Opticks (1721, 3rd Edition) — part 10 of 18

pkin the more compounded. And firfl to fhew hovv^ the Colours in the fourth nnd eighteenth Obiervarions are produced, let there be taken in any right Line from the Point Y, [in Fig. 6.1 the lengths Y A, Y B, Y C, Y D, Y E, Y F, Y G, YK, in proportion to one another, as the Cube Roots of the Squares of the Numbers, 4, t«, t» 4, ^, 4, Tj i> whereby the lengths of a mufical Cnord to found all the Notes in an eighth are reprcfcnted ; that is, in the proportion of the Numbers 63C0, 6814, 71 14, 7631, Si^^, 885-5', 9143, loooo. And at the Points A, B, C, D, E, F, G, Fi, let perpendiculars A ct, B /3, ^c. be erected, by whofe Intervals the Extent of the feveral Colours fet underneath againft them, is to be reprefented. Then divide the Line A a. in fuch proportion as the Numbers i, 2, 3, 5-, 6, 7, 9, 10, II, ^c. fet at the Points of Divifion denote. And through thofe Divifions from Y draw Lines 1 1, 2 K, 3^,5- M, 6 N, 7 O, ^c.

Now if A 2 be fuppofed to reprefent the thicknefs of any thin tranfparentBody, at which the outmofl violet is moil copiouily retlefted in the firit Ring, or Series of Colours, then by the 13th Obfervation, H K will reprefent its thicknefs, at which the utmoii: red is moil co- pioufly refledled in the fame Series. Alfo by the 5th and i6th Obfervations, A 6 and H N will denote the thicknelTes at which thofe ex- treme Colours are moft copiouily refleded in the fecond Series, arid A 10 and H Q the thick- nefles, at which they are moft copioufly reflect- ed in the third Series, and fo on. And the fhicknefs at which any of the intermediate Co- lours

C 20I ]

lours are reflefted moft copioully , will zccop{ ding to the 14th Obfervation, be defined by the diilance of the Line A H from the intermediate parts of. the Lines zK,' 6N, loQ, ^c. againd which the Names of thofe Colours are written .below,

But farther, to define the Latitude of thefe Colours in each Ring or Series, let A i defign the leaft thicknefs, and A 3 the greatefl thick- nefs, at w^hich the extreme violet in the firll Series is reflefted, and let H I, and H L, de- fign the like limits for the extreme red, and let the intermediate Colours be limited by the in- termediate parts of the Lines i I, and 3 L, a- gainfl which the Names of thofe Colours are written, and fo on: But yet wath this caution, that the Reflexions be fuppofed ftrongeft at the intermediate Spaces, x K, 6 N, 10 Q, &c. and from thence to decreafe gradually towards thefe limits, I I, 3 L, s M, 7 O, &c. oh either fide ; where you muit not conceive them to be pre- cifely Umited, but to decay indefinitely. And whereas I have aflign'd the fame Latitude to e- very Series; I did it, becaufe although the Co- lours in the firll Series feem to be a little broad- er than the refl, by reafon of a ftronger Re- flexion there, yet that inequaUty is fo infen- fible as fcarcely to be determin'd by Obferva- tion.

Now according to this Defcription, concei- ving that the Rays originally of feveral Colours are by turns refleded at the Spaces 1 1 L 3, 5 M O 7, 9 P R II, ^c. and tranfmitted at the Spaces AHIi, 3 l-^M 5", 7O P9, ^f. it is eafy to know

what

[ 202 ]

what Colour mud in the open Air be exhi- bited at any thicknefs of a tranfparent thin Bo- dy. For if a Ruler be applied parallel to A H, at that diitance from it by which the thicknefs of the Body is reprefented the alternate Spaces iIL 3, s-MOy, &c. which it crofleth will de- note the refleded original Colours, of which the Colour exhibited in the open Air is com- pounded. Thus if the conftitution of the green in the third Series of Colours be defired, apply the Ruler as you fee at tt ^ crcp, and by its paf- fing through lome of the blue at t and yellow at <r, as well as through the green at ^, you may conclude that the green exhibited at that thick- nefs of the Body is principally conftituted of original green, but not without a mixture of fbme blue and yellow.

By this means you may know how the Co- lours from the center of the Rings outward ought to fuc^ceed in order as they were defcri- bed in the 4th and i8th Obfervations. For if you move the Ruler gradually from AH through all diitances, having pafs'd over the firft Space which denotes little or no Reflexion to be made by thinnefl Subilances, it will tirft arrive at i the violet, and then very quickly at the blue and green, which together with that violet com- pound blue, and then at the yellaw and red, by whofe farther addition that blue is converted into whitenefs, which whitenefs continues du- ring the tranfit of the edge of the Ruler from I to 3, and after that by the fucceflive defici- ence of its component Colours, turns firft to compound yellow, and then to red, and laft of

all

[ 203 ]

all the red ceafeth at L. Then begin the Co- lours of the fecond Series , which fucceed in order during the tranfit of the edge of the Ruler from 5 to O, and are more Uvely than before, becaufe more expanded and fevered. And for the fame reafon, inftead of the former white there intercedes between the blue and yellow a mixture of orange, yellow, green, blue and i indigo, all which together ought to exhibit a dilute and imperfeft green. So the Colours of the. third Series all fucceed in or- der; firft, the violet, which a little interferes with the red of the fecond order, and is there- by incUned to a reddilh purple ; then the blue and green, which are lefs mixed with other Colours, and confequently more lively than be- fore, efpecially the green : Then follows the ' yellow, fome of which towards the green is di- • Hind and good, but that part of it towards the fucceeding red, as alfo that red is mix'd with the violet and blue of the fourth Series, where- by various degrees of red very much inclining to purple are compounded. This violet and blue, which fhould fucceed this red, being mix- ed with, and hidden in it, there fucceeds a green. And this at firft is much inclined to blue, but foon becomes a good green, the on- ly unmix'd and hvely Colour in this fourth Se- ries. For as it verges towards the yellow, it begins to interfere with the Colours of the fifth Series, by whofe mixture the fucceeding yel- low and red are very much diluted and made dirty, efpecially the yellow, which being the weaker Colour is fcarce able to iliew it felf.

After

C 204 ]

After this the feveral Series interfere more and more, and their Colours become more and more intermix 4, till after three or four more revo- lutions (in which the red and blue predominate by turns) all forts of Colours are in all places pretty equally blended, and compound an even whitenefs.

And fmce by the 1 5'th Obfervation the Rays endued with one Colour are tranfmitted, where thofe of another Colour are refleded, the rea- fon of the Colours made by the tranfmitted Light in the 9th and 26th Obfervations is from hence evident.

If not only the Order and Species of thefe Colours, but alfo the precife thicknefs of the Plate, or thin Body at which they are exhibited, 'be defired in parts of an Inch, that may be alfo obtained by alliltance of the 6th or 1 6th Obfer- vation. For according to thofe Obfervations the thicknefs of the thinned Air, which be- tween two GlalFes exhibited the mod luminous

parts of the firft fix Rings were —

booo' X 7 8000,

II

i78ooo> 178000' 178000' 178000 P^^'^^ ^f ^^^ Inch. Suppofe the Light refleded moft copioufly at thefe thicknefles be the bright citrine yellow, or contine of yellow and orange, and thefe thickneires willbe F A, Fft, F|, F 0, F?. And this being known, it is eafy to determine what thicknefs of Air is reprefented by G (p, or by any other diilance of the Ruler from AH.

But farther; lince by the loth Obfervation the thicknei's of Air was to., the thicknefs of Water,

which

[ 205 ]

which between the fame GlafTes exhibited the fame Colour, as 4 to 3, and by the 21ft Obfer- vation the Colours of thin Bodies are not varied by varying the ambient Medium; the thick- nefs of a Bubble of Water, exhibiting any Co- lour, will be i of the thicknefs of Air produ- cing the fame Colour. And fo according to the fame loth and xifl Obfervations the thick- nefs of a Plate of Glafs, whofe Refradtion of the mean refrangible Ray, is meafured by the proportion of the Sines 31 to lo, may be -I-t of the thicknefs of Air producing the fame Co- lours ; and the like of other Mediums. I do not affirm, that this proportion of zo to 31, holds in all the Rays ; for the Sines of other forts of Rays have other Proportions. But the differences of thofe Proportions are fo little that I do not here confider them. On thefe Grounds I have compofed the following Ta- ble, wherein the thicknefs of Air, Water, and Glafs, at which each Colour is moft intenfe and fpecifick, is expreffed in parts of an Inch divided into ten hundred thoufand equal parts.

The

[ 206 ]

fhe thicknefs of coloured Plates and Particles of

' ''Very black Black Beginning of

Jheir Colours of the g^^]^^^ firft Order, . ^^^^

Yellow Orange i^Red

f Violet I Indigo \Blue , ^ , vGreen Of tbe fecond Order, < ygHow

[Orange Bright red Scarlet

Of the third Order,

Of the fourth Order,

Of the fifth Order,

Of the fixth Order,

■ Forple

iQdigo |BIue

Green I Yellow

Red

Bluilhred

• Bluifti green

Green

kYellowifli green CRed

{Greenifh blue Red

{Greenifh blue Red

Of the fcventh Or- fGreenirti blue der, \Ruddy white

Air.

Water, Glafs.

i

1-

It

If

6^

Hi 3-I-

5f

14 i<5|-

I9f

84

74

9f

8-1?-

lOi

9

l^T

94-

I2i

io4.

'^

ii->

ni

I If

Mi

'H

21

^3f

27- ' 7

19 3^

I5i 17-14

20f

24

i3t4

I4T

174

20i

24

35f 3<5

4cf

m4

264

i7 3^

12

22|

^3^ 26

46

34i 394

^9t 34

65

44

71 77

53t S7i

38 42

45* 49i- I

Now

[207]

Now if this Table be compared with the 6th Scheme, you will there fee the conilitution of each Colour, as to its Ingredients, or the ori. ginal Colours of which it is compounded, and thence be enabled to judge of its Intenfenefs or Imperfedion ; which may fuffice in explication of the 4th and i8th Obfervations, unlefs it be farther defired to delineate the manner how the Colours appear, when the two Objeft-glaf- fes are laid upon one another. To do which, let there be defcribed a large Arc of a Circle, and a ftreigth Line which may touch that Arc, and parallel to that Tangent feveral occult Lines, at fuch diitances from it, as the Num- bers fet againft the feveral Colours in the Ta- ble denote. For the Arc, and its Tangent, will reprefent the Superficies of the GlafTes termi- nating the interjacent Air ; and the places where the occult Lines cut the Arc will fhow at what diftances from the center, or Point of contraft, each Colour is reflefted.

There are alfo other Ufes of this Table : For by its affiftance the thicknefs of the Bubble in the 19th Obfervatidn was determined by the Co- lours which it exhibited. And fo the bignefs of the parts of natural Bodies may be conje- ctured by their Colours., as fhall be hereafter (liewn. Alfo if two or more very thin Plates be laid one upon another, fo as to compofe one Plate equalling them all in thicknefs, the refult- ing Colour may be hereby determin'd. For in- ftance, Mr. Hook obferved, as is mentioned in his Mtcrographia, that a faint yellow Plate of Mufcovy Glafs laid upon a blue one conllituted

a 'very 4

L 208 J

a very deep purple. The yellow of the firff Qrder is a faint one , and the thicknefs of the Plate exhibiting it, according to the Table is 44, to. which add 9, the thicknefs exhibiting blue of the fecond Order, and the Sum will be 134) which is the thicknefs exhibiting the pur- ple of the third Order.

To explain, in the next place, the circunl- itances of the 2d and 3d Obfervations ; that is, how the Rings of the Colours may (by turning the Prifms about their common Axis the con- trary way to that exprelFed in thofe Obferva- tions) be converted into white and black Rings, and afterwards into Rings of Colours again, the Colours of each Ring lying now in an inverted order ; it muft be remember 'd, that thofe Rings of Colours are dilated by the obliquation of the Rays to the Air which intercedes the Glafles, and that according to the Table in the 7th Ob- fervation, their Dilatation or Increafe of their Diameter is moil manifeft and fpeedy when they are obliquelt. Now the Rays of yellow being more refrafted by the firit Superficies of the faid Air than thofe of" red , are thereby made more oblique to the fecond Superficies, at which they are reflected to produce the co- lour'd Rings, and confequently the yellow Cir- cle in each Ring will be more dilated than the red ; and the Excefs of its Dilatation will be fo ,much the greater, by how much the greater is the obliquity of the Rays, until at lafl it be- come of equal extent with the red of the fame Ring. And for the fame reafon the green, blue and violet, will be alfo fo much dilated by the

{till

r 205; ]

ftill greater obliquity of their Rays, as to be- come all very nearly of equal extent with the red, that is, equally diltant from the center of the Rings. And then all the Colours of the fame Ring mult be coincident, and by their mixture exhibit a white Ring. And thele white Rings muft have black and dark Rings between them, becaufe they do not fpread and interfere with one another as before. And for that rea- ibn alfo they muft become diltincler and vifible to far greater numbers. But yet the violet be- ing obliqueft will be fomething more dilated in proportion to its extent than the other Colours, and fo very apt to appear at the exterior Verges of the white.

Afterwards, by a greater obliquity of the Rays, the violet and blue become more fenfibly dilated than the red and yellow , and fo being farther removed from the center of the Rings, the Colours mull: emerge out of the white in an order contrary to that which they had before, the violet and blue at the exterior Limbs of each Ring, and the red aad yellow at the in- terior. And the violet, by realon of the great- eft obliquity of its Rays, being in proportion moft of all expanded, wall fooneft appeat at the exterior Limb of each white Ring, and be* come more confpicuous than the reit. And the feveral Series of Colours belonging to the feve- ral Rings , will by their unfolding and fpread- ing, begin again to interfere, and thereby ren- der the Rings lefs diftind, and not vifible to fo great numbers.

P If

[ 210 ]

If inflead of the Prifms the Objeift-glafres be made ufe of, the Rings which they exhibit be- come not white and diltinft by the obliquity of the Eye, by reafon that the Rays in their pailage through that Air which intercedes the Glafles are very nearly parallel to thofe Lines in which they were firlt incident on the Glafles, and con- fequently the Rays endued with feveral Colours are not inclined one more than another to that Air, as it happens in the Prifms.

There is yet another circumilance of thefe Experiments to be conlider'd, and that is why the black and white Rings which when view'd at a dillance appear diftin?t, iliould not only be- come cbnfufed by viewing them near at hand, but alfo yield a violet Colour at both the edges of every white Ring. And the reafon is, that the Rays which enter the Eye at feveral parts of the Pupil, have feveral Obliquities to the Glaf* fes, and thofe. which are moil oblique, if confi- der'd apart, would reprefent the Rings bigger than thofe which are the leait oblique. Whence The breadth of the Perimeter of every white Ring is expanded outwards by the obliquelt Rays, and inwards by the leail oblique. And this Expanfion is fo much the greater by how much the greater is the difference of the Obli- quity; that is, byhow much the Pupil is wider, or the Eye nearer to the Glailes. And the breadth of the violet mult be moll expanded , becaufe the Rays apt to excite a Senfation of that Colour are molt oblique to a fecond , or farther Superficies of the thinn'd Air at which they are refleded , and have alfo the greatefl

varia-

yariacion of Obliquity, which makes that Co- lour foonell emerge out of the edges of the white. And as the breadth of every Ring is thus augmented, the dark Intervals mull be di- miniili'd, until the neighbouring Rings become continuous, and are blended, the exterior firll, and then thofe nearer, the center, fo that they can no longer be diflinguifli'd apart, but feem to conflitute an even and uniform whitenefs.

Among all the Obfervations there is none ac- companied with fo odd circiimttances as the twenty fourth; Of thofe the principal are, that in thin Plates, which to the naked Eye feem of an even and uniform tranfparent whitenefs, without any terminations of Shadows, the Re- fraction of a Prifm fhould make Rings of Co- lours appear, whereas it ufually makes Objedts appear coloured only there where they are ter- minated with Shadows , or have parts unequal- ly luminous ; and that it jQiould make thofe Rings exceedingly diflin6l and white, although it ulually renders Objedts confufed and colour- ed. The Caufe of thefe things you will under- ftand by confidering, that all the Rings of Co- lours are really in the Plate, when view'd with the naked Eye, although by reafon of the great breadth of their Circumferences they fo much interfere and are blended together^ that they feem to conftitute an uniform v\ hitenefs. But when the Rays pafs through the Prifm to the Eye, the Orbits of the feveral Colours in every Ring are refradled, fome more than others* ac- cording to their degrees of Refrangibility : By v^'hich means the Colours on one fide of the

P % Ring

[ 212 ]

Ring (thiit is in the Circumference on one fide of its center) become more unfolded and dilated,and thofe on the other fide more complicated and contracted. And where by a due Refradion they are fo much contraCled, that the feveral Rings be- come narrower than to interfere with one ano- ther^ they muft appear diftinft, and alfo white, if the conltituent Colours be fo much contradl- cd as to be wholly coincident. But, on the o- ther fide, where the Orbit of every Ring is made broader by the farther unfolding of its Colours, it mult interfere more with other Rings than before, and fo become lefs diftinft.

To explain this a little farther, fuppofe the concentrick Circles A V, and B X, [in Fig. 7.] reprefent the red and violet of any Order, which, together with the intermediate Colours, conftitute any one of thefe Rings. Now thefe being view'd through a Prifm, the violet Circle B X, will by a greater Refraction be farther tranilated from its place than the red A V, and fo approach nearer to it on that fide of the Cir- cles, towards which the Refractions are made. For inflance , i^ the red be tranflated to a v, the violet may be tranflated to b x^ fo as to ap- proach nearer to it at x than before, and if the red be farther tranflated to a v, the violet may be fo much farther tranflated to bx as to con- vene with it at X, and if the red be yet farther tranflated to d T, the violet may be (till fo much farther tranflated to /3 | as to pafs beyond it at |, and convene with it at e and f. And this being underltood not only of the red and vio- let, but of all the other intermediate Colours,

and

[ 213 ]

and alfo of every revolution of thofe Colours, you will eafily perceive how thofe of the fame revolution or order , by their nearnefs at at i; and T|, and their coincidence at x v, e^ndfy ought to conltitute pretty diilinft Arcs of Cir- cles, efpecially at x v, or at e and /, and that they will appear feverally at x v, and at xv ex- hibit whitenefs by their coincidence, and again appear feveral atT|, but yet in a contrary or- der to that which they had before, and Itill re- tain beyond e and/ But, on the other fide, at ^ ^, a b, or a /3, thefe Colours mult become much more coufiifed by being dilated and fpread fo, as to interfere with thofe of other Orders. And the fame confufion will happen at T | be- tween e and f, if the Refraction be very great, or the Prifm very diitant from the Objeft-glaf- fes : In which cafe no parts of the Rings will be feen , fave only two little Arcs at e and f, whofe di (lance from one another, will be aug- mented by removing the Prifm ftill farther from the Objed-glafTes : And thefe little Arcs mud be didindelt and whiteit at their middle, and at their ends, where they begin to grow con- fufed they muil be coloured. And the Colours at one end of every Arc mufl be in a contrary order to thofe at the other end, by reafon that they crofs in the intermediate white ; namely, their ends, which verge towards T|, will be red and yellow on that fide next the center, and blue and violet on the other fide. But their other ends which verge from T| will on .the contrary be blue and violet on that fide to-

P 3 wards

[ 214 ]

wards the center, and on the other fide red and

yellow.

Now as all thefe things follow from the pro- perties of Light j^y a mathematical way of rea- foning, fo the truth of them may be manifefted by Experiments. For in a dark Room, by view- ing thefe Rings through a Prifm, by reflexion of the feveral prifmatick Colours, which an afliltant caufes to move to and fro upon a Wall or Paper from whence they are refleded, whilft the Spedator's Eye, the Prifm and the Objed- glalTes (as in the 13th Obfervation) are placed Iteady : the Pofition of the Circles made fuc- ceffively by the feveral Colours, will be found fuch, in refpeft of one another, as I have de- fcribed in the Figures a b x v^ or a b x v, or ct^|T. And by the fame method the truth" of the Explications of other Obfervations may be examined.

By what hath been faid, the like Phaenomena of Water, and thin Plates of Glafs may be un- derilood. But in imall fragments of thofe Plates, there is this farther oblervable, that where they iye flat upon a Table and are turned about their centers whilil they are viewed through a Prifm, they will in feme polkires exhibit Waves of va- rious Colours, and feme of them exhibit thefe Waves in one or two Pofitions only, but the rnoil of them do in all Pofitions exhibit them, and make them for the moil part appear al- moil all over the Plates. The reafon is, that the Superf cics of fuch Plates are not even, but h ive many Cavities and Swellings, which how. Ibalbw loever do a little vary the thicknefs of

the

[215]

the Plate. For at the feveral fides of thofe Ca- vities, for the Reafons newly defcribed, there ought to be produced Waves in feveral po- ftures of the Prifm. Now though it be but fome very fmall, and narrower parts of the Glafs, by which thefe Waves for the mod part are cau- fed, yet they may feem to extend themfelves over the whole Glafs, becaufe from the narrow- eft of thofe parts there are Colours of feveral Orders, that is of feveral Rings, confufedly re- flefted, which by Refraftion of the Prifm are unfolded, feparated, and according- to their degrees of Refraftion, difperfed to feveral pla- ces, fo as to conftitute fo many feveral Waves, as there were divers orders of Colours promif- cuoufly reflefted from that part of the Glafs.

Thefe are the principal Phasnomena of thin Plates or Bubbles, whofe Explications depend on the properties of Light, which I have here- tofore deliver'd. And thefe you fee do necef- farily follow from them, and a^ree with them, even to their very leaft circumltances ; and not only fo, but do very much tend to their proof. Thus, by the X4th Obfervation, it appears, that the Rays of feveral Colours made as well by thin Plates or Bubbles, as by Refradions of a Prifm, have feveral degrees of Refrangibility, where- by thofe of each order, which at the reflexion from the Plate or Bubble are intermix'd with thofe of other Orders, are feparated from them by Refraftion, and aifociated together fo as to become vifible by themfelves like Arcs of Cir- cles. For if the Rays were all alike refrangi- ble, 'tis impoffible that the whitenefs, which

P 4 ta

C 21^ ]

to the naked Senfe appears uniform, fhould by Refraftion have its parts tranlpoled and ranged into thofe black and white Arcs.

It appears aUb that the unequal Refradions of difform Rays proceed not from any contin- gent irregularities ; fuch as are Veins, an uneven PoUfli, or fortuitous Pofition of the Pores of Glafs ; unequal and cafual Motions in the Air or ^ther, the fpreading, breaking, or dividing the fame Ray into many diverging parts, or the like. For, admitting any fuch irregularities, it would be impofTible for Refraftions to render thofe Rings fo very diilind, and well defined, as they do in the 24th Obfervation. It is ne- ceflary therefore that every Ray have its proper and conllant degree of Refrangibility connate with it, according to which its refradion is ever juftly and regularly perform'd, and that feveral Rays have feveral of thofe degrees.

And what is faid of their Refrangibility may" be alfo underftood of their Reflexibility, that is of their Dil'politions to be refleded fome at a greater, and others at a lefs thicknefs, of thin Plates or Bubbles, namely, that thofe Difpofi- tions are alfo connate with the Rays, and im- mutable; as may appear by the 13th, 14th, and 15th Obfervations compared with the fourth and eighteenth.

By the precedent Obfervations it appears al- fo, that whitenefs is a diffimilar mixture of all Colours, and that Light is a mixture of Rays endued with all thofe Colours. For confider- ing the multitude of tlie Rings of Colours, in the ^d, i2.th and 14th Obfervations, it is mani-

fert,

[ 217 ]

feft, that although in the 4th and i8th Obfer- vations there appear no more than eight or nine of thofe Rings, yet there are really a far greater number, which fo much interfere and mingle with one another, as after thofe eight or nine revolutions to dilute one another whol- ly, and conilitute an even and fenfibly uniform whitenefs. And confequently that \vhitenefs muft he allow'd a mixture of all Colours, and the Light which conveys it to the Eye muft be a mixture of Rays endued with all thofe Co-^ lours.

But farther, by the 14th Obfervation, it ap- pears, that there is a conftant relation between Colours and Refrangibility , the molt refrangi- ble Rays being violet, the lealt refrangible red, and thofe of intermediate Colour? having pro- portionably intermediate degrees of Refrangibi- lity. And by the 13th, 14th and ifth Obfer- vations; compared with the 4th or i8th, there appears to be the fame conifant relation be- tween Colour and Reflexibility, the violet be- ing in like circumftances refledted at leaft thick- neiGTes of any thin Plate or Bubble, the red at greateft thickneirps, and the intermediate Co- lours at intermediate thickneiTes. Whence it follows, that the colorifick Difpofitions of Rays are alfo connate with them and immutable, and by confequence that all the Produdions and- Appearances of Colours in the World are de- rived not from any phyfical Change caufed in Light by Refradion or Reflexion, but only from the various Mixtures or Separations of Rays, by virtue of their different Refrangibility

or

[218 ]

or Reflexibility. And in this refpe^l the Science of Colours becomes a Speculation as truly ma- thematical as any other part of Opticks. I mean fo far as they depend on the Nature of Light , and are not produced or alter'd by the Power of Imagination, or by ftriking or preffing the

Eye*

THE

I 219 ]

THE

SECOND BOOK

OPTICKS.

PART III.

Of the ^permanent Colours of natural Bodies^ and the Analogy between them and^ the Colours of thin tr^nfparent Tlates.

AM now come to another part of this Defign, which is to confider how the Phaenomena of thin tranfparent Plates itand related to thofe of all o- ther natural Bodies. Of thefe Bodies I have al- ready told you that they appear of divers Co- lours,

[ 220 ]•

lours, accordingly as they are difpofed to reflect inoft copioufly the Rays originally endued with thofe Colours. But their Conftitutions, where- by they refledl fome Rays more copioufly than others, remain to be difcover'd, and thefe I ihall endeavour to manifeit in the following Proportions.

P R o p: I.

Thofe Superficies of tran/parent Bodies reflet the greateft quantity ef Light ^ which have the greateft re framing ^ower ; that is, which intercede Mediums that differ moft in their refra£iive T)enfities. And in the Confines of equally refra5iing Mediums there is no Re- fiexion.

THE Analogy between Reflexion and Re- fradtion will appear by confidering, that when Light paileth obliquely out of one Medi- um into another which refrads from the per- pendicular, the greater is the difference of their refradive Denfity , the lefs Obliquity of Inci- dence is requifite to caufe a total Reflexion. For as the Sines are which meafure the Refra- dlion, fo is the Sine of Incidence at which the total Reflexion begins, to the Radius of the Circle, and confequently that Angle of Inci- dence is lead where there is the greateft diffe- rence of the Sines. Thus in the pafling of Light out of Water into Air, where theRefra- iftion is meafured by the Ratio of the Sines 3 to 4, the total Reflexion begins when the Angle of Incidence is about 48 Degrees 35- Minutes.

In

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In paffing out of Glafs into Air, where the Re-* fradion is meafured by the Ratio of the Sines io to 31, the total Reflexion begins when the Angle of hicidence is 40 Degrees 10 Minutes ; and fo in pafling out of Cryltal, or more ftrong- ]y refradling Mediums into Air, there is flill a lefs Obliquity requifite to caufe a total Reflexion. Superficies therefore which refrad molt do foonelt reflect all the Light which is incident on them, and fo mult be allowed molt Itrongly reflexive.

But the truth of this Propofition will farther appear by obferving, that in the Superficies in- terceding two tranfparent Mediums, (fuch as are Air, Water, Oil, common Glafs, Cryltal, me- talline GlalFes, Ifland GlalTes, white tranfparent Arfenick, Diamonds, &cj the Reflexion is Itronger or weaker accordingly, as the Super- ficies hath a greater or lefs refrading Power. For in the Confine of Air and Sal-gem 'tis Itronger than in the Confine of Air and Water, and Itill llronger in the Confine of Air and com- mon Glafs or Cryltal, and flronger in the Con- fine of Air and a Diamond. If any of thefe, and fuch hke tranfparent Solids, be immerged in Water, its Reflexion becomes much weak- er than before, and llill weaker if they be im- merged in the more llrongly refracting Liquors of well redified Oil of Vitriol or Spirit of Tur- pentine. If Water be diltinguilh'd into two parts, by any imaginary Surface, the Reflexion in the Confine of thofe two parts, is none at all. In the Confine of Water and Ice 'tis very Httle, in that of Water and Oil 'tis fomething greater,

•in

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in that of Water and Sal-gem ftill greater, and in that of Water and Glafs, or Cryital, or other denfer Subdances ftill greater, accordingly as thofe Mediums differ more or lefs in their re- frafting Powers. Hence in the Confine of com- mon Glafs and Ct-yftal, there ought to be a weak Reflexion, and a ftrdnger Reflexion in the Confine of common and metalline Glafs, though I have not yet tried this. But^ in the Confine of two Glaffes of equal denfity, the;re is not any fenfible Reflexion, as was fhewn in the firlt Obfervation. And the fame may be underfl:ood of the Superficies interceding two Cryflals, or two Liquors, or any other Sub* itances in which no Refradion is caufed. So then the reafon why uniform pellucid Mediumsj (fuch as Water, Glafs, or Cryilal) have no fen- fible Reflexion but in their external Superficiesj where they are adjacent to other Mediums of a different denfity, is becaufe all their conti- guous parts have one and the fame degree of denfity,

. Prop. II.

The le aft parts of almoft all natural Bodies are in fame meaftire tranfparent : And the Opa- city of thofe Bodies arifeth from the multi- tude of Reflexions caufed in their internal Tarts,

'^r^ HAT this is fo has been obferved by o-

JL thers, and will eafily be granted by them

that have been converlant with Microicopes.

And it may be alfo tried by applying any fub-

itance

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ftance to a hole through which fome Light is immitted into a dark Room. For how opake foever that Subflance may feem in the open Air, it will by that means appear very manifeft- ly tranfparent, if it be of a fufficient thinnefs. Only white metalline Bodies mull be excepted, which by reafon of their exceflive denfity feem to refled almoft all the Light incident on their firft Superficies, unlefs by folution in Menllru- ums they be reduced into very fmall Particles , and then they become tranfparent.

Prop. III.

Between the farts of opake and coloured Bodies are many Spaces^ either empty or replenijh'dy with Mediums of other ^enjities ; as IVater between the tinging Corpufcles wherewith a- ny Liquor is impregnated-, Air between the aqueous Globules that conftitute Clouds or Mijis ; and for the moji part Spaces void of both Air and Water ^ but yet perhaps not wholly void of all Subftance^ between the parts of hard Bodies.

TH E truth of this is evinced by the two precedent Propofitions : For by the fe- cond Propofition there are many Reflexions made by the internal parts of Bodies, which, by the firlt Propofition, would not happen if the parts of thole Bodies were continued with- out any fuch Interftices between them, becaufe Reflexions are caufed only in Superficies, which intercede Mediums of a differing denfity by Trop, I.

But

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