A Letter of Mr. Isaac Newton … containing his New Theory about Light and Colors
关于光和颜色的新理论
艾萨克·牛顿 Isaac Newton（1643–1727）
1672 年（自剑桥寄出，落款 1671/2 年 2 月 6 日）

冷冻图书馆 · 开架书库 · S-006207 · https://coldlibrary.com/s/006207
权利：1672 年发表；牛顿卒于 1727 年。已按澳大利亚、欧盟、英国、中国大陆和美国的规则核对（截至 2026 年 10 月 11 日）。仅供参考，不是法律意见。
来源：Wikisource，https://en.wikisource.org/wiki/Philosophical_Transactions_of_the_Royal_Society_(1665-1886)/Volume_6/Number_80/Paper_1（取于 2026-10-11）
中文译文：Claude（AI），2026 · CC0 1.0
生成于 2026-10-14，来自 https://coldlibrary.com/open-stacks/newton-new-theory-of-light-and-colours

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Sir,

To perform my late promise to you, I shall without further ceremony acquaint you, that in the beginning of the Year 1666 (at which time I applyed my self to the grinding of Optick glasses of other figures than Spherical,) I procured me a Triangular glass-Prisme, to try therewith the celebrated Phænomena of Colours. And in order thereto having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Suns light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby; but after a while applying my self to consider them more circumspectly, I became surprised to see them in an oblong form; which, according to the received laws of refraction, I expected should have been circular.

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

Comparing the length of this coloured Spectrum with its breadth, I found it about five times greater; a disproportion so extravagant, that it excited me to a more then ordinary curiosity of examining, from whence it might proceed. I could scarce think, that the various Thickness of the glass, or the termination with shadow or darkness, could have any Influence on light to produce such an effect; yet I thought it not amiss, first to examine those circumstances, and so tryed, what would happen by transmitting light through parts of the glass of divers thicknesses, or through holes in the window of divers bignesses, or by setting the Prisme without so, that the light might pass through it, and be refracted before it was terminated by the hole: But I found none of those circumstances material. The fashion of the colours was in all these cases the same.

Then I suspected, whether by any unevenness in the glass, or other contingent irregularity, these colours might be thus dilated. And to try this, I took another Prisme like the former, and so placed it, that the light, passing through them both, might be refracted contrary ways, and so by the latter returned into that course, from which the former had diverted it. For, by this means I thought, the regular effects of the first Prisme would be destroyed by the second Prisme, but the irregular ones more augmented, by the multiplicity of refractions. The event was, that the light, which by the first Prisme was diffused into an oblong form, was by the second reduced into an orbicular one with as much regularity, as when it did not at all pass through them. So that, what ever was the cause of that length, 'twas not any contingent irregularity.

I then proceeded to examin more critically, what might be effected by the difference of the incidence of Rays coming from divers parts of the Sun; and to that end, measured the several lines and angles, belonging to the Image. Its distance from the hole or Prisme was 22 foot; its utmost length 13¼ inches; its breadth 2⅝; the diameter of the hole ¼ of an inch; the angle, with the Rays, tending towards the middle of the image, made with those lines, in which they would have proceeded without refraction, was 44 deg.56′. And the vertical Angle of the Prisme, 63 deg. 12′. Also the Refractions on both sides the Prisme, that is, of the Incident, and Emergent Rays, were as near, as I could make them, equal, and consequently about 54 deg. 4′. And the Rays fell perpendicularly upon the wall. Now subducting the diameter of the hole from the length and breadth of the Image, there remains 13 Inches the length, and 2⅜ the breadth, comprehended by those Rays, which passed through the center of the said hole, and consequently the angle of the hole, which that breadth subtended, was about 31′, answerable to the Suns Diameter; but the angle, which its length subtended, was more then five such diameters, namely 2 deg. 49′.

Having made these observations, I first computed from them the refractive power of that glass, and found it measured by the ratio of the sines, 20 to 31. And then, by that ratio, I computed the Refractions of two Rays flowing from opposite parts of the Sun's discus, so as to differ 31′ in their obliquity of Incidence, and found, that the emergent Rays should have comprehended an angle of about 31′, as they did, before they were incident.

But because this computation was founded on the Hypothesis of the proportionality of the sines of Incidence, and Refraction, which though by my own Experience I could not imagine to be so erroneous, as to make that Angle but 31′, which in reality was 2 deg.49′; yet my curiosity caused me again to take my Prisme. And having placed it at my window, as before, I observed, that by turning it a little about its axis to and fro, so as to vary its obliquity to the light, more then an angle of 4 or 5 degrees, the Colours were not thereby sensibly translated from their place on the wall, and consequently by that variation of Incidence, the quantity of Refraction was not sensibly varied. By this Experiment therefore, as well as by the former computation, it was evident, that the difference of the Incidence of Rays, flowing from divers parts of the Sun, could not make them after decussation diverge at a sensibly greater angle, than that at which they before converged; which being, at most, but about 31 or 32 minutes, there still remained some other cause to be found out, from whence it could be 2 degr. 49′.

Then I began to suspect, whether the Rays, after their trajection through the Prisme, did not move in curve lines, and according to their more or less curvity tend to divers parts of the wall. And it increased my suspition, when I remembred that I had often seen a Tennis-ball, struck with 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 press and beat the contiguous Air more violently than on the other, and there excite a reluctancy and reaction of the Air proportionably greater. And for the same reason, if the Rays of light should possibly be globular bodies, and by their oblique passage out of one medium into another acquire a circulating motion, they ought to feel the greater resistance from the ambient Æther, on that side, where the motions conspire, and thence be continually bowed to the other. But notwithstanding this plausible ground of suspition, when I came to examine it, I could observe no such curvity in them. And besides (which was enough for my purpose) I observed, that the difference 'twixt the length of the Image, and diameter of the hole, through which the light was transmitted, was proportionable to their distance.

The gradual removal of these suspitions, at length led me to the Experimentum Crucis, which was this: I took two boards, and placed one of them close behind the Prisme at the window, so that the light might pass through a small hole, made in it for the purpose, and fall on the other board, which I placed at about 12 feet distance, having first made a small hole in it also, for some of that Incident light to pass through. Then I placed another Prisme behind this second board, so that the light, trajected through both the boards, might pass through that also, and be again refracted before it arrived at the wall. This done, I took the first Prisme in my hand, and turned it to and fro slowly about its Axis, so much as to make the several parts of the Image, cast on the second board, successively pass through the hole in it, that I might observe to what places on the wall the second Prisme would refract them. And I saw by the variation of those places, that the light, tending to that end of the Image, towards which the refraction of the first Prisme was made, did in the second Prisme suffer a Refraction considerably greater then the light tending to the other end. And so the true cause of the length of that Image was detected to be no other, then that Light consists of Rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall.

When I understood this, I left off my aforesaid Glass works; for I saw, that the perfection of Telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescriptions of Optick Authors, (which all men have hitherto imagined,) as because that Light it self is a Heterogeneous mixture of differently refrangible Rays. So that, were a glass so exactly figured, as to collect any one sort of rays into one point, it could not collect those also into the same point, which having the same incidence upon the same Medium are apt to suffer a different refraction. Nay, I wondered, that seeing the difference of refrangibility was so great, as I found it, Telescopes should arrive to that perfection they are now at. For, measuring the refractions in one of my Prismes, I found, that supposing the common sine of Incidence upon one of its planes was 44 parts, the sine of refraction of the utmost Rays on the red end of the Colours, made out of the glass into the Air, would be 68 parts, and the sine of refraction of the utmost rays on the other end, 69 parts: So that the difference is about a 24th or 25th part of the whole refraction. And consequently, the object-glass of any Telescope cannot collect all the rays, which come from one point of an object, so as to make them convene at its focus in less room then in a circular space, whose diameter is the 50th part of the Diameter of its Aperture; which is an irregularity, some hundreds of times greater, then a circularly figured Lens, of so small a section as the Object-glasses of long Telescopes are, would cause by the unfitness of its figure, were Light uniform.

This made me take Reflections into consideration, and finding them regular, so that the Angle of Reflection of all sorts of Rays was equal to their Angle of Incidence; I understood, that by their mediation Optick instruments might be brought to any degree of perfection imaginable, provided a Reflecting substance could be found, which would polish as finely as Glass, and reflect as much light, as glass transmits, and the art of communicating to it a Parabolick figure be also attained. But there seemed very great difficulties, and I have almost thought them insuperable, when I further considered, that every irregularity in a reflecting superficies makes the rays stray 5 or 6 times more out of their due course, than the like irregularities in a refracting one: So that a much greater curiosity would be here requisite, than in figuring glasses for Refraction.

Amidst these thoughts I was forced from Cambridge by the Intervening Plague, and it was more then two years, before I proceeded further. But then having thought on a tender way of polishing, proper for metall, whereby, as I imagined, the figure also would be corrected to the last; I began to try, what might be effected in this kind, and by degrees so far perfected an Instrument (in the essential parts of it like that I sent to London,) by which I could discern Jupiters 4 Concomitants, and shewed them divers times to two others of my acquaintance. I could also discern the Moon-like phase of Venus, but not very distinctly, nor without some niceness in disposing the Instrument.

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

I have sometimes thought to make a Microscope, which in like manner should have, instead of an Object-glass, a Reflecting piece of metall. And this I hope they will also take into consideration. For those Instruments seem as capable of improvement as Telescopes, and perhaps more, because but one reflective piece of metall is requisite in them, as you may perceive by the annexed diagram, where A B representeth the object metall, C D the eye glass, F their common Focus, and O the other focus of the metall, in which the object is placed.

But to return from this digression, I told you, that Light is not similar, or homogeneal, but consists of difform Rays, some of which are more refrangible than others: So that of those, which are alike incident on the same medium, some shall be more refracted than others, and that not by any virtue of the glass, or other external cause, but from a predisposition, which every particular Ray hath to suffer a particular degree of Refraction.

I shall now proceed to acquaint you with another more notable difformity in its Rays, wherein the Origin of Colours is unfolded: Concerning which I shall lay down the Doctrine first, and then, for its examination, give you an instance or two of the Experiments, as a specimen of the rest.

The Doctrine you will find comprehended and illustrated in the following propositions.

1. As the Rays 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 from Refractions, or Reflections of natural Bodies (as 'tis generally believed,) but Original and connate properties, which in divers Rays are divers. Some Rays are disposed to exhibit a red colour and no other; some a yellow and no other, some a green and no other, and so of the rest. Nor are there only Rays proper and particular to the more eminent colours, but even to all their intermediate gradations.

2. To the same degree of Refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of Refrangibility. The least Refrangible Rays are all disposed to exhibit a Red colour, and contrarily those Rays, which are disposed to exhibit a Red colour, are all the least refrangible: So the most refrangible Rays are all disposed to exhibit a deep Violet Colour, and contrarily those which 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, and refrangibility, is very precise and strict; the Rays always either exactly agreeing in both, or proportionally disagreeing in both.

3. The species of colour, and degree of Refrangibility proper to any particular sort of Rays, is not mutable by Refraction, nor by Reflection from natural bodies, nor by any other cause, that I could yet observe. When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it. I have refracted it with Prismes, and reflected it with Bodies, which in Day-light were of other colours; I have intercepted it with the coloured film of Air interceding two compressed plates of glass; transmitted it through coloured Mediums, and through Mediums irradiated with other sorts of Rays, and diversly terminated it; and yet could never produce any new colour out of it. It would by contracting or dilating become more brisk, or faint, and by the loss of many Rays, in some cases very obscure and dark; but I could never see it changed in specie.

Yet seeming transmutations of Colours may be made, where there is any mixture of divers sorts of Rays. For in such mixtures, the component colours appear not, but, by their mutual allaying each other, constitute a midling colour. And therefore, if by refraction, or any other of the aforesaid causes, the difform Rays, latent in such a mixture, be separated, there shall emerge colours different from the colour of the composition. Which colours are not New generated, but only made Apparent by being parted; for if they be again intirely mix't and blended together, they will again compose that colour, which they did before separation. And for the same reason, Transmutations made by the convening of divers colours are not real; for when the difform Rays are again severed, they will exhibit the very same colours, which they did before they entered the composition; as you see, Blew and Yellow powders, when finely mixed, appear to the naked eye Green, and yet the Colours of the Component corpuscles are not thereby really transmuted, but only blended. For, when viewed with a good Microscope, they still appear Blew and Yellow interspersedly.

5. There are therefore two sorts of Colours. The one original and simple, the other compounded of these. The Original or primary colours are, Red, Yellow, Green, Blew, and a Violet-purple, together with Orange, Indico, and an indefinite variety of Intermediate gradations.

6. The same colours in Specie with these Primary ones may be also produced by composition: For, a mixture of Yellow and Blew makes Green; of Red and Yellow makes Orange; of Orange and Yellowish green makes yellow. And in general, if any two Colours be mixed, which in the series of those, generated by the Prisme, are not too far distant one from another, they by their mutual alloy compound that colour, which in the said series appeareth in the mid-way between them. But those, which are situated at too great a distance, do not so. Orange and Indico produce not the intermediate Green, nor Scarlet and Green the intermediate yellow.

7. But the most surprising and wonderful composition was that of Whiteness. There is no one sort of Rays which alone can exhibit this. 'Tis ever compounded, and to its composition are requisite all the aforesaid primary Colours, mixed in a due proportion. I have often with Admiration beheld, that all the Colours of the Prisme being made to converge, and thereby to be again mixed as they were in the light before it was Incident upon the Prisme, reproduced light, intirely and perfectly white, and not at all sensibly differing from a direct Light of the Sun, unless when the glasses, I used, were not sufficiently clear; for then they would a little incline it to their colour.

8. Hence therefore it comes to pass, that Whiteness is the usual colour of Light; for, Light is a confused aggregate of Rays indued with all sorts of Colors, as they are promiscuously darted from the various parts of luminous bodies. And of such a confused aggregate, as I said, is generated Whiteness, if there be a due proportion of the Ingredients; but if any one predominate, the Light must incline to that colour; as it happens in the Blew flame of Brimstone; the yellow flame of a Candle; and the various colours of the Fixed stars.

9. These things considered, the manner, how colours are produced by the Prisme, is evident. For, of the Rays, constituting the incident light, since those which differ in Colour proportionally differ in Refrangibility, they by their unequall refractions must be severed and dispersed into an oblong form in an orderly succession from the least refracted Scarlet to the most refracted Violet. And for the same reason it is, that objects, when looked upon through a Prisme, appear coloured. For, the difform Rays, by their unequal Refractions, are made to diverge towards several parts of the Retina, and there express the Images of things coloured, as in the former case they did the Suns Image upon a wall. And by this inequality of refractions they become not only coloured, but also very confused and indistinct.

10. Why the Colours of the Rainbow appear in falling drops of Rain, is also from hence evident. For, those drops, which refract the Rays, disposed to appear purple, in greatest quantity to the Spectators eye, refract the Rays of other sorts so much less, as to make them pass beside it; and such are the drops on the inside of the Primary Bow, and on the outside of the Secondary or Exteriour one. So those drops, which refract in greatest plenty the Rays, apt to appear red, toward the Spectators eye, refract those of other sorts so much more, as to make them pass beside it; and such are the drops on the exteriour part of the Primary, and interiour part of the Secondary Bow.

11. The odd Phænomena of an infusion of Lignum Nephriticum, Leaf gold, Fragments of coloured glass, and some other transparently coloured bodies, appearing in one position of one colour, and of another in another, are on these grounds no longer riddles. For, those are substances apt to reflect one sort of light and transmit another; as may be seen in a dark room, by illuminating them, with similar or uncompounded light. For, then they appear of that colour only, with which they are illuminated, but yet in one position more vivid and luminous than in another, accordingly as they are disposed more or less to reflect or transmit the incident colour.

12. From hence also is manifest the reason of an unexpected Experiment, which Mr. Hook somewhere in his Micrography relates to have made with two wedg-like transparent vessels, fill'd the one with a red, the other with a blew liquor: namely, that though they were severally transparent enough, yet both together became opake; For, if one transmitted only red, and the other only blew, no rays could pass through both.

13. I might add more instances of this nature, but I shall conclude with this general one, that the Colours of all natural Bodies have no other origin than this, 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 with uncompounded light of divers colours. For by that means any body may be made to appear of any colour. They have there no appropriate colour, but ever appear of the colour of the light cast upon them, but yet with this difference, that they are most brisk and vivid in the light of their own day-light-colour. Minium appeareth there of any colour indifferently, with which 'tis illustrated, but yet most luminous in red, and so Bise appeareth indifferently of any colour with which 'tis illustrated, but yet most luminous in blew. And therefore Minium reflecteth Rays of any colour, but most copiously those indued with red; and consequently when illustrated with day-light, that is, with all sorts of Rays promiscuously blended, those qualified with red shall abound most in the reflected light, and by their prevalence cause it to appear of that colour. And for the same reason Bise, reflecting blew most copiously, shall appear blew by the excess of those Rays in its reflected light; and the like of other bodies. And that this is the intire and adequate cause of their colours, is manifest, because they have no power to change or alter the colours of any sort of Rays incident apart, but put on all colours indifferently, with which they are inlightned.

These things being so, it can be no longer disputed, whether there be colours in the dark, nor whether they be the qualities of the objects we see, no nor perhaps, whether Light be a Body. For, since Colours are the qualities of Light, having its Rays for their intire and immediate subject, how can we think those Rays qualities also, unless one quality may be the subject of and sustain another; which in effect is to call it Substance. We should not know Bodies for substances, were it not for their sensible qualities, and the Principal of those being now found due to something else, we have as good reason to believe that to be a Substance also.

Besides, whoever thought any quality to be a heterogeneous aggregate, such as Light is discovered to be. But, to determine more absolutely, what Light is, after what manner refracted, and by what modes or actions it produceth in our minds the Phantasms of Colours, is not so easie. And I shall not mingle conjectures with certainties.

Reviewing what I have written, I see the discourse it self will lead to divers Experiments sufficient for its examination: And therefore I shall not trouble you further, than to describe one of those, which I have already insinuated.

In a darkened Room make a hole in the shut of a window, whose diameter may conveniently be about a third part of an inch, to admit a convenient quantity of the Suns light: And there place a clear and colourless Prisme, to refract the entring light towards the further part of the Room, which, 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-glass of a three foot Telescope,) at the distance of about four or five foot from thence, through which all those colours may at once be transmitted, and made by its Refraction to convene at a further distance of about ten or twelve feet. If at that distance you intercept this light with a sheet of white paper, you will see the colours converted into whiteness again by being mingled. But it is requisite, that the Prisme and Lens be placed steddy, and that the paper, on which the colours are cast, be moved to and fro; for, by such motion, you will not only find, at what distance the whiteness is most perfect but also see, how the colours gradually convene, and vanish into whiteness, and afterwards having crossed one another in that place where they compound Whiteness, are again dissipated, and severed, and in an inverted order retain the same colours, which they had before they entered the composition, You may also see, that, if any of the Colours at the Lens be intercepted, the Whiteness will be changed into the other colours. And therefore, that the composition of whiteness be perfect, care must be taken, that none of the colours fall besides the Lens.

In the annexed design of this Experiment, A B C expresseth the Prism set endwise to sight, close by the hole F of the window E G. Its vertical Angle A C B may conveniently be about 60 degrees: M N designeth the Lens. Its breadth 2½ or 3 inches. S F one of the streight lines, in which difform Rays may be conceived to flow successively from the Sun. F P, and F R two of those Rays unequally refracted, which the Lens makes to converge towards Q, and after decussation to diverge again. And H I the paper, at divers distances, on which the colours are projected: which in Q constitute Whiteness, but are Red and Yellow in R, r, and ρ, and Blew and Purple in P, p, and π.

If you proceed further to try the impossibility of changing any uncompounded colour (which I have asserted in the third and thirteenth Propositions) 'tis requisite that the Room be made very dark, least any scattering light, mixing with the colour, disturb and allay it, and render it compound, contrary to the design of the Experiment. 'Tis also requisite, that there be a perfecter separation of the Colours, than, after the manner above described, can be made by the Refraction of one single Prisme, and how to make such further separations, will scarce be difficult to them, that consider the discovered laws of Refractions. But if tryal shall be made with colours not throughly separated, there must be allowed changes proportionable to the mixture. Thus if compound Yellow light fall upon Blew Bise, the Bise will not appear perfectly yellow, but rather green, because there are in the yellow mixture many rays indued with green, and Green being less remote from the usual blew colour of Bise than yellow, is the more copiously reflected by it.

In like manner, if any one of the Prismatick colours, suppose Red, be intercepted, on design to try the asserted impossibility of reproducing that Colour out of the others which are pretermitted; 'tis necessary, either that the colours be very well parted before the red be intercepted, or that together with the red the neighbouring colours, into which any red is secretly dispersed, (that is, the yellow, and perhaps green too) be intercepted; or else, that allowance be made for the emerging of so much red out of the yellow green, as may possibly have been diffused, and scatteringly blended in those colours. And if these things be observed, the new Production of Red, or any intercepted colour will be found impossible.

This, I conceive, is enough for an Introduction to Experiments 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 with what success: That, if any thing seem to be defective, or to thwart this relation, I may have an opportunity of giving further direction about it, or of acknowledging my errors, if I have committed any.

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中文译文 · Claude（AI）译

先生：

为了履行我不久前对您的诺言，我就不再客套，直接告诉您：1666 年初（那时我正致力于磨制非球面形状的光学玻璃），我弄到一块三角形的玻璃棱镜，用它来试验那著名的颜色现象。为此，我把房间弄暗，在窗板上开了一个小孔，让适量的阳光进来，然后把棱镜放在光的入口处，使光经它折射到对面的墙上。起初，观看由此产生的鲜明强烈的颜色，是一种非常愉快的消遣；但过了一会儿，我开始更仔细地考察它们，却惊奇地看到它们呈长方形；而按照公认的折射定律，我原以为它应该是圆形的。

它们的两侧以直线为界，但是在两端，光的减弱是那么逐渐，很难准确地判定它们是什么形状；不过它们看来是半圆形的。

把这个彩色光谱的长度同它的宽度比较，我发现长度大约是宽度的五倍；这种不成比例是如此过分，激起了我一种非同寻常的好奇心，要去考察它可能是从哪里来的。我很难想象，玻璃的不同厚度，或者光以阴影或黑暗为界，会对光有什么影响，产生这样的效果；不过我认为，先考察一下这些情形也不无好处，于是试了试：让光透过玻璃上厚度不同的部分，或者透过窗上大小不同的孔，或者把棱镜放在外面，使光在被孔限定之前先透过棱镜、发生折射，会有什么结果：但是我发现这些情形都无关紧要。在所有这些情况下，颜色的样子都是一样的。

接着我怀疑，是否由于玻璃的某种不平，或者其他偶然的不规则，这些颜色才被这样拉长了。为了试验这一点，我拿来另一块同前一块相似的棱镜，把它这样放置：使通过两块棱镜的光沿相反的方向折射，从而被后一块棱镜送回到前一块使它偏离的那条路线上去。因为我想，用这种方法，第一块棱镜的规则效应会被第二块棱镜抵消，而不规则的效应则会因为折射次数增多而更加增强。结果是，被第一块棱镜散成长方形的光，被第二块棱镜还原成了圆形，其规则的程度，同光根本没有通过棱镜时一样。所以，无论那长度的原因是什么，都不是任何偶然的不规则。

然后我进而更严格地考察，来自太阳不同部分的光线入射角的差异，可能产生什么效果；为此，我测量了属于这个像的几条线和几个角。像到孔或棱镜的距离是 22 英尺；它的最大长度是 13¼ 英寸；宽度 2⅝ 英寸；孔的直径 ¼ 英寸；趋向像中部的光线，同它们不经折射时本应行进的路线所成的角，是 44 度 56 分。棱镜的顶角是 63 度 12 分。此外，棱镜两面上的折射，也就是入射光线和出射光线的折射，我尽可能使它们相等，因而大约都是 54 度 4 分。光线是垂直地落在墙上的。现在，从像的长度和宽度中减去孔的直径，剩下由那些通过孔的中心的光线所包含的长度 13 英寸、宽度 2⅜ 英寸，因此那宽度在孔处所张的角大约是 31 分，同太阳的直径相当；但是它的长度所张的角，却超过了五个这样的直径，也就是 2 度 49 分。

作了这些观察之后，我首先根据它们算出了那种玻璃的折射能力，发现它可以用正弦之比 20 比 31 来量度。然后，我按照这个比例，计算了来自太阳圆面相对两边、入射倾角相差 31 分的两条光线的折射，发现出射光线所包含的角应当大约是 31 分，正如它们入射之前那样。

但是，因为这个计算是建立在入射正弦与折射正弦成比例这个假说之上的，尽管根据我自己的经验，我无法想象这个假说会错到这种地步，使那个实际上是 2 度 49 分的角只有 31 分；然而我的好奇心还是使我再一次拿起了棱镜。我把它像以前一样放在窗口，观察到：把它绕着自己的轴来回转动一点，使它对光的倾角改变 4 度或 5 度以上，颜色在墙上的位置并没有因此明显地移动，所以，入射角的这种变化，并没有使折射量发生明显的变化。因此，通过这个实验，也通过前面的计算，可以明白：来自太阳不同部分的光线入射角的差异，不可能使它们在交叉之后以一个比它们先前会聚时明显更大的角发散；那个角至多不过 31 或 32 分，所以仍然要找出某种别的原因，使它成为 2 度 49 分。

于是我开始怀疑，光线在穿过棱镜之后，是不是沿着曲线运动，并且根据它们弯曲程度的大小，趋向墙上不同的部分。当我想起我常常看见一个被斜握的球拍击中的网球画出这样一条曲线时，我的怀疑就更大了。因为那一击既传给它一个前进的运动，也传给它一个旋转的运动，它在两种运动方向一致的那一边，必定更猛烈地压迫和撞击邻近的空气，从而在那里激起空气相应更大的抵抗和反作用。出于同样的理由，如果光线可能是球形的物体，并且在从一种媒质斜穿到另一种媒质时获得一种旋转运动，那么它们在两种运动一致的那一边，应当受到周围以太更大的阻力，从而不断地向另一边弯曲。但是，尽管这种怀疑有似乎合理的根据，当我去考察它的时候，却观察不到光线有任何这样的弯曲。此外（这对我的目的已经足够），我观察到，像的长度与光所透过的孔的直径之差，同它们的距离成比例。

这些怀疑逐渐被排除，终于把我引向了判决性实验，它是这样的：我拿两块板，把一块紧贴着放在窗口棱镜的后面，使光能穿过板上为此开的一个小孔，落到另一块板上；那另一块板，我放在大约 12 英尺远的地方，也先在上面开了一个小孔，让一部分入射光通过。然后，我在这第二块板后面再放一块棱镜，使穿过两块板的光也穿过这块棱镜，在到达墙壁之前再一次发生折射。做好这些之后，我把第一块棱镜拿在手里，绕着它的轴慢慢地来回转动，转动得足以使投在第二块板上的像的各个部分依次通过板上的孔，好观察第二块棱镜把它们折射到墙上的什么地方。我从这些地方的变化看出，趋向像的那一端（第一块棱镜的折射正是朝那一端进行的）的光，在第二块棱镜里受到的折射，比趋向另一端的光大得多。这样，那个像之所以长的真正原因就被发现了：它不是别的，就是光由折射性不同的光线组成，这些光线与它们入射角的差异毫无关系，而是按照它们的折射程度，被送到墙上不同的部分。

我明白了这一点之后，就停下了前面说的玻璃工作；因为我看出，望远镜的完善之所以至今受到限制，与其说是由于缺少按照光学作者的规定准确成形的玻璃（这是迄今所有的人都以为的），不如说是因为光本身就是由折射性不同的光线组成的一种不均匀的混合物。所以，即使一块玻璃成形得那样准确，能把任何一种光线聚集到一点，它也不能把另一些以同样的入射角射到同一媒质上、却容易受到不同折射的光线聚集到同一点。不，我倒奇怪，既然折射性的差别像我发现的那么大，望远镜怎么能达到它们现在这样的完善程度。因为我在我的一块棱镜里测量折射时发现：假定在它的一个平面上共同的入射正弦是 44 份，那么颜色红端最外的光线从玻璃射入空气时的折射正弦就是 68 份，另一端最外的光线的折射正弦是 69 份：所以差别大约是整个折射的二十四分之一或二十五分之一。因此，任何望远镜的物镜，都不能把来自物体上一点的所有光线聚集起来，使它们会合在焦点上一个比直径为其孔径直径五十分之一的圆还小的空间里；如果光是均匀的，那么一个圆形的透镜，像长望远镜的物镜那样截面很小，因形状不合而引起的不规则，比这要小好几百倍。

这使我考虑到反射，发现它们是规则的，一切种类的光线的反射角都等于它们的入射角；于是我明白，借助于反射，光学仪器可以达到任何可以想象的完善程度，只要能找到一种反射物质，它能磨得同玻璃一样光滑，反射的光同玻璃透过的光一样多，并且掌握了使它成为抛物线形的技艺。但是似乎有很大的困难，当我进一步考虑到，反射表面上的每一处不规则，使光线偏离它们正当路线的程度，比折射表面上同样的不规则要大五六倍时，我几乎认为这些困难是不可克服的：所以，这里需要的精细程度，要比磨制折射用的玻璃大得多。

正在这样思考的时候，我被那场突然到来的瘟疫赶出了剑桥，过了两年多才得以继续进行。但是后来我想出了一种适合于金属的细致的抛光方法，我设想用这种方法也能把形状一直校正到最后；于是我开始试验在这方面能做到什么，逐渐把一件仪器完善到这种程度（在主要部分上，它同我送到伦敦去的那一件相似），用它我能看到木星的四个伴星，并且好几次指给我认识的另外两个人看过。我还能看到金星像月亮那样的位相，不过不很清楚，而且要对仪器作些细心的调整才行。

从那时起，我一直被打断，直到去年秋天，我才做了另一件。由于那一件明显地比第一件好（尤其是看白天的物体），所以我毫不怀疑，经过那些人的努力，它们还会达到完善得多的程度；照您告诉我的，他们正在伦敦为这件事操心。

我有时想做一架显微镜，它同样用一块反射的金属来代替物镜。我希望他们也会考虑这一点。因为这种仪器看来同望远镜一样可以改进，也许更可以改进，因为它只需要一块反射金属，就像您从附图中可以看到的，图中 A B 代表物镜金属，C D 代表目镜，F 是它们共同的焦点，O 是金属的另一个焦点，物体就放在那里。

不过，回到正题上来，我告诉过您，光不是相似的或同质的，而是由不同形的光线组成的，其中一些比另一些更容易折射：所以，在以同样的方式射到同一媒质上的光线中，有些会比另一些折射得更多，这并不是由于玻璃的任何效力或其他外部原因，而是由于每一条特定的光线都有一种受到特定程度折射的预先禀性。

现在我要接着告诉您光线中另一种更值得注意的不同形，颜色的起源就是在这里展现出来的：关于这一点，我将先提出学说，然后为了检验它，举出一两个实验作为其余实验的样本。

您会发现，这个学说包含并说明在下面的命题里。

1. 正如光线在折射程度上不同，它们在显示这种或那种特定颜色的禀性上也不同。颜色不是从自然物体的折射或反射得来的光的性质（像一般人所相信的那样），而是原始的、天生的属性，在不同的光线中是不同的。有些光线倾向于显示红色而不显示别的颜色；有些倾向于显示黄色而不显示别的颜色，有些倾向于显示绿色而不显示别的颜色，其余的也是这样。而且，不仅有专属于比较显著的颜色的光线，甚至连它们之间的一切中间层次，也都有各自专属的光线。

2. 同样的折射程度总是属于同样的颜色，同样的颜色总是属于同样的折射程度。折射性最小的光线都倾向于显示红色，反过来，倾向于显示红色的光线，都是折射性最小的：同样，折射性最大的光线都倾向于显示深紫色，反过来，容易显示这种紫色的光线，都是折射性最大的。所有的中间颜色，在一个连续的系列中，都属于中间的折射程度。颜色与折射性之间的这种对应是非常精确和严格的；光线总是要么在两方面都完全一致，要么在两方面都成比例地不一致。

3. 任何一种特定的光线所固有的颜色种类和折射程度，都不能被折射改变，也不能被自然物体的反射改变，也不能被我迄今所能观察到的任何别的原因改变。任何一种光线，一旦同其他种类的光线很好地分开之后，就顽强地保持它的颜色，不管我怎样竭尽全力去改变它。我用棱镜折射过它，用白天看来是别的颜色的物体反射过它；我用夹在两块压紧的玻璃片之间的那层彩色空气薄膜截过它；让它透过有色的媒质，透过受到别种光线照射的媒质，并且用各种方法限定它；然而从来没能从它里面产生出任何新的颜色。它会因为收缩或扩散而变得更鲜明或更暗淡，在某些情况下由于损失了许多光线而变得非常模糊黑暗；但是我从来没有看见它在种类上改变过。

不过，在有不同种类光线混合的地方，可以造成表面上的颜色转变。因为在这样的混合物中，组成的颜色并不显现出来，而是由于互相冲淡，构成一种居中的颜色。因此，如果通过折射，或者通过上述任何其他原因，把潜藏在这种混合物中的不同形的光线分开，就会出现与混合物的颜色不同的颜色。这些颜色并不是新产生的，只是由于被分开而显现出来的；因为如果把它们再完全混合在一起，它们又会组成它们分开以前的那种颜色。出于同样的理由，由不同颜色会合而造成的转变也不是真实的；因为当不同形的光线再分开时，它们又会显出它们在加入混合之前的那些颜色；正如您看到的，蓝色和黄色的粉末细细地混合以后，在肉眼看来是绿色的，然而组成它的微粒的颜色并没有因此真正转变，只是混合了而已。因为用一架好的显微镜看时，它们仍然显出蓝色和黄色交错在一起。

5. 所以颜色有两种。一种是原始的、单纯的，另一种是由这些颜色复合而成的。原始的或基本的颜色是红、黄、绿、蓝和紫，还有橙、靛，以及数不清的中间层次。

6. 种类上与这些基本颜色相同的颜色，也可以通过复合产生：因为黄和蓝的混合成为绿；红和黄的混合成为橙；橙和黄绿的混合成为黄。一般说来，如果把两种在棱镜产生的颜色系列中相距不太远的颜色混合起来，它们就会由于互相冲淡，复合成在上述系列中位于它们中间的那种颜色。但是那些相距太远的颜色，就不会这样。橙和靛产生不出中间的绿，猩红和绿也产生不出中间的黄。

7. 但是最令人惊奇、最奇妙的复合，是白色的复合。没有任何一种光线能单独显示白色。白色总是复合的，它的复合需要上述一切基本颜色按适当的比例混合。我常常惊叹地看到，当棱镜的所有颜色被弄得会聚起来，从而像它们射到棱镜以前在光里那样重新混合时，就重新产生出完全纯粹的白光，同太阳的直射光没有任何可以觉察的差别，除非我所用的玻璃不够清澈；因为那样的话，它们就会使光稍稍偏向它们自己的颜色。

8. 因此就有这样的结果：白色是光通常的颜色；因为光是具有各种颜色的光线的混乱集合，它们从发光体的各个部分杂乱地射出来。如我所说，如果各种成分的比例适当，这样一种混乱的集合就产生出白色；但是如果其中某一种占优势，光就必定偏向那种颜色；就像硫黄的蓝色火焰、蜡烛的黄色火焰以及恒星的各种颜色那样。

9. 考虑到这些事情，颜色是怎样由棱镜产生的，就很明显了。因为，在构成入射光的光线中，既然颜色不同的光线在折射性上也成比例地不同，它们由于折射不等，必定被分开，散成一个长方形，按照有秩序的次序，从折射最小的猩红排到折射最大的紫。出于同样的理由，透过棱镜看物体时，物体显得有颜色。因为不同形的光线由于折射不等，被弄得向视网膜的不同部分发散，在那里显出有颜色的物体的像，正如在前一种情况下它们在墙上显出太阳的像一样。而由于折射的这种不等，它们不仅变得有颜色，而且变得非常混乱、模糊不清。

10. 为什么虹的颜色出现在下落的雨滴中，也由此可以明白。因为那些把倾向于显现紫色的光线最大量地折射到观看者眼中的雨滴，把其他种类的光线折射得少得多，使它们从眼睛旁边经过；主虹的内侧和副虹（即外虹）的外侧，就是这样的雨滴。同样，那些把容易显现红色的光线最大量地折射向观看者眼睛的雨滴，把其他种类的光线折射得多得多，使它们从眼睛旁边经过；主虹的外侧和副虹的内侧，就是这样的雨滴。

11. 肾木浸液、金箔、彩色玻璃的碎片，以及其他一些透明的有色物体，在一个位置上显出一种颜色，在另一个位置上显出另一种颜色，这些奇怪的现象，根据这些道理就不再是谜了。因为这些物质容易反射一种光而透过另一种光；在暗室里用相似的或非复合的光照射它们，就可以看出这一点。因为那时它们只显出照射它们的那种颜色，不过在一个位置上比在另一个位置上更鲜明明亮，这要看它们更倾向于反射还是透过入射的颜色而定。

12. 由此也可以明白胡克先生在他的《显微图谱》中某处所讲的一个出人意料的实验的道理：他用两个楔形的透明容器，一个装红色的液体，另一个装蓝色的液体，它们各自都相当透明，但是两个放在一起却变得不透明了；因为如果一个只透过红光，另一个只透过蓝光，就没有任何光线能通过两者。

13. 我还可以再举一些这一类的例子，但是我要用这样一个普遍的例子来结束：一切自然物体的颜色，没有别的起源，只是因为它们具有各种不同的性质，反射一种光比反射另一种光更多。我在暗室里用各种颜色的非复合光照射这些物体，试验过这一点。因为用这种方法，可以使任何物体显出任何颜色。在那里它们没有专属的颜色，而总是显出投射到它们上面的光的颜色，不过有这样一个区别：在它们自己白天颜色的光中，它们最鲜明活泼。在那里，铅丹在用什么颜色照射时就无差别地显出什么颜色，但是在红光中最明亮；同样，石青在用什么颜色照射时就无差别地显出什么颜色，但是在蓝光中最明亮。因此，铅丹反射任何颜色的光线，但是反射最多的是具有红色的光线；所以在用日光，即各种光线杂乱地混合在一起的光照射时，在反射光中最多的是具有红色的光线，由于它们占优势，就使它显出那种颜色。出于同样的理由，石青反射蓝光最多，由于反射光中这种光线过量，就显出蓝色；其他物体也是这样。这就是它们的颜色完全而充分的原因，这一点是明白的，因为对于单独射来的任何一种光线，它们都没有能力改变或更改它的颜色，而是无差别地呈现出照亮它们的一切颜色。

这些事情既然如此，那么，黑暗中有没有颜色，颜色是不是我们所看到的物体的性质，这些问题就不能再争论了，甚至光是不是一种物体，也许也不能再争论了。因为既然颜色是光的性质，以光线为它们完全而直接的主体，那么我们怎么能认为那些光线也是性质呢？除非一种性质可以是另一种性质的主体并承载它；而这实际上就是把它叫作实体。如果不是由于物体的可感性质，我们就不会知道物体是实体；而这些可感性质中最主要的一种，现在既然发现是归属于别的什么东西的，我们就有同样充分的理由相信那个东西也是一种实体。

此外，谁曾经认为任何一种性质是一个不均匀的集合，像光现在被发现的那样呢？但是，要更绝对地确定光是什么，它以什么方式被折射，又以什么方式或作用在我们心中产生颜色的幻象，就不那么容易了。我不想把猜测同确定的东西混在一起。

回顾我写下的东西，我看到这番论述本身就会引出许多足以检验它的实验：因此我不再多麻烦您，只描述其中一个我已经暗示过的实验。

在一间暗室里，在窗板上开一个孔，孔的直径大约三分之一英寸比较合适，让适量的阳光进来：在那里放一块清澈无色的棱镜，把射进来的光折射到房间的远处，正如我说过的，光就会由此散成一个长方形的彩色像。然后在离棱镜大约四五英尺的地方，放一个半径大约三英尺的透镜（比如说一架三英尺望远镜的宽大物镜），使所有那些颜色都能一下子透过它，并由于它的折射而在大约十到十二英尺远的地方会合。如果在那个距离上用一张白纸截住这光，你就会看到颜色由于被混合而重新变成了白色。但是必须把棱镜和透镜放稳，而把投上颜色的纸来回移动；因为通过这样的移动，你不仅能找到在什么距离上白色最完美，还能看到颜色怎样逐渐会合，消失成白色，然后在它们复合成白色的地方彼此交叉之后，又重新散开、分离，并以颠倒的次序保持着它们加入复合以前的那些颜色。你还可以看到，如果透镜处的任何一种颜色被截住，白色就会变成其他的颜色。因此，为了使白色的复合完美，必须注意不要让任何颜色落在透镜外面。

在附上的这个实验的图中，A B C 表示棱镜，端面朝着视线，紧靠在窗 E G 的孔 F 旁边。它的顶角 A C B 大约 60 度比较合适：M N 表示透镜。它的宽度是 2½ 或 3 英寸。S F 是一条直线，可以设想不同形的光线沿着它从太阳相继流来。F P 和 F R 是其中两条折射不等的光线，透镜使它们向 Q 会聚，交叉之后又重新发散。H I 是放在不同距离上、投上颜色的纸：颜色在 Q 处构成白色，但在 R、r 和 ρ 处是红和黄，在 P、p 和 π 处是蓝和紫。

如果你进一步去试验改变任何一种非复合颜色是不可能的（这是我在第三和第十三命题中断言的），那么房间必须弄得非常暗，以免任何散射的光同颜色混合，干扰它、冲淡它，使它成为复合的，违背实验的意图。还必须使颜色的分离比上述方法中用一块棱镜的折射所能做到的更完全；对于那些考虑过已经发现的折射定律的人来说，怎样作进一步的分离，并不困难。但是，如果用没有完全分开的颜色来试验，就必须容许发生与混合程度成比例的变化。比如说，如果复合的黄光落在石青上，石青不会显得完全是黄色，而毋宁是绿色，因为在黄色的混合物中有许多具有绿色的光线，而绿色比黄色更接近石青通常的蓝色，所以被它反射得更多。

同样，如果为了试验所断言的从被留下的其他颜色中不可能重新产生被截去的那种颜色，而截去棱镜颜色中的任何一种，比如说红色，那么必须做到：要么在截去红色之前把颜色分得非常清楚，要么在截去红色的同时，把红色暗中散布于其中的相邻颜色（也就是黄色，也许还有绿色）一起截去；要么就要容许从黄绿中出现那么多红色，可能就是散布并零星混合在那些颜色中的。如果遵守了这些事项，就会发现，重新产生红色或任何一种被截去的颜色，是不可能的。

我想，这作为这一类实验的入门已经够了；如果皇家学会有哪一位好奇地去做这些实验，我将很高兴得知结果如何：这样，如果有什么东西似乎有缺陷，或者与这篇报告相抵触，我就可以有机会对此作进一步的说明，或者承认我的错误，如果我犯了错误的话。