Opticks (1721, 3rd Edition) — part 12 of 18

Now if any Body or thing, in moving through any Space of a given breadth terminated on both fides by t-wo parallel Planes, be urged for- ward in all parts of that Space by Forces tend- ing diredly forwards towards the hil Plane, and before its Incidence on the firit Plane, had no Motion towards it, or but an infinitely Httle one ; and if the Forces in all parts of that Space, betw^een the Planes be at equal diltances from the Planes equal to one another, but at feveral diliances be bigger or lefs in any given Propor- tion, the Motion generated by the Forces in the whole palTage of the Body or thing through that Space iliall be in a fubduplicate Proportion of the Forces , as Mathematicians will" eafily underlland. And therefore if the Space of acti- vity of the refra(Sdng Superficies of the Body be confider'd as fuch a Space, the Motion of the Ray generated by the refrafting Force of the Bod5% during its palTage through that Space, . thai in the Motion B R, mult be in- a fubdupli- cate Proportion of thai refracting Force. I fay therefore that the Square of the Line BR, and by conlequence the refrading Force of the Bo- dy is very nearly as the denfity of the fame Bo- dy. For this will appear by the following Ta- ble, wherein the Proportion of the Sines which meafure thi. Refradions o[ feveral Bodies, the Square of B R fuppofing C B an unite, the Den-.

fides

C 247 ]

iTties of the Bodies eftimated by their fpecifick gravities, and their refradive Power in refped of their denfities are fet down in fever al Co- lumns. ■

Tkie H-Oj.

oritoirAi /jb ociuari

/ he den-

Lhe re

of the Sines of

^/BR, /.

ity anc

fra^live

Incidenc

e and\

which th.

fpecifick

Power

The refradling Bo-

Refratlton oj

efra£linn

gravity

of the

dies.

'yellow Light

force ofth,

f the Bo-

Body in

Body IS

ly.

'ifpe£}

proportion-

of its

ate.

den fit y.

APfeudo-Topazius,

•Seing a natural,

pellucid , brittle ,

23 to

I-:

1-699

4'i7

1919

hairy Stone, of a

yellow Colour.

Air.

3101 to

320c

3'ooo62 5

o'oof 2

5208

Glafs oi Antimony.

17 to

9

i'568

5-28

4864

A Selenitis.

6r to

41

i'2r3

2252

53b6

Glafs vulgar.

31 to

20

14025

2-58

5436

Crylhlof the Rock.

25 to

K

r'44S

x6s

54SO

IQand Cryftal.

5 to

3

('778

I'n

6536

Sal Gemmae.

17 to

II

(•3S8

2'i43

6477

Alame.

35 to

2<

i'i267

i'7i4

6570

Borax.

21 to

15

['1511

i'7r4

6716

Niter.

31 to

21

t"34J

r'9

7079

Dantzick Vitriol.

303 to

2 GO

r'295

t'715

7551

Oil of Vitriol.

10 to

7

1041

i'7

6124

Rain Water.

';29 to

396

o'7S45

i"

7845

Gum Arabick.

31 to

21

r'179

t'37j

8574

spirit of Wine well redificd.

100 to

73

o'8:6s

o'866

10121

Camphire.

3 to

2

I '25

0*996

12551

Oil Olive.

22 to

IS

i'i5 ir

09 f 3

12607

Linfeed Oil.

40 to

2.7

r'1948

0932

12819

Spirit :ofTupentine.

25 to

17

["1626

0*874

13222

Ambar.

14 to

9

['42

I '04 3 '4

r3<554

A Diamond.

roc to

41

4949

14556

The Refradion of the Air in this Table is de- termiu'd by that of the Atmofphere obferved

R 4 by

[ 248 ]

by Aflronomers. For if Light pafs through many refrading Subflances or Mediums gradu- ally, denfer and denfer, and terminated with parallel Surfaces, the fum of all the Refradions will be equal to the fingle Refraftion which it would have fuffer'd in paffing immediately out of the firft Medium into the laft. And this holds true, though the number of the refrading Sub- flances be increafed to infinity, and the diflan- ces from one another as much decreafed, fo that the Light may be refrafted in every point of its PalTage, and by continual Refradions bent into a curve Line. And therefore the whole Refradion of Light in pafling through the At- mofphere from the highell and rareit part there- of down to the loweii: and denfelt part, mull be equal to the Refraftion which it would fuf- fer in paffing at Hke obliquity out of a Vacuum immediately into Air of equal denfity with that in the lowed part of the Atmofphere.

Now although a Pfeudo-Topaz , a Selenitis, Rock Cryftal, Ifland Cryftal , Vulgar Glafs, (that is, Sand melted together ) and Glafs of Antimony, which are terreftrial flony alcahzate Concretes, and Air which probably arifes from fuch Subflances by Fermentation, be Subflan- ces very differing from one another in denfity, yet by this Table, they have their refraftive Powers almofl in the fame proportion to one another as their denfities are, excepting that the Refraftion of that ftrange Subflance Ifland Cryflal is a little bigger than the reft. And particularly Air, which is 3500 times rarer than the Pfeudo-Topaz, and 4400 times rarer than

Glafs

[ H9 ]

Glafs of Antimony, and 2000 times rarer tlian the Sejenitis, Glafs vulgar, or Cryllal of the Rock , has notwithitanding its rarity the fame refradive Power in refpeft of its denfity which thofe very denfe Subllances have in refpeft of theirs, 'excepting fo far as thofe differ from one another.

Again, the Refraftion ofCamphire, Oil Olive, Linfeed Oil, Spirit of Turpentine and Ambar, which are fat fulphureous unduous Bodies, and a Diamond, which probably is an unduous Sub- ftance coagulated, have their refraftive Powers in proportion to one anotTier as their denfities without any confiderable variation. But the refradive Powers of thefe unduous Subftances are two or three times greater in refped of their denfities than the refradive Powers of the for- mer Subllances in refped of theirs.

Water has a refradive Power in a middle de- gree between thofe two forts of Subitances , and probably is of a middle nature. For out of it grow all vegetable and animal Subftances, which confifl as well of fulphureous fat and in- flamable parts, as of earthy lean and alcalizate ones.

Salts and Vitriols have refradive Powers in a middle degree between thofe of earthy Sub- fiances and Water, and accordingly are com.- pofed of thofe two forts of Subllances. For by diftillation and redification of their Spirits a great part of them goes into Water, and a great part remains behind in the form of a dry Mx'd Earth capable of vitrification.

S

pint

[ 250 ]

spirit of Wine has a refradlive Power in a middle degree between thofe of Water and oily Subltances, and accordingly feems to be compofed of both, united by Fermentation; the Water, 'by means of fome faline Spirits with which 'tis impregnated , dilTolving the Oil, and volatizing it by the adion. For Spirit of Wine is inflamable by means of its oily parts, and be- ing diftilled often from Salt of Tartar, grows by every diftillation more and more aqueous and phlegmatick. And Chymilis obferve, that Vegetables (as Lavender, Rue, Marjoram, &c.) diftiUed J>er fe, befm-e fermentation yield Oils without any burning Spirits, but after fermen- tation yield ardent Spirits without Oils; Which lliews, that their Oil is by fermentation con- verted into Spirit. They find alfo, that if Oils be poured in fmall quantity upon fermentating Vegetables, they diitil over after fermentation in the form of Spirits.

So then, by the foregoing Table, all Bodies feem to have their refradive Powers propor- tional to their denfities, (or very nearly ;) ex- cepting fo far as they partake more or lefs of fulphureous oily Particles, and thereby have their refradive Power made greater or lefs. Whence it feems rational to attribute the refraftive Pow- er of all Bodies chiefly, if not wholly, to the fulphureous parts with which they abound. For it's probable that all Bodies abound more or lefs with Sulphurs. And ab Light congregated by a Burning-glafs ads molt upon fulphureous Bo- dies, to turn them into Fire and Flame; fo, Unce all adion is mutual, Sulphurs ought to act

moil

[ 251 ]

moft upon Light. For that the adion between Light and Bodies is mutual, may appear from this Confideration ; That the denleit Bodies which refrad and refleft Light moll: flrongly grow hottefl in the Summer Sun, by the a(^don of the refrafted or refleded Light.

I havp hitherto explain'd the Power of Bo- dies to refle6i: and refrad, and fhew'd, that thin tranfparent Plates, Fibres and Particles do, ac- cording to their feveral thicknelfes and denfi- ties, refled feveral forts of Rays, and thereby appear of feveral Colours, and by confequence that nothing more is requilite for producing all the Colours of natural Bodies than the feveral (izes and denfities of their tranfparent Particles. But whence it is that thefe Plates, Fibres and Particles do, according to their feveral thicks neflTes and denfities, refied feveral forts of Rays, I have not yet explain'd. To give fome infight into this matter, and make way for underftand- ing the next part of this Book', I ihall conclude this Part with a few more Propofitions. Thofe which preceded refped the nature of Bodies, thefe the nature of Light: For both muil be underftood before the reafon of their adlions upon one another can be known. And becaufe the lalt Propofition depended upon the velocity of Light, I will begin with a Propofition of that kind.

Prop.

[ 252 ]

P R O B. XI.

Light is' propagated from luminous Bodies in time, and fpends about feven or eight Mi- nutes of an Hour in pajjing from the Sun to the Earth.

THIS was obferved firfl by Roemer^ and and then by others, by means of the E- clipfes of the Satellites of Jupiter. For thefe Eclipfes, when the Earth is between the Sun and Jupiter^ happen about feven or eight Mi- nutes fooner than they ought to do by the Ta- bles, and when the Earth is beyond the Sun they happen about feven or eight Minutes later than they ought to do ; the reafon being, that the Light of the Satellites has farther to go in the latter cafe than in the former by the Dia- meter of the Earth's Orbit. Some inequalities of time may arife from the Excentricities of the Orbs of the Satellites ; but thofe cannot anfwer in all the Satellites,' and at all times to the po- fition and diftance of the Earth from the Sun. The mean motions of Jupiter's Satellites is alfo fwifter in his defcent from his ApheHum to his Perihelium, than in his afcent in the other half of his Orb : But this inequaUty has no refpeft to the pofition of the Earth, and in the three interior Satellites is infenfible, as I find by com- putation from the Theory of their gravity.

Prop.

[ 253 ]

Prop. XII.

Every Ray of Light in its faffage through any re framing Surface is put into a certain trail- fient Confiitution or State, which in the fro- grefs of the Ray returns at equal Intervals^ and diffofes the Ray at every return to be eafily tranfmitted through the next refracting Surface, and between the returns to be eafily refletied by it.

THIS is manifefl by the fth , 9th, nth, and i^th Obfervations. For by thofe Ob* fervations it appears, that one and the lame fort of Rays at equal Angles of Incidence on a- ny thin tranfparent Plate, is alternately refledt- ed and tranfmitted for many Succeilions accor* dingly as the thicknefs of the Plate increafes in arithmetical Progreffion of the Numbers, o, 'i, 2, 3, 4, 5", 6, 7, 8, ^c. fo that if the firft Re- flexion (that which makes the firlt or inner- moft of the Rings of Colours there defcribed) be made at the thicknefs i, the Rays ihaU be tranfmitted at the thicknelTes o, 2, 4, 6, 8, 10, II, ^c. and thereby make the central Spot and Rings of Light, which appear by tranfmiilion, and be refleded at the thicknefs i, 3, 5-, 7, 9, II, ^c. and thereby make the Rings which appear by Reflexion. And this alternate Re- flexion and TranfmifHon, as I gather by the 14th Obfervation, continues for above an hundred viciflitudes, and by the Obfervations in the next part of this Book , for many thoufands , being propagated from one Surface of a Glafs Plate to

the

C 254 ]

the other, though the thicknefs of the Plate he a quarter of an Inch or above : So that this al- ternation feetns to be propagated from every refrading Surface to all diltances without end orhmitation.

This alternate Reflexion and Refradion de- pends on both the Surfaces of every thin Plate, becaufe it depends on their diilance. By the xift Obfervation, if either Surface of a thin Plate of Mufcovy Glafs be wetted, the Colours caufed by the alternate Reflexion and Refra- 6lion grow faint, and therefore it depends on them both.

It is therefore perform'd at the fecond Sur- face ; for if it were perform'd at the firll:, be- fore the Rays arrive at the fecond, it would not depend on the fecond.

It is alfo influenced by fome aftion or difpo- fition, propagated from the firll to the fecond, becaufe otherwife at the fecond it would not depend on the firlt. And this adion or difpo- iition, in its propagation, intermits and returns by equal Intervals, becaufe in all its progrefs it inclines the Ray at one diftance from the firll Surface to be reflefted by the fecond, at ano- ther to be tranfmitted by it, and that by equal Intervals for innumerable viciffitudes. And be- caufe the Ray is difpofed to Reflexion at the dillances I, 3, $, 7, 9, ^c. and to Tranfmiflion at the diltances o, i, 4, 6, 8, 10, ^c. (for its tranfmiffion through the firlt Surface, is at the diilance o, and it is tranfmitted through both together, if their diilance be infinitely httle or much lefs than i ) the difpofition ta be tranf- mitted

[ 255 ]

mittedatthe.diflances x, 4, 6, 8, 10, ^c. is to be accounted a return of the fame difpofition which the Ray firft had at the diftance o, that is at its tranfmiilion through the firfl refrafting Surface. All which is the thing I would prove. What kind of aftion or* difpofition this is ; Whether it confifts in a circulating or a vibra- ting motion of the Ray, or of the Medium, or fomething elfe, I do not here enquire. Thofe that are averfe from alTenting to any new Dif-. coveries, but fuch as they can explain by an Hypothefis, may for the prefent fuppofe, that as Stones by falling upon Water put the Water into an undulating Notion, and all Bodies by percuflion excite vibrations in the Air ; fo the Rays of Light, by impinging on any refrafting or refleding Surface, excite vibrations in the refrading or refleding Medium or Subitance, and by exciting them agitate the folid parts of the refrading or refleding Body, and by agita- ting them caufe the Body to grow warm or hot ; that the ' vibrations thus excited are pro- pagated .in the refrading or reflefting Medium or Subftance, much after the manner that vibra- tions are propagated in the Air for caufmg Sound, and move fafter than the Rays fo as to overtake them; and that when any Ray is in that part of the vibration which confpires with its Motion, it eafily breaks through a refrading Surface, but when it is in the contrary part of the vibration which impedes its Motion, it is eafily refleded ; and , by confequence , that e- very Ray is fucceffively difpofed to be eafily re- fleded, or eafily tranfmitted, by every vibra- tion

C 256 ]

tion which overtakes it. But whether this Hy- pothefis be true or falfe I do not here confider. I "content my felf with the bare Difcovery, that the Rays of Light are by fome caufe or other alternately difpofed to be reflefted or refrad- edfor many viciflitudes.

DEFINITION.

The returns of the difpojitmi of any Ray to be rejiedied I will call its Fits of eafy Re- flexion, and thofe of its difpojition to be : -tranfmitted its Fits of eafy Tranfmiflion, and the Jpace it fajfes between every re- turn and the next return, the Interval of its Fits.

Prop. XIII.

The reafon why- the Surfaces of all thick tranf farent Bodies reflet ^art of the Light inci- dent on them, and refraEi the rejl , is, that fome Rays at their Incidence are in Fits of eafy Reflexion, and others in Fits of eafy Tranfmiffwn.

THIS may be gather'd from the 2.4th Ob- fervation, where the Light refledfed by thin Plates of Air and Glafs, which to the naked Eye appear'd evenly white all over the Plate^ did through a Prifm appear waved with many Succelfions of Light and Darknefs made by al- ternate Fits of eafy Reflexion and eafy Tranf- miflion, the Prifm fevering and dillinguifhing the Waves of which the white reflefted Light was compofed, as was explain'd above.

And

[ 257 ]

And heiice Light is in Fits of eafy Reflexion and eafy Tranfmiflion, before its Incidence on tranfparenc Bodies. And probably it is put in- to fuch Fits at its firil emiflion from luminous Bodies, and continues in them during all its progrefs. For thefe Fits are of a lading nature, as will appear by the next part of this Book.

In this Propofition I fuppofe the tranfparent Bodies to be thick, becaule if the thicknefs of the Body be much lefs than the Interval of the Fits of eafy Reflexion and Tranfmiflion of the Rays, the Body lofeth its reflecling power. For if the Rays, which at their entering into the Body are put into Fits of eafy Tranl'mifTion, ar- rive at the fartheft Surface of the Body before they be out of thofe Fits they mull be tranfm.it- ted. And this is the reafon why Bubbles of Water lofe their reflecting power when they grow very thin, and why all opake Bodies when reduced into very fmall parts become tranfpa- rent.

Prop. XIV.

Thofe Surfaces of tranfparent Bodies, which if the Ray be m a Fit of Re f ration do re frail it moji Jironglyy if the Ray be in a Fit of Re- flexion do refie6i it mofi eafily.

FOR we lliewed above in Trof. 8. that the caufe of Reflexion is not the impinging of Light on the folid impervious parts of Bodies, but fome other Power by which thofe. folid parts ^d on Light at a diftance. We Ih'ewed alio in Trop. 9. that Bodies reile6t and refrad:

S Light

[ 258 ]

Light by one and the fame Power varioufly ex- ercifed in various circumltances, and in Trop. i. that the moil llrongly refrading Surfaces reflect the moft" Light : All which compared together evince and ratify both this and the laft Propo- fition.

Prop. XV.

In any one and the fame fort of Rays emerging in any Angle out of any re framing Surface in- to one and the fame Medium^ the Interval of the following Fits ofeafy Reflexion and Tranf miff ton are either accurately or very nearly^ as the Re 6i angle of the Secant of the Angle of RefraBiony and of the Secant of another An- gle^ whofe Sine is the fir ft of 106 arithmetical mean Proportionals^ between the Sines of In- cidence and Refra^ion counted from the Sine of Refraction.

T

HIS is manifeil by the 7th and 19th Ob- fervations.

Prop.

[ 25^ ]

Prop. XVI.

In fever al forts of Rays emerging In equal An- gles out of any refraBing Surface into the fame Medium , the Intervals of the following Fits of eafy Reflexion and eajy Tra?ifmiffion are either accurately^ or very nearly^ as the Cube-Roots of the Squares of the lengths of a Chords which found the Notes of an Eighty fol, la, fa, fol, la, mi, fa, fol, with all their intermediate degrees anfwering to the Colours of thofe Raysy according to the Analogy 4^- fcribed in the feventh Experiment of the fe- cond Tart of the fir H Book.

HIS is manifefl by the 13th and 14th Ob- fervations.

T

Prop. XVII.

If Rays of any fort pafs perpendicularly into fever al Mediums , the Intervals of thi' Fits of eafy Refra6iion and Tranjmijfion in any one

. Medium^ are to thofe Intervals ' in any other as the Sine of Incidence to the Sine of Rcfrri- Bion^ when the Rays pafs out of the fir] I of thofe two Mediums into the fecond.

This is manifefl: by the icth Obfervation. '

Pii

o p.

i26o]

Prop. XVIII.

If the Rays which paint the Colour in the Cojt* fine of yellow and orange pafs perpendicularly out of any Medium into Air, the Intervals of

their Fits of eajy Reflexion are the ^-^jh

part of an Inch. And of the fame length are the Intervals of their Fits of eafyTranfmif fion.

THIS is manifeft by the 6th Obfervation. From thefe Propofitions it is eafy to col- led: the Intervals of the Fits of eafy Reflexion and eafy Tranfmiflion of any fort of Rays re- frafted in any Angle into any Medium , and thence to know, whether the Rays fliall be re- flected or tranfmitted at their fubfequent Inci- dence upon any other pellucid Medium. Which thing being ufeful for underftanding, the next part of this Book was here to be fet down. And for the fame reafon I add the two following Propofitions.

Pro

[ 2^1 ]

P lE^ o p. XIX.

If any fort of Rays falling on the polite Sur- face of any pellucid Medium be refle£led back, the Fits of eafy Reflexion which they have at the point of Reflexion , Jhall fill co7itinne to return^ and the returns Jhall be at diflances from the point of Reflexion in the arithmeti- cal progrefflon of the Numbers 2, 4, 6, 8, 10, 12, &c. and between thefe Fits the Rays Jhall be in Fits of eajy Tranjmijflon.

FOR fince the Fits of eafy Reflexion and eafy Tranfmiffion are of a returning na- ture, there is no reafon why thefe Fits, which continued till the Ray arrived at the refleding Medium, and there inclined the Ray to Refle- xion, fliould there ceafe. And if the Ray at the point of Reflexion was in a Fit of eafy Re- flexion, the progreffion of the diflances of thefe Fits from that point mud begin from o, and fo be of the Numbers o, 2, 4, 6, 8, ^c. And therefore the progreffion of the diflances of the intermediate Fits of eafy Tranfmiflion reckon'd from the fame point, muft be in the progreffion of the odd Numbers i, 3, 5, 7, 9, &c. contra- ry to what happens when the fits are propaga- ted from points of Refradion.

S3 Pro p.

[ 262 ]

Prop. XX.

The Intervals of the Fits of eafy Reflexion and eafy Tranfmijjion , propagated from points of Reflexion into any Medium^ are equal to the Intervals of the like Fits which the fame Rays would have^ if refracted into the fame Medium in Angles ofRefra^ion equal to their Angles of Reflexion.

FOR when Light is reflefted by the fecond Surface of thin Plates, it goes out after- wards freely at the firft Surface to make the Rings of Colours which appear by Reflexion, and by the freedom of its egrels, makes the Colours of thefe Rings more vivid and Itrong than thofe which appear on the other fide of the Plates by the tranfmitted Light. The re- fleded Rays are therefore in Fits of eafy Tranf- miffion ar their egrefs; which would not always happen if the Intervals of the Fits within the Plate after Reflexion were not equal both in length and number to their Intervals before it. And this confirms alfo the Proportions fet down in the former Proportion. For if the Rays both in going in and out at the firit Surface be in Fits of eafy Tranfmiiiion, and the Intervals and Numbers of thofe" Fits between the firfl and iecond Surface, before and after Reflexion, be equal ; the dillances of the Fits of eafy Tranfmiiiion from either Surface, mull be in the fame progreflion after Reflexion as before ; . that is, from the firft Surface which tranfmit- ted them, in the progreflion of the even Num- bers

[ 2^3 I

bers o, a, 4, 6, 8, ^c. and from the fecond which reflefted them, in that of the odd Num- bers I, 3, 5", 7> ^c. But thefe two Propo- fitions will become much more evident by the Obfervations in the following part of this Book.

S 4

THE

[ 2^4 I

THE

. SECOND BOOK

OF

OPTICKS.

PART IV.

Obfervatlons concerning the Reflexions and Ca- lours of thick tranfparent folijh'd Tl,ates.

HERE is no Glafs or Speculum how well foever polifh'd, but, befides the Light which it refrafts or refleds re- gularly, fcatters every way irregularly a faint Light, by meaps of which the poH/h'd Surface, when, illuminated in a dark room by a

beam

[ 2^5 ]

beam of the Sun's Light, may be eafily feen in all pofitions of the Eye. There are certain Phaenomena of this fcatter'd Light, which when I fiiit obferved them, feem'd very ftrange and furpriiing to me. My Obfervations were as fol-

' lows.

Obf. I. The Sun lliining into my darken'd Chamber through a hole one third of an Inch

• wide, I let the intromitted beam of Light fall perpendicularly upon a Glafs Speculum ground concave on one lide and convex on the other,

.' to a Sphere of five Feet and eleven Inches Ra- dius, and quick- filver'd over on the convex fide. And holding a white opake Chart, or a Quire of Paper at the center of the Spheres to which the Speculum was ground, that is, at the diltance of about five Feet and eleven Inches from the Speculum, in fuch manner, that the beam of Light might pafs through a Uttle hole made in the middle of the Chart to the Specu- lum, and thence be refleded back to the fame hole : I obferved upon the Chart four or five concentric Irifes or Rings of Colours, like Rain- bows, encompafling the hole much after the manner that thofe, which in the fourth and fol- lowing Obfervations of the firft part of this third Book appear'd between the Objeff-glafTes, en- compafled the black Spot, but yet larger and fainter than thofe. Thefe Rings as they grew larger and larger became diluter and fainter, fo that the fifth was fcarce vifible. Yet fome- times, when the Sun ihone very clear, there appear'd faint Lineaments of a fixth and fe- venth. If the diitance of the Chart from the

Spccu-

I 266 ']

Speculum was much greater or much lefs than that of fix Feet, the Rings became dilute and vanilh'd. And if the diftance of the Speculum from the Window was much greater than that of fix Feet, the reflefted beam of Light would . be fo broad at the diftance of fix Feet from the Speculum where the Rings appear'd, as to ob- fcure one or two of the innermott Rings. And therefore I ufually placed the Speculum at a- bout fix Feet from the Window; fo that its Focus might there fall in with the center of its concavity at the Rings upon the Chart. And this Pofture is always to be underftood in the following Obfervaticns where no other is ex- prefs'd.

Obf.i. The Colours of thefe Rain -bows fucceeded one another from the center out- wards, in the fame form and order with thofe which were made in the ninth Obfervation of the firft Part of this Book by Light not refleft- ed, but tranfmitted through the two Objeft- glaftes. For, firft, there was in their common center a white round Spot of faint Light, fome- thing broader than the reflefted beam of Light, which beam fometimes fell upon the middle of the Spot, and fometimes by a little Inclination of the Speculum receded from the middle, and left the Spot white to the center.

This white Spot was immediately encompaf- fed with a dark grey or ruftet, and that dark grey wJLth the Colours of the firft Iris ; which Colours on the infide next the dark grey were a little violet and indigo, and next to that a blue, which on the outfide grew pale, and then fucceeded a

little 8 .

[ 2^7 ]

little greenifli yellow, and after that a brighter " yellow, and then on the outward edge of the Iris a red which on the outlide incHned to pur- ple.

This Iris was immediately encompafTed with a fecond, whofe Colours were in order from the infide outwards, purple, blue, green, yellow, light red, a red mix'd with purple.

Then immediately follow'd the Colours of the third Iris, which were in order outwards a green inclining to purple, a good green, and a red more bright than that of the former Iris.

The fourth and fifth Iris feem'd of a bluifh green within, and red without, but fo faiatly that it was difficult to difcern the Colours."

Ohf. 3. Meafuring the Diameters of thefe Ririgs upon the Chart as accurately as I could, I found them alfo in the fame proportion to one another with the Rings made by Light tranfmitted through the two Objed-glafles. For the Diameters of the four firfl of the bright Rings meafured between the brightell parts of their Orbits, at the diftance of fix Feet from the Speculum were i^t!-, il, 2t4, 34 Inches, whofe Squares are in arithmetical progreffion of the numbers i, x*, 3, 4. If the white circular Spot in the middle be reckon'd amonglt the Rings, and its central Light, where it feems to be mod luminous, be put equipollent to an infinitely little Ring ; the Squares of the Diameters of the Rings will be in the progreffion o, i, 2, 3, 4, ^c. I meafured alfo the Diameters of the dark Circles between thefe luminous ones, and found their Squares in the progreffion of the num- bers

[ 268 ]

bers 4, i4, i-!, s-U &c. the Diameters of the lirll four at tlie diflance of fix Feet from the Speculum, being i-V, 2-tV, ^t, 4-?V Inches. If the diftance of the Chart from the Speculuni, was increafed or diminiflied, the Diameters of the Circles were increafed or diminiihed pro- portionally.

Obf. ^. By the analogy between thefe Rings and thofe defcribed in the Obfervations of the firll Part of this Book, I fufpeded that there were many more of them which fpread into one another, and by interfering mix'd their Co- lours, and diluted one another fo that they could not ;be feen apart. I viewed them there- fore through a Prifm, as I did thofe in the 24th Obfervation of the firll Part of this Book. And when the Prifm was fo placed as by refrafting the Light of their mix'd Colours to feparate them, and diftinguifli the Rings from one ano- ther, as it did thofe in that Obfervation, I could then fee them diitinder than before, and eafily number eight or nine of them, and fometimes twelve or thirteen. And had not their Light been fo very faint, I queflion not but that I might have feen many more.

Obf.^. Placing a Prifm at the- Window to refrad the intromitted beam of Light, and caft the oblong Spedrum of Colours on the Specu- lum .: I covered the Speculum with a black Pa- per which had in the middle of it a hole to let any one of the Colours pafs through to the Speculum, whilfl the reil were intercepted by the Paper. And now I found Rings of that Co- lour only which fell upon the Speculum. If

the

i 269']

the Speculum was illuminated with red , thef Rings were totally red with dark Intervals, if with blue they were totally blue, and fp of the other Colours. And when they were illumi- nated with any one Colour, the Squares of their Diameters meafured between their moll lumi- nous parts, were in the arithmetical progreflion of the numbers o, i, ^, 3, 4, and the Squares of the Diameters of their dark Intervals in the progreflion of the intermediate numbers 4, iv, 24-> 34. But if the Colour was varied they va- ried their magnitude. In the red they were lar- gell, in the indigo and violet leall, and in the intermediate Colours yellow, green and blue, they were of feveral intermediate bignefles an- fwering to the Colour, that is, greater in yel- low than in green, and greater in green than in blue. And hence I knew that when the Spe- culum was illuminated with white Light, the red and yellow on the outfide of the Rings were produced by the leall refrangible Rays, and the blue and violet by the mod refrangible, and that the Colours of each Ring fpread into the Co- lours of the neighbouring Rings on either fide, after the manner explain'd in the firlt and fe- cond Part of this Book, and by mixing diluted one another fo that they could not be diilin- guiih'd, unlefs near the center where they were lead mix'd. For in this Obfervation I could fee the Rings moredillindly, and to a greater number than before, being able in the yellow Light to number eight or nine of them, be- fides a faint fliadow of a tenth. To fatisfy my felf how much the Colours of the feveral Rings • 1 fpread

C 270 ]

fpread into one another, I meafured the Dia- meters of the fecond and third Rings, and found * them when made by the Confine of the red and orange to be to the fame Diameters when made by the Confine of blue and indigo, as 9 to 8, or thereabouts. For it was hard to determine this Proportion accurately. Alfo the Circles made fuccefTively by the red, yellow and green, difFer'd more from one another than thofe made fucceflively by the green, blue and indigo. For the Circle made by the violet was too dark to be feen. To carry on the computation, let us therefore fuppofe that the differences of the Diameters of the Circles made by the utmoft red, the Confine of red and orange, the Confine of orange and yellow, the Confine of yellow and green, the Confine of green and blue, the Confine of blue and indigo, the Confine of in- digo and violet, and outmoll violet, are in pro- portion as the differences of the lengths of a Monochord which found the Tones in an Eight ; fol^ la^ fa, fol, la, mi^ fa, fol, that is, as' the numbers 4, -^ tV, t-, -^V? -t, tV. And if the Diameter of the Circle made by the Confine of red and orange be 9 A, and that of the Circle made by the Confine of blue and indigo be 8 A

as above, their difference 9 A 8 A will be

to the difference of the Diameters of the Cir- cles made by the outmoil red, and by the Con- fine of red and orange, as -V -V tV 4- --^^ - -/t to ^, that is as^y to 4, or 8 to 3, and to the diffe- rence of the Circles made. by the outmoft vio- let, and by the Confine of blue and indigo, as

^7 -f TT 4-. -'-? 4- -i-i to t't 4- tV> that is, as 4^ to t'-? . "^- ^ '• or

[ 271 ]

or as 1 6 to $. And therefore thefe differences will be 4 A and tV A. Add the firft to 9 A and fubdud: the latt from 8 A, and you will have the Diameters of the Circles made by the leafl and

moft refrangible Rays -^ A and ~f A. Thefe

Diameters are therefore to one another as y$ to 6i4 or f o to 41, and their Squares as 2500 to 1 68 1, that is, as 3 to i very nearly. Which proportion differs not much from the propor- tion of the Diameters of the Circles made by the outmoft red and outmoll violet in the 13th Obfervation of the firit Part of this Book.