Opticks, or, A Treatise of the Reflections, Refractions, Inflections, and Colours of Light

PART I.

My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments: In order to which I shall premise the following Definitions and Axioms.

DEFINITIONS

DEFIN. I.

By the Rays of Light I understand its least Parts, and those as well Successive in the same Lines, as Contemporary in several Lines. For it is manifest that Light consists of Parts, both Successive and Contemporary; because in the same place you may stop that which comes one moment, and let pass that which comes presently after; and in the same time you may stop it in any one place, and let it pass in any other. For that part of Light which is stopp'd cannot be the same with that which is let pass. The least Light or part of Light, which may be stopp'd alone without the rest of the Light, or propagated alone, or do or suffer any thing alone, which the rest of the Light doth not or suffers not, I call a Ray of Light.

DEFIN. II.

Refrangibility of the Rays of Light, is their Disposition to be refracted or turned out of their Way in passing out of one transparent Body or Medium into another. And a greater or less Refrangibility of Rays, is their Disposition to be turned more or less out of their Way in like Incidences on the same Medium. Mathematicians usually consider the Rays of Light to be Lines reaching from the luminous Body to the Body illuminated, and the refraction of those Rays to be the bending or breaking of those lines in their passing out of one Medium into another. And thus may Rays and Refractions be considered, if Light be propagated in an instant. But by an Argument taken from the Æquations of the times of the Eclipses of Jupiter's Satellites, it seems that Light is propagated in time, spending in its passage from the Sun to us about seven Minutes of time: And therefore I have chosen to define Rays and Refractions in such general terms as may agree to Light in both cases.

DEFIN. III.

Reflexibility of Rays, is their Disposition to be reflected or turned back into the same Medium from any other Medium upon whose Surface they fall. And Rays are more or less reflexible, which are turned back more or less easily. As if Light pass out of a Glass into Air, and by being inclined more and more to the common Surface of the Glass and Air, begins at length to be totally reflected by that Surface; those sorts of Rays which at like Incidences are reflected most copiously, or by inclining the Rays begin soonest to be totally reflected, are most reflexible.

DEFIN. IV.

The Angle of Incidence is that Angle, which the Line described by the incident Ray contains with the Perpendicular to the reflecting or refracting Surface at the Point of Incidence.

DEFIN. V.

The Angle of Reflexion or Refraction, is the Angle which the line described by the reflected or refracted Ray containeth with the Perpendicular to the reflecting or refracting Surface at the Point of Incidence.

DEFIN. VI.

The Sines of Incidence, Reflexion, and Refraction, are the Sines of the Angles of Incidence, Reflexion, and Refraction.

DEFIN. VII

The Light whose Rays are all alike Refrangible, I call Simple, Homogeneal and Similar; and that whose Rays are some more Refrangible than others, I call Compound, Heterogeneal and Dissimilar. The former Light I call Homogeneal, not because I would affirm it so in all respects, but because the Rays which agree in Refrangibility, agree at least in all those their other Properties which I consider in the following Discourse.

DEFIN. VIII.

The Colours of Homogeneal Lights, I call Primary, Homogeneal and Simple; and those of Heterogeneal Lights, Heterogeneal and Compound. For these are always compounded of the colours of Homogeneal Lights; as will appear in the following Discourse.

AXIOMS.

AX. I.

The Angles of Reflexion and Refraction, lie in one and the same Plane with the Angle of Incidence.

AX. II.

The Angle of Reflexion is equal to the Angle of Incidence.

AX. III.

If the refracted Ray be returned directly back to the Point of Incidence, it shall be refracted into the Line before described by the incident Ray.

AX. IV.

Refraction out of the rarer Medium into the denser, is made towards the Perpendicular; that is, so that the Angle of Refraction be less than the Angle of Incidence.

AX. V.

The Sine of Incidence is either accurately or very nearly in a given Ratio to the Sine of Refraction.

Whence if that Proportion be known in any one Inclination of the incident Ray, 'tis known in all the Inclinations, and thereby the Refraction in all cases of Incidence on the same refracting Body may be determined. Thus if the Refraction be made out of Air into Water, the Sine of Incidence of the red Light is to the Sine of its Refraction as 4 to 3. If out of Air into Glass, the Sines are as 17 to 11. In Light of other Colours the Sines have other Proportions: but the difference is so little that it need seldom be considered.

Fig. 1

Suppose therefore, that RS [in Fig. 1.] represents the Surface of stagnating Water, and that C is the point of Incidence in which any Ray coming in the Air from A in the Line AC is reflected or refracted, and I would know whither this Ray shall go after Reflexion or Refraction: I erect upon the Surface of the Water from the point of Incidence the Perpendicular CP and produce it downwards to Q, and conclude by the first Axiom, that the Ray after Reflexion and Refraction, shall be found somewhere in the Plane of the Angle of Incidence ACP produced. I let fall therefore upon the Perpendicular CP the Sine of Incidence AD; and if the reflected Ray be desired, I produce AD to B so that DB be equal to AD, and draw CB. For this Line CB shall be the reflected Ray; the Angle of Reflexion BCP and its Sine BD being equal to the Angle and Sine of Incidence, as they ought to be by the second Axiom, But if the refracted Ray be desired, I produce AD to H, so that DH may be to AD as the Sine of Refraction to the Sine of Incidence, that is, (if the Light be red) as 3 to 4; and about the Center C and in the Plane ACP with the Radius CA describing a Circle ABE, I draw a parallel to the Perpendicular CPQ, the Line HE cutting the Circumference in E, and joining CE, this Line CE shall be the Line of the refracted Ray. For if EF be let fall perpendicularly on the Line PQ, this Line EF shall be the Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and this Sine EF is equal to DH, and consequently in Proportion to the Sine of Incidence AD as 3 to 4.

In like manner, if there be a Prism of Glass (that is, a Glass bounded with two Equal and Parallel Triangular ends, and three plain and well polished Sides, which meet in three Parallel Lines running from the three Angles of one end to the three Angles of the other end) and if the Refraction of the Light in passing cross this Prism be desired: Let ACB [in Fig. 2.] represent a Plane cutting this Prism transversly to its three Parallel lines or edges there where the Light passeth through it, and let DE be the Ray incident upon the first side of the Prism AC where the Light goes into the Glass; and by putting the Proportion of the Sine of Incidence to the Sine of Refraction as 17 to 11 find EF the first refracted Ray. Then taking this Ray for the Incident Ray upon the second side of the Glass BC where the Light goes out, find the next refracted Ray FG by putting the Proportion of the Sine of Incidence to the Sine of Refraction as 11 to 17. For if the Sine of Incidence out of Air into Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence out of Glass into Air must on the contrary be to the Sine of Refraction as 11 to 17, by the third Axiom.

Fig. 2.

Much after the same manner, if ACBD [in Fig. 3.] represent a Glass spherically convex on both sides (usually called a Lens, such as is a Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope) and it be required to know how Light falling upon it from any lucid point Q shall be refracted, let QM represent a Ray falling upon any point M of its first spherical Surface ACB, and by erecting a Perpendicular to the Glass at the point M, find the first refracted Ray MN by the Proportion of the Sines 17 to 11. Let that Ray in going out of the Glass be incident upon N, and then find the second refracted Ray Nq by the Proportion of the Sines 11 to 17. And after the same manner may the Refraction be found when the Lens is convex on one side and plane or concave on the other, or concave on both sides.

Fig. 3.

AX. VI.

Homogeneal Rays which flow from several Points of any Object, and fall perpendicularly or almost perpendicularly on any reflecting or refracting Plane or spherical Surface, shall afterwards diverge from so many other Points, or be parallel to so many other Lines, or converge to so many other Points, either accurately or without any sensible Error. And the same thing will happen, if the Rays be reflected or refracted successively by two or three or more Plane or Spherical Surfaces.

The Point from which Rays diverge or to which they converge may be called their Focus. And the Focus of the incident Rays being given, that of the reflected or refracted ones may be found by finding the Refraction of any two Rays, as above; or more readily thus.

Cas. 1. Let ACB [in Fig. 4.] be a reflecting or refracting Plane, and Q the Focus of the incident Rays, and QqC a Perpendicular to that Plane. And if this Perpendicular be produced to q, so that qC be equal to QC, the Point q shall be the Focus of the reflected Rays: Or if qC be taken on the same side of the Plane with QC, and in proportion to QC as the Sine of Incidence to the Sine of Refraction, the Point q shall be the Focus of the refracted Rays.

Fig. 4.

Cas. 2. Let ACB [in Fig. 5.] be the reflecting Surface of any Sphere whose Centre is E. Bisect any Radius thereof, (suppose EC) in T, and if in that Radius on the same side the Point T you take the Points Q and q, so that TQ, TE, and Tq, be continual Proportionals, and the Point Q be the Focus of the incident Rays, the Point q shall be the Focus of the reflected ones.

Fig. 5.

Cas. 3. Let ACB [in Fig. 6.] be the refracting Surface of any Sphere whose Centre is E. In any Radius thereof EC produced both ways take ET and Ct equal to one another and severally in such Proportion to that Radius as the lesser of the Sines of Incidence and Refraction hath to the difference of those Sines. And then if in the same Line you find any two Points Q and q, so that TQ be to ET as Et to tq, taking tq the contrary way from t which TQ lieth from T, and if the Point Q be the Focus of any incident Rays, the Point q shall be the Focus of the refracted ones.

Fig. 6.

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

Fig. 7.

Cas. 4. Let ACBD [in Fig. 7.] be any refracting Lens, spherically Convex or Concave or Plane on either side, and let CD be its Axis (that is, the Line which cuts both its Surfaces perpendicularly, and passes through the Centres of the Spheres,) and in this Axis produced let F and f be the Foci of the refracted Rays found as above, when the incident Rays on both sides the Lens are parallel to the same Axis; and upon the Diameter Ff bisected in E, describe a Circle. Suppose now that any Point Q be the Focus of any incident Rays. Draw QE cutting the said Circle in T and t, and therein take tq in such proportion to tE as tE or TE hath to TQ. Let tq lie the contrary way from t which TQ doth from T, and q shall be the Focus of the refracted Rays without any sensible Error, provided the Point Q be not so remote from the Axis, nor the Lens so broad as to make any of the Rays fall too obliquely on the refracting Surfaces.[1]

And by the like Operations may the reflecting or refracting Surfaces be found when the two Foci are given, and thereby a Lens be formed, which shall make the Rays flow towards or from what Place you please.[2]

So then the Meaning of this Axiom is, that if Rays fall upon any Plane or Spherical Surface or Lens, and before their Incidence flow from or towards any Point Q, they shall after Reflexion or Refraction flow from or towards the Point q found by the foregoing Rules. And if the incident Rays flow from or towards several points Q, the reflected or refracted Rays shall flow from or towards so many other Points q found by the same Rules. Whether the reflected and refracted Rays flow from or towards the Point q is easily known by the situation of that Point. For if that Point be on the same side of the reflecting or refracting Surface or Lens with the Point Q, and the incident Rays flow from the Point Q, the reflected flow towards the Point q and the refracted from it; and if the incident Rays flow towards Q, the reflected flow from q, and the refracted towards it. And the contrary happens when q is on the other side of the Surface.

AX. VII.

Wherever the Rays which come from all the Points of any Object meet again in so many Points after they have been made to converge by Reflection or Refraction, there they will make a Picture of the Object upon any white Body on which they fall.

So if PR [in Fig. 3.] represent any Object without Doors, and AB be a Lens placed at a hole in the Window-shut of a dark Chamber, whereby the Rays that come from any Point Q of that Object are made to converge and meet again in the Point q; and if a Sheet of white Paper be held at q for the Light there to fall upon it, the Picture of that Object PR will appear upon the Paper in its proper shape and Colours. For as the Light which comes from the Point Q goes to the Point q, so the Light which comes from other Points P and R of the Object, will go to so many other correspondent Points p and r (as is manifest by the sixth Axiom;) so that every Point of the Object shall illuminate a correspondent Point of the Picture, and thereby make a Picture like the Object in Shape and Colour, this only excepted, that the Picture shall be inverted. And this is the Reason of that vulgar Experiment of casting the Species of Objects from abroad upon a Wall or Sheet of white Paper in a dark Room.

In like manner, when a Man views any Object PQR, [in Fig. 8.] the Light which comes from the several Points of the Object is so refracted by the transparent skins and humours of the Eye, (that is, by the outward coat EFG, called the Tunica Cornea, and by the crystalline humour AB which is beyond the Pupil mk) as to converge and meet again in so many Points in the bottom of the Eye, and there to paint the Picture of the Object upon that skin (called the Tunica Retina) with which the bottom of the Eye is covered. For Anatomists, when they have taken off from the bottom of the Eye that outward and most thick Coat called the Dura Mater, can then see through the thinner Coats, the Pictures of Objects lively painted thereon. And these Pictures, propagated by Motion along the Fibres of the Optick Nerves into the Brain, are the cause of Vision. For accordingly as these Pictures are perfect or imperfect, the Object is seen perfectly or imperfectly. If the Eye be tinged with any colour (as in the Disease of the Jaundice) so as to tinge the Pictures in the bottom of the Eye with that Colour, then all Objects appear tinged with the same Colour. If the Humours of the Eye by old Age decay, so as by shrinking to make the Cornea and Coat of the Crystalline Humour grow flatter than before, the Light will not be refracted enough, and for want of a sufficient Refraction will not converge to the bottom of the Eye but to some place beyond it, and by consequence paint in the bottom of the Eye a confused Picture, and according to the Indistinctness of this Picture the Object will appear confused. This is the reason of the decay of sight in old Men, and shews why their Sight is mended by Spectacles. For those Convex glasses supply the defect of plumpness in the Eye, and by increasing the Refraction make the Rays converge sooner, so as to convene distinctly at the bottom of the Eye if the Glass have a due degree of convexity. And the contrary happens in short-sighted Men whose Eyes are too plump. For the Refraction being now too great, the Rays converge and convene in the Eyes before they come at the bottom; and therefore the Picture made in the bottom and the Vision caused thereby will not be distinct, unless the Object be brought so near the Eye as that the place where the converging Rays convene may be removed to the bottom, or that the plumpness of the Eye be taken off and the Refractions diminished by a Concave-glass of a due degree of Concavity, or lastly that by Age the Eye grow flatter till it come to a due Figure: For short-sighted Men see remote Objects best in Old Age, and therefore they are accounted to have the most lasting Eyes.

Fig. 8.

AX. VIII.

An Object seen by Reflexion or Refraction, appears in that place from whence the Rays after their last Reflexion or Refraction diverge in falling on the Spectator's Eye.

Fig. 9.

If the Object A [in Fig. 9.] be seen by Reflexion of a Looking-glass mn, it shall appear, not in its proper place A, but behind the Glass at a, from whence any Rays AB, AC, AD, which flow from one and the same Point of the Object, do after their Reflexion made in the Points B, C, D, diverge in going from the Glass to E, F, G, where they are incident on the Spectator's Eyes. For these Rays do make the same Picture in the bottom of the Eyes as if they had come from the Object really placed at a without the Interposition of the Looking-glass; and all Vision is made according to the place and shape of that Picture.

In like manner the Object D [in Fig. 2.] seen through a Prism, appears not in its proper place D, but is thence translated to some other place d situated in the last refracted Ray FG drawn backward from F to d.

Fig. 10.

And so the Object Q [in Fig. 10.] seen through the Lens AB, appears at the place q from whence the Rays diverge in passing from the Lens to the Eye. Now it is to be noted, that the Image of the Object at q is so much bigger or lesser than the Object it self at Q, as the distance of the Image at q from the Lens AB is bigger or less than the distance of the Object at Q from the same Lens. And if the Object be seen through two or more such Convex or Concave-glasses, every Glass shall make a new Image, and the Object shall appear in the place of the bigness of the last Image. Which consideration unfolds the Theory of Microscopes and Telescopes. For that Theory consists in almost nothing else than the describing such Glasses as shall make the last Image of any Object as distinct and large and luminous as it can conveniently be made.

I have now given in Axioms and their Explications the sum of what hath hitherto been treated of in Opticks. For what hath been generally agreed on I content my self to assume under the notion of Principles, in order to what I have farther to write. And this may suffice for an Introduction to Readers of quick Wit and good Understanding not yet versed in Opticks: Although those who are already acquainted with this Science, and have handled Glasses, will more readily apprehend what followeth.

PROPOSITIONS.

PROP. I. Theor. I.

Lights which differ in Colour, differ also in Degrees of Refrangibility.

The Proof by Experiments.

Exper. 1. I took a black oblong stiff Paper terminated by Parallel Sides, and with a Perpendicular right Line drawn cross from one Side to the other, distinguished it into two equal Parts. One of these parts I painted with a red colour and the other with a blue. The Paper was very black, and the Colours intense and thickly laid on, that the Phænomenon might be more conspicuous. This Paper I view'd through a Prism of solid Glass, whose two Sides through which the Light passed to the Eye were plane and well polished, and contained an Angle of about sixty degrees; which Angle I call the refracting Angle of the Prism. And whilst I view'd it, I held it and the Prism before a Window in such manner that the Sides of the Paper were parallel to the Prism, and both those Sides and the Prism were parallel to the Horizon, and the cross Line was also parallel to it: and that the Light which fell from the Window upon the Paper made an Angle with the Paper, equal to that Angle which was made with the same Paper by the Light reflected from it to the Eye. Beyond the Prism was the Wall of the Chamber under the Window covered over with black Cloth, and the Cloth was involved in Darkness that no Light might be reflected from thence, which in passing by the Edges of the Paper to the Eye, might mingle itself with the Light of the Paper, and obscure the Phænomenon thereof. These things being thus ordered, I found that if the refracting Angle of the Prism be turned upwards, so that the Paper may seem to be lifted upwards by the Refraction, its blue half will be lifted higher by the Refraction than its red half. But if the refracting Angle of the Prism be turned downward, so that the Paper may seem to be carried lower by the Refraction, its blue half will be carried something lower thereby than its red half. Wherefore in both Cases the Light which comes from the blue half of the Paper through the Prism to the Eye, does in like Circumstances suffer a greater Refraction than the Light which comes from the red half, and by consequence is more refrangible.

Illustration. In the eleventh Figure, MN represents the Window, and DE the Paper terminated with parallel Sides DJ and HE, and by the transverse Line FG distinguished into two halfs, the one DG of an intensely blue Colour, the other FE of an intensely red. And BACcab represents the Prism whose refracting Planes ABba and ACca meet in the Edge of the refracting Angle Aa. This Edge Aa being upward, is parallel both to the Horizon, and to the Parallel-Edges of the Paper DJ and HE, and the transverse Line FG is perpendicular to the Plane of the Window. And de represents the Image of the Paper seen by Refraction upwards in such manner, that the blue half DG is carried higher to dg than the red half FE is to fe, and therefore suffers a greater Refraction. If the Edge of the refracting Angle be turned downward, the Image of the Paper will be refracted downward; suppose to δε, and the blue half will be refracted lower to δγ than the red half is to πε.

Fig. 11.

Exper. 2. About the aforesaid Paper, whose two halfs were painted over with red and blue, and which was stiff like thin Pasteboard, I lapped several times a slender Thred of very black Silk, in such manner that the several parts of the Thred might appear upon the Colours like so many black Lines drawn over them, or like long and slender dark Shadows cast upon them. I might have drawn black Lines with a Pen, but the Threds were smaller and better defined. This Paper thus coloured and lined I set against a Wall perpendicularly to the Horizon, so that one of the Colours might stand to the Right Hand, and the other to the Left. Close before the Paper, at the Confine of the Colours below, I placed a Candle to illuminate the Paper strongly: 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 distance of six Feet, and one or two Inches from the Paper upon the Floor I erected a Glass Lens four Inches and a quarter broad, which might collect the Rays coming from the several Points of the Paper, and make them converge towards so many other Points at the same distance of six Feet, and one or two Inches on the other side of the Lens, and so form the Image of the coloured Paper upon a white Paper placed there, after the same manner that a Lens at a Hole in a Window casts the Images of Objects abroad upon a Sheet of white Paper in a dark Room. The aforesaid white Paper, erected perpendicular to the Horizon, and to the Rays which fell upon it from the Lens, I moved sometimes towards the Lens, sometimes from it, to find the Places where the Images of the blue and red Parts of the coloured Paper appeared most distinct. Those Places I easily knew by the Images of the black Lines which I had made by winding the Silk about the Paper. For the Images of those fine and slender Lines (which by reason of their Blackness were like Shadows on the Colours) were confused and scarce visible, unless when the Colours on either side of each Line were terminated most distinctly, Noting therefore, as diligently as I could, the Places where the Images of the red and blue halfs of the coloured Paper appeared most distinct, I found that where the red half of the Paper appeared distinct, the blue half appeared confused, so that the black Lines drawn upon it could scarce be seen; and on the contrary, where the blue half appeared most distinct, the red half appeared confused, so that the black Lines upon it were scarce visible. And between the two Places where these Images appeared distinct there was the distance of an Inch and a half; the distance of the white Paper from the Lens, when the Image of the red half of the coloured Paper appeared most distinct, being greater by an Inch and an half than the distance of the same white Paper from the Lens, when the Image of the blue half appeared most distinct. In like Incidences therefore of the blue and red upon the Lens, the blue was refracted more by the Lens than the red, so as to converge sooner by an Inch and a half, and therefore is more refrangible.

Illustration. In the twelfth Figure (p. 27), DE signifies the coloured Paper, DG the blue half, FE the red half, MN the Lens, HJ the white Paper in that Place where the red half with its black Lines appeared distinct, and hi the same Paper in that Place where the blue half appeared distinct. The Place hi was nearer to the Lens MN than the Place HJ by an Inch and an half.

Scholium. The same Things succeed, notwithstanding that some of the Circumstances be varied; as in the first Experiment when the Prism and Paper are any ways inclined to the Horizon, and in both when coloured Lines are drawn upon very black Paper. But in the Description of these Experiments, I have set down such Circumstances, by which either the Phænomenon might be render'd more conspicuous, or a Novice might more easily try them, or by which I did try them only. The same Thing, I have often done in the following Experiments: Concerning all which, this one Admonition may suffice. Now from these Experiments it follows not, that all the Light of the blue is more refrangible than all the Light of the red: For both Lights are mixed of Rays differently refrangible, so that in the red there are some Rays not less refrangible than those of the blue, and in the blue there are some Rays not more refrangible than those of the red: But these Rays, in proportion to the whole Light, are but few, and serve to diminish the Event of the Experiment, but are not able to destroy it. For, if the red and blue Colours were more dilute and weak, the distance of the Images would be less than an Inch and a half; and if they were more intense and full, that distance would be greater, as will appear hereafter. These Experiments may suffice for the Colours of Natural Bodies. For in the Colours made by the Refraction of Prisms, this Proposition will appear by the Experiments which are now to follow in the next Proposition.

PROP. II. Theor. II.

The Light of the Sun consists of Rays differently Refrangible.

The Proof by Experiments.

Fig. 12.

Fig. 13.

Exper. 3.

In a very dark Chamber, at a round Hole, about one third Part of an Inch broad, made in the Shut of a Window, I placed a Glass Prism, whereby the Beam of the Sun's Light, which came in at that Hole, might be refracted upwards toward the opposite Wall of the Chamber, and there form a colour'd Image of the Sun. The Axis of the Prism (that is, the Line passing through the middle of the Prism from one end of it to the other end parallel to the edge of the Refracting Angle) was in this and the following Experiments perpendicular to the incident Rays. About this Axis I turned the Prism slowly, and saw the refracted Light on the Wall, or coloured Image of the Sun, first to descend, and then to ascend. Between the Descent and Ascent, when the Image seemed Stationary, I stopp'd the Prism, and fix'd it in that Posture, that it should be moved no more. For in that Posture the Refractions of the Light at the two Sides of the refracting Angle, that is, at the Entrance of the Rays into the Prism, and at their going out of it, were equal to one another.[3] So also in other Experiments, as often as I would have the Refractions on both sides the Prism to be equal to one another, I noted the Place where the Image of the Sun formed by the refracted Light stood still between its two contrary Motions, in the common Period of its Progress and Regress; and when the Image fell upon that Place, I made fast the Prism. And in this Posture, as the most convenient, it is to be understood that all the Prisms are placed in the following Experiments, unless where some other Posture is described. The Prism therefore being placed in this Posture, I let the refracted Light fall perpendicularly upon a Sheet of white Paper at the opposite Wall of the Chamber, and observed the Figure and Dimensions 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 Semicircular Ends. On its Sides it was bounded pretty distinctly, but on its Ends very confusedly and indistinctly, the Light there decaying and vanishing by degrees. The Breadth of this Image answered 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 distant from the Prism, and at this distance that Breadth, if diminished by the Diameter of the Hole in the Window-shut, that is by a quarter of an Inch, subtended an Angle at the Prism 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 Rectilinear Sides about eight Inches; and the refracting Angle of the Prism, whereby so great a Length was made, was 64 degrees. With a less Angle the Length of the Image was less, the Breadth remaining the same. If the Prism was turned about its Axis that way which made the Rays emerge more obliquely out of the second refracting Surface of the Prism, the Image soon became an Inch or two longer, or more; and if the Prism was turned about the contrary way, so as to make the Rays fall more obliquely on the first refracting Surface, the Image soon became an Inch or two shorter. And therefore in trying this Experiment, I was as curious as I could be in placing the Prism by the above-mention'd Rule exactly in such a Posture, that the Refractions of the Rays at their Emergence out of the Prism might be equal to that at their Incidence on it. This Prism had some Veins running along within the Glass from one end to the other, which scattered some of the Sun's Light irregularly, but had no sensible Effect in increasing the Length of the coloured Spectrum. For I tried the same Experiment with other Prisms with the same Success. And particularly with a Prism which seemed free from such Veins, and whose refracting Angle was 62-1/2 Degrees, I found the Length of the Image 9-3/4 or 10 Inches at the distance of 18-1/2 Feet from the Prism, the Breadth of the Hole in the Window-shut being 1/4 of an Inch, as before. And because it is easy to commit a Mistake in placing the Prism in its due Posture, I repeated the Experiment four or five Times, and always found the Length of the Image that which is set down above. With another Prism of clearer Glass and better Polish, which seemed free from Veins, and whose refracting Angle was 63-1/2 Degrees, the Length of this Image at the same distance of 18-1/2 Feet was also about 10 Inches, or 10-1/8. Beyond these Measures for about a 1/4 or 1/3 of an Inch at either end of the Spectrum the Light of the Clouds seemed to be a little tinged with red and violet, but so very faintly, that I suspected that Tincture might either wholly, or in great Measure arise from some Rays of the Spectrum scattered irregularly by some Inequalities in the Substance and Polish of the Glass, and therefore I did not include it in these Measures. Now the different Magnitude of the hole in the Window-shut, and different thickness of the Prism where the Rays passed through it, and different inclinations of the Prism to the Horizon, made no sensible changes in the length of the Image. Neither did the different matter of the Prisms make any: for in a Vessel made of polished Plates of Glass cemented together in the shape of a Prism and filled with Water, there is the like Success of the Experiment according to the quantity of the Refraction. It is farther to be observed, that the Rays went on in right Lines from the Prism to the Image, and therefore at their very going out of the Prism had all that Inclination to one another from which the length of the Image proceeded, 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 possibly be so much inclined to one another.[4] For let EG [Fig. 13. (p. 27)] represent the Window-shut, F the hole made therein through which a beam of the Sun's Light was transmitted into the darkened Chamber, and ABC a Triangular Imaginary Plane whereby the Prism is feigned to be cut transversely through the middle of the Light. Or if you please, let ABC represent the Prism it self, looking directly towards the Spectator's Eye with its nearer end: And let XY be the Sun, MN the Paper upon which the Solar Image or Spectrum is cast, and PT the Image it self whose sides towards v and w are Rectilinear and Parallel, and ends towards P and T Semicircular. YKHP and XLJT are two Rays, the first of which comes from the lower part of the Sun to the higher part of the Image, and is refracted in the Prism at K and H, and the latter comes from the higher part of the Sun to the lower part of the Image, and is refracted at L and J. Since the Refractions on both sides the Prism are equal to one another, that is, the Refraction at K equal to the Refraction at J, and the Refraction at L equal to the Refraction at H, so that the Refractions of the incident Rays at K and L taken together, are equal to the Refractions of the emergent Rays at H and J taken together: it follows by adding equal things to equal things, that the Refractions at K and H taken together, are equal to the Refractions at J and L taken together, and therefore the two Rays being equally refracted, have the same Inclination to one another after Refraction which they had before; that is, the Inclination of half a Degree answering to the Sun's Diameter. For so great was the inclination of the Rays to one another before Refraction. So then, the length of the Image PT would by the Rules of Vulgar Opticks subtend an Angle of half a Degree at the Prism, and by Consequence be equal to the breadth vw; and therefore the Image would be round. Thus it would be were the two Rays XLJT and YKHP, and all the rest which form the Image PwTv, alike refrangible. And therefore seeing 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 suffer the greatest Refraction, must be more refrangible than those which go to the lower end T, unless the Inequality of Refraction be casual.

This Image or Spectrum PT was coloured, being red at its least refracted end T, and violet at its most refracted end P, and yellow green and blue in the intermediate Spaces. Which agrees with the first Proposition, that Lights which differ in Colour, do also differ in Refrangibility. The length of the Image in the foregoing Experiments, I measured from the faintest and outmost red at one end, to the faintest and outmost blue at the other end, excepting only a little Penumbra, whose breadth scarce exceeded a quarter of an Inch, as was said above.

Exper. 4. In the Sun's Beam which was propagated into the Room through the hole in the Window-shut, at the distance of some Feet from the hole, I held the Prism in such a Posture, that its Axis might be perpendicular to that Beam. Then I looked through the Prism upon the hole, and turning the Prism to and fro about its Axis, to make the Image of the Hole ascend and descend, when between its two contrary Motions it seemed Stationary, I stopp'd the Prism, that the Refractions of both sides of the refracting Angle might be equal to each other, as in the former Experiment. In this situation of the Prism viewing through it the said Hole, I observed the length of its refracted Image to be many times greater than its breadth, and that the most refracted part thereof appeared violet, the least refracted red, the middle parts blue, green and yellow in order. The same thing happen'd when I removed the Prism out of the Sun's Light, and looked through it upon the hole shining by the Light of the Clouds beyond it. And yet if the Refraction were done regularly according to one certain Proportion of the Sines of Incidence and Refraction as is vulgarly supposed, the refracted Image ought to have appeared round.

So then, by these two Experiments it appears, that in Equal Incidences there is a considerable inequality of Refractions. But whence this inequality arises, whether it be that some of the incident Rays are refracted more, and others less, constantly, or by chance, or that one and the same Ray is by Refraction disturbed, shatter'd, dilated, and as it were split and spread into many diverging Rays, as Grimaldo supposes, does not yet appear by these Experiments, but will appear by those that follow.

Exper. 5. Considering therefore, that if in the third Experiment the Image of the Sun should be drawn out into an oblong Form, either by a Dilatation of every Ray, or by any other casual inequality of the Refractions, the same oblong Image would by a second Refraction made sideways be drawn out as much in breadth by the like Dilatation of the Rays, or other casual inequality of the Refractions sideways, I tried what would be the Effects of such a second Refraction. For this end I ordered all things as in the third Experiment, and then placed a second Prism immediately after the first in a cross Position to it, that it might again refract the beam of the Sun's Light which came to it through the first Prism. In the first Prism this beam was refracted upwards, and in the second sideways. And I found that by the Refraction of the second Prism, the breadth of the Image was not increased, but its superior part, which in the first Prism suffered the greater Refraction, and appeared violet and blue, did again in the second Prism suffer a greater Refraction than its inferior part, which appeared red and yellow, and this without any Dilatation of the Image in breadth.

Illustration. Let S [Fig. 14, 15.] represent the Sun, F the hole in the Window, ABC the first Prism, DH the second Prism, Y the round Image of the Sun made by a direct beam of Light when the Prisms are taken away, PT the oblong Image of the Sun made by that beam passing through the first Prism alone, when the second Prism is taken away, and pt the Image made by the cross Refractions of both Prisms together. Now if the Rays which tend towards the several Points of the round Image Y were dilated and spread by the Refraction of the first Prism, so that they should not any longer go in single Lines to single Points, but that every Ray being split, shattered, 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 should go in those Planes to so many Lines reaching almost from one end of the Image PT to the other, and if that Image should thence become oblong: those Rays and their several parts tending towards the several Points of the Image PT ought to be again dilated and spread sideways by the transverse Refraction of the second Prism, so as to compose a four square Image, such as is represented at πτ. For the better understanding of which, let the Image PT be distinguished into five

Fig. 14

equal parts PQK, KQRL, LRSM, MSVN, NVT. And by the same irregularity that the orbicular Light Y is by the Refraction of the first Prism dilated and drawn out into a long Image PT, the Light PQK which takes up a space of the same length and breadth with the Light Y ought to be by the Refraction of the second Prism dilated and drawn out into the long Image πqkp, and the Light KQRL into the long Image kqrl, and the Lights LRSM, MSVN, NVT, into so many other long Images lrsm, msvn, nvtτ; and all these long Images would compose the four square Images πτ. Thus it ought to be were every Ray dilated by Refraction, and spread into a triangular Superficies of Rays diverging from the Point of Refraction. For the second Refraction would spread the Rays one way as much as the first doth another, and so dilate the Image in breadth as much as the first doth in length. And the same thing ought to happen, were some rays casually refracted more than others. But the Event is otherwise. The Image PT was not made broader by the Refraction of the second Prism, but only became oblique, as 'tis represented at pt, its upper end P being by the Refraction translated to a greater distance than its lower end T. So then the Light which went towards the upper end P of the Image, was (at equal Incidences) more refracted in the second Prism, than the Light which tended towards the lower end T, that is the blue and violet, than the red and yellow; and therefore was more refrangible. The same Light was by the Refraction of the first Prism translated farther from the place Y to which it tended before Refraction; and therefore suffered as well in the first Prism as in the second a greater Refraction than the rest of the Light, and by consequence was more refrangible than the rest, even before its incidence on the first Prism.

Sometimes I placed a third Prism after the second, and sometimes also a fourth after the third, by all which the Image might be often refracted sideways: but the Rays which were more refracted than the rest in the first Prism were also more refracted in all the rest, and that without any Dilatation of the Image sideways: and therefore those Rays for their constancy of a greater Refraction are deservedly reputed more refrangible.

Fig. 15

But that the meaning of this Experiment may more clearly appear, it is to be considered that the Rays which are equally refrangible do fall upon a Circle answering to the Sun's Disque. For this was proved in the third Experiment. By a Circle I understand not here a perfect geometrical Circle, but any orbicular Figure whose length is equal to its breadth, and which, as to Sense, may seem circular. Let therefore AG [in Fig. 15.] represent the Circle which all the most refrangible Rays propagated from the whole Disque of the Sun, would illuminate and paint upon the opposite Wall if they were alone; EL the Circle which all the least refrangible Rays would in like manner illuminate and paint if they were alone; BH, CJ, DK, the Circles which so many intermediate sorts of Rays would successively paint upon the Wall, if they were singly propagated from the Sun in successive order, the rest being always intercepted; and conceive that there are other intermediate Circles without Number, which innumerable other intermediate sorts of Rays would successively paint upon the Wall if the Sun should successively emit every sort apart. And seeing the Sun emits all these sorts at once, they must all together illuminate and paint innumerable equal Circles, of all which, being according to their degrees of Refrangibility placed in order in a continual Series, that oblong Spectrum PT is composed which I described in the third Experiment. Now if the Sun's circular Image Y [in Fig. 15.] which is made by an unrefracted beam of Light was by any Dilation of the single Rays, or by any other irregularity in the Refraction of the first Prism, converted into the oblong Spectrum, PT: then ought every Circle AG, BH, CJ, &c. in that Spectrum, by the cross Refraction of the second Prism again dilating or otherwise scattering the Rays as before, to be in like manner drawn out and transformed into an oblong Figure, and thereby the breadth of the Image PT would be now as much augmented as the length of the Image Y was before by the Refraction of the first Prism; and thus by the Refractions of both Prisms together would be formed a four square Figure pπtτ, as I described above. Wherefore since the breadth of the Spectrum PT is not increased by the Refraction sideways, it is certain that the Rays are not split or dilated, or otherways irregularly scatter'd by that Refraction, but that every Circle is by a regular and uniform Refraction translated entire into another Place, as the Circle AG by the greatest Refraction into the place ag, the Circle BH by a less Refraction into the place bh, the Circle CJ by a Refraction still less into the place ci, and so of the rest; by which means a new Spectrum pt inclined to the former PT is in like manner composed of Circles lying in a right Line; and these Circles must be of the same bigness with the former, because the breadths of all the Spectrums Y, PT and pt at equal distances from the Prisms are equal.

I considered farther, that by the breadth of the hole F through which the Light enters into the dark Chamber, there is a Penumbra made in the Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear Sides of the Spectrums PT and pt. I placed therefore at that hole a Lens or Object-glass of a Telescope which might cast the Image of the Sun distinctly on Y without any Penumbra at all, and found that the Penumbra of the rectilinear Sides of the oblong Spectrums PT and pt was also thereby taken away, so that those Sides appeared as distinctly defined as did the Circumference of the first Image Y. Thus it happens if the Glass of the Prisms be free from Veins, and their sides be accurately plane and well polished without those numberless Waves or Curles which usually arise from Sand-holes a little smoothed in polishing with Putty. If the Glass be only well polished and free from Veins, and the Sides not accurately plane, but a little Convex or Concave, as it frequently happens; yet may the three Spectrums Y, PT and pt want Penumbras, but not in equal distances from the Prisms. Now from this want of Penumbras, I knew more certainly that every one of the Circles was refracted according to some most regular, uniform and constant Law. For if there were any irregularity in the Refraction, the right Lines AE and GL, which all the Circles in the Spectrum PT do touch, could not by that Refraction be translated into the Lines ae and gl as distinct and straight as they were before, but there would arise in those translated Lines some Penumbra or Crookedness or Undulation, or other sensible Perturbation contrary to what is found by Experience. Whatsoever Penumbra or Perturbation should be made in the Circles by the cross Refraction of the second Prism, all that Penumbra or Perturbation would be conspicuous in the right Lines ae and gl which touch those Circles. And therefore since there is no such Penumbra or Perturbation in those right Lines, there must be none in the Circles. Since the distance between those Tangents or breadth of the Spectrum is not increased by the Refractions, the Diameters of the Circles are not increased thereby. Since those Tangents continue to be right Lines, every Circle which in the first Prism is more or less refracted, is exactly in the same proportion more or less refracted in the second. And seeing all these things continue to succeed after the same manner when the Rays are again in a third Prism, and again in a fourth refracted sideways, it is evident that the Rays of one and the same Circle, as to their degree of Refrangibility, continue always uniform and homogeneal to one another, and that those of several Circles do differ in degree of Refrangibility, and that in some certain and constant Proportion. Which is the thing I was to prove.

There is yet another Circumstance or two of this Experiment by which it becomes still more plain and convincing. Let the second Prism DH [in Fig. 16.] be placed not immediately after the first, but at some distance from it; suppose in the mid-way between it and the Wall on which the oblong Spectrum PT is cast, so that the Light from the first Prism may fall upon it in the form of an oblong Spectrum πτ parallel to this second Prism, and be refracted sideways to form the oblong Spectrum pt upon the Wall. And you will find as before, that this Spectrum pt is inclined to that Spectrum PT, which the first Prism forms alone without the second; the blue ends P and p being farther distant from one another than the red ones T and t, and by consequence that the Rays which go to the blue end π of the Image πτ, and which therefore suffer the greatest Refraction in the first Prism, are again in the second Prism more refracted than the rest.

Fig. 16.

Fig. 17.

The same thing I try'd also by letting the Sun's Light into a dark Room through two little round holes F and φ [in Fig. 17.] made in the Window, and with two parallel Prisms ABC and αβγ placed at those holes (one at each) refracting those two beams of Light to the opposite Wall of the Chamber, in such manner that the two colour'd Images PT and MN which they there painted were joined end to end and lay in one straight Line, the red end T of the one touching the blue end M of the other. For if these two refracted Beams were again by a third Prism DH placed cross to the two first, refracted sideways, and the Spectrums thereby translated to some other part of the Wall of the Chamber, suppose the Spectrum PT to pt and the Spectrum MN to mn, these translated Spectrums pt and mn would not lie in one straight Line with their ends contiguous as before, but be broken off from one another and become parallel, the blue end m of the Image mn being by a greater Refraction translated farther from its former place MT, than the red end t of the other Image pt from the same place MT; which puts the Proposition past Dispute. And this happens whether the third Prism DH be placed immediately after the two first, or at a great distance from them, so that the Light refracted in the two first Prisms be either white and circular, or coloured and oblong 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-shut a much broader hole being made to let into my darkned Chamber a large Beam of the Sun's Light; I placed a Prism behind the Shut in that beam to refract it towards the opposite Wall, and close behind the Prism I fixed one of the Boards, in such manner that the middle of the refracted Light might pass through the hole made in it, and the rest be intercepted by the Board. Then at the distance of about twelve Feet from the first Board I fixed the other Board in such manner that the middle of the refracted Light which came through the hole in the first Board, and fell upon the opposite Wall, might pass through the hole in this other Board, and the rest being intercepted by the Board might paint upon it the coloured Spectrum of the Sun. And close behind this Board I fixed another Prism to refract the Light which came through the hole. Then I returned speedily to the first Prism, and by turning it slowly to and fro about its Axis, I caused the Image which fell upon the second Board to move up and down upon that Board, that all its parts might successively pass through the hole in that Board and fall upon the Prism behind it. And in the mean time, I noted the places on the opposite Wall to which that Light after its Refraction in the second Prism did pass; and by the difference of the places I found that the Light which being most refracted in the first Prism did go to the blue end of the Image, was again more refracted in the second Prism than the Light which went to the red end of that Image, which proves as well the first Proposition as the second. And this happened whether the Axis of the two Prisms were parallel, or inclined to one another, and to the Horizon in any given Angles.

Illustration. Let F [in Fig. 18.] be the wide hole in the Window-shut, through which the Sun shines upon the first Prism ABC, and let the refracted Light fall upon the middle of the Board DE, and the middle part of that Light upon the hole G made in the middle part of that Board. Let this trajected part of that Light fall again upon the middle of the second Board de, and there paint such an oblong coloured Image of the Sun as was described in the third Experiment. By turning the Prism ABC slowly to and fro about its Axis, this Image will be made to move up and down the Board de, and by this means all its parts from one end to the other may be made to pass successively through the hole g which is made in the middle of that Board. In the mean while another Prism abc is to be fixed next after that hole g, to refract the trajected Light a second time. And these things being thus ordered, I marked the places M and N of the opposite Wall upon which the refracted Light fell, and found that whilst the two Boards and second Prism remained unmoved, those places by turning the first Prism about its Axis were changed perpetually. For when the lower part of the Light which fell upon the second Board de was cast through the hole g, it went to a lower place M on the Wall and when the higher part of that Light was cast through the same hole g, it went to a higher place N on the Wall, and when any intermediate part of the Light was cast through that hole, it went to some place on the Wall between M and N. The unchanged Position of the holes in the Boards, made the Incidence of the Rays upon the second Prism to be the same in all cases. And yet in that common Incidence some of the Rays were more refracted, and others less. And those were more refracted in this Prism, which by a greater Refraction in the first Prism were more turned out of the way, and therefore for their Constancy of being more refracted are deservedly called more refrangible.

Fig. 18.

Fig. 20.

Exper. 7. At two holes made near one another in my Window-shut I placed two Prisms, one at each, which might cast upon the opposite Wall (after the manner of the third Experiment) two oblong coloured Images of the Sun. And at a little distance from the Wall I placed a long slender Paper with straight and parallel edges, and ordered the Prisms and Paper so, that the red Colour of one Image might fall directly upon one half of the Paper, and the violet Colour of the other Image upon the other half of the same Paper; so that the Paper appeared of two Colours, red and violet, much after the manner of the painted Paper in the first and second Experiments. Then with a black Cloth I covered the Wall behind the Paper, that no Light might be reflected from it to disturb the Experiment, and viewing the Paper through a third Prism held parallel to it, I saw that half of it which was illuminated by the violet Light to be divided from the other half by a greater Refraction, especially 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 seemed contiguous at one of their Angles like the painted Paper in the first Experiment. Which also happened when the Paper was too broad.

Fig. 19.

Sometimes instead of the Paper I used a white Thred, and this appeared through the Prism divided into two parallel Threds as is represented in the nineteenth Figure, where DG denotes the Thred illuminated with violet Light from D to E and with red Light from F to G, and defg are the parts of the Thred seen by Refraction. If one half of the Thred be constantly illuminated with red, and the other half be illuminated with all the Colours successively, (which may be done by causing one of the Prisms to be turned about its Axis whilst the other remains unmoved) this other half in viewing the Thred through the Prism, will appear in a continual right Line with the first half when illuminated with red, and begin to be a little divided from it when illuminated with Orange, and remove farther from it when illuminated with yellow, and still farther when with green, and farther when with blue, and go yet farther off when illuminated with Indigo, and farthest when with deep violet. Which plainly shews, that the Lights of several Colours are more and more refrangible one than another, in this Order of their Colours, red, orange, yellow, green, blue, indigo, deep violet; and so proves as well the first Proposition as the second.

I caused also the coloured Spectrums PT [in Fig. 17.] and MN made in a dark Chamber by the Refractions of two Prisms to lie in a Right Line end to end, as was described above in the fifth Experiment, and viewing them through a third Prism held parallel to their Length, they appeared no longer in a Right Line, but became broken from one another, as they are represented at pt and mn, the violet end m of the Spectrum mn being by a greater Refraction translated farther from its former Place MT than the red end t of the other Spectrum pt.

I farther caused those two Spectrums PT [in Fig. 20.] and MN to become co-incident in an inverted Order of their Colours, the red end of each falling on the violet end of the other, as they are represented in the oblong Figure PTMN; and then viewing them through a Prism DH held parallel to their Length, they appeared not co-incident, as when view'd with the naked Eye, but in the form of two distinct Spectrums pt and mn crossing one another in the middle after the manner of the Letter X. Which shews that the red of the one Spectrum and violet of the other, which were co-incident at PN and MT, being parted from one another by a greater Refraction of the violet to p and m than of the red to n and t, do differ in degrees of Refrangibility.

I illuminated also a little Circular Piece of white Paper all over with the Lights of both Prisms intermixed, and when it was illuminated with the red of one Spectrum, and deep violet of the other, so as by the Mixture of those Colours to appear all over purple, I viewed the Paper, first at a less distance, and then at a greater, through a third Prism; and as I went from the Paper, the refracted Image thereof became more and more divided by the unequal Refraction of the two mixed Colours, and at length parted into two distinct Images, a red one and a violet one, whereof the violet was farthest from the Paper, and therefore suffered the greatest Refraction. And when that Prism at the Window, which cast the violet on the Paper was taken away, the violet Image disappeared; but when the other Prism was taken away the red vanished; which shews, that these two Images were nothing else than the Lights of the two Prisms, which had been intermixed on the purple Paper, but were parted again by their unequal Refractions made in the third Prism, through which the Paper was view'd. This also was observable, that if one of the Prisms at the Window, suppose that which cast the violet on the Paper, was turned about its Axis to make all the Colours in this order, violet, indigo, blue, green, yellow, orange, red, fall successively on the Paper from that Prism, the violet Image changed Colour accordingly, turning successively to indigo, blue, green, yellow and red, and in changing Colour came nearer and nearer to the red Image made by the other Prism, until when it was also red both Images became fully co-incident.

I placed also two Paper Circles very near one another, the one in the red Light of one Prism, and the other in the violet Light of the other. The Circles were each of them an Inch in diameter, and behind them the Wall was dark, that the Experiment might not be disturbed by any Light coming from thence. These Circles thus illuminated, I viewed through a Prism, so held, that the Refraction might be made towards the red Circle, and as I went from them they came nearer and nearer together, and at length became co-incident; and afterwards when I went still farther off, they parted again in a contrary Order, the violet by a greater Refraction being carried beyond the red.

Exper. 8. In Summer, when the Sun's Light uses to be strongest, I placed a Prism at the Hole of the Window-shut, as in the third Experiment, yet so that its Axis might be parallel to the Axis of the World, and at the opposite Wall in the Sun's refracted Light, I placed an open Book. Then going six Feet and two Inches from the Book, I placed there the above-mentioned Lens, by which the Light reflected from the Book might be made to converge and meet again at the distance of six Feet and two Inches behind the Lens, and there paint the Species of the Book upon a Sheet of white Paper much after the manner of the second Experiment. The Book and Lens being made fast, I noted the Place where the Paper was, when the Letters of the Book, illuminated by the fullest red Light of the Solar Image falling upon it, did cast their Species on that Paper most distinctly: And then I stay'd till by the Motion of the Sun, and consequent Motion of his Image on the Book, all the Colours from that red to the middle of the blue pass'd over those Letters; and when those Letters were illuminated by that blue, I noted again the Place of the Paper when they cast their Species most distinctly upon it: And I found that this last Place of the Paper was nearer to the Lens than its former Place by about two Inches and an half, or two and three quarters. So much sooner therefore did the Light in the violet end of the Image by a greater Refraction converge and meet, than the Light in the red end. But in trying this, the Chamber was as dark as I could make it. For, if these Colours be diluted and weakned by the Mixture of any adventitious Light, the distance between the Places of the Paper will not be so great. This distance in the second Experiment, where the Colours of natural Bodies were made use of, was but an Inch and an half, by reason of the Imperfection of those Colours. Here in the Colours of the Prism, which are manifestly more full, intense, and lively than those of natural Bodies, the distance is two Inches and three quarters. And were the Colours still more full, I question not but that the distance would be considerably greater. For the coloured Light of the Prism, by the interfering of the Circles described in the second Figure of the fifth Experiment, and also by the Light of the very bright Clouds next the Sun's Body intermixing with these Colours, and by the Light scattered by the Inequalities in the Polish of the Prism, was so very much compounded, that the Species which those faint and dark Colours, the indigo and violet, cast upon the Paper were not distinct enough to be well observed.

Exper. 9. A Prism, whose two Angles at its Base were equal to one another, and half right ones, and the third a right one, I placed in a Beam of the Sun's Light let into a dark Chamber through a Hole in the Window-shut, as in the third Experiment. And turning the Prism slowly about its Axis, until all the Light which went through one of its Angles, and was refracted by it began to be reflected by its Base, at which till then it went out of the Glass, I observed that those Rays which had suffered the greatest Refraction were sooner reflected than the rest. I conceived therefore, that those Rays of the reflected Light, which were most refrangible, did first of all by a total Reflexion become more copious in that Light than the rest, and that afterwards the rest also, by a total Reflexion, became as copious as these. To try this, I made the reflected Light pass through another Prism, and being refracted by it to fall afterwards upon a Sheet of white Paper placed at some distance behind it, and there by that Refraction to paint the usual Colours of the Prism. And then causing the first Prism to be turned about its Axis as above, I observed that when those Rays, which in this Prism had suffered the greatest Refraction, and appeared of a blue and violet Colour began to be totally reflected, the blue and violet Light on the Paper, which was most refracted in the second Prism, received a sensible Increase above that of the red and yellow, which was least refracted; and afterwards, when the rest of the Light which was green, yellow, and red, began to be totally reflected in the first Prism, the Light of those Colours on the Paper received as great an Increase as the violet and blue had done before. Whence 'tis manifest, that the Beam of Light reflected by the Base of the Prism, being augmented first by the more refrangible Rays, and afterwards by the less refrangible ones, is compounded of Rays differently refrangible. And that all such reflected Light is of the same Nature with the Sun's Light before its Incidence on the Base of the Prism, no Man ever doubted; it being generally allowed, that Light by such Reflexions suffers no Alteration in its Modifications and Properties. I do not here take Notice of any Refractions made in the sides of the first Prism, because the Light enters it perpendicularly at the first side, and goes out perpendicularly at the second side, and therefore suffers none. So then, the Sun's incident Light being of the same Temper and Constitution with his emergent Light, and the last being compounded of Rays differently refrangible, the first must be in like manner compounded.

Fig. 21.

Illustration. In the twenty-first Figure, ABC is the first Prism, BC its Base, B and C its equal Angles at the Base, each of 45 Degrees, A its rectangular Vertex, FM a beam of the Sun's Light let into a dark Room through a hole F one third part of an Inch broad, M its Incidence on the Base of the Prism, MG a less refracted Ray, MH a more refracted Ray, MN the beam of Light reflected from the Base, VXY the second Prism by which this beam in passing through it is refracted, Nt the less refracted Light of this beam, and Np the more refracted part thereof. When the first Prism ABC is turned about its Axis according to the order of the Letters ABC, the Rays MH emerge more and more obliquely out of that Prism, and at length after their most oblique Emergence are reflected towards N, and going on to p do increase the Number of the Rays Np. Afterwards by continuing the Motion of the first Prism, the Rays MG are also reflected to N and increase the number of the Rays Nt. And therefore the Light MN admits into its Composition, first the more refrangible Rays, and then the less refrangible Rays, and yet after this Composition is of the same Nature with the Sun's immediate Light FM, the Reflexion of the specular Base BC causing no Alteration therein.

Exper. 10. Two Prisms, which were alike in Shape, I tied so together, that their Axis and opposite Sides being parallel, they composed a Parallelopiped. And, the Sun shining into my dark Chamber through a little hole in the Window-shut, I placed that Parallelopiped in his beam at some distance from the hole, in such a Posture, that the Axes of the Prisms might be perpendicular to the incident Rays, and that those Rays being incident upon the first Side of one Prism, might go on through the two contiguous Sides of both Prisms, and emerge out of the last Side of the second Prism. This Side being parallel to the first Side of the first Prism, caused the emerging Light to be parallel to the incident. Then, beyond these two Prisms I placed a third, which might refract that emergent Light, and by that Refraction cast the usual Colours of the Prism upon the opposite Wall, or upon a sheet of white Paper held at a convenient Distance behind the Prism for that refracted Light to fall upon it. After this I turned the Parallelopiped about its Axis, and found that when the contiguous Sides of the two Prisms became so oblique to the incident Rays, that those Rays began all of them to be reflected, those Rays which in the third Prism had suffered the greatest Refraction, and painted the Paper with violet and blue, were first of all by a total Reflexion taken out of the transmitted Light, the rest remaining and on the Paper painting their Colours of green, yellow, orange and red, as before; and afterwards by continuing the Motion of the two Prisms, the rest of the Rays also by a total Reflexion vanished in order, according to their degrees of Refrangibility. The Light therefore which emerged out of the two Prisms is compounded of Rays differently refrangible, seeing the more refrangible Rays may be taken out of it, while the less refrangible remain. But this Light being trajected only through the parallel Superficies of the two Prisms, if it suffer'd any change by the Refraction of one Superficies it lost that Impression by the contrary Refraction of the other Superficies, and so being restor'd to its pristine Constitution, became of the same Nature and Condition as at first before its Incidence on those Prisms; and therefore, before its Incidence, was as much compounded of Rays differently refrangible, as afterwards.

Fig. 22.

Illustration. In the twenty second Figure ABC and BCD are the two Prisms tied together in the form of a Parallelopiped, their Sides BC and CB being contiguous, and their Sides AB and CD parallel. And HJK is the third Prism, by which the Sun's Light propagated through the hole F into the dark Chamber, and there passing through those sides of the Prisms AB, BC, CB and CD, is refracted at O to the white Paper PT, falling there partly upon P by a greater Refraction, partly upon T by a less Refraction, and partly upon R and other intermediate places by intermediate Refractions. By turning the Parallelopiped ACBD about its Axis, according to the order of the Letters A, C, D, B, at length when the contiguous Planes BC and CB become sufficiently oblique to the Rays FM, which are incident upon them at M, there will vanish totally out of the refracted Light OPT, first of all the most refracted Rays OP, (the rest OR and OT remaining as before) then the Rays OR and other intermediate ones, and lastly, the least refracted Rays OT. For when the Plane BC becomes sufficiently oblique to the Rays incident upon it, those Rays will begin to be totally reflected by it towards N; and first the most refrangible Rays will be totally reflected (as was explained in the preceding Experiment) and by Consequence must first disappear at P, and afterwards the rest as they are in order totally reflected to N, they must disappear in the same order at R and T. So then the Rays which at O suffer the greatest Refraction, may be taken out of the Light MO whilst the rest of the Rays remain in it, and therefore that Light MO is compounded of Rays differently refrangible. And because the Planes AB and CD are parallel, and therefore by equal and contrary Refractions destroy one anothers Effects, the incident Light FM must be of the same Kind and Nature with the emergent Light MO, and therefore doth also consist of Rays differently refrangible. These two Lights FM and MO, before the most refrangible Rays are separated out of the emergent Light MO, agree in Colour, and in all other Properties so far as my Observation reaches, and therefore are deservedly reputed of the same Nature and Constitution, and by Consequence the one is compounded as well as the other. But after the most refrangible Rays begin to be totally reflected, and thereby separated out of the emergent Light MO, that Light changes its Colour from white to a dilute and faint yellow, a pretty good orange, a very full red successively, and then totally vanishes. For after the most refrangible Rays which paint the Paper at P with a purple Colour, are by a total Reflexion taken out of the beam of Light MO, the rest of the Colours which appear on the Paper at R and T being mix'd in the Light MO compound there a faint yellow, and after the blue and part of the green which appear on the Paper between P and R are taken away, the rest which appear between R and T (that is the yellow, orange, red and a little green) being mixed in the beam MO compound there an orange; and when all the Rays are by Reflexion taken out of the beam MO, except the least refrangible, which at T appear of a full red, their Colour is the same in that beam MO as afterwards at T, the Refraction of the Prism HJK serving only to separate the differently refrangible Rays, without making any Alteration in their Colours, as shall be more fully proved hereafter. All which confirms as well the first Proposition as the second.

Scholium. If this Experiment and the former be conjoined and made one by applying a fourth Prism VXY [in Fig. 22.] to refract the reflected beam MN towards tp, the Conclusion will be clearer. For then the Light Np which in the fourth Prism is more refracted, will become fuller and stronger when the Light OP, which in the third Prism HJK is more refracted, vanishes at P; and afterwards when the less refracted Light OT vanishes at T, the less refracted Light Nt will become increased whilst the more refracted Light at p receives no farther increase. And as the trajected beam MO in vanishing is always of such a Colour as ought to result from the mixture of the Colours which fall upon the Paper PT, so is the reflected beam MN always of such a Colour as ought to result from the mixture of the Colours which fall upon the Paper pt. For when the most refrangible Rays are by a total Reflexion taken out of the beam MO, and leave that beam of an orange Colour, the Excess of those Rays in the reflected Light, does not only make the violet, indigo and blue at p more full, but also makes the beam MN change from the yellowish Colour of the Sun's Light, to a pale white inclining to blue, and afterward recover its yellowish Colour again, so soon as all the rest of the transmitted Light MOT is reflected.

Now seeing that in all this variety of Experiments, whether the Trial be made in Light reflected, and that either from natural Bodies, as in the first and second Experiment, or specular, as in the ninth; or in Light refracted, and that either before the unequally refracted Rays are by diverging separated from one another, and losing their whiteness which they have altogether, appear severally of several Colours, as in the fifth Experiment; or after they are separated from one another, and appear colour'd as in the sixth, seventh, and eighth Experiments; or in Light trajected through parallel Superficies, destroying each others Effects, as in the tenth Experiment; there are always found Rays, which at equal Incidences on the same Medium suffer unequal Refractions, and that without any splitting or dilating of single Rays, or contingence in the inequality of the Refractions, as is proved in the fifth and sixth Experiments. And seeing the Rays which differ in Refrangibility may be parted and sorted from one another, and that either by Refraction as in the third Experiment, or by Reflexion as in the tenth, and then the several sorts apart at equal Incidences suffer unequal Refractions, and those sorts are more refracted than others after Separation, which were more refracted before it, as in the sixth and following Experiments, and if the Sun's Light be trajected through three or more cross Prisms successively, those Rays which in the first Prism are refracted more than others, are in all the following Prisms refracted more than others in the same Rate and Proportion, as appears by the fifth Experiment; it's manifest that the Sun's Light is an heterogeneous Mixture of Rays, some of which are constantly more refrangible than others, as was proposed.

PROP. III. Theor. III.

The Sun's Light consists of Rays differing in Reflexibility, and those Rays are more reflexible than others which are more refrangible.

This is manifest by the ninth and tenth Experiments: For in the ninth Experiment, by turning the Prism about its Axis, until the Rays within it which in going out into the Air were refracted by its Base, became so oblique to that Base, as to begin to be totally reflected thereby; those Rays became first of all totally reflected, which before at equal Incidences with the rest had suffered the greatest Refraction. And the same thing happens in the Reflexion made by the common Base of the two Prisms in the tenth Experiment.

PROP. IV. Prob. I.

To separate from one another the heterogeneous Rays of compound Light.

Fig. 23.

The heterogeneous Rays are in some measure separated from one another by the Refraction of the Prism in the third Experiment, and in the fifth Experiment, by taking away the Penumbra from the rectilinear sides of the coloured Image, that Separation in those very rectilinear sides or straight edges of the Image becomes perfect. But in all places between those rectilinear edges, those innumerable Circles there described, which are severally illuminated by homogeneal Rays, by interfering with one another, and being every where commix'd, do render the Light sufficiently compound. But if these Circles, whilst their Centers keep their Distances and Positions, could be made less in Diameter, their interfering one with another, and by Consequence the Mixture of the heterogeneous Rays would be proportionally diminish'd. In the twenty third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many sorts of Rays flowing from the same disque of the Sun, do in the third Experiment illuminate; of all which and innumerable other intermediate ones lying in a continual Series between the two rectilinear and parallel edges of the Sun's oblong Image PT, that Image is compos'd, as was explained in the fifth Experiment. And let ag, bh, ci, dk, el, fm be so many less Circles lying in a like continual Series between two parallel right Lines af and gm with the same distances between their Centers, and illuminated by the same sorts of Rays, that is the Circle ag with the same sort by which the corresponding Circle AG was illuminated, and the Circle bh with the same sort by which the corresponding Circle BH was illuminated, and the rest of the Circles ci, dk, el, fm respectively, with the same sorts of Rays by which the several corresponding Circles CJ, DK, EL, FM were illuminated. In the Figure PT composed of the greater Circles, three of those Circles AG, BH, CJ, are so expanded into one another, that the three sorts of Rays by which those Circles are illuminated, together with other innumerable sorts of intermediate Rays, are mixed at QR in the middle of the Circle BH. And the like Mixture happens throughout almost the whole length of the Figure PT. But in the Figure pt composed of the less Circles, the three less Circles ag, bh, ci, which answer to those three greater, do not extend into one another; nor are there any where mingled so much as any two of the three sorts of Rays by which those Circles are illuminated, and which in the Figure PT are all of them intermingled at BH.

Now he that shall thus consider it, will easily understand that the Mixture is diminished in the same Proportion with the Diameters of the Circles. If the Diameters of the Circles whilst their Centers remain the same, be made three times less than before, the Mixture will be also three times less; if ten times less, the Mixture will be ten times less, and so of other Proportions. That is, the Mixture of the Rays in the greater Figure PT will be to their Mixture in the less pt, as the Latitude of the greater Figure is to the Latitude of the less. For the Latitudes of these Figures are equal to the Diameters of their Circles. And hence it easily follows, that the Mixture of the Rays in the refracted Spectrum pt is to the Mixture of the Rays in the direct and immediate Light of the Sun, as the breadth of that Spectrum is to the difference between the length and breadth of the same Spectrum.

So then, if we would diminish the Mixture of the Rays, we are to diminish the Diameters of the Circles. Now these would be diminished if the Sun's Diameter to which they answer could be made less than it is, or (which comes to the same Purpose) if without Doors, at a great distance from the Prism towards the Sun, some opake Body were placed, with a round hole in the middle of it, to intercept all the Sun's Light, excepting so much as coming from the middle of his Body could pass through that Hole to the Prism. For so the Circles AG, BH, and the rest, would not any longer answer to the whole Disque of the Sun, but only to that Part of it which could be seen from the Prism through that Hole, that it is to the apparent Magnitude of that Hole view'd from the Prism. But that these Circles may answer more distinctly to that Hole, a Lens is to be placed by the Prism to cast the Image of the Hole, (that is, every one of the Circles AG, BH, &c.) distinctly upon the Paper at PT, after such a manner, as by a Lens placed at a Window, the Species of Objects abroad are cast distinctly upon a Paper within the Room, and the rectilinear Sides of the oblong Solar Image in the fifth Experiment became distinct without any Penumbra. If this be done, it will not be necessary to place that Hole very far off, no not beyond the Window. And therefore instead of that Hole, I used the Hole in the Window-shut, as follows.

Exper. 11. In the Sun's Light let into my darken'd Chamber through a small round Hole in my Window-shut, at about ten or twelve Feet from the Window, I placed a Lens, by which the Image of the Hole might be distinctly cast upon a Sheet of white Paper, placed at the distance of six, eight, ten, or twelve Feet from the Lens. For, according to the difference of the Lenses I used various distances, which I think not worth the while to describe. Then immediately after the Lens I placed a Prism, by which the trajected Light might be refracted either upwards or sideways, and thereby the round Image, which the Lens alone did cast upon the Paper might be drawn out into a long one with Parallel Sides, as in the third Experiment. This oblong Image I let fall upon another Paper at about the same distance from the Prism as before, moving the Paper either towards the Prism or from it, until I found the just distance where the Rectilinear Sides of the Image became most distinct. For in this Case, the Circular Images of the Hole, which compose that Image after the same manner that the Circles ag, bh, ci, &c. do the Figure pt [in Fig. 23.] were terminated most distinctly without any Penumbra, and therefore extended into one another the least that they could, and by consequence the Mixture of the heterogeneous Rays was now the least of all. By this means I used to form an oblong Image (such as is pt) [in Fig. 23, and 24.] of Circular Images of the Hole, (such as are ag, bh, ci, &c.) and by using a greater or less Hole in the Window-shut, I made the Circular Images ag, bh, ci, &c. of which it was formed, to become greater or less at pleasure, and thereby the Mixture of the Rays in the Image pt to be as much, or as little as I desired.

Fig. 24.

Illustration. In the twenty-fourth Figure, F represents the Circular Hole in the Window-shut, MN the Lens, whereby the Image or Species of that Hole is cast distinctly upon a Paper at J, ABC the Prism, whereby the Rays are at their emerging out of the Lens refracted from J towards another Paper at pt, and the round Image at J is turned into an oblong Image pt falling on that other Paper. This Image pt consists of Circles placed one after another in a Rectilinear Order, as was sufficiently explained in the fifth Experiment; and these Circles are equal to the Circle J, and consequently answer in magnitude to the Hole F; and therefore by diminishing that Hole they may be at pleasure diminished, whilst their Centers remain in their Places. By this means I made the Breadth of the Image pt to be forty times, and sometimes sixty or seventy times less than its Length. As for instance, if the Breadth of the Hole F be one tenth of an Inch, and MF the distance of the Lens from the Hole be 12 Feet; and if pB or pM the distance of the Image pt from the Prism or Lens be 10 Feet, and the refracting Angle of the Prism be 62 Degrees, the Breadth of the Image pt will be one twelfth of an Inch, and the Length about six Inches, and therefore the Length to the Breadth as 72 to 1, and by consequence the Light of this Image 71 times less compound than the Sun's direct Light. And Light thus far simple and homogeneal, is sufficient for trying all the Experiments in this Book about simple Light. For the Composition of heterogeneal Rays is in this Light so little, that it is scarce to be discovered and perceiv'd by Sense, except perhaps in the indigo and violet. For these being dark Colours do easily suffer a sensible Allay by that little scattering Light which uses to be refracted irregularly by the Inequalities of the Prism.

Yet instead of the Circular Hole F, 'tis better to substitute an oblong Hole shaped like a long Parallelogram with its Length parallel to the Prism ABC. For if this Hole be an Inch or two long, and but a tenth or twentieth Part of an Inch broad, or narrower; the Light of the Image pt will be as simple as before, or simpler, and the Image will become much broader, and therefore more fit to have Experiments try'd in its Light than before.

Instead of this Parallelogram Hole may be substituted a triangular one of equal Sides, whose Base, for instance, is about the tenth Part of an Inch, and its Height an Inch or more. For by this means, if the Axis of the Prism be parallel to the Perpendicular of the Triangle, the Image pt [in Fig. 25.] will now be form'd of equicrural Triangles ag, bh, ci, dk, el, fm, &c. and innumerable other intermediate ones answering to the triangular Hole in Shape and Bigness, and lying one after another in a continual Series between two Parallel Lines af and gm. These Triangles are a little intermingled at their Bases, but not at their Vertices; and therefore the Light on the brighter Side af of the Image, where the Bases of the Triangles are, is a little compounded, but on the darker Side gm is altogether uncompounded, and in all Places between the Sides the Composition is proportional to the distances of the Places from that obscurer Side gm. And having a Spectrum pt of such a Composition, we may try Experiments either in its stronger and less simple Light near the Side af, or in its weaker and simpler Light near the other Side gm, as it shall seem most convenient.

Fig. 25.

But in making Experiments of this kind, the Chamber ought to be made as dark as can be, lest any Foreign Light mingle it self with the Light of the Spectrum pt, and render it compound; especially if we would try Experiments in the more simple Light next the Side gm of the Spectrum; which being fainter, will have a less proportion to the Foreign Light; and so by the mixture of that Light be more troubled, and made more compound. The Lens also ought to be good, such as may serve for optical Uses, and the Prism ought to have a large Angle, suppose of 65 or 70 Degrees, and to be well wrought, being made of Glass free from Bubbles and Veins, with its Sides not a little convex or concave, as usually happens, but truly plane, and its Polish elaborate, as in working Optick-glasses, and not such as is usually wrought with Putty, whereby the edges of the Sand-holes being worn away, there are left all over the Glass a numberless Company of very little convex polite Risings like Waves. The edges also of the Prism and Lens, so far as they may make any irregular Refraction, must be covered with a black Paper glewed on. And all the Light of the Sun's Beam let into the Chamber, which is useless and unprofitable to the Experiment, ought to be intercepted with black Paper, or other black Obstacles. For otherwise the useless Light being reflected every way in the Chamber, will mix with the oblong Spectrum, and help to disturb it. In trying these Things, so much diligence is not altogether necessary, but it will promote the Success of the Experiments, and by a very scrupulous Examiner of Things deserves to be apply'd. It's difficult to get Glass Prisms fit for this Purpose, and therefore I used sometimes prismatick Vessels made with pieces of broken Looking-glasses, and filled with Rain Water. And to increase the Refraction, I sometimes impregnated the Water strongly with Saccharum Saturni.

PROP. V. Theor. IV.

Homogeneal Light is refracted regularly without any Dilatation splitting or shattering of the Rays, and the confused Vision of Objects seen through refracting Bodies by heterogeneal Light arises from the different Refrangibility of several sorts of Rays.

The first Part of this Proposition has been already sufficiently proved in the fifth Experiment, and will farther appear by the Experiments which follow.

Exper. 12. In the middle of a black Paper I made a round Hole about a fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the Spectrum of homogeneal Light described in the former Proposition, so to fall, that some part of the Light might pass through the Hole of the Paper. This transmitted part of the Light I refracted with a Prism placed behind the Paper, and letting this refracted Light fall perpendicularly upon a white Paper two or three Feet distant from the Prism, I found that the Spectrum formed on the Paper by this Light was not oblong, as when 'tis made (in the third Experiment) by refracting the Sun's compound Light, but was (so far as I could judge by my Eye) perfectly circular, the Length being no greater than the Breadth. Which shews, that this Light is refracted regularly without any Dilatation of the Rays.

Exper. 13. In the homogeneal Light I placed a Paper Circle of a quarter of an Inch in diameter, and in the Sun's unrefracted heterogeneal white Light I placed another Paper Circle of the same Bigness. And going from the Papers to the distance of some Feet, I viewed both Circles through a Prism. The Circle illuminated by the Sun's heterogeneal Light appeared very oblong, as in the fourth Experiment, the Length being many times greater than the Breadth; but the other Circle, illuminated with homogeneal Light, appeared circular and distinctly defined, as when 'tis view'd with the naked Eye. Which proves the whole Proposition.

Exper. 14. In the homogeneal Light I placed Flies, and such-like minute Objects, and viewing them through a Prism, I saw their Parts as distinctly defined, as if I had viewed them with the naked Eye. The same Objects placed in the Sun's unrefracted heterogeneal Light, which was white, I viewed also through a Prism, and saw them most confusedly defined, so that I could not distinguish their smaller Parts from one another. I placed also the Letters of a small print, one while in the homogeneal Light, and then in the heterogeneal, and viewing them through a Prism, they appeared in the latter Case so confused and indistinct, that I could not read them; but in the former they appeared so distinct, that I could read readily, and thought I saw them as distinct, as when I view'd them with my naked Eye. In both Cases I view'd the same Objects, through the same Prism at the same distance from me, and in the same Situation. There was no difference, but in the Light by which the Objects were illuminated, and which in one Case was simple, and in the other compound; and therefore, the distinct Vision in the former Case, and confused in the latter, could arise from nothing else than from that difference of the Lights. Which proves the whole Proposition.

And in these three Experiments it is farther very remarkable, that the Colour of homogeneal Light was never changed by the Refraction.

PROP. VI. Theor. V.

The Sine of Incidence of every Ray considered apart, is to its Sine of Refraction in a given Ratio.

That every Ray consider'd apart, is constant to it self in some degree of Refrangibility, is sufficiently manifest out of what has been said. Those Rays, which in the first Refraction, are at equal Incidences most refracted, are also in the following Refractions at equal Incidences most refracted; and so of the least refrangible, and the rest which have any mean Degree of Refrangibility, as is manifest by the fifth, sixth, seventh, eighth, and ninth Experiments. And those which the first Time at like Incidences are equally refracted, are again at like Incidences equally and uniformly refracted, and that whether they be refracted before they be separated from one another, as in the fifth Experiment, or whether they be refracted apart, as in the twelfth, thirteenth and fourteenth Experiments. The Refraction therefore of every Ray apart is regular, and what Rule that Refraction observes we are now to shew.[5]

The late Writers in Opticks teach, that the Sines of Incidence are in a given Proportion to the Sines of Refraction, as was explained in the fifth Axiom, and some by Instruments fitted for measuring of Refractions, or otherwise experimentally examining this Proportion, do acquaint us that they have found it accurate. But whilst they, not understanding the different Refrangibility of several Rays, conceived them all to be refracted according to one and the same Proportion, 'tis to be presumed that they adapted their Measures only to the middle of the refracted Light; so that from their Measures we may conclude only that the Rays which have a mean Degree of Refrangibility, that is, those which when separated from the rest appear green, are refracted according to a given Proportion of their Sines. And therefore we are now to shew, that the like given Proportions obtain in all the rest. That it should be so is very reasonable, Nature being ever conformable to her self; but an experimental Proof is desired. And such a Proof will be had, if we can shew that the Sines of Refraction of Rays differently refrangible are one to another in a given Proportion when their Sines of Incidence are equal. For, if the Sines of Refraction of all the Rays are in given Proportions to the Sine of Refractions of a Ray which has a mean Degree of Refrangibility, and this Sine is in a given Proportion to the equal Sines of Incidence, those other Sines of Refraction will also be in given Proportions to the equal Sines of Incidence. Now, when the Sines of Incidence are equal, it will appear by the following Experiment, that the Sines of Refraction are in a given Proportion to one another.

Fig. 26.

Exper. 15. The Sun shining into a dark Chamber through a little round Hole in the Window-shut, let S [in Fig. 26.] represent his round white Image painted on the opposite Wall by his direct Light, PT his oblong coloured Image made by refracting that Light with a Prism placed at the Window; and pt, or 2p 2t, 3p 3t, his oblong colour'd Image made by refracting again the same Light sideways with a second Prism placed immediately after the first in a cross Position to it, as was explained in the fifth Experiment; that is to say, pt when the Refraction of the second Prism is small, 2p 2t when its Refraction is greater, and 3p 3t when it is greatest. For such will be the diversity of the Refractions, if the refracting Angle of the second Prism be of various Magnitudes; suppose of fifteen or twenty Degrees to make the Image pt, of thirty or forty to make the Image 2p 2t, and of sixty to make the Image 3p 3t. But for want of solid Glass Prisms with Angles of convenient Bignesses, there may be Vessels made of polished Plates of Glass cemented together in the form of Prisms and filled with Water. These things being thus ordered, I observed that all the solar Images or coloured Spectrums PT, pt, 2p 2t, 3p 3t did very nearly converge to the place S on which the direct Light of the Sun fell and painted his white round Image when the Prisms were taken away. The Axis of the Spectrum PT, that is the Line drawn through the middle of it parallel to its rectilinear Sides, did when produced pass exactly through the middle of that white round Image S. And when the Refraction of the second Prism was equal to the Refraction of the first, the refracting Angles of them both being about 60 Degrees, the Axis of the Spectrum 3p 3t made by that Refraction, did when produced pass also through the middle of the same white round Image S. But when the Refraction of the second Prism was less than that of the first, the produced Axes of the Spectrums tp or 2t 2p made by that Refraction did cut the produced Axis of the Spectrum TP in the points m and n, a little beyond the Center of that white round Image S. Whence the proportion of the Line 3tT to the Line 3pP was a little greater than the Proportion of 2tT or 2pP, and this Proportion a little greater than that of tT to pP. Now when the Light of the Spectrum PT falls perpendicularly upon the Wall, those Lines 3tT, 3pP, and 2tT, and 2pP, and tT, pP, are the Tangents of the Refractions, and therefore by this Experiment the Proportions of the Tangents of the Refractions are obtained, from whence the Proportions of the Sines being derived, they come out equal, so far as by viewing the Spectrums, and using some mathematical Reasoning I could estimate. For I did not make an accurate Computation. So then the Proposition holds true in every Ray apart, so far as appears by Experiment. And that it is accurately true, may be demonstrated upon this Supposition. That Bodies refract Light by acting upon its Rays in Lines perpendicular to their Surfaces. But in order to this Demonstration, I must distinguish the Motion of every Ray into two Motions, the one perpendicular to the refracting Surface, the other parallel to it, and concerning the perpendicular Motion lay down the following Proposition.

If any Motion or moving thing whatsoever be incident with any Velocity on any broad and thin space terminated on both sides by two parallel Planes, and in its Passage through that space be urged perpendicularly towards the farther Plane by any force which at given distances from the Plane is of given Quantities; the perpendicular velocity of that Motion or Thing, at its emerging out of that space, shall be always equal to the square Root of the sum of the square of the perpendicular velocity of that Motion or Thing at its Incidence on that space; and of the square of the perpendicular velocity which that Motion or Thing would have at its Emergence, if at its Incidence its perpendicular velocity was infinitely little.

And the same Proposition holds true of any Motion or Thing perpendicularly retarded in its passage through that space, if instead of the sum of the two Squares you take their difference. The Demonstration Mathematicians will easily find out, and therefore I shall not trouble the Reader with it.

Suppose now that a Ray coming most obliquely in the Line MC [in Fig. 1.] be refracted at C by the Plane RS into the Line CN, and if it be required to find the Line CE, into which any other Ray AC shall be refracted; let MC, AD, be the Sines of Incidence of the two Rays, and NG, EF, their Sines of Refraction, and let the equal Motions of the incident Rays be represented by the equal Lines MC and AC, and the Motion MC being considered as parallel to the refracting Plane, let the other Motion AC be distinguished into two Motions AD and DC, one of which AD is parallel, and the other DC perpendicular to the refracting Surface. In like manner, let the Motions of the emerging Rays be distinguish'd into two, whereof the perpendicular ones are MC/NG × CG and AD/EF × CF. And if the force of the refracting Plane begins to act upon the Rays either in that Plane or at a certain distance from it on the one side, and ends at a certain distance from it on the other side, and in all places between those two limits acts upon the Rays in Lines perpendicular to that refracting Plane, and the Actions upon the Rays at equal distances from the refracting Plane be equal, and at unequal ones either equal or unequal according to any rate whatever; that Motion of the Ray which is parallel to the refracting Plane, will suffer no Alteration by that Force; and that Motion which is perpendicular to it will be altered according to the rule of the foregoing Proposition. If therefore for the perpendicular velocity of the emerging Ray CN you write MC/NG × CG as above, then the perpendicular velocity of any other emerging Ray CE which was AD/EF × CF, will be equal to the square Root of CDq + (MCq/NGq × CGq). And by squaring these Equals, and adding to them the Equals ADq and MCq - CDq, and dividing the Sums by the Equals CFq + EFq and CGq + NGq, you will have MCq/NGq equal to ADq/EFq. Whence AD, the Sine of Incidence, is to EF the Sine of Refraction, as MC to NG, that is, in a given ratio. And this Demonstration being general, without determining what Light is, or by what kind of Force it is refracted, or assuming any thing farther than that the refracting Body acts upon the Rays in Lines perpendicular to its Surface; I take it to be a very convincing Argument of the full truth of this Proposition.

So then, if the ratio of the Sines of Incidence and Refraction of any sort of Rays be found in any one case, 'tis given in all cases; and this may be readily found by the Method in the following Proposition.

PROP. VII. Theor. VI.

The Perfection of Telescopes is impeded by the different Refrangibility of the Rays of Light.

The Imperfection of Telescopes is vulgarly attributed to the spherical Figures of the Glasses, and therefore Mathematicians have propounded to figure them by the conical Sections. To shew that they are mistaken, I have inserted this Proposition; the truth of which will appear by the measure of the Refractions of the several sorts of Rays; and these measures I thus determine.

In the third Experiment of this first Part, where the refracting Angle of the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min. is the Angle of Incidence of the Rays at their going out of the Glass into the Air[6]; and the Sine of this Angle is 5188, the Radius being 10000. When the Axis of this Prism was parallel to the Horizon, and the Refraction of the Rays at their Incidence on this Prism equal to that at their Emergence out of it, I observed with a Quadrant the Angle which the mean refrangible Rays, (that is those which went to the middle of the Sun's coloured Image) made with the Horizon, and by this Angle and the Sun's altitude observed at the same time, I found the Angle which the emergent Rays contained with the incident to be 44 deg. and 40 min. and the half of this Angle added to the Angle of Incidence 31 deg. 15 min. makes the Angle of Refraction, which is therefore 53 deg. 35 min. and its Sine 8047. These are the Sines of Incidence and Refraction of the mean refrangible Rays, and their Proportion in round Numbers is 20 to 31. This Glass was of a Colour inclining to green. The last of the Prisms mentioned in the third Experiment was of clear white Glass. Its refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays contained, with the incident 45 deg. 50 min. The Sine of half the first Angle 5262. The Sine of half the Sum of the Angles 8157. And their Proportion in round Numbers 20 to 31, as before.

From the Length of the Image, which was about 9-3/4 or 10 Inches, subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4 Inches would be the Length of the Image were the Sun but a Point, and therefore subtends the Angle which the most and least refrangible Rays, when incident on the Prism in the same Lines, do contain with one another after their Emergence. Whence this Angle is 2 deg. 0´. 7´´. For the distance between the Image and the Prism where this Angle is made, was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends an Angle of 2 deg. 0´. 7´´. Now half this Angle is the Angle which these emergent Rays contain with the emergent mean refrangible Rays, and a quarter thereof, that is 30´. 2´´. may be accounted the Angle which they would contain with the same emergent mean refrangible Rays, were they co-incident to them within the Glass, and suffered no other Refraction than that at their Emergence. For, if two equal Refractions, the one at the Incidence of the Rays on the Prism, the other at their Emergence, make half the Angle 2 deg. 0´. 7´´. then one of those Refractions will make about a quarter of that Angle, and this quarter added to, and subducted from the Angle of Refraction of the mean refrangible Rays, which was 53 deg. 35´, gives the Angles of Refraction of the most and least refrangible Rays 54 deg. 5´ 2´´, and 53 deg. 4´ 58´´, whose Sines are 8099 and 7995, the common Angle of Incidence being 31 deg. 15´, and its Sine 5188; and these Sines in the least round Numbers are in proportion to one another, as 78 and 77 to 50.

Now, if you subduct the common Sine of Incidence 50 from the Sines of Refraction 77 and 78, the Remainders 27 and 28 shew, that in small Refractions the Refraction of the least refrangible Rays is to the Refraction of the most refrangible ones, as 27 to 28 very nearly, and that the difference of the Refractions of the least refrangible and most refrangible Rays is about the 27-1/2th Part of the whole Refraction of the mean refrangible Rays.

Whence they that are skilled in Opticks will easily understand,[7] that the Breadth of the least circular Space, into which Object-glasses of Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th Part of half the Aperture of the Glass, or 55th Part of the whole Aperture; and that the Focus of the most refrangible Rays is nearer to the Object-glass than the Focus of the least refrangible ones, by about the 27-1/2th Part of the distance between the Object-glass and the Focus of the mean refrangible ones.

And if Rays of all sorts, flowing from any one lucid Point in the Axis of any convex Lens, be made by the Refraction of the Lens to converge to Points not too remote from the Lens, the Focus of the most refrangible Rays shall be nearer to the Lens than the Focus of the least refrangible ones, by a distance which is to the 27-1/2th Part of the distance of the Focus of the mean refrangible Rays from the Lens, as the distance between that Focus and the lucid Point, from whence the Rays flow, is to the distance between that lucid Point and the Lens very nearly.

Now to examine whether the Difference between the Refractions, which the most refrangible and the least refrangible Rays flowing from the same Point suffer in the Object-glasses of Telescopes and such-like Glasses, be so great as is here described, I contrived the following Experiment.

Exper. 16. The Lens which I used in the second and eighth Experiments, being placed six Feet and an Inch distant from any Object, collected the Species of that Object by the mean refrangible Rays at the distance of six Feet and an Inch from the Lens on the other side. And therefore by the foregoing Rule, it ought to collect the Species of that Object by the least refrangible Rays at the distance of six Feet and 3-2/3 Inches from the Lens, and by the most refrangible ones at the distance of five Feet and 10-1/3 Inches from it: So that between the two Places, where these least and most refrangible Rays collect the Species, there may be the distance of about 5-1/3 Inches. For by that Rule, as six Feet and an Inch (the distance of the Lens from the lucid Object) is to twelve Feet and two Inches (the distance of the lucid Object from the Focus of the mean refrangible Rays) that is, as One is to Two; so is the 27-1/2th Part of six Feet and an Inch (the distance between the Lens and the same Focus) to the distance between the Focus of the most refrangible Rays and the Focus of the least refrangible ones, which is therefore 5-17/55 Inches, that is very nearly 5-1/3 Inches. Now to know whether this Measure was true, I repeated the second and eighth Experiment with coloured Light, which was less compounded than that I there made use of: For I now separated the heterogeneous Rays from one another by the Method I described in the eleventh Experiment, so as to make a coloured Spectrum about twelve or fifteen Times longer than broad. This Spectrum I cast on a printed Book, and placing the above-mentioned Lens at the distance of six Feet and an Inch from this Spectrum to collect the Species of the illuminated Letters at the same distance on the other side, I found that the Species of the Letters illuminated with blue were nearer to the Lens than those 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 so confused and indistinct, that I could not read them: Whereupon viewing the Prism, I found it was full of Veins running from one end of the Glass to the other; so that the Refraction could not be regular. I took another Prism therefore which was free from Veins, and instead of the Letters I used two or three Parallel black Lines a little broader than the Strokes of the Letters, and casting the Colours upon these Lines in such manner, that the Lines ran along the Colours from one end of the Spectrum to the other, I found that the Focus where the indigo, or confine of this Colour and violet cast the Species of the black Lines most distinctly, to be about four Inches, or 4-1/4 nearer to the Lens than the Focus, where the deepest red cast the Species of the same black Lines most distinctly. The violet was so faint and dark, that I could not discern the Species of the Lines distinctly by that Colour; and therefore considering that the Prism was made of a dark coloured Glass inclining to green, I took another Prism of clear white Glass; but the Spectrum of Colours which this Prism made had long white Streams of faint Light shooting out from both ends of the Colours, which made me conclude that something was amiss; and viewing the Prism, I found two or three little Bubbles in the Glass, which refracted the Light irregularly. Wherefore I covered that Part of the Glass with black Paper, and letting the Light pass through another Part of it which was free from such Bubbles, the Spectrum of Colours became free from those irregular Streams of Light, and was now such as I desired. But still I found the violet so dark and faint, that I could scarce see the Species of the Lines by the violet, and not at all by the deepest Part of it, which was next the end of the Spectrum. I suspected therefore, that this faint and dark Colour might be allayed by that scattering Light which was refracted, and reflected irregularly, partly by some very small Bubbles in the Glasses, and partly by the Inequalities of their Polish; which Light, tho' it was but little, yet it being of a white Colour, might suffice to affect the Sense so strongly as to disturb the Phænomena of that weak and dark Colour the violet, and therefore I tried, as in the 12th, 13th, and 14th Experiments, whether the Light of this Colour did not consist of a sensible Mixture of heterogeneous Rays, but found it did not. Nor did the Refractions cause any other sensible Colour than violet to emerge out of this Light, as they would have done out of white Light, and by consequence out of this violet Light had it been sensibly compounded with white Light. And therefore I concluded, that the reason why I could not see the Species of the Lines distinctly by this Colour, was only the Darkness of this Colour, and Thinness of its Light, and its distance from the Axis of the Lens; I divided therefore those Parallel black Lines into equal Parts, by which I might readily know the distances of the Colours in the Spectrum from one another, and noted the distances of the Lens from the Foci of such Colours, as cast the Species of the Lines distinctly, and then considered whether the difference of those distances bear such proportion to 5-1/3 Inches, the greatest Difference of the distances, which the Foci of the deepest red and violet ought to have from the Lens, as the distance of the observed Colours from one another in the Spectrum bear to the greatest distance of the deepest red and violet measured in the Rectilinear Sides of the Spectrum, that is, to the Length of those Sides, or Excess of the Length of the Spectrum above its Breadth. And my Observations were as follows.

When I observed and compared the deepest sensible red, and the Colour in the Confine of green and blue, which at the Rectilinear Sides of the Spectrum was distant from it half the Length of those Sides, the Focus where the Confine of green and blue cast the Species of the Lines distinctly on the Paper, was nearer to the Lens than the Focus, where the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4 Inches. For sometimes the Measures were a little greater, sometimes a little less, but seldom varied from one another above 1/3 of an Inch. For it was very difficult to define the Places of the Foci, without some little Errors. Now, if the Colours distant half the Length of the Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4 Difference of the distances of their Foci from the Lens, then the Colours distant the whole Length ought to give 5 or 5-1/2 Inches difference of those distances.

But here it's to be noted, that I could not see the red to the full end of the Spectrum, but only to the Center of the Semicircle which bounded that end, or a little farther; and therefore I compared this red not with that Colour which was exactly in the middle of the Spectrum, or Confine of green and blue, but with that which verged a little more to the blue than to the green: And as I reckoned the whole Length of the Colours not to be the whole Length of the Spectrum, but the Length of its Rectilinear Sides, so compleating the semicircular Ends into Circles, when either of the observed Colours fell within those Circles, I measured the distance of that Colour from the semicircular End of the Spectrum, and subducting half this distance from the measured distance of the two Colours, I took the Remainder for their corrected distance; and in these Observations set down this corrected distance for the difference of the distances of their Foci from the Lens. For, as the Length of the Rectilinear Sides of the Spectrum would be the whole Length of all the Colours, were the Circles of which (as we shewed) that Spectrum consists contracted and reduced to Physical Points, so in that Case this corrected distance would be the real distance of the two observed Colours.

When therefore I farther observed the deepest sensible red, and that blue whose corrected distance from it was 7/12 Parts of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so is 3-1/4 to 5-4/7.

When I observed the deepest sensible red, and that indigo whose corrected distance was 8/12 or 2/3 of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to 5-1/2.

When I observed the deepest sensible red, and that deep indigo whose corrected distance from one another was 9/12 or 3/4 of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to 5-1/3.

When I observed the deepest sensible red, and that Part of the violet next the indigo, whose corrected distance from the red was 10/12 or 5/6 of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens was about 4-1/2 Inches, and as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was advantageously placed, so that its Axis respected the blue, and all Things else were well ordered, and the Sun shone clear, and I held my Eye very near to the Paper on which the Lens cast the Species of the Lines, I could see pretty distinctly the Species of those Lines by that Part of the violet which was next the indigo; and sometimes I could see them by above half the violet, For in making these Experiments I had observed, that the Species of those Colours only appear distinct, which were in or near the Axis of the Lens: So that if the blue or indigo were in the Axis, I could see their Species distinctly; and then the red appeared much less distinct than before. Wherefore I contrived to make the Spectrum of Colours shorter than before, so that both its Ends might be nearer to the Axis of the Lens. And now its Length was about 2-1/2 Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the black Lines on which the Spectrum was cast, I made one black Line broader than those, that I might see its Species more easily; and this Line I divided by short cross Lines into equal Parts, for measuring the distances of the observed Colours. And now I could sometimes see the Species of this Line with its Divisions almost as far as the Center of the semicircular violet End of the Spectrum, and made these farther Observations.

When I observed the deepest sensible red, and that Part of the violet, whose corrected distance from it was about 8/9 Parts of the Rectilinear Sides of the Spectrum, the Difference of the distances of the Foci of those Colours from the Lens, was one time 4-2/3, another time 4-3/4, another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to 5-1/4, 5-11/32, 5-31/64 respectively.

When I observed the deepest sensible red, and deepest sensible violet, (the corrected distance of which Colours, when all Things were ordered to the best Advantage, and the Sun shone very clear, was about 11/12 or 15/16 Parts of the Length of the Rectilinear Sides of the coloured Spectrum) I found the Difference of the distances of their Foci from the Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or 5-1/3 Inches.

And by this Progression of Experiments I satisfied my self, that had the Light at the very Ends of the Spectrum been strong enough to make the Species of the black Lines appear plainly on the Paper, the Focus of the deepest violet would have been found nearer to the Lens, than the Focus of the deepest red, by about 5-1/3 Inches at least. And this is a farther Evidence, that the Sines of Incidence and Refraction of the several sorts of Rays, hold the same Proportion to one another in the smallest Refractions which they do in the greatest.

My Progress in making this nice and troublesome Experiment I have set down more at large, that they that shall try it after me may be aware of the Circumspection requisite to make it succeed well. And if they cannot make it succeed so well as I did, they may notwithstanding collect by the Proportion of the distance of the Colours of the Spectrum, to the Difference of the distances of their Foci from the Lens, what would be the Success in the more distant Colours by a better trial. And yet, if they use a broader Lens than I did, and fix it to a long strait Staff, by means of which it may be readily and truly directed to the Colour whose Focus is desired, I question not but the Experiment will succeed better with them than it did with me. For I directed the Axis as nearly as I could to the middle of the Colours, and then the faint Ends of the Spectrum being remote from the Axis, cast their Species less distinctly on the Paper than they would have done, had the Axis been successively directed to them.

Now by what has been said, it's certain that the Rays which differ in Refrangibility do not converge to the same Focus; but if they flow from a lucid Point, as far from the Lens on one side as their Foci are on the other, the Focus of the most refrangible Rays shall be nearer to the Lens than that of the least refrangible, by above the fourteenth Part of the whole distance; and if they flow from a lucid Point, so very remote from the Lens, that before their Incidence they may be accounted parallel, the Focus of the most refrangible Rays shall be nearer to the Lens than the Focus of the least refrangible, by about the 27th or 28th Part of their whole distance from it. And the Diameter of the Circle in the middle Space between those two Foci which they illuminate, when they fall there on any Plane, perpendicular to the Axis (which Circle is the least into which they can all be gathered) is about the 55th Part of the Diameter of the Aperture of the Glass. So that 'tis a wonder, that Telescopes represent Objects so distinct as they do. But were all the Rays of Light equally refrangible, the Error arising only from the Sphericalness of the Figures of Glasses would be many hundred times less. For, if the Object-glass of a Telescope be Plano-convex, and the Plane side be turned towards the Object, and the Diameter of the Sphere, whereof this Glass is a Segment, be called D, and the Semi-diameter of the Aperture of the Glass be called S, and the Sine of Incidence out of Glass into Air, be to the Sine of Refraction as I to R; the Rays which come parallel to the Axis of the Glass, shall in the Place where the Image of the Object is most distinctly made, be scattered all over a little Circle, whose Diameter is (Rq/Iq) × (S cub./D quad.) very nearly,[8] as I gather by computing the Errors of the Rays by the Method of infinite Series, and rejecting the Terms, whose Quantities are inconsiderable. As for instance, if the Sine of Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the Diameter of the Sphere, to which the Convex-side of the Glass is ground, be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be two Inches, the Diameter of the little Circle, (that is (Rq × S cub.)/(Iq × D quad.)) will be (31 × 31 × 8)/(20 × 20 × 1200 × 1200) (or 961/72000000) Parts of an Inch. But the Diameter of the little Circle, through which these Rays are scattered by unequal Refrangibility, will be about the 55th Part of the Aperture of the Object-glass, which here is four Inches. And therefore, the Error arising from the Spherical Figure of the Glass, is to the Error arising from the different Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to 5449; and therefore being in comparison so very little, deserves not to be considered.

Fig. 27.

But you will say, if the Errors caused by the different Refrangibility be so very great, how comes it to pass, that Objects appear through Telescopes so distinct as they do? I answer, 'tis because the erring Rays are not scattered uniformly over all that Circular Space, but collected infinitely more densely 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, so as at the Circumference to become infinitely rare; and by reason of their Rarity are not strong enough to be visible, unless in the Center and very near it. Let ADE [in Fig. 27.] represent one of those Circles described with the Center C, and Semi-diameter AC, and let BFG be a smaller Circle concentrick to the former, cutting with its Circumference the Diameter AC in B, and bisect AC in N; and by my reckoning, the Density of the Light in any Place B, will be to its Density in N, as AB to BC; and the whole Light within the lesser Circle BFG, will be to the whole Light within the greater AED, as the Excess 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 denser in B than in N, and the whole Light within the less Circle, will be to the whole Light within the greater, as nine to twenty-five. Whence it's evident, that the Light within the less Circle, must strike the Sense much more strongly, than that faint and dilated Light round about between it and the Circumference of the greater.

But it's farther to be noted, that the most luminous of the Prismatick Colours are the yellow and orange. These affect the Senses more strongly than all the rest together, and next to these in strength are the red and green. The blue compared with these is a faint and dark Colour, and the indigo and violet are much darker and fainter, so that these compared with the stronger Colours are little to be regarded. The Images of Objects 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 those Rays which are in the middle of the orange and yellow; there where the Colour is most luminous and fulgent, that is in the brightest yellow, that yellow which inclines more to orange than to green. And by the Refraction of these Rays (whose Sines of Incidence and Refraction in Glass are as 17 and 11) the Refraction of Glass and Crystal for Optical Uses is to be measured. Let us therefore place the Image of the Object in the Focus of these Rays, and all the yellow and orange will fall within a Circle, whose Diameter is about the 250th Part of the Diameter of the Aperture of the Glass. 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) about three fifth Parts of the Light of these two Colours will fall within the same Circle, and two fifth Parts will fall without it round about; and that which falls without will be spread through almost as much more space as that which falls within, and so in the gross be almost three times rarer. 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 spread through about four or five times more space than that which falls within; and so in the gross be rarer, and if compared with the whole Light within it, will be about 25 times rarer than all that taken in the gross; or rather more than 30 or 40 times rarer, because the deep red in the end of the Spectrum of Colours made by a Prism is very thin and rare, and the willow green is something rarer than the orange and yellow. The Light of these Colours therefore being so very much rarer than that within the Circle, will scarce affect the Sense, especially since the deep red and willow green of this Light, are much darker Colours than the rest. And for the same reason the blue and violet being much darker Colours than these, and much more rarified, may be neglected. For the dense and bright Light of the Circle, will obscure the rare and weak Light of these dark Colours round about it, and render them almost insensible. The sensible Image of a lucid Point is therefore scarce broader than a Circle, whose Diameter is the 250th Part of the Diameter of the Aperture of the Object-glass of a good Telescope, or not much broader, if you except a faint and dark misty Light round about it, which a Spectator will scarce regard. And therefore in a Telescope, whose Aperture is four Inches, and Length an hundred Feet, it exceeds not 2´´ 45´´´, or 3´´. And in a Telescope whose Aperture is two Inches, and Length 20 or 30 Feet, it may be 5´´ or 6´´, and scarce above. And this answers well to Experience: For some Astronomers have found the Diameters of the fix'd Stars, in Telescopes of between 20 and 60 Feet in length, to be about 5´´ or 6´´, or at most 8´´ or 10´´ in diameter. But if the Eye-Glass be tincted faintly with the Smoak of a Lamp or Torch, to obscure the Light of the Star, the fainter Light in the Circumference of the Star ceases to be visible, and the Star (if the Glass be sufficiently soiled with Smoak) appears something more like a mathematical Point. And for the same Reason, the enormous Part of the Light in the Circumference of every lucid Point ought to be less discernible in shorter Telescopes than in longer, because the shorter transmit less Light to the Eye.

Now, that the fix'd Stars, by reason of their immense Distance, appear like Points, unless so far as their Light is dilated by Refraction, may appear from hence; that when the Moon passes over them and eclipses them, their Light vanishes, not gradually like that of the Planets, but all at once; and in the end of the Eclipse it returns into Sight all at once, or certainly in less time than the second of a Minute; the Refraction of the Moon's Atmosphere a little protracting the time in which the Light of the Star first vanishes, and afterwards returns into Sight.

Now, if we suppose the sensible Image of a lucid Point, to be even 250 times narrower than the Aperture of the Glass; yet this Image would be still much greater than if it were only from the spherical Figure of the Glass. For were it not for the different Refrangibility of the Rays, its breadth in an 100 Foot Telescope whose aperture is 4 Inches, would be but 961/72000000 parts of an Inch, as is manifest by the foregoing Computation. And therefore in this case the greatest Errors arising from the spherical Figure of the Glass, would be to the greatest sensible Errors arising from the different Refrangibility of the Rays as 961/72000000 to 4/250 at most, that is only as 1 to 1200. And this sufficiently shews that it is not the spherical Figures of Glasses, but the different Refrangibility of the Rays which hinders the perfection of Telescopes.

There is another Argument by which it may appear that the different Refrangibility of Rays, is the true cause of the imperfection of Telescopes. For the Errors of the Rays arising from the spherical Figures of Object-glasses, are as the Cubes of the Apertures of the Object Glasses; and thence to make Telescopes of various Lengths magnify with equal distinctness, the Apertures of the Object-glasses, and the Charges or magnifying Powers ought to be as the Cubes of the square Roots of their lengths; which doth not answer to Experience. But the Errors of the Rays arising from the different Refrangibility, are as the Apertures of the Object-glasses; and thence to make Telescopes of various lengths, magnify with equal distinctness, their Apertures and Charges ought to be as the square Roots of their lengths; and this answers to Experience, as is well known. For Instance, a Telescope of 64 Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120 times, with as much distinctness as one of a Foot in length, with 1/3 of an Inch aperture, magnifies 15 times.

Fig. 28.

Now were it not for this different Refrangibility of Rays, Telescopes might be brought to a greater perfection than we have yet describ'd, by composing the Object-glass of two Glasses with Water between them. Let ADFC [in Fig. 28.] represent the Object-glass composed of two Glasses ABED and BEFC, alike convex on the outsides AGD and CHF, and alike concave on the insides BME, BNE, with Water in the concavity BMEN. Let the Sine of Incidence out of Glass into Air be as I to R, and out of Water into Air, as K to R, and by consequence out of Glass into Water, as I to K: and let the Diameter of the Sphere to which the convex sides AGD and CHF are ground be D, and the Diameter of the Sphere to which the concave sides BME and BNE, are ground be to D, as the Cube Root of KK—KI to the Cube Root of RK—RI: and the Refractions on the concave sides of the Glasses, will very much correct the Errors of the Refractions on the convex sides, so far as they arise from the sphericalness of the Figure. And by this means might Telescopes be brought to sufficient perfection, were it not for the different Refrangibility of several sorts of Rays. But by reason of this different Refrangibility, I do not yet see any other means of improving Telescopes by Refractions alone, than that of increasing their lengths, for which end the late Contrivance of Hugenius seems well accommodated. For very long Tubes are cumbersome, and scarce to be readily managed, and by reason of their length are very apt to bend, and shake by bending, so as to cause a continual trembling in the Objects, whereby it becomes difficult to see them distinctly: whereas by his Contrivance the Glasses are readily manageable, and the Object-glass being fix'd upon a strong upright Pole becomes more steady.

Seeing therefore the Improvement of Telescopes of given lengths by Refractions is desperate; I contrived heretofore a Perspective by Reflexion, using instead of an Object-glass a concave Metal. The diameter of the Sphere to which the Metal was ground concave was about 25 English Inches, and by consequence the length of the Instrument about six Inches and a quarter. The Eye-glass was Plano-convex, and the diameter of the Sphere to which the convex side was ground was about 1/5 of an Inch, or a little less, and by consequence it magnified between 30 and 40 times. By another way of measuring I found that it magnified about 35 times. The concave Metal bore an Aperture of an Inch and a third part; but the Aperture was limited not by an opake Circle, covering the Limb of the Metal round about, but by an opake Circle placed between the Eyeglass and the Eye, and perforated in the middle with a little round hole for the Rays to pass through to the Eye. For this Circle by being placed here, stopp'd much of the erroneous Light, which otherwise would have disturbed the Vision. By comparing it with a pretty good Perspective of four Feet in length, made with a concave Eye-glass, I could read at a greater distance with my own Instrument than with the Glass. Yet Objects appeared much darker in it than in the Glass, and that partly because more Light was lost by Reflexion in the Metal, than by Refraction in the Glass, and partly because my Instrument was overcharged. Had it magnified but 30 or 25 times, it would have made the Object appear more brisk and pleasant. Two of these I made about 16 Years ago, and have one of them still by me, by which I can prove the truth of what I write. Yet it is not so good as at the first. For the concave has been divers times tarnished and cleared again, by rubbing it with very soft Leather. When I made these an Artist in London undertook to imitate it; but using another way of polishing them than I did, he fell much short of what I had attained to, as I afterwards understood by discoursing the Under-workman he had employed. The Polish I used was in this manner. I had two round Copper Plates, each six Inches in Diameter, the one convex, the other concave, ground very true to one another. On the convex I ground the Object-Metal or Concave which was to be polish'd, 'till it had taken the Figure of the Convex and was ready for a Polish. Then I pitched over the convex very thinly, by dropping melted Pitch upon it, and warming it to keep the Pitch soft, whilst I ground it with the concave Copper wetted to make it spread eavenly all over the convex. Thus by working it well I made it as thin as a Groat, and after the convex was cold I ground it again to give it as true a Figure as I could. Then I took Putty which I had made very fine by washing it from all its grosser Particles, and laying a little of this upon the Pitch, I ground it upon the Pitch with the concave Copper, till it had done making a Noise; and then upon the Pitch I ground the Object-Metal with a brisk motion, for about two or three Minutes of time, leaning hard upon it. Then I put fresh Putty upon the Pitch, and ground it again till it had done making a noise, and afterwards ground the Object-Metal upon it as before. And this Work I repeated till the Metal was polished, grinding it the last time with all my strength for a good while together, and frequently breathing upon the Pitch, to keep it moist without laying on any more fresh Putty. The Object-Metal was two Inches broad, and about one third part of an Inch thick, to keep it from bending. I had two of these Metals, and when I had polished them both, I tried which was best, and ground the other again, to see if I could make it better than that which I kept. And thus by many Trials I learn'd the way of polishing, till I made those two reflecting Perspectives I spake of above. For this Art of polishing will be better learn'd by repeated Practice than by my Description. Before I ground the Object-Metal on the Pitch, I always ground the Putty on it with the concave Copper, till it had done making a noise, because if the Particles of the Putty were not by this means made to stick fast in the Pitch, they would by rolling up and down grate and fret the Object-Metal and fill it full of little holes.

But because Metal is more difficult to polish than Glass, and is afterwards very apt to be spoiled by tarnishing, and reflects not so much Light as Glass quick-silver'd over does: I would propound to use instead of the Metal, a Glass ground concave on the foreside, and as much convex on the backside, and quick-silver'd over on the convex side. The Glass must be every where of the same thickness exactly. Otherwise it will make Objects look colour'd and indistinct. By such a Glass I tried about five or six Years ago to make a reflecting Telescope of four Feet in length to magnify about 150 times, and I satisfied my self that there wants nothing but a good Artist to bring the Design to perfection. For the Glass being wrought by one of our London Artists after such a manner as they grind Glasses for Telescopes, though it seemed as well wrought as the Object-glasses use to be, yet when it was quick-silver'd, the Reflexion discovered innumerable Inequalities all over the Glass. And by reason of these Inequalities, Objects appeared indistinct in this Instrument. For the Errors of reflected Rays caused by any Inequality of the Glass, are about six times greater than the Errors of refracted Rays caused by the like Inequalities. Yet by this Experiment I satisfied my self that the Reflexion on the concave side of the Glass, which I feared would disturb the Vision, did no sensible prejudice to it, and by consequence that nothing is wanting to perfect these Telescopes, but good Workmen who can grind and polish Glasses truly spherical. An Object-glass of a fourteen Foot Telescope, made by an Artificer at London, I once mended considerably, by grinding it on Pitch with Putty, and leaning very easily on it in the grinding, lest the Putty should scratch it. Whether this way may not do well enough for polishing these reflecting Glasses, I have not yet tried. But he that shall try either this or any other way of polishing which he may think better, may do well to make his Glasses ready for polishing, by grinding them without that Violence, wherewith our London Workmen press their Glasses in grinding. For by such violent pressure, Glasses are apt to bend a little in the grinding, and such bending will certainly spoil their Figure. To recommend therefore the consideration of these reflecting Glasses to such Artists as are curious in figuring Glasses, I shall describe this optical Instrument in the following Proposition.

PROP. VIII. Prob. II.

To shorten Telescopes.

Let ABCD [in Fig. 29.] represent a Glass spherically concave on the foreside AB, and as much convex on the backside CD, so that it be every where of an equal thickness. Let it not be thicker on one side than on the other, lest it make Objects appear colour'd and indistinct, and let it be very truly wrought and quick-silver'd over on the backside; and set in the Tube VXYZ which must be very black within. Let EFG represent a Prism of Glass or Crystal placed near the other end of the Tube, in the middle of it, by means of a handle of Brass or Iron FGK, to the end of which made flat it is cemented. Let this Prism be rectangular at E, and let the other two Angles at F and G be accurately equal to each other, and by consequence equal to half right ones, and let the plane sides FE and GE be square, and by consequence the third side FG a rectangular Parallelogram, whose length is to its breadth in a subduplicate proportion of two to one. Let it be so placed in the Tube, that the Axis of the Speculum may pass through the middle of the square side EF perpendicularly and by consequence through the middle of the side FG at an Angle of 45 Degrees, and let the side EF be turned towards the Speculum, and the distance of this Prism from the Speculum be such that the Rays of the Light PQ, RS, &c. which are incident upon the Speculum in Lines parallel to the Axis thereof, may enter the Prism at the side EF, and be reflected by the side FG, and thence go out of it through the side GE, to the Point T, which must be the common Focus of the Speculum ABDC, and of a Plano-convex Eye-glass H, through which those Rays must pass to the Eye. And let the Rays at their coming out of the Glass pass through a small round hole, or aperture made in a little plate of Lead, Brass, or Silver, wherewith the Glass is to be covered, which hole must be no bigger than is necessary for Light enough to pass through. For so it will render the Object distinct, the Plate in which 'tis made intercepting all the erroneous part of the Light which comes from the verges of the Speculum AB. Such an Instrument well made, if it be six Foot long, (reckoning the length from the Speculum to the Prism, and thence to the Focus T) will bear an aperture of six Inches at the Speculum, and magnify between two and three hundred times. But the hole H here limits the aperture with more advantage, than if the aperture was placed at the Speculum. If the Instrument be made longer or shorter, the aperture must be in proportion as the Cube of the square-square Root of the length, and the magnifying as the aperture. But it's convenient that the Speculum be an Inch or two broader than the aperture at the least, and that the Glass of the Speculum be thick, that it bend not in the working. The Prism EFG must be no bigger than is necessary, and its back side FG must not be quick-silver'd over. For without quicksilver it will reflect all the Light incident on it from the Speculum.

Fig. 29.

In this Instrument the Object will be inverted, but may be erected by making the square sides FF and EG of the Prism EFG not plane but spherically convex, that the Rays may cross as well before they come at it as afterwards between it and the Eye-glass. If it be desired that the Instrument bear a larger aperture, that may be also done by composing the Speculum of two Glasses with Water between them.

If the Theory of making Telescopes could at length be fully brought into Practice, yet there would be certain Bounds beyond which Telescopes could not perform. For the Air through which we look upon the Stars, is in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows cast from high Towers, and by the twinkling of the fix'd Stars. But these Stars do not twinkle when viewed through Telescopes which have large apertures. For the Rays of Light which pass through divers parts of the aperture, tremble each of them apart, and by means of their various and sometimes contrary Tremors, fall at one and the same time upon different points in the bottom of the Eye, and their trembling Motions are too quick and confused to be perceived severally. And all these illuminated Points constitute one broad lucid Point, composed of those many trembling Points confusedly and insensibly mixed with one another by very short and swift Tremors, and thereby cause the Star to appear broader than it is, and without any trembling of the whole. Long Telescopes may cause Objects to appear brighter and larger than short ones can do, but they cannot be so formed as to take away that confusion of the Rays which arises from the Tremors of the Atmosphere. The only Remedy is a most serene and quiet Air, such as may perhaps be found on the tops of the highest Mountains above the grosser Clouds.

PART II.

PROP. I. Theor. I.

The Phænomena of Colours in refracted or reflected Light are not caused by new Modifications of the Light variously impress'd, according to the various Terminations of the Light and Shadow.

The Proof by Experiments.

Exper. 1. For if the Sun shine into a very dark Chamber through an oblong hole F, [in Fig. 1.] whose breadth is the sixth or eighth part of an Inch, or something less; and his beam FH do afterwards pass first through a very large Prism ABC, distant about 20 Feet from the hole, and parallel to it, and then (with its white part) through an oblong hole H, whose breadth is about the fortieth or sixtieth part of an Inch, and which is made in a black opake Body GI, and placed at the distance of two or three Feet from the Prism, in a parallel Situation both to the Prism and to the former hole, and if this white Light thus transmitted through the hole H, fall afterwards upon a white Paper pt, placed after that hole H, at the distance of three or four Feet from it, and there paint the usual Colours of the Prism, suppose red at t, yellow at s, green at r, blue at q, and violet at p; you may with an Iron Wire, or any such like slender opake Body, whose breadth is about the tenth part of an Inch, by intercepting the Rays at k, l, m, n or o, take away any one of the Colours at t, s, r, q or p, whilst the other Colours remain upon the Paper as before; or with an Obstacle something bigger you may take away any two, or three, or four Colours together, the rest remaining: So that any one of the Colours as well as violet may become outmost in the Confine of the Shadow towards p, and any one of them as well as red may become outmost in the Confine of the Shadow towards t, and any one of them may also border upon the Shadow made within the Colours by the Obstacle R intercepting some intermediate part of the Light; and, lastly, any one of them by being left alone, may border upon the Shadow on either hand. All the Colours have themselves indifferently to any Confines of Shadow, and therefore the differences of these Colours from one another, do not arise from the different Confines of Shadow, whereby Light is variously modified, as has hitherto been the Opinion of Philosophers. In trying these things 'tis to be observed, that by how much the holes F and H are narrower, and the Intervals between them and the Prism greater, and the Chamber darker, by so much the better doth the Experiment succeed; provided the Light be not so far diminished, but that the Colours at pt be sufficiently visible. To procure a Prism of solid Glass large enough for this Experiment will be difficult, and therefore a prismatick Vessel must be made of polish'd Glass Plates cemented together, and filled with salt Water or clear Oil.

Fig. 1.

Exper. 2. The Sun's Light let into a dark Chamber through the round hole F, [in Fig. 2.] half an Inch wide, passed first through the Prism ABC placed at the hole, and then through a Lens PT something more than four Inches broad, and about eight Feet distant from the Prism, and thence converged to O the Focus of the Lens distant from it about three Feet, and there fell upon a white Paper DE. If that Paper was perpendicular to that Light incident upon it, as 'tis represented in the posture DE, all the Colours upon it at O appeared white. But if the Paper being turned about an Axis parallel to the Prism, became very much inclined to the Light, as 'tis represented in the Positions de and δε; the same Light in the one case appeared yellow and red, in the other blue. Here one and the same part of the Light in one and the same place, according to the various Inclinations of the Paper, appeared in one case white, in another yellow or red, in a third blue, whilst the Confine of Light and shadow, and the Refractions of the Prism in all these cases remained the same.

Fig. 2.

Fig. 3.

Exper. 3. Such another Experiment may be more easily tried as follows. Let a broad beam of the Sun's Light coming into a dark Chamber through a hole in the Window-shut be refracted by a large Prism ABC, [in Fig. 3.] whose refracting Angle C is more than 60 Degrees, and so soon as it comes out of the Prism, let it fall upon the white Paper DE glewed upon a stiff Plane; and this Light, when the Paper is perpendicular to it, as 'tis represented in DE, will appear perfectly white upon the Paper; but when the Paper is very much inclin'd to it in such a manner as to keep always parallel to the Axis of the Prism, the whiteness 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 posture de, or into blue and violet, as in the posture δε. And if the Light before it fall upon the Paper be twice refracted the same way by two parallel Prisms, these Colours will become the more conspicuous. Here all the middle parts of the broad beam of white Light which fell upon the Paper, did without any Confine of Shadow to modify it, become colour'd all over with one uniform Colour, the Colour being always the same in the middle of the Paper as at the edges, and this Colour changed according to the various Obliquity of the reflecting Paper, without any change in the Refractions or Shadow, or in the Light which fell upon the Paper. And therefore these Colours are to be derived from some other Cause than the new Modifications of Light by Refractions and Shadows.

If it be asked, what then is their Cause? I answer, That the Paper in the posture de, being more oblique to the more refrangible Rays than to the less refrangible ones, is more strongly illuminated by the latter than by the former, and therefore the less refrangible Rays are predominant in the reflected Light. And where-ever they are predominant in any Light, they tinge it with red or yellow, as may in some measure appear by the first Proposition of the first Part of this Book, and will more fully appear hereafter. And the contrary happens in the posture of the Paper δε, the more refrangible Rays being then predominant which always tinge Light with blues and violets.

Exper. 4. The Colours of Bubbles with which Children play are various, and change their Situation variously, without any respect to any Confine or Shadow. If such a Bubble be cover'd with a concave Glass, to keep it from being agitated by any Wind or Motion of the Air, the Colours will slowly and regularly change their situation, even whilst the Eye and the Bubble, and all Bodies which emit any Light, or cast any Shadow, remain unmoved. And therefore their Colours arise from some regular Cause which depends not on any Confine of Shadow. What this Cause is will be shewed in the next Book.

To these Experiments may be added the tenth Experiment of the first Part of this first Book, where the Sun's Light in a dark Room being trajected through the parallel Superficies of two Prisms tied together in the form of a Parallelopipede, became totally of one uniform yellow or red Colour, at its emerging out of the Prisms. Here, in the production of these Colours, the Confine of Shadow can have nothing to do. For the Light changes from white to yellow, orange and red successively, without any alteration of the Confine of Shadow: And at both edges of the emerging Light where the contrary Confines of Shadow ought to produce different Effects, the Colour is one and the same, whether it be white, yellow, orange or red: And in the middle of the emerging Light, where there is no Confine of Shadow at all, the Colour is the very same as at the edges, the whole Light at its very first Emergence being of one uniform Colour, whether white, yellow, orange or red, and going on thence perpetually without any change of Colour, such as the Confine of Shadow is vulgarly supposed to work in refracted Light after its Emergence. Neither can these Colours arise from any new Modifications of the Light by Refractions, because they change successively from white to yellow, orange and red, while the Refractions remain the same, and also because the Refractions are made contrary ways by parallel Superficies which destroy one another's Effects. They arise not therefore from any Modifications of Light made by Refractions and Shadows, but have some other Cause. What that Cause is we shewed above in this tenth Experiment, and need not here repeat it.

There is yet another material Circumstance of this Experiment. For this emerging Light being by a third Prism HIK [in Fig. 22. Part I.][9] refracted towards the Paper PT, and there painting the usual Colours of the Prism, red, yellow, green, blue, violet: If these Colours arose from the Refractions of that Prism modifying the Light, they would not be in the Light before its Incidence on that Prism. And yet in that Experiment we found, that when by turning the two first Prisms about their common Axis all the Colours were made to vanish but the red; the Light which makes that red being left alone, appeared of the very same red Colour before its Incidence on the third Prism. And in general we find by other Experiments, that when the Rays which differ in Refrangibility are separated from one another, and any one Sort of them is considered apart, the Colour of the Light which they compose cannot be changed by any Refraction or Reflexion whatever, as it ought to be were Colours nothing else than Modifications of Light caused by Refractions, and Reflexions, and Shadows. This Unchangeableness of Colour I am now to describe in the following Proposition.

PROP. II. Theor. II.

All homogeneal Light has its proper Colour answering to its Degree of Refrangibility, and that Colour cannot be changed by Reflexions and Refractions.

In the Experiments of the fourth Proposition of the first Part of this first Book, when I had separated the heterogeneous Rays from one another, the Spectrum pt formed by the separated Rays, did in the Progress from its End p, on which the most refrangible Rays fell, unto its other End t, on which the least refrangible Rays fell, appear tinged with this Series of Colours, violet, indigo, blue, green, yellow, orange, red, together with all their intermediate Degrees in a continual Succession perpetually varying. So that there appeared as many Degrees of Colours, as there were sorts of Rays differing in Refrangibility.

Exper. 5. Now, that these Colours could not be changed by Refraction, I knew by refracting with a Prism sometimes one very little Part of this Light, sometimes another very little Part, as is described in the twelfth Experiment of the first Part of this Book. For by this Refraction the Colour of the Light was never changed in the least. If any Part of the red Light was refracted, it remained totally of the same red Colour as before. No orange, no yellow, no green or blue, no other new Colour was produced by that Refraction. Neither did the Colour any ways change by repeated Refractions, but continued always the same red entirely as at first. The like Constancy and Immutability I found also in the blue, green, and other Colours. So also, if I looked through a Prism upon any Body illuminated with any part of this homogeneal Light, as in the fourteenth Experiment of the first Part of this Book is described; I could not perceive any new Colour generated this way. All Bodies illuminated with compound Light appear through Prisms confused, (as was said above) and tinged with various new Colours, but those illuminated with homogeneal Light appeared through Prisms neither less distinct, nor otherwise colour'd, than when viewed with the naked Eyes. Their Colours were not in the least changed by the Refraction of the interposed Prism. I speak here of a sensible Change of Colour: For the Light which I here call homogeneal, being not absolutely homogeneal, there ought to arise some little Change of Colour from its Heterogeneity. But, if that Heterogeneity was so little as it might be made by the said Experiments of the fourth Proposition, that Change was not sensible, and therefore in Experiments, where Sense is Judge, ought to be accounted none at all.

Exper. 6. And as these Colours were not changeable by Refractions, so neither were they by Reflexions. For all white, grey, red, yellow, green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, Indico Bise, Gold, Silver, Copper, Grass, blue Flowers, Violets, Bubbles of Water tinged with various Colours, Peacock's Feathers, the Tincture of Lignum Nephriticum, and such-like, in red homogeneal Light appeared totally red, in blue Light totally blue, in green Light totally green, and so of other Colours. In the homogeneal Light of any Colour they all appeared totally of that same Colour, with this only Difference, that some of them reflected that Light more strongly, others more faintly. I never yet found any Body, which by reflecting homogeneal Light could sensibly change its Colour.

From all which it is manifest, that if the Sun's Light consisted of but one sort of Rays, there would be but one Colour in the whole World, nor would it be possible to produce any new Colour by Reflexions and Refractions, and by consequence that the variety of Colours depends upon the Composition of Light.

DEFINITION.

The homogeneal Light and Rays which appear red, or rather make Objects appear so, I call Rubrifick or Red-making; those which make Objects appear yellow, green, blue, and violet, I call Yellow-making, Green-making, Blue-making, Violet-making, and so of the rest. And if at any time I speak of Light and Rays as coloured or endued with Colours, I would be understood to speak not philosophically and properly, but grossly, and accordingly to such Conceptions as vulgar People in seeing all these Experiments would be apt to frame. For the Rays to speak properly are not coloured. In them there is nothing else than a certain Power and Disposition to stir up a Sensation of this or that Colour. For as Sound in a Bell or musical String, or other sounding Body, is nothing but a trembling Motion, and in the Air nothing but that Motion propagated from the Object, and in the Sensorium 'tis a Sense of that Motion under the Form of Sound; so Colours in the Object are nothing but a Disposition to reflect this or that sort of Rays more copiously than the rest; in the Rays they are nothing but their Dispositions to propagate this or that Motion into the Sensorium, and in the Sensorium they are Sensations of those Motions under the Forms of Colours.

PROP. III. Prob. I.

To define the Refrangibility of the several sorts of homogeneal Light answering to the several Colours.

For determining this Problem I made the following Experiment.[10]

Exper. 7. When I had caused the Rectilinear Sides AF, GM, [in Fig. 4.] of the Spectrum of Colours made by the Prism to be distinctly defined, as in the fifth Experiment of the first Part of this Book is described, there were found in it all the homogeneal Colours in the same Order and Situation one among another as in the Spectrum of simple Light, described in the fourth Proposition of that Part. For the Circles of which the Spectrum of compound Light PT is composed, and which in the middle Parts of the Spectrum interfere, and are intermix'd with one another, are not intermix'd in their outmost Parts where they touch those Rectilinear Sides AF and GM. And therefore, in those Rectilinear Sides when distinctly defined, there is no new Colour generated by Refraction. I observed also, that if any where between the two outmost Circles TMF and PGA a Right Line, as γδ, was cross to the Spectrum, so as both Ends to fall perpendicularly upon its Rectilinear Sides, there appeared one and the same Colour, and degree of Colour from one End of this Line to the other. I delineated therefore in a Paper the Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of the first Part of this Book, I held the Paper so that the Spectrum might fall upon this delineated Figure, and agree with it exactly, whilst an Assistant, whose Eyes for distinguishing Colours were more critical than mine, did by Right Lines αβ, γδ, εζ, &c. drawn cross the Spectrum, note the Confines of the Colours, that is of the red MαβF, of the orange αγδβ, of the yellow γεζδ, of the green ηθζ, of the blue ηικθ, of the indico ιλμκ, and of the violet λGAμ. And this Operation being divers times repeated both in the same, and in several Papers, I found that the Observations agreed well enough with one another, and that the Rectilinear Sides MG and FA were by the said cross Lines divided after the manner of a Musical Chord. Let GM be produced to X, that MX may be equal to GM, and conceive GX, λX, ιX, ηX, εX, γX, αX, MX, to be in proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5, 9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth above that Key: And the Intervals Mα, αγ, γε, εη, ηι, ιλ, and λG, will be the Spaces which the several Colours (red, orange, yellow, green, blue, indigo, violet) take up.

Fig. 4.

Fig. 5.

Now these Intervals or Spaces subtending the Differences of the Refractions of the Rays going to the Limits of those Colours, that is, to the Points M, α, γ, ε, η, ι, λ, G, may without any sensible Error be accounted proportional to the Differences of the Sines of Refraction of those Rays having one common Sine of Incidence, and therefore since the common Sine of Incidence of the most and least refrangible Rays out of Glass into Air was (by a Method described above) found in proportion to their Sines of Refraction, as 50 to 77 and 78, divide the Difference between the Sines of Refraction 77 and 78, as the Line GM is divided by those Intervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3, 77-7/9, 78, the Sines of Refraction of those Rays out of Glass into Air, their common Sine of Incidence being 50. So then the Sines of the Incidences of all the red-making Rays out of Glass into Air, were to the Sines of their Refractions, not greater than 50 to 77, nor less than 50 to 77-1/8, but they varied from one another according to all intermediate Proportions. And the Sines of the Incidences of the green-making Rays were to the Sines of their Refractions in all Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And by the like Limits above-mentioned were the Refractions of the Rays belonging to the rest of the Colours defined, the Sines of the red-making Rays extending from 77 to 77-1/8, those of the orange-making from 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3, those of the green-making from 77-1/3 to 77-1/2, those of the blue-making from 77-1/2 to 77-2/3, those of the indigo-making from 77-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.

These are the Laws of the Refractions made out of Glass into Air, and thence by the third Axiom of the first Part of this Book, the Laws of the Refractions made out of Air into Glass are easily derived.

Exper. 8. I found moreover, that when Light goes out of Air through several contiguous refracting Mediums as through Water and Glass, and thence goes out again into Air, whether the refracting Superficies be parallel or inclin'd to one another, that Light as often as by contrary Refractions 'tis so corrected, that it emergeth in Lines parallel to those in which it was incident, continues ever after to be white. But if the emergent Rays be inclined to the incident, the Whiteness of the emerging Light will by degrees in passing on from the Place of Emergence, become tinged in its Edges with Colours. This I try'd by refracting Light with Prisms of Glass placed within a Prismatick Vessel of Water. Now those Colours argue a diverging and separation of the heterogeneous Rays from one another by means of their unequal Refractions, as in what follows will more fully appear. And, on the contrary, the permanent whiteness argues, that in like Incidences of the Rays there is no such separation of the emerging Rays, and by consequence no inequality of their whole Refractions. Whence I seem to gather the two following Theorems.

1. The Excesses of the Sines of Refraction of several sorts of Rays above their common Sine of Incidence when the Refractions are made out of divers denser Mediums immediately into one and the same rarer Medium, suppose of Air, are to one another in a given Proportion.

2. The Proportion of the Sine of Incidence to the Sine of Refraction of one and the same sort of Rays out of one Medium into another, is composed of the Proportion of the Sine of Incidence to the Sine of Refraction out of the first Medium into any third Medium, and of the Proportion of the Sine of Incidence to the Sine of Refraction out of that third Medium into the second Medium.

By the first Theorem the Refractions of the Rays of every sort made out of any Medium into Air are known by having the Refraction of the Rays of any one sort. As for instance, if the Refractions of the Rays of every sort out of Rain-water into Air be desired, let the common Sine of Incidence out of Glass into Air be subducted from the Sines of Refraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2, 27-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the least refrangible Rays be to their Sine of Refraction out of Rain-water into Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the Sine of Incidence, so is 27 the least of the Excesses above-mentioned to a fourth Number 81; and 81 will be the common Sine of Incidence out of Rain-water into Air, to which Sine if you add all the above-mentioned Excesses, you will have the desired Sines of the Refractions 108, 108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.

By the latter Theorem the Refraction out of one Medium into another is gathered as often as you have the Refractions out of them both into any third Medium. As if the Sine of Incidence of any Ray out of Glass into Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence of the same Ray out of Air into Water, be to its Sine of Refraction as 4 to 3; the Sine of Incidence of that Ray out of Glass into Water will be to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as the Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.

And these Theorems being admitted into Opticks, there would be scope enough of handling that Science voluminously after a new manner,[11] not only by teaching those things which tend to the perfection of Vision, but also by determining mathematically all kinds of Phænomena of Colours which could be produced by Refractions. For to do this, there is nothing else requisite than to find out the Separations of heterogeneous Rays, and their various Mixtures and Proportions in every Mixture. By this way of arguing I invented almost all the Phænomena described in these Books, beside some others less necessary to the Argument; and by the successes I met with in the Trials, I dare promise, that to him who shall argue truly, and then try all things with good Glasses and sufficient Circumspection, the expected Event will not be wanting. But he is first to know what Colours will arise from any others mix'd in any assigned Proportion.

PROP. IV. Theor. III.

Colours may be produced by Composition which shall be like to the Colours of homogeneal Light as to the Appearance of Colour, but not as to the Immutability of Colour and Constitution of Light. And those Colours by how much they are more compounded by so much are they less full and intense, and by too much Composition they maybe diluted and weaken'd till they cease, and the Mixture becomes white or grey. There may be also Colours produced by Composition, which are not fully like any of the Colours of homogeneal Light.

For a Mixture of homogeneal red and yellow compounds an Orange, like in appearance of Colour to that orange which in the series of unmixed prismatick Colours lies between them; but the Light of one orange is homogeneal as to Refrangibility, and that of the other is heterogeneal, and the Colour of the one, if viewed through a Prism, remains unchanged, that of the other is changed and resolved into its component Colours red and yellow. And after the same manner other neighbouring homogeneal Colours may compound new Colours, like the intermediate homogeneal ones, as yellow and green, the Colour between them both, and afterwards, if blue be added, there will be made a green the middle Colour of the three which enter the Composition. For the yellow and blue on either hand, if they are equal in quantity they draw the intermediate green equally towards themselves in Composition, and so keep it as it were in Æquilibrion, that it verge not more to the yellow on the one hand, and to the blue on the other, but by their mix'd Actions remain still a middle Colour. To this mix'd green there may be farther added some red and violet, and yet the green will not presently cease, but only grow less full and vivid, and by increasing 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 whiteness, or some other Colour. So if to the Colour of any homogeneal Light, the Sun's white Light composed of all sorts of Rays be added, that Colour will not vanish or change its Species, but be diluted, and by adding more and more white it will be diluted more and more perpetually. Lastly, If red and violet be mingled, there will be generated according to their various Proportions various Purples, such as are not like in appearance to the Colour of any homogeneal Light, and of these Purples mix'd with yellow and blue may be made other new Colours.

PROP. V. Theor. IV.

Whiteness and all grey Colours between white and black, may be compounded of Colours, and the whiteness of the Sun's Light is compounded of all the primary Colours mix'd in a due Proportion.

The Proof by Experiments.

Exper. 9. The Sun shining into a dark Chamber through a little round hole in the Window-shut, and his Light being there refracted by a Prism to cast his coloured Image PT [in Fig. 5.] upon the opposite Wall: I held a white Paper V to that image in such manner that it might be illuminated by the colour'd Light reflected from thence, and yet not intercept any part of that Light in its passage from the Prism to the Spectrum. And I found that when the Paper was held nearer to any Colour than to the rest, it appeared of that Colour to which it approached nearest; but when it was equally or almost equally distant from all the Colours, so that it might be equally illuminated by them all it appeared white. And in this last situation of the Paper, if some Colours were intercepted, the Paper lost its white Colour, and appeared of the Colour of the rest 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 retained its proper Colour, until it was incident on the Paper, and became reflected thence to the Eye; so that if it had been either alone (the rest of the Light being intercepted) or if it had abounded most, and been predominant in the Light reflected from the Paper, it would have tinged the Paper with its own Colour; and yet being mixed with the rest of the Colours in a due proportion, it made the Paper look white, and therefore by a Composition with the rest produced that Colour. The several parts of the coloured Light reflected from the Spectrum, whilst they are propagated from thence through the Air, do perpetually retain their proper Colours, because wherever they fall upon the Eyes of any Spectator, they make the several parts of the Spectrum to appear under their proper Colours. They retain therefore their proper Colours when they fall upon the Paper V, and so by the confusion and perfect mixture of those Colours compound the whiteness of the Light reflected from thence.

Exper. 10. Let that Spectrum or solar Image PT [in Fig. 6.] fall now upon the Lens MN above four Inches broad, and about six Feet distant from the Prism ABC and so figured that it may cause the coloured Light which divergeth from the Prism to converge and meet again at its Focus G, about six or eight Feet distant from the Lens, and there to fall perpendicularly upon a white Paper DE. And if you move this Paper to and fro, you will perceive that near the Lens, as at de, the whole solar Image (suppose at pt) will appear upon it intensely coloured after the manner above-explained, and that by receding from the Lens those Colours will perpetually come towards one another, and by mixing more and more dilute one another continually, until at length the Paper come to the Focus G, where by a perfect mixture they will wholly vanish and be converted into whiteness, the whole Light appearing now upon the Paper like a little white Circle. And afterwards by receding farther from the Lens, the Rays which before converged will now cross one another in the Focus G, and diverge from thence, and thereby make the Colours to appear again, but yet in a contrary order; suppose at δε, where the red t is now above which before was below, and the violet p is below which before was above.

Let us now stop the Paper at the Focus G, where the Light appears totally white and circular, and let us consider its whiteness. I say, that this is composed of the converging Colours. For if any of those Colours be intercepted at the Lens, the whiteness will cease and degenerate into that Colour which ariseth from the composition of the other Colours which are not intercepted. And then if the intercepted Colours be let pass and fall upon that compound Colour, they mix with it, and by their mixture restore the whiteness. So if the violet, blue and green be intercepted, the remaining yellow, orange and red will compound upon the Paper an orange, and then if the intercepted Colours be let pass, they will fall upon this compounded orange, and together with it decompound a white. So also 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 pass will fall upon this green, and together with it decompound a white. And that in this Composition of white the several Rays do not suffer any Change in their colorific Qualities by acting upon one another, but are only mixed, and by a mixture of their Colours produce white, may farther appear by these Arguments.

Fig. 6.

If the Paper be placed beyond the Focus G, suppose at δε, and then the red Colour at the Lens be alternately intercepted, and let pass again, the violet Colour on the Paper will not suffer any Change thereby, as it ought to do if the several sorts of Rays acted upon one another in the Focus G, where they cross. Neither will the red upon the Paper be changed by any alternate stopping, and letting pass the violet which crosseth it.

And if the Paper be placed at the Focus G, and the white round Image at G be viewed through the Prism HIK, and by the Refraction of that Prism be translated to the place rv, and there appear tinged with various Colours, namely, the violet at v and red at r, and others between, and then the red Colours at the Lens be often stopp'd and let pass by turns, the red at r will accordingly disappear, and return as often, but the violet at v will not thereby suffer any Change. And so by stopping and letting pass alternately the blue at the Lens, the blue at v will accordingly disappear and return, without any Change made in the red at r. The red therefore depends on one sort of Rays, and the blue on another sort, which in the Focus G where they are commix'd, do not act on one another. And there is the same Reason of the other Colours.

I considered farther, that when the most refrangible Rays Pp, and the least refrangible ones Tt, are by converging inclined to one another, the Paper, if held very oblique to those Rays in the Focus G, might reflect one sort of them more copiously than the other sort, and by that Means the reflected Light would be tinged in that Focus with the Colour of the predominant Rays, provided those Rays severally retained their Colours, or colorific Qualities in the Composition of White made by them in that Focus. But if they did not retain them in that White, but became all of them severally endued there with a Disposition to strike the Sense with the Perception of White, then they could never lose their Whiteness by such Reflexions. I inclined therefore the Paper to the Rays very obliquely, as in the second Experiment of this second Part of the first Book, that the most refrangible Rays, might be more copiously reflected than the rest, and the Whiteness at Length changed successively into blue, indigo, and violet. Then I inclined it the contrary Way, that the least refrangible Rays might be more copious in the reflected Light than the rest, and the Whiteness turned successively to yellow, orange, and red.

Lastly, I made an Instrument XY in fashion of a Comb, whose Teeth being in number sixteen, were about an Inch and a half broad, and the Intervals of the Teeth about two Inches wide. Then by interposing successively the Teeth of this Instrument near the Lens, I intercepted Part of the Colours by the interposed Tooth, whilst the rest of them went on through the Interval of the Teeth to the Paper DE, and there painted a round Solar Image. But the Paper I had first placed so, that the Image might appear white as often as the Comb was taken away; and then the Comb being as was said interposed, that Whiteness by reason of the intercepted Part of the Colours at the Lens did always change into the Colour compounded of those Colours which were not intercepted, and that Colour was by the Motion of the Comb perpetually varied so, that in the passing of every Tooth over the Lens all these Colours, red, yellow, green, blue, and purple, did always succeed one another. I caused therefore all the Teeth to pass successively over the Lens, and when the Motion was slow, there appeared a perpetual Succession of the Colours upon the Paper: But if I so much accelerated the Motion, that the Colours by reason of their quick Succession could not be distinguished from one another, the Appearance of the single Colours ceased. There was no red, no yellow, no green, no blue, nor purple to be seen any longer, but from a Confusion of them all there arose one uniform white Colour. Of the Light which now by the Mixture of all the Colours appeared 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 strike the Sensorium. If the Impressions follow one another slowly, so that they may be severally perceived, there is made a distinct Sensation of all the Colours one after another in a continual Succession. But if the Impressions follow one another so quickly, that they cannot be severally perceived, there ariseth out of them all one common Sensation, which is neither of this Colour alone nor of that alone, but hath it self indifferently to 'em all, and this is a Sensation of Whiteness. By the Quickness of the Successions, the Impressions of the several Colours are confounded in the Sensorium, and out of that Confusion ariseth a mix'd Sensation. If a burning Coal be nimbly moved round in a Circle with Gyrations continually repeated, the whole Circle will appear like Fire; the reason of which is, that the Sensation of the Coal in the several Places of that Circle remains impress'd on the Sensorium, until the Coal return again to the same Place. And so in a quick Consecution of the Colours the Impression of every Colour remains in the Sensorium, until a Revolution of all the Colours be compleated, and that first Colour return again. The Impressions therefore of all the successive Colours are at once in the Sensorium, and jointly stir up a Sensation of them all; and so it is manifest by this Experiment, that the commix'd Impressions of all the Colours do stir up and beget a Sensation of white, that is, that Whiteness is compounded of all the Colours.

And if the Comb be now taken away, that all the Colours may at once pass from the Lens to the Paper, and be there intermixed, and together reflected thence to the Spectator's Eyes; their Impressions on the Sensorium being now more subtilly and perfectly commixed there, ought much more to stir up a Sensation of Whiteness.

You may instead of the Lens use two Prisms HIK and LMN, which by refracting the coloured Light the contrary Way to that of the first Refraction, may make the diverging Rays converge and meet again in G, as you see represented in the seventh Figure. For where they meet and mix, they will compose a white Light, as when a Lens is used.

Exper. 11. Let the Sun's coloured Image PT [in Fig. 8.] fall upon the Wall of a dark Chamber, as in the third Experiment of the first Book, and let the same be viewed through a Prism abc, held parallel to the Prism ABC, by whose Refraction that Image was made, and let it now appear lower than before, suppose in the Place S over-against the red Colour T. And if you go near to the Image PT, the Spectrum S will appear oblong and coloured like the Image PT; but if you recede from it, the Colours of the spectrum S will be contracted more and more, and at length vanish, that Spectrum S becoming perfectly round and white; and if you recede yet farther, the Colours will emerge again, but in a contrary Order. Now that Spectrum S appears white in that Case, when the Rays of several sorts which converge from the several Parts of the Image PT, to the Prism abc, are so refracted unequally by it, that in their Passage from the Prism to the Eye they may diverge from one and the same Point of the Spectrum S, and so fall afterwards upon one and the same Point in the bottom of the Eye, and there be mingled.

Fig. 7.

Fig. 8.

And farther, if the Comb be here made use of, by whose Teeth the Colours at the Image PT may be successively intercepted; the Spectrum S, when the Comb is moved slowly, will be perpetually tinged with successive Colours: But when by accelerating the Motion of the Comb, the Succession of the Colours is so quick that they cannot be severally seen, that Spectrum S, by a confused and mix'd Sensation of them all, will appear white.

Exper. 12. The Sun shining through a large Prism ABC [in Fig. 9.] upon a Comb XY, placed immediately behind the Prism, his Light which passed through the Interstices of the Teeth fell upon a white Paper DE. The Breadths of the Teeth were equal to their Interstices, and seven Teeth together with their Interstices took up an Inch in Breadth. Now, when the Paper was about two or three Inches distant from the Comb, the Light which passed through its several Interstices painted so many Ranges of Colours, kl, mn, op, qr, &c. which were parallel to one another, and contiguous, and without any Mixture of white. And these Ranges of Colours, if the Comb was moved continually up and down with a reciprocal Motion, ascended and descended in the Paper, and when the Motion of the Comb was so quick, that the Colours could not be distinguished from one another, the whole Paper by their Confusion and Mixture in the Sensorium appeared white.

Fig. 9.

Let the Comb now rest, and let the Paper be removed farther from the Prism, and the several Ranges of Colours will be dilated and expanded into one another more and more, and by mixing their Colours will dilute one another, and at length, when the distance of the Paper from the Comb is about a Foot, or a little more (suppose in the Place 2D 2E) they will so far dilute one another, as to become white.

With any Obstacle, let all the Light be now stopp'd which passes through any one Interval of the Teeth, so that the Range of Colours which comes from thence may be taken away, and you will see the Light of the rest of the Ranges to be expanded into the Place of the Range taken away, and there to be coloured. Let the intercepted Range pass on as before, and its Colours falling upon the Colours of the other Ranges, and mixing with them, will restore the Whiteness.

Let the Paper 2D 2E be now very much inclined to the Rays, so that the most refrangible Rays may be more copiously reflected than the rest, and the white Colour of the Paper through the Excess of those Rays will be changed into blue and violet. Let the Paper be as much inclined the contrary way, that the least refrangible Rays may be now more copiously reflected than the rest, and by their Excess the Whiteness will be changed into yellow and red. The several Rays therefore in that white Light do retain their colorific Qualities, by which those of any sort, whenever they become more copious than the rest, do by their Excess and Predominance cause their proper Colour to appear.

And by the same way of arguing, applied to the third Experiment of this second Part of the first Book, it may be concluded, that the white Colour of all refracted Light at its very first Emergence, where it appears as white as before its Incidence, is compounded of various Colours.

Fig. 10.

Exper. 13. In the foregoing Experiment the several Intervals of the Teeth of the Comb do the Office of so many Prisms, every Interval producing the Phænomenon of one Prism. Whence instead of those Intervals using several Prisms, I try'd to compound Whiteness by mixing their Colours, and did it by using only three Prisms, as also by using only two as follows. Let two Prisms ABC and abc, [in Fig. 10.] whose refracting Angles B and b are equal, be so placed parallel to one another, that the refracting Angle B of the one may touch the Angle c at the Base of the other, and their Planes CB and cb, at which the Rays emerge, may lie in Directum. Then let the Light trajected through them fall upon the Paper MN, distant about 8 or 12 Inches from the Prisms. And the Colours generated by the interior Limits B and c of the two Prisms, will be mingled at PT, and there compound white. For if either Prism be taken away, the Colours made by the other will appear in that Place PT, and when the Prism is restored to its Place again, so that its Colours may there fall upon the Colours of the other, the Mixture of them both will restore the Whiteness.

This Experiment succeeds also, as I have tried, when the Angle b of the lower Prism, is a little greater than the Angle B of the upper, and between the interior Angles B and c, there intercedes some Space Bc, as is represented in the Figure, and the refracting Planes BC and bc, are neither in Directum, nor parallel to one another. For there is nothing more requisite to the Success of this Experiment, than that the Rays of all sorts may be uniformly mixed upon the Paper in the Place PT. If the most refrangible Rays coming from the superior Prism take up all the Space from M to P, the Rays of the same sort which come from the inferior Prism ought to begin at P, and take up all the rest of the Space from thence towards N. If the least refrangible Rays coming from the superior Prism take up the Space MT, the Rays of the same kind which come from the other Prism ought to begin at T, and take up the remaining Space TN. If one sort of the Rays which have intermediate Degrees of Refrangibility, and come from the superior Prism be extended through the Space MQ, and another sort of those Rays through the Space MR, and a third sort of them through the Space MS, the same sorts of Rays coming from the lower Prism, ought to illuminate the remaining Spaces QN, RN, SN, respectively. And the same is to be understood of all the other sorts of Rays. For thus the Rays of every sort will be scattered uniformly and evenly through the whole Space MN, and so being every where mix'd in the same Proportion, they must every where produce the same Colour. And therefore, since by this Mixture they produce white in the Exterior Spaces MP and TN, they must also produce white in the Interior Space PT. This is the reason of the Composition by which Whiteness was produced in this Experiment, and by what other way soever I made the like Composition, the Result was Whiteness.

Lastly, If with the Teeth of a Comb of a due Size, the coloured Lights of the two Prisms which fall upon the Space PT be alternately intercepted, that Space PT, when the Motion of the Comb is slow, will always appear coloured, but by accelerating the Motion of the Comb so much that the successive Colours cannot be distinguished from one another, it will appear white.

Exper. 14. Hitherto I have produced Whiteness by mixing the Colours of Prisms. If now the Colours of natural Bodies are to be mingled, let Water a little thicken'd with Soap be agitated to raise a Froth, and after that Froth has stood a little, there will appear to one that shall view it intently various Colours every where in the Surfaces of the several Bubbles; but to one that shall go so far off, that he cannot distinguish the Colours from one another, the whole Froth will grow white with a perfect Whiteness.

Exper. 15. Lastly, In attempting to compound a white, by mixing the coloured Powders which Painters use, I consider'd that all colour'd Powders do suppress and stop in them a very considerable Part of the Light by which they are illuminated. For they become colour'd by reflecting the Light of their own Colours more copiously, and that of all other Colours more sparingly, and yet they do not reflect the Light of their own Colours so copiously as white Bodies do. If red Lead, for instance, and a white Paper, be placed in the red Light of the colour'd Spectrum made in a dark Chamber by the Refraction of a Prism, as is described in the third Experiment of the first Part of this Book; the Paper will appear more lucid than the red Lead, and therefore reflects the red-making Rays more copiously 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 reflected by the red Lead in a much greater Proportion. And the like happens in Powders of other Colours. And therefore by mixing such Powders, we are not to expect a strong and full White, such as is that of Paper, but some dusky obscure one, such as might arise from a Mixture of Light and Darkness, or from white and black, that is, a grey, or dun, or russet brown, such as are the Colours of a Man's Nail, of a Mouse, of Ashes, of ordinary Stones, of Mortar, of Dust and Dirt in High-ways, and the like. And such a dark white I have often produced by mixing colour'd Powders. For thus one Part of red Lead, and five Parts of Viride Æris, composed a dun Colour like that of a Mouse. For these two Colours were severally so compounded of others, that in both together were a Mixture of all Colours; and there was less red Lead used than Viride Æris, because of the Fulness of its Colour. Again, one Part of red Lead, and four Parts of blue Bise, composed a dun Colour verging a little to purple, and by adding to this a certain Mixture of Orpiment and Viride Æris in a due Proportion, the Mixture lost its purple Tincture, and became perfectly dun. But the Experiment succeeded best without Minium thus. To Orpiment I added by little and little a certain full bright purple, which Painters use, until the Orpiment ceased to be yellow, and became of a pale red. Then I diluted that red by adding a little Viride Æris, and a little more blue Bise than Viride Æris, until it became of such a grey or pale white, as verged to no one of the Colours more than to another. For thus it became of a Colour equal in Whiteness to that of Ashes, or of Wood newly cut, or of a Man's Skin. The Orpiment reflected more Light than did any other of the Powders, and therefore conduced more to the Whiteness of the compounded Colour than they. To assign the Proportions accurately may be difficult, by reason of the different Goodness of Powders of the same kind. Accordingly, as the Colour of any Powder is more or less full and luminous, it ought to be used in a less or greater Proportion.

Now, considering that these grey and dun Colours may be also produced by mixing Whites and Blacks, and by consequence differ from perfect Whites, not in Species of Colours, but only in degree of Luminousness, it is manifest that there is nothing more requisite to make them perfectly white than to increase their Light sufficiently; and, on the contrary, if by increasing their Light they can be brought to perfect Whiteness, it will thence also follow, that they are of the same Species of Colour with the best Whites, and differ from them only in the Quantity of Light. And this I tried as follows. I took the third of the above-mention'd grey Mixtures, (that which was compounded of Orpiment, Purple, Bise, and Viride Æris) and rubbed it thickly upon the Floor of my Chamber, where the Sun shone upon it through the opened Casement; and by it, in the shadow, I laid a Piece of white Paper of the same Bigness. Then going from them to the distance of 12 or 18 Feet, so that I could not discern the Unevenness of the Surface of the Powder, nor the little Shadows let fall from the gritty Particles thereof; the Powder appeared intensely white, so as to transcend even the Paper it self in Whiteness, especially if the Paper were a little shaded from the Light of the Clouds, and then the Paper compared with the Powder appeared of such a grey Colour as the Powder had done before. But by laying the Paper where the Sun shines through the Glass of the Window, or by shutting the Window that the Sun might shine through the Glass upon the Powder, and by such other fit Means of increasing or decreasing the Lights wherewith the Powder and Paper were illuminated, the Light wherewith the Powder is illuminated may be made stronger in such a due Proportion than the Light wherewith the Paper is illuminated, that they shall both appear exactly alike in Whiteness. For when I was trying this, a Friend coming to visit me, I stopp'd him at the Door, and before I told him what the Colours were, or what I was doing; I asked him, Which of the two Whites were the best, and wherein they differed? And after he had at that distance viewed them well, he answer'd, that they were both good Whites, and that he could not say which was best, nor wherein their Colours differed. Now, if you consider, that this White of the Powder in the Sun-shine was compounded of the Colours which the component Powders (Orpiment, Purple, Bise, and Viride Æris) have in the same Sun-shine, you must acknowledge by this Experiment, as well as by the former, that perfect Whiteness may be compounded of Colours.

From what has been said it is also evident, that the Whiteness of the Sun's Light is compounded of all the Colours wherewith the several sorts of Rays whereof that Light consists, when by their several Refrangibilities they are separated from one another, do tinge Paper or any other white Body whereon they fall. For those Colours (by Prop. II. Part 2.) are unchangeable, and whenever all those Rays with those their Colours are mix'd again, they reproduce the same white Light as before.

PROP. VI. Prob. II.

In a mixture of Primary Colours, the Quantity and Quality of each being given, to know the Colour of the Compound.

Fig. 11.

With the Center O [in Fig. 11.] and Radius OD describe a Circle ADF, and distinguish its Circumference into seven Parts DE, EF, FG, GA, AB, BC, CD, proportional to the seven Musical Tones or Intervals of the eight Sounds, Sol, la, fa, sol, la, mi, fa, sol, contained in an eight, that is, proportional to the Number 1/9, 1/16, 1/10, 1/9, 1/16, 1/16, 1/9. Let the first Part DE represent a red Colour, the second EF orange, the third FG yellow, the fourth CA green, the fifth AB blue, the sixth BC indigo, and the seventh CD violet. And conceive that these are all the Colours of uncompounded Light gradually passing into one another, as they do when made by Prisms; the Circumference DEFGABCD, representing the whole Series of Colours from one end of the Sun's colour'd Image to the other, so 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 degrees of yellow, and so on. Let p be the Center of Gravity of the Arch DE, and q, r, s, t, u, x, the Centers of Gravity of the Arches EF, FG, GA, AB, BC, and CD respectively, and about those Centers of Gravity let Circles proportional to the Number of Rays of each Colour in the given Mixture be describ'd: that is, the Circle p proportional to the Number of the red-making Rays in the Mixture, the Circle q proportional to the Number of the orange-making Rays in the Mixture, and so of the rest. Find the common Center of Gravity of all those Circles, p, q, r, s, t, u, x. Let that Center be Z; and from the Center of the Circle ADF, through Z to the Circumference, drawing the Right Line OY, the Place of the Point Y in the Circumference shall shew the Colour arising from the Composition of all the Colours in the given Mixture, and the Line OZ shall be proportional to the Fulness or Intenseness of the Colour, that is, to its distance from Whiteness. As if Y fall in the middle between F and G, the compounded Colour shall be the best yellow; if Y verge from the middle towards F or G, the compound Colour shall accordingly be a yellow, verging towards orange or green. If Z fall upon the Circumference, the Colour shall be intense and florid in the highest Degree; if it fall in the mid-way between the Circumference and Center, it shall be but half so intense, that is, it shall be such a Colour as would be made by diluting the intensest yellow with an equal quantity of whiteness; and if it fall upon the center O, the Colour shall have lost all its intenseness, and become a white. But it is to be noted, That if the point Z fall in or near the line OD, the main ingredients being the red and violet, the Colour compounded shall not be any of the prismatick Colours, but a purple, inclining to red or violet, accordingly as the point Z lieth on the side of the line DO towards E or towards C, and in general the compounded violet is more bright and more fiery than the uncompounded. Also if only two of the primary Colours which in the circle are opposite to one another be mixed in an equal proportion, the point Z shall fall upon the center O, and yet the Colour compounded of those two shall not be perfectly white, but some faint anonymous Colour. For I could never yet by mixing only two primary Colours produce a perfect white. Whether it may be compounded of a mixture of three taken at equal distances in the circumference I do not know, but of four or five I do not much question but it may. But these are Curiosities of little or no moment to the understanding the Phænomena of Nature. For in all whites produced by Nature, there uses to be a mixture of all sorts of Rays, and by consequence a composition of all Colours.

To give an instance of this Rule; suppose a Colour is compounded of these homogeneal Colours, of violet one part, of indigo one part, of blue two parts, of green three parts, of yellow five parts, of orange six parts, and of red ten parts. Proportional to these parts describe the Circles x, v, t, s, r, q, p, respectively, that is, so that if the Circle x be one, the Circle v may be one, the Circle t two, the Circle s three, and the Circles r, q and p, five, six and ten. Then I find Z the common center of gravity of these Circles, and through Z drawing the Line OY, the Point Y falls upon the circumference between E and F, something nearer to E than to F, and thence I conclude, that the Colour compounded of these Ingredients will be an orange, verging a little more to red than to yellow. Also I find that OZ is a little less than one half of OY, and thence I conclude, that this orange hath a little less than half the fulness or intenseness of an uncompounded orange; that is to say, that it is such an orange as may be made by mixing an homogeneal orange with a good white in the proportion of the Line OZ to the Line ZY, this Proportion being not of the quantities of mixed orange and white Powders, but of the quantities of the Lights reflected from them.

This Rule I conceive accurate enough for practice, though not mathematically accurate; and the truth of it may be sufficiently proved to Sense, by stopping any of the Colours at the Lens in the tenth Experiment of this Book. For the rest of the Colours which are not stopp'd, but pass on to the Focus of the Lens, will there compound either accurately or very nearly such a Colour, as by this Rule ought to result from their Mixture.

PROP. VII. Theor. V.

All the Colours in the Universe which are made by Light, and depend not on the Power of Imagination, are either the Colours of homogeneal Lights, or compounded of these, and that either accurately or very nearly, according to the Rule of the foregoing Problem.

For it has been proved (in Prop. 1. Part 2.) that the changes of Colours made by Refractions do not arise from any new Modifications of the Rays impress'd by those Refractions, and by the various Terminations of Light and Shadow, as has been the constant and general Opinion of Philosophers. It has also been proved that the several Colours of the homogeneal Rays do constantly answer to their degrees of Refrangibility, (Prop. 1. Part 1. and Prop. 2. Part 2.) and that their degrees of Refrangibility cannot be changed by Refractions and Reflexions (Prop. 2. Part 1.) and by consequence that those their Colours are likewise immutable. It has also been proved directly by refracting and reflecting homogeneal Lights apart, that their Colours cannot be changed, (Prop. 2. Part 2.) It has been proved also, that when the several sorts of Rays are mixed, and in crossing pass through the same space, they do not act on one another so as to change each others colorific qualities. (Exper. 10. Part 2.) but by mixing their Actions in the Sensorium beget a Sensation differing from what either would do apart, that is a Sensation of a mean Colour between their proper Colours; and particularly when by the concourse and mixtures of all sorts of Rays, a white Colour is produced, the white is a mixture of all the Colours which the Rays would have apart, (Prop. 5. Part 2.) The Rays in that mixture do not lose or alter their several colorific qualities, but by all their various kinds of Actions mix'd in the Sensorium, beget a Sensation of a middling Colour between all their Colours, which is whiteness. For whiteness is a mean between all Colours, having it self indifferently to them all, so as with equal facility to be tinged with any of them. A red Powder mixed with a little blue, or a blue with a little red, doth not presently lose its Colour, but a white Powder mix'd with any Colour is presently tinged with that Colour, and is equally capable of being tinged with any Colour whatever. It has been shewed also, that as the Sun's Light is mix'd of all sorts of Rays, so its whiteness is a mixture of the Colours of all sorts of Rays; those Rays having from the beginning their several colorific qualities as well as their several Refrangibilities, and retaining them perpetually unchanged notwithstanding any Refractions or Reflexions they may at any time suffer, and that whenever any sort of the Sun's Rays is by any means (as by Reflexion in Exper. 9, and 10. Part 1. or by Refraction as happens in all Refractions) separated from the rest, they then manifest their proper Colours. These things have been prov'd, and the sum of all this amounts to the Proposition here to be proved. For if the Sun's Light is mix'd of several sorts of Rays, each of which have originally their several Refrangibilities and colorific Qualities, and notwithstanding their Refractions and Reflexions, and their various Separations or Mixtures, keep those their original Properties perpetually the same without alteration; then all the Colours in the World must be such as constantly ought to arise from the original colorific qualities of the Rays whereof the Lights consist by which those Colours are seen. And therefore if the reason of any Colour whatever be required, we have nothing else to do than to consider how the Rays in the Sun's Light have by Reflexions or Refractions, or other causes, been parted from one another, or mixed together; or otherwise to find out what sorts of Rays are in the Light by which that Colour is made, and in what Proportion; and then by the last Problem to learn the Colour which ought to arise by mixing those Rays (or their Colours) in that proportion. I speak here of Colours so far as they arise from Light. For they appear sometimes by other Causes, as when by the power of Phantasy we see Colours in a Dream, or a Mad-man sees things before him which are not there; or when we see Fire by striking the Eye, or see Colours like the Eye of a Peacock's Feather, by pressing our Eyes in either corner whilst we look the other way. Where these and such like Causes interpose not, the Colour always answers to the sort or sorts of the Rays whereof the Light consists, as I have constantly found in whatever Phænomena of Colours I have hitherto been able to examine. I shall in the following Propositions give instances of this in the Phænomena of chiefest note.

PROP. VIII. Prob. III.

By the discovered Properties of Light to explain the Colours made by Prisms.

Let ABC [in Fig. 12.] represent a Prism refracting the Light of the Sun, which comes into a dark Chamber through a hole Fφ almost as broad as the Prism, and let MN represent a white Paper on which the refracted Light is cast, and suppose the most refrangible or deepest violet-making Rays fall upon the Space Pπ, the least refrangible or deepest red-making Rays upon the Space Tτ, the middle sort between the indigo-making and blue-making Rays upon the Space Qχ, the middle sort of the green-making Rays upon the Space R, the middle sort between the yellow-making and orange-making Rays upon the Space Sσ, and other intermediate sorts upon intermediate Spaces. For so the Spaces upon which the several sorts adequately fall will by reason of the different Refrangibility of those sorts be one lower than another. Now if the Paper MN be so near the Prism that the Spaces PT and πτ do not interfere with one another, the distance between them Tπ will be illuminated by all the sorts of Rays in that proportion to one another which they have at their very first coming out of the Prism, and consequently be white. But the Spaces PT and πτ on either hand, will not be illuminated by them all, and therefore will appear coloured. And particularly at P, where the outmost violet-making Rays fall alone, the Colour must be the deepest violet. At Q where the violet-making and indigo-making Rays are mixed, it must be a violet inclining much to indigo. At R where the violet-making, indigo-making, blue-making, and one half of the green-making Rays are mixed, their Colours must (by the construction of the second Problem) compound a middle Colour between indigo and blue. At S where all the Rays are mixed, except the red-making and orange-making, their Colours ought by the same Rule to compound a faint blue, verging more to green than indigo. And in the progress from S to T, this blue will grow more and more faint and dilute, till at T, where all the Colours begin to be mixed, it ends in whiteness.

Fig. 12.

So again, on the other side of the white at τ, where the least refrangible or utmost red-making Rays are alone, the Colour must be the deepest red. At σ the mixture of red and orange will compound a red inclining to orange. At ρ the mixture of red, orange, yellow, and one half of the green must compound a middle Colour between orange and yellow. At χ the mixture of all Colours but violet and indigo will compound a faint yellow, verging more to green than to orange. And this yellow will grow more faint and dilute continually in its progress from χ to π, where by a mixture of all sorts of Rays it will become white.

These Colours ought to appear were the Sun's Light perfectly white: But because it inclines to yellow, the Excess 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 faint green. And so the Colours in order from P to τ ought to be violet, indigo, blue, very faint green, white, faint yellow, orange, red. Thus it is by the computation: And they that please to view the Colours made by a Prism will find it so in Nature.

These are the Colours on both sides the white when the Paper is held between the Prism and the Point X where the Colours meet, and the interjacent white vanishes. For if the Paper be held still farther off from the Prism, the most refrangible and least refrangible Rays will be wanting in the middle of the Light, and the rest of the Rays which are found there, will by mixture produce a fuller green than before. Also the yellow and blue will now become less compounded, and by consequence more intense than before. And this also agrees with experience.

And if one look through a Prism upon a white Object encompassed with blackness or darkness, the reason of the Colours arising on the edges is much the same, as will appear to one that shall a little consider it. If a black Object be encompassed with a white one, the Colours which appear through the Prism are to be derived from the Light of the white one, spreading into the Regions of the black, and therefore they appear in a contrary order to that, when a white Object is surrounded with black. And the same is to be understood when an Object is viewed, whose parts are some of them less luminous than others. For in the borders of the more and less luminous Parts, Colours ought always by the same Principles to arise from the Excess of the Light of the more luminous, and to be of the same kind as if the darker parts were black, but yet to be more faint and dilute.

What is said of Colours made by Prisms may be easily applied to Colours made by the Glasses of Telescopes or Microscopes, or by the Humours of the Eye. For if the Object-glass of a Telescope be thicker on one side than on the other, or if one half of the Glass, or one half of the Pupil of the Eye be cover'd with any opake substance; the Object-glass, or that part of it or of the Eye which is not cover'd, may be consider'd as a Wedge with crooked Sides, and every Wedge of Glass or other pellucid Substance has the effect of a Prism in refracting the Light which passes through it.[12]

How the Colours in the ninth and tenth Experiments of the first Part arise from the different Reflexibility of Light, is evident by what was there said. But it is observable in the ninth Experiment, that whilst the Sun's direct Light is yellow, the Excess of the blue-making Rays in the reflected beam of Light MN, suffices only to bring that yellow to a pale white inclining to blue, and not to tinge it with a manifestly blue Colour. To obtain therefore a better blue, I used instead of the yellow Light of the Sun the white Light of the Clouds, by varying a little the Experiment, as follows.

Fig. 13.

Exper. 16 Let HFG [in Fig. 13.] represent a Prism in the open Air, and S the Eye of the Spectator, viewing the Clouds by their Light coming into the Prism at the Plane Side FIGK, and reflected in it by its Base HEIG, and thence going out through its Plane Side HEFK to the Eye. And when the Prism and Eye are conveniently placed, so that the Angles of Incidence and Reflexion at the Base may be about 40 Degrees, the Spectator will see a Bow MN of a blue Colour, running from one End of the Base to the other, with the Concave Side towards him, and the Part of the Base IMNG beyond this Bow will be brighter than the other Part EMNH on the other Side of it. This blue Colour MN being made by nothing else than by Reflexion of a specular Superficies, seems so odd a Phænomenon, and so difficult to be explained by the vulgar Hypothesis of Philosophers, that I could not but think it deserved to be taken Notice of. Now for understanding the Reason of it, suppose the Plane ABC to cut the Plane Sides and Base of the Prism perpendicularly. From the Eye to the Line BC, wherein that Plane cuts the Base, draw the Lines Sp and St, in the Angles Spc 50 degr. 1/9, and Stc 49 degr. 1/28, and the Point p will be the Limit beyond which none of the most refrangible Rays can pass through the Base of the Prism, and be refracted, whose Incidence is such that they may be reflected to the Eye; and the Point t will be the like Limit for the least refrangible Rays, that is, beyond which none of them can pass through the Base, whose Incidence is such 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 least refrangible Rays which fall upon the Base beyond t, that is, between t and B, and can come from thence to the Eye, will be reflected thither: But on this side t, that is, between t and c, many of these Rays will be transmitted through the Base. And all the most refrangible Rays which fall upon the Base beyond p, that is, between, p and B, and can by Reflexion come from thence to the Eye, will be reflected thither, but every where between p and c, many of these Rays will get through the Base, and be refracted; and the same is to be understood of the meanly refrangible Rays on either side of the Point r. Whence it follows, that the Base of the Prism must every where between t and B, by a total Reflexion of all sorts of Rays to the Eye, look white and bright. And every where between p and C, by reason of the Transmission of many Rays of every sort, look more pale, obscure, and dark. But at r, and in other Places between p and t, where all the more refrangible Rays are reflected to the Eye, and many of the less refrangible are transmitted, the Excess of the most refrangible in the reflected Light will tinge that Light with their Colour, which is violet and blue. And this happens by taking the Line C prt B any where between the Ends of the Prism HG and EI.

PROP. IX. Prob. IV.

By the discovered Properties of Light to explain the Colours of the Rain-bow.

Fig. 14.

This Bow never appears, but where it rains in the Sun-shine, and may be made artificially by spouting up Water which may break aloft, and scatter into Drops, and fall down like Rain. For the Sun shining upon these Drops certainly causes the Bow to appear to a Spectator standing in a due Position to the Rain and Sun. And hence it is now agreed upon, that this Bow is made by Refraction of the Sun's Light in drops of falling Rain. This was understood by some of the Antients, and of late more fully discover'd and explain'd by the famous Antonius de Dominis Archbishop of Spalato, in his book De Radiis Visûs & Lucis, published by his Friend Bartolus at Venice, in the Year 1611, and written above 20 Years before. For he teaches there how the interior Bow is made in round Drops of Rain by two Refractions of the Sun's Light, and one Reflexion between them, and the exterior by two Refractions, and two sorts of Reflexions between them in each Drop of Water, and proves his Explications by Experiments made with a Phial full of Water, and with Globes of Glass filled with Water, and placed in the Sun to make the Colours of the two Bows appear in them. The same Explication Des-Cartes hath pursued in his Meteors, and mended that of the exterior Bow. But whilst they understood not the true Origin of Colours, it's necessary to pursue it here a little farther. For understanding therefore how the Bow is made, let a Drop of Rain, or any other spherical transparent Body be represented by the Sphere BNFG, [in Fig. 14.] described with the Center C, and Semi-diameter CN. And let AN be one of the Sun's Rays incident upon it at N, and thence refracted to F, where let it either go out of the Sphere by Refraction towards 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 incident Ray in Y. Produce AN and RG, till they meet in X, and upon AX and NF, let fall the Perpendiculars CD and CE, and produce CD till it fall upon the Circumference at L. Parallel to the incident Ray AN draw the Diameter BQ, and let the Sine of Incidence out of Air into Water be to the Sine of Refraction as I to R. Now, if you suppose the Point of Incidence N to move from the Point B, continually till it come to L, the Arch QF will first increase and then decrease, and so will the Angle AXR which the Rays AN and GR contain; and the Arch QF and Angle AXR will be biggest when ND is to CN as √(II - RR) to √(3)RR, in which case NE will be to ND as 2R to I. Also the Angle AYS, which the Rays AN and HS contain will first decrease, and then increase and grow least when ND is to CN as √(II - RR) to √(8)RR, in which case NE will be to ND, as 3R to I. And so 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 √(15)RR, in which case NE will be to ND as 4R to I. And the Angle which the Ray next after that Emergent, that is, the Ray emergent after four Reflexions, contains with the Incident, will come to its Limit, when ND is to CN as √(II - RR) to √(24)RR, in which case NE will be to ND as 5R to I; and so on infinitely, the Numbers 3, 8, 15, 24, &c. being gather'd by continual Addition of the Terms of the arithmetical Progression 3, 5, 7, 9, &c. The Truth of all this Mathematicians will easily examine.[13]

Now it is to be observed, that as when the Sun comes to his Tropicks, Days increase and decrease but a very little for a great while together; so when by increasing the distance CD, these Angles come to their Limits, they vary their quantity but very little for some time together, and therefore a far greater number of the Rays which fall upon all the Points N in the Quadrant BL, shall emerge in the Limits of these Angles, than in any other Inclinations. And farther it is to be observed, that the Rays which differ in Refrangibility will have different Limits of their Angles of Emergence, and by consequence according to their different Degrees of Refrangibility emerge most copiously in different Angles, and being separated from one another appear each in their proper Colours. And what those Angles are may be easily gather'd from the foregoing Theorem by Computation.

For in the least refrangible Rays the Sines I and R (as was found above) are 108 and 81, and thence by Computation the greatest Angle AXR will be found 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and 57 Minutes. And in the most refrangible Rays the Sines I and R are 109 and 81, and thence by Computation the greatest Angle AXR will be found 40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7 Minutes.

Suppose now that O [in Fig. 15.] is the Spectator's Eye, and OP a Line drawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Angles of 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min. respectively, and these Angles turned about their common Side OP, shall with their other Sides OE, OF; OG, OH, describe the Verges of two Rain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any where in the conical Superficies described by OE, OF, 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. shall be the greatest Angle in which the most refrangible Rays can after one Reflexion be refracted to the Eye, and therefore all the Drops in the Line OE shall send the most refrangible Rays most copiously to the Eye, and thereby strike the Senses with the deepest violet Colour in that Region. And in like manner the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min. shall be the greatest in which the least refrangible Rays after one Reflexion can emerge out of the Drops, and therefore those Rays shall come most copiously to the Eye from the Drops in the Line OF, and strike the Senses with the deepest red Colour in that Region. And by the same Argument, the Rays which have intermediate Degrees of Refrangibility shall come most copiously from Drops between E and F, and strike the Senses with the intermediate Colours, in the Order which their Degrees of Refrangibility require, that is in the Progress from E to F, or from the inside of the Bow to the outside in this order, violet, indigo, blue, green, yellow, orange, red. But the violet, by the mixture of the white Light of the Clouds, will appear faint and incline to purple.

Fig. 15.

Again, the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min. shall be the least Angle in which the least refrangible Rays can after two Reflexions emerge out of the Drops, and therefore the least refrangible Rays shall come most copiously to the Eye from the Drops in the Line OG, and strike the Sense with the deepest red in that Region. And the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min. shall be the least Angle, in which the most refrangible Rays after two Reflexions can emerge out of the Drops; and therefore those Rays shall come most copiously to the Eye from the Drops in the Line OH, and strike the Senses with the deepest violet in that Region. And by the same Argument, the Drops in the Regions between G and H shall strike the Sense with the intermediate Colours in the Order which their Degrees of Refrangibility require, that is, in the Progress from G to H, or from the inside of the Bow to the outside in this order, red, orange, yellow, green, blue, indigo, violet. And since these four Lines OE, OF, OG, OH, may be situated any where in the above-mention'd conical Superficies; what is said of the Drops and Colours in these Lines is to be understood of the Drops and Colours every where in those Superficies.

Thus shall there be made two Bows of Colours, an interior and stronger, by one Reflexion in the Drops, and an exterior and fainter by two; for the Light becomes fainter by every Reflexion. And their Colours shall lie in a contrary Order to one another, the red of both Bows bordering upon the Space GF, which is between the Bows. The Breadth of the interior Bow EOF measured cross the Colours shall be 1 Degr. 45 Min. and the Breadth of the exterior GOH shall be 3 Degr. 10 Min. and the distance between them GOF shall be 8 Gr. 15 Min. the greatest Semi-diameter of the innermost, that is, the Angle POF being 42 Gr. 2 Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57 Min. These are the Measures of the Bows, as they would be were the Sun but a Point; for by the Breadth of his Body, the Breadth of the Bows will be increased, and their Distance decreased by half a Degree, and so the breadth of the interior Iris will be 2 Degr. 15 Min. that of the exterior 3 Degr. 40 Min. their distance 8 Degr. 25 Min. the greatest Semi-diameter of the interior Bow 42 Degr. 17 Min. and the least of the exterior 50 Degr. 42 Min. And such are the Dimensions of the Bows in the Heavens found to be very nearly, when their Colours appear strong and perfect. For once, by such means as I then had, I measured the greatest Semi-diameter of the interior Iris about 42 Degrees, and the breadth of the red, yellow and green in that Iris 63 or 64 Minutes, besides the outmost faint red obscured by the brightness of the Clouds, for which we may allow 3 or 4 Minutes more. The breadth of the blue was about 40 Minutes more besides the violet, which was so much obscured by the brightness of the Clouds, that I could not measure its breadth. But supposing 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 2-1/4 Degrees, as above. The least distance between this Iris and the exterior Iris was about 8 Degrees and 30 Minutes. The exterior Iris was broader than the interior, but so faint, especially on the blue side, that I could not measure its breadth distinctly. At another time when both Bows appeared more distinct, I measured the breadth of the interior Iris 2 Gr. 10´, and the breadth of the red, yellow and green in the exterior Iris, was to the breadth of the same Colours in the interior as 3 to 2.

This Explication of the Rain-bow is yet farther confirmed by the known Experiment (made by Antonius de Dominis and Des-Cartes) of hanging up any where in the Sun-shine a Glass Globe filled with Water, and viewing it in such a posture, that the Rays which come from the Globe to the Eye may contain with the Sun's Rays an Angle of either 42 or 50 Degrees. For if the Angle be about 42 or 43 Degrees, the Spectator (suppose at O) shall see a full red Colour in that side of the Globe opposed to the Sun as 'tis represented at F, and if that Angle become less (suppose by depressing the Globe to E) there will appear other Colours, yellow, green and blue successive in the same side of the Globe. But if the Angle be made about 50 Degrees (suppose by lifting up the Globe to G) there will appear a red Colour in that side of the Globe towards the Sun, and if the Angle be made greater (suppose by lifting up the Globe to H) the red will turn successively to the other Colours, yellow, green and blue. The same thing I have tried, by letting a Globe rest, and raising or depressing the Eye, or otherwise moving it to make the Angle of a just magnitude.

I have heard it represented, that if the Light of a Candle be refracted by a Prism to the Eye; when the blue Colour falls upon the Eye, the Spectator shall see red in the Prism, and when the red falls upon the Eye he shall see blue; and if this were certain, the Colours of the Globe and Rain-bow ought to appear in a contrary order to what we find. But the Colours of the Candle being very faint, the mistake seems to arise from the difficulty of discerning what Colours fall on the Eye. For, on the contrary, I have sometimes had occasion to observe in the Sun's Light refracted by a Prism, that the Spectator always sees that Colour in the Prism which falls upon his Eye. And the same I have found true also in Candle-light. For when the Prism is moved slowly from the Line which is drawn directly from the Candle to the Eye, the red appears first in the Prism and then the blue, and therefore each of them is seen when it falls upon the Eye. For the red passes over the Eye first, and then the blue.

The Light which comes through drops of Rain by two Refractions without any Reflexion, ought to appear strongest at the distance of about 26 Degrees from the Sun, and to decay gradually both ways as the distance from him increases and decreases. And the same is to be understood of Light transmitted through spherical Hail-stones. And if the Hail be a little flatted, as it often is, the Light transmitted may grow so strong at a little less distance than that of 26 Degrees, as to form a Halo about the Sun or Moon; which Halo, as often as the Hail-stones are duly figured may be colour'd, and then it must be red within by the least refrangible Rays, and blue without by the most refrangible ones, especially if the Hail-stones have opake Globules of Snow in their center to intercept the Light within the Halo (as Hugenius has observ'd) and make the inside thereof more distinctly defined than it would otherwise be. For such Hail-stones, though spherical, by terminating the Light by the Snow, may make a Halo red within and colourless without, and darker in the red than without, as Halos used to be. For of those Rays which pass close by the Snow the Rubriform will be least refracted, and so come to the Eye in the directest Lines.

The Light which passes through a drop of Rain after two Refractions, and three or more Reflexions, is scarce strong enough to cause a sensible Bow; but in those Cylinders of Ice by which Hugenius explains the Parhelia, it may perhaps be sensible.

PROP. X. Prob. V.

By the discovered Properties of Light to explain the permanent Colours of Natural Bodies.

These Colours arise from hence, that some natural Bodies reflect some sorts of Rays, others other sorts more copiously than the rest. Minium reflects the least refrangible or red-making Rays most copiously, and thence appears red. Violets reflect the most refrangible most copiously, and thence have their Colour, and so of other Bodies. Every Body reflects the Rays of its own Colour more copiously than the rest, and from their excess and predominance in the reflected Light has its Colour.

Exper. 17. For if in the homogeneal Lights obtained by the solution of the Problem proposed in the fourth Proposition of the first Part of this Book, you place Bodies of several Colours, you will find, as I have done, that every Body looks most splendid and luminous in the Light of its own Colour. Cinnaber in the homogeneal red Light is most resplendent, in the green Light it is manifestly less resplendent, and in the blue Light still less. Indigo in the violet blue Light is most resplendent, and its splendor is gradually diminish'd, as it is removed thence by degrees 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 strongly reflected than the other Colours red and violet, and so of the rest. But to make these Experiments the more manifest, such Bodies ought to be chosen as have the fullest and most vivid Colours, and two of those Bodies are to be compared together. Thus, for instance, if Cinnaber and ultra-marine blue, or some other full blue be held together in the red homogeneal Light, they will both appear red, but the Cinnaber will appear of a strongly luminous and resplendent red, and the ultra-marine blue of a faint obscure 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 strongly luminous and resplendent blue, and the Cinnaber of a faint and dark blue. Which puts it out of dispute that the Cinnaber reflects the red Light much more copiously than the ultra-marine doth, and the ultra-marine reflects the blue Light much more copiously than the Cinnaber doth. The same Experiment may be tried successfully with red Lead and Indigo, or with any other two colour'd Bodies, if due allowance be made for the different strength or weakness of their Colour and Light.

And as the reason of the Colours of natural Bodies is evident by these Experiments, so it is farther confirmed and put past dispute by the two first Experiments of the first Part, whereby 'twas proved in such Bodies that the reflected Lights which differ in Colours do differ also in degrees of Refrangibility. For thence it's certain, that some Bodies reflect the more refrangible, others the less refrangible Rays more copiously.

And that this is not only a true reason of these Colours, but even the only reason, may appear farther from this Consideration, that the Colour of homogeneal Light cannot be changed by the Reflexion of natural Bodies.

For if Bodies by Reflexion cannot in the least change the Colour of any one sort of Rays, they cannot appear colour'd by any other means than by reflecting those which either are of their own Colour, or which by mixture must produce it.

But in trying Experiments of this kind care must be had that the Light be sufficiently homogeneal. For if Bodies be illuminated by the ordinary prismatick Colours, they will appear neither of their own Day-light Colours, nor of the Colour of the Light cast on them, but of some middle Colour between both, as I have found by Experience. Thus red Lead (for instance) illuminated with the ordinary prismatick 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 less compounded. For because red Lead appears red when illuminated with white Light, wherein all sorts of Rays are equally mix'd, and in the green Light all sorts of Rays are not equally mix'd, the Excess of the yellow-making, green-making and blue-making Rays in the incident green Light, will cause those Rays to abound so much in the reflected Light, as to draw the Colour from red towards their Colour. And because the red Lead reflects the red-making Rays most copiously in proportion to their number, and next after them the orange-making and yellow-making Rays; these Rays in the reflected Light will be more in proportion to the Light than they were in the incident green Light, and thereby will draw the reflected Light from green towards their Colour. And therefore the red Lead will appear neither red nor green, but of a Colour between both.

In transparently colour'd Liquors 'tis observable, that their Colour uses to vary with their thickness. Thus, for instance, a red Liquor in a conical Glass held between the Light and the Eye, looks of a pale and dilute yellow at the bottom where 'tis thin, and a little higher where 'tis thicker grows orange, and where 'tis still thicker becomes red, and where 'tis thickest the red is deepest and darkest. For it is to be conceiv'd that such a Liquor stops the indigo-making and violet-making Rays most easily, the blue-making Rays more difficultly, the green-making Rays still more difficultly, and the red-making most difficultly: And that if the thickness of the Liquor be only so much as suffices to stop a competent number of the violet-making and indigo-making Rays, without diminishing much the number of the rest, the rest must (by Prop. 6. Part 2.) compound a pale yellow. But if the Liquor be so much thicker as to stop also a great number of the blue-making Rays, and some of the green-making, the rest must compound an orange; and where it is so thick as to stop also a great number of the green-making and a considerable number of the yellow-making, the rest must begin to compound a red, and this red must grow deeper and darker as the yellow-making and orange-making Rays are more and more stopp'd by increasing the thickness of the Liquor, so that few Rays besides the red-making can get through.

Of this kind is an Experiment lately related to me by Mr. Halley, who, in diving deep into the Sea in a diving Vessel, found in a clear Sun-shine Day, that when he was sunk many Fathoms deep into the Water the upper part of his Hand on which the Sun shone directly through the Water and through a small Glass Window in the Vessel appeared of a red Colour, like that of a Damask Rose, and the Water below and the under part of his Hand illuminated by Light reflected from the Water below look'd green. For thence it may be gather'd, that the Sea-Water reflects back the violet and blue-making Rays most easily, and lets the red-making Rays pass most freely and copiously to great Depths. For thereby the Sun's direct Light at all great Depths, by reason of the predominating red-making Rays, must appear red; and the greater the Depth is, the fuller and intenser must that red be. And at such Depths as the violet-making Rays scarce penetrate unto, the blue-making, green-making, and yellow-making Rays being reflected from below more copiously than the red-making ones, must compound a green.

Now, if there be two Liquors of full Colours, suppose a red and blue, and both of them so thick as suffices to make their Colours sufficiently full; though either Liquor be sufficiently transparent apart, yet will you not be able to see through both together. For, if only the red-making Rays pass through one Liquor, and only the blue-making through the other, no Rays can pass through both. This Mr. Hook tried casually with Glass Wedges filled with red and blue Liquors, and was surprized at the unexpected Event, the reason of it being then unknown; which makes me trust the more to his Experiment, though I have not tried it my self. But he that would repeat it, must take care the Liquors be of very good and full Colours.

Now, whilst Bodies become coloured by reflecting or transmitting this or that sort of Rays more copiously than the rest, it is to be conceived that they stop and stifle in themselves the Rays which they do not reflect or transmit. For, if Gold be foliated and held between your Eye and the Light, the Light looks of a greenish blue, and therefore massy Gold lets into its Body the blue-making Rays to be reflected to and fro within it till they be stopp'd and stifled, whilst it reflects the yellow-making outwards, and thereby looks yellow. And much after the same manner that Leaf Gold is yellow by reflected, and blue by transmitted Light, and massy Gold is yellow in all Positions of the Eye; there are some Liquors, as the Tincture of Lignum Nephriticum, and some sorts of Glass which transmit one sort of Light most copiously, and reflect another sort, and thereby look of several Colours, according to the Position of the Eye to the Light. But, if these Liquors or Glasses were so thick and massy that no Light could get through them, I question not but they would like all other opake Bodies appear of one and the same Colour in all Positions of the Eye, though this I cannot yet affirm by Experience. For all colour'd Bodies, so far as my Observation reaches, may be seen through if made sufficiently thin, and therefore are in some measure transparent, and differ only in degrees of Transparency from tinged transparent Liquors; these Liquors, as well as those Bodies, by a sufficient Thickness becoming opake. A transparent Body which looks of any Colour by transmitted Light, may also look of the same Colour by reflected Light, the Light of that Colour being reflected by the farther Surface of the Body, or by the Air beyond it. And then the reflected Colour will be diminished, and perhaps cease, by making the Body very thick, and pitching it on the backside to diminish the Reflexion of its farther Surface, so that the Light reflected from the tinging Particles may predominate. In such Cases, the Colour of the reflected Light will be apt to vary from that of the Light transmitted. But whence it is that tinged Bodies and Liquors reflect some sort of Rays, and intromit or transmit other sorts, shall be said in the next Book. In this Proposition I content my self to have put it past dispute, that Bodies have such Properties, and thence appear colour'd.

PROP. XI. Prob. VI.

By mixing colour'd Lights to compound a beam of Light of the same Colour and Nature with a beam of the Sun's direct Light, and therein to experience the Truth of the foregoing Propositions.

Fig. 16.

Let ABC abc [in Fig. 16.] represent a Prism, by which the Sun's Light let into a dark Chamber through the Hole F, may be refracted towards the Lens MN, and paint upon it at p, q, r, s, and t, the usual Colours violet, blue, green, yellow, and red, and let the diverging Rays by the Refraction of this Lens converge again towards X, and there, by the mixture of all those their Colours, compound a white according to what was shewn above. Then let another Prism DEG deg, parallel to the former, be placed at X, to refract that white Light upwards towards Y. Let the refracting Angles of the Prisms, and their distances from the Lens be equal, so that the Rays which converged from the Lens towards X, and without Refraction, would there have crossed and diverged again, may by the Refraction of the second Prism be reduced into Parallelism and diverge no more. For then those Rays will recompose a beam of white Light XY. If the refracting Angle of either Prism be the bigger, that Prism must be so much the nearer to the Lens. You will know when the Prisms and the Lens are well set together, by observing if the beam of Light XY, which comes out of the second Prism be perfectly white to the very edges of the Light, and at all distances from the Prism continue perfectly and totally white like a beam of the Sun's Light. For till this happens, the Position of the Prisms and Lens to one another must be corrected; and then if by the help of a long beam of Wood, as is represented in the Figure, or by a Tube, or some other such Instrument, made for that Purpose, they be made fast in that Situation, you may try all the same Experiments in this compounded beam of Light XY, which have been made in the Sun's direct Light. For this compounded beam of Light has the same appearance, and is endow'd with all the same Properties with a direct beam of the Sun's Light, so far as my Observation reaches. And in trying Experiments in this beam you may by stopping any of the Colours, p, q, r, s, and t, at the Lens, see how the Colours produced in the Experiments are no other than those which the Rays had at the Lens before they entered the Composition of this Beam: And by consequence, that they arise not from any new Modifications of the Light by Refractions and Reflexions, but from the various Separations and Mixtures of the Rays originally endow'd with their colour-making Qualities.

So, for instance, having with a Lens 4-1/4 Inches broad, and two Prisms on either hand 6-1/4 Feet distant from the Lens, made such a beam of compounded Light; to examine the reason of the Colours made by Prisms, I refracted this compounded beam of Light XY with another Prism HIK kh, and thereby cast the usual Prismatick Colours PQRST upon the Paper LV placed behind. And then by stopping any of the Colours p, q, r, s, t, at the Lens, I found that the same Colour would vanish at the Paper. So if the Purple p was stopp'd at the Lens, the Purple P upon the Paper would vanish, and the rest of the Colours would remain unalter'd, unless perhaps the blue, so far as some purple latent in it at the Lens might be separated from it by the following Refractions. And so by intercepting the green upon the Lens, the green R upon the Paper would vanish, and so of the rest; which plainly shews, that as the white beam of Light XY was compounded of several Lights variously colour'd at the Lens, so the Colours which afterwards emerge out of it by new Refractions are no other than those of which its Whiteness was compounded. The Refraction of the Prism HIK kh generates the Colours PQRST upon the Paper, not by changing the colorific Qualities of the Rays, but by separating the Rays which had the very same colorific Qualities before they enter'd the Composition of the refracted beam of white Light XY. For otherwise the Rays which were of one Colour at the Lens might be of another upon the Paper, contrary to what we find.

So again, to examine the reason of the Colours of natural Bodies, I placed such Bodies in the Beam of Light XY, and found that they all appeared there of those their own Colours which they have in Day-light, and that those Colours depend upon the Rays which had the same Colours at the Lens before they enter'd the Composition of that beam. Thus, for instance, Cinnaber illuminated by this beam appears of the same red Colour as in Day-light; and if at the Lens you intercept the green-making and blue-making Rays, its redness will become more full and lively: But if you there intercept the red-making Rays, it will not any longer appear red, but become yellow or green, or of some other Colour, according to the sorts of Rays which you do not intercept. So Gold in this Light XY appears of the same yellow Colour as in Day-light, but by intercepting at the Lens a due Quantity of the yellow-making Rays it will appear white like Silver (as I have tried) which shews that its yellowness arises from the Excess of the intercepted Rays tinging that Whiteness with their Colour when they are let pass. So the Infusion of Lignum Nephriticum (as I have also tried) when held in this beam of Light XY, looks blue by the reflected Part of the Light, and red by the transmitted Part of it, as when 'tis view'd in Day-light; but if you intercept the blue at the Lens the Infusion will lose its reflected blue Colour, whilst its transmitted red remains perfect, and by the loss of some blue-making Rays, wherewith it was allay'd, becomes more intense and full. And, on the contrary, if the red and orange-making Rays be intercepted at the Lens, the Infusion will lose its transmitted red, whilst its blue will remain and become more full and perfect. Which shews, that the Infusion does not tinge the Rays with blue and red, but only transmits those most copiously which were red-making before, and reflects those most copiously which were blue-making before. And after the same manner may the Reasons of other Phænomena be examined, by trying them in this artificial beam of Light XY.