Fig. 9.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, wheneverthey 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.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 andabc, [inFig.10.] whose refracting Angles B andbare equal, be soplaced parallel to one another, that the refracting Angle B of the one may touch the Anglecat the Base of the other, and their Planes CB andcb, 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 andcof 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 Anglebof the lower Prism, is a little greater than the Angle B of the upper, and between the interior Angles B andc, there intercedes some Space Bc, as is represented in the Figure, and the refracting Planes BC andbc, 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 Prismought 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 Coloursof 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 fullWhite, 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 ofViride 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 thanViride 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 andViride Ærisin 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 littleViride Æris, and a little more blue Bise thanViride 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 thereforeconduced 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, andViride 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 littleshaded 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, andViride 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 severalRefrangibilities they are separated from one another, do tinge Paper or any other white Body whereon they fall. For those Colours (byProp.II.Part2.) are unchangeable, and whenever all those Rays with those their Colours are mix'd again, they reproduce the same white Light as before.
In a mixture of Primary Colours, the Quantity and Quality of each being given, to know the Colour of the Compound.
Fig. 11.Fig. 11.
With the Center O [inFig.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 Colourbetween 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. Letpbe the Center of Gravity of the Arch DE, andq,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 Circlepproportional to the Number of the red-making Rays in the Mixture, the Circleqproportional 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 shallbe 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 circumferenceI 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 Circlesx,v,t,s,r,q,p, respectively, that is, so that if the Circlexbe one, the Circlevmay be one, the Circlettwo, the Circlesthree, and the Circlesr,qandp, 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.
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 (inProp. 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.Part1. andProp.2.Part2.) and that their degrees of Refrangibility cannot be changed by Refractions and Reflexions (Prop.2.Part1.) 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.Part2.) 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.Part2.) 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.Part2.) 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 theirseveral 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 inExper.9, and 10.Part1. 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 whenby 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.
By the discovered Properties of Light to explain the Colours made by Prisms.
Let ABC [inFig.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 Raysupon 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.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.[L]
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.Fig. 13.
Exper.16 Let HFG [inFig.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 about40 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 Spand St, in the Angles Spc50 degr. 1/9, and Stc49 degr. 1/28, and the Pointpwill 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 Pointtwill 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 Pointrtaken in the middle Way betweenpandt, will be the like Limit for the meanly refrangible Rays. And therefore all the least refrangible Rays which fall upon the Base beyondt, that is, betweentand B, and can come from thence to the Eye, will be reflected thither: But on this sidet, that is, betweentandc, many of these Rays will be transmitted through the Base. And all the most refrangibleRays which fall upon the Base beyondp, that is, between,pand B, and can by Reflexion come from thence to the Eye, will be reflected thither, but every where betweenpandc, 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 Pointr. Whence it follows, that the Base of the Prism must every where betweentand B, by a total Reflexion of all sorts of Rays to the Eye, look white and bright. And every where betweenpand C, by reason of the Transmission of many Rays of every sort, look more pale, obscure, and dark. But atr, and in other Places betweenpandt, 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 CprtB any where between the Ends of the Prism HG and EI.
By the discovered Properties of Light to explain the Colours of the Rain-bow.
Fig. 14.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 theSun 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 famousAntonius de DominisArchbishop ofSpalato, in his bookDe Radiis Visûs & Lucis, published by his FriendBartolusatVenice, 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 ExplicationDes-Carteshath 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, [inFig.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 Refractionto 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.[M]
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 differentAngles, 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 [inFig.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.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 becomesfainter 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, thatI 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 byAntonius de DominisandDes-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. Andthe 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 (asHugeniushas 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 whichHugeniusexplains theParhelia, it may perhaps be sensible.
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 moremanifest, 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 andultra-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 theultra-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 theultra-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 theultra-marine doth, and theultra-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 theseColours, 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 theorange-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 (byProp.6.Part2.) 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 mustgrow 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 bothtogether. 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.Hooktried 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 ofLignum 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 allother 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.
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.