outmoft violet is moft copioufly reflected in the tirll Ring, or Series of Colours, then by the i^th Obfervation H K, will reprefent its thicknefs, at which the utmoft red is moft copioufly reflected in the fame Series. Alfo by the 5th and i6th Obfervations, A 6 and HN will denote the thicknefles at which thofe extreme Colours are moft copioufly reflated in the fecond Series, and A I o and H Q the thicknefles , at which they are moft copioufly refleded in the tliird Series, and fo on. And the thicknefs at which any of the intermediate Colours are reflected moft copioufly, will, according to the 1 4.th Obfervation, be defined by the diftanceof the line A H -from the intermediate parts of the lines a K, 6N, 10 Q, }sfc. againft which the names of thofe Co- lours are written below. But further, to define the latitude ofthefe Colours in each Ring or Series, let A i defign the lealt thicknefs, and A 3 the greateft thicknefs, at which the extreme violet in the nrft Series is refleded, and let H I, and H L, defign the like limits for the extreme red, and let the intermediate Colours be limited by the inter- mediate parts of the lines i I, and ^L, againft vvhih the names of thofe Colours are written, and fo on : But yet yet with this caution, that the refle£l:ions be fuppofed ih'ongeil at the intermediate Spaces, a K, 6 N, i o (i,^