<460r>

## Trin: Coll Cambridge. Feb. 6. 167$\frac{1}{2}$

Sr

To perform my late promise to you, I shall wthout further ceremony acquaint you, that in ye beginning of ye year 1666 (at wch time I applyed my self to ye grinding of Optick glasses of other figures then Sphericall) I procured me a triangular glasse Prisme to try therewth ye celebrated phænomena of colours. And in order thereto having darkned my chamber & made a small hole in my window-shuts to let in a convenient quantity of ye sun's light, I placed my Prism at its entrance that it might be thereby refracted to ye opposite wall. It was at first a very pleasing divertisement to view the vivid & intense colours produced thereby; but after a while applying my selfe to consider them more circumspectly, I became surprized to see them in an oblong form, wch according to ye received lawes of refraction I expected should have been circular.

They were terminated at ye sides wth streight lines, but at the ends the decay of light was so graduall that it was difficult to determine justly what was their figure, yet they seemed semicircular.

Comparing ye length of this {illeg}|Co|loured Spectrum wth its bredth I found it about five times greater, a disproportion soe extravagant that it excited me to a more then ordinary curiosity of examining frō whence it might proceed; I could scarce think that ye various thicknesse of ye glasse, or ye termination wth shaddow or darknesse could have any influence on light to produce such an effect, yet I thought it not {amis} amisse to examine first those circumstances, & soe tryed wt would happen by transmitting light through parts of ye glasse of divers thicknesses, or through holes in ye window of divers bignesses, or by setting the Prism wthout, so that the light might passe through it & bee refracted before it was terminated by ye hole: but I found none of those circumstances materiall. The fashion of ye colours was in all these cases ye same.

Then I suspected whither by any unnevenesse in ye glass or other contingent irregularity these colours might be thus dilated. And to try this I took another prism like ye former & soe placed it that ye light passing through them both might be refracted contrary wayes & so by the latter <460v> returned into that course frō which ye former had diverted it. ffor by this meanes I thought the regular effects of ye first Prism would be destroyed by the sceond Prism, but ye irregular ones more augmented by ye multiplicity of refractions. The event was that ye light wch by the first Prism was diffused into an oblong form was by the second reduced into an orbicular one wth as much regularity as when it did not at all passe through them. So that what ever was ye cause of that length 'twas not \any/ contingent irregularity.

I then proceded to examine more critically what might be effected by the difference of ye incidence of rayes coing frō divers parts of ye Sun, & to that end measured the |severall| lines & angles belonging to ye image. Its distance frō ye hole or Prism was 22 foot, its utmost length 13$\frac{1}{4}$ inches, its breadth 2$\frac{5}{8}$ inches, the diameter of ye hole $\frac{1}{4}$ of an inch, the angle which ye rayes tending towards the midle of ye image made wth those lines in wch they would have proceeded wthout refraction 44 degr. 56'. And ye verticall angle of ye Prism 63 degr 12'. Also the refractions on both sides the Prism, that is of ye incident & emergent rayes were as near as I could make them, equall, & consequently about 54 degr 4'. And ye rayes fell perpendicularly upon ye wall. Now subducting the diameter of ye hole frō ye length & breadth of ye image there remains 13 inches ye length & 2$\frac{3}{8}$ the breadth comprehended by those rayes wch passed through ye center of ye {said} hole & consequently the angle at ye hole wch that breadth su{bten}ded was about 31' answerable to ye sun's diameter, but ye ang{le} wch its length subtended was more then five such diameters, namely 2 degr 49'.

Having made these observations I first computed from them the refractive power of that glasse & found it measured by ye ratio of ye sines 20 to 31. And then by that ratio I computed the refractions of two rayes flowing frō opposite parts of ye sun's discus, so as to differ 31' in their obliquity of incidence, & found that the emergent rayes should have comprehended an angle of about 31' as they did before they were incident.

But because this computation was founded on ye Hypothesis of the proportionality of ye Sines of incidence & refraction, wch, though by my own & others experience, I could not imagine to be so erroneous as to make that angle but 31' wch in reality was 2 degr 49' yet my curiosity caused me again to take my Prism. And having placed it at my window as before I observed that by turning it a little about its axis to & fro, so as to vary its obliquity to ye light more then by an angle of 4 or 5 degrees, the colours were not thereby sensibly translated from their place on ye wall, & consequently by that variation of incidence, the quantity of refraction was not sensibly varied.

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By this experiment therefore as well as by the former computation it was evident that the difference of ye incidence of rayes flowing from divers parts of ye Sun, could not make them after decussation diverge at a sensibly greater angle then that at wch they before converged. which being at most but about 31. or 32 minutes, there still remained some other cause to be found out frō whence it could be 2 degr 49'.

Then I began to suspect whither the rayes after their trajection through the Prism did not move in curve lines & acording to their more or lesse curvity tend to divers parts of ye wall. And it increased my suspicit|o|n when I remembred that I had often seen a Tennis-ball struck wth an oblique Racket describe such a curve line. for a circular as well as a progressive motion being communicated to it by that stroak, its parts on that side where the motions conspire must presse & beat the contiguous air more violently then on ye other, & there excite a reluctancy & reaction of ye air proportionally greater. And for ye same reason, if ye rayes of light should possibly bee globular bodyes & by their oblique passage out of one medium into another acquire a circulating motion, they ought to feel ye greater resistance from ye ambient Æther on that side where the motions conspire & thence be continually bowed to the other. But notwthstanding this plausible ground of suspicion when I came to examine it I could observe noe such curvity in them. And besides (wch was enough for my purpose) I observed yt the difference betwixt ye length of ye image & diameter of ye hole through wch ye light was transmitted, was proportionable to their distance.

The graduall removall of these suspicions at length led me to ye experimentum crucis; which was this. I took two boards, & placed one of them close behind the Prism at ye window, so that ye light might passe through a small hole made in it for that purpose & fall on ye other board wch I placed at about twelve foot distance, having first made a \small/ hole in it also for some of that incident light to passe through. Then I placed another Prism behind this second board so that the light trajected through both ye boards might passe through that also <461v> & be again refracted before it arrived at ye wall. This done, I took the first Prism in my hand & turned it to & fro slowly about its axis so much as to make ye severall parts of ye image cast on ye second board, successively passe through the hole in it, that I might o{illeg}|b|serve to what places on ye wall the second Prism would refract ym. And I saw by ye variation of those places, that the light tending to that end of ye image towards wch the refraction of ye first Prism was made, did in ye second Prism suffer a refraction considerably greater then ye light tending to ye other end. And soe the true cause of ye length of that image was detected to be noe other then that light consists of rayes differently refrangible wch wthout any respect to a difference in their incidence were according to their degrees of refrangibility transmitted towards diverse parts of ye wall.

When I understood this, I left of my aforesaid glassworkes, for I saw that ye fection of Telescopes was hitherto limited, not so much for want of glasses truly figured according to ye prescriptions of Optick writers Authors, wch all men have hitherto imagined, as because that light it selfe is a heterogeneous mixture of differently refrangible rayes. So that were a Glasse so exactly figured as to collect any one sort of rayes into one point, it could not collect those also int{o} the same point which having ye same incidence upon y{e} same medium are apt to suffer a different refraction. Nay I wondered that seing the different|ce| of refrangibility was soe great as I found it, Telescopes should arrive to that fection thay are now at. ffor measuring the refractions in one of my Prisms I found that supposing the cōmon sine of incidence upon on {sic} of its planes was 44 parts, the sine of refraction of ye utmost rayes on ye red end of ye colours made out of ye glasse into ye air would be 68 parts, & ye sine of refraction of ye utmost ray rayes on ye other end 69 parts. So that the difference is about a 24th or 25t part of ye whole refraction. And consequently the objectglasse of any Telescope cannot collect all ye rayes wch come frō one point of an object, so as to make them convene at its focus in lesse room then in a circular space whose diameter is ye {illeg} \{50th}/ part of ye diameter of its spectrum. <462r> which is an irregularity some hundreds of times greater then a circularly figured lens, of so small a section as ye objectglasses of long Telescopes are, would cause by ye unfitnesse of its figure, were light uniform.

This made me take reflections into consideration; & finding them regular, so that ye angle of reflection of all sorts of rayes was equall to their angle of incidence I understood that by their mediation Optick instruments might be brought to any degree of fection imaginable if \provided/ a reflecting substance could be found which would polish as finely as glasse, & reflect as much light as glasse transmitts, & ye art of counicating to it a Parabolick figure bee also attained. But those seemed |very| great difficulties, & I almost thought them insuperable when I further considered that every irregularity in a reflecting superficies makes ye rayes stray 5 or 6 times more out of their due course then ye like irregularities in a refracting one. So that a much greater curiosity would be here requisite then in figuring glasses for refraction.

Amidst these thoughts I was forced frō Cambridge by the intervening Plague & it was more then two years before I proceeded further. But then having thought on a tender way of polishing propper for mettall, & wherby as I imagined the figure also would be corrected to ye last, I began to try what might be effected in this kind, & by degrees so far perfected an instrument (in ye essential parts of it like that I sent to London) by wch I could discern Iupiters four concomitants, & showed them divers times to two \others/ of my acquaintance. I could also discern the moon-like phase of Venus, but not very distinctly nor wthout some nicenesse in disposing the instrument.

ffrom that time I was interrupted till this last Autumn, when I made the other. And as that was sensibly better then ye first, (especially for day Objects) so I doubt not but they will be still brought to a much greater fection by their endeavours who as you inform me are taking care about it at London.

I have sometimes thought to make a microscope wch in like manner should have instead of an objectglasse a relecting piece of metall. And this I hope they will also take into consideration <462v> For those instruments seem as capable of improvement as Telescopes, & perhaps more because but one reflective peice of metall is requisite in them, as you may perceive by ye annexed diagram{illeg} where A B representeth the object metall, C D the eyeglasse, F their cōmon focus, & O the other focus of ye metall in wch ye object is placed. But to return frō this digression, I told you that light is not similar or homogeneall but consists of difform rayes, some of wch are more refrangible then others. So that of those wch are alike incident on ye same medium, some shall be more refracted then others, & that not by any virtue of ye glasse or other externall cause, but from a predisposition wch every particular ray hath to suffer a particular degree of refraction. I shall now proceed to acquaint you wth another more notable difformity in its rayes wherin the origen of colours is infolded. A naturalist would scarce beleive expect to see ye science of those become mathematicall, & yet I dare affirm that there is as much certainty in it as in any other part of Opticks. ffor what I shall tell concerning them is not an Hypoth{esis} but most rigid consequence, not conjectured by barely infer{ring} 'tis thus because not otherwise or because it satisfies all phænomena (the Philosophers universall Topick,) but evinced by ye mediation of experiments concluding directly & wthout any suspicion of doubt. To continue the historicall narration of these experiments would make a discourse too tedious & confused, & therefore I shall rather lay down the doctrine first, & then for its examination give you an instance or two of ye experiments as a Specimen of ye rest.

The Doctrine you will find comprehended & illustrated in ye following propositions.

1. As ye rayes of light differ in degrees of refrangibility, so they also differ in their disposition to exhibit this or that particular colour. Colours are not qualifications of light derived frō refractions or reflections of naturall bodies as 'tis generally beleived, but originall & connate properties, wch in diverse rayes are divers, some rayes are disposed to exhibit a red colour & noe other, <463r> some a yellow & noe other, some a green & noe other & so of ye rest. Nor are there only rayes propper & peculiar to ye more eminent colours, but even to all their intermediate gradations.

2. To the same degree of refrangibility ever belongs the same colour, & to ye same colour ever belongs the same degree of refrangibility. The least-refrangible rayes are all disposed to exhibit a red colour & contrarily those rayes which are disposed to exhibit a red colour are all ye least refrangible. So ye most refrangible rayes are all disposed to exhibit a deep violett colour & contrarily those wch are apt to exhibit such a violet colour are all the most refrangible. And so to all the intermediate colours in a continued series belong intermediate degrees of refrangibility. And this Analogy 'twixt colours & refrangibility is very precise & strict: the rayes always either exactly agreeing in both or proportionally disagreeing in both.

3. The Species of colour & degree of refrangibility propper to any particular sort of rayes, is not mutable by refraction, nor by reflection frō naturall bodies, nor by any other cause that I could yet observe. When any one sort of rayes hath been well parted frō those of other kinds it hath afterwards obstinately retained its colour notwthstanding my utmost endeavours to chang it. I have refracted it wth Prismes, & reflected it wth bodies wch in day light were of other colours; I have intercepted it wth ye coloured film of air interceding two compressed plates of Glasse, transmitted it through coloured mediums & through mediums irradiated wth other sort of rayes, & diversly terminated it, & yet could not produce any new colour out of it. It would by contracting or dilating become more brisk or faint, & by ye losse of many rayes in some cases very obscure & dark, but I could never see it changed in Specie.

4 Yet seeming transmutations of colours may be made where there is any mixture of divers sorts of rayes: ffor in such mixtures the component colours appear not, but by their mutuall allaying each other constitute a midling colour. And therefore if by refraction <463v> or any other of ye aforesaid causes the difform rayes latent in such a mixture bee seperated, there shall emerge colours different frō ye colour of ye composition. Which colours are not new generated but only made apparent by being parted. ffor if they be again intirely mixed & blended together, they will again compose that colour wch they did before seperation. And for ye same reason transmutations made by ye convening of divers colours are not reall; for when ye difform rayes are again severed they will exhibit the very same colours which they did before they entered the composition. As you see blew & yellow powders when finely mixed appear to ye naked eye green & yet the colours of ye component corpuscles are not thereby really transmuted, but only blended. ffor when veiwed wth a good Microscope they still appear blew & yellow interspersedly.

5 There are therefore two sorts of colours. The one originall & simple; the other compounded of these. The originall or primary colours are Red, yellow, Green, Blew, & a violet purple; together with Orang, Indico, & an indefinite varietie of intemediate gradations.

6 The same colours in Specie wth these primary ones may be also produced by composition: ffor a mixture of yellow & blew makes green, of red & yellow makes Orang of Orang & yellowish green makes yellow. And in generall if any two colours be mixed, which in ye series of those generated by ye Prism are not too far distant one from another, they by their mutuall alloy compound that colour wch in ye said series appeareth in ye midway between them. But those which are situated at too great a distance doe not soe. Orang & Indico produce not the intermediate green, nor Scarlet & green ye intermediate yellow.

7 But the most surprizing & wonderfull composition was that of whitenesse. There is noe one sort of rayes wch alone can exhibit this. Tis ever compounded & to its composition are requisite all the aforesaid primary colours mixed in a due proportion. I have often wth admiration beheld that all ye colours of ye Prism being made <464r> made to converge & thereby to be again mixed as they were in ye light before it was incident upon ye Prism, reproduced light intirely & perfectly white, & not at all sensibly differing from ye direct light of ye sun; unlesse when the glasses I used were not sufficiently clear, for then they would a little tinge \incline/ it wth |to| their colour.

8. Hence therefore it comes to passe that whitenesse is ye usuall colour of light: ffor light is a confused agregate of rayes indued wth all sorts of colours as they are promiscuously darted from ye various parts of luminous bodies. And of such a confused agregate as I said is generated whitenesse if there be a due proportion of ye ingredients; But if any one predominate, the light must incline to that colour as it happens in ye blew flame of Brimstone, the yellow flame of a candle & the various colours of ye fixt starrs.

9. These thinges considered, the manner how colours are produced by ye Prism is evident. ffor of ye rayes constituting ye incident light since those wch differ in colour proportionally differ in refrangibility, they by their unequall refractions must be severed & dispersed into an oblong \form/ in an orderly succession frō ye least refracted scarlet to ye most refracted violed|t|. And for ye same reason it is that objects when looked upon through a Prism appear coloured. ffor ye difform rayes by their unequall refractions are made to diverge toward severall parts of ye Retina & there expresse the images of thinges coloured as in ye former case they did the sun's image upon a wall. And by this inequality of refractions they become not only coloured but also very confused & indistinct.

10 Why the colours of ye rainbow appear in falling drops of rain is also frō hence evident. ffor those drops wch refract the rayes disposed to appear purple in greatest quantity to ye Spectators eye, refract ye rayes of other sorts soe much lesse as to make ym passe beside it; & such are ye dropes in ye inside of ye primary Bow & on ye outside of ye second or exterior one. <464v> So those drops which refract in greatest plenty the rayes apt to appear red toward ye Spectators eye, refract those of other sorts soe much more as to make them passe beside it, & such are ye drops on ye exterior part of ye Primary & interior part of ye secondary Bow.

11. The odd Phænomenon|a| of an infusion of Lignum Nephriticum, leaf-Gold, fragments of coloured glasse, & some other transparently coloured bodies appearing in one position of one colour, & of another in another are on these grounds noe longer riddles. ffor those are substances apt to reflect one sort of light & transmit another; as may be seen in a dark Room by illustrating\minating/ them wth similar or uncompounded light. ffor then they appear of that colour only wth wch they are illuminated, but yet in one position more vivid & luminous then in another, accordingly as they are disposed more or lesse to reflect or transmit the incident colour.

12 ffrom hence also is manifest the reason of an unexpected experiment wch Mr Hook somewhere in his Micrographia relates to have made wth two w|W|edg-like transparent vessells filled the one wth a red, the other wth a blew liquor: Namely that though they were severally transparent enough yet both together became opake. ffor if one transmitted only red & ye other only blew, no rayes could passe through both.

13 I might add more instances of this nature, but I shall conclude wth this generall one, that ye colours of all naturall bodies have noe other origin then th{e}|is|, that they are variously qualified to reflect one sort of light in greater plenty then another. And this I have experimented in a dark Room by illuminating those bodies wth uncompounded light of divers colours. ffor by that means any bodie may be made to appear of any colour. They have there noe appropriate colour but ever appear of ye colour cast upon them, but yet wth this difference that they are most brisk & vivid in ye light of their own day-light-colour. Minium appeareth there of any <465r> colour indifferently wth wch 'tis illustrated, but yet most luminous in red; & so Bise appeareth indifferently of any colour wth wch 'tis illustrated, but yet most luminous in blew. And therefore Minium reflecteth rayes of any colour, but most copiously those endowed wth red; & consequently when illustrated wth day-light, that is wth all sorts of rayes promiscuously blended, those qualified wth red shall abound most in the reflected light, & by their prevalence cause it to appear of that colour. And for ye same reason Bise reflecting blew most copiously, shall appear blew by ye excesse of those rayes in its reflected light; & ye like of other bodies. And that this is ye intire & adequate cause of their colours is manifest, because they have noe power to change or alter the colour of any sort of rays incident apart, but put on all colours indifferently wth wch they are enlightened.

These thinges being so, it can be no longer disputed whither there be colours in ye dark, nor whither these|y| be the qualityes of ye objects wee see, no nor perhaps whether light be a bodie. ffor since colours are qualityes of light, having its rayes for their entire & imediate subject, how can wee think those rayes qualityes also, unlesse one quality may be ye subject of & sustain another, wch in effect is to call it substance. Wee should not know bodies for substances were it not for their sensible qualityes, & the principall of them|ose| being now found due to something else, wee have as good reason to beleive that to be a substance also. Besides who ever thought any quality to be a heterogeneous agregate such as light is discovered to be. But to say \determine/ more absolutely what light is, after what manner refracted, & by what modes or actions it produceth in or minds the Phantasms of colours, is not so easie. {illeg}. And I shall not mingle conjectures wth certaintyes.

Reviewing what I have written, I see ye discours it selfe will lead to divers experiments sufficient <465v> for its examination: And therefore I shall not trouble you farther then to describe one of those which I have already insinuated.

In a darkned Room make a hole in ye shutt of a window, whose diameter may conveniently be about a third part of an inch, to admitt a convenient quantity of ye Sun's rayes \light/. And then place a clear & colourlesse Prism to refract the entering light towards the further part of ye Room: wch as I said will thereby be diffused into an oblong coloured image. Then place a lens of about three foot radius (suppose a broad object-glasse of a three foot Telescope) at ye distance of about 4 or 5 foot frō thence, through wch all those colours may at once be transmitted, & made by its refraction to convene at a further distance of about 10 or 12 foot. If at that distance you intercept this light wth a sheet of white paper, you will see the colours converted into whitenesse again by being mingled. But it is requisite that the Prism & lens be placed steddy, & that the pa on wch ye colours are cast bee moved to & fro; for by such motion you will not only find at what distance the whitenesse is most fect, but also see how ye colours gradually convene & vanish into whitenesse, & afterwards having crossed one another in that place where they compound whitenesse, are again dissipated & severed & in an inverted order retain ye same colours wch they had before they entered the composition. You may also see that if any of the colours at ye lens be intercepted, the whitenesse will be changed into ye other colours. And therefore that the composition of whitenesse be perfect, care must be taken that none of ye colours fall beside the lens.

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In the annexed designe of this experiment A B C representeth ye Prism set endwise to sight, close by ye hole F of ye window E G. Its vertical angle A C B may conveniently be about 60 degrees. M N designes ye lens. Its breadth 2$\frac{1}{2}$ or 3 inches. S F one of ye streight lines in wch difform rayes may be conceived to flow successively from ye Sun. F P & F R two of those rayes unequally refracted, which ye Lens makes to converg towards Q, & after decussation to diverge again. And H I ye paper at divers distances on which ye colours are projected: which in Q constitute whitenesse, but are red & yellow in R, r, & ρ; & blew & purple in P, p & π.

If you proceed further to try ye impossibility of changing any uncompounded colour, wch I {illeg}|have| asserted in ye 3d and 13th propositions; 'tis requisite yt ye Room be made very dark, least any scattering |light| mixing wth ye colour, disturb & allay it & render it compound, contrary to ye design of ye experimt 'Tis also requisite that there be a fecter seperation of ye colours then after ye manner above described can be made by ye refraction of one single Prism; & how to make such further seperations will scarce be difficult to them that consider ye discovered lawes of refractions. But if tryall shall be made wth colours not throughly seperated there must be allowed changes proportionable <466v> to the mixture. Thus if compound yellow light fall upon blew b|B|ise, the Bise will not appear fectly yellow, but rather green, because there are in ye yellow mixture many rayes indued wth green, because there are in ye yellow & green being lesse remote frō ye usuall blew colour of Bise then yellow, is more copiously reflected by it.

In like manner if any of ye Prismatick colours, suppose Red, be intercepted on design to try ye asserted impossibility of reproducing that colour out of |ye| others which are pretermitted 'tis necessary either that ye colours be very well parted before ye red be intercepted, or that together wth ye red ye neighbouring colours into which any red is secretly dispersed (that is the yellow & perhaps green too) bee intercepted, or {illeg}|else| that allowance be made for ye emerging of so much red out of ye yellow & green as may possibly have been diffused & scattering{ly} blended in the|o|se colours. And if these thinges be observed the new production of Red or any intercepted colour will be found impossible.

This I conceive is enough for an introduction to experimts of this kind; which if any of |the R| Society shall be so curious as to prosecute, I should be very glad to be informed wth what successe. That if any thing seem to \be defective or to/ thwart this relation, I may have an opportunity of giving further direction {in}|a|bout it, or i|o|f acknowledging my errors if I have cōmitted any.

Yor humble servt

Isaac Newton